基于主应力σ_(2)σ_(3)为参数的岩石破坏强度准则

Failure Strength Criterion for Rock Based on the Parameter of Principal Stresses σ_(2)σ_(3)

本文提出了一种基于中间主应力和最小主应力乘积(σ_(2)σ_(3))为参数的显式岩石破坏强度准则.该准则通过骨架曲线和分支曲线两部分来描述岩石的强度规律.骨架曲线即三轴压缩实验的结果,分支曲线即最小主应力固定的实验结果.通过研究岩石真三轴压缩实验结果发现岩石的破坏强度与中间主应力和最小主应力乘积的平方根(√σ_(2)σ_(3))之间存在着较强的相关性,并且平面内骨架曲线和分支曲线在交点处的斜率相等.推导出了在最大主应力和中间主应力平面内,骨架曲线的斜率在交点处是分支曲线斜率的2倍.对于同一种岩石,在最大和中间主应力平面内随着中间主应力和最小主应力的差值达到某个值,所有分支曲线其斜率逐渐衰减为0,岩石的破坏强度达到最大值.基于以上特征,得到骨架及分支曲线的函数形式.本文提出的岩石强度准则经过实验数据的检验,并与其他准则的计算结果进行对比.结果表明本文提出的岩石强度准则可以较好地拟合岩石材料在三轴受压条件下的破坏强度.此外,该强度准则可以用较少的数据拟合出相对比较稳定精确的结果,显示了该准则的稳定性与合理性.

An explicit strength criterion for rock is proposed which is based on the parameter of the product of intermediate and minimum principal stresses(σ_(2)σ_(3)).This criterion consists of two parts:the skeleton curve which is the results of triaxial compression tests,and the branch curve which is the results when the minimum stress is fixed.By studying the results of true triaxial compression experiments of rocks,a strong correlation between the failure strength of the rock and the square root of the product of intermediate and minimum principal stresses(√σ_(2)σ_(3))is observed.The slopes of the skeleton curve and the branch curve are equal at the intersection in this coordinate system.Based on this observation,the slope of skeleton curve is found two times of the slope of the branch curve at the intersection in the maximum principal stress and intermediate principal stress plane.It is observed that the failure strength for a rock always reaches a maximum value as the difference between intermediate principal stress and minimum principal stress is a constant value in all branch curves.According to the above characteristics of rocks,the functions of skeleton and branch curves are derived.The proposed criterion is validated by experimental data and compared with other criteria.The results show that the proposed failure strength criterion for rock can fit the triaxial failure strength of rock material well.This criterion can also fit relatively stable and accurate results with even less data.