Simulation of interaction problems between rock structure and soil is a challengeable subject. It involves a coupled system that considers the behaviors of both rock structure and soil, together with interaction between them. Discontinuous deformation analysis (DDA) is suitable for analyzing a blocky system, such as rock or flexible structure. On the other hand, smoothed particle hydrodynamics (SPH) is appropriate for studying flow-like behavior of soil after implementing a proper constitutive model. A coupling scheme that bridges DDA and SPH can take advantages of both methods. Therefore, a numerical method for such interaction problems using DDA and SPH is developed, in which a Drucker-Prager elasto-plastic soil constitutive model is incorporated. In the developed method, the interaction between SPH particle and DDA block is idealized through a new spring-dashpot contact model with the Mohr-Coulomb failure criterion used. Several numerical examples are studied, and satisfactory agreements between the simulation results and the experimental data or other available simulated results are obtained, suggesting the correctness of the developed method. Further, the developed method is applied to study influence of backfill on a masonry arch bridge. Conclusively, this coupled DDA-SPH method provides a potential numerical approach for studying interaction problems between rock structure and soil.

模拟岩石结构和土壤之间的相互作用问题是一个具有挑战性的课题。它涉及一个耦合系统，该系统考虑岩石结构和土壤的行为以及它们之间的相互作用。不连续变形分析 (DDA) 适用于分析块状系统，例如岩石或柔性结构。另一方面，平滑粒子流体动力学 (SPH) 适用于在实施适当的本构模型后研究土壤的类流动行为。桥接 DDA 和 SPH 的耦合方案可以利用这两种方法。因此，数值方法开发了使用 DDA 和 SPH 解决此类相互作用问题，其中包含 Drucker-Prager 弹塑性土本构模型。在开发的方法中，SPH 粒子和 DDA 块之间的相互作用通过使用 Mohr-Coulomb 失效准则的新弹簧缓冲器接触模型进行了理想化。研究了几个数值例子，模拟结果与实验数据或其他可用的模拟结果之间获得了令人满意的一致性，表明所开发方法的正确性。此外，所开发的方法应用于研究回填对砌体拱桥的影响。总之，这种耦合的 DDA-SPH 方法为研究岩石结构和土壤之间的相互作用问题提供了一种潜在的数值方法。