GEO-08

Darcy seepage discharge

Laminar discharge through a saturated soil mass.

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SeepageDarcy 1856ISO 17892-11

Governing equation

q = k i A = k \dfrac{\Delta h}{L} A

where

k: Permeability (m/s)
\Delta h: Head loss (m)
L: Path length (m)
A: Area (m²)
i: Gradient (—)
q: Discharge (m³/s)

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-08 — Darcy seepage discharge) is the form associated with Darcy 1856 · ISO 17892-11. Working symbols: $k$ , $\Delta h$ , $L$ , $A$ $\rightarrow$ $i$ , $q$ . Darcy found q proportional to hydraulic gradient i and area; k absorbs viscosity, void geometry and saturation.

Purpose

Purpose: compute

i

q

from

k

\Delta h

L

A

in Geotechnical engineering via

q = k i A = k \dfrac{\Delta h}{L} A

Laminar discharge through a saturated soil mass. 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

k = 1.000e-5\,\mathrm{m/s}

\Delta h = 2.000\,\mathrm{m}

L = 8.000\,\mathrm{m}

A = 10.000\,\mathrm{m^{2}}

, the governing relation

q = k i A = k \dfrac{\Delta h}{L} A

yields

i = 0.2500\,\mathrm{—}

q = 2.500e-5\,\mathrm{m^{3}/s}

. Uniform 1-D flow, saturated, no piping check. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Permeability k0.00001 m/sHead loss \Delta h2 mPath length L8 mArea A10 m²

Outputs

Gradient i0.2500 —
Discharge q0.000025 m³/s

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Narration of this film

Uniform 1-D flow, saturated, no piping check.

Darcy found q proportional to hydraulic gradient i and area; k absorbs viscosity, void geometry and saturation.

Reading speed

Watch on YouTube