分段黏结非连续变形分析方法及其在砂岩破裂分析中的应用

Segmented-bond based discontinuous deformation analysis method and its application in sandstone rupture

深部采煤面临高地温、高地压、高岩溶水压及开采扰动的综合影响,岩石的非连续变形及破裂行为也比浅部更为复杂,开发模拟岩石破裂行为的数值计算方法,进行从实验室尺度到工程现场尺度的分析是研究岩石破裂相关灾害规律和机理的重要手段。非连续变形分析方法 (Discontinuous Deformation Analysis,DDA)在接触理论、块体积分、计算收敛中具有严格的数学基础,采用子块体剖分和黏结处理的DDA模型可以有效模拟岩石及裂隙岩体从连续弹性变形到渐进断裂和完全破断的全过程。基于边-边黏结效应分段线性表征的朴素思想,提出分段式边-边黏结模型,将线性及非线性黏结本构关系通过分段中心点处的成对罚弹簧进行等效表征,嵌入三角形剖分的非连续变形分析求解框架内,实现模拟岩石断裂的优化DDA模型。通过简支梁中心受压、单轴压缩、巴西劈裂案例的变形、应力结果分析,验证了优化模型的准确性,获得了边-边黏结模型中分段数目、黏结刚度比、切向法向刚度比等参数的合理取值范围;通过完整及带孔洞的砂岩试样的单轴压缩试验,阐明了块体弹性模量、泊松比等变形参数及黏结单元抗拉强度、黏聚力、内摩擦角等强度参数的赋值方法,验证了优化模型在应力-应变曲线,裂纹起裂位置捕获的准确性;通过含单裂隙及组合裂隙的砂岩巴西圆盘劈裂试验的分析,验证了优化模型在裂纹起裂、裂纹扩展、多裂纹交汇等复杂裂隙扩展问题中的适用性;采用分段式边-边黏结的优化模型可推广用于包含复杂裂隙网络的岩体破坏规律和机理的分析。

In deep coal mining,the combinations of high temperature,high ground pressure,high karst water pressure and stress disturbance lead to a discontinuous deformation and complex rupture behavior of the surrounding rocks.Reproduction of the rock failure process using the numerical approaches becomes an important way to study the rock rupture phenomena and to reveal associated failure mechanisms.With a strict mathematical foundation in contact representation,numerical integration,and convergence examination,the improved DDA method with block subdivision strategy and bond representations can effectively simulate the failure process of fractured rock masses from continuous elastic deformation stage to progressive failure stage, and the complete breakage stage. Based on the idea of piecewise characterization of the edge-edge bonding effect, a segmented edge-edge bond model is proposed, where the linear and nonlinear bonding con-stitutive relationships are equivalently characterized by paired penalty springs at the center of each segment. The segmen-ted edge-edge bond models are embedded into the conventional framework of the discontinuous deformation analysis with a triangular segmentation for the optimized simulation of rock fracturing process. By the deformation and stress analysis of the simulation results in the center compression test of the simple support beam, the uniaxial compression and the Brazili-an splitting test of rock specimen, the accuracy of the proposed model is verified. The reasonable values or ranges of the segmentation number, bonding stiffness ratio, tangential-to-normal stiffness ratio and other associated parameters of the segmented edge-edge bond are obtained. In the numerical simulation of uniaxial compression test for complete and cavit-ated sandstone specimens, the assignment methods of the deformation associated parameters (e.g., block elastic modulus, block Poisson ratio) and the strength associated parameters (e.g., bond tensile strength, bond cohesion, and bond friction angle) are clarified. Also, the accuracy of the proposed model in reproducing the stress-strain curve and initial cracking po-sition is verified. In the numerical investigation of the Brazilian splitting test of sandstone with single or combined flaws, the feasibility of the proposed model in reproducing crack initiation, propagation and intersection is verified. In summary, the proposed segmented edge-edge bond model can be applied for investigating the failure phenomena and mechanisms of rock masses with complex fracture networks.