Analytical solutions to micro-bond model for particles considering width and thickness of bond

In the DEM simulation of mechanical response of methane hydrate or weathered rock, the real shape and size of inter-particle bond significantly affect the macro-mechanical properties of the materials, therefore it is necessary to build a micro-bond model considering the width and thickness of the bond. The modified high-accuracy analytical solution is proposed according to the Dvorkin theory to determine the stiffness and strength of inter-granular bond in DEM. By introducing the symmetric displacement function, the symmetry and accuracy of the stress field are improved compared with the solution by the Dvorkin theory. The provided solutions are consistent with the FEM analysis results on a qualitative and quantitative level. For an application, the parametric investigation is carried out according to the analytical solutions. The influences of width and thickness on the stiffness of the bond are discussed firstly, and then the fitting formulas for three bond stiffnesses for the common materials are provided. Subsequently, the twin shear unified strength theory is applied to give the initial failure domain for the contact model for brittle and plastic bond materials, respectively, and the tensile/compressive-shear strength envelope is also put forward. The proposed solutions can provide a large number of data for mechanical response of the bond, and assist to set up the failure criterion under complex loading, which can validate and supply the experimental data in establishing the micro-bond model in DEM.