A One-Dimensional Elastoplastic Model for Capturing the Nonlinear Shear Behaviour of Joints with Triangular Asperities Based on Direct Shear Tests

In most cases, the behaviour of rock masses is dominated by weak planes such as joints, along which shear is more likely to occur and deformation is usually nonlinear. Thus, it is of great significance to understand the shear process and mechanisms of joints. We investigated the shear process and mechanics of joints with regular and irregular triangular asperities through a series of direct shear tests, where a high-speed camera was used to record the deformation and failure of asperities. It was found that, for joints with regular asperities, the nonlinear shear behaviour is mainly related to shear failure of asperities. For joints with irregular asperities, this nonlinearity results from both shear failure of asperities and the interactions between them. Based on the findings, it was assumed that the shear stiffness/strength of a joint is the sum of shear stiffness/strength of individual asperities. By this assumption, estimation methods were developed to predict shear strength, shear displacement, and shear stiffness of joints with irregular asperities. A one-dimensional elastoplastic model was then put forward to describe the nonlinear shear behaviour of the irregular joints. In this model, a spring element is connected in series with a modified Saint Venant element. Different from the traditional Saint Venant element, this modified one incorporates the concept of alterable yield limit and thus can reflect the evolution of shear stiffness during shearing. Eventually, with these estimation methods and this new elastoplastic model, the nonlinear shear process of the joints could be expressed mathematically. The applicability of this model was verified through the comparison between fitting results and laboratory measurements. Our findings could provide insights into the evolution of shear stiffness and help to gain a better understanding on the shear process of rough joints.