UNCERTAINTIES IN ROUGHNESS COEFFICIENTS AND DIFFICULTIES OF INTERPRETATION IN RIVERINE SITUATIONS

François GAZELLE, GEODE

Associated with other parameters and dynamic vectors, notably the lengthwise gradient and the hydraulic radius, the establishment of a roughness coefficient allows the velocity of movement of water masses in the low-water and high-water channels to be estimated, information which can afterwards be used to calculate flow rates. This roughness coefficient is universally applied by hydrologists and hydraulics specialists. Many such scientists have studied the question at a fundamental level, but the names of Manning and Strickler are most often associated with it, to the point that it is commonly called Manning’s Coefficient or Strickler’s Coefficient. In theory, this approach is pertinent and brings the satisfactions and certainties associated with “hard science”. Nevertheless, the margin of error associated with its use and the ideas which may be drawn from it lead us to relativise the strict accuracy of results obtained from such calculations.

Assessment of “roughness” : The character, more or less smooth or - on the other hand - irregular and rugged, of a surface over which a liquid passes in part determines the velocity of its flow. Assigning a value to this roughness is fairly straightforward when one is dealing with conduits or pipes of regular cross-section made of materials whose physical properties are well-known ; it is almost as easy in the case of canals or stretches of river which have been artificially canalised.

The situation is far from similar when one is dealing with riverbeds which are more or less natural. The bed of the river is stony and undulating ; the banks are irregular and more or less wooded depending on the particular stretch and on the season. As for the flood plain, its roughness also varies considerably in time and space, depending on the degree of human influence. The difficulty of quantifying these rather enigmatic parameters has not prevented numerous specialists from proposing a graduating scale of roughness coefficients, on the basis of which the velocity of the current, and hence the flow rate, are calculated. It is necessary to face facts : these calculations are estimates and not precise values.

Thus in the scientific “literature” and in reports published by engineering consultancies, Strickler’s Coefficient is given in ranges as follows :  between 10 and 20 for small watercourses whose low-water channel is up to 10m wide  between 20 and 30 for larger watercourses  between 30 and 40 for canalised rivers and inland canals  between 40 and 50 for urban roads In fact, as far as roughness sensu stricto is concerned, it is indeed the nature of the surface which determines the level of the coefficient : for example, in the case of pebbles or grass, it is estimated at between 25 and 40. It may be seen that the range is large, which is not without effect on the results of calculations of water velocity and flow rates, given the nature of the mathematical formula used.

In the first place, therefore, there is a question of assessment, which may be tinged with an element of subjectivity. At what point does a small watercourse become a big one ? If the vegetation on the banks of a small watercourse is cleared, does it change category ? It must be admitted that the value of the coefficient can change by a factor of two depending on how one assesses the situation in the field, given that the assessment allows a certain latitude. In the end, all this can lead to a rather random result in the calculation of mean water velocity.

In flood conditions, it is also necessary to take into consideration the variability of the coefficient in time and space. For the same zone of flood plain which is flooded, the depth of submersion changes the roughness, in two ways which are, moreover, linked :  the hydraulic radius is modified : in the case of floods spreading over a flood plain of variable dimensions, when the depth of submersion increases, the area covered by the water does not necessarily increase in the same proportions as its perimeter. in general, the flow is better : the roughness affects above all the lower part, nearer to the river bed ;  the roughness changes with the seasons, depending on the state and the height of the crops

2 mai 2007