This paper builds the formulations of hyperplastic damage theory for rate-independent geomaterials to describe the bulk and the likely damage behavior of granular materials. Using 2 kinematic internal variables and the conjugates, dissipative and yield function can be reasonably introduced. A systematic constitutive presentation of 32 possible ways within the thermodynamical damage framework is presented, which entirely formulates the constitutive behavior through two scalar thermodynamic potentials. Combining the four common thermodynamical energy functions, two independent kinematic internal variables and the accordingly generalized stress are introduced to describe the damage behavior and structural rearrangement of the granules for any bulk deformation. A few Legendre transformations are used to establish the links between energy functions so that the complex incremental response of geomaterials can be entirely established from these four energy functions. The constitutive relations are built with the thermodynamics laws, which account for the important structural aspects of geomaterials. Some examples axe provided in the appendix to validate the applicability and implementation of the framework. This theory is based on previous work by Houlsby et al., and extends to the multi-mechanisms description. This framework paves a way in developing models for specific geomaterials with an examinable basis.
Naturally deposited or residual soils exhibit more complicated behavior than remolded clays. A dual-surface damage model for structured soils is developed based on the thermodynamics framework established in our first paper. The shift stresses and the transformation between the generalized dissipative stress space and actual stress space are established following a systematic procedure. The corresponding constitutive behavior of the proposed model is determined, which reflects the internal structural configuration and damage behavior for geomaterials. Four evolution variables κj^i（i=D, R;j=V, S） and the basic parameters λ, s, v and e0 are introduced to account for the progressive loss of internal structure for natural clays. A series of fully triaxial tests and isotropic compression tests are performed for structured and reconstituted samples of Beijing and Zhengzhou natural clays. The validation of the proposed model is examined by comparing the numerical results with the experimental data.
