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This paper presents a comprehensive study on the effect of spatial variability of the elastic modulus on vertical stress distribution in an elastic half-space due to strip loading. The modulus of elasticity is considered as a random variable which follows a log-normal probability distribution. A random field theory based on a Cholesky decomposition technique is used to generate a two-dimensional random field in the elastic half-space. Monte Carlo simulation is performed to generate various random fields with spatially varying elastic modulus. A two-dimensional random finite-element model is developed for a strip loading on an elastic half-space by coupling the random fields generated by Monte Carlo simulation with finite-element analysis. A detailed investigation of the effect of statistical variables defining spatial random variation of the elastic modulus on the vertical stress distribution and the settlement analysis in random elastic half-space is performed. The present study indicates that the spatial random variation of elastic modulus of the soil has a significant effect on the vertical stress distribution and the settlement analysis in the elastic half-space. © 2022 American Society of Civil Engineers.

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Civil Engineering

(SoE) School of Engineering

International Journal of Geomechanics

Uncertainties in Vertical Stress Distribution in Spatially Varying Random Elastic Half-Space

Interface modeling is one of the important components in the numerical modeling of soil–structure interaction problem. It is equally important as material and geometrical modeling. Inaccurate modeling of the interface between the soil and the structure may lead to unreliable results. However, in many cases, interface modeling is overlooked and the interface between the soil and the structure is generally modeled as a rigid connection. In the present paper, we have shown the influence of interface modeling in the analysis of laterally loaded deep foundations. A finite element model of laterally loaded foundation–soil system is developed wherein the foundation is modeled as a linear elastic system and the soil as nonlinear which is defined by the multi-yield surface plasticity model. The interface between the soil and the foundation is modeled using zero thickness contact element, which is defined, by constitutive relationships capable to define sliding and separation mechanisms at the interface. The results obtained from the proposed finite element model are then compared with the conventional approach of interface modeling. The present study indicates that the conventional approach overestimates the lateral load capacity of deep foundation as well as it is unable to explain the mechanisms of the deformation of laterally loaded foundation–soil system. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

Lecture Notes in Civil Engineering

Significance of Interface Modeling in the Analysis of Laterally Loaded Deep Foundations

Well foundation is commonly used in India for road and railway bridges over rivers. It is a massive structure and hence it is generally considered to be safe under laterally loaded condition. Indian Roads Congress Codes (IRC:45-1972 and IRC:78-1983) suggests limit equilibrium approach to determine lateral load capacity of well foundation. It considers well foundation as a rigid body and surrounding soils as elastic in design state and plastic in limit state. Design procedure stated in Indian standard codes determines ultimate lateral load capacity of Well-Soil system. However, it does not yield the magnitude of lateral displacement of a well foundation at the ultimate load. Because of this, it is difficult to decide whether the lateral displacement at estimated ultimate lateral load capacity of a well foundation is allowable or not. Over the years, few methods to analyze the lateral response (both force and displacement responses) of well foundation are developed. These methods consider surrounding soil as linear elastic material which is modeled by linear elastic springs, and well foundation as a rigid body. Recently developed methods consider lateral stiffness as well as rotational stiffness of the surrounding soil and represent soil by parallel combination of lateral linear springs and rotational springs. Some of these methods also consider flexibility of well foundation and model well foundation by Euler-Bernoulli beam element. In this article, we present a comparative study of the available methods of analysis of laterally loaded well foundation. This study indicates significant differences in the response of Well-Soil system obtained from different methods. Validation of existing methods is done with two-dimensional continuum model to identify accuracy in existing models. It highlights the need for proper evaluation of available methods of analysis with realistic incorporation of foundation stiffness and interface effect in modeling the Well-Soil system for pseudo static loading conditions. © Springer Nature Singapore Pte Ltd 2020.

Comparative study of methods for analysis of laterally loaded well foundation

This paper presents critical assessment of codal provisions to determine lateral stability of a well foundation. A two-dimensional finite element model of soil–well foundation system is developed for this study. The well foundation is modeled as a linear elastic body, whereas the soil as a nonlinear elasto-plastic material which is defined using multi-yield surface plasticity model. Interface between the well foundation and the adjoining soil is defined using constitutive relationships describing relative sliding and separation at the interface. Assumptions considered in the existing codal provisions to determine lateral stability of a well foundation are evaluated in light of the results obtained from the present study. The present study shows that the mechanism of deformation of laterally loaded soil–well foundation system obtained in this study differs from that considered in the existing codal provisions. It is observed that the existing codal provisions overestimate the lateral load capacity of a well foundation. © 2020, Indian Geotechnical Society.

Indian Geotechnical Journal

An Assessment of Codal Provisions for Analysis of Laterally Loaded Well foundations

This paper presents, the effect of soil spatial variability on response of laterally loaded well foundation embedded in linear elastic soil medium. The spatial variation of elastic modulus of soil along embedment depth of the foundation is modeled using random field theory. Elastic modulus of soil is considered to be random variable that follows Log-Normal probability distribution. Monte Carlo simulation technique is used to generate various random realization of spatial variability of elastic modulus of soil. Random realization is done for different values of coefficient of variation of elastic modulus with different spatial correlation distance. A finite element model is developed for laterally loaded well foundation embedded in linear soil. The finite element model is then coupled with the random field of elastic modulus of soil to analyze effect of soil spatial variability on the response of well foundation under different values of lateral load. The results obtained from this study indicate that spatial variation of soil elastic properties has small effect on lateral response of well foundation irrespective of magnitude of lateral load. © Springer Nature Singapore Pte Ltd. 2020.

Effect of soil spatial variability on lateral response of well foundation embedded in linear elastic soil

Constant rate of strain (CRS) consolidation test is a fast test method to characterize consolidation behavior of fine grained soils. In this test method, the test specimen is deformed at a constant rate of deformation, and pore water pressure at the base of the test specimen and axial reaction load are measured at successive interval during the test. This test method has several advantages over traditional incremental loading consolidation test. In the present research, a series of CRS consolidation tests have been performed on reconstituted samples of eight different clayey soils with different plasticity indices. The suitable strain rate at which the test is to be performed has been decided considering the criterion given in the literature. The test data obtained from these tests have been analyzed through the method of interpretation given in ASTM: D4186-06 (Standard Test Method for One-Dimensional Consolidation Properties ofSaturated Cohesive Soils Using Controlled-Strain Loading. 2008). The present study shows that the existing method of interpretation yields unreliable results for a significant duration at early stage of the test despite of performing the test at recommended strain rate. Analysis of present experimental data and some of the available recommendations to select suitable strain rate indicates that the theory for CRS consolidation which forms the basis for the existing method of interpretation is unable to describe rapid evolution of pore-water pressure at early stage of the test. Because of this, the existing method of interpretation fails to interpret the consolidation parameters accurately throughout the test. © 2019, Springer International Publishing AG, part of Springer Nature.

Sustainable Civil Infrastructures

Issues in Interpretation of Constant Rate of Strain Consolidation Test Data

In this paper, we present an alternative solution of consolidation at constant rate of deformation (CRD). Governing equation of CRD consolidation is formulated considering excess pore water pressure as primary variable. Formulation of the governing equation is done for soil as linear as well as nonlinear materials. An analytical solution to the governing equation is derived which consists of transient state and steady state components. The solution derived herein yields profile of excess pore water pressure distribution with depth at any time during the test. The present paper analyzes the excess pore water pressure distribution profile during CRD consolidation and factors affecting it in detail. Analysis of the obtained solution indicates the existence of moving boundary condition within the test specimen at early stage of the test where transient state condition prevails. It also indicates that the pore water pressure ratio affects significantly the excess pore water distribution profile, in turn, average value of pore water pressure and average effective stress in the specimen. An expression for consolidation parameters for steady state condition are derived using the present solution. Further, evolution of excess pore water pressure at the base of CRD consolidation test specimen during the test is predicted for normally consolidated as well as for over consolidated soils at different rates of deformation. © 2018, Springer Nature Switzerland AG.

Geotechnical and Geological Engineering

Alternative Analytical Solution of Consolidation at Constant Rate of Deformation

Compression response of fine grained soils is generally modeled by bilinear relationship between void ratio (e) and logarithmic of effective stress (σ'). In general, compression curve of overconsolidated soil is nonlinear in nature as it varies smoothly from linear portion of initial part of the curve to the linear portion of the later part of the curve. The bilinear model is unable to represent the smooth transition of the compression curve. As a result, it leads to an overestimation of the settlement and introduces a kink in the predicted stress-strain relationship of overconsolidated soil from the elasto-plasticity model wherein it is used as a component defining volumetric hardening. The present paper proposes a simple three parameters transitional plasticity model to predict the compression response of clayey soil more accurately. The proposed model considers that the irrecoverable deformation due to relative sliding between the adjacent particle and particle groups has possibility from beginning of the loading in over-consolidated region as well. © ASCE.

Geotechnical Special Publication

Transitional Plasticity Compression Model for Clays

The effect of microfabric on the mechanical behaviour of clays has been explored previously based on the response of dispersed and flocculated microfabrics only. However, the natural clays often have the geometric arrangement of particles between these two extreme cases which can be termed as intermediate microfabric. This paper explores the formation of intermediate microfabric of kaolin clay and its impact on soil's consolidation behaviour by performing self-weight consolidation, slurry consolidation and 1-D consolidation tests. The effect of calgon content (dispersing agent) on geometric arrangement of the particles has been evaluated through cluster size distribution by performing double hydrometer tests. Then these clay slurries have been used to perform the AFM (Atomic Force Microscopy) test to obtain the variation in average angle of particle orientation with respect to the calgon content present in the slurry. AFM technique provides 3D image of the clay sample and 2D image with Z-information with the potential of measuring intermediate microfabric of clayey soil quantitatively including dispersed and flocculated microfabrics. Other traditional techniques such as SEM, TEM & XRD are limited to only qualitative analysis of soil's microfabric, thus, having no capability to measure intermediate microfabric of clay. A methodology of preparing bulk specimens of clay with intermediate microfabric has been developed using slurry consolidation technique; and then these specimens have been consolidated under 1-D loading to evaluate the effect of intermediate microfabric on compressibility and permeability of clay. In this study, all the experiments reports that the dispersed type geometric arrangement increases with the increase in calgon content in soil up to 2 % and then the reverse behaviour is observed at 3 %; which may depend on the required amount of sodium cations to neutralize the negatively charged faces of the clay platelets present in the slurry. © 2012 Springer Science+Business Media Dordrecht.

Development of Intermediate Microfabric in Kaolin Clay and Its Consolidation Behaviour

Natural soil deposits commonly exhibit cross-anisotropy about a vertical axis due to their depositional environment. This paper presents a study of the vertical stress distribution in a cross-anisotropic elastic soil deposit due to a point load. The study is based upon the exact solution derived by Liao and Wang (1998) that uses Fourier and Hankel transforms to solve the governing differential equations of the displacement functions. The solution has been first modified to consider a reduced parameter elastic model for cross-anisotropy as proposed by Graham and Houlsby (1983). The vertical stress distribution in the soil has been studied for a vertical point load with a varying degrees of anisotropy. © 2010 ASCE.

Vertical stress under point load on cross-anisotropic elastic half-space with reduced parameter material model

Design of many geotechnical problems, such as the stability of slopes and excavations, are strongly governed by the shear strength of soil represented in three dimensions. In literature, a number of failure criteria have been proposed using isotropic invariant of stress tensor in three dimensional stress spaces. For a linearly pressure-dependent material, there are four basic failure criteria which have been commonly used to describe the behavior; Mohr-coulomb, Drucker - Prager (1952), Lade and Duncan (1975), and Matsuoka and Nakai (1985). Mohr-Coulomb criterion is defined in a 2-D stress space and it follows plane strain condition. The other three which are 3-D failure criteria have been considered during this study for analysis. Calibration of such a model is relatively easy when the tests are performed in axisymmetric conditions and principal stresses are applied on the specimen, e.g. triaxial tests. This paper will present the solutions for calibrating such failure criteria assuming associative flow rule and using the shear strength parameter (ps) obtained from the laboratory tests performed under plane strain conditions e.g. Direct Shear and Simple Shear Test. © 2010 ASCE.

Calibration of 3-D failure criteria for soils using plane strain shear strength data

The experimental findings on the mechanical behavior of clays with dispersed microfabric are indicative of the need for comprehensive evaluation of the constitutive theories being widely used in practice. The clay deposits can be found having all the stages of microfabrics in their natural state and the dispersed microfabric is one of those. Despite the fact that the effects of microfabric can be radical sometimes, those are seldom given due consideration during the design process. Since the success of numerical modelling of a geotechnical structure is strongly dependent on the accuracy of the constitutive equations, the results produced by commonly used constitutive models can be highly misleading. The present paper is focused on identifying such issues which make the study of dispersed clays important and show the need for incorporating the influence of microfabric into constitutive formulations. Two of the most widely known models, Modified Cam-Clay (MCC) model (Roscoe and Burland, 1968) and the single hardening (SH) model (Lade, 1990), have been calibrated for the Kaolin clay with dispersed microfabric and the predicted response has been compared with the experimental observations. This comparative study has been used to provide an insight into the important issues which still need attention.