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Das's cantilever retaining wall (Example 7.1) and 2 m square footing (Examples 3.1 and 3.2): overturning, sliding, bearing and allowable load

Tool	Retaining Wall and Footing
Source	Das, B. M. (2011). Principles of Foundation Engineering, 7th ed. Cengage Learning, Stamford, CT. Example 7.1 (cantilever wall, Figure 7.11, Rankine active pressure with a sloping backfill) and Examples 3.1 / 3.2 (Terzaghi and general bearing-capacity equations); required factors after U.S. Army Corps of Engineers (1989), Retaining and Flood Walls, EM 1110-2-2502, Table 4-1.
Level	Undergraduate

Problem

A cantilever wall has a 6 m stem (0.5 m at the top, 0.7 m at the base), a 0.7 m base slab with a 0.7 m toe and a 2.6 m heel (B = 4 m), 1.5 m of soil in front of the toe and a backfill sloping at 10°; the backfill has γ = 18 kN/m³ and φ′ = 30°, the foundation soil γ = 19 kN/m³, φ′ = 20°, c′ = 40 kN/m², and the concrete 23.58 kN/m³. Find the factors of safety against overturning, sliding (with the passive resistance) and bearing-capacity failure and the toe and heel pressures. Separately, a 2 m square footing at 1.5 m depth in soil with φ′ = 25°, c′ = 20 kN/m², γ = 16.5 kN/m³ carries a vertical load: find the allowable gross load with FS = 3 by Terzaghi's equation and by the general equation.

Inputs to Enter

Wall: stem 6 m high, 0.5 / 0.7 m wide, base 0.7 m thick, toe 0.7 m, heel 2.6 m, soil depth at toe 1.5 m; backfill γ 18 kN/m³, φ′ 30°, c′ 0, slope 10°; foundation soil γ 19 kN/m³, φ′ 20°, c′ 40 kPa; concrete 23.58 kN/m³; Rankine, passive included, δ_b = ⅔ φ′, k_2 = ⅔; required FS 2.0 / 1.5 / 3.0
Footing: 2 × 2 m, D_f 1.5 m, γ 16.5 kN/m³, φ′ 25°, c′ 20 kPa, no water table, V = 1,437 kN, FS 3, general equation (Das); settlement with E_s 30,000 kPa, μ_s 0.3, rigid

Open the Retaining Wall and Footing tool (loaded with this example)

Answers

Wall: K_a = 0.3495 (book 0.350), H′ = 7.158 m, P_a = 161.2 kN/m (book 161.4), ΣV = 470.4 kN/m, ΣM_R = 1,128.9 kN·m/m, M_o = 378.8 kN·m/m (book 379.3) → FS overturning 2.98 (book 2.98)
Wall: K_p = 2.04, P_p = 215 kN/m, resistance 433.2 kN/m → FS sliding 2.73 (book 2.73); e = 0.405 m < B/6, q_toe = 189.1 kN/m² (book 189.2), q_heel = 46.1 kN/m² (book 45.99); q_u = 571 kN/m² → FS bearing 3.02 (book about 3.0)
Footing, Terzaghi: N_c 25.13, N_q 12.72, N_γ 8.34; q_u = 1,078 kN/m², q_all = 359.5 kN/m², Q_all = 1,437 kN (book 1,078 / 359.4 / 1,437)
Footing, general equation: N_c 20.72, N_q 10.66, N_γ 10.88, F_cs 1.514, F_qs 1.466, F_γs 0.6, F_cd 1.257, F_qd 1.233; q_u = 1,374 kN/m², q_all = 458.0 kN/m², Q_all = 1,832 kN (book 1,373.2 / 457.7 / 1,830.8)
Elastic settlement (tool's own case, not in the book): rigid footing S_e = 21.2 mm under the net pressure 334.5 kN/m²

Notes

The tool's default inputs are these two examples; press Submit. The small differences from the book come from Das rounding K_a to 0.350 and the factors to three figures. The bearing-capacity check of the wall uses the 7th-edition depth factor F_cd = F_qd − (1 − F_qd)/(N_c tan φ′); older editions print 1 + 0.4 D/B′ and a slightly higher q_u.