摘要
利用随机过程的谱展开理论以及Hudson的裂纹介质模型,构造一种裂纹数密度具有空间统计分布的随机介质模型,给出了详细的理论推导过程。该模型利用Hudson理论的将裂纹微观参数(裂纹数密度、裂纹半径等)与裂纹介质的宏观性质(弹性常数)联系起来的特点,对可以用二维指数椭圆型、Gaussian型自相关函数描述裂纹数密度的裂纹介质,进行了二维随机介质的模拟。结果表明:(1) 基于这一模拟理论的随机介质模型能灵活、有效地描述实际非均匀、各向异性裂纹介质;(2) 裂纹数密度对随机裂纹介质的各个弹性常数具有不同程度的影响;(3) Gaussian型自相关函数能描述单尺度平滑的非均匀介质,而指数型随机介质具有多尺度、自相似的特性。
The model of cracked media with crack number density of spatial distribution was presented according to the theory of spectral factorization in stochastic process and Hudson's model of cracked media. The random distribution of crack number density was characterized by a 2D exponential ellipsoidal function or Gaussian auto-correlation function. Hudson's crack model can connect micro parameters of cracks, crack number density, with macro mechanical properties. By taking the advantage of Hudson's crack model, the real heterogeneous anisotropic medium can be effectively modeled. Numerical example indicates that the random distribution characteristics can be different for different elastic constants under the same random distribution of crack number density. By changing the value of the auto-correlation length pair, it is possible to model the difference of the distribution in the two coordinate directions. The random media can be modeled with different stochastic characters by choosing different auto-correlation function. In other words, the Gaussian function describes the single-scale, smooth heterogeneous media and the exponential function describes the multi-scale self-similar heterogeneous media.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2004年第13期2187-2191,共5页
Chinese Journal of Rock Mechanics and Engineering
基金
国家自然科学基金(40074025)
教育部优秀青年教师项目资助课题。
