A biconcave shape bond model for rock deformation

This paper proposes a biconcave shape bond model for the distinct element method (DEM) to simulate cementation between two circular particles in geomaterials. Rather than an original parallel bond model between particles, the proposed model adopts the more realistic shape of cementation and considers the elastic response of cementation under external loading. The stress field and force-displacement relationship of the biconcave shape bond is based on Dvorkin's theory, and three modifications are adopted: (1) A superposition method is applied to improve the correctness and symmetry of the stress field, and it also provides a method of addressing the status when both connected particles rotate; (2) To simplify the input parameters, the tangential movement is replaced by the normal deformation and rotation between particles; (3) To accelerate the calculations, variables are extracted in analytical procedures, which provide an efficient method for applying the bond model with only one matrix inversion. With these three modifications, the new biconcave shape bond model is created. To assess the validity of the proposed model, this study compared the elastic deformation in a single bond with an elastic analysis performed using the finite element method (FEM). After verification of the proposed model, a series of sensitivity analyses was performed to explore the effect of bond shape and the differences from the parallel bond model. For a single bond, the results showed that a biconcave model can represent the mechanical behavior of a biconcave shape bond and is effective with different bond shapes. The stress fields calculated by the biconcave model were more similar to the FEM results than those obtained using Dvorkin's theory. The width and thickness of a bond have a considerable effect on its stiffness, and the variation of thickness decreases with the width of the bond. In addition, the required parameters can be acquired directly from real bond material rather than using the back analysis procedure for parameters. The biconcave model was further implemented in DEM software Particle Flow Code 2 Dimension to certify its applicability in geotechnical engineering. Using this model, a series of uniaxial compression test simulations was performed to analyze the macroelastic responses of specimens. The results showed that the macrotangential elastic modulus and Poisson's ratio had a regular tendency, and they agreed with the stiffness variation in a microbond. This finding can assist in determining correlations between microand macroproperties and provides an innovative method for simulating the behavior of cemented granular material.