# A Step by Step Procedure for Calculating a Physically-based Time to Peak, Recession Time, and RDII Volume for the Three RTK Triangles

Hazem Gheith

## ABSTRACT

This paper presents a step by step procedure for educated continuous calibration of the Rain Dependent Inflow and Infiltration (RDII) using the RTK method in SWMM. The procedure starts with splitting the three distinct stages of the RDII hydrograph; inflow, delayed inflow, and groundwater infiltration, from a flow meter record. The splitting approach relies on the distinct difference in the time frame of each RDII stage. Inflow enters the system in minutes through illicit direct storm pipe connections, foundation drains, downspout connections and displaced or perforated sanitary manhole lids. Inflow ceases within minutes after the storm event. Delayed inflow enters the system within a few hours time frame through near-surface damaged pipes (e.g. lateral connections), damaged manhole castings, or leaks from storm pipe trenches near sanitary pipes. The third stage of the RDII is the infiltration of the rising groundwater surrounding the collection system as it enters through damaged joints and cracked pipes. These stages can be simulated in SWMM using the RTK unit hydrograph method. The three parameters for each unit hydrograph are R, percentage of runoff, T,,time to peak, and K, multiple T, used to define the recession time of the triangle.

One commonly accepted practice for splitting the RDII stages and determining the RTK parameters for continuous calibration is accomplished through trial and error. A best fit RTK set for one monitored RDII event is first calculated. The set is then tested in several storm events. The RTK set of parameters are then manipulated to minimize the collective errors in peak RDII flow and/or volume. In some practices, several RTK sets are calculated from several monitored storms for a sewershed and a median or average set is then accepted as the representative set for that particular system. In these practices, it is possible to generate an unlimited number of RTK sets since the RDII stages were not first split logically and the selected set of RTK parameters was based on reducing an error function (peak flow or volume). The ability of hydrology and hydraulic models using this method of RTK development to accurately simulate the collection system response in a continuous simulation becomes unpredictable. To take it one step further, these models are often used to evaluate potential system responses to improvements such as rehabilitation and/or replacement. This inherent limitation could lead to flawed improvement recommendations.

This paper presents a logical approach to defining RDII stages and developing an accurate and reliable hydraulic and hydrology model by developing a single set of RTK parameters that are based on the physical features of the system. This is accomplished by first splitting the RDII hydrograph into the three stages based on the rate of change of the flow response, which is visually represented as the slope of the flow hydrograph. The discontinuities in this slope reveal the peak and terminal recession time for each of the three stages. In this presented approach, the third RDII stage, the groundwater infiltration response, is the first to be identified since its recession limp is minimally affected by the first and second stages. Its peak time is easily identified from the discontinuity in the rate of change of the flow on the hydrograph. The R-value for the third triangle is then calculated as the percentage of the third stage hydrograph volume to the total runoff volume. Both T and K for the third unit hydrograph triangle are then calculated as functions of the peak rainfall time, core rainfall duration time of flow-routing through the collection system network and the duration of the third RDII stage. The infiltration response is then subtracted from the RDII hydrograph. The remaining hydrograph then represents the first and second RDII stages only. The procedure is repeated to split the second RDII stage, calculating the associated RTK parameters for the second unit hydrograph triangle, and once again to calculate the first RDII response unit hydrograph parameters.

This step by step approach was tested and proved to be more affective in simulating RDII response in continuous simulation for several monitored sanitary sewersheds. Additionally, this approach allows for a potentially more reliable system evaluation potentially leading to better selection and prioritization of the RDII remediation actions.