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Line 50: − + − + − + − + − + − + − + − + − + + − + − + − + − *''C'' is the runoff coefficient of the catchment area, and+ − − + − <math>Q_{p} = A_{p}\times K_{sat}\times 3.6 \times 10^{-3}</math> + − {{Plainlist|1=Where:+ − *''K<sub>sat</sub>'' is the saturated hydraulic conductivity of the filter media (mm/hr), and+ − + − ---- − + − [[File:Sizing bio1.png|thumb|The three storage areas 'bowl', 'filter media' and 'reservoir' are sized together.]] + − The bioretention facility will comprise three vertical zones: − #a 'bowl' permitting water to pond occasionally (maximum depth, ''d<sub>p</sub>'' = 0.5 m) − #a layer of [[filter media]] to support plant growth (minimum depth, ''d<sub>m</sub>'' = 0.6 m) , and − #a reservoir of [[stone]] to store and facilitate [[infiltration]] of additional water (depth, ''d<sub>R</sub>'', includes 0.1 m choking layer). − Firstly, all three zones will be sized together within the limited depth to estimate the footprint area of the whole [[bioretention]] facility. To do this the mean void ratio (''V<sub>R</sub>'') will estimated as ~ 0.4. − To calculate the required practice area (''A<sub>p</sub>'') or footprint where the depth is constrained:+ − :<math>A_{p}=\frac{V}{V_{R}d}</math> − {{Plainlist|1=Where:+ − *''V'' = Required volume of storage in m<sup>3</sup>+ − *''V<sub>R</sub>'' = Void ratio (porosity), as measured (or default to 0.4) + − *''A<sub>p</sub>'' = Area of the infiltration practice in m<sup>2</sup>+ − *''d<sub>T</sub>'' = Total depth of infiltration practice in m (= ''d<sub>b</sub>'' + ''d<sub>m</sub>'' + ''d<sub>R</sub>'')}} − ===Step 1 alternative, accounts for infiltration during a design storm event===+ − This may be desirable where the practice is located on particularly freely draining soils and/or where the design storm is of longer duration. − To calculate the required practice area (''A<sub>p</sub>'') or footprint where the depth is constrained: − :<math>A_{p}=\frac{A_{c}iD}{V_{R}d+f'D}</math> + + + − *''D'' = Duration of design storm in hrs+ − *''i'' = Intensity of design storm in mm/hr+ − *''f''' = Design infiltration rate in mm/hr+ − + − + − − − − ==Step 2, geometry and perimeter== − [[file:Hydraulic radius.png|thumb|Two practice areas of 9 m<sup>2</sup>.<br> − P = 12 m (left), P = 20 m (right)]] − <poem> − Fit the bioretention facility into the site plan. It is necessary to have an idea of the perimeter of the facility. − Narrow, linear cells drain faster than round or blocky footprint geometries. − Divide the area of the practice (''A<sub>p</sub>'') by the perimeter (''P''). − </poem> − − ==Step 3, depth of bowl,''d<sub>b</sub>''== − [[File:Sizing bio2.png|thumb|The duration of surface ponding is usually determined by the emptying of the facility below.]] − <poem> − The 'bowl' area is simply the depressed elevation of the surface compared to the surrounding areas; a space to permit temporary ponding. − The depth of the bowl would not typically exceed 0.5 m due to safety concerns. − Some jurisdictions or particular sites may demand a lower maximum depth of ponding. It is worth bearing in mind that in most cases this ponded water will only occur once or twice per year. − The ponded water within the bowl should drain within 48 hrs. This addresses public concerns about [[mosquitoes]] and reduces the probability of losing vegetation due to saturated growing conditions. − The drainage of the bowl is not usually constrained by the surface infiltration (filter media should drain > 25 mm/hr). The infiltration of water from the bowl is determined by the drainage of the filter media and reservoir into the soils. − To estimate the time (''t'') to fully drain the facility: − :<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> − </poem> − + − Check the mounding of groundwater beneath the facility to ensure no incompatibility with nearby sensitive receptors.+ +
→Calculate the remaining dimensions
This advice is specific to [[bioretention]], vegetated systems that infiltrate water to the native soil. <br>
This article is specific to [[bioretention]], vegetated systems that infiltrate water to the native soil. <br>
If you are designing a planted system which does not infiltrate water, see advice on [[flow-through planter]].
If you are designing a planted system which does not infiltrate water, see advice on [[Planters: Sizing]].
[[File:Sizing Bioretention.jpg|thumb|The vertical storage zones in a bioretention cell include: ponding, mulch, filter media, choker course, pipe diameter reservoir and the storage reservoir.]]
[[File:Sizing Bioretention.jpg|thumb|The vertical storage zones in a bioretention cell include: ponding, mulch, filter media, choker course, pipe diameter reservoir and the storage reservoir.]]
{{TOClimit|2}}
{{TOClimit|2}}
! Recommended depth (with underdrain pipe)
! Recommended depth (with underdrain pipe)
! Recommended depth (no underdrain pipe)
! Recommended depth (no underdrain pipe)
! Typical void ratio (''V<sub>r</sub>'')
! Typical void ratio (''V<sub>R</sub>'')
|-
|-
| Ponding depth
| Ponding (''d<sub>p</sub>'')
| 300 mm
| 300 mm
| See below
| See below
|
|
* 0.7 for wood based
* 0.7 for wood based
* 0.4 for aggregates
* 0.4 for [[stone]]
|-
|-
| [[Bioretention media]]
| [[Bioretention: Filter media|filter media]] (''d<sub>m</sub>'')
| colspan="2" |
| colspan="2" |
* 300 mm to support turf grass (and accept only rainwater/roof runoff)
* 300 mm to support turf grass (and accept only rainwater/roof runoff)
* 600 mm to support flowering [[perennials]] and decorative [[grasses]]
* 600 mm to support flowering [[perennials]] and decorative [[grasses]]
* 1000 mm to support [[trees]]
* 1000 mm to support [[trees]]
| 0.3
|
*[[Bioretention media storage| 0.4]] for sandy mix
* 0.35 for a more loamy mix.
|-
|-
| [[choker gravel|Choker course]]
| [[choker layer|Choker course]]
| colspan="2" |100 mm
| colspan="2" |100 mm
| 0.4 typical
| 0.4 typical
| 0.4
| 0.4
|-
|-
| Storage reservoir
| Storage reservoir (''d<sub>s</sub>'')
| See below
| See below
| See below
| See below
==Calculate the maximum overall depth==
==Calculate the maximum overall depth==
*Step 1: Determine what the planting needs are and assign appropriate depth of media, using the table above.
*Step 1: Determine what the planting needs are and assign appropriate depth of media, using the table above.
*Step 2: Select an underdrain pipe diameter (typically 100 - 200 mm), assign this as an 'embedding' depth.
*Step 2: Select an underdrain pipe diameter (typically 100 - 200 mm), assign this as an 'embedding' depth. *Note that this component does not apply if a downstream riser is being used to control an extended saturation zone.
*Step 3: Calculate the maximum possible storage reservoir depth beneath the pipe (''d<sub>s</sub>''):
*Step 3: Calculate the maximum possible storage reservoir depth beneath the pipe (''d<sub>s, max</sub>'', mm):
<math>d_{s}=f'\times38.4</math>
<math>d_{s, max}=f'\times t</math>
{{Plainlist|1=Where:
{{Plainlist|1=Where:
*''f''' = Design infiltration rate in mm/hr, and
*''f''' = Design infiltration rate (mm/hr), and
*38.4 comes from multiplying desired drainage time of 96 hours by void ratio of 0.4}}
*''t'' = [[Drainage time]] (hrs). Check local regulations for drainage time requirements.}}
===Additional step for system without underdrain===
===Additional step for system without underdrain===
*Step 4: Determine maximum permissible ponding depth (''d<sub>p</sub>''):
* Step 4: Determine maximum permissible ponding depth (''d<sub>p, max</sub>''):
<math>d_{p}=f'\times19.2</math>
<math>d_{p, max}=f'\times48</math>
{{Plainlist|1=Where:
{{Plainlist|1=Where:
*''f''' = Design infiltration rate in mm/hr, and
*''f''' = Design infiltration rate (mm/hr), and
*19.2 comes from multiplying desired drainage time of 48 hours by void ratio of 0.4. Note that conceptually the drainage of the ponded area is limited by ex-filtration at the base of the practice.}}
*48 = Drainage time of the ponding (hrs)
*Note that conceptually the drainage of the ponded area is limited by ex-filtration at the base of the practice.}}
* Step 5: Sum total depth of bioretention, and compare to available space above water table and bedrock. Adjust if necessary.
* Step 5: Sum total depth of bioretention, and compare to available space above water table and bedrock. Adjust if necessary.
==Calculate the remaining dimensions==
==Calculate the remaining dimensions==
* Step 6: Multiply the depth of each separate component by the void ratio and then sum the total to find the 1 dimensional storage (in mm).
* Step 6: Multiply the depth of each separate component by the void ratio and then sum the total to find the 1 dimensional storage (in mm).
* Step 7: Calculate the required total storage (m<sup>3</sup>):
* Step 7: Calculate the required total storage (S<sub>T</sub>, m<sup>3</sup>):
<math>Storage=RVC_T\times A_c\times C\times 0.1</math>
<math>S_{T}=RVC_T\times A_c\times 10</math>
{{Plainlist|1=Where:
{{Plainlist|1=Where:
*''RVC<sub>T</sub>'' is the Runoff volume control target (mm),
*''RVC<sub>T</sub>'' is the Runoff volume control target (mm),
*''A<sub>c</sub>'' is the catchment area (Ha),
*''A<sub>c</sub>'' is the catchment area (Ha), and
* 10 is the units correction between m<sup>3</sup> and mm.Ha.}}
* 0.1 is the units correction between m<sup>3</sup> and mm.Ha.}}
* Step 8. Divide required storage (m<sup>3</sup>) by the 1 dimensional storage (in m) to find the required footprint area (''A<sub>p</sub>'') for the bioretention in m<sup>2</sup>.
* Step 8. Divide required storage (m<sup>3</sup>) by the 1 dimensional storage (in m) to find the required footprint area (''A<sub>p</sub>'') for the bioretention in m<sup>2</sup>.
* Step 9. Calculate the peak flow rate (''Q<sub>p</sub>'', in L/s) through the filter media:
* Step 9. Calculate the peak [[flow through perforated pipe|flow rate through the perforated pipe]],
* Step 10. Calculate the peak [[flow through media|flow rate through the filter media]],
* Step 11. Determine if downstream [[flow control]] is required to achieve hydrologic objectives.
*''A<sub>p</sub>'' is the area of the practice (m<sup>2</sup>).}}
==Additional calculations==
==Step 1, total volume==
===Calculating infiltration practice drainage in 1 dimension===
This spreadsheet compares drainage in a single dimension under zero head conditions, mean head conditions and falling head conditions. It provides a more conservative measurement of the drainage time for the purposes of groundwater mounding (where a shorter drainage time causes a greater impact).
{{Clickable button|[[Media:Darcy drainage.xlsx|Download drainage time calculator(.xlsx)]]}}
===Drainage time (3D)<ref>Woods Ballard, B., S. Wilson, H. Udale-Clarke, S. Illman, T. Scott, R. Ahsley, and R. Kellagher. 2016. The SuDS Manual. 5th ed. CIRIA, London.</ref>===
[[file:Hydraulic radius.png|thumb|Two practice areas of 9 m<sup>2</sup>.<br> P = 12 m (left), P = 20 m (right)]]
In some situations, it may be desirable 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 (or [[bioswales]]) drain faster than round or blocky footprint geometries.
*Begin the drainage time calculation by dividing the area of the practice (''A<sub>p</sub>'') by the perimeter (''P'').
*To estimate the time (''t'') to fully drain the facility:
:<math>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]</math>
{{Plainlist|1=Where:
{{Plainlist|1=Where:
*''V<sub>R</sub>'' is the void ratio of the media,
*''A<sub>p</sub>'' is the area of the practice (m<sup>2</sup>),
*''f''' is the design infiltration rate (mm/hr),
*''V<sub>R</sub>'' = Void ratio (porosity), as measured (or default to 0.35 for all aggregates)
*''P'' is the perimeter of the practice (m), and
*''A<sub>p</sub>'' = Area of the infiltration practice in m<sup>2</sup>
*''d<sub>T</sub>'' is the total depth of the practice, including the ponding zone (m).}}
*''A<sub>c</sub>'' = Area of the catchment in m<sup>2</sup>
*''d<sub>T</sub>'' = Total depth of infiltration practice in m (= ''d<sub>b</sub>'' + ''d<sub>m</sub>'' + ''d<sub>R</sub>'')}}
==Final step==
===Groundwater mounding===
<poem>
<poem>
When you wish to model the extent of groundwater mounding beneath an infiltration facility. This tool uses Hantush's derivation (1967).
{{Clickable button|[[Media:Hantush.xlsm|Download groundwater mounding calculator(.xlsm)]]}}
{{Clickable button|[[Media:Hantush.xlsm|Download groundwater mounding calculator(.xlsm)]]}}
Note that this is a minor adaptation (metric units and formatting) from the original tool, written and [https://pubs.usgs.gov/sir/2010/5102/ hosted by the USGS].
Note that this is a minor adaptation (metric units and formatting) from the original tool, written and [https://pubs.usgs.gov/sir/2010/5102/ hosted by the USGS].
</poem>
</poem>
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