高地应力下砂岩力学参数和波速变化规律试验研究

基于波动方程，提出一种砂岩的纵波波速与静水围压关系的数学模型。在岩石常规三轴试验的基础上得到不同静水围压下砂岩的静弹性模量、静泊松比和纵波波速，并分别拟合得到静弹性模量-静水围压和静泊松比-静水围压关系的拟合曲线和拟合公式。试验结果表明，砂岩的静弹性模量和静泊松比随静水围压的增大而增加，且静弹性模量增加速率缓慢减少。基于波动方程求解得到纵波波速-静水围压关系的数学模型，利用数学模型计算得到的纵波波速可知，砂岩的纵波波速随静水围压的增大而增大，且增加速率逐渐变缓。计算得到的纵波波速与试验测得的纵波波速进行对比验证，误差范围为7.0%~8.3%，故基于波动方程求解的砂岩纵波波速-静水围压关系的数学模型可靠性和准确性较高，对高地应力下岩石的物理力学参数和波速变化规律的分析判定具有指导意义。

Experimental study on mechanical parameters and wave velocity variation of sandstone under high ground stress

A large number of studies showed that high ground stress had a certain influence on the wave velocity of deep buried rock, based on the wave equation, a mathematical model of the relationship between longitudinal wave velocity of sandstone and hydrostatic confining pressure was proposed. Based on the conventional triaxial test of rock, the static elastic modulus, static Poisson's ratio and longitudinal wave velocity of sandstone under different hydrostatic confining pressures were obtained, and the fitting curves and fitting formulas of static elastic modulus-hydrostatic confining pressure and static Poisson's ratio-hydrostatic confining pressure were obtained respectively. The test results showed that the static elastic modulus and static Poisson's ratio of sandstone increased with the increase of hydrostatic pressure, and the rate of increase of static elastic modulus decreased slowly. Based on the wave equation, the mathematical model of the longitudinal wave velocity-hydrostatic confining pressure was obtained, the longitudinal wave velocity calculated by the mathematical model showed that the longitudinal wave velocity of the sandstone increased with the increase of the hydrostatic pressure, and the increasing rate gradually became slower. The calculated longitudinal wave velocity was compared with the measured, the error range was 7.0%-8.3%. Therefore, the mathematical model of sandstone longitudinal wave velocity-hydrostatic confining pressure based on wave equation was reliable and accurate, it was of guiding significance to analyze and judge the physical and mechanical parameters of rock under high ground stress and the variation law of wave velocity.