中文摘要：

考虑三维结合部形貌的W-M 函数,推导了结合部静摩擦因数非线性分形理论模型.数值模拟 了考虑三维形貌的结合部静摩擦因数与法向载荷P、分形维数D、分形尺度系数G 的关系,以及在二维分形和 三维分形模型中的差异.结果表明：结合部静摩擦因数与法向载荷成单调递增关系,与分形尺度系数成单调递 减关系.当D 小于2. 5时,静摩擦因数随分形维数的增大而增大;当D 大于2. 5时,静摩擦因数随分形维数的 增大而减小;三维分形下的静摩擦因数小于二维分形下的静摩擦因数.

英文摘要：

Considering three-dimensional topography W-M function of joint surfaces, a nonlinear fractal model for static friction coefficient considering three-dimensional topography of joint surfaces was established. Relations between the static friction coefficient considering three-dimensional topography of joint surfaces and normal load,the fractal dimension,fractal roughness were numerically simulated,as well as the difference between static friction coefficients in the two-dimensional fractal model and three dimensional fractal model. The results showed that the static friction coefficient increases monotonically with the increase of normal load,and decreases monotonically with the increase of topothesy. When D is less than 2. 5, the static friction coefficient increases with the increase of fractal dimension ; when the D is greater than 2. 5 ,the static friction coefficient decreases with the increase of fractal dimension; the three-dimensional fractal static friction coefficient is smaller than that of the two- dimensional.