基于受压裂隙开裂准则的损伤模型

Damage model based on fracture cracking criteria

为了反映岩石内部裂隙对岩石本构关系的影响,建立受裂隙分布及裂隙面摩擦因数共同影响的损伤模型。类比弹簧束模型,定义与开裂裂隙长度有关的损伤模型。基于受压裂隙的开裂准则,对不同应力状态下的开裂裂隙长度范围进行求解,通过概率统计的方法计算开裂裂隙长度的数学期望,将其代入建立的损伤模型中得到损伤变量。利用模型对岩石应力-应变曲线进行计算。研究结果表明:建立的损伤模型能够反映裂隙面摩擦因数与裂隙角度对岩石强度的影响。当摩擦因数为0时,裂隙角度45o对应的岩石强度最小,随着裂隙摩擦因数增大,最小峰值强度对应的裂隙倾角逐渐减小;当裂隙角度一定时,摩擦因数越大,峰值强度越大;数值计算结果与实验结果一致。该模型还能够反映裂隙长度分布对岩石强度的影响。当长裂隙数占比较大时,岩石强度较小;反之,岩石强度较大。计算结果能够反映岩石在塑性阶段的变形特征,该损伤模型具有合理性。

In order to reflect the influence of rock internal fracture on rock constitutive relation,a damage model affected by fracture distribution and friction coefficient of fracture surface was established.Analogous to the spring beam model,a damage model related to the length of cracked fissure was defined.Based on the cracking criterion of the compression fracture,the length range of crack fracture in different stress states was solved,the mathematical expectation of crack length was calculated by probability statistics,and the damage variable was obtained in the damage model.The stress-strain curve of rock was calculated by this model.The results show that the model can reflect the influence of fracture surface friction coefficient and angle on rock strength.When the friction coefficient is 0,the corresponding angle of minimum strength of rock is 45°.With the increase of the friction coefficient,the crack angle corresponding to the minimum peak strength decreases gradually.When the angle is constant,the greater the friction coefficient is,the larger the peak strength is.The calculated results are in agreement with the experimental results.The model can also reflect the effect of crack length distribution on rock strength.When the long crack occupies a larger proportion of the crack,the strength of rock is smaller.When the long crack occupies a smaller proportion,the strength of rock is larger.The calculated results reflect he deformation characteristics of rock at plastic stage,which shows the reliability of the model.