摘要
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 accurate conformal function determines the accuracy of stress-displacement solution for the surrounding rock of roadways with the cross section of complex shape. The genetic optimization and sequential quadratic programming algorithm are thus applied to achieve the high-precision mapping for complex shapes of the cross section. The optimization scheme overcomes the low robustness and the sensitivity of initial value existed in the previous optimization algorithms and constrains the average relative error below 0.5% when thenumber of mapping coefficient is greater than 14. The elastic stress solution based on the complex function methods was derived,and utilized to systematically analyze the mechanical behaviors of the surrounding rock of three-centered arch. The tangential stress curve exhibits the double peaks of unequal heights under one-way vertical load,which correspond to the small arch and right-angle area with the stress concentration factors of 1.5–3.0 and 3.5–8.0 respectively. The stress concentration factors for side wall and floor are around 2 and-1 respectively. The stress concentration factors for large arch area are-1.0–1.5. The stress distribution of surrounding rock shows that the scope of influence for right-angle area is the largest,followed by the arch area,the side wall area and the floor area. Both the stress concentration factor and lateral pressure coefficient λ have the strict linear relationship with the slope k′ to be the growth rate of stress concentration factor. The tangential stress distribution on the boundary of roadway under different λ can be known through the distribution of k′.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2017年第2期407-419,共13页
Chinese Journal of Rock Mechanics and Engineering
基金
"十二五"国家科技与支撑计划项目(2013BAB02B08)~~
关键词
隧道工程
保角映射
遗传优化算法
序列二次规划算法
复杂巷道断面
柯西积分法
复变函数法
tunnelling engineering
conformal mapping
genetic optimization
sequential quadratic programming
complex cross section of roadway
Cauchy integral
complex function
