## Abstract

The main purpose of this study was to analyze and predict scour depth and hydraulic performance of piers using soft computing methods and to estimate scour depths using artificial neural networks and ANFIS methods. In the present study, three situations were studied: a rectangular pier without a cable (type I), a rectangular pier with a cable that has a diameter equal to 10% of the pier diameter, and a cable twist angle of 15 degrees (type II), and a rectangular pier with a cable 15% of the pier diameter and an angle of twist of 12 degrees (type III). Tests were carried out with different flow-approach angles: zero, 5, 10, and 15 degrees. Dimensional analysis based on the *π* Buckingham method was performed. Then, the effect of different parameters, and their importance for estimating scour depth was investigated. Piers with an angle of 15 degrees with respect to the direction of flow had the greatest depth of scouring. Cables can reduce scour depths at this angle; for the second and third classes of piers, the scouring is 10 and 22% compared to the first pier classification. For the second type of pier, angles of 5, 10, and 15 degrees led to increases in scouring depths of 3, 21, and 37% compared to the zero-angle situation.

## HIGHLIGHTS

Previous studies have not examined the rectangular bridge piers using cables and measuring the amount of scouring.

In the present study, the hydraulic performance of bridge piers with cable application as well as estimating scour depth by intelligent ANN and ANFIS methods have been investigated.

In this study, due to experimental limitations, the ANN and ANFIS methods for higher collision angle flow have also been used.

## INTRODUCTION

A major cause of bridge failure is the lack of attention paid to hydraulic standards in their design, implementation, and maintenance. To improve our understanding of bridge failure, a hydraulic study of piers reinforced with cables was performed with a focus on the scouring depths that can occur. There are various ways scouring around piers can be reduced. The use of slots, riprap, collars, submerged plates, and modern methods such as cables and nano clays have been studied for their ability to reduce scouring of sediments (Rezaie *et al.* 2018).

These issues have been studied in prior research. For example, Kumar *et al.* (1999), Osroush *et al.* (2019), and Saleh *et al.* (2020) studied the performance of a slot with changes to its shape and size, the arrangement and placement height of the slot, and piers with different shapes. Chiew (1995), Lauchlan & Melville (2001), Zarrati *et al.* (2010), and Froehlich (2013) investigated the stability of riprap around pier foundations and the temporal changes in geometric and hydraulic parameters. They protected the area around the pier from scouring and reduced scouring.

Zevenbergen *et al.* (2006), Lagasse *et al.* (2010), and Pagliara & Palermo (2020) evaluated scouring from a bridge pier with submerged plates at different establishment levels. In addition to examining scour reduction, they proposed relationships for estimating scour depth. Dey *et al.* (2006) studied flow splitter plates with cables at different torsion angles and different diameters. The study encompassed three bridge piers with different torsion angles and different cable diameters. The experiments showed that the scour depth was reduced by more than 43%. Pandey *et al.* (2018) studied scouring and flow patterns around a circular pier by measuring the components of the meantime velocity using a Doppler velocimeter. The main purpose of this study was to show scour changes by examining the velocity parameters radially and vertically by changing the pier diameter in the flow field. More recently, Majedi-Asl *et al.* (2021) investigated flow with bed grading and sand extraction from the riverbed around a bridge pier group. In total, they performed 22 experiments with two different substrate grades A and B, three different flow discharge rates, and different values of the Froude number. Their results showed that for a Froude number of 0.5, the presence of a pit hole downstream of the pier group causes an increase of 3 and 9.7%, respectively. Izadinia & Heidarpoor (2012a) studied cables and collars on cylindrical piers with differences in diameter and angles of cable twist. The ratio of cable diameter to pier diameter was 0.15 and the torsion angle was 15 degrees. For this situation, the upstream scour depth pier decreased to about 53%. Scouring time was more delayed with the combined use of the cable and collar compared to the collar-only situation. Ghaderi *et al.* (2020) studied the effect of downstream scouring parameters of stepped spillways by changing the flow rates and step sizes. The results of this study showed that the flow regime plays an important role in the dimensions of the scour cavity, also the scour in the side walls is more than the middle of the cross-section. Finally, a relationship was proposed to predict the maximum scour depth. Pandey *et al.* (2020a, 2020b) studied temporal changes in scour depth at the pier of collar-protected circles. The efficiency of the collar, for different diameters and different heights, was investigated in an experimental flume under clear water scouring conditions. The results showed that proper collar performance reduces the maximum scouring depth, and the collar improves the collar performance significantly when installed on the bed surface. Singh *et al.* (2019) investigated the initial scouring of gravel particles cohesionless to mixtures of silt and sand. The results of this study provided an experimental relationship to determine the critical shear stress of sand particles. Daneshfaraz *et al.* (2021a, 2021b) studied the hydraulic performance of a horizontal screen with a variable diameter on a vertical drop in the experimental. The results showed that with increasing the relative diameter of the horizontal screen, the turbulence length increased and the pool depth decreased. Ghaderi *et al.* (2019) studied scouring around the foundations of Simineh Rood Bridge in Miandoab (Iran) using HEC-RAS numerical simulation. Finally, the obtained results were compared with the results and equations of the experimental model. Ghaderi & Abbasi (2019) studied the local scouring of the airfoil-shaped piers with or without collars in the 3D simulation of flow with FLOW-3D software. The results showed that increasing the length of the airfoil reduced the maximum scour depth. The use of a collar on the pier of the airfoil pier reduces the maximum depth of the scouring hole. Pourshahbaz *et al.* (2020) studied the hydro-morphology of the parallel groynes group as a numerical simulation with FLOW-3D software. They also compared the FLOW-3D simulation results with the results of SSIIM 2.0 software. From the results, it was observed that the accuracy of the FLOW-3D simulator was affected by the landing number and the critical speed ratio (U_{avg}/U_{cr}). Singh *et al.* (2020) investigated the scouring of rectangular bridge abutment with clear water. They presented two equations to calculate the maximum scour depth in equilibrium mode and time-dependent scour depth.

Advances in data processing have also impacted hydraulic studies. As an example, data mining is a process that is performed to explore data; the main purpose of data mining is predicting future performance. Multiple data mining methods can be employed. Artificial neural networks (ANN) are made up of simple operating elements that work in parallel. Artificial neural networks can determine the relationships between the inputs and outputs of a system. Adaptive Neuro-Fuzzy Inference Systems (ANFIS) are a combination of neural networks and fuzzy systems based on fuzzy mathematics. This technique has good capabilities for training, construction, and classification.

Ismail (2018) investigated scouring around bridge piers using an evolutionary neural network. The results showed that the model produced estimates of scour equilibrium depth with many fewer constants compared to the hidden layer of neural networks. Sreedhara *et al.* (2019) investigated the prediction of scour depths near a pier bridge by a swarming group of bees based on a neural network and found that for clear water conditions, the PSO-ANN model method outperforms the ANN model. Azamathulla (2012) examined gene expression programming to estimate scour depth downstream of sills. The results showed that the equation proposed by the GEP method compared to other models, to predict the depth of scouring of the sills with different slopes of the bed performed suitably. Pandey *et al.* (2020a, 2020b) Using experimental data, previous researchers examined the maximum scouring depth using genetic algorithms and multiple linear regression. The relationship between maximum scour depth and the GA method showed more accurate results than MLR. El-Hady Rady *et al.* (2020) predicted the scour depth around a bridge pier using artificial intelligence that was based on conventional regression modeling. Their results showed that the gene programming model is superior to the neuro-fuzzy inference system model. Norouzi *et al.* (2019) used multilayer perceptron (MLP) networks, radial basis function networks, and support vector machines with different kernel functions to estimate the discharge coefficient labyrinth weirs. The results showed that the MLP model had a much higher accuracy than other models. Daneshfaraz *et al.* (2021a, 2021b) investigated the hydraulic performance of vertical drop using a support vector machine, therefore they analyzed hydraulic parameters from 120 different experimental data and 12 support vector machine models.

In previous studies, the phenomenon of scouring near bridge piers has been studied, however the effects of cable supports have not been considered. In addition, while the prediction of scour depth has been investigated previously, the present investigation goes further. Here we wrap the cable around the pier and change the collision angle of the flow to alter the intensity of the downward flow. Other objectives of the research include the following: 1. Investigating the effect of changing the diameter and torsion angle of the cable. 2. The effect of changing the collision angle of the flow to protect the pier and to reduce the scouring depth and also to increase the time required for maximum scouring depth. 3. The use of ANN algorithms and ANFIS to estimate scour depths and then the subsequent comparison of the performance of an artificial neural network with ANFIS. 4. A comparison of the results of the ANNs and ANFIS with experimental results.

## MATERIALS AND METHODS

### Dimensional analysis

*B*is the pier width, L refers to pier length,

*P*denotes the cable diameter,

*V*is the flow velocity,

*V*represents velocity threshold conditions,

_{c}*D*

_{50}is the media diameter size,

*d*is the final scour depth,

_{s}*t*refers to the scour start time,

*t*is the scour equilibrium time,

_{e}*g*is gravitational acceleration,

*y*refers to the flow depth,

*ρ*is water density,

*ρ*is the sediment particle density,

_{s}*υ*is kinematic viscosity,

*α*is the flow collision angle, and

*θ*is the angle of twist of the cable. Using Buckingham's theory of dimensional analysis, Equation (1) can be written in dimensionless format as:

*gy/V*,

^{2}*ρ*,

_{s}/ρ*V/V*,

_{c}*L/B*,

*d*

_{50}/

*B*, and

*y/B*, and the turbulence of the flow from the above parameters and the Reynolds number

*υ/ρVD*, certain simplifications are possible. By simplifying and combining dimensionless parameters, Equation (2) can be rewritten as:

In the above relation, *d _{s}/B* is the final dimensionless scour depth,

*t/t*dimensionless scouring time,

_{e}*P/B*is the dimensionless cable diameter,

*α*refers to the collision angle, and

*θ*is the cable torsion angle.

### Experimental methodologies

The experiments were performed in a rectangular experimental flume with a total length of 14 m, a useful length of 10 m, a width of 0.4 m, and a depth of 0.6 m with a fixed horizontal floor without a slope. The floor of the flume was made of PVC and the walls were made of Plexiglas with a thickness of 10 mm. There is an adjustable gate downstream of the test site that is able to control the water depth in the channel. A constant flow rate of 23 liters per second was regulated by a calibrated valve next to the pump. The range of the experimental portion of the flume is 2 meters long and 0.2 meters wide. To measure the scouring depth, a depth gauge was used. The gauge was movable in all three directions. Table 1 shows the criteria used in the present study.

Sand with a relative density of 2.65 was used to create the sediment. To ensure the uniformity of sediments, these materials have been passed through two consecutive sieves with 0.59 mm and 0.85 mm pore sizes. Residual sediments between the two sieves were selected for this experiment. These sediments were larger than 0.59 mm and smaller than 0.85 mm in diameter. In the present study, the sediments have d_{50} = 0.7 mm and *σ* = 1.23.

Raudkivi & Ettema (1983) found timewise changes in scour depth over three consecutive hours to be not more than one millimeter. In the present study, more than 90% of scouring depth occurs in the first 8 hours, so each experiment was limited to an 8-hour duration.

### Physical models and experiments

Rectangular piers made of Teflon were used in the experimental fabrication. The width and length of the rectangular pier were 30 and 90 mm, respectively. The experiments were performed according to Figure 1, and the piers were divided into three groups according to Table 2.

Research . | Criteria used . | Allowed amount . | The amount of research present . | Reason for review . |
---|---|---|---|---|

Raudkivi & Ettema (1983) | The ratio of channel width to pier width (W/B) | 6.25 | 7.65 | Due to the lack of effect of the channel walls |

Melville & Sutherland (1988) | The ratio of pier width to average grains diameter (b/d_{50}) | Larger than 25 to 25 | 42.85 | Due to the elimination of the effect of sediment grains size on scouring depth |

Melville & Sutherland (1988) | The geometric standard deviation of sediment grains (σ = d_{84}._{1}/d_{15.9}) | Less than 1.3 | 1.23 | Preventing the non-uniformity of sediment grains reduces the depth of scouring equilibrium |

Chiew (1995), Ettema (1980) and Shen et al. (1969) | Flow depth (y) | More than 4 times the pier diameter | 21 | To prevent the increase of scouring depth in shallow flows by increase the flow depth |

Raudkivi & Ettema (1983) | The average diameter of grains (d_{50}) | Greater than or equal to 0.7 mm | 0.7 mm | To prevent the formation of ripple phenomenon in non-sticky sediments |

Raudkivi & Ettema (1983) | Flow velocity (Vc) | 0.9Vc | 0.9Vc | To start local scouring in clearwater |

Research . | Criteria used . | Allowed amount . | The amount of research present . | Reason for review . |
---|---|---|---|---|

Raudkivi & Ettema (1983) | The ratio of channel width to pier width (W/B) | 6.25 | 7.65 | Due to the lack of effect of the channel walls |

Melville & Sutherland (1988) | The ratio of pier width to average grains diameter (b/d_{50}) | Larger than 25 to 25 | 42.85 | Due to the elimination of the effect of sediment grains size on scouring depth |

Melville & Sutherland (1988) | The geometric standard deviation of sediment grains (σ = d_{84}._{1}/d_{15.9}) | Less than 1.3 | 1.23 | Preventing the non-uniformity of sediment grains reduces the depth of scouring equilibrium |

Chiew (1995), Ettema (1980) and Shen et al. (1969) | Flow depth (y) | More than 4 times the pier diameter | 21 | To prevent the increase of scouring depth in shallow flows by increase the flow depth |

Raudkivi & Ettema (1983) | The average diameter of grains (d_{50}) | Greater than or equal to 0.7 mm | 0.7 mm | To prevent the formation of ripple phenomenon in non-sticky sediments |

Raudkivi & Ettema (1983) | Flow velocity (Vc) | 0.9Vc | 0.9Vc | To start local scouring in clearwater |

Tested piers . | Piers diameter (cm) . | Cable diameter . | Twist angle of the cable (degree) . | Collision angle (degree) . |
---|---|---|---|---|

P_{1} | 3 | Non-cable | Non-cable | 0-5-10-15 |

P_{2} | 3 | %10 | 15 | 0-5-10-15 |

P_{3} | 3 | %15 | 12 | 0-5-10-15 |

Tested piers . | Piers diameter (cm) . | Cable diameter . | Twist angle of the cable (degree) . | Collision angle (degree) . |
---|---|---|---|---|

P_{1} | 3 | Non-cable | Non-cable | 0-5-10-15 |

P_{2} | 3 | %10 | 15 | 0-5-10-15 |

P_{3} | 3 | %15 | 12 | 0-5-10-15 |

### Intelligent modeling

#### Artificial neural network

An ANN is a very simple approach that was developed to model the biological structures found in the human brain (Kim *et al.* 2001; Pourtaghi & Lotfollahi-Yaghin 2013).

ANN has a multilayered structure that includes many of the key elements of interconnected processing to mimic brain neurons. The neural network contains computational elements called neurons that combine inputs and determine their weight. Because ANN stores data as a template in a set of processing elements adapted from connection weights, complex maps can be identified through distributed representation features (Kim *et al.* 2001). Figure 2 is a representation of the ANN architecture.

*net*is the weighted sum of the

_{j}*j*neuron for the input received from the preceding layer with n neurons,

^{th}*w*is the weight between the

_{ij}*j*neuron and the

^{th}*i*neuron in the preceding layer;

^{th}*x*is the output of the

_{i}*i*neuron in the preceding layer. The output of the

^{th}*j*neuron (out

^{th}_{j}) is calculated using a sigmoid function as follows:

This type of layered ANN has been utilized to solve many complex problems (Kartam *et al.* 1997). Details of the learning algorithm can be found in Karayiannis & Venetsanopoulos (2013) and interested readers are directed there.

### The adaptive neuro-fuzzy inference system

The compatible ANFIS system consists of 5-layer networks and node connectors. Reasonably structured neuro-fuzzy systems are proportional to input data, membership, rules, and membership functions output. Figure 3 is a representation of neural-fuzzy network architecture with two inputs, one output, and two laws (Aghdam *et al.* 2017).

### Determine the structure of the proposed models

The values *x _{max}*, and

*x*are the maximum and minimum values in the

_{min}*x*range, respectively. Network training and network repetition rates of 0.1 and 400 are used, respectively. As the mean square error (MSE) increases, the network training process automatically stops. An ANFIS model to study two membership functions with 100 reps for a variety of membership function is intended. Considering the effect of the membership function and the use of trial and error, the psigmf membership function provided the best results.

_{i}### Evaluation criteria

*t _{k}* and

*y*are the observed results (experiments) and the output of the neural network, respectively. First, the data were normalized using a Gaussian normalization technique. In the present study, the data were normalized using Equation (6), where

_{k}*x*,

_{min}*x*, respectively, refer to the minimum and maximum data and

_{max}*x*is the normalized data.

_{n}## RESULTS AND DISCUSSION

### Temporal development of scour depth and the flow collision angle

To investigate the ability of cables to reduce the final scour depth, scour depths in the presence and absence of cables were determined and compared. The final depth was obtained at the end of each experiment. In general, for the second class of piers, the final scour depth is 9.09% less than the first type pier. For the third type of pier, the final scour depth is 10.59 and 18.72% less than the second and first pier types.

### Temporal development of scour depth for the first pier and the influence of angle

The temporal development of scour depth for the first pier type and angles of zero, 5, 10, and 15 degrees are provided in Figure 4. Over time, the appearance of horseshoe vortices has also dropped dramatically. These vortices, which enhanced vertical water motions, are primarily responsible for moving and transporting particles. For the first type of pier, a comparison of the 10- and 15-degree cases reveals very small differences, particularly for the first 90 minutes. After 90 minutes, the 15-degree case has a greater slope than the other curves. Also, as the collision angle increases, the scouring depth will increase.

Increasing the collision angle of the flow makes the pier wider and ultimately increases the strength of the horseshoe vortex and increases scouring. For experiments on the first type of pier and at angles of 5, 10, and 15 degrees increases the scouring depth by 4, 20, and 35%, respectively compared to the zero-degree case.

### Temporal development of scour depth for the second pier type and the influence of flow angle

In Figure 5, as the angle varies from zero to 5°, there is not much effect on the scour depth. The two scour depth curves coincide from the initial moment until equilibrium. Conversely, for the 10- and 15-degree angles, the scouring experiences equal slopes for 90 minutes. Thereafter, 15 degree pier has a steeper slope. Approximately 3 hours after the start of scouring, they become parallel again. The second type of pier, with an angle of 5 degrees experiences a 12% depth reduction, compared to the first type. The second type pier at an angle of 10 degrees leads to a 10% reduction in final scour depth; a collision angle flow of 15 degrees has the greatest scouring depth. The effect of cables for reducing the scour depth for this angle and for the second type pier is 10%.

For angles of 5, 10, and 15 degrees and for the second class of pier, there is an increase in horseshoe vortex activity and a consequent depth increase of 3, 21, and 37%, respectively (compared to the 0-degree case).

### Temporal development of scour depth for the third type of pier and the influence of flow angle

Figure 6 shows photographs of the experimental facility and Figure 7 shows the temporal development of scouring. As seen in the figure, for the first and second pier types, the scouring depths at angles of 10 and 15 degrees and for d_{s}/b = 0.2 differ. The piers with angles of zero and 5 degrees are also almost identical.

For the third pier type, it is observed that at an angle of 5 degrees, the scouring depth is reduced 18% compared to the first pier type. At an angle of 10 degrees, the third class of pier has a 17% reduction in the final scour depth compared to the first pier class. All experiments at the angle of 15 degrees have the most scouring and the effect of cables for reducing scour depth (15-degree angle and the third pier type) is 22%. Table 3 shows the reduction of the scour depth for the second and third pier types, compared to the first type of the pier. By comparing Figures 4, 5 and 7, it is concluded that increasing the cable the diameter will reduce the initial scouring depth and the maximum depth.

Tested piers . | Flow collision angle 0 degree . | Flow collision angle 5 degree . | Flow collision angle 10 degree . | Flow collision angle 15 degree . |
---|---|---|---|---|

P_{2} | 12 | 12 | 10 | 10 |

P_{3} | 17 | 18 | 17 | 22 |

Tested piers . | Flow collision angle 0 degree . | Flow collision angle 5 degree . | Flow collision angle 10 degree . | Flow collision angle 15 degree . |
---|---|---|---|---|

P_{2} | 12 | 12 | 10 | 10 |

P_{3} | 17 | 18 | 17 | 22 |

For the third type of pier, a cable with a diameter 15% that of the pier diameter is used and the cable has a smaller torsion angle, with angles of 5, 10, and 15 degrees compared to the pier, there is a depth increase of 3, 20, and 27%, compared to the zero-angle case. Consequently, the third pier type with a collision angle of 15 degrees has a lesser scour depth than the first and second pier types. It can be seen that the third pier leads to less total scouring. As evident in Figures 4, 5 and 7 the scour depth for the third pier with a zero-degree angle is reduced by ds/b = 1.3, 1.4, and 1.6, respectively. Such decreases can be seen from other angles as well. The final scour depth for the third pier is 17% less than for the first pier.

### Temporal development of scour depth according to the type of pier

#### Temporal development of scour depth for first, second, and third pier types at zero degrees

Typically, increasing the collision angle of the flow makes the pier wider and increases the power of the horseshoe vortices. Consequently, as the collision angle increases, the depth of scouring also increases. For the second pier type, a thin cable was used. For the first 90 minutes of scouring, the results are similar to the first pier without a cable. The initial scour depth for the third pier is less than the scour for the second pier. Furthermore, the second pier experiences less scouring than the first pier. This finding demonstrates the influence of a cable in reducing scour depth.

#### Temporal development of scour depth for all three piers at a 5 degree angle

For the three pier types, it was observed that with a flow collision angle of 5 degrees, the scour depth is increased marginally, by 4, 3, and 3%, respectively (compared to the zero-angle situation). As can be seen from Figure 9, when scouring initiates at the third pier, the scour depth is much less than that for the first pier. Therefore, it can be concluded that increasing the diameter of the cable has a significant effect on reducing the depth of scour in the early moments. A comparison of these curves in Figure 9 shows the depth of scouring at this angle for the first type of pier. It is much more than for piers equipped with a cable. The third pier initially prevented the scoured hole from deepening. The final scour depth is closer to the second and third types of piers and is most different compared to the first pier. For all three piers, and for at *t/te* = 0.2, about 90% of the scour depth has developed. Thereafter, the scouring process continues slowly. The results were obtained with a collision angle of the flow of zero and 5 degrees (Figures 8 and 9). The dimensionless depth (*ds/B*) for the first to third type piers has increased from 1.34, 1.45, and 1.6 to 1.47, 1.5, and 1.67, respectively.

#### Temporal development of scour depths for all pier types, at a 10-degree angle

For piers with a 10-degree collision angle, the first, second, and third piers experience a scouring depth increase of 20, 21, and 20% respectively, compared to the zero-degree case. This issue can be seen in Figure 10, when compared to Figures 8 and 9. The second and third pier curves are similar until *t/t _{e}*

*=*0.1. Thereafter, the first pier experiences more scouring than other piers.

Increasing the collision angle of the flow increases the width of the pier and intensifies the downward flow and horseshoe vortices, as already discussed. This leads to an enhancement of vertical flow caused by horseshoe vortices.

#### Temporal development of scour depths for all three piers, at a 15 degree angle

For all three piers, a cable with a diameter that is 15% of the pier diameter was employed. The cable has a low torsion angle. There are depth increases of 35%, 37%, and 27.5%, respectively, for the three piers, compared to the zero-flow collision angle situation. The diagram in Figure 11 for the second and third pier types shows that the scour depth for piers one and two are very similar, until *t/t _{e}* = 0.2. A slight difference is observed for the second pier and is probably due to the insufficiency of the thin cable (with a diameter of 10% compared to the pier). Table 4 shows the increase of the final scour depth with collision angles relative to the zero-degree angle case.

Tested piers . | Flow collision angle 5 degree . | Flow collision angle 10 degree . | Flow collision angle 15 degree . |
---|---|---|---|

P_{1} | 4 | 20 | 35 |

P_{2} | 3 | 21 | 37 |

P_{3} | 3 | 20 | 27.5 |

Tested piers . | Flow collision angle 5 degree . | Flow collision angle 10 degree . | Flow collision angle 15 degree . |
---|---|---|---|

P_{1} | 4 | 20 | 35 |

P_{2} | 3 | 21 | 37 |

P_{3} | 3 | 20 | 27.5 |

To compare the present study with the experimental studies of previous researches, similar models in the same (laboratory) flow conditions should be used. Therefore, similar studies using cables, collars and gaps were used to compare with the present study. For this purpose, the best results of the present study and previous researches have been used in Table 5.

Researcher . | Research specifications . | Pier mechanism . | Maximum scour reduction (%) . |
---|---|---|---|

Dey et al. (2006) | Cylindrical single pier | Cable | 51.1 |

Izadinia & Heidarpoor (2012a) | Cylindrical single pier | Cable and Collar | 52.18 |

Aghli and Zomorodian (2014) | Cylindrical bridge pier in meandering river | Cable and Collar | 69 |

Izadinia & Heidarpoor (2012b) | Cylindrical single pier | Cable and Slot | 25 |

Heidarpour et al. (2010) | Bridge Pier Groups | Collar | 45 |

Davodi et al. (2019) | Bridge Pier Groups | Cable | 56 |

Solimani-Babarsad et al. (2021) | Cylindrical single pier | Cable | 63 |

Present study | Triangular bridge pier | Cable | 37 |

Researcher . | Research specifications . | Pier mechanism . | Maximum scour reduction (%) . |
---|---|---|---|

Dey et al. (2006) | Cylindrical single pier | Cable | 51.1 |

Izadinia & Heidarpoor (2012a) | Cylindrical single pier | Cable and Collar | 52.18 |

Aghli and Zomorodian (2014) | Cylindrical bridge pier in meandering river | Cable and Collar | 69 |

Izadinia & Heidarpoor (2012b) | Cylindrical single pier | Cable and Slot | 25 |

Heidarpour et al. (2010) | Bridge Pier Groups | Collar | 45 |

Davodi et al. (2019) | Bridge Pier Groups | Cable | 56 |

Solimani-Babarsad et al. (2021) | Cylindrical single pier | Cable | 63 |

Present study | Triangular bridge pier | Cable | 37 |

#### Prediction of scour depth by ANN and ANFIS methods

To predict the scour depth using ANN methods and ANFIS, the 11 models with input parameters listed in Tables 6 and 8 were used. From the 11 models. The optimal structure was determined based on performance criteria for both the learning and testing processes. Next, a membership function was adjusted using a recursive diffusion algorithm in combination with the recursive least squares method. To reduce the MAE, the number of membership functions is gradually increased by reducing the penetration amplitude of the cluster centers using a trial-and-error method. To compare ANN and ANFIS methods, the RMSE, MAE, correlation coefficient (CC), and coefficient of determination (DC) are utilized (see Tables 6 and 8).

Row . | Models . | Max. neuron . | Train . | Test . | ||||||
---|---|---|---|---|---|---|---|---|---|---|

CC . | DC . | MAE . | RMSE . | CC . | DC . | MAE . | RMSE . | |||

1 | α, θ, t/t_{e}, P/B | 14 | 0.9821 | 0.9644 | 0.0354 | 0.0767 | 0.9843 | 0.9687 | 0.0355 | 0.0750 |

2 | α, θ, t/t_{e} | 12 | 0.9730 | 0.9466 | 0.0540 | 0.0965 | 0.9725 | 0.9457 | 0.0514 | 0.0882 |

3 | α, θ, P/B | 10 | 0.7473 | 0.5578 | 0.1872 | 0.2718 | 0.7448 | 0.5546 | 0.1872 | 0.2775 |

4 | α, t/t_{e}, P/B | 14 | 0.9731 | 0.9469 | 0.0501 | 0.0939 | 0.9726 | 0.9450 | 0.0520 | 0.0989 |

5 | θ, t/t_{e}, P/B | 6 | 0.5741 | 0.3288 | 0.2690 | 0.3363 | 0.5778 | 0.3337 | 0.2698 | 0.3338 |

6 | α, θ | 10 | 0.7517 | 0.5648 | 0.1826 | 0.2724 | 0.7254 | 0.5228 | 0.1812 | 0.2754 |

7 | α, t/t_{e} | 14 | 0.7982 | 0.6366 | 0.1716 | 0.2476 | 0.7928 | 0.6284 | 0.1676 | 0.2483 |

8 | α, P/B | 12 | 0.7546 | 0.5692 | 0.1864 | 0.2718 | 0.7135 | 0.5033 | 0.1781 | 0.2776 |

9 | θ, t/t_{e} | 10 | 0.5689 | 0.3233 | 0.2719 | 0.3395 | 0.6085 | 0.3667 | 0.2566 | 0.3179 |

10 | θ, P/B | 8 | 0.3562 | 0.1263 | 0.3048 | 0.3873 | 0.3740 | 0.1375 | 0.2823 | 0.3644 |

11 | t/t_{e}, P/B | 12 | 0.5773 | 0.3332 | 0.2692 | 0.3359 | 0.5624 | 0.3131 | 0.2686 | 0.3355 |

Row . | Models . | Max. neuron . | Train . | Test . | ||||||
---|---|---|---|---|---|---|---|---|---|---|

CC . | DC . | MAE . | RMSE . | CC . | DC . | MAE . | RMSE . | |||

1 | α, θ, t/t_{e}, P/B | 14 | 0.9821 | 0.9644 | 0.0354 | 0.0767 | 0.9843 | 0.9687 | 0.0355 | 0.0750 |

2 | α, θ, t/t_{e} | 12 | 0.9730 | 0.9466 | 0.0540 | 0.0965 | 0.9725 | 0.9457 | 0.0514 | 0.0882 |

3 | α, θ, P/B | 10 | 0.7473 | 0.5578 | 0.1872 | 0.2718 | 0.7448 | 0.5546 | 0.1872 | 0.2775 |

4 | α, t/t_{e}, P/B | 14 | 0.9731 | 0.9469 | 0.0501 | 0.0939 | 0.9726 | 0.9450 | 0.0520 | 0.0989 |

5 | θ, t/t_{e}, P/B | 6 | 0.5741 | 0.3288 | 0.2690 | 0.3363 | 0.5778 | 0.3337 | 0.2698 | 0.3338 |

6 | α, θ | 10 | 0.7517 | 0.5648 | 0.1826 | 0.2724 | 0.7254 | 0.5228 | 0.1812 | 0.2754 |

7 | α, t/t_{e} | 14 | 0.7982 | 0.6366 | 0.1716 | 0.2476 | 0.7928 | 0.6284 | 0.1676 | 0.2483 |

8 | α, P/B | 12 | 0.7546 | 0.5692 | 0.1864 | 0.2718 | 0.7135 | 0.5033 | 0.1781 | 0.2776 |

9 | θ, t/t_{e} | 10 | 0.5689 | 0.3233 | 0.2719 | 0.3395 | 0.6085 | 0.3667 | 0.2566 | 0.3179 |

10 | θ, P/B | 8 | 0.3562 | 0.1263 | 0.3048 | 0.3873 | 0.3740 | 0.1375 | 0.2823 | 0.3644 |

11 | t/t_{e}, P/B | 12 | 0.5773 | 0.3332 | 0.2692 | 0.3359 | 0.5624 | 0.3131 | 0.2686 | 0.3355 |

#### Estimations of the final depth of scouring using the ANN method

The 11 models encompass different combinations of input variables to be able to provide the best combination for scouring estimation. The goal is to adjust the models so that the effect of single variables can be analyzed and compared with models that have other input variables. By reviewing the results and considering the evaluation criteria for different models, it was observed that model number 1 is superior compared to the others. This model has the lowest RMSE and MAE (close to zero) and the largest CC and DC (close to one). Table 6 has been prepared to help compare results. It is found that by considering the ratio of cable diameter to pier width (*P/B*) and comparing scour start time to scour equilibrium time (*t/t _{e}*), the effect of the flow collision angle parameter (

*α*) is much more significant than the cable torsion angle parameter (

*θ*). It should be noted that for predictions made with an ANN, models 2 and 4 differ from model 1 by less than 3% in the CC criterion. In other words, the cable diameter parameter to pier width (

*P/B*) has very little effect on scouring.

The diagram in Figure 15 is obtained using the values in Table 6. Values of the performance criteria CC and RMSE are shown as a percentage; values of CC ∼ 1 and RMSE ∼ 0 signify better performance. According to Table 6, and as mentioned in Figure 12, it can be seen that model number 1 (the superior model) is the best, and model number 2 is next in performance quality. Therefore, these two models have the best accuracy. In addition, model 10 has minimal accuracy according to Table 6 and Figure 12, These observations show that the *P/B* and *θ* are unimportant for estimating the final scour depth.

According to the performance criteria studied by the researchers in Table 7, RMSE and R^{2} criteria are the most used compared to other criteria. By comparing RMSE and R^{2} criteria in the study of Bateni *et al.* (2007) with 98% accuracy, Ismail *et al.* (2013) estimated the scour depth around the bridge pier with 83% accuracy. The present study with RMSE and MAE of 0.075 and 0.035, respectively, has good accuracy. Many studies have been done to estimate scour depth, which is of particular importance to designers because of the importance of scour depth around the bridge pier.

Researcher . | Previous research used . | CC . | MAPE . | RMSE . | R^{2}
. | MAE . |
---|---|---|---|---|---|---|

Choi & Cheong (2006) | Laursen and Toch (1956) | – | 179.15 | – | – | – |

Neill (1973) | – | 272.33 | – | – | – | |

Jain and Fischer (1979) | – | 436.65 | – | – | – | |

CSU (Richardson and Davis, 1995) | – | 165.39 | – | – | – | |

Melville (1997) | – | 264.98 | – | – | – | |

Lee et al. (2007) | Laursen and Toch (1956) | 0.8160 | – | 1.0138 | – | – |

Shen (1971) | 0.7119 | – | 0.5994 | – | – | |

Hancu (1971) | 0.7303 | – | 1.1360 | – | – | |

Coleman (1971) | 0.6786 | – | 0.4765 | – | – | |

Ettema et al. (1999) | 0.7523 | – | 1.5825 | – | – | |

BPN (Lee et al. 2007) | 0.9559 | – | 0.1393 | – | – | |

Bateni et al. (2007) | Laursen and Toch (1956) | – | – | 0.0727 | 0.5288 | 0.0497 |

Shen (1971) | – | – | 0.0640 | 0.5815 | 0.0444 | |

Hancu (1971) | – | – | 0.1188 | 0.3284 | 0.0720 | |

Breusers et al. (1977) | – | – | 0.1039 | 0.1221 | 0.0613 | |

Melville & Sutherland (1988) | – | – | 0.1326 | 0.5350 | 0.0761 | |

Melville (1997) | – | – | 0.0589 | 0.6000 | 0.0411 | |

Melville and Chiew (1999) | – | – | 0.0519 | 0.6074 | 0.0393 | |

ANN (MLP/BP) (Bateni et al. 2007) | – | – | 0.0078 | 0.9879 | 0.0051 | |

ANN (RBF/OLS) (Bateni et al. 2007) | – | – | 0.0251 | 0.8422 | 0.0180 | |

Ismail et al. (2013) | Melville and Chiew (1999) | – | – | 0.21914 | 0.6020 | – |

Laursen and Toch (1956) | – | – | 0.21295 | 0.5195 | – | |

Shen (1971) | – | – | 0.20828 | 0.4604 | – | |

HEC-18, US DoT (1995) | – | – | 0.20065 | 0.5943 | – | |

GRNN (Ismail et al. 2013) | – | – | 0.13876 | 0.7240 | – | |

Sigmoid network (Ismail et al. 2013) | – | – | 0.10570 | 0.8366 | – | |

Optimised network (Ismail et al. 2013) | – | – | 0.09301 | 0.8725 | – | |

Zounemat-Kermani & Teshnehlab (2008) | Salim and Jones (1996) | – | – | 1.497 | 0.366 | 1.12 |

HEC-18 (2001) | – | – | 1.064 | 0.726 | 0.77 | |

Sheppard and Glasser (2004) | – | – | 0.991 | 0.818 | 0.697 | |

Ataie-Ashtiani and Beheshti (2006) | – | – | 0.821 | 0.866 | 0.649 | |

FFBP-NN (Zounemat-Kermani & Teshnehlab 2008) | – | – | 0.39 | 0.966 | 0.27 | |

RBF-NN (Zounemat-Kermani & Teshnehlab 2008) | – | – | 0.53 | 0.936 | 0.37 | |

Present study | 0.9843 | – | 0.075 | – | 0.035 |

Researcher . | Previous research used . | CC . | MAPE . | RMSE . | R^{2}
. | MAE . |
---|---|---|---|---|---|---|

Choi & Cheong (2006) | Laursen and Toch (1956) | – | 179.15 | – | – | – |

Neill (1973) | – | 272.33 | – | – | – | |

Jain and Fischer (1979) | – | 436.65 | – | – | – | |

CSU (Richardson and Davis, 1995) | – | 165.39 | – | – | – | |

Melville (1997) | – | 264.98 | – | – | – | |

Lee et al. (2007) | Laursen and Toch (1956) | 0.8160 | – | 1.0138 | – | – |

Shen (1971) | 0.7119 | – | 0.5994 | – | – | |

Hancu (1971) | 0.7303 | – | 1.1360 | – | – | |

Coleman (1971) | 0.6786 | – | 0.4765 | – | – | |

Ettema et al. (1999) | 0.7523 | – | 1.5825 | – | – | |

BPN (Lee et al. 2007) | 0.9559 | – | 0.1393 | – | – | |

Bateni et al. (2007) | Laursen and Toch (1956) | – | – | 0.0727 | 0.5288 | 0.0497 |

Shen (1971) | – | – | 0.0640 | 0.5815 | 0.0444 | |

Hancu (1971) | – | – | 0.1188 | 0.3284 | 0.0720 | |

Breusers et al. (1977) | – | – | 0.1039 | 0.1221 | 0.0613 | |

Melville & Sutherland (1988) | – | – | 0.1326 | 0.5350 | 0.0761 | |

Melville (1997) | – | – | 0.0589 | 0.6000 | 0.0411 | |

Melville and Chiew (1999) | – | – | 0.0519 | 0.6074 | 0.0393 | |

ANN (MLP/BP) (Bateni et al. 2007) | – | – | 0.0078 | 0.9879 | 0.0051 | |

ANN (RBF/OLS) (Bateni et al. 2007) | – | – | 0.0251 | 0.8422 | 0.0180 | |

Ismail et al. (2013) | Melville and Chiew (1999) | – | – | 0.21914 | 0.6020 | – |

Laursen and Toch (1956) | – | – | 0.21295 | 0.5195 | – | |

Shen (1971) | – | – | 0.20828 | 0.4604 | – | |

HEC-18, US DoT (1995) | – | – | 0.20065 | 0.5943 | – | |

GRNN (Ismail et al. 2013) | – | – | 0.13876 | 0.7240 | – | |

Sigmoid network (Ismail et al. 2013) | – | – | 0.10570 | 0.8366 | – | |

Optimised network (Ismail et al. 2013) | – | – | 0.09301 | 0.8725 | – | |

Zounemat-Kermani & Teshnehlab (2008) | Salim and Jones (1996) | – | – | 1.497 | 0.366 | 1.12 |

HEC-18 (2001) | – | – | 1.064 | 0.726 | 0.77 | |

Sheppard and Glasser (2004) | – | – | 0.991 | 0.818 | 0.697 | |

Ataie-Ashtiani and Beheshti (2006) | – | – | 0.821 | 0.866 | 0.649 | |

FFBP-NN (Zounemat-Kermani & Teshnehlab 2008) | – | – | 0.39 | 0.966 | 0.27 | |

RBF-NN (Zounemat-Kermani & Teshnehlab 2008) | – | – | 0.53 | 0.936 | 0.37 | |

Present study | 0.9843 | – | 0.075 | – | 0.035 |

Row . | models . | Train . | Test . | ||||||
---|---|---|---|---|---|---|---|---|---|

CC . | DC . | MAE . | RMSE . | CC . | D.C . | MAE . | RMSE . | ||

1 | α, θ, t/t_{e}, P/B | 0.9626 | 0.9265 | 0.0489 | 0.1009 | 0.7260 | 0.3076 | 0.2792 | 0.3082 |

2 | α, θ, t/t_{e} | 0.9626 | 0.9265 | 0.0489 | 0.1009 | 0.7626 | 0.3258 | 0.1760 | 0.2213 |

3 | α, θ, P/B | 0.7712 | 0.5947 | 0.1610 | 0.2370 | 0.5307 | 0.5846 | 0.3069 | 0.3393 |

4 | α, t/t_{e}, P/B | 0.9626 | 0.9265 | 0.0489 | 0.1009 | 0.7145 | 0.0248 | 0.2220 | 0.2662 |

5 | θ, t/t_{e}, P/B | 0.6773 | 0.4587 | 0.2135 | 0.2738 | 0.0302 | 2.3428 | 0.4357 | 0.4928 |

6 | α, θ | 0.7712 | 0.5947 | 0.1610 | 0.2370 | 0.5312 | 0.1001 | 0.2098 | 0.2557 |

7 | α, t/t_{e} | 0.8090 | 0.6545 | 0.1529 | 0.2188 | 0.5222 | 0.2193 | 0.2132 | 0.2976 |

8 | α, P/B | 0.7712 | 0.5947 | 0.1610 | 0.2370 | 0.5309 | 0.2056 | 0.2596 | 0.2960 |

9 | θ, t/t_{e} | 0.6773 | 0.4587 | 0.2135 | 0.2738 | 0.0302 | 2.3428 | 0.4357 | 0.4928 |

10 | θ, P/B | 0.4862 | 0.2364 | 0.2520 | 0.3253 | 0.0000 | 1.8596 | 0.4180 | 0.4558 |

11 | t/t_{e}, P/B | 0.6773 | 0.4587 | 0.2135 | 0.2738 | 0.0302 | 2.3428 | 0.4357 | 0.4928 |

Row . | models . | Train . | Test . | ||||||
---|---|---|---|---|---|---|---|---|---|

CC . | DC . | MAE . | RMSE . | CC . | D.C . | MAE . | RMSE . | ||

1 | α, θ, t/t_{e}, P/B | 0.9626 | 0.9265 | 0.0489 | 0.1009 | 0.7260 | 0.3076 | 0.2792 | 0.3082 |

2 | α, θ, t/t_{e} | 0.9626 | 0.9265 | 0.0489 | 0.1009 | 0.7626 | 0.3258 | 0.1760 | 0.2213 |

3 | α, θ, P/B | 0.7712 | 0.5947 | 0.1610 | 0.2370 | 0.5307 | 0.5846 | 0.3069 | 0.3393 |

4 | α, t/t_{e}, P/B | 0.9626 | 0.9265 | 0.0489 | 0.1009 | 0.7145 | 0.0248 | 0.2220 | 0.2662 |

5 | θ, t/t_{e}, P/B | 0.6773 | 0.4587 | 0.2135 | 0.2738 | 0.0302 | 2.3428 | 0.4357 | 0.4928 |

6 | α, θ | 0.7712 | 0.5947 | 0.1610 | 0.2370 | 0.5312 | 0.1001 | 0.2098 | 0.2557 |

7 | α, t/t_{e} | 0.8090 | 0.6545 | 0.1529 | 0.2188 | 0.5222 | 0.2193 | 0.2132 | 0.2976 |

8 | α, P/B | 0.7712 | 0.5947 | 0.1610 | 0.2370 | 0.5309 | 0.2056 | 0.2596 | 0.2960 |

9 | θ, t/t_{e} | 0.6773 | 0.4587 | 0.2135 | 0.2738 | 0.0302 | 2.3428 | 0.4357 | 0.4928 |

10 | θ, P/B | 0.4862 | 0.2364 | 0.2520 | 0.3253 | 0.0000 | 1.8596 | 0.4180 | 0.4558 |

11 | t/t_{e}, P/B | 0.6773 | 0.4587 | 0.2135 | 0.2738 | 0.0302 | 2.3428 | 0.4357 | 0.4928 |

#### Results of final scour depth estimation by ANFIS method

In this study, 11 models were performed (see Table 8) to estimate the scouring depth with ANFIS. The results and evaluation criteria for different models showed that model 2 is superior. This model has the lowest RMSE and MAE (close to zero) and the highest CC and DC (close to one) compared to other models. According to the results of Table 8, and by comparing models 7 and 9 and also models 8 and 10 with constant values of parameters (*t/t _{e}*) and (

*P/B*), the effect of the flow angle parameter (

*α*) is found to be much more significant than the cable torsion angle parameter (

*θ*).

The diagram in Figure 13, corresponds to the values in Table 8. The values of CC and RMSE are shown in the figure as a percentage. The greater the distance between the two lines indicates an improved performance. According to Table 8 and seen in Figure 13, model 2 (a superior model) has the lines with the greatest distance and the maximum accuracy. Model 10 has the lowest distance and minimum accuracy according to Table 8 and Figure 13.

According to Tables 6 and 8, the input parameters are the same in the methods used and in the proposed models. Therefore, the comparison of two methods with the same parameters in the input data has been made. Figure 14, shows a comparison of the top models of the neural network and ANFIS method, As can be seen, the ANN method (see Table 6 and Figure 14) (first model CC = 0.9843) has better accuracy than the ANFIS method (second model CC = 0.7626). While the ANFIS method is generally not able to predict scour depths that are in good agreement with experimental results. The numbers provide an underestimate to the final scour depth. If it is necessary to use the proposed methods in practice, it is enough to present the maximum amount of error obtained from the method to the proposed value.

The Table 9 is the results of validation data for researchers who used ANFIS to predict scour depth. Due to the large effect of the number of data and input variables on the inference and according to the fuzzy system computational algorithm, the results of this method, like the neural network method, are in an acceptable range, but it still has less adaptation than the neural network. Due to the fact that in this study only nine different experimental models have been investigated in different conditions, there is not suitable scope for adaptation to the ANFIS computational algorithm. For this reason, it has shown poorer performance in estimation, which can be remedied by performing more and various experiments.

Researcher . | MAPE . | RMSE . | R . | MAE . |
---|---|---|---|---|

Azamathulla (2012) | – | 0.290 | 0.960 | – |

Najafzadeh et al. (2013) | 0.726 | 0.530 | 0.960 | – |

Moradi et al. (2018) | 7.87 | 0.154 | 0.970 | – |

Muzzammil and Alam (2011) | 4.160 | 0.050 | 0.950 | – |

Azimi et al. (2019) | – | 0.135 | 0.978 | – |

Azamathulla & Ghani (2011) | – | 0.0046 | 0.941 | 1.426 |

Najafzadeh et al. (2016) | 27.54 | 0.0281 | 0.89 | – |

Present study | – | 0.221 | 0.762 | 0.1760 |

Researcher . | MAPE . | RMSE . | R . | MAE . |
---|---|---|---|---|

Azamathulla (2012) | – | 0.290 | 0.960 | – |

Najafzadeh et al. (2013) | 0.726 | 0.530 | 0.960 | – |

Moradi et al. (2018) | 7.87 | 0.154 | 0.970 | – |

Muzzammil and Alam (2011) | 4.160 | 0.050 | 0.950 | – |

Azimi et al. (2019) | – | 0.135 | 0.978 | – |

Azamathulla & Ghani (2011) | – | 0.0046 | 0.941 | 1.426 |

Najafzadeh et al. (2016) | 27.54 | 0.0281 | 0.89 | – |

Present study | – | 0.221 | 0.762 | 0.1760 |

#### Sensitivity analysis

By removing each parameter from the series of input parameters, the impact of the parameters could be assessed. The effect of parameter removal on the accuracy of the overall model was quantified using the statistical parameters RMSE, MAE, CC, and DC.

As can be seen from the results of the sensitivity analysis in Table 10, by removing the *α* parameter, the accuracy of the results was drastically reduced. The *α* parameter has the largest effect among the input parameters. the effect of this parameter compared to the total input parameters is a 40.31% reduction in accuracy. Data corresponding to Table 10 are shown in Figures 15 and 16. Also, the L/B parameter according to Table 10 has less sensitivity in estimating the final scour depth.

Variable . | Train . | Test . | Effectiveness (%) . | ||||||
---|---|---|---|---|---|---|---|---|---|

CC . | DC . | MAE . | RMSE . | CC . | DC . | MAE . | RMSE . | ||

α | 0.57 | 0.33 | 0.27 | 0.34 | 0.59 | 0.34 | 0.26 | 0.34 | 40.31 |

θ | 0.97 | 0.93 | 0.05 | 0.10 | 0.97 | 0.94 | 0.05 | 0.11 | 1.28 |

t/t_{e} | 0.74 | 0.55 | 0.18 | 0.27 | 0.76 | 0.57 | 0.19 | 0.28 | 22.80 |

P/B | 0.97 | 0.95 | 0.05 | 0.09 | 0.98 | 0.96 | 0.05 | 0.09 | 0.24 |

L/B | 0.98 | 0.97 | 0.04 | 0.07 | 0.98 | 0.97 | 0.04 | 0.07 | 0.15 |

V/V_{C} | 0.98 | 0.96 | 0.04 | 0.09 | 0.98 | 0.97 | 0.04 | 0.07 | 0.33 |

All Vars | 0.98 | 0.95 | 0.04 | 0.09 | 0.98 | 0.96 | 0.04 | 0.08 | – |

Variable . | Train . | Test . | Effectiveness (%) . | ||||||
---|---|---|---|---|---|---|---|---|---|

CC . | DC . | MAE . | RMSE . | CC . | DC . | MAE . | RMSE . | ||

α | 0.57 | 0.33 | 0.27 | 0.34 | 0.59 | 0.34 | 0.26 | 0.34 | 40.31 |

θ | 0.97 | 0.93 | 0.05 | 0.10 | 0.97 | 0.94 | 0.05 | 0.11 | 1.28 |

t/t_{e} | 0.74 | 0.55 | 0.18 | 0.27 | 0.76 | 0.57 | 0.19 | 0.28 | 22.80 |

P/B | 0.97 | 0.95 | 0.05 | 0.09 | 0.98 | 0.96 | 0.05 | 0.09 | 0.24 |

L/B | 0.98 | 0.97 | 0.04 | 0.07 | 0.98 | 0.97 | 0.04 | 0.07 | 0.15 |

V/V_{C} | 0.98 | 0.96 | 0.04 | 0.09 | 0.98 | 0.97 | 0.04 | 0.07 | 0.33 |

All Vars | 0.98 | 0.95 | 0.04 | 0.09 | 0.98 | 0.96 | 0.04 | 0.08 | – |

## CONCLUSION

In this study, the performance and efficiency of cable in controlling local scour around the pier of a rectangular bridge by changing the flow collision angle were investigated and presented in experimental and intelligent algorithms. Based on the results, by increasing the cable diameter, the initial and final scouring depth can be reduced. The reason for this is to reduce the downward flow and weaken the horseshoe vortices. Using different experimental models, the scouring method and the final scouring depth reduction by cable are described. The general results are as follows:

Wrapping the cable around the bridge pier (with diameters of 10 and 15% of the pier diameter) and angles of 15 ° and 12 ° will reduce the depth of the scour pit by up to 22%.

For the first, second, and third foundation types, scouring starts upstream of the bridge pier and after about 3 hours, it extends downstream of the pier at the nose.

At the beginning of scouring, the presence of horseshoe vortices on both sides of the pier deposit sediments downstream of the pier. After three hours, it reaches the initial depth and is washed.

For the second and third pier types, the rate of scouring is somewhat slower compared to the first pier type.

Reducing the angle of twist of the cable around the pier reduces the depth of scouring. If the cable twists are close together, the number of turns of available cables increases and this reduces the scouring depth.

By increasing the flow collision angle to the pier of the bridge, the scour depth increases. Changing the angle by more than 10 degrees is not recommended.

Analysis using ANN and ANFIS methods showed a high capability for estimating scour depth. It was also observed that the model with input parameters

*α*,*θ*, t/t_{e}, P/B and using a neural network method has the highest accuracy and efficiency with the highest correlation coefficient and coefficient of explanation (CC and DC) and the lowest error (RMSE).The results of the sensitivity analysis showed that by removing the input parameter

*α*, the model error rate increases to a large extent (40.31%). Therefore, this parameter is the most important variable for estimating scour depth.

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## REFERENCES

^{th}IAHR Congress, Paris, France