unsteady flow

In Coarse-grained porous media, the size of particles and pores causes complications in the flow behavior, in a way that the flow has no layered state and the Darcy relation loses its validity. In these cases, the hydraulic gradient velocity relationship is nonlinear. The coefficients of the relationships have been examined by different researchers.Surface water relations, also known as Saint-Venant relations, are among the best computational tools governing free surface water flows. Equations mentioned above were first used in 1871 by Adbemar Barre de Saint Venant in order to analyze unsteady flow with a free surface, and afterwards many researchers investigated and estimated the characteristics of free flows as well as flow in porous medium by using these equationsThe main purpose of this research is to investigate characteristics of steady and un-steady flow in porous environment. By calculating the velocity values at each point and plotting the velocity graph against the hydraulic gradient, the coefficients of Forschheimer's binomial relation were obtained for each of the discharges. By examining the changes of these coefficients, linear relationships were obtained for the changes of the coefficients against the flow rate changes.

In this study, the tilting laboratory channel of the Faculty of Civil Engineering of Zanjan University was used. In order to create a porous environment, 1.2 meters of the length of the channel has been selected and separated by two net separators. (Fig 1). The grading of pebbles used in this research is presented in Figure 2. Also, their physical characteristics are given in Table 1.The experimental program of this research was carried out in two sections of steady and unsteady flow. In the steady part, water flowed with 10 different flow rates from 8.51 to 20.62 L/s. By arranging the coefficients and the flow rates and plotting them against each other, a function can be derived to calculate each of the coefficients a and b based on the flow rate. The graphs in Figure 4 illustrates these functions.In the next part of the tests, the hydrograph in Figure 5 was passed through the porous media.Saint-Venant's equations were considered as governing equations and were solved using the method of characteristics. The equations were solved once by using fixed values and the other time by using the functions of Forschheimer coefficients.

The Saint-Venant equations for the problem were solved once by using the average values of the coefficients of Forschheimer's relation and again by using the functions of these coefficients. By solving the equations, the velocity and depth values and hence the flow rate at any moment and at any point of the porous medium were calculated. Table 3 shows the calculated flow rate error for two solution modes. In this table, the minimum and maximum values of the input hydrograph are compared with their corresponding values in the hydrograph at the point of 6 cm. Checking the error values shows that the calculated error of the maximum flow rate (which occurred at the peak of the hydrograph) in the case of constant Forschheimer coefficients is 13.36%, which is about 3 liters per second more than the actual hydrograph. In spite of this, there is only 2.16% error in the calculation hydrograph with variable coefficients of maximum discharge. This is also important in the minimum of hydrograph. So that the error value in the calculation hydrograph with fixed coefficients has 22% error (minimum of the hydrograph occurs at the beginning), while the corresponding value for the calculation mode with variable coefficients is only 1%.As can be seen in Fig 9, the calculated profile is approximately always a little lower than the observed profile and the difference between these two profiles maximize at the time of the hydrograph peak, and then the difference decreases again as the discharge decreases.Table No. 4 shows the percentage of the relative error for the observed and calculated flow profiles at different times. As mentioned, the maximum error among all times and all points is observed in 400 seconds and at the terminal point of the profile.

The results of the numerical solution in two cases of fixed and variable coefficients show that the percentage of relative error in the maximum and minimum discharge for the case of fixed coefficients is much more than the case of variable coefficients.The results indicate that the maximum discharge go smaller as we move along the medium and also occurs at a later time.The investigations determined that the average calculation error of the depth at the times of 100, 300 and 600 seconds is 4.88, 8.05 and 9.93 percent, respectively.

For a bridge pier in the flow path, a three-dimensional and complex flow pattern is formed around the pier leading to the formation of a scour hole around it. The development of the scour hole will cause the instability of the bridge pier and ultimately the destruction of the pier and the bridge. This problem becomes very important during the floods, when the flow in the river increases rapidly and has the highest potential of destruction. Most studies have investigated scouring in steady flow conditions. The maximum scour depth that occurs under a flood hydrograph can be much smaller than the equilibrium depth resulting from steady flow under peak discharge conditions (Kothyari et al., 1992; Lai et al., 2009). Therefore, the use of flood peak discharge for design can greatly overestimate the maximum scour depth compared to the actual flood conditions (Chang et al., 2004). Considering the importance of scouring investigation in the conditions of unsteady flow and the limited available studies in this regard, more research in this field is necessary. The purpose of this research is to investigate the effect of the time of the rising and falling limbs of the hydrograph, as well as the duration of the hydrograph on the temporal variations of scour depth and its maximum value around the cylindrical pier.

The experiments were carried out in a rectangular flume with glass walls and a straight length of 10 m, a width of 0.74 m and a depth of 0.6 m in the Physical and Hydraulic Modeling Laboratory of Shahid Chamran University, Ahvaz. The test section in the flume was covered with uniform sand with an average size of d50=0.7 mm and geometric standard deviation σ=1.3. In order to achieve the goals of this study, a total of 13 experiments were examined. In order to investigate the effect of the time of the rising and falling limbs of the hydrograph on the temporal variation and the maximum scour depth, a number of 6 hydrographs with a constant duration of 100 minutes and the ratio of the time to reach the peak (Tp) to the duration time (Td) of the hydrograph (skewness) equal to 0.1, 0.2, 0.4, 0.6, 0.8 and 0.9 were designed. Also, 7 hydrographs with Gaussian distribution and duration times (Td) of 10, 20, 45, 80, 100, 120 and 160 were simulated to investigate the effect of flood duration on scouring (Fig. 3 and Table 1). A hydrograph generation system was used to create unsteady flow in the flume. This system included a programmed inverter that was used to adjust the variable flow rate of the hydrograph. The inverter was connected to the pump on one side and to the electromagnetic flow meter on the other side and was run by a computer through a software.

The results of the temporal variations of scouring showed that scouring starts from the sides of the pier and reaches the nose of the pier over time, and finally, the maximum depth of scouring occurs in the nose of the pier. The results showed that the maximum scour depth in the hydrograph with a Gaussian distribution occurs after the peak time (about 10% of duration time) (Fig. 5). Investigating of the effect of the rising limb of the hydrograph showed that in hydrographs with similar duration, the time to reach the peak of the hydrograph has no effect on the maximum scour depth, but it has a significant effect on the temporal changes of shear stress and scour depth. By reducing the time of the rising limb of the hydrograph from 90 minutes to 10 minutes, the shear stress change rate increases 9 times and the scouring rate increases about 6 times. Investigating the effect of the falling limb of the hydrograph on the maximum scour depth showed that the effect of the falling limb on the maximum scour depth increases with the decrease of the time of the rising limb of the hydrograph. The results also showed that the maximum scour depth in hydrographs with skewness of 0.1, 0.2, 0.4, 0.6 and 0.8 is 51.35, 21.28, 12, 5.56 and 1.79 percent more than the scour depth at peak discharge, respectively (Fig. 6). It was also observed that in hydrographs with the same peak time but different duration time, the time of the falling limb is effective on the value of the maximum scour depth. With the increase of 9, 4, and 1.5 times the time of the falling limb of the hydrograph, the maximum scour depth increases by 30.23, 14, and 1.82 percent, respectively. Investigating the duration time of the hydrograph showed that the increase in the duration time increases the depth and dimensions of the scour hole around the pier. It was observed that the maximum scour depth for hydrographs with a duration of 20, 45, 80, 100, 120 and 160 minutes were 19.44, 38.89, 52.78, 58.33, 66.67 and 69.44% more than a hydrograph with a duration of 10 minutes, respectively (Fig. 7). In addition, the slope of the time variations of the scour depth decreases with the increase of the duration time due to the lengthening of the flow rate changes interval along the rising limb of the hydrograph (Fig. 8).

In this study, scouring around a cylindrical pier was investigated under unsteady flow conditions. The results showed that for hydrographs with similar peak discharge and duration time, the time of the rising limb of the hydrograph has a significant effect on the temporal variation of shear stress and scour depth, but it has almost no effect on the maximum scour depth. In addition, it was found that by reducing the time of the rising limb, the influence of the falling limb of the hydrograph on the maximum scour depth increases. Investigating the results of the effect of hydrograph duration time on local scour showed that with the increase of hydrograph duration time, the maximum scour depth increases and the slope of temporal variations of scour depth decreases.

Crump weir is widely used to calculate flow rate in open channels with unsteady flow regimes. In this study, flow rate calibration was experimentally investigated for unsteady free flow in crump weir using two different flow rate-time patterns. These patterns with either increasing or decreasing trends were considerd for different timeperiods. Experimental tests were performed in a laboratory flume equipped with real time data acquisition and recording system. The flume was 10 meter long and 8 meter wide and crump weir was located at 5.2 m corresponding to the enterance of the channel. The behavior of the flow rate coefficient was investigated as a function of weir height to the weir water height ratio, the weir length to weir water height ratio and weir width to weir water height ratio. Results show that flow rate coefficient is in reverse correspondence with all dimensionless parameters so that with an increase in each of these parameters, flow rate coefficient decreases. Finally using genetic algorithm, the optimization of the flow rate coefficient was performed. It was shown that the calibrated flow rate coefficient varies between 0.4 to 0.7.

Natural rivers experience significant sediment transport rates during floods.The purpose of this study was to investigate the effects of flood hydrograph intensity parameter on the amount of bed sediment transport rate. For this purpose, a real unsteady flow hydrograph was created inside a 15 meters long tilting flume by installing an interface board between the computer and the pump inverter. Sediments with a d50 of 2.69 mm have been put uniformly on the bottom of the channel and the flood hydrograph has been applied on it after saturation. 20 cases of hydrographs with different intensity parameters were tested and the erosion rate was obtained during the hydrograph time. The results show that the maximum erosion rate always occurs near the peak of the flood hydrograph and the time delay between the peak of the flood hydrograph and the peak of the sediment hydrograph is mostly positive. The erosion rate in the rising limb of the hydrograph is higher than the falling limb, and the distance between them decreases in the hysteresis diagram as the flow intensity parameter decreases. The changes of bedload transport rate (qb) in terms of flow rate (Q) are clockwise hysteresis. By decreasing the hydrograph intensity parameter by 32, 57, 75 and 87%, the total volume of transferred sediments decreases by 27, 51, 78 and 90%, respectively. A 50% decrease in the base time of the hydrograph under the same conditions has caused a 46% decrease in the total volume of transported sediments.

Investigating unsteady flows in compound channels and natural rivers is essential. Discharge measurements in medium and large rivers are often based on indirect methods of converting water level to discharge using stage-discharge curves of steady flow. However, these methods do not accurately estimate flow discharge in unsteady flow conditions. In the previous studies, many relationships have been proposed to modify the flow values in steady conditions to estimate the stage-discharge relations of unsteady flow. In most of the previous studies, the relationships are either oversimplified or have errors that make them not very generalizable. Considering the importance of estimating the rating curves in natural rivers and compound channels and the shortcomings of the studies in this field, this research aims to evaluate the stage-discharge curve and the output hydrograph in natural rivers with unsteady flow using a proposed novel method based on isovel contours.

In order to analyze the flood flows, the combination of momentum and continuity equations was used, known as Saint-Venant's equations. Saint-Venant equations do not have an analytical solution, and numerical models must be used to solve them. The numerical model used in this paper was the four-point finite difference model, which is conventionally called the Preissmann implicit model.Using the Bio-Savart law, the Maghregi’s 2006 method simulates the effect of the wall on the velocity distribution in the flow cross-section by considering the effects of the electromagnetic forces on a particle with a static charge placed in the electric field of a wire with an electric current. In the SPM method, using the Bio-Savart law, a relationship for determining the isovel contours was presented, similar to the magnetic field law. In this method, to determine the effects of the entire flow section wall on a point (uSPM), the value of uSPM was computed by integrating the impact of all boundary elements on each flow point. Then, using the power-law velocity, a relationship was obtained to calculate the average value of uSPM in the flow section known as USPM. In order to model the SPM method and estimate the parameters of this method, first, the values of the uSPM in a series of selected points of the flow section should be computed. It is worth mentioning that the pattern of arrangement of points is important in sections that do not have a regular geometric shape. One way to arrange the points was to cover the surfaces with triangular meshes. In this research, the Delaunay triangulation algorithm was used. The purpose of this was to maximize the angles of the triangles. After placing the triangular meshes on the flow section, it was enough to obtain the values of uSPM only in the centroid of each triangular element. In Wolfram Mathematica software, it is possible to use this grid type. The main effective parameters of the water discharge were listed as bed roughness (n), cross-sectional area (A), wetted perimeter (P), free water surface (T), bed slope (S0), and cross-sectional flow velocity (USPM). First, the A, P, T, and USPM should be calculated at each observation level. Having obtained the characteristics of the sections and the discharge of each section at different levels, the coefficient and exponents of the proposed discharge relation were computed using the genetic algorithm process based on error minimization.

The negligible difference between the observed data and estimated flow discharge based on the SPM method confirm the accuracy of this method. It is worth mentioning that this method can consider the effect of the shape of the section with any complexity on the water flow using the Bio-Savart law. This work was done by simulating the cross-sectional wall and water flows, respectively, with the wire flowing the electric current and the magnetic field around it. This method estimates the stage-discharge curve and flood routing with proper accuracy, even in the flow entering the floodplain where considering the shape of the cross-section is of particular importance.The field data used in this research has been provided from the Tiber River in Italy. In order to solve Saint-Venant's equations and determine the hydrograph of flood output, the system of equations consisting of numerical modeling should be resolved. The Gauss elimination method was used to solve this system of equations. In this research, instead of using Manning's relation to solve Saint-Venant's equations, the proposed discharge equation obtained based on the theory of the Maghrebi method was used to determine the flood output hydrograph. The final results of flood routing, based on the aforementioned method, showed that the values of Root Mean Square Error (RMSE), Normalized Root Mean Square Error (NRMSE) and Mean Absolute Percentage Error (MAPE) for the outflow stage hydrograph were 0.1196 (m3/s), 0.037 and 4.10%, respectively, and for the outflow discharge hydrograph were 10.12(m3/s), 0.029 and 11.97%, respectively. In addition, the error of the proposed method in estimating the peak discharge and the peak stage was less than 4% and also, in the case of their occurrence time, was about 2%.

In the proposed approach of this research, the common discharge relationships in the Saint-Venant equations have been substituted by ones extracted from the Maghrebi method (equation 24). Based on this method, the error of the discharge estimation in natural rivers can be reduced compared to other methods, especially when the flow enters the floodplain. Finally, the estimated outflow hydrographs based on the proposed approach showed that the results were entirely consistent with the observation data at the beginning and end of the flood occurrence range. Also, the error of the considered method was negligible in the range of the peak stage and discharge and their occurrence time. Besides, the peak stage and discharge and the time of their occurrence, which are accounted as the essential indicators in hydrograph estimation, have been calculated using the proposed method with excellent accuracy.

Solving the problem with the meshless method is based on selecting a series of points from inside the computational area and boundaries without meshing. In the present study, the phenomenon of seepage below the dam under steady and unsteady flow conditions has been investigated by combining the Meshless method and the Finite Difference Method. Problem solving and calibrating operations were done by coding in MATLAB software. The Meshless method was used for spatial sentences and the Finite Difference Method was used for the discretization of temporal sentences. The results showed that the shape factor (α) for low points is 0.85 and for high points is 0.52, which indicates the proximity of the initial approximations to the main answer. Considering that, the shape factor depends on the geometry and the governing equation, so the same shape factor was obtained for the steady and unsteady conditions equal to 0.52. In the unsteady condition, with the water level behind the dam remaining constant, the water head below the dam also reaches a constant value over time. Also, examination of the results showed that in numerical problem solving, a low error is not a criterion and among the various basic functions, only the MQ function has the better hydraulic performance to draw equipotential lines, so that for 133 points, the shape factor and root mean square error index are 0.52 and 0.0108, respectively.

The shallow-water equations in unidirectional form namely as Saint Venant equations (SVE) are a set of quasi-linear hyperbolic partial differential equations, having a wide range of applications in open channel and river flow analysis. Because of intrinsic non-linearity, there are no analytical solutions for these equations in most practical applications except for simplified versions. On the other hand, numerical solutions by finite difference or finite element methods are time-marching and for forecasting and timely management of floods are relatively lengthy and time-consuming. Recently, new solutions of SVE in frequency domain, using Laplace Transform (LT) or Fourier Series (FS) have been proposed to overcome these difficulties. In the LT method, input wave is converted into a unit hydrograph, a unit step, or a unit pulse. Despite of unconditional stability, the accuracy of this method depends on time step of decomposition of input information. In this research, however, the FT method is proposed to reduce the execution of real-time flood forecasting. Unlike finite difference models, this is not a marching method and the results may be generated at a given time, directly. Moreover, there is not any restriction in the decomposition of input data due to their independence from time.

The complete form of SVE, namely as full dynamic equations are used in the present work. Initial conditions are non-uniform and the up-and downstream boundary conditions are inflow hydrograph and stage-discharge rating curve. SVE are linearized around a steady-state situation using the Taylor expansion. Assuming that the changes in water depth and discharge follow a sine pattern, the linear equations of continuity and momentum are transferred from time domain to frequency domain using the FS and sine functions. The input wave to the model, not necessarily harmonic and periodic, is converted to a set of periodic waves using Fast Fourier Transform (FFT). Considering the initial condition of non-uniform flow in the model, the channel is divided into some intervals that may have equal or non-equal lengths with uniform flow at each part. All channel characteristics such as mean flow depth are computed at each interval separately. Then, transition matrices are constructed to interconnect the channel intervals at the boundaries. Finally, the frequency response of flow discharge and water level are obtained at each part of the channel.

This method could be used for all kinds of prismatic and non-prismatic channels, natural rivers with various types of flow (critical, sub-critical, and super-critical), different boundary conditions at the up- or downstream ends, and point or distributed lateral inflow. Rashid and Chaudhry (1995) performed their experiments in a rectangular flume. The flow was unsteady and non-uniform. FFT was used to decompose the input hydrograph into a complex sum of periodic waves. In this research, 256 waves with a frequency of 0.002 to 0.5 were used for accurate matching between the input hydrograph of the laboratory model and the hydrograph of the total waves analyzed by the fast Fourier transform. The result of the proposed method was compared with laboratory results of Rashid and Chaudhry, analytical model of Cimorelli, and numerical method of Preissman in time domain. The Nash–Sutcliffe efficiency coefficient (NSE) in the present study is more accurate than other models and in stations (2) and (5) are equal to 0.9893 and 0.9872, respectively. The peak of hydrograph in our model is more than the Cimorelli analytical model. The lag time of mean peak of hydrograph in the model is equal to the experimental results of Rashid and Chaudhry (1995). Execution time of the model is 11.84 seconds in comparison with Preissmann implicit method that is 54.48 seconds with the same computer. This run time is important in forecasting and warning models of floods. Visual comparison of theoretical and experimental hydrograph curves are satisfactory.

The proposed method is unconditionally stable. Full dynamic unsteady flow equations of Saint Venant is solved using FFT and Transition Matrix. The upstream boundary condition is stage-hydrograph and the downstream boundary condition is a stage-discharge relationship. The effects of lateral inflows and non-uniform initial conditions are considered in the model. To evaluate the accuracy of the model, the results compared with experimental data of Rashid and Chaudhry, analytical model of Cimorelli and numerical model of priessmann in time domain, were satisfactory both quantitatively and qualitatively. Regarding the unconditional stability and the appropriate run time of computer, the code is suitable for flood forecasting, warning and optimization models. This method can be used to analyze the flow in natural rivers and irrigation canals with any type of flow regime

The pier group is one of the important hydraulic structures that the scouring around them is affected not only by the flow characteristics, but also by their number and arrangement. Each pile in a group has an individual scouring mechanism that can influence the other piles in the group. The following are mechanisms that make pier group scouring more complicated than a single pile: 1) sheltering, 2) reinforcement, and 3) horse-shoe vortex compression (Nazariha, 1996).More recent attention has focused on the arrangement and geometric variables and their effects on the scouring size and process in steady flow. Several reviews of the angle of attack, spacing, numbers, and pier diameter have been undertaken (Hannah, 1978; Nouh, 1986; Vittal et al., 1994).As seen, most studies in the field of scouring around pier groups have only focused on steady current, and there is a relatively small body of literature that is concerned with scouring in pier groups in unsteady flow, while floods, waves and unsteady flows are the most destructive phenomena in rivers and coastal environments. This paper uses the experimental investigation of three piers in the tandem arrangement as a pier group and analyses the impact of hydrograph unsteadiness on scouring with different pier spacing in the clear-water regime and investigate the time variation of the scouring depth to understand the scouring process around pier groups in unsteady flow.

The experiments were conducted in a flume 10 m in length, 0.74 m in width and 0.6 m in depth at the Hydraulic Laboratory of Shahid Chamran University. In the flume a pump was used to drive the water from an underground reservoir to a head tank. A false bed was built at the bottom of the flume with 0.15 m height, with a 1.7 m length sand bed located 2.8 m from the inlet. The sediment part of the bed was filled with d50=0.7 mm uniform sand (Geometric standard deviation of the sand size(σ)=1.3) and the other parts were covered with the materials as rough as the sand.In this study, 36 experiments were done to evaluate the pier group scouring, which included 9 tests of steady flow in different discharge and pier spacing, and 27 tests of unsteady flow in different peak discharge, time duration and pier spacing. It is worth mentioning that all experiments were performed in the clear water regime.During the experiments, four cameras (Full High Definition (FHD) resolution) recorded the scouring process from four different angles to investigate the temporal changes (Fig. 4). All piles were scaled to extract the scouring depth from the videos and remove the light deflection effect in the water.

Steady flow

What stands out from the steady flow experiments investigation is that the scour depth around the first pier was more than the next one due to the flow attack. In other piers, because of the previous pier's protection, the scour depth was less than the first one. As shown in Figure 4, the scour depth changing rate decreased earlier at lower discharges, which may be due to the lower flow intensity to continue the scouring process. Early in the second and third pier scouring process, the scouring depth remains constant for a while, which is due to the eroded sediments from the previous pier into the next pier's scouring hole and the equal amount of deposited and eroded sediment. This issue is also seen in figures of Mahjoub et al.'s (2014) research.
Unsteady flow

The scouring depth around each pier gradually increases with increasing flow discharge during the hydrograph's rising limb. This increase occurred at the beginning of the process slower than the steady flow due to a gradual increase in flow discharge and, consequently, a gradual increase in flow intensity and shear stress to erode sediments around the pier (fig 5-8).In the unsteady flow experiments, the first pier's scouring process was gradually stopped after the peak discharge and during the falling limb due to the decrease in flow discharge. However, evaluating the recorded videos from the scouring process angles and the extracted data showed that the process proceeded differently for the second and third pier in some experiments. In these cases, four conditions around the pier were occurring by reducing the flow discharge in the falling limb. These conditions caused new phenomena called backfilling in this study..ufficient height of deposition region resulting from previous pier scouring.Sufficient flow intensity for erosion and moving the sediment Short distance for sediment to reach the next pier scouring hole. weak vortex of the next pier to re-erode the entered sediments into the hole

Evaluating the scouring hole's temporal variation during the unsteady flow shows that the scouring process around the pier group in unsteady flow can differed from steady flow around rear piers and caused a new phenomenon, which is called backfilling. This difference is due to the extra mechanisms in the pier group scouring process, and the flow changes during the hydrograph and changed with changing the pier spacing.

One of the most important parameters in the design of bridge abutments and piers is to calculate the depth of scouring. The previous relationships for measuring the scour depth were based on steady flow, and it is not expected that the amount of scour depth computed from these relationships is accommodated to the actual value during a flood wave. Inasmuch as in this condition, the flood hydrograph occurs in an unsteady state in which the discharge is variable between base and peak values. In this study, experiments were conducted to measure the clear-water scour depth of a rectangular abutment under steady and unsteady flow conditions by approaching flood waves with triangular hydrographs and equivalent stepped hydrographs in a compound channel. Then, by using the measured scour depths values in steady flows, a relationship is calculated to estimate the maximum scour depth in terms of dimensionless time parameter and flow intensity. By changing the peak discharge time parameter, the effect of slope at ascending and descending part of the triangular hydrograph on the scouring was investigated. A comparison of the scouring of two stepped hydrographs with the same time duration showed that the difference between the scouring values was 1.5%. Moreover, the results of the scour depth measurements of triangular and stepped hydrographs were compared.

Several studies have been performed to study the scouring depth at bridge piers. Due to the complication of the problem and variety of the hydraulic and geometric parameters affecting the scouring phenomena, a generalized relationship has not been presented yet. Therefore, adaptive neuro-fuzzy inference system (ANFIS) is an alternative to overcome these problems. This approach is an effective tool to provide the hydraulic engineers, precise estimation of the scouring depth around the bridge piers. Although a large number of former studies have just focused on scouring at bridge piers under steady flow condition and uniform-graded bed materials even by applying ANFIS model, a lack of studies exists on scouring under unsteady flood flow condition as well as for non-uniform bed materials. Generally, river beds are composed mainly of non-uniform materials. Motion of the finer sediment particles initiates results in the protective effect of greater particles, namely armoring effect on the bed surface, thereby eliminating further erosion of the bed. Furthermore, in most of the rivers the flow regime is commonly unsteady. During a flood, the maximum scouring depth regarding to the peak of the flood hydrograph would be smaller than the equilibrium scouring depth which is commonly estimated using a constant flow discharge. When the flow unsteadiness is pronounced, the difference between the maximum scouring depth and the equilibrium scouring depth is quite substantial and thus should be addressed.In the present study, armoring effect on local scouring under unsteady flow condition was investigated based on a comprehensive dataset collected by different former investigators using ANFIS model. For this purpose, two different models were constructed. The first model was based on 372 dataset collected in a practical study on different bridges in USA. Measurements were conducted under steady flow condition. The second model was developed for estimating the maximum scouring depth in the beds of uniform and armored materials under unsteady flow condition. To present a more accurate model, some strategies including; reduction of dimension and detection of outlier were used to improve the performance of calculations. Genetic algorithm and particle swarm optimization methods were applied to develop a novel hybrid learning algorithm for ANFIS model. The new hybrid learning algorithm train the antecedent part of the fuzzy rules. Then the least square method was applied for training the conclusion part of the rules. It was shown that ANFIS model gives more accurate results compared to the empirical equations. Results highlighted the effectiveness of the data on the estimations of ANFIS model. Furthermore, according to the results, this approach is potentially able to train the ANFIS model in both steady and unsteady flow conditions.

Local scour around bridge pier is a major factor of bridge destruction and increase in maintenance and operation cost. In addition, due to higher extension of wake region around rectangular bridge pier, more local scour depth occurs in comparison to circular bridge pier. In the present study, a new semiempirical approach was developed for calculation of local scour depth at the upstream face of round nose and tail rectangular bridge pier during hydrograph event (unsteady flow condition). In this method, in each time step, the volume of scour hole or in other words the volume of sediment transport was calculated using a sediment transport equation (MPM). Then, scour depth was determined form the volume of scour hole by simplifying the shape of it. In order to examine the accuracy of the present method, experimental data from different sources were selected. Results showed that the sediment transport equation should be modified in order to determine the volume of transported sediment around bridge pier in an unsteady flow condition. The modification factor applied to sediment transport equation was a function of hydrograph characteristics such as time to peak, duration and time from peak to base flow as well as hydrograph peak flow intensity. For example, by decreasing the time to peak, the modification factor increased (more sediment transport). Finally, the comparison of calculated scour depth based on present method and experimental data showed the acceptable accuracy of present method in comparison to other empirical equation with maximum discrepancy of lower than 10%.

In the present research, the formation and development of the delta and the interaction of the flow pattern and sediment in the reservoir under steady and unsteady flow condition of water and sediment is experimentally investigated. Laboratory observations showed that in spite of the perfect symmetry of the geometry and hydraulic conditions of the model, the flow at the reservoir entrance is randomly diverted to one side and an asymmetric but stable flow is created at the reservoir entrance. The sediment entry and its deposition in the reservoir leads to an unstable flow and a change in flow direction. The instability in unsteady flow is more severe than under steady flow condition. The results showed that with the growth of the delta, the deviation of delta decreases and approaches the symmetry. Delta development takes place in longitudinal and transvers directions and the maximum elongation of delta is about 0.8 at the initial stages, and decreases with delta development. An equation is developed for time of change in direction of flow in terms of the specific parameter of the hydrograph. In order to study the sedimentation pattern, non-dimensional parameters such as the length of delta (Xt*), deviation ratio (ψ) and delta elongation (η) are introduced. An equation is developed to estimate the length of delta using non-dimensional parameters.

In this study armoring effect on local scouring under unsteady flow condition was investigated based on model experimentation. To obtain unsteady flow condition, ten different triangular hydrographs were considered. Experiments were performed in an 8.5 m long and 0.405 m wide laboratory-scaled flume. The bed materials were overlain by a thin armor layer of coarser sediment. Different combinations of uniform bed-armor layers were employed. Three circular piers of 22, 33 and 42 mm diameters were used. For each experiment the armor-layer thickness was maintained at 3da (da, is the armor-layer material mean size). The approaching flow velocity is restricted to the clear water scour condition with respect to the armor layer particles (u*/u*ca=0.8, where u* is the flow shear velocity, and u*ca is the critical shear velocity of the armor-layer particles estimated based on the Shields’ diagram). Results indicated that the equilibrium scour depth is independent of the hydrograph shape. In addition, increasing the hydrograph base time does not affect the scouring hole formed downstream of the pier. Observations showed that the effect of n hydrographs with the same base time of T is almost identical to that of a continuous hydrograph with the base time of nT.