## The Transport and Road Research Laboratory hydrograph method

In designing storm water sewerage systems for towns, city suburbs and new developments of around 200-400 ha with varied surface characteristics, a method is required that also takes into account differences in storm rainfall over the catchment area. Developed from the time-area concept of catchment response (Chapter 12), the TRRL hydrograph method (Watkins, 1962) was applied widely in the UK.

In the time-area method, the total catchment area is deemed to be contributing to the flow after the time of concentration, Tc, the time it takes for the rain on the furthest part of the catchment to reach the outfall. Thus, in Fig. 18.5, for two drains receiving uniform rainfall from areas Aj and A^, with drain 2 joining the main channel, drain 1, a relationship of contributing area, A, versus time, T, is constructed. From the beginning of the flow in drain 1 at T = 0, there is a steady increase in area contributing until T = T which is the value of Tc for area A^. Drain 2 begins to contribute to the outfall flow at T = T3 before T = T^. After a further period, T2, area 2 reaches its own Tc at time T = (T2 + T3). Between times T3 and T both drains have been flowing and the

1

Br

/ 1

! Drain 2

' 1

Fig. 18.5 Time-area diagram.

joint contributing area (at C) at T = T is given by

From T = (T2 + T3), both areas are contributing fully. The time-area curve for the combined drains is the composite line OBCD.

The principle of the TRRL hydrograph method is outlined in Fig. 18.6. In Fig. 18.6(a), a catchment area, divided into four subareas, is drained by a single channel to the outfall where the hydrograph is required. Sub-area 1 begins contributing to the flow first, to be followed sequentially by the other three sub-areas. The individual time-area curves are shown in Fig. 18.6(b) and the composite curve for the whole catchment is drawn by summing the sub-area contributions at regular time intervals. The choice of time unit is dependent on the surface characteristics of the catchment and may range from 1 min for highly impervious areas to about 30 min for nearly natural catchments. The incremental contributing areas after each time interval are then read from the composite curve, «1, the whole area is time units.

etc. In the diagram, the time of concentration for

(a) Catchment area sub-division

Catchment boundary

Catchment boundary

(b) Time-area diagram

(c) Effective rainfall

(b) Time-area diagram

1 2 3 4 5 Time units

Fig. 18.6 Transport and Road Research Laboratory (TRRL) hydrograph method.

1 2 3 4 5 Time units

1 2 3 4 5 Time units

Fig. 18.6 Transport and Road Research Laboratory (TRRL) hydrograph method.

The next stage in the method involves the storm rainfall. The values of the areal rainfall are calculated from the rain-gauge measurements by one of the standard methods (Chapter 10) for each of the chosen time unit intervals throughout the duration of the storm. Since some of the rainfall will infiltrate the pervious areas, not all the storm rainfall will contribute to the direct runoff from the catchment area. An effective rainfall rate must be assessed for each time unit. The effective rainfalls may be obtained by assuming a runoff coefficient and, applying this to each time unit rainfall in turn, or a constant loss rate can be assumed and subtracted from each time unit rainfall rate. Fig. 18.6(c) shows the effective rates of rainfall for each time unit, ¿0 ¿1 i2, etc., for the storm duration (ten time units).

The discharge rates after each time unit interval are given by q3 = ¿2^! + ¡ia2 + ¿0^3 etc.

A worked example is shown in Table 18.3. There are four increments of area (ha) resulting in a time of concentration for the catchment equivalent to four time units. The storm duration extends over ten time units. A runoff coefficient of 0.64 has been assumed and thus the total areal rainfalls in column 2 have been multiplied by 0.64 to give the corresponding effective rainfalls (i mmh-1). The values of q for each area increment a and effective rainfall rate i are calculated from the basic form of the rational formula q1 — t0a1 q^ — i^i H- t^a^

0.36

 Time unit Areal rate Rainfall Area increment (ha) Discharge q(Ls-^ Total mm h-1 Effective rainfall i (mm h-' ) 0.25 a2 0.82 0.92 a4 0.34 I I 3.7 8.8 6. I 6. I 2 90 57.6 40 20 60 3 59.4 38 26.4 I3I .2 22.5 I80.I 4 18.3 I 1.7 8. I 86.6 I47.2 8.3 250.2 5 16.8 I0.8 7.5 26.7 97. I 54.4 I85.7 6 I 3.7 8.8 6. I 24.6 29.9 35.9 96.5 7 5.3 3.4 2.4 20 27.6 I I.I 6I.I 8 5.I 3.3 2.3 7.7 22.5 I0.2 42.7 9 6. I 3.9 2.7 7.5 8.7 8.3 27.2 10 4.6 2.9 2 8.9 8.4 3.2 22.5 II 6.6 I0 3. I I9.7 12 7.4 3.7 II.I I3 2.7 2.7

where 0.36 is a units conversion factor. The summation of the rows across a^ to a4 gives the discharge values after each time increment, and thus the required hydrograph. It will be noted that the peak flow occurs after the fourth time interval, the time of concentration of the catchment. This does not always happen, e.g. with late peaking rainfalls.

Two further considerations are necessary. A time of entry from the onset of the storm rainfall to the time of flow into the pipe is usually taken to be 2 min and must be allowed for in the computations. Secondly, experience has shown that there is a certain amount of retention of water in the pipe channel, and amendments to the hydrograph must be made to account for pipe storage (Watkins, 1962).

The procedure of the TRRL method, as presented, applies to one drainage unit, i.e. one pipe, in a system. The calculations have to be carried out for each pipe in a sewerage network as demonstrated earlier in the rational method of design. In practice, the application of the TRRL hydrograph method to even a simple configuration of drainage pipes becomes too complex for manual computation and so it has been applied in practice using software packages.