Constitutive Equation for Soils Based on the Extended Concept of “Spatial Mobilized Plane” and its Application to Finite Element Analysis

ABSTRACT A constitutive equation for soils is presented that describes the deformation and strength characteristics of soils in three-dimensional stresses. A stress-strain relationship under shear was developed introducing an extended concept of “Spatial Mobilized Plane” (named the concept of SMP*). In the present paper, paying attention to the fact that the dilatancy of soils under anisotropic consolidation is similar to that under shear, a stress-strain relationship under consolidation is obtained on the basis of the concept of SMP* in the same way as the stress-strain relationship under shear. By combining these two stress-strain relationships and the stress-strain relationship in the elastic state, a generalized constitutive equation is formulated. The validity of this proposed constitutive equation is checked by the analysis of various kinds of element tests and its comparison with the experimental results. All the soil parameters of the proposed constitutive equation can be determined from shear and consolidation tests by using a conventional triaxial compression test apparatus. Finite element analyses for bearing capacity problems are then performed by using the proposed constitutive equation. The analytical results explain well various deformation and failure behaviors of soil foundation which have been well-known empirically.

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