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_T) and practice permeable (footprint) area (A_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 catchment impervious area to practice permeable (footprint) area ratio, R (or I/P ratio) of 20.

Size a bioretention cell receiving flows directly to the storage reservoir for a constrained depth

If there is a constraint to the depth (d_T) of the practice, calculate the required storage reservoir footprint area (A_r), as: $A_{r}={\frac {i\times D\times A_{i}}{(d_{r}\times n')+(f'\times D)}}$

Where:

• A_r = Area of the infiltration practice storage reservoir (m²)
• A_i = Catchment impervious area (m²)
• D = Duration of design storm (h)
• i = Intensity of design storm (mm/h)
• f' = design infiltration rate (m/h)
• n' = Effective porosity of the fill materials within the active storage component(s) of practice, depth-weighted mean
• d_r = Storage reservoir depth, based on depth available between the elevation of the invert of the underdrain perforated pipe and one (1) metre above the seasonally high water table or top of bedrock (m) or other value determined to be suitable through groundwater mounding analysis.

If R is greater than 20, consider decreasing catchment impervious area (A_i) by draining less area to the practice.

Size a bioretention cell where drainage area and practice area are fixed

If the land area is limited, determine the I/P ratio, which is the ratio of catchment impervious area (A_i) to practice pervious footprint area (A_p):

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

Where:

• R = Ratio of catchment impervious area to practice pervious footprint area, also referred to as I/P ratio
• A_p = Practice pervious footprint area in m²
• A_i = Catchment impervious area in m²

Then calculate the required storage reservoir depth (d_r), as: $d_{r}={\frac {D\left[(R\times i)-f'\right]}{n'}}$

Where:

• D = Duration of design storm (h)
• i = Intensity of design storm (m/h)
• f' = Design infiltration rate (m/h)
• n' = Effective porosity of the storage reservoir fill material

These equations assume that infiltration occurs primarily through the base of the facility.
This spreadsheet tool has been set up to perform all of the infiltration practice sizing calculations shown above.
Download the infiltration practice sizing tool

Calculate drawdown time

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

Download the Darcy drainage time 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 storage reservoir area of the practice (A_r) by the perimeter (x).
• Use the following equation to estimate the time (t) to fully drain the facility:

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

Where:

• n is the porosity of the storage reservoir fill material
• A_r is the storage reservoir footprint area (m²),
• f' is the design infiltration rate of the native soil (mm/h),
• x is the perimeter of the practice (m), and
• d_r is the depth of the storage reservoir (m).

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

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.

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.

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 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)

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.

A perforated pipe used to assist the draining of soils.

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.

The total surface area upstream of a point on a stream that drains toward that point. Not to be confused with watershed. The drainage area may include one or more watersheds.

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

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