## The Transport and Road Research Laboratory rational method

Hydrologists are often concerned with evaluating the runoff from the subareas to be drained in order to design the necessary storm water sewers. The peak runoff from the selected design storm determines the size of sewer pipes, which are dependent on the extent of each sub-area to be drained. At the head of a catchment sub-area, the required pipe size may be quite small, but downstream, as the sewer receives water from a growing area through a series of junctions, the pipe size gradually needs to be increased.

The problem of estimating the runoff from the storm rainfall is very much dependent on the character of the catchment surface. The degree of urbanisation (extent of impervious area) greatly affects the volume of runoff obtained from a given rainfall. Retention of rainfall by the initial wetting of surfaces and absorption by vegetation and pervious areas reduces the amount of storm runoff. These surface conditions also affect the time distribution of the runoff. Thus the method used to obtain the runoff from the rainfall should allow for the characteristics of the surface area to be drained.

Calculation of runoff is the most straightforward for small impervious areas, such as roof areas and paved surfaces, in which there is very little or even no part of the ground surface into which rainfall could infiltrate. Over such limited areas, the storm rainfall can be assumed to be uniformly distributed with 100 per cent runoff occurring. The response of the impervious surfaces is rapid, resulting in a short time of concentration

Fig. 18.4 Schematic for simple pipe design using Transport and Road Research Laboratory (TRRL) methods.

of the flow in the drainage system. The Rational Formula introduced in Chapter 12 can then provide a simple estimate for peak flow.

A recommended method for the design of a piped sewer drainage system using the Rational Method was given in the Transport and Road Research Laboratory (TRRL) Road Note 35 (TRRL, 1976). The procedure may be explained by considering the simple pipe design in Fig. 18.4. The sequence of pipes must be numbered according to the convention shown. The first pipe of a branch is always labelled 1.0, 2.0, etc. and the following pipes in a line are labelled sequentially, 1.1, 1.2, etc. Here there is a line of three pipes leading to an outfall and a tributary area (pipe 2.0) drains into the junction at the end of the second pipe in line 1, pipe 1.1. The computations to determine the required pipe sizes are shown in Table 18.1. The first four columns give the surveyed particulars of level differences along each pipeline, the required length and the calculated gradient.

At the outset of the design procedure, the selected return period for a design storm will have been decided. Storm water sewers are usually designed for return periods of much less than 100 years. In the example, the expected annual storm intensities are used (1-year return period). The type of pipe will also have been chosen; the internal roughness governs the flow characteristics, and a roughness coefficient, ks, must be selected from published tables (Ackers, 1969) in order to use the Colebrook-White equation to determine the flow velocity in the pipe. Velocities and discharges for standard-sized pipes computed from this complex formula are published in tabular form for different pipe sizes, assuming full-bore conditions, a hydraulic gradient equal to the pipe gradient and appropriate roughness (Ackers, 1969). Flows larger than those derived from the tables or charts would require hydraulic gradients greater than the pipe gradient stipulated, and these could only occur by ponding (or surcharging) of

Table 18.1 Rational method drainage design example data (Pipe no. = Pipe number; Level diff. = Level difference; Grad. = Gradient; Trial pipe da. = Trial pipe diameter; V = Velocity; Q = Discharge; Time of conc = Time of concentration; Imp. A cum = Cumulative impervious area; Storm Q = Storm discharge)

Table 18.1 Rational method drainage design example data (Pipe no. = Pipe number; Level diff. = Level difference; Grad. = Gradient; Trial pipe da. = Trial pipe diameter; V = Velocity; Q = Discharge; Time of conc = Time of concentration; Imp. A cum = Cumulative impervious area; Storm Q = Storm discharge)

 Pipe Pipe Level Pipe Grad. Trial V Q Time Time Rate of Imp. A Storm Comment no. diff. length (1 in) pipe (ms- ') (Ls-1) of flow ofconc rain cum Q (m) (m) da. (min) (min) (mmh- ' ) (ha) (Ls-') (mm) 1.0 1.00 65 65 150 1.26 23.0 0.86 2.86 67.5 0. '5 28.' Surcharge partial flow 225 1.64 67.5 0.66 2.66 69.2 28.8 1.1 0.90 70 78 225 1.50 6' .7 0.78 3.44 63.2 0.25 43.9 Partial flow 2.0 1.50 60 40 150 1.61 29.4 0.62 2.62 69.5 0.20 38.6 Surcharge partial flow 225 2.10 86.0 0.48 2.48 70.7 39.3 1.2 0.90 50 56 225 1.77 72.8 0.47 3.9' 60.2 0.53 88.6 Surcharge partial flow 300 2.13 '56.0 0.39 3.83 3.83 60.7 89.4

water in the manholes at the pipe junctions. The design objective is to avoid such surcharging.

The design procedure begins with the choice of a trial pipe size for pipe 1.0 (150 mm in the example in Table 18.1). From the published tables and for ks = 0.6 for a normal concrete pipe, the velocity and discharge for a gradient of 1 in 65 are noted, 1.26 m s-1 and 23.0 Ls-1, respectively. A flow greater than 23.0 Ls-1 would result in surcharging.

The time of flow along the pipe is next calculated from the velocity and length of pipe and comes to 0.86 min. The time of concentration at the end of the first pipe is then 0.86 min plus an assumed allowance of 2 min, for the time of entry, which is assumed to cover the lag time between the onset of the storm rainfall and the entry of the overland flow into the leading manhole. With the time of concentration of the drainage to the end of the first pipe known, the design return period rainfall intensity, i over this duration to give the peak flow can be obtained from intensity-duration-frequency data. Ideally, data from a local rain gauge will be analysed to assess the design storm depth. Where there is not adequate data, a generalised model may have to be used. For durations longer than 1 hour, the FEH depth-duration-frequency model (see Chapter 9) are available, whilst shorter durations were considered in the older Flood Studies Report rainfall analysis. In this example, the rates of rainfall are taken from Table 18.2 for a location in Southern England (TRRL, 1976). The storm peak discharge for this sub-area is then calculated from the rate of rainfall, i, and its cumulated impervious area using the rational method for comparison with the unsurcharged full bore pipe flow. The first trial pipe of 150 mm diameter would clearly be surcharged, so the calculations are repeated with the next size pipe, diameter 225 mm. The calculated storm discharge, 28.8 L s-1, would be easily contained by the larger pipe.

The calculations proceed for each pipe in turn, with the previous time of concentration being added to the new time of flow to give the combined times of concentration at the end of sequential pipes. The drainage areas are also accumulated. It will be noted

Table 18.2 Rainfall intensities (in millimetres per hour) for specified durations and return periods (point location in Southern England)

Duration (min) Return period (years)

Table 18.2 Rainfall intensities (in millimetres per hour) for specified durations and return periods (point location in Southern England)

Duration (min) Return period (years)

 2 75.6 93.4 120.5 2.5 70.5 87.5 113.4 3 66.3 82.3 107.2 3.5 62.8 77.8 101.7 4 59.6 73.8 96.8

that the 2.0 min time of entry is also added to the flow time of pipe 2.0, since it is at the start of a branch pipeline. The time of concentration for the last pipe 1.2, is the sum of the time of concentration of pipe 1.1 and the flow time of pipe 1.2. The extra contribution from the greatly increased area drained by the tributary pipe results in a much larger discharge requiring the next size larger pipe, 300 mm diameter. (The pipe diameters are given as rounded metric equivalents to the old 6-, 9- and 12-in diameter pipes.)

Thus in the simple pipe design for the system in Fig. 18.4, pipes 1.0, 1.1. and 2.0 need to be 225 mm in diameter and the last pipe 1.2 must be of 300 mm diameter. These requirements conform to the normal concrete pipes specified (ks = 0.6) and 1-year return period design storm intensities, with an assumed 2 min time of entry.

It will be appreciated that the computations become complicated as more branch pipe lines are incorporated into the system. This method is most satisfactory for small impervious areas, but if more pervious fractions are included within the catchments, results from the Rational Method become less acceptable.