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

Name: Consolidation Settlement Calculator
Availability: InStock
Author: Nham Vu

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