基于分形损失理论的粗糙节理岩体中应力波波速研究

Veocity of stress wave propagating in rough jointed rock based on fractal damage theory

从损伤力学的基本理论出发,推导了应力波在节理岩石中传播波速的解析解,建立了节理面图像分形维数与波速间的关系。为了从数值角度探讨节理面图像维数对波速的影响规律,基于图像每一像素颜色可表示为一个三维空间矢量的基本假定,构建了节理面图像的粗糙"颜色表面"模型,计算了该"颜色表面"的分形维数,此维数即为节理面图像维数,并通过实例验证了该法的可行性。在此基础上,通过数值方法探讨了波速随图像维数的变化规律,研究显示:随着节理面图像维数增大,节理面粗糙程度的增加,应力波波速相应减小,且在不同的图像维数区间里,波速减小的速率也有所不同。

With fundamental theory of damage mechanics,analytical solution to velocity of stress wave propagating in jointed rock was derived,and the relation between the velocity and joint image fractal dimensions was established.In order to study influence rule of joint image dimensions on wave velocity,based on a hypothesis that color of every pixel can be expressed into a vector of a three-dimensional space,a model of rough color surface of joint surface image was built and the fractal dimensions of rough color surface were calculated.This dimension number was considered to be the image dimension number.Also,the feasibility of the theory was validated with some examples.Then,the rule of the wave velocity with the change of image dimension number was studied with numerical methods.It was indicated that with increase in joint image dimension number,joint surface roughness increases,stress wave velocity correspondingly decreases and the decreasing rate of wave velocity is distinct in different dimension ranges.