Tools › Civil and Geotechnical › Soils › Slope Stability › Example

EM 1110-2-1902 end-of-construction embankment: Simplified Bishop, Modified Swedish and Spencer on the manual's circle, with the critical-circle search

ToolSlope Stability
SourceU.S. Army Corps of Engineers (2003). Slope Stability. Engineer Manual EM 1110-2-1902, Department of the Army, Washington, DC. Appendix F, Figures F-10 to F-12 (end-of-construction example, Simplified Bishop and Modified Swedish hand calculations); Appendix C, eqs C-12, C-15 and C-19 to C-21.
LevelGraduate

Problem

An embankment rises 91 ft above a level foundation on a 3H:1V face to elevation 58 ft and a 2.5H:1V face to the crest. The compacted fill has a total unit weight of 135 lb/ft³ and undrained strengths c = 1,780 lb/ft², φ = 5°; the foundation 127 lb/ft³, c = 1,600 lb/ft², φ = 2°; there is no water. For the trial circle whose centre lies 101 ft horizontally from the toe and 259 ft above it (R = 278 ft), find the factor of safety by the Ordinary Method of Slices, the Simplified Bishop method, the Simplified Janbu method and Spencer's method, and search the centre grid for the critical circle.

Inputs to Enter

  • Ground surface (−100, 0) (0, 0) (174, 58) (256.5, 91) (400, 91) ft; one boundary at y = 0; layers: Embankment 135 / 1,780 / 5°, Foundation 127 / 1,600 / 2°
  • No piezometric line, no surcharge, k_h = 0, no tension crack; specified circle x_c = 101, y_c = 259, R = 278 ft; 30 slices; search with automatic bounds by Simplified Bishop; required F = 1.3 (Table 3-1, end of construction)
Open the Slope Stability tool (loaded with this example)

Answers

  • Manual's ten hand slices (widths 57, 44, 36, 37, 28, 26, 29, 22, 22, 17 ft from the toe): Σ W sin α = 533 kips (manual 524 with rounded values), Bishop F = 1.341 (manual 1.33), Modified Swedish at θ = 19.7° F = 1.363 (manual 1.36) with a force imbalance of 75.5 kips at the trial F = 1.6 (manual 75)
  • Tool's 33 slices on the same circle: OMS 1.310, Simplified Bishop 1.329, Simplified Janbu 1.275 uncorrected and 1.357 with f_0 = 1.064, Spencer 1.326 at θ = 9.15°; requirement F ≥ 1.3 satisfied by Bishop and Spencer on this circle
  • Search (9 × 9 centres, 7 + 2 tangent elevations, Bishop): the minimum lies at the lower tangent bound (a deep circle in the weaker foundation, F about 1.10 by Bishop and Spencer), which the page reports; the manual itself says its circle is not the most critical one

Notes

The tool's default inputs are this slope; press Submit. The manual's Figure F-11 / F-12 tables print their width, average-height and base-length columns in reverse row order (toe to crest); the c Δx column shows it. Every value is checked by test_slope_stability.php (241 checks) against the manual's Appendix F tables, the UTEXAS2 user's manual examples (Spencer 2.899 at 20.53°, the Example 3 critical circles) and the numpy script in References/Slope-Stability/checks/.