Analysis of critical safety distance between tunnel and concealing filled karst cave in the karst area
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摘要: 当隧道施工穿越喀斯特地貌发育区时，隧道应与溶洞保持一定的距离，确保隧道围岩及支护的稳定性。为探究隧道与岩溶的临界安全距离，综合采用理论计算与数值试验方法，基于强度理论，建立不同部位充填溶洞（顶部、底部、侧部）临界安全距离的计算模型，推导出隧道与环向不同位置溶洞临界安全距离计算公式；采用FLAC 3D软件建立环向不同位置溶洞与隧道间的临界安全距离数值模型，基于正交试验设计方法，分析了围岩级别、溶洞水压、溶洞尺寸对临界安全距离的影响规律和显著性。结果表明：隧道与环向不同部位溶洞间的临界安全距离均随围岩级别、溶洞水压及溶洞尺寸的增大而增大，综合影响程度从大到小可排序为围岩级别＞溶洞水压＞溶洞尺寸；结合试验结果的非线性多元回归分析建立了临界安全距离预测公式；最后将研究成果应用于阳宗隧道项目来验证临界安全距离预测模型的合理性及适用性。Abstract:
If the tunnel construction work is done in the karst area, the tunnel shall keep a certain distance from the karst cave to ensure the stability of the surrounding rock and support. If the distance between the tunnel and the filled karst cave with high water pressure is short, it is easy to cause the instability and damage of tunnel face or the circumferential surrounding rock, thus resulting in karst water inrush, mud inrush, collapse and other disasters. Especially, the karst cave concealing around the tunnel is often difficult to be accurately predicted. Therefore, the study of the critical safety distance between the karst cave and the tunnel plays a vital role in the evaluation and prevention of disasters caused by concealing filled karst cave. Studies on the critical safety distance between tunnel and karst cave can be divided into qualitative research, semi-quantitative research and quantitative research. Qualitative research, such as judging the influence degree of karst cave on tunnel through numerical analysis, is generally conducted to comprehensively analyze the factors affecting the stability of structure for water burst prevention and obtain the empirical critical safety value. Semi-quantitative research mainly focuses on theoretical calculation, which can be roughly sub-divided into three types: simplified beam slab model based on strength theory, catastrophe theory model and the model of crack tension-compression shear based on fracture mechanics. Mainly focusing on numerical simulation, quantitative research is conducted to set up multiple groups of numerical tests for calculation, and to obtain the calculation model of safety distance through linear regression. The safety distance between the tunnel and the filled karst cave can be explored by theoretical calculation and numerical simulation test. Based on the bending and shear strength theory, the mechanical calculation models of the filled karst cave at the top, bottom and side of the tunnel are established by using the fixed beam model at both ends. Meanwhile, the self-weight of the internal filler and the pore water pressure are taken into account. Given the influence of the surrounding rock pressure above the karst cave on the waterproof rock stratum, the critical safety distance between the tunnel and the karst cave can be explored, and the calculation formula of the distance in different circumferential positions can be deduced. However, this formula does not consider the excavation effect of the tunnel and the process of support, nor can it reflect the changes of the displacement, stress and plastic zone of the surrounding rock. Therefore, it is difficult to obtain a universal formula to express relationship. It is necessary to supplement the predicted safety distance with the help of numerical simulation. In this study, the numerical model of the critical safety distance between the filled karst cave and the tunnel at different circumferential positions was established by FLAC 3D software. Based on the method of orthogonal experimental design (a total of 48 numerical test schemes), the stability of surrounding rock has been evaluated by the distribution range of plastic zone of surrounding rock caused by tunnel excavation. If the plastic zone connects the tunnel with the karst cave, the distance between these two indicates that the surrounding rock is unstable, and thereby the critical safety distance can be calculated. The results of critical safety distance under different working conditions were also analyzed by range analysis and variance analysis. Besides, the law and significance of three influencing factors—the level of surrounding rock, the water pressure in karst cave and the karst cave size—on the critical safety distance were explored. Through the nonlinear multiple regression analysis of the orthogonal test results, the prediction formula of the critical safety distance between the filled karst cave and the tunnel at different circumferential positions was established respectively. The results show that the critical safety distance increases with the increase of surrounding rock level, pressure of karst cave water and the karst cave size. The comprehensive influence degree of the three factors can be ranked from the strongest to the weakest as follows: the surrounding rock level, the pressure of karst cave water and karst cave size. Finally, the research results were applied to Yangzong tunnel project to verify the rationality and applicability of the prediction model of critical safety distance. The results show that the safety distance predicted based on the strength theory is relatively conservative, and the predicted results based on the numerical test are close to the reserved distance. The predicted results have a certain reference for the project of karst tunnel with water abundance. -
图 6 溶洞位于隧道顶部临界安全距离分析
Figure 6. Analysis of critical safety distance of karst cave at the top of tunnel
图 7 溶洞位于隧道底部临界安全距离分析
Figure 7. Analysis of critical safety distance of karst cave at the bottom of tunnel
图 8 溶洞位于隧道侧部临界安全距离分析
Figure 8. Analysis of critical safety distance of karst cave at the side of tunnel
图 9 临界安全距离变化曲线（溶洞位于隧道顶部）
Figure 9. Change curve of critical safety distance (The karst cave is located at the top of tunnel.)
图 10 临界安全距离变化曲线（溶洞位于隧道底部）
Figure 10. Change curve of critical safety distance (The karst cave is located at the bottom of tunnel.)
图 11 临界安全距离变化曲线（溶洞位于隧道侧部）
Figure 11. Change curve of critical safety distance (The karst cave is located at the side of tunnel.)
表 1 溶洞充填物物理力学参数
Table 1. Physical and mechanical parameters of cave filling
参数 重度γ 粘聚力$c$ 摩擦角$\varphi $ 弹性模量E 泊松比μ kN·m−3 kPa ° MPa 溶洞充填物 18 1.0 26 7 0.26 
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表 2 各影响因素的水平值
Table 2. Level value of each influence factor
水平取值 围岩级别A 溶洞直径D 水压P m MPa 1 Ⅲ1 5 0.8 2 Ⅲ2 10 1.2 3 Ⅳ1 15 1.6 4 Ⅳ2 20 2.0
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表 3 围岩级别的各因子取值范围
Table 3. Value range of each factor of surrounding rock level
围岩级别 重度γ 粘聚力c 摩擦角φ 弹性模量E 泊松比μ kN·m−3 MPa ° GPa Ⅲ1 24 1.0 41 9 0.26 Ⅲ2 23 0.8 39 7 0.28 Ⅳ1 22 0.6 37 5 0.30 Ⅳ2 21 0.4 35 3 0.32
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表 4 L16（44）正交试验方案及结果
Table 4. Scheme and results of L16(44) orthogonal test
编号 围岩级别A 溶洞水压P 溶洞直径D 误差项e 临界安全距离 - MPa m - St/m Sb/m Ss/m 1 Ⅲ1 0.8 5 1 1.1 1.1 1.0 2 Ⅲ1 1.2 10 2 1.5 2.2 1.3 3 Ⅲ1 1.6 15 3 1.9 3.5 1.4 4 Ⅲ1 2.0 20 4 2.5 4.8 1.6 5 Ⅲ2 0.8 10 3 1.9 1.9 1.4 6 Ⅲ2 1.2 5 4 1.7 1.9 1.4 7 Ⅲ2 1.6 20 1 2.6 4.4 1.8 8 Ⅲ2 2.0 15 2 3.3 5.2 2.0 9 Ⅳ1 0.8 15 4 2.9 2.8 2.2 10 Ⅳ1 1.2 20 3 2.9 4.0 2.3 11 Ⅳ1 1.6 5 2 2.7 3.4 2.1 12 Ⅳ1 2.0 10 1 4.0 5.6 2.4 13 Ⅳ2 0.8 20 2 4.3 4.1 3.1 14 Ⅳ2 1.2 15 1 4.2 5.2 3.0 15 Ⅳ2 1.6 10 4 4.8 6.0 3.0 16 Ⅳ2 2.0 5 3 5.1 5.8 3.2
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表 5 临界安全距离极差表
Table 5. Range table of critical safety distance
影响因素 St/m Sb/m Ss/m 围岩
级别A溶洞
水压P溶洞
直径D误差列 围岩
级别A溶洞
水压P溶洞
直径D误差列 围岩
级别A溶洞
水压P溶洞
直径D误差列 K1 7.00 10.20 10.60 11.90 11.60 9.90 12.20 16.30 5.30 7.70 7.70 8.20 K2 9.50 10.30 12.20 11.80 13.40 13.30 15.70 14.90 6.60 8.00 8.10 8.50 K3 12.50 120 12.30 11.80 15.80 17.30 16.70 15.20 9.00 8.30 8.60 8.30 K4 18.40 14.90 12.30 11.90 21.10 21.40 17.30 15.50 12.30 9.20 8.80 8.20 k1 1.75 2.55 2.65 2.98 2.90 2.48 3.05 4.08 1.33 1.93 1.93 2.05 k2 2.38 2.58 3.05 2.95 3.35 3.33 3.93 3.73 1.65 2.00 2.03 2.13 k3 3.13 3.00 3.08 2.95 3.95 4.33 4.18 3.80 2.25 2.08 2.15 2.08 k4 4.60 3.73 3.08 2.98 5.28 5.35 4.33 3.88 3.08 2.30 2.20 2.05 极差R 11.4 4.7 1.7 0.1 9.5 11.5 5.1 1.4 7.0 1.5 1.1 0.3
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表 6 临界安全距离方差表
Table 6. Variance table of critical safety distance
影响
因素St/m Sb/m Ss/m 围岩
级别A溶洞
水压P溶洞
直径D误差
列围岩
级别A溶洞
水压P溶洞
直径D误差
列围岩
级别A溶洞
水压P溶洞
直径D误差
列SS 18.092 3.612 0.552 0.003 12.767 18.567 3.902 0.272 7.095 0.315 0.185 0.015 df 3 3 3 3 3 3 3 3 3 3 3 3 MS 6.031 1.204 0.174 0.001 4.256 6.187 1.301 0.091 2.365 0.105 0.062 0.005 F 6 031 1 204 174 − 46.77 67.99 14.3 − 473 21 12.4 − 显著性 显著 显著 显著 − 显著 显著 有影响 − 显著 有影响 有影响 − 注：F0.05（3，3）=9.28，F0.01（3，3）=29.46，其中：SS-离差平方和，df-自由度，MS-均方离差。
Note: F0.05(3, 3)=9.28, F0.01(3, 3)=29.46; SS: Sum of Squares, df: degree of freedom, MS: mean square deviation.
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表 7 岩溶区灰岩物理力学参数指标
Table 7. Physical and mechanical parameters of limestone in the karst area
岩性参数 重度 抗压强度 抗弯强度 抗剪强度 kN·m−3 MPa MPa MPa 灰岩 22 28 4.2 2.52
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