屈服矿柱渐进破坏及应力分布数值模拟

采用拉格朗日元法,在矿柱端面上不存在水平方向摩擦力条件下,模拟了屈服矿柱的剪切带图案、渐进破坏特征、水平应力及垂直应力分布及演变。在弹性阶段,煤的本构关系为线弹性。峰值强度后煤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。数值计算结果表明,矿柱具有渐进破坏特征。破坏首先以剪切带的形式发生在矿柱的4个角上。然后,矿柱两帮的剪切带逐渐向矿柱内部发展,形成两套剪切带网络,直到两套网络重叠,并进一步演化。倾斜的剪切带多次穿透矿柱。当矿柱处于峰值强度后,矿柱水平及垂直应力分布曲面已经变得凹凸不平。凹陷、凸起区分别对应剪切带中心及边缘。矿柱中部的水平应力较边缘大。因此,其边缘的强度较中心低。严格地讲,水平及垂直应力的分布不是单调的,呈现锯齿型。其原因是矿柱发生了条带状局部破坏。矿柱承载能力的不均匀性由矿柱水平应力的不均匀性所决定。

Numerical simulation of progressive failure and stress distribution of yield pillars

Shear strain localization,characteristics of progressive failure,distributions of horizontal and vertical stresses within yield pillars were modeled numerically by FLAC under the condition of smooth ends in horizontal direction.The failure criterion for coal was a composite Mohr-Coulomb criterion with tension cutoff,so linear elastic and strain-softening post-peak constitutive relations was adopted.Numerical simulation shows that failure of pillar in the form of shear bands is progressive from the lateral edges to the center.Shear bands are generated initially in the four corners of the pillar,and then propagate towards the center so that two sets of shear band networks near the lateral edges are formed.Finally,shear band networks overlap and further development is not prohibited.Inclined shear bands intersect the pillar from the top to the base.Surfaces of horizontal and vertical stresses are concavo-convex when the peak strength of pillar is reached.Concave and convex zones correspond to the center and the boundary of shear bands,respectively.Generally,horizontal stress in the center of the pillar is greater than that in the edges so that lower strength is reached in the edges.Strictly speaking,distributions of horizontal and vertical stresses are zigzag and not monotonous,which is due to the zonal shear failure inside the pillar.Non-uniformity of load-bearing capacity of pillar stems is controled by the non-uniformity of horizontal stress distribution.