地下开采诱发岩层复杂力学行为无网格模拟方法研究

In the process of underground mining, due to the severe disturbance to the rock strata, rock strata may be failure in the forms of large deformation, large displacement, cracking, separation, and caving; meanwhile, the mechanical properties of the rock strata may dynamically change remarkably. Currently, the numerical simulation methods with mesh dependency have obvious difficulties when used to analyze the complex mechanical behavior of rock strata. To deal with this challenging problem, this project first aims to specifically present a Local Petrov-Galerkin Mesh-free method that is suitable for the underground mining simulation, in particular by studying the following key problems: the geometrically nonlinear modeling, the construction of complex computational models and adaptive refinement, and the simulation of discontinuous interfaces. On the base of the presented mesh-free method suitable for underground mining simulation, the further objective of this project is to present a mesh-free method for modeling rock strata complex mechanical behaviors induced by underground mining, which will be accomplished by proposing a dynamic zoning method of disturbed rock strata, an adaptive method of rock mechanics characteristics, a tracking simulation method of separation and zoning interfaces, and an algorithm of underground mining modeling. The corresponding mesh-free numerical analysis software is planned to be developed; and both the mesh-free modeling method and software will also be validated and optimized using practical applications. The research results of this project can be widely used to model the movement of rock strata and surface subsidence and cracking induced by underground mining, and to analyze the distribution of stress, strain, and displacement of the surrounding rocks, which can also provide the solid basis for the mining planning and mine safety production.

地下开采过程中，由于受到剧烈扰动，岩层产生大变形、大位移、开裂、离层与冒落等形式的破坏，并且其力学特性发生显著的动态改变。具有网格依赖性的数值模拟方法在分析岩层的这种复杂力学行为时遇到很大的困难。为此，本项目在局部Petrov-Galerkin无网格法的基础上，解决几何非线性模拟、复杂计算模型构建与自适应、不连续面模拟等关键问题，建立适合地下开采数值模拟的非线性无网格法；在此基础上，研究地下开采过程中受扰动岩层动态分带、岩体力学特性自适应调整、离层和分带界面动态追踪等方法及高效的地下开采模拟算法，形成地下开采诱发岩层力学行为及其动态演变过程无网格模拟方法，并研制相应的计算程序；以典型矿井为例，对本项目的模拟方法及程序进行验证与调整。本项目的研究成果可以广泛应用于分析预测地下开采诱发的岩层移动与地表沉陷规律，分析采空区围岩的应力、变形与位移分布规律，并为采矿规划与设计、矿井安全生产提供依据。

无网格法是一种不需要计算网格的新型数值模拟方法，克服了对计算网格的依赖，在模拟大变形、非连续等问题是具有一定的优势，但在模拟地下开采诱发的岩层复杂力学行为方面的研究尚处起步阶段，亟待深入。为此，项目组采用理论研究、算法与程序研制、实例验证相结合的研究方法，开展深入研究，取得如下成果：（1）开发了基于点插值的并行插值算法，形成了复杂地质模型非均匀场结点支持域、积分域优化确定方法；实现了材料非线性无网格数值模拟算法；推导了基于局部Petrov-Galerkin无网格法非线性刚度矩阵；推导了考虑裂隙面接触作用的控制方程，将控制方程离散成可求解的矩阵形式，构建了弹塑性条件下岩体三维张开型与剪切型裂隙的无网格模拟方法；开发了适用于复杂三维地质模型高质量四面体网格划分的算法和基于K-Means聚类算法的四面体网格划分泡泡算法，用四面体剖分方法生成的网格结点作为无网格法的场结点；形成了适合地下开采模拟的非线性无网格模拟方法。（2）实现了在地下开采过程中受扰动岩体力学参数自适应方法；建立了上覆受扰动岩体的分带准则，形成了地下开采动态分带模拟算法；建立了离层判别准则，结合开采进程模拟和离层判别准则，形成了地下开采离层动态带模拟算法，实现了在地下开采模拟中反映离层与分带界面动态发育过程。（3）在上述研究的基础上，提出并实现了无网格点插值方法的并行插值算法、非均匀场节点处理方法、并行加速与压缩存储方法，研制出适合于地下开采的高性能无网格数值计算软件GeoMFree3D。本项目研究成果已在煤矿、铁矿等地下开采诱发的岩层移动、地表沉陷与地面开裂、冒落带与裂隙带发育高度等的数值模拟分析与预测方面得到初步应用。