Brea, José Daniel and
Spalletti, Pablo D.
Instituto Nacional del Agua y del Ambiente
Laboratorio de Hidráulica y del Ambiente, Autopista Ezeiza-Cañuelas Km. 1.6, CC 21 (1832) Ezeiza, Bs. As., Argentina
E-mail:
dbrea@ina.gov.ar, pspallet@ina.gov.ar
Abstract: This paper shows the results obtained from the studies on local scour on isolated elements and pile groups, with different configurations relating to element separation and current attack angles. The tests were carried out in physical models with coal beds. The objective was to minimize the scale effects in great sand river models, such as is the case of the Paraná river in Argentina (average discharge= 16000m3/s, maximum registered discharge=60000m3/s, and a river bed representative diameter in the study zone = 300 m m). The use of coal, which has a specific gravity lower that sand and enough availability in the market, allows to fulfill the objectives sought.
Of the total cases studied, those of simplest configuration are totally or partially developed in the specific bibliography on this topic. In those cases, the results have been compared to the ones of other investigators as well as with some of the most used equations for the design. There are great coincidences, both in the values of the maximum scour, as well as in the geometric configurations in the local scour, which supports the results obtained in the rest of the tests carried out.
The problem of local scour in bridge piers has been amply studied in laboratory, but generally these studies are related to isolated piers in the stream, based on models with sand as bed material, which limits their representation to extrapolate the results to prototypes with fine sand beds.
In this paper the results of the studies on physical models with coal beds are presented, with the objective of evaluating the expected scour in bridge piers in prototype, under certain conditions relating to the hydraulic functioning and to the material in the riverbed. It was analyzed the behavior of isolated piers and pile groups with different configurations, comparing the results with those of other investigators and the most used equations for the design.
In order to evaluate the similitude criteria for the execution of physical models, the local scour in bridge piles of circular section in a river, can be described by the following expression (4):
Where r : fluid density, m : fluid dynamic viscosity, U: average velocity, h: flow depth, g: gravity acceleration, d: material diameter, Uc: critical velocity at the beginning of motion of particles, B: pile diameter.
Applying the dimensional analysis to the problem, taking r , U, h as repeated variables, the following expression, is obtained:
If the length scale is not distorted, the relation h/d is sufficiently great and the flow around the pile is totally turbulent (10), there are two possible similitude criteria, one corresponding to the number of Froude and the other to the state of particle mobility.
If a simultaneous similitude cannot be maintained, and as local scour is a consequence of a complex three-dimensional flow, the hydrodynamic similitude must be respected in order to keep the flow pattern. Therefore, in the laboratory tests, hydraulic conditions were adopted in correspondence with the Paraná river prototype situations (1), respecting the equality of the Froude number.
The results of a series of tests developed in the Hydraulics Laboratory of the INA are presented, in order to study local scour in isolated piers, and pile groups specified for the hydraulic project Conexión Vial Rosario – Victoria (which crosses the Paraná river with a total length of 57 km, with a bridge of 3 km over the principal branch and 12 bridges over the flood plain (1, 2)).
A test channel 2 meters wide and 30 meters long was used, with the river bed thick equal to 60 cm, made of coal of 300 m m mean diameter. In all cases the tests lasted for more than 8 hours.
In the first instance the behavior of the isolated piles of the circular section were evaluated, with the h/B relations varying between 0.5 and 7.5, mean velocities between 0.25 and 0.32 m/s and a flow depth of 37.5 cm. The maximum scour related to the diameter of the piles for the tests with the Froude number 0.13 are indicated in Figure 1, in which the results obtained by the application of certain more frequently used expressions, have also been diagramed (5, 7). It can be seen how the maximum measured scours are located, in general, beneath the values calculated by using all the equations of the design, but maintaining the same trend of evolution of local scour in relation to the diameter of the elements, as the relation h/B varies. This is reasonable if you take into account that said formulas were developed for the design, as test groups results superior coverage, including in some cases coefficients for additional security.
In Figure 2 the results obtained from the physical coal model are compared to those obtained by other authors, who used sand beds with a mean diameter in the order of 300 m m (ripple forming materials). It can be observed that the maximum scours obtained are compatible with those of the rest of the studies (8). For the building of this graph, corrections were made where appropriate, due to the influence of h/B (3, 9), as in the basic data recompiled in reference (8).
The behavior of the groups of two circular section piles with a diameter equal to 5 cm, with separations varying between 1.25 and 3.5 times the diameter, and different current attack angles, were studied. In all the tests the flow depth was 37.5 cm and the median velocity was 0.32 m/s.
Even if the pile groups topic has not been treated in the specialized bibliography as in the case of the isolated piers, they have been treated in certain cases. Some authors have defined relations between the maximum scours registered in the groups of two piles, in relation to the separation between them and the angle that the current forms with the alignment of the elements. Breusers & Raudkivi (3, 6, 9) for two elements of circular section, for current attack angles of 0º, 45º and 90º, established relations between the separation of the piles and maximum scours in the front pile, in the back pile and in the area located between them.
The above mentioned relations are presented in Figures 3 and 4, the first one correspon-ding to a current aligned to the piers, and the latter at attack angles of 45º and 90º. In these graphics the values obtained in the physical model for the different angles of the flow’s incidence are established. The reference scour corresponds to the isolated pile, and has been adopted at the test’s value for a pile equal to those of the groups analyzed, under the same hydraulic functioning conditions.
The results can be seen to agree with those of the bibliography for the incidence angles of 0º and 45º. In the case of tests with elements located perpendicularly to the current, the relations obtained from the reference give lower values in relation to what has been observed in the model. This can also be observed in Figure 5, which presents the attack angle in relation to the maximum local scour at the end of the tests, in both piles and in the area between them.
This would be indicating that in the present study and in the one in reference (9), both the phenomenon of reinforcing and sheltering, as well as that of shed vortices together with the current deflection that the upstream pile exercises, have the same effect on the behavior of the riverbed around the elements.
But this does not occur when the groups are located perpendicularly to the current, which results in flow contraction and the interaction of the horseshoe vortices of the different elements. In this case, the experimental erosion values obtained are greater than those predicted by the reference. It is convenient to comment that in order to make said graph, the authors have used few data when the relation between separation and diameter of the piles was smaller than 4, in spite of the fact that it is the part of the curves which presents most variations.
In Figure 3 the maximum erosions in both piles and in the intermediate zone, for an attack angle equal to 22.5º and separations varying between 2 and 3.5 times the piles’ diameter, obtained in the tests are presented. It can be seen that the maximum scour values are produced by separations of about 2.5 times the diameter, due to the combined effect of reinforcing, sheltering and the shed vortices. When the separation increases, a pronounced diminution of the influence of the element located upstream can be observed.
Three aligned piles, six piles grouped in two rows and five elements with a distribution 2-1-2, with flow attack angles of 0º and 22.5º, were studied, too. The conditions of the test were equal to those previously presented, and the separation between the elements was of 2.7 and 3.4 times the diameter of the piles, while the distance between the rows was 2.5 times the diameter.
Analyzing the results in a qualitative manner, with the aligned piers to the current, the maximum local scours were registered in the elements located upstream, and a gradual scour diminution was observed downstream, with values ranging 80% and 60%. In the tests with an angle of 22.5º, the maximum local scours were produced in the downstream piles, and the relation between them and the one corresponding to the isolated pile, remained between 1.30 and 1.37.
On certain occasions, the only alternative to minimize the scale effects in the evaluation of the local scour at the bottom of structures crossed by currents, when passing from prototype to the model, is to use loose materials in the laboratory, which are different from the traditional ones, in such a way as to keep the number of Froude constant in the prototype and the model, and comply with certain requisites relating to the condition of particle mobility in the river bed. In the present study, coal was used due to its low specific gravity and the availability in the market.
From the totality of the cases studied, those of most simple configuration have been developed in the specific bibliography on the topic, totally or partially. In those cases, there was good coincidence between both the values of the maximum erosion as well as in the geometric configurations of the local scour, which upholds the results obtained in the rest of the tests carried out. The values of local scour presented are in all cases those in equilibrium, measured at the end of each test.
Finally, it can be said that even if the local scour of the isolated circular piles has been greatly studied, and the scale effects evaluated, the quantification of local scour in the most complex cases presents serious difficulties. So, it is necessary to resort to physical models in detail, in order not to overestimate their value in a gross manner, from the application of high security coefficients, due to ignorance.
References
[1] Brea J.D., Spalletti P.D. Modelación Física de la Erosión Local al Pie de las Pilas y Defensas de la Conexión Vial Rosario-Victoria. Informe LHA-180-01-99. Marzo 1999.
[2] Brea J.D., Spalletti P.D. Modelación Física de la Erosión Local al Pie de las Pilas Tipo Cofferdam de la Conexión Vial Rosario-Victoria. Informe LHA-185-01-99. Nov. 1999.
[3] Breusers H.N.C., Raudkivi A.J. Scouring. A.A.Balkema. 1991.
[4] Ettema R., Melville B., Barkdoll B. Scale Effect in Pier-Scour Experiments, Journal of Hydraulic Engineering, Vol. 124, No. 6. Jun. 1998.
[5] HEC18. Evaluating Scour at Bridges. US Department of Transportation. FHA. Nov. 1995.
[6] Hoffman G.J.G.M and Verheij H.J. Scour Manual, A.A.Balkema. 1997.
[7] Johnson P.A. Comparison of Pier-Scour Equations Using Field Data. Journal of Hydraulic Engineering, Vol. 121, No. 8. Ago. 1995.
[8] Melville B.W. Live-Bed Scour at Bridge Piers. Journal of Hydraulic Engineering, Vol. 110, No. 9. Sep. 1984.
[9] Raudkivi, Arved J. Curso Latinoamericano de Mecánica Fluvial. LHA – INCYTH. 1985.
[10]
Spalletti P.D., Brea J.D. Análisis de la erosión local en pilas circulares a
partir de modelos físicos con lecho de carbón.
XIX Cong. Latinoamericano de Hidráulica, Córdoba, Arg. 2000.
Fig. 1 Comparison with pier-scour equations (F=0.13).
Fig. 2 Comparison with data by other investigators.
Fig.
3 Two pile groups - angle 0º
Fig.4 Two pile groups – different angles of attack.
Fig. 5 Separation between piles/B = 2.6