GEO-15

Time factor Tv

Tv = cv t / Hdr². Charts map Tv to average degree of consolidation U.

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ConsolidationTerzaghi 1-D

Governing equation

T_v=\dfrac{c_v t}{H_{dr}^2}

$t \in \left[0.05, 20\right]$

where

c_v: Coefficient of consolidation (m²/yr)
t: Time (yr)
H_{dr}: Drainage path (m)
T_v: Time factor (—)

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

T_v=\dfrac{c_v t}{H_{dr}^2}

$t \in \left[0.05, 20\right]$

$t = 0.05$ $T_v = 0.1$

Along the curve

②

Domain of the variable — blue

t_{\min} = 0.05,\quad t_{\max} = 20

$t \in \left[0.05, 20\right]$

$t = 0.05$ $t = 0.05$

Along the curve

③

Response curve — green

T_v=\dfrac{c_v t}{H_{dr}^2}

$t \in \left[0.05, 20\right]$

$t = 0.05$ $T_v = 0.1$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}T_v}{\mathrm{d}t}

$t \in \left[0.05, 20\right]$

$t = 0.175$ $T_v^{\prime} = 2$

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-15 — Time factor Tv) is the form associated with Terzaghi 1-D. Working symbols: $c_v$ , $t$ , $H_{dr}$ $\rightarrow$ $T_v$ . One-dimensional diffusion of excess pore pressure. Hdr is the longest drainage path.

Purpose

Purpose: compute

T_v

from

c_v

t

H_{dr}

in Geotechnical engineering via

T_v=\dfrac{c_v t}{H_{dr}^2}

Tv = cv t / Hdr². Charts map Tv to average degree of consolidation U. 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_v = 8.000\,\mathrm{m^{2}/yr}

t = 1.000\,\mathrm{yr}

H_{dr} = 2.000\,\mathrm{m}

, the governing relation

T_v=\dfrac{c_v t}{H_{dr}^2}

yields

T_v = 2.000\,\mathrm{—}

. A clay layer, two drainage faces, a decaying isochrone. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Coefficient of consolidation c_v8 m²/yrTime t1 yrDrainage path H_{dr}2 m

Outputs

Time factor T_v2.000 —

Reading speed

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Narration of this film

A clay layer, two drainage faces, a decaying isochrone.

One-dimensional diffusion of excess pore pressure. Hdr is the longest drainage path.

Reading speed

Watch on YouTube