LID Infiltration Facility Calculator (a.k.a. Rain Garden Calculator)

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Rain Garden
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This calculator was created to provide a more user-friendly interface to the typical spreadsheet model engineers use for sizing infiltration facilities. The tool is a reservoir-routing spreadsheet model that uses a standardized NRCS Type 1a 24-hour rainfall distribution (typical of Western and parts of Central Oregon) with variables input by the user to approximate the performance of various low impact development vegetated infiltration facilities. It is to be used for modeling runoff from impervious surfaces of less than 0.25 acres (approx. 11,000 sq. ft.).

THE INNER WORKINGS OF THE LID INFILTRATION FACILITY CALCULATOR

An LID Infiltration Facility web calculator has been provided to help designers in public and private sectors size vegetated infiltration facilities including rain gardens, planters, and vegetated swales with check dams. Since the web calculator does not show the user how the calculations are being performed, this webpage presents the assumptions and calculations on which the web calculator is based and allows you to download the model in Excel format. The advantage of this format over the web calculator is that you can use it to size rain gardens for runoff from any area, not just impervious areas, and you can use it to justify the design calculations for permits.

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Planter Sizing Calculator (101 kb)
Rain Garden Sizing Calculator (101 kb)

OVERVIEW

Let's step through the logic for the Planter Sizing Worksheet by first taking a look at a screenshot.(The Rain Garden Sizing Worksheet is the same in all respects except for the last Column 12 discussed below.) The top portion is for user inputs. Once those are entered, the worksheet will automatically generate a hydrograph for the storm and calculates a few other handy items. The hydrogaph is generated using a Santa Barbara Urban Hydrograph (SBUH) Type IA rainfall distribution, but since theUrban Hydrology for Small Watersheds TR-55 model (used to size detention basins, but now is being applied sometimes for LID practices) isn't applicable for storms under 1 inch and isn't very accurate for smaller site-sized areas, this calculator uses the rational method (Q=CIA) within each 10-minute time increment to calculate the peak flow for that interval. Generally, the rational method isn't recommended for volume sensitive calculations such as this, but since we're incorporating the shape of the hydrograph into the calculations, this approach will work well to model infiltration facilities.

STORMWATER PLANTER DETAILS

Here are examples of what we might model with the stormwater planter calculator:

Fig 1. Infiltration Planter with Planting Soil

 


Fig 2. Infiltration Planter with Planting Soil & Rock Trench (Click image for high res version)

USER INPUTS

24 Hour Rainfall Depth [in]: Enter the size of the storm that you're required or wish to infiltrate.

Drainage Area [sf]: Enter the area that's draining to the stormwater planter. Some highly urbanized jurisdictions like the City of Portland only require infiltration of impervious areas; however, more rural areas or cities with lower infiltration volume requirements should include pervious drainage areas as well. Impervious and pervious areas of different types must be done in separate iterations. When you've accounted for all the areas that drain to the facility, you can add up the results to get the size of your facility.

Drainage Area Runoff Coefficient: This is the C in Q=CIA of the rational method. Click here to learn more about the rational method and to see typical values if you'd like to model this for all areas, not just impervious areas, draining to the planter. Choosing the upper end of the range for the particular land cover is safe. For instance, according to the link provided, lawns are have a runoff coefficient between 0.05 and 0.35, so enter 0.35. If you're only managing impervious area, then leave this at 0.9 or increase it to 0.98 to be more conservative.

Native Soil Infiltration Rate [in/hr]: Enter the infiltration rate of the native soils. This would come from running an infiltration test (see fact sheet provided) in the location of the infiltration facility at the depth where the constructed facility intersects with the native uncompacted soil. This number cannot be altered by the design. If the infiltration rate is low, then the facility will have to be bigger or will incorporate a rock trench.

Depth of Rock Trench Below Planter, optional [in]: As stated above, if the infiltration rate of the native soil isn't fast enough to dispose of the desired 24 Hour Rainfall Depth in the available area, then a rock trench could be added below the facility. For this model, the area of the rock trench is assumed to be the same as the footprint of the planter, but that's not necessarily required in the real world, just to use this model.

Void Ratio for Rock Trench [%]: The rock trench is made up of open graded (all almost the same size) rock. The open graded rock provides storage for the additional volume of water that must be stored in the voids between the rocks. The void ratio is ratio of solid to voids and is often 40%, but your rock supplier should be able to tell you . Some jurisdictions require you to assume 30% void ratio to account for fines moving upwards or downwards, which will reduce storage unless you account for this in your design. In Fig 2. above, the rock separation layers (3" coarse sand over 3" crushed gravel) provides protection against fine soil particles moving downward and the non-woven geotextile (aka filter fabric) beneath the uniformly graded storage rock protects against fine soil particles moving up, so no additional factor of safety is needed. (See SWAMP details for more information on design considerations.)

Planter Area: Enter any old number smaller than the drainage area. A good place to start guessing is 10% of the drainage area. Now, look at the cell asking "Planter Area Properly Sized?" under the CALCULATED DESIGN CRITERIA area. Does it say "TRUE"? Yes? Good. No? Keep trying different areas until you get a ponding depth between 6" and 12" and all parts of the facility emptying out in 30 hours after the beginning of the 24-hour design storm. OK. Now go find a place that big with appropriate setbacks to locate your planter.

CALCULATED DESIGN CRITERIA

These values will tell you whether you have correctly sized the planter.

Maximum Ponding Depth in Planter: This is the maximum depth to which the design storm will fill the planter. Make sure your overflow design actually holds the water back to the depth shown in the model.12" is considered a maximum for liability reasons. 6" is considered a minimum for optimizing the footprint of the facility but during large storms in poorly drained soils, the criteria for emptying the facility (discussed next) may coincide with a more shallow ponding depth, which is OK.

Depth of Water Left in Rock Trench After 30 Hours [in]: This should be zero whether you're using the optional rock trench in your design or not. If you're not using the rock trench (i.e. you entered zero in the Depth of Rock Trench Below Planter (optional) cell) and it has a value greater than 0, then the spreadsheet is corrupted and you should download it again from this page. If you are using the rock trench and the number is greater than 0, then that means the facility is still infiltrating the design storm after 30 hours. This is no good in Western WA. With our frequency of rain storms, the rule of thumb is that they should empty out in 30 hours to be ready for the next storm.

Depth of Water Left in Planter After 30 Hours [in]: This should be zero. No water should be ponded in the planter after 30 hours or the facility won't be ready to infiltrate the next storm.

Planter Area is Properly Sized?: This checks all three of the above criteria and tells you right away whether the planter is sized correctly. If it's FALSE, increase the Planter Area number and/or increase the Depth of Rock Trench Below Planter (optional) values until it says TRUE. (In soils where infiltration rates are low, adding more rok tThere is a range of numbers that will give a TRUE result, so feel free to experiment with the Planter Area until you've minimized the footprint of the facility.

OTHER CALCULATED VALUES

Peak Rainfall Intensity [in/hr]:

This provides the peak rainfall intensity for the storm entered.

Ratio of Planter to Drainage Area: This is provided for agencies who would like to create a SIM form similar to that of the City of Portland. If you look on page 4 of this link to Portland's SIM Form, you'll see what's called a "Sizing Factor". This number was derived in the same way as this Ratio of Planter to Drainage Area and accounts for rainfall patterns (i.e. storm type), 24-hour design storm size, the infiltration rate of the native soils, etc.

Storage Capacity of Rock Trench [cf]: If you're using a rock trench, this will calculate the storage capacity of the voids in the rock based on the Depth of Rock Trench Below Planter (optional) and Void Ratio for Rock Trench values that you entered. If you entered 0, then it doesn't exist, so the storage capacity is 0. This is used later to calculate the ponding depth.

SBUH HYDROGRAPH

You should never have to edit any of this.

Column 1,Time [min]: This is the progressive hydrograph time in 10 minute intervals.

Column 2, Rainfall Depth [in] = 24 Hour Rainfall Depth [in, user input] x a constant that represents the unit hydrograph. All the numbers in the unit hydrograph for the first 24-hours while the storm is happening add up to 1.

Column 3, Rainfall Intensity [in/hr] = Rainfall Depth [in, Column 2] x 60 min/hr /10 min [time interval]

Column 4, Inflow Rate [cfs] = Drainage Area Runoff Coefficient [unitless, user input] x Rainfall Intensity [in, Column 3] x ft/12 in x hr/3600s x Drainage Area [sf, user input]. This is the equation for the rational method Q=CIA where Q = flow [cfs], C = runoff coefficient, I = rainfall intensity [ft/s], and A = drainage area [sf].

Column 5, Inflow Volume [cf] = Inflow rate [cfs, Column 4] x 600s/time interval. We assume that for 10 minutes the flow rate is constant and we take the time out of the equation by multiplying the inflow rate by 600 seconds because that's how many seconds are in 10 minutes.

Column 6, Runoff Depth [in] = Inflow volumne [cf, Column 5] / Drainage area [sf] x 12 [in/ft, conversion factor]. This is the depth of runoff generated during the 10-minute interval spread out over the drainage area.

Column 7, Facility Infiltration Rate [cfs] = Planter Area [sf, user input] x Native Soil Infiltration Rate [in/hr, user input]/43200 [conversion factor ft/12in x hr/3600s]. The facility infiltraton rate accounts for the fact that as the planter area increases, so does the infiltration area. As the infiltration area increases, more runoff can be infiltrated even though the infiltration rate of the native soils stays the same. This number only varies with the Planter Area since the Native Soil Infiltration Rate is a constant obtained through field testing.

Column 8, Inflow Rate - Facility Infiltration Rate [cfs] = Inflow Rate [cfs, Column 4] - Facility Infiltration Rate [cfs, Column 7]. This number is negative as long as the storm is generating flows less than the infiltration capacity of the facility. That means all the runoff coming into the facility is being infiltrated over the 10-minute interval.

Column 9, Inflow Volume - Facility Infiltration Volume [cf] = (Inflow Rate-Facility Infiltration Rate) [cfs, Column 8] x 600 [conversion factor because there are 600 seconds in 10 minutes). We need this to start tracking for use in Column 10, so we know how much runoff volume is left over in the 10-minute interval because runoff rates exceed the infiltration capacity of the facility.

Column 10, Cumulative Inflow Volume to be Stored [cf] = a conditional statement that tracks cumulatively how much runoff needs to be stored. If Column 9 is negative, then no runoff volume is accumulating and the value in this cell is assigned a zero (because the storm is not exceeding the infiltration rate of the facility yet). If Column 9 is positive, then there is runoff volume and the cell is assigned a value equal to the cell above it plus the cell to the left of it in Column 9.

Column 11, Rock Trench Ponding [in] = a conditional statement that performs a stage/storage analysis of the rock trench filling with runoff. If the volume of runoff to be stored in the rock trench (Column 10) is greater than the storage capacity/depth of the rock trench, then this cell maxes out at the depth of the rock trench and volume starts accumulating in the open ponding area at the surface of the planter. If the runoff to be stored in the rock trench is less than than the storage capacity/depth of the rock trench, then runoff continues to fill the rock trench. A description of the conditional statement is worth discussing since it's a little confusing. The depth of water ponding in the rock trench [in] = Cumulative Runoff Volume to be Stored (cf, Column 10) / Planter Area [sf, user input that assumes that the rock trench has the same footprint as the planter area] x 12 [in/ft, a conversion factor] / Void Ratio for Rock Trench [unitless]. Since the rock trench in this example is 40% voids and 60% rock, dividing by the void ratio gives the true depth of the runoff as it fills the rock trench.

Column 12, Planter Ponding Depth [in] = a conditional statement that looks in Column 11 to see if there's a rock trench and then performs a stage/storage analysis of the ponding area at the surface created by the sidewalls of the planter. If there's a rock trench, this number will be zero until the rock trench is full. There may be some storage capacity in the soil between the rock trench and the surface storage, but we've assumed that to be conservatively zero. The conditional statement checks the Cumulative Inflow Volume to be Stored [cf, Column 10] to see if it's less than the Storage Capacity of the Rock Trench [cf, Other Calculated Values]. If it's less, this cell is assigned a zero because flows have already been routed to the rock trench (Column 11). If the Cumulative Inflow Volume to be Stored [cf, Column 10] exceeds the Storage Capacity of the Rock Trench, then excess volumes accumulate in the ponding area. If there's no rock trench, the Planter Ponding Depth will be zero for as long as runoff inflows can be completely infiltrated and then will be greater than zero when runoff flows exceed the infiltration capacity of the facility.

The Rain Garden worksheet is the same except that the ponding depth has been modified to account for 3:1 H:V side slopes.

 
Peak Rainfall Intesity: This is the maximum value in the Rainfall Intesity column to be discussed in the outputs section below.
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