ABSTRACT
Previous studies have generally focused on abutments located on a straight channel. Few have focused on curved channels. The present study comprised an experimental examination of the local scour that occurs around different length abutments placed on the inner and outer banks along a curved channel in a clear-water scour flow condition. The local scour around an abutment in a curved channel is a function of the upstream Froude number, flow intensity, the angle of bend curvature, and the ratios of abutment length to flow depth, abutment length to abutment width, and abutment length to channel width. The maximum scour depth around the abutments placed on the outer bank was found to be 1.45 times the scour depth on the inner bank. An empirical equation was developed to consider all dimensional parameters for equilibrium scour depth. The average percent error of the proposed equation was 2%.
Keywords : Scour, bridge abutment, curved channel, clear-water scour, flow intensity.
1Assistant Professor, Dept. of Civil Engineering, Munzur Univ., ”, 62100, Turkey (corresponding author). E-mail:meralkorkmaz@munzur.edu.tr
2Professor, Dept. of Civil Engineering, Firat Univ., Elazig 23100, Turkey. E-mail:memiroglu@firat.edu.tr
Introduction
Bridges constructed to rapidly and reliably conduct intercity transportation are urgently needed, along with an increase in transportation requirements. However, destruction or damage to bridges causes loss of life and property and negatively affects the flow of life. One of the most important reasons for the collapse of bridges is scouring (Barbhuiya and Dey, 2004). A riverbed in the vicinity of a hydraulic structure is generally protected against current, waves, and eddies (Azamathulla, 2012). Scouring can occur at any time due to the flow of the stream, but is more likely to occur during floods. Scouring is a complex phenomenon resulting from the three-dimensional powerful interaction between the scouring mechanism and flow type around the bridge abutments and piers, erodible bed material, and the turbulence flow around the bridge foundation. Figure 1 shows the flow and scour pattern at an abutment.
Fig. 1. Flow and scour pattern around an abutment
Rosgen (1994) identified seven major categories of stream that differ in terms of entrenchment, gradient, width/depth ratio, and sinuosity in various landforms. Based on both static and dynamic characteristics, streams can be classified as follows: (1) straight streams (sinuosity < 1.1), (2) braided stream (\({\tilde{B}}^{0.5}\geq F_{1}\)), and (3) meandering streams (sinuosity > 1.5), in which\(\tilde{B}(=B.S_{o}/h_{d})\) is the nondimensional parameter,B is the average river width, hd is the hydraulic depth, S o is the bed slope, and F1 is the Froude number. Straight streams generally flow with a minimal number of turns. Most are meandering rivers as long straight streams are rare (Leopold and Wolman, 1957). The curve or curvature on an open channel creates additional flow resistance similar to that caused by bridge abutments placed on linear channels or by an increase in channel roughness. This change in flow resistance results in increased depth and reduced flow rate in the upstream. The backwater pressure effect is more pronounced at sharp curves that occur at the boundary layer separation of the outer bank near the downstream. Depending on the radius of the curve, a transverse inclination is formed on the water surface.
The problem of scouring is significant and has been investigated for many years. For instance, Damaskinidou-Georgiadou and Smith (1986) experimentally examined the velocity distribution in a curved canal. All their experiments demonstrated that maximum longitudinal velocities occurred in the inside bank, and it was the approach of the vertical mean velocity distribution along the channel width. Based on tests conducted over a long period of time, Melville (1992) classified the equilibrium scour depth (dse ) based on flow depth and abutment length. If La/y ≤ 1, it is known as short abutment; whereas if La/y ≥ 25, it is known as long abutment. The equation proposed by Melville (1992) to predict equilibrium scour depth (taking into account abutment length and approach flow depth) is:
\(d_{\text{se}}=2.K_{s}.L_{a}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ }\text{for\ }\text{\ \ \ }\frac{L_{a}}{y}\leq 1\)(1)
where dse is the equilibrium scour depth,Ks is the shape factor of the abutment,La is the abutment length, and y is the approach flow depth. Melville (1992) stated thatKs is 0.75 for a vertical wall with a semicircular end. Thus, dse is equal to\(1.50L_{a}\).
Urroz et al. (1994) studied the ice conveyance of a bridge location in a sinuous channel 0.254 m wide, 0.203 m deep, and with a radius of curvature of 0.92 m, while Kandasamy and Melville (1998) investigated the maximum scour depth that could occur at bridge abutments and piers. Cardoso and Bettess (1999) then studied the effects of time and channel geometry on scouring in bridge abutments. Oliveto and Hager (2002) proposed Eq. (2) for time-dependent scour depth at a vertical wall abutment.
\(\frac{d_{\text{se}}}{L_{R}}=0.085\sigma_{g}^{-0.5}F_{d}^{1.5}\log T_{d}\)(2) in which \(L_{R}={L_{a}}^{2/3}y^{1/3}\),\(F_{d}=V/{(gd_{50})}^{0.5}\), \(T_{d}=t/t_{R}\), and\(t_{R}=L_{R}/{(gd_{50})}^{0.5}\) , where Fd is the densimetric Froude number, V is the mean approach flow velocity,σg is the geometric standard deviation of the sediment (\(\sigma_{g}={(d_{84.1}/d_{15.9})}^{0.5}\)),d 84.1 is the particle diameter for which 84.1% of the sediment is finer, d 15.9 is the particle diameter for which 15.9% of the sediment is finer, t is time,d 50 is the mean grain size, g is the acceleration due to gravity, Δ is equal to (ρs /ρ )-1= (ρs -ρ )/ρ=ρ’s /ρ ,ρs is the mass density of sediment particles, andρ is the mass density of water.
Lim (1997) proposed an empirical equation of maximum equilibrium scour depth for vertical wall abutments, as shown in Eq. (3). This includes dimensionless maximum equilibrium scour depth and dimensionless length of abutment.
\(\frac{d_{\text{se}}}{y}=1.8\left(\frac{L_{a}}{y}\right)^{0.5}\)(3)
Coleman et al. (2003) investigated the scours formed around the bridge abutment under clear-water flow conditions while Seckin (2004) investigated bridge constrictions in a compound channel. The author proposed an empirical equation to estimate the backwater at bridge constrictions in compound channels with an overbank flow. Dey and Barbhuiya (2005) presented a semi-empirical model to determine the time variation of scour depth for La/y ≤ 1. The authors proposed Eq. (4) to calculate the equilibrium scour depth for semicircular abutment.
\(\frac{d_{\text{se}}}{L_{a}}=8.689F_{e}^{0.192}\left(\frac{y}{L_{a}}\right)^{0.103}\left(\frac{L_{a}}{d_{50}}\right)^{-0.296}\)(4)
in which Fe is the excess abutment Froude number, whichVe /(ΔgLa )0.5.Ve = V -ξVc andΔ = (ρs /ρ )-1. V is the average approaching flow velocity, and Vc is the critical velocity for sediment particles. The value of ξ is 0.6 for semicircular abutment.
Rajkumar and Dey (2005) conducted experiments using uniform and non-uniform sediments to investigate clear-water scouring in circular and square bridge piers and the time taken to reach the scour depth equilibrium. Their results showed that equilibrium depth was inversely proportional to the particle diameter. Furthermore, the time required for scour depth equilibrium on bridge abutments increased with the Froude number and particle diameter for uniform material and decreased in line with a decrease in the geometrical standard deviation of particle diameter distribution for non-uniform bed material.
Kayaturk (2005) investigated the local scouring around a bridge abutment. The study was conducted in a 30 m long and 1.5 m wide open channel. The test channel was filled with uniform bed material with a median particle diameter of d 50 = 1.48 mm. The sand depth was 0.5 m at the bridge abutment. Kayaturk reported that the lateral abutment length was a more significant parameter than the abutment width. The results showed that the scour depth was reduced when the width of the plates placed at different depths around the bridge abutments to reduce the local scour depth increased, and when the plate was placed at or below sand level. Kothyari et al. (2007) proposed a formula to calculate the time-based development of clear-water scouring. Experiments were conducted on two separate 11 m long rectangular channels of 1 m and 0.50 m width, respectively. Yanmaz and Kose (2007) conducted an experimental investigation into the clear-water scour around a rectangular cross section bridge abutment using uniform bed material. They measured the scour depth and contour, and provided the spatial and volumetric changes in the scour that formed around the bridge abutment. Based on the results, they proposed a placement location for the riprap to prevent scouring.
Sanjou and Nezu (2009) experimentally studied the horizontal vortex and secondary flow in meandering compound open channel flows. They stated that the mean velocity distribution between the straight stream and the meandering stream zone is substantially different. Several horizontal vortices occurred locally in a wide zone, including over the floodplains. The rotational direction of these vortices corresponds to the velocity shear at the vortex core. They may be inclined to the channel bed because the convection velocity varies in the vertical direction, and they then disappear as they have a short life span. Moreover, the secondary flows take place in the effective circulation motion in the main channel region. Vertical downstream flow from the abutment upstream also creates tailwater vortexes and horseshoe vortexes (Sanjou and Nezu, 2009).
Cardoso and Fael (2009) found that, at the end of tests they conducted under clear-water flow conditions, the scour would be negligible if the thickness of the riprap cover layer placed on the bridge abutment is equal to at least six times the riprap diameter. Ballio et al. (2009) examined the effect of a local scour around the bridge abutment over time and the effect of convergence in the abutment under clear-water scour flow conditions. Masjedi et al. (2010) investigated the phenomenon of scouring with a collar applied to the bridge pier in a 180° curved channel. This continued to create a scour due to the downstream effect and a complex vortex system formed via the interaction with the approaching stream. This vortex system extended towards the downstream along the edges of the abutment and is referred to as a horseshoe vortex due to its shape. Thus, the horseshoe vortex developed due to the separation of the flow at the scour hole formed at the downward side as a result of the downstream flow. The horseshoe vortex is similar to the downstream vortex system. As the scour depth increased, the strength of the horseshoe vortex decreased, leading to a decrease in sediment transportation from the abutment. Dehghani et al. (2013) reported that the obstruction caused by a groyne created a horseshoe-shaped vortex around the front and sides of the groyne. Wu et al. (2014) conducted experiments to examine the maximum scour depth under ice cover around bridge abutments. Armor layer grain size has a strong impact on the dimensionless maximum scour depth. As the particle size of the armor layer increased, the maximum scour depth decreased. Conversely, as the ice cover roughness increased, the maximum scour depth increased. The relationships between maximum scour depth, water depth, densimetric Froude number, ice cover roughness, and armor layer grain size are derived through dimensionless analysis. Pagliara et al. (2015) studied the scour phenomena in the downstream of log-vanes in straight rivers under clear-water flow conditions. The results demonstrated that the tailwater depth is an important variable in determining the maximum scour depth and the vane angle is an important parameter in predicting the scour parameters. Dimensional analysis allows the derivation of design equations used to estimate the maximum scour depth, maximum length of the scour, and the maximum height and length of the dune.
The existing literature shows that, despite the importance of the abutment of a bridge in a curved channel, little attention has been paid to studying the local scour in such a case. Most studies focus on the scour on bridge abutments located on straight streams. Only a few studies focus on meandered streams. The present study therefore comprised an experimental investigation of the local scour around a bridge abutment located on the inner and outer banks of the curved channel at bend angles of α = 30°, 60°, 90°, 120°, and 150°. The effects of the flow intensity (V/Vc ), bridge abutment length (La ), and bend angle (α ) on local scouring were investigated separately and in detail for the inner and outer banks.
Dimensional Analysis
Dimensions of scour depth formed around a bridge abutment along a curved channel can be expressed as a function of the following parameters;
\(d_{\text{se}}=f({V,\ V_{c},L}_{a},\ B_{a},\ B,S_{o},\alpha,\ r_{c},\ y,g,d_{50},\mathrm{\rho}_{\mathrm{s}}^{\mathrm{{}^{\prime}}}\ ,\sigma_{g},\rho,\mu,t,K_{s})\)(5)
where dse is the equilibrium scour depth,V is the mean approach flow velocity, Vcis the velocity of approach flow corresponding to the inception of sediment particle motion in the approach flow (the critical velocity),La is the length of the abutment,Ba is the width of the abutment, B is the main channel width, So is the channel bed slope,α is the angle of bend center, rc is the radius of main channel centerline, y is the water depth, gis the acceleration due to gravity, d 50 is the location on a non-cohesive sediment bed made of uniform grains with median grain size, \(\mathrm{\rho}_{\mathrm{s}}^{\mathrm{{}^{\prime}}}\)(=ρs -ρ ) is the buoyant sediment density,σg is the geometric standard deviation of the sediment, ρ is the mass density of water, μ is the dynamic viscosity of the water, t is the scouring time, andKs is the abutment shape factor.
The Buckingham Π-theorem applied to Eq. (5), choosing ρ, y , andV as basic variables, leads to a functional relationship in terms of the dimensionless groups shown in Eq. (6):
\(\frac{d_{\text{se}}}{y}=f(\frac{L_{a}}{y},\ \frac{V}{\sqrt{\text{gy}}},\ \frac{V}{V_{c}},\frac{B_{a}}{y},\frac{B}{y},\frac{r_{c}}{y},\frac{\mathrm{\rho}_{\mathrm{s}}^{\mathrm{{}^{\prime}}}}{\rho},\frac{\text{V.y}}{\nu},S_{o},\sigma_{g},\frac{\text{V.t}}{y},\frac{d_{50}}{y},\ \alpha,\ K_{s})\)(6)
Melville (1995) proposed a shape factor Ks to express the effects of different shaped abutments on the scour. He gaveKs = 0.75 for a vertical wall abutment with a semicircular end. In the present study, the experiments were designed for an oblong abutment and therefore Ks was constant. In free surface flows, the influence of the Reynolds number in terms of viscous effects on the local scour process can be considered negligible (Melville and Chiew, 1999). The flume has constant slope. The radius of main channel centerline (rc ) in the current study was constant. Therefore, these terms were dropped.
\(\frac{d_{\text{se}}}{y}=f(\frac{L_{a}}{y},F_{d}=\frac{V}{\sqrt{g\left(\frac{\mathrm{\rho}_{\mathrm{s}}^{\mathrm{{}^{\prime}}}}{\rho}\right)d_{50}}},\frac{V}{V_{c}},\frac{L_{a}}{B_{a}},\frac{L_{a}}{B},\frac{\text{V.t}}{y},\ \alpha)\)(7)
In the equilibrium condition, the increase in dimensions of the scour geometry stops and remains unchanged. Equation (7) can be written as follows:
\(\frac{d_{\text{se}}}{y}=f(\frac{L_{a}}{y},\ F_{d},\ \frac{V}{V_{c}},\frac{L_{a}}{B_{a}},\frac{L_{a}}{B},\ \alpha)\)(8)
or
\(\frac{d_{\text{se}}}{L_{a}}=f(\frac{L_{a}}{y},\ F_{d},\ \frac{V}{V_{c}},\frac{L_{a}}{B_{a}},\frac{L_{a}}{B},\ \alpha)\)(9)
in which the scour depth is normalized with flow depth and abutment length, as shown in Eqs. (8) and (9).
Experimental Setup and Methodology
All experiments were conducted in a curved channel with an axis curvature radius of 3 m at Firat University, Hydraulic Laboratory. The curved channel width was 0.50 m. The main channel depth was 0.50 m. The channel bed slope (S o) was 0.1%. The bridge abutment was placed on the inner and outer walls of the channel with bend angles of 30°, 60°, 90°, 120°, and 150° in section I (see Fig
. 2). Bridge abutments placed on the curved channel were produced using plexiglass material. The oblong bridge abutment wasBa = 8 cm wide, 50 cm high, and three different abutment lengths were selected: La = 8, 10, and 12 cm. The tip of the abutment was semicircular with a diameter of 8 cm (Fig. 3).
Fig. 2. Experimental setup
Fig. 3. Oblong bridge abutment dimensions and the abutment placed in the channel
Quartz sand 0.25 m in height was placed between the 1st and 2nd sills on the main channel, as illustrated in Fig. 2. The uniformly graded sands used in the experiments had median diameters d 50 = 1.16, 1.34, and 3.72 mm with threshold shear velocities \(u_{c}^{*}\ \)= 2.725, 3.046 and 5.708 cm/s, respectively. The uniformity coefficient (Cu =d 60/d 10) for the sediment used was less than 3. Sediments withCu ≤ 3 were considered to be uniform. The geometric standard deviation σg of the sediment given by (d 84.1/d 15.9)0.5was less than 1.4 for uniformly graded sediment.
Prior to each experiment, the sand was mixed and the bed was leveled. The desired discharge was adjusted with a valve and measured using a Siemens brand electromagnetic flowmeter with ± 0.01 L/s sensitivity. Water for the curved channel was supplied through a pipe from a sump. A Mitutoyo brand digital point gauge with ± 0.01 mm sensitivity was used to measure water level and bed topography. Bed topography variations were measured using the digital point gauge in the abutment region. Thus, readings could be taken in both x and y directions using a special type of measurement car that moved on rails. Figures 4 and 5 show the reading spots along the curved channel and the scouring phenomenon in 3D bed topography.
Fig. 4. The bed topography measurement spots on the inner bank
Fig. 5. 3D presentation of the scour formed at the bed topography measurement spots on the inner bank and post-experimental image
The bridge abutment was placed in a curved channel on the inner and outer banks at 30°, 60°, 90°, 120°, and 150° bend angles. A series of experiments were then conducted for different abutment lengths and different flow rates under clear-water flow conditions. The main objective of these experiments was to examine the local scour depths around different length oblong abutments placed on the inner and outer banks of the channel bend. The required flow value and flow depth for predetermined flow rates were then obtained. In the first experiment, the flow rate was adjusted rapidly using the valve and flowmeter on the main channel. The butterfly valve at the end of the curved channel was initially closed and then opened slowly after the flow and flow depths were determined and flow conditions were established. The test period began after the predetermined flow depth was established. Scour depths were investigated over time and bed topography formed around the abutment was obtained when the equilibrium scour depth was established. The changes in scouring in a curved channel were examined using maximum scour depths measured as dimensionless parametersds /La andt /tm after the bridge abutment was put in place.
The critical velocity (Vc ) values that could set the bed material in motion at various flow depths were obtained using Eq. (6) given by Melville (1997),
\(V_{c}/u_{c}^{*}=5.75\log\left(5.53\ y/d_{50}\right)\) (10)
where \(u_{c}^{*}\) is the critical shear velocity. Melville (1997) proposed Eq. (10) for\(u_{c}^{*}\) (m/s) for \(1\ mm<d_{50}<100\ mm\).
\(u_{c}^{*}=0.0305d_{50}^{0.5}-0.0065d_{50}^{-1}\) (11)
Critical shear velocity (\(u_{c}^{*}\)) was calculated as 0.02725 m/s from Eq. (11) for d 50 = 1.16 mm. Equation (12) was obtained for d 50 = 1.16 mm. The critical velocity equations were similarly calculated for other median diameters. Equation (12) was tested and verified in the experimental setup.
\(V_{c}=0.1567\log\left(4767y\right)\) (12)
  1. Analysis of Results
  2. The impact of flow intensity on scour depth
In the literature, clear-water scour experiments are preferred to live bed scour experiments as they provide a steady state, greater scour depth, and a clearer idea for designers (Raudkivi and Ettema, 1983; Coleman et al., 2003; Rajkumar and Dey, 2005; Pagliara et al., 2015).
In Fig. 6 (a-f), the change in t /tmrelative to ds /La was plotted for different flow intensities V/Vc . This graph is provided for bend angle α = 60° and for both inner and outer banks and different abutment lengths. In the case of clear-water scouring, it was observed that the dimensionless scour depth increased in line with the increase in flow intensity. The scour depth initially rapidly increased over time, after which it continued asymptotically until, eventually, the change in scour depth was minimal. Thus, the scour depth reached an equilibrium. The time taken to achieve this depended on the dimensionless flow intensity (V /Vc ) and the dimensionless particle size (d50 /y ). Most of the maximum scour depth occurred up until t /tm was equal to 0.2. When t /tm was0.6, the asymptote was formed. As shown in Fig. 6 (a-f), scouring was higher on the outer bank. The impact of the secondary flow was extremely significant in this problem. One of the main reasons why the curved converging channel can be successfully used as a sediment excluder is that the secondary flow, which develops upstream from the diversion, is strong enough to move any particles traveling along the bed towards the inside wall and away from the canal entrance. Damaskinidou-Georgiadou and Smith (1986) found that the maximum longitudinal velocities occurred in the inside bank, and the values of mean longitudinal velocity approximated to a free vortex along the channel.
Fig. 6. Changes in t /tm andds /La based on differentV /Vc values for α =60°
Figure 6 shows that the effect of the flow intensity (V/Vc ) on the maximum scour depth for 60° was consistent with the literature (Melville and Chiew, 1999). Tsujimoto and Mizukami (1985) reported that the scour depth under clear-water flow conditions initially increased and then continued as an asymptote after a certain period of time. Maximum scour depth also increased in line with increasing flow intensity (V/Vc ). Table 1 presents the results of the experiment on variations in scour depth due to flow intensity at the curved channel bends at 30°, 60°, 90°, 120°, and 150° for d 50 = 1.16 mm. As shown, the maximum scour depth at all corners of the curved channel increased in line with flow intensity.