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在求解具有复杂巷道断面形状的应力解时,保角映射函数的精确性最终决定巷道围岩应力解析解的精确性。鉴于此,利用遗传与序列二次规划算法,实现任意复杂巷道断面的高精度映射,解决以往优化算法中所存在的鲁棒性较差及初值敏感性较强的问题,当映射系数个数≥14,可将平均相对误差控制在0.5%以下。以三心拱巷道为例,利用复变函数所推导的任意轴对称巷道断面的应力解,系统性地分析该巷道周边围岩的力学行为。研究结果表明:(1)在单向竖向荷载下,巷道边的切向应力曲线呈现一低一高的双峰形态,其双峰区域分别对应巷道小拱区域及直角区,应力集中系数分别为1.5~3.0,3.5~8.0。在大拱区域,切向压应力与拉应力均有表现,应力集中系数为-1.0~1.5。直墙区域与底板区域的应力集中系数相对稳定,分别维持在2与-1左右。(2)巷道周边围岩的应力分布特征表明巷道边界各点所对应的影响范围呈现不一致性,直角区所对应的影响范围最大,其次是拱形区域,再次是侧墙区域,最后是底板区域。(3)应力集中系数与侧压力系数λ保持着严格的线性关系,其斜率对应于应力集中系数增长速率k′,由k′在巷道边的分布规律,可最终掌握不同λ作用下的应力分布规律。
The accuracy of the conformal mapping function ultimately determines the accuracy of the stress analysis of the surrounding rock in solving the stress solution with the complex cross-sectional shape of the roadway. In view of this, the use of genetic and sequence quadratic programming algorithm to achieve high-precision mapping of any complex roadway section to solve the problem of poor robustness and strong initial value sensitivity in the previous optimization algorithm. When the number of mapping coefficients ≥14, the average relative error can be controlled below 0.5%. Taking Sanxin arch roadway as an example, the mechanical behavior of surrounding rock around the roadway is systematically analyzed by using the stress solution of any axisymmetric roadway section derived from the complex variable function. The results show that: (1) Under tangential vertical load, the tangential stress curve at the side of the roadway exhibits a bimodal shape with a low one and a high height. The bimodal area corresponds to the small arch area and the right angle area respectively. The stress concentration factors 1.5 to 3.0, 3.5 to 8.0. In the large arch area, the tangential compressive stress and tensile stress both show the stress concentration factor of -1.0 ~ 1.5. The stress concentration factor of the straight wall area and the floor area is relatively stable, which are respectively maintained at about 2 and -1. (2) The stress distribution characteristics of the surrounding rock mass around the roadway show that the influence range of each point along the roadway boundary is inconsistent. The right angle area has the largest influence range, followed by the arched area, the side wall area again, and finally the floor area . (3) The stress concentration coefficient and the lateral pressure coefficient λ maintain a strict linear relationship, and the slope corresponds to the growth rate of stress concentration coefficient k ’. The distribution of k’ along the roadway edge can finally grasp the stress distribution under different λ law.