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.
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 internal water 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) 	
* 125 to 400 mm (filter media Blend A or B)
* Consult local design standards where available	See below 	1
Mulch (dm) 	75 ± 25 mm 	75 ± 25 mm 	
* 0.7 for shredded wood
* 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	
* 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 	200 mm diameter pipe 	Not applicable 	0.4 for clear stone aggregate in which the pipe is embedded
Internal water storage reservoir (dr)	See below 	See below 	0.4 for clear stone aggregate below the perforated pipe; Higher effective porosity can be achieved by including void-forming structures
Before you begin you will need to know the following;
* Catchment area (i.e. contributing drainage area), Ac (m2)
* Catchment runoff coefficient, C
* Catchment impervious area, Ai (m2)
* Design storm intensity, i (mm/h)
* Design storm duration, D (h)
* Infiltration volume target for the design storm event, Vi (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 internal water storage reservoir of the practice, 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 internal water 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.
==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 (dp, max)
For practices without underdrains:
d_{p, max}=f'\times24
Note that conceptually, in designs without underdrains, when filled to their maximum storage capacity, drainage of ponded water is limited by the infiltration rate of the in-situ (native) soil at the base of the practice.
For practices with underdrains see recommended range for maximum surface ponding depth in the table above, and consult local design standards where available.
* Step 3: Select a design surface ponding depth, dp' (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
For practices with hard edges and vertical-walled ponding areas (e.g., stormwater planter, stormwater tree trench) 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, di 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})
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, dr, 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'\times t
For practices with an underdrain where the perforated pipe is installed on the bottom and connected to a riser (e.g., standpipe and two 45 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 top 90 degree coupling) and reservoir bottom, and is calculated the same way as above. See Bioretention: Internal water storage page for further design guidance and information 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 (Ap) 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)]
For practices where flow is delivered directly to a subsurface (underground) water storage reservoir:
A_{p}=i\times D\times A_{i}/[d_{i} + (f' \times D)]
* Step 6: Compare required surface area of the practice to available space.
To decrease Ap, 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 dp, di, Ap or Ai 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 internal water storage reservoir==
* Step 8: Calculate the surface area of the storage reservoir, Ar (m2) needed to capture the infiltration volume target for the design storm event: A_{r}=V_{i}/[d_{i}+(f'\times D)]
For practices where inflow is directed to a surface ponding area, if Ar is greater than Ap, use the value for Ar 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, dr (m):
d_{r}=d_{i}'/n_{r}'
To minimize the total depth of the practice, dT, 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 (nr').
==Calculate the total depth of the practice, dT==
* Step 10: Determine what the planting needs are and assign an appropriate depth of filter media (df), using the table above. 
* Step 11: Select an underdrain perforated pipe diameter (typically 150 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 two 45 degree couplings - ease for maintenance) 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 raised outlet or riser to utilize the volume of the perforated pipe and surrounding clear stone aggregate material for water storage, which helps to minimize total depth of the practice. Another option is to decrease filter media depth (and adjust 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. 
===Calculating infiltration practice drainage time assuming three dimensional (3D) drainageWoods Ballard, B., S. Wilson, H. Udale-Clarke, S. Illman, T. Scott, R. Ahsley, and R. Kellagher. 2016. The SuDS Manual. 5th ed. CIRIA, London.===
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 (Ap) by the perimeter (x)
*To estimate the time (t) to fully drain the facility
 
t = [nr' * Ap/f'*x] * ln[(dr + (Ap/x)/Ap/x]
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). 
Note that this is a minor adaptation (metric units and formatting) from the original tool, written and hosted by the USGS.
==References==