Finite Element Analysis of Large Strains in Soils

FINITE ELEMENT ANALYSIS OF LARGE STRAINS IN SOILS by RODRIGO MOLINA FERNANDEZ Submitted to the Department of Civil Engineering on August 30, 1971, in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering. Some problems of behavior of soils under given boundary conditions involve large deformations and strains, but finite element analyses of soil problems have traditionally considered only infinitesimal strain analysis. Suitable large strain formulations in cartesian coordinates for an incremental procedure are studied. One of the formulations is based on the general tensorial formulation when applied to cartesian coordinates. The fact that the constitutive equations are not easy to obtain for soils makes this formulation impractical. A second formulation is based in Biot's incremental deformation formulation, and, because physics and geometry are separated, the constitutive equations can be easily found. Two types of constitutive laws are used. One is the perfectly plastic formulation for a Tresca Material, the other one is obtained from a hyperbolic approximation of the experimental stress-strain curve for the given soil. An interpolation procedure is used to obtain the constitutive equations of an anisotropic material from active and passive tests. Finite Element programs are developed, one for each constitutive equation, for the solution of plane strain problems. An incremental procedure with a mid-point integration scheme is used. Results from test runs are inconclusive. Good results are obtained in simple problems, and some improvement over an "infinitesimal strain" approach is observed in one case. Some major problems are encountered, however, especially lack of equilibrium between stresses and nodal forces, instability of the solution after failure, impossibility of using unloading procedures, and deviation from the correct solution, especially after failure. The lack of equilibrium between stresses and forces can be traced to the midpoint integration procedure and a post yielding modification of stresses to keep them in the yield surface. The other problems are thought to be mainly caused by the imperfect constitutive equations. Thesis Supervisor: Title: John T. Christian Associate Professor of Civil Engineering