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 (e.g not less than 0.6 m to support deep rooting perennials and shrubs).
4. Bioretention has a maximum recommended I/P ratio of 20.

Size a bioretention cell for constrained depth

If there is a constraint to the depth (d_T, m) of the practice, calculate the required footprint area (A_p, m²), as: $A_{p}={\frac {A_{c}\times i\times D}{(n\times d_{T})+(f'\times D)}}$

Where:

• A_p = Area of the infiltration practice in m²
• A_c = Catchment area in m²
• D = Duration of design storm in hrs
• i = Intensity of design storm in mm/hr
• f' = design infiltration rate in mm/hr
• n = Porosity of the fill materials within the practice, depth weighted mean
• d_T = Total depth of the infiltration practice in m.

Size a bioretention cell for constrained ground area

If the land area is limited, determine the ratio of catchment (A_c) to BMP footprint area (A_p):

$R={\frac {A_{c}}{A_{p}}}$

Where:

• R = Ratio of catchment area (A_c) to area of the infiltration practice (A_p)
• A_p = Area (footprint) of the infiltration practice in m²
• A_c = Catchment area in m²

Then calculate the required depth (d_T), as: $d_{T}={\frac {D\left[(R\times i)-f'\right]}{n}}$

Where:

• D = Duration of design storm in hrs
• i = Intensity of design storm in mm/hr
• f' = Design infiltration rate in mm/hr
• n = Porosity of the fill materials within the practice, depth weighted mean
• d_T = 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 all of the infiltration BMP sizing calculations shown above
Download Infiltration Sizing.xlsx calculator tool

Calculate drawdown time

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

Download Darcy Drainage Time.xlsx calculator tool

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).
• Use the following equation to estimate the time (t) to fully drain the facility:

$t={\frac {nA_{p}}{f'x}}ln\left[{\frac {\left(d_{T}+{\frac {A_{p}}{x}}\right)}{\left({\frac {A_{p}}{x}}\right)}}\right]$

Where:

• n is the porosity of the fill materials within the practice, depth weighted mean
• A_p is the area of the practice (m²),
• f' is the design infiltration rate (mm/hr),
• x is the perimeter of the practice (m), and
• d_T is the total depth of the practice, including the ponding zone (m).

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.

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

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 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)