Underground engineering is becoming increasingly sophisticated in recent years, exemplified by shale gas recovery, nuclear waste disposal and enhanced geothermal systems. Displacement Discontinuity Method (DDM) and Fictitious Stress Method (FSM) are two branches of boundary element method which can efficiently and accurately simulate fractures and openings embedded in large spatial domains. Nevertheless, in literature, studies engaging DDM/FSM to perform the aforementioned hot-topic research are rare, and one of the key reasons lies in the inconvenient access to DDM-FSM programs. In this study, we provide DDFS^3D, a set of open-source codes incorporating the commonly used constant triangular and quadrilateral elements to implement 3D DDM, FSM and the hybrid of the two. The constant triangular element is reproduced from early studies, while the constant quadrilateral element is an independent work presented in this study. Gaussian quadrature and Hadamard finite-part integral are utilized to evaluate the regular and strongly singular integrals, respectively. To the authors’ best knowledge, DDFS^3D is the first and the only open-source codes for 3D DDM-FSM implementation. We hope it could promote the application of DDM-FSM and advance the role of DDFS in coping with the ever-increasing new challenges in underground engineering.

近年来，地下工程变得越来越复杂，例如页岩气回收、核废料处理和增强的地热系统。位移不连续法（DDM）和虚拟应力法（FSM）是边界元法的两个分支，可以高效、准确地模拟嵌入大空间域的裂缝和开口。然而，在文献中，利用 DDM/FSM 进行上述热点研究的研究很少，关键原因之一在于 DDM-FSM 程序的访问不便。在这项研究中，我们提供了 DDFS ^3D，一组开源代码，包含常用的常量三角形和四边形元素，以实现 3D DDM、FSM 和两者的混合。常三角形单元是从早期研究中复制出来的，而常四边形单元是本研究中提出的一项独立工作。高斯求积和哈达玛有限部分积分分别用于计算正则积分和强奇异积分。据作者所知，DDFS ^3D是第一个也是唯一一个用于 3D DDM-FSM 实现的开源代码。我们希望它能够促进 DDM-FSM 的应用，提升 DDFS 在应对地下工程不断增加的新挑战中的作用。