Tesis sobre el tema "Scour countermeasure"

Bridge piers within moving water are exposed to an additional failure mechanism known as scour. Upon the scour depth reaching the foundation of the pier, the structural integrity of the pier, and consequently the bridge, can be jeopardized. Bridge pier scour is the result of a three-dimensional flow separation consisting primarily of the horseshoe vortex, flow acceleration along the sides of the pier, and wake vortices. There are numerous factors that can affect bridge pier scour, of which many of them have been studied extensively. However, there are still some factors where the knowledge base is limited: one example is the presence of an ice cover around bridge piers. In order to reduce the risk of failure induced by scour, regardless of the cause, a preferred option is to use scour countermeasures. However, an ideal countermeasure does not exist. Therefore, the purpose of this research is to design and test an improved bridge pier scour countermeasure, while also better understanding the effects an ice cover has on scour. Achieving a new countermeasure design consisted of a hybrid approach that combined both numerical and experimental modelling. The numerical model was used in an iterative manner to expedite the design process, as well as to reduce experimental costs. Upon testing and improving the initial collar design numerically, physical models were constructed for the purpose of testing experimentally. Experimental tests were performed at a 1:30 scale in the presence of a sand bed. The same experimental setup was used to investigate bridge pier scour under an ice cover, except a rigid structure was constructed to replicate an ice cover. The artificial ice cover possessed either a smooth or a rough underside and was installed in such a way to replicate a floating or fixed (pressurized) ice cover. The purpose of the new countermeasure design was to improve on the flat plate collar by guiding the horseshoe vortex in a novel manner. By doing so, the quantity of erosive forces contacting the bed was greatly reduced. In order to reach a final design, a series of prototype designs were tested, and are outlined in this thesis, as they provide valuable insight into the scour problem. The final countermeasure design resembles a contoured collar but is made of riprap, where it was found to reduce the scour depth and volume by 81.0% and 92.3%, respectively, while using 18% less riprap than the conventional flat riprap countermeasure. Upon investigating scour in the presence of an ice cover, it was found that the quantity of scour increases as the ice cover becomes rougher and as the flow becomes more pressurized beneath. Specifically, the scour depth under the rough ice cover and the most pressurized condition increased by 412%. It was demonstrated that implementing any device which increases the width of the pier has inherent limitations for reducing scour. Instead, having a depression around the pier, especially made of riprap, such that it is flush with the bed and can help guide the horseshoe vortex, was found to greatly reduce scouring. Furthermore, it was observed that the presence of any ice cover on the surface of the water generates greater pier scour, therefore necessitating that ice cover always be taken into consideration when designing bridges in cold climates.

Foundations of river bridges need to be protected with respect to excessive scouring. Degree of protection depends on the severity of scouring action around bridge piers and abutments. A case study is carried out to design appropriate protective measures for sequential viaducts located on Ankara-Pozant highway in Turkey. A number of analyses are conducted to obtain water surface profiles throughout the study reach. Local scour depths at piers and abutments of the viaducts are then obtained. The design process for countermeasures is performed concerning hydraulic, hydrologic, constructional, and economical requirements. To this end, riprap, partially grouted riprap, and articulated concrete blocks are studied in these view points. A criterion based on a selection index, which is defined by the National Cooperative Highway Research Program in the USA, is applied in this study. Implementation of partially grouted ripraps at infrastructural elements is found to be an appropriate solution.

Scour at bridge piers is considered as a significant safety hazard. Hence, scour countermeasure design plays a critical role to hinder the scour potential at bridges. The selection methodology for a scour countermeasure varies with respect to site conditions, economy, availability of material and river characteristics. The aim of this study is to review the literature on this topic to gather universally accepted design guidelines. A user-friendly computer program is developed for decision-making in various sequential steps of countermeasure design against scouring of bridge piers. Therefore, the program is eventually intended to select the feasible solution based on a grading system which deals with comparative evaluation of soil, hydraulic, construction and application aspects. The program enables an engineer to carry out a rapid countermeasure design through consideration of successive alternatives. A case study is performed to illustrate the use of this program.

Riprap is the most commonly employed countermeasure where bridge piers need to be protected against possible undermining by scour. An extensive review of available design techniques revealed a wide range of equations and proposed design procedures but no generally accepted method for riprap sizing and implementation. The aim of this study was to develop a design procedure for riprap protection at piers which can be used in most river environments. The failure mechanisms and stability of riprap layers around cylindrical and rectangular shaped piers were examined in a comprehensive experimental study. The study assessed the importance of various riprap, flow, sediment, and pier parameters. Parameters for investigation were determined by dimensional analysis and included riprap placement and arrangement. A riprap size prediction formula was developed based on an allowable maximum local scour depth of up to 20%. This equation has been incorporated in a design approach which was tested through a model study of the Hutt Estuary Bridge. The influence of various parameters on riprap stability are incorporated in the equation by way of adjustment factors. The adjustment factors, KY and KD, represent the effects of riprap placement and pier/sediment size ratio effects respectively. They were deemed the most important parameters in riprap layer performance and are therefore included in the riprap size prediction formula. Additional experiments using synthetic filters have shown their ability to eliminate local scour, however they are susceptible to failure under degrading bed conditions. Degrading bed conditions cause the riprap to subside as a layer with the downward movement of the surrounding bed. Subsidence allows the layer to withstand rapid short term degradation. However long term degradation will ultimately result in failure of the stone protection. A preliminary experimental study of the use of submerged vanes as a scour countermeasure was performed. Submerged vanes have been used previously in channel protection with much success. Results indicate that vanes with a length to height ratio greater than one can reduce the maximum local scour depth in live bed conditions by as much as 34%. Further testing is required to develop a complete design procedure.

Many bridges are destroyed or completely failed during floods due to excessive scouring around bridge piers and abutments. Safe bridge design is based on joint consideration of structural, hydraulic, and geotechnical aspects. This study is concerned with the investigation of various types of countermeasures against scouring at bridge sites. The design criteria for various countermeasures are reviewed in terms of hydraulic, hydrologic, constructional, and economical requirements. (Conditions of applicability of these countermeasures are evaluated and designed for different return periods of flow, and hydroeconomic analyses are performed for Esenbosa Bridge). Based on the evaluation of the results of hydroeconomic analyses, combinations of rock riprap and grout filled bags are found to be appropriate measures for piers and abutments against scouring whereas vegetation is observed to be applicable for bank protection.

Bridge failures are generally resulted from scour of the bed material around bridge piers and abutments during severe floods. In this study, scour phenomenon around bridge abutments and collars, located at abutments as scour countermeasures, were experimentally studied. The experimental study was carried out under clear-water scour conditions with uniform non-cohesive sediment (having a grain size diameter of d50=0.90 mm). The experimental flume is a rectangular channel of 30 m long and 1.5 m wide filled with this erodible bed material. Based on the results of 97 experiments conducted during the study, the efficiency of various sizes of collars, which were used to reduce the local scour depth, located at different elevations around the abutments was determined. The results obtained were compared with previous studies, and the effect of the sediment grain size on the performance of abutment collars was emphasized. It was noticed that when the collar width was increased and placed at or below the bed level, the reduction in scour depth increases considerably. It was also found out that the change of the sediment size did not affect the optimum location of the collar at the abutment, which yields the maximum scour reduction around the abutment.

During severe floods, bed material around bridge piers and abutments are scoured by the flow and as a result, bridges are subject to damages. These damages are mostly unrepairable and can result in loss of lives and property. In this thesis study, abutment scour under clear-water condition was investigated and collars were tested as scour countermeasures around the abutments. The experimental study was carried out in a rectangular channel with an almost uniform cohesionless bed material of d50=1.50 mm for a test period of 3-hours. The channel was 28.5 m long and 1.5 m wide. The erodible bed material was placed into the test section that was 5.8 m long and 0.48 m deep. For this thesis study, 60 experiments were carried out with and without various collars placed at different elevations around the abutments. The scour formation around the abutments with collars was observed and scour reduction efficiencies of the collars were studied. Experiment results were compared with the previous studies of Dogan (2008) and Kayatü
rk (2005) in terms of sediment size, abutment shape and flow depth, and the effects of these factors on collar'
s scour reduction efficiency were studied. Based on the results of the experimental studies, it was observed that scour depths decreased as the collar width increased and the collar placed deeper into the sediment bed for a given abutment length. When the present study and the previous studies were compared, it was observed that sediment size and flow depth had no significant effect on the scour reduction performances of the collars.

Many river bridges fail or are seriously damaged due to excessive local scouring around piers and abutments. To protect a bridge from scour-induced failure, it should be designed properly against excessive scouring and its scour criticality should be checked regularly throughout the service life to take prompt action. The Federal Highway Administration of United States (FHWA) developed a program, HYRISK, as a basis for evaluation of existing scour failure risk of a bridge. It provides implementation of a risk-based model, which is used to calculate the annual risk of scour failure of a bridge or series of bridges in monetary values. A case study is carried out for a bridge crossing Fol Creek in Black Sea Region (close to Vakfikebir), for the illustration of this software. Besides, hydraulic analysis and scour depth computations of the bridge are carried out via HEC-RAS program. Also, a study is carried out to recommend scour countermeasures that can be applied to the aforementioned bridge.

The major damage to bridges occurs due to scour of the bed materials around piers and abutments during severe floods. This study involves the experimental investigations of the various scour patterns forming around abutment models tested with and without collars as scour countermeasures. The experiments were conducted in a rectangular channel under clear-water scour conditions. In the first part of this study, 34 experiments were conducted with semi-circular end abutment models with and without a collar for a period of 3 hours. Collars of various sizes were placed at different elevations on the abutment models, and the scour reduction efficiencies of collars were investigated for the different flow depths. Based on the results of the experimental studies, the optimum locations of collars on the abutments, which result in minimum scour depth around the abutments, are obtained at the bed level and below the bed level depending on the flow intensity values. In the second part of this study, the effects of flow depth and abutment length on the temporal development of local scour at bridge abutments were studied. 20 experiments were performed without collars for a time period of 8 hours. It was observed that at the upstream of the abutment, the depth of the local scour increases rapidly within the first three hours of the experiment for the different flow depths.

碩士
國立成功大學
水利及海洋工程學系碩博士班
93
Experiments of bridge pier scour are carried out under steady clear-water scour conditions with uniform sediments. The case studies on the use of penetrant structure as a pier scour countermeasure are reported. Based on the experiments of bridge pier scour to study the effect of penetrant structure of the bridge pier on the local scour. Penetrant structure’s various parameters are considered. Laboratory data are used to assess the influence of each parameter. 　The results of this study indicate that the local scour depth decreases as the penetrant structure were laid on bridge pier ahead. Penetrant structure improved the protection of bridge pier attained to 61.98％.

碩士
國立成功大學
水利及海洋工程學系專班
95
Because of the rapid flow of rivers which have steep slope and the east-west traffic system in Taiwan, there are numerous structures built in river course, such as bridge and abutment. These structures are usually in the danger of being destroyed since water elevation rise and fall fast during the storm period. For instance, the bridge pier will be imperiled when bed scour develops rapidly and causes pier to be exposed, after a flood goes by. Previous study of pier scour countermeasure used to using physical model for simulation in laboratory channel, and seldom performed field experiment in river to figure out the feasibility and the effect of scour countermeasure. Therefore, some researches of new countermeasures, which are different from present common ones, were only on theoretical step. The major work of present study was to investigate the influence of porous structure used to prevent scour by changing its distance from pier, formation of structure and arrangement. Some subjects were studied as follows: (1) the distance from pier and arrangement of a porous structure group; (2) relation between the above-mentioned two parameters and the velocity-decrease rate; (3) the relation between the porous structure formation and velocity-decrease rate; (4) the other results of experiment performed in other river. According to field experimental result, the best disposition for resisting pier scour was figured out. From the results, velocity-decrease rate reached and surpassed 70% when distance from pier was one time the diameter of pier, the structure formation was double layer, and the group arrangement was an inverted triangle form. In this situation, the down-flow strength was decreased in front of the pier. The strength of horseshoe vortex around pier was also diminished because of the flow diversion and shelter effect of porous structure, therefore, the flow was insufficient for moving sediment of bed around bridge pier. The scour depth was smallest in this case, in another word; the protective effect was the best.

碩士
逢甲大學
水利工程與資源保育研究所
98
In the west of Taiwan, bed elevations of many rivers lowered down seriously. River and bridge management bureaus often construct bridge protection works around piers to reduce the scouring of the pier foundations. However, the results are still unsatisfactory. In this study, the use of ring columns as a pier scour countermeasure is reported. The ring columns consisting of cylindrical rubber rings are placed upstream of a bridge pier to reduce the flow impacting energy and scour by its’ irregular surface roughness and porous characteristics. A series of experiment was conducted with uniform sediments under the clear-water steady flow (V/Vc=1) conditions. Various parameters including diameter, thickness, height of the ring columns and distance between ring columns and bridge pier are considered. Laboratory data are used to assess the influence of each parameter. Based on experimental results, when the diameter of the ring column is equal to the pier diameter, the ring columns could disperse the transverse flow and generate large friction to increase the protective efficiency on the pier foundation. If the thickness of each layer of the ring column is smaller than one-third of the pier diameter, the scouring depth of the pier could decrease to 61% of the original value. If the height of the ring column is higher than the water surface, the retardation cross-sectional area and friction around the ring columns will both be increased, and provide better protective efficiency than the case that the ring columns are submerged. When the distance between the ring columns and pier is equal to the diameter of the pier, it will generate a minimum scouring depth. Based on the regression equation from the experimental results, the diameter of the ring columns is the major parameter influencing the scouring depth. The influenced levels of other parameters to the scouring depth are the height of the ring columns, the distance between the ring columns and the pier, and the thickness of each layer of the ring columns in turn. The results show that the maximum scouring depth and its range of the porous ring columns are obviously less than the solid ring columns and cylindrical protection works. The porous ring columns provide the space of energy dissipation for the down-flow, and effectively reduce the flow impacting energy. The friction force of ring columns caused by the irregular geometric shape not only reduces the kinetic energy but also decreases the pier scouring. In summary, the best arrangement of this research is that the diameter of ring column equals to the diameter of the pier, the height of the ring column exceeds the flow depth, and the distance between the ring columns and pier equals to the pier diameter, which reduces the pier scour depth for 65%.

碩士
國立成功大學
水利及海洋工程學系碩博士班
94
This paper mainly studies about “Nappe Guidance Method” taken as a local scour countermeasure in a Free Overfall. From the results of the experiment, “Nappe Guidance Method”, which is under a relative hight with the surface of downstream and different contact condition of nappe, will create three different types of flow: “the First-type”, “the Second-type”, and “the Third-type.” In addition, the outcome of Hydraulic Jump, which results from the Second-type’s flow condition, has the best effective protection to the bottom bed. And the eroding rate can be reduced over than 70%. Except to the best protection of the Second-type, the flow condition of the Third-type also can effect to reduce the maximal depth of scour by lowering the topper nappe discharge. It reaches to more than 50% to reduce the eroding rate. According to the result of experiment, “Nappe Guidance Method” certainly can reduce the depth of the maximal scour by changing the flow condition, and it furthers to achieve our goals of protection.

碩士
國立成功大學
水利及海洋工程學系碩博士班
93
This paper mainly inquire about Cheng Kung Artificial Waterweeds (CKAW) as a pier scour countermeasure in a free overfall. From the experiment and the results, we know that the effect of diversion was not effectively improved by using CKAW individually in free overfall condition. It indicated that the effect of local pier scour protection is better than total scour protection. However, the efficiency of total protection was improve more than 43.5% by using CKAW with support bar. Furthermore, the effect of pier scour protection in bridges was also investigated by changing length of CKAW. The results showed that length of the CKAW was not related to the effect of pier scour protection.

The use of riprap and cable-tied blocks as scour countermeasures at bridge abutments is investigated. Riprap is the most common armouring scour protection method used at bridge abutments and approach embankments. Despite the widespread use of riprap protection, the guidelines for its use at bridge abutments are based on limited research. The aim of the experimental study was to determine the requirements of riprap and cable-tied block apron countermeasures to protect bridge abutments from scour damage, and to produce design guidelines for their use. The two types of bridge abutments used in the experimental study were a spill-through abutment situated on the floodplain of a compound channel, and a wing-wall abutment sited at the edge of the main channel. The spill-through abutment experiments were run under clear-water conditions, and the variations in the scour hole geometry were measured for different abutment and compound channel geometries, apron widths and apron types. The wing-wall abutment experiments were run under live-bed conditions, and the settled apron geometries were measured for different flow depths, flow velocities, apron widths, apron types and apron placement levels. The flow fields around the abutments were also measured for both abutment types. The clear-water spill-through abutment results show that the protection aprons do not significantly reduce the scour depth at abutments, but instead deflect the scour hole further away from the abutment, protecting it from scour failure. The experiments also show that cable-tied block aprons allow the scour hole to form much closer to the abutment compared to equivalent riprap aprons. Equations were developed to predict the scour hole position and size, and the minimum apron extent required to prevent the scour hole from undermining the abutment. For the live-bed wing-wall abutment experiments, the troughs of the propagating bed-forms undermined the outer edges of the aprons, causing them to settle. Equations were developed to predict the settled apron geometry at the equilibrium scour conditions. The predicted scour hole depth and position for clear-water scour conditions, or the predicted apron settlement geometry for live-bed scour conditions can be used in a geotechnical stability analysis of the abutment. The geotechnical stability analysis forms the basis of the abutment scour countermeasure design procedure, which was developed from the experimental study. Further experimental work is required to increase the robustness of the bridge abutment scour countermeasure design procedure and make it applicable to a wider range of situations.

Thesis (Ph.D.)--Michigan Technological University, 2005.
Includes bibliographical references. Also available online via the Michigan Technological University Library website (http://www.lib.mtu.edu/). Also available on the World Wide Web.

碩士
淡江大學
水資源及環境工程學系碩士班
106
Pier scouring can cause damage of hydraulic construction, so protecting piers against scour is an important issue in bridge construction. In the study, a series of experiments were conducted under the unsteady flow conditions to evaluate the effectiveness of different countermeasures protection arrangements for protecting the pier. Both central peak and advanced peak hydrographs were adopted and uniform sediment was used. Sacrificial piles, threaded pile, and submerged vanes were adopted. This study considered various parameter, including (1)numbers of piles, (2)threaded pile diameter and thickness, and (3)vane thickness. Temporal evolutions of pier scour are recorded by using a probe. The results show that the efficiency of submerged vanes and threaded pile are less than 50% within 30 minutes; however, after 30 minutes, the scour depth with protection exceeds that without protection. The countermeasures of submerged vanes and threaded pile do not perform well, compared to sacrificial piles. The average efficiency of sacrificial piles up to 40%, and the maximum efficiency of five sacrificial piles can exceed 100%. Consequently, sacrificial piles have the most significant efficiency in the three countermeasures.

Dissertação de mestrado integrado em Engenharia Civil (área de especialização em Perfil de Hidráulica e Ambiente)
Uma das causas associada ao colapso de pontes é o fenómeno de erosão localizada na vizinhança de pilares de pontes. É importante prever a profundidade máxima da cavidade de erosão localizada em redor dos pilares, pois a estrutura pode entrar em colapso e originar acidentes, pondo em risco vidas humanas. A presente dissertação descreve um estudo experimental da erosão localizada na proximidade de pilares de pontes. Para analisar este fenómeno, foram utilizados quatro pilares com 20 mm de dimensão transversal, sendo dois circulares e dois alongados. Um dos pilares circulares e um dos pilares alongados apresentavam uma ranhura (“slot”), correspondente a uma medida de alteração do escoamento. Os outros pilares, circular e alongado, eram simples. Foi utlizada uma areia com diâmetro médio de 0,332 mm, uma altura de água do escoamento igual a 5 cm e um caudal de 12,9 . Estudou-se a evolução temporal da profundidade máxima da cavidade de erosão. Observou-se que a profundidade máxima da cavidade de erosão evolui mais rapidamente na fase inicial do processo erosivo. Comparando os pilares com ranhura com os pilares simples, a profundidade da cavidade de erosão foi maior nos simples. Comparando as geometrias dos pilares, no pilar alongado observou-se que a profundidade da cavidade de erosão localizada foi menor. Foram retirados moldes da cavidade de erosão localizada de todos os ensaios realizados de forma a estudar o relevo da cavidade de erosão.
One of the causes associated with the collapse of bridges is the phenomenon of scour around bridges piers. It is important to predict the maximum scour depth around the piers, because the structure may collapse, originating accidents that may put human lives at risk. The present dissertation describes an experimental study of scour around bridges piers. In order to analyse this phenomenon, four piers with 20 mm of transversal dimension each were used, two of them were and the other two oblong. One circular pier and one oblong pier featured a hole (“slot”) corresponding to a flow-altering countermeasure. The others circular and oblong pier were simple. Sand with a mean diameter of 0,332 mm was used, in a free surface flow with a water depth equal to 5 cm and a flow rate equal to 12,9 m3h-1. The temporal evolution of the maximum scour depth was studied. It was observed that the maximum scour depth develops more quickly in the initial phase of the erosive process. Comparing piers with flow-altering countermeasures with simple piers, the scour hole maximum depth was higher in case of the simple piers. Comparing the piers geometries, it was observed that the scour hole maximum depth was smaller in case of oblong piers. Paraffin and vaseline casts were used to study the scour hole topography for all the experiments that were carried out.

Dissertação de mestrado integrado em Engenharia Civil
O fenómeno da erosão localizada na vizinhança de pilares de pontes é uma das causas associadas ao colapso destas estruturas. É imprescindível prever a máxima profundidade da cavidade de erosão localizada em torno dos pilares porque a estrutura poderá entrar em rotura, dando origem a acidentes que poderão colocar vidas humanas em risco. A presente dissertação descreve um estudo experimental da erosão localizada sem transporte sólido, em torno de pilares fundados em leitos não coesivos. A implementação de uma ranhura no pilar como medida de mitigação de alteração do escoamento foi avaliada no caso de pilares circulares e alongados. Foram utilizados quarto pilares com 20 mm de dimensão transversal, sendo que num dos pilares circulares e num dos pilares alongados foi implementada uma ranhura que corresponde à medida de mitigação de alteração do escoamento. Foram utilizadas duas areias, uma uniforme e outra não uniforme, ambas com diâmetro médio igual a 0.328 mm, num escoamento com superfície livre com profundidade de água igual a 5 cm e um caudal igual a 12.96 m3h-1. A evolução temporal da máxima profundidade da cavidade de erosão foi estudada, e a topografia da cavidade de erosão foi analisada. Verificou-se que a profundidade maxima da cavidade de erosão evolui a um ritmo maior na fase inicial do processo erosivo. Pôde também verificar-se que a fase de equilíbrio é atingida mais rapidamente quando se utiliza areia não uniforme, comparando com a areia uniforme. Conclui-se que a máxima profundidade da cavidade de erosão é menor em pilares alongados do que em pilares circulares. Comparando os pilares com ranhura com os pilares simples, a profundidade da cavidade de erosão foi maior nos simples, e a medida de alteração do escoamento é mais eficaz em pilares circulares do que em pilares alongados. Observou-se que o ângulo entre a linha de maior declive do talude da cavidade de erosão e o nível inicial da areia é maior a montante do pilar, quando comparado com o de jusante. Os ângulos formados entre o talude da cavidade de erosão e o nível inicial da areia diminuem com a implementação da medida de mitigação de alteração do escoamento, tanto nos pilares circulares, como nos pilares alongados.
One of the causes associated with the collapse of bridges is the phenomenon of scour around bridges piers. It is important to predict the maximum scour depth around the piers, because the structure may collapse, originating accidents that may put human lives at risk. This work describes an experimental study of clear water scour around bridge piers, placed in a cohesionless bed of sediments. The use of pier slot as a flow-altering countermeasure against bridge scour is evaluated, in the case of circular and oblong piers. Four piers with 20 mm of transversal dimension were used, with one circular pier and one oblong pier that featured a slot, corresponding to a flow-altering countermeasure. Experiments were carried out with two different sands (uniform and non uniform) of equal mean diameter (0.328 mm), in a free surface flow with a water depth equal to 5 cm and a flow rate equal to 12.96 m3h-1. The temporal evolution of the maximum scour depth was studied and the topography of the scour cavity was analysed. It was found that scour depth increases very rapidly during the initial period of the erosion process. Time for the equilibrium depth to be achieved is smaller in case of uniform sand beds, than in case of non uniform sand beds. It was observed that the scour hole maximum depth was smaller in case of oblong piers, when compared with circular piers. Comparing piers with slot with simple piers, the scour hole maximum depth was higher in case of the simple piers, and the flow-altering countermeasure is more efficient in circular piers when compared with oblong piers. The angle between the bed of the scour cavity and the initial sand level is higher upstream from the pier, when compared with the angle of the downstream scour cavity slope. The angles between the bottom of the bed of the scour cavity and the initial sand level decrease with the implementation of the flow-altering countermeasure, both in circular and oblong piers.