Generalization of three-moduli incremental non-linear constitutive models for soils

In this paper, two three-moduli incremental non-linear constitutive models are presented for triaxial stress condition. The method for the determination of three moduli (K,G,J) in one of the incremental non-linear constitutive models using conventional triaxial test data is discussed. Mathematical functions are suggested for best data fittings. The three-moduli models can consider shear-compression (or shear-dilation) by introducing the coupling modulus J (or J̄). The three moduli K,G,J are determined using data from an isotropic consolidation test and three CID triaxial shear tests. The computed results using the calibrated KGJ model are compared with the measured test data from three drained triaxial shear tests in constant p′. The main focus of the paper is on (a) a new approach in the generalization of the two three-moduli models for triaxial stress condition and (b) the interpretation of physical meanings of the two generalized models. The two new generalized forms (models) are derived based on incremental isotropic hypoelasticity theory. Both the tensor form and the matrix form of the two new generalized stress-strain relationships are presented. Physical meanings of the generalized constitutive relationships are discussed with an especial attention to the items associated with the coupling modulus J (or J̄).