Introduction

Infiltration and inflow (I&I) is an urban water resources term that describes the unwanted water existing in sewer systems that are not originated from the typical sewer sources e.g. domestic and industrial discharge. Infiltration is water seeping into the sewer pipes preferably through broken pipe cracks and joints (Figure 1). The origin of infiltration can be surface water percolated down to the sewer pipes or groundwater with the water table above the pipe invert. Inflow is surface water entering the sewer system through direct connections from runoff catchments or cross connections from storm sewer or combined sewer. The term rainfall derived infiltration and inflow (RDII) is used when I&I origin is surface runoff which is caused by rainfall.
I&I is one of the major problems affecting sewer systems in terms of flow overloading that causes sewer overflows, basement flooding, street flooding, increase in pumping costs, water pollution, and decrease in treatment efficiency in water treatment plants (Backmeyer, 1960; Field & Struzeski, 1972; Gottstein, 1976l; Lai, 2008). Based on the estimation by Petroff (1996), roughly 50% of the water entering wastewater treatment plants in the U.S. is from I&I. Depending on the age and the condition of the sewer system, the relative volume of I&I to the dry weather flow (DWF) could be ranged from 0.4 to 9 (Bishop et al., 1987; National Small Flows Clearinghouse, 1999; Ertl et al., 2002; Weiss et al., 2002; Lucas, 2003; Pecher, 2003; Jardin, 2004; Kretschmer et al., 2008; Bhaskar & Welty, 2012). For example, I&I for Baltimore City was nine times greater than the DWF and it was also larger than the gauged streamflow from the urban watershed (Bhaskar & Welty, 2012). This indicates that I&I volume can affect the capacity of a sanitary sewer system significantly.
Various I&I estimation modeling methods have been developed since the 1980s to quantify the amount of I&I (De Bénédittis & Bertrand-Krajewski, 2005). Bishop et al. (1987) developed a simple synthetic hydrograph method for 300 study basins to estimate I&I and to evaluate flow data. Gustafsson (2000) presented a leakage model that takes account of the two way interaction between pipes and the aquifer using MOUSE (Lindberg et al., 1989) and MIKE-SHE (DHI Software, 2007a;b). Karpf and Krebs (2004) also used the same leakage approach. The model was calibrated using a leakage factor that is a function of groundwater infiltration rate, groundwater level, water level in sewer pipe, and the pipe surface to which the groundwater is exposed. Schulz et al. (2005) used the same modeling approach to estimate potential benefits of sewer pipe rehabilitation with different hypothetical infiltration rates. Qiao et al. (2007) presented a groundwater infiltration model using a two-reservoir approach: one reservoir for soil storage in an unsaturated zone and another for groundwater storage in a saturated zone. The elevations of the reservoir openings determine the trigger points that initiate infiltration into sewer pipes.
One of the most common practices of estimating I&I contribution to sewer flow is the RTK method that was developed by Camp Dresser and McKee (CDM) Inc. et al. (1985). According to Lai (2008) “the RTK method is probably the most popular synthetic unit hydrograph (SUH) method” in the stormwater management field. This method uses unit hydrographs to estimate the response times associated with the effect of fast, moderate, and slow I&I by a linear convolution. A user may calibrate the model by comparing to an observed I&I hydrograph. This method is embedded in EPA SWMM5 (Rossman, 2010) and EPA SSOAP toolbox (Vallabhaneni et al., 2008). Despite its popularity, the model does not reflect the underlying physics of each I&I response and it may leave a user with a vast number of possible solutions. Also there is a little guidance for calibrating these models and for I&I modeling in general (Allitt, 2002).
InfoWorks CS (Innovyze, 2011) is another popular stormwater modeling tool that has an option for I&I simulation. InfoWorks simulates I&I using two components: rainfall-induced infiltration, and groundwater infiltration. In the InfoWorks CS infiltration module, the percolation flow from the surface depression storage is assigned to the soil storage reservoir after a runoff occurs. When the soil reaches the percolation threshold, a proportion of this percolation flow goes to the sewer network. This represents RDII. The remainder of the percolation flow goes down to the groundwater storage reservoir. When the groundwater level reaches the sewer system invert level, groundwater infiltration occurs. The method enables engineers to model groundwater infiltration into a sewer system but the full physical process is not taken into account. For example, according to the model assumption, groundwater infiltration occurs when the groundwater level is higher than the pipe invert elevation not the water level in the sewer pipe. InfoWorks CS is widely used because it provides easy to use representation of RDII and it is useful for operational design. However, the empirical approximations in this approach to model RDII and infiltration limit the ability to use this model to provide understanding of process behind I&I for a given system.
Both SWMM and InfoWorks take simple I&I estimation approaches that represent I&I with unit hydrographs or constant rates. Simplified modeling methods are labor- and cost-effective and easy to apply but such approaches do not provide understanding of processes and need much more calibration data for parameter estimation. Various I&I prediction methods, including the above methods, are well documented by Crawford et al. (1999), Wright et al. (2001), Vallabhaneni et al. (2007), and Lai (2008).
In terms of modeling, often the sources and origins of the RDII are not identified due to the complexity of the system or lack of data. Though for a convenience the I&I sources are often categorized as fast, medium, and slow sources. The RTK method is a good example of this practice where three triangular hydrographs are used to represent short-term, intermediate-term, and long-term responses, respectively (Rossman, 2010).
In physical world, the fast I&I source indicates a direct connection of impervious surface runoff catchments e.g. roof downspout, connected to a sewer pipe. The slow I&I is the infiltration component of I&I that indicates flow through porous media. The medium speed I&I falls in between the fast and slow I&I in terms of the response time. Walski et al. (2007) defined medium response as “more delayed and attenuated response to rainfall” and this is also referred to as “rapid infiltration.” Hodgson and Schultz (1995) used footer drain as an example of the medium response. Nogaj and Hollenback (1981) pointed out that foundation drains and storm sumps are not expected to be highly sensitive to changes in rainfall intensity, which makes these inflow sources classified as medium sources.
The fast and medium sources are examples of illegal connections to sanitary sewer systems that lead surface water into sewer pipes. The standard practice of treating the runoff from impervious areas is to “drain to light” or drain to a gravity flow – a ditch, a storm sewer, or an overland flow surface, ideally with a permeable soil. In case the storm sources are connected to sanitary sewer systems the extra water becomes RDII. Contrast to the fast and medium sources, slow infiltration occurs when the sewer system fails to keep groundwater out of the system. Here, the term groundwater was used loosely to indicate water exists in porous soil medium.
The objective of this paper is to identify three representative RDII sources and understand the hydrologic characteristics of the flow using the impulse response functions (IRFs). The model is calibrated using a genetic algorithm (GA) technique in a study area and eventually used to verify the relative predominance of each RDII source in the test sewershed.