基于多重分形理论的岩石试样破裂过程数值模拟

为了研究岩石破裂过程中的非线性特征,采用有限差分方法和FLAC软件,建立了服从应变软化关系的非均质二维岩石类材料数值试样,采用多重分形理论分析了在单轴加载过程中的标度不变性,并计算其多重分形谱f(α)。分析了f(α)特征参数Δf和Δα在不同加载阶段的特征,不同均匀程度的岩石试样在峰值强度前f(α)的顶点f(α)_(max)和Δα的演化规律。研究结果表明:采用合理的概率算法进行计算,在较大的尺度内标度不变性良好;f(α)曲线呈左钩形,并随着载荷的增加而趋于明显,同时Δα减小;若所有的盒子都存在可测度的参量,则f(α)_(max)随载荷增长,峰前f(α)_(max)与Δα随均匀程度的增加而下降,但在均匀性较高以后,趋于稳定。

Numerical simulation of fracture process of rock specimen based on multi-fractal spectra theory

A heterogeneous strain softening stock specimen was established by finite difference method with the FLAC in order to study nonlinear characteristics of rock fracture process. The multi-fractal theory was used to analyze the scale invariance with different probabilistic algorithm at the pre-peak of rock specimen un-der uniaxial loading. The multi-fractal spectrum f (α) was studied and the relationship between f (α) and Δαwas analyzed,with the different stages of loading process. The results show that the scale invariance was rea-sonable when the probabilities were calculated by reasonable method. The left hook shape of the multi-fractal spectrum became more apparent while the loading increased. At the same time,the Δαtrended to decrease with the loading. If the possibility of null events were not existed in the boxes,the f (α)max increased with the loading. The decrease tendency of the f (α)max and Δα became slown down, and the value of the f (α)max andΔα were stable under a certain homogeneity.