岩石单轴压缩过程变形模量的最大Lyapunov指数分析

Maximum Lyapunov Index Analysis of Rock Deformation Modulus Under Uniaxial Compression

应用Lyapunov评价准则对六种岩石单轴压缩过程的变形模量时间序列进行了分析。根据变形模量的变化定性,描述了岩石在加载过程中弹性、塑性和破坏三种状态。通过对岩石三种状态时间序列相应的最大Lyapunov指数进行分析,发现变形模量的变化和Logistic映射周期点点数的变化有着相似之处;岩石全应力-应变曲线中变形模量先由无序状态进入稳定状态,再进入强混沌状态;随着三个状态的演变,相应变形模量的平均演化距离逐渐呈现离散状态。

Based on the Lyapunov evaluation criteria, the deformation modulus time sequence in the uniaxial compressinn process of six rocks was analyzed. The change of deformation modulus during the loading process fell into three states, namely, the elasticity, plasticity and destruction. The analysis of maximum Lyapunov index of different states shows that the change of the deformation modulus is similar to the periodic points in Eogistic map; the deformation modulus in slrcss-strain process of rock changes from unordered state to stable state, and reaches strong chaos state at last; with evolution of the three states, the average evolving distances of the corresponding deformation modulus become discrete gradually.