多次冲击下砂岩粘弹性损伤本构关系

Viscoelastic damage constitutive relation of sandstone under multiple impact load

为研究砂岩的粘弹性损伤特性,开展了多次冲击压缩下的霍普金森杆试验。通过砂岩动应力应变曲线分析了中应变率范围内两种动变形模量的定义方法,表明采用等效动变形模量能反映砂岩在动态冲击压缩作用下的损伤变化特性。从微观角度出发,砂岩的统计损伤变量可由破坏的微元体数量占全部微元体数量的比例定义;从宏观角度出发,这种统计损伤变量也可由微元体破坏前后的动变形模量定义,并验证了动变形模量服从Weibull统计分布。微元体受力模型由粘性体和损伤体并联而成。粘性体的力学机制由砂岩动应力与动应变、应变率之间高度线性相关的拟合关系得到合理的解释;损伤体的应力应变关系由Drucker-Prager强度准则和Lemaitre应变等效原理基础上推导而来。通过对建立的粘弹性本构关系曲线与试验曲线进行验证,两者之间的变化趋势一致,具有较好的代表性,表明建立的粘弹性损伤本构关系是合理的;两者之间的偏差可通过增加砂岩试样数量、优化试验方案以及应用概率统计等途径解决;在获得一定概率保证率的本构关系参数后方可将粘弹性损伤本构关系用于分析和评价煤矿采动区岩质边坡的稳定性,以及为相关的地质工程安全评价提供必要的理论分析基础。

In order to study the viscoelastic damage characteristics of sandstone,the Hopkinson test under multiple impact compression was carried out. Based on the dynamic stress-strain curve of sandstone,two definitions of dynamic deformation modulus in the range of middle strain rate are analyzed. It is shown that the equivalent dynamic deformation modulus can reflect the damage characteristics of sandstone under dynamic impact compression. Microscopically,the statistical damage variable of sandstone can be defined by the ratio of the number of damaged microelements to the total number of microelements;and macroscopically it can also be defined by the dynamic deformation modulus before and after the microelement failure. It is verified that the dynamic deformation modulus obeys the Weibull statistical distribution. The force model of the microelement is composed of a viscous body and a damaged body in parallel. The mechanical mechanism of the viscoelastic body is reasonably explained by the highly linear correlation between the dynamic stress,the dynamic strain and the strain rate of sandstone. The stressstrain relation of the damaged body is derived based on the Drucker-Prager strength criterion and the strain equivalent principle proposed by Lemaitre. Through the verification of the introduced viscoelastic constitutive relation curve and the test curve of sandstone,the trend of change between them is consistent,which has good representativeness,indicating that the established viscoelastic damage constitutive relation is reasonable. The deviation between them can be solved by increasing the number of sandstone samples,optimizing the test scheme and applying probability statistics. After obtaining the viscoelastic constitutive relationship parameters with a certain guarantee rate of probability,the viscoelastic damage constitutive relation can be used to analyze and evaluate the stability of the rock slope in the coal mining area,and provide the necessary theoretical analysis basis for the related geological engineering evaluation of safety.