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
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.
(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, , 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, are 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
Fig.1
Fig.2
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
Fig.3
Fig.4
Fig.5
Fig.6
Fig.7
Fig.8
Fig.9
Fig.10
Fig.11
Fig.12
Fig.13
Fig.14
Fig.15
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
1
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