Roof stability analysis of deeply-buried cavities based on nonlinear Baker criterion
-
摘要: 针对Hoek-Brown和Mohr-Coulomb准则主要分别适用于岩体和土体的情形，采用更具适用性的广义非线性Baker准则，并结合极限分析上限方法，旨在研究深埋硐室拱顶岩土体的动力稳定性。通过构建满足Baker准则下拱顶塌落的曲线型破坏机构，考虑竖向地震荷载的影响，计算内外力功率并建立功率平衡方程，基于变分原理推导在有无竖向地震力作用时拱顶破坏机制的上限表达式，从而求解得到破坏面形状、塌落拱高度和宽度的解析解。同时采用ABAQUS数值模拟验证解析解的有效性及合理性，研究分析不同参数下拱顶破坏机制的变化规律。结果表明除岩土体特性参数外，尤其是向上的竖向地震力对拱顶破坏范围有显著影响。
-
关键词:
- 深埋硐室 /
- 拱顶稳定性 /
- 非线性Baker准则 /
- 竖向地震力 /
- 上限分析
Abstract: The dynamic roof stability analysis of deeply-buried cavities is investigated by using the upper bound limit analysis method adopting a more general nonlinear Baker criterion, in contrast to the Hoek-Brown and Mohr-Coulomb criteria which are mainly applicable to rock and soil, respectively. A curved failure mechanism for roof collapse is proposed in the realm of the Baker criterion. The vertical seismic loading is considered herein. The balance equation for work rate is then established after computing the external and internal rates of work. Based on the variational principle, the upper-bound formulation for roof collapse mechanism is derived with/without considerations of the vertical earthquake effects. Accordingly, the closed-form solutions for the failure surface, collapse height and width are explicitly obtained. At the same time, the ABAQUS modelling is used to verify the robustness and validity of closed-form solutions. The parametric studies are carried out to investigate the change laws of the roof collapse mechanism under different parameters. The results indicate that apart from rock/soil properties, the upward seismic force has a significant effect on the failure region above the cavity roof. -
-
![]()
图 1 广义非线性Baker准则在Mohr平面τn-σn
Figure 1. Generalized nonlinear Baker criterion in Mohr's plane
![]()
图 2 地震作用下Baker岩土体硐室拱顶坍塌机制
Figure 2. Collapse mechanism of cavity crown under earthquake and Baker rock/soil medium
![]()
图 4 无竖向地震荷载下数值解与解析解对比
Figure 4. Comparison of numerical and analytical solutions under no vertical earthquake
![]()
图 5 竖向地震荷载下数值解与解析解对比
Figure 5. Comparison of numerical and analytical solutions under vertical earthquake effects
![]()
图 10 参数kv影响下的塌落形状及范围
Figure 10. Collapse shapes and dimensions under varying values of kv
表 1 有限元模型几何参数
Table 1 Geometric parameters of finite element model
H/m B/m H0/m Lc/m 40 50 5 10 
下载: 导出CSV
表 2 不同破坏准则下的岩土体参数值
Table 2 Rock/soil parameters under different failure criteria
γ/
(kN·m-3)Baker强度参数 HB强度参数 MC强度 A n T pa/
kPaA B σt/
kPaσc/
kPac/
kPaϕ/
(°)25 2.08 0.7 0.3 100 0.75 0.7 30 3000 115 51.6
下载: 导出CSV
表 3 隧道围岩力学参数
Table 3 Mechanical parameters of surrounding rock of tunnel
γ/(kN·m-3) c/kPa ϕ/(°) A n T 18 30 24 0.45 0.7 0.67
下载: 导出CSV
表 4 围岩压力结果对比
Table 4 Comparative results of pressure of surrounding rock
监测点桩号 埋深/
m本文结果/kPa 规范计算结果/
kPa误差/
%ZK3+610 41.41 118.63 113.66 4.4
下载: 导出CSV
-
[1] CHEN W F. Limit Analysis and Soil Plasticity[M]. Amsterdam; New York: Elsevier Scientific Pub. Co, 1975.
[2] MICHALOWSKI R L. Slope stability analysis: a kinematical approach[J]. Géotechnique, 1995, 45(2): 283-293. doi: 10.1680/geot.1995.45.2.283
[3] 赵炼恒, 李亮, 杨峰, 等. 加筋土坡动态稳定性拟静力分析[J]. 岩石力学与工程学报, 2009, 28(9): 1904-1917. doi: 10.3321/j.issn:1000-6915.2009.09.023 ZHAO Lianheng, LI Liang, YANG Feng, et al. Dynamic stability pseudo-static analysis of reinforcement soil slopes[J]. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(9): 1904-1917. (in Chinese) doi: 10.3321/j.issn:1000-6915.2009.09.023
[4] SLOAN S W. Geotechnical stability analysis[J]. Géotechnique, 2013, 63(7): 531-571. doi: 10.1680/geot.12.RL.001
[5] 孙志彬, 潘秋景, 杨小礼, 等. 非均质边坡上限分析的离散机构及应用[J]. 岩石力学与工程学报, 2017, 36(7): 1680-1688. SUN Zhibin, PAN Qiujing, YANG Xiaoli, et al. Discrete mechanism for upper bound analysis of nonhomogeneous slopes[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(7): 1680-1688. (in Chinese)
[6] QIN C B, CHIAN S C. Kinematic analysis of seismic slope stability with a discretisation technique and pseudo-dynamic approach: a new perspective[J]. Géotechnique, 2018, 68(6): 492-503. doi: 10.1680/jgeot.16.P.200
[7] FRALDI M, GUARRACINO F. Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek–Brown failure criterion[J]. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(4): 665-673. doi: 10.1016/j.ijrmms.2008.09.014
[8] FRALDI M, GUARRACINO F. Analytical solutions for collapse mechanisms in tunnels with arbitrary cross sections[J]. International Journal of Solids and Structures, 2010, 47(2): 216-223. doi: 10.1016/j.ijsolstr.2009.09.028
[9] FRALDI M, GUARRACINO F. Evaluation of impending collapse in circular tunnels by analytical and numerical approaches[J]. Tunnelling and Underground Space Technology, 2011, 26(4): 507-516. doi: 10.1016/j.tust.2011.03.003
[10] YANG X L, QIN C B. Limit analysis of rectangular cavity subjected to seepage forces based on Hoek-Brown failure criterion[J]. Geomechanics and Engineering, 2014, 6(5): 503-515. doi: 10.12989/gae.2014.6.5.503
[11] YANG X L, HUANG F. Three-dimensional failure mechanism of a rectangular cavity in a Hoek-Brown rock medium[J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 61: 189-195. doi: 10.1016/j.ijrmms.2013.02.014
[12] QIN C B, LI Y Y, YU J, et al. Closed-form solutions for collapse mechanisms of tunnel crown in saturated non-uniform rock surrounds[J]. Tunnelling and Underground Space Technology, 2022, 126: 104529. doi: 10.1016/j.tust.2022.104529
[13] BAKER R. Nonlinear Mohr envelopes based on triaxial data[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2004, 130(5): 498-506. doi: 10.1061/(ASCE)1090-0241(2004)130:5(498)
[14] ZHANG D B, MA Z Y, YU B, et al. Upper bound solution of surrounding rock pressure of shallow tunnel under nonlinear failure criterion[J]. Journal of Central South University, 2019, 26(7): 1696-1705. doi: 10.1007/s11771-019-4126-3
[15] 刘智振. 非线性Baker破坏准则下地下硐室围岩压力上限解研究[D]. 湘潭: 湖南科技大学, 2017. LIU Zhizhen. Study on Upper Bound Solution of Surrounding Rock Pressure in Underground Cavity under Nonlinear Baker Failure Criterion[D]. Xiangtan: Hunan University of Science and Technology, 2017. (in Chinese)
[16] HOEK E, BROWN E T. Empirical strength criterion for rock masses[J]. Journal of the Geotechnical Engineering Division, 1980, 106(9): 1013-1035. doi: 10.1061/AJGEB6.0001029
[17] HOEK E, CARRANZA-TORRES C, CORKUM B. Hoek-Brown failure criterion: 2002 edition[C]// Proceedings of the North American Rock Mechanics Symposium. Toronto, 2002.
[18] XU J S, YANG X L. Seismic stability analysis and charts of a 3D rock slope in Hoek-Brown media[J]. International Journal of Rock Mechanics and Mining Sciences, 2018, 112: 64-76. doi: 10.1016/j.ijrmms.2018.10.005
[19] 黄阜, 杨小礼, 赵炼恒, 等. 基于Hoek-Brown破坏准则的浅埋条形锚板抗拔力上限分析[J]. 岩土力学, 2012, 33(1): 179-184, 190. doi: 10.3969/j.issn.1000-7598.2012.01.028 HUANG Fu, YANG Xiaoli, ZHAO Lianheng, et al. Upper bound solution of ultimate pullout capacity of strip plate anchor based on Hoek-Brown failure criterion[J]. Rock and Soil Mechanics, 2012, 33(1): 179-184, 190. (in Chinese) doi: 10.3969/j.issn.1000-7598.2012.01.028
[20] JIANG J C, BAKER R, YAMAGAMI T. The effect of strength envelope nonlinearity on slope stability computations[J]. Canadian Geotechnical Journal, 2003, 40(2): 308-325. doi: 10.1139/t02-111
[21] LIU Z Z, CAO P, LIN H, et al. Three-dimensional upper bound limit analysis of underground cavities using nonlinear Baker failure criterion[J]. Transactions of Nonferrous Metals Society of China, 2020, 30(7): 1916-1927. doi: 10.1016/S1003-6326(20)65350-X
[22] FRALDI M, CAVUOTO R, CUTOLO A, et al. Stability of tunnels according to depth and variability of rock mass parameters[J]. International Journal of Rock Mechanics and Mining Sciences, 2019, 119: 222-229. doi: 10.1016/j.ijrmms.2019.05.001
计量
- 文章访问数: 320
- HTML全文浏览量: 37
- PDF下载量: 63
