Combined identification of constitutive parameters and in-situ stress in layered rock mass formulated by Cosserat theory

Abstract

Abstract. This paper focuses on the identification of constitutive parameters and in-situ (initial) stress in the layered rock mass formulated by Cosserat theory. The direct problem is modeled by FEM (Finite Element Method), providing a platform at which the sensitivity analysis can be implemented, and the inverse problem is solved via the Gauss-Newton technique. The effects of initial guesses and noisy data on the solutions are investigated, and satisfactory results are exhibited in the numerical verification. IntroductionOccurrence of a stratified (layered) rock mass for a mineral deposit is not uncommon in mining practice and results in highly anisotropic strength and deformation characteristics. This makes it necessary to include effects of joints into the mathematical formulations describing the load-deflection behavior. In addition to the discontinuous modeling method by which the joints in the rock mass and intact rock layers are modeled individually [1,2], another kind of modeling method is the continuum one by which the whole layered rock mass with joints is represented by an equivalent continuum model providing a reasonable large scale (average) description of the material response to loading especially when closely spaced joints occur in large numbers [3,4], and make the discontinuous modeling impossible.One of the effective equivalent continuum models is that based on the couple stress theory (Cosserat theory). In a mechanical point of view, Reference[5] and its cited papers illustrated the justification for the use of the Cosserat theory in layered rock mass, and provided numerical evidence that the Cosserat model is capable of accurately reproducing complex load-deformation patterns via a comparison with calculations conducted using the discrete joint model.The couple stress theory (Cosserat theory) can be traced back to 1887 when Voigt assumed the existence of couple stress. In 1909, the Cosserat brothers first set up a framework of couple stress theory which has been further developed by [6,7,8]. Zvolinskii and Shkhinek [9] applied the Cosserat theory to formulate a model of layered material with elastic coupling between the layers and later Bogan [10] confirmed the mathematical viability of this model. Extensive development of the Cosserat theory in relation to layered rock mass has been carried out by Mühlhaus [11], Adhikary and A.V. Dyskin [5,12,13].The study of this paper is motivated by a question that if a continuum couple stress theory is adopted for modeling the layered rock mass, how to determine those equivalent constitutive