中低应变率下的岩石损伤本构模型研究

深部岩石的破碎与钻探中,岩石主要处在中低应变率的载荷作用下,而目前的研究还沿用中高应变率推导的动态损伤本构关系。从工程背景和试验角度分析了中低应变率下的岩石动力学特性,提出Maxwell体、Bingham体和损伤体的并联模型,借助拉普拉斯变换,引入基于岩石孔隙、裂隙劣化的损伤变量,导出了中低应变率下的岩石动态损伤本构模型。利用该模型对泥质砂岩和花岗岩在应变率为87 s-1、382 s-1、673 s-1时的应力-应变试验数据进行拟合,并将拟合结果与实测数值、原文献拟合曲线对比,结果表明该理论模型适用性较好。分析拟合参数可知,该动态损伤本构模型能够主动适应中低应变率两类情况,本构曲线和损伤变量的变化符合实际情况。

Damage constitutive model of rock under medium and low strain rates

When drilling is executed in the deep rock mass, rock is mainly subjected to loads with medium and low strain rates. However the medium and high strain rates damage constitutive model is still used instead, which doesn’t adapt to the real situation. The dynamic characteristics of rock under medium and low strain rates are analyzed from engineering background and practical experiments. A parallel model of rock, which is made up of Maxwell element, Bingham element and damage element, is proposed. The damage parameter based on degradation of pore and fissure is introduced with Laplace transformation. A new dynamic damage constitutive model of rock is derived. The proposed model is used to fit the stress-strain curves of argillaceous sandstone and granite at strain rates of 87 s-1, 382 s-1 and 673 s-1. By comparing fitting results with the experimental data and literature results, it is shown that the proposed model is suitable for the behavior of rock under medium and low strain rates. With analyzing the fitting parameters, the proposed model can actively adapt to medium and low strain rates. The variations of constitutive curves and damage parameters are in agreement with the practical situation.