Settlements

Settlements are computed with the service (SLS) combinations. The Settlements tab reports, for the selected combination, the elastic and oedometric contributions per layer, the optional Burland & Burbidge estimate and the time curve.

With which loads

Unlike the bearing capacity (ULS), settlements are evaluated with the service pressures. The combination selector at the top of the tab lets you switch between SLS combinations.

Elastic settlements (Timoshenko-Goodier)

Immediate settlement of an elastic half-space, computed at the centre and at the edge of the foundation:

w = q·B·(1−ν²)·I / E

where I is an influence factor depending on the shape (B/L) and on the optional rigid substratum depth (bedrock). It needs the elastic modulus E and the Poisson's ratio ν. The result is in mm.

Oedometric settlements

For layers with an oedometric modulus E_ed, the primary consolidation settlement is computed by sublayers. Loadcap offers two formulations:

• One-dimensional: w_c = Δσ·H / E_ed;
• Logarithmic (Terzaghi): w_c = H·RR·log₁₀[(σ′_v0 + Δσ)/σ′_v0], with RR = (σ′_v0 + Δσ)/(0.435·E_ed).

Choose the formulation with the Oedometric method selector. The secondary settlement (creep) is added if the C_s coefficient is defined.

Which method

The logarithmic method is consistent with classic consolidation theory; the one-dimensional one is more direct and conservative for small stress increments. For comparisons with desktop calculations, use the same formulation.

Schmertmann method

For layers with an elastic modulus E but without E_ed, Loadcap applies the Schmertmann method (1970-1978), based on the strain factor I_z:

• net pressure q = q_applied − σ′_v0(D);
• depth factor C₁ = 1 − 0.5·σ′_v0/q (minimum 0.5);
• peak I_z,max = 0.5 + 0.1·√(q/Δp);
• triangular I_z distribution (axisymmetric or plane depending on L/B);
• creep factor C₂ = 1 + 0.2·log₁₀(t/0.1).

The per-layer settlement is w = C₁·q·I_z·H_s/E, in cm.

Burland & Burbidge

Empirical estimate based on the N_SPT blow count, suited to granular soils:

w = f_s·f_h·f_t·(q − ⅔·σ′_v0)·I_c·B^0.7

with I_c the compressibility index (function of N_SPT), and the correction factors f_s (shape), f_h (thickness of the compressible layer) and f_t (time). Enable it with the dedicated checkbox; it requires N_SPT on the layers.

Time-settlement curve

For layers with a consolidation coefficient C_v, Loadcap traces the time curve of the consolidation settlement, from Terzaghi's theory:

• settlement reached at the degree of consolidation U: w(U) = w_t·U/100;
• corresponding time: t(U) = T_v(U)·H²/C_v.

The table reports the pair (consolidation percentage, time in days) up to 100%.

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