Difference between revisions of "Bioretention: Sizing and modeling"

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:<math>t=\frac{nA_{p}}{f'P}ln\left [ \frac{\left (d_{T}+ \frac{A_{p}}{P} \right )}{\left(\frac{A_{p}}{P}\right)}\right]</math>
 
:<math>t=\frac{nA_{p}}{f'P}ln\left [ \frac{\left (d_{T}+ \frac{A_{p}}{P} \right )}{\left(\frac{A_{p}}{P}\right)}\right]</math>
 
{{Plainlist|1=Where:
 
{{Plainlist|1=Where:
*''n'' is the porosity of the media,  
+
*''n'' is the porosity of the fill materials within the practice, depth weighted mean
 
*''A<sub>p</sub>'' is the area of the practice (m<sup>2</sup>),
 
*''A<sub>p</sub>'' is the area of the practice (m<sup>2</sup>),
 
*''f''' is the design infiltration rate (mm/hr),  
 
*''f''' is the design infiltration rate (mm/hr),  

Revision as of 21:43, 21 April 2020

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 (e.g not less than 0.6 m to support deep rooting perennials and shrubs).
  4. Bioretention has a maximum recommended I/P ratio of 20.

Size a bioretention cell for constrained depth[edit]

If there is a constraint to the depth (dT, m) of the practice, calculate the required footprint area (Ap, m2), as:

Where:

  • Ap = Area of the infiltration practice in m2
  • Ac = Catchment 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
  • n = Porosity of the fill materials within the practice, depth weighted mean
  • dT = Total depth of the infiltration practice in m.

Size a bioretention cell for constrained ground area[edit]

If the land area is limited, determine the ratio of catchment (Ac) to BMP footprint area (Ap):

Where:

  • R = Ratio of catchment area (Ac) to BMP footprint area (Ap)
  • Ap = Area of the infiltration practice in m2
  • Ac = Catchment area in m2

Then calculate the required depth (dT), as:

Where:

  • D = Duration of design storm in hrs
  • i = Intensity of design storm in mm/hr
  • f' = Design infiltration rate in mm/hr
  • n = Porosity of the fill materials within the practice, depth weighted mean
  • 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 aggregate.

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

Calculate drawdown time[edit]

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 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 area of the practice (Ap) by the perimeter (P).
  • Use the following equation to estimate the time (t) to fully drain the facility:

Where:

  • n is the porosity of the fill materials within the practice, depth weighted mean
  • Ap is the area of the practice (m2),
  • f' is the design infiltration rate (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.