The Wallingford procedure
From the 1970s, access to computers meant that simplifications of former methods were no longer necessary and many more relevant factors could be introduced into runoff design calculations using software packages. In 1981 the Wallingford Procedure was published. The Wallingford Procedure describes the hydraulic design and analysis of pipe networks for both new schemes and existing systems. It can accommodate both independent storm water sewers and combined sewers, but the waste water flows must be given as inflows at the appropriate junction in a combined sewer. The hydraulic analysis of a range of structures controlling the flow in a pipe system can be made and certain economic factors are also incorporated into the procedure. The whole package provides a range of methods from which a series of calculation techniques can be selected to suit the conditions of any particular design scheme. Basic data required for the design techniques were included for the whole of Great Britain and Northern Ireland so that the procedure could be applied nationwide. Almost three decades later the methods, although updated and revised, remain in widespread use within the water industry.
The Wallingford Procedure comprised several methods, as follows:
(1) a modified rational method giving peak flows only, including a routing coefficient in addition to a volumetric runoff coefficient and recommended for initial designs and for use in homogeneous catchments up to 150 ha in area;
(2) a hydrograph method to model surface runoff and pipe flow and provide a pattern of discharge in time;
(3) an optimizing method, to set the design of pipe depth and gradient as well as diameter;
(4) a simulation method to analyse the performance of existing systems or proposed designs operating under surcharge conditions.
A general outline of the four methods is given in Table 18.4, which itemises component parts of each method. In modelling the different components such as rainfall and overland flow, the methods incorporated many of the formulae derived for the Flood Studies Report. Rainfall depthdurationfrequency data and storm profiles, calculations of net rainfall and the use of catchment wetness indices were all applied in the detailing of the Wallingford Procedure.
The simulation method proved useful to practising engineers since the vexed problem of pipe surcharging is included in the analysis. As indicated in Table 18.4, the major difference from the hydrograph method lies in the modelling of the pipe flow (Bettess et al., 1978). The same flow equations are used namely the ColebrookWhite equation for velocity (Ackers, 1969) and the MuskingumCunge routing procedure (see Section 14.2.3), but instantaneous discharges are calculated throughout the sewer system at a given time increment instead of complete hydrographs being routed sequentially from one pipe to another. Thus the interactions between surcharged pipes can be modelled.
The simulation method allows for the storage of surcharged water within manholes and on the ground surface flooded to a uniform depth over an assumed area contributing to the pipe length. The extent of the temporary surface flooding related to calculated flood volumes must be assessed on the ground.
Surcharging occurs when incoming flow is greater than fullbore pipe capacity or when a raised tailwater level causes a backwater effect. It is assumed that the manhole losses are proportional to velocity head in the pipe, then head loss, Ah, in the surcharged pipe is composed of pipe friction loss plus losses at both manholes over a time increment dt.
Table 18.4 Methods and models in the Wallingford Procedure. (Reproduced from National Water Council (1981) Design and Analysis of the Urban Storm Drainage: The Wallingford Procedure, by permission.)
Method
Modified Rational Method
Rainfall models
Intensity— duration— frequency relationship
Hydrograph Rainfall Method profiles
Optimizing As for Method Modified Rational Method
Simulation Method
Overland flow models
Percentage runoff model+
time of entry
Complete surface runoff model
Model Pipe flow Sewer models
Pipe full velocity
MuskingumCunge
Sewered subarea model may be used for selected subareas
As for Pipe full Modified velocity Rational Method
Complete Muskingum— surface Cunge and runoff surcharged model flow ancillaries models
Storm overflow
Storm overflow
Storage tank
Pumping station
Construction cost model
TRRL resource cost model
As for Hydrograph Method
As for Hydrograph Method plus
Tailwater level
Sewered subarea model (without surcharging) may be used for selected subareas
Flood alleviation benefit model
Middlesex
Polytechnic
Flood
Hazard
Research
Project
Model (not included in programs)
where L and d are pipe length and diameter (m) and V is flow velocity (ms1), g is gravity acceleration (ms1), l is the friction coefficient (8gSR/V2) (s1), (with R the hydraulic radius and S the hydraulic gradient), km is the head loss coefficient for manholes (with values of 0.15 for a straight manhole, 0.50 for 30° bend and 0.90 for 60° bend manhole).
From the storage equation dS/dt = I — O where I is the total flow into the upstream manhole from the upstream pipes and direct surface runoff from its subcatchment. With h, the difference in levels in upstream and downstream manholes and the storage equation, the flow over the chosen time increment can be simulated given the
manhole and pipe geometries. The transition phases to and from free surface flow and surcharged (pressurized) flow are demonstrated in Fig. 18.7.
The state of the sewer system with the volumes stored at each surcharged manhole is determined by repeating the calculations for each time increment until the performance of the system has been established over the whole period of the storm event.
The Wallingford Procedure now incorporates several models for runoff generation. The original model is an empirical design formula for percentage runoff (PR) that was developed after monitoring of some 510 storms on 17 catchments during the period 19749. The model gave the total storm runoff depth as a product of design rainfall, catchment area and PR, hence it is essentially a variant of the rational method. The formula for PR included a parameter to describe the percentage impervious area within the catchment, along with soils information derived from Flood Studies Report maps and a catchment wetness index. The original PR formulation led to some difficulties in application. It is not always easy to work out what to include in total catchment area (e.g. whether to count areas connected by piped drainage systems) and hence how to define impervious area. The original model also assumed that the PR remained constant during a storm event. This is unrealistic, particularly for longer duration events. In response to these issues, a revised model was developed in the late 1980s and is now available in the mainstream software tools for application of the Wallingford Procedure.
The revised model remains known amongst urban drainage modelling practitioners as the 'new UK runoff model'. It separates permeable and impermeable areas. Permeable areas are represented using a simple soil moisture accounting model that calculates an increase in runoff during an event as the catchment wetness increases. It uses a dynamic antecedent precipitation index (API), which is updated during the event calculation. This is divided by a notional soil storage capacity (typically a fixed value of 200 mm) to obtain a fractional equivalent soil moisture deficit that is multiplied by rainfall to derive the predicted runoff. The API is based on the balance between rainfall and evaporation over the previous 30day period, with a time decay factor applied that varies according to soil type to represent the different rates of drying out of different soil types. This model provides consistency for both eventbased and longer 'continuous simulation' of runoff, where soil moisture can be depleted by evaporation when sequences of events are modelled over a period of time.
The model allows an initial rainfall depth to be subtracted to represent the wetting of surfaces and filling up depressions before runoff begins. Each surface, such as paved surfaces, roofs or welldrained roads has a characteristic depression storage depth that depends on the slope and the type of the surface, and is typically in the range 0.52.0 mm. If the model is run for continuous simulation, then the depression storage is dried out by evaporation after rainfall ceases.
Impermeable areas are split into two fractions. One is assumed to produce runoff with a runoff coefficient of 1.0, representing a direct connection to the drainage system. The other fraction is treated as if it were permeable, and is incorporated within the permeable area soil moisture accounting model. The fractions assumed to generate direct runoff vary according to surface type. For normal paved surfaces, the value is 0.6, which was calibrated in development of the model. Values for other surfaces are estimates. A user can calibrate these parameters when setting up a drainage model.
Further details about the Wallingford Procedure runoff models can be found in the guidance notes published and updated from time to time by the Wastewater Planning Users Group (WaPUG,1 part of the Chartered Institute of Water and Environmental Management, CIWEM).
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