The purpose of this paper is to present a new algorithm for coupling discrete-element and finite-difference methods for three-dimensional problems. The finite-difference method (FDM) and the discrete-element method (DEM) are commonly used in geotechnical engineering. However, the continuous characteristics and the computational cost are the main obstacles to accurate and efficient simulation of practical problems for these individual methods. Coupling is thought to be an effective and promising way to combine the advantages and overcome the inability of these two methods. In this paper, an algorithm for coupling of DEM and FDM is presented. A two-stage searching method—namely, global domain searching and local domain searching—is proposed for detecting contact on the interface. A calculation method for force transmitting is presented. Conventional soil element tests were simulated to verify the validity of the proposed coupled algorithm by checking the constitutive behaviors, deformation compatibility, and transmission of normal and shear contact force.

The cohesive properties of lunar regolith, combined with a low-gravity environment, result in it having a distinct mechanical behavior from sandy soil on Earth. Consequently, empirical formulas derived from cone penetration tests (CPTs) for calculating the shear strength parameters of Earth’s sand cannot be directly applied to lunar regolith. This study utilized the three-dimensional discrete element method (DEM) to numerically simulate triaxial shear tests and cone penetration tests in a lunar environment. The particle contact model for lunar regolith in the discrete element method (DEM) simulation incorporated the hysteresis effect of van der Waals forces, thereby simulating the cohesive properties of lunar regolith in a lunar environment. We proposed a relationship for calculating the shear strength index of lunar regolith based on normalized cone tip resistance using the results from triaxial and CPT simulations and referencing empirical formulas derived from ground-based CPT data. The results of this study provide a valuable reference for future lunar CPTs.

Rock–socketed pile under lateral loading is important in engineering practice. It is very significant to calculate the lateral bearing capacity of rock–socketed piles since few studies focus on this problem. The rock cohesion and instantaneous angle of friction, which have a high correlation with confining pressure, are obtained. Moreover, the strain wedge model is modified from three aspects: the assumption of nonlinear displacement; the stress level related to cohesion and friction angle; and the pile side resistance. Then, the modified strain wedge model is employed to deduce p–y criterion for rock–socketed pile considering Hoek–Brown failure criterion. The fourth-order partial differential equation constructed according to the p–y curve is solved by using the finite difference method. A numerical method with 2 m diameter rock-socketed pile is given to validate the rationality of the proposed method. It is shown that the proposed could predict the pile deformation well, and the responses are considered acceptable.