Infiltration: Sizing and modeling

• To calculate the require 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 infiltration time of ponded water on the surface of a facility footprint...
• To calculate the drawdown 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 Permeable area (P), as only one of these is required to find the other. Note that some of these parameters are limited:

1. The maximum total depth will be limited by construction practices i.e. usually ≤ 2 m.
2. The maximum total depth may be limited by the conditions underground e.g. the groundwater or underlying geology/infrastructure.
3. The minimum total depth may be limited by the need to support vegetation i.e. not < 0.6 m.
4. Green roofs, absorbent landscapes and permeable paving often receive very little flow from other surfaces, so that the I/P ratio is close to 1.
5. Infiltration trenches, chambers and bioretention cells have a maximum recommended I/P ratio of 20.

Inputs

Symbol	Units	Parameter
D	hrs	Duration of design storm (for MOECC volume based caclulations set to 1)
i	mm/hr	Intensity of design storm (for MOECC volume based calculations use whole storm depth (link to map))
q	mm/hr	Infiltration coefficient of the underlying native soil, calculated from measured infiltration rate and applied safety factor
n	-	Porosity, as measured (or default to 0.35 for all aggregates). *Note: For systems that have significant storage in clear open chambers, 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.
I	m2	Impermeable area i.e. catchment
d	m	depth of infiltration facility or BMP
P	m2	Permeable area i.e. footprint area of the facility or BMP
K	mm/hr	Infiltration coefficient of the filter media or fill used in the infiltration facility

This spreadsheet tool has been set up to perform all of the calculations shown below
Download .xlsx calculation tool

To calculate the required depth, where the area of the facility is constrained (1D)

$d={\frac {D\left[\left({\frac {I}{P}}\right)i-q\right]}{n}}$

To calculate the require facility area or footprint where the depth is constrained (1D)

$P={\frac {IiD}{nd+qD}}$

Infiltration of surface ponding time

The following equation assumes that infiltration occurs primarily through the footprint of the facility. It is best applied to calculate the limited duration ponding on the surface of bioretention cells, bioswales and enhanced grass swales. To calculate the time (t) to fully drain the facility through the footprint area only: $t={\frac {nd}{K}}$

Three dimensional infiltration

Three footprint areas of 9 m².
From left to right x = 12 m, x = 14 m, and x = 16 m

For some geometries (e.g. particularly deep facilities or linear facilities), it may be preferred to also account for lateral infiltration. The 3 dimensional equations make use of the hydraulic radius (P/x), where x is the perimeter (m) of the facility.
Maximizing the perimeter of the facility directs designers towards longer, linear shapes such as infiltration trenches and bioswales.

To calculate the required depth:

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

Where $a={\frac {P}{x}}-{\frac {iI}{Pq}}$ and $b={\frac {xq}{nP}}$

The rearrangement to calculate the required footprint area of the facility for a given depth is not available at this time. Elegant submissions are invited.

Drawdown time

The design of infiltration facilities should be checked for drawdown time. The target drawdown time for the internal storage of an infiltration facility is between 48-72 hours.
To calculate the time (t) to fully drain the facility: $t={\frac {nP}{qx}}ln\left[{\frac {\left(d+{\frac {P}{x}}\right)}{\left({\frac {P}{x}}\right)}}\right]$

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

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.

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.

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 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 slow movement of water into or through a soil or drainage system.

Penetration of water through the ground surface.

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