GEO-06

Terzaghi consolidation settlement

One-dimensional primary settlement from the compression index.

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ConsolidationTerzaghi 1925ISO 17892-5

Governing equation

s = \dfrac{C_c H}{1+e_0}\log_{10}\dfrac{\sigma'_{v0}+\Delta\sigma}{\sigma'_{v0}}

where

C_c: Compression index (—)
H: Layer thickness (m)
e_0: Initial void ratio (—)
\sigma'_{v0}: Initial effective stress (kPa)
\Delta\sigma: Stress increment (kPa)
s: Primary settlement (mm)

Lecture brief

Historical brief

Soil mechanics became a quantitative laboratory after Karl von Terzaghi’s 1925–1943 work on effective stress, consolidation and bearing. These sheets still size shallow foundations, retaining walls, piles and drainage in SI. This sheet (GEO-06 — Terzaghi consolidation settlement) is the form associated with Terzaghi 1925 · ISO 17892-5. Working symbols: $C_c$ , $H$ , $e_0$ , $\sigma'_{v0}$ , $\Delta\sigma$ $\rightarrow$ $s$ . Terzaghi linked void-ratio change to the logarithm of effective stress through Cc, giving s = Cc H/(1+e0) log10(σ'v0+Δσ)/σ'v0.

Purpose

Purpose: compute

s

from

C_c

H

e_0

\sigma'_{v0}

\Delta\sigma

in Geotechnical engineering via

s = \dfrac{C_c H}{1+e_0}\log_{10}\dfrac{\sigma'_{v0}+\Delta\sigma}{\sigma'_{v0}}

One-dimensional primary settlement from the compression index. Use it when a real geotechnical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

C_c = 0.350\,\mathrm{—}

H = 4.000\,\mathrm{m}

e_0 = 0.900\,\mathrm{—}

\sigma'_{v0} = 80.000\,\mathrm{kPa}

\Delta\sigma = 40.000\,\mathrm{kPa}

, the governing relation

s = \dfrac{C_c H}{1+e_0}\log_{10}\dfrac{\sigma'_{v0}+\Delta\sigma}{\sigma'_{v0}}

yields

s = 129.751\,\mathrm{mm}

. Normally consolidated clay, infinite layer, vertical drainage only. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Compression index C_c0.35 —Layer thickness H4 mInitial void ratio e_00.9 —Initial effective stress \sigma'_{v0}80 kPaStress increment \Delta\sigma40 kPa

Outputs

Primary settlement s129.751 mm

Reading speed

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Narration of this film

Normally consolidated clay, infinite layer, vertical drainage only.

Terzaghi linked void-ratio change to the logarithm of effective stress through Cc, giving s = Cc H/(1+e0) log10(σ'v0+Δσ)/σ'v0.

Reading speed

Watch on YouTube