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## Fredlund and Krahn Example Problem

The following example problem for verification is taken from the paper by Fredlund and Krahn, titled Comparison of slope stability methods of analysis, and is a simple 2H:1V slope, 40ft (12m) high. The slip center about which moments are calculated remains constant at (120,90).

The geometry for cases 1 and 2 are shown below. A description of all cases follows.

Case 1 Geometry
Case 2 Geometry

Case 1 - Simple 2:1 slope, 40ft (12m) high, Φ' = 20o, c' = 600 psf
Case 2 - Same as 1 with a thin, weak layer with Φ' = 10o, c' = 0
Case 3 - Same as 1 except with ru = 0.25
Case 4 - Same as 2 exception with ru for both materials
Case 5 - Same as 1 except with a piezometric line
Case 6 - Same as 2 except with a piezometric line for both materials

### Published Results

Case
Ordinary
Bishop's Simplified
Janbu's Simplified (Corrected)
Spencer
Morgenstern-Price f(x) = constant
FOS
FOS
FOS
FOS        λ
FOS        λ
1
1.928
2.080
2.041
2.073   0.237
2.076   0.254
2
1.288
1.377
1.448
1.373   0.185
1.378   0.159
3
1.607
1.766
1.735
1.761   0.255
1.765   0.244
4
1.029
1.124
1.191
1.118   0.139
1.124   0.116
5
1.693
1.834
1.827
1.830   0.247
1.833   0.234
6
1.171
1.248
1.333
1.245   0.121
1.250   0.097

### MacSlope Results

Case
Ordinary
Bishop's Simplified
Janbu's Simplified (Corrected)
Spencer
GLE f(x) = constant
FOS
FOS
FOS
FOS        λ
FOS        λ
1
1.929
2.078
2.022
2.076   0.261
2.076   0.259
2
1.299
1.381
1.431
1.378   0.168
1.382   0.176
3
1.608
1.761
1.711
1.760   0.252
1.754   0.250
4
1.039
1.122
1.166
1.121   0.152
1.125   0.154
5
1.695
1.831
1.807
1.827   0.236
1.826   0.240
6
1.173
1.242
1.306
1.240   0.115
1.245   0.124

The MacSlope calculated results are within 2.5% in all cases for all available methods.

Download the MacSlope file for case 6 of this verification example here.

Watch a tutorial video describing how to set up and analze the Fredlund and Krahn example problem below.