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Line 1: − + − − − The equation for the depth of the stone bed is as follows: − + + + + − + − *''Q<sub>c</sub>'' = Depth of runoff from contributing drainage area, not including permeable paving surface(m) + − + − + − *''q'' = Infiltration rate for native soils (m/day) + − + − + − ----+ − + − + + + − + − + − + − *''t'' = Time to drain (design for 48 hour time to drain is recommended)}} − The value for native soil infiltration rate (q) used in the above equations should be the design [[infiltration]] rate that incorporates a safety correction factor based on the ratio of the mean value at the proposed bottom elevation of the practice to the mean value in the least permeable soil horizon within 1.5 metres of the proposed bottom elevation. − 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. − + + − + +
Sahlla Abbasi moved page Permeable paving: Sizing to Permeable pavements: Sizing: Updating terminology for permeable pavings to permeable pavements
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,
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 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>
Construction, Maintenance. 3rd Edition. Interlocking Concrete Pavement Institute.
Burlington, ON.</ref>
<math>d= \frac{[Q_c\times R + P - q\times T ]}{Vr}</math>
===To calculate the total depth of the foundations (all aggregate layers)===
The equation for the depth of the stone foundation (''d<sub>f, max</sub>'', mm) is as follows:
<math>d_{f, max}=\frac{\left[\left ( RVC_{T}\times R \right )+ RVC_{T}-\left(f'\times t\right )\right]}{V_{R}}</math>
{{Plainlist|1=Where:
{{Plainlist|1=Where:
*''d'' = Stone bed depth (m)
*''RVC<sub>T</sub>'' = [[Runoff volume control target]] (mm)
*''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. R should not normally exceed 2.
*''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.
*''f''' = [[Design infiltration rate]] (mm/hr)
*''P'' = Rainfall depth (m)
*''t'' = Time to fill stone bed (typically 2 hr)
*''V<sub>R</sub>'' = Void ratio for stone bed (typically 0.4 for 50 mm dia. [[reservoir aggregate|clear stone]])}}
*''T'' = Time to fill stone bed (typically 2 hr)
*''Vr'' = Void ratio for stone bed (typically 0.35 for 50 mm dia. stone)}}
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 designs that include an underdrain, the maximum depth of the stone reservoir below the invert of the underdrain pipe can be calculated as follows:
===To calculate the invert of the underdrain from the base of the reservoir===
<math>dr_{max} = \frac{q \times t}{Vr}</math>
For designs that include an underdrain, the maximum depth of the storage layer below the invert of the underdrain pipe (''d<sub>s, max</sub>'') can be calculated as follows:
<math>d_{s, max}=\frac{f'\times t}{0.4}</math>
{{Plainlist|1=Where:
{{Plainlist|1=Where:
*''dr<sub>max</sub>'' = Maximum stone reservoir depth (m)
*''f''' = Design infiltration rate (mm/hr), and
*''q'' = Infiltration rate for native soils (m/hr)
*''t'' = [[Drainage time]] (hrs), e.g. 96 hours, check local regulations for drainage time requirements.
*''Vr'' = Void space ratio for aggregate used (typically 0.35 for 50 mm clear stone)
*''0.4'' = Void ratio of [[Reservoir aggregate|clear stone]]}}
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When sizing the area of permeable paving based on the contributing drainage area, the following equation may be used:
When sizing the area of permeable paving based on the contributing drainage area, the following equation may be used:
<math>A_p= \frac{Q_c\times A_c}{Vr \times dp – P + q\times T}</math>
<math>A_p= \frac{Q_c\times A_c}{V_R \times dp – P + q'\times t}</math>
[[category:modeling]]
Back to [[Permeable pavements]]
[[Category:Calculations]]