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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2019, Vol. 13 Issue (4) : 950-964     https://doi.org/10.1007/s11709-019-0529-3
RESEARCH ARTICLE
Seismic stability of earth slopes with tension crack
Yundong ZHOU1, Fei ZHANG1(), Jingquan Wang2, Yufeng GAO1, Guangyu DAI1
1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, ??Nanjing 210098, China
2. Key Laboratory of Concrete and Prestressed Concrete Structure of China Ministry of Education, Southeast University, ??Nanjing 211189, China
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Abstract

Cracks at the crest of slopes frequently occur during earthquakes. Such cracks result from limited tension strength of the soil. A tension cut-off in Mohr-Coulomb shear strength can represent this limited strength. Presented is an extension of variational analysis of slope stability with a tension crack considering seismicity. Both translational and rotational failure mechanisms are included in a pseudo-static analysis of slope stability. Developed is a closed-form to assess the seismic stability of slopes with zero tensile strength. The results indicate that the presence of the tension crack has significant effects on the seismic stability of slopes, i.e., leading to small value of the yield acceleration. Considering soil tension strength in seismic slope analysis may lead to overestimation on the stability, as much as 50% for vertical slopes. Imposing tension crack results in transit of the critical failure mode to a straight line from a log-spiral, except for flat slopes with small soil cohesion. Under seismic conditions, large cohesion may increase the depth of crack, moving it closer to the slope.

Keywords slope stability      tension      crack      limit equilibrium      seismic effect     
Corresponding Authors: Fei ZHANG   
Just Accepted Date: 11 March 2019   Online First Date: 26 April 2019    Issue Date: 10 July 2019
 Cite this article:   
Yundong ZHOU,Fei ZHANG,Jingquan Wang, et al. Seismic stability of earth slopes with tension crack[J]. Front. Struct. Civ. Eng., 2019, 13(4): 950-964.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-019-0529-3
http://journal.hep.com.cn/fsce/EN/Y2019/V13/I4/950
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Yundong ZHOU
Fei ZHANG
Jingquan Wang
Yufeng GAO
Guangyu DAI
item rotational mechanism translational mechanism
known parameters i, kh,ym, T i, kh,ym, T
unknown parameters A, Xc, Yc, b1, b2, B, Dc, S2, Nm C, q, X1, X2, B, Dc, S2, Nm
required equations Eqs. (8a), (8b), (8c), (11), (13a), (13b), (14), (20a), (22) Eqs. (9a), (9b), (7c), (12), (13a), (16), (20b), (22)
steps for calculation (1) assume a value for b1, b2 and Dc;
(2) use Eqs. (8a), (8b), (8c) to calculate A, Xc, Yc;
(3) use Eq. (14) to calculate Nm;
(4) substituting Eq. (22) into Eq. (11) to calculate B;
(5) integrate Eqs. (13a), (13b) and (23) to determine whether H, V, S are close to zero. If yes, the critical results are found. If no, assume new values for (b1, b2, Dc) and go to step 2. Repeat until convergence is achieved.
(1) assume a value for q and Dc;
(2) use Eqs. (9a), (9b), (7c) to calculate C, X1, X2;
(3) use Eq. (16) to calculate Nm;
(4) substituting Eq. (22) into Eq. (12) to calculate B;
(5) integrate Eqs. (13a) and (23) to determine whether H, Sare close to zero. If yes, the critical results are found. If no, assume new values for (q, Dc) and go to step 2, repeat until convergence is achieved.
Tab.1  Parameters and equations for a closed-form solution on seismic slope stability
Fig.1  Graphical representation of MC failure criteria with a tension cut-off
Fig.2  Notation and convention for the stability analysis of slope with tension crack: (a) Rotational failure mechanism; (b) Translational failure mechanism
i (°) f (°) Nm difference
variational analysis limit
analysis
TM RM TM RM TM RM
60 10 0.127 0.144 0.125 0.143 1.62% 0.66%
20 0.085 0.100 0.083 0.099 1.40% 1.23%
30 0.051 0.065 0.050 0.064 1.15% 1.36%
90 10 0.280 0.261 0.270 0.270 3.61% −3.29%
20 0.234 0.219 0.223 0.223 4.82% −1.78%
30 0.193 0.182 0.183 0.183 5.58% −0.58%
Tab.2  Stability number Nm for static slopes with tension crack
Fig.3  Yield seismic acceleration coefficients for slopes with i = 90°. (a) ϕ=10°; (b) ϕ=20°; (c) ϕ=30°; (d) ϕ=40°
Fig.4  Yield seismic acceleration coefficients for slopes with i = 75°. (a) ϕ=10°; (b) ϕ=20°; (c) ϕ=30°; (d) ϕ=40°
Fig.5  Yield seismic acceleration coefficients for slopes with i = 60°. (a) ϕ=10°; (b) ϕ=20°; (c) ϕ=30°; (d) ϕ=40°
Fig.6  Yield seismic acceleration coefficients for slopes with i = 45°. (a) ϕ=10°; (b) ϕ=20°; (c) ϕ=30°; (d) ϕ=40°
Fig.7  Yield seismic acceleration coefficients for slopes with i = 30°. (a) ϕ=10°; (b) ϕ=20°
Fig.8  Critical angle qc for slopes with translational failures. (a) i=75°; (b) i=90°
Fig.9  Normalized (a) depth and (b) location of tension crack in slopes with i = 90°
Fig.10  Normalized (a) depth and (b) location of tension crack in slopes with i = 75°
Fig.11  Normalized (a) depth and (b) location of tension crack in slopes with i = 60°
Fig.12  Normalized (a) depth and (b) location of tension crack in slopes with i = 45°
Fig.13  Normalized (a) depth and (b) location of tension crack in slopes with i = 30°
Fig.14  Critical slip surfaces for slope with or without tension crack (i = 90°). (a) ϕ=10°; (b) ϕ=20°; (c) ϕ=30°; (d) ϕ=40°
Fig.15  Critical slip surfaces for slope with or without tension crack (i = 60°). (a) ϕ=10°; (b) ϕ=20°; (c) ϕ=30°; (d) ϕ=40°
f = 10° f = 20° f = 30° f = 40°
i = 90°, N = 0.30 tension crack 0.044 0.142 0.219 0.278
No crack 0.292 0.402 0.487 0.550
difference −84.9% −64.7% −55.0% −49.5%
i = 60°, N = 0.15 tension crack 0.022 0.196 0.355 0.473
no crack 0.053 0.230 0.393 0.521
difference −58.5% −14.8% −9.7% −9.2%
Tab.3  Difference in the yield seismic acceleration for slopes with or without tension crack
1 R Q Huang, X J Pei, X M Fan, W F Zhang, S G Li, B L Li. The characteristics and failure mechanism of the largest landslide triggered by the Wenchuan earthquake, May 12, 2008, China. Landslides, 2012, 9(1): 131–142
https://doi.org/10.1007/s10346-011-0276-6
2 T Stahl, E L Bilderback, M C Quigley, D C Nobes, C I Massey. Coseismic landsliding during the Mw 7.1 Darfield (Canterbury) earthquake: Implications for paleoseismic studies of landslides. Geomorphology, 2014, 214: 114–127
https://doi.org/10.1016/j.geomorph.2014.03.020
3 R Baker. Tensile strength, tension cracks, and stability of slopes. Soil and Foundation, 1981, 21(2): 1–17
https://doi.org/10.3208/sandf1972.21.2_1
4 E A Spencer. Effect of tension on stability of embankments. Journal of the Soil Mechanics and Foundations Division, 1968, 94(5): 1159–1173
5 R Baker, D Leshchinsky. Spatial distribution of safety factors. Journal of Geotechnical and Geoenvironmental Engineering, 2001, 127(2): 135–145
https://doi.org/10.1061/(ASCE)1090-0241(2001)127:2(135)
6 R Baker, D Leshchinsky. Spatial distribution of safety factors: Cohesive vertical cut. International Journal for Numerical and Analytical Methods in Geomechanics, 2003, 27(12): 1057–1078
https://doi.org/10.1002/nag.312
7 S Utili. Investigation by limit analysis on the stability of slopes with cracks. Geotechnique, 2013, 63(2): 140–154
https://doi.org/10.1680/geot.11.P.068
8 R L Michalowski. Stability assessment of slopes with cracks using limit analysis. Canadian Geotechnical Journal, 2013, 50(10): 1011–1021
https://doi.org/10.1139/cgj-2012-0448
9 H L Ren, X Y Zhuang, Y C Cai, T Rabczuk. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476
https://doi.org/10.1002/nme.5257
10 H L Ren, X Y Zhuang, T Rabczuk. A new peridynamic formulation with shear deformation for elastic solid. Journal of Micromechanics & Molecular Physics, 2016, 1(2): 1650009
https://doi.org/10.1142/S2424913016500090
11 G Y Liu, X Y Zhuang, Z Q Cui. Three-dimensional slope stability analysis using independent cover based numerical manifold and vector method. Engineering Geology, 2017, 225: 83–95
https://doi.org/10.1016/j.enggeo.2017.02.022
12 S D Koppula. Pseudo-static analysis of clay slopes subjected to earthquakes. Geotechnique, 1984, 34(1): 71–79
https://doi.org/10.1680/geot.1984.34.1.71
13 D Leshchinsky, K San. Pseudostatic seismic stability of slopes: Design charts. Journal of Geotechnical Engineering, 1994, 120(9): 1514–1532
https://doi.org/10.1061/(ASCE)0733-9410(1994)120:9(1514)
14 H I Ling, Y Mohri, T Kawabata. Seismic analysis of sliding wedge: Extended Francais-Culmann’s analysis. Soil Dynamics and Earthquake Engineering, 1999, 18(5): 387–393
https://doi.org/10.1016/S0267-7261(99)00005-6
15 R Baker, M Garber. Theoretical analysis of the stability of slopes. Geotechnique, 1978, 28(4): 395–411
https://doi.org/10.1680/geot.1978.28.4.395
16 D Leshchinsky, A J Reinschmidt. Stability of membrane reinforced slopes. Journal of Geotechnical Engineering, 1985, 111(11): 1285–1300
https://doi.org/10.1061/(ASCE)0733-9410(1985)111:11(1285)
17 N M Newmark. Effects of earthquakes on dams and embankments. Geotechnique, 1965, 15(2): 139–160
https://doi.org/10.1680/geot.1965.15.2.139
18 J Song, Y F Gao, T G Feng, G Z Xu. Effect of site condition below slip surface on prediction of equivalent seismic loading parameters and sliding displacement. Engineering Geology, 2018, 242(2): 169–183
https://doi.org/10.1680/geot.1965.15.2.139
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