岩石滞后非线性弹性模拟的研究

在循环荷载作用下，孔隙饱和岩石呈现出闭合的应力-轴向（径向）应变滞后回线、轴向应变-径向应变滞后回线和X”形的瞬时弹性模量（杨氏模量和泊松比）等滞后非线性弹性特征，引入一种滞后非线性弹性材料的宏观模型 Preisach-Mayergoyz模型（PM模型）来描述岩石的这些特征。在PM模型中，孔隙饱和岩石的滞后非线性弹性特征由PM密度空间、施加的应力历史和岩石的滞后细观单元(HMU)的弹性特性所决定。在状态方程中，应变与关闭弹性单元数目占总单元数目的百分比成正比，而关闭弹性单元数目则与施加外力的历史有关，特别是在施加外力转向的时候。通过构造PM空间中不同的密度函数和设定HMU的弹性特性（平衡长度对）可以模拟性质不同的岩石，PM空间中不同的密度函数在一定程度上反映了岩石在循环荷载下的本构关系响应的不同性质。HMU中应变的响应与应力的路径有关，模型本身强调了施加于岩石的应力历史在决定岩石的弹性状态时的重要性，因此，可以用来模拟岩石的离散记忆，从这个意义上讲，孔隙饱和岩石的滞后特性是它具有离散记忆特性的原因。通过模拟，讨论了模型参数和岩石弹性模量之间的定量关系。

Study on simulation for hysteretic nonlinear elasticity of rock

We show the hysteretic nonlinear behavior of discrete memory, hysteresis loop and “X” shape tangent elastic moduli (Young’s modulus and Poisson’s ratio) in uniaxial cyclic loading experiments, and further clarify it using hysteretic quasi-static stress-strain equation of state in Preisach-Mayergoyz model (PM model) proposed by McCall and Guyer. Detailed curves of stress-axial strain, stress-radial strain, tangent modulus-axial strain and tangent Poisson’s ratio-axial strain are determined by space density and elastic property of hysteretic mesoscopic units (HMU) in PM model. In the equation of state, stress is proportional to the fraction of closed elastic units to total units, and the closed elastic units are related to applied pressure history, especially at the turn of pressure reversal. The response of strain is related to the stress path, and the model emphasizes the importance of stress history in determination of the elastic state of rock, hence the model can be used to simulate discrete memory. In this sense, hysteresis might be the cause of discrete memory in rock. By the simulation, we demonstrate the quantitative relationships between the parameters of PM model and elastic moduli of rock.