圆盘冲击劈裂试验中岩石拉伸弹性模量的求解算法

摘要

An analytic algorithm to estimate the tensile modulus of disk impact splitting test was presented.Combined the theoretical elastic solution of disk on cardiac force and the physical parameters obtained in actual measure of experiments,and based on the principle of calculus,the quantitative relationship between tensile modulus of rock specimen center and the total displacement of deformation on the direction of the vertical load was derived.The relationship between the deformation on the vertical-loading direction and that on the parallelloading direction was analyzed; and there is a linear relation between two deformations and this relation can be expressed with a ratio function.At last,combined with split Hopkinson pressure bar(SHPB) impact splitting test principle,measuring the deformation on the parallel-loading direction and obtaining the deformation on the vertical-loading direction by using that ratio function.And then the impact splitting tensile modulus can be obtained with a derivation function by substituting the deformation on the vertical-loading direction.Five physical parameters,including the impact loading power,sample diameter,sample thickness,rock Poisson's ratio and the total deformation on the parallel-loading direction,were used in this derivation function.This derivation function has a clear meaning and easy to use,and provide a new approach to estimate the tensile modulus in Brazilian disk splitting test.%提出圆盘冲击劈裂试验中求解岩石拉伸弹性模量的解析算法.结合圆盘对心受力的理论弹性解和实际试验过程中方便测量的物理参数,基于微积分原理,得到岩石拉伸弹性模量和垂直加载方向上总位移变形量之间的定量关系式.在此基础上,考察试样中心平行加载方向和垂直加载方向位移量之间的关系,认为两者之间存在线性关系,可以用比例函数进行表示.最后,结合SHPB冲击劈裂试验原理,通过测量得到平行加载方向位移,利用得到的比例函数进行换算,代入到拉伸模量和垂直加载方向上总位移变形量之间的定量关系式中,进而得到圆盘冲击劈裂试验中岩石拉伸模量的求解公式.该式包含冲击加载力、试样直径、试样厚度、岩石泊松比和试样中心平行加载方向上总位移变形量5个物理量,意义明确,运用简便,为求解圆盘劈裂试验拉伸弹性模量提供了一种新的方法.