MATHEMATICAL MODEL TO MONITOR STIFF CLAY COMPRESSION INDEX IN WET LAND AREA OF DEGEMA

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International Journal of Advanced Research in Engineering and Technology

(IJARET) Volume 6, Issue 12, Dec 2015, pp. 59-72, Article ID: IJARET_06_12_007

Available online at

http://www.iaeme.com/IJARET/issues.asp?JType=IJARET&VType=6&IType=12

ISSN Print: 0976-6480 and ISSN Online: 0976-6499

© IAEME Publication

___________________________________________________________________________

MATHEMATICAL MODEL TO MONITOR

STIFF CLAY COMPRESSION INDEX IN

WET LAND AREA OF DEGEMA

Eluozo. S. N

Subaka Nigeria Limited Port Harcourt Rivers State of Nigeria

Director and Principal Consultant Civil and Environmental Engineering,

Research and Development

Ode T

Department of Civil Engineering, faculty of Engineering

Rivers State University of Science and Technology Port Harcourt

ABSTRACT

The stiffness of clay in soil has lots to observe for engineering purpose,

these has been monitored through it depositions at various area, the

engineering properties of soil were applied to determined the rates of

compression in soils, lots of compression index in various types of soil has

been carried through experimental applications, empirical model has been

applied in several type of soil, these applications predict compression index

for numerous formations, but the application of mathematical model thus

mathematical methods has not been applied to predict compression index for

stiff clay, these application were used through these parameters, it express

formations characteristics to developed the system for the study, such

application generated the derived equation that produced the model to predict

compression index for stiff clay, simulation were applied and it produced

theoretical values for stiff clay at various depth, the simulation values were

compared with experimental data, both parameters express best fits validating

the developed model for the study, compression index were observed to

gradually increase with slight variation at different depth, but produced

specified compression index within the range for stiff clay.

Key words: Mathematical Model, Stiff Clay and Compression Index

Eluozo. S. N and Ode T


Cite this Article: Eluozo. S. N and Ode T, Mathematical Model To Monitor

Stiff Clay Compression Index in Wet Land Area of Degema. International

Journal of Advanced Research in Engineering and Technology, 6(12), 2015,

pp. 59-72.

http://www.iaeme.com/IJARET/issues.asp?JType=IJARET&VType=6&IType=12

1. INTRODUCTION

It has been thorough examined that saturated stiff clays exhibit a strong pore pressure

response that considerably affects the hydraulic and mechanical behaviour of the

material Genes et al 2007. Stiff sedimentary clays provide the geological background

to many civil engineering projects. In modern years, interest in these types of material

has increased, because they are being considered as possible host geological media for

underground repositories of high-level radioactive waste (Gens, 2003). They exhibit

favourable characteristics, such as low permeability, a degree of self-healing capacity

when fractured, significant retardation properties for solute transport, and no

foreseeable economic value. Possible shortcomings are the likely need for support of

the excavated openings, and sensitivity to chemical actions and to desaturation caused

by ventilation. High-level radioactive waste is heat emitting. Therefore the use of stiff

sedimentary clays in this type of application brings to the fore the thermal response of

this type of material and, especially, the interaction of thermal phenomena with

hydraulic and mechanical behaviour. The possible use of these types of clay as

geological hosts for radioactive waste has prompted the construction of several

underground laboratories. Underground laboratories allow, by the performance of

appropriate in situ tests, observation of the clay response in complex situations that

mimic some of the conditions likely to be encountered in a deep geological repository.

In particular, special attention is paid to the coupled thermo-hydro-mechanical (THM)

behaviour of the potential host clay. The observations gathered in the in situ test have

provided an opportunity to examine the integrated thermo-hydro mechanical

Consolidation is characteristically is classified to be primary consolidation settlement

and secondary consolidation settlement. Primary consolidation settlement take place

when there is an excess pore water pressure dissipates from the soil layer under the

embankment into the surrounding soil. It has been observed that it is gradual

dissipation of excess pore water produces corresponding decreases in the soil’s void

ratio as the soil consolidates. More so surface settlement consequential from

consolidation settlement may range from a few centimeters up to numerous meters;

these also depend on the thickness of the clay deposit, in previous loading history it

has been observed that the magnitude developed increased stress caused by the new

embankment load. Base on these factors predicting the amount of primary

consolidation settlement has been noted to be imperative for many civil engineering

projects. (Bartlett 2004).

The initiations of primary consolidation, the resultant from settlement are ranged

between 10 to 15 percent of the amount of embankment placed. For instance, 10-m

high embankments are observed to undergo between 1 to 1.5 m of consolidation

settlement from compression of the foundation soils. Furthermore, it has been

thoroughly observed on large amount of primary consolidation settlement, the period

of consolidation settlement is quite long, it is also noted to be between to 2 to 3 years

to complete, these are determined on the location and nature of the underlying

sediments. Thus, the time-rate of primary consolidation is an imperative design and

construction consideration. Looking at primary consolidation, secondary

Mathematical Model To Monitor Stiff Clay Compression Index in Wet Land Area of Degema


consolidation it takes long-term form of settlement to occurs under a constant vertical

effective stress (i.e., it implies that vertical effective stress may not be changing with

time). In secondary consolidation, the excess pore pressure dissipation associated with

primary consolidation has in actual fact dissipated, thus secondary consolidation is a

decrease in void ratio change that occurs after primary consolidation and progresses

under a constant vertical effective stress. Secondary consolidation is characterized by

a continuing decrease in void ratio resulting from rearrangement of the soil fabric

with time. The magnitude of secondary consolidation usually diminished with time on

a settlement versus log of elapsed time plot. Secondary consolidation is also referred

to as creep settlement. In general, secondary consolidation settlement is generally

much smaller than primary consolidation settlement and ranges from a few

centimeters to a few tens of centimeters during the lifetime of bridge structure.

(Bartlett, 2004).

Various in situ heating tests have been performed involving the observation of the

response of natural sedimentary clay. For instance, in the Hades laboratory the

following experiments have been performed: (Picard et al., 1994; Bernier & Neerdael,

1996; De Bruyn & Labat, 2002). mineralogy consists mainly of sheet silicates (illite,

illite– smectite mixed layers, chlorites, kaolinites), framework silicates (albites, K-

feldspar), carbonates (calcite, dolomite, ankerite and siderite), and quartz (Bossart et

al., 2002). Opalinus clay behaviour has been intensely studied by means of laboratory

and in situ experimental programmes. A synthesis of the main physical and

geotechnical parameters is reported in Bock (2001). A significant number of

measurements of the in situ stress have been made using different procedures

(borehole slotter, undercoring, and hydraulic fracturing). They have been

supplemented by geological observations and back-analysis of instrumented

excavations. A synthesis of the information available is reported in Wermeille &

Bossart (1999) and in Martin & Lanyon (2003). Naturally, the strength and

significance of each coupling relationship vary widely (Bai & bousleiman, 1997;

Zimmerman, 2000). Observations made during the test did not indicate any

desaturation of the clay; it is presumed that the material has remained saturated

throughout. Coupled THM formulations for saturated porous media have been

proposed by several authors (e.g. Booker & Savvidou, 1985; Katsube, 1988;

Kurashige, 1989; Wang & Papamichos, 1999; Kanj & Abousleiman, 2005).

2. GOVERNING EQUATION

02

2

dx

dc

dx

dcV

dx

cdo

(1)

Nomenclature

= Plastic Index

β = Plastic Limit

Vo = Void Ratio

= Porosity

Z = Depth

002

2

dx

dcV

dx

cd

(2)



Let

0n

n

n xaC

1

11

n

n

n xnaC

2

211 1n

n

n xannC

011

1

0

2

2

n

n

n

n

n

n xnaVxann

(3)

Replace n in the 1st term by n+2 and in the 2

nd term by n+1, so that we have;

01120

1

0

2

n

n

no

n

n

n xanVxann

(4)

i.e.

102 112 nn anVann

(5)

12

1 102

nn

anVa n

n

(6)

2

102

n

aVa n

n

(7)

for

2

,0 102

aVan

(8)

(9)

Subject equation (16) to the following boundary condition

HoCandoC 10

x

V

aaxC

0

10

010 aaoC

i.e. 010 aa (10)

x

V

aaxC

0

10



x

V

aV

xC

0

101

!2

HaV

oC

101

!2

0

1V

H

a

(11)

Substitute (10) into equation (11)

01 aa

0

0V

H

a

(12)

Hence, the particular solution of equation (16) is of the form:

x

V

V

H

V

H

xC

0

00

1

0

0

xV

V

H

xC

(13)

3. MATERIALS AND METHOD

Standard laboratory experiment where performed to monitor compression index of

stiff clay at different formation, the soil deposition of the strata were collected in

sequences base on the structural deposition at different locations, this samples

collected at different location generated variations at different depth producing

deposition of stiff clay compression at different strata, the experimental result are

applied to compare with the theoretical values to determined the validation of the

model.

4. RESULT AND DISCUSSION

Results and discussion are presented in tables including graphical representation of

compression index of stiff clay

Table 1 Predictive Values of stiff clay compression index at Different Depth

Depth [M] Predictive of Stiff Clay Cc

0.2 0.00639

0.4 0.012

0.6 0.018

0.8 0.024

1 0.03

1.2 0.036

1.4 0.04




1.6 0.048

1.8 0.054

2 0.06

2.2 0.066

2.4 0.072

2.6 0.078

2.8 0.084

3 0.09

3.2 0.096

3.4 0.102

3.6 0.108

3.8 0.114

4 0.12

4.2 0.126

4.4 0.132

4.6 0.138

4.8 0.144

5 0.15

Table 2 Predicted and Measured of compression index for stiff clay at Different Depth

Depth [M] Predictive of Stiff Clay Cc Measured Values of Stiff Clay Cc

0.2 0.00639 5.61E-03

0.4 0.012 0.0116

0.6 0.018 0.0174

0.8 0.024 0.0232

1 0.03 0.029

1.2 0.036 0.0348

1.4 0.04 0.041

1.6 0.048 0.0464

1.8 0.054 0.0523

2 0.06 0.0581

2.2 0.066 0.0639

2.4 0.072 0.0697

2.6 0.078 0.0756

2.8 0.084 0.0814

3 0.09 0.0873

3.2 0.096 0.0931

3.4 0.102 0.0989

3.6 0.108 0.1047

3.8 0.114 0.1106

4 0.12 0.1164

4.2 0.126 0.1223

4.4 0.132 0.1281

4.6 0.138 0.134

4.8 0.144 0.139

5 0.15 0.145



0.2 0.004

0.4 0.008

0.6 0.012

0.8 0.016

1 0.02

1.2 0.024




1.4 0.028

1.6 0.032

1.8 0.036

2 0.04

2.2 0.044

2.4 0.048

2.6 0.052

2.8 0.056

3 0.06

3.2 0.064

3.4 0.068

3.6 0.072

3.8 0.076

4 0.08

4.2 0.084

4.4 0.088

4.6 0.092

4.8 0.096

5 0.1

5.2 0.104

5.4 0.108

5.6 0.112

5.8 0.116

6 0.12

6.2 0.124

6.4 0.128

6.6 0.132

6.8 0.136

7 0.14

7.2 0.144

7.4 0.148

7.6 0.152

7.8 0.156

8 0.16

Table 4 Predicted and Measured of compression index for stiff clay at Different Depth


0.2 0.004 0.003

0.4 0.008 0.007

0.6 0.012 0.014

0.8 0.016 0.018

1 0.02 0.022

1.2 0.024 0.028

1.4 0.028 0.029

1.6 0.032 0.034

1.8 0.036 0.038

2 0.04 0.042

2.2 0.044 0.046

2.4 0.048 0.049

2.6 0.052 0.054

2.8 0.056 0.058

3 0.06 0.062

3.2 0.064 0.066

3.4 0.068 0.069

3.6 0.072 0.074

3.8 0.076 0.078




4 0.08 0.084

4.2 0.084 0.086

4.4 0.088 0.089

4.6 0.092 0.094

4.8 0.096 0.098

5 0.1 0.104

5.2 0.104 0.106

5.4 0.108 0.109

5.6 0.112 0.114

5.8 0.116 0.118

6 0.12 0.122

6.2 0.124 0.126

6.4 0.128 0.129

6.6 0.132 0.134

6.8 0.136 0.138

7 0.14 0.144

7.2 0.144 0.146

7.4 0.148 0.149

7.6 0.152 0.156

7.8 0.156 0.158

8 0.16 0.164



0.2 0.0048

0.4 0.0096

0.6 0.014

0.8 0.0196

1 0.024

1.2 0.028

1.4 0.033

1.6 0.0384

1.8 0.0432

2 0.048

2.2 0.0528

2.4 0.0576

2.6 0.0624

2.8 0.0672

3 0.072

3.2 0.0768

3.4 0.0816

3.6 0.0864

3.8 0.0912

4 0.096

4.2 0.1008

4.4 0.10564

4.6 0.11

4.8 0.1152

5 0.12

5.2 0.1248

5.4 0.129

5.6 0.1344

5.8 0.1392

6 0.144

6.2 0.1488

6.4 0.1536




6.6 0.158

6.8 0.162

7 0.168

Table 6 Predicted and Measured of compression iTndex for stiff clay at Different Depth


0.2 0.0048 0.00477

0.4 0.0096 0.00957

0.6 0.014 0.01437

0.8 0.0196 0.01917

1 0.024 0.02397

1.2 0.028 0.02877

1.4 0.033 0.03357

1.6 0.0384 0.03837

1.8 0.0432 0.04317

2 0.048 0.04797

2.2 0.0528 0.05277

2.4 0.0576 0.05757

2.6 0.0624 0.06237

2.8 0.0672 0.06717

3 0.072 0.07197

3.2 0.0768 0.07677

3.4 0.0816 0.08157

3.6 0.0864 0.08637

3.8 0.0912 0.09117

4 0.096 0.09597

4.2 0.1008 0.10077

4.4 0.10564 0.10557

4.6 0.11 0.11037

4.8 0.1152 0.11517

5 0.12 0.11997

5.2 0.1248 0.12477

5.4 0.129 0.12957

5.6 0.1344 0.13437

5.8 0.1392 0.13917

6 0.144 0.14397

6.2 0.1488 0.14877

6.4 0.1536 0.153357

6.6 0.158 0.1584

6.8 0.162 0.16317

7 0.168 0.16797



Figure 1 Predictive Values of stiff clay compression index at Different Depth

Figure 2 Predicted and Measured of compression index for stiff clay at Different

Depth

y = 3E-05x2 + 0.0299x + 1E-05 R² = 0.9999

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 1 2 3 4 5 6

pre

dic

tive

val

ues

fo

r st

iff

clay

Depth [M]

Predictive of Stiff Clay Cc

Poly. (Predictive of Stiff Clay Cc)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 1 2 3 4 5 6

Pre

dic

tive

an

d M

easu

red

Val

ues

fo

r St

iff

Cla

y C

om

pre

ssio

n In

dex

Depth [M]


Measured Values of Stiff Clay Cc





Depth

y = -1E-17x2 + 0.02x - 9E-16 R² = 1

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 2 4 6 8 10

Pre

dic

tive

Val

ues

fo

r St

iff

Cla

y

Depth [M]



0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 2 4 6 8 10

Pre

dic

tiva

Val

ues

fo

r St

iff

Cla

y o

n C

om

pre

ssio

n

Ind

ex

Depth [M]







Depth

The study has expressed the behaviour of stiff clay in terms its deposition, the

stiffness condition are base on the structural behaviour of the soil in terms of

engineering properties, these condition may have affected figure one and two were the

compression index of stiff clay were observed to gradually increase to the optimum

level monitored from it structural setting, slight variation of compression were noted

but it is observed to gradually increase to the optimum level, similar conditions were

found on the validation parameter i.e. figure two. The compression maintained

y = -1E-17x2 + 0.02x - 9E-16 R² = 1

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 2 4 6 8 10

Pre

dic

tive

Val

ues

fo

r St

iff

Cla

y

Depth [M]



0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 2 4 6 8

Pre

dic

tive

an

d M

easu

red

Val

ues

fo

r St

iff

Cla

y o

n C

om

pre

ssio

n In

dex

Depth [M]





gradual increase to the optimum rate, the results were found to be comparatively

fitting with the theoretical values. Figure three and four maintained similar condition

like the case of figure one and two, gradual variation of compression were found in

figure three and four respectively, variation of parameters that made up the system

were found to developed increment on the compression these figures, these were

also observed from there fitness. While in figure five and six experiences similar

condition, but with slight variation on the increment of compression to the optimum

level, the behaviour of stiff clay from it compressibility has been expressed through

the developed simulation and experimental values, these were monitored through it

fitness between the predictive and the measured values.

5. CONCLUSION

The study of stiff clay compression index in wet land area has been developed

through empirical methods, but there has been no application of mathematical method

in any latest’s literature as observed, empirical solution has been the only concept to

monitor the rate of compression of stiff clay, but the application of these modeling

techniques were able to predict the compression index of stiff at various depth as

universally specified, engineering properties soil or formation characteristics were

applied to formulate the system, these expression generated the developed

mathematical equation derived to generate model that predict compression index for

stiff clay. Such predictive values were compared with other experiment data, both

parameters developed best fits validating compression index for stiff clay, the study

express various gradual increase of compression index at different depth within the

specified rang in for stiff clay in wet land area of Degema.

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