Difference between revisions of "Bioretention: Sizing and modeling"
Jenny Hill (talk | contribs) |
Jenny Hill (talk | contribs) |
||
| Line 21: | Line 21: | ||
==Size a bioretention cell for constrained ground area== | ==Size a bioretention cell for constrained ground area== | ||
| + | {{float right|{{#widget:WolframAlpha|id=88d135fd5507a36a9770deaa8106c975}}}} | ||
If the land area is limited, determine the ratio of catchment (A<sub>c</sub>) to BMP footprint area (A<sub>p</sub>): | If the land area is limited, determine the ratio of catchment (A<sub>c</sub>) to BMP footprint area (A<sub>p</sub>): | ||
:<math>R=\frac{A_{c}}{A_{p}}</math> | :<math>R=\frac{A_{c}}{A_{p}}</math> | ||
| Line 29: | Line 30: | ||
*''A<sub>c</sub>'' = Catchment area in m<sup>2</sup>}} | *''A<sub>c</sub>'' = Catchment area in m<sup>2</sup>}} | ||
| − | + | Then calculate the required depth (d<sub>T</sub>), as: | |
| − | <math>d=\frac{D\left[ | + | <math>d=\frac{D \left[ (R\times i)-f'\right]}{V_{R}}</math> |
| − | |||
{{Plainlist|1=Where: | {{Plainlist|1=Where: | ||
Revision as of 20:25, 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:
- The maximum total depth will be limited by construction practices i.e. not usually > 2 m.
- The maximum total depth may be limited by the conditions underground e.g. the groundwater or underlying geology/infrastructure.
- The minimum total depth will be limited by the need to support vegetation i.e. not < 0.6 m.
- Bioretention has a maximum recommended I/P ratio of 20.
Size a bioretention cell for constrained depth[edit]
Depth to GW If there is a constraint to the depth (dT, m) of the infiltration 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
- VR = Mean void ratio of the fill within the practice
- 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) syn. I/P ratio.
- Ap = Area of the infiltration practice in m2
- Ac = Catchment area in m2
Then calculate the required depth (dT), as:
![{\displaystyle d={\frac {D\left[(R\times i)-f'\right]}{V_{R}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3100d19b100d30f4feda0d2db7a600b301411869)
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]
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:
![{\displaystyle 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]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7b7b4e8cd53033eb0099c43f67d3bf6288311655)
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
- 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.