Numerical simulation of a direct shear test on a rock joint using a bonded-particle model

Abstract

Rock joints were numerically simulated, and an extensive series of direct shear tests were carried out using the code PFC3D. The feasibility of reproducing a rock joint using the contact bond model was demonstrated, and the effects of the geometrical features and the micro-properties of a joint on its shear behavior were examined. Asperity failure was observed from the micro-cracks and contact force distribution, as well as the stresses and displacements in shear and normal directions. A rough joint with a joint roughness coefficient (JRC) value ranging from 10 to 20 was produced in an intact sample by defining the joint-contacts along a predefined joint surface. To simulate a decrease in joint wall strength (JCS) caused by weathering and alterations, the bond strength between particles involved in the joint-contacts was reduced by up to 70%. The shear behavior and failure progress at a given stress corresponded well to those observed in laboratory tests. The friction coefficient was the most important factor governing the shear strength and dilation angle. The variation in joint roughness and contact bond strength had a larger effect on the cohesion than peak friction angle. In addition, a new approach to represent JRC and JCS values of a joint was proposed for practical use. A numerical 3D-profile scanning technique was developed to evaluate the actual JRC of the simulated joint, and the relationship between the JCS and the contact bond strength was investigated.

Introduction

Joints are among the most important factors in understanding and estimating the mechanical behavior of a rock mass. The shear behavior of a joint is combination of complicated phenomena, such as normal dilation, asperity failure and contact area due to undulating surface. This means that the constitutive models for joint behavior need to consider a large number of assumptions and uncertainties. Considerable efforts have been devoted to explaining the shear strength and behavior of joint over the last four decades. Since Patten's bilinear model of saw-tooth joints [1], peak shear strength criteria have been developed by Ladany and Archambault [2], Barton and Choubey [3] and Amadei and Saeb [4], and the post-peak response and asperity degradation have been explained using several empirical and theoretical models [5], [6], [7], [8]. With the rapid progress of computer technology, many attempts have been made to demonstrate the joint behavior using numerical methods, such as the finite element method (FEM), boundary element method (BEM) and discrete element method (DEM) [9], [10], [11].

In terms of the explicit representation of a joint, the particle flow code PFC is a widely used simulation tool. PFC is a commercial code that was developed by the ITASCA Consulting Group based on DEM theory. It represents a material as an assembly of rigid spherical particles that move independently of one another and interact only at the contact points. The calculation scheme used in PFC requires only simple laws and a few parameters to govern the interactions at the particle and contact level to represent the behavior of a material including a joint. On the other hand, other available tools use some constitutive (stress–strain) relations, which involve many parameters and assumptions. Therefore, the PFC can simulate the effect of the joint roughness and the asperity failure in a direct and realistic manner. Moreover, an explicit finite difference scheme allows observations of the transmission of forces exerted at the contacts, and has the ability to track the propagation of bond breakage events at each stage. However, the total number of particles required to represent an actual situation is limited because of the finite computing capacity, and the properties of the microscopic constituents are usually not known. These unknown properties require tedious calibration process of micro-parameters until the macro-scale response of a model agrees with the results of laboratory tests.

Many studies have examined the effect of micro-parameters on the macro-response for an intact rock and suggested a variety of techniques for reproducing the brittle behaviors by performing uniaxial, triaxial and Brazilian tests [12], [13], [14]. On the other hand, little attention has been paid to the micro-parameters of joints. Although the micro-properties of joints have a significant effect on their shear behavior, they have been generally assumed to be small values without any calibration using direct shear tests. A direct shear test using PFC have mainly been carried out on granular materials such as soil [15], [16], [17], and a few simulations have been reported for the rock joints. Cundall [18] reported the applicability of PFC2D to a direct shear test on a virtual rough joint. In his study, Cundall examined the shear behavior of the joint by measuring its shear strength, dilation angle and micro-cracks. However, all quantities used in the simulation were without any physical units and the joint was assumed to be very rough. Kulatilake et al. [19] determined the micro-parameters of a joint model by performing a series of direct shear tests in modeling the behavior of jointed rock blocks under uniaxial loading with PFC3D. Wang et al. [20] carried out a direct shear test on a joint in an attempt to simulate the behavior of the heavily jointed rock slope using PFC2D. However, the relationship between the micro-parameters and macro-response of a rock joint has not been adequately studied in the literature.

The main aim of this study is to demonstrate the feasibility of PFC3D to reproduce a rock joint and examine the effects of the micro-properties on its shear behavior by simulating the direct shear tests at different normal stresses. A total of 25 simulation cases were established according to the particle size, roughness, friction coefficient and bond strength, and a parametric study on peak shear strength and dilation angle was carried out. The failure mechanism was observed from the micro-cracks and contact force distribution, as well as the stresses and displacements in shear and normal directions, by taking advantage of PFC calculation schemes. In addition, a new approach to represent JRC and JCS values of a joint was proposed. A numerical technique to scan the 3D-profile of a simulated joint surface was developed in order to evaluate the actual JRC. The test results were compared with the estimations from Barton's empirical model and the relationship between the contact bond strength of particles along a joint and the JCS was investigated.