Application of Finite Element Limit Analysis and Other Means to Deal with Problems Involving Foundations and Excavations

Abstract

The finite elements limit analysis (FELA) is an important tool to solve any stability problem in geomechanics. This method provides lower and upper bounds on the true solution for a material following an associated flow rule. While using this method, there is no need to compute the entire load-deformation response till failure of the structure, as is usually done for carrying out an elasto-plastic numerical analysis on the basis of finite difference/finite elements/ boundary elements methods. The solution determined on the basis of the FELA is found to be generally quite accurate, and there is absolutely no need to assume any kind of collapse mechanism as it was used to be done earlier while employing the conventional limit analysis technique without employing finite elements. The FELA has become versatile and computationally very robust on account of various mathematical advancements which took place in the field of optimization. In the field of geomechanics, a number of yield bases, namely, von-Mises, Drucker-Prager, Tresca, Mohr-Coulomb, Hoek-Brown and power type criteria, have been employed to solve a variety of problems dealing with both soils and rocks. The Mohr-Coulomb (MC) yield criterion, however, still seems to remain the most acceptable one from design point of view especially while dealing with problems involving soils. The present thesis is an attempt to employ the FELA with the usage of the MC yield criterion while dealing with a few important geomechanics problems involving foundations and excavations - for which still there appears to be a need to improve the accuracy of the existing solutions. For the purpose of validation, for a few cases, the solution has also been determined with the usage of the elasto-plastic finite elements analysis and also by performing exclusive small scale model tests in the laboratory. The first problem which is undertaken is associated with the determination of the seismic bearing capacity of a strip foundation on a soil mass which is saturated, and further, an increase in the pore water pressure occurs on account of an earthquake excitation. The problem has been solved by incorporating the variation of the pore-pressure coefficient r_u which indirectly accounts for the increase in the excess pore water pressure in terms of the total vertical overburden pressure at any point. The FELA has clearly revealed that the bearing capacity reduces with an increase in the magnitude of horizontal earthquake acceleration coefficient and for a given magnitude of earthquake acceleration coefficient, the bearing capacity reduces further with increase in the value of r_u. The results have been thoroughly examined in a detailed fashion and the effect of the variation of the various input parameters on the results, including the failure mechanism, has also been studied. Necessary comparisons have been also made for the purpose of validation. The next problem which has been taken up is to determine the improvement in the bearing capacity of the foundations of circular tanks placed over a soft clayey stratum reinforced with annular stone columns. This type of foundation is often employed for oil storage tanks. An axisymmetric FELA has been carried out to deal with this problem and the calculations clearly show that the bearing capacity of the foundation increases quite significantly with an employment of the annular stone columns. The improvement in the bearing capacity increases further once the friction angle of the column material has been increased. Apart from circular foundations, ring foundations are also employed to support structures like overhead water & oil storage tanks, chimneys, transmission towers, radar stations and silos. The pressure-settlement response of ring foundations placed on soft clay and reinforced with an annular stone column has been determined experimentally as well as numerically. The mean diameters of the ring footing and the stone column have been kept equal. The concrete ring model footing was tested in the laboratory by placing it on soft clay with and without an annular stone column. The numerical assessment is based on (i) an axisymmetric linearly elastic-perfectly plastic finite elements (FE) analysis both for associated and non-associated flow rule materials, and (ii) the axisymmetric finite elements limit analysis (FELA) for the explicit determination of the collapse loads for an associated flow rule material. It has clearly been noted, experimentally as well as numerically, that an employment of the stone column leads to (i) an extensive increase in the bearing capacity, and (ii) a remarkable decrease in the magnitudes of the footing displacements. Experiments have also revealed that to avoid the occurrence of the ring footing tilt, it is necessary that the inside of the ring is filled with the compacted soil mass (river sand during the present study). Filling the hollow portion of the concrete ring with sand also leads to a marginal increase in the bearing capacity. As compared to a solid circular footing, a ring footing provides a much greater value of the bearing capacity keeping the outside diameters of the ring and solid circular footings to be same. For an associated flow rule material, for different cases, the magnitudes of the collapse loads have also been computed with the usage of the FELA. For an associated flow rule material, the failure loads on the basis of the FELA and FE analysis compare well with each other. In geotechnical engineering, vertical excavations are often encountered in practice during construction of different foundations and various underground facilities. Therefore, performing the stability analysis of vertical excavations forms an important problem. Soil nailing is generally employed for supporting shallow excavations where steel nails can be driven into soil mass. Contiguous piled wall is also a technique used for supporting deep excavations for underground constructions where nails cannot simply be driven on account of existing adjoining structures, and moreover, piles also allow to support additional compressive loads. In this thesis, the stability analysis of both soil nailed and contiguous piled walls have been carried out by using the rigorous three-dimensional FELA. Stability numbers have been computed for both these types of reinforced excavations. Non-dimensional stability charts have been developed as a function of different non-dimensional parameters. Failure mechanisms have also been examined thoroughly and necessary comparisons have also been made for the purpose of validation and checking the accuracy of the obtained solutions. The solutions and the methodology provided for various problems undertaken in the thesis will be useful for the purpose of design.