基于残余强度修正的岩石损伤软化统计本构模型研究

Study of modified statistical damage softening constitutive model for rock considering residual strength

岩石随着围压的增大,残余强度的增加幅度比峰值强度大,残余强度逐渐成为影响岩石全应力-应变曲线峰后段的主要因素,因此,建立岩石损伤软化统计本构模型时,对残余强度进行修正是非常必要的。基于岩石应变强度理论以及岩石微元强度服从Weibull随机分布的假设,考虑岩石峰后残余强度对损伤变量进行修正,在微元破坏符合Hoek-Brown屈服准则条件下,建立了能够反映岩石峰后软化特征的三维损伤统计本构模型;依据岩石试验全应力-应变曲线的几何特征,推导出本构模型参数的数学表达式,并基于花岗岩室内试验数据对模型参数进行探讨,研究了Weibull分布参数与本构模型的关系,探讨了损伤修正系数的取值和岩石累积损伤的扩展过程;将建立的本构模型理论曲线与4种岩石(斑状二长花岗岩、细晶大理岩、砂岩和粉砂质泥岩)不同围压下的常规三轴压缩试验曲线进行对比分析,结果表明,该模型能很好地描述岩石破裂过程的全应力-应变关系和表征岩石残余强度特征。这对于岩石损伤软化问题以及岩石加固处理措施的研究均具有重要的意义。

The increase amplitude of residual strength of rock is larger than the rock peak intensity of rock with the increase of confining pressure. Gradually, residual strength becomes the main factor of complete stress-strain curve of rock at the stage after peak intensity. While establishing statistical damage constitutive model, it＇s necessary to modify the residual strength. Based on the strain strength theory and hypothesis of rock particles intensity obeying Weibull random distribution, a statistical damage constitutive model for rock under triaxial compression, which can describe the characteristics of rock post-peak softening, is established by adopting Hock-Brown criterion, and the residual strength to modify the damage parameter is considered. Then, all these model parameters analytic solutions are deduced according to the geometric features of rock complete stress-strain curve. On the basis of experimental results of granite specimens, the influences of Weibull distribution parameters on the rock damage constitutive model are studied. At the same time, the value of modified coefficient and the damage process of rock are discussed. Finally, the achieved theoretical curves by the damage model of rock under different confining pressures are comparatively analyzed with the results of conventional triaxial compression test of four kinds of rock： porphyaceous adamellite, fine-particle marble, sandstone and silty mudstone. The results indicate that this statistical damage constitutive model is able to provide an accurate description for complete stress-strain curve and residual strength for rock. All these are meaningful to the research of rock damage as well as to choose suitable measures to strengthen rock mass.