OPTIMAL DESIGN FOR POROUS LANDSCAPING DETENTION BASIN

Transcription

1 Guo, James C.Y. (00) Preservation of Watershed Regime for Low Impact Development using Detention, ASCE J. of Engineering Hydrology, Vol 5, No., January, 00 Guo, James C.Y., Kocman, S and Ramaswami, A (009) Design of Two-layered Porous Landscaping Detention Basin,, ASCE J. of Environ Engineering, Vol 45, Vol, December. OPTIMAL DESIGN FOR POROUS LANDSCAPING DETENTION BASIN Guo, J. C.Y., Kocman, S. M., Ramaswami A. 3. Professor, Civil Engineering, U of Colorado at Denver, Colorado. James.Guo@ucdenver.edu. Graduate Student, Civil Engineering, U of Colorado at Denver, Colorado. 3. Professor, Civil Engineering, U of Colorado at Denver/HSC, Colorado. Abstract Under the mandate of the Federal Clean Water Act, porous landscaping detention (PLD) has been widely used to increase on-site infiltration. A PLD system consists of a surface storage basin and subsurface filtering layers. The major design parameters for a PLD system are the infiltration rate on the land surface and the seepage rate through the subsurface medium. A low infiltration rate leads to a sizable storage basin while a high infiltration rate results in standing water if the subsurface seepage does not sustain the surface loading. In this study, the design procedure of a PLD basin is revised to take both detention flow hydrology and seepage flow hydraulics into consideration. The design procedure begins with the basin sizing according to the on-site water quality control volume. The ratio of design infiltration rate to sand-mix hydraulic conductivity is the key factor to select the thickness of sand-mix layer underneath a porous bed. The total filtering thickness for both sand-mix and gravel layers is found to be related to the drain time and infiltration rate. The recommended sand-mix and granite gravel layers underneath a PLD basin are reproduced in the laboratory for infiltration tests. The empirical decay curve for sand-mix infiltration rate was derived from the laboratory data and then used to maximize the hydraulic efficiency through the subsurface filtering layers. In this study, it is recommended that a PLD system be designed with the optimal performance to consume the hydraulic head available and then evaluated using the prolonged drain time for potential standing water problems under various clogging conditions. Keywords: Porous landscaping basin, infiltration, seepage, porous pavement, stormwater detention, LID, and BMP INTRODUCTION A porous landscaping detention basin (PLDB) in Figure reduces on-site stormwater runoff volume and peak discharge using subsurface infiltration. Beneath the porous basin bottom is an aggregate sub-base that is typically divided into an upper filtering layer comprised of fine aggregate, and a lower reservoir layer comprised of larger aggregate. The geotextile fabric provides the separation between these two layers. Stormwater that is intercepted by the surface basin will be infiltrated into the subsurface reservoir where the seepage flow is filtered, stored, and gradually released into the perforated pipes that are tied into the downstream storm sewer manhole. The water detention process is usually assumed to begin with dry subsurface layers. During an event, all the aggregate voids are filled up with water before the seepage flow can be fully developed through the saturated medium. The infiltrating rate on the basin bottom represents the inflow to the PLD system while the seepage rate through the subsurface medium represents the outflow. The operation of a PLDB is controlled by either the infiltrating rate or the seepage rate, whichever is smaller (Guo 998). If the subsurface seepage flow cannot sustain the infiltrating flow, the water mounding will be built up to balance the inflow and outflow rates. This phenomenon is manifested by standing water often observed in many water quality enhancement basins (Guo 00). The similar phenomena were also observed in the subsurface drip

2 irrigation system that has become a common method for the irrigation of field crops, trees, and landscaping. When the pre-determined discharge of the emitter is larger than the soil infiltration capacity, water pressure at the dripper outlet increases and can become built up. This pressure buildup in the soil decreases the pressure difference across the dripper and, subsequently, decreases the trickle flow (Shani et al. 996). Therefore, it is advisable that the subsurface geometry beneath the PLDB sustains the continuity of flow. Figure Layout of Porous Landscaping Basin The design of a PLD system is to seek the balance between the surface and sub-surface flows under the available hydraulic head and required water quality control storage volume. This study presents an attempt to integrate the surface and subsurface hydrology and hydraulic processes together to design a PLDB. SURFACE STORAGE BASIN A PLDB is designed as an on-site storm water disposal facility. The storage volume of a PLDB is often sized for the water quality control volume (WQCV) or equivalent to the flush volume. From previous studies, WQCV is approximately equal to 3- to 4-month event (Guo and Urbonas 996). For convenience, WQCV is directly related to the local rainfall distribution. There are many recommended probabilistic distributions derived for complete rainfall data series, such as exponential distribution (Bedient and Huber, 99), one-parameter Poisson distribution (Wanielista and Yousef, 993), and two-parameter model of Gamma distribution (Woolhiser and Pegram, 979). In this study, the one-parameter exponential distribution is adopted to fit the frequency distribution of rainfall event depths (Guo 00). The exponential distribution is described as: f ( p) = P m e p P m () in which f(p) = frequency distribution for local rainfall depth, p. Integrating Eq yields the cumulative probability distribution as: F(0 p P) = e P P m ()

3 in which F(0 p P) = non-exceedance probability for rainfall depth to be less than or equal to the design rainfall depth, P. Considering surface depression, a runoff-producing rainfall depth can be converted into its runoff volume as: P o = C P P ) (3) ( i in which P o = WQCV in mm per watershed, C= runoff coefficient used in the Rational method, and P i = incipient runoff depth. As recommended, an incipient runoff depth of.5 mm is introduced to filter out extremely small rainfall events (Guo and Urbonas in 996, Driscoll et al. in 989). Normalizing Eq 3 yields P P m Po Pi = + (4) CP P m m in which P m = local average rainfall event-depth that can be found elsewhere (EPA 986). Substituting Eq 4 into Eq yields Pi Po ( + P CP ) m m F( 0 p P o ) = e (5) in which F(0 p P o ) = probability to have an event that can be completely captured by the design water control volume, i.e. P o. In this study, Eq 5 is termed the synthetic runoff capture curve that is normalized by local average rainfall event-depth, runoff coefficient, and runoff incipient depth. Re-arranging Eq 5 yields: P o CPm (6) C v = α e P i Pm α = e (7) In which C v = runoff volume capture rate between zero and unity, and α = constant determined by incipient runoff depth. The value of α represents the watershed natural depression capacity. Figure presents a set of normalized runoff capture curves produced using Eq 6 with runoff coefficients of 0.4, 0.6, 0.8, 0.9 and.0. It is noticed that the curvature of runoff capture curve increases when the runoff coefficient decreases. This tendency reflects the fact that the higher the imperviousness in a watershed, the less the surface depression and detention. As a result, the response of a watershed to rainfall is quick and direct. For a selected runoff volume capture rate, Figure provides the required WQCV for a PLD basin as: Vo = Po A (8) where V o = WQCV in m 3 and A = catchment area tributary to basin. Safety is always a concern when designing a PLDB. Often the water depth in a PLDB is set to be 5 to 30 cm (6 to inches). With a selected basin depth, the basin cross sectional area is determined as: Vo Ao = Y (9) where A o = average cross section area, and Y= basin depth. To enhance the infiltrating process, the basin bottom shall be on a flat to mild slope. 3

4 Runoff Capture Rate C=0.40 C=0.60 C=0.80 C=0.90 C=.0 Po/Pm (Basin Size/Average Rainfall Depth) Figure Stormwater Quality Control Volume for Porous Landscaping Basin Design SUBSURFACE FILTERING SYSTEM Drain time is critically important to the operation of a PLDB because it controls the sediment removal rate. Based on the urban pollutant characteristics, a drain time for the PLDB is usually set to be between from to 4 hours (USWDCM 00). Figure 3 illustrates the flow through the two filtering layers including sand-mix and then gravel. Under a constant head, the steady flow condition is derived as: f = V = V (0) In which f = infiltrating rate, and V= seepage flow velocity through each layer, The subscriptions and represent the variables associated with the sand-mix and gravel layers, respectively. A saturated seepage flow through a medium is proportional to the energy gradient as: dh V = K () H dh V = K () H Where K = hydraulic conductivity, H = energy head, and dh = energy loss. 4

5 Figure 3 Illustration of Infiltrometer Operation In practice, the design infiltrating rate depends on the drainage nature of the selected sand-mix. With a pre-selected design infiltrating rate, the total filtering thickness for the two filtering layers is calculated as: D = f T d (3) Where D= total thickness for two filtering layers, f = infiltration rate, and T d = PLD drain time. The fundamental challenge in PLDB design is how to divide the total thickness between the two filtering layers because the layer thickness is directly related to the hydraulic gradients for seepage flow through the system. D = H + H (4) where H = sand-mix thickness and H = gravel layer thickness. As illustrated in Figure 3, the available hydraulic head for the PLD system is H = Y + D (5) where Y = water loading depth in PLDB. In this study, the optimal performance of a PLDB is defined by the infiltration flow and the subsurface thickness that allow the seepage flow to consume the hydraulic head available as: H = dh + dh (6) Aided by Eq s 0,,and, the head losses through the two filtering layers are: f dh = (7) H K f dh = (8) H K Aided by Eq s 5, 6, 7 and 8, the optimal performance of a PLDB is described as: 5

6 f Y ( ) H K D + = in which f/k >, and K >K (9) D f f ( ) K K H H = D (0) Eq 9 is valid when f/k > and K >K. In other words, the infiltration rate is greater than the seepage rate and the sand-mix layer is above the gravel layer. Eq s 9 and 0 are derived to be the guidance to divide the total required filtering thickness into two layers. OPERATION OF POROUS LANDSCAPING BASIN The operation of a PLDB is subject to clogging due to sedimentation in the basin. The pollutant deposit is often accumulated on top of the basin bottom and then diffused into the top layer of the sand-mix medium. When the infiltration rate decays on the basin bottom, the friction losses are reduced accordingly. Namely, dh dh f s H = () K f s H = () K In which f s = reduced infiltrating rate due to clogging effect. Clogging to a PLD system generally occurs as a thin, hard cake layer (0. to 0.5 cm) of sediment on the basin bottom. As reported, migration of solids only diffuses into the top 5 to0 cm of the sand-mix layer while the hydraulic conductivity in the sand-mix layer remains unchanged (Li and Davis 008a and 008b; Mays 005). As illustrated in Figure 3, the reduced infiltration flow under a clogging condition may not completely consume the hydraulic head available. As a result, the residual pressure in the system, is calculated as: H t = Y + D dh dh (3) where H t = residual pressure head. If the cake layer presents an additional friction loss, the value of H t will decrease; otherwise it represents the pressure built up in the filtering layers. The reduced infiltrating rate implies a prolonged drain time, or a period of standing water in the PLDB, as: T w D = Td (4) f s in which T w = increased drain time or period of standing water. As the basin bottom is gradually clogged, the infiltration flow rate continues to decrease and the hydrostatic head, H t, in the medium continues to build up. When the hydrostatic head in the filtering medium is close to the available head, the system is about to cease functioning because the medium layers are almost plugged. LABORATORY TESTS Previous reports recommended that a sand-mix thickness of 30 to 60 cm (or -4 inches) can effectively remove pollutants in stormwater (Hunt 00, Hunt 006, NCDENR 007, Sun 004, Toronto and Region Conservation Authority 007). As reported, metals are removed in the top 0 to 45 cm (8 to 8 inches) of sand-mix layer (Davis et al. 003; Sun 004; Winogradoff 00). In practice, the sand-mix layer thickness is recommended to be 45 cm (8 inches) to allow for both adequate pollutant removal and root zone for vegetation. In the laboratory, a 38-cm (5-inch) circular infiltrometer in Figures 4 and 5 was 6

7 utilized to represent a section of the PLDB. Sand-mix sample columns were prepared to mimic the field conditions as closely as possible. As illustrated in Figure 5, the sample column in the infiltrometer is built with an upper layer of sand-mix, a lower layer of gravel, and a perforated bottom drain. The.9 cm (¾ - inch) crushed granite was spread in the bottom. ASTM C33 washed sand and Canadian peat were combined at the ratio of 85% sand and 5% peat by volume for the sand-mix layer. Table presents the compaction and density of the sand-mix samples prepared for infiltrometer tests. For this study, the filtering layers were structured with an upper 45-cm (8-inch) sand-mix layer and a bottom layer of 0-cm (8-inch) gravel. As illustrated in Figure 5, the total thickness of a sample column is set to be 65 cm (6 inches). With a constant head of 30 cm ( inch), the total head applied to the infiltrating flow is 95 cm (38 inches) as shown in Table. To evaluate the effect of the geotextile on the infiltration rates, Sample Column I had a geotextile layer separating the sand-mix layer from the aggregate layer; and sample Columns J and F were constructed and tested without the geotextile. Manometers were installed on the infiltrometer wall at 4 stations to measure the variation of static heads. The locations of manometers are expressed by the vertical distances above the bottom of the sample column as shown in Table. Soil Column 5 diameter 38 inches of water capacity Manometers 6 4 Entry Layer 8 8 inches soil mix inches coarse aggregate Exit Layer Geotextile Drain line and valve Figure 4 infiltrometers built in Laboratory. Figure 5 Sample Column for Infiltration Tests Table Compaction and Density of Sand-mix Sample Sand-mix Sample Density grams per cubic centimeter (pounds per cubic foot) Material Loose Sand-mix Compacted Sand-mix Compaction Ratio Sand.39 (86.79).76 (09.65).6 Peat 0.4 (6.05) 0.84 (5.43).0 85% Sand and 5% Peat.6 (7.3).75 (09.).5 7

8 flow rate (cm/hr) Test Flow Rates Over Time Column I Column F Column J Horton's Estimate 0 0:00:00 4:00:00 48:00:00 7:00:00 hours:min:sec Figure 6 Variation of Infiltration Rates for Sample Columns Table Variation of Hydraulic Heads Measured at 5 Stations Column Infiltrating Locations of manometers above ground in cm Sample Rate ID entrance upper lower geotextile cm /hr sand layer sand layer sand layer layer Reading in manometers above ground in cm Col F without geotex Col I with geotex Col J without geotex Col F without geotex Col I with geotex Col J without geotex Note: Col F without geotex = Soil Column F without geotextile measured after 7 hr. Table 3 Hydraulic Conductivity in Soil Layer at 7 hours Column Sample ID Infiltration Rate cm/hr Hydraulic Conductivity for Sand-mix cm/hr Col F without geotex Col I with geotex.4 6. Col J without geotex

9 The sample columns were tested with the wet initial condition by filling each column to 30.5 cm ( inches) of water and soaking the sample column overnight with the drain valves closed. The next morning the valve was opened and outflow measurements were recorded. The outflow rates from sample columns were recorded for 7 hours continuously. Figure 6 is the plot of the decayed infiltration rate through the sand mix layer over 7 hours. The best fitted Horton s infiltration equation for the sandmix tested is (Horton 933): 0.44t = (5) f t e Where f t = infiltration rate in cm/hr at elapsed time t in hours. Eq 5 has a correlation coefficient, r = The differences in the infiltration decay among sample columns are attributed to sample preparations, compaction condition, and test operations. Sand-mix compaction alone can have a significant impact on infiltration rates in sandy soils (Pitt et al. 999). Although the impact of the geotextile fabric on the flow rate was not measurable through the sample columns, the sand-mix particles were found to migrate into the gravel layer (Haliburton and Wood, 98). Based on three sannd-mix column tests, the average final infiltration rate is found to be.6 cm/hr (or 4.6 inch/hr). The hydraulic conductivity coefficients were found to be 6. cm/hr (or.4 inch/hr) for sand-mix and 64.0 cm/hr (or 5. inch/hr) for gravel. As listed in Table 3, these values are within the range reported before (Schwartz and Zhang, 003). DESIGN EXAMPLE AND SCHEMATICS The PLD basin located in the City of Denver, Colorado is employed as an example to illustrate the design procedure. The catchment draining into this basin has a tributary area of.0 hectare (.5 acre) and runoff coefficient of As reported, the average event depth for the Denver metropolitan area is.0 cm (or 0.4 inch) (EPA 986). With a runoff volume capture rate of 80%, the WQCV for this basin is calculated as: α = Pi P e m = e = 0.79 Po CP P m C = α e = 0.79 e = 0.8 or P o = 0.86 cm V v = P A = 0.86 cm.0 ha 86 m o o = o 3 From the laboratory test, f =.6 cm/hr (or 4.6 inch/hr), K = 6. cm/hr (or.4 inch/hr) for sand mix and K = 64.0 cm/hr (or 5. inch/hr) for gravel. Consider a drain time of 6 hours. The required dimension for the subsurface filtering system is calculated as: D = f Td =.6 6 = cm H = Y + D = = 00. cm H D f ( ) K = f f ( K K Y D ) ( ) = ( ) = 0.73 or H = 5.0 cm and H = 8.6 cm Substituting the above dimension into Eq s 7 and 8 yields 9

10 f.6 dh = H = 5.0 = cm K 6. f.6 dh = H = 8.6 = 3. cm K 64.0 As expected, the total friction losses for the seepage flow through the two layers satisfy Eq 5. This is the optimal performance for this PLD basin, according to Eq 9. In practice, the infiltration rate at the site is estimated with uncertainties. Secondly, the infiltration rate is subject to the clogging effect. For comparison, the performance of this PLDB is further assessed for the condition that the infiltration rate is reduced to 7.5 cm/hr. The corresponding head losses are calculated as: dh dh f s H K = 6. = = f sh K = 64.0 = = 6.7 cm. cm H t = H dh dh = cm T = D 69.6 = Td = 6.0 = 3. hr -- an extended period of standing water. f 7.5 w 3 s Under the clogging condition, this PLDB drains slowly. After the design drain time of 6 hours, standing water is developed in the basin. The residual pressure head, H t, is either dissipated through the cake layer or built up in the sand medium. The above analysis was repeated for the bio-retention medium studies (Li and Davis 008a and 008b). In the laboratory, the clean sand column was used as the subsurface medium to filter the solids in storm water. After several loading cycles of stormwater, a 0. to 0.6-cm cake layer was formed on the basin bottom. The deposited solids were also diffused into the top layer of the sand medium up to 3 to 7 cm. Table 4 summarizes the laboratory measurements and observed data. The clean sand medium started with a hydraulic conductivity of 45 cm/hr. After the top layer is clogged, the equivalent hydraulic conductivity coefficients for the sand medium were measured as listed in Table 4. Table 4 Observed Case Studies for Bi-Retention Medium (Li and Davis 008a and 008b) Laboratory Dimension Calibrated Parameters Observed Thickness Infiltrating Filtering Bottom Equivalent Water Upper Upper Bottom Cake Flow Media Conductivity Conductivity Depth Conductivity Clogged Clean Layer Rate Thickness Coeff Coeff in Basin Coeff Layer Layer f D K K e Y K H H cm/h cm cm/h cm cm cm/h cm cm cm

11 Predicted Thickness Ratio Observed Thickness Ratio H/H -Top Layer H/H - Bottom Layer Figure 7 Comparison between Observed and Calculated Filtering Thickness Consider that the clogged top layer is equivalent to a sand-mix layer and the bottom clean layer is equivalent to a gravel layer. Eq 9 was applied to 5 case studies to predict the thickness ratio between the top and bottom layers. Figure 7 presents good comparison between the calculated and observed thickness ratios. CONCLUSION. A PLDB shall be designed using the concept of hydrologic system to take both the surface and sub-surface flows into consideration. In this study, it is recommended that the PLDB be sized for the on-site storm water quality control volume according to the selected drain time and target pollutant removal rate. The total filtering thickness underneath the PLDB shall be determined by the selected drain time and infiltration rate.. The filtering layers beneath a PLDB shall be structured to completely consume the hydraulic head available in the system. The optimal dimension of the sub-base medium is found to be closely related to the design infiltrating and seepage rates. In this study, Eq 9 was derived to provide the optimal thickness ratio between the sand-mix and gravel layers. The optimal sub-base dimension delivers the highest seepage flow rate for the unclogged condition. 3. Eq 9 is numerically sensitive to f/k, but not to f/k because the hydraulic conductivity coefficient of granite gravel is usually much higher than the infiltrating rate or the ratio, f/k, numerically close to zero. For simplicity, the thickness for the sand-mix layer is approximated as: H K K = ( D + Y (6) f f ) In practice, it is critically important that the ratio, f/k, is properly selected to avoid undesirable prolonged standing water in the PLDB. 4. In this study, the infiltration rate for the sand-mix layer varies from 50 to 7.5 cm/hr (0 to 3 inch/hr). The final infiltration rate is approximately 7.5 to.5 cm/hr (3 to 5 inch/hr) after an operation of 7

12 hours. The hydraulic conductivity coefficient was varied within a small range through the sandmix column. All these uncertainties are attributed to the residual pressure in the PLD system. As a common practice, perforated pipes are installed in the subsurface system. A sub-drain pipe creates an accelerated hydraulic gradient to collect the excessive water and to alleviate the buildup pressure. 5. This study is a research project supported by the Urban Drainage and Flood Control District, Denver, Colorado and the Urban Watersheds Research Institute. The detailed construction plan and drawings to design a porous landscaping detention basin can be found elsewhere (USWDCM 00). REFERENCES Bedient, P.B., and Huber, W.C. (99). "Hydrology and Floodplain Analysis", nd Edition, Addison Wesley Inc., New York. Environmental Protection Agency (EPA) (986). Methodology for Analysis of Detention Basins for Control of Urban Runoff Quality, U.S Environmental Protection Agency, EPA440/ , September. Davis, A. P., Shokouhian, M., Sharma, H., Minami, C., and Winogradoff, D. (003). "Water Quality Improvement through Bioretention: Lead, Copper, and Zinc Removal." Water Environment Research: A Research Publication of the Water Environment Federation, 75(), 73. Driscoll, E.D., Palhegyi, G.E., Strecker, E.W. and Shelley, P.E. (989). Analysis of Storm Events Characteristics for Selected Rainfall Gauges Throughout the United States. U.S. Environmental Protection Agency, Washington, D.C. Guo, J. C. Y. (998). "Surface-Subsurface Model for Trench Infiltration Basins." J. of Water Resources Planning and Management, 4(5), Guo, J. C. Y. (00). "Design of Circular Infiltration Basin under Mounding Effects." Journal of Water Resources Planning and Management, 7(), Guo, J. C. Y. (00). "Overflow Risk Analysis for Stormwater Quality Control Basins." Journal of Hydrologic Engineering, 7(6), Guo, J. C.Y. (003). Design of Infiltrating Basin by Soil Storage and Conveyance Capacities, IWRA International J. of Water, 8(4) Guo, J. C. Y., and Hughes, W. (00). "Storage Volume and Overflow Risk for Infiltration Basin Design." Journal of Irrigation and Drainage Engineering, 7(3), Guo, J. C. Y., and Urbonas, B. (996). "Maximized Detention Volume Determined by Runoff Capture Ratio." ASCE J. of Water Resources Planning and Management, (), Guo, J. C. Y., and Urbonas, B. (00). "Runoff Capture and Delivery Curves for Storm Water Quality Control Designs." ASCE J. of Water Resources Planning and Management, 8(3). Haliburton, T.A. and P.D. Wood (98) Evaluation of the U.S. Army corps of Engineers Gradient Ratio Test for Geotextile Performance." The Second International Conference on Geotextiles, Las Vegas, NV, USA. Horton, R. E. (933). "The role of infiltration in the hydrologic cycle." Transactions, American Geophysical Union, 4,

13 Hunt, W. F., Jarrett, A. R., Smith, J. T., and Sharkey, L. J. (006). "Evaluating bioretention hydrology and nutrient removal at three field sites in North Carolina." Journal of Irrigation and Drainage Engineering- Asce, 3(6), Hunt, W. F., and White, N. M. (00). "Designing rain gardens/ bioretention areas." North Carolina State University, Raleigh, NC. Li, H., and Davis, A. P. (008a). "Urban Particle Capture in Bioretention Media. I: Laboratory and Field Studies." Journal of Environmental Engineering, 34(6), Li, H., and Davis, A. P. (008b). "Urban Particle Capture in Bioretention Media. II: Theory and Model Development." Journal of Environmental Engineering, 34(6), Mays, D. C., and Hunt, R. H., (005). Hydrodynamic Aspects of Particle Clogging in Porous Media, Environmental Science and Technology.,39, NCDENR. (007). "NCDENR Stormwater Best Manament Practices Manual." D. o. W. Quality, ed. Pitt, R., Lantrip, J., Harrison, R., and O'Connor, T. P. (999). "Infiltration Through Disturbed Urban Soils and Compost-Amended Soil Effects on Runoff Quality and Quantity." USEPA, Washington, D.C. Schwartz, F.W. and Zhang, H. (003) Fundamentals of Groundwater, John Willey and Sons, Inc, New York. Shani, U., Xue, S., Gordin-Katz, R., and Warrick, A. W. (996). "Soil-Limiting Flow from Subsurface Emitters. I: Pressure Measurements." Journal of Irrigation and Drainage Engineering, (5), Sun, X. (004). "Dynamic Study of Heavy Metal Fates in Bioretention Systems," University of Maryland, College Park, Maryland. USWDCM (00), (999). "Urban Storm Drainage Criteria Manual s Volume 3 Best Management Practices " Urban Drainage and Flood Control District, Denver, Colorado. Wanielista, M.P. and Yousef, Y.A. (993) "Storm Water Management", John Wiley and Sons, Inc., New York. Winogradoff, D. A. (00). "The Bioretention Manual, 00 Update." M. Programs & Planning Division Department of Environmental Resources Prince George s County, ed. Woolhiser, D.A. and Pegram, G.G. S. (979). Maximum Likelihood Estimation of Fourier Coefficients to Describe Seasonal Variations of Parameters in Stochastic Daily Precipitation Models. J. of Applied Meteorology, 8, NOTATIONS A = catchment area tributary to basin A o = average cross section area C= runoff coefficient C v = runoff volume capture rate between zero and unity. D= total filtering thickness f = infiltrating rate, design infiltrating rate defined by land surface f s = reduced infiltrating rate due to clogging effect f t = infiltration rate at time t f(p) = frequency of rainfall event-depth F(0 p P o ) = non-exceedance probability for runoff volume 3

14 F(0 p P) = probability to have complete runoff volume capture dh = energy loss H = energy head or total head H = sand-mix thickness H = gravel layer thickness H t = residual pressure head K = hydraulic conductivity P o = WQCV in mm per watershed P i = incipient runoff depth p = rainfall event depth P = design rainfall depth P m = average rainfall event-depth T d = drain time T w = increased drain time or period of standing water V = seepage flow velocity through each layer V o = WQCV in m 3 Y= water loading depth in basin α = constant determined by incipient runoff depth The subscriptions and represent the variables associated with the two layers of medium 4