Bioretention: Sizing and modeling

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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 i.e. not < 0.6 m.
  4. Bioretention has a maximum recommended I/P ratioThe ratio of the catchment (impervious area) to the footprint area of the receiving BMP (pervious area). of 20.

Size a bioretentionA shallow excavated surface depression containing prepared filter media, mulch, and planted with selected vegetation. cell for constrained depth

If there is a constraint to the depth (dT, m) of the practice, calculate the required footprint area (Ap, m2), as\[A_{p}=\frac{A_c\times i\times D}{(V_{R}\times d_{T})+(f'\times D)}\]

Where:

  • Ap = Area of the infiltration practice in m2
  • Ac = CatchmentThe land draining to a single reference point (usually a structural BMP); similar to a subwatershed, but on a smaller scale. 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
  • VR = Mean void ratio of the fill within the practice
  • dT = Total depth of the infiltration practice in m.

Size a bioretentionA shallow excavated surface depression containing prepared filter media, mulch, and planted with selected vegetation. cell for constrained ground area

If the land area is limited, determine the ratio of catchmentThe land draining to a single reference point (usually a structural BMP); similar to a subwatershed, but on a smaller scale. (Ac) to BMPBest 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. footprint area (Ap): \[R=\frac{A_{c}}{A_{p}}\]

Where:

  • R = Ratio of catchmentThe land draining to a single reference point (usually a structural BMP); similar to a subwatershed, but on a smaller scale. area (Ac) to BMPBest 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. footprint area (Ap)
  • Ap = Area of the infiltration practice in m2
  • Ac = CatchmentThe land draining to a single reference point (usually a structural BMP); similar to a subwatershed, but on a smaller scale. area in m2

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

Where:

  • D = Duration of design storm in hrs
  • i = Intensity of design storm in mm/hr
  • f' = Design infiltration rateThe rate at which stormwater percolates into the subsoil measured in inches per hour. in mm/hr
  • VR = Void ratio
  • dT = 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 aggregateA 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..

This spreadsheet tool has been set up to perform either of the above calculations.
Download .xlsx calculation tool

Calculate drawdown timeThe period between the maximum water level and the minimum level (dry weather or antecedent level).

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

Download Darcy drainage time calculator(.xlsx)

In some situations, it may be possible to reduce the size of the bioretentionA shallow excavated surface depression containing prepared filter media, mulch, and planted with selected vegetation. required, by accounting for rapid drainageNatural or artificial means of intercepting and removing surface or subsurface water (usually by gravity).. Typically, this is only worth exploring over sandy soils with rapid infiltrationThe slow movement of water into or through a soil or drainage system.Penetration of water through the ground surface.. Note that narrow, linear bioretentionA shallow excavated surface depression containing prepared filter media, mulch, and planted with selected vegetation. features drain faster than round or blocky footprint geometries.

  • Begin the drainage timeThe period between the maximum water level and the minimum level (dry weather or antecedent level). calculation by dividing the area of the practice (Ap) by the perimeter (P).
  • To estimate the time (t) to fully drain the facility:

\[t=\frac{V_{R}A_{p}}{f'P}ln\left [ \frac{\left (d_{T}+ \frac{A_{p}}{P} \right )}{\left(\frac{A_{p}}{P}\right)}\right]\]

Where:

  • VR is the void ratio of the media,
  • Ap is the area of the practice (m2),
  • f' is the design infiltration rateThe rate at which stormwater percolates into the subsoil measured in inches per hour. (mm/hr),
  • P is the perimeter of the practice (m), and
  • dT is the total depth of the practice, including the ponding zone (m).

This 3 dimensional equation makes use of the hydraulic radius (Ap/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.