P. K. Basudhar

Generalized stability analysis of reinforced embankments on soft clay

By modifying Janbus generalized procedure of slices (GPS), the stability of a reinforced embankment constructed on a non-homogeneous clay deposit of finite depth is analysed to compute the factor of safety. The non-circular critical surface corresponding to the minimum factor of safety is obtained by a sequential unconstrained minimization technique in conjunction with a conjugate direction method for a multidimensional search and a quadratic interpolation technique for a unidimensional search. The effect of the thickness of the desiccated zone and the variation of undrained shear strength of clay with depth on the factor of safety is considered in the analysis. The influence of the tensile reinforcement force on the location of the critical surface is presented. The effects of the tensile reinforcement force and its orientation as well as the number of reinforcing layers on the stability of embankment have also been studied. The results obtained from the present analysis are compared with solutions reported in the literature.

Applicability of Burger Model in Predicting the Response of Viscoelastic Soil Beds

This paper presents a critical review of various viscoelastic lumped parameter models (Maxwell model, Kelvin-Voigt model, Poynting-Thompson model and Burger model) commonly used to represent the stress-strain-time behavior of a compressible viscoelastic medium. Efficacy of such models has been checked to suggest a rational model so as to represent the time-dependent behavior of such media. Though Burger’s four element model can incorporate all the phenomena of viscoelastic behavior of materials and all other models can be degenerated to other lower order models, it has not yet found general acceptability amongst the soil engineers to model such behavior of soils. Through this study, an effort has been made to demonstrate that it is probably the most effective model to predict the behavior of structures resting on such soils. Therefore, the efficacy of the model so chosen has been demonstrated through a case-study available in literature. Based on the studies, it has been inferred that the Burger model possesses an excellent potential for proper representation of the time-dependent behavior of a saturated viscoelastic medium when subjected to loading an unloading phenomena.

Interference of Two Asymmetric Closely Spaced Strip Footings Resting on Nonhomogeneous and Linearly Elastic Soil Bed

AbstractThis paper presents a study using the FEM on the effect of interference on the settlement of two closely spaced rough rigid strip footings resting on the surface of linearly elastic finite and infinite nonhomogeneous soil beds with the modulus of elasticity linearly varying with the depth. Both symmetric and asymmetric cases with respect to its geometry and applied loading have been considered in the analysis. The finite-element (FE) mesh was created using four-noded isoparametric elements. The results are presented in terms of the interaction factors, which are defined as the ratio of the settlement of the interfering footings with the corresponding value of the settlement of the isolated footing identifying the influence of the size of the footings, loading on the footings, and clear spacing between the footings. The settlement of the interfering footings is observed to be greater than the settlement of the isolated footing of the same width and loading. With an increase in the stiffness of the ...

Determination of the optimal lower-bound-bearing capacity of reinforced soil-retaining walls by using finite elements and non-linear programming

Abstract In this paper, the application of a generalized approach to the estimation of the lower-bound-bearing capacity of reinforced soil-retaining walls by using the finite-element technique in conjunction with non-linear programming to isolate the optimal solution is successfully demonstrated. The analysis is based on a rigid-plastic model for reinforced soil, treating it as a macroscopically homogeneous anisotropic material. The results obtained are found to be in good agreement with the theoretical and experimental data reported in the literature.

Flexural response of surface strip footings resting on reinforced viscoelastic foundation beds

Abstract A generalized method of analysis has been proposed to determine the flexural response of a surface strip footing resting on a compacted granular foundation bed overlying a clay layer of soft to medium consistency with geogrid/geomat/ geocell reinforcement at their interface. The footing and the reinforcement are idealized as beams with sufficient flexural rigidity. The compacted granular bed and the clay layer are idealized by Winkler springs and four-element standard viscoelastic Burger element respectively. The rationality of choosing Burger model to represent the time-dependent behavior of compressible viscoelastic medium has been elucidated. A non-uniform variation of the subgrade modulus is assumed along the width of the footing at the soil-structure interface. Governing differential equations, predicting the response of the reinforced foundation bed under the given loading condition, are developed; and solved using the Finite Difference Method (FDM). Based on the convergence study, optimal size of mesh segment is determined; and the correctness of the study has been established by comparing the solution from a degenerated case with the standard solutions available in literatures. Effect of variation in the viscoelastic parameters of the Burger model on the flexural response of the reinforced foundation bed has been discussed. It is shown that the Burger model can be degenerated to any lower order models by proper modifications in the viscoelastic parameters of the Burger model. Significant variation in the bending moment of footing is observed with elapsed time, thus revealing the necessity of considering the effect of time in the design of reinforced viscoelastic foundation beds.

Parameter Optimization of Rock Failure Criterion Using Error-in-Variables Approach

Parameters of rock failure criteria are estimated using an optimization procedure based on appropriate objective function. In the development of objective function, it is assumed that the independent variables are free from errors. But, as measurement error is attributed to equipment and random testing effects, all the measuring variables may have some error. In such cases, a statistical approach known as error-in-variables (EIVs) method has been proposed in literature. In EIV, the parameter vectors and reconciled values of the measured variables are estimated. The parameter estimation of such problem is associated with increase in dimensions of the optimization problems, and due to chosen nonlinear models, the resulting optimization problem is generally nonconvex. In the present study, the EIV approach has been applied for estimation of rock strength parameter for multiaxial rock failure criteria using evolutionary optimization algorithms. The rock strength parameters and the mean square error values so ...

Estimation of Burger model parameters using inverse formulation

Abstract This paper reports the development of a generalized inverse analysis formulation for the parameter estimation of four-parameter Burger model. The analysis is carried out by defining the problem as a mathematical programming formulation in terms of identification of the design vector, the objective function and the design constraints. Thereafter, the formulated constrained nonlinear multivariable problem is solved with the aid of fmincon: an in-built constrained optimization solver module available in MatLab. In order to gain experience, a synthetic case-study is considered wherein key issues such as the determination and setting up of variable bounds, global optimality of the solution and minimum number of data-points required for prediction of parameters is addressed. The results reveal that the developed technique is quite efficient in predicting the model parameters. The best result is obtained when the design variables are maintaining a lower bound while providing a full slack on the upper bound. Global optimality of the solution is achieved using the developed technique. A minimum of 4-5 randomly selected data-points are required to achieve the optimal solution. The developed technique has also been tested for real-time field and laboratory investigations with encouraging results.

Flexural Response of Beams on Reinforced Foundation Beds

The paper aims to study the flexural response of the foundation of a surface reservoir resting on a dense granular foundation bed overlying a weak clay layer with the reinforcement possessing sufficient bending stiffness placed at their interface. The footing and reinforcement are idealized as free-ended beams. The overlying compacted granular layer and the underlying clay layer are idealized respectively by Winkler Springs and four-element standard visco-elastic Burger model. A quadratic variation of the subgrade modulus is assumed along the length of the footing at the soil-structure interface with the corresponding maximum value being at the centre and progressively decreasing to minimum at the edges. The resulting differential equations are discretized by using Finite Difference Method (FDM), and the set of linear equations so obtained is solved by Gauss-Seidel iterative technique. Studies were carried out to obtain the optimal element size for convergent solution and establish its correctness by comparing the same with available solutions. Parametric studies to find the effect of time, relative stiffness and viscosity, interface friction and the distribution of subgrade reaction on the flexural behavior of the footing are also reported here. INTRODUCTION Very often geotechnical engineers are called upon to build structures on soft ground. Under such condition it is common to place a layer of geosynthetics reinforcement (geotextile, geogrid, geomat, geocell etc.) over it and then place a dense compacted layer of sand and construct the structure over the reinforced foundation bed, so made, for improved performance. Shukla and Chandra (1994) studied the settlement behavior of such reinforced beds. However, they considered the settlement of the soft clay layer as a function of the degree of consolidation and thus took into account indirectly the time dependency of the solution in the analysis. But, it will be more appropriate if this effect can be incorporated directly in the analysis, modeling the soft clay layer by four element standard visco-elastic model (Burger model) (Flugge, 1967). Such a study has not yet 17 ANALYSIS AND COMPUTATION SPECIALTY CONFERENCE th Copyright ASCE 2006 17th Analysis and Computation Conference been made to analyze the flexural response of beams resting on reinforced beds and therefore, in the present article such an attempt has been made. STATEMENT OF THE PROBLEM A surface reservoir resting on a densely compacted granular fill laid over a weak clayey deposit of medium to soft consistency (100 25 kN/m) (Murthy, 2001) with a layer of reinforcement placed at their interface is depicted in Figure 1. Both the footing and the reinforcing layer are idealized as elastic beams of flexural rigidity and respectively. The lengths of the footing and reinforcing beam are and respectively. Two concentrated loads of magnitude each, representing the wall loads from the tank, are acting at the edges of the beam. The self weight of the footing is neglected in comparison to the water pressure (w/unit length) acting on it. Edge moments also act when the tank is either fully or partially filled with water. The unit weights of the upper and lower soil media are 1 1I E

Optimal lower-bound solutions of plane-strain metal indentation and extrusion problems

Abstract A generalized procedure based on finite elements and non-linear programming to obtain lower-bound solutions for indentation and extrusion through a frictionless flat die is presented in this note. The validity of the method has been demonstrated successfully by comparing the values predicted with those of solutions available in the literature.

Flexural response of beams on viscoelastic foundations with predictions beyond the loading area

Abstract The present study presents a generalized analysis and solution procedure for finding the flexural response of beams on viscoelastic foundations. The foundation soil is modelled as a tension membrane interconnecting a series of Burger model representing the time-dependent behaviour of saturated clayey soils and maintaining continuity of stresses and displacement beyond the loaded area as well. The governing differential equations are developed and solved using finite difference scheme. Studies were made to find the optimal mesh size for getting convergent solution matching excellently with those reported in the literature. The relative importance of the different parameters controlling the flexural response of the foundation was assessed and reported.