Calculation method of semi-ellipsoid loose load on tunnel in weak and fragmented stratum
-
摘要: 为有效控制隧道围岩压力，优化隧道支护结构，研究了软弱破碎地层作用在隧道衬砌结构上的松散荷载；根据相关文献中砂性地层隧道周边围岩松动变形试验，采用半椭球体拟合了地层松动范围，提出了软弱破碎地层半椭球体松散荷载模型，给出了松散荷载随隧道收敛变形的计算表达式，分析了松散荷载的分布特征及其随隧道收敛变形的变化特征；为提高松散荷载计算效率，将半椭球体松动边界离散为多个线段，提出了松散荷载离散求和的数值计算流程；为进一步增强计算模型的工程实用性，采用二次多项式拟合松散荷载，得到了松散荷载随隧道收敛变形的简化计算方法。研究结果表明：提出的半椭球体模型可较为准确地描述隧道所受的松散荷载及其随隧道收敛变形的动态变化特征，由于滑动面上摩阻力的作用，松动区范围内的地层竖向应力小于地层初始自重应力，松动区荷载通过滑动面上的摩阻力向周边地层转移，松动区土拱效应显著；随着隧道收敛变形的增加，隧道周边地层松动范围增大，松散椭球体受周边地层的约束作用减弱，地层土拱效应减弱；地层内摩擦角和椭球体偏心率对松散荷载的计算结果影响较大，需根据地质条件测试确定；将半椭圆曲线分为3段时，离散求和的数值计算结果与解析解的相对误差约为3.9%，具有较好的一致性。Abstract: To effectively control the tunnel pressure from the surrounding rock and optimize the support structure of the tunnel, the loose load applied in the tunnel lining structure in the weak and fragmented stratum was studied. Based on an experiment in the literature about the loose deformation of the surrounding rock in sandy stratum, the semi-ellipsoid loose load model for the weak and fragmented stratum was put forward by using the semi-ellipsoid to fit the loose range of the stratum. The calculation equations of the loose load with the tunnel convergence deformation were developed. The distribution characteristics of the loose load and its changing with the tunnel convergence deformation were analyzed. For quickly calculating the loose load, a numerical calculation procedure by scatter and summation of the loose load was developed by dividing the semi-ellipsoid boundary of the loose zone into many short straight lines. To further improve the engineering practicability of the calculation model, the quadratic polynomial was used to fit the loose load, and the simplified calculation method of the loose load with the tunnel convergence deformation was obtained. Research results show that the proposed semi-ellipsoid model can accurately represent the loose load applied to the tunnel and its dynamically developing process with the tunnel convergence deformation. Due to the presence of frictional resistance on the slide surface, the vertical stress of the stratum in the loose range is less than the initial gravity stress, and the load in the loose range is transferred to the surrounding stratum by the frictional resistance on the slide surface, which obviously manifests a soil arching effect in the loose range. The increase in the tunnel convergence deformation causes an extended loose range of the surrounding stratum of the tunnel and weak constraints on the loose ellipsoid from the surrounding stratum, and the soil arching effect of stratum weakens. The internal friction angle of the stratum and the eccentricity of the ellipsoid have great influences on the calculation results of the loose load, so these two parameters should be determined according to the test of geological conditions. When the semi-ellipse boundary is discretized into three segments, the results of the numerical calculation by scatter and summation can have a good consistency with the analytical solution, and the error is about 3.9%.
-
图 1 隧道周边地层松动范围随隧道埋深的动态变化
Figure 1. Dynamic changes in loose range of surrounding stratum of tunnel with tunnel buried depth
图 6 松动区外荷载应力竖向分布
Figure 6. Distriubtions of applied loads in loose zone along vertical direction
图 7 松动区合外荷载竖向分布
Figure 7. Applied combined external load distributions in loose zone along vertical direction
图 8 松动区内压应力竖向分布
Figure 8. Distributions of compression stress in loose zone along vertical direction
图 9 隧道收敛变形对松动区内压应力竖向分布的影响
Figure 9. Effects of tunnel convergence deformation on distributions of compression stress along vertical direction in loose zone
图 10 隧道收敛变形对松动区高度和松散荷载的影响
Figure 10. Effects of tunnel convergence on height of loose zone and loose load
图 12 地层内摩擦角对松散荷载的影响
Figure 12. Effect of stratum internal friction angle on loose load
图 16 半椭球体松动区松散荷载计算流程
Figure 16. Calculation process of loose load on semi-ellipsoid loose zone
图 17 松散荷载与隧道收敛变形的关系
Figure 17. Relationship between loose load and tunnel convergence deformation
表 1 离心模型试验结果拟合
Table 1. Fitting of centrifugal model test results
C/D 1 2 3 4 bG/m 3.64 3.89 4.33 4.65 aG/m 5.10 10.15 16.86 23.17 ε 0.70 0.92 0.97 0.98 
下载: 导出CSV
表 2 滑动面上的侧压力系数
Table 2. Lateral pressure coefficients at sliding surface
滑动面位置 侧压力系数 0°≤θ＜φ/2 K≥1(σh≥σv) φ/2≤θ＜90°+φ/2 K≤1(σh≤σv) 90°+φ/2≤θ≤180° K≥1(σh≥σv)
下载: 导出CSV
表 3 不同理论分析结果对比
Table 3. Comparison of analysis results among different theories
C/D 模型试验所得p′c/kPa Terzaghi公式所得p′c/kPa 普氏压力拱所得p′c/kPa 文献[6]计算结果 本文计算结果 m p′c/kPa ε ω/m σa /kPa 1 28.4 37.87 2.281 25.2 0.93 0.21 23.64 1 28.8 38.40 2.281 25.2 0.93 0.21 23.64 2 37.5 51.56 75.35 2.461 34.4 0.94 0.80 41.21 2 37.0 55.52 75.35 2.461 34.4 0.94 0.80 41.21 3 33.7 56.76 75.35 2.513 38.5 0.95 1.64 46.49 3 36.4 58.24 75.35 2.513 38.5 0.95 1.64 46.49
下载: 导出CSV
表 4 隧道周边地层基本参数
Table 4. Basic parameters of stratum around tunnel
参数 取值 参数 取值 P0/MPa 0.5 R/m 6 c/MPa 0.003 ω/m 0.3 φ/(°) 20 β 1.07 γ/(kN·m-3) 18 ε 0.92 γs/(kN·m-3) 17
下载: 导出CSV
表 5 松散荷载离散计算结果
Table 5. Discrete calculation results of loose load
计算方法 数值积分计算结果 不同椭圆曲线沿竖向小区间总数n下的离散求和计算结果 1 2 3 4 5 10 15 20 25 σa(ω=0.70 m) 0.209 2 0.158 9 0.192 7 0.204 0 0.208 8 0.210 9 0.211 7 0.210 7 0.210 0 0.209 7 σa(ω=0.30 m) 0.173 5 0.113 9 0.158 0 0.173 2 0.179 2 0.181 5 0.180 4 0.177 9 0.176 4 0.175 5 σa(ω=0.10 m) 0.144 8 0.077 9 0.130 3 0.148 5 0.155 5 0.157 9 0.155 4 0.151 7 0.149 4 0.148 1 σa(ω=0.05 m) 0.133 4 0.063 4 0.119 2 0.138 6 0.146 0 0.148 5 0.145 4 0.141 2 0.138 6 0.137 1
下载: 导出CSV
-
[1] TIEN H J. A literature study of the arching effect[D]. Taipei: National Taiwan University, 1990. [2] 王建宇. 对形变压力的认识——隧道围岩挤压性变形问题探讨[J]. 现代隧道技术, 2020, 57(4): 1-11. doi: 10.13807/j.cnki.mtt.2020.04.001WANG Jian-yu. The key way is to release the genuine rock pressure—discussion on problems of tunnelling in squeezing ground[J]. Modern Tunnelling Technology, 2020, 57(4): 1-11. (in Chinese) doi: 10.13807/j.cnki.mtt.2020.04.001 [3] 陈仁朋, 李君, 陈云敏, 等. 干砂盾构开挖面稳定性模型试验研究[J]. 岩土工程学报, 2011, 33(1): 117-122. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201101022.htmCHEN Ren-peng, LI Jun, CHEN Yun-min, et al. Large-scale tests on face stability of shield tunnelling in dry cohesionless soil[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(1): 117-122. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201101022.htm [4] 汪大海, 贺少辉, 刘夏冰, 等. 地层渐进成拱对浅埋隧道上覆土压力影响研究[J]. 岩土力学, 2019, 40(6): 2311-2322. doi: 10.16285/j.rsm.2018.1475WANG Da-hai, HE Shao-hui, LIU Xia-bing, et al. Studies of the progressive ground arching on the loosening pressure above shallow tunnels[J]. Rock and Soil Mechanics, 2019, 40(6): 2311-2322. (in Chinese) doi: 10.16285/j.rsm.2018.1475 [5] JANELID I, KVAPIL R. Sublevel caving[J]. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 1966, 3(2): 129-132. [6] 武军, 廖少明, 张迪. 于颗粒流椭球体理论的隧道极限松动区与松动土压力[J]. 土工程学报, 2013, 35(4): 714-721. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201304017.htmWU Jun, LIAO Shao-ming, ZHANG Di. Loosening zone and earth pressure around tunnels in sandy soils based on ellipsoid theory of particle flows[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(4): 714-721. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201304017.htm [7] 宫全美, 张润来, 周顺华, 等. 基于颗粒椭球体理论的隧道松动土压力计算方法[J]. 岩土工程学报, 2017, 39(1): 99-105. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201701010.htmGONG Quan-mei, ZHANG Run-lai, ZHOU Shun-hua, et al. Method for calculating loosening earth pressure around tunnels based on ellipsoid theory of particle flows[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(1): 99-105. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201701010.htm [8] 方焘, 梁连, 颜建伟. 不同埋深下盾构隧道施工引起的地层变形试验[J]. 长江科学院院报, 2023, 40(3): 85-92. https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB202303014.htmFANG Tao, LIANG Lian, YAN Jian-wei. Experimental study on stratum deformation caused by shield tunnelling at different buried depths[J]. Journal of Yangtze River Scientific Research Institute, 2023, 40(3): 85-92. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB202303014.htm [9] 梁连, 方焘, 方立建, 等. 基于PIV技术的隧道施工引起的地层变形规律试验研究[J]. 隧道建设(中英文), 2023, 43(4): 625-633. https://www.cnki.com.cn/Article/CJFDTOTAL-JSSD202304007.htmLIANG Lian, FANG Tao, FANG Li-jian, et al. Experimental study on deformation law of stratum caused by tunnel construction based on particle image velocimetry technique[J]. Tunnel Construction, 2023, 43(4): 625-633. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSSD202304007.htm [10] 方焘, 梁连, 陈其志. 基于修正椭球体理论的隧道松动区及松动土压力研究[J]. 岩土工程学报, 2023, 45(6): 1113-1122. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202306002.htmFANG Tao, LIANG Lian, CHEN Qi-zhi. Loosening zone and earth pressure around tunnels based on modified ellipsoid theory[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(6): 1113-1122. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202306002.htm [11] CARRANZA-TORRES C, FAIRHURST C. Application of the convergence-confinement method of tunnel design to rock masses that satisfy the Hoek-Brown failure criterion[J]. Tunnelling and Underground Space Technology, 2000, 15(2): 187-213. [12] ORESTE P. P. Analysis of structural interaction in tunnels using the convergenc-confinement approach[J]. Tunnelling and Underground Space Technology, 2003, 18(4): 347-363. [13] GONZÁLEZ-NICIEZA C, ÁLVAREZ-VIGIL A E, MENÉNDEZ-DÍAZ A, et al. Influence of the depth and shape of a tunnel in the application of the convergence-confinement method[J]. Tunnelling and Underground Space Technology, 2008, 23(1): 25-37. [14] PARASKEVOPOULOU C, DIEDERICHS M. Analysis of time-dependent deformation in tunnels using the convergence-confinement method[J]. Tunnelling and Underground Space Technology, 2018, 71: 62-80. [15] 孙振宇, 张顶立, 房倩, 等. 隧道初期支护与围岩相互作用的时空演化特性[J]. 岩石力学与工程学报, 2017, 36(增2): 3943-3956. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2017S2027.htmSUN Zhen-yu, ZHANG Ding-li, FANG Qian, et al. Spatial and temporal evolution characteristics of interaction between primary support and tunnel surrounding rock[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(S2): 3943-3956. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX2017S2027.htm [16] 李奥, 张顶立, 黄俊, 等. 软弱破碎围岩深埋隧道拱顶渐进性塌方机理及控制[J]. 工程科学与技术, 2022, 54(6): 85-96. https://www.cnki.com.cn/Article/CJFDTOTAL-SCLH202206010.htmLI Ao, ZHANG Ding-li, HUANG Jun, et al. Progressive collapse mechanism and safety control of deep buried tunnel vault in soft and broken surrounding rock[J]. Advanced Engineering Sciences, 2022, 54(6): 85-96. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SCLH202206010.htm [17] 于丽, 吕城, 王明年. 基于非线性M-C准则的深埋土质隧道三维塌落破坏上限分析[J]. 岩土工程学报, 2019, 41(6): 1023-1030. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201906007.htmYU Li, LYU Cheng, WANG Ming-nian. Three-dimensional upper bound limit analysis of deep soil tunnels based on nonlinear Mohr-Coulomb criterion[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(6): 1023-1030. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201906007.htm [18] 汪成兵, 朱合华. 隧道塌方机制及其影响因素离散元模拟[J]. 岩土工程学报, 2008, 30(3): 450-456. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200803029.htmWANG Cheng-bing, ZHU He-hua. Tunnel collapse mechanism and numerical analysis of its influencing factors[J]. Chinese Journal of Geotechnical Engineering, 2008, 30(3): 450-456. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200803029.htm [19] 房倩, 张顶立, 王毅远, 等. 圆形洞室围岩破坏模式模型试验研究[J]. 岩石力学与工程学报, 2011, 30(3): 564-571. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201103016.htmFANG Qian, ZHANG Ding-li, WANG Yi-yuan, et al. Model test study of failure modes of surrounding rock for circular caverns[J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(3): 564-571. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201103016.htm [20] IGLESIA G R, EINSTEIN H H, WHITMAN R V. Validation of centrifuge model scaling for soil systems via trapdoor tests[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2011, 137(11): 1075-1089. [21] 汤旅军, 陈仁朋, 尹鑫晟, 等. 密实砂土地层盾构隧道开挖面失稳离心模型试验研究[J]. 岩土工程学报, 2013, 35(10): 1831-1838. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201310010.htmTANG Lyu-jun, CHEN Ren-peng, YIN Xin-sheng, et al. Centrifugal model tests on face stability of shield tunnels in dense sand[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(10): 1831-1838. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201310010.htm [22] 汪成兵, 朱合华. 埋深对软弱隧道围岩破坏影响机制试验研究[J]. 岩石力学与工程学报, 2010, 29(12): 2442-2448. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201012011.htmWANG Cheng-bing, ZHU He-hua. Experimental study of influence mechanism of buried depth on surrounding rock failure of tunnel constructed in soft rock[J]. Chinese Journal of Rock Mechanics and Engineering, 2010, 29(12): 2442-2448. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201012011.htm [23] 刘飞香. 铁路隧道智能化建造装备技术创新与施工协同管理展望[J]. 隧道建设(中英文), 2019, 39(4): 545-555. https://www.cnki.com.cn/Article/CJFDTOTAL-JSSD201904003.htmLIU Fei-xiang. Prospects for intelligent construction equipment technology innovation and collaborative construction management of railway tunnel[J]. Tunnel Construction, 2019, 39(4): 545-555. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSSD201904003.htm [24] 田四明, 王伟, 李国良, 等. 川藏铁路隧道设计理念与主要原则[J]. 隧道建设(中英文), 2021, 41(4): 519-530. https://www.cnki.com.cn/Article/CJFDTOTAL-JSSD202104002.htmTIAN Si-ming, WANG Wei, LI Guo-liang, et al. Design concept and main principles of tunnel on Sichuan-Tibet Railway[J]. Tunnel Construction, 2021, 41(4): 519-530. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSSD202104002.htm [25] 武松, 汤华, 罗红星, 等. 浅埋大断面公路隧道渐进破坏规律与安全控制[J]. 中国公路学报, 2019, 32(12): 205-216. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201912022.htmWU Song, TANG Hua, LUO Hong-xing, et al. Progressive failure law and control criterion for safe construction of shallow buried highway tunnel with different grades of surrounding rock[J]. China Journal of Highway and Transport, 2019, 32(12): 205-216. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201912022.htm [26] 李利平, 李术才, 赵勇, 等. 超大断面隧道软弱破碎围岩渐进破坏过程三维地质力学模型试验研究[J]. 岩石力学与工程学报, 2012, 31(3): 550-560. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201203016.htmLI Li-ping, LI Shu-cai, ZHAO Yong, et al. 3D geomechanical model for progressive failure progress of weak broken surrounding rock in super large section tunnel[J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(3): 550-560. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201203016.htm [27] 张成平, 韩凯航, 张顶立, 等. 城市软弱围岩隧道塌方特征及演化规律试验研究[J]. 岩石力学与工程学报, 2014, 33(12): 2433-2442. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201412008.htmZHANG Cheng-ping, HAN Kai-hang, ZHANG Ding-li, et al. Test study of collapse characteristics of tunnels in soft ground in urban areas[J]. Chinese Journal of Rock Mechanics and Engineering, 2014, 33(12): 2433-2442. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201412008.htm [28] 李英杰, 张顶立, 宋义敏, 等. 软弱破碎深埋隧道围岩渐进性破坏试验研究[J]. 岩石力学与工程学报, 2012, 31(6): 1138-1147. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201206008.htmLI Ying-jie, ZHANG Ding-li, SONG Yi-min, et al. Experimental research of progressive damage of surrounding rock for soft fractured deep tunnel[J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(6): 1138-1147. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201206008.htm [29] 叶飞, 毛家骅, 刘燕鹏, 等. 软弱破碎隧道围岩动态压力拱效应模型试验[J]. 中国公路学报, 2015, 28(10): 76-82, 104. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201510012.htmYE Fei, MAO Jia-hua, LIU Yan-peng, et al. Model test on effect of dynamic pressure arch of tunnel in soft broken surrounding rock[J]. China Journal of Highway and Transport, 2015, 28(10): 76-82, 104. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201510012.htm [30] LEE C J, CHIANG K H, KUO C M. Ground movement and tunnel stability when tunneling in sandy ground[J]. Journal of the Chinese Institute of Engineers, 2004, 27(7): 1021-1032. [31] 于学馥, 乔端. 轴变论和围岩稳定轴比三规律[J]. 有色金属, 1981, 33(3): 8-15. https://www.cnki.com.cn/Article/CJFDTOTAL-YOUS198103001.htmYU Xue-fu, QIAO Duan. Theory of axial variation and three rules of axial ratio for stabilizing country rock[J]. Nonferrous Metals, 1981, 33(3): 8-15. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YOUS198103001.htm [32] MCNULTY J W. An experimental study of arching in sand[R]. Vicksburg: US Army Engineer Waterways Experiment Station, 1965. -
点击查看大图
图(18) / 表(5)
计量
- 文章访问数: 344
- HTML全文浏览量: 97
- PDF下载量: 47
- 被引次数: 0
