裂隙岩体三维柔度张量的数值试验方法

A numerical test method for three-dimensional elastic compliance tensor of fractured rock masses

在裂隙岩体二维柔度张量数值试验的基础上,建立了裂隙岩体三维柔度张量及其表征单元体积(REV)尺度研究的简化数值试验方法。首先根据岩体裂隙的统计参数及分布规律,运用蒙特卡罗方法在研究域内获得与实际岩体裂隙同分布的三维随机裂隙网络,提取位于不同方位的岩体试件,运用二维柔度张量的数值试验方法求出各个平面方向上的二维柔度张量,然后根据二维与三维柔度张量的拓扑关系,用数学方法求解裂隙岩体的三维柔度张量。对于含3组正交全贯通裂隙的岩体,通过数值试验获得的柔度张量与理论解相比,其主对角线上各参数的误差在5%以内,表明该数值试验方法较为可靠。最后将此方法运用到小湾水电站工程中,确定左岸坝区裂隙岩体的应力REV为11 m×11 m×11 m,并获得该区域裂隙岩体的三维柔度张量。

A simplified numerical testing method is developed to estimate the three-dimensional（3D） elastic compliance tensor and study the mechanical representative element volume（REV） of fractured rock mass, on the basis of the numerical test for two-dimensional（2D） elastic compliance tensor. Firstly, 3D stochastic discrete fracture networks are randomly generated using the Monte Carlo method, according to the statistical parameters and the probability distribution functions. Then rock samples are collected in varied directions and the 2D elastic compliance tensors of the examples are further calculated using the 2D numerical test. Thus the 3D elastic compliance tensors are obtained, regarding to the topological relationship between the 2D and 3D elastic compliance tensors. For rock samples with three sets of orthogonal and continuous fractures, it is found that the maximum relative error of the main diagonal components of the elastic compliance tensor is less than 5%, comparing the results of the numerical test with analytical solutions. Therefore, the reliability and effectiveness of the numerical tests are verified. Finally, this method is applied to determine mechanical properties of Xiaowan Hydropower Station and the REV is approximately estimated as REV≈11×11×11m3.