Difference between revisions of "Bioretention: Sizing and modeling"

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[[file:Hydraulic radius.png|thumb|Two footprint areas of 9 m<sup>2</sup>.<br>
 
[[file:Hydraulic radius.png|thumb|Two footprint areas of 9 m<sup>2</sup>.<br>
 
Perimeter = 12 m (left) Perimeter = 20 m (right)]]
 
Perimeter = 12 m (left) Perimeter = 20 m (right)]]
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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.
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Note that narrow, linear bioretention features drain faster than round or blocky footprint geometries.
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*Begin the drainage time calculation by dividing the area of the practice (''A<sub>p</sub>'') by the perimeter (''P'').
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*To estimate the time (''t'') to fully drain the facility:
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:<math>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]</math>
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{{Plainlist|1=Where:
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*''V<sub>R</sub>'' is the void ratio of the media,
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*''A<sub>p</sub>'' is the area of the practice (m<sup>2</sup>),
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*''f''' is the design infiltration rate (mm/hr),
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*''P'' is the perimeter of the practice (m), and
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*''d'' is the total depth of the practice, including the ponding zone (m).}}
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To calculate the time (''t'') to fully drain the facility:  
 
To calculate the time (''t'') to fully drain the facility:  
 
:<math>t=\frac{V_{R}A_{p}} {q'P}ln\left [ \frac{\left (d+ \frac{A_{p}}{P} \right )}{\left(\frac{A_{p}}{P}\right)}\right]</math>
 
:<math>t=\frac{V_{R}A_{p}} {q'P}ln\left [ \frac{\left (d+ \frac{A_{p}}{P} \right )}{\left(\frac{A_{p}}{P}\right)}\right]</math>

Revision as of 20:06, 2 April 2018

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 ratio of 20.

Size a bioretention cell[edit]


Determine if there is a constraint to the depth (d) of the bioretention practice:

Depth to GW

or if the land area is limited, determine the I/P ratio::

Where:

  • R = Ratio of catchment area (Ac) to BMP footprint area (Ap) syn. I/P ratio.
  • Ap = Area of the infiltration practice in m2
  • Ac = Catchment area in m2
Then
To calculate the require facility area or footprint where the depth is constrained:

To calculate the required depth, where the area of the facility is constrained:

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Where:

  • D = Duration of design storm in hrs
  • i = Intensity of design storm in mm/hr
  • q' = Infiltration coefficient in mm/hr (accounting for SCF)
  • SCF = Safety correction factor
  • VR = Void ratio (porosity), as measured (or default to 0.35 for all aggregates)
  • R = Ratio of catchment area (Ac) to BMP footprint area (Ap) syn. I/P ratio.
  • Ap = Area of the infiltration practice in m2
  • Ac = Catchment area in m2
  • d = 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)

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).
  • To estimate the time (t) to fully drain the facility:

Where:

  • VR is the void ratio of the media,
  • 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
  • d is the total depth of the practice, including the ponding zone (m).

To calculate the time (t) to fully drain the facility:

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.