圆形巷道围岩应力场的自然边界元法

Natural boundary element method for the stress field of circular roadway's surrounding rock

根据复变函数法和复Fourier级数法,通过自然边界归化分别得到了圆形巷道在整体平衡支护及局部非平衡支护时围岩内Airy应力函数的边界积分公式,并得到了各自应力场的解析解或数值解;对比分析了这两种应力场随侧压系数或支护角度变化的分布规律,计算表明,局部支护时随着侧压系数或支护角度的增加,压应力峰值下降,使得上覆岩层的稳定性得到提高.

In terms of the complex-variable function method and the complex Fourier series method, the boundary integral formulas based on the natural boundary reduction were produced respectively for the surrounding rock's Airy stress function of the circular roadway with the whole equilibrium or the non-equilibrium partial supporting resistances, and the analytical or numeric solutions to the each stress field were obtained.Also the different distribution laws for the two stress fields varying with the lateral pressure coefficient and the supporting angle were analyzed comparatively.The calculations show that, with the increasing of the lateral pressure coefficient and the supporting angle of the local supporting, the peak value of the compressive stress declines, thus the stability of the overlaying strata is improved.