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Derived Empirical Relations and Models of Vital Geotechnical Engineering Parameters

Based on Geophysical and Mechanical Methods of Testing

John MUKABIa,1 a

Kensetsu Kaihatsu Consultants, Nairobi, Kenya

Abstract. Due to the increasing frequency of seismic action and other natural hazards on one hand, and population explosion culminating in the development of megacities on the other, the need for mega structures cannot be overemphasized. Precise determination of geotechnical engineering parameters for the design and construction control for foundations of high rise buildings, bridges, highways, tunnels, underground space development and other civil engineering structures is one of the greatest challenges to engineers and scientists. As a result, various destructive and non-destructive methods of laboratory and in-situ testing have been developed. However, the cost of constructing such structures is usually high and depends on the precision of the design parameters adopted. This Study proposes some empirical equations that can be useful in determining not only the elastic stiffness directly from geophysical measurement but also derive such essential parameters as bearing capacity and shear strength from the same. Application of the GECPRO Model in bridging the small strain parameters determined from the field and sophisticated laboratory tests, and the failure parameters measured in the laboratory, which are vital in geotechnical engineering design, whilst probing geo-changes, are also demonstrated.

Keywords. Elastic, stiffness, shear, strength, geotechnical, testing, modeling

Introduction

The recent tendency by most geotechnical engineers is to adopt field techniques for the measurement of stiffness due to large error factors that are associated with laboratory testing within the linear elastic range, which various researchers have determined to be very small, averaging (𝜀𝑎)𝐸𝐿𝑆 < 0.01% for clayey geomaterials [1]. These errors are mainly as a result of sampling disturbance, bedding errors and system compliance. Menzies [2] states that many field tests, however, are unsuitable for measuring soil parameters in the direction of foundation load application whereas plate loading tests

1 John MUKABI: CEO, Kensetsu Kaihatsu Limited, A6 Mac Apts., Lavington, P. O. Box 35246-

00200, Nairobi, KENYA; E-mail: mukabinj@gmail.com

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simulating the size and loading of real foundations are normally very expensive. This necessitates the employment of geophysical methods which measure the ground property in terms of maximum stiffness as distinct from a ground parameter such as strength which is dependent on the method of measurement. Consequently, establishing a correlation of appreciable precision between the elastic/shear modulus and shear strength for application in modeling ground behavior over a wide range of strain, design and construction control is considered essential.

In this study, Geotechnical Investigation (GI) was undertaken at four bridge sites for purposes of determining design parameters for bridge foundations in Juba, the capital of South Sudan. The GI was part of the Juba Urban Transport Infrastructure (JUTI) Study, which was grant aid funded by The Government of Japan, through its implementing Agency, Japan International Cooperation Agency (JICA).

1. Testing and Geotechnical Investigation

The Standard Penetration Test (SPT), Dynamic Cone Penetration Test (DCPT), Geophysical Survey and Soil Classification were carried out at 1m intervals. The geo-electromagnetic probing was carried out with two coils; a transmitter and a receiver, which was placed within the borehole vicinity on land as shown in Figure 1.

Figure 1. Sampling, testing and measurement at the bridge sites in Juba, South Sudan

The system is based on the transient electromagnetic method (TEM) sounding technology which enables the conduction of near surface and subsurface soundings to a depth of up to 300m, depending on the geological formation and the frequency applied, whereby lower frequencies sense deeper into the ground. The measured data presented in Figure 3 was determined using a similar method of geophysical survey.

Disturbed samples were extruded at 1m intervals or at points where the soil type and/or characteristics varied. This was for purposes of measuring basic physical and mechanical properties such as specific gravity, bulk and dry densities, Atterberg Limits, grading, moisture content and compaction characteristics. The data applied for modeling was determined from sophisticated laboratory tests and field seismic survey.

2. Typical Test Results

The typical characteristics curves of the test results determined from the geophysical survey and SPT are compared in Figure 2 for borehole log BH-01.

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The similarity in the trends at the respective depths from the geophysical and mechanical (SPT) methods of testing can be verified accordingly.

Figure 2. Comparison of geophysical survey and Standard Penetration Test (SPT) data

3. Derived Basic Empirical Relations

The mathematical and regression analysis carried out with consideration to various environmental factors yielded the following equations applicable for ρ >25Ω-m.

( ) NNSPT BAN −= ρln (1)

BCBC BACBR −= )ln(ρ (%) (2)

[ ]qqu BAq −= )ln(ρ (MPa) (3)

EE BAE −= )ln(max ρ (MPa) (4)

On the other hand, the relations between the N-value and Unconfined Compressive Strength (UCS) as well as initial stiffness expressed as Emax and UCS are presented in Eqs. (5) and (6) respectively.

[ ] qNqNSPTu BAABNq −×+= }/{ (MPa) (5)

[ ] EqEqu BAABqE −+= }/{max (MPa) (6)

where, NSPT is the number of blows from a Standard Penetration Test (SPT), CBR is the California Bearing Ratio (a measure of bearing capacity), qu is the Unconfined Compressive Strength (UCS), Emax is the elastic (Youngs’) modulus, ρ is the geo-electromagnetic resistivity, and AN=19.6, BN=48.4, ABC=40, BBC=98, Aq=0.96, Bq=2.37, AE=1024 and BE=280 are material and ground related constants.

4. Application of the Empirical Relations for Design and Modeling

Figure 3 depicts the geotechnical engineering parameters derived over a geo-formation thickness of up to 56metres. These parameters were quite useful in determining the appropriate type and mode of piling as well as simulating the interactive behavior.

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

0 200 400 600 800 1000

Depth

(m)

Resistivity (Ohm-m)Depth Vs Resistivity for Borehole 01

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

0 10 20 30 40 50 60

Pene

tratio

n Dep

th (M

)

SPT N-ValuePenetration Depth vs SPT N-Value for BH-01

N>50 therefore NO measurements taken

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Figure 3. Computed design parameters over relevant depth of geological formation

Note 1: The UCS, qu, the elasctic modulus, E0 and and shear modulus, G0 are measured in MPa.

5. Introducing the GECPRO Empirical Model

Rigorous testing can be economically, technically, and time-wise prohibitive and yet, with the increasing necessity for the development of mega structures against the backdrop of the prevalence of large scale destructive natural and manmade disasters, it is practically compelling, on the part of the geotechnical engineer, to determine relatively precise and reliable Value Engineering (VE) based cost-effective design parameters taking into serious account prevalent seismicity, environmental factors and structural sustainability. An appreciably versatile geo-mathematical model (GECPROM) is proposed. GECPROM is designed to probe and estimate changes in vital geo-properties for clayey geomaterials and ground for a wide range of strain (very small strains to large pre-failure strains). The significant advantage of this model is that various geotechnical changes and geo-structural behavior can be modeled from a single sophisticated experimental test, whilst simultaneously catering for the effects of drainage conditions, loading rate, and consolidation stress-strain-time history even in the small strain region.

Consequently, as one of the most integral modules of the GECPROM, a method of mathematically determining the Elastic Limit Strain (ELS) within which range the elastic stiffness and shear modulus can be measured or derived more precisely, is

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developed [Eqs. (7) ~ (11)]. This is extended to determining the subsequent sub-yield strain limits. The importance and application of this method is demonstrated in Fig. 5.

Figure 4. Graphical representation of stress~strain parameters applied for YSL [Mukabi, 1995a]

Considering the intersection properties of the parameters in Figure 4, a square relation is developed as expressed in Eq. (7).

( ) ( )[ ] ( ) ( )[ ]2max oaiaoaiaa

oi aEqq εεεε −−−=∆−∆ . (7)

The tangent moduli αE at point α and βE at point β are thence expressed as;

( ) ( ) ( )[ ]oaaa

a aEddqE εεεε ααα −−== 2max (8)

( ) ( ) ( )[ ]oaaa

a aEddqE εεεε βββ −−== 2max (9)

• ( )IYaε : Initial Yield Strain (ELS)

( ) ( ) ( ) ( ) ( )[ ]αββα

αβ εεεε aa

a

aYa EEEE

I−×

−−

−=2

max . (10)

( ) ( ) ( ){ }( ) ( )[ ]

( ) ( )[ ] 1002

22

×−

−×

−−

+∆−∆

=oaia

oaia

aaoi

EEqq

Eεε

εε

εε αβ

βα

max (11)

where,

( ) ( )∆×= aa E

Eεε

α

βα

, %.010==a

EE εβ β , aEE maxαα = .

• ( )SYaε : Secondary and Tertiary Yield Strain

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The secondary and the tertiary yield strains, which quantitatively define the intermediate strain boundary limit and the pre-failure large scale plastic strain boundary limit respectively, are computed from the equations proposed by Mukabi [3].

Figure 5. (a) Yield surfaces traced from computed YS and, (b) Zoning of sub-yield surfaces based on

computed Yield Strains for Long Term (LT) and Short Term (ST) Consolidated specimens

The basic equation developed from CSSR functions [4] for the GECPROM shear modulus module is expressed as:

[𝐺𝑜]𝑝′ = �𝒜𝑝𝑜′ �(𝐾𝑐𝑠)𝛼 × �𝑝′

𝑝𝑜′�𝛽� + ℬ𝑝𝑜′

𝐾𝑐𝑠� × [𝐺𝑜]𝑝𝑜′ (12)

where, [𝐺𝑜]𝑝′ is the initial shear modulus at a variable stress point 𝑝′, 𝐾𝑐𝑠=𝜎𝑟′ 𝜎𝑎′⁄ is the arbitrary or designated consolidation stress ratio traced to 𝑝′, [𝐺𝑜]𝑝𝑜′ is the initial shear modulus determined at in-situ overburden pressure, 𝒜𝑝𝑜′ =0.95 and ℬ𝑝𝑜′ =0.35 are material constants, the values of which are applicable for most natural stiff and hard clayey geomaterials, while 𝛽=1.16 and 𝛼=0.4 for stress states in the 1st quadrant and 𝛼=-1 for stress states in the 4th quadrant accordingly [3].

In developing the model functions it is important to consider the relativistic rates of change of [𝐺𝑜]𝑝′(Δ, 𝛿) within only the 1st quadrant of the {p’,q} stress plane for stress ratio and orientation whereby, 𝜓𝑝′ =𝑝′ 𝑝𝑜′⁄ and 𝛿𝑘=𝐾𝑐𝑠 , the total derivative is expressed in the general form as: 𝑑[𝐺𝑜]𝑝′

𝑑𝜓𝑝′=

𝜕[𝐺𝑜]𝑝′

𝜕𝜓𝑝′+ �

𝜕[𝐺𝑜]𝑝′

𝜕𝛿𝑘� × 𝑑𝛿𝑘

𝑑𝜓𝑝′ (13)

∴𝑑[𝐺𝑜]𝑝′

𝑑𝜓𝑝′= 𝒜𝑝𝑜′ �(𝐾𝑐𝑠)𝛼 × 𝛽 �𝑝

′

𝑝𝑜′�𝛽−1

� + �𝒜𝑝𝑜′ �𝛼𝐾𝑐𝑠𝛼−1 × �𝑝

′

𝑝𝑜′�𝛽� + ℬ𝐾𝑐𝑠

𝐾𝑐𝑠� × 𝑑𝛿𝑘

𝑑𝜓𝑝′ (14)

The change of variables within the model is made by applying Leibnitz’s theorem of the chain rule expressed as: 𝜕[𝐺𝑜]𝑝′

𝜕𝜉𝑗= ∑

𝜕[𝐺𝑜]𝑝′

𝜕𝜓𝑝′∙ 𝜕𝜓𝑖

′

𝜕𝜉𝑗, 𝑗 = 1,2,⋯ ,𝑚,𝑛

𝑖=1 ; 𝑓(𝑛) = ∑ 𝑛!𝑟!(𝑛−𝑟)!

𝑢(𝑟)𝑣(𝑛−𝑟)𝑛𝑟=0 (15)

Based on the (𝜀𝑎)𝑌𝐼𝑅 Analytical Function Model (AFM) [3], the following initial sub-

yield zone and shear strength GECPROM functions for simulating various geo-changes, are derived.

I. Stress States (𝜎𝑠𝑠) BL The basic generalized equation defining the impact of stress states is expressed as:

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[𝜀𝑎]𝑌𝐼𝜎𝑠𝑠 =

�𝒜𝑝𝑜′𝜀 �(𝐾𝑐𝑠)𝑙×�𝑝

′

𝑝𝑜′�𝑚�+ℬ

𝑝𝑜′ ,𝜀𝐾𝐶𝑆𝑟�𝛼

𝜓(𝜀𝑎)𝑌𝐼

× �(𝜀𝑎)𝑌𝐼�𝑝𝑜′ , �𝜓(𝜀𝑎)𝑌𝐼>1,𝛼=−1≦1,𝛼=+1 (16)

Considering 𝜌𝑝′=𝑝′ 𝑝𝑜′⁄ and 𝜅 = 𝐾𝑐𝑠 then the Boundary Conditions (BC) are

defined as:

𝜕2(𝜀𝑎)𝑌𝐼𝜎𝑠𝑠

𝜕𝜌𝑝′2 < 0 𝑜𝑟

𝜕2(𝜀𝑎)𝑌𝐼𝜎𝑠𝑠

𝜕𝜅2< 0 𝑎𝑛𝑑

𝜕3(𝜀𝑎)𝑌𝐼𝜎𝑠𝑠

𝜕𝜌𝑝′3 ≠ 0 𝑜𝑟

𝜕3(𝜀𝑎)𝑌𝐼𝜎𝑠𝑠

𝜕𝜅3≠ 0 (17)

Carrying out 2nd order partial differentiation w.r.t 𝜌 we obtain,

�𝜕2(𝜀𝑎)𝑌𝐼

𝜎𝑠𝑠

𝜕𝜌𝑝′2 �

𝜅= 𝒜𝑝𝑜′ �(𝐾𝑐𝑠)𝑙 × 𝑚(𝑚 − 1) �𝑝

′

𝑝𝑜′�𝑚−2

�−1

× �(𝜀𝑎)𝑌𝐼�𝑝𝑜′ < 0 (18)

Performing the same w.r.t 𝜅 we obtain,

�𝜕2(𝜀𝑎)𝑌𝐼

𝜎𝑠𝑠

𝜕𝜌𝑝′2 �

𝜌𝑝′

=

⎩⎪⎨

⎪⎧𝒜𝑝𝑜′ �𝑙(𝑙 − 1)𝐾𝑐𝑠𝑙−2 × �𝑝

′

𝑝𝑜′�𝑚�

+ �𝐾𝑐𝑠ℬ𝐾𝐶𝑆

(𝑛−2)−𝑚𝐾𝐶𝑆

(𝑛−1)ℬ𝐾𝐶𝑆(𝑛−1)

(𝐾𝑐𝑠𝑛 )2�⎭⎪⎬

⎪⎫−1

× �(𝜀𝑎)𝑌𝐼�𝑝𝑜′ < 0 (19)

𝛿𝑅�𝜀𝑎Δ𝑛1�, which is indicated in the lower BL of the second component, which defines

the interface of the transition and transposition from the end of 𝜓𝑙𝑖𝑚[𝜎𝑠𝑠] to the beginning of 𝜓𝑙𝑖𝑚[ℒ𝐶𝑆𝑆𝐻] is solved analogous to Eq. (14) and Taylor’s Remainder Theorem resulting in the function;

𝛿𝑅�𝜀𝑎Δ𝑛1� = �

�(𝜀𝑎)𝐸𝐿𝑆ℒ𝐶𝑆𝑆𝐻�

𝑛−�(𝜀𝑎)𝐸𝐿𝑆

ℒ𝐶𝑆𝑆𝐻�𝑛−1

𝑛!� × 𝑓(𝑛)(𝜉), |lim𝑛→∞ 𝛿𝑅 → 0 (20)

II. Consolidation Stress-strain history (𝓛𝑪𝑺𝑺𝑯)

[𝜀𝑎]𝑌𝐼𝜎𝑠𝑠 = 𝒜ℒ𝐶𝑆𝑆𝐻

𝜀 ln(𝛿𝑆𝐶𝑇 × 𝜙𝑂𝐶𝑅) + �(𝜀𝑎)𝑌𝐼�𝑁𝐶𝑡𝑝

(21)

where 𝒜ℒ𝐶𝑆𝑆𝐻𝜀 =1.9×10-3 is a strain level dependent constant, 𝛿𝑆𝐶𝑇 is the secondary

consolidation factor, 𝜙𝑂𝐶𝑅 is the overconsolidation factor and �(𝜀𝑎)𝑌𝐼�𝑁𝐶𝑡𝑝

is the initial yield strain determined under normally consolidated conditions at a standard time period designated after the end of primary consolidation [5].

III. Drainage conditions (𝜑𝐷𝐶)

[𝜀𝑎]𝑌𝐼𝜑𝐷𝐶 = ��𝛥𝜎𝑎

′−2𝜈𝛥𝜎𝑟′��𝛥𝜎𝑎′−𝛥𝜎𝑟′�

�𝛽�𝑑 𝑢� �

× �𝜎𝑟′

𝜎𝑎′�𝐾𝐶

× �(𝜀𝑎)𝑌𝐼��𝑑 𝑢� � (22)

where Δ𝜎𝑎′ , Δ𝜎𝑟′ are the effective axial and radial stresses respectively determined at the threshold of �(𝜀𝑎)𝑌𝐼��𝑑 𝑢� �

, [𝜎𝑟′ 𝜎𝑎′⁄ ]𝐾𝐶 is the stress ratio during consolidation, 𝛽(𝑑)=-1,

𝛽(𝑢)=+1 (𝑑 : drained and 𝑢 : undrained) and 𝜈 is the Poisson’s ratio. For perfectly drained conditions 𝜈≑0.2 and 𝜈≑0.5 for perfectly undrained state.

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IV. Cyclic prestraining (𝛼𝑐𝑝)

[𝜀𝑎]𝑌𝐼𝛼𝑐𝑝 = 𝒜𝛼𝑐𝑝

𝜀 ln𝛼𝑐𝑝 + �(𝜀𝑎)𝑌𝐼𝑅 �

(𝑡𝑝), �𝜕

2(𝜀𝑎)𝑡𝑝𝜕𝛼𝑐𝑝2

= 0 𝑎𝑛𝑑, �𝜕3(𝜀𝑎)𝑡𝑝𝜕𝛼𝑐𝑝3

�𝛿𝑅

< 0 (23)

V. Strain rate (𝜀𝑎)𝑌𝐼�̇�𝑆𝑅

[𝜀𝑎]𝑌𝐼�̇�𝑆𝑅 = �𝒜�̇�𝑆𝑅 ln ��̇�𝐴𝑆𝑅

�̇�𝑅𝑆𝑅� + ℬ�̇�𝑆𝑅� × (𝜀𝑎)𝑌𝐼

�̇�𝑆𝑅 (24)

where, the subscripts SR denote Strain Rate, ASR: Applied Strain Rate during testing or arbitrary designation and RSR: Reference Strain Rate. VI. Deriving shear strength from elastic stiffness and introducing some modeled results Developing an appreciably reliable correlation between shear strength at failure and the elastic (Initial) stiffness is important in determining a more precise parameter (qmax) closely related to a ground property (E0). The GECPROM module for this relation is:

𝑞𝑚𝑎𝑥 = 𝐴𝜓𝐸0 × exp [𝐵𝜑𝐶𝑆𝑆 ln�𝑚−1 × (𝜎𝑎)𝑚𝑎𝑥 × 𝐸0� − 𝐶𝜑𝐶𝑆𝑆 (25)

𝐴𝜓𝐸0 = 0.134, 𝐵𝜑𝐶𝑆𝑆 = 0.418, 𝐶𝜑𝐶𝑆𝑆 = 0.936, 𝑎𝑛𝑑 𝑚−1 = 1.32

Figures 6 and 7 depict the experimental and modeled characteristic curves for small stress ~ strain behavior and the decay of stiffness plotted as a function of strain level respectively. Figure 7(b) includes curves that predict ageing effects on the characteristics of the decay curves. The results conform to the tendency of experimental data reported by various researchers [1] [6]. In these figures all the curves modeled by the GECPRO show a very good agreement in comparison to the experimental trends. It can also be inferred that the curves for the reconstituted specimens deviate significantly from those of the intact ones in all cases.

Figure 6 Comparison of modeled and experimentally measured relations for intact and reconstituted Overconsolidated (OC) OAP clay from Osaka, Japan, for (a) small stress ~ strain characteristics (𝜀𝑎 ≤0.01%) and, (b) very small stress ~ strain characteristics (𝜀𝑎 ≤ 0.003%)

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Figure 7 Comparison of modeled and experimentally determined strain level dependency of stiffness decay curves for Overconsolidated (OC) OAP clay from Osaka, Japan, for (a) Intact and reconstituted specimens and, (b) Prediction curves for ageing effects for intact and slightly disturbed specimens

It can be further derived that the elastic modulus measured from field seismic survey, 𝐸𝑓 plotted in Figure 7(b) confirms the reliability of the laboratory experimental data. For generating the prediction curves that characterize 𝐸𝑠, and 𝐸0, Eqs. (26) and (27) were applied in conjunction with Eqs. (16) ~ (24).

𝐸𝑆 = 𝑑𝛥𝑞𝑑𝛥𝜀𝑎

= 𝜓𝐸𝑆 × �𝐺 = 𝐸𝑆

2(1 + 𝜈)� 𝛼𝐸𝑆(𝜀𝑎)𝑚

+𝛽𝐸𝑆(𝜀𝑎)𝑛 + 𝛾𝐸𝑆� × 10(𝑀𝑃𝑎) (26)

�𝑚 = 1𝑛 = 0𝑎𝑛𝑑 𝜓𝐸𝑆

= 1.257 𝑤ℎ𝑒𝑛 0 ≦ 𝜀𝑎 ≦ 0.1 and, �𝑚 = 2𝑛 = 1 𝑎𝑛𝑑 𝜓𝐸𝑆

= 1.77𝑤ℎ𝑒𝑛 𝜀𝑎 > 0.1 and,

𝐸𝑜 = �𝛼𝐸𝑜(𝜀𝑎)=0.001% + 𝛽𝐸𝑜� × 10(𝑀𝑃𝑎) (27)

where 𝜈 = 𝑃𝑜𝑖𝑠𝑠𝑜𝑛𝑠 𝑟𝑎𝑡𝑖𝑜, 𝑤ℎ𝑖𝑙𝑒 𝛼𝐸𝑜 and 𝛽𝐸𝑜 are determined by employing simultaneous equations at designated strain levels 𝜀𝑎=0.001% and 𝜀𝑎=0.01%.

6. Conclusions

Vital geotechnical engineering parameters were determined from experimental testing based on geophysical surveys and mechanical methods of testing. The main conclusions that can be drawn from this study include the following.

1. The proposed empirical relations for bearing capacity, strength and elastic modulus (initial stiffness) may be useful in correlating design parameters for versatility, enhanced precision and actual ground simulation.

2. As demonstrated in this paper, the method of quantitatively determining the zonal sub-yield strain magnitude proposed in this study is not only important in modeling but can also be useful in the prediction of the magnitude of ground movement under loading and construction control.

3. The proposed GECPROM is versatile and appreciably effective in probing, simulating, modeling and predicting geotechnical changes in ground.

4. Remolding (reconstitution) completely destroys the intrinsic structure of structured clays. Theories and concepts based on reconstituted clay behavior are therefore inadequate in modeling the behavior of natural clays.

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References [1] Mukabi J.N, Deformation Characteristics at Small Strains of Clays in Triaxial Tests, PhD Thesis, Institute of Industrial Science, University of Tokyo, Tokyo, Japan, 1995. [2] Menzies, B.K., Near-surface site characterisation by ground stiffness profiling using surface wave geophysics," Instrumentation in Geotechnical Engineering. H.C.Verma Commemorative Volume, Oxford & IBH Publishing Co. Pvt. Ltd., New Delhi, Calcultta. pp 43-71, 2001. [3] Mukabi J.N., Characterization and Modeling of Various Aspects of Pre-failure Deformation of Clayey Geomaterials, to be published. [4] Mukabi J.N., Kotheki S. (2010a) - Mathematical Derivative of the Modified Critical State Theory and its Application in Soil Mechanics. Procs. 2nd International Conf. on Applied Physics & Mathematics, 2010 IACSIT, Kuala Lumpur, Malaysia. [5] Mukabi J.N, Tatsuoka F. (1999c) - Effects of stress path and ageing in reconsolidation on deformation characteristics of stiff natural clays. Proc. 2nd I.S Pre-failure characteristic of geomaterials, Torino, Italy. [6] Tatsuoka F., Jardine R.J., Presti D.L., Benedetto H. D. Kodaka T. ( 2000) – Characterising the pre-failure deformation of geomaterials. XIV ICSMFE in Hamburg, Theme Lecture.