Refined Simulation Analysis of Water Pressure of Tunnel Lining Based on Temperature Analogy Method
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摘要: 为验证温度比拟法在隧道衬砌水压计算中的精度与可行性，在隧道开挖未支护、施作衬砌以及围岩注浆3种工况下，将该法的计算结果与理论解析法轴对称解、流固耦合法进行对比.针对高速公路典型双车道马蹄形断面建立含有隧道防排水系统的精细化模型，研究衬砌外水压力在隧道横断面和纵断面上的分布规律.结果表明：施作衬砌后，衬砌外水压力明显增大，围岩注浆则可在围岩和衬砌之间形成水压过渡缓冲区，使衬砌外水压力减小；衬砌外水压力在纵向排水管以上呈周期性分布，在排水节间中部最大，在环向排水管处最小；横断面水压则呈现倒葫芦形，在拱脚处最小，在拱顶和仰拱处较大；在既定的计算假设下，温度比拟法与轴对称解的最大误差为0.3%，与流固耦合法的最大误差为14.8%，满足工程精度要求.Abstract: In this study, the distribution of a lining's water pressure is calculated under different construction states including excavation, lining construction, and grouting to verify the accuracy and feasibility of the temperature analogy method in water pressure calculations. The results were compared with those of the theoretical analytical method and fluid-structure coupled method. Subsequently, the distribution of the lining's water pressure on transverse and longitudinal section was numerically explored through a refined model that includes a drainage system of a double lane highway tunnel. The results indicate that the water pressure of the lining significantly increases after lining construction and that a grouting circle can effectively reduce water pressure. The longitudinal distribution presents the characters of periodic variation above the longitudinal drain pipe, maximum water pressure occurs in the centre of two annular drain pipes, and minimum water pressure occurs in annular drain pipes. The transverse distribution presents an inverted gourd shape, minimum water pressure occurs in the arch foot, and maximum water pressure occurs in the vault and invert. Under the given computational assumptions, the maximum error between the temperature analogy method and theoretical analytical method is 0.3%, and the maximum error between the temperature analogy method and fluid-structure coupled method is 14.8%. Hence, the calculation precision satisfies the required engineering accuracy.
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图 3 H=20 m工况下开挖未施作衬砌时水压分布
Figure 3. Distribution of water pressure after excavation under H=20 m
图 4 H=20 m工况下施作衬砌后水压分布
Figure 4. Distribution of water pressure after lining under H=20 m
图 5 H=20 m工况下围岩注浆后水压分布
Figure 5. Distribution of the water pressure after grouting under H=20 m
表 1 开挖未支护时衬砌外侧水头值
Table 1. Water pressure of the lining after excavation under different operation conditions
m 计算方法 H/m 20 40 60 80 100 轴对称解 0.841 1.121 1.407 1.681 1.945 温度比拟法 0.841 1.122 1.409 1.685 1.951 误差/% 0.000 0.057 0.137 0.231 0.333 
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表 2 施作衬砌后衬砌外侧水头值
Table 2. Water pressure of the lining after lining construction under different operation conditions
m 计算方法 kl/(cm·s-1) H/m 20 60 100 轴对称解 1×10-6 17.954 49.660 79.868 温度比拟法 17.954 49.708 80.088 误差/% 0.000 0.097 0.275 轴对称解 1×10-7 19.775 58.776 97.541 温度比拟法 19.775 58.792 97.628 误差/% 0.000 0.027 0.089 轴对称解 1×10-8 19.977 59.875 99.749 温度比拟法 19.977 59.877 99.760 误差/% 0.000 0.003 0.011
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表 3 围岩注浆后衬砌外侧水头值
Table 3. Water pressure of the lining after grouting under different operation conditions
m 计算方法 kg/(cm·s-1) H/m 20 60 100 轴对称解 2×10-5 12.292 34.856 56.651 温度比拟法 12.293 34.864 56.686 误差/% 0.009 0.022 0.062 轴对称解 4×10-6 5.118 14.993 24.717 温度比拟法 5.119 14.997 24.729 误差/% 0.019 0.027 0.048 轴对称解 2×10-6 2.959 8.756 14.500 温度比拟法 2.959 8.757 14.505 误差/% 0.000 0.016 0.033
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表 4 围岩参数
Table 4. Parameters of the rock
项目 弹性模量/GPa 泊松比 密度/(kg·m-3) 粘聚力/MPa 内摩擦角/(°) 孔隙率 Ⅳ级围岩 2 0.35 2 000 0.30 30 0.25 二次衬砌 30 0.20 2 500 — — 0.10 注浆圈 20 0.20 1 850 — — 0.20
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表 5 各工况下衬砌外侧水头值比较
Table 5. Comparison of the water pressure of the lining under different operation conditions
m 计算方法 开挖未支护 施作衬砌 围岩注浆 计算时间/s 拱顶 边墙 仰拱 拱顶 边墙 仰拱 拱顶 边墙 仰拱 温度比拟法 1.702 1.941 2.298 68.564 77.732 87.447 19.978 24.562 29.148 15 流固耦合法 1.861 1.943 2.198 74.132 78.913 83.798 22.935 24.617 26.733 9.7×103 误差/% 9.342 0.103 -4.352 8.121 1.519 -4.173 14.801 0.224 -8.285 —
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表 6 围岩及结构物等效渗透系数
Table 6. Permeability coefficient of the rock and structure
cm/s 排水管 围岩 初衬 注浆圈 二砌 防水板 透水垫层 4 2×10-4 5×10-7 4×10-6 2×10-8 4×10-9 4×10-4
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表 7 衬砌外侧各部位的水头值
Table 7. Water pressure of the lining in different parts
m 计算方法 注浆前 注浆后 计算时间/s 拱顶 拱腰 边墙 仰拱 拱顶 拱腰 边墙 仰拱 温度比拟法 28.160 27.236 19.346 47.915 12.672 11.859 9.092 26.353 50 流固耦合法 28.462 27.437 20.798 53.224 12.899 12.011 9.919 30.183 2.9×104 误差/% 1.072 0.738 7.505 11.080 1.791 1.282 9.096 14.533 —
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