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物质点强度折减法边坡失稳判据选择方法

蒋先平 张鹏 卢艺伟 刘磊磊 张明辉

蒋先平, 张鹏, 卢艺伟, 刘磊磊, 张明辉. 物质点强度折减法边坡失稳判据选择方法[J]. 地质科技通报, 2022, 41(2): 113-122. doi: 10.19509/j.cnki.dzkq.2021.0075
引用本文: 蒋先平, 张鹏, 卢艺伟, 刘磊磊, 张明辉. 物质点强度折减法边坡失稳判据选择方法[J]. 地质科技通报, 2022, 41(2): 113-122. doi: 10.19509/j.cnki.dzkq.2021.0075
Jiang Xianping, Zhang Peng, Lu Yiwei, Liu Leilei, Zhang Minghui. Slope failure criterion for the strength reduction material point method[J]. Bulletin of Geological Science and Technology, 2022, 41(2): 113-122. doi: 10.19509/j.cnki.dzkq.2021.0075
Citation: Jiang Xianping, Zhang Peng, Lu Yiwei, Liu Leilei, Zhang Minghui. Slope failure criterion for the strength reduction material point method[J]. Bulletin of Geological Science and Technology, 2022, 41(2): 113-122. doi: 10.19509/j.cnki.dzkq.2021.0075

物质点强度折减法边坡失稳判据选择方法

doi: 10.19509/j.cnki.dzkq.2021.0075
基金项目: 

国家自然科学基金青年基金项目 41902291

湖南省自然科学基金项目 2020JJ5704

中南大学中央高校基本科研业务费专项资金项目 2021zzts0810

详细信息
    作者简介:

    蒋先平(1980—),男,高级工程师,主要从事复杂地质条件下的岩土工程设计方法方面的研究工作。E-mail: 41555767@qq.com

    通讯作者:

    刘磊磊(1987—),男,副教授,主要从事地质灾害防治与风险控制方面的研究工作。E-mail: csulll@foxmail.com

  • 中图分类号: P642.22

Slope failure criterion for the strength reduction material point method

  • 摘要: 用物质点强度折减法求解边坡安全系数时, 需要选择一定的失稳判据, 而采用不同的失稳判据获得的安全系数通常存在一定差异。为此, 采用物质点强度折减法对两个边坡算例进行了稳定性分析, 对比研究了文献中常用的4种边坡失稳判据(计算不收敛、特征点位移突变、塑性应变贯通及界限值判据)在计算边坡安全系数时的合理性及适用性。同时, 将Spencer极限平衡法获得的安全系数作为参考, 进一步验证了结果的合理性与准确性。结果表明: ①数值计算的收敛性不能作为边坡失稳判据; ②将特征点位移突变视为边坡失稳判据时, 获得的安全系数与极限平衡法获得的结果基本一致, 故特征点位移突变可以作为边坡失稳判据; ③塑性应变贯通和边坡最大位移随迭代时间步趋于稳定的界限值不宜单独作为边坡失稳判据。

     

  • 图 1  算例1边坡几何尺寸

    Figure 1.  Slope geometry of example 1

    图 2  算例2边坡几何尺寸

    Figure 2.  Slope geometry of example 2

    图 3  边坡特征点位移随折减系数变化曲线

    Figure 3.  Variation curve of slope characteristic point displacement with reduction coefficient

    图 4  不同强度折减系数下的等效塑性应变区(算例1)

    Figure 4.  Equivalent plastic strain zone for different Ft values (example 1)

    图 5  不同强度折减系数下的等效塑性应变区(算例2)

    Figure 5.  Equivalent plastic strain zone for different Ft values (example 2)

    图 6  不同折减系数下计算时间步与特征点最大位移曲线

    Figure 6.  Curve of calculation steps and maximum displacement under different reduction coefficients

    图 7  同一折减系数下算例2边坡塑性应变随计算时间步分布图

    Figure 7.  Plastic strain zone with calculation steps for example 2 under the same reduction coefficient

    图 8  算例2边坡潜在滑动面

    Figure 8.  Potential sliding surface of example 2

    表  1  边坡基本计算参数

    Table  1.   Fundamental calculation parameters of slope

    土体参数 算例1[25] 算例2[37]
    重度γ/(kN·m-2) 20 20
    内摩擦角φ/(°) 12.38 20
    黏聚力c/kPa 20 15
    弹性模量E/kPa 100 100
    泊松比υ 0.35 0.30
    膨胀角ψ/(°) 0 9
    下载: 导出CSV

    表  2  不同方法得到的安全系数

    Table  2.   Fs obtained by various methods

    方法 算例1(Fs) 算例2(Fs)
    Spencer极限平衡法 0.996[38] 1.593
    有限元法(塑性区贯通) 0.98[38]
    有限元法(位移突变) 0.99[38] 1.60[39]
    有限元法(计算不收敛) 1.06[38]
    下载: 导出CSV

    表  3  不同折减系数下算例1和2边坡位移

    Table  3.   Displacement of example 1 and 2 for different Ft

    Ft yAyC/m xA, xC/m xB, xD/m
    算例1 0.95 0.013 0.001 0.003
    0.96 0.014 0.002 0.003
    0.97 0.015 0.002 0.004
    0.98 0.016 0.003 0.004
    0.99 0.019 0.005 0.005
    1.00 0.026 0.010 0.008
    1.01 1.313 0.923 0.426
    1.02 1.384 0.977 0.169
    1.03 1.484 1.051 0.500
    算例2 1.10 0.018 0.000 0.002
    1.20 0.019 0.000 0.003
    1.30 0.020 0.002 0.004
    1.40 0.020 0.003 0.005
    1.50 0.024 0.006 0.007
    1.60 0.028 0.012 0.016
    1.70 0.054 0.041 0.060
    注:表中yAyC分别为算例1和算例2的坡顶点竖向位移,xAxC分别为算例1和算例2的坡顶点横向位移,xBxD分别为算例1和算例2的坡脚点横向位移
    下载: 导出CSV
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