改进的岩石节理弹性非线性法向变形本构模型研究

Improved nonlinear elastic constitutive model for normal deformation of rock fractures

回顾了已有的几类岩石节理法向变形本构模型,指出以往模型在中应力水平条件下模拟结果与试验结果发生偏离的现象。针对这一问题,引入"半值节理最大闭合量应力"σ1/2概念,着重论述了传统的BB模型与经典指数模型本身所固有的数学缺陷。随后,以Malama和Kulatilake(2003)提出的统一指数模型为例,进一步阐明模型改进的必要性,同时分析了该模型因采用对σn/σ1/2项添加幂函数n的修正方式而丢失节理法向初始刚度Kni的物理意义这一不足之处。基于上述研究,根据前人试验数据分析建立单调加载条件下岩石节理法向应力–位移关系曲线的控制微分方程,定义拟节理最大允许闭合量Dmax=ξdmax的概念,提出一种新的三参数本构模型——改进的岩石节理弹性非线性法向变形本构关系,并在数学上严格证明了BB模型与经典指数模型是新模型的两个特例。新模型克服了前述模型数学上的缺陷,弥补了以往模型模拟结果与试验结果发生偏离的不足,且没有因新参数ξ的添加丢失Kni的物理意义。最后采用新模型对他人试验结果进行预测,建议了修正参数ξ的确定方法。模型预测结果与试验结果吻合良好,进而验证了本文模型的可行性。

Some nonlinear elastic constitutive models for normal deformation of rock fracture were reviewed and the significant deviation of these models from experimental results at median stress level was pointed out. A new concept named half-closure stress σ1/2 was introduced to lay emphasis on the analysis of the mathematical defects of both the BB model and the classical exponential model. The generalized exponential model proposed by Malama and Kulatilake （2003） was treated as an example for further explanation of the necessity for model improvement, meanwhile the deficiency of physical meaning of the initial normal stiffness of fracture K,i because of the modification by accession of power function n on σn/σ1/2 was analyzed. Based on the above researches, a governing differential stress-displacement equation of fractures under monotonically raising normal compressive loading was established, and the concept of maximum allowable closure of pseudo fracture Dmax=ξdmax was defined. Then a new 3-parameter constitutive model which could improve the nonlinear elastic normal deformation behavior of fractures was proposed. It was strictly proved that the BB model and the classical exponential model were two special cases of the new model. The new parameter was easy to be determined, and the mathematical defects of the BB model and the classical exponential model were overcome. Counteracting the deviation of the simulated results of these traditional nonlinear models with the test results at median stress level, the physical meaning of Kni would not be lost with the accession of the new parameter. The predicated results fitted with the test results well in adopting the new model for the predication of other test data, which verified the feasibility of the new model.