A Case Study of the Retention Efficiency of a Traditional and Innovative Drainage System

To determine the effectiveness of the retention capacity utilization of traditional and innovative drainage systems equipped with damming partitions, the detailed model tests were carried out. The research results allowed indicating what values of the hydraulic parameter of the innovative drainage system should be adopted in order to effectively use the retention capacity of drainage collectors. The adoption of short distances between the LKR damming partitions and a high level of permissible rainfall of stormwater Hper turned out to be the most effective solution. In the most favorable conditions, the peak flow was reduced by up to 60% (717.46 dm3/s) compared to the values established in the traditional drainage system (1807.62 dm3/s). The benefits obtained resulted from the increased retention efficiency of the drainage system after equipping it with the damming partitions. It was found that the innovative system always achieved the maximum retention capacity with longer rainfall compared to the traditional system. In the real catchment area, an increase in the use of the retention capacity of the drainage system, from an initial value of 65% for a traditional system to almost 88% for an innovative system, was also found. Very large variability of the volume of accumulated stormwater in the conduits of the traditional and innovative drainage system was observed during rainfall, which generated the peak rainfall discharge in the innovative system. With rainfall of TRK duration, the innovative system accumulated up to 746.50 m3 more stormwater compared to a traditional system, which was 49.2% of the total retention capacity of the drainage system, with a value of 1515.76 m3. The approach to reduce the growing flood risk in cities provided the right approach to long-term urban drainage system planning, especially since traditional drainage systems are still the leading way to transport stormwater in cities. In addition, the innovative sewage system gives the possibility of favorable cooperation with any objects (LID) and retention tanks with any hydraulic model. The implementation of an innovative system allows achieving significant financial savings and reducing the need to reserve areas designated for infrastructure investments.


Introduction
Due to the increasing concentration of greenhouse gases in the atmosphere, climate changes cause significant transformations in the characteristics of extreme weather phenomena [1,2] manifested by an increase in the incidence of short-term torrential rainfall [3,4]. This implies a more frequent incidence of local urban floods, whose range shows great variability due to natural and human impacts, with particularly severe adverse effects in high-density urban catchments and a significant proportion of impervious surfaces [5][6][7]. The proper assessment of future hydrological changes in cities caused by uncertain climates is very important and is required for the proper management of stormwater [8][9][10]. Many studies have determined the potential impact of climate changes on the frequency and patterns drainage system in global terms. Thus, the use of the retention capacity of the drainage system is undoubtedly part of the policy of sustainable stormwater management, bringing many benefits to the environment, operators of drainage systems and people living in drained areas. This method of stormwater management allows to minimize social losses, which can manifest in the forms of damage to the infrastructure, damage to human health and even loss of life. Unfortunately, these types of drainage systems will not increase the overall area of urban greenery and more recreational space for society.
This paper aims to present the possibilities of controlling the process of stormwater retention in conduits of the drainage system. This approach makes an increased hydraulic and retention efficiency of the drainage system by introducing special partitions. This concept allows determining the exact value of the peak stormwater discharge and their volumes retained in the drainage system, depending on the geometry and the number of damming partitions used and the height of the stormwater damming.

Case Study
The studies on the effectiveness of the drainage of urbanized areas were carried out for the real urban catchment area, which is located in Southeastern Poland ( Figure 1).
Resources 2020, 9, x FOR PEER REVIEW 3 of 19 effectiveness of the drainage system in global terms. Thus, the use of the retention capacity of the drainage system is undoubtedly part of the policy of sustainable stormwater management, bringing many benefits to the environment, operators of drainage systems and people living in drained areas. This method of stormwater management allows to minimize social losses, which can manifest in the forms of damage to the infrastructure, damage to human health and even loss of life. Unfortunately, these types of drainage systems will not increase the overall area of urban greenery and more recreational space for society. This paper aims to present the possibilities of controlling the process of stormwater retention in conduits of the drainage system. This approach makes an increased hydraulic and retention efficiency of the drainage system by introducing special partitions. This concept allows determining the exact value of the peak stormwater discharge and their volumes retained in the drainage system, depending on the geometry and the number of damming partitions used and the height of the stormwater damming.

Case Study
The studies on the effectiveness of the drainage of urbanized areas were carried out for the real urban catchment area, which is located in Southeastern Poland ( Figure 1).
Parameters characterizing the catchment are presented in Tables 1 and 2. The values of the parameters were assumed based on the author's own research and the literature [72].  Parameters characterizing the catchment are presented in Tables 1 and 2. The values of the parameters were assumed based on the author's own research and the literature [72]. The parameters characterizing the designed traditional drainage system are presented in Table 3.

Precipitation Model
The precipitation model of Bogdanowicz and Stachy (recommended in Poland) was used to calculate the unit precipitation intensity [73]. It determines the correlations between the intensity of precipitation and its duration (1): where h max is the maximum total amount of precipitation with a duration t d and a probability of occurrence p (mm); α is a parameter (scale) adopted depending on the region of Poland and the duration of precipitation t d , p is the probability of rainfall: p ∈ (0, 1] and R is a region of Poland. All simulations were carried out assuming the probability of rainfall of p = 0.5. Precipitation intensity estimated according to the Bogdanowicz and Stache formula concerned block precipitation with uniform intensity throughout their duration. Figure 2 shows the IDF curve determined on the basis of Formula (1).

Hydrodynamic Simulation-Storm Water Management Model
The simulation of hydrological and hydraulic phenomena occurring in the "rainfall-drainage, basin-drainage and system-receiver" system was mapped using the Storm Water Management Model (SWMM) version 5.1 program.
Hydrodynamic models of the drainage system, made in the SWMM program, allow determining hydraulic values that describe its operation in variable conditions (static and dynamic), including flow rate and liquid stream velocity, hydrostatic pressure and stormwater-filling heights in canals [72].

Innovative Drainage Systems (Retention Sewage Canal)
A significant improvement in the hydraulic efficiency of traditional drainage systems was obtained as a result of the use of an innovative solution [70], whose idea resulted in the intentional installation of damming partitions across the direction of stormwater flow in gravity conduits of existing or planned drainage systems ( Figure 3).

Hydrodynamic Simulation-Storm Water Management Model
The simulation of hydrological and hydraulic phenomena occurring in the "rainfall-drainage, basin-drainage and system-receiver" system was mapped using the Storm Water Management Model (SWMM) version 5.1 program.
Hydrodynamic models of the drainage system, made in the SWMM program, allow determining hydraulic values that describe its operation in variable conditions (static and dynamic), including flow rate and liquid stream velocity, hydrostatic pressure and stormwater-filling heights in canals [72].

Innovative Drainage Systems (Retention Sewage Canal)
A significant improvement in the hydraulic efficiency of traditional drainage systems was obtained as a result of the use of an innovative solution [70], whose idea resulted in the intentional installation of damming partitions across the direction of stormwater flow in gravity conduits of existing or planned drainage systems ( Figure 3).

Hydrodynamic Simulation-Storm Water Management Model
The simulation of hydrological and hydraulic phenomena occurring in the "rainfall-drainage, basin-drainage and system-receiver" system was mapped using the Storm Water Management Model (SWMM) version 5.1 program.
Hydrodynamic models of the drainage system, made in the SWMM program, allow determining hydraulic values that describe its operation in variable conditions (static and dynamic), including flow rate and liquid stream velocity, hydrostatic pressure and stormwater-filling heights in canals [72].

Innovative Drainage Systems (Retention Sewage Canal)
A significant improvement in the hydraulic efficiency of traditional drainage systems was obtained as a result of the use of an innovative solution [70], whose idea resulted in the intentional installation of damming partitions across the direction of stormwater flow in gravity conduits of existing or planned drainage systems ( Figure 3).  According to the features of the invention [70], the damming partition has an outflow orifice (4) in the bottom part, and the upper edge of the partition is a typical frontal overflow (2). For the analysis of the research on the hydraulic processes, an outflow orifice (4) with a circular cross-section was adopted, which was mapped in the SWMM program using the Orifice link function. The emergency overflow (2) was designed using the Weir link function. The hydraulic parameters of nine models of the innovative drainage system variants are presented in Table 4. Variant 0 is a traditionally functioning drainage system. The study also analyzed in detail nine different variants of the hydraulic operation of the innovative drainage system (drainage system with damming partitions). In Variants 1-9 adopted, they differ in the distances between the L RK damming partitions and the permissible level of stormwater accumulation H per in canals. In all the adopted variants, the drainage system has the same canal geometry presented in Table 1.

Results
In order to assess the possibility of controlling the transport, the volume of the accumulated and the amount of stormwater discharge from the drained catchment and the functioning of the adopted drainage system was examined by separating the ten designed variants, simultaneously creating their hydrodynamic models.
First, the impact of the damming partitions was determined on the volume of Q D stormwater discharges during rainfall with different durations (Figure 4). It was done by turning the traditional drainage system into a retention canal system that creates an innovative drainage system.
The results of the tests confirmed the close dependence of the degree of reduction of the stormwater outflow from the drained catchment due to the assumed distances between the damming partition (L KR ) and the admissible stormwater damming heights before the damming partitions H per , regardless of the considered duration of the rainfall t d . It was established that, with the simultaneous reduction of the distance between the damming partitions L KR and increasing the stormwater damming heights before the damming partitions H per , the value of the parameter Q D is gradually reduced. Therefore, regardless of the rainfall duration t d , the most favorable variant in terms of reducing the risk of urban flooding is Var1.
A significant hydraulic effect results from the favorable flattening of the hydrograph and the simultaneous slowdown of the stormwater discharge from the drainage system equipped with a retention canal system. A practical benefit of stormwater damming in the innovative drainage system is the hydraulic relief of the traditional system located below the retention canal system-in particular, the negative effects of rapid short-term rainfall discharges into the receiver. The transformation of time-varying flows as a result of the use of a retention canal system is particularly important in a situation where the drainage system cooperates with retention facilities or when the construction of such facilities will be planned in the future. The flattened hydrograph of stormwater outflow from the innovative drainage system allows a significant reduction in the required usable capacity of retention tanks and selected LID devices (objects for retention and the temporary retention of stormwater, e.g., stormwater retention pound) cooperating with it. In special cases, and in the event of favorable local conditions, a properly designed system of retention canals allows taking over part or all of the tasks set for retention tanks and/or other unloading facilities. Thus, it even enables to abandon the construction Resources 2020, 9, 108 7 of 19 of such facilities. This situation will occur when the determined maximum allowable stormwater flow rate Q D,DT from the planned retention tank exceeds the critical storm fall flow rate Q D,IDS,M from the drainage catchment with a drainage system equipped with a retention canal system at the intended location of the tank.
variants, the drainage system has the same canal geometry presented in Table 1.

Results
In order to assess the possibility of controlling the transport, the volume of the accumulated and the amount of stormwater discharge from the drained catchment and the functioning of the adopted drainage system was examined by separating the ten designed variants, simultaneously creating their hydrodynamic models.
First, the impact of the damming partitions was determined on the volume of QD stormwater discharges during rainfall with different durations (Figure 4). It was done by turning the traditional drainage system into a retention canal system that creates an innovative drainage system.  The results of the tests confirmed the close dependence of the degree of reduction of the stormwater outflow from the drained catchment due to the assumed distances between the damming partition (LKR) and the admissible stormwater damming heights before the damming partitions Hper, regardless of the considered duration of the rainfall td. It was established that, with the simultaneous reduction of the distance between the damming partitions LKR and increasing the stormwater The inclusion of a sufficiently wide range of rainfall times t d in the study allowed confirming the interesting relationship. Each rainfall corresponds to a precisely defined value of the maximum stormwater outflow Q D,M from the drainage system. When analyzing the functioning of the traditional drainage system and retention canal system with the changing duration of the rainfall t d , the critical value of stormwater outflow from the system examined was determined ( Figure 5). outflow from the innovative drainage system allows a significant reduction in the required usable capacity of retention tanks and selected LID devices (objects for retention and the temporary retention of stormwater, e.g., stormwater retention pound) cooperating with it. In special cases, and in the event of favorable local conditions, a properly designed system of retention canals allows taking over part or all of the tasks set for retention tanks and/or other unloading facilities. Thus, it even enables to abandon the construction of such facilities. This situation will occur when the determined maximum allowable stormwater flow rate QD,DT from the planned retention tank exceeds the critical storm fall flow rate QD,IDS,M from the drainage catchment with a drainage system equipped with a retention canal system at the intended location of the tank.
The inclusion of a sufficiently wide range of rainfall times td in the study allowed confirming the interesting relationship. Each rainfall corresponds to a precisely defined value of the maximum stormwater outflow QD,M from the drainage system. When analyzing the functioning of the traditional drainage system and retention canal system with the changing duration of the rainfall td, the critical value of stormwater outflow from the system examined was determined ( Figure 5). Using the simulation by means of hydrodynamic modeling, the lowest critical value of stormwater outflow from the retention canal system was determined with QD,IDS,C = 717.46 dm 3 /s. This outflow will occur in the Var1 variant, where the system is equipped with 42 damming partitions with an average distance of every LKR = 75 m and with the permissible momentary level of stormwater accumulation just before the damming partitions Hper/dk = 0.99 but ensuring the drainage system of all canals.
It is obvious that the adoption of a higher level of stormwater accumulation in front of damming partitions Hper/dk directly affects the beneficial decrease in the value of the peak critical stormwater outflow rate QD,IDS,C from the innovative drainage system, since a larger volume of stormwater remains in the system. Additionally, the reduction of the distance between the LKR damming partitions affects the successive decrease of the QD,IDS,C parameter values for all permissible system fillings specified by the Hper/dk parameter. The scenarios of the functioning of the designed drainage system equipped with a retention canal system confirmed the validity of each variant of the concept of hydraulic transport and stormwater accumulation in an innovative drainage system in order to determine the optimal solution in the given design conditions. Formulated theoretical foundations and models describing the process and the impact of the Hper/dk and LKR parameters of the drainage system with the retention canal system on the conditions of its hydraulic functioning each time give a possibility to determine clearly the amount of stormwater outflow intensity reduction from the innovative drainage system. Therefore, through the assumptions made at the design stage, it is possible to control the degree of stormwater flow Using the simulation by means of hydrodynamic modeling, the lowest critical value of stormwater outflow from the retention canal system was determined with Q D,IDS,C = 717.46 dm 3 /s. This outflow will occur in the Var1 variant, where the system is equipped with 42 damming partitions with an average distance of every L KR = 75 m and with the permissible momentary level of stormwater accumulation just before the damming partitions H per /d k = 0.99 but ensuring the drainage system of all canals.
It is obvious that the adoption of a higher level of stormwater accumulation in front of damming partitions H per /d k directly affects the beneficial decrease in the value of the peak critical stormwater outflow rate Q D,IDS,C from the innovative drainage system, since a larger volume of stormwater remains in the system. Additionally, the reduction of the distance between the L KR damming partitions affects the successive decrease of the Q D,IDS,C parameter values for all permissible system fillings specified by the H per /d k parameter. The scenarios of the functioning of the designed drainage system equipped with a retention canal system confirmed the validity of each variant of the concept of hydraulic transport and stormwater accumulation in an innovative drainage system in order to determine the optimal solution in the given design conditions.
Formulated theoretical foundations and models describing the process and the impact of the H per /d k and L KR parameters of the drainage system with the retention canal system on the conditions of its hydraulic functioning each time give a possibility to determine clearly the amount of stormwater outflow intensity reduction from the innovative drainage system. Therefore, through the assumptions made at the design stage, it is possible to control the degree of stormwater flow reduction in a wide range, which was proposed to be determined by the β KR factor. The value of this coefficient is closely related to the capacity of the drainage system and decreases as this capacity grows [21]. When designing an innovative drainage system, its value is determined using the relationship (2): where β KR is stormwater flow reduction factor in an innovative drainage system (-), Q D,IDS,C is the value of the determined critical intensity of stormwater outflow from the drainage system equipped with damming partitions (d m 3 /s) and Q D,TDS,C is the determined value of the critical intensity of stormwater outflow from the traditional drainage system (d m 3 /s).
Resources 2020, 9, 108 9 of 19 The value of the β RK flow reduction factor shows the scale of the advisability of implementing damming partitions in an operated stormwater drainage system. The lower the value β RK is, the more justified the implementation of the retention canal system. The results of the research in this area that were carried out in the real catchment area analyzed are presented in Figure 6.
where βKR is stormwater flow reduction factor in an innovative drainage system (-), QD,IDS,C is the value of the determined critical intensity of stormwater outflow from the drainage system equipped with damming partitions (d m 3 /s) and QD,TDS,C is the determined value of the critical intensity of stormwater outflow from the traditional drainage system (d m 3 /s). The value of the βRK flow reduction factor shows the scale of the advisability of implementing damming partitions in an operated stormwater drainage system. The lower the value βRK is, the more justified the implementation of the retention canal system. The results of the research in this area that were carried out in the real catchment area analyzed are presented in Figure 6. Based on the adopted for the design values of the Hper/dk parameters from 0.80 to 0.99 and LKR from 75 m to 235 m, the values of the stormwater flow reduction coefficient βKR were determined separately for each of the nine variants, which ranged from 0.40 to 0.75. Thus, in the study case, it was proven that, in each design variant, the distances at which subsequent LKR partitions were placed had significant impact on the determined value of the βKR coefficient. This was regardless of the assumed value of the permissible instantaneous level of stormwater accumulation Hper just before the partitions.
The simulation tests carried out on the catchment area allowed the dependence of the reliable rainfall time to dimension the innovative drainage system (TRK) to be determined on the basis of the accepted values of variable parameters that characterize the object (Figure 7) in nine assumed variants. TRK values for this time range from 17 min to 34 min. On the other hand, in the variant allowing the highest filling, i.e., at Hper/dk = 0.99, and, at the same time, minimizing the LKR distance between damming partitions, the set TRK valid rainfall time for dimensioning the innovative drainage system was almost three times longer than the reliable time tdm, which was determined when dimensioning the designed, traditional drainage system.
The basic effect of implementing the idea of an innovative drainage system is, in addition to the hydraulic transport of stormwater in the network, the occurrence of the phenomenon of their effective accumulation in drainage system pipes. The volume of stormwater that is accumulated in the classic VTDS(t) and innovative VIDS(t) drainage pipes is constantly changing during rainfall (Figure 8). Based on the adopted for the design values of the H per /d k parameters from 0.80 to 0.99 and L KR from 75 m to 235 m, the values of the stormwater flow reduction coefficient β KR were determined separately for each of the nine variants, which ranged from 0.40 to 0.75. Thus, in the study case, it was proven that, in each design variant, the distances at which subsequent L KR partitions were placed had significant impact on the determined value of the β KR coefficient. This was regardless of the assumed value of the permissible instantaneous level of stormwater accumulation H per just before the partitions.
The simulation tests carried out on the catchment area allowed the dependence of the reliable rainfall time to dimension the innovative drainage system (TRK) to be determined on the basis of the accepted values of variable parameters that characterize the object (Figure 7) in nine assumed variants. TRK values for this time range from 17 min to 34 min. On the other hand, in the variant allowing the highest filling, i.e., at H per /d k = 0.99, and, at the same time, minimizing the L KR distance between damming partitions, the set TRK valid rainfall time for dimensioning the innovative drainage system was almost three times longer than the reliable time t dm , which was determined when dimensioning the designed, traditional drainage system.  The basic effect of implementing the idea of an innovative drainage system is, in addition to the hydraulic transport of stormwater in the network, the occurrence of the phenomenon of their effective accumulation in drainage system pipes. The volume of stormwater that is accumulated in the classic V TDS(t) and innovative V IDS(t) drainage pipes is constantly changing during rainfall (Figure 8).

Figure 7.
Values of reliable TRK rainfall durations (rainfall generating a critical value QD,IDS,C) for dimensioning an innovative drainage system, taking into account different variants of its functioning. Considering any rainfall of a specific duration td and adopting a specific way of hydraulic functioning of the drainage system, one can determine:  the maximum value of the instantaneous variable volume of accumulated stormwater VTDS(t),M in the drainage system:

VIDS(t),M = max(VIDS(t)) − an innovative system (4)
 the value of the instantaneous difference in the variable volume of accumulated stormwater ΔV(t) in a drainage system that works traditionally and innovatively:  the value of the maximum instantaneous difference in the variable volume of accumulated stormwater ΔV(t),M in the traditional and innovative drainage system:  the difference in the maximum stormwater volume ΔV accumulated in the drainage system functioning in a traditional and innovative way: Considering any rainfall of a specific duration t d and adopting a specific way of hydraulic functioning of the drainage system, one can determine: • the value of the instantaneous difference in the variable volume of accumulated stormwater ∆V (t) in a drainage system that works traditionally and innovatively: • the value of the maximum instantaneous difference in the variable volume of accumulated stormwater ∆V (t),M in the traditional and innovative drainage system: • the difference in the maximum stormwater volume ∆V accumulated in the drainage system functioning in a traditional and innovative way: When conducting an in-depth analysis of the functioning of many formulated variants of the drainage system, it was found that the use of damming partitions changed the process described so far related to the hydraulic transport of stormwater into a more complex one. It also covers the transport and accumulation of stormwater in the drainage system during and after rainfall. It turns out that the most favorable results were obtained in the variant VarI, where the largest volume of stormwater with V IDS(t),M = 1212.48 m 3 was retained in the drainage system at the same time with the longest retention time in the pipes of the system. In a situation where the drainage system operated traditionally, the maximum value of the instantaneous variable volume of accumulated stormwater was V TDS(t),M = 982.64 m 3 . Adoption of a greater distance between the L KR damming partitions or/and reducing the permissible level of stormwater damming H per /d k will reduce the retention efficiency of the innovative drainage system, as well as the value of the V IDS(t),M parameter.
Performing many hydrodynamic simulations in various models of the hydraulic functioning of the drainage system, taking into account the wide range of variable rainfall times t d , allowed determining four important parameters that characterize the innovative drainage system.

•
Critical value of the instantaneous variable volume of accumulated stormwater in the drainage system: • Maximum difference in the maximum volume of stormwater accumulated in a drainage system that operates in a traditional and innovative way: • Critical difference of critical volumes of stormwater accumulated in the drainage system functioning traditionally and innovatively: • Critical value of the maximum instantaneous difference in the variable volume of accumulated stormwater in a drainage system that operates in a traditional and innovative way: In the tested, real drainage system, including ten design variants, the maximum volumes of accumulated stormwater V IDS(t),M and V TDS(t),M were determined, assuming different rainfall durations t d , which are presented in Figure 9.
When conducting an in-depth analysis of the functioning of many formulated variants of the drainage system, it was found that the use of damming partitions changed the process described so far related to the hydraulic transport of stormwater into a more complex one. It also covers the transport and accumulation of stormwater in the drainage system during and after rainfall. It turns out that the most favorable results were obtained in the variant VarI, where the largest volume of stormwater with VIDS(t),M = 1212.48 m 3 was retained in the drainage system at the same time with the longest retention time in the pipes of the system. In a situation where the drainage system operated traditionally, the maximum value of the instantaneous variable volume of accumulated stormwater was VTDS(t),M = 982.64 m 3 . Adoption of a greater distance between the LKR damming partitions or/and reducing the permissible level of stormwater damming Hper/dk will reduce the retention efficiency of the innovative drainage system, as well as the value of the VIDS(t),M parameter.
Performing many hydrodynamic simulations in various models of the hydraulic functioning of the drainage system, taking into account the wide range of variable rainfall times td, allowed determining four important parameters that characterize the innovative drainage system.


Critical value of the instantaneous variable volume of accumulated stormwater in the drainage system:

VIDS(t),C = max(VIDS(t),M) − an innovative system (9)
 Maximum difference in the maximum volume of stormwater accumulated in a drainage system that operates in a traditional and innovative way:  Critical difference of critical volumes of stormwater accumulated in the drainage system functioning traditionally and innovatively:  Critical value of the maximum instantaneous difference in the variable volume of accumulated stormwater in a drainage system that operates in a traditional and innovative way: In the tested, real drainage system, including ten design variants, the maximum volumes of accumulated stormwater VIDS(t),M and VTDS(t),M were determined, assuming different rainfall durations td, which are presented in Figure 9.   Figure 9 allow determining the difference in critical volumes of accumulated wastewater ∆V C . On the other hand, the results of simulation tests carried out in this area for nine variants of the hydraulic functioning of the innovative drainage system are shown in Figure 10.
Resources 2020, 9, x FOR PEER REVIEW 12 of 19 It was agreed that the determined values of the VIDS(t),M and VTDS(t),M parameters depended strictly on the duration of rainfall td. For instance, the highest value of the parameter VTDS(t),C = 987.29 m 3 in the variant Var0 was determined during the rainfall with a duration of td = 12 min. However, in the variant VarI, the maximum value of the parameter is equal, VIDS(t),C = 1329.20 m 3 , with the rainfall duration td = 24 min, i.e., twice as long. The curves illustrated in Figure 9 allow determining the difference in critical volumes of accumulated wastewater ΔVC. On the other hand, the results of simulation tests carried out in this area for nine variants of the hydraulic functioning of the innovative drainage system are shown in Figure 10. Comparing the hydraulic functioning of the drainage system in the Var0 and Var1 variants, it was found that the parameter ΔVC reached the highest value of 341.91 m 3 and constituted 23% of the total retention capacity VDS of the designed drainage system. The determined value is also extreme for this parameter in the analyzed model catchment variants.
Ensuring However, the peak flows of QD,IDS,C, as well as the critical volumes of stormwater VIDS(t),C accumulated in the drainage system in the Var0 and VarI variants, are achieved at other times of the rainfall duration td. Therefore, the determined critical value of the ΔVC parameter does not directly translate into the determined reduction of the peak outflow QD. With this in mind, in-depth simulation studies were conducted to determine the course of variation in the volume of accumulated stormwater in the innovative drainage system IDS during rainfall with different td duration times.
The use of damming partitions in drainage systems turns a typical stormwater transport system into a complex one where it is also possible to control the process of the accumulation of a significant part of the transported stormwater, which is shown in detail in Figure 11. Along with the change in the duration of the rainfall, the maximum difference also changes the stormwater volume ΔV, as well as the value of the maximum instantaneous difference in the variable stormwater volume ΔV(t),M accumulated in the traditional and innovative drainage systems.
The variability of the determined values of the parameters ΔV and ΔV(t),M, depending on the assumed duration of the rainfall, is shown in Figures 11 and 12.
It turns out that the differences in the volume of accumulated stormwater in the innovative and traditional drainage system reach values much higher than results from the set value of the ΔVC parameter. It was shown that traditional and innovative drainage systems achieved maximum retention capacity at different durations of rainfall td (Figures 11 and 12). By analyzing the hydraulic functioning of both systems during the rainfall of any duration td, each retention capacity of the innovative drainage system was confirmed. However, the differences in the maximum volumes of accumulated stormwater ΔV during a strictly determined duration of rainfall significantly exceed Comparing the hydraulic functioning of the drainage system in the Var0 and Var1 variants, it was found that the parameter ∆V C reached the highest value of 341.91 m 3 and constituted 23% of the total retention capacity V DS of the designed drainage system. The determined value is also extreme for this parameter in the analyzed model catchment variants.
Ensuring the largest accumulation of stormwater with a volume of 341.91 m 3 in the variant Var1 of the innovative drainage system at H per /d k = 0.99 and L KR = 75 m in relation to the value in the Var0 variant with the traditional drainage system allowed reducing the peak outflow of stormwater from the catchment 1807.62 d m 3 s to just 717.45 d m 3 /s ( Figure 5).
However, the peak flows of Q D,IDS,C , as well as the critical volumes of stormwater V IDS(t),C accumulated in the drainage system in the Var0 and VarI variants, are achieved at other times of the rainfall duration t d . Therefore, the determined critical value of the ∆V C parameter does not directly translate into the determined reduction of the peak outflow Q D . With this in mind, in-depth simulation studies were conducted to determine the course of variation in the volume of accumulated stormwater in the innovative drainage system IDS during rainfall with different t d duration times.
The use of damming partitions in drainage systems turns a typical stormwater transport system into a complex one where it is also possible to control the process of the accumulation of a significant part of the transported stormwater, which is shown in detail in Figure 11. Along with the change in the duration of the rainfall, the maximum difference also changes the stormwater volume ∆V, as well as the value of the maximum instantaneous difference in the variable stormwater volume ∆V (t),M accumulated in the traditional and innovative drainage systems.
The variability of the determined values of the parameters ∆V and ∆V (t),M , depending on the assumed duration of the rainfall, is shown in Figures 11 and 12.
It turns out that the differences in the volume of accumulated stormwater in the innovative and traditional drainage system reach values much higher than results from the set value of the ∆V C parameter. It was shown that traditional and innovative drainage systems achieved maximum retention capacity at different durations of rainfall t d (Figures 11 and 12). By analyzing the hydraulic functioning of both systems during the rainfall of any duration t d , each retention capacity of the innovative drainage system was confirmed. However, the differences in the maximum volumes of accumulated stormwater ∆V during a strictly determined duration of rainfall significantly exceed those determined by assigning the value of the ∆V C parameter. For instance, in the Var1 variant, the ∆V parameter reaches the maximum value of 620.79 m 3 with the rainfall duration of t d = 34 min.
At the same time, the td value is equal to the TRK rainfall value, which generates the critical stormwater runoff Q D,IDS,C . However, in the case of the eight other analyzed variants of the functioning of the innovative sewage network (from Var2 to Var9), the t d times proved to be longer than the TRK times.
Resources 2020, 9, x FOR PEER REVIEW 13 of 19 those determined by assigning the value of the ΔVC parameter. For instance, in the Var1 variant, the ΔV parameter reaches the maximum value of 620.79 m 3 with the rainfall duration of td = 34 min. At the same time, the td value is equal to the TRK rainfall value, which generates the critical stormwater runoff QD,IDS,C. However, in the case of the eight other analyzed variants of the functioning of the innovative sewage network (from Var2 to Var9), the td times proved to be longer than the TRK times. Figure 11. Dependence of the established differences in the maximum stormwater volume ΔV accumulated in the traditional and innovative drainage system conduits from the duration of the rainfall td. To sum up, one should state that the duration of the rainfall, at which the greatest differences in the maximum fillings of the conduits in a traditional and innovative drainage system with stormwater is achieved, is equal to or slightly longer than the time of TRK, determined for the design of the retention canal systems.
When analyzing the curves illustrating the change in the volume of accumulated stormwater during the rainfall td = 13 min (Figure 8), the momentary maximum difference in their volume was determined, ΔV(t),M = 689.03 m 3 . On the other hand, the performance of a full analysis, taking into account the full range of rainfall times, enabled the determination of the highest value of the parameter, ΔV(t),C = 789.84 m 3 , in the Var1 variant ( Figure 12). This value is achieved at the rainfall with a duration of td = 24 min, and it is much shorter than the time set for dimensioning the innovative drainage system, which, in the Var1 variant, is TRK = 34 min. During the rainfall with a duration of td = TRK = 34 min, the maximum instantaneous volume of accumulated stormwater is ΔV(t),M = 746.50 m 3 and is only slightly lower than the critical value of this parameter by ΔV(t),C = 789.84 m 3 . Figure 11. Dependence of the established differences in the maximum stormwater volume ∆V accumulated in the traditional and innovative drainage system conduits from the duration of the rainfall t d .
Resources 2020, 9, x FOR PEER REVIEW 13 of 19 those determined by assigning the value of the ΔVC parameter. For instance, in the Var1 variant, the ΔV parameter reaches the maximum value of 620.79 m 3 with the rainfall duration of td = 34 min. At the same time, the td value is equal to the TRK rainfall value, which generates the critical stormwater runoff QD,IDS,C. However, in the case of the eight other analyzed variants of the functioning of the innovative sewage network (from Var2 to Var9), the td times proved to be longer than the TRK times. Figure 11. Dependence of the established differences in the maximum stormwater volume ΔV accumulated in the traditional and innovative drainage system conduits from the duration of the rainfall td. To sum up, one should state that the duration of the rainfall, at which the greatest differences in the maximum fillings of the conduits in a traditional and innovative drainage system with stormwater is achieved, is equal to or slightly longer than the time of TRK, determined for the design of the retention canal systems.
When analyzing the curves illustrating the change in the volume of accumulated stormwater during the rainfall td = 13 min (Figure 8), the momentary maximum difference in their volume was determined, ΔV(t),M = 689.03 m 3 . On the other hand, the performance of a full analysis, taking into account the full range of rainfall times, enabled the determination of the highest value of the parameter, ΔV(t),C = 789.84 m 3 , in the Var1 variant ( Figure 12). This value is achieved at the rainfall with a duration of td = 24 min, and it is much shorter than the time set for dimensioning the innovative drainage system, which, in the Var1 variant, is TRK = 34 min. During the rainfall with a duration of td = TRK = 34 min, the maximum instantaneous volume of accumulated stormwater is ΔV(t),M = 746.50 m 3 and is only slightly lower than the critical value of this parameter by ΔV(t),C = 789.84 m 3 . To sum up, one should state that the duration of the rainfall, at which the greatest differences in the maximum fillings of the conduits in a traditional and innovative drainage system with stormwater is achieved, is equal to or slightly longer than the time of TRK, determined for the design of the retention canal systems.
When analyzing the curves illustrating the change in the volume of accumulated stormwater during the rainfall t d = 13 min (Figure 8), the momentary maximum difference in their volume was determined, ∆V (t),M = 689.03 m 3 . On the other hand, the performance of a full analysis, taking into account the full range of rainfall times, enabled the determination of the highest value of the parameter, ∆V (t),C = 789.84 m 3 , in the Var1 variant ( Figure 12). This value is achieved at the rainfall with a duration of t d = 24 min, and it is much shorter than the time set for dimensioning the innovative drainage system, which, in the Var1 variant, is TRK = 34 min. During the rainfall with a duration of t d = TRK = 34 min, the maximum instantaneous volume of accumulated stormwater is ∆V (t),M = 746.50 m 3 and is only slightly lower than the critical value of this parameter by ∆V (t),C = 789.84 m 3 .
Thus, the use of damming partitions allows increasing significantly the retention capacity of gravity drainage systems, especially in relation to the rainfall, which generates a peak rainfall discharge from the drained catchment. For example, in the Var1 variant, the determined temporary increase in volume is as much as 52.1% (789.84/1515.76) of the volume of the drainage system analyzed. During the rainfall of TRK, which causes the occurrence of peak outflow Q D,IDS,C , this volume accounts for 49.2% (746.50/1515.76) of the retention capacity of the IDS drainage system.
The high degree of reduction of the reliable stormwater flow rate at the outflow (node K) from the real catchment is, in practical terms, the effect of the full use of the retention capacity of the drainage system after it is equipped with an innovative retention canal system. However, the measure of its effectiveness is determined by the hydrodynamic modeling values of the coefficients λ TDS and λ IDS , which show the degree of utilization of the retention possibilities of the traditional and innovative drainage system. The values of the coefficients λ TDS and λ IDS are described by the following Equations (13) and (14): where λ TDS is the coefficient of percentage capacity utilization of the traditional drainage system (-), λ IDS is the coefficient of percentage capacity utilization of the innovative drainage system (-), V TDS(t),C -the critical value of stormwater volume stored in a traditional drainage system (m 3 ), V IDS(t),C is the critical value of stormwater volume stored in the innovative drainage system (m 3 ) and V DS -total retention volume of the drainage system (m 3 ). The values of the coefficients λ TDS and λ IDS are shown in Figure 13. Thus, the use of damming partitions allows increasing significantly the retention capacity of gravity drainage systems, especially in relation to the rainfall, which generates a peak rainfall discharge from the drained catchment. For example, in the Var1 variant, the determined temporary increase in volume is as much as 52.1% (789.84/1515.76) of the volume of the drainage system analyzed. During the rainfall of TRK, which causes the occurrence of peak outflow QD,IDS,C, this volume accounts for 49.2% (746.50/1515.76) of the retention capacity of the IDS drainage system.
The high degree of reduction of the reliable stormwater flow rate at the outflow (node K) from the real catchment is, in practical terms, the effect of the full use of the retention capacity of the drainage system after it is equipped with an innovative retention canal system. However, the measure of its effectiveness is determined by the hydrodynamic modeling values of the coefficients λTDS and λIDS, which show the degree of utilization of the retention possibilities of the traditional and innovative drainage system. The values of the coefficients λTDS and λIDS are described by the following Equations (13) and (14): where λTDS is the coefficient of percentage capacity utilization of the traditional drainage system (-), λIDS is the coefficient of percentage capacity utilization of the innovative drainage system (-), VTDS(t),Cthe critical value of stormwater volume stored in a traditional drainage system (m 3 ), VIDS(t),C is the critical value of stormwater volume stored in the innovative drainage system (m 3 ) and VDS-total retention volume of the drainage system (m 3 ).
The values of the coefficients λTDS and λIDS are shown in Figure 13. With the most favorable scenario marked as Var1 variant, an increase in the use of the network retention capacity from 65% in the traditional system to 88% using an innovative drainage system with damming partitions was determined. Thus, the use of an appropriate number of damming partitions and the adoption of a high level of stormwater accumulation in the conduits allows incorporating virtually all the free space of the drainage system conduits into the retention volume.

Conclusions
The analysis of the hydraulic functioning of the traditional and innovative drainage system allowed drawing the following conclusions: Figure 13. Values of the λ TDS and λ IDS coefficients in the innovative drainage system depending on the adopted variants of its functioning.
With the most favorable scenario marked as Var1 variant, an increase in the use of the network retention capacity from 65% in the traditional system to 88% using an innovative drainage system with damming partitions was determined. Thus, the use of an appropriate number of damming partitions and the adoption of a high level of stormwater accumulation in the conduits allows incorporating virtually all the free space of the drainage system conduits into the retention volume.

Conclusions
The analysis of the hydraulic functioning of the traditional and innovative drainage system allowed drawing the following conclusions: (1) Reducing the distance between damming partitions L KR (implementation of a greater number of damming partitions) reduces the peak runoff of stormwater from the drained catchment.
(2) The level of stormwater accumulation H per in canals affects the hydraulic functioning of the drainage system. Increasing the level of stormwater accumulation H per reduces the peak flows in the drainage system. (3) A modern approach to the design of innovative drainage systems is a competitive alternative in terms of usability and economy in relation to fairly commonly used retention tanks or other cubature facilities. (4) The transformation of the traditional drainage system into an innovative drainage system requires only the implementation of damming partitions in the existing manholes.
A multi-variant analysis of the functioning of the hydraulic drainage system, equipped with damming partitions, confirmed the practical need to transform known, traditional gravity drainage systems into innovative systems that are equipped with damming facilities. The results of the application of the concept in the drainage system are highly satisfactory, as the costs associated with the implementation and operation of an innovative drainage system are disproportionately small to the benefits obtained.
As with any solution, the concept of an innovative drainage system also has some negative aspects. Determining the required geometry of the damming barriers requires the use of hydrodynamic modeling and spending more time designing a solution in relation to the traditional drainage system. Additionally, these types of drainage systems will not increase the overall areas of urban greenery and more recreational spaces for society. However, it should be mentioned that an innovative drainage system can interact with LID devices, maximizing the effectiveness of the drainage system in global terms.
All things considered, the application of the concept of an innovative drainage system is part of a modern approach to the design of systems for the drainage and management of stormwater. Traditional drainage systems that operate in a gravitational way are still the leading way of draining and managing stormwater both in Poland and internationally. For this reason, there is a large area of practical applications of the results of the tests conducted whose measurable effects will be an increase in the degree of hydraulic safety of drained and designed drainage systems, while achieving significant financial savings and reducing the area allocated for infrastructure investments.