Skip to main content
CalcStack

Terzaghi 1D Consolidation Settlement Calculator

When structures are constructed over saturated cohesive clay soils, the added vertical load initially squeezes pore water, transferring stress slowly from pore pressure to the soil skeleton.

Total thickness of the consolidating clay layer.

Ratio of void volume to solid volume before loading (typically 0.6 - 1.5).

Slope of virgin consolidation e vs log(sigma') curve from oedometer test.

Pre-construction effective vertical overburden stress.

Net vertical stress increase induced by building foundation.

Calculated Result
166.6 mm

Primary Consolidation Settlement (S_c)

Vertical Consolidation Strain

3.33%

Final Clay Void Ratio (e_f)

0.788

Stress Overburden Ratio

1.50×

Calculation Breakdown

  1. S_c = [C_c·H / (1 + e₀)] · log₁₀[(σ₀' + Δσ') / σ₀']166.6 mm
  2. Δe = C_c · log₁₀(σ_f / σ₀)Void Ratio Change

What Is the Terzaghi 1D Consolidation Settlement Calculator?

Consolidation settlement is the time-dependent vertical compression of saturated cohesive soil under sustained static loading.

Unlike immediate elastic settlement, consolidation can take years or decades to reach completion.

How Does the Terzaghi 1D Consolidation Settlement Calculator Work?

Calculates stress ratio (sigma_0' + Delta_sigma') / sigma_0'.

Applies the logarithmic compression formula to determine primary settlement in millimeters.

Computes void ratio reduction and vertical strain percentage.

Terzaghi 1D Consolidation Settlement Calculator Formula & Variables

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

S_c = \frac{C_c H}{1 + e_0} \log_{10}\left( \frac{\sigma_0^\prime + \Delta\sigma^\prime}{\sigma_0^\prime} \right), \quad \Delta e = C_c \log_{10}\left( \frac{\sigma_f^\prime}{\sigma_0^\prime} \right), \quad e_f = e_0 - \Delta e

Terzaghi one-dimensional consolidation settlement equation for normally consolidated clay.

How to Use the Terzaghi 1D Consolidation Settlement Calculator

  1. Enter clay layer thickness H in meters.
  2. Input initial void ratio e0 and compression index Cc from laboratory oedometer tests.
  3. Enter in-situ overburden effective stress and foundation stress increment in kPa.

Step-by-Step Example Calculation

Multistory Building Mat Foundation on Marine Clay

Input Values:

layerThicknessM:5
initialVoidRatioE0:0.85
compressionIndexCc:0.35
initialEffectiveStressKpa:100
stressIncreaseDeltaSigmaKpa:50
Worked Steps: Long-term primary settlement of a 5 m normally consolidated silty clay layer.

Understanding Your Result

Total settlement indicates cumulative downward displacement of the foundation.

Differential settlement between building columns is the primary cause of architectural cracking and structural damage.

Factors That Affect the Result

  • Overconsolidation Ratio (OCR): Preconsolidated clays experience much smaller recompression settlement governed by recompression index Cr.
  • Drainage boundary conditions: Single drainage (impermeable rock on bottom) takes 4 times longer to consolidate than double drainage (sand top and bottom).

When Should You Use This Calculator?

  • Foundation engineering for buildings, bridge abutments, embankments, and earth dams.
  • Predicting post-construction settlement of reclaimed land and airport runways.

Assumptions & Limitations

  • Assumes 1D vertical strain and 1D upward/downward pore water flow.
  • Applies to normally consolidated clay (OCR = 1.0).

Frequently Asked Questions

Calculation Accuracy & Reference Note

Foundational equation of modern soil mechanics established by Karl von Terzaghi (1925).

Related Calculators

Explore more tools and calculators in Physics Calculators

Three-Phase Subtransient Short-Circuit Current Calculator

Calculates the initial subtransient symmetrical short-circuit current (I"k), short-circuit MVA capacity, and base rated current for a bolted three-phase power system fault.

Ferranti Effect Transmission Line Voltage Rise Calculator

Calculates the open-circuit receiving-end voltage rise, percentage voltage surge, and charging reactive power on long high-voltage AC transmission lines caused by the Ferranti effect.

Ohm's Law & Electrical Power Calculator

Calculate Voltage (V), Current (I), Resistance (R), and Electrical Power (P) across DC circuits.

Density, Mass & Volume Calculator

Calculate density (ρ = m/V), material mass, or physical volume for solids, liquids, and gases.

Steam Turbine Surface Condenser Cooling Water Duty Calculator

Calculates surface condenser thermal heat rejection (MWth), circulating cooling water pumping volume (m³/h), and steam condensation rate.

SCARA Robot Arm Workspace Envelope Calculator

Calculates the maximum reach, inner dead-zone radius, horizontal swept reach area, and optimal dexterity sweet spot for a two-link SCARA robotic manipulator.