# Evaluating the Road-Bioretention Strip System from a Hydraulic Perspective—Case Studies

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## Abstract

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## 1. Introduction

_{b}), as an important design parameter, is the grate inlet height above the ground surface of the RBS (Figure 1). When the rainfall starts, runoff generated from the road flows into the RBS through curb inlets and infiltrates into the soil first. Then, after the soil is saturated, surface ponding occurs inside the RBS. When the ponding depth is greater than the overflow height, the runoff begins to flow into the grate inlet and then to the underground stormwater sewage system. When the infiltrated runoff reaches the storage layer of the RBS it can drain through the perforated pipe.

## 2. Materials and Methods

#### 2.1. Road-Bioretention Strip (RBS) Design

#### 2.1.1. Curb Inlet Interception Efficiency Calculation

_{ci}) of undepressed curb inlets is calculated using the following Equations (1)–(3) adopted from HEC-22:

_{T}(m) is the theoretical curb-inlet length required to intercept 100% of the flow; E

_{ci}(%) is the inlet interception efficiency; L

_{ci}(m) is the curb inlet length; S

_{x}and S

_{0}are the cross slope and longitudinal slope of the road/street, Q is the flow rate on the road/street surface; T is the spread width of the flow on the road/street surface; and n (-) is Manning’s roughness of the road surface.

#### 2.1.2. Bioretention Ponding Volume and Infiltration Capacity

#### 2.2. FullSWOF-ZG Program and Model Test

_{i}(x, y) (m/s) is the cell’s rainfall intensity; f(x, y) (m/s) is the cell’s infiltration rate; h (m) is the cell’s water depth; z (m) is the cell topography elevation as a function of the cell location or x and y coordinates; u (m/s) and v (m/s) are the cell’s depth-averaged velocities in the x and y directions, respectively; S

_{fx}and S

_{fy}are the cell’s friction slopes in the x and y directions, respectively; g (m/s

^{2}) is the gravity acceleration; and t (s) is time.

_{gr}, m

^{3}/s) from the 2D overland flow to the 1D drainage pipe flow is calculated using the weir Equation (7) [34] applied to the k cells within the grate inlet:

_{w}(-) is the discharge coefficient of the weir flow = 0.368 [45]; g (m/s

^{2}) is the gravity acceleration; L

_{w}(m) is the flow length (=cell size); h

_{2D}

_{(i)}(m) is the overland-flow water depth for the ith cell; and k is the total number of the cells within the grate inlet. Each grate inlet in the simulation domain is considered to have an elevation difference (e.g., 5 cm lower) from the surrounding road cells.

#### 2.2.1. Pervious Surface Modeling Cases

^{−6}m (0.0001 in) resolution every minute. The discharge depth was measured with a 22.5° V-notch weir box. The rainfall intensity was monitored using an inline flowmeter connected to the rainfall simulator. The tipping bucket rain gauge was also used to double check the rainfall depth. The rainfall was stopped at 10 min after the peak discharge was attained and the discharge measurement was done until the runoff ceased. The slope of the test bed was 0.02%, 0.1%, 0.2%, 0.5%, and 1.04%. Different slopes for the overland flow were achieved by raising or lowering the steel-framed bed. Six rainfall events were tested for each slope, with a total of 30 events for the experiment.

_{oi}(m

^{3}/s) is the ith observed runoff rate, Q

_{si}(m

^{3}/s) is the corresponding simulated runoff rate, $\overline{Q}$ (m

^{3}/s) is the mean observed runoff rate, and m (-) is the total number of observed runoff rates. The NSE values for eight rainfall events were calculated to evaluate the FullSWOF-ZG performance.

#### 2.2.2. Curb Inlet Modeling Cases

_{i}) divided by the number of the cells within the spread and was equal to 0 for other boundary cells outside of the spread. The top and right (downstream) boundary of the simulation domain were set as a Neumann condition that allows the flow to get out of the simulation domain. At the top of the simulation domain, those cells outside the curb inlet had higher elevations to prevent the outflow. The bottom boundary of the simulation domain (Figure 3b) had the highest elevation along the y-direction and was set as a wall boundary condition to guarantee that the flow would not pass through the bottom boundary.

#### 2.3. Road-Bioretention Modeling Cases

_{0}), cross slope (S

_{x}), curb inlet interception efficiency (E

_{ci}), bioretention depth (D

_{b}), overflow height (h

_{b}), and the RBS’s soil infiltration parameters, such as the saturated hydraulic conductivity (K), suction head (φ), and moisture deficit (Δθ). Different modeling cases were established to explore the influence of these design parameters on the RBS performance. Even when the RBS was flat in the y-direction with a lower elevation (i.e., bioretention depth, D

_{b}) than the road surface, the RBS had the same length and longitudinal slope, S

_{0}, in the x-direction as the road did (Figure 4).

_{b}above the RBS ground surface. The elevation difference between the grate inlet opening and the RBS ground surface is called the overflow height, h

_{b}, ranging from 0.25 m (10 in) to 0.45 m (18 in) in this study (Table 1). In the USA, the initial concept of bioretention has a shallow ponding depth of 0.15 m (6 in), but recent green infrastructure design manuals allow for 0.30 m (12 in) to 0.45 m (18 in) of ponding depth [14]. Only when the water depths near the grate inlet are greater than h

_{b}, will the runoff in RBS flow into the grate inlet then to the underground drainage pipe system. There is a berm at the end of the RBS (Figure 1 and Figure 4) to pond the runoff inside the RBS, which facilitates infiltration downward and possible overflow into the grate inlet. The berm height was set as the same as the bioretention depth, D

_{b}, to prevent the longitudinal outflow from the RBS since D

_{b}> h

_{b}.

_{ci}in Figure 4), then, a part of the bypass runoff from the inlet is captured by the grate inlet on the road (Q

_{rg}) and leaves the simulated road surface through the grate inlet. Finally, the remainder of the runoff is discharged downstream along the road (Q

_{bp}). The runoff into the bioretention infiltrates downward or overflows through the bioretention grate inlet (Q

_{og}) when the ponding depth is greater than h

_{b}.

_{pc}) was calculated for each modeling case in this study when the overflow occurred, and did not consider the vegetation volume fraction of the bioretention facility. The impact of the longitudinal slope was included when calculating V

_{pc}using the following Equation (9). The V

_{pc}is calculated with two situations: (1) The ponding length is larger than the upstream catchment length, L ($L\times {S}_{0}<{h}_{b}$); and (2) the ponding length is equal to or smaller than the upstream catchment length ($L\times {S}_{0}\ge {h}_{b}$):

_{pc}(m

^{3}) is the calculated ponding volume based on the RBS geometry; w

_{b}(m) is the RBS width (1 m); L (m) is the RBS length, which is the same as the road length; S

_{0}is the RBS’s longitudinal slope; h

_{b}(m) is the RBS overflow height; and A

_{gr}(m

^{2}) is the overflow grate inlet area.

_{ci}, were increased also as real design situations for the curb inlet to intercept a similar amount of the runoff. When the contributing watershed was enlarged by increasing L, a longer L

_{ci}allowed more runoff to flow into the RBS. Other corresponding RBS’s parameter values were changed correspondingly as shown/summarized in Table 1. The RBS system has eight key modeling parameters, and to fully understand the RBS system performance and the influence from each parameter, a large number of modeling cases is required, which was not studied here. For all 20 cases (Table 1), the roadway width was 10 m (y-direction, Figure 4) for a two-lane road, including necessary space for shoulders and gutters [49]. The curb width, which was the same as the curb-inlet width, was 0.1 m (4 in) to separate the road and the RBS. The RBS width was 1.0 m (40 in), and the maximum ponding depth or the bioretention depth, D

_{b}, was set as 0.05 m above the grate-inlet overflow height, h

_{b}, i.e., D

_{b}= h

_{b}+ 0.05 m for all 20 modeling cases. The road grate inlet was a rectangle of 0.75 m (30 in, along with the x-direction) by 0.45 m (18 in) and was made to be 0.05 m (2 in) lower than the surrounding road-surface cells for the model simulation here. The grate inlet in the RBS was the same size for all modeling cases.

_{ci}= 0.45 m) was 18 cells [(0.45/0.05) × (0.1/0.05)] in the simulation domain of RBS04.

_{0}and S

_{x}) for the road surface as the corresponding RBS modeling case (Table 1).

^{−5}m/s (250 mm/h, 10 in/h) and lasted 1200 s (20 min) to generate enough runoff reach the ponding volume, but the total simulation period was 2400 s. A portion (virtual road-surface in Figure 4a) of the simulation domain just downstream of the curb inlet was simulated without rainfall because the focus of the study was to investigate the impact of the runoff generated upstream of the curb inlet.

## 3. Results and Discussion

#### 3.1. FullSWOF-ZG Testing Results

#### 3.1.1. Results for Pervious Surfaces

#### 3.1.2. Results of Curb Inlet Interception

_{in}0.1031–0.2453 m

^{3}/s). All these model input parameter values were exactly the same as the experimental setup information [36,48]. The curb inlet interception efficiency (E

_{ci}) was evaluated with the curb intercepted flow rate (observed Q

_{cio}or simulated Q

_{cis}) divided by the upstream inflow rate (Q

_{in}) after the system reached equilibrium.

^{2}) of the linear relationship between the simulated and observed curb inlet interception efficiencies was 0.94. The high R

^{2}value with lower differences (∆E) is evidence to support that the FullSWOF-ZG model, which predicted the curb inlet interception efficiency with good performance.

_{E}) of the simulated and observed intercepted efficiencies ranged from −6.0% to 28.7%, with an average ± standard deviation of 6.6 ± 7.3%. In a previous study by Fang et al. [48], a three-dimensional fluid simulation software, FLOW-3D, was applied to simulate complex 3D shallow flow over the drainage pavement and flow leaving through type C and type D inlets. The differences (∆E) ranged from −7.0% to 17.6%, with an average ± standard deviation of 1.0 ± 4.87% for type C cases in their 3D simulations. The percent differences (PD

_{E}) for Fang’s study ranged from −19.7% to 6.1%, with an average ± standard deviation of −0.8 ± 5.7%. These 2D SWEs models using the FullSWOF-ZG program were almost as good as the FLOW-3D models used in the previous study when trying to simulate the interception efficiency of the type C curb inlet under different operation conditions. The results for all 20 modeling cases (Table 3) showed that the FullSWOF-ZG program was not only able to simulate the complicated flow over type C curb inlets, but also predicted the curb inlet interception efficiency well.

#### 3.2. Results of Rd and RBS Modeling Cases

#### 3.2.1. Example Modeling Results

_{bp}), and the flow into the road grate inlet (Q

_{rg}) of the 30 min simulation period. The runoff generated from the road surface took 32 s to reach the grate inlet, the discharge into the grate inlet then increased rapidly to a 98% peak in 85 s, and reached the equilibrium discharge of 11.96 L/s at 180 s under the constant rainfall. The grate inlet discharge took about 300 s to decrease to 0 L/s after the rainfall stopped. The rest part of the overland runoff that was not captured by the grate inlet discharges to the downstream as the bypass flow, which had a peak discharge of 1.91 L/s at 91 s. The sum of the peak flows of Q

_{rg}and Q

_{bp}was 13.87 L/s, which was the same as the peak discharge from the rational formula.

_{rg}, Q

_{bp}, the curb inlet intercepted flow (Q

_{ci}), and the overflow from the grate inlet in bioretention (Q

_{og}) as well as the bioretention water depth (y

_{b}) of the modeling case, RBS19. The peak or equilibrium discharges of Q

_{rg}, Q

_{ci}, and Q

_{bp}were 8.03 L/s, 4.94 L/s, and 0.50 L/s, respectively. The flow interception by the curb inlet seemed to slow down the flow a little bit to make more runoff into the grate inlet. Therefore, the sum of the peak Q

_{rg}and Q

_{ci}for RBS 19 was 12.97 L/s, which was larger than the Q

_{rg}of 11.96 L/s for the Rd19 case.

_{ci}, of a curb inlet is not constant, but changes with time. For RBS19, the runoff first reached the curb inlet at 11 s, and E

_{ci}was 100% when the runoff rate was small at 11 s < t < 31 s, then E

_{ci}decreased with time and became 36.7% when Q

_{ci}reached the equilibrium discharge. At the end of the 40-min simulation, the runoff volume, intercepted by the curb inlet and generated from the road, can be computed and the volumetric interception efficiency was computed as 37.4% for the RBS19 case, which will be further discussed later using Table 5. Therefore, for RBS19, the grate inlet on the road still intercepted a large percent (~60%) of the incoming runoff and only about 2.6% of the runoff volume was bypassed downstream. This is important information to the road and bioretention design since many designers think the curb inlet can intercept all runoff and adding or keeping the grate inlet on the road is not necessary. Figure 6 also shows that the geometry of the experiment and the model allowed for a fully developed flow by the time the flow reached the inlet. This was true for all modeling cases.

_{og}started at 748 s, reached the peak discharge of 6.16 L/s (at 1200s), and decreased after the rainfall stopped (Figure 6b). The red dash line in Figure 6b shows that the ponding depth (y

_{b}) adjacent to the bioretention overflow grate inlet increased to become higher than the bioretention overflow height (h

_{b}= 0.3 m) at 748 s and decreased to 0.3 m slowly after the rainfall stopped. There was a time period when Q

_{og}was larger than Q

_{ci}, which seemed impossible in the first impression. This was because the grate inlet discharge capacity was usually higher than the curb inlet capacity. In this study, the corresponding overflow weir length of the grate inlet [2 × (0.45 + 0.75) m] was much larger than the curb inlet opening (0.6 m) and the hydraulic head above the grate inlet could be larger also. It was verified that the mass conservation of the runoff in the simulation domain was valid (Figure 6) and the simulated larger Q

_{og}was correct.

_{i}) at every time step. The bioretention infiltration rate was equal to the rainfall intensity, R

_{i}, when the calculated soil infiltration capacity was larger than R

_{i}. The infiltration rate started to decrease at 263 s and decreased to 80.1 mm/h at the end of the simulation. The cumulative infiltration, F, kept increasing during the simulation period and reached 0.07 m at 30 min, which seemed small, but the infiltration continued at ~80 mm/h to gradually deplete all ponding water in the bioretention cell. The heavy rainfall (250 mm/h) over 20 min was used for the simulation in order to generate the overflow in the grate inlet at the RBS so that FullSWOF-ZG was fully tested.

#### 3.2.2. Modeling Results for Road-Only (Rd) Cases

_{rd}, was transformed into the runoff volume captured by the road grate inlet (V

_{rg}) and the bypass runoff volume (V

_{bp}). The percent differences (∆V

_{rd}) between the simulated runoff volume, V

_{srd}= V

_{rg}+ V

_{bp}, and the rainfall volume V

_{rd}for 20 road-only cases ranged from −3.3% to 0.1%. The average ± standard deviation of ∆V

_{rd}was −0.6 ± 0.8% for 20 road-only cases (Table 4), which indicated FullSWOF-ZG had a higher accuracy in mass balance. These 20 modeling cases were regrouped into five groups (by alternating two colors in Table 4): The road length L decreased from 40 m to 10 m as the modeling case number increased when S

_{0}is the same in each group (Table 1). Since the same rainfall was used for all modeling cases, all runoff volumes decreased with the decrease of the road length (Table 4), e.g., V

_{rg}decreased from 22.96 m

^{3}(Rd17, L = 40 m) to 7.67 m

^{3}(Rd20, L = 10 m); and the corresponding V

_{bp}decreased from 10.31 m

^{3}to 0.64 m

^{3}. Because of the volume decrease or less flow velocity due to less L, the percent of V

_{rg}(P

_{rg}= V

_{rg}/V

_{srd}) increased with the additional influence of the increase of the cross slope, e.g., Rd01–Rd04 from 70.9% to 98.3% (Figure 7a). The percent of V

_{rg}ranged from 53.4% (Rd09, S

_{x}= 2%) to 98.3% (Rd08, S

_{x}= 4%), with an average ± standard deviation of 80.7 ± 21.5%. The percent of V

_{bp}(P

_{bp}= V

_{bp}/V

_{srd}) ranged from 1.7% (Rd08) to 46.6% (Rd09), with an average ± standard deviation of 19.3 ± 13.0%. The relatively large variations of P

_{rg}and P

_{bp}were due to the change of the road length or upstream inflow.

_{rg}for the same L cases decreased from 96.2% to 64.3% for L increases from 10 to 40 m, but the standard deviation from the mean increased from 2.5% to 7.0%. Therefore, L had more influence on P

_{rg}than S

_{0}did. When L was smaller, the incoming runoff from the upstream road was small, more runoff as intercepted by the grate inlet, and less runoff was bypassed downstream. Only 20 individual road-only cases (4 L × 5 S

_{0}) were modeled here; when S

_{0}was increased, the cross slope, S

_{x}, was also increased to allow and guide more runoff to the grate inlet. S

_{x}ranged from 3.0%–6.5% at L = 10 m to 1.0%–4.0% at L = 40 m (Table 1). For Rd09, both V

_{bp}and P

_{bp}were the highest and indicated a high potential of the local flooding on the road. For all road-only cases, the peak discharges of the grate inlet (Q

_{prg}) were 6.68 ± 0.17 L/s for the L = 10 m group, 11.66 ± 0.61 L/s for the L = 20 m group, 15.92 ± 1.51 L/s for the L = 30 m group, and 17.43 ± 1.91 L/s for the L = 40 m group. The peak discharges of the bypass flow (Q

_{pbp}) were 0.26 ± 0.17 L/s for the L = 10 m group, 2.22 ± 0.61 L/s for the L = 20 m group, 4.90 ± 1.51 L/s for the L = 30 m group, and 10.33 ± 1.91 L/s for the L = 40 m group. Both Q

_{prg}and Q

_{pbp}increased with the increase of the catchment length.

#### 3.2.3. Modeling Results for Road-Bioretention Strip (RBS) Cases

_{srd}) was intercepted by the curb inlet (V

_{ci}), resulting in a reduction of the runoff incepted by the road grate inlet (V

_{rg}) and bypass runoff (V

_{bp}). For the 20 RBS cases (Table 5), V

_{ci}increased from 3.27 ± 0.05 m

^{3}(L = 10 m) to 13.6 ± 1.54 m

^{3}(L = 40 m) (Table 6), but the percentage (P

_{ci}= V

_{ci}/V

_{srd}= V

_{ci}/(V

_{ci}+ V

_{rg}+ V

_{bp})) of runoff volume intercepted by the curb inlet (or curb inlet efficiency by volume) was similar: 40.0 ± 3.3%. This was because the curb inlet length, L

_{ci}, was also increased from 0.45 m to 1.2 m for L = 10–40 m. The corresponding runoff volume (V

_{rg}) captured by the road grate inlet increased from 4.53 ± 0.21 m

^{3}(L = 10 m) to 15.46 ± 1.00 m

^{3}(L = 40 m); the bypass runoff volume (V

_{bp}) from 0.28 ± 0.25 m

^{3}to 3.38 ± 0.81 m

^{3}. The percentage of the runoff captured by the grate inlet on the road (P

_{rg}= V

_{rg}/V

_{srd}) decreased from 56.1 ± 2.6% (L = 10 m) to 47.6 ± 3.1% (L = 40 m), with an overall average ± standard deviation of 54.6 ± 5.2%. Due to the curb inlet interception, each RBS system diverted a part of the runoff from the impervious road to the bioretention strip for infiltration and treatment (e.g., to allow sediments to settle and improve water quality), therefore, less runoff flowed into the grate inlet on the road, and then the P

_{rg}for the RBS (Table 5) was always smaller than for the corresponding road-only case (Table 4). The differences of P

_{rg}between the road-only and corresponding RBS modeling cases ranged from 5.2%–40.8%, with an average difference of 26.0 ± 9.6%.

_{bp}, for the RBS cases (Figure 7 and Table 5) ranged from 0.3% (RBS04) to 12.9% (RBS05), with an average ± standard deviation of 5.4 ± 3.6%. The V

_{bp}and P

_{bp}for all RBS cases (Table 5) were lower than them for the corresponding road-only cases (Table 4), which means the curb inlet and grate inlet combination was more efficient than the grate inlet only for intercepting the road surface runoff. The mass balance as percent differences of the whole simulation domain (∆V), on the road (∆V

_{rd}) and in the bioretention strip (∆V

_{rb}), were small (Table 5).

_{ci}) and generated on the bioretention surface from rainfall (V

_{rb}). The bioretention outflow included the infiltration (V

_{inf}) and the overflow through the grate inlet near the check dam (Figure 1, V

_{bog}in Table 5). The difference between the inflow and the outflow was the ponding volume (V

_{bio}) in the bioretention strip. V

_{rb}was the rainfall depth (250 mm/h × 20 min) times the area (L × 1 m) of the bioretention strip and linearly increased from 0.83 m

^{3}to 3.33 m

^{3}for L = 10 m to 40 m.

_{inf}) was calculated (Table 5) and the mean V

_{inf}ranged from 1.24 m

^{3}for the L = 10 m group to 3.75 m

^{3}for the L = 40 m group over 40 min simulation periods. To understand the soil infiltration performance of the bioretention, loamy sand was used for the L of 10 m and 40 m cases, sandy loam for L of 20 m cases, and loam for L of 30 m cases. The average and standard deviation of the infiltrated runoff percentage, i.e., V

_{inf}/(V

_{ci}+ V

_{rb}), were 30.4 ± 0.3% for loamy sand (L = 10 m group), 21.3 ± 0.8% for sandy loam (L = 20 m group), 20.7 ± 6.5% for loam (L = 30 m group), and 22.5 ± 8.5% for loamy sand (L = 40 m group).

_{inf}, decreased from RBS01 (4.28 m

^{3}) to RBS17 (3.09 m

^{3}, Table 5, L = 40 m group), mainly because the smaller longitudinal slope, S

_{0}, increased the ponding area, since h

_{b}and the infiltration parameters were the same for these five modeling cases. For RBS01, RBS05, and RBS09, L × S

_{0}≤ h

_{b}, so that the maximum ponding area was 40 m × 1 m (width of the bioretention strip); for RBS13 and RBS17, L × S

_{0}> h

_{b}, so that the maximum ponding area was less than 40 m × 1 m (only covered 28.6 m and 20 m, respectively).

_{bog}= 0) because the overflow height of the grate inlet (h

_{b}) was the largest (0.4 m, D

_{b}—0.05 in Table 1), but the maximum ponding depth (h

_{max}, Table 7) was less than h

_{b}for these cases. All other three modeling groups (L = 20, 30, and 40 m) overflowed through the grate inlet in the bioretention (h

_{max}> h

_{b}, Table 7). The increase of the overflow grate-inlet volume V

_{bog}(Table 5) was mainly because of the increase of the longitudinal slope (S

_{0}) when L and h

_{b}were unchanged. The mean V

_{bog}increased from 1.59 m

^{3}(L = 20 m group) to 10.11 m

^{3}(L = 40 m group) when h

_{b}decreased from 0.3 to 0.2 m. This indicated that the overflow height, h

_{b}, was a key design parameter of the RBS to retain the runoff inside the bioretention.

_{bog}percentage, i.e., V

_{bog}/(V

_{ci}+ V

_{rb}), increased when h

_{b}decreased: 20.7 ± 12.7% for the L = 20 m group (h

_{b}= 0.30 m), 44.4 ± 8.8% for the L = 30 m group (h

_{b}= 0.25 m), and 58.4 ± 10.2% for the L = 40 m group (h

_{b}= 0.20 m). When h

_{b}was small, the grate-inlet overflow became the main mechanism to remove the extra runoff in the bioretention strip as indicated by the larger V

_{bog}percentage.

_{pog}, increased from 4.81 L/s to 12.65 L/s for L = 20–40 m groups (Table 7) when the total inflow (V

_{ci}+ V

_{rb}) increased, h

_{b}decreased also. The bioretention overflow-start-time, (T

_{bog}) and Q

_{pog}, were mainly related to V

_{ci}and h

_{b}. T

_{bog}decreased from 974.8 ± 188.2 s (L = 20 m group) to 391.6 ± 252.5 s (L = 40 m group). The bioretention overflow was delayed when the overflow height, h

_{b}, increased. The bioretention overflow was first projected to start at 163 s in the RBS17 modeling case and reached the peak discharge of 14.92 L/s. The main reason was the largest curb inlet intercepted runoff volume of RBS17 (15.72 m

^{3}) due to the large L and S

_{x}and the lowest h

_{b}= 0.20 m.

_{bio}) were 3.10 m

^{3}for the L = 10 m group, 4.86 m

^{3}for the L = 20 m group, 4.93 m

^{3}for the L = 30 m group, and 3.93 m

^{3}for the L = 40 m group when the rainfall intensity was large (250 mm/h). V

_{bio}is a function of time and shows the integrated/cumulative effects of different flow processes (inflow from curb inlet, outflow through the overflow grate inlet, rainfall, and infiltration). V

_{bio}(t) is also related to the bioretention strip’s ponding capacity, which was determined by the bioretention-strip geometry as shown in Equation (9). There are four modeling cases (RBS09, 13, 17, and 18; Table 1) with L × S

_{0}≥ h

_{b}; therefore, the overflow height, h

_{b}, was the only controlling factor for V

_{bio}(t), independent of L × S

_{0}for these four cases.

_{bio}(t) was zero. When the ponding depth increased from zero to h

_{b}, V

_{bio}(t)/V

_{pc}increased from zero to 1.0, since V

_{pc}(Equation (9) is the calculated maximum bioretention ponding volume at h

_{b}. When the overflow through the grate inlet took place in the bioretention strip, V

_{bio}(t)/V

_{pc}was greater than 1.0. After the rainfall stopped, eventually, V

_{bio}(t) was zero when the ponding depth decreased to zero. In this study, V

_{bio}(t) at the end of the simulation (t = 40 min) for each RBS case is shown in Table 5 and was used to calculate the runoff-volume mass-balance percent difference (∆V) in the whole simulation domain. These percent differences (Table 5) were very small, with an average of −0.02%, and indicated that the RBS simulation results were reasonable.

_{bio}(40) percentage, V

_{bio}(40)/(V

_{ci}+ V

_{rb}) at the end of simulation, t = 40 min, was larger when h

_{b}was larger: 75.6 ± 0.2% for the L = 10 m group (h

_{b}= 0.4 m), 64.3 ± 11.8% for the L = 20 m group, 40.3 ± 26.7% for the L = 30 m group, and 24.2 ± 26.3% for the L = 40 m group (h

_{b}= 0.2 m). The higher V

_{bio}(40) percentage means that more runoff was ponded and waited for infiltration when the simulation ended. The ponding volume, V

_{bio}(40), for each case was compared with V

_{pc}, and the ratio ranged from 0.73 to 0.96 (Table 7).

_{bio}(40) was smaller than V

_{pc}

_{,}and the mean ratios of V

_{bio}/V

_{pc}were 0.77–0.95 for the changing L. The results in Table 7 and Equation (9) indicate that it is necessary to consider three parameters, S

_{0}, L, and h

_{b}, when calculating the ponding capacity of the bioretention; this was especially important in the continuous RBS system when these three parameters changed in different RBSs. In this study, the vegetation volume fraction was not considered when calculating V

_{pc}, therefore, we need to use a safety factor to calculate the actual ponding volume based on the bioretention geometry and vegetation volume fraction when designing a continuous RBS system.

#### 3.3. Implications of the Simulation Results on RBS Design

_{prgb}, Table 7) were compared with the corresponding Q

_{prg}for the road-only modeling cases. For all 20 RBS cases, the average Q

_{prgb}increased from 3.84 L/s to 13.14 L/s for an L increase from 10 to 40 m. Comparing with Q

_{prg}, the average ratio of Q

_{prgb}/Q

_{prg}were from 0.57 to 0.76 for L = 10–40 m groups. The overall average ± standard deviation of Q

_{prgb}/Q

_{prg}for 20 modeling cases was 0.69 ± 0.09, which indicates that the curb inlet and grate inlet combination could reduce the road grate inlet peak discharge and help to relieve road local flood inundation. Therefore, the curb inlet and grate inlet combination greatly benefits the runoff control, local flood inundation relief, and traffic safety, especially for continuous road-bioretention. Eliminating the grate inlets on the road for the RBS system is not a recommended design practice.

_{pc}) multiplied by the safety factor used for RBS design. The berm at the end of a bioretention cell (Figure 1 and Figure 2) is typically to pond the runoff for infiltration and to ensure that the overflow discharges through the grate inlet rather than flowing into the bioretention downstream. For the RBS13, RBS17, and RBS18 modeling cases, L × S

_{0}> h

_{b}, so that the maximum ponding and infiltration area was less than the total bioretention surface area (e.g., 40 m × 1 m in this study), which is not a recommended design configuration for the bioretention strip. The distance between the ditch dikes should be small enough to have L × S

_{0}≤ h

_{b}or pond the runoff in the whole bioretention area. The bioretention ponding volume is influenced by the bioretention cells’ geometry, including the length, longitudinal slope, and overflow height; it can be computed using Equation 9, but the vegetation volume fraction can be important when the vegetation density in the bioretention is very high (Figure 2a) so that a ponding volume safety factor should be introduced. The EPA-SWMM model suggests the vegetation volume fraction of 0.1–0.2, therefore, the safety factor used for RBS design in computing the ponding volume should be 0.8–0.9.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

BMP | Best Management Practice |

D_{b} | bioretention depth |

DEM | digital elevation model |

E_{ci} | curb inlet interception efficiency |

f | bioretention infiltration rate |

F | cumulative infiltration depth |

h_{b} | overflow height |

HEC-22 | Urban Drainage Design Manual: Hydraulic Engineering Circular No. 22 |

h_{max} | bioretention maximum ponding depth |

K | saturated hydraulic conductivity |

φ | suction head |

∆E | differences of simulated and observed interception efficiencies |

Δθ | moisture deficit |

∆V | percent difference between simulated RBS runoff volume and rainfall volume |

∆V_{p} | percent difference of simulated and observed runoff volume |

∆V_{rb} | percent difference between simulated bioretention runoff volume and rainfall volume |

∆V_{rd} | percent difference between simulated road runoff volume and rainfall volume |

∆Q_{p} | percent difference of simulated peak discharge |

L | upstream catchment length |

L_{ci} | curb inlet length |

LID | Low impact development |

L_{T} | theoretical curb-inlet length required to intercept 100% of the flow |

NSE | Nash-Sutcliffe Efficiency |

P_{bp} | percent of bypass runoff volume |

P_{ci} | percent of runoff volume intercepted by curb inlet |

PD_{E} | percent differences of simulated and observed intercepted efficiencies |

P_{inf} | percent of bioretention cumulative infiltration volume |

P_{rg} | percent of road grate inlet captured runoff volume |

Q_{bp} | remainder of runoff discharged downstream along the road |

Q_{ci} | road runoff intercepted by the curb inlet |

Q_{cio} | observed curb intercepted flow rate |

Q_{cis} | simulated curb intercepted flow rate |

Q_{i} | total inflow rate |

Q_{og} | overflows runoff through the bioretention grate inlet |

Q_{pbp} | peak discharges of the bypass flow |

Q_{po} | observed peak runoff rate |

Q_{pog} | overflow grate inlet peak discharge |

Q_{prg} | peak discharges of the grate inlet |

Q_{prgb} | road grate inlet peak discharge for RBS cases |

Q_{ps} | simulated peak runoff rate |

Q_{rg} | road runoff captured by the road grate inlet |

RBS | Road-bioretention strip |

S_{0} | longitudinal slopes of the road/street |

SPC | Sponge city |

SWEs | Shallow-Water Equations |

S_{x} | cross slope of the road/street |

T_{bog} | bioretention overflow-start-time |

V_{bio} | bioretention ponding runoff volume |

V_{bio}(t) | runoff volume stays in the bioretention strip |

V_{bog} | bioretention overflow grate inlet discharge volume |

V_{bp} | bypass runoff volume |

V_{ci} | runoff volume intercepted by curb inlet |

V_{inf} | bioretention cumulative infiltration volume |

V_{ob} | observed total runoff volume |

V_{pc} | calculated bioretention ponding volume |

V_{r} | calculated rainfall volume |

V_{rb} | runoff generated on the bioretention surface from rainfall |

V_{rd} | road rainfall volume |

V_{rg} | runoff volume captured by the road grate inlet |

V_{si} | simulated total runoff volume |

V_{srd} | simulated road runoff volume |

y_{b} | bioretention water depth |

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**Figure 2.**Continuous road-bioretention strip in (

**a**) Beijing (curb inlet length L

_{ci}= 0.5 m) taken by Yongwei Gong, (

**b**) Shenzhen (L

_{ci}= 0.4 m) taken by Yongwei Gong, (

**c**) Jinan (L

_{ci}= 0.4 m) taken by Xiaoning Li, and (

**d**) Ningbo (L

_{ci}= 0.3 m) taken by Jianlong Wang. Red boxes show curb inlets and yellow boxes show overflow grate inlets in the bioretention cells.

**Figure 3.**(

**a**) Layout of type C curb inlet evaluation experiment (top view), and (

**b**) DEM of case C01 with a longitudinal slope, S

_{0}= 0.004, and cross slope, S

_{x}= 0.0208.

**Figure 4.**(

**a**) Plan view and (

**b**) DEM for RBS04 (Table 1) with a longitudinal slope, S

_{0}= 0.001, and cross slope, S

_{x}= 0.030.

**Figure 5.**Simulated and observed hydrographs of one pervious surface under four events: (

**a**) S01R1, (

**b**) S01R2, (

**c**) S01R3, and (

**d**) S01R4 (Table 2).

**Figure 6.**Simulation results of case Rd19 (

**a**) and case RBS19 with an undepressed curb inlet (

**b**,

**c**). All symbols are defined in the text and summarized in Appendix A.

**Figure 7.**Runoff volumes and corresponding percentages captured by the road grate inlet (V

_{rg}and P

_{rg}), bypassed downstream (V

_{bp}and P

_{bp}) for (

**a**) 20 road-only (Rd01–Rd20) and (

**b**) 20 RBS modeling cases, and (

**b**) intercepted by the curb inlet (V

_{ci}and P

_{ci}) for RBS modeling cases. Percentages are shown as a 100% stacked column diagram using a major y-axis and volumes (m

^{3}) are shown as lines with symbols using a secondary y-axis.

**Table 1.**Parameter values of 20 modeling cases of the road-bioretention strip (RBS) systems with an undepressed curb inlet and grate inlets (Figure 4a).

Case No. | L | S_{0} | S_{x} | L_{ci} | D_{b} | K | φ | Δθ | V_{pc} |
---|---|---|---|---|---|---|---|---|---|

(m) | (-) | (-) | (m) | (m) | (mm/h) | (m) | (-) | (m^{3}) | |

RBS01 | 40 | 0.001 | 0.010 | 1.20 | 0.25 | 51 | 0.090 | 0.410 | 7.44 |

RBS02 | 30 | 0.001 | 0.015 | 0.90 | 0.30 | 25 | 0.218 | 0.435 | 7.33 |

RBS03 | 20 | 0.001 | 0.020 | 0.60 | 0.35 | 13 | 0.478 | 0.451 | 6.08 |

RBS04 | 10 | 0.001 | 0.030 | 0.45 | 0.45 | 51 | 0.090 | 0.410 | 4.28 |

RBS05 | 40 | 0.003 | 0.015 | 1.20 | 0.25 | 51 | 0.090 | 0.410 | 5.68 |

RBS06 | 30 | 0.003 | 0.020 | 0.90 | 0.30 | 25 | 0.218 | 0.435 | 6.33 |

RBS07 | 20 | 0.003 | 0.030 | 0.60 | 0.35 | 13 | 0.478 | 0.451 | 5.62 |

RBS08 | 10 | 0.003 | 0.040 | 0.45 | 0.45 | 51 | 0.090 | 0.410 | 4.16 |

RBS09 ^{1} | 40 | 0.005 | 0.020 | 1.20 | 0.25 | 51 | 0.090 | 0.410 | 3.93 |

RBS10 | 30 | 0.005 | 0.030 | 0.90 | 0.30 | 25 | 0.218 | 0.435 | 5.32 |

RBS11 | 20 | 0.005 | 0.040 | 0.60 | 0.35 | 13 | 0.478 | 0.451 | 5.16 |

RBS12 | 10 | 0.005 | 0.045 | 0.45 | 0.45 | 51 | 0.090 | 0.410 | 4.03 |

RBS13 ^{1} | 40 | 0.007 | 0.030 | 1.20 | 0.25 | 51 | 0.090 | 0.410 | 2.79 |

RBS14 | 30 | 0.007 | 0.040 | 0.90 | 0.30 | 25 | 0.218 | 0.435 | 4.32 |

RBS15 | 20 | 0.007 | 0.045 | 0.60 | 0.35 | 13 | 0.478 | 0.451 | 4.71 |

RBS16 | 10 | 0.007 | 0.055 | 0.45 | 0.45 | 51 | 0.090 | 0.410 | 3.91 |

RBS17 ^{1} | 40 | 0.010 | 0.040 | 1.20 | 0.25 | 51 | 0.090 | 0.410 | 1.93 |

RBS18 ^{1} | 30 | 0.010 | 0.045 | 0.90 | 0.30 | 25 | 0.218 | 0.435 | 3.04 |

RBS19 | 20 | 0.010 | 0.055 | 0.60 | 0.35 | 13 | 0.478 | 0.451 | 4.02 |

RBS20 | 10 | 0.010 | 0.065 | 0.45 | 0.45 | 51 | 0.090 | 0.410 | 3.72 |

^{1}—for the modeling case, L × S

_{0}≥ h

_{b}Equation (9). L (m) is the length of the road and the RBS upstream of the curb inlet (Figure 4), L

_{ci}(m) is the opening length of the curb inlet, h

_{b}(m) is the overflow height of the grate inlet inside the RBS, and the bioretention depth, D

_{b}= h

_{b}+ 0.05 m, K (mm/h) is the saturated hydraulic conductivity, φ (m) is the soil suction head, and Δθ is the soil moisture deficit, V

_{pc}(m

^{3}) is the calculated bioretention ponding volume when overflow occurs.

**Table 2.**Comparison of simulated and observed discharge and volume results for eight rainfall events.

Events | S_{0} | NSE | V_{r} | V_{ob} | V_{si} | ∆V_{p} | Q_{po} | Q_{ps} | ∆Q_{p} |
---|---|---|---|---|---|---|---|---|---|

(-) | (-) | (m^{3}) | (m^{3}) | (m^{3}) | (%) | (L/s) | (L/s) | (%) | |

S01R1 | 0.001 | 0.85 | 0.35 | 0.20 | 0.25 | 22.2 | 0.18 | 0.21 | 15.4 |

S01R2 | 0.001 | 0.93 | 0.32 | 0.20 | 0.21 | 4.9 | 0.18 | 0.19 | 5.4 |

S01R3 | 0.001 | 0.83 | 0.32 | 0.19 | 0.22 | 14.6 | 0.15 | 0.19 | 23.5 |

S01R4 | 0.001 | 0.92 | 0.20 | 0.13 | 0.11 | −16.7 | 0.12 | 0.12 | 0.0 |

S02R5 | 0.002 | 0.83 | 0.21 | 0.12 | 0.12 | 0.0 | 0.12 | 0.15 | 22.2 |

S02R6 | 0.002 | 0.84 | 0.27 | 0.15 | 0.15 | 0.0 | 0.12 | 0.15 | 22.2 |

S02R7 | 0.002 | 0.79 | 0.25 | 0.16 | 0.14 | −13.3 | 0.15 | 0.14 | −6.9 |

S05R8 | 0.005 | 0.87 | 0.19 | 0.09 | 0.10 | 10.5 | 0.12 | 0.16 | 28.6 |

_{0}(-) is the testing bed’s surface slope, V

_{r}(m

^{3}) is the calculated rainfall volume, V

_{ob}(m

^{3}) is the observed total runoff volume, V

_{si}(m

^{3}) is the simulated total runoff volume, ∆V

_{p}(%) is the percent difference of the simulated runoff volume = (V

_{si}− V

_{ob})/[(V

_{ob}+ V

_{si})/2] × 100%, Q

_{po}(L/s) is the observed peak runoff rate, Q

_{ps}(L/s) is the simulated peak runoff rate, ∆Q

_{p}(%) is the percent difference of the simulated peak discharge = (Q

_{ps}− Q

_{po})/[(Q

_{po}+ Q

_{ps})/2] × 100%.

Case No. | S_{0} | S_{x} | T | Q_{in} | Q_{cio} | E_{cio} | Q_{cis} | E_{cis} | ∆E | PD_{E} |
---|---|---|---|---|---|---|---|---|---|---|

(-) | (-) | (m) | (m^{3}/s) | (m^{3}/s) | (%) | (m^{3}/s) | (%) | (%) | (%) | |

C01 | 0.004 | 0.0208 (1:48) | 4.27 | 0.2400 | 0.1256 | 52.3 | 0.1306 | 54.4 | 2.1 | 3.9 |

C02 | 0.004 | 0.0208 | 4.27 | 0.1076 | 0.0829 | 77.0 | 0.0872 | 81.0 | 4.0 | 5.0 |

C03 | 0.010 | 0.0208 | 4.27 | 0.2361 | 0.1098 | 46.5 | 0.1185 | 50.2 | 3.7 | 7.7 |

C04 | 0.010 | 0.0208 | 4.27 | 0.1806 | 0.0983 | 54.4 | 0.1047 | 58.0 | 3.5 | 6.3 |

C05 | 0.020 | 0.0208 | 3.45 | 0.1246 | 0.0741 | 59.5 | 0.0793 | 63.6 | 4.2 | 6.8 |

C06 | 0.020 | 0.0208 | 4.27 | 0.2424 | 0.0979 | 40.4 | 0.1139 | 47.0 | 6.6 | 15.1 |

C07 | 0.040 | 0.0208 | 4.07 | 0.1281 | 0.0698 | 54.5 | 0.0734 | 57.3 | 2.8 | 5.1 |

C08 | 0.040 | 0.0208 | 4.07 | 0.1589 | 0.0762 | 48.0 | 0.0823 | 51.8 | 3.8 | 7.7 |

C09 | 0.060 | 0.0208 | 4.07 | 0.1166 | 0.0653 | 56.0 | 0.0615 | 52.8 | −3.2 | −6.0 |

C10 | 0.060 | 0.0208 | 4.27 | 0.2451 | 0.0853 | 34.8 | 0.0896 | 36.6 | 1.8 | 4.9 |

C11 | 0.004 | 0.0417 (1:24) | 3.87 | 0.2316 | 0.1488 | 64.2 | 0.1539 | 66.4 | 2.2 | 3.4 |

C12 | 0.004 | 0.0417 | 3.21 | 0.1439 | 0.1182 | 82.1 | 0.1194 | 83.0 | 0.8 | 1.0 |

C13 | 0.010 | 0.0417 | 2.84 | 0.1433 | 0.1133 | 79.1 | 0.1145 | 79.9 | 0.9 | 1.1 |

C14 | 0.010 | 0.0417 | 3.37 | 0.2320 | 0.1369 | 59.0 | 0.1436 | 61.9 | 2.9 | 4.8 |

C15 | 0.020 | 0.0417 | 2.97 | 0.2433 | 0.1215 | 49.9 | 0.1359 | 55.9 | 5.9 | 11.2 |

C16 | 0.020 | 0.0417 | 2.28 | 0.1031 | 0.0870 | 84.4 | 0.0886 | 86.0 | 1.6 | 1.9 |

C17 | 0.050 | 0.0417 | 2.16 | 0.1724 | 0.0874 | 50.7 | 0.0983 | 57.0 | 6.3 | 11.7 |

C18 | 0.050 | 0.0417 | 3.09 | 0.2381 | 0.0940 | 39.5 | 0.1255 | 52.7 | 13.2 | 28.7 |

C19 | 0.070 | 0.0208 | 4.07 | 0.1542 | 0.0700 | 45.4 | 0.0682 | 44.2 | −1.2 | −2.6 |

C20 | 0.070 | 0.0417 | 3.05 | 0.1535 | 0.0803 | 52.3 | 0.0927 | 60.4 | 8.1 | 14.3 |

_{0}(-) is the road longitudinal slope, S

_{x}(-) is the road cross slope, T (m) is the upstream flow spread width, Q

_{in}(m

^{3}/s) is the upstream inflow rate, Q

_{cio}(m

^{3}/s) is the observed curb inlet intercepted flow rate, E

_{cio}(%) is the observed curb inlet intercepted efficiency, Q

_{cis}(m

^{3}/s) is the simulated curb inlet intercepted flow rate, E

_{cis}(%) is the simulated curb inlet intercepted efficiency, ∆E (%) is the difference of the simulated intercepted efficiency = E

_{cis}− E

_{cio}, PD

_{E}(%) is the percent difference of the simulated intercepted efficiency = (E

_{cis}− E

_{cio})/[(E

_{cis}+ E

_{cio})/2] × 100%.

Case No. | V_{rd} | V_{srd} | ∆V_{rd} | V_{rg} | P_{rg} | V_{bp} | P_{bp} | Q_{prg} | Q_{pbp} |
---|---|---|---|---|---|---|---|---|---|

(m^{3}) | (m^{3}) | (%) | (m^{3}) | (%) | (m^{3}) | (%) | (L/s) | (L/s) | |

Rd04 (10 m) ^{1} | 8.33 | 8.24 | −1.02 | 8.10 | 98.3 | 0.14 | 1.7 | 6.81 | 0.13 |

Rd08 | 8.33 | 8.30 | −0.34 | 8.16 | 98.3 | 0.14 | 1.7 | 6.82 | 0.12 |

Rd12 | 8.33 | 8.31 | −0.21 | 8.06 | 97.0 | 0.25 | 3.0 | 6.74 | 0.20 |

Rd16 | 8.33 | 8.31 | −0.17 | 7.92 | 95.3 | 0.39 | 4.7 | 6.62 | 0.32 |

Rd20 | 8.33 | 8.31 | −0.18 | 7.67 | 92.3 | 0.64 | 7.7 | 6.42 | 0.52 |

Rd03 (20 m) | 16.66 | 16.45 | −1.25 | 14.85 | 90.3 | 1.60 | 9.7 | 12.43 | 1.45 |

Rd07 | 16.66 | 16.60 | −0.33 | 13.10 | 78.9 | 3.50 | 21.1 | 10.80 | 3.08 |

Rd11 | 16.66 | 16.63 | −0.17 | 13.81 | 83.0 | 2.82 | 17.0 | 11.43 | 2.45 |

Rd15 | 16.66 | 16.63 | −0.13 | 14.05 | 84.5 | 2.58 | 15.5 | 11.66 | 2.22 |

Rd19 | 16.66 | 16.64 | −0.11 | 14.39 | 86.5 | 2.25 | 13.5 | 11.97 | 1.91 |

Rd02 (30 m) | 24.98 | 24.49 | −2.00 | 21.52 | 87.9 | 2.97 | 12.1 | 18.01 | 2.81 |

Rd06 | 24.98 | 24.84 | −0.58 | 19.98 | 80.4 | 4.86 | 19.6 | 16.55 | 4.27 |

Rd10 | 24.98 | 24.92 | −0.24 | 17.00 | 68.2 | 7.93 | 31.8 | 13.94 | 6.88 |

Rd14 | 24.98 | 24.95 | −0.13 | 18.50 | 74.1 | 6.45 | 25.9 | 15.25 | 5.57 |

Rd18 | 24.98 | 24.96 | −0.10 | 19.18 | 76.8 | 5.78 | 23.2 | 15.86 | 4.96 |

Rd01 (40 m) | 33.31 | 32.22 | −3.28 | 22.85 | 70.9 | 9.37 | 29.1 | 19.02 | 8.73 |

Rd05 | 33.31 | 33.02 | −0.88 | 21.87 | 66.2 | 11.15 | 33.8 | 17.97 | 9.79 |

Rd09 | 33.31 | 33.16 | −0.44 | 17.71 | 53.4 | 15.45 | 46.6 | 14.38 | 13.38 |

Rd13 | 33.31 | 33.24 | −0.22 | 20.61 | 62.0 | 12.62 | 38.0 | 16.87 | 10.89 |

Rd17 | 33.31 | 33.27 | −0.13 | 22.96 | 69.0 | 10.31 | 31.0 | 18.89 | 8.87 |

^{1}—the road length, L, is given in brackets and there is the same length for other modeling cases in the same group, V

_{rd}(m

^{3}) is the total rainfall volume fell on the road surface, V

_{rg}(m

^{3}) is the runoff volume captured by the road grate inlet, V

_{bp}(m

^{3}) is the bypass runoff volume (to the road downstream), P

_{rg}(%) is the percent of runoff captured by the grate inlet = V

_{rg}/(V

_{rg}+ V

_{bp}) = V

_{rg}/V

_{srd}, P

_{bp}(%) is the percent of the bypass runoff = V

_{bp}/V

_{srd}, ∆V

_{rd}(%) is the percent difference of the simulated runoff volume = (V

_{srd}− V

_{rd})/V

_{rd}× 100%, Q

_{prg}(L/s) is the peak discharge of the runoff captured by the road grade inlet, Q

_{pbp}(L/s) is the peak discharge of the bypass runoff.

Case No. | V_{ci} | P_{ci} | V_{rg} | P_{rg} | V_{bp} | P_{bp} | V_{rb} | V_{inf} | V_{bog} | V_{bio} | ∆V | ∆V_{rd} | ∆V_{rb} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

(m^{3}) | (%) | (m^{3}) | (%) | (m^{3}) | (%) | (m^{3}) | (m^{3}) | (m^{3}) | (m^{3}) | (%) | (%) | (%) | |

RBS04 (10 m) ^{1} | 3.30 | 40.8 | 4.76 | 58.9 | 0.02 | 0.3 | 0.83 | 1.24 | 0.00 | 3.13 | 0.0 | −2.9 | 5.8 |

RBS08 | 3.33 | 41.2 | 4.64 | 57.5 | 0.10 | 1.3 | 0.83 | 1.25 | 0.00 | 3.16 | 0.0 | −3.0 | 5.9 |

RBS12 | 3.22 | 39.9 | 4.62 | 57.2 | 0.23 | 2.9 | 0.83 | 1.24 | 0.00 | 3.06 | 0.0 | −3.0 | 6.1 |

RBS16 | 3.27 | 40.5 | 4.42 | 54.7 | 0.39 | 4.8 | 0.83 | 1.25 | 0.00 | 3.10 | 0.0 | −3.0 | 5.9 |

RBS20 | 3.21 | 39.8 | 4.22 | 52.3 | 0.64 | 8.0 | 0.83 | 1.24 | 0.00 | 3.05 | 0.0 | −3.0 | 6.0 |

RBS03 (20 m) | 5.61 | 34.6 | 10.00 | 61.7 | 0.60 | 3.7 | 1.67 | 1.63 | 0.26 | 5.83 | 0.0 | −2.7 | 6.1 |

RBS07 | 5.85 | 36.1 | 9.89 | 61.1 | 0.44 | 2.7 | 1.67 | 1.63 | 1.03 | 5.33 | 0.0 | −2.8 | 6.3 |

RBS11 | 6.09 | 37.7 | 9.76 | 60.4 | 0.32 | 2.0 | 1.67 | 1.62 | 1.73 | 4.89 | 0.0 | −2.9 | 6.3 |

RBS15 | 5.99 | 37.1 | 9.76 | 60.4 | 0.41 | 2.6 | 1.67 | 1.61 | 2.09 | 4.45 | 0.0 | −3.0 | 6.4 |

RBS19 | 6.04 | 37.4 | 9.50 | 58.8 | 0.61 | 3.8 | 1.67 | 1.58 | 2.82 | 3.80 | 0.0 | −3.0 | 6.5 |

RBS02 (30 m) | 9.24 | 38.0 | 14.28 | 58.7 | 0.80 | 3.3 | 2.50 | 2.70 | 2.66 | 7.03 | 0.0 | −2.6 | 5.5 |

RBS06 | 9.13 | 37.5 | 13.61 | 56.0 | 1.59 | 6.5 | 2.50 | 2.65 | 3.72 | 5.91 | 0.0 | −2.6 | 5.6 |

RBS10 | 10.05 | 41.4 | 12.57 | 51.7 | 1.68 | 6.9 | 2.50 | 2.60 | 5.69 | 4.94 | 0.0 | −2.7 | 5.4 |

RBS14 | 10.78 | 44.4 | 12.59 | 51.8 | 0.92 | 3.8 | 2.50 | 2.54 | 7.45 | 3.98 | 0.0 | −2.8 | 5.2 |

RBS18 | 10.49 | 43.2 | 12.89 | 53.1 | 0.89 | 3.7 | 2.50 | 2.30 | 8.60 | 2.80 | 0.0 | −2.8 | 5.4 |

RBS01 (40 m) | 12.18 | 37.5 | 16.87 | 52.0 | 3.40 | 10.5 | 3.33 | 4.28 | 5.01 | 7.06 | −0.1 | −2.6 | 5.4 |

RBS05 | 12.47 | 38.4 | 15.81 | 48.7 | 4.19 | 12.9 | 3.33 | 4.12 | 7.45 | 5.07 | 0.0 | −2.5 | 5.2 |

RBS09 | 12.96 | 39.9 | 15.64 | 48.2 | 3.87 | 11.9 | 3.33 | 3.85 | 9.85 | 3.43 | 0.0 | −2.5 | 5.1 |

RBS13 | 14.75 | 45.4 | 14.34 | 44.2 | 3.37 | 10.4 | 3.33 | 3.42 | 13.09 | 2.42 | 0.0 | −2.6 | 4.7 |

RBS17 | 15.72 | 48.4 | 14.67 | 45.2 | 2.06 | 6.3 | 3.33 | 3.09 | 15.14 | 1.68 | 0.0 | −2.6 | 4.5 |

^{1}—the road length, L, is given in brackets and there is the same length for other modeling cases in the same group, V

_{ci}(m

^{3}) is the runoff volume intercepted by the curb inlet, V

_{rg}(m

^{3}) is the runoff volume captured by the road grate inlet, V

_{bp}(m

^{3}) is the bypass runoff volume, P

_{ci}(%) is the percentage of the total runoff volume that is intercepted by the curb inlet (V

_{ci}/V

_{rd}), P

_{rg}(%) is the road grate inlet captured runoff percentage, P

_{bp}(%) is the road end bypass runoff percentage, V

_{rb}(m

^{3}) is the runoff generated on the bioretention surface from the rainfall, V

_{inf}(m

^{3}) is the bioretention infiltrated runoff volume, V

_{bog}(m

^{3}) is the bioretention overflow grate inlet discharge volume, V

_{bio}(m

^{3}) is the runoff ponded in bioretention at the end of the simulation, ∆V (%) is the runoff volume percent difference of the whole simulation domain = (V

_{rg}+ V

_{bp}+ V

_{inf}+ V

_{bog}+ V

_{bio}− V

_{rd}− V

_{rb})/(V

_{rd}+ V

_{rb}) × 100%, ∆V

_{rd}(%) is the runoff volume percent difference of the road surface = (V

_{ci}+ V

_{bp}+ V

_{rg}− V

_{rd})/V

_{rd}× 100%, ∆V

_{rb}(%) is the runoff volume percent difference of the bioretention cell = (V

_{inf}+ V

_{bog}+ V

_{bio}− V

_{ci}− V

_{rb})/(V

_{ci}+ V

_{rb}) × 100%, P

_{inf}(%) is the infiltrated runoff percentage = V

_{inf}/(V

_{ci}+ V

_{rb}) × 100%.

**Table 6.**Mean and standard deviation (numbers inside brackets) of parameters calculated from each of the five road-bioretention cases with the same L (10 m–40 m).

Length (L) | V_{ci} | P_{ci} | V_{rg} | P_{rg} | V_{bp} | P_{bp} | V_{rb} | V_{inf} | V_{bog} | V_{bio} |
---|---|---|---|---|---|---|---|---|---|---|

(m^{3}) | (%) | (m^{3}) | (%) | (m^{3}) | (%) | (m^{3}) | (m^{3}) | (m^{3}) | (m^{3}) | |

10 m RBS ^{1} | 3.27 | 40.5 | 4.53 | 56.1 | 0.28 | 3.4 | 0.83 | 1.24 | 0.00 | 3.10 |

(0.05) | (0.6) | (0.21) | (2.6) | (0.25) | (3.1) | (0.00) | (0.00) | (0.00) | (0.05) | |

20 m RBS ^{2} | 5.91 | 36.6 | 9.78 | 60.5 | 0.48 | 2.95 | 1.67 | 1.61 | 1.59 | 4.86 |

(0.19) | (1.2) | (0.18) | (1.1) | (0.12) | (0.8) | (0.00) | (0.02) | (0.98) | (0.78) | |

30 m RBS ^{3} | 9.94 | 40.9 | 13.19 | 54.3 | 1.17 | 4.8 | 2.50 | 2.56 | 5.62 | 4.93 |

(0.74) | (3.07) | (0.74) | (3.0) | (0.42) | (1.7) | (0.00) | (0.16) | (2.48) | (1.65) | |

40 m RBS ^{4} | 13.62 | 42.0 | 15.46 | 47.6 | 3.38 | 10.4 | 3.33 | 3.75 | 10.11 | 3.93 |

(1.54) | (4.76) | (1.00) | (3.1) | (0.81) | (2.5) | (0.00) | (0.50) | (4.10) | (2.16) |

^{1}for RBS04, 08, 12, 16, and 20;

^{2}for RBS03, 07, 11, 15, and 19;

^{3}for RBS02, 06, 10, 14, and 18; and

^{4}for RBS01, 05, 09, 13, and 17.

**Table 7.**Mean and standard deviation (numbers inside brackets) of additional simulation results calculated from each of the five road-bioretention cases with the same L (10–40 m).

Length (L) | h_{max} | T_{bog} | Q_{pog} | V_{pc} | V_{bio}(40)/V_{pc} | Q_{prgb} | Q_{prgb}/Q_{prg} |
---|---|---|---|---|---|---|---|

(m) | (s) | (L/s) | (m^{3}) | (-) | (L/s) | (-) | |

10 m RBS ^{1} | 0.36 | - | 0.00 | 4.02 | 0.77 | 3.84 | 0.57 |

(0.02) | (0.00) | (0.22) | (0.03) | (0.19) | (0.02) | ||

20 m RBS ^{2} | 0.32 | 975 | 4.81 | 5.12 | 0.95 | 8.30 | 0.71 |

(0.01) | (188) | (2.17) | (0.80) | (0.01) | (0.19) | (0.04) | |

30 m RBS ^{3} | 0.29 | 650 | 9.43 | 5.27 | 0.93 | 11.23 | 0.71 |

(0.00) | (255) | (1.15) | (1.67) | (0.02) | (0.72) | (0.03) | |

40 m RBS ^{4} | 0.24 | 392 | 12.65 | 4.36 | 0.89 | 13.14 | 0.76 |

(0.01) | (252) | (1.81) | (2.22) | (0.03) | (0.92) | (0.10) |

^{1}for RBS04, 08, 12, 16, and 20;

^{2}for RBS03, 07, 11, 15, and 19;

^{3}for RBS02, 06, 10, 14, and 18;

^{4}for RBS01, 05, 09, 13, and 17; h

_{max}(m) is the maximum ponding depth (water height) in the bioretention, T

_{bog}(s) is the time when the bioretention overflow starts, Q

_{pog}(L/s) is the bioretention overflow peak discharge, V

_{pc}(m

^{3}) is the calculated maximum bioretention ponding volume based on bioretention-strip geometry, V

_{bio}(40)/V

_{pc}is the percentage of the bioretention ponding volume at the end of the 40-min simulation to the calculated bioretention ponding volume, Q

_{prgb}(L/s) is the road grate inlet peak discharge for RBS cases, Q

_{prgb}/Q

_{prg}is the ratio of the road grate inlet peak discharge for RBS case to corresponding Rd case.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, X.; Fang, X.; Gong, Y.; Li, J.; Wang, J.; Chen, G.; Li, M.-H.
Evaluating the Road-Bioretention Strip System from a Hydraulic Perspective—Case Studies. *Water* **2018**, *10*, 1778.
https://doi.org/10.3390/w10121778

**AMA Style**

Li X, Fang X, Gong Y, Li J, Wang J, Chen G, Li M-H.
Evaluating the Road-Bioretention Strip System from a Hydraulic Perspective—Case Studies. *Water*. 2018; 10(12):1778.
https://doi.org/10.3390/w10121778

**Chicago/Turabian Style**

Li, Xiaoning, Xing Fang, Yongwei Gong, Junqi Li, Jianlong Wang, Gang Chen, and Ming-Han Li.
2018. "Evaluating the Road-Bioretention Strip System from a Hydraulic Perspective—Case Studies" *Water* 10, no. 12: 1778.
https://doi.org/10.3390/w10121778