Bioretention: Sizing and modeling

Before beginning the sizing calculations most of the following parameters must 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. not 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. The area P for a green roofs, absorbent landscapes and permeable paving may be very similar or equal to the catchment area, 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, calculated from measured infiltration rate and applied safety factor
n	-	Porosity, as measured (or default to 0.35)
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

The following equations assume that infiltration occurs primarily through the base of the facility. They may be applied for any shape and size of infiltration facility.

To calculate the required depth, where the area of the facility is constrained: $d={\frac {D\left(\left[{\frac {I}{P}}\right]i-q\right)}{n}}$

To calculate the require facility area or footprint where the depth is constrained: $P={\frac {IiD}{nd+qD}}$

This spreadsheet tool has been set up to perform either of the above calculations.
Download .xlsx calculation tool

To calculate the time (t) to fully drain the facility: $t={\frac {nd}{2q}}$

Accounting for lateral 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 $a={\frac {P}{x}}-{\frac {iI}{q}}$ 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.

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

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

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)

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

Penetration of water through the ground surface.