DETERMINATION OF LOCAL SCOUR DEPTH OF PROTOTYPE CYLINDRICAL PIER USING PHYSICAL MODEL DATA COLLECTION

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 9, September 2018, pp , Article ID: IJCIET_09_09_124 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed DETERMINATION OF LOCAL SCOUR DEPTH OF PROTOTYPE CYLINDRICAL PIER USING PHYSICAL MODEL DATA COLLECTION Dr. Ihsan A. Abdulhussein Assistant Professor, Basrah Engineering Technical College Southern Technical University Rafi M. Qasim Basrah Engineering Technical College Southern Technical University ABSTRACT Rivers can be considered as a very important natural hydraulic system conveys water. During water motions the bed material mixture will be subjected to erosion force and erosion processes will reflect especially on the behavior of any structural element that constructed in this region. Thus, the bridge pier is influenced by scouring processes. In order to study the hydraulic effect and interaction between stream flow and depth of scouring, many researchers working on scouring processes theoretically and experimentally. Some researchers predict equations based on experiments to calculate scour depth depend on the model (small scale). The present research is focused to convert collection data of previous works from model to prototype (large scale) by two different methods depend on linear scale factor (length scale ) and (roughness scale ) supported by dynamic similitude. During conversion processes, scour depth is considered as dependent variable while flow velocity, water depth, pier diameter and particle size are considered as independent variables. The authors are derived three predict equations which build on data result obtained from conversion. These equations give a good agreement with Froehlich formula. Because two different criteria adopted in the conversion from model to prototype, the Sheppard-Melville method is adopted to check the type of scour for model and prototype. In spite of the two methods give a good agreement between model and prototype, but during the investigation, it is observed that the type of scour will change regardless of flow field type. Also, all the results of large-scale scour depth are checked with maximum potential scour, and they are found mostly be the less value. Key words: Prototype Cylindrical, Pier, Physical Model, Data Collection editor@iaeme.com

2 Determination of Local Scour Depth of Prototype Cylindrical Pier Using Physical Model Data Collection Cite this Article: Dr. Ihsan A. Abdulhussein and Rafi M. Qasim, Determination of Local Scour Depth of Prototype Cylindrical Pier Using Physical Model Data Collection. International Journal of Civil Engineering and Technology, 9(9), 2018, pp INTRODUCTION The components of the total scour are long term aggradation and degradation, contraction scour, and local scour. The resultant depth from local scour is always larger than the other two, often by a factor of ten. The local scour comprises of clear-water scour and live bed scour. The maximum depth of clear-water scour is greater than live-bed scour by about 10 percent. Because of the equations predict the maximum scour, there is no need to increase the scour depths. The bed material size, flow characteristics, fluid properties and the geometry of the pier are the main factors that affect local scour at piers. The scour at piers is studied extensively in the laboratory and a number of investigations in field. There are many equations implemented from these studies which give similar results. These equations will be as follows, Colorado State University's (CSU) equation (Richardson et. al. 1975, 1988), Jain and Fisher's (1979) equation, Graded and/or armored streambed equations, Froehlich's (1987, and 1988) equations, and Sheppard et. al. (2014) equations. These equations are compared with field data measurements. The CSU equation encloses all the observed data and estimates lower, more reasonable, values of scouring than Jain, Laursen and Niell's equations [1]. Kaya (2010) investigated different input variables with various ANNs models, the sensitivity analysis indicated that pier scour depth can be estimated using four variables: pier shape, pier skew, flow depth and flow velocity [2]. Several researchers study the above four variables (Chabert and Engeldinger, 1956) [3], (Dey et. al.,1995) [4], (Maatooq J. S., 1999) [5], (Mia and Nago, 2003) [3], (Yanmaz and Altinbilek, 1991) [6], and (Khassaf and Abdulwahab, 2016) [7]. The above studies concluded that, the depth of local scour increases as the diameter of the pier, flow velocity, and depth of water increases and the size of particles decreases. In this research, equations are implemented to convert the values of different input variables (pier diameter, flow velocity, flow depth and size of particles) from model (small scale) to equivalent prototype values (large scale). Further, the prototype values are treated to find equations used to predict the value of local scouring for any given prototype state variables mentioned above. 2. METHODOLOGY (DYNAMIC SIMILITUDE FOR MODEL AND PROTOTYPE) The relationship between the full-scale physical system (prototype) and its smaller version having similar or partially similar boundaries (model) is investigated. Physical model studies of a proposed fluvial system are frequently undertaken in the laboratory as an aid to the design engineers. If accurate quantitative results are to be obtained from a laboratory model study, there should be a thorough dynamic similitude between the model (small scale) and the prototype (large scale) [8]. To achieve a desired similitude between the model (small scale) and the prototype (large scale), scaling laws or criteria of similitude must be fulfilled. If a model and its prototype are identical in shape but differ only in size, it is represented by the geometric similarity of the editor@iaeme.com

3 Dr. Ihsan A. Abdulhussein and Rafi M. Qasim model and prototype, keeping the corresponding angles the same, all dimensions are replicated at the same scale. What requires to be deliberated most toward a geometric similar model is that the flow feature is to be geometrically similar [8]. Method 1: The linear dimensions Lp of the prototype to the corresponding dimensions Lm of the model are transformed by a length scale Lr, such that: Lp = Lr. Lm (1) Here, subscripts p, m, and r denote the prototype, model, and ratio of the prototype to model conditions, respectively. The requirements for kinematic similarity between the model and the prototype are that, along with geometric similarity, similar velocities at all corresponding points in the flow field must be found. Therefore, it is the similitude between the parameters involving space and time, implying that the velocity scale Ur is: Ur = Vp/Vm (2) The clear water scour at circular piers of the model will depend directly on Reynolds number, Froud number and flow intensity. ( ) Where (Re) m is the Reynolds number of the model, U m is the flow velocity of the model (m/sec), h m is the flow depth of the model (m), and (V) is the kinematic viscosity of the water (m 2 /sec). If Reynolds number greater than 1400 the flow is turbulent (Allen, 1947). ( ) Where (Fr) m is the Froud number of the model, and (g) is the acceleration due to gravity (m/sec 2 ). Froud number divided into three categories depending on its value, if Fr less than 1 the flow considered as subcritical, else if Fr equal 1 the flow consider as critical and if Fr greater than 1 the flow considered as supercritical flow. Due to shear resistance or friction force which is developed when flow occurs above grain media, therefore, it is necessary to utilize the relationship between the shear velocity of particles media and critical water flow velocity. The shear velocity of the media can be obtained using the following equations ( Melville, 1997 ) [9].When d 50 is greater than 0.1mm and less than 1mm, the following equation used to compute the critical shear velocity of media particles in the model and prototype. ( ) (5a) When is greater than 1mm and less than 100mm, the following equation used to the computation of the critical velocity in the model and prototype. = ( ) ( ) -1 (5b) The critical water flow velocity (V c ) can be obtained from the equation (Melville & Sutherland 1988) [10]. ( ) (6) Where, V c is the critical flow velocity (m/sec), V *c is the critical shear velocity (m/sec.) for media particles, y is the flow depth which is equal to in model and d 50 is the median diameter of particle size (mm). (3) (4) editor@iaeme.com

4 Determination of Local Scour Depth of Prototype Cylindrical Pier Using Physical Model Data Collection Having calculated the value of V c, the flow intensity (V/V c ) is computed. If this ratio less than 0.5, no scour occur, whereas if (V/V c ) greater than or equal 0.5 and less than or equal 1, then the scour occurs and the local scour type in the model is the clear water scour. Then, if (V/V c ) is greater than 1, the scour occurs and the local scour type in the model is the live bed scour [11]. Additionally, if water flow velocity is less than or equal to critical flow velocity then clear water scour will occurs, whereas if water flow velocity is greater than critical flow velocity then live bed scour will occurs [12]. For the prototype all assumption must check based on the Reynold number, Froud number and flow intensity. Also, the length scale and velocity scale are defined in equations 1 and 2 respectively. For the computation of Fr or Re, the length L must be a specific characteristic length that is significant in the flow field. For an open channel flow, the gravity force is the determining law. Hence, the Froude number Fr is the relevant nondimensional number or the similitude criterion (scaling law) being extensively used in model studies. Using a Froude similitude criterion, the velocity scale can be obtained as: (7) (8) (9) (10) ( ) ( ) (11) When d 50 is greater than 1mm and less than 100mm, the following equation used to compute the critical shear velocity of the particles media in the prototype. ( ) ( ) (12) ( ) (13) Where, y is the flow depth which is equal to in the prototype. Having calculated the values of V c the ratio of flow intensity (V/ ) is computed. This ratio greater than or equal 0.5 and less than or equal 1, then the scour occur and the local scour type in the model is the clear water scour. The value of local scour in the prototype can compute as follow: ( ) ( ) (14) Example Design The data obtained from (Dey, 1995) [4] included the followings: A long sand-bed model carries a flow with a flow depth of m and flow velocity of m/sec. If the median size of sand is 0.26 mm, the diameter of the single cylinder is m, and the result local scour depth is m, simulate a prototype model for arbitrary length scale. Dynamic Similitude For the model, d 50 =0.26 mm, Dm=0.057 m, Vm= m/sec, hm = m, with (ds)p = m. From equation (3) and for kinematic viscosity of (10-6 m 2 /sec) (Re)m=6020. Since (Re)m greater than 1400, so the flow in the model is turbulent. Then, from equation (4) the value of (Fr)m= 0.29, and because of (Fr)m less than 1, the flow is subcritical. The value of V *c and the corresponding value of Vc are calculated using equation (5) and (6) and it found equal to m/sec and m/sec, respectively. The ratio (Vm/Vc)=0.778, and since this ratio greater than 0.5 and less than 1, the scour occurs and the type is clear water scour. For the prototype, the length scale is selected arbitrarily to be Lr = 50. The velocity scale is computed using equation (7) and it is found equal to Ur = Then, the prototype flow velocity and flow depth are calculated using equations (8) and (9) and found equal to Vp=1.216 m/sec and hp = 1.75 m, respectively. From equations (10) and (11), the prototype editor@iaeme.com

5 Dr. Ihsan A. Abdulhussein and Rafi M. Qasim pier diameter and bed material size are calculated and equal to Dp= 2.85 m and (d 50 )p = 13 mm, respectively. The prototype Reynold's number (Re)p= , and since (Re)p greater than 1400, so the flow in the prototype is turbulent. The prototype Froude number is (Fr)p= and because of (Fr)p less than 1, the flow is subcritical. The value of V *c and the corresponding value of Vc are calculated using equation (12) and (13) and it found equal to m/sec and m/sec, respectively. The ratio (Vp/Vc)=0.672, and since this ratio greater than 0.5 and less than 1, the scour occurs and the type is clear water scour. Finally, the prototype depth of scour is calculated from equation (14) and found equal to (ds)p=2.6m. Method 2 The complete geometric similarity in many problems on sediment transport is a difficult proposition. For instance, the sediment particles of a small model could not be reduced in proportion, maintaining a length scale. For such situations, the term most frequently used is geometric distortion in which a model has a departure from a scaling law by not satisfying one or more of the geometric similarities [8]. Model distortion in three dimensions thus implies a different horizontal Lxr, lateral Lyr, and/or vertical Lzr length scales, according to a Cartesian coordinate system. Here, x, y, and z are stream wise (that is, horizontal or longitudinal), span wise (that is, transverse), and vertical coordinates, respectively. The roughness scale (geometric distortion) is calculated as follow [8]: dr= ( ) ( ) Where, dr is particle length scale (roughness scale), (d 50 )p is prototype particle size (mm), and (d 50 )m is model particle size (mm). The range of dr is assumed between one and small value above zero to ensure the same media for both model and prototype. Thus, all the generated values of (d 50 )p will be less than or equal (d 50 )m. For modeling of rivers, as reported by (Stevens et. al, 1942) [8], the horizontal scale (Lxr) should be always greater than vertical scale (Lzr). The range of Lxr should be between (100 to 2000) whereas the range of Lzr between (50 to 150). The relation linked between Lxr and Lzr is as follow : dr= Also, the velocity scale, prototype flow velocity, prototype flow depth, prototype pier diameters and prototype scour depth can be obtained as follow: (15) (16) Ur= Lzr 0.5 (17) Vp= Ur. Vm (18) hp= hm. Lzr (19) Dp= Dm. Lzr (20) (ds)p= (ds)m. Lzr (21) The values of (Re)m, (Re)p, (Fr)m, and (Fr)p are calculated using equation (3) and (4). The critical flow velocity can be calculated from the equation (22) which adopt by FHWA [13]. Because it comprises all soil particle diameter and the critical flow velocity will compare with mean flow water velocity. Additionally, if water flow velocity less than or equal critical flow velocity clear water scour occurs, while if water flow velocity greater than critical flow velocity live bed scours occurs [12]. Also, the critical flow velocity at which grain media begin to move can be calculated by using the following formula [13] editor@iaeme.com

6 Determination of Local Scour Depth of Prototype Cylindrical Pier Using Physical Model Data Collection = 6.19 (22) Where, represents the critical flow velocity of water above bed material at which cohesionless grain move, y represents the water flow depth and D represents the particles diameter of mixture or. Example Design The data obtained from (Yanmaz and Altinbilek, 1991)[6] included the followings: A long sand-bed model carries a flow with a flow depth of m and flow velocity of m/sec. If the median size of sand is 1.07 mm, the diameter of the single cylinder is m, and the result local scour depth is m, simulate a prototype model for arbitrary roughness and horizontal length scale. Dynamic Similitude For the model, d 50 =1.07 mm, Dm=0.047 m, Vm= m/sec, hm = m, with (ds)p = m. From equation (3) and for kinematic viscosity of (10-6 m 2 /sec) (Re)m=14925> 1400, so the flow in the model is turbulent. Then, from equation (4) the value of (Fr)m= < 1, the flow is subcritical. The value of Vc of the model is calculated using equation (6b) and it found equal to 0.38 m/sec. The value of Vm= m/sec, and since this value less than Vc, the scour occurs and the type is clear water scour. For the prototype, the roughness scale is assumed to be equal to 0.8. Then, by using equation (15) the value of (d 50 )p=0.856 mm. The horizontal length scale is selected arbitrarily to be Lxr = 200. Therefore, the vertical length scale is calculated using equation (15) and found equal to (Lzr=50). The velocity scale is computed using equation (17) and it is found equal to Ur = Then, the prototype flow velocity and flow depth are calculated using equations (18) and (19) and found equal to Vp= m/sec and hp = 3.25 m, respectively. From equation (20), prototype pier diameter is calculated and equal to Dp= 2.35 m. The prototype Reynold's number (Re)p= > 1400, so the flow in the prototype is turbulent. The prototype Froude number is (Fr)p= 0.288< 1, the flow is subcritical. The value of Vc of the prototype is calculated using equation (6b) and it found equal to 0.68 m/sec. The value of Vp=1.628 m/sec, and since this value greater than Vc, the scour occurs and the type is live bed scour. Finally, the prototype depth of scour is calculated from equation (21) and found equal to (ds)p=2.05m. Model Verification One of the important purposes of the present work is to estimate an equation from the data results from dynamic similitude used to compute the prototype local scour (ds)p for any given data ( (d 50 )p, Dp, Vp, and hp). The predictions of the estimated equations are compared with Froehlich (1988) formula [14]: ( ) ( ) ( ) ( ) ( ).. (23) Where, K 1 the coefficient taking in the account the pier shape, g the acceleration due to gravity, d 50 the median grain size, D the diameter of the pier, V the flow velocity, and h the flow depth. Froehlich (1988) classified his data as to being either clear-water or live-bed scour data on the basis of Neill's (1968) equation which compute the value of critical mean velocity (Vc). If Vc is larger than the mean velocity of the flow, then the scour would be clear water scour. In actuality, all the clear water scour depths in the data that Froehlich used were less than the magnitude of Vc. Therefore, the live bed pier scour equation developed by Froehlich, can be used for clear-water scour also [1] editor@iaeme.com

7 Dr. Ihsan A. Abdulhussein and Rafi M. Qasim Another method used to estimate the depth of scour is Sheppard et. al. (2014). This method proposed the following equations to predict the depth of scouring [8]...(24a) [ ( ) ( )] (24b)..(24c) Where b e is the effective pier diameter and U peak is the live bed flow velocity. The equations and procedure to calculate the values of f 1, f 2, f 3, U cr, and U peak can found in [8]. Also, we should be known that there are three categories of pier flow field, which produce significantly different pier scour morphologies; narrow piers, transitional piers, and wide piers [13]. In term of estimating a potential maximum scour depth, related to the scale of the pier flow filed, the Sheppard- Melville method simplifies to: (( ) ).(25) The value of scour should be less than the maximum potential scour depth [13]. Efficiency Criteria In this section, the efficiency criteria used in this study are presented and evaluated. These are the two criteria: coefficient of determination, Nash-Sutcliffe efficiency, together four modified forms that may prove to provide more information on the systematic and dynamic errors present in the model simulation. 1. Coefficient of determination r 2 The coefficient of determination r 2 is defined as the squared value of the coefficient of correlation according to Bravais-Pearson. It is calculated as (Krause, 2005) [16]: ( )( ) { } (26) ( ) ( ) With O observed and P predicted values. The range of r 2 lies between 0 and 1 which describes how much of the observed dispersion is explained by the prediction. A value of zero means no correlation at all whereas a value of 1 means that the dispersion of the prediction is equal to that of the observation. The fact that only the dispersion is quantified is one of the major drawbacks of r 2 if it is considered alone. A model which systematically over- or under predicts all the time will still result in good r 2 values close to 1.0 even if all predictions were wrong. If r 2 is used for model validation it, therefore, is advisable to take into account additional information which can cope with that problem. Such information is provided by the gradient (b) and the intercept (a) of the regression on which r 2 is based. For a good agreement the intercept a should be close to zero which means that an observed runoff of zero would also result in a prediction near zero and the gradient b should be close to one. In method 1 the intercept is closer to zero but the gradient is only 0.85 which reflects the under prediction of 15% at most time steps. For a proper model assessment, the gradient b should always be discussed together with r 2. To do this in a more operational way the two parameters can be combined to provide a weighted version (w r 2 ) of r 2. Such a weighting can be performed by: editor@iaeme.com

8 Determination of Local Scour Depth of Prototype Cylindrical Pier Using Physical Model Data Collection { ) (27) By weighting r 2 under- or over predictions are quantified together with the dynamics which results in a more comprehensive reflection of model results. 2. Nash-Sutcliffe efficiency E The efficiency E proposed by Nash and Sutcliffe (1970) is defined as one minus the sum of the absolute squared differences between the predicted and observed values normalized by the variance of the observed values during the period under investigation. It is calculated as [16]: ( ) ( ) (28) The range of E lies between 1.0 (perfect fit) and 1. An efficiency of lower than zero indicates that the mean value of the observed time series would have been a better predictor than the model. The largest disadvantage of the Nash-Sutcliffe efficiency is the fact that the differences between the observed and predicted values are calculated as squared values. As a result, larger values in a time series are strongly overestimated whereas lower values are neglected (Legates and McCabe, 1999) [16]. For the quantification of runoff predictions, this leads to an overestimation of the model performance during peak flows and an underestimation during low flow conditions. Similar to r 2, the Nash-Sutcliffe is not very sensitive to systematic model over- or under prediction especially during low flow periods, (Krause, 2005) [16]. 3. RESULTS AND DISCUSSION The phenomenon of fluid- grain media interaction is considered as complex matter due to the interaction between the factors that control the process of sour regardless of these factors related to the pier, bed sediment, flow condition, and fluid. The target of this paper is represented by extraction of large-scale (prototype) from small-scale (model). This can be carried out by the built program have the ability to convert the model to prototype taken into consideration the fundamental concept of similitude. This program feed by collection data obtains from previous experimental work. Scale length basically the main point which controls the conversion and supported by flow intensity or critical velocity which determine the type of scour. Depending on flow intensity scour can be classified into three type, if the flow intensity less than 0.5 no scour occurs, when flow intensity have ranged between (0.5-1) clear water scour occurs, and if the flow intensity greater than 1 live bed scour occurs. Additionally, if water flows velocity less than or equal critical flow velocity clear water scour occurs, and if water flow velocity greater than critical flow velocity live bed scour occurs. The occurrence of scours bed material can be considered as mobile material. The convert can be performed by two methods. The first method adopts the length scale factor while the second adopt the particle length scale. The main feature of this conversation based on the values of Froude number and Reynolds number will not equal to unity. For mobile material, the following criteria must be satisfied or inevitable these criteria are resistance, Froude number, and Reynolds number. The experimental data obtained from previous researchers shown in Table (1) is used to carry out the dynamic similitude between model and prototype using the procedures explained in method 1 and 2. The primary goal of the present study is to convert the experimental data and its results of the model to equivalent prototype values. In order to accomplish this goal, a Fortran 90 program has been written and implemented to input all the data and model equations required for conversion. Also, the compatibility between model and prototype with respect to flow condition and type of scour has been observed editor@iaeme.com

9 Dr. Ihsan A. Abdulhussein and Rafi M. Qasim The scale factor and roughness factor are the important parameters control the conversion process. The values of scale factor used are ranges between (Lr=30 to 100) with the step equal to 5 in method1, while the values of roughness factor range between (dr=0.1 to 1) with the step equal to 0.1 in method2. By using the above values of Lr and dr, and the input data as shown in Table 1, the predicted (prototype) values of ((d 50 )p, Dp, Vp, hp, and (ds)p) are obtained. Then, the input data (model) and predicted values (prototype) should examine for flow condition and type of scour. The number of data set generated by method1 is around 2880 whereas the data set generated by method2 is Appendixes (1) and (2) illustrate the input data model and its prediction values with the flow condition and type of scour for method1 and method2, respectively. Table 1 Range of Input Data Model Range of Range of Input Data (model) No. of Output The Researcher Data Dm Vm hm (ds)m (d 50 )m (cm) (m) (m) (m) (m) Chabert and Engeldinger Dey et. al Maatooq J.S Mia and Nago Yanmaz and Altinbilek Khassaf and Abdulwahab The obtained result in Appendix (1) shows that the turbulent flow is satisfied for both model and prototype and this depends on the values of length scale. It is necessary to assume or select scale such a way to maintain turbulent flow, and the value of Froude number of the model should matching the value of prototype. In spite of the coincide in Froude and Reynolds number respectively, it does not have to be similar in type of scour. This reflects the vital role of flow intensity or critical velocity and grain diameter. Appendix (2) shows flow characteristics which are similar to Appendix (1). In second method result shows turbulent flow and subcritical flow. This depends on the selection one degree of freedom in the solution of the problem and the obtained result will not conflict with confirmation of turbulent flow. We inferred that the selection values of particle scale will reflect on the values of laboratory data and this has significant effect on result. Due to matching in flow characteristics between two conversion methods regardless of flow intensity and critical velocity limitation the obtained result can be considered as comparable value take in consideration the way of check in method (1) which depend on flow intensity differed from the method (2) which depend on critical velocity Derivation of New Formulas The main goal of any experiment is making the results as widely applicable as possible in the field conditions. Based on the procedures and ideas that are discussed above and by using the data resulted from the dynamic similitude (method1) and by assisting with curve expert professional software, the first formula is derived: ( ) ( ) (29) editor@iaeme.com

10 Determination of Local Scour Depth of Prototype Cylindrical Pier Using Physical Model Data Collection The coefficient of determination (r 2 ) for this formula is (0.97) whereas the value of the weighted coefficient, wr 2, and coefficient of intersection are and respectively. This result indicated the good agreement between computed and calculated data and reflecting the perfect simulation better than r 2 alone. For the dynamic similitude (method2) and by assisting with curve expert professional software, the relationship is: ( ) ( ) (30) The coefficient of determination (r 2 ) for this formula is (0.97) whereas the value of the weighted coefficient, wr 2, and coefficient of intersection are and 0.26 respectively. This result indicated the fair agreement between computed and calculated data and reflecting the good simulation better than r 2 alone. Then, the data obtained from method1 and method2 are merged and the regression is carried out to derive the following formula: ( ) ( ) (31) The coefficient of determination (r 2 ) for this formula is (0.942) whereas the value of the weighted coefficient, wr 2 and coefficient of intersection are 1.0 and 0.19 respectively. This result indicated the perfect agreement between computed and calculated data and reflecting the good simulation better than r 2 alone. It is well-known that most of the practical problems of the fluvial system are highly intricate in nature so that a desirable solution of the hydrodynamic equations is rather hoping against hope. Even on many occasions, the equations are not at all applicable. The obvious benefit of using a laboratory model is that if it is carefully fabricated representing a simulated miniature prototype, and then it could lead to a much more accurate prediction being applicable to that field. Figures 1 to 3 show that the values of the coefficient of determination r 2, are 0.94, 0.93 and 0.96 while the values of the weighted coefficients, wr 2, are 0.85, 0.83 and 0.84 for method1, method2 and merge method respectively. Also, the values of intercept (a) are 0.03, and 0.08 for method1, method2 and merge method respectively. These results are reflecting the fair simulation better than r 2 alone and the predictive results are underestimation by about 15%. The values of the Nash-Sutcliffe efficiency E are 0.9, 0.83 and 0.91 for method1, method2 and merge method respectively. This results indicating that this criterion is not very sensitive to the quantification of systematic under prediction errors editor@iaeme.com

11 Dr. Ihsan A. Abdulhussein and Rafi M. Qasim

12 Determination of Local Scour Depth of Prototype Cylindrical Pier Using Physical Model Data Collection Figures 4 to 6 show the matching between the predictive values and Froehlich formula, with the perfect agreement lines and the ±10%, ±15%, and ±20% bands for method1, method2 and merge method respectively. The percentage of simulated points located over, inside and below the band is presented in Table 2. For example, data obtained from method2 yields in 84%, 16% and 0% of simulated conditions ±15% furnishes respectively values smaller than, almost equal to, and higher than those given by the Froehlich formula ( equation 23) in the same condition. The agreement between predictive values and Froehlich formula can be considered as strong, moderate or weak if 75 to 100%, 50 to 75% and 0 to 50% of simulated points fall inside the ±10% band, respectively. Table 2 shows that a strong agreement between the two formulae is never found. Only the method1 is in moderate agreement, with only 50% of simulated data falling inside the ±15% band. Also, method1 and merge method are in moderate agreement, with only 63% and 58% of simulated data falling inside the ±20% band. The other simulated data show weak agreements. The Froehlich formula produced overestimations with respect to the predictive value in most simulated conditions editor@iaeme.com

13 Dr. Ihsan A. Abdulhussein and Rafi M. Qasim Table 2 Percentage of Points falling inside the asymmetric band Equation -10% to 10% -15% to 15 % -20% to 20% Method 1 62, 34, 4 48, 50, 2 36, 63, 1 Method 2 92, 8, 1 84, 16, 0 72, 28, 0 Merged 76, 23, 1 58, 41, 1 41, 58, 1 Table (3) gives additional verification between the extraction prototype data and showing comparison between obtain predict equations in this work the minimum range of equation 31 is the same as the minimum range of first convert method which adopts (equation 29) while the maximum range of equation 31 is same as of second convert method which adopts (equation 30) this mean equation 31 have intermediate position. Table 3 The Minimum and Maximum Values of Prototype Output Method D50p (m) Dp (m) Vp (m/sec) Yp (m) Dsp (m) Equation (m) Min. Max. Min. Max. Min Max Min. Max. Min. Max Min. Max. Method Method Merged Velocity Level and Maximum Potential Scour This work includes two ideas the first convert the model to prototype and the second predict equation to calculate scour depth. During conversion from model to prototype two different methods are used to implement this conversion depend on and. Also, two different methods are used to determine the type of scour (clear or live bed) depend on flow intensity or comparison between critical and mean flow velocity respectively. As shown in Appendix 1 and 2, the type of scour is similar for both conversion methods for the model (clear) but different for the prototype (clear, bed, and no scour). But if we consider additionally variable which is defined by live-bed peak flow velocity as mentioned in the Sheppard-Melville method, the type of scour change from clear to bed during conversion or remain without change clear or bed for both model and prototype respectively. Therefore, Sheppard-Melville method is used to check the type of scour and the variation in the type of scour related to variation in velocity level. Figures (7-9) preview the conversion date of the prototype which extraction by and collected model data are compared with maximum potential scour and scour depth which calculated from the Sheppard-Melville method. It is evident from these figures that the conversion data limited by maximum potential scour at the top and the obtained scour depth from the Sheppard-Melville method in the bottom. This is accepted results because it avoids conflict with the permissible limit of maximum potential scour. Figure (9) shows the value of conversion data above the upper limit (Max. potential scour) in some regions. This due to the calculated maximum potential scour depth depends on water depth and pier diameter while the calculated scour depth in the present study depends on flow velocity, particles diameter, water depth and pier diameter. Also, it is clear from figures (10-12) that the conversion data of prototype which extraction by and collected model data are located below the upper limit. Figures (13-16) representing the comparison between equation (31) with Froehlich formula, Sheppard-Melville method and maximum potential scour depth. This figures based on data collected from the range of conversion prototype data. These figures are drawn to show the variation of scour depth with any independent variables (d50p, Dp, Vp, and hp). Figures 13 and 14 show the relationship between the depth of scouring with pier diameter and editor@iaeme.com

14 Determination of Local Scour Depth of Prototype Cylindrical Pier Using Physical Model Data Collection depth of water respectively. Equation (31) is bounded by Froehlich formula at the top and Sheppard-Melville method at the bottom, so this equation gives an accepted prediction and always this equation below the maximum potential scour. The same result is obtained from figure 15 which represent the relationship between scour depth and particles size while figure 16 which represents the relationship between scour depth and flow velocity shows equation (31) exceeds the maximum potential scour because this equation depends on flow velocity as compare with equation of maximum potential scour depth (equation 25). In spite of equation (31), Froehlich, Sheppard-Melville depends on flow velocity but equation (31) overtaken Froehlich and Sheppard-Melville due to change in velocity level and exponential value of velocity in equations will reflect on resultant of scour depth. In spite of the change in scour type, figures from 13 to 15 prove that the predict equation (31) always below maximum potential scour taken in consideration the pier flow field type

15 Dr. Ihsan A. Abdulhussein and Rafi M. Qasim

16 Determination of Local Scour Depth of Prototype Cylindrical Pier Using Physical Model Data Collection

17 Depth of Scour (m) Dr. Ihsan A. Abdulhussein and Rafi M. Qasim Authers Shepperd Potential Froehlich Velocity (m/sec) Fig. (16) Variation of scour depth with velocity for D50p=0.001m, Yp=5m, Dp=1m 4. CONCLUSIONS The diameter of pier and flow velocity has the major effect on the scour around pier while water depth has the minor effect. The selection of scale factor in the extraction of the prototype has a vital role in the computation of fluvial hydrodynamics parameters. Froude number and Reynolds number satisfy dynamic similarity and do not equal to unity. The second conversion includes the large range of particles size diameter as compared with the first conversion. For large scale the obtained value of scouring generally less than the maximum potential scour. The change in scour type related directly to flow velocity level at the field as compare with critical flow velocity. Turbulent flow can be considered as the sufficient and necessary condition for the obtained prototype. The predict equations give an accepted result as compare with Froehlich (1988) and Sheppard et.al. (2014) formula. Pier flow field has a significant effect on scouring type and scours value. LIST OF SYMBOLS ds Depth of scouring around the pier d 50 Median size of the sediment particle Fr Froude number g Acceleration due to gravity D Diameter of pier Re Reynolds number V Mean approach flow velocity Vc Critical velocity V*c Critical shear velocity of media particles editor@iaeme.com

18 Determination of Local Scour Depth of Prototype Cylindrical Pier Using Physical Model Data Collection h Flow depth μ Dynamic viscosity Lr Length scale Ur Velocity scale dr Roughness scale Lxr Horizontal scale Lzr Vertical scale REFERENCES [1] Richardson, E. V., and Richardson, J. R. (2000) "Bridge Scour" Civil Engineering Dept., Colorado State University, Collins, Colorado. [2] Kaya, A., (2010) Artificial Neural Network Study of Observed Pattern of Scour Depth around Bridge Piers. Computers and Geotechnics, 37: [3] Mia, M.F. and Nago, H., (2003) "Design Method of Time Dependent Local Scour at Circular Bridge Pier" Journal of Hydraulic Engineering, Vol.129, NO.6, pp [4] Dey, S., Bose, S.K. and Sastry, L.N., (1995) "Clear Water Scour at Circular Piers: Model", Journal of Hydraulic Engineering, Vol. 121, NO.12, pp [5] Maatooq, J.S. (1999) "Evaluation, Analysis and New Concepts of Scour Process around Bridge Piers", Ph.D. thesis, University of Technology, Iraq. [6] Yanmaz, A.M. and Altinbilek, H.D., (1991) "Study of Time-Dependent local Scour Around Bridge Piers" Journal of Hydraulic Engineering, Vol. 117, NO.10, pp [7] Khassaf, S. I. and Abdulwhab, A. Q. (2016) "Modeling of Local Scour Depth Around Bridge Piers Using Artificial Neural Network", Advances in Natural and Applied Sciences, July 10(11): [8] Dey, S. (2014) "Fluvial Hydrodynamics: hydrodynamic and sediment transport phenomena". Springer-Verlag Berlin Heidelberg. [9] Melville, B W Pier and abutment scour: Integrated approach. Journal of Hydraulic Engineering 123(2): [10] Melville, B W & Sutherland, A J Design method for local scours at bridge piers. Journal of Hydraulic Engineering, 114(10): [11] Breusers, H. N. C, Nicollet, G., and Shen, H. W. (1977) "Local Scour around Cylindrical Piers." J. of Hydraulic Research, Vol. 15, No. 3, pp [12] Raudkivi, A.J. (1986) Functional Trends of Scour at Bridge Piers Journal of Hydraulic Engineering, Vol.112, NO.1, pp [13] Arneson, L.A., Zevenbergen, L.W., Lagasse, P.F., and Clopper, P.E. (2012) "Evaluating Scour at Bridges" fifth edition. Publication NO. FHWA HIF , Hydraulic Engineering Circular NO.18. [14] Muller, D. S., and Wagner, C. R. (2005) "Field Observations and Evaluations of Stream Bed Scour at Bridges." Published No. FHWA-RD [15] Ettema, R., Constantinescu, G., and Melville, B. (2011) " Evaluation of Bridge Research: Pier Scour Processes and Predictions" NCHRP web-only document 175. [16] Krause1, P., Boyle D. P., and ase1 F. B (2005) "Comparison of different efficiency criteria for hydrological model assessment", Advances in Geosciences, 5, editor@iaeme.com

19 Dr. Ihsan A. Abdulhussein and Rafi M. Qasim APPENDIX (1) Selected Input Data model and its Corresponding Output Prototype Predictive Values (Method1) APPENDIX (2) Selected Input Data model and its Corresponding Output Prototype Predictive Values (Method2)