Shear behaviour of idealized rock joints – microscale analysis

Abstract

Reliable estimation of shear strength of rock mass is important for design of tunnels or underground structures. Especially, the assessment of shear strength of a rock joint is critical because a rock joint is one of the weakest points of rock masses due to its discontinuity. Until now, numerous works have been performed through experimental tests, but it is hard to find a microscale study focusing on asperity geometry or asperity size of a rock joint surface and its spatial distribution. This paper explores the effects of microscale characteristics of joint asperities on rock joint shear behaviours through theoretical and numerical analyses. First, the shear strength and failure mode of a rectangular asperity are theoretically obtained from force equilibrium analysis and its basic mechanism is experimentally verified with idealized rock joints. Rectangular-shaped asperities can reflect the microscale asperity of a rough joint surface and evolve its shear behaviour in small deformation regime. Two failure modes of a rectangular asperity can be determined depending on its shape and critical aspect ratio: one mode is a dilative failure with an inclination of 45 – /f/2 and the other is a non-dilative failure with shearing of asperity. The critical aspect ratio, which is used as a failure mode criterion, is a function of peak friction angle, cohesion, and normal stress, and is the most sensitive to peak friction angle. The range of critical aspect ratio is 0.15–0.32 for general rocks. The shear strength of a rectangular asperity also can be determined with peak friction angle, cohesion, basic friction angle, aspect ratio, and normal stress. Upon this basic analysis, the effect of asperity size distribution, asperity shape distribution, normal stress, and specimen size are discussed on the shear behaviour of idealized rock joints. Asperity size distribution has a significant influence on the shear behaviour of rock joints, altering peak shear strength and shear displacement at peak. Numerical analysis results show that the joint of different asperity sizes experiences progressive failure in order of asperity size, while the joint of an identical asperity size approaches failure simultaneously. The joint of more various asperity sizes renders the more ductile shear behaviour. Asperity shape distribution also affects the shear strength. Although joints have the same average aspect ratio, their shear strength can vary depending on the variation of asperity shape. Numerical simulation shows that surface roughness alone may not be appropriate for reliable estimation of rock joint shear strength. Thus, a parameter for characterization of joint surface roughness should be able to reflect the effect of asperity shape distribution. Smaller-sized asperities contribute to peak shear strength at lower normal stresses while larger-sized asperities do at higher normal stresses. Thus, the increase of normal stress alters the evolution of rock joint shear behaviour due to the progressive failure of joint asperities and makes the joint shear behaviour ductile (or deformation-hardening). The mechanism of hardening behaviour of a rock joint with the increase of normal stress is related to reduction of cohesion effect relative to normal stress. Smaller specimens cause much bigger variation of shear strength and their shear behaviours become uniform when the number of asperity approaches or is greater than 100. The effect of specimen size worsens with the increase of variation of asperity size. Therefore, when the rock joint specimen is sampled for reliable estimation of shear strength, the specimen size has to be longer than a minimum required length (i.e., 100 times greater than mean asperity size).