The present thesis illustrates the application of the lower bound limit analysis in combination with finite elements and linear programming for obtaining the numerical solutions for various plane strain and axisymmetric stability problems in geomechanics. For the different plane strain problems dealt in the thesis, the existing formulation from the literature with suitable amendments, wherever required, was used. On the other hand for various axisymmetric problems, the available plane strain methodology was modified and a new formulation is proposed. In comparison to the plane strain analysis, the proposed axisymmetric formulation requires only three additional linear constraints to incorporate the presence of the hoop/circumferential stress (σθ). Several axisymmetric geotechnical stability problems are solved successfully to demonstrate the applicability of the proposed formulation. In the entire thesis, three noded triangular elements are used for carrying out the analysis. The nodal stresses are treated as basic unknowns and the stress discontinuities are employed along the interfaces of all the elements. To ensure that the finite element formulation leads to a linear programming problem, the Mohr-Coulomb yield surface is approximated by a polygon inscribed to the parent yield surface. For solving different problems, computer programs are developed in ‘MATLAB’. The variation of the bearing capacity factor Nγ with footing-soil interface roughness angle δ is obtained for different soil friction angles. The magnitude of Nγ is found to increase extensively with an increase in δ. With respect to variation in δ, the obtained values of Nγ were found to be generally smaller than the results available in literature. The effect of the footing width on the magnitude of Nγ has been examined for both smooth and rough strip footings. An iterative computational procedure is introduced to account for the dependency of φ on the mean normal stress ( σm). Two well defined φ- σm curves from literature, associated with two different relative densities, are being chosen for performing the computational analysis. The magnitude of Nγ is obtained for different footing widths, covering almost the entire range of model and field footing sizes. For a value of the footing width greater than approximately 0.2 m and 0.4 m, for a rough and smooth footing, respectively, the magnitude of Nγ varies almost linearly on a log-log scale. The bearing capacity factors Nc, Nq and Nγ are computed for a circular footing both with smooth and rough footing interface. The bearing capacity factors for a rough footing are found to be consistently greater than those with a smooth interface, especially with grater values of soil friction angle (φ). An encouraging comparison between the obtained results and those available from the literature is noted. Bearing capacity factor Nc for axially loaded piles in clays whose cohesion increases linearly with depth has been estimated numerically under undrained (φ = 0) condition. The variation of Nc with embedment ratio is obtained for several rates of the increase of soil cohesion with depth; a special case is also examined when the pile base was placed in the stiff clay stratum overlaid by a soft clay layer. It has been noticed that the magnitude of Nc reaches almost a constant value for embedment ratio approximately greater than unity. The bearing capacity factor Nγ has been computed for a rough conical footing placed over horizontal ground surface. The variation of Nγ with the cone apex (interior) angle (β), in a range of 30º - 180º, is obtained for different values of friction angle ( φ). For φ< 30º, the magnitude of Nγ is found to decrease continuously with an increase in β from 30º to 180º. On the other hand, for φ > 30º , the minimum magnitude of Nγ is found to occur generally between β = 120 and β = 150º. In all the cases, it has been noticed that the magnitude of Nγ becomes maximum for β = 30o. The vertical uplift resistance of circular plate anchors, embedded horizontally in a clayey stratum whose cohesion increases linearly with depth, has been obtained under undrained ( φ = 0) condition. The variation of the uplift factor (Fc) with changes in the embedment ratio (H/B) has been computed for several rates of the increase of soil cohesion with depth. It has been noted that in all the cases, the magnitude of Fc increases continuously with H/B up to a certain value of Hcr/B beyond which the uplift factor becomes essentially constant. The results obtained from the analysis are noted to compare quite well with those published in literature. From the investigation reported in this thesis, it is expected that the proposed axisymmetric formulation will be quite useful for solving various axisymmetric geotechnical stability problem in a rapid manner. The available plane strain formulation has also been found to yield quite satisfactory solutions even for a problem where the soil friction angle depends on the state of stress at a point.

Use of geosynthetics for reinforcing soil beds supporting shallow foundations has gained tremendous popularity in recent times. In this thesis, to study and understand the behaviour of geosynthetics reinforced soil foundations, model load tests are carried out on square footings resting on sand beds reinforced with geosynthetics. The effects of various parameters like type and tensile strength of geosynthetic material, depth of reinforced zone, spacing of reinforcement layers, width of reinforcement and form of reinforcement on the performance of square footings on reinforced sand beds are studied. Results from these tests are analyzed to understand the effect of various parameters in improving the bearing capacity and reducing the settlement of footings. An equation is developed to estimate the ultimate bearing capacity of square footings resting on geosynthetic reinforced sand beds by multiple regression analysis of the experimental data. The model loading tests on reinforced soil foundations are simulated in the numerical model using the computer program FLAC3D (Fast Lagrangian Analysis of Continua in 3D). Finally parametric studies on a full scale reinforced soil foundation are conducted. From the experimental, analytical and numerical investigations carried out in this thesis, some important conclusions are drawn regarding the effective depth of reinforced zone, optimum spacing and quantity of reinforcement layers. Relative efficiency of various forms of reinforcement is discussed. Validity of the regression and numerical models developed is verified through experimental data from present study and also for data from other researchers.

Due to close proximity of different civil engineering structures, the ultimate bearing capacity and failure pattern of adjoining footings/anchors are often influenced by their mutual interference. The present thesis is an attempt to examine the interference effects on the ultimate failure loads and the elastic settlements for a group of closely spaced strip footings and anchors. In this thesis, a new experimental setup has been proposed to examine the response of interfering strip footings and strip anchors subjected to vertical loads but without having any eccentricity. Through out the investigation, it has been assumed that the magnitudes of loads on all the footings/anchors at any stage of settlement remain exactly the same. Unlike the existing experimental works of the previous researchers reported in literature, in the proposed experimental setup, there is no need to use more than one footing/anchor. As a result a much smaller size of the tank, in which the soil sample needs to be prepared, is required. In the proposed setup, it has been attempted to satisfy the boundary conditions existing along the vertical planes of symmetry midway between any two adjoining footings/anchors. To satisfy the governing boundary conditions, along the planes of symmetry, the interface friction angle is kept as small as possible, with the employment of a very smooth high strength glass sheet, and the associated horizontal displacements are made equal to zero. For two interfering footings/anchors case, only single plane of symmetry on one side of the footing needs to be modeled. On the other hand, for an infinite number of multiple footings/anchors, two vertical planes of symmetry on both the sides of the footing need to be simulated in the experiments. The proposed experimental setup is noted to yield reasonably acceptable results both for the cases of interfering footings and interfering anchors. The magnitudes of ultimate failure loads for the interfering footings/anchors are expressed in terms of the variation of the efficiency factor ( ξγ) with respect to changes in the clear spacing(s) between the footings/anchors; wherein, an efficiency factor is defined as the ratio of the magnitude of the failure load for an intervening strip footing/anchor of a given width to that of an isolated strip footing/anchor having exactly the same width. From the experiments, the values of the efficiency factors are obtained for a group of two and an infinite number of multiple strip footings/anchors. The effect of two different widths of the footing/anchor on the magnitudes of the failure load is also studied. It is noted that for a group of two and infinite number of multiple footings, the magnitude of the ultimate failure load for an interfering footing becomes always greater than that for a single isolated footing. For the case of two footings, the value of ξγ becomes maximum corresponding to a certain critical s/B between two footings. At a given spacing, the value of ξγ is found to increase further with an increase in the value of φ. It is observed that, for a group of an infinite number of equally spaced multiple strip footings, the magnitude of ξγ increases continuously with a decrease in s/B; when the clear spacing between the footings approaches zero, the magnitude of ξγ tends to become infinity. The value of ξγ associated with a given s/B for the multiple footings case is found to become always greater than that for a two footing case. The effect of s/B on ξγ is found similar to that reported in theories in a qualitative sense. The value of ξγ at a given s/B associated for B = 4 cm both for two and multiple footings is found to become smaller as compared to that with B = 7 cm. In contrast to a group of interfering footings under compression, the magnitude of ξγ in the case of both two and multiple interfering anchors decreases continuously with a reduction in the value of s/B. For given values of s/B and embedment ratio ( λ = d/B ), the values of ξγ for the case of multiple anchors are found to be always lower than those for the case of two anchors; d = depth of the anchor. In comparison with the available theoretical values from the literature, the values of ξγ are found to be a little lower especially for smaller values of s/B. The comparison of the present experimental data with that reported from literature reveals that the interference of strip anchors will have relatively more reduction in the uplift resistance on account of interference as compared to a group of square and circular anchors; the present experimental data provides relatively lower values of ξγ as compared to the available experimental data (for square and circular footings). The value of s/B beyond which the response of anchors becomes that of an isolated anchor increases continuously with an increase in the value of λ. The magnitude of ξγ for given values of s/B and λ associated for B = 4 cm is found to become slightly greater as compared to that with B = 7 cm. Both for the cases of interfering footings and anchors, the ratio of the average ultimate pressure with the employment of the rough central plane (glass sheet glued with a sand paper) to that with the smooth central plane, is found to increase with (i) a decrease in the value of s/B, and (ii) an increase in the value of φ. The finite element analysis, based on a linear elastic soil-constitutive model, has also been performed for interfering footings and anchors to find the effect of interference on elastic settlements. The computations have revealed that for both the footings and anchors, a decrease in the spacing between the footings leads to a continuous increase in the magnitudes of the settlements. The increase in the settlement due to the interference becomes quite substantial for an infinite number of footings/anchors case as compared to two footings/anchors case. The effect of the Poisson’s ratio on the results is found to be practically insignificant.

The present thesis is an attempt to investigate the interference effects on the magnitudes of the ultimate failure loads for a group of closely spaced strip footings and strip plate anchors. On account of an increase in the number of different civil engineering structures, footings and anchors are often need to be placed very close to each other. In such a situation, the ultimate bearing capacity/pullout capacity of an interfering footing/anchor becomes significantly different from that of a single isolated footing/anchor. The effect of interference on the magnitude of failure load is usually expressed in terms of an efficiency factor (%y); where £,y is defined as the ratio of the magnitude of the failure load for a strip footing/anchor of a given width in the presence of other footings/anchors to that of the magnitude of the failure load for an isolated single strip footing/anchor having exactly the same width. No rigorous analysis seems to have been carried out so far in literature to investigate the interference effect for a group of footings and anchors. In the present study, it is intended to use rigorous numerical upper bound limit analysis in combination with finite elements and linear programming in order to determine the collapse loads for the problems of both isolated and a group of footings and anchors. Three noded triangular elements are used throughout the thesis for carrying out the analysis for different problems. The velocity discontinuities are employed along the interfaces of all the elements. The plastic strains within the elements are incorporated by using an associated flow rule. The Mohr Coulomb yield surface is linearised by means of an exterior regular polygon circumscribing the actual failure surface so that the finite element formulation leads to a linear programming problem. In solving the different problems taken in this thesis, computer programs were developed using 'MATLAB' with the usage of 'LINPROG' - a library subprogram for doing the necessary optimization. The bearing capacity factor Ny for an isolated single rigid strip footing placed on a cohesionless ground surface has been computed and its variation with respect to the footing-soil roughness angle (8) has been examined in detail. It is clearly noted that an increase in 8 leads to a continuous increase in Ny. The solution is also obtained for a perfectly rough footing without considering any velocity discontinuity surface along the footing-soil interface. With 5 = <|), the magnitude of NY becomes almost the same as that for a perfectly rough footing. The size of the plastic zone increases with an increase in the values of 8 and <j). The obtained values of Ny for 5=0 and § compare quite favorably with the solutions reported earlier in literature. The ultimate bearing capacity for a group of two and an infinite number of multiple interfering rough strip footings placed on a cohesionless medium has been computed; all the footings are assumed to be perfectly rigid. It is specified that the footings are loaded simultaneously to failure exactly at the same magnitude of the failure load. For different clear spacing (S) between the adjacent footings, the magnitude of the efficiency factor (£,y) is determined. In the case of two footings, the value of E,y at S/B = 0 becomes exactly equal to 2.0, and the maximum ^occurs at a critical spacing (Scr). For S/B < Sor/B, the ultimate bearing pressure for a footing becomes equal to that of an isolated footing having the width (2B+S), and the ground mass encompassed between the two footings deforms mainly in the downward direction. In contrast, for S/B > Scr/B, ground heave is noticed along both the sides of the footing. As compared to the available theories in literature, the analysis presented in this thesis provides generally lower values of ^y for S/B > Scr/B. ' In the case of a group of multiple strip footings, the value of £y is found to increase continuously with a decrease in S/B. The effect of the variation of spacing on §y is found to be very extensive for small values of S/B; the magnitude of ^y approaches infinity at S/B = 0. For all the values of S/B ground heave is invariably observed on both the sides of the footings. The magnitudes of ^Y for given values of S/B and <|) for the two footings case are found to be smaller than the multiple footings case. The vertical uplift capacity of an isolated strip anchor embedded horizontally at shallow depths in sand has been examined; the anchor plate is assumed to be perfectly rigid and rough. The collapse load is expressed in terms of a non-dimensional uplift factor FY, the value of which needs to be known before calculating the failure load for an interfering anchor. The magnitude of Fr is found to increase continuously with increase in both embedment ratio (k) and the friction angle (<|>) of sand. Even though the analysis considers the development of plastic strain within all elements, however, at collapse, the soil mass just above the anchor is found to move as a single rigid block bounded by planar rupture surfaces; the rupture surfaces emerging from the anchor edges are seen to make approximately an angle <|> with the vertical. The vertical uplift capacity of a group of two and an infinite number of multiple interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. At collapse, it is specified that all the anchors in the group are loaded to failure simultaneously exactly at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (£Y) is determined. On account of interference, the magnitude of 4y is found to reduce continuously with a decrease in the spacing between the anchors. For all values of X and §, the magnitude of ^y for the multiple anchors case is found to be always smaller than that for the two anchors case. In contrast to a group of footings under compression, the magnitude of ^v for a group of anchors is found to decrease invariably with an increase in $ for a given value of S/B. For S > 2c/tan<j) , the uplift resistance of anchors in the group becomes equal to that of an isolated anchor, and no interference is seen to exist; where d is the depth of anchor. By examining the nodal velocity patterns, it was noted that in the event of collapse, a wedge of soil mass just above the anchors and encompassed within linear rupture surfaces moves vertically upward almost as a single rigid unit with the velocity same as that of the anchor plate itself. On this basis, a closed form solution of the problem has been developed. The results from the closed form solution for the group of two anchors as well as for multiple anchors are found to provide an excellent comparison with the rigorous upper bound numerical solution especially for the value of § greater than or equal to about 35°. For all the problems taken in this study, it has been seen that an upper bound limit analysis in combination with finite elements and linear programming is a very useful numerical tool for determining the magnitudes of collapse loads.