Priti Maheshwari

Nonlinear response of footings on granular bed-stone column-reinforced poor soil

Abstract In this paper, an attempt has been made to model and analyze the footings, having finite flexural rigidity, lying on granular bed-stone column-reinforced poor soil system. The granular bed placed over stone column reinforced earth beds has been idealized by the Pasternak shear layer. The natural occurring poor soil has been idealized as Winkler springs and stone columns have been idealized as stiffer Winkler springs. Nonlinear behavior of granular bed, natural occurring soil and the stone columns has been considered in the analysis and has been incorporated by means of hyperbolic constitutive relationships. Governing differential equations for the soil-foundation system have been obtained and finite difference method has been adopted for solving these by means of Gauss-Elimination iterative scheme. A detailed parametric study for a combined footing subjected to concentrated column loads at its edges has been carried out to study the influence of various parameters on the flexural response of the footing. These parameters include magnitude of applied load, flexural rigidity of footing, diameter of stone column, spacing of stone column, ultimate bearing capacity of granular fill, poor foundation soil and stone column and relative stiffness of stone columns. It has been found that ultimate resistance of granular fill in shear has negligible effect on the response of soil foundation system. However, other parameters have been found to significantly affect settlement and the bending moment in the footing.

Strip footings on a three layer soil system: theory of elasticity approach

Abstract An attempt has been made in this paper to predict deformations and stresses built up in a three layer soil medium supporting a strip footing. Soil layers have been considered to have different elastic modulii. The governing differential equations have been derived in terms of horizontal and vertical displacements using the theory of elasticity and solved numerically using the finite difference method. This paper also includes the parametric study which was undertaken to understand the influence of both relative thicknesses and the relative elastic modulii of various soil layers on vertical displacements and stresses in the entire medium. Due consideration has been given to the range of parametric values, normally found valid in case of foundations of conventional and the industrial structures. The analysis clearly highlights that vertical displacement of the footing reduces with increase in upper and middle soil layer thicknesses and with the ratio of modulii of these layers. Presence of a stiffer middle layer helps in reducing the vertical stresses at the top of lower soil layer.

Response of Infinite Beams on Geosynthetic-Reinforced Granular Bed over Soft Soil with Stone Columns under Moving Loads

AbstractThis paper pertains to the development of a simplified model for an infinite beam subjected to a concentrated load moving with constant velocity and resting on geosynthetic-reinforced granular bed over soft soil improved with stone columns. The granular fill has been modeled as a Pasternak shear layer while naturally occurring saturated soft soil has been idealized by a Kelvin-Voigt model, stone columns by Winkler springs, and geosynthetic as rough elastic membrane. Nonlinear behavior of granular fill, stone columns, and the soft soil has been represented by means of hyperbolic constitutive relationships. An iterative finite difference scheme has been adopted for obtaining the system response by employing the Gauss-Seidel technique. The system response has not been found to be sensitive at lower velocities of the applied load. Damping has been found to influence the response at higher velocities. Ultimate shear resistance of granular fill has a negligible effect on the response of the system.

Generalized model for footings on geosynthetic-reinforced granular fill-stone column improved soft soil system

Abstract The present study pertains to the modeling and analysis of combined footings resting on geosynthetic reinforced granular fill overlying stone column improved soft soil. The footing has been assumed to have finite bending stiffness. Granular fill layer below the footing has been idealized as Pasternak shear layer. The geosynthetic layer has been provided in between the granular fill layer and assumed as an elastic membrane. Stone columns and saturated soft soil have been represented by nonlinear Winkler springs and Kelvin - Voigt body respectively. Nonlinear behaviors of granular fill layer, stone columns and the soft soil have been considered by means of hyperbolic stress strain relationships. Results of a detailed parametric study have been presented, for a footing supporting typically five columns, in non-dimensional form in respect of deflection and bending moment in footing and mobilized tension in the geosynthetic layer. Influence of applied loads, flexural rigidity of footing, diameter and spacing of stone columns, ultimate resistance of soft soil, stone columns and granular fill layer, relative stiffness of stone column with respect to the surrounding soft soil and average degree of consolidation has been studied considering wide range of physically possible model parameters of soil - foundation system. The effect of inclusion of geosynthetic layer has also been studied. Geosynthetic layer has been found to significantly reduce the deflection of the footing and the same has also been quantified by means of parametric study.

Stochastic design of beams on reinforced random earth beds in deterministic mode

One of the main soil parameters in analysis and design of foundations is modulus of subgrade reaction (MSR) which is a stochastic process. However, design engineers prefer a deterministic approach invoking mean of MSR and rather empirical factors of safety to account for the uncertainty. The present study includes the stochasticity in the deterministic designs by linking the factors of safety (in respect of maximum deflection and bending moment) to the allowable risk of failure through a Monte Carlo simulation on a lumped parameter deterministic model. A parametric study reveals that for a given risk level, the factors of safety are strongly dependent upon the coefficient of variation of MSR, and only mildly upon other geometric parameters of foundation system. This facilitates development of closed form equations for the upper bounds on factors of safety exclusively in terms of allowable risk of failure and the coefficient of variation of MSR.

Rationalization of factors of safety in analysis of beams on geosynthetic reinforced random earth beds by Monte Carlo simulation

Abstract The paper presents an approach for rationalizing the factors of safety in the analysis and design of foundations, wherein a single lumped value is assigned to an uncertain soil parameter on the basis of multiple field testing. A soil-foundation system, comprising a geosynthetic layer (idealized as a beam) placed over a random poor soil and overlain by a compacted sand layer and the foundation beam, has been modeled in a lumped parameter mode. The model parameters comprise among other, the relative stiffness of the random poor soil that has been treated as a lognormally distributed random variable. Monte Carlo simulation has been performed on the model at various levels of the coefficient of variation (COV) of the uncertain/random parameter to arrive at the probability distribution functions (PDF) of the state variables viz., the normalized mid-span deflection and bending moment in the foundation beam. These PDFs have been subsequently invoked to correlate the factors of safety to the COV and the risk of failure. It has been suggested that factors of safety should be introduced in the foundation design by considering COV of the uncertain soil parameters and the allowable risk.

Stochastic analysis of beams on reinforced earth beds

The present study comprises Monte-Carlo simulation assisted analysis of foundations resting on reinforced earth beds using the concept of beams on an elastic foundation, treating the modulus of subgrade reaction (MSR) as a stationary stochastic field characterised by mean, variance, autocorrelation function (ACF) and the autocorrelation distance (ACD). Realisations of the MSR, generated by solving a stochastic differential equation, are fed to a deterministic distributed parameter model to generate realisations of two dependent stochastic fields, namely deflection and bending moment in the foundation beam, and two random variables, namely the location of occurrence of maximum deflection and the bending moment. Subsequently these realisations are analysed to evolve probability distribution functions, variance and ACF of the dependent stochastic fields and the random variables. It is revealed that the ACF of these fields is independent of the ACF of the MSR. Further, variance of deflection is found to increase as the ACD of the MSR increases, implying requirement of a larger factor of safety when random soils display low frequency (macro level) variations. On the other hand, variance of the bending moment is larger at smaller ACDs of the MSR, indicating that for bending moments a larger factor of safety is required when the random soils display high frequency (micro level) variations.

Strengthening of clay by geogrid reinforced granular pile

Abstract In the present work an attempt has been made to study the behavior of a single pile reinforced with the layers of geogrid and installed in soft clay. Laboratory tests have been conducted to study the response of a geogrid reinforced granular pile under a rigid circular footing. The influence of spacing of geogrid layers and reinforced depth of pile (depth of bottom most geogrid layer), on the performance of reinforced pile has been investigated. Finite element numerical analysis has also been carried out employing rocscience, Phase2, version 6 and the comparison of results has been done with those from the experimental study. In order to validate the general findings from the study, results have also been compared with those from relevant published literature. Geogrid reinforced granular pile has been found to result in significant increase in load carrying capacity. The bulge diameter of pile has been found to reduce due to the incorporation of geogrid layers as reinforcement.

Settlement of shallow footings on layered soil: state-of-the-art

Abstract Shallow footings form the foundations of conventional structures like residential as well as industrial framed buildings and also other industrial structures like silos, chimneys, cooling towers, overhead tanks, etc. The foundations are checked both for shear failure and settlement criterion. Most of the conventional analyses consider the soil to be homogeneous, however, soil strata comprise of different soil layers with inherent variability. Several analytical, numerical, and experimental research works are available for the analysis of shallow footings on layered soil system. This paper presents comprehensive overview of literature pertaining to the settlement analysis of shallow foundations on layered soil system. It was aimed to provide all the references at one place to facilitate the research workers in this area. Deterministic as well as probabilistic studies have been compiled and it is felt that deterministic methods should be used in conjunction with the stochastic approaches for more rational analysis of shallow foundations on layered soils.

Infinite beams on stone column reinforced tensionless earth beds under moving loads

Abstract In the present study, an analysis of a rail, idealized as an infinite beam, resting on a granular bed-stone column reinforced earth bed has been carried out under a load moving with constant velocity. The granular fill layer just below the rail has been modeled as the Pasternak shear layer, while stone columns as non-linear Winkler springs and foundation soil as non-linear Kelvin–Voigt body. As the load moves on rail, the rail tends to separate from the ground. This separation has been modeled (tensionless foundation) by means of appropriate deflection and soil reaction conditions. Governing differential equations of the soil–foundation system have been obtained and have been solved with proper boundary and continuity conditions. The Gauss–Siedel iterative method has been employed to obtain the solution of finite difference form of these equations. Detailed parametric study revealed that the velocity of load, the damping of the soil–foundation system, and the ultimate resistance of soft soil and granular fill layer has the least influence on the response of system. However, the magnitude of load, ultimate resistance of stone columns, diameter and spacing of stone columns, and degree of consolidation and relative stiffness of stone columns with respect to the surrounding soil have been found to significantly affect the response of the system. The influence of all these parameters has been quantified and presented in the form of readily usable non-dimensional charts.