裂隙化岩体不连续面密度的分形研究

 不连续面密度是表征岩体内部不连续面分布特征的重要参数之一，但是岩体内不连续面的分布是随机的、不规则的，要想准确获得岩体不连续面密度的真实值是不可能的。基于现场调查的岩体露头不连续面特征，借助计算机模拟技术建立岩体不连续面分布的二维、三维随机裂隙网格模型，从数理统计学的角度计算岩体不连续面密度数值。并基于分形理论计算岩体不连续面分布的二维、三维分布特征，尝试建立岩体不连续面密度与分维数的数学关系。计算结果表明，岩体不连续面密度与分维数具有相同的变化趋势，随着不连续面分维数的增大，不连续面密度增大，不连续面密度与分维数之间存在线性关系。研究结果表明，不连续面分布的体密度和三维分形维数，可以更加综合地反映岩体内部不连续面的分布特征和空间信息及对岩体强度参数的影响，对工程应用具有更好的实际作用。且在此基础上，提出基于不连续面分布的体密度和三维分形维数的岩体等效抗剪强度指标的折减计算。

STUDY OF DISCONTINUITY DENSITY OF FRACTURED ROCK MASSES BASED ON FRACTAL THEORY

The discontinuity density is one of the most important parameters，which can express the distribution of rock masses discontinuities. However，the distributions of discontinuities in rock masses are random and irregular. It is impossible to obtain the true value of discontinuity density accurately in practical engineering. Based on the discontinuities data of rock mass outcrops in field investigation，two-dimensional(2D) and three-dimensional(3D) stochastic fracture network models are established by using computer simulation technology. The discontinuity density approximate value of rock masses is calculated based on mathematical statistics；and 2D and 3D distribution characteristics of discontinuity in rock mass are calculated by using fractal theory. The authors try to establish the mathematical relationship between discontinuity surface density，volume density and 2D，3D fractal dimensions. The calculation results show that discontinuity density and fractal dimension have the same change law that they increase with the increasing factual dimension. The discontinuity density increases linearly with the increasing fractal dimension of discontinuities. The volume density and 3D fractal dimension of discontinuities comprehensively reflect the spatial distribution characteristics of discontinuities in rock mass and the influence for rock mass mechanical strength parameters. The two indices are effective for engineering practice. The equivalent shear strength indices of rock masses can be calculated based on the volume density and 3D fractal dimension of discontinuities.