岩石非弹性特性的内时理论模型

An Endochronic Model for Anelasticity in Rock

针对岩石的非弹性特性,将内时理论引入到岩石特性的研究中来。首先对内时理论的方程作了简要推导和说明。将核函数作四阶的Prony展开,将积分方程用一组微分方程来代替,最后得出可以进行数值运算的内时方程。在MTS压机上进行了砂岩、花岗岩等不同岩石样品的多种循环加卸载实验,得到一系列应力—应变曲线。根据滞回曲线的拐点,用最小二乘拟合法来具体确定内时方程中的有关参数。将理论产生的各种滞回曲线与实验滞回曲线作比较,可以看出在滞回曲线和残余应变这二个岩石非弹性特性最明显的标志上,非常一致。说明在中等应变强度时,利用内时理论可以对岩石非弹性特性作很好的研究。与塑性理论比较,可以免去确定屈服面的困难。最后对岩石滞回特性的微观机制用P-M模型作了简要讨论和分析。

For anelasticity in rock, endochronic theory was introduced into the study on the characteristic of rock. First, we explained and deduced the endochronic equation briefly. Then, we expanded the kernel function by fourth-order. Thus, we can replace the integral equation with a set of differential equations and get the endochronic equations that can be used for numerical calculation at last. On the MTS pressure machine, a set of hysteresis graphs of stress-strain under uniaxial cycling loadings for different rock samples such as sandstone and granite were obtained. According to stress and strain values at hysteresis loop reversal points, the corresponding parameters in the endochronic equations can be determined by the method of a least squares fitting. Comparing the stress-strain curves of simulation and the observed results of experiments, we can get very consistent results for both hysteresis and residual strain which are the most distinct signs for the anelasticity of rock. It indicates that the anelasticity in rock can be explained well by endochronic theory at intermediate strain levels. Therefor endochronic theory can overcome the obstruction of getting yield surface accurately comparing with plastic theory. Finally, we discuss and analyze the microcosmic mechanism of the characteristic of rock hysteresis briefly using P-M model.