Rectangular Piers Research Articles

Research and Modification on the Park-Ang Damage Index for Railway Rectangular Piers

ABSTRACT This study addressed the issue of distortion in evaluating the seismic damage state of railway bridge piers using the original Park-Ang damage index. By constructing a parameterized co-simulation program with two finite element models, OpenSees and Abaqus, five sets of flexural failure and five sets of flexural-shear failure rectangular pier quasi-static test results were selected to validate the rationality of the calculation program. Four hundred and eighty parameterized calculations were conducted using this program. The combination coefficient β and critical damage index DI within the Park-Ang damage index were modified using nonlinear regression algorithm and convolutional neural network algorithm. The adaptability of the damage index calculation was ultimately verified through an engineering case study of a simply supported beam bridge. The research findings are as follows: 1) The main factor influencing β is the longitudinal reinforcement ratio, while the axial compression ratio, shear span ratio, volumetric stirrup ratio, aspect ratio, concrete strength, and steel strength are secondary parameters influencing β. 2) Compared to the nonlinear regression algorithm, the convolutional neural network algorithm can better establish a calculation model between pier structural parameters and β, clarifying their relationship. 3) It is recommended to use critical values of 0.11, 0.29, 0.49, and 1.00 for assessing pier damage as no, slight, moderate, severe, and collapse damage when using the damage index calculation model. 4) The Park-Ang index corrected by convolutional neural networks demonstrates improved accuracy and computational stability, making it suitable for practical assessment of seismic damage in bridge structures.

Experimental, Analytical, and Numerical Evaluation of Bridge Pier Scouring

Abstract Due to the rising number of incidents of bridge failure, scouring around bridges has received a lot of attention. Accurate scour depth prediction is a challenge for researchers and experts, despite massive global research efforts. Estimation the scour depth is crucial for both a safety and economy. Numerous factors affect the scour depth. In this work, the scour depth of three distinct pier geometries – circular, oblong, and rectangular – is thoroughly investigated, and the effect of water depth and discharge on the scour depth of a given geometry is evaluated. Three pier shapes were the subject of a total of 27 trials, nine of which combined three discharges with varying flume water depth. Experimental observation of scour depth shows good agreement with analytical and numerical scour depth values. A comparative examination of analytical, experimental, and numerical findings indicates that numerical models can effectively estimate scour depth, offering a cost-effective and time-saving methodology. Results showed that circular and oblong pier geometry shows lesser scour depth than rectangular pier geometry for a specific combination of flow depth and discharge. Scour depth decreased with increasing flume water depth for the same discharge. For the constant flume water depth, higher discharge results in greater scour depth.

Predicting the scouring depth around a rectangular pier with a round nose by artificial intelligence methods

Local scour around bridge piers constitutes a significant phenomenon in river engineering. The development of artificial intelligence models and their capabilities has resulted in the widespread adoption of these models. In the experiments, various factors were considered, encompassing three different pier angles (0, 5, and 10°), six submerged vanes with two angles (20 and 30°) aligned with the flow direction, three vane heights (0, 1.25, and 2.5 cm) on the bed, and a collar. The study evaluated the performance of distinct machine learning models, namely, the multi-linear regression (MLR) model, radial basis function neural network (RBF), multilayer perceptron neural network (MLP), support vector machine (SVM), and adaptive neuro-fuzzy inference system (ANFIS) in predicting the scouring depth. Application of these models (RBF, MLP, ANFIS, SVM, and MLR) yielded positive outcomes, with corresponding R2 values of 0.99, 0.98, 0.97, 0.96, and 0.90 for scour depth assessment. The results demonstrated that the RBF artificial neural network model exhibited excellent generalizability in comparison to the other models. It consistently provided accurate predictions with minimal errors across varying training set sizes. Conversely, the ANFIS model exhibited limited generalizability compared to the other models, as reducing the training set size resulted in a significant increase in prediction errors during testing. Furthermore, although the MLR model demonstrated good generalizability, its prediction error was relatively high compared to the alternative models.

Effects of pier inclination angle and direction on local scour at rectangular and circular piers

Effects of pier inclination angle and direction on local scour at rectangular and circular piers

Hydrodynamic and morphologic investigating of the discrepancy in flow performance between inclined rectangular and oblong piers

Accurate estimation of local scour is crucial for designers and stakeholders that involved in bridge pier construction. Understanding the scour mechanisms at different cross sections is essential. This study aims to re-evaluate how the inclined rectangular and oblong piers influence the local scour. The flow behaviour around two rectangular and oblong shaped piers with vertical and inclination angles (10⁰,21⁰ and 30⁰ downstream flow direction) under steady-current, shallow flow and clear water conditions was numerically investigated. To achieve this, a hydrodynamic coupled with morphological model are created and tested using experimental data sets on flow and scour. The reliability of flow velocity predictions was verified with high accuracy. The maximum scour depth around inclined rectangular and vertical oblong pier was reduced by 19 and 21% respectively compared with vertical rectangular pier. The simulation results reveal that although oblong piers play a significant impact in minimizing scour development in comparison to rectangular piers, inclined rectangular piers may experience significantly less scour. However inclined oblong piers, regardless of their round nose shape (low intensity of the downward flow), demonstrate a less reduction in eroding the bed around the pier compared to the vertical oblong piers.

Scour pattern around a pier in a 180° sharp bend: influence of pier shape under unsteady currents

ABSTRACT The effect of unsteady currents on scour at piers was investigated. The tests were run for nine pier shapes, three installation positions along a 180° bend, four flood durations, and four ratios of rising limb to flood duration for the 100-minute flood durations. Overall, including seven tests performed in the bend without piers, 196 tests were performed. The flow rapidity ranged from the movement threshold to live bed situations. The results indicated that the deepest scour-hole in front of the piers with different shapes was a function of flood duration and the ratio of ascending branch to descending branch had little effect on the final maximum scour-hole depth around the pier. The scour-hole volume is affected by the nose and the cross-sectional shape of the pier. For the rectangular pier, the scour-hole volume is greater than that of the other piers. The average shape coefficient was calculated.

Study on the hydrodynamic added mass of rectangular pier under sine wave actions

As for deep-water bridges in river, sea, and reservoirs, the water-structure interaction is non-negligible when investigating its seismic performance. Morison equation and radiation wave theory are two main methods for calculation of hydrodynamic pressure resulted from water-structure interaction, which cannot truly simulate the complicated interaction between water and structures. This study conducts a series of underwater shaking table tests on seven rectangular steel tubes to predict the hydrodynamic added mass of rectangular piers considering water-pier interaction. The influence of action amplitude, action frequency, water depth, depth of cross section, and width of upstream face of the pier on hydrodynamic added mass is investigated. The results show that the hydrodynamic added mass of pier first decreases and then increases with action frequencies. The hydrodynamic added mass is proportional to a-th (a > 1) power of water depth due to the influence of structures on the movement of water. The hydrodynamic added mass increases with depth of cross section and width of upstream face of pier, and changes slightly with the action amplitude with maximum percentage of 10% and thus can be neglected. Therefore, except for the water depth, depth of cross section, and width of upstream face, the frequency characteristics of ground motions should be considered when analyzing the water-pier interaction under earthquake actions.

Assessment the local scour around vertical and inclined oblong piers under shallow flow condition

Scour around abutment and piers of water structures cause a failure for these structures in most developing countries. Most of the existing scour prediction equations are mainly produced for circular and square piers. However, in reality, many bridge piers behave as oblong piers (round noses). The dimensionless maximum scours depths (ys/D) were extensively investigated for ten pier configurations under shallow flow operating conditions. The length-to-width (L/D) ratio was optimized for the development of the scour hole around inclined and vertical oblong piers. The ys/D depths around vertical and inclined oblong piers are slightly affected by the L/D ratios in contrast to rectangular piers. However, the ys/D value was reduced by values of 5.9–11.6% around the oblong piers compared to the circular one. Furthermore, the appropriate prediction equations were assessed for determining the maximum ys/D for different pier configurations. CSU and Vagfhi equations are modified to give an accurate prediction for the maximum ys/D around vertical and inclined oblong piers, respectively.

Effects of increasing the width of collar on reduction of scouring surrounding the rectangular piers in a 180-degree bend

Employment of protective structures is vital for reducing the effect of the local scour created surrounding the bridge piers. One of the most effective protective structures used for controlling and reducing scour surrounding the bridge piers is the collars. Hence, research on the mechanism of scouring surrounding the combination of pier and collar as well as the effect of collar on reduction of scouring surrounding the pier is of great significance. In this study, the effect of various collar width-to-pier width ratios on reduction of scouring parameters surrounding the rectangular piers has been investigated experimentally in various 180-degree sharp bend positions. The experiments were conducted under clear water and threshold of sediment motion in the upstream straight path. Results indicated that collars with collar width-to-pier width ratios equal to 3 to 4 perform the best at reducing the maximum depth of scouring in front of the nose of piers. Increasing the width of collar surrounding the piers reduces the maximum depth of scouring. Increasing the length of pier reduces the efficiency and effectiveness of the collar in delaying the scour process at the pier nose as well as the amount of the maximum scour reduction. The highest amount of scour depth reduction occurred in the vicinity of the pier and the collar at the 90-degree section with the collar installed with a ratio of collar width to pier width equal to 4 surrounding the piers with a ratio of length to width equal to 2 and 3 by approximately 75 and 70%, respectively.

Experimental investigation and flow analysis of clear-water scour around pier and abutment in proximity

Local scour around bridge piers and abutments is one of the most significant causes of bridge failure. Despite a plethora of studies on scour around individual bridge piers or abutments, few studies have focused on the joint impact of a pier and an abutment in proximity to one another on scour. This study conducted laboratory experiments and flow analyses to examine the interaction of piers and abutments and their effect on clear-water scour. The experiments were conducted in a rectangular laboratory flume. They included 18 main tests (with a combination of different types of piers and abutments) and five control tests (with individual piers or abutments). Three pier types (a rectangular pier with a rounded edge, a group of three cylindrical piers, and a single cylindrical pier) and two abutment types (a wing–wall abutment and a semi-circular abutment) were used. An acoustic Doppler velocimeter was used to measure the three-dimensional flow velocity for analyses of streamline, velocity magnitude, vertical velocity, and bed shear stress. The results showed that the velocity near the pier and abutment increased by up to 80%. The maximum scour depth around the abutment increased by up to 19%. In contrast, the maximum scour depth around the pier increased significantly by up to l71%. The presence of the pier in the vicinity of the abutment led to an increase in the scour hole volume by up to 87% relative to the case with a solitary abutment. Empirical equations were also derived to accurately estimate the maximum scour depth at the pier adjacent to the abutment.

Assessing local scour at rectangular bridge piers

The scour depth at bridge piers depends on a large number of variables. This study aims at revisiting the influence of rectangular piers' shape on local scouring. The scour around circular and rectangular bridge piers with length to width (L/D) of 1, 3, 4.5, 6, 7.5, and 9 was experimentally and numerically investigated at shallow water conditions (water depth to pier width (h/D) ratio varied from 1.4 to 2.32). Fifty-two experimental runs were carried out with a mobile bed made of non-ripples uniform sand with a median sediment grain size (d50) of 0.6 mm. The results show that L/D would influence the dimensionless scour depth (ys/D). The rectangular pier with L/D of 4.5 had the maximum ys/D and at L/D of 7.5 and 9 the ys/D was highly reduced. The Flow 3D model was used to verify the effect of downflow, shear stress, streamwise velocity and turbulence (energy and intensity) on the ys/D. The numerical results emphasized that the maximum scour would occur in terms of downflow and shear stress at L/D of 4.5. A new empirical equation (R2 = 0.904 and RMSE = 0.238) for predicting the maximum ys/D at rectangular piers was obtained. Compared with the similar formulas in the literature for predicting ys/D, accurate predictions at the rectangular pier with L/D of 1–9 were registered in this study.

EXPERIMENTAL AND NUMERICAL STUDY OF THE EFFECT OF A PIER ON SHIP TRAJECTORIES IN CURRENTS

A study is presented of the effect of a pier on ship trajectories in currents. The current flow field around the pier is investigated. Experiments on ship manoeuvring and drift motion in the vicinity of a rectangular pier were carried out in a tank. Different current velocities and current angles were taken into account. The characteristics of the deviations of the ship trajectories from the initial course around the pier are investigated. Experimental findings indicate that the minimum required distance for safety navigation becomes larger with an increase of the current velocity. To obtain the details of continuous three-dimensional flow field around a pier, numerical simulation based on CFD calculations is conducted. The validity of the numerical simulation is demonstrated by comparison with experimental results.

Reduction of local scouring at round-nosed rectangular piers using a downstream bed sill

This study investigated the effectiveness of bed sills in reducing the scour depth with time at rectangular piers in a laboratory. Experiments were conducted just below the threshold of sediment motion (U/Uc = 0.95) for round-nosed piers with the length-to-width ratios of L/b = 1, 2, 3 and 4. Accordingly, a 1 cm thick PVC section as wide as the channel was used as the bed sill, which was flush with the bed and located at various distances, D, in the downstream of the piers, i.e. D/b = 0, 1, 2 and 3. It was found that the efficiency of the bed sill for a rectangular pier was significantly less than that for the circular one; there was a decrease in efficiency and scour depth with an increase of the pier length. The maximum efficiency obtained for the round-nosed piers with L/b = 1, 2, 3 and 4 was 32.5%, 21.3%, 14.4% and 5.7%, respectively. The application of a bed sill to reduce the local scour in round-nosed rectangular piers, when the length-to-width ratio exceeds 2, is therefore not recommended. Furthermore, the efficiency of the bed sill is the best when it is attached to the downstream end of the pier; its efficiency is decreased when increasing its distance from the pier.

Development an empirical formula to calculate the scour depth at different shapes of non-uniform piers

The study of local scour around foundation of bridge piers is very important for safe design of piers and other hydraulic structures. Various studies about local scour around uniform bridge piers but a few studied non-uniform bridge piers, Non-uniform bridge pier is one for which the cross-sectional dimension varies over the length of pier (piers with footings). In this study, the effect of main parameters (pier shapes, foundations shapes, level of foundation, flow intensity, and Froude number) on local scour with different shapes of non-uniform piers were experimentally investigated with five different velocities 0.16, 0.18, 0.21, 0.24, and 0.27) m/sec. The tests were occurred using laboratory flume, operated under the clear water condition using sand as a bed material. The test program was done on five different piers Rectangular, Chamfered, oblong, Octagonal, and Hexagonal, foundation shapes were rectangular, oblong, and hexagonal. The results showed that the rectangular pier with rectangular foundation gives the maximum scour depth about 6.5 cm when foundation is placed above bed level, while the hexagonal pier with hexagonal foundation gives the minimum scour depth 2 cm, when foundation is placed below bed level.

The impact of cables on local scouring of bridge piers using experimental study and ANN, ANFIS algorithms

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.

Experimental and numerical study on thin-walled hollow bridge piers

Research on thin-walled hollow bridge piers is of great importance to the large bridge. To study the nonlinear behavior of the thin-walled hollow bridge piers, two rectangular pier specimens have been tested under quasi-static cyclic lateral displacement and different axial loads. For easier comparison, these two specimens have been tested with constant load and varied load separately. Then an MSC. Marc model is built to compare the skeleton line and energy dissipation properties with experimental results. In consideration of the impact of some important parameters, a parametric numerical model has been built to test its performance with experimental results adopting different axial force and wall height-to-thickness ratio.

Experimental Investigation of Scour Hole Characteristics for Different Shapes of Piers Caused by Flood Hydrograph Succeeding Steady Flow

In this study, the scour depth and dimensions of the scour hole around different shaped piers for the cases of hydrographs succeeding steady flow were studied experimentally. The experiments were carried out by using circular, square, rectangular, lenticular and rectangular with trapezoidal nose to compare the various scour hole geometries at the same flow conditions. Numerous experiments were conducted in a rectangular flume (18.6 m long, 0.80 m wide and 0.75 m deep) with different triangular shaped hydrographs. The flume bed of 26 cm thickness consists of uniform graded material with D50 =1.68 mm. The experiments were carried out in clear water conditions. The temporal variations of the equilibrium scour depths in front of the pier and the scour hole dimensions were recorded by two different cameras. The equilibrium scour depths at lateral sides and downstream of the piers were also measured. Regression analysis was performed in order to derive empirical relations to predict temporal variations of the scour depth in the case of unsteady flow. The shape factor values were also investigated based on the experimental findings and the obtained values were compared to those available in literature. The performance of the obtained empirical relation for circular pier was tested by using limited experimental data available in the literature. The smallest scour hole was observed for the rectangular with trapezoidal noses pier. The increase in the scour hole dimensions for other cross-sections was in the following order: rectangular with circular noses, circular, square and rectangular piers.

Investigation of Flow Pattern around Rectangular and Oblong Piers with collar Located in a 180o Sharp Bend

Flow in river bends is associated with generation of secondary flows that leads to a rather complicated flow pattern around bridge piers located in the bend. In this study, the flow patterns around rectangular and oblong piers models with collar located at the 90o angle of a 180-degree sharp bend in an experimental plume were investigated. The 3D flow velocity data were collected using a Vectrino velocimeter. The experimental results indicated that the presence of the rectangular pier caused more intense deviation of the streamlines towards the outer bank of the bend. Furthermore, installation of the oblong pier, the maximum secondary flow power and angular velocity were decreased, respectively, by 35% and 45% in comparison with the installation of the rectangular pier. In addition, it was found that the maximum turbulence kinetic energy around the two piers was not significantly different, but by installing the rectangular pier, a region with high values of turbulence kinetic energy is formed at 90° near the inner bank. Also, installation of oblong pier reduces the values of shear stress in comparison with the use of the rectangular pier.

Experimental study of the effect of the length-to-width ratio and skewness angles of the pier installed at the bend on scour pattern

One of the causes of the destruction or damage of many bridges in the world is the local scour around the bridge piers. Accordingly, research on effective factors on the scouring pattern around the bridge piers is a necessity. In this study, the parameters of the scour hole created around rectangular piers, such as the depth, area and volume of the scour hole, and the effects of increasing the rectangular pier’s length-to-width ratio and its skewness angle towards the banks on scour hole parameters, bed topography changes and the downstream straight path in a 180° sharp bend has been investigated. The results showed that in a 180° sharp bend, the length of the rectangular pier should be at least 3 and at most 5 times its width. The pier with a length-to-width ratio of 3 had a better performance in terms of reducing scouring along the bend. The maximum depth of the scour hole around the piers occurs when the piers are located at 90°. Increasing the angle of attack caused by skewing the pier towards the inner and outer bank at 90° increases the depth and volume of the scour hole.

Influence of bridge piers shapes on the flow of the lower Yellow River

Abstract The shape of bridge piers across rivers is one of the significant factors that affect the backwater in the river. The study on the influence of bridge pier shapes on the flow patterns of the river is valuable to the design of the bridge and river flooding. Based on the MIKE21 Flow Model hydrodynamic model, dynamic numerical simulations were conducted to investigate the effect of different shapes of bridge piers on water flow. The result shows that rectangular, circular and elliptical piers have a water blocking effect on the river. The flow patterns changed in local areas near the piers. Under the same flow rate, the backwater of the rectangular pier was the largest, followed by the circular piers, and the elliptical pier was the smallest. The value of backwater volume caused by the rectangular pier was 1.95 times the elliptical pier. The elliptical bridge piers basically do not change the overall flow patterns of the river, and have little effect on the river regime. This work provides a reference for the layout of river bridge piers.