KSCE Journal of Civil Engineering (2009) 13(2):129-136 DOI 10.1007/s12205-009-0129-1
Water Engineering
www.springer.com/12205
Sediment Transport on Block Ramp: Filling and Energy Recovery Stefano Pagliara*, Michele Palermo**, and Ilaria Lotti*** Received May 22, 2008/Revised 1st: October 14, 2008; 2nd: November 28, 2008/Accepted December 1, 2008
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Abstract The effect of sediment transport on both morphology and energy dissipation in presence of non conventional stream rehabilitation structures, such as block ramps or rock chutes, is a not well explored topic on hydraulic engineering. Namely, in normal functioning conditions, these types of structures are generally located in mountain rivers, which are characterized by an elevated sediment transport which can be deposited and trapped between the rocks constituting the ramp. This causes a change in the bed roughness and in the energy dissipation process that is present on a block ramp. This occurrence was experimentally investigated at the Hydraulic Laboratory of the University of Pisa. Different experimental conditions were tested and the main hydraulic and geometric parameters controlling the filling phenomenon and its effects were highlighted. Namely, it was experimentally proved that both the median diameters of the filling material and of the ramp blocks, the ramp slope and the discharge are the most relevant parameters governing the ramp filling. Thus, experimental formulae were derived to foresee the ramp morphological changes and the interaction between the filling process and the geometric and hydraulic parameters. Moreover a comparison of the energy dissipation on block ramp was conducted and the energy recovery in presence and absence of filling material was compared. Keywords: block ramp, rock chutes, sediment transport, sediment filling, energy dissipation ···································································································································································································································
1. Introduction Block ramps or rock chutes consist of rocks placed on a sloped bed. The presence of a hydraulic structure generally modifies the natural sediment transport as it constitutes a discontinuity in the river bed morphology. This occurrence is minimized by a block ramp but, according to different hydraulic conditions, river sediments can be alternatively transported or deposited on it. For this reason, it is very important to analyze the filling phenomenon in order to foresee and determine the hydraulic conditions which consent the transport or the deposition on block ramp of the approaching sediments. Two examples of block ramps are shown in Fig. 1a-b. The initiation of uniform sediment motion has been widely studied. The most known theory was proposed by Shields (Shields, 1936), who gave the well known Shields threshold curve as a suitable criterion to identify the initiation conditions of sediment motion. Successively, many other Authors developed new approaches in order to account for other parameters such as the bed slope or the relative submergence which were found extremely important for the definition of the incipient motion conditions (Chew and Parker, 1994; Graf and Suszka, 1987; Rice et al., 1998). The peculiarity of block ramp structures built in mountain rivers is that they are generally characterized by small relative submergences and large slopes. Because of these occur-
rences, flow depth and bed size material are almost of the same order of magnitude (macro-roughness condition). Many authors investigated the incipient motion for negligible or relatively small bed slopes (White, 1940; Iwagaki, 1956; Coleman, 1967; Yang, 1973), but few papers analyzed the sediment threshold in case of high slopes (Smart and Jaeggi, 1983; Schoklitsch, 1983; Bathurst et al., 1987). Moreover, the effect of the relative submergence was found very important. In fact it was proved (Ashida and Bayazit, 1973; Suszka, 1991; Pagliara and Chiavaccini, 2006) that the dimensionless critical shear stress θ can be expressed as a function of the relative depth, h/D50, where h is the water depth and D50 the mean size of sediments. The results show that the dimensionless critical shear stress increases considerably as the flow becomes shallower. The presence of the filling material between the ramp rocks changes the ramp morphology and influence the energy dissipation process. Previous works investigated the stability of these types of structures (Whittaker and Jaggi, 1986; Robinson et al., 1995) and analyzed the stability of rock chutes for bed slopes ranging between 0.10 and 0.40. Pagliara and Chiavaccini (2007) investigated the stabilization effect of boulders with three boulder configurations (boulders in rows, randomly or in a arc configuration) and illustrated the different steps of failure mechanisms. But all these studies are related to a ramp configuration in which
*Professor, Dept. of Civil Engineering, University of Pisa, 56126 Pisa, Italy (Corresponding Author, E-mail:
[email protected]) **Ph.D. Student, Dept. of Civil Engineering, University of Pisa, 56126 Pisa, Italy (E-mail:
[email protected]) ***Ph.D., Dept. of Civil Engineering, University of Pisa, 56126 Pisa, Italy (E-mail:
[email protected]) − 129 −
Stefano Pagliara, Michele Palermo, and Ilaria Lotti
Fig. 1. (a) Downstream View of a Block Ramp in the Magra River (Italy), (b) Side View of a Block Ramp in the Cecina River (Tuscany, Italy)
no filling material is present between the rocks and so all the deductions can be limited to this case. The aim of this paper is to analyze both the influence of sediment transport on the ramp filling phenomenon and the energy recovery which occur in a filled ramp respect to the configuration of “empty” ramp (i.e. in absence of filling material on block ramp).
2. Experimental Setup and Procedure Tests were carried out at the Hydraulic Laboratory of the University of Pisa, Pisa Italy. Block ramps were built in a rectangular flume 0.35 m wide, 0.60 m deep, and 7 m long, with smooth glass side walls. The discharge Q was measured by means of a calibrated magnetic flow meter located in the supply line. The block ramp materials tested were uniform (σ QE).
Three different ramp materials and three filling materials were tested: M1, M2 and M3, and m2, m3 and m4, respectively. The granulometric characteristics of both the ramp blocks and the filling materials are reported in Table 1. Table 2 synthesizes the
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KSCE Journal of Civil Engineering
Sediment Transport on Block Ramp: Filling and Energy Recovery
between 0.073-0.298, where d50 is the mean diameter of the filling material and D50 is the mean diameter of the ramp material. In all the tests the bed and the water level were accurately measured before and after the input of the sediment into the flow, using a point gauge whose accuracy is 0.1 mm. Moreover, when the finer material was supplied, also the filling level was measured in order to obtain the filling percentage Px/Lr (%). Px/Lr (%)=1− δ/D50 is defined as the complementary to 1 of the ratio of δ to D50, where δ is the distance of the horizontal average level of sediments tops (L.T.), which reasonably coincides with D50 (mean diameter of the ramp material), from the horizontal average level of filling material (L.R.) in the measured transversal sections (see section A-A of Figs. 2d). L.L. represents the liquid level and d50, the mean diameter of the filling material. The filling material was carefully supplied in the transversal section x/Lr =0. It was uniformly distributed on this cross section
Table 1. Block Ramp and Filling Materials Characteristics Material (-)
Symbol (-)
d50 (m)
σ = (d84/d16)0.5
ρs
(-)
(kg/m3)
Block ramp
M1
0.0318
1.074
2585
Block ramp
M2
0.0380
1.050
2710
Block ramp
M3
0.0518
1.076
2744
Filling material
m2
0.0038
1.368
2241
Filling material
m3
0.0065
1.202
2325
Filling material
m4
0.0095
1.174
2498
different flow and setup experimental conditions. About 130 tests were performed. Tests were carried out in three different slope configurations (1V:8H, 1V:6H and 1V:4H, respectively) and for different combinations of the ratios d50/D50, ranging
Table 2. Different Flow and Setup Conditions Experimental arrangement (−)
Material of block ramp (−)
Material of sediment transport (−)
Q (l/s)
S (−)
d50/D50 (−)
k/D50 (−)
Fr (−)
Re (−)
1
M1
m2
1-20.9
0.125
0.119
0.30-2.24
0.75-2.2
11000-238000
2
M1
m3
1.6-21.5
0.125
0.203
0.40-2.28
1.07-2.1
18000-245000
3
M1
m4
2.1-22
0.125
0.298
0.48-2.32
1.08-2.15
24000-251000
4
M2
m2
1.3-20.7
0.125
0.100
0.29-1.87
0.95-2.01
5000-237000
5
M2
m3
1.9-22.1
0.125
0.170
0.38-1.95
1.08-2.22
2000-253000
6
M2
m4
2.4-24.7
0.125
0.250
0.44-2.10
1.15-2.52
7000-282000
7
M3
m2
1.3-25
0.125
0.073
0.22-1.55
1.05-2.61
5000-286000
8
M3
m3
2-25
0.125
0.125
0.29-1.55
1.11-2.72
3000-286000
9
M3
m4
2.5-27.8
0.125
0.183
0.33-1.67
1.18-3.22
9000-318000
10
M1
m2
0.8-15
0.166
0.119
0.25-1.80
0.9-1.8
9000-171000
11
M1
m3
0.9-15
0.166
0.203
0.28-1.80
1-1.8
10000-171000
12
M1
m4
1.3-15
0.166
0.298
0.35-1.80
1.05-1.85
15000-171000
13
M2
m2
0.8-15
0.166
0.100
0.21-1.51
0.82-1.75
9000-171000
14
M2
m3
0.9-15
0.166
0.170
0.23-1.51
0.75-1.7
10000-171000
15
M2
m4
1.2-16
0.166
0.250
0.28-1.57
1.05-1.91
4000-183000
16
M3
m2
1.35-15
0.166
0.073
0.22-1.10
1.15-1.81
5000-171000
17
M3
m3
2-15
0.166
0.125
0.29-1.10
1.25-1.85
23000-171000
18
M3
m4
3-15
0.166
0.183
0.38-1.10
1.3-1.78
34000-171000
19
M1
m2
0.6-6
0.25
0.119
0.21-0.98
0.75-1.8
7000-69000
20
M1
m3
0.6-6
0.25
0.203
0.21-0.98
0.72-1.9
7000-69000
21
M1
m4
1-15
0.25
0.298
0.30-1.80
1.05-3.71
1000-171000
22
M2
m2
0.6-6
0.25
0.100
0.18-0.82
0.78-1.85
7000-69000
23
M2
m3
0.6-6
0.25
0.170
0.18-0.82
0.8-1.7
7000-69000
24
M2
m4
0.8-8
0.25
0.250
0.21-0.99
0.95-1.9
9000-91000
25
M3
m2
0.6-6
0.25
0.073
0.13-0.60
0.73-1.92
7000-69000
26
M3
m3
0.6-6
0.25
0.125
0.13-0.60
0.8-2
7000-69000
27
M3
m4
0.8-8
0.25
0.183
0.16-0.73
0.98-2.3
9000-91000
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Stefano Pagliara, Michele Palermo, and Ilaria Lotti
in such a quantity that could be gradually transported by the approaching flow. Tests were carried out with different discharges. At the beginning of each experiment, the ramp was completely clean as no filling material was present (initial condition). The experimental procedure is described by the following steps: 1) At the beginning, tests are conducted with a very low discharge value Q1 (Fig. 2a). The filling material is gradually dosed until the flow had not enough energy to transport it further downstream. The ramp slope changes in the upper part due to the material accumulation. For this step only the upper sectors of the ramp result filled of transported material. 2) The test is repeated increasing the discharge Q2 (Fig. 2b). In this case the supplied material is transported in further downstream sectors. Anyway, also in this case, the flow had not enough energy to transport filling material until the last section x/Lr =1. 3) The discharge is further increased until it reaches the value QF, defined as the “filling discharge” (Fig. 2c). QF results the minimum discharge which has enough energy to transport the supplied material until the last ramp section (x/Lr =1) and if a further quantity of material is inserted it is transported downstream of the ramp, without substantially varying the L.R. level reached in the various sectors of the ramp. This means that a condition of dynamic equilibrium is reached. In this configuration, for 0.25 < x/Lr QF (Fig. 2d). Also in this case, the sediment transport dynamic equilibrium described in the step 3 occurs and further supplied material is entirely transported downstream of the ramp. But the equilibrium level L.R. results to be lower than the one reached for QF. This means that the filling in this case is less than the one obtained for Q=QF. 5) The discharge is further increased up to Q4 (Fig. 2e), the same occurrence described in the step 4 is observed also in this case. The main difference is that the equilibrium level L.R. further decreases. 6) Increasing the discharge up to QE (Fig. 2f), the equilibrium level L.R. further decreases, reaching its minimum for 0.25 < x/Lr < 0.75. Thus, QE is defined as the “emptying discharge”. When this configuration is reached the only filling material that remains on the ramp is the one that is hidden by the ramp blocks or got trapped by them (filling percentage less than 15%). 7) A further increase of the discharge (Q5 in Fig. 2g) does not modify significantly the equilibrium level L.R. reached in the step 6, and the ramp configuration remains almost the same of that described in the previous step. Moreover, for each hydraulic condition and combination of ramp and filling material, the energy dissipation was evaluated
between sections 1-1 and 2-2, in order to compare it in case of filled and clean ramp conditions.
3. Results and Discussion 3.1 Evaluation of the “Filling” and “Emptying” Discharges (QF and QE) A similar analysis of the critical conditions for the incipient motion on a sloped bed in case of clean ramp (absence of filling material) was conducted by Bathurst et al. (1987). They proved that the unit critical discharge q can be expressed as function of the bed slope, the mean diameter of the material constituting the bed D50 and the gravitational acceleration g, thus resulting in the following functional relationship: q = f (g, D50, S)
(1)
When a filling material is present on the ramp another parameter has to be taken into account, i.e. the mean diameter d50 of the filling material, thus resulting in the following functional relationship: q = f (g, D50, S, d50)
(2)
rearranging in non dimensional parameters, k/D50 = f1 (d50/D50, S)
(3)
where k is the critical depth relative to the unit discharge q. According to the procedure illustrated in the previous paragraph, the values of the filling discharge QF and of the emptying discharge QE were collected for each run and the data were elaborated in order to find simple relationships to predict them. Surely, the uniform flow conditions are not strictly attained on the ramp but for design purposes a simplified approach is to consider the flow condition as uniform. This simplification is commonly adopted in literature for such structures (see also Rice et al., 1998). In the case in which filling material is present on the ramp, the functional relationship Eq. (3) was experimentally validated and both the non dimensional critical heights kF/D50 and kE /D50 were expressed as function of both the ramp slope and the ratio d50 / D50, in which d50 is the mean diameter of the filling material, D50 the mean diameter of block ramp material, kF and kE are the critical heights relative to the discharges QF and QE respectively. Moreover, for the limiting case d50/D50=1, it can be considered that the filling discharge coincides with that given by Bathurst et al. (1987) (see Eq. (4)), as in this case the filling material would have the same mean diameter of the blocks constituting the ramp and QF coincides with the discharge of incipient motion. The relationship of Bathurst et al. (1987) is the following: qF /(g · D503)0.5 = 0.15 ·S -1.12
(4)
where qF is the unit critical discharge of incipient motion for a uniform clean ramp. Thus, plotting kF /D50 versus d50 /D50 with the ramp slope S as parameter, it can be seen a clear trend of experimental data. In
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Sediment Transport on Block Ramp: Filling and Energy Recovery
fact, Fig. 3 shows that for the same value of the ratio d50 /D50, kF/ D50 increases if the ramp slope decreases. It means that, being the same filling and block ramp materials, a bigger discharge is needed to reach the dynamic equilibrium. Moreover, the same figure shows that, being the ramp slope constant, kF/D50 increases if the ratio d50/D50 increases. Thus proving that if the filling material mean diameter increases a bigger discharge is needed to reach the dynamic equilibrium, as to be expected. A simple relationship can be given to describe the physical phenomenon as follows: d50 ------D50 kF -------- = ---------------------------------------------------------d 50 D50 ( 3.54S + 0.11 ) + 0.23 ------D50
(5)
Fig. 4 shows an acceptable agreement between measured and calculated data of the unit discharge qF. The same methodology was adopted also to furnish a simple relationship to foresee the value of the emptying discharge QE. Also in this case kE/D50 was plotted versus d50 /D50 with slope ramp S as parameter. The same considerations done for kF /D50 are valid also in this case.
The following relationship, valid for 0.05 < d50/D50 < 0.35 is proposed: d50 ------kE D50 -------- = --------------------------------------------------------------d50 D50 0.0175 + ( 5.12S – 0.24 ) ------D50
(6)
Fig. 5 shows the ratio kE /D50 as function of d50 /D50 with ramp slope as parameter, whereas Fig. 6 shows that there is an acceptable agreement between measured and calculated data of unit discharge qE. It has to be noted that sediment transport formulae are generally empirical or semi empirical relationships and many authors noted that there is an objective difficulty to collect experimental data (and also to identify a unique criterion to fix the motion conditions). Thus, many relationships known in literature have standard deviations which are of the same order of the proposed Eqs. (5) and (6) (see also Whitehouse et al., 2000). 3.2 Block Ramp Filling Evaluation One of the aim of this paper is to evaluate the filling percentage Px/Lr (%) in different hydraulic and geometric conditions. The analysis was limited to the first six sectors of the ramp (0
