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
dc
V
dx
cd
o


(1)
Nomenclature
 = Plastic Index
β = Plastic Limit
Vo = Void Ratio
 = Porosity
Z = Depth
  002
2

dx
dc
V
dx
cd


(2)

Let




0n
n
n xaC





1
11
n
n
n xnaC
 




2
211
1
n
n
n xannC
    01
1
1
0
2
2
 






n
n
n
n
n
n xnaVxann


(3)
Replace n in the 1st
term by n+2 and in the 2nd
term by n+1, so that we have;
       0112
0
1
0
2  






n
n
no
n
n
n xanVxann


(4)
i.e.
      102 112   nn anVann


(5)
  
  12
1 10
2


 

nn
anV
a n
n


(6)
 
 2
10
2


 

n
aV
a n
n


(7)
for
 


2
,0 10
2
aV
an


(8)
(9)
Subject equation (16) to the following boundary condition
    HoCandoC  1
0
 
 x
V
aaxC 



0
10 
  010  aaoC
i.e. 010  aa (10)
 
 x
V
aaxC 



0
10 

   
 x
V
a
V
xC 






0
1
01
!2

    Ha
V
oC 

 1
01
!2




0
1
V
H
a


(11)
Substitute (10) into equation (11)
01 aa 



0
0
V
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
x
V
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
predictivevaluesforstiffclay
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
PredictiveandMeasuredValuesforStiffClay
CompressionIndex
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
PredictiveValuesforStiffClay
Depth [M]
Poly. (Predictive of Stiff Clay
Cc)
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
PredictivaValuesforStiffClayonCompression
Index
Depth [M]
Clay Cc

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
PredictiveValuesforStiffClay
Depth [M]
Poly. (Predictive of Stiff
Clay Cc)
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 2 4 6 8
PredictiveandMeasuredValuesforStiff
ClayonCompressionIndex
Depth [M]
Clay Cc

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.
REFERENCES
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Lake Valley, Utah Report Prepared for the Utah Department of
Transportation Research Division Civil and Environmental Engineering
Department University of Utah
[2] A. Gene A Vaunat Garitte B and Wileveau Y In situ behaviour of stiff
layered clay subject to thermal loading: Observations and interpretation
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[3] Gens, A. (2003). The role of geotechnical engineering in nuclear energy
utilisation (Special Lecture). Proc. 13th Eur. Conf. Soil Mech. Geotech.
Engng, Prague 3, 25–67.
[4] Bernier, F. & Neerdael, B. (1996). Overview of in situ thermomechanical
experiments in clay: concept, results and interpretation. Engng Geol. 41, Nos
1–4, 51–64.
[5] Bock, H. (2001). RA experiment. Rock mechanics analyses and synthesis:
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[6] Bossart, P., Meier, P. M., Moeri. A., Trick, T. & Mayor, J.-C. (2002).
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[7] Bai, M. & Abousleiman, Y. (1997). Thermoporoelastic coupling with
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[8] De Bruyn, D. & Labat, S. (2002). The second phase of ATLAS: the
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[16] Kanj, M. & Abousleiman, Y. (2005). Porothermoelastic analyses of
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MATHEMATICAL MODEL TO MONITOR STIFF CLAY COMPRESSION INDEX IN WET LAND AREA OF DEGEMA