ENERGY DISSIPATION IN THE STILLING BASIN DOWNSTREAM OF BLOCK RAMPS IN PRESENCE OF ROCK MADE SILLS S. Pagliara1 and M. Palermo2 1 Department of Civil Engineering, University of Pisa, Italy, Via Gabba 22, 56122, Pisa 2 Department of Civil Engineering, University of Pisa, Italy, Via Gabba 22, 56122, Pisa Abstract: The dissipative process is one of the main topics for river engineers. It is deeply affected by both river morphology and the geometric configuration of the structures which can eventually be present in the river branch. In presence of a block ramp, previous studies allowed to analyze the energy dissipation mechanism for prismatic channels. The analysis was conducted for both submerged and free hydraulic jumps located at the toe of the block ramp with different stilling basin materials and different scale roughness conditions for scour equilibrium configuration, but in the absence of any protection structure in the stilling basin. Conversely, the aim of the present study is to analyze the dissipative process which occurs in correspondence and downstream of a block ramp when a rock made sill is located in the stilling basin. Moreover, the analysis of the dissipative process was conducted varying the spatial positions of the sill and the results were compared with the cases where no protection sills are present. The tests were performed using different stilling basin materials and varying the ramp slope. Moreover, in all the tests, the hydraulic jump was entirely located in the stilling basin, never submerging the ramp toe. INTRODUCTION The energy dissipation which occurs in correspondence of hydraulic structures is a fundamental topic for hydraulic engineers. Different types of structures produce different dissipative mechanisms which has to be carefully analyzed for their optimal design. Namely, block ramps are peculiar hydraulic structures which produce high energy dissipation. They are structures made of loose or fixed blocks and either a fixed or a mobile stilling basin can be present downstream. They have become more popular in the last decades as they can assure a great energy dissipation and, in the meantime, they have the characteristic to be eco-friendly structures. Generally the approaching flow is in sub-critical condition and a passage from sub- to super-critical condition occurs in correspondence with the ramp entrance. The sudden slope variation downstream of the block ramp and the downstream hydraulic conditions in the stilling basin determine a further passage from super- to sub-critical condition resulting in a hydraulic jump which can be entirely localized in the stilling basin or partially submerge the ramp. The presence of a hydraulic jump in the downstream stilling basin causes a bed erosion in the case in which it is movable. The scour process has to be carefully controlled in order to avoid structural risks that can even lead to a structural collapse. The optimal functionality of the ramp is assured if the ramp bed is stable. Thus, one of the main problem which was studied and solved in the past is the ramp stability (see for example Whittaker and Jäggi 1986 and Robinson et al. 1997). In the case of mobile bed, the erosion occurring in the downstream stilling basin is another important factor which has to be carefully analyzed. In the last years, many studies have been conducted in order to understand the erosive mechanism downstream of hydraulic structures (among these Bormann and Julien 1991, Breusers and Raudkivi 1991, Hoffmans and Verheij 1997, Hoffmans 1998, D’Agostino and Ferro 2004, Dey and Raikar 2005). More recently, scour downstream of block ramps was deeply analyzed both in the case in which protection structures are present or absent in the stilling basins. Pagliara (2007) analyzed the scour mechanism in various geometric and hydraulic conditions furnishing useful relationships in order to calculate the scour lengths. Successively, Pagliara and Palermo (2008a-b) studied the effect of the presence of different sills located in various spatial positions in the stilling basin in order to reduce the maximum scour depth and the scour hole length. The dissipative process occurring in correspondence of a block ramp was deeply analyzed in different hydraulic conditions and geometric configuration. Pagliara and Chiavaccini (2006) analyzed the energy dissipation occurring in correspondence with the block ramp between the entering section and the toe of the ramp. They conducted experiments for fixed stilling basins and in presence of a hydraulic jump entirely occurring downstream of the ramp itself. Successively, Pagliara et al (2008) extended the analysis of the dissipative process to the case in which the stilling basin was movable and the hydraulic jump submerged the ramp. Moreover, they analyzed the complete energy dissipation process as they evaluated the energy dissipation between the entering section of the ramp and downstream of the hydraulic jump. No studies known by authors deal with the energy dissipation process in correspondence and downstream of a block ramp when protection structures, namely rock sills are located in the stilling basin. The present paper aims to evaluate the energy dissipation occurring between the entering section of the ramp and downstream of the hydraulic jump varying the spatial positions of rock made sills located in the stilling basins. Moreover, both the energy dissipations occurring on the ramp and in the stilling basin were evaluated in order to understand each single contribute to the entire dissipative process. EXPERIMENTAL SET-UP Experiments were conducted in one channel whose geometric dimensions are: 0.25 m wide, 3.5 m long and 0.30 m high. The ramp was simulated using an iron sheet on which stones were glued. The stones used for the ramp had the following granulometric characteristics: D50 = 0.01046 m, D65 = 0.01094 m, D90 = 0.0117 m and σ=(D84/D16)0.5=1.17. Three different ramp slopes i were tested: 0.25, 0.125 and 0.083. The mobile bed was simulated using two different granular materials, m1 and m2, both non-uniform, whose main granulometric characteristics are synthesized as follows: for material m1 d50=0.0053 m, d90=0.0105 m and σ=(d84/d16)0.5=1.8, whereas for material m2 d50=0.0051 m, d90=0.0168 m and σ=(d84/d16)0.5=2.8. The rock made sill was simulated using crushed rocks whose mean diameter was 0.046 m. The rock made sills were located in the stilling basin in different spatial positions. Some preliminary tests were conducted without any type of protection (reference test) in order to evaluate the energy dissipation in absence of sills and in the same hydraulic and geometric conditions. Moreover, the preliminary tests allowed to evaluate the average maximum scour depth zm (obtained averaging the transverse depth measurements in the section of maximum scour), and the scour hole length l0 (see Fig. 1a). The sills were located in two different vertical positions and four different longitudinal positions. The vertical positions Zop=zop/zm tested were 0 and 0.5, in which zop is the vertical position of the upper sill corner point measured from the original bed level and zm is the maximum average scour depth for the respective reference test. The longitudinal positions λ=xs/l0 tested were 0.25, 0.5, 0.75 and 1, in which xs is the longitudinal position of the protection structure measured from the ramp toe and l0 the scour hole length of the respective reference test (see Fig. 1b). Prior to each experiment the channel bed was carefully levelled. When the asymptotic scour equilibrium was reached, the bed morphology and the water depths were measured. Particular attention was paid in measuring the water depth h1 in section 1-1, which is the water depth at the ramp toe, and h2 in section 2-2 which is the water depth downstream of the hydraulic jump (see Fig. 1). All tests were conducted in clear water conditions and the discharge varied between 2.9 and 9.3 l/s. Moreover, all the experiments were done in intermediate scale roughness condition (see Pagliara and Chiavaccini 2006), thus for 2.5<k/D50<6.6, where k is the critical depth. In Fig. 2a-b two pictures of the experimental apparatus are shown. In fig. 2a the rock made sill is located at Zop=+0.5 and λ=1 and in Fig. 2b Zop=+0.5 and λ=0.25. 0 1 2 k l0 (a) H h1 h2 zm 0 1 2 0 1 2 k ls (b) H xs h1 h2 zms zop 0 1 2 Figure 1 Definition sketch of (a) ramp in reference test condition and (b) with sill protection with the indication of the main geometric and hydraulic parameters Figure 2 Pictures of experimental apparatus: (a) view from upstream and (b) side view RESULTS AND DISCUSSION The energy dissipation between the sections 0-0 and 2-2 was analyzed in presence of rock made sill located in the stilling basin in different spatial positions and compared with the respective dissipation obtained in preliminary reference tests. The data relative to reference tests confirmed the findings of Pagliara et al (2008), who furnished an equation by which it is possible to estimate the relative energy dissipation ΔE2=(E0-E2)/E0, in which E0=1.5k+H is the total upstream energy and E2=h2+q2/(2gh22) is the energy at downstream end of jump, where H is the ramp height and q is the unit discharge. Pagliara et al. (2008) analyzed the dissipative phenomenon both in the case in which the hydraulic jump submerges the ramp and in the case in which it is entirely located in the stilling basin, proposing the following formula: ΔE2 = A + (1 − A)e( B )k / H (1) In which A and B are parameters depending on the scale roughness and the submergence condition of the ramp. In case of intermediate scale roughness condition and for hydraulic jump entirely located in the stilling basin, A=0.249 and B=-1.863. Note that in the tested range ΔE2 does not depend on the uniformity of stilling basin material and on the ramp slope. A preliminary analysis was conducted in order to understand if there is any effect of non uniformity in the dissipative process being the same hydraulic conditions, geometric configuration and location of the sill in the case of either m1 or m2 was the stilling basin material. It was experimentally proved that the effect of material non uniformity is negligible also in presence of a protection structure in the stilling basin. Successively, the data were distinguished for various Zop and i values and for all λ tested, in order to put in evidence the dependence of the dependent variable ΔE2 on these parameters. Figure 3 shows the result of the comparison. 1 ΔE 2 Equation (1) for IR i=0.25, Zop=+0.5 i=0.25, Zop=0 0.8 i=0.125, Zop=+0.5 i=0.125, Zop=0 i=0.083, Zop=+0.5 i=0.083, Zop=0 0.6 0.4 k/H 0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Figure 3 ΔE2(k/H) for various i and Zop and all λ tested It is worth noting that in the case in which a stilling basin is protected by a rock made sill, the energy dissipation between sections 0-0 and 2-2 is slightly bigger than in the case in which the stilling basin is unprotected. This mainly due to the fact that the sill presence partially deflects the flow creating a local recirculation upstream of the structure itself which contributes to dissipate energy. Moreover, it is clearly visible that practically there is no difference in data trend varying λ and Zop in the tested range. Thus, it can be stated that the effect of the sill position on the dissipative phenomenon is negligible. As the differences in energy dissipation between the reference tests (whose trend is represented by Eq. (1) in Fig. 3) and the respective tests conducted in the same geometric and hydraulic conditions but in presence of a rock sill is very slight, Eq. (1) can satisfactorily estimate also the data relative to the last case. The comparison between measured and calculated (with Eq. 1) values of the variable ΔE2 for protected basins is shown in Fig. 4. 1 ΔE 2 meas 0.8 0.6 data 0.4 perfect agreement 20% deviation 0.2 ΔE 2 calc 0 0 0.2 0.4 0.6 0.8 1 Figure 4 Comparison between measured and calculated (with Eq. 1) values of the variable ΔE2 for protected basin tests The analysis of the dissipative process was further specialized and developed. Especially for practical purposes it is very useful to know where the energy is mainly dissipated, namely on the ramp itself or in the stilling basin. Thus the following non dimensional variables were introduced and estimated: ΔE1-2=(E1-E2)/E0 and ΔE’1-2=(E1-E2)/(E0-E2). ΔE1-2 represents the amount of the total upstream energy (in section 0-0) dissipated in the stilling basin (between sections 1-1 and 2-2), whereas ΔE’1-2 represents the amount of the total energy dissipation (between sections 0-0 and 2-2) which is dissipated in the stilling basin (between sections 1-1 and 2-2). E1 is the energy in section 1-1 evaluated using Eq. (2) proposed by Pagliara and Chiavaccini (2006), who found that the relative energy dissipation between section 0-0 and 1- 1 can be expressed as follows: E0 − E1 ΔE1 = = A + (1 − A)e( B + C ⋅i ) k / H (2) E0 Where A,B,C are parameters depending on the scale roughness conditions of the ramp. In particular for intermediate scale roughness condition Pagliara and Chiavaccini (2006) found that A=0.25, B=-1.2 and C=-12.0. Based on Eq. (2) and knowing the hydraulic and geometric conditions (discharge, ramp configuration and material) one can easily derive the value of E1. It is worth noting that ΔE1-2= ΔE2- ΔE1, in which ΔE1 is evaluated using Eq. (2). Also in this case the analysis was conducted by steps. It was experimentally proved that the effect on non-uniformity σ, Zop and λ on both the dependent variables ΔE1-2 and ΔE’1-2 can be considered negligible for practical purposes. Both the variables ΔE1-2 and ΔE’1-2 were plotted versus k/H for all Zop and λ tested as shown in Figure 5a-b respectively. 1 (a) ΔE 1-2 0.8 data Eq. (3) 0.6 0.4 0.2 k/H 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1 ΔE ' 1-2 (b) data Eq. (4) 0.8 0.6 0.4 0.2 k /H 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Figure 5 (a) ΔE1-2 (k/H) and (b) ΔE’1-2 (k/H) for all the data relative to protected basin For both the variables ΔE1-2 and ΔE’1-2 two different experimental equations are proposed: E1 − E2 ΔE1− 2 = = 0.42 ⋅ e −1.77⋅( k / H ) (3) E0 and E1 − E2 ΔE '1− 2 = = 0.53 ⋅ e −1.1⋅( k / H ) (4) E0 − E2 both valid for 0.2<k/H<1.6. In figure 6a-b the comparison between measured and calculated values with Eq. (3) and (4) of the variables ΔE1-2 and ΔE’1-2 is shown. 0.3 ΔE 1-2 meas (a) 0.2 data 0.1 perfect agreement 30% deviation ΔE 1-2 calc 0 0 0.1 0.2 0.3 0.5 (b) ΔE ' 1-2 meas 0.4 0.3 0.2 data perfect agreement 30% deviation 0.1 ΔE ' 1-2 calc 0 0 0.1 0.2 0.3 0.4 0.5 Figure 6 (a) Comparison between measured and calculated (with Eq. 3) values of the variable ΔE1-2 and (b) between measured and calculated (with Eq. 4) values of the variable ΔE’1-2 for all the data relative to protected basins From Figure 5a-b it is evident the effect of the presence of a block ramp on the entire dissipative process. In fact, from fig. 5a, it is clearly visible that in the stilling basin it can be dissipated an amount of available energy which is less than 0.2 E0. The amount of energy dissipated in the stilling basin decreases increasing the ratio k/H and it results to be independent from the parameters Zop and λ. Moreover, Figure 5b proves that the most part of energy dissipation occurs on the ramp itself as the energy which can be dissipated in the stilling basin is always less than the 40% of the total energy dissipation. This last result has a considerable practical importance as it proves that block ramps are structures which can be satisfactorily used to dissipate energy. The energy dissipation process mainly occurs on them even if in the stilling basin are located rock made sills which can be used to reduce the scour lengths, but which have not a substantial effect on the dissipative process, if compared to the condition in which they are not present. CONCLUSIONS In the present paper the energy dissipation process in presence of both a block ramp and a protected granular stilling basin was analyzed. The effect of the longitudinal and vertical position of rock made sills on the dissipative mechanism was deepened. Namely, the energy dissipation between the upstream ramp section and downstream of the hydraulic jump was evaluated and it was experimentally proved that the presence of protection structures slightly contributes to increase the total amount of the dissipated energy. Moreover, a more detailed analysis was conducted to understand the quantity of available energy which is dissipated on the ramp itself and in the stilling basin. The main result which was achieved is that, in the tested range of parameters, in the stilling basin is dissipated less than 0.2E0. Moreover, if the energy dissipation which occurs in the stilling basin is compared with that occurring both on the ramp and in the stilling basin, it was proved that it decreases increasing the ratio k/H and it is always less than 0.4(E0-E2). 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