What is the formula used?

S = (Cc / (1 + e₀)) × H × log₁₀((σ'₀ + Δσ') / σ'₀). This is Terzaghi's primary consolidation equation for normally consolidated clay, where Cc is the compression index, e₀ is the initial void ratio, H is the layer thickness, σ'₀ is the initial effective stress, and Δσ' is the stress increment.

What is the compression index and where do I get it?

The compression index (Cc) is the slope of the linear portion of the e–log σ' curve from a laboratory oedometer (consolidation) test. Typical values range from 0.1–0.5 for soft clays to above 1.0 for very soft organic soils. It can also be estimated from correlations with liquid limit: Cc ≈ 0.009(LL − 10).

What is the initial void ratio?

The initial void ratio (e₀) is the ratio of void volume to solid volume in the soil at the start of loading. It is measured in the laboratory from moisture content and specific gravity tests. For soft clays, e₀ commonly ranges from 0.6 to 2.0 or higher.

Where is the initial effective stress measured?

Use the effective vertical stress at the mid-depth of the clay layer: σ'₀ = γ' × z, where γ' is the submerged unit weight of the overlying soil and z is the depth to the layer midpoint. For saturated soils above the water table, use total unit weight minus water pressure.

Is this for normally consolidated or overconsolidated clay?

This form of the equation applies to normally consolidated (NC) clay, where the current effective stress equals the preconsolidation pressure. For overconsolidated clay where the stress increment crosses the preconsolidation pressure, the swelling index (Cs) and two separate terms are needed.

Does this account for secondary consolidation or creep?

No. The calculator computes primary consolidation only, which is due to drainage of excess pore water. Secondary compression (creep) is a separate, time-dependent process and requires the secondary compression index (Cαε) plus an assumed time horizon.

Consolidation Settlement Calculator

Enter soil parameters to compute the expected primary consolidation settlement of a clay layer under an applied load.

Soil & Load Parameters

Based on Terzaghi one-dimensional consolidation (normally consolidated clay).

Initial Void Ratio (e₀) — dimensionless

Typical range for soft clay: 0.6 – 2.0

Compression Index (C_c) — dimensionless

From oedometer test; estimate: C_c ≈ 0.009(LL − 10)

Clay Layer Thickness (H) — meters

Initial Effective Stress (σ'₀) — kPa

Effective vertical stress at mid-depth of clay layer

Stress Increase (Δσ') — kPa

Increase in effective stress from foundation load at mid-depth

Enter soil parameters and click Calculate

Results appear here after calculation

Terzaghi Primary Consolidation Formula

S = (C_c / (1 + e₀)) × H × log₁₀((σ'₀ + Δσ') / σ'₀)

S — settlement (m)
C_c — compression index (from oedometer)
e₀ — initial void ratio
H — clay layer thickness (m)
σ'₀ — initial effective vertical stress (kPa)
Δσ' — stress increase from applied load (kPa)

Summary

This tool computes primary consolidation settlement — the long-term compression of a clay layer caused by drainage of pore water as effective stress increases under an applied load. It applies Terzaghi's one-dimensional consolidation theory, which is the standard method used in geotechnical engineering for foundations on soft clay. Results are expressed in millimeters and reflect final settlement once excess pore pressure has fully dissipated.

How it works

Enter the initial void ratio (e₀) of the clay layer.
Enter the compression index (Cc) from laboratory oedometer tests.
Input the clay layer thickness (H) in meters.
Provide the initial effective vertical stress (σ'₀) in kPa at the mid-depth of the layer.
Enter the increase in effective stress (Δσ') in kPa caused by the foundation load.
Click Calculate — the tool returns settlement using S = (Cc / (1+e₀)) × H × log₁₀((σ'₀ + Δσ') / σ'₀).

Use cases

Estimate foundation settlement on soft clay deposits.
Check whether calculated settlement is within tolerable limits for a structure.
Compare settlement under different foundation loads during design iteration.
Verify hand calculations from geotechnical lab and oedometer test data.
Support slope stability and embankment design studies.
Educational reference for soil mechanics coursework on consolidation theory.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu