Darcy's law, and the parameter that swamps it
Flow through soil is the permeability times the hydraulic gradient times the gross cross-sectional area. Three terms, and two of them are geometry that can be measured to a few per cent.
The third cannot. PERMEABILITY spans roughly ten orders of magnitude across the soils encountered in construction — from a clean gravel that drains as fast as you can pump, to a clay through which water effectively does not move on any timescale that matters. No other geotechnical parameter has that range, and it sits as a direct multiplier on the answer.
The practical consequence is that a seepage calculation's precision is an illusion unless the permeability came from a test on the actual ground. A figure taken from a table against a soil description is a starting point that could be out by an order of magnitude in either direction, and the honest way to present a result from one is as an order of magnitude rather than a number.
- Q
- volumetric flow rate
- k
- coefficient of permeability — the term that varies over ten orders of magnitude
- i
- hydraulic gradient: head loss divided by the distance over which it occurs
- A
- GROSS area including the solids, not the pore area
The velocity in the formula is not the speed of the water
Darcy's velocity — flow divided by gross area — is a bulk figure spread over the whole face of the soil, solids included. Water does not move through the solids, so the actual speed in the pores is higher, by the reciprocal of the porosity.
The distinction matters whenever a TRAVEL TIME is wanted rather than a flow rate: how long until a contaminant reaches a well, how long a drawdown takes to propagate, how quickly a filter will be reached. Using the bulk velocity for a travel time over-estimates the time available, which is the wrong direction for anything involving contamination.
It also matters for filter design. It is the pore velocity that carries fines, so a geotextile or graded filter is designed against the seepage regime rather than against the bulk flow, and the criterion is about particle sizes rather than about litres per second.
The radius of influence is an empirical fudge, and says so
The classic well equations need a radius at which the drawdown is taken to be zero — the radius of influence. It appears in the formula as a logarithm, which is the saving grace, because the answer is relatively insensitive to it.
It is worth being plain about what that radius is: an EMPIRICAL fitting parameter with no rigorous theoretical basis. The common expressions for it — Sichardt's among them — are correlations, and different sources give different ones. A real aquifer has no boundary at which drawdown becomes zero; it has a cone of depression that thins with distance and interacts with rivers, boundaries and other wells.
Because it enters logarithmically, a factor-of-two error in the radius changes the computed yield modestly, which is why the fudge survives. That is a fortunate property rather than a justification, and where the answer matters the route is a PUMPING TEST: pump at a measured rate, monitor drawdown in observation wells, and fit the aquifer parameters to what actually happened.
Where it fails: layers, and the neighbours
Real ground is layered, and layering makes permeability DIRECTIONAL. A sequence of sand and clay laminations conducts water readily along the layers and barely at all across them — horizontal and vertical permeability can differ by an order of magnitude in a deposit that a borehole log describes with one word. A calculation using a single value has already averaged away the thing that controls the flow.
The consequence that reaches other people is settlement. Lowering a water table increases the EFFECTIVE STRESS in the soil beneath — the water was carrying part of the load and now is not — and that consolidates compressible layers. The ground settles, and it settles across the whole cone of depression rather than only inside the excavation.
So a dewatering scheme is a liability question as much as a construction one. Buildings on shallow foundations within the drawdown area can settle; timber piles above a lowered water table can rot; a nearby well can go dry. Recharge wells and cut-off walls exist to contain the drawdown rather than to make it cheaper, and the monitoring that goes with them is the evidence that it worked.
The alternative: test it, or cut it off
The alternative to estimating permeability is measuring it. Falling and rising head tests in a borehole give a local value cheaply; a PUMPING TEST with observation wells gives a mass value that already includes the layering, the boundaries and the anisotropy — and it is the only method that produces a number for the ground rather than for a sample of it.
The alternative to dewatering at all is to stop the water instead: a sheet-piled or secant-piled cut-off, a slurry wall, ground freezing, or working under water and sealing with a tremie plug. These substitute a construction cost for a pumping cost and for the settlement risk described above, and on a congested site they are frequently the cheaper answer once the neighbours are counted.
The calculators here size a first pass — a flow rate, an indicative yield, a drawdown time. They are a planning tool. Any dewatering scheme that affects a third party is a designed system with a monitoring regime, and the honest use of these pages is to find out roughly what scale of system is in question before commissioning one.
Calculators that use this method
Basis
- Darcy, H. (1856), Les Fontaines Publiques de la Ville de Dijon. The original experiment and the law.
- Dupuit-Thiem well equations for steady radial flow to a well in confined and unconfined aquifers, and the radius-of-influence term they require.
- Sichardt's empirical expression for the radius of influence, cited here as the correlation it is rather than as a derivation.
- CIRIA C750, Groundwater control: design and practice. Dewatering methods by permeability range, and the settlement and third-party risks of drawdown.
- Powers, J.P. et al., Construction Dewatering and Groundwater Control. Pumping tests, wellpoint and deep well systems, and cut-off alternatives.
- ASTM D4050 (field pumping tests) and BS EN ISO 22282 for borehole permeability testing — the measurements that replace a table value.
- Terzaghi's effective stress principle, which is why lowering a water table loads the soil and settles what is standing on it.