正弦波下砂岩ms级损伤预测模型

Damage Prediction Model for Sandstone at Millisecond Level under Sinusoidal Wave

为获得毫秒(ms)级正弦波损伤变量预测模型,对岩样在不破坏情况下进行了不同波形不同频率的轴向力加卸载试验。提出了不同步时间段的定义,进而获得不同峰值荷载下不考虑不同步时间条件下的动态泊松比分别与即时荷载、即时横向长度、即时轴向高度之间的线性关系,从而得到线性关系中系数与峰值荷载间的拟合公式,即可联立不同已知条件,通过少量几个加载力峰值下的试验数据,对任意峰值荷载下动态泊松比与相关参数间的线性关系进行预测。以此为基础研究得到,在误差允许的范围内,采用动态泊松比与即时横向长度的线性关系,推导出体积应变、损伤变量的计算公式和方法,可以很好地对加卸载过程中岩样的体积应变、损伤的变化做出ms级的精确预测,也为在已知少量循环试验下获得岩石动态参数,即可对ms级的损伤进行精确预测的模型提供了方法。

An accurate(millisecond level)prediction method for sandstone damage by determining the dynamic Poisson’s ratio is put forward in this paper.First of all,axial loading and unloading tests are performed on rock specimens under different waveforms at varied frequency on the prerequisite that failure does not occur.Tests reveal asynchronous lateral strain and axial strain,which give rise to dynamic Poisson’s ratio under cyclic loading and unloading.The time intervals of such asynchronous phenomenon are defined.The linear relations of dynamic Poisson’s ratio against instantaneous load,instantaneous transverse length,and instantaneous axial height under different load peaks are acquired without considering the asynchronous time.Hence,the fitting formula between relational coefficients and peak load can be obtained.Through only a small amount of test data at the peak of loading force,the linear relationship between dynamic Poisson’s ratio and relevant parameters at any peak load can be predicted.Furthermore,according to the linear relation between Poisson’s ratio and instantaneous lateral length,the equations and methods for volumetric strain and damage variable can be derived within allowable error range.The present model could precisely(at millisecond level)predict volumetric strain and damage variable of rock under cyclic loading and unloading with no need to measure displacement values when load type is known.