Bioretention: Sizing

Many of the dimensions in a bioretention system are relatively constrained by the performance requirements of the individual component. There is greatest flexibility in the ponding depth and the depth of the storage reservoir beneath the optional underdrain pipe. The order of operations in calculating these dimensions depends on whether an underdrain is desired.

Component	Typical void ratio (Vr)	Recommended depth (with underdrain pipe)	Recommended depth (no underdrain pipe)
Ponding depth	300 mm	See below	1
Mulch	75 ± 25 mm		0.7 for wood based 0.4 for aggregates
Biofiler media	300 mm to support turf grass (and accept only rainwater/roof runoff) 600 mm to support flowering perennials and decorative grasses 1000 mm to support trees		0.3
Choker course	0.4 typical	100 mm
Pipe reservoir	Is equal to underdrain pipe diameter	Not applicable	0.4
Storage reservoir	See below	See below	0.4

Calculate the maximum overall depth

• Step 1: Determine what the planting needs are and assign appropriate depth of media, using the table above.
• Step 2: Select an underdrain pipe diameter (typically 100 - 200 mm), assign this as an 'embedding' depth.
• Step 3: Calculate the maximum possible storage reservoir depth beneath the pipe (d_s):

$d_{s}=f'\times 38.4$

Where:

• f' = Design infiltration rate in mm/hr, and
• 38.4 comes from multiplying desired drainage time of 96 hours by void ratio of 0.4

Additional step for system without underdrain

• Step 4: Determine maximum permissible ponding depth (d_p):

$d_{p}=f'\times 19.2$

Where:

• f' = Design infiltration rate in mm/hr, and
• 19.2 comes from multiplying desired drainage time of 48 hours by void ratio of 0.4. Note that conceptually the drainage of the ponded area is limited by ex-filtration at the base of the practice.

• Step 5: Sum total depth of bioretention, and compare to available space above water table and bedrock. Adjust if necessary.

Calculate the remaining dimensions

• Step 6: Multiply the depth of each separate component by the void ratio and then sum the total to find the 1 dimensional storage (in mm).
• Step 7: Calculate the required total storage (m³):

$Storage=RVC_{T}\times A_{c}\times C\times 0.1$

Where:

• RVC_T is the Runoff volume control target (mm),
• A_c is the catchment area (Ha),
• C is the runoff coefficient of the catchment area, and
• 0.095 is the product of a typical runoff coefficient for impermeable surfaces (0.95) and the units correction between m³ and mm.Ha. (0.1)

• Step 8. Divide required storage (m³) by the 1 dimensional storage (in m) to find the required footprint area (A_p) for the bioretention in m².
• Step 9. Calculate the peak flow rate (Q_p, in L/s) through the filter media:

$Q_{p}=A_{p}\times K_{sat}\times 3.6\times 10^{-3}$

Where:

• K_sat is the saturated hydraulic conductivity of the filter media (mm/hr), and
• A_p is the area of the practice (m²).

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To size a bioretention facility using this page, the design infiltration rate (q' in mm/hr, after correction) of the native underlying soils must estimated, and the maximum available excavation depth (d in m) is the primary constraint to sizing.
If the space on the ground is the tighter constraint to design, try this article on sizing bioretention for space.

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Step 1, total volume

The three storage areas 'bowl', 'filter media' and 'reservoir' are sized together.

The bioretention facility will comprise three vertical zones:

1. a 'bowl' permitting water to pond occasionally (maximum depth, d_p = 0.5 m)
2. a layer of filter media to support plant growth (minimum depth, d_m = 0.6 m) , and
3. a reservoir of stone to store and facilitate infiltration of additional water (depth, d_R, includes 0.1 m choking layer).

Firstly, all three zones will be sized together within the limited depth to estimate the footprint area of the whole bioretention facility. To do this the mean void ratio (V_R) will estimated as ~ 0.4.

To calculate the required practice area (A_p) or footprint where the depth is constrained:

$A_{p}={\frac {V}{V_{R}d}}$

Where:

• V = Required volume of storage in m³
• V_R = Void ratio (porosity), as measured (or default to 0.4)
• A_p = Area of the infiltration practice in m²
• d_T = Total depth of infiltration practice in m (= d_b + d_m + d_R)

Step 1 alternative, accounts for infiltration during a design storm event

This may be desirable where the practice is located on particularly freely draining soils and/or where the design storm is of longer duration. To calculate the required practice area (A_p) or footprint where the depth is constrained:

$A_{p}={\frac {A_{c}iD}{V_{R}d+f'D}}$

Where:

• D = Duration of design storm in hrs
• i = Intensity of design storm in mm/hr
• f' = Design infiltration rate in mm/hr
• V_R = Void ratio (porosity), as measured (or default to 0.35 for all aggregates)
• A_p = Area of the infiltration practice in m²
• A_c = Area of the catchment in m²
• d_T = Total depth of infiltration practice in m (= d_b + d_m + d_R)

Step 2, geometry and perimeter

Two practice areas of 9 m².
P = 12 m (left), P = 20 m (right)

Fit the bioretention facility into the site plan. It is necessary to have an idea of the perimeter of the facility.
Narrow, linear cells drain faster than round or blocky footprint geometries.
Divide the area of the practice (A_p) by the perimeter (P).

Step 3, depth of bowl,d_b

The duration of surface ponding is usually determined by the emptying of the facility below.

The 'bowl' area is simply the depressed elevation of the surface compared to the surrounding areas; a space to permit temporary ponding.
The depth of the bowl would not typically exceed 0.5 m due to safety concerns.
Some jurisdictions or particular sites may demand a lower maximum depth of ponding. It is worth bearing in mind that in most cases this ponded water will only occur once or twice per year.
The ponded water within the bowl should drain within 48 hrs. This addresses public concerns about mosquitoes and reduces the probability of losing vegetation due to saturated growing conditions.
The drainage of the bowl is not usually constrained by the surface infiltration (filter media should drain > 25 mm/hr). The infiltration of water from the bowl is determined by the drainage of the filter media and reservoir into the soils.
To estimate the time (t) to fully drain the facility:
$t={\frac {V_{R}A_{p}}{f'P}}ln\left[{\frac {\left(d+{\frac {A_{p}}{P}}\right)}{\left({\frac {A_{p}}{P}}\right)}}\right]$

Final step

Check the mounding of groundwater beneath the facility to ensure no incompatibility with nearby sensitive receptors.
Download groundwater mounding calculator(.xlsm)
Note that this is a minor adaptation (metric units and formatting) from the original tool, written and hosted by the USGS.

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.

A perforated pipe used to assist the draining of soils.

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)

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 portion of water precipitated onto a catchment area, which then flows as surface discharge from the catchment area past a specified point.

Water from rain, snow melt, or irrigation that flows over the land surface.

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 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).

The technique of removing pollutants from runoff as it infiltrates through the soil.

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 portion of water precipitated onto a catchment area, which then flows as surface discharge from the catchment area past a specified point.

Water from rain, snow melt, or irrigation that flows over the land surface.

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

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.

A parameter that describes the capability of a medium to transmit water.

A body of water smaller than a lake, often artificially formed.

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)