裂隙岩体损伤局部化破坏分岔模型及其应用

DISCONTINUOUS BIFURCATION MODEL OF DAMAGE LOCALIZATION FOR JOINTED ROCKS AND ITS APPLICATION

采用概率统计方法分析节理裂隙岩体的几何特征,定义了反映裂隙岩体几何特征的组构张量。基于不可逆热力学理论,通过裂纹扩展的细观分析,得出了损伤的发展机理和演化方程,把损伤演化和裂隙的几何特征的变化联系起来,建立了弹塑性损伤本构关系。为分析含有节理裂隙岩体在发生局部化破坏时的特征,通过对发生局部化时的裂隙岩体的分析,构造了适用于节理裂隙岩体局部化分析的不连续分岔模型。利用非线性规划数值解法,可以得出局部化破坏的方向特征。在有限元方法中,根据该模型给出了节理裂隙岩体相关的算例,分析表明该模型用于分析裂隙岩体的局部化破坏是有效的。

A fabric tensor is defined in this paper based on the statistical analysis of geometrical characteristics, i.e., orientation, length, inclination, of cracks in jointed rocks. In the frame of irreversible thermo-dynamics, a damage tensor is assumed to respond to the variation of the compliance tensor of jointed rocks. According to the accumulation of strain energy caused by each crack, the compliance tensor can then be determined by the fabric tensor. Therefore, relationship between damage tensor and fabric tensor is established. Afterwards, the mechanism of crack propagation is investigated and the fabric tensor is associated with the propagation of cracks in jointed rocks, thus both the compliance tensor and the damage tensor can be computed. Actually, the evolution of the damage tensor has close relationship with the propagation of cracks. Within the frame of irreversible thermo-dynamics, the constitutive law for jointed rocks is formulated. In order to analyze localization modes of jointed rocks, a classical discontinuous bifurcation model, namely weak discontinuous bifurcation model, is adopted for the analysis of the characteristics of tangent stiffness tensor of jointed rocks. Nonlinear programming procedure is formulated to calculate the directions of localization bands. The implementation of this model can be achieved by modifying standard FEM procedures. Finally, localization failures of several specimens with randomly distributed initial cracks under tension or compression are studied by this model and results demonstrate its applicability. However, two problems remain unresolved for this model. The pedestal problem lies in the neglect of interactions between cracks in the determination of the compliance tensor from the fabric tensor. This neglect will induce a great deviation especially when distances between cracks are quite small. Another problem lies in the lack of analysis of strong discontinuous bifurcation condition for jointed rocks. Recent studies show that the classical discontinuous localization band is usually followed by a much more narrow one characterized as strong discontinuous band. The condition for the onset of strong discontinuous bands in jointed rocks is under study.