GEO-32

Compression-index settlement

ΔH = [Cc H /(1+e0)] log10(σ′f / σ′0) for NC clay (σ′0 ≥ σ′p).

Reading speed

ConsolidationTerzaghi Cc

Governing equation

\Delta H=\dfrac{C_c H}{1+e_0}\log_{10}\dfrac{\sigma'_f}{\sigma'_0}

$\sigma'_f \in \left[15, 800\right]$

where

C_c: Compression index (—)
H: Layer thickness (m)
e_0: Initial void ratio (—)
\sigma'_0: Initial effective (kPa)
\sigma'_f: Final effective (kPa)
\Delta H: Settlement (mm)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\Delta H=\dfrac{C_c H}{1+e_0}\log_{10}\dfrac{\sigma'_f}{\sigma'_0}

$\sigma'_f \in \left[15, 800\right]$

$\sigma'_f = 15$ $\Delta H = -727$

Along the curve

②

Domain of the variable — blue

\sigma'_f_{\min} = 15,\quad \sigma'_f_{\max} = 800

$\sigma'_f \in \left[15, 800\right]$

$\sigma'_f = 15$ $\sigma'_f = 15$

Along the curve

③

Response curve — green

\Delta H=\dfrac{C_c H}{1+e_0}\log_{10}\dfrac{\sigma'_f}{\sigma'_0}

$\sigma'_f \in \left[15, 800\right]$

$\sigma'_f = 15$ $\Delta H = -727$

Along the curve

④

Rate of change — amber

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

$\sigma'_f \in \left[15, 800\right]$

$\sigma'_f = 19.94$ $\Delta H^{\prime} = 22.25$

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-32 — Compression-index settlement) is the form associated with Terzaghi Cc. Working symbols: $C_c$ , $H$ , $e_0$ , $\sigma'_0$ , $\sigma'_f$ $\rightarrow$ $\Delta H$ . Virgin compression is a straight line in e–log σ′. Cc is the slope.

Purpose

Purpose: compute

\Delta H

from

C_c

H

e_0

\sigma'_0

\sigma'_f

in Geotechnical engineering via

\Delta H=\dfrac{C_c H}{1+e_0}\log_{10}\dfrac{\sigma'_f}{\sigma'_0}

ΔH = [Cc H /(1+e0)] log10(σ′f / σ′0) for NC clay (σ′0 ≥ σ′p). 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 = 6.000\,\mathrm{m}

e_0 = 1.100\,\mathrm{—}

\sigma'_0 = 80.000\,\mathrm{kPa}

\sigma'_f = 160.000\,\mathrm{kPa}

, the governing relation

\Delta H=\dfrac{C_c H}{1+e_0}\log_{10}\dfrac{\sigma'_f}{\sigma'_0}

yields

\Delta H = 301.0\,\mathrm{mm}

. A clay layer, a log-stress jump, a settlement. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Compression index C_c0.35 —Layer thickness H6 mInitial void ratio e_01.1 —Initial effective \sigma'_080 kPaFinal effective \sigma'_f160 kPa

Outputs

Settlement \Delta H301.0 mm

Reading speed

Watch on YouTube

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Narration of this film

A clay layer, a log-stress jump, a settlement.

Virgin compression is a straight line in e–log σ′. Cc is the slope.

Reading speed

Watch on YouTube