基于对数正态分布的岩石损伤统计分析方法研究

以Mohr强度理论为基础，利用岩石微元强度服从对数正态随机分布的特点，得到了三轴压缩条件下的岩石损伤统计本构模型，并根据试验曲线采用最小二乘法确定出模型参数．与试验结果比较，该模型可以很好地模拟岩石破裂过程的全应力应变关系，真实反映了岩石软化特性、岩石强度随围压变化等特性．在此基础上，讨论了对数正态参数R0,S0对岩石应力应变全过程曲线的影响．结果表明，参数R值的变化对岩石的强度有影响；参数S0值的变化对岩石的脆性有影响．

Study on the Statistical Analysis of Rock Damage Based on Lognormal Distribution

Based on Mohr strength theory, by considering the characteristic that the strength of rock microunit is of lognormal stochastic distribution, a statistical damage constitutive model is obtained under rock triaxial compression test. Using the method of least squares, these model parameters are determined according to the experimental curve. Compared with rock triaxial compression test results, this model can well simulate the relation of stress - strain during the full process of rock failure, being capable of reflecting the characteristic of strain softening and the phenomenon that rock strength is affected by confining pressure. Moreover, the effect of which tognormal distribution parameters F0 and So have on complete stress - strain curves of rock failure is also discussed. The results show that the change of Fo has some effect on the rock strength and that the value of So has effect on the brittleness of rock.