Bearing capacity and settlement
The geotechnical check of a shallow foundation: the ultimate bearing capacity of a strip, square, rectangular or circular footing on one bearing stratum, by the general bearing capacity equation in the form of FHWA GEC 6 (2002) Eq. 5-14 with the factors of the method the engineer chooses, checked against the bearing pressure on Meyerhof's effective footing; and the settlement of a layered profile below the base (immediate settlement of granular layers, primary consolidation of clay layers). The footing's concrete design is done in the footing types (spread, wall, combined footing); this type answers the soil questions they take as inputs.
Inputs of the bearing capacity check #
- Footing: shape (strip: loads per ft of length), width B (diameter of a circle), length L (rectangular), depth Df from grade to the base, and, when its weight is included as dead load, the footing thickness (concrete at 150 pcf, the backfill above at the unit weight above the base).
- Bearing stratum: cohesion c and friction angle φ (undrained: c = su with φ = 0; drained: c', φ'), the total unit weight below the base and above it, and the groundwater depth below grade (the highest anticipated level). These come from the geotechnical report; GEC 6 Figs. 4-1 and 4-2 correlate SPT values with φ.
- Method (engineer's choice): Terzaghi (1943; his own shape factors 1.3 / 0.8 / 0.6), Meyerhof (1963), Hansen (1970) or Vesić (1973), the set FHWA GEC 6 Table 5-1 and AASHTO use, with the shape factors of GEC 6 Table 5-2. Depth factors are off by default: GEC 6 5.2.3.3 includes them only when the cover is high-quality compacted granular fill that will stay in place.
- Factor of safety (ASD, 3.0 usual, GEC 6 5.2.6) or resistance factor φb (LRFD; 0.45 prefilled, the AASHTO value for the theoretical method in sand, to confirm against the code text). The method switch picks the ASCE 7-22 2.4.1 (ASD) or 2.3.1 (LRFD) combinations.
- Loads: per load type, unfactored, at the base center: P down, MB (moves the resultant across B) and ML (along L).
- Settlement: the stress below the center (Boussinesq or 2:1), the part of L in the settlement load (sustained live load for consolidation), net or gross pressure, the layers below the base (granular: Es; clay: Cc, Cr, e0, OCR = σ'p/σ'0) and the limit set by the structure.
Auto-design varies the footing width B in 0.5-ft steps (a rectangular footing keeps its L/B ratio); depth, soil, method, loads and factor of safety are the engineer's. See Auto-design.
Checks performed #
| Check | Basis |
|---|---|
| Bearing: P / (B'L') ≤ qult / FS (ASD) or φb qult (LRFD), every combination | GEC 6 Eq. 5-14: qult = c Nc sc dc + q Nq sq dq Cwq + 0.5 γ B' Nγ sγ dγ Cwγ |
| Factors | Vesić: Nq = e^(π tan φ) tan²(45° + φ/2), Nc = (Nq − 1) cot φ (5.14 at φ = 0), Nγ = 2(Nq + 1) tan φ; Meyerhof Nγ = (Nq − 1) tan 1.4φ; Hansen Nγ = 1.5(Nq − 1) tan φ; Terzaghi Nq = e^(2(3π/4 − φ/2) tan φ)/(2 cos²(45° + φ/2)) |
| Shape factors | GEC 6 Table 5-2: sc = 1 + (B/L)(Nq/Nc) (1 + B/5L at φ = 0), sq = 1 + (B/L) tan φ, sγ = 1 − 0.4 B/L; Meyerhof with Kp; Hansen sq with sin φ |
| Groundwater | GEC 6 Eqs. 5-9, 5-10: Cwq = 0.5 + 0.5 Dw/Df ≤ 1, Cwγ = 0.5 + 0.5 (Dw − Df)/(1.5B) between 0.5 and 1 |
| Eccentric load | Meyerhof: B' = B − 2eB, L' = L − 2eL; the resultant inside the footing (else not feasible); an advisory when it leaves the middle third |
| Settlement ≤ limit | Δσ below the center (Boussinesq: Newmark's corner solution, strip and circle closed forms; or 2:1); granular Δσ H/Es; clay Cc H/(1 + e0) log((σ'0 + Δσ)/σ'0), with Cr up to σ'p |
The drawings show the section (footing at its depth, grade, groundwater, the settlement layers) and, for a finite footing, the plan with the effective area of the governing combination hatched.
Limitations #
- One bearing stratum: a weaker layer within about 2B below the base (punching) is not checked; enter the weaker layer's strength or use a layered method.
- Vertical loads only: load inclination factors are not applied (GEC 6 notes they should not be combined with shape factors); sliding and overturning are checked in the footing types.
- Level ground; footings on or near slopes (GEC 6 5.2.3.5, Ncq and Nγq) and rock are not covered.
- A moment on a circular footing is not covered (enter an equivalent square).
- Terzaghi's Nγ uses Coduto's closed approximation of his chart (to confirm against the source).
- The settlement is the immediate and primary consolidation settlement below the center; time rate, secondary compression and differential settlement are not computed. Δσ H / Es is a one-dimensional estimate with the modulus the engineer enters.
Verification examples #
Verification status: 20 values compared in 8 examples (3 published, 5 hand calculations from the cited equations): 19 within tolerance, 1 recorded deviations. Code basis: the provisions it uses were read in the target edition.
Published worked examples (backend/tests/test_verify_bearing_capacity.py):
| Source | What it checks | Published | ILX Calcs |
|---|---|---|---|
| FHWA GEC 6 (2002) Table 5-1 | Nc, Nq, Nγ at 30° and 35° | 30.1, 18.4, 22.4; Nq 33.3, Nγ 48.0 | ≈ 30.14, 18.40, 22.40; 33.30, 48.03 (hand-checked) |
| FHWA GEC 6 Appendix B Example 1, Step 7 (interior pier, φ = 35°, Df = 2.3 m) | sq, sγ, surcharge term | 1.7, 0.6, 2,553 kPa | ≈ 1.700, 0.6, 2,552 kPa |
| same | unit weight term at Bf = 6 m (deviation: the example rounds Cwγ to 0.9) | 1,524 kPa | ≈ 1,487 kPa |
| GEC 6 Tables 5-1, 5-2 | undrained Nc and sc of a square | 5.14, 1.2 | 5.14, 1.2 |
Hand calculations cover Terzaghi's, Meyerhof's and Hansen's factors, Meyerhof's effective width of an eccentric strip, and the consolidation of a normally consolidated clay layer under the 2:1 stress. No published worked settlement example with these inputs was found on disk (the open textbook of Kouretzis has settlement examples, but their numbers are figures in the text copy).