Bioretention: Sizing

This article is specific to bioretention, vegetated systems that infiltrate water to the native soil.
If you are designing a planted system which does not infiltrate water, see advice on Planters: Sizing.

The vertical storage zones in a bioretention cell include: ponding, mulch, filter media, choker layer, embedded pipe diameter depth and the storage reservoir.

Many of the dimensions in a bioretention system can be predetermined according to the function of the component. There is greatest flexibility in the ponding depth, filter media depth and the depth of the storage reservoir beneath the optional underdrain pipe. The table below describes some recommended values to use to begin the design process.

Component	Recommended depth (with underdrain pipe)	Recommended depth (no underdrain pipe)	Typical porosity (n)
Surface ponding, maximum (dp, max)	300 mm; filter media Blend A 350 mm; filter media Blend B	See below	1
Mulch (dm)	75 ± 25 mm		0.7 for wood based 0.4 for stone
Filter media (df)	300 mm to support turf grass and accept only roof runoff 600 mm to support shrubs, flowering perennials and deeply rooting decorative grasses and accept both roof and pavement runoff 1000 mm to support trees and accept both roof and pavement runoff		0.4 for sandier Blend A (drainage rate priority) 0.35 for more loamy Blend B (water quality treatment priority)
Choker layer	100 mm	Not applicable	0.4
Perforated pipe and surrounding aggregate	200 mm (i.e. pipe diameter)	Not applicable	0.4
Storage reservoir (dr)	See below	See below	0.4

Before you begin you will need to know the following;

• Catchment area (i.e. contributing drainage area), A_c (m²)
• Catchment runoff coefficient, C
• Catchment impervious area, A_i (m²⁾
• Design storm intensity, i (mm/h)
• Design storm duration, D (h)
• Infiltration volume target for the design storm event, V_i (m³), based on average annual water budgets for the catchment for pre- and post-development scenarios and equal to the infiltration volume deficit (pre-development minus post-development annual infiltration)
• Drainage time, t (h), time required to fully drain the active water storage components of the practice (i.e surface ponding and active storage reservoir depths), based on local criteria or long term average inter-event period for the location
• Field measured infiltration rate of the underlying native soil, f (mm/h), median of field measurements or based on interpolation from median grain-size distribution results
• Design infiltration rate of the underlying native soil, f' (mm/h), median field measured value, f divided by a safety factor, z
• Safety factor, z (dimensionless value between 2 and 3) chosen by designer based on consideration of risk factors
• Proposed surface grade elevation at the practice location (metres above sea level, masl)
• Elevation of the seasonally high water table or bedrock surface (metres above sea level, masl), below the practice location
• Effective porosity of the storage reservoir fill material, including any void-forming structures (e.g. pipes, chambers, tanks, soil cells, etc.) and surrounding aggregate, n'
• Types of plants to be supported by the filter media bed (i.e. grasses vs. mix of grasses, plants and shrubs vs. trees)
• How runoff will be delivered to the practice (i.e. to surface ponding area, or directly to storage reservoir)

This spreadsheet tool has been set up to perform all of the bioretention sizing calculations shown below and allows side-by-side comparison of equation outputs for each potential design approach or constraint scenario.
Download the infiltration practice sizing tool

Decide if an underdrain will be included

• Step 1: Based on the median measured infiltration rate of the native soil at the proposed location and bottom elevation of the practice, or estimated infiltration rate from median grain-size distribution results, decide if an underdrain will be included in the design. See Design infiltration rate for guidance on field tests, methods and number of test locations and tests (i.e. measurements) to be performed.
  

If the median field measured or estimated infiltration rate of the underlying native soil (f) is less than 15 mm/h, include an underdrain.

Select a surface ponding depth to begin sizing with

• Step 2: Determine a maximum surface ponding depth (d_{p, max})

For practices without underdrains: $d_{p,max}=f'\times 48$

Where:

• f' = Design infiltration rate (mm/h), and
• 48 = Maximum permissible drainage time for surface ponded water (h)

Note that conceptually, in designs without underdrains, when filled to their maximum storage capacity, drainage of ponded water is limited by the infiltration rate at the base of the practice.

For practices with underdrains see recommended maximum surface ponding depth for each filter media blend in the table above.

• Step 3: Select a design surface ponding depth, d_p' (m) to begin sizing with:
  

For practices with soft (i.e. landscaped) edges and bowl-shaped ponding areas calculate the mean surface ponding depth: $d_{p}'=d_{p,max}\times 0.5$

Where:

• d_{p, max} = maximum surface ponding depth (m)

For practices with hard edges and vertical-walled ponding areas (e.g., stormwater planter, soil cell) use the maximum ponding depth: $d_{p}'=d_{p,max}$

Determine the infiltration water storage depth of the practice

• Step 4: Calculate the infiltration water storage depth of the practice, d_i which is the depth of water stored by the practice that can drain by infiltration alone.
  

For practices without an underdrain, components contributing to infiltration water storage include the surface ponding, mulch and filter media depths (i.e. total depth of the practice). The infiltration water storage depth of the practice can be calculated as: $d_{i}=d_{p}'-(d_{m}\times (1-n_{m}))+(d_{f}\times n_{f})$

Where:

• d_p' = Design surface ponding depth (m)
• d_m = Depth of mulch (m)
• n_m = Porosity of mulch
• d_f = Depth of filter media (m)
• n_f = Porosity of filter media

For practices with an underdrain where the perforated pipe is elevated off the bottom, infiltration water storage is provided by the depth of the storage reservoir below the invert of the underdrain perforated pipe, d_r, and only the portion that can reliably drain by infiltration within the specified inter-event drainage time, t. So the infiltration water storage depth of the practice can be calculated as: $d_{i}=f't$

Where:

• f' = Design infiltration rate of underlying native soil (m/h)
• t = Drainage time (h), time required to fully drain the active storage components of the practice (i.e. surface ponding and infiltration water storage depths), based on local criteria or long term average inter-event period for the location

For practices with an underdrain where the perforated pipe is installed on the bottom and connected to a riser (e.g., standpipe and two 90 degree couplings), infiltration water storage is provided by the storage reservoir depth between the inverts of the riser outlet (i.e invert elevation of the 90 degree coupling) and reservoir bottom, and is calculated the same way as above. See Bioretention: Internal water storage page for guidance on water quality treatment benefits of internal water storage reservoirs or zones in partial infiltration bioretention designs.

To boost drainage performance on fine-textured, low permeability soils, consider designing storage reservoirs even deeper than those calculated using the above approach, that many not fully drain between storm events (i.e. includes inactive water storage), which increases hydraulic head and thereby, infiltration rate at the base of the practice. See Low permeability soils for more information.

Determine the required surface area of the practice

• Step 5: Calculate the surface area of the practice (A_p) needed to capture the volume of runoff produced from the catchment by the design storm event.
  

For practices where flow is delivered to a surface ponding area: $A_{p}=i\times D\times A_{i}/[d_{p}'+(K_{f}\times D)]$

Where:

• i = Design storm intensity (m/h)
• D = Design storm duration (h)
• A_i = Catchment impervious area (m²)
• d_p' = Design surface ponding depth (m)
• K_f = minimum acceptable saturated hydraulic conductivity of the filter media (m/h), see Filter media for guidance

For practices where flow is delivered directly to the storage reservoir: $A_{p}=i\times D\times A_{i}/[d_{i}+(f'\times D)]$

Where:

• d_i = Infiltration water storage depth (m), see above for equations for with and without underdrain designs
• f' = design infiltration rate of the underlying native soil (m/h)
• D = Design storm duration (h)

• Step 6: Compare required surface area of the practice to available space.
  

To decrease A_p, consider increasing ponding depth if feasible and would not create a safety hazard (recommended maximum of 0.45 m), using the Darcy 3D drainage equation or tool (see below) to optimize the infiltration water storage depth assuming both vertical and horizontal drainage, or decreasing the catchment area.

• Step 7: Calculate catchment impervious area to practice permeable (footprint) area ratio, R, also referred to as I/P ratio:

$R=A_{i}/A_{p}$
You can use the infiltration practice sizing tool noted above to adjust d_p, d_i, A_p or A_i to find practice dimensions that provide the required storage volume and will drain within the specified drainage time, while keeping R between 5 and 20.

Determine the required surface area of the storage reservoir

• Step 8: Calculate the surface area of the storage reservoir, A_r (m²) needed to capture the infiltration volume target for the design storm event: $A_{r}=V_{i}/[d_{i}+(f'\times D)]$

Where:

• V_i = Infiltration volume target for the design storm event (m³), based on average annual water budgets for pre- and post-development scenarios, and the estimated infiltration volume deficit (pre-development minus post-development infiltration).
• d_i = Infiltration water storage depth of the practice (m), see equations above to calculate for with and without underdrain designs.
• f' = Design infiltration rate of the underlying native soil (m/h)
• D= Duration of design storm (h)

For practices where inflow is directed to a surface ponding area, if A_r is greater than A_p, use the value for A_r as the required footprint area of the practice and adjust the ponding depth down to limit surface storage to what is required to fully capture the design storm runoff volume.

• Step 9: Calculate the required storage reservoir depth, d_r (m):

$d_{r}=d_{i}'\times 1/n_{r}'$

Where:

• d_i' = Design infiltration water storage depth (m)
• n_r' = Effective porosity of the storage reservoir fill material(s).

To minimize the total depth of the practice, d_T, and save aggregate, consider installing void-forming structures (e.g. Permavoid, D-Raintank, low profile stormwater chamber, large diameter perforated pipes etc.) embedded in clear stone aggregate in the storage reservoir instead of aggregate alone, which will provide a greater effective porosity (n_r').

Calculate the total depth of the practice, d_T

• Step 10: Determine what the planting needs are and assign an appropriate depth of filter media (d_f), using the table above.
• Step 11: Select an underdrain perforated pipe diameter (typically 100 or 200 mm), assign this as an 'embedded' depth equal to the pipe diameter. The perforated pipe depth can be made part of the infiltration water storage of the practice when a riser (standpipe and 90 degree coupling) are used to design the underdrain.
• Step 12: Sum total depth of bioretention components, and compare to available space (i.e. depth) between the elevations of the proposed surface grade and one (1) metre above the seasonally high water table or top of bedrock in the practice location.
• Step 13: Adjust component depths to maintain a separation of one (1) metre between the base of the practice and the seasonally high water table or top of bedrock elevation, or a lesser or greater value based on groundwater mounding analysis. See below and Groundwater for more information.
  

For practices without an underdrain in locations constrained in the vertical dimension, consider decreasing filter media depth (and adjusting supported plant types) and/or catchment impervious area.

For practices with an underdrain in locations constrained in the vertical dimension, consider installing the perforated pipe on the bottom of the storage reservoir and including a riser (saves the depth of aggregate needed to embed the pipe), and/or decreasing filter media depth (and adjusting supported plant types), storage reservoir depth and/or catchment impervious area.

For more on sizing bioretention practices on constrained sites see Bioretention: Sizing and modeling.

Calculate peak flow rates

• Step 14. Calculate the peak flow rate through the perforated pipe,
• Step 15. Calculate the peak flow rate through the filter media,
• Step 16. Determine if downstream flow control is required to achieve hydrologic objectives.

Calculating infiltration practice drainage time assuming one dimensional (1D) drainage

This spreadsheet allows calculation of drainage time assuming one dimensional drainage under zero head conditions, mean head conditions and falling head conditions. It provides a conservative estimate of drainage time for the purposes of groundwater mounding analysis, where shorter drainage times cause a greater impact.

Download the Darcy drainage time calculator tool

Calculating infiltration practice drainage time assuming three dimensional (3D) drainage

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

In some situations, it may be desirable to optimize the size of the bioretention practice, by accounting for drainage in three dimensions rather than one. Typically, this is only worth exploring over sandy textured native subsoils with rapid infiltration.

The drainage time calculator noted above can be used to calculate drainage time assuming both one and three dimensional drainage and allows for comparison between the estimates.

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

t = [n_r' * A_p/f'*x] * ln[(d_r + (A_p/x)/A_p/x]

Where:

• n_r' is the effective porosity of the storage reservoir fill material(s),
• A_p is the area of the practice (m²),
• f' is the design infiltration rate of the native soil (mm/h),
• x is the perimeter of the practice (m),
• ln is the natural logarithm and,
• d_r is the depth of the storage reservoir (m).

Note that narrow, linear bioretention features (or bioswales) drain faster than round or blocky footprint geometries because they have larger perimeters (see above right figure).

Groundwater mounding

To model the extent of groundwater mounding beneath an infiltration facility use the tool below to determine if there is potential for interaction between groundwater levels and the base of the practice during drainage. This tool uses Hantush's derivation (1967).
Download the Hantush groundwater mounding tool
Note that this is a minor adaptation (metric units and formatting) from the original tool, written and hosted by the USGS.

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

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

a top dressing over vegetation beds that provides suppresses weeds and helps retain soil moisture in bioretention cells, stormwater planters and dry swales.

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.

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

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.

A hard surface area (e.g., road, parking area or rooftop) that prevents or retards the infiltration of water into the soil.

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

refers to the characteristics and functions of a system prior to urban development.

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

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.

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).

A vegetated practice that collects and treats stormwater through sedimentation and filtration. Contributions to water cycle/water balance are through evapotranspiration only; no infiltration.

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

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

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