GEO-36

Secondary compression Cαe

ΔHs = [Cαe H /(1+e0)] log10(t2/t1) after primary ends.

Reading speed

ConsolidationMesri Cαe

Governing equation

\Delta H_s=\dfrac{C_{\alpha e} H}{1+e_0}\log_{10}(t_2/t_1)

$t_2 \in \left[1, 200\right]$

where

C_{\alpha e}: Secondary index (—)
H: Thickness (m)
e_0: Void ratio (—)
t_1: Start of secondary (yr)
t_2: Time of interest (yr)
\Delta H_s: Secondary 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_s=\dfrac{C_{\alpha e} H}{1+e_0}\log_{10}(t_2/t_1)

$t_2 \in \left[1, 200\right]$

$t_2 = 1$ $\Delta H_s = 0.019$

Along the curve

②

Domain of the variable — blue

t_2_{\min} = 1,\quad t_2_{\max} = 200

$t_2 \in \left[1, 200\right]$

$t_2 = 1$ $t_2 = 1$

Along the curve

③

Response curve — green

\Delta H_s=\dfrac{C_{\alpha e} H}{1+e_0}\log_{10}(t_2/t_1)

$t_2 \in \left[1, 200\right]$

$t_2 = 1$ $\Delta H_s = 0.019$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta H_s}{\mathrm{d}t_2}

$t_2 \in \left[1, 200\right]$

$t_2 = 2.252$ $\Delta H_s^{\prime} = 9.314$

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-36 — Secondary compression Cαe) is the form associated with Mesri Cαe. Working symbols: $C_{\alpha e}$ , $H$ , $e_0$ , $t_1$ , $t_2$ $\rightarrow$ $\Delta H_s$ . Mesri: Cαe/Cc ≈ 0.04 ± 0.01 for inorganic clay. Creep on log-time after Tv charts have finished.

Purpose

Purpose: compute

\Delta H_s

from

C_{\alpha e}

H

e_0

t_1

t_2

in Geotechnical engineering via

\Delta H_s=\dfrac{C_{\alpha e} H}{1+e_0}\log_{10}(t_2/t_1)

ΔHs = [Cαe H /(1+e0)] log10(t2/t1) after primary ends. 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_{\alpha e} = 0.015\,\mathrm{—}

H = 6.000\,\mathrm{m}

e_0 = 1.100\,\mathrm{—}

t_1 = 1.000\,\mathrm{yr}

t_2 = 30.000\,\mathrm{yr}

, the governing relation

\Delta H_s=\dfrac{C_{\alpha e} H}{1+e_0}\log_{10}(t_2/t_1)

yields

\Delta H_s = 63.3\,\mathrm{mm}

. A clock after primary, a slow settlement. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Secondary index C_{\alpha e}0.015 —Thickness H6 mVoid ratio e_01.1 —Start of secondary t_11 yrTime of interest t_230 yr

Outputs

Secondary settlement \Delta H_s63.3 mm

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Narration of this film

A clock after primary, a slow settlement.

Mesri: Cαe/Cc ≈ 0.04 ± 0.01 for inorganic clay. Creep on log-time after Tv charts have finished.

Reading speed

Watch on YouTube