考虑塑性应变率梯度的单轴压缩岩样轴向响应

Axial response of rock specimen considering strain rate gradient effect in uniaxial compression

基于剪切应变率梯度格式,采用解析方式研究了岩石材料在单轴压缩条件下的应变软化的结构响应。根据非局部连续介质模型,提出了一维二阶剪切应变率梯度格式。非局部剪切应变率与局部剪切应变率及其二阶梯度有关。将经典塑性理论中的局部剪切应变率替换为非局部剪切应变率,可以直接得到局部剪切应变率的封闭解析解,而不必通过将局部剪切应变对时间求导获得。通过对局部剪切应变率积分,得到了沿剪切带方向的相对剪切速度。试件峰值强度后的端部速度由弹性及塑性两部分构成。前一部分由虎克定律描述;后一部分与相对剪切速度有关。对弹性及塑性两部分速度求和,得到了单轴压缩岩样剪切破坏问题轴向响应的解析式。研究表明:试样高度越大、内部长度越小、剪切软化模量越大及泊松比越小,则岩样的轴向响应倾向于脆性。根据岩样与矿柱的相似性,岩样响应倾向于脆性,意味着矿柱将失去稳定性,发生矿柱岩爆。目前的基于剪切应变率梯度格式的主要优点是简洁。

Strain softening structural response of rock material in uniaxial compression is investigated analytically based on shear strain rate gradient formation. One dimensional shear strain rate gradient formation of the second order is proposed based on the non-local continuum model. Non-local plastic shear strain rate is dependent on local shear strain rate and its second spatial derivatives. The closed-form analytical solution of the local shear strain rate is straightly obtained by substitution of the non-local plastic shear strain rate into the local one in classical plastic theory, instead of differentiating the local shear strain with respect to time. Relative shear velocity along shear band is calculated by integrating the local shear strain rate. Velocity at the end of rock specimen beyond the peak compressive stress can be divided into two parts. One is elastic part described by Hooke抯 law; the other is plastic part dependent on the relative shear velocity. Summing the two parts yields analytical solution of structural response for uniaxial compressive rock specimen subjected to shear failure. It is shown that sudden snap-back instability can occur as internal length parameter (or thickness of shear band) of rock material is decreased. Higher shear softening modulus, lower Poisson抯 ratio or inclination angle of shear band can lead to brittle axial response. Based on analogy between specimen and pillar in mines, the brittle axial response of rock specimen means that pillars in mine will lose their stability and pillar bursts will occur. Main advantage of the present analytical process based on strain rate gradient formation is concise.