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 will be limited by the need to support vegetation i.e. not < 0.6 m.
4. Bioretention has a maximum recommended I/P ratio of 20.

Size a bioretention cell

Determine if there is a constraint to the depth (d) of the bioretention practice: Depth to GW	or if the land area is limited, determine the I/P ratio::$R={\frac {A_{c}}{A_{p}}}$ Where: R = Ratio of catchment area (Ac) to BMP footprint area (Ap) syn. I/P ratio. Ap = Area of the infiltration practice in m2 Ac = Catchment area in m2
Then
To calculate the require facility area or footprint where the depth is constrained: $A_{p}={\frac {IiD}{V_{R}d+q'D}}$	To calculate the required depth, where the area of the facility is constrained: $d={\frac {D\left[Ri-q'\right]}{V_{R}}}$

Where:

• D = Duration of design storm in hrs
• i = Intensity of design storm in mm/hr
• q' = Infiltration coefficient in mm/hr (accounting for SCF)
• SCF = Safety correction factor
• V_R = Void ratio (porosity), as measured (or default to 0.35 for all aggregates)
• R = Ratio of catchment area (A_c) to BMP footprint area (A_p) syn. I/P ratio.
• A_p = Area of the infiltration practice in m²
• A_c = Catchment area in m²
• d = Depth of infiltration practice in m.

The following equations assume that infiltration occurs primarily through the base of the facility. They may be easily applied for any shape and size of infiltration facility, in which the reservoir storage is mostly in an aggregate.

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

Calculate drawdown time

Two footprint areas of 9 m².
Perimeter = 12 m (left) Perimeter = 20 m (right)

In some situations, it may be possible to reduce the size of the bioretention required, by accounting for rapid drainage. Typically, this is only worth exploring over sandy soils with rapid infiltration. Note that narrow, linear bioretention features drain faster than round or blocky footprint geometries.

• Begin the drainage time calculation by dividing the area of the practice (A_p) by the perimeter (P).
• To estimate the time (t) to fully drain the facility:

$t={\frac {V_{R}A_{p}}{f'P}}ln\left[{\frac {\left(d+{\frac {A_{p}}{P}}\right)}{\left({\frac {A_{p}}{P}}\right)}}\right]$

Where:

• V_R is the void ratio of the media,
• A_p is the area of the practice (m²),
• f' is the design infiltration rate (mm/hr),
• P is the perimeter of the practice (m), and
• d is the total depth of the practice, including the ponding zone (m).

To calculate the time (t) to fully drain the facility:

$t={\frac {V_{R}A_{p}}{q'P}}ln\left[{\frac {\left(d+{\frac {A_{p}}{P}}\right)}{\left({\frac {A_{p}}{P}}\right)}}\right]$

This 3 dimensional equation makes use of the hydraulic radius (A_p/P), where P is the perimeter (m) of the facility.
Maximizing the perimeter of the facility directs designers towards longer, linear shapes such as bioswales.

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

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

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

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

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.

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

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

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).

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

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