Useful Equations

A working index of classic analytical groundwater equations

This page presents a curated collection of well-established, back-of-the-envelope analytical equations that engineers and geoscientists use for early-stage estimates and conceptual checks. These equations are distinct from the analytic element modeling approach on which Anaqsim is based.

Most of the equations link to an information card which provides the equations, how to use them, and what limitations are associated with each approach. Some also include case-studies to show how these analytical equations perform on real projects.

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Construction Dewatering & Mining

ApplicationConceptual Model
Excavation Dewatering – Unconfined Aquifer

Equivalent Well model with axially symmetric radial flow. Typical applications include Mines, pits, quarries and construction dewatering with sidewall seepage.

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Excavation Dewatering – Confined Aquifer

Equivalent Well model with axially symmetric radial flow. Typical applications include mines, pits, quarries and construction dewatering with sidewall seepage

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Excavation Dewatering – Mixed Aquifer

Equivalent Well model with axially symmetric radial flow. Typical applications include mines, pits, quarries and construction dewatering with sidewall seepage. Applicable for confined aquifers transitioning to unconfined.

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Excavation Dewatering – Confined Aquifer (Superposition of Wells)

Superposition of wells method is applicable to confined aquifers, but can also be used on unconfined and mixed aquifers if drawdown is relatively small (<10% aquifer thickness). Applicable for mines, pits, quarries and construction dewatering with sidewall seepage

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Discharge into excavation through base

Equivalent Well model with axially symmetric radial flow where flow is through base of excavation only. Applicable to mines, pits, quarries and construction dewatering with impermeable walls (secant piles)

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Discharge into excavation through base and pit walls

Equivalent Well model with axially symmetric radial flow applicable for 2 layer dewatering of mines, pits, quarries and construction dewatering

Excavation Dewatering – Unconfined Aquifer

Flow to slot model with linear flow – applicable for mines, pits, quarries, construction dewatering with sidewall seepage and rivers and streams.

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Conceptual Model for slot flow to excavation in unconfined aquifer
Excavation Dewatering – Confined Aquifer

Flow to slot model with linear flow – applicable for mines, pits, quarries, construction dewatering with sidewall seepage and rivers and streams

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Conceptual Model for slot flow to excavation in confined aquifer
Excavation Dewatering – Mixed Aquifer

Flow to slot model with linear flow – applicable for aquifers transitioning from confined to unconfined. Used in mines, pits, quarries, construction dewatering with sidewall seepage and rivers, streams and drains

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Further Reading

Construction Dewatering and Groundwater Control: New Methods and Applications.
By J. Patrick Powers, Arthur B. Corwin, Paul C. Schmall, and Walter E. Kaeck.
Copyright © 2007 John Wiley & Sons, Inc.
Print ISBN:9780471479437 | Online ISBN:9780470168103 | DOI:10.1002/9780470168103
https://onlinelibrary.wiley.com/doi/book/10.1002/9780470168103

Groundwater Lowering in Construction: A Practical Guide to Dewatering
By Pat Cashman and Martin Preene
Copyright 2021 CRC Press
ISBN 9780367504755
https://www.routledge.com/Groundwater-Lowering-in-Construction-A-Practical-Guide-to-Dewatering/Cashman-Preene/p/book/9780367504755

Groundwater control: design and practice (second edition) (C750)
By R. Preene, M. T. Roberts, and W. Powrie.
Copyright 2016 CIRIA
https://www.ciria.org/CIRIA/CIRIA/Item_Detail.aspx?iProductcode=C750&Category=

Simple Analytical Equations for Estimating Ground Water Inflow to a Mine Pit
By Fred Marinelli, Walter L. Niccoli
Groundwater Volume 38, Issue 2
https://doi.org/10.1111/j.1745-6584.2000.tb00342.x
https://ngwa.onlinelibrary.wiley.com/doi/10.1111/j.1745-6584.2000.tb00342.x

Application of Forchheimer’s Formula to Dewatered Excavation as a Large Circular Well
By Otohiko Suzuki and Hideo Yokoya
Soils and Foundations. Vol. 32, No. 1, pp. 215–221, March 1992.
Japanese Society of Soil Mechanics and Foundation Engineering.
https://www.sciencedirect.com/science/article/pii/S0038080620319119
https://doi.org/10.3208/sandf1972.32.215

Analytical techniques for the estimation of mine water inflow.
By Singh, R.N., & Atkins, A.S.
International Journal of Mining Engineering, 3, 65–77.
https://link.springer.com/article/10.1007/BF00881342
https://doi.org/10.1007/BF00881342

For more on Successive Steady State method see:

Analytical Modeling of Ground-Water Impacts by Mining.
By D. Koch
Groundwater. Volume 24, Issue 2.
https://ngwa.onlinelibrary.wiley.com/doi/10.1111/j.1745-6584.1986.tb00998.x
https://doi.org/10.1111/j.1745-6584.1986.tb00998.x

Dynamics of Fluids in Porous Media
By Jacob Bear
Copyright 1972 American Elsevier Publishing Company
1988 Dover Books Edition
ISBN: 9780486656755
Dynamics of Fluids in Porous Media