Volume 41 Issue 2
Mar.  2022
Turn off MathJax
Article Contents
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

Slope failure criterion for the strength reduction material point method

doi: 10.19509/j.cnki.dzkq.2021.0075
  • Received Date: 07 Apr 2021
  • It is necessary to select an instability criterion for the material point strength reduction method (SRMPM) to solve the slope safety factor (Fs), and there are some differences in the obtained Fs values with different instability criteria. To examine the rationality and applicability of the four common instability criteria (i.e., calculation nonconvergence, displacement mutation of the feature point, transfixion of the plastic zone and the limit value), this paper uses the SRMPM to analyse the stability of two slope examples. The Fs obtained by the Spencer limit equilibrium method (LEM) is taken as a reference to further verify the rationality and accuracy of the results. The results show that ① the material point calculation is convergent, so the calculation nonconvergence cannot be used as the slope instability criterion; ② when the displacement mutation of the feature is regarded as the criterion of slope instability, the Fs is basically consistent with the LEM, so the displacement mutation of the feature point can be used as the slope instability criterion; and ③ the limit value and the transfixion of the plastic zone cannot be used alone as the slope instability criterion.

     

  • loading
  • [1]
    吴益平, 卢里尔, 薛阳. 基于临界状态的边坡渐进破坏力学模型分析及应用[J]. 地质科技通报, 2020, 39(5): 1-7. doi: 10.19509/j.cnki.dzkq.2020.0501

    Wu Y P, Lu L E, Xue Y. Application of landslide progressive failure mechanical model based on the critical stress state[J]. Bulletin of Geological Science and Technology, 2020, 39(5): 1-7(in Chinese with English abstract). doi: 10.19509/j.cnki.dzkq.2020.0501
    [2]
    陈祖煜. 土质边坡稳定分析[M]. 北京: 中国水利水电出版社, 2003.

    Chen Z Y. Soil slope stability analysis[M]. Beijing: Water Publication of China, 2003(in Chinese).
    [3]
    Zheng Y, Tang X, Zhao S, et al. Strength reduction and step-loading finite element approaches in geotechnical engineering[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2009, 1(1): 21-30. doi: 10.3724/SP.J.1235.2009.00021
    [4]
    Klar A, Aharonov E, Kalderon-Asael B, et al. Analytical and observational relations between landslide volume and surface area[J]. Journal of Geophysical Research Earth Surface, 2011, 116: F02001.
    [5]
    Bai B, Yuan W, Li X C. A new double reduction method for slope stability analysis[J]. Journal of Central South University, 2014, 21(3): 1158-1164. doi: 10.1007/s11771-014-2049-6
    [6]
    Isakov A, Moryachkov Y. Estimation of slope stability using two-parameter criterion of stability[J]. International Journal of Geomechanics, 2014, 14(3): 613-624.
    [7]
    Yang T, Zou J F, Pan Q J. Three-dimensional seismic stability of slopes reinforced by soil nails[J]. Computers and Geotechnics, 2020, 127: 103768. doi: 10.1016/j.compgeo.2020.103768
    [8]
    吴凯峰, 郑志勇, 余海兵. 基于应变软化特征的含软弱层公路边坡稳定性研究[J]. 地质科技情报, 2019, 38(6): 150-156. https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201906018.htm

    Wu K F, Zheng Z Y, Yu H B. Stability evaluation of highway slope with soft layer based on strain softening characteristics[J]. Geological Science and Technology Information, 2019, 38(6): 150-156(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DZKQ201906018.htm
    [9]
    唐宇峰, 施富强, 廖学艳. 基于SPH的边坡稳定性计算中失稳判据研究[J]. 岩土工程学报, 2016, 38(5): 904-908. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201605016.htm

    Tang Y F, Shi F Q, Liao X Y. Failure criteria based on SPH slope stability analysis[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(5), 904-908(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201605016.htm
    [10]
    涂义亮, 刘新荣, 钟祖良, 等. 三类边坡失稳判据的统一性[J]. 岩土力学, 2018, 39(1): 180-187, 197. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201801022.htm

    Tu Y L, Liu X R, Zhong Z L, et al. The unity of three types of slope failure criteria[J]. Rock and Soil Mechanics, 2018, 39(1): 180-187, 197(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201801022.htm
    [11]
    裴国平, 陈培帅. 基于参数化训练模型的边坡强度折减法研究[J]. 山西建筑, 2012, 38(21): 101-103. doi: 10.3969/j.issn.1009-6825.2012.21.054

    Pei G P, Chen P S. Research on side slope strength reduction method based on parametric training model[J]. Shanxi Architecture, 2012, 38(21): 101-103(in Chinese with English abstract). doi: 10.3969/j.issn.1009-6825.2012.21.054
    [12]
    郑颖人, 赵尚毅. 有限元强度折减法在土坡与岩坡中的应用[J]. 岩石力学与工程学报, 2004, 23(19): 3381-3388. doi: 10.3321/j.issn:1000-6915.2004.19.029

    Zheng Y R, Zhao S Y. Application of strength reduction FEM in soil and rock slope[J]. Chinese Journal of Rock Mechanics and Engineering, 2004, 23(19): 3381-3388(in Chinese with English abstract). doi: 10.3321/j.issn:1000-6915.2004.19.029
    [13]
    Griffiths D V, Lane P A. Slope stability analysis by finite elements[J]. Geotechnique, 1999, 49(3): 387-403. doi: 10.1680/geot.1999.49.3.387
    [14]
    Ugai K, Leshchinsky D O V. Three-dimension limit equilibrium and finite element analysis: A comparison of results[J]. Soils Found, 1995, 35(4): 1-7. doi: 10.3208/sandf.35.4_1
    [15]
    栾茂田, 武亚军, 年廷凯. 强度折减有限元法中边坡失稳的塑性区判据及其应用[J]. 防灾减灾工程学报, 2003, 23(3): 1-8. https://www.cnki.com.cn/Article/CJFDTOTAL-DZXK200303001.htm

    Luan M T, Wu Y J, Nian T K. A criterion for evaluating slope stability based on development of plastic zone by shear strength reduction FEM[J]. Journal of Disaster Prevention and Mitigation Engineering, 2003, 23(3): 1-8(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-DZXK200303001.htm
    [16]
    连镇营, 韩国城, 孔宪京. 强度折减有限元法研究开挖边坡的稳定性[J]. 岩土工程学报, 2001, 23(4): 407-411. doi: 10.3321/j.issn:1000-4548.2001.04.005

    Lian Z Y, Han G C, Kong X J. Stability analysis of excavation by strength reduction FEM[J]. Chinese Journal of Geotechnical Engineering, 2001, 23(4): 407-411(in Chinese with English abstract). doi: 10.3321/j.issn:1000-4548.2001.04.005
    [17]
    宋二祥. 土结构安全系数的有限元计算[J]. 岩土工程学报, 1997, 19(2): 4-10. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC702.000.htm

    Song E X. Finite element analysis of safety factor for soil structures[J]. Chinese Journal of Geotechnical Engineering, 1997, 19(2): 4-10(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC702.000.htm
    [18]
    Zienkiewicz O C, Humpheson C, Lewis R W. Associated and non-associated visco-plasticity and plasticity in soil mechanics[J]. Geotechnique, 1975, 25(4): 671-689. doi: 10.1680/geot.1975.25.4.671
    [19]
    刘金龙, 栾茂田, 赵少飞, 等. 关于强度折减有限元方法中边坡失稳判据的讨论[J]. 岩土力学, 2005, 26(8): 1345-1348. doi: 10.3969/j.issn.1000-7598.2005.08.035

    Liu J L, Luan M T, Zhao S F, et al. Discussion on criteria for evaluating stability of slope in elastoplastic FEM based on shear strength reduction technique[J]. Rock and Soil Mechanics, 2005, 26(8): 1345-1348(in Chinese with English abstract). doi: 10.3969/j.issn.1000-7598.2005.08.035
    [20]
    吴春秋. 非线性有限单元法在土体稳定分析中的理论及应用研究[D]. 武汉: 武汉大学, 2004.

    Wu C Q. Theory and application study on the non-linear FEM for soil stability analysis[D]. Wuhan: Wuhan University, 2004, (in Chinese with English abstract).
    [21]
    张培文, 陈祖煜. 弹性模量和泊松比对边坡稳定安全系数的影响[J]. 岩土力学, 2006, 27(2): 299-303. doi: 10.3969/j.issn.1000-7598.2006.02.025

    Zhang P W, Chen Z Y. Influences of soil elastic modulus and Poisson's ratioon slope stability[J]. Rock and Mechanics, 2006, 27(2): 299-303(in Chinese with English abstract). doi: 10.3969/j.issn.1000-7598.2006.02.025
    [22]
    刘新荣, 涂义亮, 钟祖良, 等. 基于能量突变的强度折减法边坡失稳判据[J]. 中南大学学报: 自然科学版, 2016, 47(6): 2065-2072. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201606034.htm

    Liu X R, Tu Y L, Zhong Z L, et al. Slope's failure criterion based on energy catastrophe in shear strength reduction method[J]. Journal of Central South University : Science and Technology, 2016, 47(6): 2065-2072(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201606034.htm
    [23]
    柴红保, 曹平, 林杭, 等. 采用边坡稳定性强度折减法分析弹性应变能突变判据[J]. 中南大学学报: 自然科学版, 2009, 40(4): 1054-1058. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD200904037.htm

    Chai H B, Cao P, Lin H, et al. Criteria of elastic strain energy in slope stability analysis using strength reduction method[J]. Journal of Central South University: Science and Technology, 2009, 40(4): 1054-1058(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD200904037.htm
    [24]
    王双, 李小春, 石露, 等. 物质点强度折减法及其在边坡中的应用[J]. 岩土力学, 2016, 37(9): 2672-2678. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201609033.htm

    Wang S, Li, X C, Shi L, et al. Material point strength reduction method and its application to slope engineering[J]. Rock and Soil Mechanics, 37(9), 2672-2678(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201609033.htm
    [25]
    史卜涛, 张云, 张巍. 边坡稳定性分析的物质点强度折减法[J]. 岩土工程学报, 2016, 38(9): 1678-1684. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201609018.htm

    Shi B T, Zhang Y, Zhang W. Strength reduction material point method for slope stability[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(9): 1678-1684(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201609018.htm
    [26]
    王安礼, 王双, 石露, 等. 物质点局部强度折减法及其在边坡中的应用[J]. 交通科学与工程, 2016, 32(4): 1-9. doi: 10.3969/j.issn.1674-599X.2016.04.001

    Wang A L, Wang S, Shi L, et al. Local strength reduction method for material points and its application in slope engineering[J]. Journal of Transport Science and Engineering, 2016, 32(4): 1-9(in Chinese with English abstract). doi: 10.3969/j.issn.1674-599X.2016.04.001
    [27]
    张雄, 廉艳萍, 刘岩, 等. 物质点法[M]. 北京: 清华大学出版社, 2013.

    Zhang X, Lian Y P, Liu Y, et al. Material point method[M]. Beijing: Tsinghau University Press, 2013(in Chinese with English abstract).
    [28]
    Sulsky D, Chen Z, Schreyer H L. A particle method for history-dependent materials[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 118(1): 179-196.
    [29]
    张静静, 董龙雷. 考虑冲击温度影响的物质点法算法[J]. 计算机辅助工程, 2018, 27(5): 37-41. https://www.cnki.com.cn/Article/CJFDTOTAL-JSFZ2018Z1007.htm

    Zhang J J, Dong L L. Material point method algorithm considering impact temperature influence[J]. Computer Aided Engineering, 2018, 27(5): 37-41(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-JSFZ2018Z1007.htm
    [30]
    张雄, 廉艳平, 杨鹏飞, 等. 冲击爆炸问题的三维物质点法数值仿真[J]. 计算机辅助工程, 2011, 20(4): 29-37. doi: 10.3969/j.issn.1006-0871.2011.04.007

    Zhang X, Lian Y P, Yang P F, et al. 3D simulation based on material point method for impact and explosion problems[J]. Computer Aided Engineering, 2011, 20(4): 29-37(in Chinese with English abstract). doi: 10.3969/j.issn.1006-0871.2011.04.007
    [31]
    刘康琦, 刘红岩, 祁小博. 基于强度折减法的土石混合体边坡长期稳定性研究[J]. 工程地质学报, 2020, 28(2): 327-334. https://www.cnki.com.cn/Article/CJFDTOTAL-GCDZ202002013.htm

    Liu K Q, Liu H Y, Qi X B. Numerical study in long-term stability of soil-rock mixture slope using strength reduction technique[J]. Journal of Engineering Geology, 2020, 28(2): 327-334(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-GCDZ202002013.htm
    [32]
    赵尚毅, 郑颖人, 时卫民, 等. 用有限元强度折减法求边坡稳定安全系数[J]. 岩土工程学报, 2002, 24(3): 343-346. doi: 10.3321/j.issn:1000-4548.2002.03.017

    Zhao S Y, Zheng Y R, Shi W M, et al. Analysis on safety factor of sloep by strength reduction FEM[J]. Chinese Journal of Geotechnical Engineering, 2002, 24(3): 343-346(in Chinese with English abstract). doi: 10.3321/j.issn:1000-4548.2002.03.017
    [33]
    Zhao T, Sun J, Zhang B, et al. Analysis of slope stability with dynamic overloading from earthquake[J]. Journal of Earth Science, 2012, 23(3): 285-296. doi: 10.1007/s12583-012-0257-2
    [34]
    廉艳平, 张帆, 刘岩, 等. 物质点法的理论和应用[J]. 力学进展, 2013, 43(2): 237-264. https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201302003.htm

    Lian Y P, Zhang F, Liu Y, et al. Material point method and its applications[J]. Advances in Mechanics, 2013, 43(2): 237-264(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-LXJZ201302003.htm
    [35]
    孙玉进, 宋二祥. 大位移滑坡形态的物质点法模拟[J]. 岩土工程学报, 2015, 37(7): 1218-1225. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201507008.htm

    Sun Y J, Sun E X. Simulation of large-displacement landslide by material point method[J]. Chiese Journal of Geotechnical Engineering, 2015, 37(7): 1218-1225(in Chinese with English abstract). https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201507008.htm
    [36]
    Xu Z, Stark T D. Runout analyses using 2014 Oso landslide[J]. Canadian Geotechnical Journal, 2021, 59(1): 55-73.
    [37]
    Liu K, Wang Y, Huang M, et al. Postfailure analysis of slopes by random generalized interpolation material point method[J]. International Journal of Geomechanics, 2021, 21(3): 04021015. doi: 10.1061/(ASCE)GM.1943-5622.0001953
    [38]
    费康, 张建伟. ABAQUS在岩土工程中的应用[M]. 北京: 水利水电出版社, 2010.

    Fei K, Zhang J W. Applications of ABAQUS in soil engineering[M]. Beijing: Water Publication of China, 2010(in Chinese).
    [39]
    Smith I M, Griffiths D V, Margetts L. Programming the finite element method[M]. London: John Wiley & Sons, 2014.
    [40]
    Lax P D, Wendroff B. The Courant-Friedrichs-Lewy(CFL) condition[J]. Communications on Pure and Applied Mathematics, 1962, 15(4): 363-371. doi: 10.1002/cpa.3160150401
    [41]
    Strikwerda J. Finite difference schemes and partial difference equations[J]. Mathematics of Computation, 1990, 55: 869-870. doi: 10.2307/2008454
    [42]
    裴立建, 屈本宁, 钱闪光. 有限元强度折减法边坡失稳判据的统一性[J]. 岩土力学, 2010, 31(10): 3337-3341. doi: 10.3969/j.issn.1000-7598.2010.10.049

    Pei L J, Qu B N, Qian S G. Uniformity of slope instability criteria of strength reduction with FEM[J]. Rock and Mechanics, 2010, 31(10): 3337-3341(in Chinese with English abstract). doi: 10.3969/j.issn.1000-7598.2010.10.049
    [43]
    赵尚毅, 郑颖人, 张玉芳. 极限分析有限元法讲座: 有限元强度折减法中边坡失稳的判据探讨[J]. 岩土力学, 2005, 26(2): 332-336. doi: 10.3969/j.issn.1000-7598.2005.02.035

    Zhao S Y, Zheng Y R, Zhang Y F. Study on slope failure criterion in strength reduction finite element method[J]. Rock and Mechanics, 2005, 26(2): 332-336(in Chinese with English abstract). doi: 10.3969/j.issn.1000-7598.2005.02.035
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article Views(833) PDF Downloads(107) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return