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中文摘要：
采用拉格朗日元法，模拟了具有粗糙端面的屈服矿柱的宏观力学行为、曲线剪切带图案及渐进破坏特征。矿体在弹性阶段的本构关系取为线弹性；峰值强度后的本构模型取为莫尔库仑剪破坏与拉破坏复合的应变软化模型。计算表明，矿柱的宽度越窄、强度越低。矿柱的破坏是逐渐发生的，剪切带从矿柱的四角开始启动，向矿柱的内部传播，最终形成了由曲线剪切带构成的剪切破裂网络。该网络与塑性力学中的曲线滑移线网非常类似。矿柱中心弹性区两侧的软化区的压缩应力由表至里波动上升，反映了矿柱内部条带状的局部剪切破坏。软化区厚度随时间步（或轴向应变）的变化率为常量。矿柱弹性区的应力水平及软化区的应力分布不受矿柱宽度的影响，前者与矿柱的轴向应变有关。
英文摘要：
Using FLAC, the macroscopically mechanical behavior, curved shear bands and progressive shear failure of yield mine pillar with rough ends are modeled. In elastic stage, constitutive relation for ore is linear elasticity. The failure criterion is a composite Mohr-Coulomb criterion with tension cut-off. Beyond the peak stress, the linear strain-softening constitutive relation is adopted. For wider pillar, the strength is higher. The failure of the pillar is progressive. Shear bands are initiated at the corners of the pillar and then propagate into the pillar. Finally, the shear fracture network is formed. The shear fractures are similar to the curved slip lines in plastic theory. The compressive stress, acting on the strain-softening zone outside the central elastic zone of the pillar, increases in a fluctuation fashion toward the center of the pillar from the two lateral edges. The ratio of the thickness of strain -softening distribution zone to the timestep （or axial strain） remains a constant. The stress level in elastic zone and the stress in strain-softening zone are not affected by the pillar thickness. The former is related to the axial strain of the pillar.
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