In order to estimate the water flow into drainage pipes, one should differentiate between the two distinct situations introduced earlier:
• pipes above the water level (intersection drains); and
• pipes below the water level (groundwater lowering) drains.
When the drainage system is above the water level, the infiltration water from edges, channels and gutters, and from some of the transverse drainage that is covered by permeable surfacing, must also be considered according to the relationship of Eq. 13.2.
qL = R ■ B ■ L (13.2)
where qL is the water flow through the pipe (m3/s), R is the surface runoff water flow (m3/(s. m2)), L is the section’s length (m) (see Eq. 13.3) and B is the width of the section requiring calculation (m) (see Eq. 13.3 as shown in Fig. 13.39).
B ■ L = Y, bi x I, (13.3)
i = 1
where b and l are individual widths and lengths, respectively (Fig. 13.39). Other non-runoff flows can be added into Eq. 13.2 by simple addition, provided they are expressed in units of m3/s.
In cases where the drainage system is used not only as an interceptor but also to lower the water level, dimensioning should consider specific calculations for the underground flow into the drain. In this situation the projected flow should be the sum of the aforementioned value and that estimated through the application of Darcy’s Law.
Such a flow estimate and the depth of installation for the drain are based on the assumption of specific tests and sophisticated calculations. Nevertheless, in most
Fig. 13.39 Drainage zones for a section of carriageway and hinterland (adapted from Carreteras (2004))
cases they are revealed to be of limited practical relevance because, in the range of commercial diameters, perforated pipes have a considerably larger capacity for in-flow than is strictly required and the depths at which they are installed usually guarantees the lowering of the water level in the zone between drains.
Having said this, and in order to simplify dimensioning, some authors consider that the in-flow to the drain amounts to approximately 35% of the total flow generated as slope runoff with 20% of the surface runoff from the road pavement being added to cater for flows originating in the road platform, i. e.:
qL = 0.35qE + 0.20qp (13.4)
where qL is the water flow to the pipe (m3 /s); qE is the surface runoff water from slopes (m3/s) and qP is the surface runoff water from the platform (m3/s).
Regarding the depth of installation of the drains, one can make a first estimate using the formula:
z = zro + 0.5 ■ b ■ к (13.5)
where z is drain depth (m), zw is the depth at which the groundwater level should stabilize (m), b is the distance between drains (m), IR is the rate of infiltration into soil (m/s) and K is the soil permeability (m/s).
A specific hydro-geological calculation must be done whenever the drainage system aims to lower the water level. When deciding on the transverse profile to use in a new road’s project, the details of the subterranean drainage, based on tables and criteria, are very important.
Finally, one should add that in order to satisfy the criteria for self-cleansing and guarantee an adequate geometry, the drains should have a minimum longitudinal inclination of 0.5%, which, in exceptional cases, can be reduced to 0.25%. This inclination should not exceed 20%.
There are various computer software codes on the market that can perform calculations of flow as described, e. g. CANALIS, HYDRA and MOUSE.