基于幂函数分布的砂岩损伤本构模型研究

Study on sandstone damage constitutive model based on power function distribution

为了能够准确地描述岩石应力应变关系和损伤演化规律,假定微元的统计强度概率服从幂函数分布,推导了单轴应力条件下岩石的损伤本构方程;考虑围压条件下岩石峰后的残余强度,推导了三轴应力下岩石修正的损伤本构方程,并分别采用砂岩试样进行了实验验证.研究结果表明:(1)单轴载荷下岩石的损伤本构方程能够较好的表述全应力-应变曲线的弹性阶段、屈服阶段、应变软化阶段以及峰值应变和峰值强度特征;(2)单轴应力下岩石的损伤演化和加载过程中岩石裂隙的演化有良好的相关性;(3)修正的损伤本构方程可较好地反映三轴应力状态下岩石峰前非线性、应变软化以及峰后残余强度特征;(4)随着围压的增大,损伤-应变曲线逐渐变缓,岩石抵抗损伤的能力将逐步加强.以上研究成果可为工程岩体损伤失效性分析提供重要理论指导.

To accurately describe the stress-strain relationship and the evolution law of the rock damage,under the assumption that the statistical strength probability of micro element follows the power function distribution,the damage constitutive equation of rock under uniaxial stress is derived.Taking the residual strength after rock peak under the confining pressure into consideration,the revised damage constitutive equation of the rock under the triaxial stress is developed and verified separately through the experiments with sandstone samples.The following conclusions can be drawn from the experiments.Firstly,the damage constitutive equation of the rock under the uniaxial load provides a more accurate descriptions of the characteristics of elastic stage,the yield stage,the strain softening stage,the peak strain and the peak strength of the total stress-strain curve.Secondly,a strong correlation has been identified between the damage evolution of rock under uniaxial stress and the evolution of rock fractures during loading.Thirdly,the modified damage constitutive equation can well reflect the pre-peak nonlinearity,the strain softening and the post peak residual strength of rock under triaxial stress state.Fourthly,with the increase of the confining pressure,the damage strain curve gradually slows down along with the gradually improved damage resistance of the rock.It is expected that this study results can provide important theoretical guidance for the damage failure analysis of engineering rock mass.