Difference between revisions of "Bioretention: Sizing and modeling"

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:<math>b=\frac{xq}{nP}</math>
:<math>b=\frac{xq}{nP}</math>


The rearrangement to calculate the required footprint area of the facility for a given depth is not available at this time. Submissions are welcome.  
The rearrangement to calculate the required footprint area of the facility for a given depth is not available at this time. Elegant submissions are invited.  


To calculate the time (''t'') to empty the facility:  
To calculate the time (''t'') to fully drain the facility:  
<math>t=\frac{nP}{qx}ln\left [ \frac{\left (d+ \frac{P}{x} \right )}{\left(\frac{P}{x}\right)}\right]</math>
<math>t=\frac{nP}{qx}ln\left [ \frac{\left (d+ \frac{P}{x} \right )}{\left(\frac{P}{x}\right)}\right]</math>


[[category: modeling]]
[[category: modeling]]
[[category: infiltration]]
[[category: infiltration]]

Revision as of 21:21, 18 August 2017

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 may be limited by the need to support vegetation i.e. not < 0.6 m.
  4. The area P for a green roofs, absorbent landscapes and permeable paving may be very similar or equal to the catchment area, so that the I/P ratio is close to 1.
  5. Infiltration trenches, chambers and bioretention cells have a maximum recommended I/P ratio of 20.
Inputs
Symbol Units Parameter
D hrs Duration of design storm (for MOECC volume based caclulations set to 1)
i mm/hr Intensity of design storm (for MOECC volume based calculations use whole storm depth (link to map))
q mm/hr Infiltration coefficient, calculated from measured infiltration rate and applied safety factor
n - Porosity, as measured (or default to 0.35)
I m2 Impermeable area i.e. catchment
d m depth of Infiltration facility or BMP
P m2 Permeable area i.e. area of the facility or BMP

The following equations assume that infiltration occurs primarily through the base of the facility. They may be applied for most shapes and sizes of infiltration facility. For some geometries (e.g. where a particularly deep facility is both possible and desired), it may be preferred to also account for lateral infiltration.

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

To calculate the require facility area or footprint where the depth is constrained:

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

Accounting for lateral infiltration[edit]

Three footprint areas of 9 m2.
From left to right x = 12 m, x = 14 m, and x = 16 m

The 3 dimensional equations make use of the hydraulic radius (P/x), where x is the perimeter (m) of the facility.
Maximizing the perimeter of the facility directs designers towards longer, linear footprint shapes such as infiltration trenches and bioswales.

To calculate the required depth:

Where:

and

The rearrangement to calculate the required footprint area of the facility for a given depth is not available at this time. Elegant submissions are invited.

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