Debarghya Chakraborty

Bearing Capacity of Strip Foundations in Reinforced Soils

AbstractA method is proposed to determine the ultimate bearing capacity of a strip footing placed over granular and cohesive-frictional soils that are reinforced with horizontal layers of reinforcements. The reinforcement sheet is assumed to resist axial tension but not bending moment. The analysis was performed by using the lower bound theorem of the limit analysis in combination with finite elements. A single layer and a group of two layers of reinforcements were considered. The efficiency factors ηγ and ηc that need to be multiplied with the respective bearing capacity factor Nγ and Nc to account for the inclusion of the reinforcements were established. The results were obtained for different values of the soil internal friction angle (ϕ). The critical positions of the reinforcements, which would result in a maximum increase in the bearing capacity, were established. The required tensile strength of the reinforcement to avoid its breakage during the loading of the foundation was also computed. The resu...

Solving Axisymmetric Stability Problems by Using Upper Bound Finite Elements, Limit Analysis, and Linear Optimization

A numerical formulation has been proposed for solving an axisymmetric stability problem in geomechanics with upper bound limit analysis, finite elements, and linear optimization. The Drucker-Prager yield criterion is linearized by simulating a sphere with a circumscribed truncated icosahedron. The analysis considers only the velocities and plastic multiplier rates, not the stresses, as the basic unknowns. The formulation is simple to implement, and it has been employed for finding the collapse loads of a circular footing placed over the surface of a cohesive-frictional material. The formulation can be used to solve any general axisymmetric geomechanics stability problem.

Bearing capacity of foundations on slopes

By applying the lower bound finite element limit analysis in conjunction with non-linear optimisation, the bearing capacity factors, Nc, Nq and Nγ, due to the components of cohesion, surcharge and unit weight, respectively, have been estimated for a horizontal strip footing placed along a sloping ground surface. The variation of Nc, Nq and Nγ with changes in slope angle (β) for different soil friction angle (φ) have been computed for smooth as well as rough strip footings. The analysis reveals that along a sloping ground surface, in addition to Nγ, the factors Nc and Nq also vary considerably with changes in footing roughness. Compared to the smooth footing, the extent of the plastic zone around the footing becomes greater for the rough footing. The results obtained from the analysis are found to compare well with those previously reported in literature.

Seismic Bearing Capacity of Shallow Embedded Foundations on a Sloping Ground Surface

By using the lower-bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization, bearing-capacity factors, N-c and N-gamma q, with an inclusion of pseudostatic horizontal seismic body forces, have been determined for a shallow embedded horizontal strip footing placed on sloping ground surface. The variation of N-c and N-gamma q with changes in slope angle (beta) for different values of seismic acceleration coefficient (k(h)) has been obtained. The analysis reveals that irrespective of ground inclination and the embedment depth of the footing, the factors N-c and N-gamma q decrease quite considerably with an increase in k(h). As compared with N-c, the factor N-gamma q is affected more extensively with changes in k(h) and beta. Unlike most of the results reported in literature for the seismic case, the present computational results take into account the shear resistance of soil mass above the footing level. An increase in the depth of the embedment leads to an increase in the magnitudes of both N-c and N-gamma q

Stability of a long unsupported circular tunnel in soils with seismic forces

By using the lower-bound finite element limit analysis, the stability of a long unsupported circular tunnel has been examined with an inclusion of seismic body forces. The numerical results have been presented in terms of a non-dimensional stability number (γH/c) which is plotted as a function of horizontal seismic earth pressure coefficient (kh) for different combinations of H/D and ϕ; where (1) H is the depth of the crest of the tunnel from ground surface, (2) D is the diameter of the tunnel, (3) kh is the earthquake acceleration coefficient and (4) γ, c and ϕ define unit weight, cohesion and internal friction angle of soil mass, respectively. The stability numbers have been found to decrease continuously with an increase in kh. With an inclusion of kh, the plastic zone around the periphery of the tunnel becomes asymmetric. As compared to the results reported in the literature, the present analysis provides a little lower estimate of the stability numbers. The numerical results obtained would be useful for examining the stability of unsupported tunnel under seismic forces.

Linearization of Drucker-Prager yield criterion for axisymmetric problems: implementation in lower-bound limit analysis

The linearization of the Drucker-Prager yield criterion associated with an axisymmetric problem has been achieved by simulating a sphere with the truncated icosahedron with 32 faces and 60 vertices. On this basis, a numerical formulation has been proposed for solving an axisymmetric stability problem with the usage of the lower-bound limit analysis, finite elements, and linear optimization. To compare the results, the linearization of the Mohr-Coulomb yield criterion, by replacing the three cones with interior polyhedron, as proposed earlier by Pastor and Turgeman for an axisymmetric problem, has also been implemented. The two formulations have been applied for determining the collapse loads for a circular footing resting on a cohesive-friction material with nonzero unit weight. The computational results are found to be quite convincing

Seismic Bearing Capacity of Foundations on Cohesionless Slopes

By applying the lower bound theorem of limit analysis in conjunction with finite elements and nonlinear optimization, the bearing capacity factor N has been computed for a rough strip footing by incorporating pseudostatic horizontal seismic body forces. As compared with different existing approaches, the present analysis is more rigorous, because it does not require an assumption of either the failure mechanism or the variation of the ratio of the shear to the normal stress along the footing-soil interface. The magnitude of N decreases considerably with an increase in the horizontal seismic acceleration coefficient (kh). With an increase in kh, a continuous spread in the extent of the plastic zone toward the direction of the horizontal seismic body force is noted. The results obtained from this paper have been found to compare well with the solutions reported in the literature

Bearing Capacity of Circular Footings on Reinforced Soils

A method is presented for determining the ultimate bearing capacity of a circular footing reinforced with a horizontal circular sheet of reinforcement placed over granular and cohesive-frictional soils. It was assumed that the reinforcement sheet could bear axial tension but not the bending moment. The analysis was performed based on the lower-bound theorem of the limit analysis in combination with finite elements and linear optimization. The present research is an extension of recent work with strip foundations reinforced with different layers of reinforcement. To incorporate the effect of the reinforcement, the efficiency factors eta(gamma) and eta(c), which need to be multiplied by the bearing capacity factors N-gamma and N-c, were established. Results were obtained for different values of the soil internal friction angle (phi). The optimal positions of the reinforcements, which would lead to a maximum improvement in the bearing capacity, were also determined. The variations of the axial tensile force in the reinforcement sheet at different radial distances from the center were also studied. The results of the analysis were compared with those available from literature

Bearing capacity of strip footings by incorporating a non-associated flow rule in lower bound limit analysis

A plane strain lower bound limit analysis technique in combination with the finite elements and nonlinear programming has been used to investigate the effect of considering a non-associated flow rule on the bearing capacity of a rigid strip footing. The results are derived in terms of bearing capacity factors Nc, Nq, and Nγ on account of the components of soil cohesion (c), surcharge pressure (q), and unit weight (γ), respectively. The results clearly indicate the increase in the magnitude of bearing capacity factors with an increase in the magnitudes of dilative coefficient (η). It is expected that the charts provided in this note will be quite helpful for the practicing engineers.

Vertical Uplift Resistance of Pipes Buried in Sand

By incorporating the variation of peak soil friction angle (phi) with mean principal stress (sigma(m)), the effect of pipe diameter (D) on the vertical uplift resistance of a long horizontal pipeline embedded in sand has been investigated. The analysis has been performed by using the lower bound finite-element limit analysis in combination with nonlinear optimization. Three well-defined phi versus sigma(m) curves reported from literature for different sands have been used. It is observed that for a given embedment ratio, with an increase in pipe diameter, the magnitude of the uplift factor (F-gamma) reduces quite significantly, which indicates the importance of considering scale effects while designing buried pipe lines. The scale effects have been found to become even more substantial with an increase in the embedment ratio. The analysis compares well with various theoretical results reported from literature. On the other hand, as compared to available centrifuge test results, the present analysis has been found to provide quite a higher magnitude of the uplift resistance when the theoretical prediction is based on peak soil friction angle. However, if the theoretical analysis is performed by using the friction angle that accounts for the progressive shear failure, the difference between the theoretical and centrifuge test results decreases quite significantly.(C) 2013 American Society of Civil Engineers.