GEO-33

Coefficient of volume compressibility

ΔH = mv H Δσ′. Linearised 1-D compression for a stress increment.

Reading speed

Consolidationmv

Governing equation

\Delta H=m_v H\Delta\sigma'

$\Delta\sigma' \in \left[5, 400\right]$

where

m_v: mv (1/MPa)
H: Thickness (m)
\Delta\sigma': Stress increment (kPa)
\Delta H: Settlement (mm)

The figure, part by part

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①

Governing law — red

\Delta H=m_v H\Delta\sigma'

$\Delta\sigma' \in \left[5, 400\right]$

$\Delta\sigma' = 5$ $\Delta H = 6.25$

Along the curve

②

Domain of the variable — blue

\Delta\sigma'_{\min} = 5,\quad \Delta\sigma'_{\max} = 400

$\Delta\sigma' \in \left[5, 400\right]$

$\Delta\sigma' = 5$ $\Delta\sigma' = 5$

Along the curve

③

Response curve — green

\Delta H=m_v H\Delta\sigma'

$\Delta\sigma' \in \left[5, 400\right]$

$\Delta\sigma' = 5$ $\Delta H = 6.25$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta H}{\mathrm{d}\Delta\sigma'}

$\Delta\sigma' \in \left[5, 400\right]$

$\Delta\sigma' = 7.484$ $\Delta H^{\prime} = 1.25$

Along the curve

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-33 — Coefficient of volume compressibility) is the form associated with mv. Working symbols: $m_v$ , $H$ , $\Delta\sigma'$ $\rightarrow$ $\Delta H$ . mv = Δεv / Δσ′ = Cc / [2.3 σ′ (1+e0)] on the virgin curve. Direct from an oedometer increment.

Purpose

Purpose: compute

\Delta H

from

m_v

H

\Delta\sigma'

in Geotechnical engineering via

\Delta H=m_v H\Delta\sigma'

ΔH = mv H Δσ′. Linearised 1-D compression for a stress increment. 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

m_v = 0.250\,\mathrm{1/MPa}

H = 5.000\,\mathrm{m}

\Delta\sigma' = 50.000\,\mathrm{kPa}

, the governing relation

\Delta H=m_v H\Delta\sigma'

yields

\Delta H = 62.5\,\mathrm{mm}

. A spring of modulus 1/mv, a layer, a ΔH. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

mv m_v0.25 1/MPaThickness H5 mStress increment \Delta\sigma'50 kPa

Outputs

Settlement \Delta H62.5 mm

Reading speed

Watch on YouTube

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Narration of this film

A spring of modulus 1/mv, a layer, a ΔH.

mv = Δεv / Δσ′ = Cc / [2.3 σ′ (1+e0)] on the virgin curve. Direct from an oedometer increment.

Reading speed

Watch on YouTube