2,681
edits
Changes
Jump to navigation
Jump to search
Line 37:
Line 37: − + Line 49:
Line 49: − + Line 57:
Line 57: − + Line 64:
Line 64: − + − + − + − + − + − + − + − + − + − + − + − + Line 104:
Line 104: − +
→Time to drain the storage reservoir
|''i''||mm/h||Intensity of design storm
|''i''||mm/h||Intensity of design storm
|-
|-
|''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]]
|-
|-
|''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
|-
|-
|''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
|}
|}
==To calculate the required storage reservoir footprint area where the depth is fixed or 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>:
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>
<math>d_{r} = (\frac{f'}{1000}) \times t </math>
Where <br>
Where <br>
''f''' = [[design infiltration rate]] of the native soil (mm/h) <br>
''f''' = [[design infiltration rate]] of the native soil (mm/h) <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>
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:
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>Ar=\frac{iDAi}{ndr+f'D}</math>
<math>A_{r}=\frac{i \times D \times Ai}{(n\times d_{r})+f'D}</math>
==To calculate the required storage reservoir depth where the area is fixed or 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 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>:
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>d=\frac{D\left[\left( \frac{Ai}{Ap} \right )i-f' \right]}{n}</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 3 dimensional drainage.
Note that in most cases the results of this calculation will be very similar to those from the equation below assuming three-dimensional drainage.
==To calculate the required storage reservoir depth, where the area is fixed or constrained (3D drainage)==
==To calculate the required storage reservoir depth, where the area is fixed or 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:
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=a[e^{\left ( -bD \right )} -1]</math>
:<math>d_{r}=a[e^{\left ( -bD \right )} -1]</math>
Where
Where
<math>a=\frac{Ar}{x}-\frac{i Ai}{x f'}</math>
:<math>a=\frac{A_{r}}{x}-\frac{i\times A_{i}}{x\times f'}</math>
and
and <br>
<math>b=\frac{xf'}{nAr}</math>
:<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 using three dimensional drainage is not available at this time. Elegant submissions are invited.)<br>
(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>
<br>
==Time required to drain surface ponded water==
==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>
<br>
<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{nAr}{f'x}ln\left [ \frac{\left (d+ \frac{Ar}{x} \right )}{\left(\frac{Ar}{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 <br>
Where "ln" means natural logarithm of the term in square brackets <br>
Adapted from CIRIA, The SUDS Manual C753 (2015).
Adapted from CIRIA, The SUDS Manual C753 (2015).