单轴拉伸岩样破坏过程及尺寸效应数值模拟

由于从实验及理论角度研究岩样单轴拉伸条件下的破坏全过程及尺寸效应难度都很大。因此采用拉格朗日元法来研究这些问题。在峰值强度之前后，岩石材料的本构模型分别取为线弹性及拉破坏线性应变软化模型。为了使拉伸塑性区不出现在试样的端部，在试样的两侧面中部预制了2个凹槽。数值模拟结果表明，全程拉应力-拉应变曲线分为峰前和峰后阶段。在接近峰值的峰前阶段，由于两凹槽附近具有明显的拉应力集中现象，拉伸塑性区最先出现在两凹槽附近。随着轴向拉应变的增加，发生拉伸破坏的单元的数目增加，新发生拉伸破坏的单元越来越接近试样的中心，直到两块拉伸塑性区在应变软化阶段贯通。两凹槽连线上各单元拉应力的分布呈现3个阶段，“澡盆型”（“U型”）阶段，“双峰型”（“M型”）阶段及“单峰型”（“Π型”）阶段。“澡盆型”阶段对应于全程拉应力-拉应变曲线的弹性阶段。“双峰型”阶段及“单峰型”阶段对应于全程拉应力-拉应变曲线的非弹性阶段（包括峰值强度之前的一小段，即应变硬化阶段及峰后的应变软化阶段）。增加试样高度及降低试样宽度，拉应力-拉应变曲线的软化段变得越来越陡峭，因而试样越容易发生失稳破坏。由于试样宽度较大时，试样内部的单元并非处于单向拉应力状态，因此，增加试样宽度，全程拉应力-拉应变曲线的峰值强度增加。当试样宽度较小时，从出现塑性区，到塑性区贯通所需要的时间步较小，或应变范围较窄。这说明试样的脆性较强，前兆不明显。前兆不明显的脆性破坏对应常见的是洞室岩爆、冲击地压及地震等灾害。

Numerical simulation of failure process and size effect of rock specimen in uniaxial tension

Due to the fact that there is a great deal of experimental and analytical difficulty in investigating the failure process and the size effect of rock specimen in uniaxial tension, in the present paper these problems are modeled numerically by FLAC. In elastic and strain-softening stages, the adopted constitutive relations of rock are linear elastic and linear strain-softening due to tensile failure, respectively. To ensure that elements subjected to tensile failure are localized into a narrow band within the specimen, two null elements at two edges of specimen are prescribed to model two notches. It is found from numerical results that the complete tensile stress-tensile strain curve exhibits pre-peak and post-peak branches. Prior to the peak stress, tensile stress concentration appears near the two notches so that two elements close to the two notches due to tension yield. The number of yielded elements is increased with axial tensile strain and the new plastic elements are even closer to the center of specimen until a horizontal and longer plastic zone is formed. Tensile stress distribution undergoes three distinct stages: upward concave stage, stage of downward concavity with two peaks and stage of downward concavity with one peak. The first stage corresponds to the elastic stage of complete stress-strain curve; however, the latter two stages correspond to the inelastic stage including strain-hardening and strain-softening stages. Softening branch of complete stress-strain curve becomes steeper so that the instability of rock specimen easily occurs as the height of specimen is increased or the width of specimen is decreased. Peak stress of complete stress-strain curve increases with the width of specimen, which is due to the fact that the stress state within the specimen is not a simple uniaxial state of stress for wider specimen. For thinner specimen, the needed time steps form the initial formation of yielded elements to the full development of a plastic zone are less than those for wider specimen. This reflects that the precursor for thinner specimen is less apparent. Brittle failure without obvious precursor is concerned with seriously natural hazards, such as rockburst and earthquake.