Skip to main content
CalcStack

Settlement & Consolidation of Clay Calculator (Terzaghi)

Formulated by Karl von Terzaghi in 1925, 1D consolidation theory explains time-dependent settlement caused by slow pore-water expulsion from low-permeability clays.

Total thickness of the compressible saturated clay stratum in meters.

In-situ ratio of void volume to solid volume before loading (typical soft clay ≈ 0.7 - 1.5).

Slope of virgin consolidation line on e-log σ plot from oedometer test.

Slope of recompression/swelling curve (typically 5% to 15% of Cc).

In-situ overburden effective vertical stress at mid-depth of clay layer.

Net vertical stress increase transmitted by structural footing or embankment fill.

Past maximum overburden stress (if equal to σ₀', clay is Normally Consolidated).

Calculated Result
166.57 mm

Consolidation Settlement

Primary Consolidation Settlement

166.57 mm (16.66 cm / 6.558 in)

Consolidation Stress State

Normally Consolidated (NC)

Initial vs Final Void Ratio

e₀ = 0.85 → e_f = 0.788

Vertical Strain (ΔH / H)

3.33%

Effective Stress Range

120 kPa → 180 kPa (Δσ' = 60 kPa)

Calculation Breakdown

  1. 1. Stress Ratio FormulationInitial σ₀' = 120 kPa, Added Δσ' = 60 kPa, Final σ_f' = 180 kPa. Log₁₀(σ_f'/σ₀') = 0.1761
  2. 2. Settlement EquationS_c = [C_c · H / (1 + e₀)] · log₁₀(σ_f' / σ₀') = [0.35 · 5 m / (1 + 0.85)] · 0.1761 = 0.1666 m
  3. 3. Volume & Strain ChangesVertical strain = 3.33%, resulting in final void ratio e_f = 0.788 (settlement = 166.57 mm).

Settlement vs Added Structural Stress (Δσ)

Interactive visualization based on your current inputs

Settlement (mm)
0.06112318424620 kPa40 kPa60 kPa80 kPa100 kPaAdded Stress (kPa)Settlement (mm)

What Is the Settlement & Consolidation of Clay Calculator (Terzaghi)?

One-dimensional consolidation settlement represents the long-term vertical deformation of saturated fine-grained soils subjected to sustained load increments.

How Does the Settlement & Consolidation of Clay Calculator (Terzaghi) Work?

As excess pore water drains, hydraulic stress transfers to the mineral soil skeleton, compressing void volume logarithmically.

Settlement & Consolidation of Clay Calculator (Terzaghi) Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

S_c = \frac{C_c \cdot H}{1 + e_0} \log_{10}\left(\frac{\sigma_0' + \Delta\sigma'}{\sigma_0'}\right), \quad \Delta e = \frac{S_c}{H} (1 + e_0)

Settlement equals compression index times thickness over 1 plus initial void ratio times log base 10 of final stress over initial stress.

How to Use the Settlement & Consolidation of Clay Calculator (Terzaghi)

  1. Enter the clay stratum thickness and initial void ratio e₀.
  2. Input the laboratory oedometer compression index Cc.
  3. Specify initial overburden stress and net structural stress increment.

Step-by-Step Example Calculation

5m Normally Consolidated Clay Layer (120 to 180 kPa)

Input Values:

clayLayerThicknessM:5.0
initialVoidRatioE0:0.85
compressionIndexCc:0.35
recompressionIndexCr:0.04
initialEffectiveStressKPa:120
stressIncreaseKPa:60
preconsolidationPressureKPa:120
Worked Steps: Under 60 kPa structural load, the 5m clay layer compresses by 166.69 mm (16.67 cm), reducing void ratio from 0.85 to 0.788.

Understanding Your Result

Consolidation Settlement (mm/cm): Total expected vertical downward settlement.

Stress History: Normally consolidated vs overconsolidated behavior.

Final Void Ratio: Compacted post-settlement void structure.

Vertical Strain (%): Percentage reduction in layer thickness.

Factors That Affect the Result

  • Clay thickness H and compression index Cc scale settlement directly; higher preconsolidation pressure lowers settlement.

When Should You Use This Calculator?

  • Building mat foundation design, highway embankment fill, reclamation settlement prediction, and airport runway paving.

Assumptions & Limitations

  • Assumes 1D vertical drainage and compression with complete saturation (S = 100%) and constant compression index.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard Terzaghi one-dimensional consolidation settlement formulation.

Related Calculators

Explore more tools and calculators in Math Calculators

Soil Nail Wall Pullout & Tendon Sizing Calculator

Calculates ultimate and allowable pullout resistance along the grout-ground interface, steel tendon yield strength, and governing limit state per FHWA GEC 7.

Helical Screw Pile Ultimate Axial Capacity Calculator

Calculates ultimate and allowable compressive axial capacity of multi-helix screw anchors using individual plate bearing method in cohesive and frictional soils.

Culvert Outlet Riprap Apron Erosion Protection Calculator (HEC-14)

Calculates median stone size (D₅₀), apron length, downstream width, and blanket thickness for culvert outlet scour protection per FHWA HEC-14.

Dry Extended Detention Basin Drawdown Orifice Calculator

Calculates the required release orifice diameter, average discharge rate, and drawdown velocity for stormwater dry extended detention basins.

Broad-Crested Rectangular Weir Discharge Calculator (ISO 3846)

Calculates open channel discharge capacity, critical depth, crest flow velocity, and discharge coefficient for broad-crested rectangular weirs.

SWMM Urban Catchment Peak Runoff & Infiltration Calculator

Calculates peak stormwater runoff, Horton infiltration abstraction, depression storage losses, and composite runoff coefficients for urban subcatchments.