Rigid Vertical Wall Research Articles

Effects of the soil on the noise attenuation of environmental berm barriers

Berm mounds are a commonly used technique to reduce the environmental noise levels produced by highways. A berm is a natural noise barrier constructed of soil, stone, rock, or rubble, often landscaped, running along a highway to protect adjacent communities from noise pollution. An earth mound may be constructed using surplus materials at project site, provided there is sufficient land area available for its construction. Therefore, berms are natural environmental barriers, having relative low costs and they are subjectively well perceived by residents. However, exact noise attenuation provided by berms has not been enough explored in the technical literature, as opposed to common barriers made of vertical rigid walls. Although, some highway noise prediction models assign a noise reduction bonus of 3 dB(A) to sound barriers made of earth mounds, experimental assessments have yielded mixed results. Few theoretical reports have studied this particular problem. In this work, numerical analysis using the classical theory of diffraction is performed on a berm made of different types of soil. The model assumes a line source and includes flow resistant data as boundary conditions. By integrating the results, noise attenuation is given in third-octave bands. It is concluded that soil's properties significantly influence the measured results and that this may be one of the causes of varied in-site empirical evidence.

Dynamic Behavior of Bubble near Vertical Plate in Underwater Explosion

In this study, the volume-acceleration model was introduced to determine the initial condition for bubble motion during underwater explosion. Subroutines, which defined the initial and boundary conditions of the fluid field, were developed based on MSC.DYTTAN software. Numerical simulations were compared with the results of validated experimental data. From the basic phenomenon of interaction between a bubble and a vertical rigid wall, the dynamic behavior of a bubble near a vertical rigid wall was simulated and analyzed. The dynamic behavior of bubble and the jet were studied systematically and summarized relative to the law that both of the motion of bubble and water jet are closely related with the standoff distance parameter. The results of this study have valuable implications for correlative theory research and engineering calculation.

Impulsive Singularity in a Stratified Fluid; Diffraction by a Vertical Half-Plane

The anisotropy created by stratification places severe restrictions, as in rotating fluids, on the construction of analytic solutions to wave-scattering problems. With emphasis on the time evolution, this paper considers a fundamental disturbance, an impulsive dipolar mass singularity in the presence of a semi-infinite vertical rigid wall. The initial Laplacian response is subsequently modified by internal waves that everywhere propagate within the local St Andrew's double cone. But the edge diffraction is found to propagate outside this cone.

Coupled free vibration analysis of a fluid-filled rectangular container with a sagged bottom membrane

Abstract In the present paper, two-dimensional coupled free vibrations of a fluid-filled rectangular container with a sagged bottom membrane are investigated. This system consists of two rigid walls and a membrane anchored along two rigid vertical walls. It is filled with incompressible and inviscid fluid. The membrane material is assumed to act like an inextensible material with no bending resistance. First, the nonlinear equilibrium equation is solved and the equilibrium shape of the membrane is obtained using an analytical formulation neglecting the membrane weight. The small vibrations about the equilibrium configuration are then investigated. Along the contact surface between the bottom membrane and the fluid, the compatibility requirement is applied for the fluid–structure interactions and the finite element method is used to calculate the natural frequencies and mode shapes of the fluid–membrane system. The vibration analysis of the coupled system is accomplished by using the displacement finite element for the membrane and the pressure fluid-finite element for the fluid domain. The variations of natural frequencies with the pressure head, the membrane length, the membrane weight and the distance between two rigid walls are examined. Moreover, the mode shapes of system are investigated.

Asymptotic reflection of linear water waves by submerged horizontal porous plates

On the basis of linear water-wave theory, an explicit expression is presented for the reflection coefficient R ∞ when a plane wave is obliquely incident upon a semi-infinite porous plate in water of finite depth. The expression, which correctly models the singularity in velocity at the edge of the plate, does not rely on knowledge of any of the complex-valued eigenvalues or corresponding vertical eigenfunctions in the region occupied by the plate. The solution R ∞ is the asymptotic limit of the reflection coefficient R as a → ∞, for a plate of finite length a bounded by a rigid vertical wall, and forms the basis of a rapidly convergent expansion for R over a wide range of values of a. The special case of normal incidence is relevant to the design of submerged wave absorbers in a narrow wave tank. Modifications necessary to account for a finite submerged porous plate in a fluid extending to infinity in both horizontal directions are discussed.

Water-wave trapping by floating circular cylinders

Under the assumptions of the linearized theory of small-amplitude water waves, it is proved that plane waves, normally incident upon a semi-immersed cylinder of uniform circular cross-section floating freely on the surface of a fluid of infinite depth, are capable of being totally reflected. Numerically, this is shown to occur at a single non-dimensional frequency. This remarkable result is used to construct examples of motion-trapped modes, involving pairs of freely floating cylinders moving either in phase or out of phase. The former case is equivalent to having a motion-trapped mode for a single such cylinder next to a rigid vertical wall. In the latter out-of-phase case, the pair of cylinders move as if they form the wetted sections of a single rigidly connected catamaran structure.

On the waves in two superposed liquids in the presence of a wall

An exact analysis, based on a simple reduction procedure, is described in this work for finding the linear solution of the normally incident incoming waves in the presence of surface tension (ST) in two liquids, where the liquids are bounded on the left by a rigid vertical wall. Analytical expressions for the velocity potentials in each of the two liquids are obtained here assuming the lower liquid to be of uniform finite depth and the upper liquid to be of uniform finite height.

Buoyancy and local friction effects on rockfill settlements: A discrete modelling

Measured displacements in the upstream shell of rockfill dams show some settlements which can reach a few meters with water levels changes, especially during the first impounding, whereas downstream displacements are smaller. Complementary phenomena are responsible for rockfill collapse due to wetting. Here we numerically investigate the effects of buoyancy forces and the decrease in the coefficient of friction with water on a rockfill column maintained by vertical rigid walls and progressively filled with water. Numerical simulations of the settlements of the rockfill column, using the Contact Dynamics method, are presented. Buoyancy forces seem to have only a negligible influence on the granular pile. Decrease in the friction angle of the rock with water induces rearrangements of the medium, all the more as the decrease is significant. These dynamic rearrangements exhibit an irregular temporal evolution of the granular medium which can be characterized by a phenomenon of local “crisis”. Analysis of the settlements shows that these two combined effects are not the major cause of the settlements observed in rockfill dams and that they cannot in particular explain the settlements.

1002 フリーラグランジュ法による粘性自由表面流れの数値解析(OS10.メッシュフリー/粒子法とその関連技術(1))

Free-Lagrange method has been combined with the free-mesh FEM and applied to the numerical simulation of viscous free surface flows. The nodes distributed over the fluid region are regarded as fluid particles and moved in a Lagrangian manner every time step. In this paper, we report a new numerical technique for calculating the interaction between the fluid and rigid walls. The proposed method has been applied to the broken-dam problem in a bounded region in which flowing liquid strikes a rigid vertical wall and run up along it. Encouraging numerical results have been obtained.

Liquefied soil pressures on vertical walls with adjacent embankments

Horizontal earth pressures on rigid vertical walls in liquefied soils have extensively been studied by many researchers for the level ground surface condition. In this paper, a series of centrifuge tests was conducted to investigate the effects of embankments resting on ground surfaces on the pressure on the rigid vertical walls. In the tests, earth pressures on the rigid walls were successfully measured with built-in earth pressure cells with small accelerometers attached on them. The earth pressure cells are capable of measuring both normal and shear stresses simultaneously with a good accuracy. It appears that dynamic component of the earth pressure of liquefied sand is in proportion to the acceleration of the rigid wall irrespective of amplitude and frequency of the input motion, and increases with increasing average embankment load. On the other hand, the residual component of the earth pressure is found to be well estimated from FEM assuming the liquefied soil as an incompressible elastic body. A practical formula of the earth pressures is established for the purpose of practical use. Another series of centrifuge tests was carried out on models with solidification or densification zones below embankment toes as a remedial countermeasure against liquefaction-induced embankment failure. It was found that the proposed formulae holds valid independently of the movement of walls as long as the liquefied soil behaves as a heavy fluid, and the countermeasure does not soften significantly.

Impact of an oblique breaking wave on a wall

The intention of this paper is to study impact force of an oblique-angled slamming wave acting on a rigid wall. In the present study the analytical approach is pursued based on a technique proposed by Shu (Proceedings of the International Conference on Applied Mathematics & Mathematical Physics, Sylhet, Bangladesh, 2000). A nonlinear theory in the context of potential flow is presented for determining accurately the free-surface profiles immediately after an oblique breaking wave impingement on the rigid vertical wall that suddenly starts from rest. The small-time expansion is taken as far as necessary to include the accelerating effect. The analytical solutions for the free-surface elevation are derived up to the third order. The results derived in this paper are of particular interest to the marine and offshore engineering industries, which will find the information useful for the design of ships, coastal and offshore.

Study on the efficiency of the digging process using the model of excavator bucket

In the first part of the paper, an experimental program is presented investigating the soil cutting problem, with the application of vertical rigid walls at various widths as the working tools. It was found that when the tool width equalled the width of the soil bin, the soil cutting problems might be treated as plane strain processes. For the tools for which no interaction with the sidewalls of the bin was observed, the zone of the plane strain deformations occurred in the central part of the tools. In the second part of this paper a new experimental program of laboratory tests is presented, for a tool model in the shape of an excavator’s bucket equipped with teeth. The experimental verification of the influence of teeth (number of teeth and the position of teeth on the bucket’s inside lip) on the efficiency of the digging cycle is the aim of this paper. For high values of teeth spacing, the superposition of the plane strain deformation mechanism with three-dimensional failure modes within the soil was observed. For the low values of teeth spacing, the teeth did not act as separate three-dimensional objects but as one wide tool built up from several modules. As a consequence, the deformation pattern in front of such an assembly of teeth was again the plane strain deformation pattern.

Dynamic pressures on a pair of rigid walls retaining poroelastic soil

This work deals with the evaluation of the dynamic pressures and the associated forces on a pair of rigid vertical cantilever walls retaining a uniform, fully saturated poroelastic layer of soil. Hysteretic damping in the soil skeleton may also be present. Wall pressures and forces are induced by horizontal ground shaking harmonically varying with time and spatially invariant. The problem is solved analytically under conditions of plane strain. The governing partial differential equations of motion, after separation of variables and the simplifying assumptions of zero vertical normal stresses and zero horizontal variation of vertical displacements, reduce to a system of two ordinary differential equations for the amplitudes of the solid skeleton horizontal displacement and the pore water pressure, which are easily solved. The parameters examined include the ratio of the distance between walls to the height of the retained soil material and the soil material properties such as porosity, permeability and damping. The comprehensive numerical data presented indicate that the displacements, wall pressures and resultant forces are highly dependent on the distance between the walls for any values of porosity and permeability.

Passive Earth Pressure with Critical State Concept

This paper presents experimental data of earth pressure acting against a vertical rigid wall, which moved toward a mass of dry sand. The backfill had been placed in lifts to achieve relative densities of 38, 63, and 80%. The instrumented retaining-wall facility at National Chiao Tung University in Taiwan was used to investigate the effects of soil density on the development of earth pressure. Based on the experimental data, it has been found that the Coulomb and Terzaghi solutions calculated with the peak internal friction angle significantly overestimated the ultimate passive thrust for the retaining wall filled with dense sand. As the wall movementS exceeded 12% of the wall height H, the passive earth thrust would reach a constant value, regardless of the initial density of backfill. Under such a large wall movement, soils along the rupture surface had reached the critical state, and the shearing strength on the surface could be properly represented with the residual internal-friction angle. The ultimate passive earth pressure was successfully estimated by adopting the critical state concept to either Terzaghi or Coulomb theory. CE Database keywords: Passive pressure; Earth pressure; Sand; Vertical angles.

Green Water Loading on a FPSO

Abstract Green Water Loading in the bow region of a Floating Production Storage and Offloading unit (FPSO) in head sea waves is studied by numerical means. A 2-D method satisfying the exact nonlinear free-surface conditions within potential-flow theory has been developed as a step towards a fully 3-D method. The flow is assumed 2-D in a plane containing the ship’s centerplane. The method is partly validated by model tests. The importance of environmental conditions, 3-D flow effects, ship motions, and hull parameters are summarized. The wave steepness of the incident waves causes important nonlinear effects. The local flow at the bow is, in general, important to account for. It has become popular to use a dam-breaking model to study the propagation of water on the deck. However, the numerical studies show the importance of accounting for the coupled flow between the deck and outside the ship. When the water is propagating on the deck, a suitable distance from the bow can be found from where shallow-water equations can be used. Impact between green water on deck and a vertical deck-house side in the bow area is studied in details. A similarity solution for impact between a wedge-formed water front and a vertical rigid wall is used. Simplified solutions for an impacting fluid wedge with small and large interior angles are developed, both to support the numerical computations and to provide simpler formulas of practical use. It is demonstrated how the local design of the deck house can reduce the slamming loads. The importance of hydroelasticity during the impact is discussed by using realistic structural dimensions of a deck house. This indicates that hydroelasticity is insignificant. On the contrary, first results from an ongoing experimental investigation document blunt impacts against the deck during the initial stage of water shipping, which deserve a dedicated hydroelastic analysis.

Indentation of a continent with a built-in thickness change: experiment and nature

Orogens oblique to the direction of plate convergence are currently attributed to obliquity between the margins of one or both of the sutured continents to their direction convergence. We use a single analogue experiment and natural examples to illustrate a potential additional factor: variations in strength of the indented continent at a high angle to the convergence direction. The wavelengths of structures in laterally shortened lithosphere depend on the strength of the most competent layers. Lateral variations in crustal thickness must therefore lead to structures oblique to any applied lateral compression. An analogue experiment was performed to explore this phenomenon. A two-layer ‘indented continent’ was modelled by a brittle upper crust of sand above a lower crust of high-viscosity polymer floating on a single layer of low-viscosity syrup representing the mantle. The well-known strike-slip structures allowing lateral escape to distant weak boundaries were hindered by lateral boundaries in front of the indenter. This allowed us to focus on the effects of a thickness change built into the ‘indented continent’ along a zone parallel to the direction in which a vertical rigid wall advancing at a steady rate represented the indenter. Vertical escape led to an ‘orogenic belt’ oblique to the advancing wall; this obliquity influences subsequent lateral escape. Model scaling and interpretations are based on Extended Thin Sheet Approximation (ETSA) and standard theories of faulting. Four sectors of the Alpine–Himalayan orogen (Iran, Tunisia, the Eastern Alps and the Himalaya) are oblique to the continental convergence direction, and we point to thickness changes at high angles to the suture that may account for this geometry. As crustal thicknesses north of oblique sectors of the Himalayas are not yet known, we speculate on them. We infer from the main difference between our experiment and all our examples chosen from nature that vertical orogenic escape was oblique to our model suture but can be parallel to natural sutures.

Vibration of vertical rectangular plate in contact with water on one side

In this paper, the vibratory characteristics of a rectangular plate in contact with water on one side are studied. The elastic plate is considered to be a part of a vertical rectangular rigid wall in contact with water, the edges of which are elastically restrained and parallel to those of the rigid wall. The location and size of the plate on the rigid wall may vary arbitrarily. The water with a free surface is in a rectangular domain infinite in the length direction. The effects of free surface waves, compressibility of the water and the hydrostatic water pressure are neglected in the analysis. An analytical-Ritz method is developed to analyse the interaction of the plate–water system. First of all, by using the method of separation of variables and the method of Fourier series expansion, the exact expression of the motion of water is derived in the form of integral equations including the dynamic deformation of the plate. Then the Rayleigh–Ritz approach is used to derive the eigenfrequency equation of the system via the variational principle of energy. By selecting beam vibrating functions as the admissible functions of the plate, the added virtual mass incremental (AVMI) matrices for plate vibration are obtained. The convergency studies are carried out. The effects of some parameters such as the depth and width of water, the support stiffnesses, location and aspect ratio of the plate and the plate–water size and density ratios on the eigenfrequencies of the plate–water system are investigated. Several numerical examples are given. The validity of AVMI factor approach is also confirmed by comparing the AVMI factor solutions with the analytical-Ritz solutions. The results show that the approach presented here can also be used as excellent approximate solutions for rectangular plates in contact with water of infinite width and/or infinite depth. Copyright © 2000 John Wiley & Sons, Ltd.

COMPARISON OF NUMERICAL METHOD WITH ANALYTICAL METHOD FOR PREDICTING GEOMETRIC AND MIGRATION CHARACTERISTICS OF ALTERNATE BARS

We have tested the suitability of two non-linear analyses of the geometric and migration characteristics of alternate bars formed between rigid vertical walls of a straight channel. The development of alternate bars were predicted. The wave height obtained by an analytical method is higher than that obtained by a finite difference method (FDM). The difference is caused by higher wave number components in the simulated flow. The difference in the migration velocity between these analyses is large, which is caused by the difference of the bed geometry structure. It is found that the secondary flow which is estimated in the FDM by the stream line curvature affects the wave height very much. The wavelength of alternate bars produced by a bed disturbance located in the upstream end of the computational domain was found to be close to the wavelength obtained by a linear analysis.

Earth Pressures with Sloping Backfill

This paper presents experimental data of earth pressure acting against a vertical rigid wall, which moved away from or toward a mass of dry sand with an inclined surface. The instrumented retaining-wall facility at National Chiao Tung University (NCTU) Taiwan, was used to investigate the variation of earth pressure induced by the translational wall movement. Based on experimental data, it has been found that the earth-pressure distributions are essentially linear at each stage of wall movement. Both the wall movement required for the backfill to reach an active state and the wall movement needed for the backfill to reach a passive state increase with an increasing backfill inclination. The experimental active and passive earth-pressure coefficients for various backfill sloping angles are in good agreement with the values calculated by Coulomb's theory. It may not be appropriate to adopt the Rankine theory to determine either active or passive earth pressure against a rigid wall with sloping backfill.

Simulation of plunging wave impact on a vertical wall

We present a numerical study of the impact of a two-dimensional plunging wave on a rigid vertical wall in the context of potential flow. The plunging wave impinging the wall is generated using a mixed-Eulerian-Lagrangian (MEL) boundary-integral scheme. The initial stage of the impact is characterized by an oblique impact of a liquid wedge on the wall and is solved using a similarity solution. Following the initial impact, the MEL simulation is continued to capture the transient impact process. The effect of an air cushion trapped between the plunger and the wall is considered. In addition to details such as temporal evolutions and surface profiles, the main interests are the maximum impact pressure on the wall and its rise time. To arrive at appropriate scaling laws for these, simulations are performed and correlations are explored for a broad range of local plunging wave kinematic and geometric parameters. To assess the present results, direct comparisons are made with the experiment of Chan & Melville (1988). Reasonable quantitative agreement is obtained and likely sources for discrepancies are identified and discussed.