# Permeable pavements: Sizing

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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 taken from the ICPI Manual [1]

### To calculate the total depth of the foundations (all aggregateA broad category of particulate material used in construction, including sand, gravel, crushed stone, slag, recycled concrete and geosynthetic aggregates, and available in various particulate size gradations. layers)

The equation for the depth of the stone foundation (df, max, mm) is as follows$d_{f, max}=\frac{\left[\left ( RVC_{T}\times R \right )+ RVC_{T}-\left(f'\times t\right )\right]}{V_{R}}$

Where:

• RVCT = Runoff volume control target (mm)
• R = Ac/Ap; the ratio of contributing drainage areaThe total surface area upstream of a point on a stream that drains toward that point. Not to be confused with watershed. The drainage area may include one or more watersheds. (Ac) to permeable pavingAn alternative practice to traditional impervious pavement, prevents the generation of runoff by allowing precipitation falling on the surface to infiltrate through the surface course into an underlying stone reservoir and, where suitable conditions exist, into the native soil. area (Ap). Note that the contributing drainage areaThe total surface area upstream of a point on a stream that drains toward that point. Not to be confused with watershed. The drainage area may include one or more watersheds. (Ac) should not contain pervious areas. R should not normally exceed 2.
• f' = Design infiltration rate (mm/hr)
• t = Time to fill stone bed (typically 2 hr)
• VR = Void ratioThe void ratio (e) of a mixture is the ratio of the volume of void-space to the volume of solids. It is closely related to the concept of porosity (n) where porosity is the ratio of the volume of void-space to the total or bulk volume of the mixture. e = Volume of voids/Volume of solids = n/(1-n) for stone bed (typically 0.4 for 50 mm dia. clear stone)

On highly permeable soils (e.g., infiltration rateThe rate at which stormwater percolates into the subsoil measured in inches per hour. of 45 mm/hr or greater), a maximum stone reservoirAn underlying bed filled with aggregate or other void-forming fill material that temporarily stores stormwater before infiltrating into the native soil or being conveyed by an underdrain pipe. depth of 2 metres is recommended to prevent soil compaction and loss of permeability from the mass of overlying stone and stored water.

### To calculate the invert of the underdrainA perforated pipe used to assist the draining of soils. from the base of the reservoir

For designs that include an underdrainA perforated pipe used to assist the draining of soils., the maximum depth of the storage layer below the invert of the underdrainA perforated pipe used to assist the draining of soils. pipe (ds, max) can be calculated as follows$d_{s, max}=\frac{f'\times t}{0.4}$

Where:

• f' = Design infiltration rateThe rate at which stormwater percolates into the subsoil measured in inches per hour. (mm/hr), and
• t = Drainage time (hrs), e.g. 96 hours, check local regulations for drainage timeThe period between the maximum water level and the minimum level (dry weather or antecedent level). requirements.
• 0.4 = Void ratioThe void ratio (e) of a mixture is the ratio of the volume of void-space to the volume of solids. It is closely related to the concept of porosity (n) where porosity is the ratio of the volume of void-space to the total or bulk volume of the mixture. e = Volume of voids/Volume of solids = n/(1-n) of clear stone

When sizing the area of permeable pavingAn alternative practice to traditional impervious pavement, prevents the generation of runoff by allowing precipitation falling on the surface to infiltrate through the surface course into an underlying stone reservoir and, where suitable conditions exist, into the native soil. based on the contributing drainage areaThe total surface area upstream of a point on a stream that drains toward that point. Not to be confused with watershed. The drainage area may include one or more watersheds., the following equation may be used$A_p= \frac{Q_c\times A_c}{V_R \times dp – P + q'\times t}$

Back to Permeable pavements
1. Smith, D. 2006. Permeable Interlocking Concrete Pavements; Selection, Design, Construction, Maintenance. 3rd Edition. Interlocking Concrete Pavement Institute. Burlington, ON.