基于梯度塑性理论的岩石等间距破坏分析

Analysis on Spaced Fractures in Rock Based on Gradient Plastic Theory

等间距断裂属应变局部化范畴,这是传统的宏观连续介质理论无法预测和解释的。应变梯度理论是传统塑性理论的推广和完善,本文在屈服函数中引用应变梯度项分析了岩石等间距破坏问题。首先建立了平面应力状态下应变梯度塑性理论模型,通过解析岩样边界在水平压应力作用下的塑性应变场,得出其曲面的分布具有等间距规律,其网络的分布格局及幅值大小受岩样尺度、边界应力、降模量等多种因素的影响。这一结论不仅与一些文献结果相吻合,而且说明用梯度塑性理论能够近似描述等间距现象。本文对深入研究等间距断裂提供了一个新思路。

The phenomenon of the same fracture spacing exists extensively in seismic and geological field, which belongs to strain localization. The phenomenon can not be predicted and explained by classical macroscopical continuum theory, in the paper, the strain gradient term is introduced into the yield function to analyze the phenomenon of the same fracture spacing. The model of strain gradient theory is established in plane strain state. The field of plastic strain in rock specimen is analyzed on the condition of horizontal stress acting on the edges of the specimen. It is found that the distribution of plastic strain exhibits the phenomenon of the same spacing. The pattern and the magnitude of the distribution of plastic strain are influenced by the size of specimen, the compressive stress acting on the edges of the specimen, and the softening modulus, etc. The present conclusion agrees with some previous experiments. The gradient plastic theory can approximately describe the phenomenon of the same fracture spacing. The present discussion offers a new thinking that contributes to further investigate fracture spacing.