Analytical Method for Calculation of Surrounding Rock Pressure of Shallow-Buried and Unsymmetrically Loaded Tunnel Adjacent to Variable Slope
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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.
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图 2 变坡条件下浅埋偏压隧道滑动体受力
Figure 2. Force analysis of the shallow-buried and unsymmetrically loaded tunnel with variable slope
图 7 浅埋偏压隧道受竖直围岩压力示意
Figure 7. Vertical pressure analysis of the shallow-buried and unsymmetrically loaded tunnel
图 8 浅埋偏压隧道围岩压力示意
Figure 8. Surrounding rock pressure analysis of the shallow-buried and unsymmetrically loaded tunnel
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 
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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
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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
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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
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