1D Consolidation Calculator — Terzaghi
In saturated fine-grained soils, settlement does not occur during construction but months or years afterwards. Terzaghi's one-dimensional consolidation theory is the standard model for predicting how much clay will settle and in what time. This calculator combines oedometer test parameters (Cc, Cr, e0, σ'p) with project stresses to estimate primary settlement and characteristic times t50 and t90 from the coefficient of consolidation Cv and drainage length Hd.
What is it and when is it applied?
1D consolidation applies to saturated clays and silts under vertical load, where the dissipation of excess pore water pressure controls the settlement time. It is used to estimate settlements of buildings, fills on soft ground, port embankments, and to design construction schedules (preloading, wick drains, etc.). It does not apply to sands or rocks, where settlement is essentially immediate and is resolved with Schmertmann or other elastic methods.
Applied formulas
Primary settlement (normally consolidated soil, σ'0 + Δσ > σ'p):
S = [Cc / (1 + e0)] · H · log((σ'0 + Δσ) / σ'0)
Settlement with preconsolidated section:
S = [Cr / (1 + e0)] · H · log(σ'p / σ'0) + [Cc / (1 + e0)] · H · log((σ'0 + Δσ) / σ'p)
Preconsolidation ratio: OCR = σ'p / σ'0
Time factor: Tv = Cv · t / Hd²
Degree of consolidation: U(Tv): U = 50 % → Tv = 0.197; U = 90 % → Tv = 0.848
Times: t50 = 0.197 · Hd² / Cv; t90 = 0.848 · Hd² / Cv
Drainage length: Hd = H if drainage is on one face only; Hd = H/2 if drained from top and bottom.
Calculation example
| Parameter | Value |
|---|---|
| Stratum thickness H | 4.0 m |
| Initial void ratio e0 | 0.95 |
| Compression index Cc | 0.32 |
| Recompression index Cr | 0.045 |
| Initial effective stress σ'0 | 80 kPa |
| Preconsolidation pressure σ'p | 120 kPa |
| Increment Δσ | 100 kPa |
| Cv | 1.2 × 10⁻⁷ m²/s |
| Drainage | Double (sand above and below) |
OCR = 120 / 80 = 1.5 (slightly preconsolidated). Final stress σ'0 + Δσ = 180 kPa, greater than σ'p = 120. The settlement has two sections: S1 (preconsolidated section) = (0.045 / 1.95) · 4.0 · log(120/80) = 0.0231 · 4 · 0.176 = 0.0163 m. S2 (normally consolidated section) = (0.32 / 1.95) · 4.0 · log(180/120) = 0.1641 · 4 · 0.176 = 0.1155 m. Total S = 0.0163 + 0.1155 = 0.132 m = 132 mm. Hd = 4.0 / 2 = 2.0 m (double drainage). t50 = 0.197 · 4 / (1.2·10⁻⁷) = 6.57·10⁶ s = 76 days. t90 = 0.848 · 4 / (1.2·10⁻⁷) = 2.83·10⁷ s = 327 days.
Result: S = 132 mm · t50 = 76 days · t90 = 327 days (≈ 11 months).
Interpretation of results
132 mm is a significant settlement requiring measures: preloading with temporary surcharge, vertical wick drains to accelerate, deep foundations (piles to underlying firm stratum) or a flexible structure capable of absorbing the movement. t90 close to one year requires planning construction considering prior consolidation before paving or installation of sensitive equipment. Piles passing through the stratum may experience negative skin friction during consolidation.
Reference standards
- BS 1377-5 — Methods of test for soils for civil engineering purposes. Compressibility, permeability and durability tests
- BS EN ISO 17892-5 — Geotechnical investigation and testing. Laboratory testing of soil. Incremental loading oedometer test
- Terzaghi, K. (1943). Theoretical Soil Mechanics — Chapters 13-15
- BS EN 1997-1 — Eurocode 7: Geotechnical design. General rules
- Casagrande, A. (1936). Determination of the preconsolidation load and its practical significance
Frequently asked questions
How do I obtain σ'p from the test?
Casagrande method: on the e vs log σ' curve, identify the point of maximum curvature and draw the tangent and horizontal; σ'p is the intersection with the bisector. The Schmertmann method is more reproducible. Laboratory software usually provides the value directly.
What about secondary consolidation?
After completing pore pressure dissipation, the soil continues to settle at a decreasing rate due to creep. It is estimated with Cα (secondary compression index) and can represent 10-30 % of primary settlement in highly compressible clays and peats.
How do I accelerate consolidation on site?
Preloading with a surcharge greater than the final load plus prefabricated vertical drains (PVD or sand wick). Reduces t90 from years to weeks. It is the most economical technique before opting for piles or deep treatments.
When is the soil underconsolidated?
When σ'p < σ'0, i.e., it has not yet finished consolidating under its own weight. Typical in recent fills or young alluvial deposits. Requires a different analysis because it already has "committed" settlement before applying new loads.