In this paper, the behavior of hardening in the stress-strain curves from the true tri-axial tests for a schist rock has been simulated using a multi-laminate constitutive model. In this regards, a multi-laminate based model capable of predicting the behavior of rocks on the basis of sliding mechanisms and its elastic behavior is presented. The capability of the model is to predict the behavior of rock under the true tri-axial compression condition. The constitutive equations of the model are derived within the context of the linear elastic behavior of the whole medium and the plastic sliding of interfaces of predefined multi-planes. The predicted model results and their conformity with experimental results show the capability of the mode so that simulation results show a good qualitative agreement with the experimental data.
The stress states in the earth's crust are generally complex and non-axisymmetric compressive conditions. Therefore, studies on the deformation and failure behavior of rocks and rock masses under the general stress states are very important. The experiments on rock deformation and strength have been usually carried out under axisymmetric compressive stress conditions (σ2=σ3). Whereas a large number of studies have been demonstrated importance of the intermediate stress effect on the mechanical and hydromechanical behavior of rocks, however, the number of experiments on rock samples under true tri-axial stress is very limited . A major goal of rock mechanics laboratory testing is to characterize deformation and strength behavior under stress conditions simulating those encountered in situ. However, most experiments are conducted on cylindrical specimens subjected to uniform lateral confining pressure. Such conventional tri-axial tests simulate a special case of crustal condition, in which the intermediate and the least principal stresses, σ2 and σ3, are equal. Tri-axial tests have been widely used for the study of mechanical characteristics of rocks because of equipment simplicity and convenient specimen preparation and testing procedures. Moreover, researchers have increasingly faced situations in which the above- mentioned criteria were found lacking. For example, Vernik and Zoback (1992) found that use of the linearized Mohr-coulomb criterion of strength in relating borehole breakout dimensions to the prevailing in situ stress conditions in crystalline rocks did not provide realistic results. They suggested the use of a more general criterion that accounts for the effect on strength of the intermediate principal stress . Furthermore, many geo-mechanical problems require a full knowledge of the mechanical behavior of the soils/rocks in order to ascertain viability in terms of economics and safety plans. Accordingly a large numbers of constitutive models have been proposed. One of them is called multilaminate model which was originally introduced by Zienkiewicz and Pande (1977) for modeling the behavior of rock masses. In this paper, a multilaminate elasto-plastic model for the true tri-axial stress state (σ1>σ2>σ3) of rock is presented. 1144
The multilaminate framework was originally developed by Zienkiewicz & Pande (1977) for jointed rock mass. Pande & Sharma (1983), Pietruszczak & Pande (1987, 2001) have also proposed this model for soils.