Difference between revisions of "Permeable pavements: Sizing"

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The following calculation is used to size the stone storage bed (reservoir) used as a base course for designs without underdrains. It is assumed that the footprint of the stone bed will be equal to the footprint of the pavement. The following equations are taken from the ICPI Manual <ref>Smith, D. 2006. Permeable Interlocking Concrete Pavements; Selection, Design, Construction, Maintenance. 3rd Edition. Interlocking Concrete Pavement Institute. Burlington, ON.</ref>
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The following calculation is used to size the stone storage bed (reservoir) used as a base course. It is assumed that the footprint of the stone bed will be equal to the footprint of the pavement. The following equations are derived from the Interlocking Concrete Pavement Institute (ICPI) manual <ref>Smith, D. 2017. Permeable Interlocking Concrete Pavements; Selection, Design, Specifications, Construction, Maintenance. 5th Edition. Interlocking Concrete Pavement Institute. Chantilly VA</ref>
==To calculate the total depth of the stone reservoir (all graded layers)==  
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The equation for the depth of the stone bed is as follows:  
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===For full infiltration design, to calculate the total depth of clear stone aggregate layers needed for the water storage reservoir===  
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The equation for the maximum depth of the stone reservoir (''d<sub>r, max</sub>'', m) is as follows:  
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<math>d_{r, max}=\frac{(RVC_{T}\times R) + RVC_{T} - (f'\times D)}{n}</math>
  
<math>d= \frac{[Q_c\times R + P - f'\times t ]}{V_{R}}</math>
 
 
{{Plainlist|1=Where:
 
{{Plainlist|1=Where:
*''d'' = Stone bed depth (m)  
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*''RVC<sub>T</sub>'' = [[Runoff volume control target]] (m)
*''Q<sub>c</sub>'' = Depth of runoff from contributing drainage area, not including permeable paving surface (m)  
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<math>RVC_{T}= D\times i </math>
*''R'' = ''A<sub>c</sub>''/''A<sub>p</sub>''; the ratio of contributing drainage area (''A<sub>c</sub>'') to permeable paving area (''A<sub>p</sub>''). Note that the contributing drainage area (''A<sub>c</sub>'') should not contain pervious areas.
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<br>
*''P'' = Rainfall depth (m)  
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*''D'' = Duration of the design storm event event (hr)
*''f''' = Design infiltration rate (m/day)
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*''i'' = Intensity of the design storm event (m/hr)
*''t'' = Time to fill stone bed (typically 2 hr)  
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*''R'' = the ratio of impervious contributing drainage area to permeable pavement area; ''A<sub>i</sub>''/''A<sub>p</sub>''
*''V<sub>R</sub>'' = Void ratio for stone bed (typically 0.4 for 50 mm dia. [[reservoir aggregate|clear stone]])}}  
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*''A<sub>i</sub> = Impervious contributing drainage area (m<sup>2</sup>)
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*''A<sub>p</sub> = Permeable pavement area (m<sup>2</sup>)
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*''f''' = [[Design infiltration rate]] of underlying native soil (m/hr)
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*''n'' = Porosity of the stone bed aggregate material (typically 0.4 for 50 mm dia. [[reservoir aggregate|clear stone]])}}  
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It is important to note that R should not exceed 1 to limit hydraulic loading and help avoid premature clogging.  Also important to note is that the contributing drainage area should not contain pervious areas that are sources of sediment that can lead to premature clogging.
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<br>
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<br>
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On highly permeable soils (e.g., infiltration rate of 45 mm/hr or greater), a maximum stone reservoir depth of 2 metres is recommended to prevent soil compaction and loss of permeability from the mass of overlying stone and stored water.
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===For partial infiltration design, to calculate the depth of the storage reservoir needed below the invert of the underdrain pipe===
  
===To calculate the invert of the underdrain from the base of the reservoir===
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For designs that include an underdrain, the depth of the storage reservoir below the invert of the underdrain pipe (''d<sub>r'') can be calculated as follows:<br>
For designs that include an underdrain, the maximum depth of the stone reservoir below the invert of the underdrain pipe (''d<sub>s, max</sub>'') can be calculated as follows:  
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<math>d_{r}=\frac{f'\times t}{n}</math>
<math>d_{s, max}=\frac{f'\times t}{0.4}</math>
 
 
{{Plainlist|1=Where:
 
{{Plainlist|1=Where:
 
*''f''' = Design infiltration rate (mm/hr), and
 
*''f''' = Design infiltration rate (mm/hr), and
*''t'' = [[Drainage time]] (hrs), e.g. 96 hours, check local regulations for drainage time requirements.   
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*''t'' = [[Drainage time]] (hrs), e.g. 72 hours, check local regulations for drainage time requirements.   
*''0.4'' = Void ratio of [[reservoir gravel|clear stone]]}}
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*''n'' = Porosity of the stone bed aggregate material (typically 0.4 for 50 mm dia. [[reservoir aggregate|clear stone]])}}  
  
 
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----
(f') used in the above equations should be the [[design infiltration rate]] that incorporates a safety correction factor. On highly permeable soils (e.g., infiltration rate of 45 mm/hr or greater), a maximum stone reservoir depth of 2 metres is recommended to prevent soil compaction and loss of permeability from the mass of overlying stone and stored water.
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Where the total contributing drainage area (A<sub>c</sub>) and total depth of clear stone aggregate needed for load bearing capacity of the pavement are known (i.e., storage reservoir depth is fixed) or if available space is constrained in the vertical dimension due to water table or bedrock elevation, the minimum footprint area of the water storage reservoir, A<sub>r</sub> can be calculated as follows:<br>
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<math>A_{r}=\frac{D(i - f')\times A_{c}}{d_{r} \times n}</math>
When sizing the area of permeable paving based on the contributing drainage area, the following equation may be used:
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<br>
<math>A_p= \frac{Q_c\times A_c}{V_R \times dp – P + q'\times t}</math>
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<br>
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Where:<br>
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A<sub>c</sub> = A<sub>i</sub> + A<sub>p</sub>, and<br>
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A<sub>r</sub> = A<sub>p</sub> (i.e., assumed that the water storage reservoir area and permeable pavement area are the same)
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<br>
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<br>
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Then adjust A<sub>r</sub> accordingly to keep R between 0 and 1, which reduces hydraulic loading and helps avoid premature clogging.
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Back to [[Permeable pavements]]
  
[[category:modelling]]
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==References==
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[[Category:Calculations]]

Latest revision as of 21:33, 3 November 2022

The following calculation is used to size the stone storage bed (reservoir) used as a base course. It is assumed that the footprint of the stone bed will be equal to the footprint of the pavement. The following equations are derived from the Interlocking Concrete Pavement Institute (ICPI) manual [1]

For full infiltration design, to calculate the total depth of clear stone aggregate layers needed for the water storage reservoir[edit]

The equation for the maximum depth of the stone reservoir (dr, max, m) is as follows:

Where:


  • D = Duration of the design storm event event (hr)
  • i = Intensity of the design storm event (m/hr)
  • R = the ratio of impervious contributing drainage area to permeable pavement area; Ai/Ap
  • Ai = Impervious contributing drainage area (m2)
  • Ap = Permeable pavement area (m2)
  • f' = Design infiltration rate of underlying native soil (m/hr)
  • n = Porosity of the stone bed aggregate material (typically 0.4 for 50 mm dia. clear stone)

It is important to note that R should not exceed 1 to limit hydraulic loading and help avoid premature clogging. Also important to note is that the contributing drainage area should not contain pervious areas that are sources of sediment that can lead to premature clogging.

On highly permeable soils (e.g., infiltration rate of 45 mm/hr or greater), a maximum stone reservoir depth of 2 metres is recommended to prevent soil compaction and loss of permeability from the mass of overlying stone and stored water.

For partial infiltration design, to calculate the depth of the storage reservoir needed below the invert of the underdrain pipe[edit]

For designs that include an underdrain, the depth of the storage reservoir below the invert of the underdrain pipe (dr) can be calculated as follows:

Where:

  • f' = Design infiltration rate (mm/hr), and
  • t = Drainage time (hrs), e.g. 72 hours, check local regulations for drainage time requirements.
  • n = Porosity of the stone bed aggregate material (typically 0.4 for 50 mm dia. clear stone)

Where the total contributing drainage area (Ac) and total depth of clear stone aggregate needed for load bearing capacity of the pavement are known (i.e., storage reservoir depth is fixed) or if available space is constrained in the vertical dimension due to water table or bedrock elevation, the minimum footprint area of the water storage reservoir, Ar can be calculated as follows:


Where:

Ac = Ai + Ap, and
Ar = Ap (i.e., assumed that the water storage reservoir area and permeable pavement area are the same)

Then adjust Ar accordingly to keep R between 0 and 1, which reduces hydraulic loading and helps avoid premature clogging.


Back to Permeable pavements

References[edit]

  1. Smith, D. 2017. Permeable Interlocking Concrete Pavements; Selection, Design, Specifications, Construction, Maintenance. 5th Edition. Interlocking Concrete Pavement Institute. Chantilly VA