A three-dimensional dual-scale coupled approach and its application in geotechnics

To study the microscopic and macroscopic behaviour of geotechnical engineering materials, attention is increasingly being paid to the dual-scale coupled computation of continuum and discrete models. However, two-dimensional dual-scale coupling cannot reveal the actual behaviour of materials. Therefore, a three-dimensional dual-scale coupled approach to accomplish the information transmission between discrete-element model and finite-difference model was deduced, and a corresponding coupled program was developed. The point of application of the resultant force on the interface in the discrete-element model was sought by introducing the principle of least squares, and the element nodal forces at the interface in the continuum model were obtained based on the formulation of load transfer from the literature. The velocities acting on the interface in the discrete-element model were calculated by bilinear interpolation according to the nodal velocities of the interface in the continuum model, which achieved the velocity transmission from the continuous zone to the discrete-element zone. The coupling was accomplished through the velocity and force transmissions at the interface between discrete-element model and finite-difference model. Finally, the algorithm and program were validated through an example of dynamic compaction.