Cylindrical Pier Research Articles

Numerical Modeling of Tsunami Wave Run-Up and Effects on Sediment Scour around a Cylindrical Pier

AbstractThe linked two-dimensional hydrodynamic and sediment-scour models have been enhanced to simulate tsunami wave run-up on a sloping beach to determine its effects on sediment scour around a cylinder pier located in the wave breaking and run-up zone. To resolve the steep wavefront of the tsunami bore, the kinetic flux vector splitting scheme was adopted to solve the hydrodynamic model equations in the unstructured triangular mesh. The models have been validated by comparing model simulations with experimental data. The results indicate that the model predictions of water surface elevations and velocity match well with the measured data. The error for peak flood elevation ranges from 0.01 to 0.11 m, and the maximum error for the peak velocity is 6%. The model simulations adequately characterize the tsunami wave propagations and transformations as the wave approaches the beach from offshore, especially for the sharp tsunami front before it breaks and the tsunami bore runs up in the beach slope. The mod...

“Temporal variation of scour around circular bridge piers” by U.C. Kothyari and Ashish Kumar, ISH Journal of Hydraulic Engineering, 16(Suppl 1), 2010

The authors are congratulated for developing a new mathematical model and algorithm for computation of local scour in cylindrical bridge piers. It may be pointed out that local scour is only a part...

Numerical Modeling of Turbulent Kinetic Energy of 2D Horizontal Flow for Scouring Simulation in Cohesive and Granular Bed around Circular Piers

In order to simulate the bed scouring around piers, many researchers have developed sophisticated numerical algorithms. In this work, the numerical modeling of souring around cylindrical piers are performed by solution of the shallow water equations flow and depth averaged turbulent model equations coupled with the empirical relations for cohesive and granular beds. The shallow water flow equations include to the depth average continuity and motion and depth average turbulent model equations in horizontal Cartesian coordinate systems. For computation of bed erosion at each time step, the numerical results of turbulent flow model are combined with SRICOS empirical bed erosion empirical relations, which are derived from laboratory experiments. The governing partial differential equations of depth average turbulent flow are converted to discrete form using a vertex base finite volume method suitable for triangular unstructured meshes. Therefore, scouring due to flow around piers with arbitrary shape can be modeled. Several test cases of scouring on the cohesive and sandy beds around circular piers are modeled using the developed numerical model and the computed results are compared with the laboratory measurements reported for scouring in cohesive and granular bed around circular piers by the previous experimental workers. Despite of the simplicity and light computational work load of the introduced algorithm, the computed results show promising agreements with the anticipated trends.

Initial stages of erosion and bed form development in a turbulent flow around a cylindrical pier

[1] Bed load transport and erosion in fine sediment beds are mainly driven by the dynamics of the near-bed turbulent flow. In situations when the shear stress is not sufficiently high to produce significant transport, the presence of an obstacle can initiate erosion and trigger the development of bed forms, which are produced by the emergence of the turbulent horseshoe vortex (THV) system. We develop a numerical model to investigate the initial stages of erosion and the development of ripples produced by the THV system in the vicinity of a surface-mounted cylindrical pier. The flow is simulated using the detached eddy simulation approach, which has been shown to accurately resolve most of the turbulent stresses produced by the THV. To compute the erosion, the Exner equation is coupled to a new bed load transport model that directly incorporates the effect of the instantaneous flow field on sediment transport. The morphodynamic model is integrated simultaneously with the flow equations using an arbitrary Lagrangian-Eulerian method for moving boundaries. Even though the time rate of scour is slower compared to the observations, the computed results exhibit essentially all the dynamics of erosion, including the emergence of ripples reported in the experiments of Dargahi (1990). The bed forms show similar velocities as reported in the experiments and are shown to be statistically similar to ripples measured in laboratory experiments and in nature. To our knowledge, this is the first three-dimensional simulation to capture the ripple dynamics that evolve naturally from the nonlinear interactions between the flow and the bed.

Numerical simulation of flood waves and calculation of exerted forces on the cylindrical piers in contraction channels with different cross section profiles

A numerical model based on two-dimensional shallow water equations is presented. The depth-averaged velocity components with free-surface elevation have been used as independent variables in the model. The finite element technique is applied to discretize the spatial derivatives. Triangular elements with quadratic and linear interpolating functions are employed for two horizontal velocity components and the free-surface elevation, respectively. The standard Galerkin method is applied for discretization of the governing equations. Time discretization is performed using an implicit scheme. The resulting linear system of equations is solved by the GMRES method. The model is validated using three test cases and the results are compared with an analytical solution, the result of numerical work and experimental data, respectively. Favorable agreement was achieved in all three cases. Subsequently, the developed model is applied to simulate free-surface elevation through a channel contraction. The effects of width of the narrow section as well as the profile of the cross section of the channel on the wave forces exerted on a circular cylinder were studied. This was done in a channel with a quartic narrow section. Plots of time histories of the drag coefficient on the cylinder were produced, demonstrating the effects of the mentioned parameters.

Vortex scouring process around bridge pier with a caisson

An experimental investigation to predict the characteristics of scour vortices related to the scour depth of caisson piers was conducted. Two median size sediments were used as bed materials. Three types of piers, namely a cylindrical pier, a cylindrical pier with a caisson, and a nose pier were considered. The size and the rotational speed of the primary vortex were measured and correlated to the flow and pier parameters. The vortex power available to scour the sediment is related to the power provided by the vortex in the scour process. The equilibrium scour depth was predicted based on the concept of power available in the primary scour vortex equal to the resisting power of sediment in the scour hole. The prediction of the scour depth agrees well with literature data.

Estimating Equilibrium Scour Depth at Cylindrical Piers in Experimental Studies

Using data from six very long experiments on local scour at single cylindrical piers, some of the existing equilibrium criteria found in the literature are assessed. It is found that common criteria, which consider scour depth increments in 24 h or the observation of horizontal plateaux in records of scour depth time evolution, can incur important errors on the equilibrium scour depth. Using some of the expressions for time evolution found in the literature to fit the experimental data and infer equilibrium scour depth through extrapolation to infinite time, it is found that the equilibrium scour depth cannot be specified, in general, for experiments shorter than one to two weeks.

Effect of suspended sediment concentration on local scour around cylinder for clay–sand mixed sediment beds

Suspended sediments present in the flow are known to affect the flow resistance, velocity distribution and turbulent characteristics. Experiments were conducted in the laboratory flume to see the effect of suspended sediment concentration (SSC) on local scour around a cylindrical pier for a wide range of clay–sand mixed sediment beds for SSC up to 2700 mg/L. It has been observed that the effect of SSC on equilibrium scour hole parameters such as maximum equilibrium scour depth, and longitudinal and transverse extent of scour hole can be significant. Present data showed that the presence of SSC in the range 993–1332 mg/L can increase maximum equilibrium scour depth as much as 1.54 times compared to the clear water case. However, tests made for SSC in the range 2456–2700 mg/L showed that the maximum equilibrium scour depth reduced compared to that for SSC in the range 993–1332 mg/L, but these maximum equilibrium scour depths were still larger than that obtained for clear water. The effect of SSC on time variation of scour and equilibrium scour hole geometry was further investigated.

Scour countermeasures for cylindrical piers using riprap and combination of collar and riprap

Various methods are proposed to control scouring around bridge piers. In the present study application of riprap alone and combinations of riprap and collar were examined experimentally for scour control around cylindrical bridge piers. Tests were conducted with seven riprap sizes and with two different sizes of collars. Empirical equations were developed for stable riprap diameter for two cases of piers with and without collar protection. Extent of riprap layer is also presented for these two cases. The results showed that in the range of b/ d R =7.5 (where b is pier diameter and d R is riprap size) using a collar reduced the stable riprap size. It was also concluded that using collar reduced the riprap layer extension in front and sides of the pier.

Suitable Bridge Pier Section for a Bridge over a Natural River

Estimation of maximum scour depth at the bridge pier is necessary for the safety and economy of the bridge design. Therefore, the phenomenon of scour around bridge piers was extensively studied from the literature to find the effect of pier shapes and inclined flow on scour depth at bridge piers. It was found from the analysis that scour depth increases with the increase of the flow angle relative to the pier axis, but for a cylindrical pier, maximum scour depth does not change with flow angle. When the flow angle is at 300, the scour depth for the cylindrical pier is smaller than other pier shapes; hence circular pier shape is more suitable for natural rivers which have possibility of changing flow direction.

Temporal Variation of Scour Depth at Nonuniform Cylindrical Piers

The paper proposes a semiempirical model to estimate the temporal development of scour depth at cylindrical piers with unexposed foundations. A cylindrical pier with a foundation is considered as nonuniform pier. The concept of primary vortex and the principle of volumetric rate of sediment transport are used to develop a methodology to characterize the rate of evolution of the scour hole at nonuniform cylindrical piers. The model also simulates the entire scouring process at nonuniform cylindrical piers having the discontinuous surface located below the initial bed level. The scouring process includes three zones; viz Zone 1 having the scouring phenomenon similar to that of a uniform pier, Zone 2 in which the scour depth remains unchanged with its value equal to the depth of the top level of foundation below the initial bed level while the dimensions of the scour hole increase, and in Zone 3 the geometry pier foundation influences the scouring process. A concept of superposition using an effective pier diameter is proposed to simulate the scouring process in Zone 3. In addition, the laboratory experiments were conducted to utilize the laboratory results for the validation of the model. The simulated results obtained from the proposed model are in good agreement with the present experimental results and also other experimental data. Also, the effect of unsteadiness of flow is incorporated in the model and the results of the model are compared with the experimental data. The model agrees satisfactorily with the experimental data.

DRAG CHARACTERISTICS OF CYLINDRICAL PIERS WITH SLOTS AND/OR COLLARS IN SUBCRITICAL FLOW

ABSTRACT The flow field around a circular bridge pier is a complex three-dimensional phenomenon. Notwithstanding the considerable effort made in the study of local scour by many researchers, an understanding of the mechanics of local scour around a bridge pier remains far from complete. The drag force exerted on the structure is related to the wake. Larger the wake, higher is the drag force and scour potential. Efforts to reduce the drag by reducing/altering the wake structure are widely reported in literature. Use of slot-collar combination is one among them. In this study, an attempt has been made to establish the drag characteristics of cylindrical pier models, with different slot-collar combinations. This experimental study is conducted using a physical hydraulic model operated under clear-water and rigid bed conditions. All the experiments are conducted in a re-circulating tilting flume. Experiments are run for different combinations of slot and collar. Drag coefficient of the pier is computed using the momentum equation. The drag studies indicate that the drag coefficient in general is found to decrease with the provision of slot/collar. The value of drag coefficient is reduced by about 33 % for a bottom slot/collar combination.

Laboratory experiments on local scour around cylinder for clay and clay–sand mixed beds

New data on scouring around cylinders embedded in clay–sand mixed beds are reported and the mechanism of the scouring process is described. The effects of clay-content, water content, bed shear strength and pier Froude number on maximum equilibrium scour depth, equilibrium scour hole geometry, scouring process, and time variation of scour were investigated. Existing literature on scouring around cylinders in cohesive sediment beds suggested that the maximum equilibrium scour depth in clay beds was similar to that of sand, while increase in the clay fraction for clay–sand mixed beds reduced maximum equilibrium scour depth. The present study attempted to fill this gap between observations made by different investigators in cylindrical pier scour in clay–sand mixed sediment beds. Further, equations for estimation of non-dimensional maximum scour depth for cylinders embedded in clay–sand mixtures were proposed as functions of pier Froude number, clay content, water content, and bed shear strength, while the clay–sand mixtures had clay content in the range of 20–100% and water content in the range of 20%–45.92%.

Reduction of Local Scour around Cylindrical Bridge Piers Using Upstream Protective Piles

AbstractCylindrical bridge piers are widely used and equations exist that can predict the maximum depth of local scour around such piers. Scour around piers is an undesirable phenomenon, as it requires the foundation to be placed to a greater depth resulting in increased cost, making it worthwhile to investigate scour-reducing measures. A number of scour-reducing measures have been tried out for cylindrical bridge piers including placing a concrete collar around the pier, having a delta-wing projecting upstream in front of the pier, placing riprap around the pier, using a group of piers instead of a single pier, having a slot in the pier aligned in the longitudinal direction. The objective of this study is to investigate the effect of upstream protective piles on reduction of maximum local scour depth around a cylindrical bridge pier. The upstream piles are placed at different radial distances in front of the pier and the scour depths are observed. The proposed equation of Dey (1997) for determining the m...

Effect of submerged vanes on the scour occurring at a cylindrical pier

The principal purpose of this research was to study the effect of a submerged vane as a countermeasure technique on local scour at a cylindrical pier. For this purpose, several heights of vane, angles of orientation, and flow depths were evaluated, all for a constant Froude number. It was found that for an isolated vane, a greater depth of scour was experienced at higher flow rates and/or at greater flow depths with all vane combinations and orientations. It was also found that not all types of single isolated submerged vanes can be used as a scour countermeasure at cylindrical piers. The highest reduction in scour was achieved for an angle of 8.5° and a flow depth of 20 cm for a vane height equal to 0 cm while the most exacerbated case occurred with a vane angle of 18.5° and a flow depth of 10 cm for a vane height equal to 5.7 cm. So, it was concluded that for vane heights other than the 0 cm investigated in this study, an increasing scour depth is experienced at cylindrical piers compared to control. For two vanes attached to the pier, a reduction of 87.7% in scour depth next to the pier was achieved for a constant flow depth (i.e., 15 cm), a constant vane angle (i.e., 18.5), and at 0 distance upstream from the pier for a vane height of 0 cm

Characteristics of Horseshoe Vortex in Developing Scour Holes at Piers

The outcome of an experimental study on the turbulent horseshoe vortex flow within the developing (intermediate stages and equilibrium) scour holes at cylindrical piers measured by an acoustic Doppler velocimeter (ADV) are presented. Since the primary objective was to analyze the evolution of the turbulent flow characteristics of a horseshoe vortex within a developing scour hole, the flow zone downstream of the pier was beyond the scope of the investigation. Experiments were conducted for the approaching flow having undisturbed flow depth (=0.25 m) greater than twice the pier diameter and the depth-averaged approaching flow velocity (=0.357 m/s) about 95% of the critical velocity of the uniform bed sand that had a median diameter of 0.81 mm. The flow measurements by the ADV were taken within the intermediate (having depths of 0.25, 0.5, and 0.75 times the equilibrium scour depth) and equilibrium scour holes (frozen by spraying glue) at a circular pier of diameter 0.12 m. In order to have a comparative study, the ADV measurements within an equilibrium scour hole at a square pier (side facing the approaching flow) of sides equaling the diameter of the circular pier were also taken. The contours of the time-averaged velocities, turbulence intensities, and Reynolds stresses at different azimuthal planes (0, 45, and 90°) are presented. Vector plots of the flow field at azimuthal planes reveal the evolution of the characteristics of the horseshoe vortex flow associated with a downflow from intermediate stages to equilibrium condition of scour holes. The bed-shear stresses are determined from the Reynolds stress distributions. The flow characteristics of the horseshoe vortex are discussed from the point of view of the similarity with the velocity and turbulence characteristic scales. The imperative observation is that the flow and turbulence intensities in the horseshoe vortex flow in a developing scour hole are reasonably similar.

LOCAL SCOUR AND BED EVOLUTION AROUND A SUBMERGED CYLINDRICAL PIER

Laboratory experiments were conducted on local scour and bed evolution around a cylindrical pier. Not only with a traditional non-submerged pier, but some cases with a submerged pier were explored. Experiments were carried out in both static and dynamic scouring conditions. Shape of a scouring hole around the pier, as well as backwater caused by the pier, is of particular interest. The shape of the scouring hole in the submerged conditions is similar to that in the non-submerged condition, thus the maximum scour depth appears in vicinal front of the pier. The maximum scour depth reduces as the height of the pier decreases. A refined equation for estimating the maximum scour depth including the effect of variable pier height is proposed and shows good performance in the range tested here. Backwater in the upstream is not so noteworthy in the submerged cases.

Fluid Flow and Fluid Force Acting on a Cylindrical Pier Standing in a Scour

Local clear water scour around a cylindrical pier have been studied in a wind tunnel. Characteristics of fluid flow and fluid force acting on the pier standing in a scour were investigated with a pier and five different depth scours (scour depth/pier diameter=0, 0.5, 0.7, 1.0 and 1.5). The diameter of the pier is 40mm and free stream velocity is 16m/s, so that the Reynolds number is 4.2×104. The flow visualization was carried out by the surface oil-flow pattern and smoke-wire methods. The surface pressure distributions on the pier and scour were measured and the drag coefficient of the pier was determined by integration of surface pressure distribution on the pier. Characteristics of the horseshoe vortex and drag acting on the pier in the scour are clarified. The results show that the two horseshoe vortices are observed in near the root the pier as the scour grows deeper and the stagnant area is formed in the bottom of the scour for the deepest depth.

604 洗掘孔内の円柱橋脚まわりの流れ(流体工学VII)

604 洗掘孔内の円柱橋脚まわりの流れ(流体工学VII)

320 すり鉢状洗掘孔内の円柱橋脚まわりの流れ(流体工学IV)

320 すり鉢状洗掘孔内の円柱橋脚まわりの流れ(流体工学IV)