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锚杆不确定性对加固边坡失稳概率的影响

王上上 陈富 李东贤 林后来 刘志良 李亮

王上上, 陈富, 李东贤, 林后来, 刘志良, 李亮. 锚杆不确定性对加固边坡失稳概率的影响[J]. 地质科技通报, 2022, 41(2): 282-289. doi: 10.19509/j.cnki.dzkq.2022.0055
引用本文: 王上上, 陈富, 李东贤, 林后来, 刘志良, 李亮. 锚杆不确定性对加固边坡失稳概率的影响[J]. 地质科技通报, 2022, 41(2): 282-289. doi: 10.19509/j.cnki.dzkq.2022.0055
Wang Shangshang, Chen Fu, Li Dongxian, Lin Houlai, Liu Zhiliang, Li Liang. Influence of anchor uncertainty on the failure probability of reinforced slope[J]. Bulletin of Geological Science and Technology, 2022, 41(2): 282-289. doi: 10.19509/j.cnki.dzkq.2022.0055
Citation: Wang Shangshang, Chen Fu, Li Dongxian, Lin Houlai, Liu Zhiliang, Li Liang. Influence of anchor uncertainty on the failure probability of reinforced slope[J]. Bulletin of Geological Science and Technology, 2022, 41(2): 282-289. doi: 10.19509/j.cnki.dzkq.2022.0055

锚杆不确定性对加固边坡失稳概率的影响

doi: 10.19509/j.cnki.dzkq.2022.0055
基金项目: 

国家自然科学基金项目 51778313

详细信息
    作者简介:

    王上上(1996-), 男, 现正攻读建筑与土木工程专业硕士学位, 主要从事边坡稳定分析研究。E-mail: 295547041@qq.com

    通讯作者:

    李亮(1977-), 男, 教授, 主要从事岩土工程防灾减灾研究。E-mail: liliang@qut.edu.cn

  • 中图分类号: TU457

Influence of anchor uncertainty on the failure probability of reinforced slope

  • 摘要: 为了探究锚杆不确定性对加固边坡失稳概率的影响, 建立了施加锚杆后的边坡模型, 通过以下两种途径来考虑锚杆的不确定性: 其一是假定锚杆与锚固体之间接触面上的单位表面摩擦力为对数正态分布变量, 其二是引入锚杆与锚固体之间接触面上的单位表面摩擦力衰减系数来考虑运营过程中锚杆的不确定性。采用极限平衡分析法并结合蒙特卡罗抽样法, 计算并对比分析了两种途径下锚固边坡失稳概率变化曲线, 最后以深圳假日酒店基坑边坡支护工程为例, 证明所提方法的有效性。结果表明: 对于途径一, 在相同土体统计参数下, 随着锚杆与锚固体之间接触面上单位表面摩擦力变异系数的增加, 加固边坡的失稳概率缓慢增加, 增幅介于18.03%~41.90%之间。对于途径二, 随着锚杆衰减系数自1.0逐步减小至0, 加固边坡失稳概率迅速增加, 增幅介于55.64%~124.90%之间; 在同一衰减系数下, 加固边坡失稳概率随着锚杆衰减根数的增加而增大。研究结果可以为锚杆施工与运营期间的管理提供决策支持。

     

  • 图 1  条块受力分析

    hibi分别为第i个条块的高度和宽度;αi为底面倾角;Wi为重力;Pi为锚杆有效的最大抗拔力;ωiPi与竖直方向的夹角;Ni为滑动面上的有效法向力;Si为滑动面上基底下滑剪力;EiEi+1分别为条块i, i+1间的法向作用力;ZiZi+1分别为Ei, Ei+1与底面的垂直距离; λ为待定系数; fi, fi+1为条间(i, i+1)力函数f(s)计算结果

    Figure 1.  Force analysis of slice

    图 2  设计的不稳定边坡

    Figure 2.  An unstable slope of design

    图 3  施加锚杆后的设计边坡

    Figure 3.  Design slope after anchor applied

    图 4  黏聚力c、内摩擦角φ和单位表面摩擦力Ff样本频率直方图

    Figure 4.  Sample frequency histograms of cohesion, internal friction angle and unit surface friction force

    图 5  锚杆与锚固体之间接触面上的单位表面摩擦力Ff变异性对边坡失稳概率的影响

    Figure 5.  Influence of variation of unit surface friction Ff on the contact surface between the anchor and the anchor solid on the failure probability of slope

    图 6  变异系数增加后失稳概率增幅图

    Figure 6.  Increase graph in failure probability with increasing of coefficient of variation

    图 7  锚杆局部失效下边坡失稳概率变化曲线

    Figure 7.  Change curve of slope failure probability under local anchor failure

    图 8  深圳假日广场深基坑边坡支护图

    Figure 8.  Slope retaining project of Shenzhen Holiday Inn foundation pit

    图 9  不同锚杆失效模型下的边坡失稳概率

    Figure 9.  Slope failure probability under different anchor failure models

    表  1  锚杆与锚固体之间接触面上的单位表面摩擦力Ff对数正态分布模型下边坡失稳概率

    Table  1.   Slope failure probability under the log-normal distribution model of unit surface friction Ff on the contact surface between the anchor and the anchor solid

    黏聚力c 内摩擦角φ 锚杆与锚固体之间接触面上的单位表面摩擦力Ff
    均值/kPa 分布类型 COV 均值/(°) 分布
    类型
    COV 均值/kPa 分布类型 COV
    0 0.1 0.2 0.3 0.4
    不同COV下的失稳概率pf/%
    5.0 LN 0.3 25 LN 0.3 50 LN 38.55 38.90 41.30 41.70 45.50
    7.5 LN 0.3 25 LN 0.3 50 LN 26.00 26.20 29.50 30.10 33.20
    10.0 LN 0.3 25 LN 0.3 50 LN 17.90 18.20 19.40 25.30 25.40
    注:COV为变异系数(coefficient of variation),LN为对数正态分布
    下载: 导出CSV

    表  2  随机1根锚杆局部失效下的边坡失稳概率

    Table  2.   Slope failure probability under partial failure of on eanchor at random

    黏聚力c 内摩擦角φ 衰减系数
    Ki
    其中1根锚杆
    Ffi/kPa
    另外2根锚杆
    Ffi/kPa
    失稳概率/%
    均值/kPa 分布类型 COV 均值/(°) 分布类型 COV
    5 LN 0.3 25 LN 0.3 0 0 50 60.00
    5 LN 0.3 25 LN 0.3 0.1 5 50 58.75
    5 LN 0.3 25 LN 0.3 0.3 15 50 53.60
    5 LN 0.3 25 LN 0.3 0.5 25 50 49.30
    5 LN 0.3 25 LN 0.3 0.7 35 50 45.75
    5 LN 0.3 25 LN 0.3 0.9 45 50 39.00
    5 LN 0.3 25 LN 0.3 1.0 50 50 38.55
    下载: 导出CSV

    表  3  随机2根锚杆局部失效下的边坡失稳概率

    Table  3.   Slope failure probability under partial failure of two anchors at random

    黏聚力c 内摩擦角φ 衰减系数
    Ki
    其中两根锚杆
    Ffi/kPa
    另外一根锚杆
    Ffi/kPa
    失稳概率/%
    均值/kPa 分布类型 COV 均值/(°) 分布类型 COV
    5 LN 0.3 25 LN 0.3 0 0 50 86.70
    5 LN 0.3 25 LN 0.3 0.1 5 50 82.60
    5 LN 0.3 25 LN 0.3 0.3 15 50 71.30
    5 LN 0.3 25 LN 0.3 0.5 25 50 62.55
    5 LN 0.3 25 LN 0.3 0.7 35 50 52.20
    5 LN 0.3 25 LN 0.3 0.9 45 50 41.15
    5 LN 0.3 25 LN 0.3 1.0 50 50 38.55
    下载: 导出CSV

    表  4  各岩土层参数

    Table  4.   Parameters of each rock layer

    岩土层名称 层厚/m 重度γ/(kN·m-3) 泊松比 黏聚力c/kPa 分布类型 COV 内摩擦角φ/(°) 分布类型 COV
    素填土 1.75 18.0 0.45 10.0 LN 0.3 8 LN 0.3
    粉质黏土 16.25 18.9 0.38 24.9 LN 0.3 20 LN 0.3
    花岗岩 6.40 26.0 0.30 160.0 LN 0.3 35 LN 0.3
    下载: 导出CSV

    表  5  锚杆物理力学参数

    Table  5.   Physical and mechanical parameters of anchors

    锚杆编号 起点坐标/m 终点坐标/m 锚杆长度/m 黏结直径d/m 锚杆水平间距/m 层面夹角δ/(°) 单位表面摩擦力均值Ff/kPa 抗剪强度σs/MPa 抗拉强度σtb/MPa
    锚杆1 (19.18, 21.35) (32.34, 16.56) 14 0.3 2 20 70 300 168
    锚杆2 (18.37, 18.35) (29.64, 14.25) 12 0.3 2 20 70 300 168
    锚杆3 (17.55, 15.35) (26.95, 11.93) 10 0.3 2 20 70 300 168
    锚杆4 (16.74, 12.35) (24.25, 9.61) 8 0.3 2 20 70 300 168
    下载: 导出CSV

    表  6  4根锚杆中随机1根、2根和3根锚杆局部失效模型下的失稳概率

    Table  6.   Failure probability of one, two and three anchors of four anchors under partial failure

    衰减系数
    Ki
    随机1根锚杆局部失效 随机2根锚杆局部失效 随机3根锚杆局部失效
    Ffi/kPa 失稳概率/% Ffi/kPa 失稳概率/% Ffi/kPa 失稳概率/%
    0 0 21.40 0 34.20 0 56.70
    0.1 7 21.10 7 31.10 7 50.80
    0.3 21 17.90 21 25.00 21 41.20
    0.5 35 17.80 35 23.20 35 31.80
    0.7 49 13.40 49 17.20 49 24.60
    0.9 63 13.00 63 12.40 63 12.80
    1.0 70 12.10 70 12.10 70 12.10
    下载: 导出CSV
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