数值岩石试样破裂过程多重分形特征

采用数值分析的方法和FLAC3D软件,建立服从应变软化关系的非均质岩石试样模型。引入多重分形理论,通过盒计数法计算了单轴加载过程中峰前某一阶段单元体积应变的多重分形谱f(α)。分析了f(α)-α曲线特征参数#f和#α随加载过程的阶段特征,不同均匀程度的岩石试样在临近峰值强度前#α和f(α)max的变化规律。研究结果表明,采用多重分形理论对单元体积应变的空间分布特征进行描述,可以在较大的尺度内满足标度不变性。通过不同的参量进行概率计算得出的f(α)略有不同,但动态变化规律相近,f(α)曲线呈左钩形状,随着载荷的增加#f变大,而#α变小。当不是所有的盒子内都存在可测度的参量时,f(α)max随载荷的增加而增长。对于均匀程度不同的试样,峰前f(α)max与#α随均匀性的增加而减小,但在均匀性较高以后,逼近于某一常数。

Multi-fractal spectra characteristics of numerical rock specimen during the fracture

A heterogeneous strain softening rock specimen was established with the numerical code FLAC3D .The multi-fractal spectrum f(α)of the elements volumetric strain at the pre-peak of rock specimen under uniaxial loading was obtained by using the box-counting method.The change rules of multi-fractal spectrum characteristic parameters,Dαand Df,with the different stages of loading process were analyzed.The characteristics of the f(α)curve vertex f(α)max and Dαwith different heterogeneity of rock specimen near the peak strength was studied.The results show that the double logarithmic diagram would keep scale invariance in a wide range when the multi-fractal was used to describe the spatial structure of elements volumetric strain.The f(α)curves shape and variation are similar to different parameter probabilistic calculation method.The shape of the multi-fractal spectrum show left hook.The Df increase with the loading process.At the same time,the Dαtrend to decrease.If the possibility of null events exist in some of the boxes,the f(α)max increase with the loading.There is an obviously decrease tendency of the f(α)max and Dαwith the decrease of the heterogeneity within limit at the pre-peak of rock specimen.However,they would be constants while the homogeneity increased to a certain extent.