مجله هیدرولیک
سال هجدهم شماره 2 (تابستان 1402)

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.

A retaining wall is a structure that maintains the pressure due to the situation in the level difference caused by an embankment, excavation, or natural factors. Since comparing the performance of two different types of walls from retaining walls is the subject of this article, in this research, from rigid walls, weight retaining wall (concrete) and flexible walls, gabion retaining wall (in weight form) with almost the same conditions, It is evaluated in terms of stability and performance. The geometry of the concrete weight retaining wall is chosen so that the result of the forces acting on it (including weight and lateral forces) is in the core of the base or its horizontal sections. The expected results of this study include the study of retaining wall performance in terms of soil material change behind the wall, river water depth, and retaining wall slope, and finally, comparison and selection of suitable retaining wall to protect the river wall between two types of concrete and gabion walls.

Software SLOPE/W is the most advanced slope stability software for soil and rock slopes from the GEO-STUDIO 2012 software suite. SLOPE/W effectively analyzes various types of slip surface shapes and determines factors of safety, pore water pressure conditions, soil properties, and loading conditions. In this study, the Morgenstern-Price method has been used. In this method, the balance of forces and anchors for sliding sections is determined, and by Entry and Exit method, the factor of safety is determined.In this study, different factors such as type of wall and river bed materials, water depth in the river, type of retaining wall materials, the slope of retaining wall, and soil adhesion were investigated. Based on the critical conditions in the evaluation of the stability of retaining walls, the saturation state (the most critical state possible) was considered for the wall and river bed materials. To apply the soil properties behind the retaining wall in modeling, a homogeneous porous medium and isotropy (Kx/Ky = 1) were considered, and for the slip criterion of the Mohr-Coulomb resistance model, which is the most common method for expressing shear strength in geotechnical materials, used. To compare the results, the retaining wall was designed and modeled in mirror conditions, i.e. the vertical part of the wall on the riverside and the stair part of the wall under the soil.

Since the permeability and hydraulic conductivity of medium gravel are higher than that of average sand, it has a greater capacity to drain excess water. It was observed that the active force and torque of the average gravel are 7% and 11% lower than the average sand, respectively. This is also true for the gabion retaining wall as well as the state of the river with a water depth of 2 meters and 4 meters. In a river, without water, the amount of active force and torque is about 20% more than in a river with a water depth of 2 meters and about 40% more than in a river with a water depth of 4 meters. In the retaining wall in the mirror state, in the river without water, the active force and torque have both increased by about 16%, and in the river water depth of 2 meters, it has increased by about 17% and in the depth of 4 meters, it has increased by 23%. The results of stability and factor of safety for two wall slopes in the conditions of water level drop showed that the factor of safety at a depth of 2 meters decreases by about 20% compared to a depth of 4 meters and Also, the factor of safety of the river without water is reduced by about 30% compared to a depth of 4 meters. The results showed that the retaining wall in mirror conditions has a better performance than other models in terms of factor of safety. Also, the index wall in the vertical position, at a depth of 4 meters, which is the same depth equal to the total height of the wall from the riverbed, has the lowest factor of safety.

In this research, the stability and performance of two types of concrete and gabion retaining walls were examined with SLOPE/W software under similar river conditions. A total of 24 models were designed using two types of bank material (gravel and sand), two slopes of the retaining walls, and three river water depths. Also, 6 models of vertical walls were considered for comparison. The results indicated that the coarser-grained bank material produces a lower level of pore pressure, which in turn results in lower values of active force and torque by 11% and 7%, respectively, compared with the sand material. The results of this applied research can be used as a guideline for selection between two types of retaining walls (i.e. Concrete or masonry walls, and gabion walls) in different river conditions.

The newest type of nonlinear labyrinth weirs are piano key weirs. The initial study on this weir indicated that it increases the discharge significantly and has a simple and economical structure. In the past years, different researches are done to check effective factors on flow discharge and optimization of this weir. But to a limited extent is referenced about ventilation mechanism and aeration of this weir at outlet and the only solution that has been presented for aeration at outlet is gallery aeration at downstream. Another problem that is discussed in the case of piano key weirs and generally over flow of weirs is Nappe oscillation after the cross of weirs crest. Past research considered the use of splitter to be effective in reducing the nappe oscillation in linear weir. By getting ideas from this method (use of splitter), three piers with different geometries (circular, square, and rectangular) has been used in piano key weir to reduce nappe oscillation.

All experiments of this research were performed in a rectangular channel with a width of 75 cm, metal floor, unbreakable glass walls and a height of 80 cm in the hydraulic laboratory of the Department of Water Engineering and Hydraulic Structures, Tarbiat Modares University, Tehran The water flow from the underground tank is entered to the flow calming tank by two pumps with a maximum discharge of 85 liters each per second, and it reaches to weirs after passing through the calming plates, and falls into the underground tank by passing over weir at the end of the flume. This cycle continues during various tests under different hydraulic conditions.The discharge was measured by ultrasonic flowmeter with an accuracy of 0.01 liters per second, after the pumping and before entering to the calming tank. All experiments were performed under free flow conditions. Upstream flow deep was measured by a point gauge with an accuracy of ±1 mm. This depth gauge is moved by rails on the wall of the channel and the water depth is measured at desired points.The piano key weir used in this research is of three types of A piano key weir with different rectangular, triangular and trapezoidal designs in the plan. splitter with three circular, square and rectangular cross-section geometries were installed on the weir crown and in the downstream corners of the weir keys.

The results showed that splitter, in addition to separating the flow after the splitter and creating a space for the connection of free surface air with the lower part of the outflow from the weir, also reduces the nappe oscillation intensity of passing through it. The use of splitter does not have a negative effect on the flow discharge in the rectangular and trapezoidal piano key weir and only in the triangular piano key weir, it has reduced the discharge by 3%.The performance of square and rectangular splitter was similar on water discharge and separation. The effect of flow separation in a rectangular splitter is evaluated better than on a square base. Also, the effect of these two splitter on the current separation is more appropriate than a circular splitter. Regarding the comparison of the discharge coefficient of these three types of weir, it was observed that at H_t/P<0.2, the discharge coefficient in the rectangular and trapezoidal piano key weir is higher than the triangular piano key weir, which is due to more flow suction (due to vacuum created below the weir inlet key) in this head for these two weirs. By increasing H_t/P up to 0.4, the difference between the discharge coefficient of the rectangular and trapezoidal piano key weir relative to the triangle gradually decreases to the point that after H_t/P>0.4, the discharge coefficient of the triangular piano key weir relative to the trapezoidal and rectangular piano key weir has increased, which ventilation performance of this weir type is one of the main reasons for that.

Regarding the increasing use of piano key weir due to its advantages and the need for aeration in the downstream to improve its performance, this study aims to provide an economic solution (using splitter instead of aeration gallery) to improve ventilation performance in the downstream of the piano key weir. Therefor it has studied the effect of splitter with different circular, square and rectangular sections on the flow discharge of this weir type with three rectangular, triangular and trapezoidal designs in the plan. In general, the results obtained in this study can be summarized as follows: In the total head less than 0.08 m, the rectangular piano key weir in constant discharge, about 5 and 15%, has a smaller head than the trapezoidal and triangular piano key weir. But at a total head greater than 0.08 m, a trapezoidal piano key weir at a constant discharge, has a smaller head than a rectangular piano key weir about 5% and on average about 8% than a triangular piano key weir. Splitter show the best flow separation performance in the case of H_t/P<0.6, but in the case of H_t/P>0.6 this performance is affected by high water flow, so that with increasing discharge, the correlation the bottom of flow is reduced with open air and it is not possible to ensure relative to the complete correlation of the open air with the downstream and the outlet of the piano key weir. In terms of the splitter geometric shape, square and rectangular splitter showed similar performance in flow discharge and separation. But the separation of the current at the rectangular splitter is evaluated better than the square splitter. Also, the geometry of these two splitters is more suitable for flow separation than circular geometry.

Hydraulic jump is a fast and irreversible variable flow that occurs downstream of hydraulic structures and the result of which is the rapid transformation of supercritical flow into subcritical flow, which increases the depth of the flow and causes a significant loss of energy. By examining the previous studies, it is clear that the roughness bed or the divergence plays an important role in hydraulic jump characteristics.  FLOW-3D is one of the suitable software in hydraulic Phenomenon modeling. In order to ensure the appropriate capability of FLOW-3D software in simulating hydraulic jump, first, a research related to this issue which has been investigated in the past in a laboratory, is simulated in the software. Then, by comparing the results of the numerical simulations with the laboratory data and ensuring the proper functioning of the software, new simulations are made. The experiments related to the physical model used were carried out in a laboratory flume with walls and floors made of transparent plexiglass, 5 meters long, 0.3 meters wide, 0.45 meters high, and zero longitudinal slope. To create a supercritical flow, a steel valve with a height of 0.65 meters and a thickness of 3 mm and an opening height of 1.7 cm was used for a non-prismatic channel with a divergence ratio of 0.33. In order to create symmetrical opening ratios of 0.33, glass boxes with a length of 0.5, a height of 0.2 and a width of 0.1 meters were placed on both sides of the flume. After the simulation and by checking the R2, MAE and RMSE parameters, the k-ɛ model and the mesh with the number of 687600 cells were selected as the optimal mesh. In this research, according to the selection of four types of bed (smooth bed, rough bed with hemispherical roughness and diameter of 3, 4 and 5 cm) and three divergence angles (7, 14 and 90 degrees) and five Froude numbers (Froude number: 4.34, 5.71, 6.95, 8.17, and 9.37) in total, Simulated for 60 different experiments.  The results showed that for the maximum discharge for the sudden divergent channel, the roughness of the bed with a diameter of 5 cm causes the amount of the flow depth to decrease by 19.77% compared to the smooth bed. Also, the sudden divergence of the bed reduces the flow level by 23.75%. In all cases, the value of y2/y1 increases with increasing Froude number. With the increase of the Froude number from 4.34 to 9.37, the value of y2/y1 on the flat bed increases by 15.54%. With the increase of the Froude number from 4.34 to 9.37, the value of y2/y1 on the rough bed with a diameter of 3 cm decreases by 5.67% on average compared to the smooth bed. As the roughness diameter increases from 3 to 5 cm, the value of (Lj/y1) decreases by 15.58% on average. The results show that the (EL/E1) ratio increases with the application of bed roughness. So that by applying a roughness with a diameter of 5 cm, the value of (EL/E1) compared to a smooth bed increases by about 5% on average, and by applying a sudden divergence, the value of (EL/E1) compared to a bed diverging under an angle of 7 degrees The average increases by 4.58%. FLOW-3D is a good software to prediction of hydraulic jump characteristics in divergent channel with smooth bed and rough bed and The k-ɛ turbulence model was selected as the optimal turbulence model. Increasing the bed roughness size decreases the secondary depth for all values ​​of 𝐹𝑟1. The sudden expanding of the rough bed with a roughness of 4 cm reduces the y2/y1 by 12.98% compared to the bed with a divergence under 7 degrees. Increasing the size of the roughness decreases the length of the hydraulic jump. According to the results, the length of the hydraulic jump in the rough bed with a diameter of 5 cm compared to the smooth bed decreased by 26.12%. Also, by increasing the roughness diameter from 3 to 5 cm, the value of (Lj/y1) decreases by 15.58% on average. By applying roughness with a diameter of 5 cm, the value of (EL/E1) increases by about 5% on average compared to the smooth bed. Results show that the divergence angle of the bed is effective on streamlines. But, increasing the roughness of the bed, there is no noticeable change in the streamlines. However, increasing the bed roughness size, increases the amount of disturbance energy in the section.

Today, due to the high statistics of erosion globally, the importance of continuous monitoring of rivers that carry most of the eroded rich soil in the form of suspended sediments is vital. In Iran, almost one billion tons of eroded soil are destroyed annually. One hundred million cubic meters will reduce the volume of dams. In such a situation, most sediment measurement stations worldwide still use traditional methods to monitor suspended sediments, which are costly and time-consuming and are associated with human error. In recent decades, attention to new methods of monitoring suspended sediments in rivers has increased. One of these methods is Hydroacoustic technologies such as Acoustic Doppler Current Profiler (ADCP), which transmit sound waves with different frequencies underwater. The analysis of its speed and intensity and the number of sound waves attenuation due to collisions with suspended sediment particles can measure the mean suspended sediment concentration and particle size estimating the mean suspended sediment concentration using a single frequency is possible only by sampling the river. Therefore, in this study, for the first time, with the development of tomographic relationships and the simultaneous dual frequencies, the possibility of estimating the mean particle size and suspended sediment concentration in the river using the Fluvial Acoustic Tomography (FAT) method without the need for sampling by using 10 and 30 kHz are presented.

The acoustic tomography consists of two sources of sound production and a sound receiver installed diagonally on both sides of the river; They monitor the river cross-section by sending and receiving sound waves. This system is considered an active measurement system due to its sound production source. The systems are synchronized using nanosecond satellites using GNU satellites and transmit sound waves at a single time. Sound waves propagate throughout the water depth, and changes in water depth do not affect the measurement of this method, and there is no need to install several devices at different depths. These waves propagate forward in contact with the water surface and the bed of the aquatic environment. One of the disadvantages of the acoustic tomography method is trapping the foliage of plants around the transducers, which disrupts the measurement operation (Bahreinimotlagh et al., 2019; Bahreinimotlagh et al., 2018; Bahreinimotlagh et al., 2015)

In this study, to test the ability of the proposed equation in acoustic tomography, three hypothetical probabilities (A1, A2, and A3) were considered with SNR (36 and 23 dB), (39 and 26 dB), and (37 and 24 dB) respectively. First, by using the proposed equation, estimate the sediment absorption coefficient by using frequencies (10 and 30 kHz) as the hypothetical probability A1, A2, and, A3 are (0.013 and 0.025 dB), (0.009 and 0.020 dB) and, (0.011 and 0.023 decibels) respectively. Finally, by solving two equations and two unknowns for each hypothetical occurrence probability (A1, A2, and A3), the average concentration and size of suspended sediments in the river section are equal to (1.43 kg / m3 and 24.89 μm), (0.54 kg / m3 and 9.64 μm) and (0.93 kg / m3 and 16.43 μm) were estimated respectively.In general, with increasing frequency, the measured SNR values decrease. The noise increases with increasing frequency, and the SNR decreases. Similarly, by reducing the SNR, the values of the sediment absorption coefficient also increase. It only could measure SNR between 10 and 40 dB.

This research showed that acoustic tomography could estimate PS and SSC with dual frequency using the proposed equation. The results showed that the acoustic tomography method could monitor suspended sediment particles with a radius between 105 to 0.1 μm and mean sediment concentrations between 7.17 to 0.1 kg/m3 at 10 and 30 kHz.

Stepped spillways are one of the types of weirs used in waterway systems. This structure is used to discharge measurement, energy dissipation, and water aeration. Due to engineers' tendency towards environmental sustainability and not manipulating natural landscapes, porous spillways made of stone in the form of gabions are a suitable alternative to impermeable concrete spillways. These spillways have technical, economic, environmental, and hydraulic priorities compared to conventional concrete stepped spillways. Porous spillways are a suitable alternative to the usual concrete spillways in water transmission and distribution systems due to their high hydraulic and technical performance on the one hand and negligible negative environmental impact on the other hand.In this research, the hydraulic performance of the porous stepped spillway under free flow conditions has been investigated in a laboratory manner. This research investigates the effect of different variables including flow rate, upstream blockage, and porosity, on the discharge coefficient of the porous spillway. The materials used in the porous spillway were selected from four gradations between 1.13 and 4 cm with a uniformity coefficient close to 1. Each porous spillway was tested for seven blockages between zero and 100%. Also, the results were compared with a solid stepped spillway model with and without blockage. In the following, it has been extracted to present the empirical relationship of the discharge coefficient in these spillways under blockage conditions, using the dimensional analysis of effective dimensionless parameters under free flow conditions.Finally, in the final part, based on the dimensional analysis, two empirical relationships are presented using SPSS and GEP (gene-expression programming) for calculating the free flow discharge coefficient for porous stepped spillways.The results showed that the free flow discharge coefficient increases with the size of the filling material. The percentage increase in discharge coefficient for porous stepped spillways is approximately 34 to 230% higher than that of solid spillways. Unlike solid spillways, whose free flow discharge coefficient increases with increasing the flow rate, in porous stepped spillways, the trend of free flow discharge coefficient changes in low flow rates is downward. With an increasing flow rate, it gradually becomes horizontal and then increases with a slight slope. As the blockage increases, the flow coefficient in the porous stepped spillway gradually decreases. In blockages above 80%, the flow coefficient of the porous stepped spillway is insignificantly different from the solid stepped spillway. In the solid stepped spillway, in the percentage of obstructions below 80%, the obstacle does not affect the free discharge coefficient. The presence of blockage upstream of the porous stepped spillways sometimes reduces the discharge coefficient by more than 70%. The extraction of empirical relationships based on the GEP meta-heuristic model has higher accuracy than those extracted from the nonlinear multivariate regression using SPSS. The average error of the relation of the GEP porous stepped spillway free discharge coefficient was 4%, and the nonlinear multivariate regression model was 7%.