Infiltration: Sizing and modeling

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• To calculate the required depth of an infiltration facility in a specified footprint area...
• To calculate the required footprint area of an infiltration facility with a known depth constraint....
• To calculate the drainage time of ponded water on the surface of a facility footprint...
• To calculate the drainage time of an underground infiltration facility...

The sizing calculations require that most of the following parameters be known or estimated. The exceptions are the depth (d) and the permeable footprint area of the practice (Ap), as only one of these is required to find the other. Note that some of these parameters can be limited by site conditions and factors influencing constructability:

1. The maximum total depth will be limited by construction practices i.e. usually ≤ 2 m to avoid the need for benching and shoring open cut excavations.
2. The maximum total depth may be limited by the conditions underground (e.g. water table or underlying geology/infrastructure).
3. The maximum total depth may be limited by the desire to install the practice below the maximum frost penetration depth in the proposed location.
4. The maximum total depth may be limited by the desire to support vegetation cover over it (e.g. at least 30 cm of planting soil backfill over the BMP to support grasses)
5. Infiltration trenches, chambers and bioretention have a maximum recommended I/P ratio of 20.

Inputs

Symbol	Units	Parameter
D	h	Duration of design storm
i	m/h	Intensity of design storm
f'	m/h	Design infiltration rate of the underlying native soil, calculated from measured infiltration rate and applied safety factor
n	-	Porosity of the aggregate or other void-forming fill material(s) in the storage reservoir of the practice. *Note: For systems that have significant storage in open chambers surrounded by clear stone aggregate, an effective porosity value (n') may be estimated for the whole installation and used in the calculations below. Effective porosity will vary according to the geometry of the storage chambers, so advice should be sought from product manufacturers. Permit applications should include the basis for n' estimates.
Ai	m2	Catchment impervious area
dr	m	Water storage reservoir depth. For practices without an underdrain (i.e. full infiltration design), dr is the total depth of the practice (i.e. includes surface ponding and filter media depths). For practices with an underdrain (i.e. partial infiltration design), dr is the depth below the invert of the underdrain perforated pipe or riser pipe upturn.
Ap	m2	Permeable footprint area of the practice. For practices where runoff is directed to a surface ponding area, Ap is the surface ponding area. For practices where runoff is directed to a subsurface water storage reservoir, Ap is the footprint area of the internal water storage reservoir, Ar.
x	m	Perimeter of the practice
Kf	m/h	Minimum acceptable saturated hydraulic conductivity of the filter media or growing medium (i.e., planting soil) used in the practice, when compacted to 85% maximum dry density

This spreadsheet tool has been set up to perform all of the infiltration practice sizing calculations shown below
Download the infiltration practice sizing tool

To calculate the required storage reservoir footprint area where the depth is fixed or constrained (1D drainage)

To ensure that the water storage capacity of the facility is available at the onset of a storm event, it is recommended to size the storage reservoir despth, d_r, based on the depth of water that will drain via infiltration between storm events. So d_r can be calculated as:
$d_{r}={\frac {f'\times t}{n}}$ Where
f' = design infiltration rate of the native soil (m/h)
t = drainage time, based on local criteria or long-term average inter-event period for the location (e.g. 72 hr in southern Ontario).
n = Porosity of the stone bed aggregate material (typically 0.4 for 50 mm dia. clear stone)
In many locations there may be a limited depth of soil available above the seasonally high water table or top of bedrock elevation into which stormwater may be infiltrated. In such cases the required storage needs to be distributed more widely across the landscape.
Where the storage reservoir depth is fixed or constrained the footprint area of the water storage reservoir, A_r can be calculated: $A_{r}={\frac {i\times D\times Ai}{(n\times d_{r})+f'D}}$

To calculate the required storage reservoir depth where the area is fixed or constrained (1D drainage)

On densely developed sites, the surface area available for the practice may be constrained. In such cases the required storage reservoir depth, d_r of the bioretention cell or infiltration trench can be calculated based on available surface area, A_p:

$d_{r}={\frac {D\left[\left({\frac {Ai}{Ap}}\right)i-f'\right]}{n}}$

Note that in most cases the results of this calculation will be very similar to those from the equation below assuming three-dimensional drainage.

To calculate the required storage reservoir depth, where the area is fixed or constrained (3D drainage)

On densely developed sites, the surface area available for the facility may be constrained. In such cases the required water storage reservoir depth of the bioretention cell or infiltration trench, d, can be calculated assuming three-dimensional drainage as follows

$d_{r}=a[e^{\left(-bD\right)}-1]$

Where

$a={\frac {A_{r}}{x}}-{\frac {i\times A_{i}}{x\times f'}}$

and

$b={\frac {x\times f'}{n\times A_{r}}}$

(The rearrangement to calculate the required footprint area of the facility for a given depth assuming three-dimensional drainage is not available at this time. Elegant submissions are invited.)

Time required to drain surface ponded water (1D drainage)

The following equations assume one dimensional drainage over the surface ponding area. It is best applied to calculate the maximum duration of ponding on the surface of bioretention cells and stormwater tree trenches, and upstream of check dams of bioswales and enhanced grass swales to ensure all surface ponding drains within 24 hours.
To calculate the time (t) to fully drain surface ponded water through the filter media or growing medium: $t={\frac {d_{p}'}{K_{f}}}$
Where
d_p' is the effective or mean surface ponding depth (mm).
K_f is the minimum acceptable saturated hydraulic conductivity of the filter media and growing medium when compacted to 85% maximum dry density (mm/h); minimum of 25 mm/hr is recommended for bioretention filter media; minimum of 15 mm/hr is recommended for enhanced grass swale and stormwater tree trench growing medium.

For full infiltration design practices that do not feature an underdrain, once the internal water storage capacity has been filled, the length of time required to fully drain surface ponded water is limited by the saturated hydraulic conductivity of the underlying in-situ (native) subsoil. To calculate the time (t) to fully drain surface ponded water once filled to capacity: $t={\frac {d_{p}'}{f'}}$
Where
d_p' is the effective or mean surface ponding depth (mm).
f' is the design infiltration rate of the underlying native soil.

Time to drain internal water storage reservoir

The target drainage time for the internal water storage reservoir portion of an infiltration facility is typically between 48 and 72 hours or based on the average inter-event period for the location. Contact the local municipality or conservation authority for criteria. See Drainage time for more information about how inter-event periods vary across Ontario and to help select what is suitable for the site.

Try the Darcy drainage time calculator tool for estimating the time required to fully drain the water storage reservoir of the facility assuming either one or three-dimensional drainage:
Download the Darcy drainage time calculator

Three footprint areas of 9 m².
From left to right x = 12 m, x = 20 m

For some geometries, particularly deep or linear facilities, it desirable to account for lateral drainage, out the sides of the storage reservoir. The following equation makes use of the hydraulic radius (A_r/x), where A_r is the area of the reservoir and x is the perimeter (m) of the reservoir.

Maximizing the perimeter of the water storage reservoir of the facility will enhance drainage performance and directs designers towards longer, linear shapes such as infiltration trenches and bioswales. See illustration for an example.
To calculate the time (t) to fully drain the facility assuming three-dimensional drainage: $t={\frac {n\times A_{r}}{f'\times x}}ln\left[{\frac {\left(d_{r}+{\frac {A_{r}}{x}}\right)}{\left({\frac {A_{r}}{x}}\right)}}\right]$ Where "ln" means natural logarithm of the term in square brackets
Adapted from CIRIA, The SUDS Manual C753 (2015).

The period between the maximum water level and the minimum level (dry weather or antecedent level).

The upper surface of the zone of saturation, except where the surface is formed by an impermeable body.

Subsurface water level which is defined by the level below which all the spaces in the soil are filled with water; The entire region below the water table is called the saturated zone.

Best management practice. State of the art methods or techniques used to manage the quantity and improve the quality of wet weather flow. BMPs include: source, conveyance and end-of-pipe controls.

The ratio of the impervious catchment (drainage) area to the pervious (footprint) area of the receiving BMP.

The natural ground material characteristic of or existing by virtue of geographic origin.

The porosity (n) of a mixture is the ratio of the volume of void-space to the total or bulk volume of the mixture. It is closely related to the concept of void ratio (e) where void ratio is the ratio of the volume of void-space to the volume of solids. n = Volume of voids/Total volume of mixture = e/(1+e)

A broad category of particulate material used in construction, including sand, gravel, crushed stone, slag, recycled concrete and geosynthetic aggregates, and available in various particulate size gradations.

An underlying bed filled with aggregate or other void-forming fill material that temporarily stores stormwater before infiltrating into the native soil or being conveyed by an underdrain pipe.

The porosity (n) of a mixture is the ratio of the volume of void-space to the total or bulk volume of the mixture. It is closely related to the concept of void ratio (e) where void ratio is the ratio of the volume of void-space to the volume of solids. n = Volume of voids/Total volume of mixture = e/(1+e)

The land draining to a single reference point (usually a structural BMP); similar to a subwatershed, but on a smaller scale.

A hard surface area (e.g., road, parking area or rooftop) that prevents or retards the infiltration of water into the soil.

A perforated pipe used to assist the draining of soils.

The engineered soil component of bioretention cell or dry swale designs, typically with a high rate of infiltration and designed to retain contaminants through filtration and adsorption to particles.

The portion of water precipitated onto a catchment area, which then flows as surface discharge from the catchment area past a specified point.

Water from rain, snow melt, or irrigation that flows over the land surface.

A parameter that describes the capability of a medium to transmit water.

Natural or artificial means of intercepting and removing surface or subsurface water (usually by gravity).

A shallow excavated surface depression containing prepared filter media, mulch, and planted with selected vegetation.

Structures constructed of a non-erosive material, such as suitably sized aggregate, wood, gabions, riprap, or concrete; used to slow runoff water. Can be employed in practices such as bioswales and enhanced grass swales.

Vegetated open channel, with check dams; designed to convey, treat and attenuate stormwater runoff.

The rate at which stormwater percolates into the subsoil measured in inches per hour.