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Question 15.9: A given slope under steady-state seepage has the following: ...

A given slope under steady-state seepage has the following: H = 21.62 m, \phi ^\prime = 25°, slope: 2H:1V, c′ = 20 kN/m², γ = 18.5 kN/m³,  r_u = 0.25. Determine the factor of safety, F_s. Use Table 15.3.

Table 15.3 Values of m′ and n′ [Eq. (15.62)]
a. Stability coefficients m′ and n′ for c′/γH = 0
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
10.0 0.353 0.441 0.529 0.588 0.705 0.749 0.882 0.917
12.5 0.443 0.554 0.665 0.739 0.887 0.943 1.109 1.153
15.0 0.536 0.670 0.804 0.893 1.072 1.139 1.340 1.393
17.5 0.631 0.789 0.946 1.051 1.261 1.340 1.577 1.639
20.0 0.728 0.910 1.092 1.213 1.456 1.547 1.820 1.892
22.5 0.828 1.035 1.243 1.381 1.657 1.761 2.071 2.153
25.0 0.933 1.166 1.399 1.554 1.865 1.982 2.332 2.424
27.5 1.041 1.301 1.562 1.736 2.082 2.213 2.603 2.706
30.0 1.155 1.444 1.732 1.924 2.309 2.454 2.887 3.001
32.5 1.274 1.593 1.911 2.123 2.548 2.708 3.185 3.311
35.0 1.400 1.750 2.101 2.334 2.801 2.977 3.501 3.639
37.5 1.535 1.919 2.302 2.558 3.069 3.261 3.837 3.989
40.0 1.678 2.098 2.517 2.797 3.356 3.566 4.196 4.362
b. Stability coefficients m′ and n′ for c′/γH = 0.025 and D = 1.00
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
10.0 0.678 0.534 0.906 0.683 1.130 0.846 1.367 1.031
12.5 0.790 0.655 1.066 0.849 1.337 1.061 1.620 1.282
15.0 0.901 0.776 1.224 1.014 1.544 1.273 1.868 1.534
17.5 1.012 0.898 1.380 1.179 1.751 1.485 2.121 1.789
20.0 1.124 1.022 1.542 1.347 1.962 1.698 2.380 2.05
22.5 1.239 1.150 1.705 1.518 2.177 1.916 2.646 2.317
25.0 1.356 1.282 1.875 1.696 2.400 2.141 2.921 2.596
27.5 1.478 1.421 2.050 1.882 2.631 2.375 3.207 2.886
30.0 1.606 1.567 2.235 2.078 2.873 2.622 3.508 3.191
32.5 1.739 1.721 2.431 2.285 3.127 2.883 3.823 3.511
35.0 1.880 1.885 2.635 2.505 3.396 3.160 4.156 3.849
37.5 2.030 2.060 2.855 2.741 3.681 3.458 4.510 4.209
40.0 2.190 2.247 3.090 2.993 3.984 3.778 4.885 4.592
c. Stability coefficients m′ and n′ for c′/γH = 0.025 and D = 1.25
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
10.0 0.737 0.614 0.901 0.726 1.085 0.867 1.285 1.014
12.5 0.878 0.759 1.076 0.908 1.299 1.098 1.543 1.278
15.0 1.019 0.907 1.253 1.093 1.515 1.311 1.803 1.545
17.5 1.162 1.059 1.433 1.282 1.736 1.541 2.065 1.814
20.0 1.309 1.216 1.618 1.478 1.961 1.775 2.334 2.090
22.5 1.461 1.379 1.808 1.680 2.194 2.017 2.610 2.373
25.0 1.619 1.547 2.007 1.891 2.437 2.269 2.879 2.669
27.5 1.783 1.728 2.213 2.111 2.689 2.531 3.196 2.976
30.0 1.956 1.915 2.431 2.342 2.953 2.806 3.511 3.299
32.5 2.139 2.112 2.659 2.686 3.231 3.095 3.841 3.638
35.0 2.331 2.321 2.901 2.841 3.524 3.400 4.191 3.998
37.5 2.536 2.541 3.158 3.112 3.835 3.723 4.563 4.379
40.0 2.753 2.775 3.431 3.399 4.164 4.064 4.958 4.784
d. Stability coefficients m′ and n′ for c′/γH = 0.05 and D = 1.00
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
10.0 0.913 0.563 1.181 0.717 1.469 0.910 1.733 1.069
12.5 1.030 0.690 1.343 0.878 1.688 1.136 1.995 1.316
15.0 1.145 0.816 1.506 1.043 1.904 1.353 2.256 1.567
17.5 1.262 0.942 1.671 1.212 2.117 1.565 2.517 1.825
20.0 1.380 1.071 1.840 1.387 2.333 1.776 2.783 2.091
22.5 1.500 1.202 2.014 1.568 2.551 1.989 3.055 2.365
25.0 1.624 1.338 2.193 1.757 2.778 2.211 3.336 2.651
27.5 1.753 1.480 1.380 1.952 3.013 2.444 3.628 2.948
30.0 1.888 1.630 2.574 2.157 3.261 2.693 3.934 3.259
32.5 2.029 1.789 2.777 2.370 3.523 2.961 4.256 3.585
35.0 2.178 1.958 2.990 2.592 3.803 3.253 4.597 3.927
37.5 2.336 2.138 3.215 2.826 4.103 3.574 4.959 4.288
40.0 2.505 2.332 3.451 3.071 4.425 3.926 5.344 4.668
e. Stability coefficients m′ and n′ for c′/γH = 0.05 and D = 1.25
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
10.0 0.919 0.633 1.119 0.766 1.344 0.886 1.594 1.042
12.5 1.065 0.792 1.294 0.941 1.563 1.112 1.850 1.300
15.0 1.211 0.950 1.471 1.119 1.782 1.338 2.109 1.562
17.5 1.359 1.108 1.650 1.303 2.004 1.567 2.373 1.831
20.0 1.509 1.266 1.834 1.493 2.230 1.799 2.643 2.107
22.5 1.663 1.428 2.024 1.690 2.463 2.038 2.921 2.392
25.0 1.822 1.595 2.222 1.897 2.705 2.287 3.211 2.690
27.5 1.988 1.769 2.428 2.113 2.957 2.546 3.513 2.999
30.0 2.161 1.950 2.645 2.342 3.221 2.819 3.829 3.324
32.5 2.343 2.141 2.873 2.583 3.500 3.107 4.161 3.665
35.0 2.535 2.344 3.114 2.839 3.795 3.413 4.511 4.025
37.5 2.738 2.560 3.370 3.111 4.109 3.740 4.881 4.405
40.0 2.953 2.791 3.642 3.400 4.442 4.090 5.273 4.806
f. Stability coefficients m and n for c/GH 0.05 and D 1.50
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
10.0 1.022 0.751 1.170 0.828 1.343 0.974 1.547 1.108
12.5 1.202 0.936 1.376 1.043 1.589 1.227 1.829 1.399
15.0 1.383 1.122 1.583 1.260 1.835 1.480 2.112 1.690
17.5 1.565 1.309 1.795 1.480 2.084 1.734 2.398 1.983
20.0 1.752 1.501 2.011 1.705 2.337 1.993 2.690 2.280
22.5 1.943 1.698 2.234 1.937 2.597 2.258 2.990 2.585
25.0 2.143 1.903 2.467 2.179 2.867 2.534 3.302 2.902
27.5 2.350 2.117 2.709 2.431 3.148 2.820 3.626 3.231
30.0 2.568 2.342 2.964 2.696 3.443 3.120 3.967 3.577
32.5 2.798 2.580 3.232 2.975 3.753 3.436 4.326 3.940
35.0 3.041 2.832 3.515 3.269 4.082 3.771 4.707 4.325
37.5 3.299 3.102 3.817 3.583 4.431 4.128 5.112 4.735
40.0 3.574 3.389 4.136 3.915 4.803 4.507 5.543 5.171
g. Stability coefficients m′ and n′ for c′/γH = 0.075 and toe circles
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
20 1.593 1.158 2.055 1.516 2.498 1.903 2.934 2.301
25 1.853 1.430 2.426 1.888 2.980 2.361 3.520 2.861
30 2.133 1.730 2.826 2.288 3.496 2.888 4.150 3.461
35 2.433 2.058 3.253 2.730 4.055 3.445 4.846 4.159
40 2.773 2.430 3.737 3.231 4.680 4.061 5.609 4.918
h. Stability coefficients m′ and n′ for c′/γH = 0.075 and D = 1.00
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
20 1.610 1.100 2.141 1.443 2.664 1.801 3.173 2.130
25 1.872 1.386 2.502 1.815 3.126 2.259 3.742 2.715
30 2.142 1.686 2.884 2.201 3.623 2.758 4.357 3.331
35 2.443 2.030 3.306 2.659 4.177 3.331 5.024 4.001
40 2.772 2.386 3.775 3.145 4.785 3.945 5.776 4.759
i. Stability coefficients m′ and n′ for c′/γH = 0.075 and D = 1.25
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
20 1.688 1.285 2.071 1.543 2.492 1.815 2.954 2.173
25 2.004 1.641 2.469 1.957 2.972 2.315 3.523 2.730
30 2.352 2.015 2.888 2.385 3.499 2.857 4.149 3.357
35 2.728 2.385 3.357 2.870 4.079 3.457 4.831 4.043
40 3.154 2.841 3.889 3.428 4.729 4.128 5.603 4.830
j. Stability coefficients m′ and n′ for c′/γH = 0.075 and D = 1.50
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
20 1.918 1.514 2.199 1.728 2.548 1.985 2.931 2.272
25 2.308 1.914 2.660 2.200 3.083 2.530 3.552 2.915
30 2.735 2.355 3.158 2.714 3.659 3.128 4.128 3.585
35 3.211 2.854 3.708 3.285 4.302 3.786 4.961 4.343
40 3.742 3.397 4.332 3.926 5.026 4.527 5.788 5.185
k. Stability coefficients m′ and n′ for c′/γH = 0.100 and toe circles
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
20 1.804 2.101 2.286 1.588 2.748 1.974 3.190 2.361
25 2.076 1.488 2.665 1.945 3.246 2.459 3.796 2.959
30 2.362 1.786 3.076 2.359 3.770 2.961 4.442 3.576
35 2.673 2.130 3.518 2.803 4.339 3.518 5.146 4.249
40 3.012 2.486 4.008 3.303 4.984 4.173 5.923 5.019
l. Stability coefficients m′ and n′ for c′/γH = 0.100 and D = 1.00
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
20 1.841 1.143 2.421 1.472 2.982 1.815 3.549 2.157
25 2.102 1.430 2.785 1.845 3.458 2.303 4.131 2.743
30 2.378 1.714 3.183 2.258 3.973 2.830 4.751 3.372
35 2.692 2.086 3.612 2.715 4.516 3.359 5.426 4.059
40 3.025 2.445 4.103 3.230 5.144 4.001 6.187 4.831
m. Stability coefficients m′ and n′ for c′/γH = 0.100 and D = 1.25
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
20 1.874 1.301 2.283 1.558 2.751 1.843 3.253 2.158
25 2.197 1.642 2.681 1.972 3.233 2.330 3.833 2.758
30 2.540 2.000 3.112 2.415 3.753 2.858 4.451 3.372
35 2.922 2.415 3.588 2.914 4.333 3.458 5.141 4.072
40 3.345 2.855 4.119 3.457 4.987 4.142 5.921 4.872
n. Stability coefficients m′ and n′ for c′/γH = 0.100 and D = 1.50
\phi ^\prime Stability coefficients for earth slopes
Slope 2:1 Slope 3:1 Slope 4:1 Slope 5:1
m′ n′ m′ n′ m′ n′ m′ n′
20 2.079 1.528 2.387 1.742 2.768 2.014 3.158 2.285
25 2.477 1.942 2.852 2.215 3.297 2.542 3.796 2.927
30 2.908 2.385 3.349 2.728 3.881 3.143 4.468 3.614
35 3.385 2.884 3.900 3.300 4.520 3.800 5.211 4.372
40 3.924 3.441 4.524 3.941 5.247 4.542 6.040 5.200
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