GEO-30

Dupuit–Thiem well

Q = π k (H² − hw²) / ln(R/rw). Unconfined radial flow to a well.

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SeepageDupuit–Thiem

Governing equation

Q=\dfrac{\pi k(H^2-h_w^2)}{\ln(R/r_w)}

where

k: Permeability (m/s)
H: Far-field head (m)
h_w: Head at well (m)
R: Influence radius (m)
r_w: Well radius (m)
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-30 — Dupuit–Thiem well) is the form associated with Dupuit–Thiem. Working symbols: $k$ , $H$ , $h_w$ , $R$ , $r_w$ $\rightarrow$ $Q$ . Dupuit assumes nearly horizontal flow and hydrostatic pressure. Thiem integrates Darcy between rw and R.

Purpose

Purpose: compute

Q

from

k

H

h_w

R

r_w

in Geotechnical engineering via

Q=\dfrac{\pi k(H^2-h_w^2)}{\ln(R/r_w)}

Q = π k (H² − hw²) / ln(R/rw). Unconfined radial flow to a well. 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-4\,\mathrm{m/s}

H = 12.000\,\mathrm{m}

h_w = 6.000\,\mathrm{m}

R = 200.000\,\mathrm{m}

r_w = 0.150\,\mathrm{m}

, the governing relation

Q=\dfrac{\pi k(H^2-h_w^2)}{\ln(R/r_w)}

yields

Q = 0.00472\,\mathrm{m^{3}/s}

. A well, a drawdown cone, a recharge radius. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Permeability k0.0001 m/sFar-field head H12 mHead at well h_w6 mInfluence radius R200 mWell radius r_w0.15 m

Outputs

Discharge Q0.00472 m³/s

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Narration of this film

A well, a drawdown cone, a recharge radius.

Dupuit assumes nearly horizontal flow and hydrostatic pressure. Thiem integrates Darcy between rw and R.

Reading speed

Watch on YouTube