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University of Nigeria Research Publications
APAGU, Joseph tanko
Aut
hor
PG/ Ph.D/00/32171
Title
The Relationships Between Design Parameters and
Cost of Some Functional Earth Dams
Facu
lty
Engineering
Dep
artm
ent
Civil Engineering
Dat
e
May, 2006
Sign
atur
e
THE RELATIONSHIPS BETWEEN DESIGN PARAMETERS AND COST OF SOME FUNCTIONAL EARTH DAMS
JOSEPH APAGU TANK0 (REG. NO. UNN/PG/Ph.D/00/32171)
DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF NIGERIA NSUKKA
MAY, 2006
Certification
This is to certify that Joseph Apagu Tanko a Post Graduate student of Civil
Engineering Department with registration number PG/Ph.D/00/32171 has
successfully completed the requirement of research for the award of
Doctor of Philosophy (Ph. D) in Civil Engineering (Water Resources).
The work is original and has not been submitted either in parts or in full
for the award of any certificate in Institutions, Universities, Referred
Journals, Book or any publication.
ENGR PROF. N. EGBUNIWE ENGR. PROF J.C. AGUNWAMBA SUPERVISOR SUPERVISOR
ENGIY. PROF. EFEY NWAOGAZIE EXTERNAL EXAMINER
ENGR.\D~. C. U. NWOJI HOD CIVIL ENGINEERING
~ f i i . 7 croofk is ded i ca ted to t h e "IJN+'W!ICO I J N " hose
'Wisdomj Poweer, ?feaCt/i, Wealth. . . I relied on for this
'Work Wone Is ~ i / @ On to 7l iee, 0 Lord
Acknowledgement
My Profound gratitude goes to Engr. (Prof.). N. Egbuniwe and Cnqr. (Prof.) J. C. Agunwamba, my supervisors who in the course of this study and my academic career have inspired me through their objective arid purposeful direction. I owe them a lot. My gratitude also goes t o the entire staff of Civil Engineering and the lhcl.rlty o f Engineering. University of Nigeria, Nsukka especially my
rC
I + d of Department Engr. Dr. C. U. Nwoji. Engr. Prof. Eze Uzomaka, Prof. Osadabe, Prof. David Enyejekwe. Prof. Ademuliyi whose individual contributions toward the success of this work are too numerous t o tnention here.
My gratitude also goes to Prof. (Engr.) Salihu Mustafa. Federal University of Technology, Yola whose visionary academic steps have made me achieve what I have f o r now. His elderly pieces of advice and never failing kindness encouraged and influenced my thinking toward achieving this feat in academic world. He is an umbrella shielding many from the scorching sun.
My sincere gratitude also goes t o Prof. (Or) Pande 0. 0. Lal (an expatriate from India), Dr. A. A. Musa (Survey Dept. FUTY), and Prof. Muluneh Yitayew (A Visiting Professor to Addis Ababa University. Ethiopia from Arizona University USA) who both contributed immensely, materially and academically toward the Success o f this work.
My hearty appreciation t o the members of my family (Waiziro - - - - - - - - -
Ruth--J-.-Tmko A k - J a b u n J- Tanka, A t o Dqv id J Tanko. Waizirit - - - - - - - - - - - - - - - - - - - - - - - - - -
i . Theriza J. Tanko, and Ato James J. Tanko) and Ato Buba AP. Ankidawa (my junior) who all sacrificed everything f o r the success of this work. 1 owe them a lot.
Many thanks t o my head of department and a fr iend Engr. Victor Anametemfiok whose cooperation, understanding and personal sacrifices prepared a conducive environment for this work. I will not Forget the individual e f fo r t of the staf f of Civil Engineering Department. FUT Yola in persons of Engrs. 5. Balla. Hijab Mahmoud. Ernmanuel W. Gadzama, Toma James, Sini Pembi and the non- academic stnf f of the department.
.r My gratitude also goes to the entire s ta f f of school of Engineering and Engineering Technology. FUT-Yola whose individual contributions are too numerous to mention (ere. However, I must mention Mr. Raf el Mailabari (Mechanical Engineering Dept FUN) , Mrs Martha Amadi (Civil Engr'g.. F U N ) . Jacob 5. Maianguwa (Mech. F U N ) . Mohammed Nura Adamu and Paul Meshek (both of Civil, F U N ) , Harriet. Bassah Emmanuel and Josephine (all of UNN), s ta f f and management of Shammah Computers. CEC, UNN and best of all Waizirit Endalche Dea (Electrical Engineering Dept.. Arba Minch University. Ethiopia). Woizoro Misra k K i f le (Department of Library and Documentation Service. Arba Minch University. Ethiopia), and most of all Woizoro Wosene Te kele Ireland whose various e f f s r ts made this
rr work possible. I have t o appreciate my Co-Technical Aid corps Volunteers deployed t o Arba Minch University, Ethiopia in persons of late Dr. A j i E. Kalu. Dr. K.R.E. Okoye. Alh. Tahir and Engr. Elemuwa Emeka whose cooperation and advice helped in actualizing this work.
I have to thank the entire management of Arba Minch University. Ethiopia whose effective management prepared a conducive environment fo r academic work.
Engr. Joseph A. Tanko.
C'hapter one : Introduction
13ack ground o f study
I'urpose of study
Statenlent o f rcsearcli prohlcnl
Scope of research
Aims and objectives
Study Area
Chapter two: Literature Review
l':conomy o f hydraulic s t ru~ tunx
I'rc~jecl al tcmat ives cvaluat ion tcclin iquc
Project appraisal in dcvcloping counlrics.
llarth dams
Spillways
ISarlli dam's top width analysis
t k t h cia111 design principles
Rclated cost functions
Maintenance cost
Lartl~ dams maintcnance stratcgy
Iyailure modes in carth dam structures
I
. . I I
... . I l l - I V
v-vii
viii-x
xi-xiii
xiv
Ageing and degradation process
Risk cost analysis
Maintenance modelling
Failure ofsome earth dams experienced and likcly causes
Work quantities for earth dams
I Jnit price of work clua~itities
I:ormulation ofcost functions for earth dams
C h a l ~ t e r Three: Methods and materials
I>ala col lect ion
Data analysis
Regression analysis
Chapter Four : Earth dam design and cost analysis
I'arth dam design
Iiarth dam cost minimi7ation in terms of side slopes
Seepage analysis
1':arth dam's cost analysis
I'rice Index
Earth dam construction cost and salient fealurcs.
Earth dam parameters and costs
Summary or the relations hetween dam parameters and costs
Relationships between datn paratneters
(;e~ieral cost runctiotls
Optimising cost functions using 1,agrange Multipliers with
constraints and solution techniques. - - - - - - - - - - - - - - -
Chapter Five: Results and discussions
Project appraisal a d evaluation
Earth dams design
I'roject cost analysis
Inflation index and cost analysis
Earth dam coristn~ction cost salient features
Earth dam's parameters and costs
5.5.0 Rclationsliips between earth dam's parameters
5 h.0 Optimisation tcchli iquc
0 Chapter six: <:oncl~~sions, Limitations and Jiecommenclatian
6 . I Conclusions
References
Appendic~s
Appendix A (Small earth dams)
Appendix I3 (I ,arge earth ~RIIIS)
Appendix C (General earth dams)
Appendix 11 (Computer I'rograms)
Appendix 1' (Tables 4.26 -- 4.3 1)
vii
I;igure 1 . I Map of Nigeria showing the Northern states where the 13nrtli (lams are located.
Figure 2.1.0 17ault Iree logic diagrams.
I'igure 2.2 Failure rate distributions for time a k r dam completion.
I,'igure 2.3: Steps in probabilistic study.
I'igr~rc 4.01 a: A sketch o f a typical homogeneous earth fill d a d
Figure 4.0 I b: A sketch o f a typical diaphragm earth f i l l darn
Figure 4 . 0 1 ~ : A sketch ofa lypical zoned earth f i l l dam
I:igut-e 4.0 1 d: A monograph for estimating spillway parameters
I;igut-e 4.0le: Relationship between medium dam's Lop widths and their heights
17igure 4.02: Relationship between large dam's top widths and their heights
Figure 4.03: Assumed earth dam cross section
Figure 4.04: A cross-section of the typical dam studied
Vignre 4.05: Relationsliip hetween height and cost for general dams
Figure 4.06: Relationsh ip between dam height and costs large dams
Figure 4.07: Relationship between dam height and cost for small dams
Figure 4.08: Relationship between dam length and cost for large dams
Figure 4.09: Relationship between dam lengths and cosls for m a l l dams
Figure 4.10: Relationship between dam lengths and costs for general dams
Figure 4.1 1 : Relatioriship between dam capacities and costs Tor large dams.
I:igure 4.12: Relationship bctwecn darn capacilies and cosls for general dams.
Page 6
1:igtrrc 4.1 3 : I<elationsli ip bctween dam capacities and cosls h r smal l dams
I< igure 4.1 1 : Relationship between d a ~ n sile clearance areas and costs f i~r general danis
I : i g ~ ~ r c 4.1 5: Relationship between dam sile clearance arcas and costs Tor large dams.
Figure 4.16: Relationship betwecn dam sitc clearance areas and costs Tor smal l dams.
l : i p ~ ~ r e 4.1 7: Relal ionship between volumes ofexcavat ion and costs for general datns case
b
Figure 4.1 8: Relat io~ is l i ip betwcen vol i lmcs ofexcavat ion and costs Tor largc dams.
I;igure 4.19: I<elationsliip betwcen volumes o fcxcava t ion and costs i'or smal l datns.
Figure 4.20: Relationship hetwcen volumes o f pervious (granular) f i l l and costs for general datns.
Figure 4.2 1 : Relationship between volumes o f pervious (granular) fill and costs for smal l dams.
Figure 4.22: Relationship between volvmes o fperv ious (granular) fill and costs Tor large darns.
Figure 4.23: Relat ionship between volumes o f impervious (hard core) fill and costs Tor general dams dams.
1;igure 4.24: Relationship between volumes o f impervious (hard core) fill and costs h r large dams.
- - - - - - - - - - - - - - - - - - - - -
I;igure 4.25: I<elationship between volumes o f impervious (hard cow) fill and costs for stnall dams.
Figure 4.26: Relationship bctwecn rock fill volumes and costs for general dams
Figure 4.27: Relat ionship bctween rock fill volumes and costs fo r large dams
Figure 4.28: Relationship bc twee~ i rock fill vo lu~nes and costs for smal l danis
Figure 4.2%: l<elationsliip between riprap fill volumes and costs fbr general dams. 172
Figure 4.2%: Relationship between volumes ofriprap liII and costs Tor largc dams 174
1;igure 4.2%: Relationship between volun~es of riprap fill and costs for slnall dams. 176
Figure 4.30a: Relatiorlship between plain concrete volu~nes and costs lor gelicral (lams 178
Vigure 4.30b: Relationship between plain concrete volu~nes and costs Tor large dams 1 80
Figure 4 . 3 0 ~ : Relationship bctween plain concrete volu~iics and costs for small danis 18 1
17igure 4.3 la: Relationship between rcinlbrced concrete volumes and costs Tor general dams
Figure 4.3 1 b: Kelationship betwcen reinforced concrete volunles and costs fiw large dams 185
Figure 4.3 I c: Relationship hctweer~ reinforced concrete volumes and costs fi~r srnall dams
Figure 4.32: Relationship betwecu rock drilling and cosl Ihr large dams 189
I;igure 4.33: Relations between dam heights and lengths for small dams 199
Figure 4.34: Relations between tiam capacities and lengths Tor small dams 20 1
Figure 4.35: Relations between dam capacities a d heights for small dams 203
% Figure 4.36: Relations between dam heigllts and lengths for large dams 209
Figure 4.37: Relations between dam capacities and lengths for large dams 210
I;igure 4.38: Relations between dam capacities and heights for large dams 21 1
17igure 4.39: Relations between dam heights and lengths for general dams 216
Figure 4.40: Relations betweer1 dam capacities and lengths for general dams 217
Figure 4.4 1 : Relations between dam capacities and heights for general dams 218
'I'ahle I . I R iver basins i n Nor thern Niger ia a ~ i d their approximate Ionti mass
'fable 2.1 Weights fiw (h ject ives comparison
Table 2.2 Multi-ob,jectivc dccision matr ix
Table 2.3 Sowe earth dams i n Northern Niger ia and their construction cost
'I'able 2.4 M i n i m u m inlet widths and f lood f lows.
'I'able 2.5
Table 2.8
'Table 2.9
Tahle 2. I 0
' fable 2.1 I
'I'ahle 4.0 1
'I'able 4.02
Table 4.03
'fable 4.04
'fable 4.05 -
Table 4.06
. Table 4.08 \
', 'I'able 4.09
'Table 4.1 Oa
Table 4. l Ob
Table 4. 1 Oc
' fable 4. t I a
M i n i ~ n u ~ n outlet widths and f lood f lows and t l ic i r return slopcs. #
1:ailure defect mechanisms and preventive mcasurcs Ihr cmbankmenl dams
Causes o f hydraul ic structure failure in percentage
Fai lure probabil i t ies Ihr some common hydraul ic structures
Maintenance alternative procedures
Relations between dam hcight, sp i l lway type and freeboard
'I 'ypical l iceboard values fhr various rcscrvoir I'ctches
M e d i u m earth dams i n the study area and their top widths
f'redicted top widths for med ium earth dams i n the study area.
Side slopes suggested b y 'T'erzaghi (in I 'nn~nia and I ,al, 1992) for various materials.
Side slopes suggested b y ' f e r ~ a g l i i i n (I'ummia and I,al, 1992) for various ~na le r ia ls and opt i lnal height, section and cost.
Side slopes suggested by 'l'erzaghi (in I'unmia and Lal, 1992) Tor various materials and opt imal height, cross- section and costs In f la t ion index h r the period 1970-1 994.
I'redicled and actual in l la t ion rates fiw 1 970-20 1 0.
I la r lh dam costs and heights relationship Ibr general dams.
Earth dam costs and heights relationship for large darns.
Earth dam costs and heights relationship for small dams.
Earth dam costs and Iengtlis relationship for large dams
Table 4.1 l b
'I'ablc 4.1 I c
'I'able 4.12a
'I'ablc 4.12b
'Table 4 . 1 2 ~
Tahle 4.13
'l'able 4 . l h
Table 4.13b
.D Table 4.132
Table 4.14a
Table 4.14b
'l'ahle 4 . 1 4 ~
'Table 4.15a
Table 4.1%
Table 4 . 1 5 ~
Table 4. l6a
D
'I'ablc 4.16b
Table 4.1 Gc
v Tahle 4.17a $
'\ 'I'able 4.171,
Table 4 . 1 7 ~
I'able 4.18a
Table 4.1%
'Table 4 . 1 8 ~
Icarth dam costs and lengths relationship Tor small dams
I;artli dam costs and lengths relatic,nship fhr general dams
Earth dam costs and reservoir capacitics rclationship for large dams
tarth dam costs and reservoir capacities relationship for general dams I'arth dam costs and reservoir capacities rclationship fi,r small dams
Storage ratio and economic e~nbankincnt.
Site clearance areas and dam costs h r general dams
Si te clearance areas and dam costs lbr large darns
Site clearance areas and dam cost Tor small dams
Open cut excavation volunie and cost h r general dams
Open cut excavation volume and cost for large dams
Open cut excavation volume and cost I'or small dams
I'ervious granular lill volumes and cost Tor general dams in the study area
I'ervious granular fill volumes and cost li)r small dams in he study area
I'ervious granular 1711 volumes and cost Tor large dams in the study area
impervious (hard core) earth f i l l volumes and cost for general dams in the study area
Impervious (hard core) earth f i l l volunies and cost Ibr large dams in the study area
Impervious (hard core) earth lill volunies and cost Tor small dams in the study area - - - - - - - - - - - - - - - - - - - -
Rock fills volulncs and their cost Tor general dams in the study area.
Rock fills volumes and their cost h r large dams in the study area
Rock fills volumes and their cost for small dams in the study area
Riprap fills volumes and their cost Tor general dams in the study area liiprap fills volumes and their cost for large dams in the study area
Kiprap fills voluines and their cost for small dams in the study area
xii
Table 4.1%
'Table 4.1%
Tahle 4.1%
'fablc 4.20a
'I'able 4.20b
'I'ahle 4 . 2 0 ~
'fable 4.2 1 a
- Table 4.22a
Table 4.22b
'I'ahle 4 . 2 2 ~
Table 4.23
Table 4.24
Table 4.25
'fable 4.26
Table 4.27
'I'able 4.28
Table 4.29
Table 4.30
,q
'I'able 4.3 1
Plain concrete volumes and cost for geticral dams in the study area
Plain concrcte volunics and cost ibr large dams i l l the sludy arca
I'lain concrctc vohrmes and cost Tor small dams in thc study area
Reinforced concretc (class A) volumes and cost h r gcncral dams in t lie study area Reinforced concrcte (class A) volumes and cost for largc dams in the study area Reinforced concrete (class A) volulnes and cost Tor small clams in the study area Ihilling Tor grouting (0- 40m) and cost Tor large dams in the study
area Summary of rclations between gencral dam's para~nctcrs and costs.
Summary of relations betwcen large dam's parameters and costs.
Summary of rclations bctwcen small dam's paralnetcrs and costs.
Earth darns Icngths and heights (small dams)
Earth dams lengths and capacities (small dams)
llarth dams heights and capacities (small d a m )
Earth dams lengths and heights (large dams)
Earth dams lengths and capacities (large dams)
Garth dams heights and capacities (large dams)
Ikrth dams Icngths and heights (general dams)
Earth dams lengths and capacities (general dams)
Ibrtti dams heights and capacities (general dams)
ABSTRACT
I<ar t l i dams arc necessary hydraulic structures for sustainahlc water rcsourccs development. 'Thc
i~ ic~casi~tg cost o f dcsign and construction makes it a primc conccrn to stakeholders in the water
rcsourccs developmen t suh-sector. Against this background, i t i s nccessary to develop working
w tools in forms o f design rclations and cost functions to aid dcsign and cost estimation
respxtively. Design rclations fijr earth dam top width, k p h a r d , spillway inlct and outlet siLes
werc tlerivetl using the existing data from functional earth dams. The data were obtained from
River 13asins in Northern Nigcria and thc Slates and Fcdcr~l Ministries of water resources. Cost
functions were also derivcd in lerms o f dam parameters from site clearance area to
instru~ncntation using Microsoft cxcel chart wimrd on cxisting data. 'l'he functions reduced to
functions in terms o f dam salicnt features o f length, heiglit and reservoir capa$y for small and
large dams respectively. 'l'he cost functions were ~ninicnized using Lagrange multipliers with
constraints and solved with computer sollware developcd in Visual Basic using data for earth
darns selected randomly in the study area. Spillway inlct width rclation showed correlation
coefficienl o f 0.9979, in rclation to actual. Top width relations for small and large dams showed
co~relation coefficients o f 0.6900 and 0.001 4 respcctively. C'ost fi~nctions minimization reduced 1
cost of earth dams by 45% to 87% for large and small earth dams respectively. Cost functions are
necessary during biding prooess like the Jhc J'rocess to set standard against over or under
estimation o f cost.
xiv
CHAPTER ONE
- INTRODUCTION
1.1 BACKGROUND OF STUDY
Earth dams are designed and constructed for the purpose of controlling and storing surface
water for later use. The roles earth dams' plays are very vital especially for a sustainable water
resources development and utilization (Dawes, 1970). This is because the level of development
reached in water resources sector is proportional to the developments in food production to
feed the teeming world population through irrigation (Lattiff and Bartlle, 2001). However, to v
provide an earth dam, initial investment and maintenpce cost are involved which most of the
times are very high and unaffordable even when they are needed. However, because of their
importance, earth dam projects have to compete with other responsibilities for the little or no
find available to Government or Private Water Agencies. Therefore, it becomes necessary to
frnd ways of ensuring only cost effective earth dams are provided especially in the engineering
world. Cost effectiveness of earth dams could reduce problems of over estimation which may
ultimately lead to expensive dams to construct or under estimation which may encourage the !?
use of inferior materials for construction with a risk of failure of part or whole of the structure. t
Failure of dams generally could cause excessive flooding that may lead to loss of lives and
property. The following are among the recorded failure events of some important dams in i '
History. The failure of St. Francis dam in 1928 in USA, caused flood that resulted in loss of
%
Basin Authority failed and the consequence was great on both the lives and the properties of . I '
the area. At present, flooding alone causes about 40% of the world's catastrophes as observed
by Lattiff and Bartle (2001). This figure is too high, and steps should be taken to reduce it. It is r /
w against this background that some design relationships and management tools for analysis of I
earth dam costs fast. This is necessary especially in Northern Nigeria where much resources , 1
(both human and finds) go for surface water resources development to avert the consequences
of drought experienced intermittently. Such design relationships and management tools or cost
C
functions were derived from existing relationships and costs of existing earth dams constructed
previously. The cost functions derived were limited to earth dams because of their diversity in
the study area and due to their relatively low investment cost compared to concrete dams as
observed by Lattiff and Bartle, (2001). Most of these earth dams support man and agriculture
dircctly for irrigation, water supply, power generation etc. In formulating the cost fbnctions for
earth dams, some parameters wcre selected and related to their costs to yield some relations.
Optimisation techniques was applied to the cost functions for optimum cost functions for
estimation of earth dam's cost in the study area. This study also considered maintenance cost b
because it also affects the life-span of earth dams either positively or negatively especially if
avoided right at the design stagc to the operation. According to Rai and Anyata (1999)
adequately maintained structure helps to:
(i) Keep n~inimum total operating cost of an equipment or structure.
(ii) Keep an equipment or structure in good working conditions, and
(iii) Keep equipment or structure in operation for a givcn percentage of time in their
lives spans.
The above claims are very necessary especially for earth dams which are required to
impound water for a reasonable period of time.
1.2 PURPOSE OF STUDY - - - - - - - - - - - - - - - - - - - - - - -
Resource managers, engineers, consdtantt ~niractors e t c , -offer spend t ime and
i resources in trying to evaluate and choose between alternative structures and the growing cost t
is of concern as suggested by Hoang Dong (1980). The evaluation was based on their cost and
design relationships meant for the study area. However, because of the time and resources
involved, very few alternatives are oflen considered for evaluation. This study suggested some
management tools (cost models), and some design relationships derived particularly for the
study area. This wpuld form a basis for design and comparing alternative earth dams in terms
2
of their costs faster. In addition it will also help to eliminate the process of either over or under +.
design and the rigorous process of pricing each work conlponent especially at the
preliminary stage of evaluating between several alternatives. The cost estimate resulting fiom
the cost functions could also:-
* Enhance proper planning and budgeting for earth dams under Nigerian environment.
Ilclp in checking misappropriation through under or over estimated contracts.
Set standards that could indicate the level of investment required to achieve
government objectives.
Help contractors 'and engineers tenderin~for competitive jobs.
1.3 STATEMENT OF RESEARCH lDROBLER4
Hydraulic structures are very important for a sustainable water resources development and
use, however their designs are mostly based on foreign design relationships and investment
costs are often over estimated. Perhaps because of the cost involved only few alternatives are
usually considered during cost analysis. As a result, optimum or economical structures are left
out and resource managers become discouraged by the large initial investment costs, and
become sceptical about implementation. Those implemented are either abandoned on the way
- for lack of fund because of under cstimation or are hurriedly completed below standard with
consequential failure. Waya Dam in Upper Henue River Basin Developnient Authority, Yola
suffered incompletion while Alau dam failed because of poor construction in 1995 with high
loss of lives and properties in Chad 13asin Development Authority, Maiduguri-Nigeria.
Unrealistic cost estimates which is often associated with embezzlement of public hnd or poor
construction due to low material quality usage could be avoided. Failure of earth dams could
also lead to loss of lives and properties. It is necessary that cost functions and design relations
that could ensure a fast method of evaluating the cost of structures be made available and aid rl*
design. IJse of cost hnctions that resulted fioin adequately related dam parameters and costs
could help make sound cconomic decisions beneficial to all stake holders in the water
resources development sector.
1.4 SCOPE OF RESEARCH.
This research had suggested some design relation~hips for aiding design and cost
functions (management tools) for cost estimation for some parameters of active earth dams
whose cost estimates and design were made bctwcen 1980 and to date. Important components
that affect design and the overall dam cost, would be selccted with the aim of formulating some
relations that could be used to predict their costs reasonably. Some of the parameters for the
design relationships and cost parameters to be utilized for formulating design relations and cost b
functions for earth dams included:-
(i) Design relationship parameters: These include top widths, fieeboards, spillway
inlet and outlet widths, seepage analysis, up and downstream slopes.
(ii) Parameters for cost functions: Construction cost and the dam storage capacity;
construction cost and the dam height construction cost and the dam length; relationships
between unit costs fiom site clearance area to instrumentation. The cost hnctions formulated
was optimized using Lagrange Multipliers with constraints for minilnuin cost estimation.
"I Computer software was developed for easy and fast solution.
1.4 AIMS AND OBJECTIVES
Among the objectives of this study are:
7'0 derive relationships between earth dams's cost and their salient features like height, - - - - -
- - - - - - - - - - - - - - - - - - - - - - - -
reservoir capacity and length.
To establish design relationships between earth dam parameters for various components
like top widths, side slopes, seepages, spillways inlet and outlet width.
To derive general cost hnctions for earth darns in terms of salient features using
parameters right fiom site clearance area to instrumentation after relating with their
costs.
TO optimize the general cost functions for least cost estimation using Lagrange's
Multipliers with constraints.
'To develop ~omputer software for fast and easy cost estimation.
1.5 THE STUDY AREA
.w The study did not cover the whole of Nigeria but only Northern region because of the earth
dams diversity. The study was limited to only earth dams from the Northern Nigeria River
Basins and owned by individuals, Governmcnts or Private Sectors. The choice of the Northern
Region was because earth dams are common and used for surface water devclopment as a
result of the low rainfall experienced in the region comparcd to the Soutllern region with high
rainfall. 'The Northern region is characterized by relatively dry spells to semi desert areas and
needs to impound excess rain water during rainy seasons with the dams for protective or
V
productive irrigation. #
The River Basins in Northern Nigeria with their land masses are as shown in Table 1 . I
'Table 1.1 River Basins in Northern Nigeria and their approximate land mass.
Basins States Covered Land Mass kmL
. . . - ...--. ... - ~ ~ ~
Chad Basin Borno, Yobe 108,900
Lower nenue E3enue 146,900
Lower Niger Niger 146,900
r, Kaduna River Basin Kaduna 104,700
Uppcr Bcnue Gombe. Rauchi. Adamawa. 203.2( i: Taraba
Upper Niger Kogi, Niger 1 16,300
(After Offodile, 2002).
The approximate landmass of the study area obtained by summing the individual Basin
areas in Table 1.1 above was about 1,133,800 square kilonietres. Figure I . 1 below is the map
of Nigeria showing the Northern States where the earth dams were located.
thern States
Figure 1.1: Map of Nigeria showing the Northern States (LacaUon of the earth dams).
CHAPTER TWO * LITERATURE REVIEW
2.1.0. ECONOMY OF HYDRAULlC STRUCTURES
A hydraulic structure is an important structure for water resources development, and
management strategies (Dawes, 1970). 'The eficicncy arid effectiveness of such structures are
also vcry important if the most talked sustainability is to be ensured. Sustainable water
resource has a direct or indirect link with the national economy. This is because the food
security of any country depends on advances made in irrigation ensured by sustaiiiable
developments in the water sector (water supply, power generation etc), which are functions of
efficient earth dams. Although earth dams have a lot of benefits, their number is still low in
developing countries especially in the study area. This may be attributed to several hctors
among which are their high initial investment costs, which are n~akes them unaffordable even
by governments especially in developing countries. When it becomes absolutely necessary,
resources managers, policy makers and engineers have to spend valuable time on questions like
"Why do it at all"? "Why do it now"? , and "Why do it this way"? These questions imply that
apart fiom technical know how, political, economical and social justifications are necessary
'w before decisions are finalized for implementation as observed by Findley (1982). Usually the
money values are placed on a comparable basis by appropriate conversions factors like interest
rates - - - and minimum attractive rates of return which are only appropriate in some particular - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
circumstances. 1
\
Even when final decisions arc: taken, several alternatives may be possible and would
prompt a question like "which of these will pay more?' An answer to this question implies that
an optimum alternative based on economic and engineering principles a.re necessary as
suggested by Hoang Dong (1980). Linsely and Franzini (1979) and Agunwamba (2000,)
suggested some guide lines that could help in selecting the best alternatives as follows:
(i) Promisiqg alternatives are identified in physical terms.
( i i ) The physical terms are translated into money values.
(iii) Usually the nioney values are placed on a comparable basis by appropriate
conversions through interest rate and minimum attractive ratc of return which could
bc appropriate in a particular circumstance or any othcr economic analysis.
(iv) IJsually a choice is madc among various alternatives, which are usually influenced
by money units and by irreducible or inta~igiblcs.
Although this approach is important, it lacks dircct relationships between parameters and
data on each component may not be readily available. Structures of unequal live spans are
generally difficult to compare in terms of cost because their life-cycle cost vary. However,
# 'I'aylor (1980); 'l'huesen, and others, (1980). and Sexena and Garg (1990) suggested two
methods for comparing short and long life spans of structures. The first method considers the
lowest common multiple of life spans of the alternatives while the other method involves
selecting a common study period, which is usually equal to the life of the structure with the
shorter life span. Both methods deal with projects with unequal life span problem adequately
for service type structures. Service type structures are those structures that do not produce
revenues and profits, but only the needed service. These approaches were not adopted for this
Q study because of their peculiarity to othcr Foreign environments and the fact that they do not
relate the costs of structure components directly to their quantities.
F'arth dams are usually designed as multipurpose structures which are more popular - - - - - - - - -
e$ecially in devebping C6untrfes of the world &awe they arc more ecnncrmical a s t h q serve- a
t several purposes. This is because in most cases, revenues accrued to single purpose structures
can hardly balance its investment cost as observed by (Agunwamba, 2000a). Economical
structures are those structures whose marginal benefit of producing output is equal to or greater
than the marginal cost of producing it as suggested by Dioxion (1964). This could be
represented by cost and ttenefit per unit out put at the determined level for one purpose as:
c 3 ~ , / ac,=ap2 x2= ...= api / aci=l (2.2)
Forj=l ton
Where, MPi = marginal gross benefits or productivity and MCj = Marginal cost.
For high economic benefit of the system, the niargitial cost of producing the last
increment of benefit must be equal to unity for all-purpose.
apI / X ~ = ~ E ' ~ I ac2= . . .= ap,,/ ac,,-i (2.3)
.- For a sound economic analysis to be undertaken, cost benefit analysis, capital recovery
+ factor, cost effectiveness etc are some of the simple techniques adopted as suggested by
Franzini and 1,insely (1979). In an earth dam, the benefit cost may include the following as
suggested by Olugbekan (2004):
Reduction in out put cost (electricity, water used for supply or irrigation, fish,
recreat ion);
Reduction in future maintenance cost; and
Reduction in economic losses due to failure
* Cost effective technique is another method for analysing earth dam costs which, considers
both quantitative as well as qualitative aspects of earth dams. But for cost and benefit
technique, it must be kept in mind that its application will necessitate consideration of resource - - - - - - - - - - - - - - - - - - - - - - - -
development policies of the study areathatutilizG the ratios ofbotlihenefrt and catSn-this-
basis, economical design of an earth dam means the design with the highest excess value of
benefit over cost as suggested by Agunwamba (2000a). Although the cost benefits ratios do not
in them selves provide enough information to make an economic choice between several
alternative designs, its use as a means for sound design evaluation needs additional analysis. 7
Cost benefit analysis needs information on money values of services which are unavailable for
the study area. If however, the choice of economic structure is based on cost-benefit ratio, then
the ratio should be greater than unity for additional cost to be justified as suggested by Dixion
I
(1 964), Agunwainba (2000a), and Osara, (1 997). Ihis can be expressed mathematically as:
A plot of benefit-cost ratio against the project cost yields a parabolic curve whose
maximum value coincides with the most economical design (Franzini and Linsely, 1979). It is
however becoming apparent that a need for water resource development models or
management tools be done to assist in analysing water resource problems, and for evaluating
- between alternative solutions, thus aiding the understanding of the economic, technical, social
and political aspects of the alternatives. Such models couldpoint out the types of inputs and
outputs necessary and how each relates to each others (Dawes, 1970). The above components
are normally considered in terms of cost, environmental quantities, reliability, implement
ability (as related to institutional and other factors) and energy utilization. Although several
alternative combinations are possible, mixed integer programming screening model could be
used to reduce the large number alternatives down to a manageable number based on cost as T
pointed out by Goodman (1984). Further approaches could be used to evaluate between the 1
screened alternatives. I
2.2.0 Project alternative evaluation techniques
To every engineering problem there are several approaches and golutions, however, only
one bpttmum -or -be& - resdt- fbr t h e -variables available, - T h e , A first - - - approach - - - - - - involves - - - -
\ administering questionnaires to estimate citizen's preferences for the,selected objectives. The \
second approach involves a technical evaluation of each alternative based on how well it
satisfied each objective. The third approach utilizes the results of the first and second approach
to generate ranking for the final alternative. For convenience, the approaches were classified
as. # r
Citizen participation;
Technical evaluation; and
Multi objective decision matrix.
2.2.1 Citizen participation: Citizen groups that benefit directly or indirectly fiom Hydrau
structures and whose interest span on economic growth through the provision of citizen welfare
as Farmers Association (FA), River Basins Technical Advisory Board (RBTAB), Public
Welfare Board (PWB) etc. could be selected to represent the voice of the citizens. General
discussion could be made with each group involving questions and answers period carried out
by the evaluator. Questionnaires could also be administered to aid in estimating the weight the +
citizens attached to the following objectives.
9 Cost of the project
ii) Effect on environment
iii) Reliability of the project
iv) Implementability of the project , "
v) Energy requirement to sustain the project.
The weights are rated in percentages and tabulated as shown below in Table 2.1
Table 2.1 : Weights for objectives comparison
objective
1. cost
2. Environment
3. Reliability
4. Implement ability
5. Energy requirement
(After Philip, 1987)
RBTAT !%) PWB (%!
'I'he cost effectiveness of a structure is broad in scope and may include considerations
of all means for enhancing water resource development in addition to social, political,
environmental and economic costs as criteria for evaluation. Reliability is determined in terms
of the percentage of time an existing hydraulic structure meets its water resources development
requirements.
lniplement ability could be estimated in terms or response fiom appropriate officials
based on citizen's acceptance, existence of a capable management agency, acceptance by
existing institutions, regulatory agency acceptance, and adequate iinancial base. The energy
requirement objective could be rated by evaluating the total annual energy budget for each b
alternative.
2.2.2 Technical Evaluation. Technical evaluation could be made to determine how each
alternative compares with all other alternatives in fulfilling specified objectives listed in Table
2.1 above.
2.3.3 Multi objective Decision Matrix. In this approach, the aim is to estimate an overall
evaluation Index (I) by combining the technical evaluation and objective weights using a
technique of additive weighting as shown in Table 2.2. Each objective weight is multiplied by
an appropriate relative value for an alternative. The combinations arc summed in the vertical
direction giving the final score (index) for each alternative (Good man, 1984). Thc alternative
with the highest score (indices) will determine the final alternative. Mathematically, the
objective function is to be niaximizcd as suggestcd by Good man ( 1 984).
Where, j varies fiom 1 to m.
IF number of objectives (is this case five); m= number of alternatives; Wi= weight of
importance the citizen places on objective I and Vij= relative value of alternative j in fulfilling
Table 2.2: Multi objective decision matrix
Objectives - Alternatives
1 Cost
2. Environment
3. Reliability
4. Implement ability
5. Energy requirement
Total (I)
(After Philip, 1978)
In general, components of water resource development structures are structures needed
for storing finished and unfinished water, transmission facilities, treatment plant, distribution
system, reconditioning, reuse and disposal, wells and pumps etc. Important among them are
dams (earth and concrete dams), wells and pumps. Only earth dams were covered by this
study.
2.3.0 Project appraisal in developing countries by financing Organizations
Project Appraisal refer to the process of reviewing a particular project by an authority,
government to determine whether the project meet appropriate criteria for authorization and/or
funding, or whether a regional plan meets appropriate standards for proceeding with
implementation studies. Project appraisal in developing countries is based largely on the
appraisal guidelines of the World Bank, an organization that reviews applications for a loan by
governmental or quasi- governmental organizations. The World Bank's approach places more
emphasis on criteria to implement and its concern on other impacts, such as the effect of the i
intended project(s) on low income groups in the society. This multi objective broadening of
criteria makes the cess more generally applicable and requires an agency in a developing
country to submit a loan application in order to fulfil its responsibility of providing services to
a particular area. The proiect is also expected to be important to the rcgional or national
economy and to the improvement of thc general welfare and standard of living. Among the
important factors considered for appraisal by the World Bank, include the following as listed in
Goodman, (1984): the Economic aspects, technical aspects, commercial and financial aspects,
institutional, organiix~tional and managerial aspects.
2.3.1 Economic aspect: The appraisal here sets to ensure that the sector (pro-ject) involved is a
priority for the economic development of the country concerned and whether the project is
* sufficiently of high priority to justify thc investment into it. Other economic aspect should also
+ be considered when establishing an order of priority for the various pro.jects. This is because a
basic investment in a pro-ject with lower economic returns may set a stage for the development
of other project(s) with much more attractive returns. As an example, a dam may be
constructed to impound water for irrigating farm that produces a raw material for a factory (
Kiri dam in Upper Benue River Basin Development Authority provides water for sugar-cane
plantation irrigation which generates raw material Ibr Savanah sugar company, in Numan,
Nigeria)
fl 2.3.2 Technical aspects: This appraisal is much concerned about the reviewing of the detailed
engineering plan for construction and operation of the project. It also ensures that qualified
engineering staff prepares the plan. Apart fi-om the adequate pro-ject layout, the design criteria - - - - - - - - - - -
employed for preliini%ypla~ii expccted fot subsequent detailed designs o n theapproval of the
project are also reviewed. 'Thc appraisal also considers proposed plans of least cost or I
otherwise best solution among the alternatives, The constriction schedules should be clear
enough to check delays. Cost estimates should be comprehensive and contain adequate
contingencies for omissions, physical contingencies and price increases due to market &
fluctuation caused by inflation or deflation. Project operation cost should also be provided to
safe guard the pro.jqt alter completion.
2.3.3 Commercial aspects:
w The appraisal at this stage seeks to know the arrangements fbr purchasing materials and
services needed for the project construction. World Dank's guideline however, emphasises on
obtaining best value for money expended and this might involve competitive bidding even
internationally when practicable. The evaluation of bids take account of price, quality of work,
experience and reliability of the supplier, efficiency of the project, tern? of delivery and
payment arrangements. Arrangements for obtaining the materials, power, labour to maintain
and operate the project, and marketing of the goods and services provided by the project are all
appraised.
2.3.4 Financial aspects:
The appraisal at this stage determines the soundness of the financial plans for both
construction and operation of the project. For construction, the plan should cover all the
monies involved and their sources, the amount involved and terms for repayment of loans.
Financial analysis should also include financial liquidity, prqject costs expected during the
operation phase, and the revenues and other finds to pay such costs and to repay both foreign
exchange and domestic loans.
- 2.3.5 Institutional, organizational and managerial aspects: The appraising body at this stage
seeks to review the organizational arrangements for construction and operation of the project.
It would like to be assured that the organization functions as a business like manner and, in - - - - - - - - - - - - - - - -
some projects, assistance isbased o n credion-of an autonomous aperating authority free from -
political pressures and rigidities of governmental administrative procedures. Another condition li
stressed by appraising body is on the availability of adequate management skills. However, if
the needed skills are not fully available locally especially engineers, accountants, lawyers and
other disciplines, outside organization or individuals may be needed especially at the initial
stages of operation to provide management training to local person. Among the managerial
task is developme@ and administration of rate policies, monitoring financial performance, and
settjng technical standards for operation. Training programs should be provided for both office
and field operations.
2.4.0 Earth dams
Dams are usually constructed as multipurpose that is, dams constructed for a
combjnatio~i of the following functions; diverting or storing water for irrigation, water supply,
flood control, electricity generation, and navigation purposes (Agunwamba, 2000a) or as
mono-purpose. Earth dams could be classified according to the nature of filling materials as
homogenous earth fill, earth and rock filled (zoned), and rock filled dams as shown by Twort
and others, ( 1994), Garge (1990), Arora (2001) . A simple earth embankment dam is t
essentially homogenous throughout however, most at times a blanked of relatively impervious
material is usually placed on the upstream face of the dam. Zoned embankment earth dams
usually have a central zone made of selected soil material to for111 an impermeable core against
seepage. The rock filled earth dams are built with coarse rock pebbles to provide structural
stability with either an in~pervious membrane on the upstream slope or an impervious earth
core within the body of the dam as a water barrier. Dams mostly encountered in the study area
are mostly earthhock filled and homogenous earth filled dams. The distributions of the earth
dams and their costs in the study area are as shown in Table 2.3.
setting technical standards for operation. Training programs should be provided for both office
and field operations.
2.4.0 Earth dams
Dams are usually constructed as nlultipurpose that is, dams constructed for a
combination of the following functions; diverting or storing water for irrigation, water supply,
flood control, electricity generation, and navigation purposes (Agunwamba, 2000a) or as
mono-purpose. Earth dams could be classified according to the nature of filling materials as
homogenous earth fill, earth and rock filled (zoned), and rock filled dams as shown by Twort
and others, ( 1994), Ciarge (1990), Arora (2001) . A simple earth embankment dam is b
essentially homogenous throughout however, most at times a blanked of relatively impervious
material is usually placed on the upstream face of the dam. Zoned embankment earth dams
usually have a central zone made of selected soil material to form an impermeable core against
seepage. 'The rock filled earth dams are built with coarse rock pebbles to provide structural
stability with either an impervious membrane on the upstream slope or an impervious earth
core within the body of the dam as a water barrier. Dams mostly encountered in the study area
are mostly earWrock filled and homogenous earth filled dams. The distributions of the earth
- dams and their costs in the study area are as shown in Table 2.3.
Table 2.3: Earth fill dams in Northern Nigeria and their construction costs
Dams Year
completed
1 .D/Kowa
2. SA.
3. JBNL, I
4. SGE 1 I981
5. FNI, t - i ? r
8. Alau 1988
9. Gubi ---p@-
I I . Kura
12. Mayo Belwa
1 3. Mangu t?i%T--
14. Panshanu 7 15. Farakwai 1 2 0 0 4
16. Giwa pix- 17. Gwaraji -- i 1 8. Sabon Birni 2003
I
20. Shagari 1 I990
(Culled from URRBDA,
Height I Lengt [TopTReservoirr (m) I h I width 1 Capacity I Actual cost
I I I I - j78 and 1984; FMWRRD, 1995).
Inflatior Adjusted to Factor 2006
3446353754 114.99
47905533 14 114.99
' 4187796127 114.99
4695354467 114.99
4939619876 114.99
7864752669 114.99
7429842465 121.35
35449742 - 2 . . 2 4 8
1224685000 3.181
2366175850 1 7 . 3 . 0
586270795 34.3
114399721 6.693
7090896202 - 2.248
70873024 2 . 2 4 8
70439909 2.248
680325 12 2.212
56980437
Key ENGR- Engineen estimate SA- Starllng Astakli, Nigeria Ltd l B N G lalims B e q r , Nigerb Ud SGE - ~ w l e b Genera* Entevrlses FNL- P o o ~ d e NIgerIa Ltd AV-Ar.dran Volke; Civil Fngg. Ltd
An earth dam usually has several structures called the appurtenances. These may include.
(i) Dam embankment;
(ii) Spillway;
(iii) Intake structure;
(iv) Outlet structure (surface and bottom.);
(v) Power house; and
(vi) Diversion tunnels or coffer dams (especially at construction stage).
?'he dam embankment is expected to:
- provide stability against external forces; and
+ ensure water tightness of the structure
Stability against water forces could be achieved mainly by the weight of the dam and
anchorages. Water tightness of dams on the other hand does not mean absoIute water tightness.
But that the seepage must stay within tolerable limits to avoid the danger of failure due to
excessive loss of water as suggested by Ademmuliyi (1987). This gives rise to three technical
possibilities, such as:
(i,
(ii) .9
1 Jsing water tight materials in construction especially concrete dams.
FIaving earth dams that allow a steady tolerable flow through an embankment by
seepage. In such cases; the upstream and downstream slopes should be flat enough.
The fill material properties like cohesion coefficient (c) and angle of internal
&ictiGn(+J ShXld IE comtjiired~ptirndly-to give-adequak-fac_tar_of safety. - - - - - - - - - - - - - - -
- - - -
Rock fill dams, whose slopes could be remarkably steeper than those of earth dams
because the shear strength of rock fill dams is oAen much higher than that of
homogeneous earth dams.
Seepage control measures in earth dams. Ts
The control measuses that could be adopted to reduce the catastrophes associated with dam
failures caused by seepage include the following:-
Reduction of seepage volume quantity: Seepage volume could be reduced in earth
m
dams by the provision of an inlpervious barrier called the hard core. With recent technologies,
synthetic membranes could be adopted in earth dams for controlling seepage as suggested by
Oskoorouchi (1988). The hard core could extend to foundation in which case, it is called partial
or complete cut off lrench. Tt could also be a horizontal impervious blanket at the upstream side
or combination of both cut off and horizontal impervious blanket.
At the design stage of earth dams; determination of the particulars of the cores are necessary.
These includes:-
- Selection of material: 'The desirable qualities of earth dam core material are flexibility and
b erosion resistance. Flexibility refers to a deformation without cracking. Shearad (1976)
suggested that materials with plasticity index (PI < 15) and grain size ranging between 2x10"
to 1.20 mm are susceptible to cracking but observed that plasticity index higher than 15
improves the material flexibility. Erosion resistance on the other hand is the material's ability
to withstand erosive action of water leaking through possible cracks. Experimental
investigations carried out at the Water Resources Development Training Centre by Venkatesh
(1 973) and Marjono (1 974), indicated that erosion resistance normally increases with plasticity
index except for highly plastic expansive and organic clays. Stabilizing the material by
bentonite or by compaction improves its erosion resistance. Recent studies have suggested
using anthills especially where they are available for core material fill (Yohanna and others,
I \
Determination of core size: Earth dam hard core usually has smaller shear strength than
material of the pervious zones (Oskoorouch, 1988), and because of its imperviousness, it
would have natural pressure and tends to reduce its stability. In addition, during construction,
adequate compaction of soil is required which is usually done in layers at fairly accurate d)
moisture content. These factors indicate that the use of minimum thickness of hard core
consistent with the dam's safety is important. Theoretically, minimum core thickness is
19
governed by the requirements for permissible seepage losses which could be estimated fiom
Darcy's equation. Therefore, the core thickness would depend on the permeability of the core
material but generally on the designer's premium to safety against piping. Davidenkoff (1 955)
conducted an experiment on material composition for rock dams which indicated that hydraulic
gradients of 300 -- 600 was found to be suitable for the movement of soils with permeability
ranging from 4.0~10-'" to 3.0~10-" rids. For these type of soils, provision of filters are
necessary really for a defensive design measure to ensure safety in the event of leakage through
cracks. Sherard (1 967) suggested the following measures for hard core design.
* Cores with widths of 30% to 50% of the water head proved satisfactorily under
+ diverse conditions;
* Cores with width of 15% to 20% of the water head are considered thin but, if
adequately designed and constructed filter layers are used, they are satisfactory under
most circumstance; and
* Cores with widths much less than 10% of the water head have not been used widely
and probably should be considered only in situations where leakage through the core
would not lead to the dam failure.
v
Core location in Earth dam section: Generally cores are located as central, moderately
slanting and slanting positions in earth dams. The central core location has the following
advantages:
* having high pressure on the contact between core and foundation thereby reducing
possibility of leakage;
* Provides opportunity for grouting;
* Cracks on Cores could be remedied by grouting through vertical holes; and
* Location of contact area with foundation is independent on the depth of excavation.
A moderately thick central core with pervious shells gives slightly flatter upstream slope
compared to the downstream slope as suggested by Oskoorrouchi (1 988).
This means that by slanting the core towards upstream, the downstream slope can bc made
steeper while the upstream slope remains flatter.
Reinius (1 973) estimated pressure distribution on the base of the shell downstream of the
cores at various inclinations and concluded that an inclined core results in more advantageous
stress and deformation conditions of the fill material downstream of the core than a vertical
core. For cores flatter than 0.5: 1, no advantage is gained in respect of stress conditions in the
- downstream side of the dam.
b 2.4.1 Spilhvrys
The function of a spillway in dams generally is to release flood or excess water that cannot
be contained in the storage reservoir downstream safely. At times, to allow the water simply to
overtop the dam would result in a catastrophic failure of thc dam structure. For this reason
carefully designed out flow passages known as spillways are incorporated as part of the dam
design. The spillway capacity must be sufficient to accon~nlodate thc largest flood discharge
likely to occur in the life of the dam without endangering the dam structure. There are several
types of spillways in use and their classification. Based on their prominent features, spillways L
could be classified as follows (Arora, 2001 ; Novalk and others, 1990):
(iii)
Free over fall or straight drop spillway;
Overflow er-ogee+pillway: T h e over flow-or agee spillways g e - - - - - by far the most - - - -
widely adopted for either masonry or concrete dams with sufficient crest length to
obtain the required discharge;
Chute or open channel or trough spillway;
Conduit or tunnel spillways (usefirl for dams sited in narrow gorges);
Shaft or morning glory spillways oflen used on earth dams. Morning glory
spillways consist of four parts namely:- A circular weir at the entry, a flared
transition which conforms with the shape of the shaft, vertical drop shaft and
horixontal (or gently sloping) outlet shall;
(vi) Siphon Spillway; and
(vii) Cascade spillway
Spillways could also be classified as suggested by USRR (1974) as
* Combined service and auxiliary spillways, and
* Emergency spillways
The combined service and auxiliary spillway types are suitable where site conditions are
f'dvourable. This includes the existence of saddle or depression along the rim of the reservoir d
that leads into a natural waterway. Another site condition is for a site with a gentle slopping
abutment that can allow excavation beyond the dam structures. Emergency spillways are those
designed to release flood during emergency situations caused by either of the following
* Enforced shutdown of outlet structures;
* Malfunctioning of spillway gates; and
* Necessity to bypass the regular spillway during unprecedented flood that may result
in failure or damage of the dam structure.
Spilhvay components: The major components of spillways include control structures,
discharge channel, terminal structure, etc. The control structure regulates water releases
especially when reservoir water rises above the level of the control structure. The design
principles involve achieving a component that could pass all released water without difficulty.
The control structures may include sill, weir, orifice, tube or pipe, etc.
Discharge channel: 'The discharge channels on the other hand, refer to the structures
that usually carry flood water downstream. The design involves getting an adequate cross-
section that could easily carry the flood water downstream without spillage or scouring. The
selection of profile, cross-sectional area, widths, lengths etc depend on geologic and
transition which conforms with the shape of the shaft, vertical drop shaft and
horizontal (or gcntly sloping) outlet sha It;
(vi) Siphon Spillway; and
(vii) Cascade spillway
Spillways could also be classified as suggested by IJSRR (1974) as
* Combined service and auxiliary spillways, and
* Emergency spillways
The combined service and auxiliary spillway typcs arc suitable where sitc conditions are Y-
favourable. This includes the existence of saddle or depression along the rim of the r e se~o i r b
that leads into a natural waterway. Another site condition is for a site with a gentle slopping
abutment that can allow excavation beyond the dam structures. Emergency spillways are those
designed to release flood during emergency situations caused by either of the following
means:-
* Enforced shutdown of outlet structures;
* Malfunctioning of spillway gates; and
* Necessity to bypass the regular spillway during unprecedented flood that may result
in failure or damage ofthe dam structure.
Spillway components: Thc major components of spillways include control structures,
discharge channel, terminal structure, etc. The control structure regulates water releases - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - - - - - - - - -
especially when reservoir water rises above the level of theconfiol~structufer -The design
i !. % principles involve achieving a component that could pass all released water without dificulty.
The control structures may include sill, weir, orifice, tube or pipe, etc.
Discharge channel: The discharge channels on the other hand, refer to the structures
that usually carry flood water downstream. The design involves getting an adequate cross-
section that could easily carry the flood water downstream without spillage or scouring. The
selection of profile, cross-sectional area, widths, lengths etc depend on geologic and
topographic characteristics of the site. Common cross-sections are rectangular, trapezoidal,
- circular or other shapes. The terminal structure is basically an energy dissipation mechanism.
Energy is normally dissipated utilizing devices like hydraulic jump, stilling basin with baffles,
a roller bucket, a sill block, apron, some times a basin i~icorporating impact baffles and walls;
and some other energy dissipators that may be appropriate.
Erosion control devices: Because the spillway is associated with disposing off flood
water with high kinetic energy, there is tendency that such energy may not be dissipated
completely. As a result, if control measures are not put in place, then scouring could damage
" the control stnictures and at times affect the dam itself.
b Control measures may include use of rock paved chute or by using impact forces on the main
stream downstream.
Spillway Design: In the design of spillways, the main objectives are for the spillway to be able
to withstand the worst and variable flood loading conditions (Arora, 2001; Novalk and others,
1990; Punmia and Lal, 1990; Singh and Vershney, 1979). Spillways are more important to
earth dams because of their susceptibility to erosion during over topping as observed by
Roberson and others, (1 988). Spillway inadequacy often results because of under estimation of
v the peak flow rate or volume of the design flood. In view of this, flood estimation should be
handled by an experienced hydrologist.
Spillway size and type selection: In order to make the best combination of storage and
spillway capacity to accommodate the selected inflow design flood, all pertinent factors of
hydrology, hydraulics, design, cost and damage risk be considered (USBR, 1974). Attention t
should also be given to the following factors:-
* Characteristics of the flood hydrograph;
* Damage that may result if the dam is not in place or when it is in place;
4
* Damages that would occur if the spillway were breached; and
*Relative costs of increasing the capacity of spillways.
Minimum inlet and outlet widths for spillwavs
Considering the design flood and cost. the spillwav control device size. then the maximum
spillway discharge and the maximum reservoir water level can be determined by flood routing
as suggested by USBR (1974). Other features of the spillway could then be proportioned to
conform to the required capacity and to the specific site conditions to establish the complete
spillway layout. Nelson (1985) gave values for relating spillway inlet widths for a given flood
flow and was extended to give Table 2.4.
Table 2.4: Minimum inlet width for given flood flow.
l%od flow (m'ls) - - -
Upto 3
4
5
6
7
8
9
10
11
12
13
14
Inlet width (m) 4 . . - . - .
5.50
7.50
9.00
1 1.00
12.50
14.50
16.50
18 50
20.00
22.00
23.50
25.00
(Source: Nelson, t 9851
Minimum inlet and outlet widths for spillways
Considering the design flood and cost. the spillwav control device size. then the maximum
spillway discharge and the maximum reservoir water level can be determined by flood routing
as suggested by USBR (1974). Other features of the spillway could then be proportioned to
conform to the required capacity and to the specific site conditions to establish the complete
spillway layout. Nelson (1985) gave values for relating spillway inlet widths for a given flood
flow and was extended to give Table 2.4.
Table 2.4: Minimum inlet width for given flood flow.
Flood flow (mqs) Inlet width (m)
(Source: Nelson, 1985)
T l w v:~lues in Table 2.4 were l~setl to derive n relntioii for estimating inlet width for a
piven flood or vice versa. The relations between the outlet widths and the flood flow at
various return slopes is given in Table 2.5 as suggested by Nelson ( I 985)
'['able 2.5: Minimum outlet width for a given Ilood flows and return slopes
Flood flow
(m3)
- .
Outlet width at various return slopes (m)
14 12 10 8 6 4%or less 24 2_2_-20_18 16
15 100 94 87 81 74 67 59 52 44 3530 -- - -
(Source: Nelson, 1985)
Table 2.5 was used to construct a monograph for estimating discharge, outlet width or return
slope when two of the parameters are given as shown in Figure 4.01d.
Environmental effects: In recent times attention has been on environmental consequences of
" every project. Thus, environmental considerations have become very important in the design of
earth dams and can have a major influence on the dam type selected. Some of the
environmental effects includes the presence of pathogens, growth of animals that complete
their lives cycles in water, encouraging the breed of insects that breed in or near water bodies
(Dirk Vander Waal and Mintesinot Behailu, 2001), denudation of land masses, consequences
of dam failure, etc.
Economic effect: The final selection of the type of dam should be made only after carefhl
" analysis and composition of possible alternatives based on economic analysis and costs of
# spillway, power house, control structures and foundation treatment.
Settlement: The magnitude and rate of settlement depend upon a number of factors such as the
character of the soil in the earth dam embankment and foundation, the drainage conditions, the
height of the dam, depth of weak strata and the method of construction adopted. Generally,
settlement allowance of 1 to 2% of the dam height is made. For large dams with height up to
30 m, an extra allowance of 1% is made to account for the settlement due to earth quakes as
suggested by Novalk and others (1 990).
Cut off in foundation: The effect of seepage could be reduced to tolerable value through the 't*r
foundation as to avoid piping failure. Cut off wall is usually provided when the foundation is I
pervious to moderate depth. An impervious core is usually provided at the centre of zoned
earth dams to control the loss of water by seepage through the dam embankment. The site
slopes of the core should not be greater than (x - 0.5): 1 on the upstream and (y - 0.5): 1 on the
downstream, where x: 1 and y: 1 are the upstream and downstream slope of the shell (Arora,
Earth dams top width analysis: The top width has little effect on the earth dam's stability but
w is governed by whatever purpose the top width will serve. Depending on the height of the dam,
the minimum top width should be between 7.50 and 12.0m (American Corps of Engineers,
1994). lhpirical relations for estimating the top width of earth dams exists as suggested by
(I JSI3I<, 1964; Singh and V;dima. 1990; Novalk and others, 1990: Sharma, 1979;
Agunwamba, 2000b) as shown in Ilqualions (2.26), (2.27) and (2.28).
'I'he relationships between the top widths and the darn heights for medium and large earth dams
in the study area are as follows.
'I'able 2.6 Medium earth dams in the study area.
slNo. Dam Owner
- - -- - 1 Achida SRBDA
Dinawa
Karkiro
Marnoma
Misbil
Suru
Wurno
Rijau
Girei
Yola
Ankwill II
Jekko l
Kogingiri
Kwall
Lamigo
Kubani
Umogidi
BlKudu
DaurX
RIGado
Alau
IlAdamu
Naka
SRBDA
SRBDA
SRBDA
SRBDA
SRBDA
SRBDA
NRBDA
UBRBDA
UBRBDA
NESCO
NESCO
MOW
NESCO
MOW
ABU
FMW
WRECA
BSWB -
WRECA
CBDA
MANR
LBRBDA
State
-.
Sokoto
Sokoto
Sokoto
Sokoto
Katsina
Kebbi
Sokoto
Niger
Adarnawa
Adamawa
Plateau
Plateau
Plateau
Plateau
Plateau
Kaduna
Benue
Jigawa
Bomo -
Jigawa
Borno
Kano
Benue
Year length width Height Capacity Purpose
In a similar manner the above analysis was repeated for large d a m using Table 2.7.
'I'able 2.7: I x g e earth dams in thc sludy area (1 1, 3 0 )
slNo. Dam Owner State Year length width Height Capacity Purpose
~
1 DlKowa UBRBDA Bauchi 1988 520 8 4 2 5 HE,IR,WS
2 Kiri UBRBDA Adaniawa 1982 1300 10 3 7 615 WS.IR
3 Usuma WRA FCT 1984 1350 10 4 5 120 WS
4 Omi NRBDA Kwara 1976 6 4 2 250
5 Pedan FCDA Abuja 1993 357 7 33 5.5 WS
6 Shiroro NEPA Niger 1984 700 7.5 105 7000 HE,IR,WS
7 Kainji NEPA Niger 1968 7750 8.7 6 5 15000 HE,IR,WS b
8 Kontogora NRBDA Niger 1400 10 32 350 IR
9 Jebba I NEPA Niger 1984 670 10 4 0 3800 HE,IR,WS
10 Jebba l l NEPA Niger 1984 540 7 2 9 3800 WS,IR
11 Kagara NSWB Niger 1995 1313 10 3 1 43 WS,IR
12 Gurara 6 54 WS,IR
2.4 Earth dam design principles
The preliminary design principles involved in estimation of suitable cross section at a
minimum cost. 'l'hus, it is iniportant that the construction matcrials be made of most
- - - eeolmntic& waterid ,wahMe ~ i U i ( w t xo~11pm111Lsi~g _ s a k t r durillg sonstr@ion and post - - - - -
1
&. conslrnction of reservoir operations (Suresh, 2000; Singh and Varshney, 1995, Novalk and
others, 1990; Arora, 2001 ; Nelson, 1985; I'unmia and I,al, 1992; Agunwamba, 2000; Garg,
1990 and IJSBR (1 965 and 1974).
The darn should be safe against overtopping due to large inflows;
I lave adequate, freeboard against wave actions;
* Have stable upstream and downstream slopes during construction, post construction
and during reservoir operations;
Have adequate provision for seepage control either in the dam body, or its foundation
and abutment to a tolerable level;
Ensure downstream slope is not cut by seepage lines to avoid sloughing; and
Provide protection for upstream and downstream slopes against wave action, water and
wind erosion.
The preliminary design estimates the following components of earth dam: Top width (W),
freeboard (FB), casing or outer shell, central impervious core and cut off, and downstream #
drainage system.
Empirical Relations: Earth dams were classified based on height as (USABR, 1974)
(a) Small dams (H< 10)
Top width (W) = 0.2H+3 I , (2.6)
(b) Medium height dams (lo< H< 30)
Top width (W) = 0.55H1 ' +0.2H
(c) High dams (H > 30)
Top width (W) = 1.65(H+1.5) " (2.8)
Where, H = maximum dam height (m) and W= crest width (m)
Embankment volume
Methods fix estimatingeartk wkms far eartkdams include horizontals@ce, average - area, - -
prismoidal methods etc. Nelson (1985) suggested a less accurate methQd as I
V = 1 .OSKBH (H+1) (2.9)
Where, K= Coefficient depending on gully shape (0.5-1.6), B= Length of dam measured along
Its crest (m), V= Volume of earth fill (m') and H = dam height (m). *rr
However, another simplified embankment volume could be estimated through the end area
method suggested by Water for the World (2004).
Freeboard
" Earth dam fieeboard varies with the dam height as suggested by USER (1965), Punmia and
La1 (1 992) and Arora (200 1). The effects of wave action should be considered in estimating the
freeboard as:
FB = 1.5 hw+ SF (2.10)
Agunwamba (2001), Saville and others, (1962) and Falvey (1974) suggested a relationship in
terms of wave height as:
' Where, hw = height of wave (m), SF = safety factor (0.6 -3.0)
b The wave height hw may be estimated from the relationship suggested by Agunwamba (2000)
Where, F = wind fetch in kilometre, UF = wind speed kmlh \
2.6 Related cost functions
Engineering decisions involving design, construction and operation needs economical
estimates (Rai and Anyata, 1999). However, for many projects in developing countries
political, economic and social factors play a big role, and such factors should be considered
when selecting a project in addition to its profitability as suggested by Findley (1982). Cost
estimates that are reliable and consistent with the local factors such as environment,
technological know how etc., are also important especially if an pptimum cost is to be
estimated for hydraulic structures.
Hydraulic structures have the major objectives of cost minimization as they involve large
investment cost profit or service maximization. Their major productisn factors include labour,
materials and services. 1
Formulation of cost functions may start with the definitions of the production fbnction for the
process under view. The production function approach is limited to cases where outputs and I
inputs are defined. The production fimction suggested by (Musgrave and Rasche, 1976;
Herzlinger, 1980) is of the form:
Where XI, x2, x3 ... xn are economic inputs and Q is the output.
For a productive project,
Taking Equation (2.13) above to represent the proposed cost function, Q, could represent the i
total cost, while xj,xl, ..... x, are the individual cost components ofthe structure.
An alternative functional form could be selected on the basis bf statistical analysis. In
selecting a functional form, alternative behavioural constraints based on economic systems and t
statistical analysis are considered as suggested by Musgrave and Rasche (1976). The various
behavioural constraints on the economic systems to be considered are the three optimising
rationales which seem appropriate for economic systems and include:
(i) Maximization of profits;
(ii) Maximization of output given a predetermined level of cost; and
(iii) Minimization of cost given a predetermined expected level of output.
Considering cost minimization case, the total cost could be defined for linear relations as ? '
suggested by Musgrave and Rasche (1976) as:
1. I
Where, CT= Total cost, Pi = Unit price of the i'h input and Xi= the i'h input or quantity.
In Equation (2.15), Pi could represent unit prices in a cost hnction and Xi the components
whose cost is to be estimated. In Equation (2.1 5), the unit prices of components Xi need to be
known. I
Cost factoring technique had often been used by Engineers to forecast unknown cost of a
pro-ject with a given level of expected output fiom the cost and output of a similar project of
known cost as suggested by Musgrave and Rasche (1976). The cost factoring technique is
represented as:
Where, CI and C2 are costs of projects 1 and 2, respectively
QI and QZ are the output of projects 1 and 2, respectively
X is the "cost output" or "cost-capacity power factor", which are standards. #
Writing Equation (2.16) for the unknown project as:
In Equation (2.17), 4 is a constant represented by
The ratio of the two cost functions is given by,
The exponent I/r is greater than one for the diseconomies of scale. The term l/r is less than one
when economies of scale r equal to or greater than one for constant returns to scale. This result
can be extended to account for general trend in inflation in various locations as suggested by
Musgrave and Rasche (1976). Suppose it is meant to estimate the impact on cost of component
rates in a region where only one labour input has different rate and in an area where input
receives an increase in its rate of variables. The cost function in an area one would be
represented by
And in area two, the cost fimction is represented by
Thus, the cost factoring function technique would yield:
'C-l Solving for C1 results in
I l r
CI = pi c2 /Ian
In a general inflation where all inputs are expected to increase by the same percentage in the
future, the procedure above could be used to determine the effect of inflation on the cost. If C1 is
the cost being forecasted, then cost would be
And our base period cost (C2) would be
Thus, adopting the cost fhctoring model theory, the relation could be written as:
t Another method of making investment decisions is by comparing alternative use of the available
fbnd, through life cycle cost analysis (Noel, 1985). Life-cycle costs are the total costs of a project
over its lifetime and may include initial project cost (research, developh&nt, design, c?nstruction,
start up, etc.) plus the operating costs (maintenance and operations) etc., over the life of the project
as suggested by Remer and others, (1 98 1) and Fisaha (2002). Life-cycle costing becomes popular
if operating costs are rwognized to be large fractions of or may even be greater than the initial
investment cost. But beqause the components required for effective
life- cycle cost
functions.
Another efficient
through statistical
analysis are mostly unavailable, it is difficult to apply it for deriving cost
procedure for obtaining cost functions and the variables that affect them, is
functions approach as suggested by Herzlinger, (1980). Statistical cost function
approach could predict the level of cost given the projected value of the independent variables.
Parameters for statistical cost functions could be data for a large number of similar projects at one
point in time called "cross-sectional analysis", or for one project over a number of years called
"time series" analysis (Herzlinger, 1980). The cross-sectional analysis assumes that all of the
organizations in the data base use the same production process but, the time series analysis
assumes that production process is held over constant time. This statistical cost function
formulation also assumes that relationship between total costs and independent variables are either
additive or multiplicative. The additive model assumes that marginal cost is given by
d (Total costs)/d (Q) (2.27)
Applying the cost factoring technique would yield
The above equations show that an increase in the cost of each factor of production leads to an
increase in the total cost of out put assuming all other parameters are held constant. However,
in most applications, the output rate is not constant and the input prices do not increase at
uniform rate. For a differential inflation where the input prices increase at various rates can be
represented by.
And the base cost C2 is given by
Applying the cost factoring model would give values that are independent of the other
variables in the regression equation, but contains polynomial expressions of value in order to
account for economies and dis-economies of scale as illustrated by Herzlinger (1 980)
Total cost= CL+ ljlQi - p2Q2 + p3Q3 +.....+ biQn + E (2.32)
Where a and Pi = constants of fixed and variable costs to be estimated.
Q= quantity of out put, and E= the error term.
# The relation shown in Equation (2.32) is a non linear polynomial function whose constants
could be estimated to represent the general cost function model for estimating cost of earth
dams in the study area.
Fixed costs constitute project cost or the cost accrued to the whole project and may include the
construction cost, engineering and legal services, contingencies and land cost. Dawes (1970)
estimated the engineering and legal services to account for about 15% and contingencies to be
10% of the construction cost. The operation and maintenance cost vary over the live of the
structure.
2.7 Maintenance cost
In the design and construction of an earth dam, an element of uncertainty and experience come
into play. As a result of the uncertainty an element of risk is involved. Thus, maintenance
becomes unavoidable especially in keeping the structure in a functional condition throughout
its life span.
Few civil engineering structures are maintenance free (passive structures) that is, those
structures whose performances are assured throughout the design live without maintenance.
Passive structures require no inspection or maintenance as suggested by Modarres and others
(1999), however, no9 passive structures require maintenance right at planning and design stage
for sustainability and avoidance of failure. This makes maintenance important in the life of
- engineering structures. Although the estimation of maintenance cost could be done based on
probability and consequence of the failure, Negede, (2002) and Agunwamba (2000b) suggested
using 10-25% of the project cost as maintenance cost. Gubrernariame and others, (2002)
suggested 2% of the total investment cost for operation and maintenance and 5% for
replacement cost. 2% to 5% was used as maintenance and operation costs for this study.
Maintenance cost could be of direct or indirect cost (Okoh-Avae, 1995); corrective or
preventive cost (FisaRa, 2002; Rai and Anyata, 1999; and Cairncross and others, (1 98 1).
Direct cost of maintenance +
Direct maintenance costs are the direct cost expended on labour, materials and fixed assets and
may be called corrective maintenance. Labour cost includes costs accrued to salaries,
allowances, overtimes and other forms of allowances paid to the maintenance team. Materials I
cost constitute the cost of materials required for the maintenance operation especially t I
consumables. Fixed asset on the other hand constitute the cost of equipment and tools acquired
exclusively for maintenance operation.
Indirect cost of maintenance 1 '
The indirect maintenance cost provides the necessary yardstick for measuring the effectiveness .B
of a maintenance system. Although it is difficult to quantify especially in developing countries
where data keeping is poor, it is an indispensable factor for comprehensive and meaningfbl
(a) Structures secondary damage;
(b) Structures failure; and ,
(c) Structures depreciation.
Estimation of indirect cost could be easier through valuation of depreciated project as
(91
suggested by Dutta (2000) while the structure's failure mechanisms and the consequence of the
failure would be tre ed in later sections.
2.7.1 Earth dams maintenance strategy
w In order to undertake a comprehensive maintenance of earth dams effectively, the
knowledge of the deterioration effects, failure modes, and how they could be reduced or
avoided is necessary. In earth dam maintenance, two maintenance options are common that is
the preventive and corrective maintenance. Corrective maintenance takes place after the
failure of the dam has occurred, but preventive maintenance is the maintenance carried out
before the failure of the dam. Choice between the two could be based on the cost involved and
the importance of the dam structure. Preventive maintenance is associated with low cost
\"
compared to the corrective maintenance cost but has to be periodic. This is because preventive b
maintenance is undertaken at early deterioration stage in its function or structurally but
corrective maintenance is after the whole or part of the structure has failed in function or
structurally. Therefore, it is important to understand the sequences and causes of these i
functional and/or structural failures. I I
Functional Failure: Earth dams or any civil engineering structure is usually designed with
some objectives in mind. 'These objectives are called functions and it is expected that the . I '
structure fulfils their functional requirements throughout the design life of the structure.
llsl However, the efficiency of the structure to meet its designed function I starts to diminish or is
halted due to ageing or unexpected uncertainties. A structure is also suppose to guarantee
certain minimum level of function through out its life, however defline below the minimum
designedlevel could-mean failure - in - function or hctional failure has occurred. - - - - -
- A , i , - - \ - - - - -
Structural Failure: Structural failure is characterized by the collapsing of part or the complete i
structure due to loss of strength, durability, appearance (aesthetic) etc. Use of inferior
materials, poor workmanship, earth quake, landslide, unprecedented floods etc, contributes to
structural failure in earth dams. In most structural designs, safety factors are introduced to *r
reduce structural failure. It should be clear however; that functionally active structure could be
structurally unsafe v d structurally safe structure could be functionally in adequate.
Fault Tree failure: This failure mechanism is called fault tree because logic diagrams are used
* to represent partial failures similar to branches or roots of a tree. The partial failures aggregate
to result in the structure's failure in parts or a whole. It is important however, to note that fault
tree could be of two types called series or parallel systems. A series system is represented in a
fault tree by a prefix "OR". This means that failure of one of the components (elements) leads
to the failure of the system or structure under consideration. A parallel system on the other
hand is represented by a prefix "AND7'. This means failure of both branches is necessary for
the failure of the structure or system under consideration. Tree fault failure could be
* exemplified by a sedimentation problem in a canal serving Savannah Sugar company ( Kiwi
#
dam in Adamawa State, Nigeria as shown in Figure 2.1)
2.7.2 Failure modes in earth dam structures. Failure in hydraulic structures
generally was pointed out earlier to be either failure in function or structural failure.
The failures for earth dams were grouped into three major groups (Punmia and Lal,
1992, Arora, 2001) with their likely probabilities as:-
i) Hydraulic Failures : 40%;
ii) Seepage Failures : 30%; and I
.a% iii) Structural Failures : 30%
The hydraulic failures include failures due to over-topping, wave erosion, toe erosion
and gulling. Seepage failure on the other hand, includes failure due to piping and
sloughing. Structural failures may include the following. : ;
P Upstream slope failures due to sudden drawdown; * 1
9 Drawdown slope failure during ful l reservoir condition; I I
P Foundation slide caused by spontaneous ejection;
P Failure caused by spreading;
Failure due to natural event (earthquake, seismic etc.);
P Failure due to damage caused by burrowing animals; and
P Failure due to damage caused by soluble minerals in water.
Interriai emsbn and overtopping arcafgaakular concernto - - - - - dams - - - - - - as they could constitute - - - - - - - - - -
60-70% of serious incidents of failures (Novalk and others, 1990). The failure defects,
characteristics, causes, and comctivelpreventive measures are sumrnirized in Table 2.8.
'"
Table: 2.8: Failure defect mechanisms and preventive measures for earth dam
I Characteristics I Causes I I
A. External
1 . Overtopping
2. Wave erosion
3. Toe erosion
4. Gull eying
B .. Internal seepage
5. Loss of water
6. seepage erosion -
(concealed internal
erosion)
---- I
-- - -pp
Flow over dam and possible I in adequate spill way,
washout; less cohesive soils under estimation of I most at risk; most serious if design flood, in
localized I I adequate freeboard.
Seniement reducing
free-board, spillway b
shoulder
toe.
of down streamer face by
andlor irregularities in formation, cut-off
on slopes or downstream
drainage system
perimeter of culverts,
measure
Adequate spillway capacitj
and initial fieeboard,
Accurate design flood, and or
reinforced grass surface to
slope. Restoration of
settlement crests protection.
Proper design and
maintenance. 4
Good hydraulic design;
'tramping walls.
Vegetation, surface
~einforcement and/or
drainage
Gut off and core grouting
Carehl design grouting.,
f
Internal - - - - drainage; - - - - filters; - - - -
careful zoning of fi l l detail
design; use of collars;
grouting
C. Instability
7. Foundation slip
8. Down and Change in morphology;
upstream face bulging and deformation
leading to rotational or
transitional slip
flow mechanism
d. Deformation Loss of freeboard; local low
10. Settlement spots
I
Source: Novak and others ( 1990).
Soft or weak
formation and/or high
pore water pressures
High pore water
pressure, slopes too
steep; rapid draw
down on upstream
slope.
Triggered by shock or
movement, silty soils
at risk
Deformation and
zonsolidation of dam
and/ or foundation;
result of internal
x-osion
Consolidate soil; drainage,
grout improvement.
Drainage; flatten slope or
construct stabilizing berms
Adequate compaction/
consolidation or toe berm
added.
Restoration of fieeboard;
good internal detailing to
reduce risk of cracking eg.
Protective filter. Good
detailing, with wide transition
zones etc.
Bis-was and Chatter (1971) in their study of over 1600 dams identified the causes of
"5
Table 2.9: Causes of hvdraulic structure failure in percentage
Causes of failure
Foundation problems
Inadequate spillway
Poor construction
Uneven settlement
High pore pressure
Acts of war
Embankment slips
Defective Materials
Incorrect operation
Earth quakes c Source: Good man (19114)
Baecher and others (1908) however, estimated dam failure rates to be in the range of
as 2x10'~ to 7x10" failureldam per year. They were of the opinion that historical
occurrences of structural failures seem to indicate possibly as few as 10% which is
attributed to mechanisms within the scope of either present or prospective methods of
engineering analysis. Thus it was concluded that, on the average, there is I .O chance
- - - - i m 10,QQO thata damwillfailinany yec.I t was also assumed that such failures occur - - - -
- - - - - - - - - - - - - - - - -
during the initial filling of a reservoir (first 5 years) and the remainder are spread over
the life of the structure as shown in the Figure 2.2.
5 Design life (in years).
Figure 2.2: Failure rate distribution for time after completion (from US
Water
Resources Council, 1979)
Maintenance of an infrastructure may be to remedy the causes that hinder the
fulfilment of a required fimction(s). These functions need be identified for
maintenance requirement. Functional losses could be grouped into three (Negede,
2002) as:
i) Technical causes;
ii) External causes; and
For the technical cause, either a component of the structure under consideration or the I
whole structure may fail due to ageing. Ageing is the gradual diminishing of strength,
loss of serviceability or complete loss of finction with time.
The external cause or malfunction failure however. includes unprecedented natural
happenings like flash floods, sediment load, earth quakes, lightening strokes on the
structures, power fluctuation, drought, stealing and accidents etc.
Human cause of structure's service failure may include errors made by human 1
activities which could occur at any of the following stages
P Design stage (wrong conception, defective data etc.);
h Construction stage( using poor materials, inaccurate specifications);
h Operation stage of the structure (improper opgration of zppurtenances, in
prompt response to an eminent danger like flash floods etc.); and
P Maintenance stage (lack of effective maintenance plan to rectify defects
before it could reach uncontrollable state). ' 1
Generally hydraulic structure's failure mechanisms may be grouped into three as , / .
suggested by Fisaha (2002) as:
i) Near- Field Neighbourhood failure mechanism: This include local erosion
or deformation in the vicinity of the structure among which are scour, surface
runoff erosion, sliding etc, caused by effects of water on the immediate
surrounding of the structure. . .
ii) Macro- failure mechanism: This failure mechanism includes all
visible externaL failures o fpaesor all the structure. This failure may be - - - - - - - - - - - - - - - - - - - - -
caused by:-
* dope instability: This failure becomes eminent when actual shear stress along
potential failure sections exceeds the shearing resistance along the section.
* Settlements (due to consolidation and/or creep effects): ere the
submergence of the structure is experienced with resultant decrease in
functional requirements.
iii) * Wear out of the structure or its components (ageing): This type
of failure is likely to occur in every structure no matter how reliable the design
and construction. This failure may also be caused by an unprecedented natural
happening like natural disaster
iv) Micro-failure mechanism: This failure mechanism includes internal
failures which control the behaviour ofthe constitugnts or units of the structure,
but not the whole structure and may include the following.
* Liquefaction: Failure characterized by the movement of loose sand with
resultant displacement of larger pebbles, sand mass or local sliding. I I
* Piping: This failure is caused by erosion in which soil particles are
transported by strong ground water flow through pipe like flow channels.
2.7.3 Ageing and degradation process
Dutta (2000) defined ageing as depreciation that result in the gad;al exhaustion of
w the usefulness of a structure's service life. In simple terms, ageingldegradation refers
to the gradual decrease in structural (strength, durability, and aesthetic) and finctional 3 ' 1
requirement. Dutta (2000) compared the value of a structure after some service life to - - - - - - - - - - - - - - - - - - - - - - - - - - -
its initial value to determine its level of bepreciation.-However, fora choice-of
t maintenance, the processes of degradation and ageing are important. Negede (2002) t
suggested the following processes as the causes of degradation.
i ) Linear degradation: This process may be caused by corrosion, wear, tear 11
over years.
ii) Accelerated degradation: This is the process caused by fatigue or load
resulting in a creeping effect of the structure over time (ageing). Example of this
degradation is the eroding of canal lining, erosion of dam slopes etc.
iii) Sudden loading: Sudden application of load to a structure could result in
degradation especially when the load is substantially big to cause failure of some
components or the whole structure (initial filling of reservoir after construction).
*r iv) Protection appurtenances or structural element attack: Most structures are
designed to have appurtenances or protection units in addition to the main structure.
Thus, this type of degradation could start on the appurtenances at the first stage. At
the second stage, the real structural elements are attacked (as an example, the failure
of a spillway could lead to the entire dam failure).
The minimization of degradation process results in minimum maintenance which " I ,
ultimately translates into cost effective structure. Thus, in the design of a structure,
the main objective is for the structure to carry out its functions with little or no I '
maintenance and reduce degradation. However, in most cases, the information and
gl process involved in the design and maintenance of earth dams are approximated
values, and most often inaccurate. Therefore, knowledge of the techniques for
quantifying, managing uncertainties is necessary. One approach to this problem is
I
required. This element of probability assurance is referred to as reliability as
suggested by Halder (2000)
Another approach is through a technique which measures the probability of failure
with some tolerable level of risk. The aim is to design a hydraulic structure that is
reliable in function and less risk of failure or degradation. Probability is a measure of
uncertainty and uncertainty in Engineering generally could be either be cognitive or
non-cognitive sources (Halder, 2000).
Non- cognitive uncertainty sources are classified into the following:
P Inherent randomness or uncertainty in all physical a observations:
Repeated measurements of same physical quantities may not yield the same
value due to numerous fluctuations in the environment, test procedure,
instruments used, ability of the observer etc. In such ti situation, a large
number of observations could reduce the variability of uncertainty.
P Statistical uncertainty: In most Civil Engineering designs, especially
hydraulic structures, precise information is lacking on the variability due to
non-availability of data. Thus, quantitative measure of confidence based on
the amount of data available adds up to their reliability evaluation.
9 Model uncertainties: In most hydraulic structure designs, data are obtained
through the use of computational models which most at times only strive to X
capture the essential characteristics of the system behaviour using idealized
mathematical relationships or numerical procedures. In doing this, some
minor determinants of system behaviour are ignored leading to difference
between computational predictions and actual behaviour. To reduce this
effect, past experience on the difference between computational values and
actual behaviour could be used to develop a statistical description for
modelling error. This could be included as an additional 'variable in the
reliability analysis.
The cognitive (or qualitative) uncertainty source on the other hand relates to
the vagueness of the problem arising from intellectual abstractions of reality.
This uncertainty may come tiom some parameter definitions (eg. structural
performance which could either be a failure or survival, quality deterioration,
experience of workers and engineerdor human factors like management;
politics etc). This source of uncertainty would not be covered by this study.
Uncertainty (Non-Cognitive): The necessary statistical information for the
quantification of non-cognitive uncertainty source may include some of the
steps in Figure 2.3 as suggested by Halder (2000).
Real World l------ . ample space ----+F=
- Relevant information
-
-
r- i 7
Mathematical representation of
I uncertain quantities t-
parameters
'-4 Density of dislribution fl~nctlon
RiskIReliabiIity evaluation (probability)
I:igurc 2.3: Steps in probabilistic study (from 1 laltlar, 2000)
2.7.4 Risk cost analysis 'I'lie design and construction o f hydraulic structures are
usually done with an element of risk (US Army Corps o f Engineers, 1994) but to a
tolerable value. Risk may bc defined as the probability o f loss o f production and asset
during the life of a structure. Kisk could be ~ninitnii.cd for a particular structure by
improving the design and increasing the investment and the maintenance cost. The
designer and the operator (engineer) o f tlie structure need to know the amount o f
money that could reduce the risk involved to its minimum and to guarantee adequate
production.
Risk could be quantified by taking the product o r the consequence o f damage of a
b specified failure incidence and the probability o f its occurrence as suggested by
Negede (2002). Mathemalically, i t can be reprcscnted as
Risk C'ost ((',) = 1'1 x C'p (2.3 1)
Where, C,= Risk cost
PI. = probability or failure
(II, - cost associated with failure or damage.
Fisaha (2002), suggestctl similar runction that uses present value cost and discounting
factor that takes the effect o f time and rate o f return as:
Where, I'VR - Present Value Risk Costs. - - - - - - - - - - - - - - - - - - - - -
P,, = I'robability o f failure with inspection
MVR = Monetary Value Risk o f consequence or Tailure.
I , I' = Design life o f the structure.
The estimation o f the monetary value o f the risk cost could be based on cost o f human
and property loss to flood, cost o f environ~nental damage, cost of decline in
anticipated benetit, maintenance and repair cost o f the structure aRer the failure etc.
'Thus. the acceptable risk should be based on optimal cost of the structure (i.e.
structure with more benefit but less cost and risk).
The Water Resources Council (1 979) suggested the following four major components
of failure consequences. These include:
i) The direct physical damage due to flooding after dam failure;
ii) The cost of emergency relief and rescue operations;
iii) The loss of economic activity due to loss of land, loss of facilities and
equipment and loss of capital ( a secondary economic loss might occur in
economic sectors linked by supply and demand to those that have been
affected by flooding); and
iv) The loss of foregoing future benefits (all benefits evaluated in cost benefit , I
analysis fiom time to time when an earth dam fails).
Al-Mashidani and others (1979), suggested a relationship for estimating the , I . .
probability of risk for flood of equal or greater magnitude that would occur at least
once during a hydraulic life time of the structure as:-
Where. U.P= urobabilitv of flood event ris. T,= Return period of flood r= Life span or design life of the structure.
The above Equation (2.33) could be used for our case, but making the return period of
flood to represent time for maintenance interval.
w An alternative to Equation (2.33) above was represented by t
Al- Mashidani and others. ( 1 979) as
Where. P=U=probabilitv of flood event risk e= an exponent.
The result obtained by Equation (2.34) was reported to be close to that of Equation
(2.34). After the evaluation of the risk associated with the design of a hydraulic
structure, the designer may accept it as it is or make some modification in the design
or in its maintenance strategy as to reduce the risk level.
Evaluation of risks with more complex events or actions other than just one as
assumed above needs the break down of the actions or events into their components.
If these components are assumed to be additive, then Equation (2.3 1 ) becomes
)I
Risk Cost (CR) = L ( P , xC, x W , ) (2.33) / = I
Where, Wi= weighting factor for a component failure event
PFi = pmbabilify of failure of il\omponent event.
CFi= cost associated with ?%component failure event.. I -
The failure probabilities for some common hydraulic structures are given by (Fisaha,
2002) are presented in Table 2.10
Table 2.10: Revetment failure Probabilities for some common hydraulic stmcture
-- Failure type Probability of failure
Revetment failure 1 . 4 ~ 1 o-'
(a) Overall instability
* Micro- Instability
* Unstable geometry
* Toe Erosion
b. Local Instability
* Unstable filter
* Instability of top layer
* Extreme currents
* Wave over topping
* Subsidence
2.7.5 Maintenance Modelling - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
In order to model maintenance adequately, knowledge of the level of risk to be
tolerated is very important. A structure could be risked to deteriorate without
maintenance. Of importance therefore, is whether increase in investment and
construction quality could reduce the overall life-cycle cost due to reduced
maintenance and risk cost. To access these conditions well, a model that could predict
the level of critical deterioration and optimal maintenance level is necessary. Inability
to predict with reliability the general performance of an earth dam in service and
other uncertainties had often lead designers to either over or under design earth dams
with detrimental effects. Over design is associated with high investment cost due to
resource wastage on construction materials, while under design is associated with
high maintenance cost or even a threat of failure in fimction and/or structurally as
earlier pointed out. The question then is, "How does one know the maximum
allowable deterioration to call for maintenance"? There is a link between design, risk
of failure and maintenance and inter dependable as suggested by the US Army Corps
of Engrs.(1994). These factors should be chosen to give minimum investment,
maintenance and risk costs. Mathematically, it can be represented as suggested by
Negede (2002) as
, I
Where, 1 = Investment cost of a structure, PV = Present Value okrator
Mc = Maintenance cost, PI: = probability of failure
CF = Cost associated with failure and CTotal = Total cost
If the components of an earth dam are considered and assuming additive, Equation
(2.36) takes the form
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Where, all terms in Equation (2.37) retain their meaning in Equation.(Z.36) but for the
il"component of the structure. A typical dam would be used to test the' above models
Maintenance procedure:
Maintenance procedure may bc defined as the niainteniince action a ~ i d its timing for a
parlicular componetit o f a structure or the whole structure (Anthony, 1984). The
procedure for maintenance may hc carried out as lbllows:
i) Maintenance carried out to prevent failure shown by numbers 1-3 in Table
2.1 1 ;
ii) Maintenance undertaken after the occurrence o f failure show by number 4
in Tablc 2.1 I ; and b
. . . III) I h n e as an opportunity maintcnance shown by number 5 i ~ ? Table 2.1 I .
'These maintenance procedures are summarized in 'l'ablc 2.1 I.
'l'able 2.1 I : Maintenance procedure alternatives
1.0. Fixed time maintenarice
2.0. I:ixed time Illspection
Maintenance.
3.0. Conti~iuous Inspection.
Maintenance.
4.0. Operate to Failure
maintenance
5.0. Opportunity
Maintenance - - - -- - - -. - -- - - - - - - - - (I rom Anlhory, 1984)
.. . ~ ~~- . - - . . - .. . . ~ - . Actions
Adjust or repair o r replace any damage to a
structure at fixed periods
Inspect via equal o r variable inspection periods
thcn adjust1 repairlreplacc on condition.
Inspect hydraulic structures on continuous basis
and then adjustlrcpairlreplacc on condition.
Replace or repair afler failure has occurred.
Inspect item at time based on some other
i. Fixed Time Maintenance
The Fixed- Time Maintenance refer to the type of maintenance actions carried out at
regular intervals, or after a fixed cumulative output , fixed number of cycles of
operations etc. Most often, the periodicities, actions and resources for such work
could be anticipated and scheduled well before hand with ample time tolerances. The
fixed time maintenance is only effective where the failure mechanism of a structure is
clearly time dependent (e.g. siltation problem of canals and reservoirs). The Fixed-
time maintenance cost is relatively lower than that of operate-to-failure maiptenance.
(ii) Condition based Maintenance
If the time for performing maintenance is determined by monitoring condition andlor
performance, and that a readily monitor able parameter of deterioration can be found,
the probabilistic element in failure prediction could be reduced or almost eliminated $
with the life span of the structure maximized and its effects on failure minimized
(Anthony , 1984). The monitored parameter may provide information about a single
component or provide information that may lead to a change in a number of
components of the structure. As a result, condition maintenance could be applied in
r \ \ . three ways as:
Simple Inspection: Here qualitative checks are based on look and feel. The - - - - - - - - - -
cost 7 s Tow- and asuaHy carried out as part of a r m t i n e inspection with - - periodicity - - - - - - -
t sufficiently short to detect minor and often unexpected problems before they develop
high.
Condition checking: It is also done routinely and most at times with the 1 1
measuring of some parameters which are most often not recorded. It could only be w
< y b
used for comparison with control limit especially where there is extensive experience
of identical systems.
Trend Monitoring: Here measurements are made and plotted in order to
detect the gradual departures from the normal. It is most effective where little is
known about the deterioration characteristics. Hence, trend monitoring is the most
widely applied condition based maintenance. Y
2 Operate to Failure maintenance: In this type of maintenance, it, is done after
failure of the structure or its component has occurred both finctionally and
structurally. Usually actions are not taken to defect the inset of or to prevent this
failure. Corrective work that results may occur with random incidence and with little
or no warning. If such failures occur in hydraulic structures, it can cause the complete
outage of the structure or its component. It is usually catastrophic and most often
associated with high cost in comparison to condition maintenance.
3 Opportunity Maintenance: The timing for opportunity maintenance is
determined by procedure adopted for some other items is the same unit of a 1
rC structure. This is because the failure of the components is only discovered when
carrying out a maintenance operation on a different component.
Actions for Maintenance: I '
Actions may be defined as activities carried out in the maintenance procedure. The
main "first line" actions may include "Replace", and "Adjust". In practice however,
each of these groups could be firther sub-divided (e.g. perman&t or temporary
repairs)
Among a l l the actions involved in a maintcnancc procedure, only for a lixed
maintenance is action established beli~re hand. I1 could also be called corrective
maintenance as i t arises not only when an item fails, but also when there i s an
indication from condition monitoring. It becomes clear only after the maintenance
causing even is established that the influencing factors like l j i lure cause, replacement
or repair cost, availability o f resources. cost o f unavailability, time to nexl window
etc., can be assessed and type o f repair determined. It becomes difficult however,
after the occurrence o f failure as a result o f opchte lo failure policies which
ultimately results in [he structure's abandonment. Condition monitoring helps avoid
this situation because it provides time for decision making and scl~eduiir~g. Some
failures do not stop the action o f tlie structure immediately, but rather could allow for
a time for a decision to be taken. Once such work i s identilied sonietimes (called
deferred work or jobs) the repair maintenance could be scheduled for a more suitable
time and date.
2.7.6 Failure of some earth dams and likely causes
In assessing an earth dam failure, the Following should be considered as suggested by
the IJS Corps o f Engineers (1994).
The consequence or hilure
Life span ofthe dam structural components
Nature o f the dam with respect to tlie Ibundation and cxtcrnal loading, and
Past performance and remedial measures
Although several dam failures were experienced will1 serious threat to lives and
properties, the following are among those reported in literature.
1. Teton Dam Failure (USA)
Teton dam was an embankment dam designed bv llnited States Bureau of Reclamation.
The dam was designed with approximately 92.0 m above the river bed level. The dam
failed in I 976.
Causes of Failure: The causes of failure was investigated by two groups of experts
(Singh and Varshney, 1995)
Tll i) Interior Review Group of Agencies of the U.S. Government; and
ii) Independent Panel of Experts 6
The result of their investigations is as follows:-
* Several unsealed open joints were discovered under the grout cap of the key trench
of the failed portion of the dam. The flow of water through the unsealed open joints
against the highly erodible and unprotected key trench fill and the consequent
development of an erosion tunnel across the base of the key trench fill were 1 " .
considered as the possible mechanism that triggered the failure
* The second likely triggering mechanism may be cracking caused by differential
I' T strains or hydraulic fracturing of the core filling material ofthe key trench.
It was concluded by the investigators that in either of the two triggering mechanisms ) I
above, leakage occurring through the key trench ultimately initiated fbrther erosion - - - - - - - - - - - - - - - - - - - - -
along the downstream contact of the core anii ibiitiiie"t-r6cl.
Although the Teton dam was constructed to specification, it could have failed as a I i
result of in-adequate protection of zone one impervious core material from internal
erosion. The most probable physical mode of failure could have been the cracking of
zone one material which allowed the initiation of erosion. However, the erosion could t
have been initiated by piping at the contact of zone one and rock surface. It is logical
that Teton dam failed structurally. (US Interior Review Group, 1980; Independent
panel Review Experts, 1976; Seed and Dun-can, 1982)
Remedy: The provision of a shot-crate mat or concrete block at the core contact with
rock foundations for several numbers of dams is to ensure a good seal and eliminate
the possibility of erosion by flow through an open joint left untreated. (Singh and
r* Varshney, 1995)
Consequent of Failure: The failure of Teton dam resulted in flooding downstream
which caused the loss of fourteen human lives and several thousand of livestock.
Property loss was assessed to be about four hundred million U.S. dollars
i ' 2. Failure of Panshet Dam (India):
I '
The Panshet embankment dam was about 56.5m above the river bed level and about
820m long. The dam failed in 1961
Causes of Failure: The Causes of Panshet dam failure was inquired by h e
w Maharashtra Government, India. 1 I
According to the Commission of Enquiry, the final cause of the' failure was the
subsidence of about 30m length of the dam and its consequent over-topping. The '1 r
subsidence could have been caused by the following.
material ofthe dam might have been removed through leakage;
Failure of Conduit: Stress analysis of the conduit indicated that its arch roof
was overstressed. This could have resulted in squeezing out of mortar fiom ir
between the voussoirs. The intermittent surging inside the conduit could have
contributed to the opening of joints and the entry of embankment material into
the conduit which could have led to the observed subsidence;
The rapid rising of earth work during the construction and the subsequent
rapid filling of the reservoir also contributed; and
In adequate compaction due to the urgency of the dam to be completed did not
allow the earthen embankment to have sufficient time to attain normal
settlement under its own weight. The saturation'of the in adequately settled
embankment to it full height immediately after construction could have
resulted in some settlement. This failure could be of structural and function
type (Commission of Enquiry , 1963)
Remedy: The filling of a reservoir behind and embankment dam should not be started
without assurance of arrangements for the regulation of the filling rate and to stop or
even reverse the filling process if necessary. Letting too large a difference in level to ' r '
develop between different portions of the embankment and of raising the lower level - portion too rapidly under pressure could have been avoided. Conduits shouldn't have
been allowed through an embankment fill, but, if it must have been done out of
necessity, stringent precautions in design and construction should have been taken.
- - - - - - - Failure_Cons~quence:Jot readily available. - - - - - - - - - - - - - - - - - -
3. Nanak Sagar dam failure (India):
The Nanak Sagar embankment dam was a U-shaped dam in aerial view. The
embankment consisted of two flanks (Eastern flank- about 10.70 km and Western
flank-about 8.0 km long) and 0.6 km long spillway separating the two flanks. This
*
makes the total length of the embankment to be about 19.30 km. The maximum
height of the dam was 16.50 m. The dam was designed as a mixture of homogeneous.
impervious section with a small rock on the downstream, and part as a zoned section
with semi-pervious shells, an upstream impervious blanket and a.downstream rock
toe. The dam failed in 1967.
Causes of Failup: The failed section was located at about 1.5 km on the Western
- flank fkom the spillway which is almost mid-way between the two flanks. The top
layer silt clay thickness was about 3.0 m and with a far more pervpus stratum of silty
sand underneath. The relief well system adopted was unable to relief the high
pressures built up in the stratum. This condition was aggravated in the reach by the
existence of a small local stream joining river Deoha downstream of the dam. The
sandy stratum was then connected to the bed of the stream causing a strong seepage
to be maintained which could only find an exit into the stream. The intermittent
boiling of water removed finer sand particles, there by reducing resistance to seepage
flow causing progressive intensification and ultimately piping through the
P foundations of the dam could have been responsible for the failure. This dam failed
both structurally and in function. (Harkauli and others, 1970)
Remedy: The remedial measures that could have prevented the failure include.
0 Using effective relief well system to reduce pressure; and
The installation of piezometers in the sand stratum downstream of the dam
and a continuous monitoring.
Consequence of Failure: Not available
4. Waco dam slide failure (USA).
The Waco embankment dam was designed with a maximum height of 42.70 m and
length ofabout 5.50 m. 'The dam suffered a sliding failure in 1961.
Causes of slidiqg Failure: Investigation into the cause of the sliding failure showed
that the central portion of the dam subsided along a roughly circular arc that extended
through the cut-off trench down to a bedding plane approximately mid-depth of the
pepper formation. The movement continued horizontally downstream until it
encountered a zone that was weak enough to permit a rise to the ground surface. The
movement was slow; hence there was no danger to personal or equigment. The failure
cause was analysed as follow (Singh and Varshnery, 1995)
0 Pore pressures: No piezometers were installed prior to construction;
however, 127 piezometers were installed during the analysis of the failure cause. It I
was discovered that within the area of the slide, excess pore pressure at mid-depth of
the pepper formation was about 70% that of the imposed embankment load under the 1
axis of the dam. The pore pressure dropped to about normal ground water level at a I
distance a way fiom the dam axis. This might have been so because of drainage
through cracks that developed during the slide. ,
Shear strength: As a result of the presence of bedding planes, the main
investigation was done by direct shear tests. The typical values for an undisturbed - - - - - - - - - - - - - - - - - - - - 1 1
- - - - - - - - - -
samples were frictional angle (b=14" and pore pressure c = 4.30 tonesrm'. However,
stability analysis on the slide surface, assuming pore pressures to be 70% of the
superimposed load, indicated an effective fi-ictional angle (4) value of only 8".
Evidently, the material in the seam was over consolidated and the residual shear
strength was much less than the peak value. Summarily, the slide failure of Waco
dam was caused by the presence of an over consolidated weak-shale layer and the
consequent development of high pore pressures on embankment loading. This made
the shear stress beneath the embankment to exceed the effective peak shearing
resistance. And this resulted in the reduction of the strength to a low residual value
with progressive movement and overstressing proceeded in a downstream direction.
- This is again a structural and functional failure type.
Remedy: The embankment in the slided area was redesigned for a residual friction
angle (J of 8" and an anticipated pore pressures for full dam height using a factor of
safety of 1.2. Berms extending to about 270 m both upstream and downstream of the
axis were provided. A series of vertical sand drains were drilled beneath the
downstream berm into the two faults to control seepage passing through the faults.
High pore pressures varying fiom 70% of the superimposed load (under the axis of
the dam) to 50% (in the general area of the pepper formation) was developed during
the reconstruction and continued to persist afterwards
I Consequence of slide failure: Not readily available.
5. Draw down slope failure of Sampan dam (India): The Sampan embankment
dam was constructed with a maximum height of 21.30 m. The dam was designed as a - - - - - - - - - - - - - - - - - k - - - - - - - - - - - - - - - - -
zoned f i l l with a thick core or hearting whose clay content was 47% and fiictional
angle, pore pressure were 2 4 and 4.9 toneslm" respectively on saturation. Pre- 1 .
construction tests on samples of shells or casing material indicated a clay content of 3 t I
18%, pore pressure ( c ) value of 1.10 toneslm" and fiictional angle of material Q =
26". Thus, the shell material was considered semi-pervious and the factor of safety for '(.
9
upstream slope was worked out to be 1.80. The, the assumption of shell material
being free draining and the calculated value of safety factor of 1.8 were erroneous.
The dam failed twice (in 196 1 and 1 964).
Causes of the two failures: An inquiry in to the cause of the failure was undertaken
by an
Enquiry committee and found that:
The clay content of the fill material was 50% of the value adopted in the T
design; #
Compaction dry density was also found to be about 81.70% of the design
value;
The frictional angle (0) was about 70% the design value;
The section of the dam embankment was supposed to be zoned but was found
to be nearly homogeneous as constructed;
Compaction was in adequate and the actual shear strength was much less than
the design value; and
C
Factor of safety of the upstream slope was found to be 0.92 only.
After about three years from the first failure, another failure occurred in 1964. The
failure was more serious and occurred in a different reach of the embankment that is*
at a portion where the maximum height was 20.40m. The recommendations of the
Enquiry Committee were as follows:
The upstream should have been loaded to a level below water level by
dumping boulders under water Level;
Trimming the upstream slope above low- water level to a flatter slope, which
may be 3:l up to final reduced level (F.K.L.) and 2:l above the top, subject to
detailed stability analysis; and
Putting additional earth fill well compacted on the downstream slope of the
dam to compensate for the soil trimmed fiom the upstream slope in order to
maintain an adequate top width and a stable downstream slope.
T Summarily, the slip failures in both cases were evidently due to inadequate
exploration and testing, wrong assumption of design values and lack of needed
quality control during construction. (Singha and Vashma, 1995).
Remedy: Improving the stability of the upstream slope could have been done by
installing drains at moderate cost. The Enquiry committee however, did not favour 1 ,
extensive work involving the flattening of the upstream slope. On the contrary, the I
site engineers found that the drains could only be installed after dismantling almost
the entire pitching fiom the upstream face. As a result, no hrther action was taken
after the construction of the retired (or degraded) portion of the embankment. I . , ! , *
PC Consequent of Failure: Not readily available. i
6. Overtopping failure of Machhu I1 dam (India): The Machhu I1 embankment : I
dam was constructed by the state of Gujarat. The dam consisted of a central masonry
spillway in the river main section with about 2.4 km long earthen embankment on the
Pefi side and about 1.5 km earth fill on the right side. The top width of the
embankment was 6.10 m while the masonry section consisted of a 206 m long
spillway with a 92.0 m long non-overflow section equipped with radial gates.
At Machhu I dam (Masonry) located about 48 km upstream of Machhu II dam, had
about 700 m long earthen embankment on the right side and 1070 m long on the left
side of the masonry dam which were washed off by flood fiom an unprecedented
rainfall whose average gauge reading was about 530 mm in 21 hours. This resulted in
an inflow of 19800m'/s while the maximum outflow was only estimated at about
13450 mJ/s only before the failure in 1979.
i.',
Cause of Failure: Two Inquiry Committees were set up by the qujarat Government
to ascertain the pause of the Machhu I1 dam failurr b
The two commi$tee's main finding was that the embankment secti~n was adequately
designed. The dam also was found to conform to specification with respect to
construction quality. However, the rainfall intensity and the resulting flood inflow I
were indeed highly unusual for that type of arid zone (Jagdish and others., 1980) and ! t
could be the main cause of the failure.
Remedy: Maximization technique with maximum probable precipitation (MPP)
could have been used to estimate the design flood not less than 15000 m'/s for
Machhu I1 dam, more so that the risk of human lives is involved.
The lessons learnt fiom the Machhu I1 dam failure was more of disaster management
than that of dam engineering. Power failure, transport and communication disruption
Consequence of the Failure: The Machhu I1 dam was reconstructed at a cost much
more than the'initial construction cost, mainly because of the augmentation of the
spillway ffom 5550 m'/s to 19822 m'/s capacities. The damage caused was very
extensive; the most tragic of all was the human lives lost which was estimated at
:thor~t 3000. An indr~strial town located ahout 8.0 km downstream of the failed dam
(Morvi town) also suffered most compared to the above 68 villages washed off'.
I'ower supply, transportation and communication system were daniaged.
7. The failure of Alau dam, Nigeria. The major cause of the datn failure in 1985
was seepage through the foundation str~rctures as suggested hy Ademuliyi (1987).
# Possible measures to reduce failr~res in earth dams
I t could be generally concluded that the above failures could be averted with a
contim~ous routine observations ensure the datns retnain in a fairly good condition.
The observations to IX made are numerous; however, the following are important
indications of possible deterioration (l'wott and others, 1994).
1. Recording Instrument
* presence of higher than r~sual pore water pressures
* Pore pressures remaining persistently high especially those in the lower part of
the downstream shoulder aqjacent to the core wall or forniation. which do not
appear to vary with rainfall, hut are influenced by reservoir.
* Settlement and inclinometer gauge readings (if installed) which do not show a
declining range of movement with time
2. Under drain Flows.
* Flows not decreasing with dry weather;
* Out flows cloudy in appearance (Test for clay and silt colitent); and
* The presence of clay or silt in weir boxes, or in any tunnel or culvert taking
drainage water away fiom the dam.
3. Dam crest
* Appearance of any irregular settlement; ? .
* Absence of any slight bow upwards towards the middle of the dam, denoting
that if settlement allowance had been given to the dam (as would normally
have been the case), and all these allowance could be taken up; and
* Tilting of any wave wall or road way dong the crest.
4. Shoulders.
* Appearance of damp patches on the downstream slope or at its, toe, growth
of rushes at or near the toe;
* lmgular settlement, hollows, declivities, slight bulges on the downstream
slope, unusually luxuriant grass or weed growth in any location;
* Slabs or facings on the water face irregularly settling; and
* the line of impounded water against the upstream shoulder not following a
consistent smooth curve.
5. Others. I
* Tilting of the spillway weir crest or bell mouth lip as shown by uneven
overspill;
* New leakage into inspection galleries, draw off tower, bell mouth shaft,
culvert or tunnel with-in the dam or its abutments; and
* Valves or gates which are inoperable or difficult to operate. 8 1 %
2.8.0 Work quantities for dams
A good job and a successful cost control depend on the development of a good cost
estimate. The cost estimate represents the cost of services and materials that would
guide the Contractor make a profit. However unrealistic costing could lead the
contractor loose money on the job which may lead to job delay, abandonment or use
of inferior materials for the job construction. Consequently, failure or high
maintenance cost might result.
Cost estimate therefore entails looking into the htbre and predicting the cost of
materials and services with certainty. Studies have shown that the major cause of
failures in construction firms is incorrect or unrealistic cost estimating and bad
building practices. The preparation of detailed cost estimate requires the estimator to
break the project into "cost centres" or "cost sub-elements", so that unit rates could be
' , estimated for a particular material or service. A procedure suggested by Halpino and
I ( '
Woodhead (1 998) include the following:
1. Break the project into cost centres (e.g. site clearance, excavation, earth filling,
concreting, etc).
Estimate the quantities required for completing the project at hand often referred to as
quantity take-off. For non physical items (bonding premiums, fees for licence), lump
sum amounts are allocated based on experience.
The physical quantities determined in (2) above are priced based on historical data, . ,
vendor quotation, supplier catalogues and other pricing information that may be
available. Pricing of physical quantities may require detailed analysis as follows:- Y ! ,
i) Assume a work team composition to include a number of workers (skilled
and unskilled) and equipmcnt required;
ii) Estimate an hourly production rate bascd on the technology being uscd;
iii) 1;stimatc also the efficiency to bc achieved on the job putting into
consideration the prevailing sitc conditions and other factors;
iv) Calculate the effective unit pricc; and
v) Calculate the total price for each cost centre by ~nultiplying the estimated
quantity takc-off by the unit pricc.
# Quantity take o f f refers to the development o f work to he placed in an appropriate
2 1 units (m , m. kg, tons, etc).
Ek-ors incurred in quantity take-off include the following:-
(i) Arithmetic errors: Errors incurred due to addition, subtraction, multiplication;
(i i ) Transportation error: Errors incurred in copying or transferring figures /dimensions or quantities;
(iii) Errors o f omission: Errors incurred for overlooking items required to accomplish the work;
(iv) I'oor reference error: Error incurred from scaling drawings rather than using the dimensions indicated hy the designer; and
(v) IJnrealistic waste or loss factors.
Two approaches com~nonly used for detailed cost estimation arc "unit pricing or unit
cost" and "rcsourcc enumeration". Only the unit pricing or unit cost mcthod would be
adopted for cost analysis in this study because o f i l s versnlility.
Dams, wells and pumps arc accomplished through scries of ~ o r k quantities like
excavation earth and rock filling, geotechnical instrumentation etc. I t is usually
difficult to estimate the exact quantity o f some materials like earth vo!umcs, concrete
volumes, excavations, site clearance etc. I lowever, lo be on the safe side allowance is
rlsually made to take care of the followi~lg:
(i) Wasted or unsuitable materials hauled to site;
(ii) Shrinkage as a result of excavation to cotnpacted fills;
(iii) Excavation in rocks is usually subjected to swells;
(iv) Out break excavations.
I;or earth dams, soil or rock fills depending on which of them is available locally on
the construction site are used for filling and threc principal sit8 conditions or states
exist as suggested by Nunnally (200 I) as :-
Bank condition: This refers to a soil condition in its natural state before disturbance
and could be called in-situ or in-place soil. Its unit volume is identified as bank cubic
metre ( f K M ) .
Loose condition: This refers to the soil condition that has been excavated or loaded.
Its volume is identified as a loose cubic metre ( IXM).
Thus, a unit volume of soil in bank condition will occupy more than one unit volume
aflcr excavation and is computed in terms of its swcll as
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Shrinkage on the other hand occurs when the soil is compacted. This is bccause air is \ 4 , displaced from the pore spaces and the soil occupies less volume than under bank or
loose conditions. This value of shrinkage may be determined as
Weigh p r . hunk volt~rtte I - ; I 00
Weighr per cnmpacled voltme
'1'0 simplib the conversion o f loose soil volume lo batik volume, a load factor i s
i~sr~al ly used. A soil load factor i s computed as
Siniilarly, the conversion o f bank volume to compacted volume is done by a
slirilikage factor. Hank volume may be multiplied by the shrinkage factor to obtain
bank volume as
As R rcsull of the above met~tioned soil characteristics, earth for embankments may
usually shrink by 10-30 perccnt o f thcir borrow pit volume. 'l'hus, allowance o f 15%
may be generally adequate to rake care oF the shrinkage effect as suggested by
Nunnally (2001). For out break or rock excavation, 20-40% with a typical value o f
25%) be made for the swells o f rock excavation (IJSl)lBJ<, 1074; Oskoorouchi. 1988).
(knerally, contingency percentage is added to an estimated quantity for the purpose
of covering these unforeseen dificulties, changes in plans or a detail o f an item o f
design changed or omittcd.
2.81 Unit prices of work quantities
Each item o f the work quantity is priced bascd on several factors in addition to the
- - - - - - - - - - - - - - - -
following factors which an estimator i s supposed to 6nlrriarGe k i ~ n i e l T w M ~ aurhg
pricing:
(i) I,ocal market price conditions:
(ii) Probable sources o f material to be used for the work and labour supply;
and
(iii) Probable changes in material cost and labour cost that may occur within
the contract period.
Most at times, economic fluctuation during the contract period normally affect the
unit prices (or rates) to the detriment of either the contractor or the client. To reduce
these fluctuations, construction cost index should be forwarded along with the 1
contract document. There are many cost adjusting methods among which sliding price
formula (SPF) is one. However, because of data unavailability, these approaches
would not be applied to this study. The sliding price formuh for Earth and Civil
Engineering works presented by (WDSC, 1993) is of the form:
Where, . I f
A= Civil Engineering works contract price as defined by terms of payment
adjusted with the sliding formula i
Ao= Civil Engineering works contract price according to the price schedules 4 ; .
L = Average labour index of Nigeria from the same authority at escalation
point - - - - - - - - - - - - - - - - - - -
Lo = Average labour cost index of Nigeria published by the joint industrial FountrZs
P= Average index figure for construction plant and equipment issued by same
Authority at escalation point
Po = Average index figure for construction plant and equipment issued by an
Accepted official authority of the country of origin, at base point.
Fo= Official price of fuel published by NNPC at base point
F = Official price of fuel published by the same source at escalating point 1
Co = Cement price published by the Nigerian cement control board at base
point
C= Cement price Rom the same source at escalation point
So= Average steel cost index ofNigeria Rom an a~ce~ted'official authority
at base point
S= Average steel cost index of Nigeria from same authority at escalation point.
t
The sliding price formula for imported equipment presented by (WDSC, 1993) is of
the form
Where,
A= Contract price adjusted by the sliding formula
Ao= portion of contract price in the BOQ before adjustment.
IF average labour cost index issued by an accepted authority at escalation point
Lo= average labour cost index in the machinery and metal working industry in the
country of origin issued by an accepted authority at base point.
S= index for steel in the country of origin at escalation point
So= index for steel in the country of origin at base point
'I'lie sliding price Ihr~nrtla for transport insurance and sea transport i s o f the limn
( W DSC. 1993).
A= A. (0.1 tO.YO'l'/'l'o) (2.44)
Where.
A- portion o f transport cost from tlie shipping port to the Nigerian entry port
including loading and unloading adjusted with the sliding formula
Afl = transport cost from the shipping port o f the base country to the Nigerian entry
# port including loading and unloading according to tlie bill o f quantities
'r= Conference tariff rates and relevant charges, Surcharges etc for transport
from the shipping port to the Nigerian entry port at escalation point
To- Conference tarifr rates and relevant charges, surcharges etc for transport from the
shipping port of base country to tlie Nigerian entry port
2.9.0 Formulation of cost function for dams
'There are several cost functions derived for di ffercnt Furposes by many
researchers, but only few relevant ones were sighted and would be modified for the
analysis o f this study. Aniong them are the cost minimization n~odels suggested by
Musgrave and Kasch ( 1 976) stated earlier.
In tlie above model, P and X could represent unit prices and work quantities
respectively. This cost model is linear but the actual earth dam cost relations may
itivolve non-linearity. 'I'hus the cost model suggested by I lerzlinger (I 980) considers
the effect o f non-linearity.
C' tx-t [VJ + P ~ Q ~ t ...I\, -1- fl,> Q" + 1;
In the above Equation (2.46) a and E are constants to be estimated from the cost
variables. The two equations (2.45) and (2.46) could be re-written as a generalised
multiple regression models similar to that suggested by (Idama, 1999)
Where, a = constant that may represent preliminaries and other fixed sums in the bill
of quantities
E = Computational error, Pi = unit prices of the varisus work components, and Xi =
work component quantities
Equation (2.47) is similar to the cost function derived by Leton and Rodriqueze-
lturbe (1 977). In general, the cost relations for earth dam components could be related
either linearly, exponentially, power function or as a polynomial 'function to their
cost.
Linear function
Exponential function
CT =k en'
Power function
CT=kxn
Polynomial function
CT =alx" + a2 xn-' +...+ a ,x + Q
Where, k, a, Q = constants to be estimated from the existing cost data
x = hydraulic parameter whose cost is estimate
CHAPTER THREE
3 METHODOLOGY AND MATERIALS
.This research was carried out by assessment and evaluation of existing raw cost data
on earth dams. Almost all the Northern River Basins were visited for data collection,
however only very few cooperated. The few that were collected were separated into
their cost centres for further analysis. The deriving of design parameter's
relationships and cost functions (models) was fiom earth dams whose priced Bills of b
Engineering Measurements and Evaluations (BEME) were made between 1980 and
date. Cost functions (models) were derived for the components of earth dams that
correlated highly with their costs. The models were optimised for least cost
estimation using Lagrange's Multipliers with constraints.
3.1 Data collection.
For the purpose of this study, cost data in form of bills of quantities of earth dams
constructed from 1980 to date were collected fiom appropriate so$ces. This period
was chosen because of data availability and avoidance of much variation in cost due
to changes in technology, construction methods, difference in materials, labour and
equipment efficiency associated with very old cost data as suggested by Osara (1 994)
and Dawes (I 970).
It is normally difficult to get enough cost data on completed or ongoing projects
especially in developing countries where data keeping is poor and most at times for
fear of exposing financial misappropriation. It could have been better to have used
the project cost which is supposed to be comprised of construction cost, land
acquisition cost, engineering and legal services costs and contingencies, but, only I,
project construction cost was used for the analysis. This was because construction
cost is more definite and could be evaluated fiom the work components which are
summarized in contract bills of quantities.
Specifically, cost data on dams would include among others the following
components to be utilized for the analysis.
Construction cost and dam height;
Construction cost and dam length;
Construction cost and storage capacity; b
Work component quantities (site clearance to instrumentation):
Year of completion of dam;
Cost index or its equivalent; and
Inflation index
The cost data was collected fiom Water Survey Files, Consulting Firms, River
Basins, and Federal and State Ministries of Water Resources, etc.
3.2 Data analysis.
The earth dam cost data estimated in the past was first updated using appropriate
inflation index from Nigeria's Central Bank, so that there was harmony between costs
of the earth dams at the time of study. Costs of earth dams estimated at different times
was analysed by updating it to the time of study through the application of
appropriate inflation index, inflation rate (IR), and the minimum rate of return (MRR)
for the study area from a reliable source as to keep harmony between the costs as
suggested by Osara (1994). This approach reduced the effect of inflation and
variation in value. Earth dam components costs were used to determine the cost
functions through regression analysis.
3.3 Regression analvsis.
In a standard notation of regression analysis. two variables called independent
variable (X) and dependent variable (Y) are correlated. 'The variable to be forecasted
(dependable variable is expressed as a mathematical hnction of the independent
variable. Linear finction is represented as suggested by Frederick and Lieberman
( 1995). +
=PX! +a (3.1)
The regression Equation (3.1) represents a line through the data points that minimizes
the least squares given by
The values of the constants are determined by setting the partial derivatives of
Equation (3.1) with respect to a and /3 to zero and solving the resulting equations.
The analysis was done by Excel Microsoft Chart Wizard- Step i of 4 and the
expected regression equations were either
* Linear functions;
* Power hnct ions;
* Natural logarithms functions;
* Exponential functions; and
* Polynomial functions
Earth dam components were correlated using appropriate statistical methods in order
to determine useful cost functions. The cost hnctions were optimized using Lagrange
Multipliers with constraints. Computer software and monographs were developed for
fast, easy design and cost analysis. Although it is expected that the cost estimated
using the cost functions (models) would have a high reliability, it should not
substitute the detailed cost estimate prepared by Engineers for specific conditions.
CHAPTER FOUR
4. EARTH DAM DESIGN AND COST RELATIONS ANALYSIS
4.1 Earth dam design
The-design of earth dams used to be more of an art than science, but has improved
remarkably with the developments in soil mechanics. These developments include the
technique of determining the soil properties and their control during placement and rational
methods of stability analysis. These analyses have increased high reliability and accuracy b
in dam design especially earth dams.
The basic principles in design include the estimation of a satisfactory cross-section
at a minimum cost. It is therefore, essential that the dam structures be made fiom the most
economical material on site which is safe and stable during construction, post construction
and reservoir operations as observed by USBR (1965); USBR (1974); Nelson (1985);
Novak and others (1990); Punmia and La1,(1992); Garg (1990); Suresh (1992); Suresh
(2000); Agunwanba (2000); and Arora (2001).
The preliminary section design of an earth dam is usually selected based on
experience, considering various design factors holistically. Among the earth dam types
include the following:-
pHomo_geneous earth dams. - - - - -
I t Usually built fiom a single material preferably material that contain 20 to 30% clay
I: with the balance made up of silt, sand and some gravel as suggested by Nelson (1985) and
Arora (200 1 ). See Figure 4.01 a.
Zoned earth dams (Composite earth and rock fill dams).
This type of dam is made of casings (shells) both upstream and downstream of the
imperious core usually located in the heart of the dam for checking seepage. This type of
dam is preferable provided the right kinds of soils are available at the site. This is because
it has the advantage of maintaining steep slopes, thus reducing earth volumes and costs.
The upstream pervious shell prevents the build up of water pressure while the downstream
pervious shell forestalls the build up of water pressure in the clay core by keeping the
seepage line within the downstream toe (See Figure 4.01 b). b
Diaphragm earth dams.
Diaphragm dams essentially consist of a thin impervious core surrounded by
pervious shells. The main difference between zoned and diaphragm earth dams is the
thickness of core. If the thickness of core is less than the height of the embankment above I
the elevation or 10 m, the dam is considered to be of the diaphragm type. This type of dam
is preferable especially when the amount ofclay is available at the site. (See Figure 4. 01c).
toe
The whole elrbanla\lent materid is rrade 14 one materid preferabbbly sandy clay (Sharrm and Dandekar, 1 979)
#
7 mid dlaphrqmas bpmiols fill or hard core X Y
I I I
Wrviols or shell
Th15 1s a modtfled form of a homogeneous dam ~n whlch the entae embankment 15 constructed using
perviols nrterids (sand,gr& or rock) and a thin draptrrgm (haxi core) checks the flow of seepse wder
from the d m *st ream to the dolrurst ream
.-us MI (hard core)
t rasit ion zone - . -. . . ... .. - --
Fig 4.0lcZoned eathdan
The following sholld dso be notted (Sharrre and M e k , 1979) 1 , The rrin'mm M t h of hard core sholld mt be less than the dam Milt or 0.2 -0.5 t irnes rrmjmrn
head of Heter &ow the sect ion
2 , The depth of d - o f f coud range between 15 ad 45% of the d m heiith.
Design Features: Foundation treatment; abutment stability, seepage conditions, stability of
slopes; stability of reservoirs, slopes, and ability of the reservoir to retain water stored.
Other design considerations may include the influence of climate which governs the length
of the construction season and its effects, decisions on the type of fill materials to be used,
the relationship of the width of the valley and its influence on the river diversion and the
type of the dam (United States A m y Corps, 1994). The planned utilization of the project
(whether embankment will have a permanent pool or be used for short-term storage),
* influence of valley configuration and topograph~c features on wave action and required
slope protection, the seismic activity of the area and the effect of construction on the
environment.
Earth Dams Basic Design Requirements
The following conditions are basic design requirements for earth dams:
1 . The embankment, foundation, and abutments must be stable under all conditions of
construction and reservoir operation including seismic action.
2. Seepage through the embankment, foundation, and abutments must be collected and
controlled to p ~ v e n t excessive uplift pressures, piping, sloughing, and removal of material
by solution or erosion of material by loss into cracks, joints, and activities. The design
should consider seepage control measures such as foundation cut offs, adequate and non-
brittle impervious zones, transition zones, drainage blankets, upstream impervious blankets
and relief wells.
3. Freeboard must be sufficient to prevent over topping by waves and include allowance for
the normal settlement of the foundation and embankment as well as for seismic effects
where possible.
4. Spillway and outlet capacity must Re sufficient to prevent overtopping of the
embankment.
Special attention should Re given to possible development of pore pressures in
foundations.
Embankment type selection
1 . Topography: A relatively narrow valley with high rocky walls would suggest a rock fill
or concrete dam. However, a wide valley with deep overburden would suggest a
homogeneous earth dam. Irregular valley h a y suggest composite dam (earth and concrete)
2. Geology and foundation: The geology and foundation conditions at the dam site may
also dictate the type of dam that is suitable. Special attention and precaution should be
given for adequate seepage control andlor effective water cut offs or seals.
3. Materials available: The most economical type of dam is often the type for which
materials can be sourced within a reasonable haul distance h m the site including
excavated materials for the dam's foundation, spillways, outlet works, power houses and
other appurtenant structures. Materials that may be available near or on the dam site may
4 include soils for embankments, rock for embankments and rock especially for earth dams,
4. Spillway. The size, shape and type of spillway and restrictions on its location often
control the choice of the dam type.
Design factors to be considered for the following parameters. t
I: t
1.0 Freeboard: Freeboard is the vertical distance of a dam crest above the maximum
reservoir water elevation adopted for the spillway design flood. Freeboard should be
able to prevent overtopping of the dam by wind setup, wave action or earth quake
effects. A relation exists between freeboard and the type of spillway available in
relation to the dam heights as suggested by USBR (1964), Puma and Lal (1992),
American Corps of Engineers (I 994); and Arora (200 1) sliown in Table 4.0 1 .
Table 4.01 Relations between dam height, spillway type and freeboard
Nature of spillway Dam height Free board
-- I . Free fall Any 22 <1:13<3m.
2. Controlled Less than 6Om 2.5, above the top of gates
3. Controlled - Over 6Om 3.0m above the top of gates
(Source: USBR, 1965; Punmia and Lal, 1992)
The actual freeboard should include the effects of wave action as suggested by
Arora (200 1).
Freeboard = 1 S h , + SF (4 -0 1 a)
Where, h w - - height of wave, SF =Safety factor (0.6 - 0 .3m).'
Saville and others, (1962), Falvey (1 974) and Agunwamba C2001), expressed the
Freeboard for medium size reservoirs as: i
2
Freeboard =0.75hW, +
In Equation (4.01b), wave height depends on the wind fetch and wind speed and are
related as:
'Vlierc. ! If: - wind st>ecd in kilometrt: ncr hour 1: - wind fctcli i l l kilometres
A relation hetween rcscrvoir ktch arid tlic f iccl~ard WIS cstal~lislicd Ily Nelson
( 1 0 8 5 ) s~~mrnarized in 'r'ahlc 4.03..
'I'al~le 4.02: Typical freehoa~d values fiw various rcscrvoir ktches.
.- -- - - - . -
(Source: Nelson, 1985
Minimwm inlet and orrtlet widths design.
A relationship was estahlisl~cd wing the values ol'tlic ITlood I:low, Rct11t-11 Slopes
and Rct~~rn Widths in Table 2.5 aller extrapolation ~rsing l5cel Microsoft ('11ar.t Wizard
Soflware. The resulting cquatio~i is shown hclow
Inlet Width (Win)-? 1.8433 Q " " ' ~ ~ (4.0ld)
'T'he ahove relation gave a coefficient of correlation of O.W77.
'l'ahle 2.5 was used to propose a monograph for estimating discharge; outlet width
or re tun^ slope or when two of the parameters are given as shown in 1:igure 4.01(d).
0 0
0
0 - E
0 - 0 g
I 0 % -
c u
0
0
0
Return slope (O/O)
Fig. 4.01d: Monograph for estimating the parameters for spillway design
Earth dam top widths analysis.
Using the values in Table 2.6 for small earth dams, a relationship was established
between the dam top widths and their heights using Excel MicrosoR Chart wizard of a
linear form function shown below:-
Top width (w) = 0.5323H + 1.5 The correlation coefficient = 0.6900
I:qi~ation 4.04 shows a diffcrcnce fioni tlic equation sl~ggestctl hy tJSDK (1965, 1975) of
ti)r.m (Scc Ilquation 2.6):
'I'op witltll (W) - 0.21 I t 3
Where, I I - dam height in Inctcrs
rkluation (4.04) was used to predict the top witlths h r the: various dams in this category as
slrniniarised in 'l'ahle 4 .03 . b
Table 4.03: Predicted top widths Tor small earth darns in the study area.
~ ~~ ~ ~ . ---.-.-.--..--....--.-----.p-
Predicted % prediction Top error
TOP width year s/No. Dam length width Height
m rn rn ~ ------- ~ ~
1 Achida 135 3 4 3.6 -2 1
2 Dinawa 126 5.6 4 3.6 -36
3 Karkiro 180 6 7 5.2 13
4 Marnorna 220 6 7 5.2 13
5 Misbil 1535 3.4 3.3
6 Sum 800 6.3 4.8
7 Wurno 4500 3.5 8 5.8 -65 1960
8 Rijau 350 5.5 7 5.2 05 1990
9 Girei 250 5.5 4.4
10 Yola 5 4.2 1983
11 Ankwill ll 203 3 9 6.3 -1 10 1963
12 Jekko I 128 10 6.0 1937
13 Kogingiri 280 3 8.23 5.9 -96 1935
14 Kwall 2 74 9 6.3 1923
15 Larnigo 410 3 11.5 7.5 -1 50
16 Kubani 823 8.5 6.0 1975
17 Umogidi 310 6 5.5 4.4 27 1986
19 Daura 6 4.7 i 980
20 RIGado 210 4 5 4.2 05 1980
21 Alau 344 6 9.5 6.6 10 1992
23 Naka 600 5.5 8.5 6.0 09 1986
location
Sokoto
Sokoto
Sokoto
Sokoto
Katsina
Kebbi
Sokoto
Niger
Adarnawa
Adamawa
Plateau
Plateau
Plateau
Plateau
Plateau
Kaduna
Benue
J igawa
Borno
Jigawa
Borno
Kano
Benue
The graphical relationship between dam height and top width for medium darns is
shown in Figure 4 . 0 1 ~ .
0 2 4 6 8 10
Dam's he ig ht(m)
Fig.4.Ole: Relationship between medium dam's top widths and their heigths.
The values in Table 2.7 for large dams were used to derive a relation of linear form
for the dams under consideration as shown below:-
Top width (W) = 0.133H + 1.63 (4.05)
The correlation coefficient = 0.9014
Equation 4.05 shows a difference fi-om the equations suggested by USBR (1965 and
1975) for medium and large earth dams respectively of form (See Equations 2.7 and 2.8):
Top Width(W)dl.55H0.5 +0.2H
And
Top Widths = l.65(H + 1 .5)0.333
4v Equation 4.05 was used to re-predict the top widths for the various dams as shown in Table 4.04.
'l'ablc 4.04: I'rcdicted top widths h r large carth d a m in the study area
- Predicted 1 OP Top O h predict~on
length width Height width error slNo Dam m m m . - -- --- - - -
1 D / ~ o w a 520 8 42 7 20 I 0
2 Kiri
3 Usuma
4 Omi
5 Pedan
6 Shiroro
7 Kainji
8 Kontogora
9 Jebba I
10 Jebba I1
1 1 Kagara
12 Gurara
year .. . .-
1988
Location .- -- -- Bauchi
1982 Adamawa
1984 FCT
1976 Kwara
1993 Abuja
1984 Niger
1968 Niger
Niger
1984 Niger
1984 Niger
1995 Niger
'l'he graphical relationship between dam height and top width Tor large dams i s shown in
Figwe 4.02.
Dam's heighqm)
Fig. 4.02: Relationship between large dam's top widths and their heigths.
4.3 Earth dam cost minimization in terms o f side slopes.
'I'lie cross section ofan earth dam is approximately trapemidal as suggested by
Water for the World (2004). The upslrcam and downstream slopes may bc same or
differelit depending on the soil characteristics (angle of i~iler~ial friction,$, cohesion
coeflicient, c, and height) ofthe structure.
'I'he cross- sectiotid parameters include the following
'I'op width (W)
13ase width (13)
1 leight (I 1)
lJpstream and downstream slopes (in and n )
'I'heir relationships is shown o n the sketch below in Figure 4 9 3
W A - ' I f n
Figure 4.03 Assurned earth (lain cmss --section
'I'aking an earth dam cross-section as shown in Fig. 4.03, and assuming a
Ilomogeneous filling material, the volume of filling material per unit length (sectional area)
can be estimated using the sectional parameters. Although there are several methods of
estimating the fill volume, trapezoitlal method was used based on its simplicity.
4.3.1 Basic eqr~a tions.
'I'he top width (W) of earth dams could be expressed in terms of height as suggested
by (JSBR, Garge. ( 1 909). I'unmia and l , n l , ( l W 2 ) and N o v n l k otid others. ( 1 990) atid
Water (2005) for small, medium and high dams as in Equations (4.0l), (4.02), and (4.03)
Rercrring to Figure 4.03, the vol~rnie orthe f i l l material could be estimated as
Where, 13 = 13ase width ( I I n t 1 I m .t W)
m and n = upstream ~ n d downstream slopes
I , - tlie lcngth ofthe dam (rn), W= top widtli (rn)
'I'lie cross- sectional area (volume per unit Icngth) is givcn by
A,- % 111 m -t I1 n t 2 W ) I l (4.07)
'I'he minimum cost o f fill matcrial o f a dam scction given in I%pation (4.07) must
b be solved such that tlie cost function for the type o f fil l ing matcrial is minimized. This can
hc expressed mathenlatically as a microcconomic problem o f minimizing production cost
through minimizing inputs. In our case, tlie inputs arc the sectional parameters o f height
(ll), slopes (m and n), top width (W) and basc width (R). The output is tlie sectional area
(volume per unit length). The sol~~t ion involves tlie determination o f the input mix for
which the marginal products equal the ratio o f the marginal cost. This mix can be
determined Tor any nu~nber o f inputs utilizing tlic I ,angragc multiplier technique as in
Slrout (1 982) as
Where, As = sectional area, C: I -cost function
For the optimum val~~e, the side slopes are chosen to be the constrained parameters
t
\
&, because under most conditions, the choice o f side slopes is limited to some extent by soil
characteristics (cohesion coeflicient, c, and angle o f internal friction,$), foundation, and
seepage characteristics. For the three categories o f dams described by Equations (4.03),
(4.04) and (4.05), the sectional area could be estimated as follows:
Case 1 : Small dams ( l lomogeneous earth fill with top width = 0.2111 +3)
'T'he sectional area Tor small dams can be estimated by substituting Equation (4.03)
into I'quation (4.07) lo give
A,= l/Z (I 12m -t i i2n 4- 2(0.211-t 31 1)
The cost function estimated for a homogeneous earth fill Tor small, large, and
(4.1 la)
Differentiating Iiquations (4.10) arid (4.1 I) using "MA'I'IAU sonware and
inserting in Equation (4.09) gives
Equation (4.12) can be simplified to a quadratic cquation of the form
I,et KI= Abs (-m-n-0.4) 9,
K l 112-611 -- 1367 -0
Equation (4.15) can be solved Tor positive Il values as
'T'hus, from [<quation (4.16) above, i t is logical to say that the dam height is a
function of the side slopes only. [:or the side slopes suggested by 'T'erzaghi Ior various
filling material, the optimal cross- section and optimal cost were estimated and shown in
o 'I'able 4.05 for small dams.
Tahle 4.05: Side slopes suggested by 'I'erzaghi (in I'nmnia and I A , 1992) for various
f i l l material and optimal section and cost
Fill material type Side slopes I leight
Upstream Ihwnstreatn (m)
I .O I lomogeneous
wellgraded 2:l
2.0 14omogeneous
coarse, silt 3:l
3 .O 1 lomogeneous
silty clay or
day
II<15m 2 ' :I II>151n 3:l
4.0 Sand or sand
and gravel
with clay core 3:l
5.0 Sand or sand
and gravel
with IIC core
wall 2 % :I
As cos t Cost
(m7/m) ( ~ 1 1 n ~ ) (Nlm)
'l'he heights (H), cross sectional area (A,), and total cost (C-,) were re-computed.
Case 11: Medir~ni dams antl homogeneous fill (FI < 30111 antl top
width, W = ~ . S S / ~ ' ~ + l l 1 2 ) :
The scctional arca (A,) fix medium dams can be estiniatcd by substituting Equation (4.07) in
Equation (4.09) to give
Differentiating ['quation (4.10) and I<quation (4. I I ) amd inserting in Equation (4.09)
gives
k21l2- 1.10t1 -1367 -0 (4.18)
Where, kz= abs (- m-n-0.2)
Solving Eqi~ation (4.1 8) for positive value o f t i , gives
The optimal values o f height ( I ] ) , cross-section (As) and cost (CT) for various f i l l
material and recommended slopes are shown in Table 4.06.
'l'able 4.06: Ilecommended side slopes by 'I'erzaghi (in I'u~itnia and I,al, 1992) for various f i l l materials and optimum scctions and costs.
~ ~ - ~
Material 'I'ypes Side slopes I I As C.,, c.,. -- -- - -- . -- -.
l lpstream 1)ownstrcam (m) (m'lm) ( ~ l m ' ) (Nlrn)
well graded 2: 1 2: 1 18.17 1033.05 08.27 8,543.32
coarse silt
silty clay or clay
4. Sand or sand and
gravel with clay
core
5. Sand or sand and
gravel with I<C
core wall 2 % : I 2: 1 17.17 907 .2 10.77 107,440.49
The values of height (l l) , cross- sectional area (A,), and total cost ( e l ) were recomputed as 2 .
before.
Case ll I: High dams and homogeneo~~s fill (1 P3Om and top
widlh - 1.05(11 t 1 .5)17 ):
l 'he cross- sectional area (A,) Tor high dams could be estimated by substituting
ecpation (4.48) into 1:quation (4.49) lo give
+ Similarly, differentiating liquations (4.19) and (4.1 I ) mid inserting into lcluation
(4.09) gives
K ~ I 12- 3.3 t 1 (I l t 1.5)"'- 1367 -0 (4.20)
Where k3- abs (-m-n).
Equation (4.20) was solved for positive values oTheighl (I I) Tor the various slopes
recommended by 'l'erzaghi using *MA'll,AB software.
'l'lie oplimal cross sectional arca (A,), height atid cost were computed from
equations (4.19) and (4.20), respectively. The values are shown in Table 4.07.
*MArI'I,AH i s a commercial software lbr solving nu~nerical mathcmatics.
various fi l l materials and optimal section and cost
..
Material type Side slopes I I
Table 4.07: Kecommended side slopes by 'I'erzaghi (in I'unmia and IA,
-
- -
I . I iomogeneous
well graded
2. I lo~nogeneous
coarse silt
3. I lomogeneous
silly clay
11~15m
11>15m
4. Sand or sand
and gravcl
with clay core
5. Sand or sand
atid gravel
with RC core
wall
L - - - - - - - - - - - -
1992) for
Cost
( ~ / m ~ ) (Nlm)
4.4. Seepage analysis
There are some suggested factors for t l ie typc o f under sccpagc control mcasurc
(Slierard, 1 968).
I . Economic analysis should bc done to compare tlie valuc o f the watcr o r hydropower that
may be lost and cost o f complc t ing cut of f .
2. Resistance of foundation a l luv iun i w i th luspect to potential progressive backward
erosion o f leaks o r p ip ing. For foundations w i th l inc and cohesion less siit, w i th soils
b exposed on tl ie surface o f the val lcy f loor o r walls, a coniplete cut-off' is more desirable
than if the foundation is basically gravely o r coarse sand.
3. I f tail-water a l lows for water p o ~ i d s downstream o f the dani so that under secpage wou ld
emerge underwater and could no t be observed, i t is desirable to be more co~iservat ive in
evaluating the need for a complcte scepagc cut-ofl..
4. 'The amount o f s i l t and clay sized particles i n suspension i n the r iver watcr which
contribrltes t o si ltation o f the reservoir w i t h t ime and tends to d imin ish under seepage.
'I'heory and model tests suggest that cu t -o f f should penctrate a homogeneous
isotropic foundaticm at least 95% o f thc fu l l depth beforc there is any appreciable reduction
i n seepage beneath the earth embankment as suggested b y 'T'clling and others (1978);
Mnnsur and Pnrret (1949). 'I'hc effectiveness o f thc pnrl in l cu l - o f f i n reducing the quant i ty
o f under seepage decreases as the ratio o f the width o f the dam to depth of penetration o f
the cut o f f increase. Partial c ~ ~ t ofCs are on l y effectivc on ly when they extend d o w n in to an
immediate stratum o f lower permeabil i ty. I n such a case, the stratum must be continuous
across the val ley Ihundat ion to ensure that a three dimensional seepage around a
discontinuous stratum does no t negate the effectiveness o f the partial cu t of f . The cu t o f f
efliciency could be assessed either in terms of the flow efficiency as suggested by
Casagrande (1 761) or by head efliciency as suggested by 1,ane and Wohlt (1 961) and
Ade~nuliyi ( 1 987).
I;or flow efiiciency,
And for head efficiency,
f $ l r h l l l
Where,
- Oo -- Itare of under seepage withoul cut oll'
-. 0 - Rate of under seepage with cul ofT
l$, - -- Flow elliciency ofci~f oII'
- 1 lead efficiency ofcut ofP
h = I lead loss between points ininiediately upstream and downstream of
up streams oftlie cut offwall at its funclion with the base ofthe dam
I I = 1 lead loss across the clam.
' I le head efficiency is more widely used because its field perhrmance may be
estimated by peizo~netric data taken during construction before and alter initial reservoir
filling (Ademuliyi 1987). A partial cut off' in a hornogeneous isotropic foundation will
- - - - lower - the - line - - of - seepage - - in - the downstream embankment but exit gradients at the - - - - - - - - - - - - - - -
7
downstream toe are reduced only slightly as suggested by Cedergten (1973). When the 'I,
pervious foundation is cut off by a compacted backfill or slurry trench, the rate of i~nder
seepage rnay be established using equalion suggested by Arnbraseys (1983)
Where,
Q,,= rate o f u~ ider seepage in rn3/scc pcr dam Icngth
K o - permeability o f the foundation in m/sec
I I - hcatl o f water in the reservoir in ~n
13 - width o f thc base o f tlie dam in m
K permeability o f the compacted backfil l o r s l u r~y trcnch backfill in nilsec.
1) -'l'liickriess o f the cut o f f in In
I) -'l'hickness ofpcrvious laycr. fi
For a concrete wall or stcel sheet pi l l ing with defects (openings in the cut off) the
rate o f under seepage per unit length o f cut o f f is given by equation below as suggested by
Ambraseys (I 963) and Marshal and Rescndiz ( I97 1 ).
Whcre,
W = Total area o f openings in rn'.
4.4.0 Excessive Seepage Assessnie~it: 'I'he choice o f cut o f l trench for seepage conbol
could be done based on foundation depth, strata and material including permeability o f the
diflerent layers making the foundation material. 'l'hus, the likely seepage losses and degree
t o f control requires the economics o f different alternatives, acceptable risk and the
seriousness o f the failure consequences as suggested by (irima (200 I ) .
The seepage assessment involvcs the checking o f the effectiveness o f the cut o f f
through the hydraulic computation o f seepagc watcr through the foundation material. If
materials availability i n the vicinity o f the projcct area is taken into consideration
especially clay material, construction ofupstrcaln cut OK up to thc impcrvious stratum and
keying info i t appropriatcly is necessary. A typical dnm with thc following data was used to
demonstralc the seepage asscsslncnt.
I)a ta :
I . Average conccntralion leakage flow rncasurcti downstrcam o f the dam body using the
floating ~ncthod was 20 11s.
2. Ilcservoir level (end of.luly 1998) - 1976.86 m a.s.1.
3. Reservoir water level (end o f 1)ecernber 1998 = 1974.47 In a.8.1.
4. Reservoir water volumc (end o f .luly 1998) = 280,000 nl' (Arca curve)
5. Reservoir water volumc (cntl o f t)eccmber, 1998) - 166,520 in' (Arca capacity curve)
1 6. I<xpected evaporation loss - 28,620 m
7. Ihpected sediment load - 3.1 87.5 nl'
8. I'recipitation on rcservoir = 7,200 m '
9. Surface runoff(end o f August 19%) - 159,4373 in'
10. Surface runofT(cnd o f lleccmbcr,) - 62,687.5 m'
I l . Final storagc - 166.520 ~ n '
The typical cross-section of the carth dam is shown in Figure 4.04.
Inpenious fill (hard core)
Fg. 4 .O4 A typicd cross section of the dam studied
W e , B= Danbottomwidth B Depth of ctlt off trench D= Depth of pervious fouddion H= Height of d m W Top width of d m Wkdk b= Fkrrneabirty of the fonddion in (ds) k Fkmi&ihty of conpacted back fill or slury
in trench (M) KG Wect ive pefined>iity
Calculations
CASE I : (Measured using water budget for a dam without cut off)
Net loss (end o f July 1998 to end o f December 1008) = initial storage + surface
runoff t precipitation t Sedimentation load -- evaporation - final storage
(4.25)
Net loss- 280000 i ( 159437.5 t 62687.5) +7200+3 187.5-28620- 166520 - 3 17372 m'
The expected amount o f concentrated average seepage measured downstream from
+ end o f July 1988 to the end of!>ecemhcr 1988 including evaporation i s given by:
Net loss (end o f .luly 1988 to end o f December 1988) = total seepage volume + evaporation
(4.26)
Net loss - 20x l 0 ' ~ 5 x 3 0 ~ 2 4 ~ 6 0 ~ 6 0 t 28620 = 287820 rn'
Comparing tlie result o f volume loss in Equation (4.25) and that o f lkpation (4.26),
we find that they are 90.7% identical or only about 10% o f the water seeped.
CASE 11 (Seepage estimation for dams with a cut off trench)
The volume o f the under seepage which may be expected, i t is necessary to estimate
C the coefficient of permeability ofthe foundation material at tlie field. The approximate
arnount o f under seepage may be made using Darcy's equation.
P (4.2 7)
2. Where, I = !I113 atid for tlie dam selectcti,
~ r = 2 0 x 1 0 ~ ' m ' / s , l l = 15m,13=45m,11=8m
Q - 20x 10-' x ( 1 5/45) x 8x 1 =5.33x l 0-\n3/s/ni
'1 l ie total volume o f water seeping through the fbundation f'rom end of.luly to end
of'llecembcr 1988 along thc crest lcngth o f a dam 470 m may bc cstimatcd from
Volume (V) = () I, t (4.28)
Where, Q = discharge per unit Icngth, I, = datn crest Icngth, and t = time (end of.luly to
end o f Ikcemher. 1988)
Volume = 5.33x10-~ x 5 x 30 x 24 x 60 x 60 = 324864 111'
I lowever. when a cut o f f i s provided in a porous foutidation and back filled with an
impervious material, the rate o f seepage can be obtained using lkpation (4.07) by inserting
a l l the dam data i r i which +
K r z 2 . 0 ~ 10-5 mls, K, 2.1 x 10-6 ctnls, I < - 9.0 m, I) - 8.0 In, B - 45 111, and l l = 15 m
'I'liis gives the value o f tllc <lischarpc (qc) as2.78~ 10.' m'lsltn.
Girma (2001) suggested that with 50% cut o f f penetration. 25% seepage could be
reduced. 'l'herefore, the amount or'sccpage with 50% cut oll'penetration i s given by
q,, - 0.75 x ()
Where. Q i s the discharge without cut ofS
q, - 5.33 x 1 0-' x 0.75 - 3.99 x 10.' m'lslm
And volume (V) - q,, x dam length x time o f monitoring
= 3.99 x 10.' x 470 x 5 x30 x 24 x 60 x 60 = 243038.80 m'
Net loss (Thd of.luly to cnti o f I)eccmbcr, 1088) - total sccpnge volume 1. evaporation
(4.29)
Net loss = 243038.80 1 28620 -- 27 1658.80 in'
Again comparing the net loss computed in llquation (4.29) and that computed in
Ikpation in (4.28), and about are about 94.4% identical or 6.60% water seeped
Limits of seepage: In the design ofrescrvoirs, the hl lowing scepagc limits suggested by
Nelson ( 1980) could be adopted: 833x1 0 ? too pernicable reservoir; Clp to 1 39x1 o - ~ : the
reservoir is doubtl'ul and acccptablc only on proressional's advice and less than 1 .39x104:
acceptable seepage
4.5.0 Earth dam's cost analysis
4.5.1 Price Index: A price itrdex could be expressed as weighted average o f prices o f
service, construction materials, cclilipmetit etc., expressed as a percentage o f price existing
in base ycar. Mathematically, the price index could be represcr~ted by the following relation
(ISNR, 1990; IJdu, 1990). +
I'r ice of cwrenl yeur I)rice index (I'I)= ---L- -- .
I'r ice hnsc. yecw
I3ase year: 13ase year is ~rscd to dcscribe the year that satisfies the necessary economic
criteria. The choice oTa basc ycar could be done in consideration orthe following.
'I'he base ycar should be chosen to adequately reflect the current economic developments
and the base be periodically updated to maintain a realistic weight.
'I'hc base year should be cyclically neutral, thus, others preSer several years as base
years.
For this study, the basc year could be the year the earth dam was constructed. For
this analysis, the present cost could be estimated according to the labour cost index
suggested by I larbold, ( 1982) as
I'r esenl itidex wtlitc Present cost - original cost x - - -
Originul index v c h e
I lowever. the present and original index values are rarely known for the study area.
Inflation rate: 'I'he English O x h r d Advanced 1,earner's dictionary defines inflation as the
rise in prices and wages caused by an increase in the money supply and demand for goods
and services, with rcsulting Shl l in tlic value 01' the Inoncy. 'l'hus inflation is said to have
taken placc i r t l ic valuc o f ~ n o n c y ralls hclow tlic valuc at a basc year. Inflation in economic
ternis i s defined as a silualion when the cost o r an item tcnds to increaqe over time, or, to
p ~ ~ t it in another way, thc same moncy valuc buys less orsame item over time (Park, 1997).
Inflation is o l k n associated with thc appreciation o r intcrnational currencies. This means
that the extent o f inflation could bc indicated by thc cn'ective exchatige rate (LXR). The
inllalion rate Tor Nigeria is prcscnted in Table 4.08 (CBN, 1994) Tor the period 1970 to the
first quarlcr o r 1994 b
'I'able 4.08: In flat ion indcx for the pcriod of l 970- 1 994
* I "' Quarter Sourcc I 'ctlcral OTTicc a T S t a l ~ s l i c s , I.agos
The inflation rate in 'I'able 4.08 was used to calibrate a linear regression Fquation of the
fo urn (1) = 171 i- ( I (4.32)
Where cl) - Inflation rate
b - slopc o f line of best lit
t = time in years
a = inlerccpt of a line ofbest fit on the y-axis
The assumption made was that the inflation rate was increasing linearly with time.
rI'lius. thc rnodel was calibrated to give Equation (6.33).
(I, -= 1.23 t t 6.90 (4.3 3)
'I'he analysis gave a correlation coefficient ofO.60
Other forms of regression like non-linear, power, logarithmic, exponential etc, but
only linear gave a relationship with the highest correlation coefficient. 'Ihe non-linear gave
a relation of fonn:
(D = 0.1 1 5712 - 1.82351 t 19.392
The correlation coefficient = 0.3985
Equation (4.33) was used to predict the inllation rates as presented in 'fable 4.09.
Table 4.09: Actual and predicted inflation rates Ihr 1970-20 I0
Year
1 070
1971
1972
1073
1974
1975
1976
1977
1978
1970
1980
198 1
1982
1983
1984
1985
I986
I987
1988
1989
1990
199 1
1992
1993
---- - - - -
lullation Kate ((4)
13.80
1 5.60
03.20
05.40
13.40
33.90
2 1.20
1 5.40
1 6.40
1 1.80
09.90
20.90
07.70
23.20
39.60
05.50
05.40
10.20
38.30
40.90
07.50
1 3 .OO
44.50
5 7.20
- --
-. - - - -- -
Predict td iufla tian
8.13
9 3 6
10.59
1 1.82
13.05 6
14.28
15.51
16.74
1 7.92
1 0.20
20.43
2 1 .66
22.89
24.12
25.35
26.93
27.8 1
29.09
30.27
3 1 .so
3 2.74
3 3.96
35.19
36.42
- -
Error of Prediction ( %")
4 1
4 0
-23
-188
03
-58
2 7
-09
-10
-106
04
- 197
-04
36
-383
-415
- 185
2 1
2 3
-336
-161
121
136
Average Inflation Kate (f)
' lo account Tor the erfect of yearly varying inflation rates over a period of several
7 years, a single rate can be cotnputed to represent an average inflation rate as suggested by I
(Park, 1 997 and Goodman, 1984) as:
Where, I: = the current price; I' - the previous price,
f = the average inflation rate; and n= period of forecasting
Ilquatiori (4.34) would be used lo determine thc current price bccausc thc inflation rates arc
known.
4.6.0 Earth (lam construction cast and salient features
'l'lie rclationship between constri~ction cost and tlic carth dam colnponents that are
cost dcpcndcnt to be considcrcd included ((hodman, 1984):
i) Ilani construction cost as a Siinctioti of cla~n height in metrcs;
i i ) Ilani constructiori cost as a li~nction of' dam Ixngth in metres;
iii) 1)am conslruction cost as a fi~nctioti o f d a m I<cscrvoir storage in cubic
metres; and
iv) Dan1 construciion cosl as a function of lake surfacc area in heclarcs.
'l'hc darn construction cost and their various coniponents arc shown in Tables 4.1 Oa,
4.1% and 4 . 1 0 ~ for Gcneral, I,argc and Small darns.
Analysis of dam construction cost and height
'l'hc dam consln~ction cost was hutid to be a Si~nction of thc darn height related as a
powcr f~~nct ion of the h n n :
(',, K , > l P
Where, (',,= pro.jeet cost in naira;
I I.= tiam height in ntclcrs; and
- - - - - - . . . . . . . . . . . . . . . . . . . . - - - - - - -
I K,, and n,-constants to be estimated
2 . tlquation (4.35) was calibrated using the dam adjusted cost and their corresponding
hcighls as shown below.
General dams ('Table 4.10a): 'l'hc equation Tor gcncral danis was estimated with a powcr
function of the Sorm:
C1, - ~ ? J S ~ O I I ' '""
'I'lie corrclatio~i coefiicient Tor the above relation is 0.8496
Signiiicance levcl could be testcd using the t- test as suggested by Millcr and Miller
( 1 993) given hy
Where, n - sarnple size;
X- sample meall:
p == population sample; arid
s - standard devi a t' lon.
The degree of rreedorn is given by n-2; n being lhc nurnber of sample population
but corrclalion coefkicnt fiom 0.6000 was acceptable Tor this studies exccpt otherwise.
'I'ahle 4.1 0 a ; Ilarth darn's costs and hcights for a gcneral darn casc.
Aclual cost per
Height length cost in 2006
Wlrn 6627640
9212602 5
8053454 2
9029527 8
9499269 1
15124524
5715342 3
23636320
1428309 3
l744OOlO
15723806
2331 888 1
308144 6
213454 34
271136 2
170091 74
706591 95
Predicted cost
Hlrn - - - - . . 12068390
12068390
12060390
12068390
120683p0
12068390
10002346
4675506
1653926
6271 770
1334651
675650
593938
398336
398336
441202
330143
SINo. Dam Prediction error Inflation factor Dale
(rn) Wlrn . - .. ...
42 57637
42 80117
JBNL
4 SGE
S FNI
7 Kiri
8 Mangu
9 Shagari
10 Guhi
1 1 Alau
12 Paki
13 Panshanu
14 Farakwai
I6 Gwaraji
'I'he graphical relationship betweon dam hcight and cosf for general dams is shown in
1;igurc 4.05.
0 I 0 20 30 40 50
Dam's heig ht(m)
Fig .4.05:Relationship between dam's heights and costs for general dams.
Large clanis (l'abte 4.10h)
'I'he relationship is represented by a power fi~nction of the Tom:
( ', = 0.003 11 ' '40"
- - - - - - - - - - -
('orrelation coefficient: 0.92.64
'l':iblc4.l0b: I>am cosls and darn heights for large darns.
SINo. Dam
. . - - - - - - - - - 1 D kwa(Engr)
2 S A
JBNI
4 SGF
5 FNL
6 AV
7 Kin
8 Mangu
9 Shagari
10 Guhi
1 1 Jada
12 Dugwaha
13 Mararaba donga
Actr~al cost per length
Nlm . - - --- - 57637
80117
70036
78525
82610
131529
47098
10514377
449013
100786
3290710 16
31 3486 68
275064 73
41 26653 93
-
Pred~cted 2006 cost cost
Nlm Nlm - -- --
6627640 7935899
9212602 5 7935899
80534542 7935899
0029527 8 7935899
9499269 1 7935899
15124524 7935899 1
5715342 3 9064212
23636320 16017640
14283093 32409793
25201 539 1261 3793
3290710 16
3l,Y86 68
275064 73
41 26653 93
. .
Date inflalion dam
Prediction error faclor consl.
Wlm % Wlm -- - -- - - -1308259 -20 114.99 1981
l'hc graphical relalionship bctwecn dam hcighr and cost fix large dams is shown in
I;igure 4.06.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
0 10 20 30 40 50
Dam height (m)
1:ig 4.06 Rclationship between dam heights and costs lor large dams
Small dams (Table 4.10~): 'l'lw. eqmtion is again a power function ofthe form:
Correlation coefficietit: 0.9370
Table 4.1 Oc: [)am costs and heights for small dams.
cosl per 2006 I'retlicled inflation SINo. I)am I leighl length cost cosl I'rcdiction error factor Date.
'I'hc graphical relationship bctwccn dam height and cost fiv small dams i s shown in Figure
4.07.
0 2 4 6 8 10
Dam's heig ht(m)
Fig A.07: Relationship behnreen dam's heights and costs for small dams.
Ikpations (4.36), (4.38), and (4.39) were used lo re-compute the construclion cost for the
respective heights as shown in Tables 4.10a. 4.1 Ob, and 4 .10~ respectively.
'l'he plot o f height against construction cost would give a fairly linear curve as shown in a
sketch in Figure 4.07a (i). 'l'hc economic height o f a dam i s that dam height corresponding
to the height which, the construction cost per unit o f storagc is minimum as suggested by
Garg ( 1 990). l 'he reservoir capacity could be estimated from reservoir-capacity curve for
each dam height. 'l'lie construction cos( per unit o f storage for all possiblc dam heighL~
could be worked out and plotted as sliown in tlie sketch shown in 17igure 4.07a (ii). 'l'he
lowest point on the curve in Figure 4.07a (ii), gives the dam height for which tlie cost per
unit o f storage i s minimum, and hence, tlie most econo~nical.
I I
Mort ecul,n.lin~ I,,=~~I* fm) Dam height (m) *
- -I (i) 0 (i i)
r ig. 4 07a Relatiunships I,etwecn dam Iiciglits and constt-i~ctior? cost
Analysis of dam construction cost and length: I h m length was another colnponent that
has effect on the construction cost and is going to be analysed.
Large dams (Table 4.1 la): The relationship could be estimated by a power function o f
Correlation coeflicient: 0.9006
J<quation (4.40) was then used to rc-compute the dam co~istri~clion cost for the respective
lengths as shown in Table 4.1 1 a.
'I'able 4.1 1 a I ,engths and construction costs Tor large darns.
SlNo
- 1
2
3
4
- 5
6
7
8
9
10
11
12
13
Dam
D-kwa(Er1gr).
S A
JBNL
SGE
FNI-
AV
Kiri
Mangu
Shagari
Gubi
Jada
Dugwaba
Kaltungo
Length Height
(m) . - -- -_ .
520 42
520 4 2
520 42
520 42
520 42
520 42
1300 37
300 21 5
119260 1098
3820 2 7
1150 20
900 11
356 32 8
Actual cost per length
Nlm - --- - 57637
801 17
70036
78525
8261 0
131 529
4 7098
10514378
449013
1 01E+O5
3290710 16
31 3486 68
4 126653 93
2006 cost
Nlm . .
6627679
9212654
8053440
9029528
9499324
151 24520
57 15264
23636321
1128310
25201375
3290710.16
31 3486.68
41 26653.93
Prediction error
Nlm Yo - - --- -- - - - -- -3496295 -53
-91 1320 -1 0
-2070534 -26
1094446 12
-624650 0 7
5000546 33
28801 37 50
1 9001 96 08
-1 108870 7 7
24567057 97
infln. Factor
Mlm ---- 114.99
114.99
114.99
114.99
114.99
114.99
121.35
2.248
3.181
173.04
1 .ooo
1.000
1.000
Date
-- 1981
1981
1981
1981
1981
1981
1983
2004
1990
1992
2006
2006
2006
'lhc graphical relationship betwecti dam lerigtl~ and cost for large dams is shown in Figure
4.08.
Dam length (m)x1 o2
Fig. 4.08 Relationship between dam lengths and costs tbr large dams
Small dams ('l'able 4.1 1 I)):
Equation is power filnclion oflhe fonn
(', -5/i+071, 0 9752
('orrelalion coefficient: 0.85 1 3
Iiquation (4.41) was then ~ ~ s e d to re-compute the dam conslruction cost for the respective
lengths as shown in 'l'able 4. I 1 b.
Table 4.1 1 b: [)am adjr~stcd construction cost and dam length Tor small dams
Dam - - - - -- . - Alau
Paki
Panshanu
Farakwai a
G~wa
Gwaraji
SI Birni
MI Belwa
~ ~~ ~
Predicted Height Actual cost 2006 cost cost
Nlm . . . . _- -.
9.5 45842 15723618 2249812
Prediction error .- - Nlm
1347381
375094
-1 8368
-20343
-25647
-60477
62 76
-74570
inflation factor
34 3
6.693
2.248
2.248
2.248
2.212
2.212
3.181
Date.
I988
2001
2004
2004
2004
2003
2003
1990
The graphical relationship between dam length and cost h r small dams is shown in 1;igul.e
4 .O9.
0 100 200 300 400 500
Dam's length(m)
Fig.4.09: Relationship between dam's length and costs for large dams.
General dams (Table 4.1 Ic)
J2quation is power fi~nction ofthe Som
Table 4.1 1 c: 1)arn adjusted constn~ction cost and darn length for general dams
SIN o
. --- I
2
3
4
5
6 %.
7
8
9
10
11
12
13
14
15
16
17
18
I 12
13
14
Dam
- - - .- - . . -- Alau
Pak~
Panshanu
Farakwai
Giwa
Gwaraji
Sabon Rirn~
Mayo Belwa
D-kowa(Engr)
S A
JBNL
SGE
FNL
AV
Kiri
Mangu
Shagari
Gubi
Dugwaba
Mararaba D
Kaltungo
Height Aclual cost 2006 cost
(m) . . .. .. Nlrn Nlm 9.5 45842 1572361 8
Preti~c cosl Prediction error
Wrn Nlm YO - - -- -- -- 18999249 -3275632 -21
inflatn.factor Date
343 1988
6.693 2001
2..248 2004
2..248 2004
2..248 2004
2..212 2003
2..212 2003
173.04 1992
114.99 1981
1 14.99 1981
11 4.99 1981
11 4.99 1981
11 4.99 1981
11 4.99 1981
121.35 1983
2.248 2004
6.09 1990
173.04 1992
1.000 2006
1.000 2006
1.000 2006
The graphical relationship between darn length and cosl f'or general dams is shown in
Figure 4.1 0.
Dam's length (m)x103
Fig -4.10: Relationship between dam's lengths and costs for general dams.
Analysis o f dam constrr~ction cost and reservoir storage capacity
In a similar approach, the dam construction cost was assuincd to bc rclatcd directly to the
reservoir storage capacity by a power function of the form.
I ',, = K ,( H "
Wherc, C,- the dam construction cost in Naira
n and KK- ~ ~ n ~ t i l t l t ~ to be estimated, and
K= lleservoirs storage capacity in cubic meter.
'I he adjusted darn cost to 2006 and the respective reservoir storage capacity i n Tables
4.12a, 4.12b, and 4.1 2c were used to calibrate Equation (4.43) to:
1,arge dams ('l'able 4.12a): I'quation is o r t h e power runction o r t h e Torln:
( '1-21it2 1 K 1 1 2 5 1 (4.44)
Correlat ion coerficient: 0.8968
I kluat ion (4.44) was then i ~ s e d to rc-compute the const ruc i io~ i cost Ihr the respective
reservoir storage capacity as shown i n 'l'able 4.12a.
'I'able 4.12a: 1-arth darn's adjusted construction costs ant1 reservoir storage capacities Tor large dams.
~
Prediction. infln. Capacity Actual cost 2006 cost Predic cost error Factor Date
-. --
D -kwa( f ngr).
S.A
JBNI.
SGE
FNL
AV
Kiri
Mangu
Shagari
10 Gubi I
t 11 Jada '.
13 Kaltungo
Height
-(111).. 42
42
42
42
42
42
37
21.5
10.98
27
20
11
32.8
I'he graphical relationship between dam reservoir capacity and cost for large dams is
shown in Figure 4.1 I .
Dam's capacity (m"xl0
Fig.4.11: Relationship between dam's capacity and costs for large dams.
General Dams ('I'a ble 4.1211): i
1':quation is of the exponential lirnction of the form:
- - - - - - - - - - -
Correlation coefficient: 0.8583 . ', Ilquation (4.45) was then used to re-compute the constn~ction cost h r the respective
reservoir storage capacity as shown in 'l'able 4.12b.
el
Table 4.1 2b: Dam's ad-justed construction costs and reservoir capacities for general dams.
Predic. Prediction. infln. Date Smo. Dam Height Capacity Actual cost 2006 cost cost error Fador const.
A m ) m Nlm BWrn Nlm Nlrn YO 1 D-kwa(Engr). 42 2.80E+03 57637 6627640 6127514 500000 08 11 4.99 1981
S.A
JBNL
SGE
FNL
AV
Kiri
Mangu
Gubi
Alau
Paki
Panshanu
Farakwai
Giwa
Gwaraji
SlBirni
MlBelwa
Jada
Dugwaba
Kaltungo
'The graphical relationship between dam reservoir capacity and cost for general
dams is shown in Figure 4.12.
+OO +03 +03 +03 +03 +03
Dam reservoir capacity(m3)x104
I '
Fig. 4.12: Relationship between dam reservoir capacity and costs for general dams
Small dams (Table 4.12~)
X Equation is of the exponential function of the form:
Correlation coefficient: 0.8380
Table 4.1 2c: Dam adjusted construction cost and reservoir capacity for small dams
- . -. -. -- - - - -- - . ... Actual Predic. infln.
Dam Height Capacity cost 2006 cost cost Prediction. error Factor Date const.
(m) m #/m #/m #/m % #/m -. Alau 9.5 1.12€+03 45842 15723806 3981196 117426 75 343 1988
Paki 6 1.02€+03 348407 2331888 2722586 -39098 -17 6.693 2001
Panshanu 5.5 5.41 E+02 137075 308145 41 I0410 -132896 -46 2.248 2004
Farakwai 4 2 3.70E-01 94953 213455 56528 156927 72 2 248 2004
Giwa 4.2 2.62€+02 120612 271136 152771 118365 41 2.248 2004
Gwaraji 4.5 5.10€+02 76895 170092 392029 221937 130 2.212 2003
'The graphical relationship between dam reservoir capacity and cost for small dams is shown
in Figure 4.13.
Reservoir capacity (m3)x102
Fig .4.13: Relationship between dam's capacity and costs for small dams
'I'he capacity of a reservoir cou Id be estimated by summing the embankment
volume and the natural reservoir storage volume. The embankment volume is included
because most of the time construction material is taken from the reservoir area of the dam
and this contributes to the volume of the storage
The natural storage volume is estimated as (Nelson, 1985)
Where: W = Width of water across the dam wall (m);
K= the site factor depending on the cross-sectional storage basin (0.5-1.6);
I)= maximum depth of water at reservoir; and
l,= length ofthe longest stretch of water surface at the reservoir.
The storage ratio as a measure of the economy of the dam could be checked easily.
The storage ratio is the ratio of the total storage to the embankment volume (Nelson, 1985)
y,+y, Storage Ratio =
v,
Where: V,= volume of embankment; and
V, = volume of natural storage.
Table 4.1 3 shows a guide to the rating for various storage ratios
Table 4.1 3 : Storage ratio and economic embankment
Storage Rating
-- -. ~- . ~ ~ ~
1,ess than 2.00 I'oor
2.00 to 4.00 Moderate
6.00 and above Very high
- . - -- - (From Nelson, 1985)
b
4.7 Earth dam parameters and costs.
'lie unit cost of a particular Civil engineering service: labour, equipment and
construction materials refer to the cost of a unit of the item in question. The best estimate
of a unit cost of an engineering project is best based o n "Contractor type" estimates
(Goodman, 1984) as follows:-
i ) Cost of pr~rchased materials;
ii) Equipment rental or ownership costs;
iii) Wages and salaries paid to construction and /or i~istallalion personnel;
iv) Cost of management and supervision; and
v) Other overhead costs and profits.
- - - - - - - - Mathem&ially,-theunit cost canbe~epresented by. - - - - - - - - - - - - - - -
Total cost of a service, equipment or mulerid - (', lJn i t cost (C,,) - -- . . . . (4.49)
Quanlilyqf ,ser.vicq equipment or nralerial (2,
Wherc, C,,- unit cost. CT- total cost of service, equipment or material; and
Ql-- quantity of service, equipment or material.
Equation (4.49) can be represented generally for all the work components in terms of the
uni t cost and the total quantity as
For embankment dams, discrete cost units o f services, equipment and materials sum
up to form the dam pro-ject investment cost. Among the important items that affect the
project investment cost includes:- b
i > i i)
... 111)
iv)
v > v i)
vii)
Preliminaries
Site clearance
Excavation (normal or rock excavation)
Iilling (rock and earth f iH) and compaction.
Instrumentation and geotechniques
Drilling
Grouting ( cement or chemical)
viii) Relief drains
ix) Concrete (plain and reinforced)
x) Form work and shutters
xi) Water testing etc.
Although there are several other components that add up to the total investment
cost, only the important ones mentioned above would be discussed further.
Site Clearance cost analysis.
The site to be cleared for dam construction inclr~des the construction area and the
working area. The clearance may inchde removal of top soils, grasses, shrubs, rock
outcrops, and trees. The measurement of the cleared area is usually in terms of surface area
(either in hectare, m2 or ~ r n ~ ) . d e ~ e n d i n ~ on the size ofthe area.
The relationship between the average of site clearing and grubbing per unit length of dam
( m 2 / ~ m ) could be represented by a power fimction of the form (Gichaga and Parker, 1988):
Where, SA = the average area of site clearing and grubbing per unit length of dam ( m 2 / ~ m ) .
GRI: - the rise and fall in ground (in m/Km) . . 3
D, = dam width (m)
KlrK2, n,, and n;! arc constants depending on the prevalent sitc conditions.
llowever, the cost of site clearance was assumed to be related to the area cleared by
a power fimction as
C I=kASu (4.52)
Where, Cr= total cost of site clearance
As= total surface area cleared in m2
k and n= constants to be estimated
Equation (4.52) was calibrated using existing dam cost data and valrles of k and n ..
were estimated and results shown in Tables 4.13a, 4.13b, and 4 .13~ .
General dam case (Table 4.13a):
Equation is ofthe linear function of the form:
C7 =O.OO~A' 85h0
Correlation coefficient: 0.8861
'Table 4.13a: Site clearance areas and dam costs for general dam case in the study area.
Adual SlNo Dam Height Area cost 2006 cost Pred cost Predict~on error factor
-- rn -- rn Nlrn Nlrn Nlm Wrn % Date 1 Paki 6 5 10E+04 947 5 6342 20889 -14547 -2.29 6.693
2 Shagari 10.98 7.00E+04 17902.1 56947 29488 27459 48 3.181 1990
3 Farakwai 4.2 1.75€+03 523 1176 5329 644 55 2.248 2004
4 Panshanu 5.5 1.50E+03 737 1657 2890 -1273 -73 2.248 2004
5 Giwa 4.2 1.60E-rO3 729 1639 2602 -1023 -62 2.248 2004
6 Gwaraji 4.5 1.60E+03 44 1 992 482 51 0 52 2.248 2004 1
7 SlBirni 3.7 1.75€+03 42 7 94 5 532 413 44 2.214 2003
8 MlBelwa 3 5 4.75Et03 520 3167 1554 ' 1613 5 1 6.09 1990
9 D-kowa(Engr). 42 3.00E+06 8430 969029 1763736 -794707 -82 114.95 1981
11 JBNL 42 3.00€+06 30600 351747 1763736 17753704 50 114.95 1981
12 SGE 42 3.00€+06 21300 2448435 1763736 681699 28 114.95 1981
13 FNL 42 3.00€+06 11310 1300085 1763736 -4636511 -36 114.95 1981
16 Monkin 25 1.29E+05 27144 25271064 167163 145541 58 9.31 2000
17 Alau 9.5 3.73E+05 55950 19190850 1170706 748379 39 343 1988
18 Durpaba 11 1.22Et06 67944.44 67944.44 1,000 2006
19 Kaltungo 32.8 8.21E+04 11528.09 11528.09 1.000 2006
20 ~ u r e 5.66 4.41€+05 42000 42000
21 Mararaba D. 12 2.35€+04 3776.79 3776.79
The graphical relationship between dam site clearance area and cost for general dams is
shown in Figure 4.1 4.
Clearance area (m2) x103
Fig. 4.14: Dam site clearance areas and costs for general dams
Large dams (Table 4.1 3b)
I'quation is o f the power function of the form:
(', =28.409A
w Correlation coefficient: 0.8242
v
Table 4.1 3b: Site clearance areas and dam cost for large dams in the study area
- ---. - -- -- -- - - Adual 2006 Pred infln
SIN0 Dam He~ght Area cost cost cost Prediction error factor Date m m2 Nlrn Nlm Wrn ---- -- - - - -- -- - -. -. - - -- - - .
1 Shagari 1098 7 00E+04 17902 1 56947 56972 -25 -0 04 3 181 1990
JBNL
SGE
TNL
AV
Gubi
Monkin
Dugwaba
Kaltungo
12 Wure 5.66 4.41E+05 42000 42000 1.000 2006
13 Mararaba D. 12 2.35E+04 3776.79 3776.79 1.000 2006
-. .- - ~
'17he_graphical relalis~ulip-between-damt sitectearanc;e area and cost t\,r large-dams %
i t is shown in Figure 4.15.
0.00Et00 2.00Et02 4.00Et02 6.00Et02 8.00Et02
Clearance area(m2)x104
Fig 4.15: Dam site clearance area and costs for large dams
Small dams (Table 4.13~)
P Equation is of the linear function of the form:
(', =53.694A-IE+06
Correlation coefficient: 0.9939
.~~ ~~ ~ . - . ~ . . ~. ~~. ~. ~ ~~. ~ .
SINo. Dam Length Height Area Actilal cast
m m m Nlm 1 Paki 400 6 5.10E+04 947.5
2 Farakwai 330 4.2 1.75E+04 52 3
3 Panshanu 230 5.5 1.75E+03 737
4 Giwa 225 4.2 1.75E+04 729
5 Gwaraji 335 4.5 1.50E+04 44 1
6 SlBirni 390 3.7 1.75E+04 427 , 7 MIBelwa 305 3.5 4.00E+04 52 0
8 Alau 344 9.5 3.73E+05 55950
Site 4.1 3c: Site clearance areas and dam cost Tor small dams in the study area.
--
-- - -. mflat
2006 cost factor Date Nlm -- - 6342 6.693 2004
The graphical relationship between dam site clearance area and cost for small dams is
shown in Figure 4.16.
0 50 100 150 200 250 300 350 400
Clearance area (m2)x lo3
Fig .4.16: Earth dam's site clearance areas and costs for small dams
The site clearance cost in Northern Nigeria could be estimated from the calibrated
equation (4.56) used to re-compute the total site clearance cost for the various dam sites in
Tables 4.13a, 4.13b, and 4 . 1 3 ~
Excavation cast analysis
Excavation refers to the digging of a geometric shape into the earth crust. 'The
important dimensions are the depth, width and length as the quantity of the excess earth
removed is accounted for in volu~nes of cubic meter (in3). Excavations could be in normal
earth or in rock excavation based on the prevailing soil conditions. Excavation cost most at
times accounts for digging, backfilling, hauling of excess material and disposal of the
hauled excess material. The cost of excavation is a function o f the volume and may be
assumed to be related to the cost as power function and linear relations.
(a). Normal soil excavation cost analysis: This i s the type o f excavation that is common
and is done in norrnal soil. The ma-jor problems encountered in normal excavation that
could affect its cost are caving and bank instability as a rcsult o f swelling caused by pore
water. If the ground water table is within the excavation depth, more problems o f bank
- instability are encountered. The excavation volume could be assumed to be related to its
b cost either linearly or as a power function
General Dam case (Table 4.14a)
Equation is o f the exponential function o f the fortn:
C, =0.3222~: 'I2.'
Correlation coefficient: 0.869 1
Table 4.14a: Open cut excavation volumes and costs for general dam case in the study area
Predic. infln. SlNo Dam Hdght excavation Actual cost 2006 cost cost Prediction error factor Date
-. m PUm Wm Mlrn BUm O h m3 - 1 Paki 6 44400 33498 224202 200574 23628 1 1 6.693 2001
2 Shagari 10.98 193202 156507 4562805 4508150 54655 0 1 29.154 1996
3 Farakwai 4.2 16170 26593 59781 115008 -55227 -92 2.248 2004
4 Panshanu 5.5 19780 4561 5 102543 128506 -25963 -25 2.248 2004
5 G'wa 4.2 17100 40667 91420 118605 -27185 -30 2.248 2004
6 Gwaraji 4.5 14405 2269 1 50193 107916 -57723 -115 2.212 2003
1 1 JBNL 42 7.29€+05 4258 489457 936691 -447434 -91 114.95 1981
12 SGE 42 7.29E+05 6064 697057 936691 -239634 -34 114.95 1981
13 FNL 42 7.29E+05 3642 418648 936691 -510043 -123 114.95 1981
14 AV 42 7.29E+05 5560 639122 936691 -297569 -47 114.95 1981
15 Monkin 25 6.71E+05 197310 1836956 894887 942069 51 9.31 2000
16 Alau 9.5 8 28E+05 10132 3475276 1004735 2470541 71 343 1988
1 1 Kallungo 32.8 4.417E+03 51844 51 51844.51 1.000 2006
12 Dugwaba 11 2 60E+04 481 80.00 48180 00 1.000 2006
13 Mararaba D. 12 2.23E+03 1688.83 1688.83 1.000 2006
1
The graphical relationship between dam volumes of excavations and cost for general dams
is shown in Figure 4.1 7 .
0 20 40 60 80
Volume of excavation (m)xl o4
Fig. 4.1 4b: Volumes of excavation and cost for general dams
Large dams (Table 4.14h)
Equation is of a linear fimction of the form:
C I = -7.3973Ve+ 6E+06
Y
Correlation coefficient: 0.9757
'Table 4.14 b: Open cut excavation volumes and their adjusted actual costs for large dams in Northern Nigeria.
Date Actual infln. dam
SINo. Dam Length excavation cost 2006 cost Pred. cost Prediction error factor const. Nlm . ~. . . .
M rn m3 Nlm w m Nlm pp----p.p..-- % 1 Shagari 92.6 93202 56507 4562805 4570827 -8022 -0.2
JBNL 520 7.29E+05 4258 489457 607368 .117,1, -24 114.95 1981 w
SGE 520 7 29E+05 6064 697057 607368 89689 13 114.95 1981 + FNL 520 7.29E+05 3642 41,648 607368 -188720 -45 114.95 1981
8 Monkin 1300 6.71E+05 197310 1836956 1036412 800544 44 9.31 2000
'I'he graphical relationship between dam volumes of excavations and cost for large dams is
shown in Figure 4.18
Volume of excavation (m3)x I o5
Fig .4.18: Volumes of excavation and cost for large dams
w Small dams (Table 4 . 1 4 ~ )
Equation is o f a linear function ol'the form:
C.,. " 4.1 504V,+ 363 1 5
Correlation coefficient: 0.9982 t
Table 4 . 1 4 ~ : Open cut excavation volumes and thcir adjusted actual costs for small dams in Northern Nigeria.
C__-___-_.__ ______ _ _- _ __ - - . Actual 2006 Predic
SlNo Dam Length excavation cost cost cost Prediction error in Inflation Year
m rnJ P U ~ ~ r n PJ1p- _ .PUm % factw 1 Paki 400 44400 33498 224202 220575 3627 02 6.693 2001
4 Giwa 225 17100 40667 91420 107287 -15867 -17 2,248 2004
- 5 Gwaraji 335 14405 22691 50193 9 6 1 0 ~ -45909 -91 2.212 2004
'J'he graphical relationship between dam volumes of excavations and cost for small dams is
shown in Figure 4.19.
Volume of excavation (m3)x104
Fig.4.19: Volumes of excavation and cost for small dams
Equation (4.58) was used lo re-compute the excavation cost as shown in Table 4.1 4c
Granular earth fill cost analysis: Filling with materials of different permeability is
common in zoned embankment dam. Zoned embankments are usually provided with a
central impervious core, covered by a coinparatively pervious transition zone, which is
finally surrounded by much more pervious outer zone. 'l'he transition zone prevents piping 0
through cracks while the outer zone gives stability to the central impervious fill and also
distribute load over a large area of foundation. The materials are selected based on their
availability. The granidar fill materials used for the dams in the study area are given in
i
:&
Tables 4.15a, 4.15b, and 4.1 5c below.
General dams (Table 4.15a): t'quation is a power function of form:
Correlation coefficient: 0.8234 rJ
'fable 4.15a: Pervious (granular) earth fills volumes and costs for general dams in the study area
- - - -- - - -- -- - - -- --- -- - -- SIN0 Dam rill Actual 2006 Predic. Predic.
Length Height volume cost cost cost Error inflat.
-- Wrn "3' Wrn Wm____- Wrn % factor Year
Paki
Shagari
Farakwai
Panshanu
Giwa
Gwaraji
SlBirni
MlBelwa
D-kowa(Engr)
S A
JRNL
SGE
FNL
AV
Monkin
Dugwaba
Kaltungo
Mararaba
The graphical relationship between darn volumes of' pervious (granular) fill and cost
for general dams is shown in Figure 4.20 below.
10 20
Fill wlurne (rn3)x104
Fig. 4.20: Volume o f pervious (granular) fill and cost for general dams
Small dams (Table4.15b): 7'he equation is o f a linear function oftlie form:
C, 30.288 lVK + I0 (4.60)
Correlation coefficient: 0.8000
Table 4.1 5b: Pervious (granular) earth fills volumes and costs Tor small dams in the study area.
-- -. - - - ... - .
Ian. SINo. Dam Length Height volume cost cost cost Prediction error factor Date
m ' Nlm Nlm Nlm - .- - - - - - Nlm % 1 Paki 400 6 16330 22454 150285 96750 53535 36 6.693 2001
2 Farakwai 330 4.2 14315 20628 46372 52850 -6487 -1 4 2 248 2004
3 Panshanu 230 5.5 17650 39207 ,,,,, 143758 -78101 6 3 2 248 2004
4 Giwa 225 4 2 15145 17079 38394 67805 .29411 -77 2 248 zoo4
5 Gwaraji 335 4.5 12500 19888 ,,,,, 30665 I,327 -30 2 212 2003
6 SIBirni 390 3.7 14650 29675 65641 58448 71930 11 2 212 zoo3
7 MlBelwa 305 3.5 6450 46258 134 6, 4994 1343612 99 29 154 1996 B 8 Wure 560 35.66 90300 241875 241875 241875 1 0 0 0 2006
The graphical relationship between dam volumes of pervious (granular) fill and cost for
small dams is shown in Figure 4.21.
Fill wlurne (&)XI o3
Fig. 4.2 1 : The volume ofpervious (granular) f i l l and cost for small dams
General earth dams: The equation is orthe form
( ', = 1 2.707V1,, - 3II; -t 06
Correlation coefficient (r) -0.9875
Table 4.1 5c: Pervious (granular) earth fills volumes and costs Tor general dams in the study area
Shagari
D-kowa(Engr)
S A
JBNL
SGE
FNL
AV
Monkin
Length rn
1193
520
520
520
520
520
520
1300
F~ll volume m
18330
2 41E+05
2 4lE+O5
2 4lE+O5
2 4lE+O5
2 4lE+O5
2 4lE+O5
3 5lE+O5
Actual cost Nlm
24515
105479
52879
51616
42041
51 125
51597
6791 80
2006 cost Wlrn
714711
130353
6078441
5933259
4832613
5876819
593075
6323168
Prediction Predicted cost error
Nlm Nlm
Pred. error in-?
55
50
0 2
02
-25
-03
-22
-18
Inflation factor . . . . . . . . . - -
29.154
114.95
114.95
114.95
114.95
114.95
114.95
9.31
'I'he graphical relationship between dam volumes of pervious (granular) f i l l and cost for
large dams is shown in Figure 4.22 v
20 25
Fill Volume (m3)x 1 o4
Fig A.22: Volume of pervious (granular) fill and costs for lage dams
b
Impervious fill volumes (Hard core): The earth fills volumes and their cost for the study
area is shown in Tables 4. I 6a, 4. I6b, and 4.1 6c.
f General dams (Table 4.16a): Equation is a power function of the form: i
3.
Correlation coefficient: 0.8000
Table 4 . 1 6 ~ lrnpervious (hard core) earth fills volumes and costs fbr general dams in the study area
- -. -- . ---- - - -. -- ... . -- -- -- -- - - -- .- - - Actual inflat.
SINo. Dam Height Fill volume cost 2006 cost Predic. cost Prediction error factor Date
-- 1 Paki
Shagari
Farakwai
Panshanu
Giwa
Gwaraji
SlBirni
MlBeCa
D-kowa(Engr)
S. A
JBNL
SGE
F NL
14 AV 42 7.10E+04 1584 183575 97295 86280 47 114.95 1981
15 Monkin 25 3.51E+05 169795 1580792 149886 1430906 91 9.31 2000
16 Dugwaba 11 1.53E+05 5077.80 5077.80 1 ,000 2006
17 Kaltungo 32.8 2.38E+5 184515.53 184515.53 1.000 2006
18 Wure 5.66 0.48E+05 293.61 293.61 1.000 2006
The graphical relationship between volumes of impervious (hard core) f i l l and cost for
general dams is shown in Figure 4.23.
+ I I
I0 20
Fill wlume (m3)xl o4
Fig.4.23: Volume o f impervious (hard core) fills and costs for general dams
Large dams (Table 4.16b): I<quation is a linear function o f the form:
'*. C, =0.003~,:, -9791 IV,,, + 6BO6
Correlation coefficient: 0.9258
'Table 4.1 6h: Impervious (hard core) earth fills volumes and costs for large dams in the study area
Adual 2006 inflat. SINo. Dam Length Height Fill volume cost cost factor Dale
m m m3 Nlrn Wlrn I Shagari 1 1 9 2 . 6 3 . 9 8 - 61100 24515 714711 29,154 1996
JBNL 52 0 42 2.41E+05 264 ,0809 114.95 1981
5 SGE 52 0 42 2.41E+05 2321 234613 113.95 1981 b
FNL 520 42 2.41E+05 718 129319 114.95 1981
'The graphical relationship between volumes of impervious (hard core) lill and cost for
large dams is shown in Figure 4.24.
0 5 10 15 20 25 30
Fill Volume (m3)xlo4
Fig 4.24: Volume of impervious (hard core) fill and costs for large dams
* Small dams (l'ahle4.16~): I'qnation is a linear function ofthe form:
Correlation coefficient: 0.9000
Table4. t6c: Impervious (hard core) earth fills volumes and costs fbr small darns in the study area
~
2006 Predic. inflat. SlNo Dam
. - - 1 Paki
2 Farakwai
3 Panshanu
4 Giwa
5 Gwaraji
6 SlBirni
7 MlRelwa
8 Monkin
9 Wure
Height Fill volume
m m3 - - ... -- 6 421 5
4.2 2005
5.5 21 10
4.2 1920
4.5 1745
3.7 3260
3.5 1820
25 3.51E+05
5.66 4766
Actual cost cost
Nlm . .- - - --- 150285
238924
234386
226589
240847
242601
234398
1580792
27234 29
cost
Wrn 242520
233980
234386
233652
232976
b 238830
233265
1582497
Prediction error factor Dale
N/m -- % - -92235 -61 6.693 2001
4944 02 2.248 2004
.04 0 2.248 2004
-7063 -03 2.248 2004
7871 03 2.212 2003
3771 02 2.212 2003
1133 0.5 29 154 1996
-1705 0 9.31 2000
1 .OOO 2006
The graphical relationship between volurr~es o f impervious (hard corc) fill and cost for
small dams is shown in Figure 4.25.
Fill volume(rr?)x 1 03 +
Fig 4.25: Vo lume o f irnpervious fill (hard core) and costs for smal l dams
The earth f i l l vo lume could be approximated b y the relation suggested by Nelson
(I 985) that gives a less accurate estimate as:
V,= 1 .65KBH (H-t I)
Where, K- coeff ic ient depending on the gul iey section (0.5-1 A);
D- dam length across the r iver channel (m); and
1 I- dam height (m)
Other methods include the average end area, pr ismoidal methods or combinat ion o f
the t w o are in use as indicated i n Gay and [;air ( 1 971 ) as
Where: aland a2 =-end areas w i t h centre heights and c2;
I , - distance between the sections; and
b, and b ~ = base widths.
Earth filling i s l~sually o f homogeneous earth. llomogeneous earth fill dam are
being replaced by modified homogeneous section in which internal draining system i s
provided to contml seepage and permit steeper slopes. Zoned embankments are also used
for earth dams in which the embankment is made up o f more than one niaterial.
Embankment filling could be done in two ways as
i) 1 Iydraulically filled, and
ii) Rolled fill method #
In a hydraulically filled method, thc dam body i s constructed by excavating and
transporting soils by hydraulic means (using water).'l'he soil material i s mixed with water
and pumped through pipes via flumes to the dam site.
In a Ilolled filled method, suitable materials for the f i l l i s placed in layers o f 150 to 300mm
and compacted with rollers. The soil is brought to the site from burrow pits which are
rlsually within a haul distance from the dam construction site. 'l'his is the common method
of filling and adopted for the study area.
Rock fill cost analysis: The rock fill dams are relatively cheaper than concrete dams and
can even be constructed more quickly especially when rock ~naterials are available
economically. Their characteristics vary between concrete dams and earth dams. They are
less flexible compared with homogeneous earth dams but more flexible than concrete
dams. Their foundation need not be very strict and rigid as in concrete dam but more rigid
than those o f homogeneous earth darns.
The sizes o f rock used for the f i l l vary from small stones to LIP to 3m size stones.
Rock fill dams are niore resistant to seismic forces but are liable to large settlements.
The volumes of rock fills used for the darns in the study area and their cost are
shown in 'fables 4.17a, 4.1 7h, and 4 . 1 7 ~ respectively.
General dams (Table 4.1 7a): tlquatiori is a power li~riction of the form:
I ', -982.22~'~~~'"" (4.67)
Clorrelatior~ coefficient: 0.9568
'I'ablc 4.1 7a: Rock lill volrrmcs and costs Tor general dams ill the s~udy area.
-- -. -- .. - - -- Actual 2006 Predic. inflan.
SINo. Dam kleigtit Rock fill cost cod cost Prediction error factor Date
-- m Nlm Nlm Nlm N/m % m3 -. - - _____. .
1 Paki 6 6300 24650 164983 103690 6129323 37 6693 2001
2 Shagari 10.98 3992 2989 87142 81321 5820 07 29.154 1996
3 Farakwai 4.2 381 10504 23613 23271 342 02 2.248 2004
4 Panshanu 5.5 37 5 9131 20527 23075 -2548 -12 2.248 2004
5 Giwa 4.2 341 8382 18843 21936 -3093 -16 2.248 2004
6 Gwaraji 4.5 335 9825 21733 21729 3.9 0 2.212 2003
9 D-kowa(Engr). 42 8.26E-605 13855 1592632 1391850 200782 13 114.95 1981
10 S.A 42 8.26E+05 9104 1046505 1391850 -345345 -33 114.95 1981
11 JBNL 42 8.26E4.05 7452 856608 1391850 -535242 -62 114.95 1981
12 SGE 42 8.26E405 11488 1320546 1391850 -71304 -08 114.95 1981
13 FNL 42 8.26E+05 7960 915002 1391850 476848 -52 114.95 1981
15 Monkin 25 1.04Ec04 9693 90242 135419 -45177 -50 9.31 2000
The graphical relationship between rock lill volurnes and cost for general dams is shown in
Figure 4.26.
0 10 20 30 40 50 60 70 80 90 100
~ o c k fill volumes (M~)XIU~
Fig.4.26: Rock fill volumes and costs for general dams in the study area
Large dams (Tahle4.11 h):
Equation i s an exponential function ofthe form:
( ', = 2 1 3 5 2 (k !' " ""'N
Correlation coeflicient: 0.827 i
Table 4.1 7b: Rock fill volumes atid costs Tor large dams in the str~dy area.
. . - -- inflan.
SINo. Dam Height Rock till Prediction error factor Date
1 Shagari
D kowa(Engr)
3 S A
JBNL
SGE
6 FNI
7 A,
8 Monkin
'T'he graphical relationship between rock f i l l volumes and cost for large dams is shown in
Figure 4.27.
Rock fill volumes (m3)x1v3
Fig.4.27: Rock fill volumes and costs for large dams in Re study area
Small dams (Table4.17~)
Rock filling volume and cost Tor large clams t
2 % Equation i s a linear function or the form:
C.', = 36.33 IV ,<,,. +2760
Correlation coefficient: 0.9992
'fable 4 . 1 7 ~ : Rock f i l l volumes and costs h r small dams in the study area.
~ ~ ~ . ~ - -
Rock Actual 2006 Predic. inflan. SlNo Dam Length Heighl fill cosl cost cost Prediction error factor Date
2 Farakwai 330 4.2 381 6504 14671 16602 -1981 -14 2.248 2004
4 Giwa 225 4.2 34 1 8382 18843 15149 3694 20 2.248 2004
5 Gwaraji 335 4.5 335 5725 12664 14931 -2267 -18 2.212 2003
'The graphical relationship between rock f i l l volumes and cost Tor small dams is shown in
f7igure 4.28.
0 10 20 30 40 50 60 70
Rock fill volumes (m3)x102
Fig.4.28: Rock fill volumes and costs for small dams in the study area
Riprap fill cost analysis: Riprap is the upstream protection against the erosive action o f
waves by stone pitching o r stone dumping. 'fhe thickness o f the protection should be up to
-clr I .Om and placed over a gravel filter o f about 300 m m thick. The filter prevents the washing
o f lines from the darn into tlie riptap.
'To reduce failure. the riprap is made in Inore than one layer. Concrete slabs may also be
adopted instead o f thc stone gravels but with filter underneath. 'The slabs sliould be 7
c b. '. providcd
with weep holes to avoid the washing o f fines from (lie dani embankment, a situation that
could lead to tlie cracking o f the slab. The downstream protection is o f more to protect
against the erosive action o f rain. Protection against the rainfall r ~ r n ~ ~ o f ' f is collected by
horizontal benns located at suitable intervals o f u p to 15 In. They intercept the rainfal l run-
o f f and discharge i t safely downstream. I n the study a m , stone p i tch ing Tor upstream
protections and grass p i tch ing Tor d o w n stream protect ion are the commonest. ' f he r iprap
fill for some dams it1 the study area and the i r cost is s l iowti i n 'I'able 4.1 8a.
General dams (Table 4.18a): Equation i s a power funct ion o r t h e Tonn:
Correlat ion coefl icient: 0.8547
'fable 4.1 8a: Riprap fill volumcs and costs for some earth dams in the study area.
--- -- 1
D 2
3
4
5
6
7
8
9
10
11
12
13
14
RID
15
Dam
Dams
--- - Paki
Shagari
Farakwai
Panshanu
Giwa
Gwaraji
SlBirni
MlBdwa
D-kowa(Engr).
S A
JBNL
SGE
FNL
AV
Monkin
Height
m
6
10.98
4.2
5.5
4.2
4.5
3.7
3.5
42
42
42
42
42
42
25
Riprap fill
m3 --
5400
9200
1143
1125
1022
1004
1713
6.4
5.88Ei 04
5.88E+04
5.08€.+04
5.88E+04
5.88E+ 04
5.88E+04
3.51E+04
Actual
cost
Nlm
1 m - '
3575
9429
14131
11795
12725
11579
52
2680
1832
2422
2886
2445
2233
2006
cost
Pllm
- 7201 7
104226
21197
31767
2651 5
28148
2561 3
1516
308066
21 0589
278409
331746
281053
256684
Predic
cost
Nlm
72029
98378
29037
28768
27197
2691 5
36792
1398
291237
291237
291237
291237
291237
291237
Prediction error
Infln
factor Date
1 he graphical relalionsli ip between riprap fill volumes and cost Ibr general darns is shown
in 1?ig11rc 4 2 9 a .
0 10 20 30 40 50 60 70
Riprap fill volumes (m3)x103
Fig.4.29a: Riprap,fill volumes and costs k r general dams in the study are a
Correlation coefficient: 0.892 1 l'able 4.1 8b: Riprap f i l l volumes and costs for large earth dams in the str~dy area.
~ - ~ - -- .~. .....
Pr edid: re diction infln. SINo. Dam Length Iieight Ripap f~ll cost cost cost errw factor Date
m m m3 Ulm Nlrn Nlm Nlm ~ ~ ~ ~ ~ -- %
1 Shagari 1192 6 10.98 9200 15390 448680 29.154 1996
FNL 520 42 5.88E+04 7445 ,5,,,3 214549 641254 75 114.95 1981
8 Monkin 1300 25 3.51E+04 61'78 ,,,,, 6286 51231 89 9.31 2000
-~ ~ .~
'I'he graphical relationship belweeli riprap fill volurnes and cost for large dams i s shown in
I;igure 4.29b.
Riprap fill volumes (m3)xlo3
Fig.4.29b: Riprap fill volumes and costs for large dams in the study area
Small dams (Tahle4.18~): Equation was a linear function of the form:
Correlation coefficient: 0.9802
Table 4.1 8c: Kiprap lilt volumes and costs Tor small earth dams in the study area.
. . . . . . . . . . . . . . . . _. -_ . - . . . . _ .. -. ___ . _ . - .. . . . . . _ .. - - .. - Actual 2006 infln.
SINo. Dam Weight Riprap fill cost cost Predic. cost Prediction error factor Date
m rn3 PUm Nlm Nlrn Wm % _ _ __ -
1 Paki 6 5400 29700 198782 190825 7957 04 6.693 2001
2 Farakwai 4.2 1143 9429 21197 26634 -5437 -26 2.248 2004
3 Panshanu 5.5 1125 14131 31767 25940 5827 18 2.248 2004
4 Giwa 4.2 1022 11795 26515 21967 4548 17 2.248 2004
5 Gwaraji 4.5 1004 5725 12664 21272 -8608 -6 8 2.212 2003
The graphical relationship belween riprap fill volumes and cost for small dams i s shown in
Figure 4 . 2 9 ~ .
0 10 20 30 40 50 60
Riprap fill volumes (m3)x102
Fig.4.29~: Riprap fill volumes and costs for small dams in the study area
Concrete volume cost analysis: Concrete is another material most often utilized in any
construction bccausc of its quick setting property and high strength on setting. On setting
concrete is impermeable to watcr. Another important factor Ihr utilizing concrete i s that it
could be formed into any desircd shapc.
Ilased on the magnitirde of load it will withstand in service, concrete could be of
two types or even more
i plain concrete(mass concrete), and
ii) Reinforced concrete(or 1 ligh grade concrete)
Although various grades o f concrete could bc utilized Tor a dam construclion, the
concrete was grouped into two as mentioned above for convenience
General dams ('rahle4.19a): fquation was a linear function of the form:
(', =- 5408.7 l1<,,. -- 59429
Correlation coefficient: 0.9402
'lahle4.19a: Plain concrete volu~ncs and costs Tor general dams in (hc study area
2 Shagari
3 Farakwai
4 Panshanu
5 Giwa
6 Gwaraji
JBNL
l2 SGE
l3 FNL
t
14 AV ;+
15 Monkin
16 Alau
Height
m .- 6
10.98
4.2
5.5
4.2
4.5
3.7
42
42
42
42
42 - -
42
2 5
9.5
volume cost cost cosl Prediction error faclor Date
m ' Hlm Hlrn % Prim ------ 16 400 2677 2711 -34 -01. 6.693 2001
'I he graphical tctationship bctween plain concrete lill volumes and cost for general dams is
shown in I:igure 4.3Oa.
Plain concrete fill volumes (m")
Fig.4.30a: Plain concrete fill volumes and costs for general dams in {he study area
I7able4.l9b: Plain concretc fill volumes and costs for large dams in thc study area.
Adual 2006 Predic. infln. SINo. Dam Height volume cost cost cost Prediclion error factor Date
rn r n ' l ~ - Wrn -- Nlrn Wrn N h - "/-- 1 Shagari 16 98 42 5510 189793 190024 -232 29.154 1996
D kowa(Engr). (92 1 17 3080 354046 572801 -218755 -62 114.95 1981
S A 42 117 5848 6,2228 572801 99427 15 114.95 1981
' JBNL 42 1 17 4965 5,072, 572801 -2074 0.4 114.95 1981
SGE 42 117 5144 59,303 572801 18502 03 114.95 1981 "1
FNL 42 117 6490 74,026 572001 173225 23 114.95 1981 +
8 Monkin 25 027 15693 ,46102 113468 32634 -29 9.31 2000
-- .- - -- -- --
'The graphical relationship hctween riprap {ill volu~nes and cost for largc dams is shown in
Figure 4.30b.
Plain concrete fill volumes (m3)
Fig.4.30b: Plain concrete volumes and costs for large dams in the study area
Small dams (Table4.19~): Equation was a linear furiction o f the form:
(', =- 19874V,<,. t 271 352 1
r'
Correlation coefficient: 0.8458
'l'i1bl~4.19c: Plain concrete volumes and costs Tor small darn in thc study arca. - . ~ ~ -
2006 SlNn D:-vi Height volume Actual cosl cosl Predic, cost Prediction error infln. factor Date
m m3 Wlm PUm Nlrn Nlrn % ~. ~ . ~
1 F':~ki 6 16 400 2677 15309 12632 82 6.693 2001
2 f ~rakwai 4.2 14 84 9 1909 2330
3 F'snshanu 5 5 I4 1339 3010 2330
4 (hwa 4.2 14 1316 29 59 2330
5 ' ;waraji 4 5 14 94 1 2082 2330 I
6 SIBirni 3 7 14 771 1706 2330
7 Alau 9.5 3.65 765 262395 198812 ~- ~ ~- ~~ ~ .- ~ -
'l'lie graphical relationship hetwecn riprap fill volu~nes and cosl for small dams is shown in Figure 4,30c.
Plain concrete volumes (m3)
Fig.4.30cPlain concrete volumes and costs for small dams in the study are a
( 'hss 2 concrete
I;ene~:*I dams (Table4.20a): Ilquation was oSa powcr f~~nct io~i oftlie form
- 0 8818 C' , - 17'J.6% , (4.73)
( 'orre1 ~ t io~ i coeflicievl: 0 .94074
l'able 4.20a: Rcinforccd concrcte volumes (class A) and costs for general dams
P,~ki
!; liagari
17arakwai
I'a~~slianu
Giwa
(;wara,ji
S/llirni
1)-kowa(l<tigr).
S.A
JDNI,
SG13
FNI,
AV
Monkin
Alan
-
Actual 2006 iriflan. cost cosl factor Date H/m Hhn
- -- 3275 219120 6.693 2001
'!'he grapliical relationship between classes A concrete fill volurncs and cost for general
tl:iiiis is slioivn in 1:igurc 4.3 1 a.
0 5 10 15 20
Reinforced concrete volumes (m3)xlo3
Fig.4.31a: Reinforced concrete (Class A) volumes and costs for general dams in the study area
I Large dams ('rable4.19a): Equation was ofcxponetitial function o f tlic form I b
b
Correlation coefficient: 0.9402
Table 4.20b: Reinforced concrete volumes (class A) for large dams
SINo. Darn
- .. - -. -
1 Shagari
D-kowa(Engr)
S A
JBNL
SGE
FNL
AV
8 Monkin
tieighl Volutne. rn rn3
- - - . -- 10.98 370
42 17160
42 17160
42 17160 , 42 17160
42 17160
42 17160
25 2.60E+03
cost
Wrn
. . -- - - - - 10549
71215
10308
8490
8987
1 I854
10116
23244
cost
AIlm
307548
8186165
11 84905
975928
1033056
1362618
1 162835
216402
factor Date
'The graphical relationship between classes A concrete f i l l volumes and cost for general
Ijams are shown in Figure 4.3 I b.
Reinforced concrete volumes (m3)xlo3
Fig.31 b: Reinforced concrete (Class A) volumes and costs for large dams in fie study area
Small clams (Table4.19a): I'quation is a linear function o f fonn
Correlation coefficient: 0.9964
Table 4 . 2 0 ~ : Reinforced concrete volumes (classes A) for small dams.
.. ~ .~ --- 2006 inflari.
SINo Darn [Length Height Volume. Actual cost cost factor Date
rn rn m7 Nlm Nlm . - - . -.. . . - -- . . - . . -. .- .- - -- - . - - -- . . - .. -. - - - - -
1 Paki 400 6 40 3275 219120 6.693 2001
2 Farakwai 330 4.2 4 5 32 8 738 2248 2004
3 Panshanu 230 5.5 4.5 453 I0l9 2248 20,
4 Giwa 225 4.2 4.5 46 1 2.248 20,
5 Gwaraji 335 4.5 4.5 329 728 2.212 2003
6 SlBirni 390 3.7 1.5 270 598 2.212 2003
b 7 Alau 314 9.5 9976 7172 2459996 343 1988
'1 hc graphical relationship between class A concrete lill volu~nes 2nd cast for small dams is
shown in Figure 4.3 1 c
Reinforced concrete volumes (m3)
Fig 4.31~: Reinforced concrete (Class A) volumes and costs for small dams in the study area
1)rilling (0-40m depth) cost analysis
Ikilling operation in adopted for either of lhe following
i) I'reparing the surface. and
ii) (;routing the foundation
Surface preparation involves removing the entire loose soil till a sound bed rock is
cxposctl. 'l'lie exposed surhce may be grooved by stepping, so as to increase the frictional
w ~csistance of the dam against sliding. Whcre faults, seams, or shattered rock zones are
+ dc(ectcd. geological investigations should be undertaken for remcdial measures.
(;routing on the other hand, involves drilling holes into the exposed rock (that is
af'let. surface preparation) and concrete grout is fi)rcctl into the holes pre-selected pressures.
Ikpending on the depth of the grouting holes, the grouting technique could be of two
types.
Consolidated grouting, and
curtain grouting
In consolidated grouting holes of depth from I 0- 15 In are drillcd at about 5 to 20 m
w apad and cement grout forced at low pressures of ahout 30 - 40 N/cln2. In a curtain
grouting however, the depths of the holes may vary from 30 to 40% of the total upstream
waler head for slrong hundations, and may be up to about 70% of the upstream water head
for poor rocks. Cement grout is forced into the holes at high pressures of about 2.5D
N/cm2, (where 1) is the depth of the hole in meters below the rock surface).
Grouting material could be ofchemical also but both cement and chemical grouting
were used for grouting in the study area. 'l'he drilling depth, chemical and cement grouting
used for the dams in the study and their quantities and cost are as shown in l'able 4.21 a.
I'al~lc 4.2 1 a: Ilrilling Tor grouting (0-40m dcpths), and their costs for some earth dams in the slrdy arca
2006 Drill Actual cost Inflation
SlNo Darns Length Height depth Cost ate in 2006
SGE 52 0 42 3640 675 46095 1981 114.95
FNL 52 0 42 3640 36 7 46095 1981 114.95
7 Monkin 1300 25 540 2693 25072 2000 9.31
The graphical relationship between the depth of drill for grouting and cost for large dams is
shown in ligure 4.32.
Depth of drill (rn)x10"
Fig.4.32: Depth of drill for grouting and cost for large dams
'I'he eqr~ation for drilling was calibrated from Table 4.2 1 a as
CI-6.7X161>,1t21410; r = l . O
Where, IIa = Depth ol'drill in normal soil (m)
The equation for hard rock drilling was calibrated as
(:1-29 r ) ~ 0 0759
Where, IIR - Ikpth of drill in rock (in)
The equation for cement grouting w as calibrated as
C 1=30 G, + I28
Wherc, (ire-- Cement grout quant ity (tons)
'l'lic eqr~ation for chemical grouting was calihratcd as
- Arwllorage cost analysis:
Anchorages are devices fbr guiding against displ;kcnient forces. Srd i anchorages
rcwld be in form of kcys on good ground b make the fountlation and the dam monolithic
struclure. At the basc of a dam, concrete-rock bond and the resulting interface shear
slrcngth are critical factors. Anchorages are to forestall discontinuities to faults, joints or
surface with reduced shear resistance. 'l'lic geological structure of the foundation should be
thoroughly investigated and the presence, naturc, frequency and orientation of such
disconl inuitics including critical intersections established. 'l'he resistance to sliding or
shearing which can be mobilized across a place is expressed through its angle of internal
v shearing resistance (6) and cohesion (c ) which represents the unit shearing strength of
concrete or rock utitler conditions of zero normal stress.
'I'he equation for rock anchorage was calibrated as
C'1-448 1000001<~-~ 70
Where, RA- Rock anchor clual~lity (tons)
Geotechnical instrumentation (control) cost analysis
(;coteclinical instrumentation refers to the application of mon i to r ing instruments for
geotechnical parameters o f the tiani. I t has rt lot o f roles among which include the
.- '1 '0 p o v i t l e an indicn(ior1 o f t h e v:ilitlity o fdes ign assumptio~is, and
- To determine an in i t ia l datum pattern o f performance against wh ich subsequent observations cou Id be assessed.
I'o achieve tlie above, men tioncd ot?jcctive, suites o f instruments are installed to
'C
provide a lricasure o r rc-assurance. Such instrumentation scrves to detect any signi f icant +
a b ~ i o ~ ~ r ~ a l deviations in thc long t e r ~ n behaviour and abnor~na l deviations in the short term
hcl iaviour o f the darn. Suites o f instruments varies great i n sophistication, attention should
be given to specification, dcs ig~i , and correct installation which arc cr i t ical to their
satisfactory performance. Suites o f instruments may he classif ied according to their
pr imary f i ~nc t i on o f installation (Novak and others, 1997) as
- construction control: veri f icat ion o f cr i t ica l design parameters w i t h immediate looped feedback to design and construction
- post construction perforniance: val idat io~r o f design determination o f in i t ia l o r datum behavioural pattern
iP
- Service performance/survei1lance: Reassurance o f structural adequacy, defection o f regressive change in established hehavioural pattern, investigation o f identif ied o r suspcctcd problems.
- Hesearch/development: Academic researcli equipment prov ing and development.
'I'he equation for geo techn ical instrumentation was calibrated as
Where, G I = Geotechnical instrumentation (m)
I'r-essare drains and wells cost analysis
I lplifl pressure in dams refers to the upward p~cssu~c o f water under the foundation
ilrcn. 'l'lie water may be those that seeps or flows through the dam body or to its
li)uridations via joints and water stops. 'l'he upward pressure reduces the net dam vertical
force. l 'he I.I.S. h r e a u for reclamation recornrnends that the total area o f the foundation on
wl\icli the uplilt pressure acts should be considered as cf'f'ective to account for uplift
P pcssure. To redr~cc the effect of the uplin pressure, so~netimcs drainage galleries are
~wv i t le t l in the hody o f Llic dam which releases thc upl i l i pressure built up under it.
0rain:ige holes or wells drilled subsequent to grouting in the hundation are also
effective in giving a partial relief to the effect o f the r~p l i f l pressure intensities under and in
the body orthe dam. Its effectiveness depends upon the character of the foundation and the
effective maintenance o f the drainage system.
The equation for pressure drains and wells was calibrated as
Where, P I ) = Depth o f pressure drain (m) '*
1701-mworks cost analysis
'These are structural members used to support concrete in the desired shape until i t
gets set. 1:ormwork could I,c o f wood, steel or plastic. The niosl comrnonly used are the
- , - - - - - - - - - - - - - - - - - - - P - - - -
I wooden and steel formworks. 7'hc equation Tor formwo7k utiIked iii tTieTtuTIyarEi was L.
Where, Fw = Formwork surface area and cost (mZ)
Sun~mary of the relations between various clam parameters and costs
' I ' a l~ lc 4.22a: S u m n ~ a r y o f c o s t relatioris for s m a l l earth d a m s
Correlation Darn parameters Equations derived
... ~. ~ -~ ~~ ~ ~ - - - coefficients
1 tieight and cost 169.381 I""'~' 0.9370
51: t071, -0 9252 2 Length and cost
3 Capacity and cost 56449e0 "3RR b
Unit costs 1 Site clearance and cost
2 Excavation cost 4.1504Ve+ 36315 0.9982
3 Pervious. fill cost 0.288 !IfR i - 10 0.8000
4 Imp. fill (Hard core) -0.0816 V,, +22.65 0.9000
5 Rock fill C O S ~ 36.33vRF 0.9992
6 Riprap fill cost
7 Plain concrete cost -19874 (',, + 271 352 0.8458
8 Reinforced concrete 243.1 9cA + 34570 -- --- -- - 0.9964
'1 :d,le 2.22h: Summary o f cost rclations Tor large earth darns
. - -. ~- -- -- - -- - .- . . Correlation
Dam parameters Equations derived ~ ~ I coefficient
1 Height and cost
2 Length and cost
3 Capacity and cost
1Jnit costs
Site clearance and cost
Excavation cost
Perv. fill cost
Imp. fill. (Hard core)
Rock fill cost
Riprap fill cost
Plain concrete cost
Normal drilling cost
Rock drilling cost
Cement grouting cost
Chemical grouting
Geotech. Inst. cost
Pressure drain cost
Form work
Rock anchorage
'l'ablc 11.22~: Sr~~ntnary o f cost relations for gencral csrth dams
. .---
1 Height and cost
7 Length and cost
Capacity and cost
Site clearance and cost
Excavation cost
Perv. fill cost
Imp. fill (Hard core)
Rock fill cost
Riprap fill cost
Plain concrete cost
Concrete A cost
Normal drilling cost
Rock drilling cost
Cement grouting cost
Chemical grouting
Geotech. Inst. cost
Pressure drain cost
Form work
C 16 Rock anchorage
- -. .- . -- -- -- -
--- - - - - - - .- .- - - . - -.
Correlation Eauations derived coefficient
Whcr-e,
2 AS, - Arca of silc cle;~rancc (111 )
Vil. Volume in-pervious fill (m')
\IR1. - VOhIlne ofrock f i l l ( d )
Crl = Volume of plain concrctc (m3)
I I - h i 1 height (ni)
CIA - ~ c i n forced concrete (m3)
I) , ( - Ikptli of drilling in rock (111)
(;,I, - C~liernicat grouting (tones)
Fw = Fi,rni work (m2)
1 V,. - Volr~mc ofcxcavation (m )
VPr' Volume ol'pervious fill (m3)
VrI - Volr~~nc oS riprap f i l l (m')
1, = Ilam length (m)
I<( - -= Reservoir capacity (m')
I),, - normal soil drilling (m)
(;,r: - ('cn~ent gror~ling (tones)
(il - Instrumentation
4.11.0 Relationships between clam parameters
'I'he dam para~nelcrs considered include heights, lengths, capacities, site clearance
areas, excavation volumes, embankment fills (homogeneous earth fill, pervious fills or
shell, impervinus fills or hard corc, rock fills etc); concrete fills (plain and reinhrced)
w grouting pit (normal or rock), grouting (cement and chemical), instrumentation, pressure
drai~is wells, form work area, etc.
All the parameter may not be applicable to all categories ofdams, however, where
- - - - - - - -,applicable,-tky- are considcrecl. 'Ille-c-orrelations wou Id be derived for small, large and 7 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
b b general dam cases. The correlations that give high correlation coeflicient (0.60- 100)
would bc selected for the general cost function Sor~nulation. The parameters considered
included the following:-
.rc
Dam l~eights and lengths: The dam hcight and length were correlated for small, large and
gcricral dam cases. 'Hie correlation coeflicients fiv sniall, large and general dam cases are
0.5305.0.5567 and 0.5883 respectively.
r ? 1hnr r-cscrvoir capacities and l e ~ ~ g t h s : I hc relationship bctwccn dam reservoir capacity
;r~id ils length correlated well, tlie correlation coeficient Tor small, large and general dam
c-a.;c were 0.8730,0.6962 and 0.7545 wspectivcly.
% Ilese~*voir capacities and clam heights: 'I he relationship between dam reservoir capacity
t n~id Iieight was fitted with corrclntion coefficients or 0.4050, 0.6836, and 0.8260 for small,
large and general dams respectively.
(a) Small dams. Small dams have heights less than I O meters ~ncasurcd from the lowest
portion of'the general f'onndation area to tlie crest and ilnpounding not more than 5 million
cubic meters of water (J~MWIIRT>, 1995)
I . 'l'he dam heights Tor small dams werc lilted to the dam lengths with a power function of
the ro1.111
l i =3 1.62 1, 02xxx (4.82)
P Correlation coefficient = 0.5395
The above relation was used l o estimate the dam hcighls for the various dam
lengths as shown in Table 4.23.
l 'ahlc 4.23: Earth dam's lengths and heights for srnall dams
. . . .......... . . . -~ -
SINo. Dams Length Height Predicted Capacity Location (m) (m) Height m . m3
. . . . -
'1 Achida 135 4 7.60 Sokoto
2 Dinawa 126.5 4 7.80 1.50E+05 Sokoto
3 Karkiro 180 7 7.10 2.38E+05 Sokoto
4 Marnoma 220 7 6.70 2.75E+05 Sokoto
5 Misibil 1535 3 3.80 7.66E+05 Katsina
6 Suru 800 6 4.50 Kebbi
7 Wurno 4500 8 2.80 Sokoto
8 Rijau 350 7 5.80 1.30E+06 Niger
9 Girei 250 5 6.40 2.50E+05 UBRBDA
10 MIBelwa 305 4 6.10 6.60E+05 UBRBDA
11 Apkwill II 203 9 6.80 1 .16E+06 Plateau
12 Kogingiri 280 8 6.20 2.50E+05 Plateau
13 Kwall 274 9 6.30 6.30E+05 Plateau
14 Kubani 853 4.50 ABU
15 Omogidi 31 0 5.5 6.00 2.50E+06 LBRBDA
16 BlKudu 1931 7 3.60 1. 19E+06 Jigawa
17 Daura 6 1.20E+06 Borno
18 RIGado 21 0 7 6.80 2.60E+05 Jigawa
19 Alau 344 9.5 5.90 5.60E+05 CBDA
20 Panshanu 230 5 6.60 5.40E+05 Niger
21 Paki 400 6 5.60 1.02E+06 Niger
22 Farakwai 330 4 6.00 5.40E+05 Niger
23 Giwa 255 4 6.40 5.34E+05 Niger
24 Gwaraji 335 4.5 5.90 5.09E+05 Niger
I 25 SIBirni 390 4 5.64 4.04E+05 Niger
' I he graphical relationship between dam heights and lengths for srnall dams is shown in
I'igurc 4 . 33.
Depth of drill (m)xlo2
Fig. 4.33: Relationship between dam's heights and lengths for small dams
I 2. The relationship between dam reservoir capacities and dam lengths were fitted with a
power fimction o f a the form:
R, =1230.701!~'~"
Correlation coefficient for the relation = 0.8730.
The relation was used to estiniate the reservoir capacity for various dam Icngths.
The results are shown in Table 4.24.
l':ll)lc 4.24: Earth dams lengths and capacities for small dams
Predicted SIfJo. Darns Length Height Capacity capacity Location
m' m" . ._ .. .- 1m1 . . @... ..~ - -
1 Achida 135 4 2.02E+05 Sokoto
2 Dinawa 126.5 4 1.50E+05 1.88E+05 Sokoto
3 Karkiro 180 7 2.38E+05 2.71 E+05 Sokoto
4 Marnoma 220 7 2.75E+05 3.34E+05 Sokoto
5 Misibil 1535 3 7 66E+05 2.52E+06 Katsina
6 Suru 800 6.3 1.28E-t-06 Kebbi
b 7 Wurno 4500 8 7.69E+06 Sokoto
13 Rijau 350 7 1.30E+06 5.42E+05 Niger
9 Girei 250 5 2.50E+05 3.82E+05 UBRBDA
10 MlBelwa 305 4 6.60E+05 4.70E+05 UBRBDA
11 Apkwill 11 203 9 1.16E+06 3.08E+05 Plateau
12 Kogingiri 280 8.23 2.50E+05 4.30E.tO5 Plateau
13 Kwall
14 Kubani
15 Omogidi
16 BlKudu
17 Daura
18 RlGado
19 Alau
20 Panshanu
21 Paki
22 Farakwai
23 Giwa
24 Gwaraji
25 SlBirni
Plateau
ABU
LBRBDA
Jigawa
Bomo
Jigawa
CBDA
Niger
Niger
Niger
Niger
Niger
Niger
'I ' l ie graphical relatinnsti ip hetween darn reservoir capacities and lengths Tor smal l
t l n~ns i s s lwwn in 17igr1re 4.34.
Lengths (m)x 1 o2 Fig. 4.34: Relationship between reservoir capacities and lengths for
small dams.
*s 3. 'The relationship between dam reservoir capacities and heights fo r smal l dams were
fitted b y a power runct ion o f t h e form.
R e2'32.3 151/" "'"
'I'he relation gave a correlal ion coc f f ic ient or0.4050.
'I'he relation was then used to re- estimate the dam reservoir capacities for the
various dam heights as shown i n Table 4.25.
'1';tl)le 4.25: Earth dam's heights and capacities and prediction errors for small dams - - . .. ~~ ~- ~
Predicted SINo. Dams Length Height Capacity capacity Location
Im) fm) m m3 . I._,
1 Achida 135 3.77E+04 Sokoto
2 Dinawa
3 Karkiro
4 Marnoma
5 Misibil
6 Suru
7 Wurno
8 Rijau
9 Girei
10 MIBelwa
11 Apkwill II
12 Kogingiri
13 Kwall
14 Kubani
15 Omogidi
16 BIKudu
17 Daura
18 RIGado
19 Alau - - - - - - -
7 20 PaKhaEu
2,. 21 Paki
22 Farakwai
23 Giwa
24 Gwaraji
w 25 SIBirni
Sokoto
Sokoto
Sokoto
Katsina
Kebbi
Sokoto
Niger
U BR BDA
U BR BDA
Plateau
Plateau
Plateau
ABU
LBRBDA
J igawa
Bomo
Jigawa
CODA
N w r - -
Niger
Niger
Niger
Niger
Niger
l'he graphical relationship between dam reservoir capacities arid heights for small
tl:~nis is show11 in 1;igrrre 4. 75.
heights (m)
Fig 4.35: Relationship between reservoir capacity and heights for general dams.
I'he equations and the correlation coefficients Tor the fbllowing parameters are
shown in appendix A.
t
i 4. Site clearance areas and dam heights: 'These two parameters were correlated using c,
linear and power functions. This was because these two Tirnctions gave higher correlation
coeficient between these parameters than other functions. The correlation coefficients
ranged from 0.5045 to 0.9003 Tor power and litiear ft~nctions. respectively.
II 5. Site clearance and dam lengths: These parameters were correlated using linear and
power fi~nctions. 'l'he relation had corrclation coefficients ol'0.6125 and 0.5538 for power
attd liticar li~nctions, respectively.
(1. Site clearance antl reservoir capacities: 'l'hcse two relations resulted in correlation
cocTficicnt 01'0,0207 and 0.7402 Ihr power and liticnr ht ict ions, rcspcclivcly.
7. Kxcavatior~ volumes and dams heights: ' l l i c volumes of excavation on the dam sites
\\,cle correlated to the dam hcights. 'l'hc corrclation cocrficients were 0.7699 and 0.9396 for
[irwar arid power runctions.
8 ICxcavation volemes antl dam Icngths: 'l'hcsc parameters Qcre also corrclatcd in linear
and power ft~nctions. 'l'hc corrclation cocficicnts Tor power and linear functions were
0.3762 and 0.4665 rcspcctivcly.
9. Excavation volumes and dam capacities: The relalionship between these parameters
gave a correlation coerficicnt o f 0.1253 and 0.7323 fiv power and lincar functions,
respectively.
10. Impervious fill volunics and lengllis: Impervious fill volumcs which is the hard core
used for controlling seepage were correlated with the darn lengths in the study area. The
a, correlations gave corrclations coeficient o f 0.9498 and 0.9842 Ibr power and linear
functions, rcspectively.
11. ln~pervious fill vola~mes and dam heights: 'l'he correlation cocflicients betwecn these
two parameters for small dams arc 0.9650 and 0.9936 for power and lincar functions, 1
b
respcctivcly.
12. Impervious fills volumes and reservoir capacities: 'I'liese parameters were correlated
~~..;ing power and linear functions for small earth dams in thc study area. 'l'he correlations
g w c correlation coefficients of0.2090 and 0.6423 Tor power and linear functions,
~rspt:clivcly.
I.?. I'ervic~us fills volumes and dam heights: Pervious till materials arc common in zoned
( : i l l 1 1 1 tla~ns or rock fill. 'I licse dams are relatively chcaper because tlie pcrvious nlatcrial
w, givrs ~ttore of stability to the darn and could be sourced locally. The pervious material
wl~isli is also callcd tlie shell could he made of porous matcrhls that arc available on the
t h n sik. 'l'he pervious f i l l volumes were correlated to thc dam heights giving correlation
coeflicicnt of 0.6650 and 0.684 1 for power and linear functions, respectively.
14. I'rrvious fills volrmes and dam lengths: Thcse parameters were correlated for small
dams in the study area and the relations gave a correlation coeflicient of 0.35 16 and 0.3 192
Tor power and linear functions.
15. I'ervio~rs fills volrrnics and darn capacilics: 'l'licsc parameters wcre related for small
earth dams in the study area giving a correlation coefficient of 0.6350 and 0.2032 for
u power aid li~icar functions, respcctivcly.
16. Rock fills volumes and dam heights: 'I'hcsc parameters were correlated for small earth
dams and tlieir relation gave a correlation coeflicicnt of0.7473 and 0.7232 for power and
linear ftlnctions, respectively.
17 Hock fill volume aed clam lengths: The rock fill volumes fiw small carth dams were
correlated to their heights. The correlations for power and littear functions gave correlation
coeflicient of 0.3 898 and 0.5486, respectively.
18. Dam rock fill volurnes and reservoir capacities: These parametcrs were correlated
h r small dam using power and linear f'unctions. 'l'he rclation gavc correlation coefficients
o S O . 1304 and 0.8259 for power and linear functions, rcspcctively
19 Riprap fill volumes and dam heights: Riprap f i l l refer to the medium sized stones
()laced on the upstrcam slope li,r protection against wave action and othcr f oms o f erosion.
'I he riprap f i l l volumes wcre correlatcd with the dam hcights hi small earth dams in the
s(tltly arm. 'l'he correlations gave correlation coefficients o f 0.6402 and 0.7344 for power
"I
and lincar functions, respectively. +
20 Hiprap fill volumes and clam lengilis: The riprap volumes were correlatcd to the dam
lengths in the study area. 'fhe correlations gave correlation coefficients o f 0.1008 and
0.58 17 for power and lincar frrnctions, respectivcly.
21. Riprap fill volumes and reservoir capacities: 'l'hese parameters were fitted using
power and linear functions giving correlation coeflicients o f 0.0 100 and 0.7909 for power
and linear functions, respectivcly.
22 Concrete fill volumes: ' f w o c:~tegcwies o f concrete were generally common for use.
'I'hese include plain arid reinfbrccd concretes.
(a) I'lain co~icrete:
(i) J'lain concrete fill volumes and dam heights: The plain concrete volumes used
were fitted to the dam heights for small darns. The correlations gave correlation
coetlicients o f 0.8664 and 0.9834 for power and linear functions, respectively.
(ii). Plain concrete fill volumes and clam lengths: 'l'hese variables werc fitted using
power and linear relations. 'T'hc rclalions gave correlation coeflicients o f 0.4922 and 0.5277
for power and linear functions, respectively.
(iii). I'lain concrete volames and reservoir capacities:
I l i c p la in concrete volumes were fitted to the rcscrvoir capacities Ihr smal l earth dams in
t l ic s t r dy area. 'l'lie correlations gave correlation cocf l ic ients o f 0.8664 and 0.9834,
~cspecl ive ly .
(I,). Hciaforced concrele ((;rade A).
fi). I<eiaforced concrete volemes and clam I~e ig l~ts: ' l ' l ie reinlbrced concrete volumes for
- w i a l l t i a m were related to their heights. The correlations gave correlation coefficients o f
0.02 18 and 0.9 I 6 0 Tor power and l incar relation, respect if ely.
(ii). Reinforced concrete volames and dam lengths: 'l'hese parameters were correlated
usiug power and linear functions. 'l'lie correlation cocl'ficients for the correlations are
0.4022 atid 0.5277 Tor power and l inear functions, respeclively.
iii). Reinforced concrete volen~es a ntl (la111 capacities: 'I'liese parameters were
correlated using power arid linear functions. The correlation coefficients o f 0.8920 and
1.000 were obtained for power and l inear functions.
(h) l a r g e dams:
iC These arc dams that have heights greater than 10 metres. Al t l iougt i the lntcrnational
(:ommission o n l a r g e Dams (ICOLI)) suggested from 15 meters and above, I 0 meters and
above could he i n c l ~ ~ d e d . Other si lent features of these categories o!' darns include the
fo l lowing:
'The crest length should no t he less than 500 mercrs;
I'he capacity o f the reservoir formed b y the dam should not be less than 1 m i l l i on 3
m ;
The max imum f lood discharge dealt w i t h b y the sp i l lway should no t be less than
2000 1n3/s; and
e 'I tie dani design and foundation pmblems should be handled specially
Tliesc catcgories ofearth darns require more paranielers than sriiall dams. The other
p:w:~uiclers that such darns may be required include drilling Tor grouling (normal soil and
twk) , grouting (cement and chemical), rock anchorage, pressure drains, instrumentation,
k)l-mwork etc. Some orlhese parameters lack enough data for comprehensive analysis such
a:: l l ~ i s one. I lowever, the hl lowing parameters were correlated as follows.
?w 1 . '1 he dam licights and its lengths were fitted with a linear relation o f the form
+
l~d).OO2l,-t 16. I 3
' I lie correlation coefficient - 0.5567.
'I'he equation was usecl to re-estimate the dani heights for the various lengths as
sulnmarised in Table 4.26 o f Appendix E.
'I'he graphical relalionship betwcen dam heights and lengths for small dams is
dP shown in Figure 4. 36.
Length (m)xlo2 Fig .4,36:Relationship between dam heights and lengths for large dams.
'II 2. The relationship between dam reservoir capacities arid their lengths werc fitted with a
linear fimction of the form.
R,=16067/,-587677
'l'he correlation coefficient Tor thc relationship -- 0.6962.
The relation was then used to re-estimate the reservoir capacity fix various dam
lengths as shown in 'Table 4.27 of Appendix E.
'l'hc graphical relalionship hctwecn dam rcscrvoir capacitics and Icngths for large
tlatiis is shown in I:igui-e 4.37.
Le ng h (m)x lo2 Fig 4.37:Relationship bebeen dam reservoir capacities and lengths tor
large dams.
3. The relation between dam rcservoir capacities and thcir hcights were fitted by a linear
N, -21-t07IJ -t 150
't'he above relation gave a correlation cocficient of 0.6836.
I he relation was then used to cstimatc the reservoir capacities for the various dam
Iicighfs as shown in 'l'ablc 4.28 of Appcndix I:.
I he graphical relationship lxtween dam reservoir capacities and heights for large
ci:r~ns i s shown in i*igulc 4.38.
Height (m)xlo2 Fig.4.38: Relationship between dam reservoir capacity and heights for
large dams.
For the following parameters equations and correlation cocf'ficicnts are shown in
Appendix 13.
4.0 Site clearaiice areas and (lam heights: The areas ofsi tc clcamnce were correlated to
the darn heights For large dams. The correlation coefficients were 0.9573 and 0.9412 for
power and linear functions, respectively.
5.0 Site clearance areas and clam lengths: 'l'he site clearance areas were correlated to the
tlam lengths, using power and linear filnctions. 'l'he relation gavc correlation coefl7cienls of
0.747 1 and 0.0970 Tor power and linear rclations, respcctivcly.
6.0 Site clearance areas ancl dam capacities: 'I'hese paralneters were correlated and the
co~lelalions yielded correlation coeflicients of 0.3362 and 0.7218 Tor power and linear
f i~~icl io~n, respectively.
- 7.0 l xcava t ion volumes and clam heights: The vo lumcs of excavation were correlated to
the dam lengths. 'l'lie correlations yielded correlation cocfficientsbf 0.6586 and 0.6020 for
~ ~ o w e r and linear functions, rcspcctively.
9.0 Excavation volumes ancl reservoir capacities: ' I hc excavation volumes were
corrclaled with the dam reservoir capacities. The rclations yielded correlation coefficients
of 1.000 for both power and linear fi~~~ctions.
10. Impervious fill volumes and dam heights: l h c impervious f i l l volumes were
correlatcd with the dam heights in the s t d y area. The correlations gave coefficient of
correlation of05349 and 0.5025 for power and relations, respectively.
a 11. Irnpervioss fill volr~mes and darn lengths: 'I'hc corrclotions bctwcen thesc parameters
yielded correlation coefficients of 0.5349 and 0.5025 as the case of height above for power
and linear fonctions, respectively.
12. Impervious fill volumes and clam capacities: 'I'he correlations between these
parameters yielded correlation coefficients o r 0.5349 and 0.5025 for power and linear
relations as the case above.
15. I'ervioas fill volumes and dam heights: 'l'hese parameters w x e correlated with each
orllcr and gave corrclation cocflicicnt o f 0.865 I and 0.5733 li)r power and lincar functions,
~c:.;pcctivcly.
14. I'trvioas fill vol l~nles aml dams lengths: 'l'hc relationships bctwccn tlicsc parameters
gave correlation coefficients of0.4936 and 0.1987 Tor power and linear functions,
rcy?cctivcly.
.- 1.5. I'rrvious fill volumes and dam capacities: 'l'hc correlation coefficients between these
p;~ranlrfers were 1 .OO h s both power and linear fi~nctions.+
16. Pervious fills volumes and dam capacities: ' lhc correlation coefficients Tor relating
tl~cse parameters using power and linear functions are 0.9363 and O.O4!, 1, rcspcctively.
17. Pervious fills volumes and dam lengths: 'l'hc rock volumes for large dams were
related using power and linear functions. 'l'he correlations yield correlation coefficients o f
0.9856 and 0.9960 for power and linear functions, respectively.
18. Hiprap fill volnnies and dam heights: 'T'hcse parameters were correlated k)r using
power and lincar functions giving correlation coefficient o f 1.000 for both the functions.
o 19. Hiprap fill v o l ~ l m e s and dam lengths: 'l'hese parameters were correlated for large
dams resulting in a relation with correlation coeficient o f 0.9945 and 0.3980 for power and
linear fi~nctions, respectively.
- - - - - - - - 2 k R i p m f l K v d u m e s a t l ~ l 4 a m keigl&:ll'lu: rdaLionst~s_belwe_en_the~e~w~ - - - -
\, parameters gave correlation coefficient o f 0.8052 and 0.8904, respectively.
21. Riprap fill volumes and dam capacities: These two parameters were also correlated
using power and linear functions. l ' l ~ e i r correlation coellicients wcrc 1.00 for both power
and linear functions.
22. I'lain concrete volumes and clam heights: 'T'hcsc parameters were fitted by power and
linear functions. 'I'hc cotrclatio~is yicldcd correlalion coellicients o f 0.6020 and 0.8637 for
powcr and linear filnctions, respectively.
25. IUlsin concrete volumes and clan1 lengths: I llcsc para~nctcrs wcrc corrclatcd giving
c-orrclation coefficients o f O.%Z!8 and 0.993 1 for powcr and lincar fimctions, respectively.
24. I'lain coacrete volrrnes and clam capacities: 'l'hcse parameters yielded correlation
- cocflicients o f 1.00 for bolh functions.
+ 25. <:lass a concrete volrlnies and tlain heights: 'l'hcsc parameters wcrc correlated with
each ot l~cr giving correlalion cocflicienls of 0.9922 and 0.9706 for power and linear
f i~nct ions, respectively
26. Class a concrete volnmes and dam lengths: 'l'he correlation coeflicients for relations
between ttlesc panrnetcrs were 0.9083 and 0.9861 for linear and power functions,
respectively.
27. Class a concrete volumes s nrl dam capacities: Relations between these pannieters
yielded correlation coefficients or 1 .OO for both powcr and linear functions, respectively.
u 28. Normal soil drilling deptl~ and dam heights: 'l'hese para~netcrs were correlatcd and
their relations yielded correlation coefficients o f 1.00 for both power and linear functions.
29. (:emen[ groi~ting also gave 1.00 correlation coefficients for relations with datn heights. - - - - . . . . . . . . . . . . . . . . . . . . .
- - - - - - - - - - - - - - - - - - - - - - -
length and reservoir capacities. ' l ' l~ correlations between the surhcc areas o f form work I
' \ i~sed and darn heights, length and capacities gavc corrclatio~i coefficients of 1.000.
('. General clams
(icneral dams consist of' both small and large dam's characteristics. Thus.
~lnra~nckrs i~tclude site clearance areas, excavation volumec, embankment fill volumes
(pwvious. itiipcrvio~~s, rock fill ck), nor~nal soil and rock drilling for grouting, cement and
cl~emical grouting, plain and reinforced concretes, rock anchorage, pressure drains,
i~isl~~lrnentation, form work ek. Although not all p:lramcters are applicable in the study
%- are~, r hose applicable arc analyscd below.
#
I. The relationship between dam heights and its Icngths for general dam case were fitted
with a linear function o f form:
I f 2.30 E-03 I, -t 12.28
The relationship gave a correlation coefficient o f 0.5883,
'I'he relation was again used lo re-eslimate the darn heights Tor the various dam
lengths. 'fhe results are shown in 'fable 4.29 of appendix 1:.
9 The graphical relalionship belwecn dam Iieiglits and lengths for general dams is
shown in Figure 4.39.
Fig.4.39: Relafionship between dam heights and lengths for general dams.
2. The relationship between darn reservoir capacity and length were correlated using a
power function o f the form.
R( =700.861! '""
The relalion gave a correlation coefficient of 0.7545.
The relation was then used to reestimate the reservoir capacities for the various
dam lengths along with their errors of estimate as shown in Table 4.30 o f Appendix I.:.
*r
' I he graphical relationship between dam reservoir capacities and lengths for general dams
is shown in Figure 4.40.
Leng h (m)x103 Fig.4.40: Relationship between dam reservoir capacity and lengths for
general dams.
3 . The relationship between reservoir capacity and height was fitted with a power function
of form.
The relation gave a correlation coefficient of 0.8260.
The relation was then used to re-estimate the reservoir capacities for various dam
heights. The results of estimate are shown in Table 4.3 1 of Appendix E.
The graphical relationship between dam reservoir capacities and heights for general
dams is shown in Figure 4.4 1 .
Fig .4.41: Relationship between dam reservoir capacity and heights for general dams.
The equations and correlation coefficients are shown in Appendix C.
4. Area of site clearance and dam heights: Dam site clearance areas were correlated to
the dam heights for general dam case in the study area. The result gave correlation
coefficients of 0.91 55 and 0.9636 for power and linear functions, respectively.
5. Area of site clearance and dam lengths: These parameters were correlated to each
other giving correlation coefficients of 0.691 8 and 0.2270 for power and linear functions,
respectively.
6. Site clearance area's and dam capacities: These parameters were fitted with power
and linear functions. The correlations yielded torrelation coefficients of 0.8177 and 0.7436
for power and linear functions, respectively.
7. Volumes of excavation and dam heights: The volumes ofexcavation were correlated
to the dam heights using power and linear functions. The correlations gave correlation
coefficients of 0.9760 and 0.981 0 for power and linear functions, respectively.
8. Volumes of excavations and dam lengths.
The excavation volumes were correlated to the dam lengths. The correlations gave
correlation coefficients of 0.7595 and 0.5920 for power and linear functions, respectively.
9. Volumes of excavations and dam capacities: These parameters were correlated with
each other giving correlation coefficients of 0.4696 and 0.3497 for power and linear
functions, respectively.
10 Pervious fill volumes and dam heights: The pervious fill volumes and dam heights
were correlated giving correlation coefficients of 0.9663 and 0.8982 for power and linear
hnctions, respectively.
1 1 . Pervious fill volumes and dam lengths: The relation between these parameters yielded
correlation coefficients of 0.785 1 and 0.7736 for power and linear functions, respectively.
12. Pervious fill volumes and dam capacities: The pervious f i l l volumes were related
using power and linear functions. The relations resulted in correlation coefficients of
0.6350 and 0.2032 for the power and linear functions, respectively.
13. Impervious f i l l volumes and dam heights: The correlations between these two
parameters using power and linear functions resulted in correlation coefficients of 0.91 16
and 0.9038, respectively.
14. Impervious fill volumes and dam lengths: These parameters were correlated using
power and linear functions. The relation gave correlatioA coef'ficients of 0.8822 and 0.9844
for power and linear functions, respectively.
15. Impervious fill volumes and dam capacities: These two parameters were correlated
using power and linear functions and the result gave correlation coefficients of 0.05857 and
0.9855, respectively.
16. Pervious fills volumes and dam capacities: Relations between these two parameters
using power and linear functions gave correlation coefficients of 0.9619 and 0.9594
respectively.
17. Volumes o f rock fill and dam lengths: The correlations between these two parameters
using power and linear functions were 0.8775 and 0.9078, respectively.
18. Pervious fills volumes and dam capacities: The relationship between these to
parameters gave correlation coefficients of 0.5505 and 0.9843 for power and linear
functions, respectively.
19. Riprap fill volumes and dam heights: These parameters were correlated using power
and linear functions giving correlation coefficients of 0.3709 and 0.9992, respectively.
20. Riprap fill volumes and dam lengths: Relation between parameters using power and
linear functions gave correlation coefficients of 0.7709 and 0.91 63, respectively.
21. Riprap fill volumes and dam capacities: These parameters were correlated using
power and linear functions and gave correlation coefficients of 0.4274 and 0.9875,
respectively.
22. Plain concrete volumes and dam heights: The correlations for these parameters gave
correlation coefficients of 0.9454 and 0.7945 using power and linear hnctions,
respectively. b
23. Plain concrete volumes and dam lengths: These two parameters were correlated
using power and linear functions resulting in correlation coefficients of 0.8989 and 0.9454,
respectively.
24. Plain concrete volumes and dam capacities: Relations between these two parameters
gave correlation coefficients of 0.9850 and 0.5932 for power and linear functions,
respectively.
25. Reinforced concrete volumes (class a) and dam heights: These relations gave
correlation coefficients of 0.941 6 and 0.9415 for power and linear functions, respectively.
26. Reinforced concrete volumes (class a ) and dam lengths: Relations between these
parameters gave correlation coefficients of 0.8745 and 0.8999 for power and linear
hnctions, respectively.
27. Reinforced concrete volumes (class a) and dam capacities: These parameters were
correlated resulting in correlation coefficients of 0.6138 and 0.9838 for power and linear
functions, respectively.
28. Normal soil drilling for grouting and dam heights: These parameters gave
correlation coefficients of 1.000 for both functions.
29. Normal soil drilling for grouting and dam lengths: Relations between these two
parameters also gave correlation coefficients of 1.000 for both power and linear functions.
30. Normal soil drilling for grouting and dam capacities: The correlations gave
correlation coefficients of 1.000 for both power and linear functions. For rock drilling,
adequate data was not available to make a reliable analysis.
31 Cement grouting qualities and dam heights: These parameters were correlated giving
correlation coet'ficients of 1.000 for both functions.
32 Cement grouting quantities and dam lengths: These parameters were correlated and
gave correlation coefficient of 1 .OO for both functions.
33. Formwork areas and dam parameters: The areas of formwork used were correlated
with dam heights, lengths and reservoir capacities. The correlations gave correlation
coefficient of 1.000 for power and linear functions. The relationship between these
parameters also gave correlation coefficients of 1.000 for both functions.
4.9.0 General cost functions
The derivation of a cost hnction needs the input variables which are the parameters
in this case of earth dams. The total cost function involves the addition of the cost of all the
parameters that made up the whole earth dam. This may include site clearance cost,
excavation cost, embankment f i l l cost (Pervious fill, impervious fill, rock fill), grouting
cost (cement and chemical), concrete f i l l cost (plain and reinforced), instrumentation cost
etc. These parameters are not applicable to all dam sites; however, for larger dams most of
them are applicable.
The generalization of cost function to all the categories of dams has its own limitations and
as such the limitations could be reduced by deriving cost functions for the various
categories of earth fill dams possible (homogeneous earth fill, Rock and earth fill, and
diaphragm earth fill dams). Data is not available to make such analysis as most of the
dams are either earth and concrete dams, mixture of rock and earth f i l l and diaphragm
dams. In view ofthis variation, grouping the dams as small, large and general cases was
adopted for this study.
1.0 Small dams @
Small earth dams as pointed out earlier are dams constructed with heights less than
10 meters. The most common parameters include site clearance, excavation, embankment
f i l l (pervious, impervious, rock etc), concrete, riprap f i l l , instrumentation etc. The
parameters were related with each other. The relationships that yielded higher correlation
coefficients were selected as shown below:
The general cost functions for small dams were derived by adding the costs of the dam
parameters in equations above.
C.,, = 53.69 Asc+4.1 5 Ve+721.18e (O.oM3V ) ,, + 3.86VlF + 36.33vRF + 38.57Vd - 19874Cp +
243.19 CA -431704.53 + E 4.90
Where,
2 As, = Area of site clearance (m ) V, = Volume of excavation (m')
V,f =Volume in-pervious fill (m3) V P f = t/olume of pervious fill (mi)
VKI: = Volume of rock f i l l (m') Vrf.= Volume of riprap fill (m')
C p = Volume of plain concrete (m3) L = Dam length (m)
H = Dam height (m) Rc = Reservoir capacity (m')
CA = Volume of reinforced concrete (m3) = operation and maintenance cost (Taken as 2-5% of the investment or construction cost)
Equation 4.89 was substituted in Equation 4.90 to yield Equation (4.91).
The dam total cost could be summarized in terms of dam height, length and
reservoir capacity only.
The operation and maintenance cost should be taken as a percentage of the total
cost as suggested by Caimicross and others (1981) and Gubremariame and others (2002).
2. Large dams
Large dams as pointed out earlier refer to dams with heights greater than 10 meters.
w
Where, all the parameters retain their meaning in Equation (4.90) except for the
following
Dd = Depth ofdrilling in normal soil (m), DR = Depth of drilling in rock (m)
GI = Cement grouting (m), GI = Instrumentation
Fw = Form work (m2) ~2 = operation and maintenance cost (taken as 2-5% of the investment or the construction cost).
Equation (4.92) was substituted in Equation (4.93) and after simplification the ff
resulting Equation reduced to Equation (4.94). +
0.7095 1.4384 Cr =20.51 (1 151 25H - 2E + 06) - 0.02Rc + 8.5E-05(Rc) -
0.7 192 5.21(Rc) +0.022e ( ~ . ~ S E - O B R - 0.58) 6.8421 + 5E - 27 (1559.2H - 64897) -
663.48L + 377.65(-21.28L + + 12366217H + 3 0 . 4 1 ( ~ ) ~ . ~ ~ ~ ~ + 33 (4.47H
The general equation for large dams reduced to length, height and capacity
parameters.
3. General dams
o These categories of dams as pointed out earlier refer to the dams with the
combination of both small and large dams characteristics. Thus, they reflect the parameters
for small and large dams. The parameters for general dams include all the parameters in
Equation (4.90) and (4.92).
The correlations between the parameters for the general dam case with the highest
correlation coefficient are as shown in Equation (4.95).
Vp :: 9X.h3K( - 35875 r -= 0.9975
V 0 I I I - 47087 r = 0.98 10
VII = 29.23 R( - I I95 1 r = 0.9855
VKl 351.14K( -- 171 177 r = 0.9843
VrS= 153111-5401 r = 0.9992
C,, 0.043K(' - 5.84 F 0.9850 (4.95)
( ' A 7.324KC' - 3343 r = 0.9838
I , - 187.3511 - IOI8.80 + r -- I ,000
- -3.7-311
(;(. - 1.05 t 1 + 65.47 r = l . O O O
1 : ~ -= 4.471 1 - 85.77 r = l . O O O
7'he general cost functions For gcneral dam case was estimated as shown in
[:quation (4.96) on substituting Equation (4.95) in the general cost function derived fbr
gencral earth darns.
' ."887 + 553.34(V, ) 0.5507 = 0.16 (As( , ) + 46992e - "('V ,,,' + 4745.80(Vlp ) 02704 +
0.585 I v82.22(VuF) 471 .72(VrI) + 5408.70 + 37765(C\ ) 0.AAJH + 678 16
I.O(I8 + 2 9 ( 1 ) ~ ) ".035"+ 30G(.+ (33Fw) - 37891+ EJ 4.96
l.:cluations (4.05 ) was substituted into cquation (4.96) and reduced to equat inn (4.97)
Vpi - ')X.h3K[. 35875
V 9 0 I I I - 47087
V I ~ - 29.23f<(. 1 195 1
Vnl - 351.14Kc. - 171 177
V,,.- 15.31 I1 -- 5401
C,, = 0.043K(' - 5.84
( ' A - 7.224KC' 3343
I - I I I 40 18.80
[In ;' 3.731 1
(;(,; - 1.05t1 + 65.47 r = 1.000
I.'w - 4.4711 -- 85.77 r = 1.000
'l'he general cost functions fbr general dam case was estimated as shown in
1:quation (4.96) on substituting Equation (4.95) in the general cost hnc t i on derived for
general earth dams.
(: 1 = 0.1 6 ( A s c , ) I .OHH7 + S53.34(Ve) 0.5507 + 4699Ze (" "- 0" ) + 474S.X0(VIb )02704 +
982.22(VKk, 11.5335 + 47 1 . 72(Vr~. ) ".'*I + 5408.70 (I'p + 3 7 7 6 5 ( ~ : ~ ) " . ~ ~ - " + 678 16 l),,
0.03 5 ' ) +29(1IK) + 30<;(,+ (33Fw) '."'- 37891+ E~ 4.96
I cluatron\ (4.05) was substituted into equation (4.96) and reduced to equation (4.97)
(I', = 0.16 (7897H - 453473)' + 553.34 (19021H - 4 7 0 8 7 ) ~ ) . ~ ~ ~ ' +
46992e ( " 'W'hK 0.221 + 4745.80 (0.30Rc - 1 1 9 ~ 1 ) " ~ ~ ~ " + 982.22 (0.3S4Uc -
77)fl.5335 0.585 1 + 471.72 ( l531 .8H - 5401) + .0233R( + 377.65 (O.OOXR( -
I ~ U ~ ~ I O T I ( 4 0 0 ) provldcd that I ' ( Y , ) and g, (x,) for i = I . 2 , 3.. .rn all havc contlnuou\ lir\t
s p:irlial clcrivari\ies (Kich;irtJ and (;ovind:rsa~ni. 1907 and ( ioodmun. 1084) +
1. Small e a r t h d a m s
Where. t i = dam height in metres (m), I,= dam length in metres (m) 1 K, = datn reservoir capacity in cubic metres (m )
r : ~ = operation and maintenance cost taken as 2 to 3% ofproject cost
1,et P - I: (x , ) - h, g, ( x , ) (i = 1 . 2 . 3. . . ..m) w
A n d
Substituting the objective function and the constraints in Equation ( 4 . 9 9 ~ ) gives
Where, A, and A? are thc penaltics associated with constraints for filling thc objective
P I ( on\tant in 1;quation (4.99i) suggests that the length for 5mall earth dams has no
much significance.
Subst i~ut ing 11-3, into I:quation (4.99') and K,=51-3+05, gives the value ol
i.,- 331465 and h2 0.38 respectively.
Substituting the values of h l and hz in equation (4.99d) gives the min imi~ed cost function
ti,r small earth dams (I) ')
Where. ti- dam height in metres (m), L = dam length in metres (m), Rc = dam
reservoir capacity in cubic metres (m' ) . and E I = operation and maintenance cost taken as 2
(o 3% o f project cost. klquation (4.99.;) is the minimized cost function for estimating small
earth dam's cost in the study area while Equation (4.91) reproduced as l.quation (4.09b) is
the un-optimized cost function
Solution technique
The salient fkatures fbr Alau dam located in Chad River Basin Ikvclopment Area. w
"vlaidi~guri was ~ ~ s e d li,r solving the cost tunetion using a computersoft ware developed by
the author.
Alau d a m salient features in Tab le 2 3
Dam height ( t I) = 9.50 m
[>am length (1,) - 344 tn
I>am reservoir capacity (R,) = 1 . l24x 1 0' m'
Ad,justed actual cost:
Optimized cost function 1,;quation (4.99i):
\ ~ ~ h l c c ~ 1 0
i l i I l l 0 I I - I 0 0
i1 ( I< ) 0 I - I 0 0 i111cl
Substituting k'(s,) - C 1 in Equation (4.90L) above, gives
P = C , - XI g, (sl) (Ihr i - 1 , 2 and 3 ) (4.99 m)
Substituting Equation (4.99k), h l , hz, and h3 in Equation (4.991~1) gives P'
4
Differentiating Equation (4.9%) with respect to H , R,, L, hi, 1 2 , and h? and equating to
1
Where. hz and h, are the penalties associated with constraints for filling the objective
function.
I rom tquations (4.9911) to (4.09t1, the values of 'r,~ hz and hi arc 1236621 7.12, 1055 and
660.40. respectively.
Yubstituting the values of hl and h, into Equation (4.990) gives the optimized cost
[,quation ( 4 . 9 9 ~ ) is the minimized cost function for estimating the cost of large earth dams
:i
in the study area.
Solution techniques
Kiri dam located in lipper Henue River Basin Development Authority, Yola was
randomly selected for solving the cost functions using a computer software developed by
the author,
w The dam salient features (Table 2.3)
Dam height (H) = 37 m
Dam length ( I . ) = 1300 m
- - - X 3 - I h ~ n r r e m v & r c-apsi ty(R4 =3.1JxlQ r n - - - - - - -
Adi~~sted actual cost: N7429842465 .OO
Optimized cost function Equation ( 4 . 9 9 ~ ) : 818 12234425 .OO
Iln-optimited cost function Equation (4.99b): 8S1473700284.00
Differences between:
I Optimi7ed and un-optimi~ed cost functions: S 6 6 1.46S.8SO.OO (45% cost savings)
2 Optimized and adjusted actual cost function: 44661 7608040.00 (89% cost savings)
3 Actual and un-optimized cost function: 81 59561421 81.00( about 80% difference)
3. General earth dams.
Similarly. the cost function h r general earth dams was rcprexented by Equation (4.97). a
w A n d
P = 0.16 (7897H - 4 ~ 3 4 7 3 ) ' . " ~ " + 553.34 (19021H - 47087)".""~ +
Differentiating Equation (4.99aa) with respect to the variables and substituting the
constraints givcs
Situilal ly, ?I' -. --- = 0 - 0.0 12 1 t- 0.023 + 0.0233 -t 0.079 - /1, (31(
A tid I
Substitutitig the valucs of k , , 1 2 and k3 into I3patio11 (4099ab) gave the function for
the minimum cost for general earth dams ofthe form:
1: - 0.16 (789711 - 4~3473) '""~ + 553.34 (19021 H - 47087)'LSS" +
Solution techniqr~es
Since general earth dams comprise of small and large dams, salient features of small
and large dams taken randomly in the study area were used for testing the cost function.
1. Small earth dams(Alau dam, Chad Hasin)
I jeiglit = 9.50 m
Length = 344 m a.
('apacity - l . l 2 4 x i 0 ~ m'
' I hese salient features were substituted in 1:yuations (4.97) and (4.99al) and gave
wlut ion~ a5 follows:
Actual contract cost 81 35,449,742.19
Optimi~ed cost function Equation (4.99af) 81 72,189,586.66
Iln-opti~nized cost function I'qunlion (4.97) N 88.270.566.47
- Differences between
1 . Opti1ni7ed and un-optimized cost functions W 16,080,959.8 1 (1 8.20%)
2. Optimized and actual contract cost W 36,739,844.47 (50.90%)
3. Actual contract cost and 1111-optimized cost P4 52,820,824.28 (59.84%)
2. Large earth dams (Kiri dam, Upper Uenue Basin)
1 leight - 37 m
I ,en& - 1300 m
('apacily = 3 . 1 5 ~ 10' m7
These salient features were substituted in Equations (4.99ab) and (4.99af) and gave the
following results.
Actual contract cost N 7429,842,465 .OO
- - - - - - - - - Opti~nked - - cost function Fquation (4.99af) - - - - -
- - - - - - - - - - -
W 163,592.874.40 - - - - - - - - - - - - - - -
- - - - - -
IJn-optimized cost function Equation (4.97) 44 2 1 1,6 12,045.40
Ilifferences hetween
1 . Optimized and un-optimized cost functions W 48,O 19,170.96 (22.70%)
2. Optimized and actual contract cost W 7266,249,59 1 .OO (97.80%)
3. Actual and un-optimized cost 44721 8,230,420.00 (97.15%)
CHAPTER FIVE
5.0 HESIJLrl'S AND DISCIJSSION.
5 . I Project appraisal and evaluation:
Ilam prc!jects are cost intensive and most at times unaffordable especially the
nee&xl number by peasant farmers, farmcrs associations, or even governments in
developing countries for social development. Ilowever, because of their direct link with
- sustainable water resources developments and food security, they become very necessary.
4
' l 'lietehrc for these hydraulic structures to be provided, the stake holders may need aids or
loans from donor countriesJorganisations and agencies with stronger economy. The donor
organisations and agencies have to depend on effective pro-ject evaluation and appraisal
technique before awarding such aids and loans. Two methods of pro-ject evaluation were
suggested which include citizen participation and multi-ob-jective approaches. These
evaluation approaches needs field data for verification which was not done in the course of
this study. !{owever, guidelines to arrive at the solution were discussed and any of the two
methods suggested could be adopted for project appraisal and evaluation in the study area. w
After evaluation and appraisal, design techniques become an important ob.jective.
5.2 Earth dam design
Earth dams are very costly structures. Ibwever their failure could cause a huge loss
of economic resources and lives. Although there are numerous dam parameters that need
economic. safe and convenient design, only the following few important ones were
considered in this study. These include: 'l'op width, free board, seepage analysis, and
spillway inlet and outlet sizing.
Top width: I'mpirical relations that relate the earth dam top widths and heights have been
rcported in literature (United States I3ureau for Reclamation, 1974; United Stales Corps of
I:ngineers, 1994; Arora, 2002; Novak and others, 1992). I lowever, these relations were
chived for other regions of the world. In this study, relations between the dam top width
and height were derived were derived for the study area. Some of the various earth dams
designed in some locations of the study area are listed i n Tables 4.03 and 4.05 for small
** and large dams, respectively. The relations obtained are shown in Equations (4.04) and
(4.05) for small and dams in the study area respectively. he relations were derived using
I'xcel Microsofl Soltware Chart Wizard - Step I of 4. 'l'he relations obtained were used to
re-compute the top width for the given dam heights. These values were compared with the
actual values and the estimated errors varied from 15% to 13% for small earth dams and
from 33% to 46% for the large dams. 'l'he sumnary of the results are shown in Tables 4.04
and 4.05 for the categories of dams considered.
Free board: 'l'he provision for free board helps to guidc against overtopping of an earth
dam especially under most adverse conditions such as full storage coping with a maximum
w flood flow, and maximum wave action. Earth dams havitig long fetches (greater than 600
m) need to have increased freeboard as suggested by Nelson (1987); Garge (2002); Novak
( 1 992); Puntnia and 1.81 (1990); and Arora (2002). Also suggested are values of free board - - - -
- - - - - - - - - - - - -
in relation to dam fetch lengths a n b h e i g k t ~ ~ ~ n S i d i % i n g a n y h~ight;freeBoar&of 2 3 -
metres was suggested; for heights less than 6 meters, freeboard of 3 meters and above was
suggested. Considering fetch lengths, values suggested by Nelson (1 982) given in Table
4.02 could be used for estimating freeboard give11 the fetch lengths.
Seepage analysis: Seepage in earth dams is inevitable because o f geologic factors as
suggested by Novak and others, (1992), however, measures could be adopted to reduce its
~(Tccts lo a tolerable limits. Conseyucnces o f seepage in carth dams arc numerous and may
i~ lchde piping, sloughing and even the total failure o f the wholc dam as suggested by Singh
and Vershney ( I 992); Pumia and Lal ( 1 990); and Arora (2002). '1'0 reduce seepage in earth
dams, provision o f hard core in the embankment, cut offtrcnch, and provision o f filters etc
linvc heen common. In this study, a data that was obtained by monitoring a dam in the
slt~dy atca Tor five months (from end o f .li~Iy to end o f I)ecehber, 1998) was used to
cxc~nplify the phenomenon. I:irst o f all the seepage analysis was considered assuming no
cut of( trench was in place using Darcy's Equation. The data included the dam length (I,)
of 470 m, coeficient o f permeability (K) o f 2 0 x 10-'m/s, dam bottom width o f 45 m and
height o f 15 m. For the period o f monitoring, the volume o f seepage that would be
expected was estimated as 324864 m'. When a cut o f f trcnch i s to be in placc in a pewious
foundation o f thickness (I)), 8 m, and depth o f cut ofT trench (I) to be Y .O m, filled with
an impervious materials o f coefficient o f permeability (K) o f 2.10 x I (Y4 ,n/s resulted in a
volume o f seepage o f only 1693.35 m'. Therefore by comparing the two volumes o f
324864 m3 with 1693.35 m3,it was found that by providing a cut o f f trench at the centre
line o f the dam axis with the conditions described above would reduce the under seepage
by 4948%.2'his confirms_thewjdeug! qfcut off trench as a means o f reducing seepage to - - - - - - - - - -
- - - - - - -
tolerable limits by many designers.
Spillway inlet and ar~tlet sizing.
Spillway in darns especially earth dams act as the main safety device against over
topping by unprecedented flood as a guide against failure. The spillways adopted for earth w
h t n s are numemus depending on site conditions and purpose ofthe dam.
Generally. spillway sizes, types, control structures, discharge channels, energy dissipaters,
etc needs to be designed carefully. Ilowever, this study considered only the inlet and outlet
witlrh sining.
Inlei Widths: The inlet widths refer to the channel from which flood water flows from the
reservoir directly onto the spillway. Nelson (1978) suggested minimum inlet widths for
given flood flows in cubic meters. The values are shown in Table 4.02a. The values were
fitted with a regression equation and the result given by I<quation 4.0 Id. 'l'he relations gave
a high correlation coefficient of 0.9977 which suggests that the t1~o parameters had
correlated well.
Outlct widths: 'l'hcse parameters refer to the channcl that conveys flood water from the
spillway weirs to the downstream. If the channel is not adequately sized, then the problem
o f over flooding would also be experienced. Nelson (1987) also suggested values of the
outlet widths for given flood volumes and the channel return slopes that varied between
24% to 4% and less. The maximum flood volumes were 15 m3. The values given were used
rgr to construct a monograph for easy solution when two of the other parameters arc known.
The monograph is shown in Figure 4.0 I . 'l'he error of estimate between results from the
monograph and that suggested by Nelson (1 987) were not significant for the same slope. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
5.3 Project cost analysis:
Project cost includes the cost of engineering and legal services, contingency, and
the construction cost of the project. Dawes (1970) suggested 15% of the project
constn~ction cost for engineering and legal 10% to 15% as the contingency sum depending
on the project size. Therehre, adding 25 to 30% of the project construction cost to the
project construction cost would give the project cost.
5.3.1 Inflation index and cost index:
This study depended on data on earth dams estimated at different periods. Thus,
usiug s ~ ~ c l i data Tor analysis at tlie selected time for study would definitely be affected by
inflation. i 'o take care of this elred, inflation factors and minimum rate of return (MKK)
for tlie study area were used to forecast the expected cost from the time of estimation to the
em time of study. This technique was used to harmonize the costs at the study time for
effective analysis. +
Another approach was to have derived effective cost index for the study area on such
pr(!jects, however, hecausc of inadequate data, cost index was not derived.
5.3.2 Earth dam constrtrction cost and salient features:
'I'he construction cost of earth dams in the study area were correlated to the various
dam parameters like height, length reservoir capacity, excavation volume, embankment fill
volume, rock fill volume, etc. The following are the resrrlts of the various analysis carried
out.
Earth dam length and cost:
The earth dam's updated costs were correlated with the dam lengths for small, large
and general dams as shown by I3quations (4.41). (4.40), and (4.42) for the small, large and
general dams; mpmtively; Theretations shewed t h a t ear* Barn's costs conelated be t t e r
with their lengths. Their correlation coefficients were 0.7247, and 0.7625 for small, large
and general dams. I o r the dam lengths shown in Tables 4.1 1 b, 4.1 l a and 4.1 lc, their
costs were re-estimated. 'l'hc predicted costs were compared with the actual updated
costs, and showed prediction errors of 46% to 85%, 53% to 97%, and 76% to 87% for
small. large and general dams, respectively. The results are shown i n Tables 4.1 I b, 4.1 1 a,
:tnd 4.1 Ic f i j r s~n:iII, large and general dams, respectively. The predict ion errors are higher
perhaps because o f s i t e factors attributed to geographical locations o f t h e sites.
Kart11 dam h e i ~ l ~ t a ~ ~ d costs:
I'arth dam costs were correlated to the dam heights i n the study area and the relations
are shown i n Equations (4..39), (4.38) and (4.36) Tor small, large and general darns,
I respcctively. The relations showed higher correlation coefficients than that fo r costs and
b lengtlls. ?'he corrclation coefficients werc 0.9370, 0.77, and 0.8496 fo r small, large and
general dams, respectively. 'l'lle dam heights were then rlsed to re-estimate the dam costs
for the various Iieiglits. The result and their estimation error when cornpared w i t h their
actual updated costs are shown i n Tables 4 . 1 0 ~ 4.10b and 4.10a for small, large and
general dams respectively. Garg ( 1 902) suggested a relationship between dam heights and
cost f rom wh ich an opt imal height could be estimated. The suggestion however could no t
g ive direct mathematical relation bu t a graphical solution.
Darn reservoir capacity and costs
The reservoir capacities fo r the earth dams i n the s t i ~ d y area were correlated to their
costs as represented b y Equations (4.46), (4.44) and (4.45) f o r small, large and general
dams. respectively. 'l 'heir corrclation coefficients wcrc 0.8382, 0.8958 and 0.7951 for
small, large and general earth dams i n the study area, respectively. F o r the earth dam
reservoir capacities, their costs were re-estimated us ing the relations derived. The results
and estimation error when compared w i t h their actual updated costs are shown i n Tables
4.1 2c, 4.1 2 a and 4.12b f o r small, large and general dams, respectively
Generally, earth dam construction cost could be estimated w i th data o n length,
height and reservoir capac ities. Site conditions should be considered for effective relations.
5.4 Earth clam's parameters and costs
The units ol'costs in this study refer to the parameters whose costs add up to the
total earth dam costs and were analysed. Among these are site clearance areas,
embankment f i l l volume, excavation volumes, pervious and impervious f i l l volumes, rock
fill volumes, grouting depths etc. 'Ihe most significant and generally applicable parameters
'P were selected for analysis.
Site clearance area 4
The site clearance area is a parameter applicable to all earth dams if not all Civil
lingineering pro-jects. 'l'he site clearance area is aff'ected by the topography ofthe site.
Ondulating and sloping terrains need levelling in addition to clearance before the
commencement of construction. tlecause these factors are site specific, its efTect was not
incorporated in the analysed. Ilowever, the site factors suggested by Nelson, (1 987) could
be applied which varied from 0.5 to 1.6. The site clearance area for earth dams in the study
area were correlated to their costs and relations are shown in Equations (4.55), (4.54) and
w (4.53) for small, large and general dams, respectively. The relations gave correlation
coeflicients of 0.9939,0.7951 and 0.500 for small, large and general dams, respectively.
The high correlation coefficient for small ealdi darns shows that the area cleared is
uneven topography. The site clearance areas Tor the earth dams in the study area were used
to re-estimate their costs which were compared with their actual updated costs. The results
and errors of estimate are shown in Tables 4.13c, 4.1% and 4.1 3a for small, large and
general dams, respectively
Kxcavation volumes and costs
Excavation vohmes for earth dams in !he study area were correlated to their costs.
The relations are shown in Ikpations (4.58), (4.57) and (4.56) for small, large, and general
dams, respectively. The relations showed good correlation with correlation coefficients of
0.9982, 0.7576 and 0.9757 for small, large and general dams, respectively. For the
volumrs of excavation of earth dams in the study area, their respective costs were re-
estimated as shown along with their errors of estimate on comparing with their updated
acti~al costs. The results are summariscd in Tables 4.146, 4.14b and 4.14a for small, large
and general dams, respectively.
I'ervions fill volurnes and costs.
'1 hc pervious fill volumes for earth dams in the study area were correlated to their costs
as shown in Equations (4.00), (4.61). and (4.59) for small, large and general dams,
respectively. The relations gave correlation coefficients of 0.62 18, 0.9875 and 0.6255 for
small, large and general dams, respectively. The relations fitted well for large dams as
indicated by its height correlation coeficient because only large dams have significant
volumes of impervious fills (hard cores). Small dams are generally made of homogeneous
earth. pervious fill also called the shell are more conspicuous in zoned earth dams. This is
because pervious fills are used to increase the stability of the dam in addition to reducing
relation derived in equations above. The estimated costs were compared with their updated
actual costs and the results and estimation errors are shown in Tables 4.1 5b, 4.1 5c and
4.1 5a for small, iarge and general dams, respectively.
Impervioas fill volumes and Costs
'I he impervious lill volumes (hard core) serve the function of' reducing seepage to
tolerable limits either in the embankment or in the foundation. Ilard cores are commonly
located in the dam heart and extend to the foundation as a cut off trench. However,
diaphragm dams have their hard cores located upstream with thickness that vary with the
water level in the reservoir as observed by United States Corps of Engineers (1994). The
volunies of impervious f i l l materials were correlated with their costs and gave Equations
(4.64), (4.63) and (4.62) for stnall, large and general da~ns, ' res~ectivel~. The relations had
cor.re!ation coefficients of 0.7205, 0.9258 and 0.6254 Tor small, large and general darns,
respectively. l o r the given impervious lil l volu~nes, their respective costs were estimated.
'l'he estimated costs were compared with the updated costs. The results and estimation
errors are shown in Tables 4.l6c, 4. l6b and 4.l6a for small, large and general dams,
respectively.
Rocks fill volumes and costs.
'I'he rock fill volumes were correlated with their respective costs and relations derived
are shown in Equations (4.69), (4.68) and (4.67) for stnall, large and general dams,
respectively. l 'he relations gave correlation coeficients of 0.9992, 0.8271 and 0.9568 for
small, large and general dams. respectively. 'I'liis high correlation coefficient indicates high - - - - - - - - - - - - - - -
- - - - - - - - - - - - - - - - - -
correlation between rnck f i l l volumes and their costs. For the given rocks fill volumes, their
respective costs were estirnated using the equations derived for each dam category. The
estimated costs were compared with the actual updated costs. The results and estimation
errors are shown in Tables 4.1 7c, 4.17h 4.17a for small, large and general dams,
respectively
Ripraps fill volumes and costs.
Riprap fills differ from rock fills because riprap fills are assorted rocks that can
withstand abrasion and erosion wears. Rock f i l l on thc othcr hand, constitute ordinary
locks of varior~s sizes and quality whose main Sunction is to reduce earth volume, cost and
iricrcase stability. 'The riprap volumes were correlated with their respective costs and the
relations gave Equations (4.72), (4.71) and (4.70) for small, large and general dams,
w respectively. 'I'hese relations gave correlation coefficients of 0.9802, 0.892 1 and 0.8547 for
small, large and general dams, respectively. 'l'he rfiprap f i l l volumes were then used b
estimate their respective costs using the equations derived above. 'I'he estimated costs were
compared with their actual updated costs. 'l'he result and estimation errors are shown in
Tables 4.1 812.4.1 8b and 4.1 8a for small, large and general dams, respectively.
Concrete volsmes and costs
In dam construction works, two categories of concretes are used which include
plain and reinforced concretes. Plain concrete volumcs were correlated to their costs and
the relation rcsulted in TZquations (4.75), (4.74) and (4.73) for small, large and general
e dams, respectively. The relations gave correlation coefficients of 0.8458, 0.8467 and
0.9402 Tor small, large and general dams, respectively. The equations derived were used to
re-estimate their respective costs for each plain concrete volurne. The estimated costs were
compared with their actual updated costs and rcsult and estimation errors are shown in
Tables 4.lOc, 4.1% and 4.1% for small, large and general dams, respectively.
For reinforced concrete volumes, grout drilling (normal and rock drill), chemical
and cement grout, rock anchorage, geotechnical instrumentation, pressure drains, etc werc
also analysed. Ilowever, becar~sc of insufficient data, the result may require further
analysis.
5.5.0 Relations between earth dam's parameters.
)lam lengths and heights.
For small earlh dams, the relations between dam heights and lengths were
correlated using power, linear, exponential, logarithmic functions. Power function resulted
~ I I equatio~i ofthe form:
b 'I'lie relation gave the highest correlation coefficient ofO.5095.
l o r large dams, the parameters were correlated using all the possible functions. A
linear function gave the highest correlatiori coeflicient as shown in Equation (5.02).
I I =0.0021, + 16.13 (5.02)
The correlation coefficient = 0.5567
For general dams, the parameters were correlated using all the possible functions. A linear
fi~nction gave the highest correlation coefficient as shown in Equation (5.03).
I1 =2.30E - O3I,t-l2.28 a*
'The correlation coefficient = 0.5883
All the relations for small, large and general dam case gave low correlation
cocf ic ic~i ts of 0.5395, 0.5567 and 0.5883, respectively. 'This may bc due to the fact that - - - - - - - - - - - - - - - - - -
- - - - - - - - - - -
dam heights does not depend its length. A high dam may have a short crest length and vice
versa.
Dam reservoir capacities and lengths
For small dams the above parameters were correlated using power, linear,
exponential, logarithmic functions. Power function gave the highest correlation coefficient
as sliown in Equation (5.04)
'l'he correlation coefficient - 0.8730
For large dams, the parameters were correlated again using all the functions, but
linear function gave the highest correlation coefficient as shown in Equation (5.05).
'I'hc: correlation coefficient - 0.6962 +
For general dams case, the pararneters were correlated again using all the functions,
hut a power fhction gave the highest correlation coefficient as shown in Equation (5.06).
'i'he correlation coefficient = 0.7545
Frotn the slightly higher correlation coefficients recorded in the relations above, it
could be logical to suggcst that reservoir capacities are functions of the dam's lengths. This
is because the more the darn lengths, the larger the pond age ratio of the dam (Nelson,
1985).
Earth dam Reservoir capacities and heights.
For small dams the above parameters were correlate using power, linear,
as shown in Equation (5.07)
R,. =2923 1 5 ~ ' '"'" (5 .07)
The correlation coefficient = 0.4050
For large dams, the parameters were correlated again using all the frmctions, but
linear function gave the highest correlation coeflicient as shown in Equation (5.08).
'l'hc correlation coeflicient = 0.6836
I;or general dams case, the parameters were correlated again using all the functions,
hut a power function gave the highest correlation coefficient as shown in Equation (5.09).
'I'he correlation coefficient = 0.8260
'I'lie relations between the parameters showed slight increase in correlation b
cocIX-icients especially for large and general dam cases. Although dam capacities could
depend on heights, capacities depend more on lengths as shown earlier above. See Tables
4.24 and 4.25 and also Appendix E, 'Tables 4.27 and 4.28
Site clearance and dam heights, lengths and capacities
The above parameters were correlated by a power and linear fimctions for small.
large and general dam case (see Appendix A, t 3 and C). The relation that resulted in the
highest correlation coefficient was selected as the besc representative.
170r small darns, relation between site clearance area and darn heights gave the highest F
correlation coefficient. The relation was represented by equation in Equation (5.10).
C'orrelation coeflicient = 0.9003 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
For large dams, the relation that had the highest correlation coeflicient was between
site clearance area and dam heights given by.
Asc= 11512511-2Et-06 (5.1 1 )
Correlation coefTkicnt= 0.94 12.
For general dam case, the relation that gave the highest correlation coeficient was between
sile clearance areas and darn heights represented by Equat ion (5.1 2):
As(. = 7897 1 1 1 1 -- 453473
Correlation coeff ic ient - 0.9636.
I:roni the above, the site clearance areas for small, large and general dams depend
o n reservoir capacilies and heights respectively.
'I'he volumes of excavation: l ' he volumes o f excavation were correlated w i th dam
(Z heights, lengths and reservoir capacities for small, large and general dam cases,
~ c s l x x t i v e l y (see Appendices A, 13 and C:) . @
I:or stnall dams, the relation bctween the above parameters was fitted w i t h a l inear funct ion
hav ing highest correlation coeff ic ient as:
V, = 9888.301 1 -- 24678
Correlation coefficient - O.76c)O
For large dams, the relation was fitted w i t h a l inear function o f t h e rorm:
V, 259.09Rc 1- 3548.20
('orrelation coeff ic ient = 1.00
8 For general dam case, the relation was f i t ted w i th a l inear f i ~nc t i on o f the form:
V, = 1902 1 kJ - 47087 (5.15)
capacity.
Pervious fill volumes and dam height, lcngth and reservoir capacities
These parameters were correlated using power and linear f i~nc t ions fo r stnall large
and general dam cases (See Appendices R and C).
For small dams, the relation that had the highest correlation coefficient was
twtwecn pervious fill volumes and dam heights givcn by:
V1.l -2712.9011 t 1615.9
C:o~.rdation coefficient = 0.684 1
For large darns, thc relation that gave the highcst correlation coenicient was
\vtnrce~i pervious lill volumes and darn capacities represented by:
Vrl - 1 07.67Rc - 60487 (5.17)
Correlatirm coefficient = 1.000 +
For general dam case, the rclation that gave the highest correlation coefficient was between
pc~vious f i l l voh~ncs and dam reservoil-capacilics represented by:
Vp( = 98.63Rc 35875
Correlation cocfficicnt - 0.2975
Impervious fill volumes and clam heights, lengths and reservoir capacities.
The pararneters were fitted using power and linear funclions as shown in
Appendices A, 13 and C.
C For small dams. the relation that gave the highest correlation coefficient was
between impervious fill volumes and darn lengths given by:
Vpy: 3431, - 104697
Correlation coefficient = 0.9842
For large dams, the relation that gave the highest correlation coefficient was
between impervious fill volrtmes and dam reservoir capacities given by:
VIp = 53 I .87Rc - 60487 (5.20)
Correlation coeflicient - 1.000
For general darn case, the relation that gave the highest correlation coefficient was
Ixtween tlic impervious f i l l volumes and dam reservoir capacities represented by:
Vl1: = 29.23 Kc - 1 195 1
Correlation cocfficienl= 0.9855.
71ie corrclations between impervious fill volumcs and dam parameters could be
I x ~ t represented by relations with darn lenglhs and capacities.
,* Rocks fill volumes and dam heights, lengths and reservoir capacities.
These parameters were fittcd with power and lihcar functions for small, large and
general dam cascs as sliown in Appendices A, 13 and C.
S~~la l l dams:
The vo lumes of rock f i l l were correlated with dam heights, lengths and reservoir
capacities. The relation that gave the highest cnrrelation coefficient was between the rock
f i l l volurnes and reservoir capacities given in Equation (5.22).
VRI: = 5.862 Rc - 1283.90 (5.22)
Correlation coefficient = 0.8259
r0: Large dams: The correlations between rock f i l l volumcs and the above parameters that
had the highest correlation coefTicient was between rock f i l l volumes and reservoir
Correlation coefficient = 1.000
General dam case: 'l'he relation between the rock fill volumes and the above parameters
that gave the highest correlation coefficient was bctween rock fill volumes and reservoir
capacities as shown in Equation (5.24).
VRI.=351.14 k(3- 171 177
('orrelation coefficient = 0.0843
'1 he relations between rocks till volumes and dam parameters depend more on
reservoir capacities for small, large and general dam case
Ripraps fill volumes and dam heights, lengths and capacities.
'I'he ripraps f i l l volu~nes were correlated to the dam heights, lengths and capacities
w with power and linear functions. 'T'he equations are shown in Appendices A, B and C for
small, large a d general dam cases, respectively. ' Small dams
'I he riprap f i l l volu~nes were correlated to the dam parameters of lengths, heights and
capacities. The relations between riprap till volumes and reservoir capacities gave the
highest correlation coefficient shown in Equation (5.25).
Correlation c,oefficicnt = 0.7909
Large dams: The relation that gave the highest correlation coeficient for the above
1 parameters was between the riprap f i l l volumes and dam heights given by:
V,[ = 1559.2011 - 64897.
Correlation coefficient = 0.9980
- - - - - - -
7;cneral~ams:Thextetation t h a t ~ ~ tkehfgltest currelatiotxcseffiientfi the -riprtq- - - - - - - - -
f i l l volumes and dam heights, lengtlls and reservoir capacities was between riprap fill
volumes and dam heights given by.
Vrr = 153 1.8011 - 540 1 (5.27)
Correlation coefficient= 0.9992.
'I'he relation between riprap f i l l volumes and dam parameter could be best
represented by relations between riprap fill volumes and dam heights and reservoir
I'lain concrete volumes antl dam heights, lengths antl capacities
The volumes of plain concrete were correlated tu the dam heights, lengths and
a. The volumes of plain concrete were correlated to the dam hcights, lengths and
rcscrvoir capacities for small, large and ge~icral dams. 'l'hc rehtion equations arc shown in
t~ppentlices A, 13 and C for small, large and general dams, respectively.
Small dams: The volumes of plain concretc were correlated to the dam heights, lengths
and reservoir capacities. The relation that gave the highest correlation coefficient was
hetween plain concrete volumcs and reservoir capacities given by:
Correlation coefficient = 0.9834
Large dams: The plain concrete volumes were correlated to the dam heights, lengths and
'PP reservoir capacities using power and linear functions. 'l'lie relation that gave the highest
correlation coefTicient was between plain concrete volumes and reservoir capacities given
Correlation coefficient = 0 . W 1
General dams: The plain concrete volumes were correlated to the dam heights, lengths
and reservoir capacities using power and linear functions. The relation that gave the highest
correlation coe Fficient was between plain concrete volumes and reservoir capacities given
Cp - 0.043 I<(. = 5.84
<'orrelation coeff ic ient = 0.9850
Generally. the p la in concrete volumes depend on reservoir capacities for small,
I n ~ g e and gcneral dam cases as shown b y the above relations.
w R e i ~ ~ f o r r e c l concrete (C'lsss A) and d a n ~ heights, lengths a n d reservo i r capacit ies
'I'he correlations between reinforced concrete voll lhles and dam heights, lengths and
~eservo i r capacities were fitted irsing power and linear f i~nct ions. 'l'lle relation equations are
shown in appendices A, R and C Tor small, large and general dams, respectively.
Sma l l dams: 'l'he correlations k ~ r the above parameters that gave the highest correlation
coe f l k i e n t were the relation between rein lbrcetl concrete volumes and dam heights given
b y a relation o f the form.
C A - 213 - 05 1 1' '37' (5.3 1 )
Correlation coef l ic ient = (1.92 1 8
L a r g e dams: 'I'he relation between reinforced concrete dams and dam lengths, heights and
reservoir capacity for large dams was fitted r ~ s i n g linear f i~nct ions o f the form.
CA=-21 .28 [>=28168 (5.3 2 )
- - - - - - - -
- This relation gave + h e - h i g l t e s t c ~ r d a t i o ~ - ~ w d f i c i e n t a f 4 . 9 8 6 1 f o r r d a t j o n w i t h
dam lengths.
( jenera l dams: The re inhrced concrete volumes were fitted to the dam parameters
(heights, lengths and reservoir capacities) using power and linear functions. 'The relation
that gave the highest correlation coeff ic ient was that between concrete volumes and
reservoir capacities o f t h e hnn
VA =- 7.224 I<( 3313
Correlalion coef l ic ient = 0.9838
(kneral ly. rhe re inhrced concrete relates better w i th dam 1ieigl:ts and reservoir capacilies.
I)epth of drilling for grouting and dam heights, lengths and reservoir capacities.
I k p l h s of pits l i ~ r grout ing were correlated to the dam parameters (lengths, heights
and rcservoir capacities) For large dams and general cases. The correlations are shown i n
aplwndiccs 13 and C for large and general dams, respeclively!
I,arge dams: 'l'he depths o f drill Tot grout ing were correlated w i th dam heights, lengths
and capacities using power and l inear f i~nct ions. A l l the relations gave highest correlation
cocfl icients o f 1.000. Thus for convenience the relation between drill depths and dam
heights Tor l inear f i ~nc t i on was selected shown i n Equation (5.34):
1 ) ~ = 182.35fI -- 401 8.80
C'orrelalion coeff ic ienl = 1 .000
The above relation was estimated for the general dam case also.
Cement grouting and dam lengths, heights and reservoir capacities.
Again the correlations for large dams and general dams had same equation w i th
Clorrelation coef l ic ient = 1.00
Form work surface area and dam lengths, heights and reservoir capacities.
'I'he correlations between the for inwork surface area arid dain lengths, heights and
reservoir capacities gave relations that had correlation coeff ic ient o f 1.00. Ifowever, for
convenience the linear relation was selected given by:
I:, = 4.471 1 -- 85.77
(:orrelation coefficient = 1.000
5.6 Optimisation techniqw
C)ptiniisation techniques available in watcr rcsources planning systems may include
linear, dynamic, goal, quadratic. geometric 1,agrange multipliers etc. These programming t
techniques may be generally grouped into linear (constrained or unconstrained) and non
lincar (const rained or unconstrained)
Objective function and constrsints
In any optimization problem, i t would include an objective fi~nction that is to be either
maximized or minimized. This would serve as a basis for ranking alternative solutions and
plans. Apart from lhe oh.jective firnction, planning problems incorporates a number of
requirements formulated as constraints. The optimal solution o f a planning problem is that
the plan achieves the largest or smallest value of the ob.jective function while satisfying the
constraints. 'J'he constraints could be of two types:-
* The one that exprcsses the actual physical lin~itations that can not be violated at
any cost (e.g c lonse~at ic ln , fm~, magnitude - of - a - fixed - resource) - - - - -
An implicit ob-jective or goal which could be violated although the cost of such
violation may be high (e.g. restriction on stream flows to maintain water quantity
and quality, budgetary limitalions etc).
It should also be clear that when goals are formulated as constraints, all feasible
solutions must not satisfy these goals and no explicit incentive for fulfilling these goals are
pc~mitled to be reduced if the cost o r meeting such action is high. These adjustment9 are
oflen made aRer the examination of the optimal solutions of the planning problem as
initially formulated. Decision makers are oRen interested in knowing how much money can
he saved. 'fhus, a solution lo any particular planning problem provides dccision
~nnkerlanalysts with an estimate of what is possible and such information would be
necessary for a point ofdeparture for searching a more deqirable alternative.
1 agrange Multipliers
Optimization using 1,agrange multipliers involves the multiplication of the constraint
equation by a variable or multiplier (1) called the Lagrange multiplier and the product
subtracted from the ob-jective function. The solurion is determined by setting the partial
derivatives of the resulting function with respect to cach unknown variable and equating lo
zero. 'l'he resulting equations in terms of the variables and the multipliers are solved
simultaneously.
1. Small earth darns
The optimized cost function for small earth dams was derived in terms of the dam
height (Il), length (I,) and reservoir capacity (R,) as shown in Equation (4.91). Alau dam
in Chad Basin Development Authority, Maiduguri was randomly selected for checking.
'I'he salient features Tor the dam are as follows:-
- -Ihml1ei&L(F1) =. P50 rn - - - - - - - - - - - - - - - - - - - - - - - -
Dam length (I,) = 344 m
Dam reservoir capacity (R,) = 1 . I 24x1 0' m'
Adjusted actual dam cost = 4435,449.742.19
'lhe derived cost function was optimized using 1,agrange Multipliers with constraints
(SCC' I<quation (4.99i)) and the resulting equat io~i solvcd by computer sonware developed in
Vissal J3asic (see appendix I))
I he sol~ltion Ihr the 1111-optimizeti cost fi~nction h r thc above dam parameters gave
$44'7, 327,177.83 and that of optimized cost function gave $46, 054,045.1 23. The difference
hetneen the solutions of the optimized and thc un-optimized cost functions is W
41,273,132.69 (about 87%) decrease in cost. '['he difference between the solution of the w
cy~irni7ctl cost function and the actual adjusted dam cost is N 29,395897.05 (about 83%)
decrease i n the dam cost. 'l'his means that optimizing the earth dam cost function for
optimum dam height, length and reservoir capacity could reduce the dam cost by about
83% to 87%.
2. Large earth dams
In a similar manner, the cost function Tor large earth dams was derived in terms of the
dam's parameters of height (I I), length (I.) and reservoir capacity (R,) as shown in equation
(4.94). Kiri dam located in llpper f3enue River I3asin 1)evelopment Authority, Yola was
b selected randomly for solution o f the cost function. The salient feature of the earth dam
shown in Table 2.3 reproduced bellow.
I)am height (1 1) - 37.00 111 - - - - - - - -
Dam length (I,) - 1300 m
R 3 Dam reservoir capacity (Kc) -; 3.1 5x10 In
Ad.justed actual dam cost - W 742,9842,465.00
'I'he derived cost filnction was optimized for optimum cost estimation (Equation 4 . 9 9 ~ )
and solved using the soft ware developed in Visual Basic (see Appendix D). The solution
Tor the un-optimized cost function for the abovc darn paramefers gave $41, 473,700,284.00
and that o f optimized cost fi~nction gave H8 12, 234.425.00. The difference between the
solution o f the optimized and the un-optimized cost functions i s W 661,465,859.00 (about
45%) decrease in cost. 'I'he dil'ference between the solution o f the optimized cost function
a l~d the actual a$jusled dam cost i s $4 6617,608,040.00 (about 89%) decrease in the dam
cost. This means that optimizing the earth dam cost function for optimum dam height,
length and reservoir capacity could reduce the dam cost by about 4.5%. On the other hand,
the optimization decreased thc valuc o f the un-optimifed cost function by about 89%.
CHAPTER SIX
CONCLUSION AND RECOMMENDATION
6. I Conclusions
Most hydraulic structures especially earth danis are either under estimated or over
cstimatcd because of the variations i n materials cost and time and financial resources are
wasted. N o much work was done on relating the cost paranieters of earth dams; thus, it is
.41
tw:essary lo develop a function that could relate the parameters and their cost
4 ~liatlie~natically for predictive purposes.
Earth dams whose costs were estimated previously were used to develop the cost
filnctions. Eartli dam parrmelers Tor small, large and gcncral dams wcre related with their
costs using regression analysis. Before the regression analysis, inflation factors in
c,o~~.junction to the minimum rate of return for the study area were used to harmonise the
dam costs at study period. The earth dams cost parameters were inter related with each
other and the cost functions could be reduced lo only three parameters of length, height and
reservoir capacity for the small, large and general dam case to give the cost Sunctions. The I
cost Srinctions for small and large dams were optimized using Lagrange Multipliers with
constraints for optimal costing.
The solutions for the cost functions were estimated using customized software. The - - - - - - - - - - - - - - - - - - - - - - - - - - -
solution showed that a decrease of about 87% in cost between the resun oTthT optimizFa
and the un-optimized cost firnctions for small earth dams. Similarly, a decrease of about
83% was recorded between the optimized cost function and the adjusted actual cost.
l o r large earth dams, 45% decrease in cost was recorded between the solution of the
* optimized cost function and the un-optimized cost function. About 89% decrease in the
cod was recortfed between the solution of the optimized cost function and the adjusted
ac tua! cost.
Ilesign relations for earth dam parameters like top widths; freeboard, spillways,
cores ctc were checked for effective design in the study area. In most cases deriving direct
~natheniatical relationships were not possible because unavailability of adequate data.
I lowcver, few parameters considered include seepage control, freeboard, and spillway inlet
and outlet width sizes. The estimation of freeboard involves the determination o f wave
heights, winrl fetcl~ and its speed. 'l'he estimation of spillway in ld and outlet widths could
he done by the aid of the monograph proposed in this study using the table of values fi)r
relations between the flood rates, inlet and outlet widths and the return slopes as suggested
by Nelson (1 984). The seepage volume could be estimated using Darcy's equation.
In conclusion, the cost of earth dams in the study area could be determined using
m~hemat ica l relations to relate the dam parameters and their costs. Inter relationships
between the para~rieters reduced the cost function to only three parameters of height,
length, and reservoir capacity.
This work is I-ecomniended for prospective tfesigners as an alternative approach to
earth dam's designs using the suggested relationships. The work further suggested a
niethodology for obtaining least cost using I,agrange's Multipliers with constraints. - - - -
- - - - - - - - - - - - - - - - - - - - - - -
- - - - - - - - - - -
Consultants in Ilydraulic Structures especially eadh dams would find this work useful for
tender evaluation and processes. 7'his work would also be useful for the present Federal
Governments Due Process intended to reduce corrupt practices in 'Tendering processes o f
either under estimation or inflated contracts to the detriment of the public generally.
6.2.0 Limitations of the study
'I'he cost hnctions should have consiclered the co~~struction materials on
constnrction site, hence dam classification according to malcrial ofconstruction as: -
f Ioniogeneous cnrth dams
Rock and earth fill dams. and
Rock filled earth dams.
Which were not used in this study, but the dams were classified as small, large and
gencral earth dams. I>uc to in adcquate data on inf l~r ion f i g h s , extrapolations using
regression analysis wcrc cmployecl. Recause inflation does not usually follow a d e h i k
paltern, the use o fa direct relation could have introduced some crrGrs in the predicled costs
in thc study.
6.3.0 Hecom mendat ion
'I his work is necessary for fast tender preparation and processing especially for
earth dams in Northern Nigeria.
'f'he cost functions should have been derived in terms o f materials for construction
so that cost o f earth dams could also be estimated based on materials available on site but
fix lack o f data availability, relationships considered only the dam salient features o f
height, leng[h andreservoir - - capacity. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Cost hnctions should also he estimated for other civil engineering structures like
roads, buildings, bridges, sewers, water supply networks etc.
Cost- Indices should he prepared regularly by a recognised and capable Agency or
Institution for reliable cost estimation in Nigeria.
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-- Site ('Ic:trancc at~tl d m Itcights
. -. . . -- Ilxcavation and l leight
.-
tnperuior~s lill and I lcipllts
-- - - - 'crvious Pil l and llrigltts
'ervious I ~ i l l and ('apilc,ity
- !ock 1 3 1 and I leighls
Lock Fill and I~.engtIis
16;qar lions
. - - - As(:= 27.37811 - 228123
Correlation
I'bin Concrete 1,cngllis
Class A amcrelc and I m g t l i
-- - -- Class A concrete and I I c i ~ h l s
Class A mncrclc and C'apncily
APPENDIX B
I ,;I rge (la rr~s
and capacit ics --
I I \ ~ ; ~ ~ : ~ l i o n ~ ~ i d hcights
+ 5 I:\cavation a n d I.cngths V, =- -373,631. + 916907
I S A o
i 1 i l
! 2 I I
IT 1 Impervious fill and capacities 1 V,F = 59,59Rc + 17480
-- -, 12 / I 'cn lous fill and capacittes v p F = ~ ~ 7 k 7 ~ c -60487
I h m pammeters
sllc clearance
and dam heights
Site clearance
and dam lengths
i V,, = 0.018~~ ' 920' -- r" Kock fill and heights V K ~ =30W9H - 482704
VKF ~0.053~~''~~ ~
! l 4 K Z k f n l aTd EngitTs - - - Tl i f~ l l f f ( .g t+ t i?+*h - - - - -
I V,, ;7~+20~-' "'45
I l 5 Rock till and capacities V, = 397.49Rc-286970
V, = 2 E - 0 8 ~ ~ " ' ~ ~ ~
IF--- - ~~
Riprap till and heighls Vd= 1559.20H - 64897
1:qualions
A~~ z 11 125H - 28106
Asc ; 26.47~"~~"
Asc = -892.441, + 317.+00
( 'omlat ion
coellicicnt
o (1 4 I 2
0.9573 .- ~-
0.6970
Asc = 4~+l01," "" ' 0 7471
l i lprap ti l l and capaclty
I'la~n concrctc Icng~h\
('lass A concrctc and Icngths.
('lass A w~ncrclc and heights
-- ('lass A concrete and
capacities
Normal soil dri l l ing and heights
Normal soil drilling and lengths
Korlnal soil drilling and
ca[ )ac I lu
Iiock dri l l ing and hcights
('ernenl grouting and heights
('ement groutlng and Icngthh
('crncnt grouting and capac~tics
I. o r n ~ work arcas and heights
Fo rm work arcas and
lengths
Form work areas and
capacities
APPENDIX C
I -- I
I / Site clcarance 1 A,, = 78971-1 - 453473 / 00636 -1 1 and dam heights
1 and capacities I0 .8177 1 I
V, .= 1327.50HL 7 ~ ~ ' ' 0.0760
0.5920
v, .: 7 ~ 4 5 l,'JqOq 0.7505
I:uuavat~on and capacities V, - T.&e 343304 03497
Inipcrvious fill and lcngths V,, = 342.18L- I05440
0.8822 --
In~pcrvious lill a n d hciglits 0.4088
Irnpcrvious till and capacilics Vl+ =29.23Rr - 11951 0.9855
I Vik = 646.1 1 K ~ ~ " " " 0.5857 I l'crvio~is f i l l and heights V p~ = 6294.60H - 67 13 . X O 0.8982
10 ( VpF = 1754t1'"49 0.9663 IFZI~ f i l l and lengths VPF = 379.99L - 44904 0 7736
1 V,,, = 0.0031."~~~ 0.785 I
~ E - - ~ G ~ ~ ~ ~ \ fill
I
v K P = 2 . 2 1 ~ ~ ~ ~ ~
Rock fill and lengths VKF = 3335.91,- 987 113
i VKF = [ E - ~ ~ L I I 547(1
r-'l+li[l and capacities V,=351.14Rc-171 177 0.9843
I 17 / Riprap lill and lengths
I I K~prap lill and cdpaclty V,, =24.44Rc- 10471 0 9875 4
--
Plain concrete lengths -1 Cl,= 0.43L - 1 I 6 -
. .~~~
I'lirin concrctc ('I!= 1 -07R, + 14.33 0 9834
capacily c1,:20, 1 1 ~ ~ - ~ 0 ~ 7 5 0.8664 -- ('lass A concretc and lengths CAz=68.85L - 20274 0 .X990
c,, = 71;-2g L ' 1 ""5" 0 .X 74 .- . ~ -..~ ~
('lass A concrcle and Iicighth CA=4A$21H - 1801 0.94 l 6 C' -0 .(;kH 1.4745
A - 0 9 4 1 5
('1. . . AS A cc~ricrwte and C,,= 7 4 3 R c - 3343 0.0838
I C.~=O,T R~ IOIKS 0.6138 I
Normal soil dri l l ing and 182.35 kI - 401X.80 1 .(I00
hcigh~s Dd=0.O043 11 3 6 7 g 1 1 000 - Normal soil dri l l ing and Dd= -3.98 1, - 5707 1.000
Icn gths D,,= 2 ~ + 0 9 0a2r 1 .ooo
Nor~r la l soil d r~ l l i ng and I.)d= -2E-05 Rr + 3640 1 ,000
capacities I), ,=- 1 4 0 8 0 ~ ~ . - ~ 17" 1 .OOO
Koch dri l l ing arid hcigh~s 11,- 3.73 H -- -
Cenicnt grou ti11g and heights (i(.= -1.06 H + 65.47 1 .OOO
I.'w=0.005 13 70'J7 1.000 - I:or~n work arcas and lcngths 0.43L - 123 1 .OOO
APPENDIX D
1 . 0 Programs for small earth dams.
Form - I
l'rivatt. Sub Cornrnand I _Click ( j
I > = 3 12 106 * l'extl .Text I
c ' l-z 7 7 1 , I 8 * Exp (0.82 * 'l'ext 1 . I'ext + 0.49)
13 - I323,YX * Text2.Text + 0.38 * Text3.Text - 323465 * ('Textl .'l'ext -3 j
'I ANS - 1) + C B - A - 185264 + El
1 ext4.1 rxt = ANS
End Sub
I ' r i~ate S u b Command2_Click()
lind
End S u b
I
2.0 Progrdam for large earth dams
Pr~vate S u b Cornand2-Click ()
A = 20 I2 * ( I 1512 * 7ex t I . Text - 2 * 10") ^0.7095 -0.02 * Text3.Text + 8.5 * I0 ' -5
* 7 ext3 rext A 1.4384 - 5.21 * 'rext3. rext A 0.7192 + 0.022 * Exp (7.95'4 * 1 ext3.Text3.Text A
-0 F8)
L 2 1.28 * Text I I ext)^O 8848 + 123662 17 * Text1 .Text + 30 4 1 *Text1 7 ext A 0 0359
1 ext4.Trxt - ANS 1
APPENDIX E
I able 4.26: Earth dam's lengths and heights for large d a m s
SIN0 Dams
1 Cham
2 Waya
3 Swash1
4 Tagwa~
5 Tungan K
6 UsmaS
7 Zana
8 Nasko
9 Kanglm~
10 Kontogora
11 Kubl
12 Agba
13 Bgoma
14 B o w
75 Guzan
16 Lamlngo
17 lbrah~m A
18 Jekko l
19 Iku
20 Jab1
21 Jeba(aux)
22 Malruwa
23 MlNufashl
24 Zobe
25 Zum
26 Dallaje
27 Dutslnma
28 Goronyo
29 J ~ b ~ y a
30 Shagar~
31 Sulelja
32 DlKowa
33 Klr~
34 UsmaM
35 Om1
Predicted
Heights (rn) Capac~ty ,\
Locat~on
UBRBDA
UBRBDA
NRBDA
NRBDA
NRBDA
FCT
Kaduna
NRBDA
Kaduna
NRBDA
NRBDA
Kwara
Kaduna
NRBDA
NRBDA
Plateau
Kana
Plateau
FCT
FCT
NRBDA
Katslna
Katsma
Kats~na
Kebbl
Kats~na
Katana
Sokoto
Kats~na
Sokoto
N~ger
UBRDA
UBRDA
FCT
Kwara
Pedan
Sh~roro
Kontogora
Jeba(m)
Ruwan K
T ~ g a
Bagauda
BIU
Challawa
Galala
Gar1
Tomas
Tudun W
Warwade
Watarl
Karaye
Magaga
Marash~
Pada
Guzuguzu
Jakara
Kafinchn
Kafin Zakt
Kango
Ouree
Pansh~n
Shendam
Tent1
YakubuG
Bokos
Lang tang
Lamnga
~ i r a - -
Doma
FCT
Niger
Niger
Niger
Kano
Kano
Kano
Bomo
Kano
Bauchi
Kano
Kano
Kano
Jigawa
Kano
Kano
Kano
Kano
Kano
Jlgawa
Kano
Kano
Bauchi
Kano
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
P-lakau
Plateau
'l'able 4.27: Larth dam's lengths and capacities for large dams
SINo. Dams
-.
1 Cham
2 Waya
3 Swash1
4 Tagwai
5 Tungan K.
6 Usma S.
7 Zar~a
8 Nasko
9 Kangimi
10 Kontogora
11 Kubi
12 Agba
13 Bgoma
14 Boso
15 Guzan
16 Lamingo
17 lbrahim A.
18 Jekko I
19 Iku
20 Jabi
21 Jeba(aux)
22 Mairuwa
23 MINufashi
24 Zobe
25 Zuru
26 Dallaje
27 Dutsinma
28 Goronyo
29 Jibiya
30 Shagari
31 Suleija
32 DlKowa
Length
(m)
1300
400
800
1770
3300
350
54 9
645
1525
1000
110
31 0
1067
132
950
41 0
183
128
870
850
275
457
55
2750
700
41 70
5285
3680
1193
51 2
520
Height
(m) ----
10
2 3
21
25
12
20
15
12
19
20
17
16.5
14.32
17
20
11.5
11
10
28
15
14
12
12
19
15
13
10
20
21.5
11
27.8
42
Pred.Capacity Location
(m3)
2.03E+07 UBRBDA
U BR BDA
NRBDA
NRBDA
NRBDA
FCT
Kaduna
NRBDA
Kaduna
NRBDA
NRBDA
Kwa ra
Kaduna
NRBDA
NRBDA
Plateau
Kano
Plateau
FCT
FCT
NRBDA
Katsma
Katsma
Katsrna
Kebb~
Katsma
Katsma
Sokoto
Katsma
Sokoto
N~ger
UBRDA
Klrl
Usma M
Om I
Pedan
Sh~roro
Kontogora
Jeba(m)
Ruwan K
T ~ga
Bagauda
BIU
Challawa
Galala
Gar1
Tomas
Tudun W
Warwade
Watar~
Karaye
Magaga
Marash~
Pada
Guzuguzu
Jakara
Kafinchr~
Kafin Zak~
Kango
Ouree
Panshm
St rendam -
Tent1
YakubuG
Bokos
La ng ta ng
Lamr~ga
Ku ra
Doma
UBRDA
FCT
Kwara
FCT
Niger
N~ger
Niger
Ka no
Ka no
Ka no
Bomo
Kano
Bauch~
Kano
Ka no
Ka no
Jigawa
Kano
Kano
Kano
Kano
Ka no
Jigawa
Ka no
Kano
Bauchi
Kano
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
I :rhle 3 38. I a ~ f h dam s helghts and capacltlesfor large dams
SIN0 Dams
1 Cham
2 Waya
3 Swash1
4 Tagwa~
5 Tungan K
6 UsmaS
7 Zana
8 Nasko
9 Kang~m~
10 Kontogora
I I K i i b ~
11 Ayba
13 Bgorna
14 Boso
15 Guzan
16 Larnlngo
17 lbrahlrn A
18 Jekko I
19 Iku
20 Jab1
21 Jeba(aux)
22 Ma~ruwa
23 MINufash~
24 Zobe
25 Zuru
26 Dallaje
27 Duts~nrna
28 Goronyo
29 J ~ b ~ y a
30 Shagar~
31 Suleha
32 DIKowa
33 K I ~ I
-
Length
(4 1300
400
800
1770
3300
350
549
64 5
1525
1000
110
310
1067
132
950
41 0
183
128
870
850
275
457
5 5
2750
700
41 70
5285
3680
1193
512
520
1300
He~ght Capacity Pred Capac~ty
(m3)
2 00E+07
4 60E+07
4 20E+07
5 OE+07
2 40E+07
4 00E+07
3 00E+07
@ 40E+07
3 80E+07
4 00E+07
3 40E+07
3 30E+07
2 86E+07
3 40E+07
4 00E+07
2 30E+07
2 20E+07
2 00E+07
5 60E+07
3 00E+07
2 80E+07
2 40E+07
2 40E+07
3 80E+07
3 00E+07
2 60E+07
2 00E+07
4 00E+07
4 30E+07
2 20E+07
5 56E+07
8 40E+07
7 40E+07
-- -
Locat~on
- - -- U BR BDA
UBRBDA
NRBDA
NRBDA
NRBDA
FCT
Kaduna
NRBDA
Kaduna
NRBDA
NRRUA
Kwara
Kaduna
NRBDA
NRBDA
Plateau
Kano
Plateau
FCT
FCT
NRBDA
Katsma
Katsma
Katsma
Kebb~
Katsma
Katsma
Sokoto
Kats~na
Sokoto
N~ger
UBRDA
UBRDA
34 Usma M
35 Om1
36 Pedan
37 Sh~roro
38 Kontogora
39 Jeba(m)
40 Ruwan K
41 Tiga
42 Bagauda
43 BIU
44 Challawa
45 Galala
46 Gar1
47 Tomas
48 Tudun W
49 Warwade
50 Watar~
51 Karaye
52 Magaga
53 Marash~
54 Pada
55 Guzuguzu
56 Jakara
57 Kafmchr~
58 Kafm Zak~
59 Kango
60 Ouree
61 Panshm
62 Shendam
63 Tent1
64 YakubuG
65 Bokos
66 Langtang
67 Lamr~ga
68 Kura
69 Doma
FCT
Kwara
FCT
N~ger
N~ger
N~ger
Kano
Kano
Kano
Bomo
Kano
Bauch~
Kano
Kano
Kano
J lgawa
Kano
Kano
Kano
Kano
Kano
J~gawa
Kano
Kano
Bauch~
Ka no
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau --
I able 4.39 l k t h darn's lengths and heights for general dams
--
Dams
- - -
Achlda
Dlnawa
Kark~ro
Marnoma
Mlslbll
Suru
Wurno
R I] au
G~rel
MIBelwa
Apkwlll II
Koglngm
Kwall
Kubanl
Omogldl
BIKudu
Daura
RIGado
Alau
Panshanu
Pakl
Farakwa~
Glwa
Gwarajl
S/Bm I
Cham
Waya
Swash1
Tagwal
Tungan K
Usma S
Zara
Nasko
--
Predicted Length
_A!!LL 135
126.5
180
22 0
1535
800
4500
350
250
30 5
203
280
27 4
853
31 0
1931
21 0
344
230
400
330
255
335
390
1300
400
800
1770
3300
350
54 9
64 5
Heights (m) -- .
12.60
12.60
12.69
12.79
15.89
14.12
22.63
13.09 I
12.86
13.04
12.75
12.92
12.91
14..24
12.99
16.72
12.76
13.07
12.81
13.20
13.04
12.87
13.05
13.18
15.27
13.20
14.12
16.35
19.87
13.09
13.54
13.76
Locat~on
~ o k o t o
Sokoto
Sokoto
Sokoto
Katsma
Kebb~
Sokoto
N~ger
UBRBDA
UBRBDA
Plateau
Plateau
Plateau
ABU
LBRBDA
Jlgawa
Borno
J~gawa
CBDA
UBRBDA
UBRBDA
NRBDA
NRBDA
NRBDA
F CT
Kaduna
NRBDA
Kangrm I
Kontogora
K u b ~
Agba
Bgoma
Boso
Guzan
Lammgo
lbrah~m A
Jekko l
Iku
Jab1
Jeba(aux)
Ma~ruwa
MINufash~
Zobe
Zuru
Dallaje
Dutsmma
Goronyo
J ~ b ~ y a
Shagar~
Sule~ja
DIKowa
K I ~ I
Usma M
Om I
Pedan
Sh~roro
Kontogora
Jeba(m)
Ruwan K
T~ga
Bagauda
B iu
Challawa
Galala
Kaduna
NRBDA
NRBDA
Kwara
Kaduna
NRBDA
NRBDA
Plateau
Kano
Plateau
FCT
FCT
NRBDA
Katsina
Katsina
Katsina
Kebbi
Katsina
Katsina
Sokoto
Katsma
Sokoto
Niger
UBRDA
UBRDA
FCT
Kwara
FCT
Niger
Niger
Niger
Kano
Kano
Kano
Borno
Kano
Bauch~
69 Gar1
70 Tomas
71 Tudun W
72 Warwade
73 Watarl
74 Karaye
75 Magaga
76 Marash~
77 Pada
78 Guzuguzu
79 Jakara
80 Kaf~nchr~
81 Kafln Zak~
82 Kango
83 Ouree
84 Panshm
85 Shendarn
86 Tent1
87 YakubuG
88 Bokos
89 Langtang
90 Larnnga
91 Kura
92 Dorna
Kano
Kano
Kano
Jigawa
Kano
Kano
Kano
Kano
Kano
Jigawa
Kano
Kano
Bauch~
Kano
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Table 4.30: Earth dam's lengths and capacities for general dams
SIN o Dams
Achida
Dinawa
Kark~ro
Marnoma
Misibil
Suru
Wurno
Rijau
Girei
MIBelwa
Apkwill II
Koging iri
Kwall
Kubani
Omogidi
BIKudu
Daura
RlGado
Alau
Panshanu
Paki
Farakwai
Giwa
Gwaraji
SIBirn I
Cham
Waya
Swash1
Tagwai
Tungan K
Usma S.
Zarla
Nasko
Length
A 135
126.5
180
22 0
1535
800
4500
350
250
305
203
280
274
853
31 0
1931
210
344
230
400
330
255
335
39 0
1300
400
800
1770
3300
350
54 9
64 5
He~g ht Capacity
-(m)--_ (m3)
Capacity
--.I!?.- 4.54E+05
4 16E+05
6.63E+05
8.65E+05
1 .l2E+O7
4.75E+06
4,67E+07
1.60E+06
1.02 E+O6
1 .33 E+06
7.78E+O5
1. IgE+O5
1 16E+06
5.17E+06
1.36E+06
1.52E+07
8.13E+05
1.56 E+O6
9.17E+05
1.91 E+06
1.48E+06
1.05E+06
1.63E+06
1 .84 E+O6
9.02E+06
1.91 E+06
4.75E+06
1.36E+07
3.08E+07
1.60E+06
2.89 E+O6
3.58E+06
Locatron
- Sokoto
Sokoto
Sokoto
Sokoto
Katsma
Kebb~
Sokoto
Nlger
UBRBDA
UBRBDA
Plateau
Plateau
Plateau
ABU
LBRBDA
J~gawa
Borno
Jlgawa
CBDA
N~ger
N~ger
N~ger
N~ger
N~ger
N~ger
UBRBDA
U BRBDA
NRBDA
NRBDA
NRBDA
FCT
Kaduna
NRBDA
Kangirni
Kontogora
Kubi
Agba
Bgoma
Boso
Guzan
Lamingo
lbrahm A.
Jekko l
Iku
Jabi
Jeba(aux)
Mairuwa
MINufashi
Zobe
Zuru
Dallaje
Dutsinrna
Goronyo
Jibiya
Shagari
Suleija
DIKowa
Kiri
Usma M.
Om I
Pedan
Shiroro
Kontogora
Jeba(rn)
Ruwan K.
Tiga
Bagauda
Biu
Challawa
Galala
Kaduna
N R BDA
NRBDA
Kwara
Kaduna
NRBDA
NRBDA
Plateau
Kano
Plateau
FCT
F CT
NRBDA
Katsina
Katsina
Katsina
Kebbi
Katsina
Katsina
Sokoto
Katsina
Sokoto
Niger
UBRDA
UBRDA
FCT
Kwara
FCT
Niger
Niger
Niger
Kano
Kano
Kano
Borno
Kano
Bauchi
69 Gari
70 Tomas
71 Tudun W
72 Warwade
73 Watart
74 Karaye
75 Magaga
76 Marashi
77 Pada
78 Guzuguzu
79 Jakara
80 Kafinchri
81 Kafin Zaki
82 Kango
83 Ouree
84 Panshin
85 Shendam
86 Tent1
87 YakubuG.
88 Bokos
89 Langtang
90 Lamriga
91 Kura
92 Doma
Kano
Kano
Kano
Jigawa
Kano
Kano
Kano
Kano
Kano
Jigawa
Kano
Kano +
Bauch~
Kano
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
Plateau
1 able 4.3 1 : 1:arth dam's he~ghts and capacit~es for general dams
Dams
Achlda
Dinawa
Karkiro
Marnorna
M~s~b i l
Suru
Wumo
R~jau
G~rei
MIBelwa
Apkw~ll II
Kogingiri
Kwall
Kubani
Omogld~
B/Kudu
Daura
RIGado
Alau
Panshanu
Paki
Farakwa~
Giwa
Gwaraji
SlBirni
Cham
Waya
Swashi
T a g w a ~
Tungan K.
Usma S
Zar~a
Nasko
Kangim~
Kontogora
Kub~
Agba
Length
-0 135
126 5
180
220
1535
80 0
4500
350
250
305
203
280
274
853
31 0
1931
21 0
344
230
400
330
255
33 5
390
1300
400
800
1770
3300
350
54 9
64 5
1525
1000
110
31 0
-
Height Capacity Capacity
-- (rn) (m3 (m3) 2.74E+05
Locat~on
~ o k o t o
Sokoto
Sokoto
Sokoto
Katsina
Kebb~
Sokoto
N~ger
UBRBDA
UBRBDA
Plateau
Plateau
Plateau
ABU
LBRBDA
J~gawa
Bomo
J~gawa
CBDA
LBRBDA
LBRBDA
LBRBD A
LBRBDA
LBRBDA
LBRBDA
UBRBDA
UBRBDA
NRBDA
NRBDA - - - -
NRBDA
FCT
Kaduna
NRBDA
Kaduna
NRBDA
NRBDA
Kwara
38 Bgoma
39 Boso
40 Guzan
41 Lamlngo
42 lbrahim A.
43 Jekko I
44 Iku
45 Jabi
46 Jeba(aux)
47 Mairuwa
48 MlNufashi
49 Zobe
48 Zum
49 Dallaje
50 Dutsinma
51 Goronyo
52 Jib~ya
53 Shagarl
54 Sule~ja
55 DlKowa
56 Kiri
57 UsmaM
58 Omi
59 Pedan
60 Shiroro
61 Kontogora
62 Jeba(m)
63 Ruwan K
64 Tga
65 Bagauda
66 BIU
67 Challawa
68 Galala
69 Gari
70 Tomas
71 Tudun W
Kaduna
NRBDA
NRBDA
Plateau
Kano
Plateau
FCT
FCT
NRBDA
Katsina
Katsina
Katsina
Kebbi
Katsina
Katsina
Sokoto
Katsina
Sokoto
N~ger
UBRDA
UBRDA
FCT
Kwara
FCT
Niger
Niger
Niger
Kano
Kano
Kano
Borno
Kano
Bauchi
Kano
Kano
Kano
