Behavior of Post-Yielding Parameters of Marble During Plastic Deformation
Authors: Sarkar S. , Kumar R. 
Published: August 2024

ABSTRACT:
Triaxial compression tests are used for the evaluation of the behavior of marble rock in the plastic region. Marble samples with a diameter of 60 mm are experimented on a servo-controlled universal testing machine (UTM). The marble rocks are tested under various confining stresses of 4 MPa, 8 MPa, 12 MPa, 20 MPa, and 28 MPa. During the testing, the volume change of samples is determined by quantifying the flow of hydraulic fluid into and out of the triaxial chamber. The test results reveal that marble rock is brittle at low confinement and softens with increasing confinement. The data analysis shows that cohesion () and dilation angle (ψ) have a negative exponential correlation with plastic shear strain and both these parameters become almost constant in the residual zone. The internal angle of friction (ϕ) remains almost constant after attaining its peak value as plastic shear strain increases. The existing dilation angle model (Zhao and Cai, 2010) and the post-peak cohesion degradation model (Pourhosseini and Shabanimashcool, 2014) are compared with experimental data and their parameters are calculated. In essence, these parameters provide useful information about post-yielding parameters.

1. INTRODUCTION
Understanding intact rock and rockmass behavior is crucial for designing mining and civil excavation and structure. Both laboratory experiments and field studies have revealed that rocks exhibit nonlinear failure behavior. The simple elastic analysis is insufficient for describing rock deformation. Therefore, it is essential to understand the entire stress-strain relationship of rocks, particularly the post-yield region where significant changes occur.
When rocks are subjected to stress beyond their yield point, dilation occurs as a result of microcrack initiation, propagation, and the expansion of void spaces. This phenomenon illustrates the volumetric strain of rocks. Consequently, plastic deformation occurs, causing the volume of the rock to increase, this phenomenon is referred to as dilation.
Reynolds (1885) studied the phenomenon of shear dilatancy in granular materials, which refers to the increase in volume resulting from the distortion caused by shear forces acting on the material's components. Dilatancy is often quantified using the dilatancy angle (), which serves as a convenient way to portray dilatant materials. The idea of the dilation angle was first introduced by Hansen (1958), who demarcated it as the proportion of the plastic volumetric change to plastic shear strain. Brace et al., (1966) formulated the relationship between rock dilatancy, stress-volumetric strain, and the impact of confining pressure. Cook, (1970) further recognized that dilation in compression is not merely a surface-level phenomenon, but a volumetric characteristic inherent to rocks. The dilation angle which measures the extent of dilation of rock, can be determined through tri-axial testing of rocks (Vermeer and De Borst, 1984). This laboratory testing underscores the interaction between confining pressure and plastic shear strain in determining the dilation behavior of the material, shedding light on its mechanical response under different confinements.