Analytical Method for Calculation of Surrounding Rock Pressure of Shallow-Buried and Unsymmetrically Loaded Tunnel Adjacent to Variable Slope
-
摘要: 目前浅埋偏压隧道围岩压力主要采用隧规计算方法,而对于左右洞隧道洞门不在同一里程,一侧需要开挖路基边坡,使隧道从自然放坡状态转为邻路基变坡状态的工况,隧规不适用于计算其围岩压力. 依托安徽某高速公路,运用极限平衡原理推导了邻路基变坡条件下浅埋偏压隧道围岩压力解析解. 计算结果表明:由于变坡的存在,深埋侧修正算法计算竖向围岩压力小于规范法,相对误差为15.98%,水平围岩压力保持不变;浅埋侧修正算法计算竖向围岩压力及水平压力均小于规范法,其竖向压力相对误差为24.93%,水平压力相对误差为5.50%,变坡的存在对浅埋侧影响较大;对比围岩竖向及水平偏压率,有变坡围岩偏压率更大;围岩位移、应力及等效应力,有变坡约为无变坡的1~5倍,围岩及结构更加偏于不安全.Abstract: At present the surrounding rock pressure of shallow-buried and unsymmetrical loading tunnels is generally calculated by code for design of road tunnel. However, when the two portal parts of twin tunnels are not located at the same mileage, one of them will be constructed adjacent to the excavated subgrade slope, rather than under a natural mountain slope. In this case, the code is not applicable to the calculation of surrounding rock pressure of the tunnel. To solve this problem, an analytical solution for calculating the surrounding rock pressure of the shallow-buried and unsymmetrically loaded tunnel adjacent to variable slope is proposed using the limited equilibrium theory, taking a highway tunnel in Anhui province as a prototype. The results indicate that due to the variable slope, the vertical pressure in the surrounding rock of deep-buried side calculated by the modified algorithm is smaller than that calculated by the code with a relative error of 15.98%, while values of horizontal pressure in the deep-buried rock remain unchanged. However, in the surrounding rock of shallow-buried side, both vertical and horizontal rock pressures calculated by the modified algorithm are smaller than that by the code, with relative errors being 24.93% and 5.50% for vertical and horizontal pressures, respectively. Therefore, the variable slope has a greater influence on the shallow side. In addition, the surrounding rock with variable slope has a larger bias rate than that with a natural slope. Values of stress, equivalent stress and rock displacement of the former are approximately 1–5 times larger than those of the latter, indicating that the tunnel with variable slope is more unsafe.
-
表 1 围岩压力对比
Table 1. Comparison of surrounding rock pressures
kPa 变量 深埋侧 浅埋侧 规范法 修正算法 相对误差/% 规范法 修正算法 相对误差/% q1 104.42 90.03 15.98 72.06 57.68 24.93 e1 21.85 21.85 0 13.61 12.90 5.50 e2 51.37 51.37 0 41.48 39.32 5.49 表 2 计算结果对比
Table 2. Comparison of calculation results
压力类型 位置 压力(规范法)/kPa 偏压率 压力(修正算法)/kPa 偏压率 内侧 外侧 内侧 外侧 竖直压力 拱腰 104.42 72.06 1.45 90.03 57.68 1.56 水平压力 拱腰 41.13 31.20 1.32 41.13 29.57 1.39 拱底 51.37 41.48 1.24 51.37 39.32 1.31 表 3 计算参数
Table 3. Calculation parameters
类别 $\gamma $/
(kN•m–1)弹性模量
E/GPa泊松比$\mu $ 粘聚力C/MPa ${\varphi _{\rm{c}}}$/
(°)Ⅴ级围岩 1 800 2.5 0.40 0.5 35 加固圈 2 100 6.0 0.35 0.7 39 初期支护 2 300 29.5 0.20 表 4 围岩变形及应力对比
Table 4. Comparison of surrounding rock deformation and stress
项目 有变坡 无变坡 比值 围岩最大 x 向移位/mm 1.132 0.861 1.31 围岩最大 y 向移位/mm 2.433 2.264 1.05 围岩最大 x 向应力/MPa 0.667 0.540 1.24 围岩最大 y 向应力/MPa 0.723 0.615 1.18 围岩第 1 主应力/MPa 0.121 0.021 5.76 围岩第 3 主应力/MPa –0.796 –0.702 1.13 等效应力/MPa 0.490 0.410 1.20 -
邱建业,彭立敏,雷明峰. 浅埋偏压隧道围岩压力上限法解析解[J]. 土木工程学报,2015,48(6): 105-113.QIU Jianye, PENG Limin, LEI Mingfeng. Upper bound solutions for surrounding rock pressure of shallow bias tunnel[J]. China Civil Engineering Journal, 2015, 48(6): 105-113. 重庆交通科研设计院. 公路隧道设计规范: JTGD70—2004[S]. 北京: 人民交通出版社, 2004. 杨峰,阳军生. 浅埋隧道围岩压力确定的极限分析方法[J]. 工程力学,2008,25(7): 179-184.YANG Feng, YANG Junsheng. Limit analysis method for determination of earth pressure on shallow tunnel[J]. Engineering Mechanics, 2008, 25(7): 179-184. 王书刚, 李术才, 王刚, 等. 浅埋偏压隧道洞口施工技术及稳定性分析研究[J]. 岩土力学, 2006, 27(增刊1): 364-368.WANG Shugang, LI Shucai, WANG Gang, et al. Research on construction technique and stability analysis of outlet in shallow tunnel under unsymmetrical pressure[J]. Rock and Soil Mechanics, 2006, 27(S1): 64-368. 王亚琼,张少兵,谢永利. 埋偏压连拱隧道非对称支护结构受力性状分析[J]. 岩石力学与工程学报,2010,9(1): 3265-3272.WANG Yaqiong, ZHANG Shaobing, XIE Yongli, et al. Mechanical characteristics of unsymmetrical support structure of shallow-buried bias multi-arch tunnel[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 9(1): 3265-3272. 邓之友,彭立敏,刘正初. 埋偏压隧道围岩渐进破坏机制分析[J]. 隧道建设,2012,32(2): 150-155.DENG Zhiyou, PENG Limin, LIU Zhichu. Study on progressive failure mechanisms of rock mass of asymmetrically-loaded tunnel under shallow cover[J]. Tunnel Construction, 2012, 32(2): 150-155. 周晓军,高扬,李泽龙,等. 地质顺层偏压隧道围岩压力及其分布特点的试验研究[J]. 现代隧道技术,2006,43(1): 12-22. doi: 10.3969/j.issn.1009-6582.2006.01.003ZHOU Xiaojun, GAO Yang, LI Zelong. Experimental study on the uneven rock pressure and its distribution applied on a tunnel embedded in geologically bedding strata[J]. Modern Tunneling Technology, 2006, 43(1): 12-22. doi: 10.3969/j.issn.1009-6582.2006.01.003 刘小军,张永兴. 浅埋偏压隧道洞口段合理开挖工序及受力特征分析[J]. 岩石力学与工程学报,2011,30(1): 3066-3073.LIU Xiaojun, ZHANG Yongxing. Analysis of reasonable excavation sequence and stress characteristics of portal section of shallow tunnel with unsymmetrical loadings[J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(1): 3066-3073. 王兵,谢锦昌. 偏压隧道模型试验及可靠度分析[J]. 工程力学,1998,15(1): 85-93.WANG Bing, XIE Jinchang. Model test and reliability analysis for an unsymmetrically loaded tunnel[J]. Engineering Mechanics, 1998, 15(1): 85-93. 雷明峰,彭立敏,施成华,等. 浅埋偏压隧道衬砌受力特征及破坏机制试验研究[J]. 中南大学学报(自然科学版),2013,44(8): 3316-3325.LEI Mingfeng, PENG Limin, SHI Chenghua, et al. Model research on failure mechanism and lining stress characteristics of shallow buried tunnel under unsymmetrical pressure[J]. Journal of Central South University (Science and Technology), 2013, 44(8): 3316-3325. 钟新樵. 土质偏压隧道衬砌模型试验分析[J]. 西南交通大学学报,1996,31(6): 31-35.ZHONG Xinqiao. An analysis of model tests on earth tunnel under unsymmetrical loading[J]. Journal of Southwest Jiaotong University, 1996, 31(6): 31-35. 张志强,何川. 偏压连拱隧道优化施工的研究[J]. 岩土力学,2007,28(4): 723-727. doi: 10.3969/j.issn.1000-7598.2007.04.017ZHANG Zhiqiang, HE Chuan. Research on optimized construction procedure for double-arched tunnel in unsymmetrical pressure[J]. Rock and Soil Mechanic, 2007, 28(4): 723-727. doi: 10.3969/j.issn.1000-7598.2007.04.017