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Line 55: − + − On densely developed sites, the surface area of the practice may be constrained. In such cases the required storage reservoir depth, d<sub>r</sub> of the bioretention cell or infiltration trench can be calculated based on available surface area, A<sub>p</sub>:+ − :<math>d=\frac{D\left[\left( \frac{Ai}{Ap} \right )i-f' \right]}{n}</math>+ − Note that in most cases the results of this calculation will be very similar to those from the equation below assuming 3 dimensional drainage.+ + + + + + + − + − In many locations throughout Ontario, there may be limited depth of soil available into which stormwater may be infiltrated. In such cases the required storage needs to be distributed more widely across the landscape. The footprint area of the water storage reservoir, A<sub>r</sub> can be calculated:+ − + + − + + + + + + + + + + + + − + Line 76:
Line 94: − + − ==To calculate the required depth, where the area of the facility is constrained (3D drainage)== − On densely developed sites the surface area of the facility may be constrained, in this case the required water storage reservoir depth of the bioretention cell or infiltration trench, d, can be calculated assuming three dimensional drainage as follows: − :<math>d=a[e^{\left ( -bD \right )} -1]</math> − Where − <math>a=\frac{Ap}{x}-\frac{i Ai}{x f'}</math> − and − <math>b=\frac{xf'}{nAp}</math> − − (The rearrangement to calculate the required footprint area of the facility for a given depth using three dimensional drainage is not available at this time. Elegant submissions are invited.)<br> − <br> − Try the Darcy drainage calculator tool for estimating drainage time assuming either one or three-dimensional drainage from the practice: <br> Line 97:
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→Time to drain the storage reservoir
|''i''||mm/h||Intensity of design storm
|''i''||mm/h||Intensity of design storm
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|''f'''||mm/h||Design infiltration rate of the underlying native soil, calculated from measured [[Infiltration: Testing| infiltration rate]] and applied [[Infiltration|safety factor]]
|''f'''||mm/h||[[Design infiltration rate]] of the underlying native soil, calculated from measured [[Infiltration: Testing| infiltration rate]] and applied [[Infiltration|safety factor]]
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|''n''||-||Porosity of the aggregate or other void-forming fill material(s) in the storage reservoir of the practice.<br> *Note: For systems that have significant storage in open chambers surrounded by clear stone aggregate, an effective porosity value (''n<nowiki>'</nowiki>'') may be estimated for the whole installation and used in the calculations below. Effective porosity will vary according to the geometry of the storage chambers, so advice should be sought from product manufacturers. Permit applications should include the basis for ''n<nowiki>'</nowiki>'' estimates.
|''n''||-||Porosity of the aggregate or other void-forming fill material(s) in the storage reservoir of the practice.<br> *Note: For systems that have significant storage in open chambers surrounded by clear stone aggregate, an effective porosity value (''n<nowiki>'</nowiki>'') may be estimated for the whole installation and used in the calculations below. Effective porosity will vary according to the geometry of the storage chambers, so advice should be sought from product manufacturers. Permit applications should include the basis for ''n<nowiki>'</nowiki>'' estimates.
|''x''||m||Perimeter of the practice
|''x''||m||Perimeter of the practice
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|''K<sub>f</sub>''||mm/h||Minimum acceptable saturated hydraulic conductivity of the filter media or planting soil used in the practice, when compacted to 85% maximum dry density
|''K<sub>f</sub>''||mm/h||Minimum acceptable saturated hydraulic conductivity of the [[Bioretention: Filter media|filter media]] or [[Topsoil| planting soil]] used in the practice, when compacted to 85% maximum dry density
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{{Clickable button|[[Media:Infiltration Sizing 20200525 locked.xlsx|Download the infiltration practice sizing tool]]}}
{{Clickable button|[[Media:Infiltration Sizing 20200525 locked.xlsx|Download the infiltration practice sizing tool]]}}
==To calculate the required storage reservoir depth where the area of the facility is constrained (1D drainage)==
==To calculate the required storage reservoir footprint area where the depth is fixed or constrained (1D drainage)==
To ensure that the water storage capacity of the facility is available at the onset of a storm event, it is recommended to size the storage reservoir despth, d<sub>r</sub>, based on the depth of water that will drain via infiltration between storm events. So d<sub>r</sub> can be calculated as <br>:
<math>d_{r} = (\frac{f'}{1000}) \times t </math>
Where <br>
''f''' = [[design infiltration rate]] of the native soil (mm/h) <br>
''t'' = [[drainage time]], based on local criteria or long-term average inter-event period for the location.<br>
<br>
In many locations there may be a limited depth of soil available above the seasonally high water table or top of bedrock elevation into which stormwater may be infiltrated. In such cases the required storage needs to be distributed more widely across the landscape. <br>
Where the storage reservoir depth is fixed or constrained the footprint area of the water storage reservoir, A<sub>r</sub> can be calculated:
<math>A_{r}=\frac{i \times D \times Ai}{(n\times d_{r})+f'D}</math>
==To calculate the required storage reservoir footprint area where the depth is constrained (1D drainage)==
==To calculate the required storage reservoir depth where the area is fixed or constrained (1D drainage)==
On densely developed sites, the surface area available for the practice may be constrained. In such cases the required storage reservoir depth, d<sub>r</sub> of the bioretention cell or infiltration trench can be calculated based on available surface area, A<sub>p</sub>:
<math>Ar=\frac{iDAi}{nd+f'D}</math>
:<math>d_{r}=\frac{D\left[\left( \frac{Ai}{Ap} \right )i-f' \right]}{n}</math>
Note that in most cases the results of this calculation will be very similar to those from the equation below assuming three-dimensional drainage.
==Time required to drain surface ponded water==
==To calculate the required storage reservoir depth, where the area is fixed or constrained (3D drainage)==
On densely developed sites, the surface area available for the facility may be constrained. In such cases the required water storage reservoir depth of the bioretention cell or infiltration trench, d, can be calculated assuming three-dimensional drainage as follows
:<math>d_{r}=a[e^{\left ( -bD \right )} -1]</math>
Where
:<math>a=\frac{A_{r}}{x}-\frac{i\times A_{i}}{x\times f'}</math>
and <br>
:<math>b=\frac{x\times f'}{n\times A_{r}}</math>
(The rearrangement to calculate the required footprint area of the facility for a given depth assuming three-dimensional drainage is not available at this time. Elegant submissions are invited.)<br>
<br>
==Time required to drain surface ponded water (1D drainage)==
The following equation assumes one dimensional drainage over the surface ponding area.
The following equation assumes one dimensional drainage over the surface ponding area.
It is best applied to calculate the maximum duration of ponding on the surface of [[bioretention cells]], and upstream of the [[check dams]] of [[bioswales]] and [[enhanced grass swales]] to ensure all surface ponding drains within 48 hours.
It is best applied to calculate the maximum duration of ponding on the surface of [[bioretention cells]], and upstream of the [[check dams]] of [[bioswales]] and [[enhanced grass swales]] to ensure all surface ponding drains within 48 hours.
To calculate the time (''t'') to fully drain surface ponded water through the filter media or planting soil:
To calculate the time (''t'') to fully drain surface ponded water through the filter media or planting soil:
<math>t=\frac{dp'}{Kf}</math>
<math>t=\frac{d_{p}'}{K_{f}}</math>
Where <br>
Where <br>
d<sub>p</sub>' is the effective or mean surface ponding depth (mm).<br>
d<sub>p</sub>' is the effective or mean surface ponding depth (mm).<br>
The target [[drainage time]] for the active storage reservoir depth of an infiltration facility is typically between 48 and 72 hours or based on the average inter-event period for the location. Contact the local municipality or conservation authority for criteria. See [[Drainage time]] for more information about how inter-event periods vary across Ontario and to help select what is suitable for the site. <br>
The target [[drainage time]] for the active storage reservoir depth of an infiltration facility is typically between 48 and 72 hours or based on the average inter-event period for the location. Contact the local municipality or conservation authority for criteria. See [[Drainage time]] for more information about how inter-event periods vary across Ontario and to help select what is suitable for the site. <br>
<br>
<br>
Try the Darcy drainage time calculator tool for estimating the time required to fully drain the water storage reservoir of the facility assuming either one or three-dimensional drainage: <br>
{{Clickable button|[[Media:Darcy drainage 20200528 locked.xlsx|Download the Darcy drainage time calculator]]}}<br>
{{Clickable button|[[Media:Darcy drainage 20200528 locked.xlsx|Download the Darcy drainage time calculator]]}}<br>
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<br>
To calculate the time (''t'') to fully drain the facility assuming three-dimensional drainage:
To calculate the time (''t'') to fully drain the facility assuming three-dimensional drainage:
<math>t=\frac{nAp}{f'x}ln\left [ \frac{\left (d+ \frac{Ap}{x} \right )}{\left(\frac{Ap}{x}\right)}\right]</math>
<math>t=\frac{n\times A_{r}}{f'\times x}ln\left [ \frac{\left (d_{r} \frac{A_{r}}{x} \right )}{\left(\frac{A_{r}}{x}\right)}\right]</math>
Where "ln" means natural logarithm of the term in square brackets
Where "ln" means natural logarithm of the term in square brackets <br>
Adapted from CIRIA, The SUDS Manual C753 (2015).
[[category: modeling]]
[[category: modeling]]
[[category: infiltration]]
[[category: infiltration]]