Tools › Civil and Geotechnical › Soils › Bearing Capacity and Settlement › Example
2 m square footing in a c-φ soil: Terzaghi, Meyerhof, Hansen and Vesić side by side with USACE EM 1110-1-1905's factors, allowable pressure and settlement
| Tool | Bearing Capacity and Settlement |
| Source | U.S. Army Corps of Engineers (1992). Bearing Capacity of Soils. Engineer Manual EM 1110-1-1905, Department of the Army, Washington, DC. Tables 1-2, 4-1, 4-2, 4-4, 4-5 and 4-6; U.S. Army Corps of Engineers (1990). Settlement Analysis. Engineer Manual EM 1110-1-1904, eq. 3-18 and Table 3-3a. |
| Level | Undergraduate |
Problem
A 2 m square footing bears 1.5 m below grade in a soil with c = 10 kPa, φ = 30° and γ = 18 kN/m³, no water table, under a concentric column load of 1,000 kN. Find the ultimate bearing capacity by the Terzaghi, Meyerhof, Hansen and Vesić equations with the shape and depth factors of EM 1110-1-1905, the allowable pressure at the manual's factor of safety of 3.0 (Table 1-2, footings), the applied pressure and the immediate settlement of the rigid footing for E_s = 67.7 MPa (silty sand, EM 1110-1-1904 Table D-3) and ν = 0.30.
Inputs to Enter
- Square footing B = 2 m, D_f = 1.5 m; soil γ = 18 kN/m³, c = 10 kPa, φ = 30°, no water table
- Vertical load Q = 1,000 kN, no moments, no horizontal load; governing method Vesić; FS = 3.0
- Immediate settlement: E_s = 67.7 MPa, ν = 0.30, rigid footing, semi-infinite soil; allowable settlement 25 mm
Answers
- N factors at φ = 30°: Terzaghi 37.16 / 22.46 / 19.7 (Table 4-1); Meyerhof, Hansen, Vesić N_c 30.14, N_q 18.40, N_γ 15.67 / 15.07 / 22.40 (Table 4-4)
- q_u: Terzaghi 1,373 kPa (ζ_c 1.3, ζ_γ 0.8), Meyerhof 1,752, Hansen 1,747, Vesić 1,826 kPa (De Beer shape 1.611 / 1.577 / 0.600, Hansen depth 1.300 / 1.217 / 1.000)
- Vesić: q_all = 1,826.3 / 3.0 = 608.8 kPa, net allowable 599.8 kPa, Q_all = 2,435 kN; applied q = 1,000 / 4 = 250 kPa ≤ 608.8 kPa (FS available 7.31)
- Immediate settlement: Δp = 223 kPa, I = 1.122 (Table 3-3a 1.12), flexible centre 6.7 mm, rigid 0.99/1.12 × centre = 5.9 mm ≤ 25 mm; Schmertmann 4.6 mm for information
Notes
The tool's default inputs are this footing; press Submit. The factors and the manual's own worked examples (paragraph 4-5: 8.0 / 7.196 ksf for the clay wall footing, 5.25 / 4.69 / 5.86 ksf for the inclined load) are reproduced in test_bearing_capacity.php; the default case itself is checked against the closed forms and a numpy script, not against a printed example.