Local scour around complex abutments

ISH Journal of Hydraulic Engineering ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/tish20 Local scour around complex abutments Reza Mohammadpour, Aminuddin Ab. Ghani, Tooraj Sabzevari & Mohamad Fared Murshed To cite this article: Reza Mohammadpour, Aminuddin Ab. Ghani, Tooraj Sabzevari & Mohamad Fared Murshed (2021) Local scour around complex abutments, ISH Journal of Hydraulic Engineering, 27:sup1, 165-173, DOI: 10.1080/09715010.2019.1607783 To link to this article: https://doi.org/10.1080/09715010.2019.1607783 Published online: 26 Apr 2019. Submit your article to this journal Article views: 203 View related articles View Crossmark data Citing articles: 2 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=tish20 ISH JOURNAL OF HYDRAULIC ENGINEERING 2021, VOL. 27, NO. S1, 165–173 https://doi.org/10.1080/09715010.2019.1607783 Local scour around complex abutments Reza Mohammadpour a,b , Aminuddin Ab. Ghani c , Tooraj Sabzevaria and Mohamad Fared Murshedb a Department of civil engineering, Estahban Branch, Islamic Azad University, Estahban, Iran; bSchool of Civil Engineering, Universiti Sains Malaysia, Engineering Campus, Nibong Tebal, Malaysia; cREDAC (River Engineering and Urban Drainage), Universiti Sains Malaysia, Engineering Campus, Nibong Tebal, Malaysia ABSTRACT ARTICLE HISTORY Local scour around complex abutment and pier is the main reason for bridges to collapse. Although the complex abutment/pier has been used in most rivers, there is limited research in the literature about the flow pattern and local scour at complex abutment/pier. In this study, a series of experimental test was conducted to predict local scour at complex abutments and provided results were compared with complex piers. The trend of local scour at compound abutments and piers was similar and considerably sensitive to the foundation level (Z). The top of foundation stops development of scour depth for several hours which depends on the abutment/pier size (L), foundation size and its level (Lf and Z). The minimum scour depth was observed for 1.0 < Z/L < 1.5. A novel equation with high accuracy (R2 = 0.97 and RMSE = 0.06) was developed for prediction of local scour at compound abutment based on effective length. This research highlights that the bridge cost can be reduced with a suitable design for the foundation level. Received 21 February 2019 Accepted 10 April 2019 1. Introduction Local scour at compound abutment and pier is the main reason for bridge failure. Due to financial and geotechnical reasons, a foundation or pile cap is located under actual abutment and pier (Coleman 2005; Ashtiani and Beheshti 2006; Ashtiani et al. 2010). A rectangular compound pier is a rectangular bridge pier resting on a larger foundation or caisson. Kumar et al. (2012) reported that due to the effect of shape, the flow pattern around compound piers is more complicated than the uniform pier. Numerous studies have been carried out on abutments/piers with uniform cross-section and many equations are suggested for prediction of the local scour (Froehlich 1989; Lim 1997; Sturm and Janjua 1994; Barbhuiya and Dey 2004; Mohammadpour 2013a, 2013b, 2013c; Mohammadpour et al. 2014b; Azamathulla et al. 2010, 2014; Dehghani et al. 2013; Gendaszek et al. 2013). Lately, a number of studies reported local scour at compound piers under clear-water conditions (Sheppard et al. 1995; Jones 1989; Parola et al. 1996; Coleman 2005). Melville and Raudkivi (1996) recommended a procedure for prediction of local scour depth at compound piers, identifying three levels for foundation relative to the existing bed level (Figure 1). Melville and Coleman (2000) showed that scour depth increases with increasing pile cap level. Jones and Sheppard (2000) proposed a superposition method for forecasting scour depth around the pilesupported pier. They showed that local scour around the compound pier is equal to the summation of local scour around all components such as pier column, pile cap, and pile group. The effect of pile group on local scour around compound pier was studied by Coleman (2005) and Akib et al. (2014). Ashtiani et al. (2010) employed a wide range of pile cap to determine the effect of pile cap level on the local scour at compound piers. Mohammadpour (2017) employed two techniques of M5-tree and Gene Expression CONTACT Reza Mohammadpour © 2019 Indian Society for Hydraulics reza564@gmail.com KEYWORDS Local scour; complex abutment; complex pier; bridge foundations; scour time; mechanism of scour Programming (GEP) for the prediction of local scour at compound piers. The result indicated that for practical purposes, the equations provided by GEP and M5-Tree are more useful and can be easily employed for prediction the local scour at complex piers. There are few research conducted on the local scour at compound abutments (Mohammadpour et al. 2014a, 2016; Ghani and Mohammadpour 2015; Mohammadpour et al. 2017). The Federal Highway Administration (FHWA) recommended that the abutment foundation should be located below scour-resistant rocks or ripraps (Richardson and Davis, 2001). However, the flow usually erodes ripraps during a flood and due to scour caused by the abutment the foundation may be exposed to flow (Ettema et al. 2010). It can be concluded that if the effect of foundation or pile cap taken into account, the conservative method will not be necessary. Therefore, a new approach is necessary for the prediction of scour depth at complex abutments by considering both abutment and foundation sizes. The main objective of this research is to compare the local scour around complex abutments and piers. All experiments were conducted for vertical wall abutment which is located on a foundation with a rectangular shape at a different level. To find the mechanism of local scour, the time variation of depth of scour around both compound piers and abutment were compared. Finally, a novel equation was recommended to predict local scour at compound abutments. 2. Dimensional analysis The following parameters are the main independent variables to estimate scour depth at abutment in open channel:
ds ¼ f L; U ; y ; Uc ; d50 ; g ; ρ ; ν ; σ D ; ρs ; KG ; Kθ ; Ks (1) 166 R. MOHAMMADPOUR ET AL. where, L = abutment length; U = mean flow velocity, y = approach flow depth; Uc = critical velocity; d50 = median size of sediments; g = the gravity acceleration; ρ = fluid density; ν = kinematic viscosity; σ D = the sediment standard deviation; ρs = the sediment density; KG = the coefficient of channel cross-section geometry; Kθ = alignment coefficient and Ks = shape coefficient. If the bed material is composed of uniform material with d50 > ≈0.6, ρs  constant and σ D < 1.5–1.8 then ρs and σ D can be eliminated (Cardoso and Fael 2010). The following relationship can be developed using Buckingum’s-π theorem:  2  ds U y d50 ; ; ¼f ; Kθ ; Ks ; KG (2) gd50 L L L If a vertical-wall and right angle abutment is used then the effect of angle and shape will be negligible (Kθ = 1; Ks = 1). In uniform flow condition and wide rectangular channel, the KG has no effect on scour depth. Finally, Equation (2) can be rewritten as:  2  ds U y d50 ; ¼f ; (3) L L gd50 L Melville (1992) and Simarro et al. (2007) reported that in the channel with uniform sediment, the ratio of I = U/Uc Figure 1. Complex pier configuration. Figure 2. Three cases for complex abutment below the initial bed. can be used instead of U 2 =gd50 , therefore the Equation (3) can be expressed as follows:   ds y U d50 ; (4) ¼f ; L Uc L L Three cases are shown in Figure 2 for complex abutment when the foundation level is located under the initial bed. In Case I, the top of the foundation remains below the maximum scour depth, therefore the foundation size and its level have no effect on the scour depth. In Case II and Case III, the foundation is exposed within the scour hole and it is similar to an obstacle or armour layer in front of down flow, then the local scour is typically less than Case I. However, in these cases (Case II and III), the foundation changes the flow pattern around complex abutment and the scour depth depends on both abutment dimensions (Bu and Lf) and foundation level (Z). Therefore Equation (4) can be expressed as follows:   ds y U d50 Lf Z Bu ; ; ; ¼f ; (5) ; L Uc L L L L L where Bu = extension of foundation at upstream of the abutment; Lf = foundation length (Figure 2). In this study, short abutments were chosen and the effect of water depth (y/L) is ignorable. Melville and Coleman (2000) showed that ISH JOURNAL OF HYDRAULIC ENGINEERING for L/d50 > 50 the effect of sediment size (d50/L) is negligible. Hence, Equation (5) can be described as follows:  Lf Z Bu ds U ¼f ; ; ; Uc L L L L  (6) 3. Experimental setup A laboratory flume with 6.0 m long, 0.6 m deep, and 0.6 m wide was selected for all experiments. The flume was equipped with a 0.25 m deep sand recess (Figure 3). Several energy depleting screens were designed at the flume entrance for reduction of flow turbulence. To adjust the flow depth, a controlling gate was used at the end of the flume. A camera inside the abutment and a transparent ruler were employed to detect variation of scour depth with time at the nose of the abutment (Figure 4). As shown in Table 1, four short compound abutments (FA) with L/y < 1 and three uniform abutments (AB) were considered in this study. The uniform sediment was selected in all experiments with σD = 1.2 and d50 = 0.60 mm. To remove the effect of flow depth on scour depth, a value of 120 mm was selected for flow depth (y) and in this conditions ratio of L/y is less than 1. A point gauge was used to measure the topography of scour hole with an accuracy of  1 mm. To maintain the clear water condition, the ration of U/Uc was selected between 0.94 and 1. Three cases were chosen to determine the foundation level effect on the complex abutment. As shown in Figure 2, the location of foundation in Case I is below the maximum scour depth. In Case II, the top of the foundation is reached to the scour hole, and in Case III, the foundation is located between the initial bed and maximum scour depth (within the scour hole). To determine the test duration required, two long-time tests with t ~ 67 h (4004 min) and ~84 h (5080 min) were performed for uniform abutments of AB-II and AB-III. Figure 5 shows the time variation of scour depth at AB-II and AB-III. The result indicates that after 2500 min (42 h), approximately 96% of the scour has occurred. According to Oliveto and Hager (2002), development of the scour hole never stops. Ettema (1980) indicated that in the equilibrium time, the scour depth is approximately fixed. Therefore, the time of 42 h was selected as a criterion for semi-equilibrium time in all experiments. Figure 3. Laboratory flume. 167 4. Local scour at the complex abutment In this study, the experiment conditions and its results are shown in Table 2. In this table, the uniform and compound abutments are represented by AB and FA, respectively. The maximum depth of scour (ds) in terms of foundation level (Z) is shown in Figure 6. In this figure, both axes are normalized using abutment length (L). In Case I, where Z/ L ≥ 2.0, the level of the foundation is under the scour hole and the maximum depth of scour is always above the top of foundation, then the flow pattern around compound abutment is similar to the uniform abutment. In Cases II and III, the top of the foundation exposes to scour hole, therefore the dimension of foundation effects on the vortices around the abutment. Starting from Z/L ≈ 2.0 and then decreasing, the foundations gradually rises to the hole of scour and relatively scour depth (ds/L) decreases and reaches to Z/L ≈ 1.0. In Case II (1 ≤ Z/L < 2), the horseshoe vortices are weakened by the foundation and the scour depth will be reduced. In this case, the top of foundation stops development of scour depth, then the maximum depth is in the level of foundation (ds = Z). In Case III, the foundation level ratio is located between 0.0 and 1.0 (0 < Z/L < 1) and it rises more within the hole of scour. Due to the presence of the foundation within a hole of scour, a strong vortex is formed in front of the abutment and increasing the depth of scour. Generally, in this Case, the relative scour depth (ds/L) increases with decreasing Z/L. In Case III, the scour depth around a compound abutment is also dependent on the foundation length (Lf). For instance, in FA 33 and FA 43 the dimensions of the abutment are similar (L = 7.0 cm) while the dimension of foundation for FA 43 (Lf = 12.0 cm) is bigger than FA 33(Lf = 9.0 cm). The results show that the uniformity of complex abutment is depended on the foundation size and the uniformity increases with reduction of the dimension (FA 33), therefore, the principle vortices produced by the foundation in compound abutment of FA33 are smaller than those produced by FA43. Consequently, the scour depth for FA 33 is less than those for FA43. The main causes of the local scour at pier or abutment are the down-flow and principal vortex at upstream of these structures. The results show that the location of the foundation is the main case to increase or decrease the depth of 168 R. MOHAMMADPOUR ET AL. Table 2. Summary of experimental results for the present study. Figure 4. transparent abutment and ruler with a camera. Table 1. Abutment-geometry characteristics for the present study. Foundation Experiment No. AB 1 AB 2 AB 3 FA 21 FA 33 FA 42 FA 43 Lf (cm) – – – 5.5 9.0 12.0 12.0 Bf (cm) – – – 11.0 18.0 24.0 24.0 Case I I I II III III II II II III III II II III III II II III III III Experiment AB I AB II AB III FA 21 FA 21 FA21 FA33 FA33 FA33 FA33 FA33 FA42 FA42 FA42 FA42 FA43 FA43 FA43 FA43 FA43 Q (lit/sec) 18 18.6 16 18 18.3 18.4 21.4 17.7 19.4 18.5 18 21.3 17.65 20.8 20 18.5 17.9 18 18.4 18.5 U/Uc 0.96 0.98 0.95 0.96 0.96 0.98 0.94 0.98 0.97 0.96 0.95 0.94 0.99 0.99 0.98 0.95 0.97 0.97 0.96 0.95 L (cm) 4 5.5 7 4 4 4 7 7 7 7 7 5.5 5.5 5.5 5.5 7 7 7 7 7 Z (cm) – – – 1.5 3.5 5 3 3.5 7 8 9 3 5 7 8 3 5 7 8 9 L/y 0.36 0.5 0.72 0.36 0.36 0.38 0.54 0.66 0.61 0.62 0.64 0.42 0.54 0.46 0.46 0.62 0.65 0.64 0.63 0.62 Z/L – – – 0.38 0.88 1.25 0.43 0.50 1.00 1.14 1.29 0.55 0.91 1.27 1.45 0.43 0.71 1.00 1.14 1.29 ds/L 1.68 1.73 1.68 1.50 0.88 1.25 1.93 1.47 1.07 1.14 1.29 1.98 1.33 1.27 1.45 2.07 2.01 1.00 1.14 1.29 Abutment L (cm) 4.0 5.5 7.0 4.0 7.0 5.5 7.0 B (cm) 8.0 11.0 14.0 8.0 14.0 11.0 14.0 Length ratio L/Lf – – – 0.73 0.78 0.46 0.58 Figure 6. Scour depth as a function of top elevation of the foundation. 5. Compound abutments in comparison with compound piers Figure 5. Time variation of scour depth at the abutment of AB-II and AB-III. scour in front of the complex abutment. Melville and Raudkivi (1996) reported similar results for the compound pier. In Case III where 0 < Z/L < 1, the foundation is similar to an obstacle and decreases the effects of principle vortices. Although the foundation reduces the effect of principle vortex, the maximum depth usually occurs in the nose of the compound abutment and this location is independent to the foundation or abutment size. This is due to maximum shear stress in the nose of the compound abutment. On average, the bed shear stress near the nose of a uniform abutment is amplified nearly 3.63 times (Ahmad and Rajaratnam, 2000). Figure 7 shows local scour and sediment deposition around FA 21 and FA 43. It can be observed that topography of local scour around abutment is sensitive to the level and size of the foundation. To compare local scour around compound pier and abutment, a set of experimental data was collected from previous study given by Chabert and Engeldinger (1956), Coleman (2005), Jones et al. (1992), Melville and Raudkivi (1996), Parola et al. (1996), and Ashtiani et al. (2010). Table 3 shows a summary of the collected dataset for compound pier and abutment. As shown in this table all data for the compound pier is collected from the previous study, whereas the data for a compound abutment is selected from this study. The range of length ratio for compound abutment (L/Lf) and piers (D/Df or bc/bpc) is between 0.46 and 0.82. A comparison between local scour around compound abutments and piers is shown in Figure 8. Melville and Coleman (2000) reported that the maximum scour depth at uniform piers and the abutment is 2.4D and 2L, respectively. Therefore it can be concluded that for foundation level bigger than these values the foundation has no effect on scour depth and the local scour at compound abutment/pier is similar to uniform abutment/pier. 169 ISH JOURNAL OF HYDRAULIC ENGINEERING Figure 7. local scour topography around complex abutment (a) FA 21; (b) FA 43. Table 3. Summary of experimental data. Researcher(s) Ashtiani et al. (2010) Coleman (2005) Parola et al. (1996) Melville and Raudkivi (1996) Chabert and Engeldinger (1956) FA-42 FA-43 FA-33 FA-21 Shape Rectangular Pier Rectangular Pier Circular Pier Circular Pier Circular Pier Rectangular abutment Rectangular abutment Rectangular abutment Rectangular abutment Flow depth (cm) 14 to15.5 d50 (mm) 0.60 33 to 60 0.84 15.0 0.58 20.0 0.80 10.0 1.50 10 to13 0.60 10 to13 0.60 10 to13 0.60 10 to13 0.60 Dimension (cm) bc = 4.20 bpc = 9.00 bc = 10.00 bpc = 19.00 D = 3.75 Df = 7.50 D = 3.00 Df = 6.30 D = 4.90 Df = 8.00 L = 5.50 Lf = 12.00 L = 7.00 Lf = 12.00 L = 7.00 Lf = 9.00 L = 4.00 Lf = 5.5 length ratio 0.47 to 0.54 U/Uc 0.72 to 0.85 Experiment time (hr) 10.5 to 75 0.53 0.72 to 0.85 – 0.50 ~1 8.00 0.48 to 0.82 ~1 >34 0.61 ~1 8 to 20 0.46 0.94 to 0.99 43 to 53 0.58 0.95 to 0.97 37.5 to 59 0.78 0.94 to 0.98 36 to 57 0.73 0.96 to 0.98 36 to 50 Figure 8. Comparison of scour depth between complex abutment and pier. As shown in Figure 8 the trend of variation for both abutment and pier is similar. The result indicates that the scour depth around compound abutments can be qualitatively and quantitatively compared with those for compound piers. Starting from Z/L (or Z/D) = 2.4, the scour depth (ds/L or ds /D) decreases with decreasing Z/L to reach a minimum value at Z/L between 1.0 and 1.5. In this range, for U/Uc close to 1.0, all points will be located on the line of ds = Z. Generally, the maximum scour depth occurs in threshold condition (U/Uc ≈ 1) and for some cases with a small value of U/Uc, the scour depth is less than those for U/Uc ≈ 1.0. For example the points in the hatched area in Figure 8, the value of U/Uc is less than 0.80 and all points are under the line of ds = Z. This fact shows that for the low value of U/Uc the foundation level has no effects on the local scour since the maximum local scour depth is higher than foundation level; and the foundation remains under the scour hole (ds < Z). As shown in Figure 8, after the minimum value of ds/L, the trend increases with a decrease in foundation level (Z/L). 170 R. MOHAMMADPOUR ET AL. Mohammadpour (2017) reported that the flow pattern at complex pier can be classified into four elements, foundation horseshoe vortices, pier horseshoe vortices, down-flow, and wake vortices (Figure 9). The main causes for the development of scour hole at complex pier and abutment are the down-flow and the pier horseshoe vortices. It is expected that with the increasing level of foundation on the bed, the scour depth increases due to the formation of more vortices in front of the foundation. However, more investigation is needed to find the effect of foundation on complex piers and abutments. 6. Development of scour with time Figure 10 illustrates the time variation of scour depth at compound abutments, the results indicate that the local scour increases with increasing time. Normally, the scour depth develops to the upper surface of the foundation and in the next step, the extension of foundation in front of abutment decreases the vortices strength and delays development of local scour. In FA 42, for a big value of Z (AB-II in Table 2), the scour hole at a uniform and compound abutment are similar to each other (Case I, Figure 2). For Z/L = 1.27 (Z = 7 cm) and Z/L = 1.45 (Z = 8 cm), the foundation is located within the scour hole and depth of scour reaches to the top of the foundation. The maximum scour depth in these cases is equal to Z. Finally, for Z/L = 0.55 (Z = 3cm) and Z/L = 0.55 (Z = 5cm), the foundation postpones scour time which depends on foundation level (Case III). For FA 42 and Z/L = 0.55 (Z = 3.0, Table 2), the depth of scour reaches to the top of the foundation after 30 min and stays at this level for around 7 h. In this step, the flow develops the scour hole parallel to the abutment and in the flow direction. The horseshoe vortices enlarge the area of local scour in front of the abutment and upstream side of the foundation. The vortices create and gradually develop a groove with a small depth parallel to the foundation in the flow direction. Subsequently, due to the formation of vortices, the scour depth increases at the upstream part of the foundation. The sediments around foundation are translated to abutment downstream by the flow and the scour hole gets bigger and deeper due to the effect of vortices. Figure 9. Flow pattern around complex pier (Mohammadpour 2017). 7. Time variation of local scour around compound piers and abutments Figure 11 shows a comparison between the compound abutment of FA 42 with L= 5.5 and Lf = 12.0 cm (L/Lf = 0.46) and piers gave by Melville and Raudkivi (1996) with a dimension of D = 3.0 and Df = 8.1 cm (D/Df = 0.37). The variation of scour depth at abutment with Z = 3.0 cm is shown in Figure 11(a). The provided result is compared to three compound piers with Z = 2.5, 3.0, and 3.5 cm. The results show that time variation of scour depth at compound abutment and pier is similar. The scour depth is developed to the upper surface of foundation and then the foundation stops it for several hours which is recognized as the lag time at this study. Lag time duration is around 400 and 100 min for compound abutment and pier, respectively. With increasing time of scour, the scour depth increases and the flow carries the sediments around the foundation to downstream. Due to the large size of the compound abutment, development of scour depth at abutment is bigger and faster than those at the compound pier, it increases dramatically and reaches to 11.0 cm after approximately 2000 min (33 h). Figure 10. Development of scour depth around the complex abutment. ISH JOURNAL OF HYDRAULIC ENGINEERING 171 Figure 11. Time variation of local scour at complex abutment FA 42 and pier. (a) Foundation level for abutment Z = 3.0; (b) Foundation level for abutment Z = 5.0. In Figure 11(b) the complex pier with Z = 5.0 and 6.5 cm is compared to FA 42 with Z = 5.0 cm. The dimension of compound abutment and pier is similar to Figure 11(a). In compound pier, the scour depth is confined by the top of foundation and variation of scour depth after 500 min is approximately fixed. The large dimension of compound abutment contributes to generating strong vortices and the scour depth is increased after 500 min. It can be concluded that although the extension of foundation in front of pier/ abutment decreases the strength of vortices produced by pier/abutment, big size of pier/abutment has a huge effect on the scour depth. 8. Estimation of scour depth at a compound abutment As mentioned in the last section, the variation of scour depth around compound abutments is similar to compound piers. Therefore, the recommended approach for compound piers has been used to develop an equation for prediction of local scour around compound abutment. Generally, the suggested method by Melville and Coleman (2000) was previously used in a wide range of conditions. The following equation was suggested based on experimental data to predict the scour depth at short abutments (L/y < 1): ds ¼ 2L Kd KI Kθ Ks Kt KG Le ¼ Lðy þ ZÞ þ Lf ðds ds þ y ZÞ (8) Melville and Coleman (2000) reported that the maximum scour depth at abutment is ds = 2L. In this study, a value of ds = 2mL is considered for compound abutment then another form of Equation (8) can be expressed as: Le ¼ Lðy þ ZÞ þ Lf ð2mL 2mL þ y ZÞ (9) Figure 6 shows that the scour depth can be divided into three parts. In Case I, the maximum scour depth is equal to 2L (uniform abutment). In Case II, The maximum depth of scour is equal to the level of foundation (Z). Finally, in Case III, the scour depth is smaller than 2L. It can be concluded that the value of m should be equal to 1.0 in Case I and less than 1 in Case II and III. Melville and Raudkivi (1996) suggested the method of trial-and-error to determine m value. This value is determined equal to 0.3 using the collected data and trial-anderror method. Therefore the equations of effective length (Le) at compound abutment can be expressed as follows: Le ¼ L Le ¼ Z 2 for Z=L  2 (10) for 1  Z=L < 2 (11) (7) where L = abutment length; Kd = sediment size factor; KI = flow intensity factor; Kθ = abutment alignment factor; Ks = abutment shape factor; Kt = time of scouring and KG = channel geometry factor. This approach can be used to estimate local scour at compound abutment if the effective length of the abutment (Le) is used instead of abutment length (L). The effective length is the length of the compound abutment that produces similar scouring at uniform abutment. Melville and Raudkivi (1996) recommended the method of weighted average for estimation of the effective length. In this method, the effective length is a weighted average of both foundation and pier diameters and the exposed length is used as the weighting factor. Yaroslavtziev (Maza Alvarez 1969) recommended a similar technique for a pier with a rectangular shape that is located on a rectangular foundation. Therefore, the following equation was developed for a compound abutment: Le ¼ Lðy þ ZÞ þ Lf ð0:6L 0:6L þ y ZÞ for 0 < Z=L < 1 (12) Equation (12) indicates that for a similar size of the foundation and abutment (L = Lf) the effective length will be abutment length (Le = L). Finally, the following equation can be used to predict local scour at compound abutments: ds ¼ 2 Kd KI Kθ Ks Kt KG Le (13) A comparison between observed and calculated scour depth using recommended equations is shown in Figure 12. The recommended method predicts the local scour at complex abutment with in high accuracy (R2 = 0.97 and RMSE = 0.06). The results indicate that the suggested method can be easily used with high precision in practical proposed. This research highlights that with a suitable design for the foundation level, not only the conservative 172 R. MOHAMMADPOUR ET AL. Figure 12. Predicted and observed (Experimental) local scour around the complex abutment. approach would be unnecessary but also bridge cost can be reduced. 9. Conclusions The local scour depth at complex pier and abutment is the main reason for bridge failure. In this study, local scour at complex abutment was investigated with different dimension for abutment and foundation. The obtained results showed that time variation of local scour at compound abutments and piers are similar to each other and considerably sensitive to the foundation level (Z). Three cases for scour depth were recognized in terms of foundation level. In both compound abutment and pier, the scour depth is developed to the upper surface of foundation and then the foundation stops it for several hours which is recognized as the lag time at this study. The lag-time duration is depended to the foundation size (Lf), abutment/pier size (L) and foundation level (Z). Furthermore, in both compound pier and abutment, the minimum depth of scour was observed for 1.0 < Z/L < 1.5. The results indicated that with a suitable design for foundation level, bridge cost can be considerably reduced and the conservative approach is unnecessary. Finally, Equation (8) with high accuracy is recommended to predict local scour at compound abutment. Disclosure statement No potential conflict of interest was reported by the authors. ORCID Reza Mohammadpour Aminuddin Ab. Ghani http://orcid.org/0000-0002-7940-5101 http://orcid.org/0000-0002-8912-9569 References Ahmed, F., and Rajaratnam, N. 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