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ALFA et al: HYDROLOGIC AND MORPHOMETRIC ANALYSIS OF OFU RIVER SUB-BASIN 49
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.1
ABSTRACT: The morphometric characteristics of a river basin are very important factors in watershed hydrology.
The morphometric analysis of the Ofu River sub-basin was carried out in this study to assess its morphologic and
hydrological characteristics as well as its flood potentials based on the morphological characteristics. The study was
carried out using remotely sensed spatial data analysed using Geographical Information Systems (GIS). The
morphometric parameters analysed were the areal, linear, and relief aspects of the sub-basin. The results showed that
Ofu river sub-basin covers a total area of 1604.56 km2 and a perimeter of 556.98 km covering parts of Kogi and
Enugu States in Nigeria. The sub-basin has 3rd order river network based on the Strahler’s classification with a
dendritic drainage pattern and moderate drainage texture. The values of bifurcation ratio, drainage density,
circularity ratio, elongation ratio, form factor, stream frequency and drainage intensity indicate that the sub-basin is
elongated and would produce a flatter peak of direct runoff for a longer duration implying that the sub-basin is
morphometrically less susceptible to flood and that any flood flow that may emanate from it would be easy to
manage.
KEYWORDS: Delineation, GIS, Morphometric analysis, Ofu river sub-basin, Remote sensing.
[Received December 31, 2017; Revised July 01, 2018; Accepted October 01, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110
I. INTRODUCTION
Morphometric analysis of a river basin refers to the
measurement and mathematical evaluation of the surface,
shape and dimension of its landform (Agarwal, 1998; Obi et
al., 2002; Kulkarni, 2015). The morphometric characteristics
of a river basin are very important factors in watershed
hydrology. They reflect the hydrological behaviour of the
river basin and are useful in evaluating the hydrologic
response of the basin. There are relationships between river
basin morphometric parameters and flood potential. For
instance, higher drainage density indicates faster runoff and a
more significant degree of channel abrasion for a given
quantity of rainfall (Withanage et al., 2014). Rivers and
fluvial processes are the most dominant geomorphic systems
of earth’s surface responsible for morphometric changes in
drainage basin or the watershed (Horton, 1945). Sapkale
(2013), in buttressing this stated that the geological nature of
basin and its landform generally controls the river, influence
the channel slope and reveals possibilities of erosion and
depositions of the river.
Quantitative morphometric analysis of a river basin
facilitates an understanding of the drainage characteristics
and development, surface runoff generation, infiltration
capacity of the ground as well as groundwater potential
(Ibrampurkar, 2012; Raj and Azeez, 2012).
The systematic description of the geometry of a river
basin and its stream channel requires the measurement of
linear aspects of the drainage network, areal aspects of the
drainage basin, and relief or gradient aspects of the channel
network and contributing ground slopes (Strahler, 1964;
Withanage et al., 2014). Various researchers across the world
have carried out morphometric analysis of various river
basins in different continents of the world. Waikar and
Nilawar (2014) carried out morphometric analysis for the
drainage basin in Charthana, located in Parbhani district of
Maharashtra state in India, extracting linear, areal and relief
aspects of the basin characteristics. The parameters estimated
include stream length, bifurcation ratio, drainage density,
stream frequency, texture ratio, elongation ratio, circularity
ratio and form factor ratio amongst others. Similarly, Raj and
Azeez (2012) carried out morphometric analysis for
Barathapuzha River in Southern India. GIS and remote
sensing tools were used to study the morphometric
characteristics of the basin. They also determined the linear,
areal and relief aspects of the watershed characteristics. They
noted that the Barathapuzha River, the second longest river in
the state of Kerala was a seventh order river formed by
several lower order streams resulting to a dentritic flow
pattern. Similarly, Withanage et al. (2014) carried out
morphometric analysis of the Gal Oya River Basin in Sri
Lanka to assess its hydrological characteristics and flood
potentials based on the morphological characteristics. They
Hydrologic and Morphometric Analysis of Ofu
River Sub-Basin using Remote Sensing and
Geographic Information System M. I. Alfa1*, M. A. Ajibike2, D. B. Adie2, O. J. Mudiare3 1Department of Civil Engineering, University of Jos, Jos, Nigeria.
2Department of Water Resources & Environmental Engineering, Ahmadu Bello University, Zaria, Nigeria. 3Department of Agricultural & Bioresource Engineering, Ahmadu Bello University, Zaria, Nigeria.
50 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.1
utilized spatial data obtained from Geographical Information
Systems (GIS) to estimate the linear, areal and relief aspects
of the basin characteristics. They noted that the Gal Oya
River was a 6th order river network following the Strahler’s
classification with a dendritic drainage pattern and moderate
drainage texture. Martins and Gadiga (2015) also carried out
morphometric analysis of upper Yedzaram catchment of
Mubi in Adamawa State, Nigeria using Geographic
Information System (GIS). The study focused on the
hydrological and geometrical analysis with emphasis on the
linear and areal morphometric characteristics of the
catchment.
Morphometric analysis of Ofu River sub-basin became
necessary to form a basis for the detailed assessment of the
flood hazard, vulnerability and risk within the catchment.
This will also provide a sound basis for the management of
the watershed for optimum development of the resources
within it. The morphometric analysis of the Ofu River sub-
basin was carried out in this study to assess its morphologic
and hydrological characteristics as well as its flood potentials
based on the morphological characteristics.
II. MATERIALS AND METHODS
A. The Study Area
Ofu River sub-basin lies between latitudes 6o 46ˈ 48.38ˈˈ
N and 7o 38ˈ 31.2ˈˈ N and longitudes 6o 42ˈ 43.56ˈˈ E and 7o
20ˈ 54.6ˈˈ E covering parts of Dekina, Ofu, Igalamela/Odolu,
Idah and Ibaji Local Government Areas in Kogi State and
Uzo-Uwani Local Government Area in Enugu State, Nigeria
(Fig. 1), within the humid tropical rain forest of Nigeria. It
falls within the Lower Benue River Basin Development
Authority in North Central Nigeria. Rainfall within the
catchment is concentrated in one season lasting from
April/May to September/October. The main river within the
sub-basin (Ofu) is perennial and parallel in pattern to Imabolo
and Okura rivers which are close to the study area. It took its
root from Ojofu, in Dekina Local Government area in Kogi
State flowing in the eastward direction with a catchment area
amounting to about 1,604 km2 most of which is covered by
dense forest. Okura River joined Imabolo River in Egabada
(Kogi State) and further flow southwards before joining the
Ofu River and the ‘three-in-one’ river empties into the
famous Anambra River in Anambra State (Gideon et al.,
2013).
B. Delineation of Ofu River Watershed
The delineation of Ofu River Catchment was carried out
using the Shuttle Radar Topographic Mission Digital
Elevation Model (SRTM-DEM) version 3 and the drainage
network extracted from the River map of Africa. The pre-
processing was done using ArcHydro extension in ArcGIS
10.2.2 while the actual delineation was done using HEC-
GeoHMS extension in ArcGIS 10.2.2 with the DEM and
drainage network as input.
C. Estimation of Morphometric Parameters
Areal characteristics such as basin area, perimeter,
longest flow path and main stream length were extracted from
the attribute tables of the sub-basin and the main river in
ArcGIS while the other parameters were estimated using the
respective equations developed previously as shown in Tables
1-3.
III. RESULTS AND DISCUSSION
The boundaries of Ofu River catchment delineated in this
study using remote sensing and GIS is shown in Fig.2. The
figure shows the basic areal characteristics of the catchment.
Fig. 1: Map of Study Area Source: Adapted from the
Administrative Map of Nigeria, LOC (n.d); www.nationsonline.org
Fig. 2: Areal Characteristics of Ofu River Catchment.
ALFA et al: HYDROLOGIC AND MORPHOMETRIC ANALYSIS OF OFU RIVER SUB-BASIN 51
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.1
Table 1: Methods used for Estimation of Areal Morphometric Parameters.
Parameter Symbol Formula Reference
Area A GIS Analysis - Perimeter P GIS Analysis -
Basin Length Lb GIS Analysis Schumm (1956)
Longest Flow Path Lfp
GIS Analysis -
Main Stream Length SL GIS Analysis -
Basin Centroid Longest Flow Path Lcfp
GIS Analysis -
Elongation ratio Re Re = 2√(A/п)/Lb Schumm (1956)
Circularity ratio Rc R
c = 4пA)/P
2
Miller (1953)
Form factor Ff F
f = A/L
b
2
Horton (1932)
Compactness coefficient Cc C
c = 0.282038P/A
0.5
Horton (1945)
Shape Factor Bs B
s = L
b
2
/A Horton (1932)
Stream frequency F F = ΣNu/A Horton (1945)
Drainage Density Dd D
d = ΣL
u/A Horton (1932; 1945)
Drainage Texture Dt D
t = ΣN
u/P Horton (1945)
Drainage Intensity Id I
d = F/D
d Faniran (1968)
Constant of Channel Maintenance Cm C
m = 1/D
d Strahler (1952)
Length of Overland Flow Lo L
o = 1/2D
d Langbein & Leopold (1964)
Channel Sinuosity Sc S
c = ΣL
u/L
fp Le Roux (1992)
Time of Concentration Tc 𝑇𝑐 = 0.000323𝐿𝑓𝑝
0.77𝑆−0.385 Kirpich (1940)
Time to Recession N 𝑁 = 0.84𝐴0.2 Mustafa & Yusuf, 2012
Table 2: Methods used for Estimation of Linear Morphometric Parameters.
Parameter Symbol Formula Reference
Stream order U GIS Analysis Strahler (1964)
Stream Number Nu GIS Analysis Horton (1945)
Stream Length Lu GIS Analysis Horton (1945)
Mean Stream Length Num
Lum
= Lu
/ Nu
Strahler (1964)
Bifurcation Ratio Rb R
b
= Nu
/Nu+1
Schumm (1956)
Stream Length Ratio RL R
L
= Lu
/ Lu-1
Horton (1945)
Table 3: Methods used for Estimation of Relief Morphometric Parameters.
Parameter Symbol Formula Reference
Basin Relief H H = Z-z Strahler (1957)
Relief Ratio Rh R
h = H/Lb Schumm (1956)
Relative Relief Rhp
Rhp
= H*100/P Melton (1957)
Ruggedness Number RN R
N=D
d×(H/1000) Patton and Baker (1976)
Basin Slope S GIS Analysis -
A. Areal Characteristics of Ofu River Catchment
The areal characteristics of the catchment estimated in
this study are presented in Table 4. The results show that Ofu
River catchment covers a total area of 1,604.56 km2 and is
bounded by a perimeter of 556.98 km. 41.89 % of this area
falls in Dekina LGA, 24.4 % in Ofu LGA, 19.72 % in
Igalamela/Odolu LGA, 0.23 % in Idah LGA and 13.30 % in
Ibaji LGA all in Kogi State while 0.42 % falls in Uzo-Uwani
LGA in Enugu State.
In addition, the percentage of each LGA land mass
drained by Ofu River are 27.02 %, 23.48 %, 14.06 %, 9.25 %,
14.04 % and 0.80 % for Dekina, Ofu, Igalamela/Odolu, Idah,
Ibaji and Uzo-Uwani LGAs respectively. Schumm’s basin
length of Ofu River catchment is 100.93 km. the longest flow
path is 159.14 km while the length of main stream (Ofu
River) is 121.37 km. The basin’s centroid longest flow path is
89.32 km.
52 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.1
Table 5: Morphologic Characteristics of Ofu River Catchment (Linear Aspects)
Stream Order
(U)
Stream
Number (Nu)
Stream Length
(Lu)
Mean Stream Length
(Lum)
Bifurcation Ratio
(Rb)
Stream Length Ratio
(RL)
1 20 98.76 4.94 1.25
2 16 101.17 6.32 5.33 1.02
3 3 41.47 13.82 0.41
ΣNu = 39 ΣLu =241.40 - Av. Rb = 3.29 Av. RL = 0.72
Table 4: Morphometric Characteristics of Ofu River Catchment (Areal
Aspects).
Parameters Symbol Unit Value
Basic Parameters
Area A km2 1604.56
Perimeter P km 556.98 Basin Length Lb km 100.93
Longest Flow Path Lfp km 159.14
Main Stream Length SL km 121.37 Basin Centroid Longest Flow Path Lcfp km 89.32
Derived Parameters
Elongation ratio Re - 0.45 Circularity ratio Rc - 0.07
Form factor Ff - 0.16
Compactness coefficient Cc - 3.92 Shape Factor Bs - 6.35
Stream frequency F km-2 0.11
Drainage Density Dd km/ Km2 0.26
Drainage Texture T km-1 0.31
Drainage Intensity Id km-1 0.42
Constant of Channel Maintenance Cm km2/km 3.90 Length of Overland Flow Lo km 1.95
Channel Sinuosity Sc - 2.59
Time of Concentration Tc Hrs 6.17 Time from peak to Recession N Days 3.68
The results further show that the catchment has an
elongation ratio of 0.45, circularity ratio of 0.07, form factor
of 0.16, compactness coefficient of 3.92 and a shape factor of
6.35. More so, the stream frequency of the catchment is 0.11
km-1 while the drainage density is 0.26 km/km2. The drainage
texture is 0.31 km-1, the drainage intensity 0.42 km-1, while
the constant of channel maintenance is 3.90 km2/km. Finally,
the length of overland flow is 1.95 km, and the channel
sinuosity is 2.59 while the time of concentration and time
from peak to recession were 6.17 hours and 3.68 days
respectively implying that while it will take a drop of water
6.17 hours to flow from the remotest part of the catchment to
get to the outlet, it will take approximately four days for flood
water to recede after peak.
The low value of Drainage density (Dd) of 0.29 km/km2
indicates that the catchment has highly permeable subsoil and
thick vegetative cover. In addition, the low Circularity ratio
(Rc) of 0.07 obtained also indicates that as the catchment is
almost elongated in shape, it has a low discharge rate of
runoff and highly permeable subsoil conditions. More so, the
low elongation ratio (Re) of 0.45 and Form factor (Ff) of 0.16
confirm that the basin is elongated and thus the basin has a
flatter peak with a longer duration.
The lower values of Stream frequency (Fs) and Drainage
intensity (Id) values further confirm that the surface runoff is
not quickly removed from the river basin. The results reveal
that the basin is well capable of absorbing water into the soil
and recharging groundwater while reducing the risk of
flooding. If such floods happen, they could be managed easily
from this type of elongated Catchments than from circular
basins. The results of the areal morphologic characteristics
show that Ofu river catchment is inherently and
morphometrically capable of reducing the flood risk but
sustainable management plans should be made in advance to
cope with the potential floods that can occur due to high
rainfalls as has been the case with the low lying flood plains
for years.
B. Linear Morphometric Characteristics of Ofu River
Catchment
The analyzed drainage network of the Ofu river
catchment is presented in Fig. 3 while the linear aspects of
the morphometric analysis conducted for the river network
are given in Table 5.
A total of 39 streams are found in Ofu River catchment.
These streams are linked up to the 3rd order spreading over an
area of 1,604.56 km² (Fig. 3). There are a total of 20, 16 and
3 streams of orders 1, 2 and 3, respectively with stream
lengths 98.76 km, 101.17 km and 41.47 km in respective
orders. This small number of streams indicates mature
topography in the catchment (Zaidi, 2011). The mean stream
lengths for order 1, 2 and 3 were, respectively 4.94 km, 6.32
km and 13.82 km. A plot of the respective logarithm of
stream number (Nu), stream length (Lu) and mean stream
length (Lum) versus stream order are presented in Figs.4, 5
and 6.
There was a decrease in stream length (Fig. 5),
respectively with increasing order which agrees with Horton
(1945). The mean stream length (Lum) on the other hand
showed an increase with increasing order (Fig. 6) as
explained by Strahler (1964). These trends agree with those
of previous studies carried out on other similar catchments
(Withanage et al., 2014; Waikar et al., 2014).
Dendritic drainage pattern can be observed in Ofu River
basin (Fig. 3) which is probably the most common drainage
pattern identified in Nigerian river basins and the world at
large. This is a randomly developed, tree-like pattern
composed of branching tributaries and a main stream,
characteristic of essentially flat-lying and/or relatively
homogeneous rocks and impervious soils (Zernitz, 1932).
.
ALFA et al: HYDROLOGIC AND MORPHOMETRIC ANALYSIS OF OFU RIVER SUB-BASIN 53
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.1
Fig.5: Logarithm of Stream Length (Lu) versus Stream Order (U).
Fig. 6: Logarithm of Mean Stream Length (Lum) versus Stream
Order (U).
Fig. 4: Logarithm of Stream Number (Nu) versus Stream Order (U).
This pattern develops on rocks of uniform resistance which
indicate a complete lack of structural control (Withanage et
al., 2014). It is more likely to be found on nearly horizontal
sedimentary rocks or on areas of massive igneous rocks and
sometimes on complex metamorphosed rocks (Garde, 2006).
Ofu River shares similar geological characteristics with
Ankpa which according to Imasuen et al. (2011) falls within
the Anambra Basin whose genesis has been linked with the
development of the Niger Delta Miogeosyncline and the
opening of the Benue Trough. According to them, the Benue
Trough is underlain by the rocks of Anambra Sedimentary
Basin consisting of the Ajali and Mamu formations.
Furthermore, the bifurcation ratios were 1.25 and 5.33
while the average bifurcation ratio was 3.29. According to
Horton (1945), bifurcation ratio is an index of reliefs and
dissections. The bifurcation ratios were not the same from
one order to the next which according to Strahler, (1964) and
Withanage et al. (2014) is attributable to the geological and
lithological development of the drainage basin. Strahler
(1964) and Nag (1998) stated that lower values of bifurcation
ratios are characteristics of watersheds which have suffered
less structural disturbances. The higher bifurcation ratio of
5.33 obtained for order 2 streams in this present study
indicates that strong structural disturbances have occurred in
the basin when the underlying geological structure underwent
transformations.
In addition to the forgoing, Chorley et al. (1957) noted
that bifurcation ratio could be an index of flood risk level. He
Fig. 3: Strahler’s Stream Order of Ofu River Basin.
54 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.1
Fig. 7: Digital Elevation Model (DEM) of Ofu River Catchment.
stated that the lower the bifurcation ratio, the higher the risk
of flooding, particularly of parts and not the entire basin. This
explains why the flooding within the Ofu River catchments
affects only a part of the basin amongst other factors. The
values of bifurcation ratio (Rb) obtained in this study (1.25
and 5.33), the high average of 3.29 together with the
elongated shape of Ofu River basin would result in a lower
and extended peak flow, which will reduce the risk of
flooding within the basin.
C. Relief Morphologic Characteristics of Ofu River
Catchment
The Digital Elevation Model (DEM) of Ofu River
catchment is shown in Fig.7 while the relief characteristics of
the catchment are presented in Table 6.
The highest and lowest elevations of Ofu River basin are
extracted from the DEM (Fig. 7) were 436 and 11 m above
mean sea level (m asl.), respectively. The Basin relief (H),
Relief ratio (Rh) and Relative relief (Rhp) are 425 m, 0.0042
and 0.0008, respectively while the Ruggedness number and
Basin slope are respectively 0.109 and 0.19. The Relief ratio
according to Schumm (1956) is equal to the tangent of the
angle formed by two planes intersecting at the mouth of the
basin. It is also a measure of the overall steepness of a river
basin which is an indicator of the intensity of erosion process
operating on the slope of the basin.
The Rh value of 0.0042 obtained for Ofu River basin
reveals that the basin is morphometrically less susceptible to
severe erosion. From the reconnaissance survey conducted, it
was observed that the catchment is not affected by serious
erosion characteristic of a major part of Kogi East Senatorial
district. The relief ratio (Rhp) is an important morphometric
variable used for the overall assessment of morphological
characteristics of terrain.
V. CONCLUSION
A quantitative morphometric analysis using remotely
sensed data and GIS has been demonstrated to be a fast,
convenient and effective method of studying the
characteristics of a river basin. Ofu River catchment has a
dendritic drainage pattern showing a 3rdorder stream network
and a total of 39 streams. The high values of bifurcation ratio
reveal that a lower and extended peak flow would result from
the basin which will reduce the risk of flooding. The low
drainage density indicates that the basin has highly permeable
sub-soil and thick vegetative cover. This is further buttressed
by the low circularity ratio, elongation ratio and form factor.
As the basin is elongated in shape, it has a low discharge rate
and highly permeable sub soil conditions. The low values of
stream frequency and drainage intensity further confirm that
the surface runoff is not quickly removed from the basin.
Morphometrically, the basin is well capable of absorbing
water into the soil and recharging groundwater while
reducing the risk of flooding and possibly increasing the risk
of ground water flooding as it is in some parts of the
catchment. If such flood will emerge, it could be managed
easily from this type of elongated basins than from circular
basins by adopting suitable precautionary measures. Although
the studied Ofu river basin is not morphometrically
susceptible to flood, sustainable management plans should be
made in advance to cope with the potential floods that can
occur due to high rainfalls.
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ALFA et al: HYDROLOGIC AND MORPHOMETRIC ANALYSIS OF OFU RIVER SUB-BASIN 55
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.1
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Zaidi, F. K. (2011). Drainage basin morphometry for
identifying zones for artificial recharge: A case study from
the Gagas River Basin, India. Journal of the Geological
Society of India, 77(2): 160-166.
Zernitz, E. R. (1932). Drainage patterns and their
significance. The Journal of Geology, 498-521.
56 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.2
ABSTRACT: In this study, oil was extracted from butter fruit (Dacrydes edulis). To model and optimize the process
conditions of oil extraction, Response Surface Methodology (RSM) and Artificial Neural Network (ANN) were
used. Physicochemical analysis of the oil was carried out in order to determine the suitable of oil for industrial
applications. Dacryodes edulis seeds were collected from Ikot Abasi Village in Eket Local Government of Akwa
Ibom State, Nigeria. The seed was washed with clean water to remove dirt, and open with a sharp stainless knife to
remove the seed from the pulp. The seeds were cut into small pieces and sundried for 5 days and were grinded into
powder. Oil extraction from the powder seed was carried out using Sohxlet extraction method. The experiment was
designed using Box-Behnken Design approach on three levels, three factors which generated 17 experimental runs.
Independent factors considered were extraction time (X1), solvent volume (X2) and sample weight (X3). The
accuracy of the regression model obtained from the optimization software was determined using the co-efficient of
determination (R2). Results showed the highest oil yield of 17.878% (w/w) was obtained at solvent volume of 200
ml, sample weight of 50 g and extraction time of 55 min, respectively. However, response surface methodology
predicted an oil yield of 17.826% (w/w), while the artificial neural network predicted 17.875% (w/w) at the same
variables condition. The predicted values were validated in triplicate, and an average of 17.46% (w/w) and 17.72%
(w/w) were obtained for RSM and ANN, respectively. The predicted values obtained were well within the range
predicted. The coefficient of determination, which determines the model accuracy, was obtained to be 0.8454 for
RSM and 0.8712 for ANN. Physicochemical analysis of the oil showed the oil is highly unsaturated with high
saponification value and high iodine value. The study concluded that Dacryodes edulis seeds are found to be rich in
oil and the oil can be applicable in industries as raw materials for products formation.
KEYWORDS: Dacryodes edulis seeds, response surface, artificial neural network, optimization, extraction, physicochemical
properties.
[Received April 16, 2018; Revised September 06, 2018; Accepted September 19, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110
I. INTRODUCTION
The use of oil in Industries for production of cosmetic,
biofuel, bio lubricant and other products has become greatly
increase, which has necessitated the needs to search for
alternative source through biomass (Agricultural oilseeds). To
meet up with the needs of the incessant increase in the
demand for oil by both domestic and industries have resulted
in search for using underutilized seeds as sources of oil to
supplement the already current traditional sources of oil
(Ugbogu et al., 2014). In some nation, specifically Nigeria,
different oil crops exist from the largely used and highly-
utilized to under-utilized seed oils that have not been
investigated for their potential uses.
Dacryodes edulis, an annual fruit known as African plum
or African pear or Safou seed is one of the under-utilized seed
oil. It is an indigenous fruit tree in the humid low lands and
plateau regions of West, Central African and Gulf of Guinea
countries. Usually, the trees are grown around homesteads
and flowering always takes place from January to April, with
fruiting season between May and October (Nwosuagwu et al.,
2009). The pear is locally called ’Ube’ among the Igbos in
South eastern part of Nigeria belongs to the family of
Burseraceae and genus Dacryodes (Ogunsuyi, 2015). It has
the qualities of butter apart from the pulp outlook which
contains 48% oil; the overall plantation can produce 7-8
tonnes of oil per hectare.
Generally, the extraction of oil from the seeds can be
achieved via various methods such as mechanical, (Joglekar
and May, 1987; Haidar and Pakshirajah, 2007; Schinas et al.,
2009) pressurized solvent extraction (Mcginely, 1991),
soxhlet extraction (Meher et al., 2006), ultrasonic extraction
(Ramos et al., 2009; Rodríguez et al., 2012), Aqueous
Enzymatic Oil Extraction (AEOE) (Perez-Serradilla et al.,
2002; Pan et al., 2002), stirring and shaking extraction (Kim
et al., 2004) to mention but few. These methods have been
reported used for extraction of vegetable oils and other plant
essential components, each with intrinsic advantages and
shortcomings (Umer et al., 2011). Mechanical pressing is the
oldest and easiest method used widely, but, the oil produced
always with low value. Meanwhile, (Betiku and Adepoju,
Oil Extraction from Butter Fruit (Dacryodes Edulis)
Seeds and its Optimization via Response Surface
and Artificial Neural Network T. F. Adepoju1*, I. O. Esu1, O. A. Olu-Arotiowa2, E. Blessed1
1Chemical/Petrochemical Engineering, Department, Akwa-Ibom, State University, Ikot Akpaden, Nigeria. 2Chemical Engineering, Ladoke Akintola University of Technology, Ogbomosho, Nigeria.
ADEPOJU et al: OIL EXTRACTION FROM BUTTER FRUIT SEEDS AND ITS OPTIMIZATION 57
*(corresponding author) [email protected], [email protected] doi: http://dx.doi.org/10.4314/njtd.v14i2.1
2013) reported the use of supercritical CO2 extraction; the oil
yield obtained was higher than what was obtained from using
solvent extraction and of high purity, but the high operating
and investment costs make this method not suitable to be
used. Solvent extraction has various advantages including
high yield, less turbidity, environmentally friendly and cost
effective (Adepoju et al., 2013; Betiku et al.,2012), which
was why solvent extraction of oil from Jatropha curcus was
carried out by (Kian et al., 2011), while (Umer et al., 2011)
studied the solvent extraction of oil from Moringa oleifera.
Betiku et al. (2012) extracted oil from sorrel seed using
solvent extraction while solvent extraction of oil from
Chrysophyllum albidium oilseeds and its quality
characterization was carried out by (Adepoju et al., 2013). In
another study, Betiku et al. (2012) worked on solvent
extraction of oil from Beniseed (Sesamum indicum) oilseeds.
This work therefore employed the possibility of using
Dacryodes edulis seed for oil production. For modelling and
optimization, response surface methodology (RSM) and
artificial neural network (ANN) were employed so as to
generate the number of experimental runs, determine the
predicted yields, compare the error values, and analyse the
various variable factors responsible for optimum production
of oil so as to increase the process efficiency. Lastly, the
properties of oil were evaluated with a view to determining
its suitability as edible or non-edible oil.
II. MATERIALS AND METHODS
A. Materials
The Dacryodes edulis seeds used in this work was
collected from Ikot Abasi Village in Eket Local Government
of Akwa Ibom State, Nigeria. The seed was washed with
clean water to remove dirt, and open with a sharp stainless
knife to remove the seed from the pulp. The seeds were cut
into small pieces and sundried for 5 days. Finally, the cleaned
seeds were grinded into powder with a Corona grinder. All
the chemicals used in this study are of analytical grades.
B. Methods
1) Experimental design
To optimize the oil extraction from Dacryodes edulis
seeds powder, three level-three factors were considered. Box-
Behnken Design (BBDRSM) was employed which generated
17 experimental runs used to study the effects of selected
factors on oil yield. Table 1 showed the selected factors
which are solvent volume (X1), sample weight (X2) and the
extraction time (X3) and their levels. These factors were also
used for ANN Modeling and optimization. For the coefficient
of the quadratic model of the response fitting, multiple
regressions model was adopted using design expert software
10 version 15.5 (Stat Inc., Tulsa, OK, USA) and Neural
Power _21356. Regression analysis and test of significance
are the computationally intensive process that is best carried
out via statistical software; hence the quality of the fitted
model was evaluated using test of significance and regression
analysis of variance (ANOVA) via Eq. 1. To compare the
results of the model chosen and validate the coefficient of
determination of the experimental result, artificial neural
network (ANN) was incorporated.
𝑅𝐹 = 𝜏0 + ∑ 𝜏𝑖𝑋𝑖
𝑘
𝑖=1
+ ∑ 𝜏𝑖𝑖𝑋𝑖2
𝑘
𝑖=1
+ ∑ 𝜏𝑖𝑗𝑋𝑖𝑋𝑗
𝑘
𝑖<𝑗
+ 𝑒 (1)
where, RF is the response (oil yield), 𝜏0 is the intercept term,
𝜏𝑖, 𝜏𝑖𝑖, 𝜏𝑖𝑗 are the coefficient terms for linear (𝑋𝑖), quadratic
(𝑋𝑖2) and interaction (𝑋𝑖𝑋𝑗), 𝑋𝑖 is the selected factors, 𝑖= 1, 2,
3. Table 1: Factors and their Levels for Box - Behnken Design. Variable Symbol Coded factor levels
-1 0 +1
SV (ml) X1 180 200 220
SW (g) X2 40 50 60
ET (min) X3 50 55 60
SV = Solvent volume, SW = Sample weight, ET= Extraction time
2) Description of oil extraction procedure
Based on the experimental design by Box Behken
Design, seventeen experimental runs were generated and
were carried out. Soxhlet extractor was used for the
extraction process; the powdered sample was weighed and
placed in the extractor through the muslin cloth. N-hexane
was used as organic solvent for extraction. Three level three
factors were considered, the excess n-hexane was recovered
using rotary evaporator, and the yield of the oil was obtained
using Eq. (2).
𝑂𝑖𝑙 𝑦𝑖𝑒𝑙𝑑 (%) =𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑜𝑖𝑙
𝑤𝑒𝑖𝑔ℎ𝑡 𝐷𝑎𝑐𝑟𝑦𝑜𝑑𝑒𝑠 𝑒𝑑𝑢𝑙𝑖𝑠 𝑝𝑜𝑤𝑑𝑒𝑟 𝑢𝑠𝑒𝑑 (2)
3) Physicochemical analysis of the extracted Dacryodes
edulis seed oil
The properties of the oil were evaluated using standard
of AOAC (1997), official methods of analysis and Wij’s
iodine method as described below:
0.52 g of oil sample was dissolved in 10 ml of
cyclohexane. 20 ml of Wij’s solution was added, the stopper
flask was allowed to stand for 30 min in the dark at room
temperature, and 20 ml of 10% potassium iodide solution was
added. The resulting mixture was then titrated with 0.1 M
Na2S2O3 using starch as indicator. Iodine value was calculated
using equation 3.
𝐼𝑜𝑑𝑖𝑛𝑒 𝑉𝑎𝑙𝑢𝑒 = [𝜌𝑜−𝜌] 𝑋 𝑀𝑋12.69
0.26 (3)
where M = concentration of sodium thiosulphate used;
𝜌𝑜 = volume of sodium thiosulphate used as blank; 𝜌 =
volume of sodium thiosulphate used for determination.
4) Variable interactive effects
To study the effects of independent variables on oil yield,
three factors were taking into consideration (Table 1). The
interactive effects of the variables on the oil yield were
considered by allowing for the linear (X1, X2, X3), the
interaction (X1X2, X1X3, X2X3) and the quadratic (X12, X2
2,
58 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.2
Table 3: Test of Significance for All Regression Coefficient Term.
Source Sum of
squares
df Mean
Square
F-
value
p-value
X1 18.23 1 18.23 12.45 0.01617
X2 13.10 1 13.10 13.89 0.0391 X3 16.67 1 16.67 8.96 0.0613
X1X2 12.65 1 12.65 11.76 0.0437
X1X3 3.82 1 3.82 10.13 0.04600 X2X3 4.03 1 4.03 1.20 0.3101
X12 1.49 1 1.49 10.44 0.05277
X22 0.038 1 0.038 0.011 0.9186
X32 14.63 1 14.63 4.35 0.0755
Table 4: Analysis of variance (ANOVA) of regression equation.
Source Sum of
squares
df Mean
Square
F-
value
p-
value
Model 175.16 9 19.46 12.48 0.0122
Residual 23.55 7 3.36
Lack of fit 21.08 3 7.03 11.37 0.199 Pure error 2.47 4 0.62
Correction for
total sum 98.71 16
R2RSM: 84.54% R2
ANN: 87.12%
Table 2: Box-Behnken Experimental Design for Three Independent
Factors.
Std.
run
X1 X2 X3 Oil
yield
%(w/w)
Predicted Residual
RSM ANN RSM ANN
1 1 1 0 13.1102 13.0282 13.129 1.69 0.019236
2 0 0 0 17.8780 17.826 17.875 6.47 0.0030479 3 0 1 1 13.5602 13.5082 12.476 0.40 1.0838
4 0 -1 1 12.6760 12.624 12.476 -0.55 0.19955
5 1 -1 0 9.6400 9.588 9.7187 -1.77 0.078717 6 0 1 -1 8.8878 8.8358 8.9299 -1.85 0.042103
7 -1 0 -1 9.0790 9.027 9.0722 -0.16 0.0067995
8 0 0 0 12.1744 12.1224 12.476 0.55 0.30205 9 0 0 0 9.9718 9.9198 9.958 -2.25 0.013816
10 -1 0 1 11.4024 11.3504 12.476 -8.34 1.074
11 0 0 0 9.4003 9.3483 9.3893 -1.69 0.011029 12 -1 1 0 12.5876 12.5356 12.476 2.25 0.11115
13 1 0 1 8.1188 8.0668 8.5722 -3.29 0.4534
14 1 0 -1 9.2843 9.2323 8.7767 -0.40 0.50758 15 -1 -1 0 14.1445 14.0925 14.151 1.85 0.0062827
16 0 -1 1 11.3265 11.2745 11.305 0.16 0.021387
17 0 0 -1 10.0145 9.9625 10.034 -1.40 0.019628
X32) on the response. The variable interactive effects also lead
to the formation of regression equation (Eq. 1) and explained
vividly how the contour and three-dimensional plots are
obtained.
C. Optimization of Dacryodes edulis Seed Oil Extraction
The important part of any regression analysis is to
determine whether or not the standard assumptions of the
simple linear regression model are satisfied. The relationship
between the response variable (oil yield) and selected
variables (X1; X2; X3) are assumed to be in form of linear,
interactions and quadratic (Eq. 1). To check the model
accuracy and model estimation capabilities, the coefficient of
determination (R2) was determined by estimating these
parameters using Eqns. (4). Their values were used together
to juxtapose the Box Behnken design and genetic algorithm
models by comparing the evaluated values for the models.
𝑅2 = 1 − ∑(∅𝑖,𝑐𝑎𝑙−∅𝑖,𝑒𝑥𝑝)2
(∅𝑎𝑣𝑔,𝑒𝑥𝑝−∅𝑖,𝑒𝑥𝑝)2𝑛𝑖=1 (4)
where ∅𝑖,𝑒𝑥𝑝 is the experimental value, ∅𝑖,𝑐𝑎𝑙 is the
calculated value and ∅𝑎𝑣𝑔,𝑒𝑥𝑝 is the average experimental
value.
IV. RESULTS AND DISCUSSION
D. Optimization of oil extraction
Table 2 depicts the 17 experimental generated, the oil
yield results obtained together with the predicted oil yield and
the residual values. It was observed that the lowest yield
obtained was 8.1188% (w/w) and the predicted values for
RSM and ANN couple with genetic algorithms were 8.0668%
(w/w) and 8.5722% (w/w), respectively. Meanwhile, the
highest yield obtained was 17.8780% (w/w), while the
predicted values for RSM and ANN were 17.726% and
17.876% (w/w), respectively. The predicted values were
validated in triplicate, and an average of 17.46 % (w/w) and
17.72% (w/w) were obtained for RSM and ANN,
respectively.
Table 3 showed the results of test of significance for all
coefficient of regression. The F-values of X1, X2, X1X2 and
X1X3, implies the significant model terms. Values of "Prob >
F" less than 0.0500 indicate model terms are significant.
Table 4 showed the results of the Analysis of Variance
(ANOVA). The analysis of variance is important to test
significance and suitability of the model and to determine
whether the variation from the model is significant when
compared to the variation due to residual error at 95%
confidence level. The “Lack of Fit” compares the residual
error to the pure error from simulated design points. The lack
of fit F-value of 11.37 with p-value 0.199 implies
insignificant lack of fit relative to pure error.
The mathematical expression of the relationship
between oil yield and the variable factors is given by the
model equation 4. All negative values have reduction impact
on the yield while positive values have ability to increase the
yield (Table 5).
OY (%) = +12.48 – 1.01X1 + 1.28X2 – 1.44X3 – 1.78X1 X2
– 0.98X1X3 – 1.00X2X3 – 0.59X12 + 0.095X2
2 – 1.861X32
To test the fit of the model equation, the regression model
was established using R2 as a measure of how much
variability in the observed response values can be explained
by the experimental factors and their interactions (Sudamalla
et al., 2012). The R2 value is always between 0 and 100%
(Haider and Pakshirajah, 2007; Schinas et al.,
2009). However, to create a good-fit model, it was
recommended that R2 should not be less than 80% (Joglekar
and May 1987). The results in Table 4 indicated an R2 value
of 84.54% for RSM and 87.12% for ANN, which leaves only
15.46% and 12.87% of the variability, not explains by oil
yield, this indicates that an unexplainable total variation could
be caused by other factors, which were not included in the
model. Figure 1 shows the relationship between the predicted
plots (RSM and ANN) and the actual experimental oil yield.
A graphical drawing depicts a functional relation
between two or three variables by means of a curve or surface
containing only those points, whose coordinates satisfy
ADEPOJU et al: OIL EXTRACTION FROM BUTTER FRUIT SEEDS AND ITS OPTIMIZATION 59
*(corresponding author) [email protected], [email protected] doi: http://dx.doi.org/10.4314/njtd.v14i2.1
Table 5: Regression Coefficients and Significance of Response
Surface Quadratic
Factor Coefficient
estimate
df Standard
error
95%
CI
Low
95%
CI
High
VIF
Intercept 12.48 1 0.82 10.54 14.42
X1 -1.01 1 0.65 -2.55 0.52 1.00
X2 1.28 1 0.65 -0.25 2.81 1.00 X3 -1.44 1 0.65 -2.98 0.090 1.00
X1X2 -1.78 1 0.92 -3.95 0.39 1.00
X1X3 -0.98 1 0.92 -3.15 1.19 1.00 X2X3 -1.00 1 0.92 -3.17 1.17 1.00
X12 -0.59 1 0.89 -2.71 1.52 1.01
X22 0.095 1 0.89 -2.02 2.21 1.01
X32 -1.86 1 0.89 -3.98 0.25 1.01
Design-Expert® SoftwareFactor Coding: Actual% OY
Design Points17.878
8.1188
X1 = A: SV (ml)X2 = C: ET (min)
Actual FactorB: APSW (g) = 50
180 190 200 210 220
50
52
54
56
58
60% OY
SV (ml)
ET
(m
in)
8
9
10
11
12
125
Design-Expert® SoftwareFactor Coding: Actual% OY
Design points above predicted valueDesign points below predicted value17.878
8.1188
X1 = A: SV (ml)X2 = C: ET (min)
Actual FactorB: APSW (g) = 50
50
52
54
56
58
60
180
190
200
210
220
6
8
10
12
14
16
18
% O
Y
SV (ml) ET (min)
Fig. 2(a)
the relationship between the response and the experimental
levels of each variable on the one side, and the type of
interactions between the test variables, on the other, which
allows for deducing the optimum conditions. The interaction
effects of solvent volume (SV), sample weight (SW) and
extraction time (ET) on the oil yield were studied using the
contour plots and 3D surface plots of RSM (Figure 2 (a-d)).
From the plots, it was observed that the oil yield increased
with decreases in ET and SV while keeping SW constant at
zero level. The curvature nature of the surface plots in
Figures 2 (b-e) depict mutual interactions between ET and SV
Figures 2 (b-e) depict mutual interactions between ET
and SV on oil yield. It was observed that an increased in SW
and SV favoured the high yield of the oil, while low SV and
low SW reduced the oil yield. Figures 2 (c-f) showed the
interaction between the SW and ET on the yield of oil. It was
also observed that the high SW with low ET produced the
highest oil yield. Further increase in ET reduced the yield of
the oil.
The RSM and ANN plots of contours and the 3 D’s showed
that the highest oil yield was obtained at high SW, low ET
and low SV (Figures 2(b-e & c-f)).
RSM ANN
Figure 1: Actual yield Vs. Predicted values.
60 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.2
Design-Expert® SoftwareFactor Coding: Actual% OY
17.878
8.1188
X1 = A: SV (ml)X2 = B: APSW (g)
Actual FactorC: ET (min) = 51.3609
40
45
50
55
60
180
190
200
210
220
8
10
12
14
16
18
% O
Y
SV (ml)APSW (g)
12.07612.076
Design-Expert® SoftwareFactor Coding: Actual% OY
17.878
8.1188
X1 = A: SV (ml)X2 = B: APSW (g)
Actual FactorC: ET (min) = 51.3609
180 190 200 210 220
40
45
50
55
60% OY
SV (ml)
AP
SW
(g
)
10
12
14
Prediction 12.076
Fig. 2(b)
Design-Expert® SoftwareFactor Coding: Actual% OY
Design Points17.878
8.1188
X1 = B: APSW (g)X2 = C: ET (min)
Actual FactorA: SV (ml) = 180
40 45 50 55 60
50
52
54
56
58
60% OY
APSW (g)
ET
(m
in)
8
10
12
14
16
Prediction 12.076
Design-Expert® SoftwareFactor Coding: Actual% OY
Design points above predicted valueDesign points below predicted value17.878
8.1188
X1 = B: APSW (g)X2 = C: ET (min)
Actual FactorA: SV (ml) = 180
50
52
54
56
58
60
40
45
50
55
60
6
8
10
12
14
16
18
% O
Y
APSW (g)ET (min)
12.07612.076
Fig. 2(c)
Fig. 2(e)
Fig. 2(d)
ADEPOJU et al: OIL EXTRACTION FROM BUTTER FRUIT SEEDS AND ITS OPTIMIZATION 61
*(corresponding author) [email protected], [email protected] doi: http://dx.doi.org/10.4314/njtd.v14i2.1
Table 6: Physiochemical Properties of oil.
Parameters Values
Physical properties
Absorbance @660oC 2.032
Moisture content (%) 0.04549 Specific gravity 0.9217
Mean Molecular mass 434.008
Viscosity @34.2oC (N.s/m2) 1.282
Chemical Properties
Free Fatty Acid 13.036
Acid Value (mg KOH/g oil) 27.072 Saponification Value (mg KOH/g oil) 129.03
Iodine Value (g I2/100g oil) 78.09
Peroxide Value (meq O2/kg oil) 37.60 Higher Heating Value (MJ/kg) 42.968
Other Properties
Cetane number 71.0299
E. Physiochemical Properties of African Pear Oil (APO)
Table 6 showed the results of the physicochemical
properties of the extracted oil obtained using (AOAC, 1997)
standard methods. The oil obtained was liquid, brownish in
colour with the moisture content of 0.04549% and specific
gravity of 0.9217. The high acid value of 27.072
corresponding to high FFA of 13.036 obtained in this study
indicated the good resistance of the oil to hydrolysis.
Peroxide value measures the content of hydroperoxides in the
oil (Mcginely, 1991) and its high value (37.60 meq.
O2/kg) indicates high resistance to oxidation.
High saponification value of 129.03 mg KOH/g with a
high iodine value of 78.09 gI2/100 g indicated a low
concentration of triglycerides and the oil contained a
substantial level of unsaturation. The high heating value of
42.968 MJ/kg takes into account the latent heat of
vaporization of water in the combustion products. Fuel
properties such as Cetane number, a measure of the fuel’s
ignition delay and combustion quality, and its fuel standard is
a minimum of 40 (Meher et al., 2006; Ramos et al., 2008).
The high value of 71.03 obtained in this study showed the oil
has high fuel potential.
V. CONCLUSION
Dacryodes edulis seeds oil extraction showed the highest
oil yield of 17.878% (w/w) at solvent volume of 200 ml,
sample weight of 50 g and extraction time of 55 min,
respectively. However, response surface methodology
predicted an oil yield of 17.826 % (w/w), while the artificial
neural network predicted 17.875 % (w/w) at the same
variables condition. The predicted values were validated in
triplicate, and an average of 17.46 % (w/w) and 17.72%
(w/w) were obtained for RSM and ANN, respectively. The
predicted values obtained were well within the range
predicted. The coefficient of determination, which determines
the model accuracy, was obtained to be 0.8454 for RSM and
0.8712 for ANN. Physicochemical analysis of the oil showed
the oil is highly unsaturated with high saponification value
and high iodine value.
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OHIAMBE et al: ASSESSING THE SURFACE RAINWATER HARVESTING POTENTIAL FOR ABUJA, NIGERIA 63
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.3
ABSTRACT: This study aimed at assessing the surface rainwater harvesting potential in Abuja as a means of
mitigating the problem of water scarcity. Surface rainwater harvesting potential for the year 2046 was assessed using
Geographical Information System (GIS) and Spatial Multi-criteria Evaluation (MCE). The criteria considered were
annual rainfall, land use/land cover (LULC), slope and soil. The spatial MCE was used to estimate the extent of
surface rainwater harvesting and rank the potential. Analytical Hierarchy Process (AHP) was employed to determine
the priority weights of the criteria which gave; rainfall 55.9%, LULC 26.3%, slope 12.2% and soil 5.7%. A potential
map for surface rainwater harvesting was produced showing moderate, good and excellent with the percentages of
Abuja 10.7, 34.4 and 54.9% respectively. After considering an increased rainfall from (1170 mm-1470 mm) in 2016
to (1230 mm-1910 mm) in 2046, expansion in built-up areas, bare surfaces due to urbanisation and population
growth, the result showed that Abuja will have a minimum of 5.8 billion litres of water harvestable from rainfall per
year which is about 14.8% increase compared to the estimated harvestable quantity for 2016. Therefore, the potential
for surface rainwater harvesting in 2046 is significantly greater than it was in 2016.
KEYWORDS: Surface Rainwater Harvesting Potential, Water Scarcity, Analytical Hierarchy Process, Multi-Criteria
Evaluation.
[Received May 14, 2018; Revised September 07, 2018; Accepted September 27, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110
I. INTRODUCTION
Water is an important resource in every area of life, it is
essential for all aspects of life ranging from agriculture to
commerce, manufacturing and several types of energy
including electrical energy. The existence of humans, animals
and plants is solely dependent on water (Pandey et al., 2003;
Rutherford, 2000). As important as water is, it cannot be
manufactured yet it can be polluted, recycled, desalinated or
treated (Eletta et al., 2018). Even though water is never lost,
different parts of the world are experiencing water scarcity as
a major environmental problem (Mahmoud and Alazba,
2014).
Water scarcity is an inequality of supply in response to
demand for water with respect to existing institutional
arrangements and prices; where demand is excessively high
compared to available water supply; especially if the supply
potential is difficult or expensive to tap (Stratfor, 2018; Food
and Agriculture Organisation, 2010; Kisakye et al., 2018).
Water scarcity can be caused by artificial and natural causes.
The artificial causes are basically human activities and
behavior while natural causes include geographical terrain
and climate (Eletta et al., 2018; Stratfor, 2018). In Nigeria
water scarcity problem is also prominent especially in the
ASAL regions which are situated in the northern part of the
country. However, the water scarcity issue in Abuja is unique
because Abuja is not classified as an ASAL region. In fact,
Abuja actually experiences an average annual rainfall of
about 1100 mm-1600 mm and its temperatures are not as high
as the ASAL regions. But, the population growth in Abuja
has been very rapid within a short period. The population
grew from 107,069 in 1991 to 2,238,800 in 2011 which is
only 20 years and has grown even more to 3,564,100 in 2016.
Urbanization has led to a lateral expansion of the cities which
is leading to a higher demand for water, strain on the existing
water sources and distribution systems. In recent times, both
urban and rural areas in Abuja have suffered from water
scarcity, this is because the rate at which the available water
is consumed is significantly greater than the rate at which the
tapped sources are replenished.
During the Pan-African Conference on Water in Addis
Ababa, 2003, and at the African MDGs on Hunger meeting in
2004, rainwater harvesting was identified as an important
way of meeting the African Water Vision of minimizing
water scarcity and reducing poverty (Maimbo et al., 2005). In
Abuja, since the problem of water scarcity is as a result of an
increase in population and expansion of the cities and towns,
rainwater harvesting would be ideal as it will provide water
close to where it is needed. Rainwater harvesting is the
systematic concentration, collection and storage of rainwater
Assessing the Surface Rainwater Harvesting
Potential for Abuja, Nigeria: A Short-term
Projection E. Ohiambe1*, P. G. Home1, A. O. Coker2, J. Sang1
1Pan African University of Basic Science, Technology and Innovation, Jomo Kenyatta University of
Agriculture & Technology, Nairobi, Kenya. 2Department of Civil Engineering, University of Ibadan, Ibadan, Nigeria.
64 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author’s e-mail address: [email protected] doi: http://dx.doi.org/10.4314/njtd.v15i4.1
Figure 1: Location of Abuja in Nigeria (inset), River Niger and Benue and the rainfall grids in Abuja.
and surface runoff for different uses by linking the collection
area or runoff catchment area with the storage facility or
runoff receiving area (Mbilinyi et al., 2005). Rainwater
harvesting is not a new concept, it is an ancient practice
which can be traced back thousands of years BC. Harvested
rainwater was used for many purposes, including drinking
(both for animals and humans alike), domestics, agricultural,
prevention of environmental issues like minimize risk of
drought ASAL areas, flooding, erosion (Intergovernmental
Panel on Climate Change, 2007). It was also used as a means
for groundwater recharge (Rainwater Harvesting, 2006;
Rutherford, 2000). Rainwater harvesting is being encouraged
and promoted in many countries including China, Brazil,
Australia and India.
In New Delhi and Chennai, India, it is mandatory to have
a rainwater harvesting plan for a building plan to be
approved. Rainwater can be harvested through several
mediums, all of which can be summed into three major
categories; roof tops, surface and in-situ rainwater harvesting
(Gould and Nissen-Peterson, 1999; Maimbo et al., 2005).
Surface rainwater harvesting provides natural soft water
which can serve all non-potable water usages. It involves the
collection of runoff from open surfaces such as roads, home
compounds, hillsides, rocks, open pasture lands, bare grounds
(Gould, 1992; Pacey and Cullis, 1989). It may also include
collecting runoff from water courses and gullies. It is an
intervention that could be implemented almost anywhere and
by anyone; however, it would be better implemented by
governmental bodies so that it can be done in large scales to
collect more water from strategic locations. To harvest
rainwater the climatic conditions of a place should be studied
and understood (Gould and Nissen-Peterson, 1999).
The present climatic condition of Abuja is such that
rainwater harvesting can be implemented effectively.
However, climate change might affect rainfall in Abuja either
positively or negatively. Climate change is a change in the
statistical distribution of weather patterns usually over a
short-term period of at least 30 years (Australian Academy of
Science, 2018). The Global climate change estimates show a
variation in weather patterns but most of the estimates concur
that some areas will have increased precipitation while others
will experience a drought (Kisakye et al., 2018). A short-term
projection of the climate change in Abuja will help to
estimate if the change will affect RWH potential positively or
negatively.
Therefore, the objective of this research was to assess the
surface rainwater harvesting potential in Abuja by
considering the short-term (at least 30 years), in which
significant change in climate and land use/land cover could
occur. The aim is to inform decision makers of an additional
source of water to minimize water scarcity and ultimately
balance the existing imbalance between supply and demand
of water in Abuja. This can be done by assessing and
highlighting potential sites for surface RWH. The selection of
potential areas depends on several factors including climate,
hydrology, topography, soils, socioeconomic criteria even
agronomy as highlighted. Mahmoud and Alazba (2014) citing
Kahinda et al. (2008). Several studies have used different
parameters. Mahmoud and Alazba (2014) used soil texture,
elevation, land use/land cover, slope, rainfall surplus and
potential runoff coefficient to identify in-situ rainwater
harvesting potential in Al-Baha, Saudi Arabia. Kahinda et al.
(2008) used soil texture, soil depth, rainfall, land cover
ecological importance to produce suitability maps for in-field
and ex-field rainwater harvesting.
Multi-Criteria Evaluation (MCE) plays a significant role
in life-problems, at some point almost every organization
from private to public sector are involved in the evaluation of
alternatives in decision making especially with conflicting
criteria (Udezo, 2017). Analytical Hierarchical Process
(AHP) is a MCE tool introduced by Saaty (1980). It is one of
the GIS databased MCE which sums and transforms spatial
data to a result decision (Mahmoud and Alazba, 2014). AHP
is the major decision-making tool employed in this study.
Weighted overlay tool is also another relevant for the
selection of potential sites for surface RWH. The overlay
process produces maps with ranks from 1-5 where 1 is the
lowest and 5 is the highest rank. However, some researchers
have classified these ranks using terms like unsuitable,
suitable, low, high, medium, moderate, poor, excellent
(Mahmoud and Alazba, 2014; Kahinda et al., 2008; Maimbo
et al., 2005).
II. MATERIALS AND METHODS
A. Study Area
Abuja is located in the North Central zone, at the center
of Nigeria just north of the confluence of the Niger and
Benue River with a total land area of 7,315 km2. Abuja, also
known as Federal Capital Territory (FCT) has six local
OHIAMBE et al: ASSESSING THE SURFACE RAINWATER HARVESTING POTENTIAL FOR ABUJA, NIGERIA 65
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.3
government areas; Abaji, Bwari, Gwagwalada, Kwali, Kuje
and Abuja Municipal as shown in (Figure 1). Abuja lies
between the range of 300-760 m above sea level, the highest
part of Abuja is in the northeast where there are major peaks
some above 760 m. Abuja has three distinct weather
conditions per annum; a warm, rainy season, a hot dry season
and a short period of harmattan between the rainy and dry
season. The rainy season begins in April till October, with
temperatures reaching about 28-30 C in the day and
temperatures range around 22-23 C at night, the total annual
rainfall is about 1100 mm to 1600 mm making it a potentially
good region for rainwater harvesting. During the dry season,
daytime temperatures can increase to 40 C and night
temperatures sometimes drop to 12 C (Cyblug, 2016).
B. Assessing the RWH Potential of Abuja
The criteria necessary in assessing the potential of RWH
are; rainfall data, land use maps, elevation maps, soil maps
(Maimbo et al., 2005; Mahmoud and Alazba, 2014). To
assess the surface RWH potential in the study area, the
following activities were carried out;
1) Rainfall forecast
The rainfall data is a relevant component in estimating
the rainwater harvesting potential for Abuja, however, in
order to estimate the rainwater harvesting potential for the
range of years 2046-2065, there must be a forecast of the
climatic conditions expected at that time. In this study, the
rainfall forecasted data was directly collected from the World
Bank Climate Change Portal (WBCCP) where the forecasting
had already been done. With the data, a spatial representation
of the rainfall was done on GIS using the Interpolated
Distance Weighted (IDW) which according to Mahmoud and
Alazba (2014) is a suitable method for the spatial
representation of rainfall. The extent was set to fit the study
area and the rainfall grids shown in Figure 1.
2) Slope data
The Shuttle Radar Topography Mission (SRTM) 30m
DEM of the study area was obtained from United State
Geological Survey/National Aeronautics and Space
Administration/Shuttle Radar Topography Mission
(USGS/NASA SRTM). The slope ranges were reclassified
into four (0-5, 5.1-10, 10.1-19 and 19.1-71.9) like
Mahmoud and Alazba (2014) giving a view of the flat,
moderate, steep and hilly regions in the study area using their
rise in degrees. This data is assumed to remain constant and
so was not be projected.
3) Land use/Land cover data
In this study the Landsat imagery was used to create the
land use/land cover (LULC) map for the study area. The
spatial resolution 30m of Landsat imagery is adequate for
vegetative analysis particularly, to identify vegetative cover
(Jonathan et al., 2017). Two scenes of Landsat images from
the Landsat7 and Landsat8 were acquired for the LULC of
the years 2001 and 2016 respectively. These were all
obtained online from the data archive of Global Land Cover
Facility (GLCF) under the United States Geological Survey
(USGS). The images acquired for the use of this study were
cloud free. The land use/land cover maps for the years 2001
and 2016 were created using the maximum likelihood
algorithm for supervised image classification on ERDAS
Imagine 2014 after forming a false color composite with
bands 4, 3 and 2 which are the infrared, red and blue bands
respectively. The image classification gave nine different
classes which helped to assess the changes in land use over
15 years (2001-2016).
4) Land use/land cover projection
LULC is an important component of the study of
rainwater harvesting as stated by Maimob et al. (2005) and
especially for this study because surface rainwater harvesting
technologies are dependent on the different land use and land
cover classifications. In this study, the LULC of the years
2001 and 2016 was used to aid the projection of the LULC
for the year 2046. After creating the LULC maps for 2001
and 2016, the Markov model on IDIRISI change was adopted
to produce the LULC for 2046 and the area occupied by each
LULC was calculated using the area calculator on IDIRISI.
Markov model is a reliable tool for simulating LULC change
in situations where changes and processes in the LULC prove
to be complex to describe (Logsdon, 1996).
A Markov process is one in which the later state of a
system can be defined simply by the immediately preceding
state. This is done by creating a transition probability matrix
for LULC change from one time to the next time. It shows the
characteristics of the change as well as serves as the
foundation for projecting to a future time-period (Dongjie et
al., 2008; Zhang et al., 2011; Huang et al., 2008; Muller and
Middleton, 1994). Markov model gives a simple
methodology with which a dynamic system can be dissected
and explained. Several researchers like Zhang et al. (2011)
and Jianping et al. (2005) have attested to the efficiency of
the Markov model.
5) Soil data
The soil map for Abuja was obtained from Harmonised
World Soil (HWS) database. There exist five soil types in
Abuja which are loam, sand, loamy sand, sandy clay and
sandy loam as stated by Kogbe (1978). The composite runoff
coefficient for different soil types in relations to slope and
land use was calculated using the information for runoff
coefficient given by Mohamed et al. (2014).
Composite runoff coefficient is given as;
𝐶 =𝐶1𝐴1+ 𝐶2𝐴2+⋯ 𝐶𝑛𝐴𝑛
𝐴𝑡𝑜𝑡𝑎𝑙 (1)
where: C is the composite runoff coefficient
C1 to Cn are the corresponding runoff coefficients for
different landuses, soil type or slope
A1 to An are corresponding areas of different landuses,
soil types or slopes
Atotal is the sum of the areas considered from A1 to An
(Odot Hydraulics Manual)
66 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author’s e-mail address: [email protected] doi: http://dx.doi.org/10.4314/njtd.v15i4.1
6) Application of the analytical hierarchical process
(AHP)
The Analytical Hierarchy Process (AHP) developed by
Saaty (1980) is a method used for analyzing and supporting
decisions in which several competing objectives are involved
with multiple available alternatives. The technique was used
on the basis of three principles: decomposition thereby
forming a hierarchy of decision, comparative judgment and
combination of priorities (Saaty, 1980).
The AHP and weighted overlay for assessing the surface
RWH potential was done using Saaty’s pairwise comparison
scale. The hierarchy is the final goal which is to determine
the potential for surface RWH. The next stage in the
hierarchy is the criteria needed to determine the potential. For
this study, the criteria used are rainfall, soil, slope and LULC.
The ranking in this stage helps to reclassify each of the
criteria maps into their different ranks. The advantage of this
hierarchical decomposition is simply to clearly understand the
decisions as well as results to be obtained, the criteria to be
used and the alternatives present (Decision Lens, 2015).
C. Determining Priorities Weight for each Criteria
The rainfall, LULC, slope and soil as determinant criteria
for rainwater harvesting potential are of different importance.
The second step in the AHP process is to determine the
relative weight of each criteria. This is called relative weight
because the derived criteria priorities are measured with
respect to each other.
1) Pairwise comparison for surface RWH
This is the comparison between the criteria used for the
analysis. Table 1 shows the pairwise comparison matrix of
the criteria for surface RWH. The weight of each criterion is
obtained using the normalized matrix generated from Table 1.
The average value of each row in the normalized matrix is the
weight.
The second stage is the calculation for the weight of each
criterion used in the pairwise comparison. It is obtained by
summing up the values in each column, a normalized matrix
is formed by dividing each value in the pairwise comparison
matrix by the total of its column as shown in Table 2.
2) Consistency
Once judgment is made and the criterion weights
obtained, it is important to verify the consistency of the
judgment made. This is illustrated below.
a) Start with the matrix showing the judgment
comparisons and derived weights which is presented in
Table 1.
b) Use the weights as factors (priority) for each column.
c) Multiply each value in the first column of the pairwise
comparison matrix in Table 1 by the first criterion
weight (i.e., 1 x 0.0565 = 0.0565; 3 x 0.0565 = 0.1694;
5 x 0.0565 = 0.2823; 7 x 0.0565 = 0.3952) multiply
each value in the second column with the second
weight; continue this process for all the columns of the
comparison matrix (in our case, we have four
columns).
d) Add the values in each row to obtain a set of values
called the weighted sum
e) Divide the values of the weighted sum vector (obtained
in the previous step) by the corresponding weight of
each criterion. Calculate the average of the values from
the previous step; this value is called λmax.
λmax = (4.0290 + 4.0203 +…4.2109)/4 = 4.1057.
f) Then we calculate the consistency index (CI) as
follows:
CI= (λmax - n) / (n-1) (2)
Where n is the number of compared elements (in
this example n =4).
Consistency index is therefore,
CI= (λmax - n) / (n-1) = (4.1057-4) / (4-1) = 0.0352
g) Now, the Consistency Ratio can be calculated thus:
CR = CI/RI (3)
CR = 0.0352/0.9 = 0.0396
where the Random Index (RI) is 0.89 for n=4
given by Saaty (1980) and Mahmoud & Alazba
(2014).
Since this value (0.0396) for the proportion of
inconsistency CR is less than 0.10, we can assume that our
judgments matrix is reasonably consistent, so we may
continue the process of decision-making using AHP
(Mahmoud and Alazba, 2014).
3) Weighted Overlay Process
The Weighted Overlay Process (WOP) allows the
implementation of several steps in the general overlay
analysis process all in one tool. It combines the following
steps:
a) It reclassifies values in all input raster layers
(rainfall, LULC, slope, soil) into a common
evaluation scale of suitability or preference.
b) It multiplies the values of the cells in each input
raster file by the raster’s weight of importance.
c) It then sums the resulting values of each cell to
produce the final raster file which is the suitability
raster file (Udezo, 2017).
Assuming Point A in the study area of the four criteria
maps used in the AHP example above have a ranking of 5 in
all four maps, (i.e., the rain class as 5, LULC class 5, slope
class 5 and soil class also 5) the overlay result would show
Table 1: Pairwise judgment matrix and weights.
Surface RWH Soil class Slope class LULC class Rain class
Soil class 1 0.33 0.2 0.14
Slope class 3 1 0.33 0.2
LULC class 5 3 1 0.33
Rain class 7 5 3 1
Column addition 16 9.33 4.53 1.67
Table 2: Normalized Matrix.
Surface
RWH
Soil
class
Slope
class
LULC
class
Rain
class
Weight
Soil class 0.0625 0.0354 0.0442 0.0838 0.0565
Slope class 0.1875 0.1072 0.0728 0.1198 0.1218
LULC class 0.3125 0.3215 0.2208 0.1976 0.2631
Rain class 0.4375 0.5359 0.6623 0.5988 0.5586
OHIAMBE et al: ASSESSING THE SURFACE RAINWATER HARVESTING POTENTIAL FOR ABUJA, NIGERIA 67
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.3
that exact point to have a suitability of 5 (i.e., soil – 5 x
0.0565 = 0.2823… rain – 5 x 0.5586 = 2.7931). The final
potentiality value is the sum of the resulting values for all
criteria, in our example the suitability of Point A is 5.
The spatial distribution of the suitability map which
shows the surface RWH potential was done using spatial
Multi-criteria evaluation (MCE) to rank. The identification of
suitable sites was considered as a multi-objective and multi-
criteria problem (Mahmoud and Alazba, 2014). The quantity
of rainwater harvestable is given by the formula;
Qa = Ra x A x C (4)
where Qa is the annual harvestable rainwater, Ra is the
annual rainfall, A is the Area and C is the runoff coefficient
(Maimbo et al., 2005).
III. RESULTS AND DISCUSSION
A. Slope Map
The slope map generated using ArcGIS is presented in
Figure 2. The distribution of the slope for the study area
ranged from 0 – 71.86. This means there are areas with
steepness as low as 0 and hilly areas with steepness as high
as 71.86. Areas with steep slopes would allow for easy flow
of water along the path while water would stagnate around
areas with gentle slopes.
The slope maps were classified from 0 – 5, 5 – 10,
10 – 19 and 19 – 72 (Figure 2). The slope of the area
explains how rapidly water will move during the event of
rains, example areas above 5 will generate runoff quickly
which will increase the potential for surface RWH compared
to areas with slopes less than 5 which will result in the
increase of stagnated water (Mahmoud and Alazba, 2014).
B. Soil Map
The soil data for Abuja collected from Harmonised
World Soil (HWS) database showed five soil textural classes
which are clay loam, sand, loamy sand, sandy clay and a
predominant sandy loam as shown in Figure 3. The soil
textures with a higher percentage of sand allows infiltration
therefore has less runoff, while soil textures which limit
infiltration will lead to more runoff.
C. Forecasted Rainfall
The 2046 rainfall map in Figure 4 was created with the
forecasted rainfall data collected from World Bank Climate
Change Portal (WBCCP) for 2046 and the 2016 rainfall map
was created using satellite data from Tropical Rainfall
Measuring Mission (TRMM). They highlight the changes in
the precipitation between 2016 and 2046. In 2046, according
to (WBCCP), the minimum rainfall in Abuja would be about
1225 mm/year and the maximum would be 1908 mm/year.
The rainfall map for 2016 according to the rainfall satellite
data from Tropical Rainfall Measuring Mission (TRMM)
showed the minimum rainfall to be 1170 mm/year and the
maximum was 1470 mm/year.
The forecasted rainfall map in Figure 4 shows 5 different
ranges of the total annual rainfall for 2046 in Abuja. This
shows a more precise spatial view of the rainfall interpolation
in the study area (Maimbo et al., 2005). The global climate
change has made it widely accepted that changes in climate
will lead to intensified drought in some areas while others
would experience excessive rainfall which could lead to
Figure 2: Slope Map for identifying surface RWH potential.
Figure 3: Soil Texture for Abuja.
68 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author’s e-mail address: [email protected] doi: http://dx.doi.org/10.4314/njtd.v15i4.1
Figure 4: Abuja Rainfall maps for 2016 and 2046 respectively.
floods (Kisakye, 2018). From Figure 4, it is obvious that in
total there would most likely be an increase of the annual
rainfall in Abuja up till 2046 and beyond which will affect the
surface RWH potential positively.
D. Land use/land cover Map
The LULC map for 2046 signified distinct changes in the
areas occupied by each LULC class as shown in Figure 5 and
Table 3.
The areas occupied by each LULC class differ in size
from one year to another, some continuously increasing like
built-up areas, some decreasing and others varying from one
year to another as illustrated in Table 2. However, for classes
like built-up areas which were seen to be continuously
increasing, the explanation is obvious considering that the
population is increasing massively as a result of birth rate and
urbanization. The forested areas decreased between the years
2001 and 2016 due to deforestation problem in Nigeria and
Abuja specifically (Adeniyi et al., 2014; Mongaby.com 2018)
and so that decrease was reflected in the 2046 projection. The
LULC classes for 2046 is shown in Figure 5, having 9 classes
as the other years with which, it was predicted.
A. Surface rainwater harvesting Potential for 2046
The suitable sites for surface RWH are shown in Figure
6. Three categories were obtained in the surface RWH
potential map, moderate potential, good potential and
excellent potential. These categories were based on
reclassification of each criterion map, the weight of each
criterion and the weighted overlay of the criteria maps with a
minimum ranking of 3.1 and maximum of 5 after the overlay
operation. This means that every area in Abuja has at least
moderate potential (i.e. 3.1 of 5) for surface RWH. The
difference in RWH potential was based on the criteria
considered, rainfall, soil texture, slope and the LULC in the
areas. Some areas had less rainfall with 0 slope, sandy soil
texture and maybe wetlands. The area enclosed by the
moderate potential region was 781.6 km2, the area enclosed
by the sites with good potential was 2513.9 km2 while the
sites with excellent potential enclosed the largest area of
Figure 5: Projected LULC map for Abuja. Figure 6: Surface RWH Suitability Map for 2046.
OHIAMBE et al: ASSESSING THE SURFACE RAINWATER HARVESTING POTENTIAL FOR ABUJA, NIGERIA 69
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.3
about 4019.5 km2.
The spatial distribution showed minimum ranking to be
3.1 and maximum 5, this means that the entire study area was
above the average ranking for RWH potential. These areas
were classified as moderate, good and excellent adopting the
classification done by Mahmoud and Alazba (2014). The
percentage area enclosed by each class were estimated to be
about 10.7%, 34.4 and 54.9% respectively; making the whole
of Abuja 100% potentially viable for surface RWH. The
composite runoff coefficients for the suitable, more suitable
and most suitable sites were estimated to be 0.53, 0.62 and
0.72 respectively.
Therefore, quantifying the potential of surface rainwater
harvesting in terms of harvestable rainwater gave 5,840,287
m3 at minimum rainfall and at maximum rainfall 9,247,121
m3. This water can be harvested and used for several
purposes. This quantity shows that Abuja will be harvesting
about 14.8% more at minimum rainfall in 2046 than the
5,087,765 m3 it would have harvested in 2016. Although
every area in Abuja was found to have potential for RWH, a
larger part of Abuja was found to have an excellent potential.
IV. CONCLUSION
Identification of suitable sites for surface rainwater
harvesting is an important step towards minimizing water
scarcity in Abuja, Nigeria. Surface rainwater can be used to
provide water for all non-potable water needs very close to
where it is needed, which will reduce the stress on
distribution systems and stop the over exploitation of existing
and tapped water sources. The study showed within the years
2016 to 2046, the maximum annual rainfall of the state will
increase from 1470 mm to about 1908 mm due to climate
change.
The result showed that from 2016 to 2046, the rainwater
harvesting potential will increase by about 14.8%. Despite the
results of the potential Abuja has for RWH, some other
factors like environmental, socioeconomical and quality
factors need to be carefully considered to improve the
usefulness of these research findings. It is therefore
recommended that further study be carried out on the
environmental impact of RWH and the quality of rainwater in
Abuja.
V. ACKNOWLEDGMENT
The authors acknowledge both the African Union
Commission and Pan African University, Institute for Basic
Science Technology and Innovation (PAUSTI) for their
financial support to the first author towards the completion of
this research.
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ODETOYE et al: PYROLYSIS AND CHARACTERIZATION OF JATROPHA CURCAS SHELL AND SEED COAT 71
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.4
ABSTRACT: The utilization of dedicated energy crops and agricultural residues for producing biofuels and bio-oil in
a range of energy conversion technology is attracting more research interests. Pyrolysis is one of such important
thermochemical method for converting lignocellulosic biomass into biofuels. This work investigates the pyrolysis of
residues from a dedicated energy crop, jatropha of Nigerian origin using intermediate pyrolysis. Pyrolysis of
Jatropha biomass residues [Jatropha fruit shells (JFS) and Jatropha seed coat (JSC)] was carried out in a tubular
fixed bed reactor at a temperature of 450oC, using intermediate pyrolysis method. Bio-oils were obtained and
subsequently characterised for their physico-chemical properties. The yields of the resulting bio-oil, biochar and gas
were determined. The compositions of the bio-oils obtained were also determined by gas-chromatography mass
spectrometry (GC-MS) and carbon, hydrogen, nitrogen, sulphur (CHNS) elemental analysis. The main constituents
of the bio-oils obtained from JFS and JSC were acetic acid, guaiacol, 2,6-dimethoxyphenol and phenol. The
empirical formula of the obtained JFS and JSC bio-oils were found to be CH1.77 O0.28 N0.04 and CH2.03 O0.47 N0.04
respectively. The bio-oil samples that were produced from JSC and JFS of Nigerian origin were found suitable for
bio-oil production. Valuable compounds found in the bio-oils indicated potential industrial applications.
KEYWORDS: Jatropha shell, pyrolysis, biomass waste, biofuel, bio-products.
[Received June 29, 2018; Revised September 10, 2018; Accepted October 23, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110
I. INTRODUCTION
The utilization of biomass as alternative renewable
energy source to meet growing energy needs and to reduce
carbon emission, has attracted global attention in recent times
due to its economic potential and environmental concerns
(Titiloye et al., 2013; Odetoye et al., 2014; Aysu et al., 2016;
Thapa et al., 2018). Biomass is an important source of
energy especially in the developing countries (Akinrinola et
al, 2014).
Jatropha curcas is a widely cultivated plant for energy
purpose as it has been regarded as one of the most suitable
feedstocks for biodiesel production (Pambudi et al, 2017).
Extensive studies have been done on the production of
biodiesel from jatropha oil (Ajala et al., 2015; Thapa et al.,
2018), therefore several researches have been extended
towards the utilization of biomass residues generated from
Jatropha fruits and seeds (Biradar et al., 2014; Adinurani,
2015; Kaewpengkrow, 2017; Patel, 2018).
In Nigeria, jatropha has been listed as one of the
potential feedstocks considered for biofuel production and
diversification of the monolithic petroleum-based economy
by the Government (PPRA, 2010, Ohimain, 2013). More so,
jatropha grows locally in Nigeria and the oil yields of up to
53% had been reported for jatropha of Nigerian origin
(Aransiola et al., 2012; Somorin et al., 2017). Subsequently,
large scale cultivation of jatropha has been recently embarked
on by the Nigerian Government to encourage the industrial
application of the seed oil for biodiesel production (Lateef et
al., 2014). Jatropha seed coat and the fruit shell are wastes
generated during the processing of jatropha oil that can be
converted to bio-oil as value added product (Patel et al.,
2018).
One of the effective technologies for converting such
biomass wastes to bio-oil is by pyrolysis, a method which
involves thermal decomposition of the lignocelluosic biomass
waste in the absence of air at high temperatures of about 400 oC (Aysu et al., 2016; Patel et al., 2018). Two main types of
pyrolysis technology widely practiced had been the slow and
fast pyrolysis (Yang et al., 2014; Abu Bakar and Titiloye,
2013). The classification was based on the variation in
heating rate, residence time and the product distribution
(char, bio-oil, gas). Fast pyrolysis involves rapid cooling of
the short-residence-time-heated finely ground biomass to
room temperature so as to obtain higher yield of the liquid
products. Slow pyrolysis which is characterised by longer
residence time, produces higher yield of char. Intermediate
pyrolysis is a recently emerged pyrolysis technology which
offers the opportunity of process integration as extended
involvement of char in the pyrolysis process seems to
Pyrolysis and Characterization of Jatropha Curcas
Shell and Seed Coat T. E. Odetoye1,2*, M.S. Abu Bakar1,3, J. O. Titiloye1,4
1European Bioenergy Research Institute, CEAC, Aston University, Birmingham, B4 7ET, United Kingdom. 2Department of Chemical Engineering, University of Ilorin, PMB 1515, Ilorin, Nigeria.
3Faculty of Integrated Technologies, Universiti Brunei Darussalam, Jalan Tungku Link, Gadong, BE1410,
Negara Brunei Darussalam. 4Chemical & Environmental Engineering, College of Engineering, Swansea University, SA1 8EN, United Kingdom.
72 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author’s e-mail address: [email protected] doi: http://dx.doi.org/10.4314/njtd.v15i4.1
improve the bio-oil quality. This is a technology that has
recently been patented by Aston University, the designer of a
Pyroformer, an intermediate pyrolysis reactor (Yang et al.,
2014).
Although several works have been done on pyrolysis of
Jatropha of various origins (Sing et al., 2008; Manurung et
al., 2009; Murata et al., 2011; Wever et al., 2012), there is
dearth of report about bio-oil production from Jatropha
wastes of Nigerian origin. This study investigates the
suitability of the biomass residues of Jatropha of Nigerian
origin for the production of bio-oil via intermediate pyrolysis.
The intermediate pyrolysis method on a fixed bed reactor was
chosen over fast pyrolysis method because the method is
relatively more affordable for growing economies.
II. MATERIALS AND METHOD
A. Materials preparation
The jatropha fruit shell (JFS) and jatropha seed coat
(JSC) residues were obtained from the matured jatropha fruits
collected at Ilorin, Kwara State, Nigeria. 5 kg of the residues
were sundried for five days and ground using Fritsch blade
heavy-duty cutting mill (USA) fitted with a 2 mm particle
size screen and characterized according to standard methods
as reported in another work (Odetoye et al., 2018).
B. Pyrolysis
The intermediate pyrolysis experimental set up
was as shown in Figure 1. The experiments were carried out
on a bench scale fixed – bed vertical tubular reactor at
reaction temperature of 450 oC. The internal diameter and
height of the quart glass reactor was about 8 cm and 35 cm,
respectively. The reactor was filled with 90 g of JFS or JSC
as required. A Carbolite vertical split furnace was used as a
source of heating while the reactor temperature and pressure
were monitored by AALBORG model DFM digital monitor.
Nitrogen gas flow into the reactor was maintained at a flow
rate of 50 cm3/min. The heating rate of the reactor was 25 oC/min while the residence time was 25 minutes. The primary
condenser was cooled with dry ice to enable the collection of
condensable bio-oil in the oil pot while the non-condensable
gases were scrubbed with isopropanol before sending a
stream of the gases to the GC-MS HP Series 5890 for
analysis. The remaining gases were vented through the fume
cupboard.
The bio-oil yield was obtained considering the oil
entrapped in the glass wares, condensers, by weighing each
part of the glassware apparatus before and after each
pyrolysis experiment since the pyrolysis procedures included
setting up and running the experiment with a good
consideration of mass balance. The mass of the bio-oil,
biogas and biochar produced were accounted for by
measuring the mass of each component of the apparatus
(reactor tube, connecting tubes, and oil pots) before and after
each pyrolysis experiment. The biogas was also accounted for
by difference (Abu Bakar and Titiloye, 2013).
C. Characterization of bio-oil
The bio-oils obtained were characterized to determine the
quality and composition. The following characteristics were
determined: acid number, pH value, density and water
content determinations. Acid number, pH value, density and
water contents were carried out using apparatuses based on
standard methods. The acid number of the oil was determined
using Mettler Toledo acid number analyser G20 Compact
Titrator, which was based on the standard method ASTM
D664-04 (ASTM, 2011) for the determination of acid number
in motor oil while the pH values of the bio-oils were
determined using the Sartorius pH meter model PB-11.
Mettler Toledo PortableLab Densimeter was used to
determine the density of the bio-oil. The water content of the
bio-oil was determined with Karl –Fischer volumetric
titration using a Metrohm 758 KFD Titrino water content
analyser that was based on the standard ASTM method
D1744 (ASTM,2011). The heating values of the bio-oil
samples as well as the elemental analyses of the samples were
carried out by MEDAC Ltd. Surrey, U.K. using standard
method on biomass characterization with Carlo-Erba 1108
elemental analyser. Metals and inorganic components were
also determined using a PerkinElmer Optima 7300DV
Induced Coupled Plasma (ICP) Emission Spectrometer.
The composition of the bio-oils produced were
determined using the Hewlett Packard 5890 Series II Plus
Gas Chromatograph incorporated with a Hewlett Packard
5972 mass selective detector. Helium was used as the carrier
gas with a DB 1706 non-polar capillary column. The initial
oven temperature was 40 °C and ramped up to 290 °C at a
rate of 3 °C/min. The injection temperature was held at 310
°C with a volume of 5µl. The dilution solvent used was
ethanol and the dilution rate was 1:5. Identification of
compounds in the spectral and chromatograph data was done
with the aid of NIST mass spectra database.
1 = primary reactor, 2 = secondary reactor, 3 = dry ice condenser, 4 = oil pot
1, 5 = secondary condenser, 6 = scrubber
Figure 1: Experimental set up for intermediate pyrolysis experiment
III. RESULTS AND DISCUSSION
A. Characterization of the bio-oils produced
The relatively semi-homogenous bio-oil obtained clearly
separates into aqueous and organic phases when stored. The
properties of the bio-oils obtained from Jatropha seed coat
and Jatropha fruit shells are as shown in Table 1.
ODETOYE et al: PYROLYSIS AND CHARACTERIZATION OF JATROPHA CURCAS SHELL AND SEED COAT 73
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.4
Figure 3: GC-MS chromatogram for Jatropha fruit shell.
Figure 2: Jatropha residue bio-oils from (a) JSC and (b) JFS.
The bio oil samples obtained from the JFS and JSC biomass
residues were dark brown in colour as shown in Figure 2.
The pH values of 5.3 and 5.8 of the Jatropha waste bio-
oils obtained for JFS and JSC are relatively higher than the
value of 3.3 obtained in literature for JSC (Manurung et al.,
2009). Higher pH values (as the values approach 7, being
neutral) are desirable for bio-oils since acidity can wear out
the engine components when the bio-oil is used as fuel.
Sulphur contents are desirably low in both JSC and JFS bio-
oils indicating that the formation of sulphur dioxide is at
lower risk (Tsai et al, 2018).
The higher heating value (HHV) of the Jatropha fruit
shell bio-oil (29.84 MJ/kg) is relatively higher than that
obtained for Jatropha seed coat (25.24 MJ/kg). However, the
heating values of both bio-oil samples prepared were
comparable to the value of 25.63 MJ/kg (Jourabchi et al.,
2016), 30 MJ/kg (Das et al., 2015) available in literature for
jatropha seed cake bio-oil.
Carbon contents were found to be desirably relatively
higher in JFS (62.4%) compared to JSC bio-oil (52.6%) while
the oxygen content was lower in JFS. The chlorine and the
sulphur contents were desirably low in both bio-oil samples.
Hence, there is a lower risk of sulphur dioxide formation
which can lead to environmental pollution (Tsai et al, 2018).
B. Composition of the Bio-oil Produced
Analysis of the bio-oil samples indicated the presence of
a vast number of complex mixtures of compounds which
include alkenes, phenols, carboxylic acids and their
derivatives. The GC-MS chromatograms for JFS and JSC
pyrolysis oils were as shown in Figures 3 and 4. The most
prominent peaks identified, corresponding chemical names,
retention time, chemical formulae, molecular weight and %
peak area measured are summarised in Tables 2 and 3.
Table1: Some physicochemical characteristics properties of the prepared Jatropha waste bio-oils.
Properties Jatropha Seed Coat
(This study)
Jatropha Fruit shell
(This study)
Jatropha Seed Coat
(Manurung et al., 2009)
Jatropha Seedshell cake
Kim et al., 2013)
pH 5.2 5.8 3.3
Density (g/cm3) 1.006 1.008
Water content (wt %) 18.47 21.76 23.3 Elemental composition (wt %)
C 52.6 62.4 65.6 65.8
H 8.89 9.19 9.5 8.92 N 2.29 2.73 0.9 5.62
O 33.04 23.14 nd 18.8
S 0.25 0.26 nd 0.19 Cl 2.93 2.31 nd
HHV(MJ/kg) 25.24 29.84 39
Empirical Formula CH2.03O0.47N0.04 CH1.77O0.28N0.04 H/C molar ratio 2.0 1.8 1.63
O/C molar ratio 0.47 0.28 0.11
74 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author’s e-mail address: [email protected] doi: http://dx.doi.org/10.4314/njtd.v15i4.1
The main identified components of the Jatropha seed
coat include dimethoxyphenol, guiacol and acetic acid while
the main identified components of the fruit shells are acetic
acid, 2-cyclopenten-1-one, phenol, guaiacol and 2,6-
dimethoxyphenol as shown in Figures 5, 6 and 7. These
compounds are characteristic components of bio-oil that are
candidates for biorefinery. They are useful precursor for
the synthesis of industrial products and can be used as fuels
chemicals and food bioproducts after refining (Demiral et
al, 2012). Guaiacol is useful for medicinal purposes, 2,6-
dimethoxyphenol has been recognized as a volatile flavor
component (Bridgwater et al., 2008) found in soy sauce,
wine and smoke.
Lignin which is a phenolic bio-polymer (Das et
al.,2015) was responsible for the phenolics and aromatics
constituents in the bio-oils. The presence of acetic acid, an
organic acid, undesirably contributes to low pH values in
bio-oils. Such relatively high content of acetic acid
indicates the need for upgrading procedure to be performed
on the oil prior to applications as fuel in engines (Odetoye et
al, 2014).
Figure 4: GC-MS chromatogram for Jatropha seed coat.
Table 2: Most prominent identified compounds of Jatropha Fruit Shell.
Peak
ID
RT
(min)
Compound Name Area
%
1 9.184 Acetic Acid 6.9
2 10.242 Hydroxyacetone 1.05
3 10.794 Toluene 1.12 4 11.518 Pyridine 1.79
5 15.059 Ethylbenzene 0.35
6 15.45 p-Xylene 0.44 7 16.462 Cyclohexanone 0.75
8 16.922 m-Xylene 0.23
9 20.659 2-Cyclopenten-1-one, 2-methyl- 2.89
10 21.452 2-Furyl Methyl Ketone 0.61
11 22.199 Mesitylene 0.24 12 25.545 3-Methyl-2-Cyclopentenone 0.66
13 25.717 3-Methyl-2-Cyclopentenone 3.04
14 26.718 3-Picoline 0.58 15 27.304 2,4-dimethyl-2-oxazoline-4-methanol
Maple lactone /2-hydroxy-3-methyl-2
2.11
16 28.776 Cyclopenten-1-one 4.64 17 30.351 Phenol 3.67
18 31.374 Guaiacol 2.83
19 32.869 2-Methylphenol 2.44 20 33.375 3-Ethyl-2-hydroxy-2-cyclopenten-1-
one
1.17
21 34.697 p-Cresol 1.95 22 36.996 2,4-Dimethylphenol 2.31
23 39.043 4-Ethylphenol 0.37
24 40.02 Decane 0.47 25 40.653 4-Ethylguaiacol 1.07
26 45.574 2,6-Dimethoxyphenol 2.63
27 60.141 4-Allyl-2,6-dimethoxyphenol 0.46
Table 3: Peak assignment for Jatropha seed coat bio-oil.
Peak ID RT
(min)
Compound Name Area %
1 6.771 2-butanone 1.33
2 9.105 Acetic Acid 14.68
3 10.796 Toluene 0.69 4 11.612 Pyridine 0.52
5 13.302 Hydroxyacetone 2.43
6 14.383 Cyclopentanone 1.66 7 14.498 1-hydroxy-2-butanone 1.74
8 17.602 2-Cyclopenten-1-one 2.86
9 19.913 2-Furanmethanol 3.25 10 20.66 2-Cyclopenten-1-one, 2-methyl- 2.06
11 21.454 2-Furyl Methyl Ketone 0.73
12 25.719 3-Methyl-2-Cyclopentenone 2.5 13 26.214 Tetrahydro-2-furanmethanol 1.13
14 28.778 cyclopenten-1-one 3.6
15 30.341 Phenol 4.31 16 31.365 Guaiacol 12.14
17 32.871 2-Methylphenol 2.53
18 33.377 3-Ethyl-2-hydroxy-2-cyclopenten-1-one
0.76
19 34.687 m-Cresol 3.52
20 36.573 Isocreosol / 5-methylguaiacol 3.12 21 38.746 2,4-Dimethylphenol 1.17
22 38.918 4-Ethylphenol 0.83 23 40.137 Dianhydromannitol 0.91
24 40.655 4-Ethylguaiacol 5.06
25 45.576 2,6-Dimethoxyphenol 6.04 26 49.163 Isoeugenol 2.57
27 49.611 1,2,4-Trimethoxy-benzene 2.13
28 52.75 1,2,3-trimethoxy-5-methylbenzene 1.97 29
55.9
2,4-hexadienedioic acid, 3,4-
diethyl-, dimethyl ester, (EZ)- 0.73
30 60.143 4-Allyl-2,6-dimethoxyphenol 0.72
ODETOYE et al: PYROLYSIS AND CHARACTERIZATION OF JATROPHA CURCAS SHELL AND SEED COAT 75
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.4
Figure 5: Main chemical constituents of Jatropha bio-oils.
0 2 4 6 8 10 12 14 16
Acetic Acid
Hydroxyacetone
Toluene
Pyridine
2-Cyclopenten-1-one, 2-methyl-
3-Methyl-2-Cyclopentenone
2,4-dimethyl-2-oxazoline-4-methanol
2-hydroxy-3-methyl-2-cyclopenten-1-one
Phenol
Guaiacol
2-Methylphenol
p-Cresol
m-cresol
2,4-Dimethylphenol
2,6-Dimethoxyphenol
Isoeugenol
JSC
JFS
Area %
Figure 6: Main ketones constituents of Jatropha bio-oils.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Hydroxyacetone
Cyclohexanone
2-Cyclopenten-1-one
2-Furyl Methyl Ketone
3-Methyl-2-Cyclopentenone
2-hydroxy-3-methyl-2-cyclopenten-1-one
2-Cyclopenten-1-one
2-Furyl Methyl Ketone
3-Ethyl-2-hydroxy-2-cyclopenten-1-one
JSC
JFS
Area %
76 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author’s e-mail address: [email protected] doi: http://dx.doi.org/10.4314/njtd.v15i4.1
Figure 7: Phenols and its derivatives in Jatropha bio-oils
0
2
4
6
8
10
12
14
JFS
JSC
V. CONCLUSION
Jatropha wastes (seed coat and fruit shell) of Nigerian
origin, have been found suitable for use as renewable energy
feedstock with potential for bio-oil production. The
characteristics of the bio-oils produced were found to be
similar to those reported in literature. The presence of
valuable compounds such as phenolic compounds suggests
useful potential for industrial applications. Jatropha fruit shell
(JFS) and Jatropha seed coat (JSC) bio-oils need to be
upgraded before they can be utilized as a fuel substitute
particularly in engines as they consist of various complex
organic compounds with varying composition. This work has
provided database on some properties of Jatropha residues
bio-oils of Nigerian origin, that are applicable for bio-energy,
bio-refinery, waste management and vegetable oil industries.
VI. ACKNOWLEDGEMENT
The authors are thankful for the financial support
obtained from European Bioenergy Research Institute/School
of Engineering and Applied Sciences, Aston University,
Birmingham, UK.
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78 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.5
ABSTRACT: Recent catastrophic events, involving the accidental loading of structures caused either intentionally for
example aircraft crashes on structures, blast loadings, or unintentionally due to object impact, gas explosions etc, has
changed our view from something connected to the stage of war to a much more domestic scene. This makes it
imperative to study the response of structural elements under such accidental loading conditions in an attempt to
assess structures vulnerability and characteristic performance. The study presented in this paper investigates the
response of steel beams under impact loads by using the energy principles in assessing the capacity of the steel beam
to absorb impact energy in deflecting before fracture ensues. In addition, the point at which the ductile material is
considered to have failed was also examined, in an attempt to give safety recommendations to steel structures under
impact. This study also looks at the evaluation of dynamic loads, different impact scenarios, behaviour of steel
material at high strain rates (i.e. dynamic increase factor DIF) as well as influence of joint rotation on failure. The
findings from this study show that the maximum strain energy beyond which the beam is considered to have failed is
largely influenced by joint rotation.
KEYWORDS: Structural behaviour, Impact scenario, High strain rate, Joint rotation and Dynamic load.
[Received April 26, 2018; Revised August 06, 2018; Accepted September 04, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110
I. INTRODUCTION
Impact loads are dynamic in nature. They are generally
of great magnitudes and usually of very short duration with a
time rise of typically less than a second, so that it is the
response of structures to such loading which produces large
inelastic deformations leading to failure, which is of
particular interest to engineers (Johnson, 1972). In studying
the dynamics of impact, ‘the critical factor is not the stress
distribution in the elastic range but the capacity of the
structure to absorb energy without collapse and that the proof
resilience of a ductile continuous structure is insignificant in
comparison with energy that can be absorbed in the elastic-
plastic range’ (Baker, 1948).
An understanding of this concept of energy absorption by
structural elements will enable structural engineers to predict
likely responses of structures subject to impact loading, thus
facilitating their design to sufficiently withstand the effect of
impact load, ensuring the safety of personnel and valuables
(Corbett et al. 1996). Generally, structures having low
frequencies when loaded very rapidly, fails in a sudden brittle
manner as the structure does not have sufficient time to react
to rapid low period (less than 0.05 s) high frequency loads; in
this scenario the localized effects are considered more
dominant (Wessman and Rose 1942).
However, where the period of impact loading is high
(e.g. < 2 s) and the frequency of loading is low, the structure
is able to respond in a ductile manner before brittle fracture.
This study is however, limited to a low frequency high period
impact loading of a steel beam from an impactor generated
missile. The aim here is to investigate the deformation (i.e.
the strain energy absorption capacity) of the steel beam in
absorption of impact energy before brittle fracture ensues and
the influence joint rotation has on failure in other to give
safety recommendations that will guard against such failure.
For this study, the strain energy model developed by Mugah
et al. (1994) was adopted and the results validated using
ANSYS nonlinear finite element package.
II. ANALYSIS PROCEDURE
For this study the impact loads were as a result of
concrete cubes of specific weights dropped from the
following heights: a 500 kg concrete cube dropped from a
height of 15m; a 1 tonne concrete cube dropped from a height
of 20 m and a 2 tonne concrete cube dropped from the highest
point of 25m The concrete cubes used for this study had a
self-weight of 25 kN per cubic meter (Mosley et al 2007).
The steel beam which was 30 m long was impacted at the
following positions; at the quarter span and mid-spans as this
is where the main connections for the beam are located.
Although it is not possible to predict the actual size of
impactors in actual impact situations, for this study however,
the following sizes of impactors were selected and dropped
from the above respective heights.
Design Recommendation for Steel Beams Subject to
Impact Load to Prevent Brittle Fracture
Ohunene Hafsa Aliyu*
Department of Building, Federal University Birnin Kebbi, PMB 1157, Kebbi State, Nigeria.
ALIYU: DESIGN RECOMMENDATION FOR STEEL BEAMS SUBJECT TO IMPACT LOAD 79
*(corresponding author) [email protected] doi: http://dx.doi.org/10.4314/njtd.v14i2.1
Figure 1: The size of impactors dropped onto the steel beam at different
positions from different heights.
The velocity of impact was evaluated using the technique
suggested by Jones (1993). In his views, the velocity of
impact resulting from dropped weights can be evaluated
using the principles of conservation of energy which is
normally derived from the following principle.
𝐾. 𝐸 𝑔𝑎𝑖𝑛𝑒𝑑 = 𝑃. 𝐸 𝑙𝑜𝑠𝑡 𝑖. 𝑒. Mgh = 1
2M𝑣2 (1)
Figure 2: The portal frame roof (rafter beam) as datum level.
III. THE ANALYTICAL MODELLING
A. Structural Response Due to Impact Loading
Since the response of a structure to dynamic (impact)
load depends as much on the dynamic properties of the
structure as well as on the force-time history of the applied
loading, in establishing the principles for predicting these
structural responses, a number of simplifications have been
made to facilitate the analysis procedure which includes the
following: idealization of the structure to an equivalent single
degree of freedom system, the force-time and resistance
functions where possible are expressed in simple
mathematical forms, idealization of the deformation
characteristics in terms of an elasto-plastic resistance function
B. Single Degree of Freedom (SDOF) System
The simplest representation of discrete transient
problems is by means of a single degree of freedom system.
Although, only a small number of structures respond in this
manner because structures ideally have distributed masses
and stiffness characteristics but, in such situations, the actual
structure is replaced by an equivalent single degree of
freedom system where the structural elements are idealized in
terms of equivalent concentrated mass, load and resistance
displacement function. The response of the actual structure
will then be obtained by use of transformation factors which
offers a comparable system for analysis. The equation of
motion for the equivalent single degree of freedom system is
formed using the actual system properties given as:
𝑀𝑒�̈� + 𝐾𝑒𝑥 = 𝐹𝑒(𝑡) (2)
Figure 3: Single degree of freedom system.
C. Effective Mass
Effective mass (𝑀𝑒) is used to ensure a balance of
kinetic energy between the equivalent and actual system. The
ratio of these masses however, gives the mass factor (𝐾𝑚 )
𝐾𝑚 = 𝑀𝑒
𝑀𝑡⁄ (3)
In their full deformation mode, the assumed deflected
shape is taken to be the same as that resulting from the static
application of the dynamic loads. For this study where the
stress wave travel time 𝑡𝑐 is much less than the duration of
impact 𝑡𝑖 the deflected shape during impact is approximated
from the first mode shape. Therefore, (𝑀𝑒) is given as:
𝑀𝑒=𝑘𝜔2⁄ or 𝑀𝑒 = 𝑘 ⌊𝑇𝑛
2𝜋⁄ ⌋2 (4)
D. Effective Load
The effective load as used in the expression in
equation (1) is obtained by equating work done by actual
system in deflecting to the assumed deflected shape, to the
work done by the equivalent system. The load factor 𝐾𝐿 is
given as the ratio of equivalent load to actual load and can be
based on either the elastic or plastic deformation shape.
𝐾𝐿 =𝐹𝑒
𝐹𝑡⁄ (5)
E. Effective Resistance
The resistance of an element is the materials internal
force (strength), tending to restore the element to its unloaded
equilibrium position. The equivalent stiffness and maximum
resistance are defined in terms of the actual load distribution,
such that 𝐾𝑅 equals the load factor 𝑘𝐿.
𝐾𝑅 = 𝑅𝑚𝑒
𝑅𝑚⁄ = 𝑘𝐿 (6)
𝐾𝑅 = 𝐾𝑒
𝐾⁄ = 𝑘𝐿 (7)
F. Natural Period of Vibration
The natural period (𝑇𝑛) of the equivalent system is given
by (Mughal et al. 1994):
𝑇𝑛 = 2𝜋√𝑀𝑒𝐾𝐸
⁄ = 2𝜋√𝐾𝑀𝑀𝑡
𝑘𝐿𝐾⁄ = √𝐾𝐿𝑀𝑀𝑡
𝐾⁄ (8)
𝐾𝐿𝑀 is the load-mass factor = 𝐾𝑀
𝐾𝐿⁄ (9)
80 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.5
The maximum response of the equivalent system to dynamic
load (i.e. excitation force) is usually measured in terms of
displacement, velocity, and acceleration.
G. Material Behaviour at High Strain Rates
Impact loading according to Johnson (1972) tends to
produce strain rates in the range of 102/𝑠𝑒𝑐. Some materials
are however strain rate sensitive; a condition where the
materials stress versus strain relationship is highly dependent
on the rate of loading. Wei et al. (1992) however suggests
that because mild steel materials are highly strain rate
sensitive, their effect needs to be accounted for under impact
situations which according to Li et al. (2005) is best
addressed through the use of a dynamic increase factor (DIF).
This is the ratio between the unconfined dynamic uniaxial
compression strength and its corresponding quasi static value.
H. Dynamic Properties of Steel under High Strain Rates
Scholars such as (Johnson 1972 and Mughal et al. 1994)
are of the opinion that materials tend to behave differently
under dynamic loading situations than their more familiar
behaviour under static loading. Mughal et al. (1994), further
went on to say that this variation in behaviour represents the
increase in strength observed in these materials over their
characteristic value which can be accounted for in design by
basing the dynamic capacity of structural members on their
dynamic properties which as mentioned earlier can be
obtained by applying a DIF to the static strength value i.e.
𝑓𝑦𝑑𝑛 = 𝐷𝐼𝐹𝑓𝑠𝑡𝑎𝑡; 𝜎𝐷
𝜎𝑆⁄ = DIF (10)
where: 𝑓𝑦𝑑𝑛= Allowable dynamic strength; 𝑓𝑠𝑡𝑎𝑡=
Allowable static strength.
Johnson (1972) has tried to explain this phenomenon of
strength increase above their characteristic value by saying
that a delay in time usually exists between the time of load
application and the onset of plastic flow in low carbon steels
which is particularly important when considering the impact
loading of mild steels beams.
I. Ductility Requirement
The term ductility according to the United States
Department of Defence in “The effects of nuclear weapons”,
(1964) can be described as the ability of a structure or its
component members to absorb energy in the inelastic range
without fracture, implying that the more ductile a structure or
its components are, the more its resistance to failure. In
simple terms however, ductility can be viewed in terms of
displacement. In considering the example a single degree of
freedom system with a clearly defined yield point, the
displacement ductility (𝜇), can be expressed as the ratio of
displacement at first yield to maximum displacement.
where: 𝜇 =𝑋𝑚
𝑋𝑒⁄ is the allowable ductility and
𝜇′ =12 is the maximum ductility (Mughal et al. 1994)
In design it is essential to ensure that the ductility supply
be greater than the ductility demand. Where ductility supply
is the maximum ductility that the structure can sustain
without collapse implying that it is only a structural property
independent of the impact load. Ductility demand on the
other hand is the maximum ductility that the structure
experiences during impact and as such a function of both load
and structure.
Figure 4: Idealized Resistance displacement curve for an elastic-
plastic SDOF system (adapted from Mughal et al. 1994).
J. Analysis Method
The method adopted for this study was based on the
energy and momentum balance solution which is an
analytical approach. According to Mughal et al. (1994) this
procedure should ideally give the upper bound estimate of the
structural response. It involves establishing the displacement,
𝑋𝑚 at which the available strain energy of the system equals
the Kinetic Energy of the system after impact(𝐾𝐸′). The
upper limit estimate of 𝐾𝐸′ was however, determined by
assuming that the resisting spring back force (𝑅𝑥), did not act
during impact and that the coefficient of restitution ‘e’ was
zero which characterised the impact situation as a completely
inelastic collision between two solid bodies namely a missile
with velocity 𝑉𝑆 and mass 𝑀𝑚 striking a beam of mass 𝑀𝑒
which originally was at rest. The kinetic energy of the system
after the completely inelastic impact is derived from the
expression
𝐾𝐸′= 𝑀𝑚
2𝑉𝑆2
2(𝑀𝑚+𝑀𝑒) (13)
Since the coefficient of restitution was assumed to be
zero and given the fact that an elasto-plastic response was
assumed. The maximum displacement 𝑋𝑚 at which the
available strain energy equalled the kinetic energy was
derived from the expression.
𝑋𝑚=𝐾𝐸′
𝐾(𝑋𝑒−𝑋𝑜)+
𝑋𝑒+𝑋𝑜
2..14 𝑋𝑚 >
𝑋𝑒
𝜇 =𝐾𝐸′
𝑅𝑚(𝑋𝑒−𝑋𝑜) +
𝑋𝑜
2𝑋𝑒+ 1
2⁄ (15)
Available strain energy capacity of beam was obtained
by equating the internal strain energy (U) to the external work
done by the impactor.
(16)
The maximum allowable displacement 𝑋𝑚 is obtained from
the allowable ductility ratio given by 𝜇 where 𝜇 =𝑋𝑚
𝑋𝑒
ALIYU: DESIGN RECOMMENDATION FOR STEEL BEAMS SUBJECT TO IMPACT LOAD 81
*(corresponding author) [email protected] doi: http://dx.doi.org/10.4314/njtd.v14i2.1
Figure 5: Resistance displacement function with associated structural
response with effect of other loads. Adapted from Mughal et al (1994:
53).
Where: 𝑋𝑜 = displacement due to other loads; 𝑋𝑒= yield
displacement; 𝑋𝑚= maximum combined displacement; 𝑅𝑚 =
yield resistance; 𝐾 = elastic spring constant; Μ = ductility
ratio. However, adequacy of the beam under the impact load
was checked by ensuring that the strain energy (𝑆𝐸) utilized
in resisting the impact loading was not greater than half the
available strain energy at failure(𝑆𝐸𝑓). Conversely, according
to Mughal et al. (1994) when the strain energy is analytically
defined then the strain energy should not exceed 0.5𝑆𝐸𝑓.
IV.MODEL SIMULATION
A. Plastic Deformation
For large plastic deformations to be acceptable, the
stability of the structure under investigation must be assured.
With this type of deformation, the behaviour of the beam is
most likely to change from bending to centenary actions.
(This is a curve that an idealized hanging chain of cable
assumes, when fixed at its ends) (Yin, Y. Z and Wang, Y.C,
2004). For this behaviour to be modelled properly, both
linear and bilinear material properties have been specified as
nonlinearities in steel members could be both geometric as
well as material making them very important when high
levels of deformation are being investigated.
B. Modelling of the Beam Using Ansys
Ansys (finite element analysis software) is generally
applicable to a wide variety of engineering problems. In the
numerical simulation of the beam, a Beam 4 element has been
used with an encastre boundary condition specified. A total
number of 30 finite element mesh was used.
C. Beam 4
This element is a uniaxial element having tension,
compression, torsion and bending capabilities with stress
stiffening and large deflection capabilities also included and
has six degrees of freedom at each node (Ansys library, 10.0).
D. Material Model
For small deflections, it can be assumed that the
geometric effects are small and as such can be neglected but
with large deformations, this needs to be specified. In
analysing the beam to determine its plastic deformation
capacity the following material properties have been
specified.
Linear Isotropic and
Bilinear Isotropic
This is to ensure that the beam is properly modelled in
both the elastic and the plastic range. The values of the
material properties adopted are:
Modulus of elasticity 2.1 x 1011 𝑁 𝑚2⁄
Passion ratio 0.3
Yield stress 4.10 x 108 𝑁 𝑚2⁄
Tangent modulus of elasticity 0
Figure 6: Idealized elasto-plastic stress strain curve adapted
for Johnson, (1972).
where:
𝐸𝑇 = tangent modulus
𝐸𝑡 = elastic modulus
E. Analysis Type
Transient dynamic analysis technique has been used to
determine the displacement response of the beam under time
varying load. For this analysis, a triangular pulse has been
assumed with a rise time of about half the impact duration
which has been taken as 2 s.
Figure 7: Triangular pulse shape with equal rise and decay times.
82 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.5
Although, it can be argued that true dynamic loads would
probably be characterised by a load–unload cycle of less than
a second, this is not a hard and fast rule. The structure under
investigation has a low natural frequency and hence a high
period of loading therefore should respond well by deflecting
when subjected to impact load which also has high loading
periods.
IV. RESULTS AND DISCUSSION
For structures in general, the integrity of design must be
guaranteed over its service life, therefore there is a need to
ensure that the structure is safe under normal and accidental
loading situations.
A. Evaluation of Displacement from Drop Test using Hand
Calculation
A 2-tonne, 1-tonne, and a 500 kg concrete cube were
dropped from heights of 25 m, 20 m and 15 m respectively,
unto a 533 x 210 UB 92 mild steel beam with a span of 30 m
at both the quarter-span and mid-span positions respectively.
The results obtained are as shown in the graph below.
The graph shows that the displacement at mid span of
1.98 m coincides with the maximum allowable deflection (see
Figure 9) while the displacement 1.6 m at quarter span (See
Figure 10) exceeds the maximum allowed (1.55 m). Implying
that in considering the effects other loads have on the
allowable ductility, the strain energy available for resisting
the impact loading is significantly reduced. This option of
considering the effects other loadings have on the available
ductility ratio which in turn affects the available strain energy
of the beam should be considered especially where the risk of
collapse or failure is extremely severe. The deflections as
shown in Figures 9 and 10 will however be limited by
rotation capacities of the member which ensure the deflection
sustained is not too excessive.
0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
0 15m/500kg 20m/1000kg 25m/2000kg
d
e
f
l
e
c
t
i
o
n
Height of drop / Mass of impactorFigure 9: A graph of actual versus allowable displacement considering the effects of other loads for mid-span
deflection.
Actual Deflection Allowable Deflection
0
0.3
0.6
0.9
1.2
1.5
1.8
0 15m/500kg 20m/1000kg 25m/2000kg
d
e
f
l
e
c
t
i
o
n
Height of drop/Mass of impactor
Mid Span Deflection Quarter Span Deflection
Figure 8: A combined graph of the mid-span and the quarter-span deflection versus the drop heights.
ALIYU: DESIGN RECOMMENDATION FOR STEEL BEAMS SUBJECT TO IMPACT LOAD 83
*(corresponding author) [email protected] doi: http://dx.doi.org/10.4314/njtd.v14i2.1
Figure 10: A graph of actual versus allowable displacement considering
the effects of other loads for mid-span deflection.
B. Ansys Model Simulation (Transient Analysis)
A transient analysis simulation was carried to validate
the results obtained from the hand calculation using the
energy momentum balance analytical approach. The transient
analysis simulation showed that the deflection sustained at
mid span due to the 2-tonne impactor load dropped from a
height of 25 m was 1.962 m at a stress level of 358 N/𝑚𝑚2
(see Figure 11).
While the quarter span deflection due to the 2-tonne
impactor load dropped from a height of 25 m gave a value of
1.301 m at a stress level of 460 N/𝑚𝑚2 (see figure 12). The
safe rotation capacity beyond which the beam is considered to
have failed is 20, which corresponds to a deflection of 0.25
m. This implies that for the mid-span and quarter-span
deflection of 1.98 m and 1.301 m respectively, the beam is
considered to have failed.
C. Comparison of Results
Comparing the results from the hand calculation to the
Ansys model shows that, the static deflection, from the hand
calculation with a value of 0.047 m compares closely to the
Ansys result of 0.0426 m (see Figure 13). Similarly, for the
dynamic deflection, the maximum value of 1.984 m at mid
span as well as the quarter span deflection of 1.6 m (see
Figure 9 and 10) due to the 2000 kg (2tonne) from the hand
calculation compared closely with those from the Ansys
simulation of 1.984 m and 1.301 m (see Figure 11 and 12).
V. CONCLUSION
A 30 m long mild steel beam was subjected to drop
weights (impact loading) from heights of 15 m, 20 m, and 25
m respectively. The deflection sustained was evaluated using
the energy method by Mughal et al. (1994) and validated
using the Ansys transient analysis which was performed to
simulate the beams response to the impact loading. As the
results for the hand calculation matched those from the Ansys
model, it was concluded that the presence of other static loads
significantly reduced the beam’s stiffness thus reducing the
Figure 11: Ansys model for midspan span deflection.
Figure 13: Static deflection.
Figure 12: Ansys model for quarter-span deflection.
84 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.5
capacity of structural elements in absorbing impact energy by
deflecting. Also, the maximum allowable deflection for safety
depending on structures classification should be controlled by
rotation capacity.
VI. RECOMMENDATION
For the safe design of steel structures, it is important to
identify the modes of failure that is the weak links in a
structure. This is because a structure can only be as strong as
its weakest link. For steel structures this will mostly be the
connections and welded joints. It is therefore recommended
that these weak link positions are designed to develop their
full strength. Implying that the ductility capacity of
connections and welded joints are crucial in ensuring the
safety of steel structures under impact loads as unanticipated
accidental loadings will ultimately have to be accommodated
by the connections.
To further ensure safety of design, it is recommended
that the ductility supply of the connection must at least be
20% greater than the ductility demand on it so that brittle
failure does not occur.
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ABDULLAHI: NUMERICAL ANALYSIS OF STRUCTURES OF REVOLUTION USING UNIVERSAL MATRICES 85
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.6
ABSTRACT: Stress and displacement analysis of structures of revolution under axisymmetric loading is of
considerable interest in engineering. Many practical problems can be idealized as an axisymmetric case, which
simplifies the analysis and reduces the computational work. The axisymmetric triangular element is commonly used
for modeling these cases. This paper proposes a method of generating stiffness matrix for the axisymmetric
triangular element using universal matrices instead of numerical integration. The computation time of the proposed
method was compared against the Gaussian numerical integration. The CPU time ratio for the 3-node element was
1:1.56, 1:1.79, and 1:1.89 for the proposed method against 1-point, 3-points, and 4-points Gaussian numerical
integration respectively. The accuracy of the proposed method was 0.012% against the exact integration method.
The 1-point, 3-points, and 4-points Gaussian numerical integration have an error of 0.059%, 0.001%, and 0.0006%
respectively. Nodal displacements from this method were compared against the results of some commercially
available finite element packages. The proposed method has a deviation of 0.44% from the theoretical values, while
ABAQUS, ANSYS, and Optistruct has a deviation of 1.26%, 1.29%, and 1.44% respectively using the default
number of integration points provided by the packages.
KEYWORDS: Stiffness matrix; explicit formulation; closed-form; universal matrix; axisymmetric triangular elements.
[Received April 26, 2018; Revised August 10, 2018; Accepted September 19, 2018] Print ISSN: 0189-9546 | Online ISSN: 2437-2110
I. INTRODUCTION
In Finite Element Analysis, some cases of 3D problems
associated with the structures of revolution (SOR) can be
reduced to a 2D problem by using axisymmetric elements,
which simplifies the analysis and reduces computational work
(Cui and Xu, 2013). These structures are generated by
rotating a cross-section about an axis, as shown in
Figure 1. The cross-section can be of any 2D shape; the
resulting structure is said to be axisymmetric (O. C.
Zienkiewicz et al., 2014). These structures are paramount in
engineering applications due to their ease of manufacture and
optimality in strength-weight ratio, by hollowing the structure
it can further be used as a container. Axles, bottles, cans,
cups, nails, piles, pipes, tanks, vessels, and wheels are all
examples of structures of revolution. In the transportation of
fluids at different atmospheric conditions such structures are
widely used (Gill, 1970).
For an axisymmetric structure to be defined as an
axisymmetric problem, it is imperative that the boundary and
loading conditions be rotationally symmetric, with these two
conditions, the mechanical response of the structure is
regarded as axisymmetric and the displacement, strains, and
stress are not affected by the circumferential position (O. C.
Zienkiewicz et al., 2014).
Figure 1: Axisymmetric cylinder.
The finite element technique predicts deformation and its
intensity on a given structure, this is achieved by dividing the
structure into a network of elements called mesh, the
elements are non-complex shapes for which the finite element
code can evaluate the stiffness matrix (Chandrupatla and
Belegundu, 2001; Pachpor et al., 2011). The nodes, which are
the points at which the elements are connected are used to
determine the unknown field variables such as displacement
or temperature. Element stiffness matrices are further
combined into a global stiffness matrix for the whole model
Numerical Analysis of Structures of Revolution
using Universal Matrices Approach
Hamza Sulayman Abdullahi*
Department of Mechanical Engineering, Bayero University, Kano, 700241, Nigeria.
86 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author’s e-mail address: [email protected] doi: http://dx.doi.org/10.4314/njtd.v15i4.1
and then solved for the unknowns. Elements can either have a
constant, linear or cubic strains within the element
(Zienkiewicz et al., 2005). The first archival-journal on the
axisymmetric finite element using solid elements was applied
to a rocket nozzle problem presented by Wilson (1965).
Shape functions are used to describe the elements
behavior between element nodes (Huttton, 2004). The
coefficients in the interpolation polynomial denote the shape
function, which is written for each individual node of a finite
element and its magnitude is 1 at that node and 0 for all other
nodes in that element. The local coordinate system x and y
can be converted into another coordinate system that allows
for specifying a point within the element by a dimensionless
number whose magnitude never exceeds unity called natural
coordinate system (Huttton, 2004).
Numerical Integration has been widely applied in finite
element analysis mainly due to its simplicity. It provides an
approximate solution of the exact integration. Researchers
over the past few decades have been studying and developing
better approximation than the conventional numerical
integration. An alternate method was presented by
Subramanian (Subramanian and Bose, 1982) for plane
triangular elements which result in a closed-form solution i.e.
same as exact integration. Another method for computing
stiffness matrix that results in closed-form solution and
reduction in computational effort for quad elements was
presented by Zhou and Vecchio (2006). McCaslin et al.
(2012) considers isoparametric and subparametric higher
order tetrahedral element and proposed yet another closed-
form approach. Symbolic computation was used to reduce
computation time by 50% for exact integration (Videla et al.,
2008). An alternate midpoint quadrature was suggested by
Jeyakarthikeyan et al. (2017) to enhance the stiffness matrix
of quad elements. For axisymmetric triangular element under
axisymmetric loading, using a closed-form approach is
possible only when the radius of the element is much larger
than the element thickness (Subramanian and Bose, 1982;
Jeyakarthikeyan et al., 2015).
Familiarity with the stiffness matrix is essential to
understanding the stiffness method. A stiffness matrix K is
a matrix such it relates the local forces F on an element
with the displacement u on the nodes as F K u ,
the stiffness matrix indicates the defiance of the element to
axial, bending, shear, or torsional deformation (Zienkiewicz
et al., 2005). In fluid flow and heat transfer analyses, the
stiffness matrix represents the resistance of the element to
change when subjected to motion or temperature gradient
(O.C. Zienkiewicz et al., 2014). Element stiffness matrices
are always symmetric and positive for definitive structural
problems, the diagonal coefficients are always positive and
relatively large when compared to the off-diagonal values in
the same row, it is banded and singular (Zienkiewicz et al.,
2005).
The objective of this paper is to generate stiffness matrix
for the axisymmetric triangular element using universal
matrices instead of numerical integration. First, the
foundation of finite element formulation and the development
of universal matrices is described. The accuracy and
computation time of the proposed method was analyzed.
Lastly, a linear-static finite element study of a cylinder
subjected to internal pressure was carried out, the result from
three commercially available packages was compared against
the results of the proposed method.
II. SYSTEM MODELLING The axisymmetric triangular elements have 2 degrees of
freedoms (u, v) per node which is represented by the nodal
displacements. For the purpose of illustration in this paper,
the three-node axisymmetric triangular element will be used,
it is usually referred to as Constant Strain Triangle (CST) as
the strain is constant along its sides. The radius of the element
is approximated as
3
1
1
3ix x (1)
where x is the radial coordinate of the element nodes.
The strain-displacement equation gives
x
y
xy
u
x
v
y
u v
y x
u
x
(2)
where , ,x y are the three normal strains and xy is
the shear strain. The subscripts ,x y and denotes the radial,
axial and tangential directions. The field variable
(displacements) are denoted by u and v . The shape
functions for the CST are
*
1
*
2
*
3
,
,
1
N
N
N
(3)
Where ξ and η are interpolating terms with values
ranging from 0 to 1. For a 3-node CST element with the
isoparametric formulation, the geometry ( x and y ) and field
variable ( u and v ) are of the same order.
1 1 2 2 3 3
1 1 2 2 3 3
* * *
1 1 2 2 3 3
* * *
1 1 2 2 3 3
u N u N u N u
v N v N v N v
x N x N x N x
y N y N y N y
(4)
The Jacobian matrix for the transformation is given by
[ ]
x y
Jx y
ABDULLAHI: NUMERICAL ANALYSIS OF STRUCTURES OF REVOLUTION USING UNIVERSAL MATRICES 87
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.6
Figure 2: Axisymmetric problem formulation (Chandrupatla and Belegundu, 2001).
The strain-displacement equation becomes
1
2P g
(5)
where
23 13
23 13
23 13 23 13
0 0 0
0 0 0
0
20 0 0 0
y y
x x
P x x y y
x
,
ij i j
ij i jy
x x x
y y
,
T u v u vg u
and is the
area of the triangular element.
The internal energy of the element is given by
11
0 0
(2 )2
TtU D d d
where 2t x and [ ]D is
the elasticity matrix for axisymmetric problems.
Substituting the strain-displacement equation we have
11
0 02
TxU g G g d d
Where T
G P D P a 5 x 5 matrix of constants,
we can also express [g]T as:
0 0
0 0 0
T T T
T
g u v N
N NN
NN N
Which yields
11
0 0
1
2
T T
T
xU u v N G N u v d d
U u v K u v
Where the stiffness matrix [K] is given by
11
0 0
TxK N G N d d
(6)
The universal matrices are denoted by [A], [B], [C], [E],
[H] and [J], they are the result of integration over the shape
functions of the field variable (Abdullahi, 2015).
11
0 0
1 0 11
0 0 02
1 0 1
TdN dNA d d
d d
11
0 0
0 1 11
0 0 02
0 1 1
TdN dNB d d
d d
11
0 0
0 0 01
0 1 12
0 1 1
TdN dNC d d
d d
11
0 0
2 1 11
1 2 124
1 1 2
TE N N d d
11
0 0
1 0 11
1 0 16
1 0 1
T dNH N d d
d
11
0 0
0 1 11
0 1 16
0 1 1
T dNJ N d d
d
Substituting the universal matrices into equation (6), the
element stiffness matrix of the 3-noded constant strain
triangle (CST) can be written as:
T
X YxK
Y Z
(7)
where
11 12 22 25 15 55
13 23 53 14 54 24
33 43 44
T T T
T
T
X G A G B B G C G J J G H H G E
Y G A G B G H G B G J G C
Z G A G B B G C
ijG are the terms of the G matrix.
An algorithm was developed to explicitly compute the
stiffness matrix terms and save it in memory for retrieval,
these explicit equations will be used instead of evaluating the
integrals or matrix multiplication when solving the problem,
therefore the stiffness matrix becomes a simple algebraic
computation and reduces the computation time.
88 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author’s e-mail address: [email protected] doi: http://dx.doi.org/10.4314/njtd.v15i4.1
An axisymmetric problem (Figure 2) which consists of a
cylinder subjected to internal pressure was used to assess the
capability of the method presented in this paper. The cylinder
has an internal diameter of 80mm and an external diameter of
120mm subjected to internal pressure of 2MPa, the Young
modulus of the cylinder wall material is 200Gpa with a
Poisson ratio of 0.3.
The axisymmetric problem depicted in Figure 2 was
modeled using three finite element packages; ABAQUS,
ANSYS, and Optistruct. Modeling procedure for each
package is explained in the following subsections. The
material of the cylinder wall has a Young Modulus of 200
GPA and Poisson Ratio of 0.3.
A linear-static analysis was employed using
Abaqus/Standard (ABAQUS, 2015). The part was set to be a
deformable axisymmetric shell, an isotropic elastic property
was defined. A general static step was created. A three-node
linear stress/displacement element without twist (CAX3) was
used to mesh the model, the model consists of 2 elements and
4 nodes. Fixed boundary conditions were employed on the
outer radius nodes while the inner nodes are only allowed to
move in a radial direction. The inner radius edge was
subjected to a uniform pressure of 2Mpa.
A static analysis using Plane182 element was employed,
the element is a four-node rectangular element that was
further degenerated to a triangular element by merging the
last two nodes (ANSYS, 2013). The axisymmetric option was
selected along with full integration and pure displacement.
An isotropic elastic property was defined. Uniform pressure
of 2MPa was resolved into forces and applied on the inner
radius nodes.
Axisymmetric triangular element CTAXI was used to
define the problem, all the nodes were placed on the x-z plane
with x as the radius. The pressure was applied using
PLOADX1, which is a bulk unsupported card for static
pressure load on axisymmetric elements. Material and
property were defined as MAT1 and PAXI cards respectively.
A linear static load step with two set of constraints for the
inner and outer radius was defined.
IV. RESULTS AND DISCUSSION
A. Accuracy and Computation Time
In non-axisymmetric triangular elements, the Universal
Matrix Method (UMM) gives the exact solution
(Subramanian and Bose, 1982). Due to the approximation of
the radius of the element shown in equation (1) the proposed
method gives another approximation. Therefore, the need for
determining the deviation of UMM and numerical integration
from the exact integration becomes paramount.
To assess the computational efficiency of the proposed
method, we consider the cylinder in Figure 2 and compute the
stiffness matrices using the universal matrices and Gaussian
numerical integration for the 3-node (CST) and the 6-node
(LST) axisymmetric triangular elements. The CPU time is
taken for 10,000 elements. The numerical integration was
coded as explicit equations this is aimed at providing a
common ground for the execution time comparison.
The test was carried out on a desktop computer with
Intel® Core™ CPU i5-6400 (2.70 GHz) and 16GB of RAM
running on a 64-Bit Windows operating system for all the
steps to ensure a fair comparison. For each of the elements a
problem is solved using the methods and then the stiffness
matrix generated is compared and the error is estimated using
the expression presented by Videla et al. (2008) as follows
, 1
100| |
nT
ij ij
i j
T
ij
K K
eK
(8)
where T
ijK the stiffness matrix is terms using exact
integration and ijK is the stiffness matrix term using UMM
or Gaussian numerical integration. The CPU time ratio for
element 1 with radius x = 46.67mm is shown in Table 1.
Table 1: Computation time ratio for 10,000 elements. Elements Method CPU time ratio
CST
Current Work 1.00
NI 1 point 1.56
NI 3 points 1.79
NI 4 points 1.89
LST
Current Work 1.00
NI 1 point 5.64
NI 3 points 12.84
NI 4 points 16.69
NI 7 points 28.12
The CPU time ratio for the 3-node CST element was
1.00 for UMM while Gaussian numerical integration has
1.56, 1.79 and 1.89 for 1-point, 3-points, and 4-points
integration respectively. The computation time increases with
an increase in the number of points due to re-computation
loop for each point and then taking the weighted sum. While
UMM uses only one computation loop. Similarly, for the 6-
node LST element, the CPU time ratio was 1.00 for the
universal matrix method and 5.64, 12.84, 16.69 and 28.12 for
1-point, 3-points, 4-points, and 7-points Gaussian numerical
integration.
Figure 2 shows the percentage error for UMM and
Gaussian numerical integration with 1, 3 and 4 points against
the exact integration. CST elements with radius x =
46.67mm and 53.33mm were used for the cylinder problem
shown in Figure 2. The result indicated that UMM has a
better approximation (0.012% error) than the 1-point
numerical integration (0.059%) which is the most commonly
used by commercial packages. However, by increasing the
number of integration points to 3 and 4 the error drastically
decreases to 0.001% and 0.0006% respectively. This clearly
shows that when using a 3-node constant strain triangle, a
minimum of 3 points is required in the commercial finite
element packages.
Figure 44 shows the percentage error for UMM and
Gaussian numerical integration with 1, 3, 4 and 7 points
against exact integration. Six-node linear strain triangle
ABDULLAHI: NUMERICAL ANALYSIS OF STRUCTURES OF REVOLUTION USING UNIVERSAL MATRICES 89
*Corresponding author: [email protected] doi: http://dx.doi.org/10.4314/njtd.v16i2.6
Figure 2: Percentage Error for CST using UMM and Numerical
Integration.
Figure 4: Percentage Error for LST using UMM and Numerical
Integration.
(LST) elements with radius x = 46.67mm and 53.33mm
were used for the cylinder problem shown in Figure 2. Three
mid-nodes are added to the CST to create the LST. The result
indicated that UMM has a better approximation (1.873%
error) than the 1-point numerical integration (27.1%).
However, by increasing the number of integration points to 3,
4 and 7 the error drastically decreases to 0.43%, 0.032%, and
0.00015% respectively. This clearly shows that when using a
6-node linear strain triangle, a minimum of 3 points is
required in the commercial finite element packages.
B. Nodal Displacement
The axisymmetric problem illustrated in Figure 2 was
solved using the explicit equations generated. To further
understand the computational accuracy of the proposed
method, the nodal displacements from the current work,
ABAQUS, ANSYS, and Optistruct was compared against the
theoretical values obtained using exact integration. The result
for node 1 of element 1 is shown in Figure 5.
The universal matrix method has a deviation of 0.44%
from the theoretical values, while ABAQUS, ANSYS, and
Optistruct has a deviation of 1.26%, 1.29%, and 1.44%
respectively using the default number of integration points
provided by the packages. A similar trend was observed on
node 2 as shown in Figure . The deviation of the current work
from the theoretical values on the second node displacement
is 0.54%, while ABAQUS, ANSYS, and Optistruct have a
deviation of 1.62%, 1.64%, and 1.84% respectively using the
default number of integration points provided by the
packages. These deviations shown by the commercial
packages considered in this study is highly associated with
fewer integration points for the numerical integration of the
shape functions.
ABAQUS uses 1-point integration for the 3-node linear
axisymmetric triangular element (CAX3). The 6-node
quadratic axisymmetric triangular element (CAX6) and the 4-
node bilinear axisymmetric quadrilateral element (CAX4) are
recommended by ABAQUS because of the number of
integration points (ABAQUS, 2015). The CAX6 uses 3
integration points while the CAX4 has the option for full (4-
point) and reduced (1-point) integration. ANSYS and
Optistruct both use 1-point integration for the Plane182 and
CTAXI elements. ANSYS recommends using the 4-node
version of Plane182 without degeneration (ANSYS, 2013).
Figure 5: Displacement of node 1.
Figure 6: Displacement of Node 2.
90 NIGERIAN JOURNAL OF TECHNOLOGICAL DEVELOPMENT, VOL. 16, NO. 2, JUNE 2019
*Corresponding author’s e-mail address: [email protected] doi: http://dx.doi.org/10.4314/njtd.v15i4.1
V. CONCLUSION
A method of generating stiffness matrix for triangular
axisymmetric elements was presented, the method utilizes
universal matrices generated by integrating the shape
functions once and saved for retrieval in memory.
Furthermore, a set of explicit equations were generated for
each term of the stiffness matrix to improve the
computational efficiency. Unlike other closed-form
approaches to finite elements, the stiffness matrix
computation method presented in the current work results in
yet another approximation, due to the element radius
estimation.
However, the method shows a better approximation to
the theoretical baseline, with better acceptable percentage
error and lower computation time. The proposed method has
a deviation of 0.44% and 0.54%, while the commercial finite
element packages considered in this work have deviations up
to 1.44% with the default number of integration points.
Increasing the number of the integration points decreases the
error significantly and increases the computation time.
Therefore, careful consideration should be given when
choosing the element and the number of points to find a
balance between accuracy and computation time.
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