Elastic Settlement Calculator — Schmertmann
The Schmertmann method is the most widely used tool for estimating the immediate settlement of footings on granular soils. Based on the modulus Es derived from CPT, SPT or pressuremeter, and the influence factor Iz which distributes strain with depth, this calculator provides the total settlement with correction factors C1 (embedment) and C2 (creep). It applies to sands, silty sands and gravels where consolidation is not the governing mechanism.
What is it and when is it applied?
Schmertmann proposed in 1970 (updated 1978) that settlement under a footing is calculated by integrating vertical strains over a zone of influence of depth 2B (square footing) or 4B (strip footing). The method applies to granular soils where settlement is mostly elastic-plastic and occurs during construction. It is not appropriate for saturated clays, which require consolidation analysis. It is used in residential, industrial and road foundation buildings on sand.
Applied formulas
Settlement: s = C1 · C2 · Δp · Σ (Iz / Es) · Δz
Embedment factor: C1 = 1 − 0.5 · (σ'0 / Δp) ≥ 0.5
Creep factor: C2 = 1 + 0.2 · log (t_years / 0.1); for t = 1 year, C2 = 1.2
Elastic modulus from CPT: Es = α · qc; α = 2.5 square footing, α = 3.5 strip footing
Elastic modulus from SPT: Es (kPa) ≈ 766 · N60 (normal sands); Es ≈ 1 930 · N60 (dense gravels)
Iz factor (square footing): increases linearly from 0.1 at the base to Iz,max = 0.5 + 0.1·√(Δp/σ'_zp) at z = B/2; decreases linearly to 0 at z = 2B.
Iz factor (strip footing): Iz,max at z = B, zero at z = 4B.
Calculation example
| Parameter | Value |
|---|---|
| B × L | 3.0 × 3.0 m (square) |
| Δp (net pressure) | 150 kPa |
| Df | 1.5 m |
| γ | 18 kN/m³ |
| Average qc (CPT) 0-6 m below base | 8 MPa |
| Design working life considered | 25 years |
σ'0 at footing level = 18 × 1.5 = 27 kPa. C1 = 1 − 0.5 · (27 / 150) = 1 − 0.09 = 0.91. C2 for t = 25 years: 1 + 0.2 · log(25 / 0.1) = 1 + 0.2 · log(250) = 1 + 0.2 · 2.40 = 1.48. Iz,max ≈ 0.5 + 0.1·√(150/σ'zp); with σ'zp at depth B/2 = 1.5 m below base = 18 × (1.5 + 1.5) = 54 kPa → Iz,max = 0.5 + 0.1·√(150/54) = 0.5 + 0.167 = 0.67. We divide the zone 0-2B = 0-6 m into two segments with average Iz: segment 0-1.5 m → Iz avg ≈ 0.38 (from 0.1 to 0.67); segment 1.5-6 m → Iz avg ≈ 0.37 (from 0.67 to 0). Modulus Es = 2.5 × 8 000 = 20 000 kPa. Σ(Iz/Es)·Δz = (0.38/20000)·1.5 + (0.37/20000)·4.5 = 2.85·10⁻⁵ + 8.33·10⁻⁵ = 1.12·10⁻⁴. Settlement s = 0.91 · 1.48 · 150 · 1.12·10⁻⁴ = 0.0226 m = 22.6 mm.
Result: s (25 years) ≈ 23 mm; immediate settlement (t→0, C2=1) ≈ 15 mm.
Interpretation of results
23 mm is a tolerable settlement for a rigid warehouse structure, generally accepted up to 25 mm for isolated footings of ordinary buildings. If the result exceeds 50 mm, the footing should be enlarged, a raft foundation constructed, or the ground improved. Differential settlements between adjacent footings are more concerning than total settlements: typically limited to L/500 where L is the column spacing.
Reference standards
- Schmertmann, J.H. (1970). Static cone to compute static settlement over sand. JSMFD, ASCE 96(SM3)
- Schmertmann, J.H.; Hartman, J.P.; Brown, P.R. (1978). Improved strain influence factor diagrams. JGED, ASCE 104(GT8)
- BS EN 1997-1 (Eurocode 7) — Geotechnical design of foundations
- BS EN ISO 22476-1 — Cone Penetration Test (CPT)
- BS EN ISO 22476-3 — Standard Penetration Test (SPT)
Frequently asked questions
Does Schmertmann work for clays?
No. The method assumes the soil is granular with elastic-plastic behaviour. In saturated clays, consolidation settlement dominates and requires Terzaghi analysis (Cc, Cv). Applying Schmertmann to soft clay grossly underestimates the actual settlement.
How do I estimate Es if I only have SPT?
Typical correlations: Es (kPa) ≈ 766 · N60 for natural sands, 1 930 · N60 for dense gravels, and 500-700 · N60 for silty sands. These are estimates with high scatter (±30 %). If possible, use CPT (qc–Es relationship better established).
What time do I use for C2?
Usually s is reported at t = 1 year (C2 = 1.2) and s at t = 25-50 years (C2 = 1.4-1.5) for design working life. For warehouses and light structures, 1 year is sufficient. For bridges or tall buildings, it is recommended to report both.
Why is Iz not maximum at the base of the footing?
Due to the distribution of elastic stresses: at the base, vertical strain is restrained by the footing itself. The peak occurs at B/2 (square) or B (strip) where the soil response is maximum. This is an empirical result validated with hundreds of field measurements.