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Stability and failure pattern analysis of bimslope with Mohr-Coulomb matrix soil: From a perspective of micropolar continuum theory

基于微极连续体理论视角的Mohr-Coulomb 基质土的土石混合体边坡 稳定性及破坏模式分析

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Abstract

For the stability and failure pattern analysis of bimslopes, a novel second-order cone programming optimized micropolar continuum finite element method (mpcFEM-SOCP) incorporating the micropolar Mohr-Coulomb (MC) model is developed. Based on two bimslopes, the effectiveness and superiority of the present method is examined. Numerical analyses disclose that the presence of rock blocks “intruding” the potential slip surface may increase the ultimate bearing capacity of the rigid footing and contribute to the stability of bimslopes. Compared to the second-order cone programming optimized classical continuum finite element method (FEM-SOCP), it is interesting to note that mpcFEM-SOCP may reveal different failure mechanisms evidently from those predicted by FEM-SOCP in some cases. For the bimslope with square-cluster rock blocks, it is observed by FEM-SOCP and mpcFEM-SOCP that the presence of scattered rock blocks complicates the failure patterns of bimslopes. Compared to the generalized limit equilibrium method in the Pybimstab package assuming a single slip surface, FEM-SOCP and mpcFEM-SOCP may produce finger-pattern slip surfaces, and particularly the width of slip surfaces in matrix soil may be adequately modeled by the internal characteristic length /c bridging the particle characteristics of matrix soil and the macroscopic strain localization behavior.

摘要

针对土石混合体边坡稳定性和破坏模式分析, 提出了一种基于微极Mohr-Coulomb(MC)模型 的二阶锥规划微极连续体有限元法(mpcFEM-SOCP)。以两个土石混合体边坡为例, 验证了所提方法的 有效性和优越性。数值分析表明, 块石“侵入”潜在滑面会增加刚性基础的极限承载力以及边坡的稳 定性。与二阶锥规划经典连续体有限元法(FEM-SOCP)相比, 在某些情况下mpcFEM-SOCP 可以揭示不 同的土石混合体边坡破坏机制。通过FEM-SOCP 和mpcFEM-SOCP 可以观察到, 对于方形簇块石土石 混合体边坡, 分散的块石会使土石混合体边坡破坏模式更为复杂; 与Pybimstab 程序包中(假设单滑移 面)的广义极限**衡方法相比, FEM-SOCP 和mpcFEM-SOCP 会提供手指分叉式滑移面; 通过关联基质 土颗粒特性和宏观应变局部化行为的内部特征长度l c 能够较好地模拟基质土滑移面的宽度。

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Abbreviations

DOF:

Degree of freedom

FEM:

Finite element method

FEM-SOCP:

Second-order cone programming optimized classical continuum finite element method

FOS:

Factor of safety

FOSf :

FOS corresponding to the static force equilibrium

FOSm :

FOS corresponding to the moment equilibrium

GLE:

Generalized limit equilibrium

LAM:

Limit analysis method

LEM:

Limit equilibrium method

MC:

Mohr-coulomb

mpcFEM-SOCP:

Second-order cone programming optimized micropolar continuum finite element method

SSRFEM:

Shear strength reduction finite element method

UCS:

Uniaxial compressive strength

VBP:

Volumetric block proportion

a :

Vector of linear equation

A :

Coefficient matrix of linear equation

b :

Vector of body force

c :

Cohesion

c :

Coefficient vector

c 0 :

Initial cohesion

ℂq :

Quadratic cone

ℂr :

Rotated quadratic cone

d b :

Rock block size

d thr :

Threshold of rock block sizes

D e :

Elastic stiffness matrix

E :

Elastic modulus

F mc :

Micropolar MC yield function with compression positive

G :

Lamé constant (or shear modulus)

G m :

Micropolar shear modulus

h 1, h 2 and h 3 :

Constant coefficients

h cp :

Negative softening modulus of cohesion

I :

Index diagonal matrix

I R :

Roundness index

I SPH :

Sphericity index

k 0 :

Parameter denoting the hardening exponent of the material

l c :

Internal characteristic length

l e :

Average mesh size

l v :

Evolving internal characteristic length

L f :

Length of engineering features or the slope dimensions

m ij :

Couple stress components

nels :

Total number of finite elements in mesh

n o :

Total number of integration points in the whole solution domain

N u :

Shape (or interpolation) function for displacement

N o :

Shape (or interpolation) function for stress

R o :

Mean surface roughness

\({{{\boldsymbol{\hat r}}}_{k + 1}}\) :

Unknown nodal reaction force

u :

Displacement vector

u x, u y :

Translational displacement components in two plane coordinates Prescribed nodal displacement vector

û :

Nodal displacement vector of each element

v :

Poisson ratio

x :

Solution vector

σ :

Stress vector

σ ij :

Stress components

σ m :

Mean normal stress

\({{\boldsymbol{\hat \sigma }}}\) :

Stress vector at stress integration points in each element

τ*:

Generalized shear strength

ε :

Strain vector

ε ij :

Strain components

\(\overline \varepsilon _{\rm{p}}^{{\rm{ip}}}\) :

Total accumulated equivalent plastic strain at each integration point

κ ij :

Micro-curvature components

α m :

Shear modulus ratio

γ b :

Unit weight of rock blocks

γ m :

Unit weight of matrix soil

λ :

Lamé constant

∇:

Differential operator

φ :

Internal friction angle

ω z :

Micro-rotation component

References

  1. GUAN Wen-jie, WU Wen-bing, JIANG Guo-sheng, et al. Torsional dynamic response of tapered pile considering compaction effect and stress diffusion effect [J]. Journal of Central South University, 2020, 27: 3839–3851. DOI: https://doi.org/10.1007/s11771-020-4503-y.

    Article  Google Scholar 

  2. WEN Min-jie, TIAN Yi, WU Wen-bing, et al. Influence of thermal contact resistance on dynamic response of bilayered saturated porous strata [J]. Journal of Central South University, 2022, 29(6): 1823–1839. DOI: https://doi.org/10.1007/s11771-022-5053-2.

    Article  Google Scholar 

  3. ZONG Meng-fan, TIAN Yi, LIANG Rong-zhu, et al. One-dimensional nonlinear consolidation analysis of soil with continuous drainage boundary [J]. Journal of Central South University, 2022, 29(1): 270–281. DOI: https://doi.org/10.1007/s11771-022-4916-x.

    Article  Google Scholar 

  4. WU Wen-bing, LU Chun-hua, CHEN Li-bo, et al. Horizontal vibration characteristics of pile groups in unsaturated soil considering coupled pile-pile interaction [J]. Ocean Engineering, 2023, 281: 115000.

    Article  Google Scholar 

  5. LINDQUIST E, GOODMAN R. Strength and deformation properties of a physical model melange [C]//1st North American Rock Mechanics Symposium. ARMA, 1994: 843–850.

  6. SONMEZ H, GOKCEOGLU C, MEDLEY E W, et al. Estimating the uniaxial compressive strength of a volcanic bimrock [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(4): 554–561. DOI: https://doi.org/10.1016/j.ijrmms.2005.09.014.

    Article  Google Scholar 

  7. AFIFIPOUR M, MOAREFVAND P. Mechanical behavior of bimrocks having high rock block proportion [J]. International Journal of Rock Mechanics and Mining Sciences, 2014, 65: 40–48. DOI: https://doi.org/10.1016/j.ijrmms.2013.11.008.

    Article  Google Scholar 

  8. LIU Yong, XIAO Hua-wen, YAO Kai, et al. Rock-soil slope stability analysis by two-phase random media and finite elements [J]. Geoscience Frontiers, 2018, 9(6): 1649–1655. DOI: https://doi.org/10.1016/j.gsf.2017.10.007.

    Article  Google Scholar 

  9. MEDLEY E W. Observations on tortuous failure surfaces in Bimrocks[J]. Felsbau Rock Soil Eng, 2004, 5(22): 35–43.

    Google Scholar 

  10. AFIFIPOUR M, MOAREFVAND P. Failure patterns of geomaterials with block-in-matrix texture: Experimental and numerical evaluation [J]. Arabian Journal of Geosciences, 2014, 7(7): 2781–2792. DOI: https://doi.org/10.1007/s12517-013-0907-4.

    Article  Google Scholar 

  11. NAPOLI M L, BARBERO M, SCAVIA C. Effects of block shape and inclination on the stability of melange bimrocks [J]. Bulletin of Engineering Geology and the Environment, 2021, 80(10): 7457–7466. DOI: https://doi.org/10.1007/s10064-021-02419-8.

    Article  Google Scholar 

  12. MONTOYA-ARAQUE E A, SUAREZ-BURGOA L O. Automatic generation of tortuous failure surfaces in block-inmatrix materials for 2D slope stability assessments [J]. Computers and Geotechnics, 2019, 112: 17–22. DOI: https://doi.org/10.1016/j.compgeo.2019.04.002.

    Article  Google Scholar 

  13. DENG Dong-**, ZHAO Lian-heng, LI Liang. Limit equilibrium method for slope stability based on assumed stress on slip surface [J]. Journal of Central South University, 2016, 23(11): 2972–2983. DOI: https://doi.org/10.1007/s11771-016-3361-0.

    Article  Google Scholar 

  14. LI **ong-wei, ZHU Jian-qun, LI Zheng-wei, et al. 3D stability assessment of stepped slopes in inhomogeneous soils [J]. Journal of Central South University, 2020, 27(1): 221–230. DOI: https://doi.org/10.1007/s11771-020-4290-5.

    Article  Google Scholar 

  15. CHEN **, WU Yong-kang, YU Yu-zhen, et al. A two-grid search scheme for large-scale 3-D finite element analyses of slope stability [J]. Computers and Geotechnics, 2014, 62: 203–215. DOI: https://doi.org/10.1016/j.compgeo.2014.07.010.

    Article  Google Scholar 

  16. BAI Bing, YUAN Wei, LI **ao-chun. A new double reduction method for slope stability analysis [J]. Journal of Central South University, 2014, 21(3): 1158–1164. DOI: https://doi.org/10.1007/s11771-014-2049-6.

    Article  Google Scholar 

  17. TSCHUCHNIGG F, SCHWEIGER H F, SLOAN S W. Slope stability analysis by means of finite element limit analysis and finite element strength reduction techniques. Part I: Numerical studies considering non-associated plasticity [J]. Computers and Geotechnics, 2015, 70: 169–177. DOI: https://doi.org/10.1016/j.compgeo.2015.06.018.

    Article  Google Scholar 

  18. WANG Dong-yong, CHEN **, QI Ji-lin, et al. Assessment on strength reduction schemes for geotechnical stability analysis involving the Drucker-Prager criterion [J]. Journal of Central South University, 2021, 28(10): 3238–3245. DOI: https://doi.org/10.1007/s11771-021-4828-1.

    Article  Google Scholar 

  19. SMITH I M, GRIFFITHS D V, MARGETTS L. Programming the finite element method [M]. Chichecter: John Wiley & Sons, 2013.

    MATH  Google Scholar 

  20. CHEN **, WANG Dong-yong, YU Yu-zhen, et al. A modified Davis approach for geotechnical stability analysis involving non-associated soil plasticity [J]. Géotechnique, 2020, 70(12): 1109–1119. DOI: https://doi.org/10.1680/jgeot.18.p.158.

    Article  Google Scholar 

  21. de BORST R. Simulation of strain localization: A reappraisal of the cosserat continuum [J]. Engineering Computations, 1991, 8(4): 317–332. DOI: https://doi.org/10.1108/eb023842.

    Article  Google Scholar 

  22. WANG Dong-yong, CHEN **, LYU Yan-nan, et al. Geotechnical localization analysis based on Cosserat continuum theory and second-order cone programming optimized finite element method [J]. Computers and Geotechnics, 2019, 114: 103118.

    Article  Google Scholar 

  23. CHEN **, WANG Dong-yong, TANG Jian-bin, et al. Geotechnical stability analysis considering strain softening using micro-polar continuum finite element method [J]. Journal of Central South University, 2021, 28(1): 297–310. DOI: https://doi.org/10.1007/s11771-021-4603-3.

    Article  Google Scholar 

  24. RATTEZ H, SHI Yao-zhong, SAC-MORANE A, et al. Effect of grain size distribution on the shear band thickness evolution in sand [J]. Géotechnique, 2022, 72(4): 350–363. DOI: https://doi.org/10.1680/jgeot.20.p.120.

    Article  Google Scholar 

  25. ALSHIBLI K A, ALSALEH M I, VOYIADJIS G Z. Modelling strain localization in granular materials using micropolar theory: Numerical implementation and verification [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(15): 1525–1544.

    Article  MATH  Google Scholar 

  26. SHARBATI E, NAGHDABADI R. Computational aspects of the Cosserat finite element analysis of localization phenomena [J]. Computational Materials Science, 2006, 38(2): 303–315. DOI: https://doi.org/10.1016/j.commatsci.2006.03.003.

    Article  Google Scholar 

  27. TANG Jian-bin, WANG **ang-nan, CHEN **, et al. Geotechnical strain localization analysis based on micropolar continuum theory considering evolution of internal characteristic length [J]. International Journal of Geomechanics, 2022, 22(8): 06022016. DOI: https://doi.org/10.1061/(asce)gm.1943-5622.0002462.

    Article  Google Scholar 

  28. VOYIADJIS G Z, ALSALEH M I, ALSHIBLI K A. Evolving internal length scales in plastic strain localization for granular materials [J]. International Journal of Plasticity, 2005, 21(10): 2000–2024. DOI: https://doi.org/10.1016/j.ijplas.2005.01.008.

    Article  MATH  Google Scholar 

  29. KARAPIPERIS K, ORTIZ M, ANDRADE J E. Data-driven nonlocal mechanics: Discovering the internal length scales of materials [J]. Computer Methods in Applied Mechanics and Engineering, 2021, 386: 114039. DOI: https://doi.org/10.1016/j.cma.2021.114039.

    Article  MathSciNet  MATH  Google Scholar 

  30. TANG Hong-xiang, WEI Wen-cheng, LIU Feng, et al. Elastoplastic Cosserat continuum model considering strength anisotropy and its application to the analysis of slope stability [J]. Computers and Geotechnics, 2020, 117: 103235. DOI: https://doi.org/10.1016/j.compgeo.2019.103235.

    Article  Google Scholar 

  31. WANG Sheng-nian, LI Yue, GAO **n-qun, et al. Influence of volumetric block proportion on mechanical properties of virtual soil-rock mixtures [J]. Engineering Geology, 2020, 278: 105850. DOI: https://doi.org/10.1016/j.enggeo.2020.105850.

    Article  Google Scholar 

  32. MONTOYA-ARAQUE E A, SUAREZ-BURGOA L O. pyBIMstab: Application software for 2D slope stability analysis of block-in-matrix and homogeneous materials [J]. SoftwareX, 2018, 7: 383–387. DOI: https://doi.org/10.1016/j.softx.2018.11.003.

    Article  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Urban Underground Engineering of Ministry of Education, Bei**g Jiaotong University, Bei**g, 100044, China

    ** Chen  (陈曦), Jian-bin Tang  (唐建彬), Liu-sheng Cui  (崔柳生) & Zong-qi Liu  (刘宗祺)

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  1. ** Chen  (陈曦)
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  2. Jian-bin Tang  (唐建彬)
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  3. Liu-sheng Cui  (崔柳生)
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Contributions

CHEN ** provided the concept and methodology and wrote the original draft; TANG Jian-bin provided the methodology and performed some numerical analysis; CUI Liu-sheng performed some investigations; LIU Zong-qi conducted data curation.

Corresponding author

Correspondence to ** Chen  (陈曦).

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CHEN **, TANG Jian-bin, CUI Liu-sheng and LIU Zong-qi declare that they have no conflict of interest.

Additional information

Foundation item: Project(52178309) supported by the National Natural Science Foundation of China; Project(2017YFC0804602) supported by the National Key R&D Program of China; Project(2019JBM092) supported by the Fundamental Research Funds for the Central Universities, China

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Chen, X., Tang, Jb., Cui, Ls. et al. Stability and failure pattern analysis of bimslope with Mohr-Coulomb matrix soil: From a perspective of micropolar continuum theory. J. Cent. South Univ. 30, 3450–3466 (2023). https://doi.org/10.1007/s11771-023-5452-z

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