弹性-脆性-损伤模型及其在岩石局部破坏研究中的应用

在弹性-脆性-损伤本构模型中,采用了由线性的莫尔-库仑剪切屈服函数和非线性的虎克-布朗屈服函数复合后的屈服函数,以适应高压应力条件下岩石变形及破坏规律的研究.为了考虑脆性岩石在应力突然跌落过程中的弹性模量的变化,引入了一个损伤因子,以描述损伤的程度.此外,还考虑了围压对弹性模量的增强作用.对平面应变压缩条件下的矩形岩样的破坏过程进行了计算,并与接近脆性的带拉伸截断的应变软化莫尔-库仑模型的结果进行了对比,发现了它们之间的差异.又对静水压力条件下的平面应变模型开挖圆形巷道之后的破坏区、轻微的剪切及拉伸岩爆区和体积模量的分布进行了计算.研究发现,当考虑围压对弹性模量的影响后,体积模量的高值区位于V形坑的尖端,而V形坑内部的损伤程度随着损伤因子的增加而增加.如果不考虑围压对弹性模量的影响,V形坑尺寸大、较钝.研究结果表明,不同岩石脆性破坏过程中的损伤程度及围压对弹性模量的影响程度不相同是导致V形坑形态差别的原因之一.

An Elastic and Brittle Model with Damage and Application in Study on Rock Localized Failures

To model rocks’ deformations and failures at high compressive stresses,a composite yield function was proposed in an elastic and brittle constitutive model with damage,which includes a linear shear yield function with tension-off(i.e.,the Mohr-Coulomb criterion)and a nonlinear shear yield function(i.e.,the Hoek-Brown criterion).A damage factor was introduced into the model to take the decrease of elastic modulus into account in the stress drop process of brittle rocks.The factor describes the damage extent.The influence of confining pressure on the elastic modulus was considered.The failure process of a rectangular specimen in plane strain compression was modeled.The obtained results were compared with those of the quite brittle strain-softening Mohr-Coulomb model with tension-off.Apparent difference was found.A plane strain model after a circular tunnel was excavated in hydrostatic pressure was modeled and the distribution of failed elements,slight rockburst regions due to shear and tensile failures and bulk modulus was presented.It is found that when the influence of confining pressure on the elastic modulus is considered,there exists higher bulk modulus at tips of V-shaped notches.In notches,the damage extent of rock elements is increased with an increase of the damage factor.If the elastic modulus is independent of the confining pressure,then blunt V-shaped notches with larger sizes are expected.The present results show that the one reason for the difference in pattern of V-shaped notches of different rocks is the different damage extent in the brittle failure process and the different influence extent of confining pressure on the elastic modulus.