What's the difference between primary and secondary settlement?

Primary settlement is from pore water dissipation under load (Terzaghi). Secondary is creep at constant effective stress, typically 5–20% of primary for inorganic clays, much more for peat. This calculator handles primary only.

When does C_c apply vs C_r?

C_c (compression index) applies on the virgin compression curve (σ' > σ'_p, normally consolidated). C_r (recompression index) applies below σ'_p (over-consolidated). Mixed path uses C_r up to σ'_p, then C_c. C_r ≈ C_c/10 typical.

What's a typical C_c for clay?

Soft NC clay: C_c = 0.2–0.5. Stiff OC clay: 0.05–0.15. Organic clay or peat: 1.0–5.0+. Empirical Skempton (1944): C_c ≈ 0.009(LL − 10) for normal inorganic clays.

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One-Dim Consolidation Settlement

Primary consolidation settlement of saturated clay from compression index C_c, recompression index C_r, initial void ratio e₀, and stress change. Auto-detects normally consolidated vs over-consolidated stress path.

Units

Clay layer thickness, Hft

Initial void ratio, e₀— (typically 0.5–2.0)

Compression index, C_c— (≈ 0.009 (LL−10) for normal clays)

Recompression index, C_r— (≈ Cc/10)

Initial effective stress, σ'₀psf

Pre-consolidation pressure, σ'_ppsf (= σ'₀ for NC clay)

Stress increment, Δσ'psf (from new fill or footing load)

Final effective stress, σ'_f—psf

OCR——

Stress path——

Settlement, S—in

Defaults: 20 ft soft clay layer, e₀ = 1.1, OCR = 1.5 (slightly over-consolidated), 2500 psf surcharge. Output unit "in" for US (settlement is small) or "mm" for SI.

Normally consolidated (σ'₀ = σ'_p, σ'_f > σ'_p):

$$ S = H \cdot \frac{C_c}{1 + e_0} \cdot \log_{10}\!\!\left(\frac{\sigma'_f}{\sigma'_0}\right) $$

Over-consolidated, σ'_f ≤ σ'_p (recompression only):

$$ S = H \cdot \frac{C_r}{1 + e_0} \cdot \log_{10}\!\!\left(\frac{\sigma'_f}{\sigma'_0}\right) $$

Over-consolidated, σ'_f > σ'_p (mixed path):

$$ S = H \cdot \frac{C_r}{1 + e_0} \log\!\frac{\sigma'_p}{\sigma'_0} + H \cdot \frac{C_c}{1 + e_0} \log\!\frac{\sigma'_f}{\sigma'_p} $$

S primary consolidation settlement · H compressible layer thickness · C_c compression index (slope of e-log σ on virgin curve) · C_r recompression index (slope of unload-reload portion) · e₀ initial void ratio · σ'₀ initial effective stress at midpoint of layer · σ'_p pre-consolidation pressure (max past stress) · Δσ' applied stress change · σ'_f = σ'₀ + Δσ'.

What this calculator does NOT include

Time-rate of settlement (Terzaghi consolidation theory, U vs T_v). Use a separate calc for that.
Secondary compression (creep) — typically 5–20% of primary for inorganic clays, much more for peat/organic soils.
Differential settlement across a footing — distortion is what cracks structures, not total settlement.
Stress distribution from a footing — Δσ' must be the in-situ value at midpoint of the clay layer (use Boussinesq, Westergaard, or 2:1 method to compute).

Pre-consolidation pressure σ'_p

σ'_p is the maximum stress the clay has ever experienced — set by Pleistocene glacial loading, past surcharges, water-table fluctuations, or weathering. Get it from a 1-D consolidation test (oedometer) per ASTM D2435; the Casagrande construction or strain-energy method picks σ'_p off the e-log σ curve.

Ratio of σ'_p/σ'₀ is the over-consolidation ratio (OCR). OCR = 1: normally consolidated (NC), the worst case for settlement. OCR > 4: heavily over-consolidated, settlement is small (recompression only).

Typical Cc values

Soft normally-consolidated clay: C_c = 0.2 to 0.5
Stiff over-consolidated clay: C_c = 0.05 to 0.15
Organic clay or peat: C_c = 1.0 to 5.0+
Empirical (NC inorganic): C_c ≈ 0.009 (LL − 10) where LL is liquid limit (Skempton 1944)
Recompression: C_r ≈ C_c / 10 (typical)

Stress increment Δσ' from a footing

The applied stress at the midpoint of the clay layer is reduced from the footing contact pressure by stress distribution. For a square footing of width B at depth z below the footing base:

Δσ ≈ q × B² / (B + z)² (2:1 method, simple but conservative); or use Boussinesq's elastic point-load solution. For thick layers (clay layer thicker than ~B), use multi-layer integration: divide the clay into 3–5 sub-layers, compute Δσ at each midpoint, settlement of each sub-layer, sum.

Drainage path length and time

Time to consolidate scales with the square of drainage path length H_dr. Two-way drainage (sand layer above and below) gives H_dr = H/2 — much faster than one-way drainage where H_dr = H. For T_v = c_v t / H_dr², U(T_v) read from textbook chart. Typical c_v = 0.5–10 ft²/day (5–100 cm²/day) for clay.

Reference: Terzaghi, K. (1943). Theoretical Soil Mechanics. Wiley. Skempton, A.W. (1944). "Notes on the Compressibility of Clays." Quarterly Journal Geological Society, London. Das, B.M. (2014). Principles of Geotechnical Engineering, 8th ed., Cengage, ch. 11.

One-Dim Consolidation Settlement

What this calculator does NOT include

Pre-consolidation pressure σ'p

Typical Cc values

Stress increment Δσ' from a footing

Drainage path length and time

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Pre-consolidation pressure σ'_p