The Design of Minimum Energy Loss Structures

 

F. B. WINSTON and R. J. KELLER

 

Cooperative Research Centre for Catchment Hydrology

Department of Civil Engineering, Monash University,

Clayton, Victoria, Australia 3168

e-mail: frank.winston@eng.monash.edu.au

bob.keller@eng.monash.edu.au

Phone: +61 3 9905 4971, Fax: +61 3 9905 5033

 

 

ABSTRACT

A method is developed for the design of minimum energy loss (MEL) structures for stream crossings. Such structures are characterised by smoothly transitioned inlet and outlet fans and a depressed invert. MEL structures can accumulate sediment in the depressed invert under conditions of low flow. It is essential that the sediment is swept out prior to the arrival of the peak flow. The design procedure includes a model for computing the sediment sweepout characteristics under an imposed inflow hydrograph. The procedure has been tested against experimental results from a physical model and excellent agreement is noted.

 

Keywords: Minimum energy loss structures, design procedure, sediment sweepout

 

INTRODUCTION

The technique of minimum energy loss (MEL) design involves the design of a culvert or bridge waterway such that the flow in the upstream approach channel is contracted over the length of an inlet fan into the throat or barrel before expanding in a streamlined outlet fan to eventual release into the downstream channel.

The over-riding consideration in the design strategy is that energy losses are kept as small as possible. In the inlet and outlet fans, this is achieved by careful shaping to ensure that there is no significant form loss. The net result is that the energy loss through the engineered structure may be equal to or even less than the energy loss in the original natural stream.

Concurrent with a minimisation of energy loss, it is often desirable to minimise the width of the structure barrel to reduce costs. The greater the available specific energy, the less is the required structure width. The specific energy may be increased by depressing the invert of the structure. However, depressing the invert of the structure leads to the likelihood of sediment deposition during periods of low flow. It is; therefore, a feature of properly designed minimum energy loss structures that accumulated sediment is swept out of the barrel during large flow events.

In this paper, the basic features of the MEL structure are described first. Theoretical considerations are then addressed. The theory is then tested against the results of an experimental study and conclusions drawn.

 

BASIC FEATURES OF THE mel STRUCTURE

A typical structure is shown schematically in Figure 1. The stream flow is transitioned from the river channel or flood plain upstream into the barrel section via the inlet fan and transitioned back into the river channel via the outlet fan.

Figure 1: Basic Shape of Minimum Energy Loss Structure

 

A mathematical model of the path formed by a naturally meandering river is used to design the shape of the walls directing the contraction and expansion of the flood flow. Chang (1983) suggested that the natural course followed by an hydraulically stable river represents the course of minimum stream power expended. Thus, using a natural meander model to train the direction of flow in the fans would seem to be energy efficient. Ferguson (1973) suggested that the path of a meandering channel can be specified by a relation between local path direction and distance along the path from an arbitrary origin. Among the models which he described, that adopted for the current study is a linearly varying curvature model developed by Fargue, where curvature increases linearly from the point of inflection of the bend to its apex. Details are presented in Cade and Keller (1994).

Following specification of the fan wall shape, the bed profile throughout the structure is determined, taking proper account of energy losses due to friction. In principle, it is possible to design the structure for critical flow conditions throughout. This method was advocated in the past on the basis that critical flow represents the condition of maximum flow rate per unit width for a given specific energy level and, hence, minimum structure width (McKay, 1978). However, it is now widely felt that the inherent instability of critical flow mitigates against this philosophy and that, consequently, the assurance of sub-critical flow under design conditions is necessary.

 

THEORY OF MINIMUM ENERGY LOSS STRUCTURES

The basis of subcritical MEL design was first suggested by Isaacs, (1990). His approach is adopted and extended herein.

The fundamental defining equations, assuming a rectangular cross-section, are:

Specific energy, (1)

Froude Number, (2)

Depth, y=ly_c (3)

where Q= flow rate, w= width, g=gravitational acceleration, l= subcriticality factor, and subscript "c" refers to critical conditions.

For critical flow, Fr = 1 and Equation (2) may be transposed to:

(4)

The result is a system of three independent equations, (1,3,and 4), describing the interrelationships among six variables, (Q, E, l, w, y, y_c). Two variables, Q and l are chosen by the designer and in the approach adopted, the plan profile is prespecified, providing the width, w, at successive cross-sections.

Manipulation of Equations (1, 3, and 4) yields

(5)

Equation (5) may be used to determine the bed elevation from a calculated total energy level. The known total energy level on the downstream floodplain is the starting point for the design procedure, following which, the exit loss at the lip of the outlet fan and friction losses within the structure are calculated to determine the total energy level throughout the structure. Details are presented in Winston (1998).

The design procedure incorporates a performance model to check conditions at flows other than design flow and to calculate sediment sweepout characteristics under an imposed flood hydrograph. This is described in the following.

The flow through the MEL structure is described by a simplified form of the St. Venant equations, in which the time-dependent terms are neglected because of the relatively short length of the structure and the relatively slow rate of change of the inflow.

(6)

and

(7)

Under a prevailing inflow hydrograph, discretised according to a prescribed elemental time increment, Equations (6) and (7) are used to calculate the water surface profile at a particular inflow, assuming that the bed profile remains fixed during the elemental time increment.

Once a new water surface profile has been calculated, a new bed profile is computed. The first step in this process is the calculation of the sediment transport rate at each cross section based on the flow variables. The total load equation, developed by Ackers and White (1973), is used for this purpose.

The change in bed elevation is then computed using the sediment continuity equation:

(8)

where x = distance in downstream direction, q_s is the volumetric sediment transport rate per unit width, and p is the porosity of the bulk sediment, defined as the volume of the voids divided by the total volume of the bulk sediment.

The change in depth, Dz, over the time increment Dt, is then given by:

(9)

where Q_s is the volumetric sediment transport rate (m³/s), B is the average width over the incremental length Dx, and subscripts (k-1) and (k) refer to the upstream and downstream boundaries of the reach Dx.

 

EXPERIMENTAL VERIFICATION

These procedures have been incorporated into a spreadsheet-based MEL design package, and the software has been used to design a prototype structure with validation based on the performance of a physical model. Model testing is completed and this section addresses the prediction of water surface profiles and sediment sweepout characteristics and the comparable performance of the physical model.

The prototype creek has an annual flood of 12m³/s and transports large quantities of sand, much of which deposits under the existing bridge deck, which is quite low in comparison with the general level of the stream. After extended periods of low flow, the sand fills the space beneath the bridge deck, leaving very little clearance for water flow. Consequently, even mild floods regularly overtop the bridge. The local authority removes the sand from under the bridge approximately every two years.

A minimum energy loss structure was designed for this site for a design flow of 32 m³/s, which has a 10-year ARI. The bridge throat has a width of 7 m, and the fan lips have orthogonal widths of 48.7 m (u/s) and 42.0 m (d/s).

An undistorted physical model was built to a scale of 1/16 and tested with and without sediment. With no sediment, the water surface profile was measured and compared with the design profile.

Figure 2 compares design and measured water surface profiles. Excellent agreement is noted.

Figure 2: Experimental Model and Design Water Surface Profiles

 

For the sediment sweepout tests, the structure was filled with sediment to the level of the outlet lip. The sediment used comprised plastic granules with a specific gravity of 1.1, porosity of 0.45, and mean particle size of 2.1 mm. Tests were conducted at flowrates representing average return periods of one year, (12 m³/s) and two years, (18 m³/s).

The sediment level and water surface elevation in the barrel were measured continuously throughout each test. The tests were continued until the downstream fan was approximately 90% clear of sediment.

The sweepout prediction computer simulations were carried out using the model dimensions and sediment properties. Two runs were performed - the first at 11.7 l/s and the second at 17.6 l/s, replicating in the model, values of the one and two year return interval flows. Typical results for the flow of 17.6 l/s are shown in Figure 3, together with the corresponding observed levels in the physical model.

Figure 3: Comparison Of Sediment Sweepout Results From Computer Simulation And Physical Model - Q = 17.6 L/S.

 

Very close agreement between experimental and predicted water surface elevations and bed levels is evident. Although this agreement gives confidence in the use of the procedure, it is emphasised that verification against a prototype structure has not yet been carried out. It is anticipated that the prototype bridge crossing will be built in the near future and full verification will follow.

 

CONCLUSIONS

This paper has presented a design procedure, utilising MEL principles, for stream crossings, which shows many advantages over conventional designs. The very low energy losses associated with MEL designs leads to structures with reduced afflux and narrower waterway widths with consequent construction economies.

Sediment deposition under low flow conditions is a recognised characteristic of MEL structures. In this study, a predictive procedure was developed to determine the sediment sweepout characteristics, under high flows, of a MEL structure, which was tested against the results from a physical model. Excellent agreement with regard to the variation of water surface and bed elevation with time was noted, indicating the fundamental soundness of the approach. The sediment sweepout modelling procedure represents a useful aid for the design of minimum energy loss structures, enabling engineers to verify that sediment accumulation in the depressed invert will not disrupt the structure's performance under flood conditions.

In the light of the comprehensive model tests and prototype experience, minimum energy loss structures can be confidently recommended for many situations, where their reduced cost and afflux will make them an attractive design option.

 

ACKNOWLEDGEMENTS

Financial assistance was provided by VicRoads and the NSW Road Traffic Authority and is gratefully acknowledged.

 

REFERENCES

Ackers, P. and White, R. (1973): "Sediment Transport: New Approach and Analyses," J. Hydr. Div., ASCE, Vol. 99, No. HY11, pp 2041-2060.

Cade, L.E. and Keller, R.J., (1995), "Design Procedure and Performance of a Minimum Energy Designed Culvert", I.E.Aust Civil Engg Trans., Vol. CE37, No.1, pp 1-8.

Chang, H.H. (1983): Energy Expediture in Curved Open Channels, Journal of the Hydraulics Division, ASCE, Vol. 108, HY5.

Ferguson, R.I. (1973): Regular Meander Path Models, Water Resources Research, Vol. 9, No. 4, pp 1079-1086.

Isaacs, L.T. (1990), "Design Calculations for Minimum Energy Loss Culverts," I.E.Aust Civil Engg Trans., Vol CE32, No.2, pp. 87-92

McKay, G.R. (1978), "Design principles of Minimum Energy Waterways," Proc Workshop on Minimum Energy Design of Culverts and Bridge Waterways, ARRB, Melb., December.

Winston, F.B. (1998): "Minimum Energy Loss Waterways, Design and Numerical Performance Modelling", Thesis towards the requirements of the degree of M. Eng. Sci., Monash University, Melbourne