Scaling Issues in Hydraulic Modelling

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The uncertainties involved in many coastal issues and the lack of complete scientific background in some knowledge fields, especially to evaluate extreme coastal-forcing events, the cumulative environmental evolution and impacts on beaches and coastal structures as well as to confirm design procedures, for instance, lead to the need of using physical modelling. There is also little public awareness of the physics behind several coastal processes and physical modelling can help in describing and illustrating them.

In this paper a brief revue on the importance of physical modelling, its advantages in relation to numerical modelling, some basic aspects of physical modelling, related scaling issues and how to control hydraulic modelling and scale effects as well as three case studies and future challenges will be presented.

The Importance of Physical Modelling

Physical models have played a pivotal role in the growth of coastal engineering as a profession [1]. They have given us insight into the complex hydrodynamic regime of the nearshore region, and they have provided us with reliable and economic design solutions to support man’s activities in the coastal zone. Many of our present-day engineering design techniques were developed using laboratory measurements, and numerous theoretical developments have relied on laboratory experiments for validation.
However, many of us can still list some of the limitations of those design approaches, being in some case considered as empirical formulations. This means further tests and measurements are needed to increase the reliability of those formulations, specially performed at scales closer to the prototype, avoiding scale effects and testing new forcing situations. Especially due to climate change and the demand for bigger structures located at higher depths, more accurate design formulations are needed and this will be the most important role of large laboratories of maritime hydraulics. However, as these large tests in large facilities are more expensive they need to work in close relation with other small/medium facilities for preliminary/cheaper analyses.

Physical and numerical modelling tools have developed enormously during the last years. However several issues need still further developments, namely the physics and modelling of sediment transport, the wave-structure interaction analysis and loads determination, erosion and scour near coastal structures as well as medium to long term accurate simulation tools.

From the management side, for instance, plans should be based on an adequate understanding of coastal dynamics. It is necessary to pursue research on many aspects of coastal dynamics in order to better assess and understand erosion and sedimentation problems, predictions of shoreline positions for various scenarios and time scales of climate variability and direct human influence, the vulnerability of beaches, dunes and coastal structures to storms and other extreme events, the impact of artificial coastal structures and ecological changes.

Physical Modelling versus Numerical Modelling

Numerical models represent the real problem but with some simplifications. Thus, the modeller is forced to make a compromise between the details of the model and the prototype. Several advantages and disadvantages of physical model testing are usually reported.

An incorrectly designed model always provides wrong predictions, independently of the sophistication of the instrumentation and measuring methods. The cost of physical modelling is often more than that of numerical modelling, and less than that of major field experiments, but this depends on the exact nature of the problem being studied. Physical modelling has gathered new perspectives due to the development of new sophisticated equipment, allowing the measurement of variables in complex flows, which was previously impossible. New experimental techniques, automated data acquisition and analysis systems, rapid processing and increased data storage capabilities also provide useful information for the validation of numerical models, Frostick et al. (2011[2])

Other advantages of physical models are the study of new phenomena, the lower level of simplification, to confirm through measurements theoretical results, to obtain measurements from complex phenomena inaccessible from theory, to test extreme conditions, to test a wide variety of environmental conditions and the immediate visual feedback. Despite all these advantages there are still some problems of physical modelling to solve such as the scale effects, the incomplete modelling, the laboratory effects and the costs of installation and maintenance.

With relation to numerical models it can be said that despite the huge developments made they still exhibit deficiencies and limitations when applied to complex flows and situations like breaking, overtopping, wave structure interaction, etc. However, recent developments such as SPH and in computing capacity have made these tools more powerful than even before, leading to a better description of the complexity of the hydraulic phenomena (physical environment and borders as well as non-linear aspects of the equations used). From another perspective this tool is in general more attractive to researchers and practitioners.

To obtain theoretical solutions, simplifications of the physical environment (especially the boundaries) are needed as well as of the equations that govern the phenomena. As a result of that mathematical solutions may have lower quantitative value, and therefore could be more useful for qualitative or comparative analyses. The geometry can be reproduced with the desired detail but it is not enough to ensure a correct reproduction of the reality in the model as this can generate a behaviour sometimes different from the prototype. So calibration is needed. Physical modelling reproduces both linear and nonlinear aspects of the phenomena, avoiding the simplifications of the numerical modelling that simplifies not only the geometry but also fundamental equations.
Other advantages of physical modelling are intermediate and controllable cost; they represent reality at a certain scale; the involved variables and boundaries can be controlled; measurements are in general easy to perform and the comprehension of the processes is facilitated.

Other disadvantages of physical modelling are the time spent and the cost of building alternatives, the particle similarity, the partial control of boundaries and the difficulty in measuring parameters in some model areas. The actual level of research needs common efforts between the various available tools, namely physical and numerical modelling in order to decrease the lack of knowledge in some areas of Maritime Hydraulics. The problems to solve or which are not solved yet are so complex that only this integrated approach is feasible in order to obtain better accurate results not only for researchers but also for designers and practitioners.
There is still a need to design and construct new and more advanced laboratory facilities, develop new reliable measuring instruments and techniques, minimize laboratory effects, and understand the scale effects that arise from incomplete modelling.

Physical and numerical model input conditions can be controlled and systematically varied, whereas field studies have no such control. However, many problems in coastal engineering are not amenable to mathematical analysis because of the nonlinear character of the governing equations of motion, lack of information on wave breaking, turbulence or bottom friction, or numerous connected water channels. In these cases it is often necessary to use physical models for predicting prototype behaviour or observing results not readily examined in nature. The growing use of numerical models in coastal engineering has not stopped the use of physical models and in some cases they made progress in conjunction with each other. Recent trends have included the concept of “hybrid modelling” where results from a physical model of complex region are used as input or boundary conditions for a comprehensive numerical model covering a wider region of interest. Alternatively, numerical model results may be used to provide input conditions at the boundaries of the physical model.

The rationale for continued support of physical modelling in support of project design is that “Theory cannot cover all the complications that are encountered in practice. Consequently, most major hydraulics projects are model tested to optimize design”.
Due to the quantitative deficiencies and limitations of predictive numerical models when applied to complex flows, the need for physical modelling still remains and investments in laboratory facilities, equipment and new techniques are more and more needed, highlighting the need for synergies between the various research tools, physical and numerical modelling included, not only because of the actual complexity of the maritime hydraulics problems, but also to improve some design approaches.

Basic Aspects of Physical Modelling

A physical hydraulic model represents a real prototype and is used to find or confirm solutions for engineering problems. Differences between the model and prototype behaviour and results may be due to scale (similarity laws considered and incomplete reproduction of the forces involved), laboratory (model geometry – 2D or 3D influences, reflections; flow or wave generation techniques – turbulence intensity levels, linear wave theory approach; fluid properties, etc.) or measurement (different equipments used in model and prototype – intrusive or not, probe sizes) effects. The estimation of these effects (qualitatively and quantitatively) affects the results and to know if they can be neglected is a challenge for physical modellers, Heller (2011[3]). They can also justify differences between physical and numerical models (e.g. kinematic viscosity). The examples of the overflow spillway or a wave breaking are classic ones.

Considering the usual geometric scale parameter [math]\lambda=L_m/L_p[/math] or [math]N=L_p/L_m[/math], the required space, time and cost of experiments decrease with [math]\lambda^2,\lambda^{1/2}[/math] and [math]\lambda^3[/math], respectively, but scale effects will increase, and the results cannot be properly extrapolated to the prototype. So a proper selection of [math]\lambda[/math] is an economic and technical issue and if related effects cannot be neglected this must be known and taken into account.

The basic aspects of mechanical similarity (geometric - dimensions, kinematic – time, velocity, acceleration and discharge, and dynamic – forces: inertial, gravitational, viscous, surface tension, elastic, pressure) are well known, leading to the different numbers (similarities or laws) when considering the ratios of all the forces in relation to the inertial one (the most relevant in fluid mechanics) – Froude [math]Fr[/math], Reynolds [math]Re[/math], Weber [math]We[/math], Cauchy, Euler.

It is also known that although a perfect similarity would need the same value of these numbers between the prototype and the model, this is in general not possible as some of these similarities are incompatible (when using the same fluid or considering the same environment – gravity). So the most relevant force(s) present in the prototype must be selected and if compatible the model must be build according to the related similarity.

The relevant forces for most coastal hydrodynamics problems are the gravitational forces, friction, and surface tension (Dalrymple, 1985[4]). Thus, the dimensionless products are combinations of the Froude, Reynolds, and Weber numbers. Neglected are compressibility and elasticity effects. Yet the use of the same fluid on both model and prototype prohibits simultaneously satisfying the Froude, Reynolds and Weber number scaling criteria and thus, most coastal models are run respecting Froude’s similarity only, which implies assuming that gravitational effects are the most significant and that the viscosity and surface tension of water do not play significant roles.

For coastal sediment models, another set of scale relationships governing the initiation of motion, the transport mode, and the transport rate have to be introduced into the model, again with inevitable scale effects. The coastal mobile bed sediment transport and morphology model is perhaps the most difficult of all physical hydraulic models (Kamphuis, 2009[5]); yet despite the shortcomings it is, in many cases, the most important available instrument to bring about improvements with respect to sediment transport, and erosion.

Scaling Issues in Hydraulic Modelling

As was referred before the differences between the model and the prototype behaviour are due to several reasons, however:

  • Scale effects are always present. When can they be neglected?
  • As smaller is [math]\lambda[/math] larger will be the scale effects. Can a given value of [math]\lambda[/math] indicate if scale effects can be neglected?
  • Scale effects do not affect in the same way all phenomenon/parameter under investigation – qualitatively they may be differently reproduced between model and prototype, but quantitatively they can be properly scaled (discharge vs air entrainment). How to evaluate these differences?
  • In general some parameters are smaller in the model than in prototype – relative wave height, relative discharge, transported relative volume of sand, etc. How small is this damping effect?

Froude similarity is normally considered in open-channel hydraulics, where friction effects are negligible (deep-water wave propagation) or highly turbulent phenomena, since the energy dissipation depends mainly on the turbulent shear stress terms which are statistically correctly scaled even though the turbulent fine structures and the average velocity distribution differ between the model and prototype flows [1]. The gravitational acceleration is not scaled as well as the other numbers. Note: for the most important scaling ratios see Hughes (1993) [1] and Martin and Pohl (2000[6]). To avoid scale effects the influence of the gravity force on fluid flow should be negligible in a Reynolds model.

Reynolds similarity is normally considered in air models, laminar boundary layer problems, intake structures, seepage flows, creeping around immersed bodies or head losses elements (for lower values of [math]Re[/math]). The other force ratios (numbers) are not properly modelled. A serious disadvantage is the scale velocity which will lead, for the same fluid, to higher velocities rather than in prototype. For that the use of air models is more appropriate. Hydraulic Froude models should be run under the same hydraulic rough regime as in nature in order to have the same losses’ level and not a faster decay as append sometimes with waves in a model.

It is not normal to build a model according to Weber similarity, so this can lead to some scale effects. Surface tension is negligible in most of hydraulic prototypes, but is important in scale models for air entrainment (wave breaking), small water depths, small wave heights and periods (capillary waves) or large fluid paths. Since many dimensions are smaller in the model this can lead to a dominant surface tension – larger relative air bubbles’ sizes, faster air detrainment and smaller volume fractions of air. Phenomenon that includes air flow (that depends also on the atmospheric pressure) needs a relative large scale.

Cauchy number is related with Young’s modulus [math]E[/math], which in the case of water is not scaled, so its behaviour in impact phenomena, like wave-structure interaction, should be analysed with precaution. In fact a distensible structure (with [math]Est[/math]) must be scaled without changing the Poisson number. In a Froude model, [math]Est[/math] scales linearly with [math]1/\lambda[/math], so if same material as the prototype is used the model structure will be [math]\lambda[/math] too stiff which lead to erroneous resistance obtained in the model. This is also the case of air-water mixtures, for instance during the interaction of waves with a vertical quay. To model fenders is another example, where sometimes its [math]Est[/math] is modelled with a spring system that includes the non-linear behaviour.

The Euler number considers pressure forces as relevant especially for high pressures (pipes, cavitation of turbines, pumps or hydraulic structures). If the cavitation number is not correctly modelled in a Froude model, the cavitation phenomena will be not observed.

Control of Hydraulic Modelling and Scale Effects

When trying to control hydraulic modelling some “tools/procedures” are available:

  • If a certain physical phenomenon can be described mathematically (Navier-Stokes equations) both the model and prototype should follow the related equations (inspectional analysis);
  • A physical problem can be reduced to a product of dimensionless parameters (geometrical and forces ratios), that must have the same values both in the model and in the prototype (dimensional analysis);
  • Perform tests of known prototype situations, from which there is data available, allowing testing of other unknown situations (calibration);
  • Performing tests with at least three [math]\lambda[/math] being the smallest considered as the prototype; deviations of the dimensionless results of the smaller compared with largest one are due to scale effects; this requires large experimental efforts and does not inform about the scale effects of the larger model (scale series).

When trying to control scale effects some “tools/procedures” are available:

Avoidance: The best way to avoid scale effects would be to satisfy the force ratios limits for which there are no differences between the model and the prototype. There are also some practical rules/guidelines resulting from many tests and theoretical analysis if such a relation model/prototype is to be made. For limiting criteria and reference model scales with “reasonable size” and moderate scale effects (not necessary negligible) see Heller (2011[7]).

Replacement of Fluid: In order to avoid scale effects due to kinematic viscosity, sometimes air is used in the model instead of water, also because of the more advanced measurement techniques (turbulence e.g.). Although inertial and viscous forces are correctly modelled, however gravity, free-surface and cavitation effects are not reproduced. Example: ripple forms (water and sediments) were simulated with coal dust in glycerine with a surfactant to lower surface tension effects; a mixture of distilled water with isopropyl alcohol solution changed the breaker’s shape and evolution, air entrainment and energy dissipation.

Compensation: The model geometry is distorted in order to obtain a better similarity when compared to the prototype: roughness, vertical distortion and grain diameter.

Roughness: many models are built with a fixed bed (Froude similarity) leading to important scale effects due to surface tension and viscosity; as the Reynolds number is lower in the model the boundary roughness coefficient is higher and as geometric roughness similarity is ignored same friction coefficient can be achieved, resulting in a compensation of scale effects and a similarity of the water surface and energy gradients (only for models not too small and for a certain range of [math]Re[/math]); the boundary friction is also relevant for the drag force in small-scale ship models – artificial roughness elements are included on the hull of the ship to shift boundary layer roughness to the turbulent rough regime leading to an appropriate prototype roughness modelling.

Vertical distortion: more used in fluvial hydraulics increases water depth, decreases scale effects since [math]Re[/math] and [math]We[/math] will be higher, higher flow velocities, a shift from hydraulic smooth to the rough flow regime, improvement of relative measurement accuracy and the duration of a run is reduced; as negative effects, 2D and 3D flow processes are incorrectly modelled and the model roughness must be calibrated.
Movable bed: Among many factors that influence sediment transport ([math]Fr^*, Re^*[/math], Energy line slope - [math]SE[/math], etc) the grain density and diameter may be the most critical ones as they cannot follow any scale without being affected by cohesion or changing in its transport mode (bed load to suspended load) in the model; This is only possible satisfying various similarity criteria that need to be fulfil simultaneously and for that only with a distorted model; the sediment density may be reduced and a larger grain diameter can be used, leading to an unknown time scale that can only be evaluated through prototype data; if [math]\lambda[/math] is used to scale [math]d_{50}[/math] the corresponding value in the model will be smaller than 0.22 mm that would change the flow-grain interactions and related sediment transport. Limit model [math]d_{50}[/math] references state values of 0.5, 0.8 or 1.0 mm.

Correction: Sometimes the model is small for economic, limited space or time reasons and for that scale effects are expected; however some model results can be corrected afterwards for phenomena where enough information on the quantitative influence of scale effects is available; ex: correction factors for: solitary waves decay – boundary layer effects and fluid viscosity; coefficients for the stability of rubble mound breakwaters; equilibrium scour-depth estimates in cylinders; slopes of movable surf zone beach profiles; wave impact pressures and air leakage in the impact zone.

The Future of Physical Modelling

Similitude theory is quite old, new modern laboratory techniques and instrumentation exists and better field data is known allowing better calibrations. However several questions can be raised:

  • What’s the role of un-scaled atmospheric pressure in air entrainment?
  • How the scaling of [math]g[/math] would affect the results?
  • How numerical simulations can be used to improve physical ones (composite modelling) specially for phenomena that are difficult to reproduce in models – turbidity currents, distensible structures, turbulent flows and bridge pier scour?
  • Can numerical models used for a certain scale confirm some model scale effects as the effect of kinematic viscosity;
Another important issue is related with the development of harbours and related challenges. For several reasons the volume of goods actually transported by ships is increasing, and in order to optimize this, the size of ships has also been increasing. These bigger ships need bigger water depths for their pathways that can only be obtained, in general, further away the coast. This leads also, in general, to higher wave design conditions and other safety problems related with the foundations, currents, scour, breaking, etc. Many new harbour facilities are reaching dimensions never reached before. Taking in mind all this it will result in new interesting problems for hydraulic engineers namely for the development of design tools for these new sea conditions and harbour structures’ dimensions.

Finally, as it was referred physical hydraulic modelling is an important field within civil engineering and others scientific areas that can use several tools to resolve complex problems. How to avoid completely duplication of work and how to stimulate the exchange of information as each laboratory has their particular method for conducting model studies that sometimes makes difficult the comparison of results and data transfer will be a future challenge.

Case Studies

Behaviour of Moored Ships

The study of the behaviour of moored ships combines different areas of research, namely: propagation of offshore sea states to the port considering nonlinear wave-wave interactions and sub-harmonic generation; hydrodynamic interaction between the ship and waves, taking into account the influence of nearby port structures; simulation of the ship response considering the nonlinear characteristics of its mooring system and other forcing loads (wind, currents, ice, etc.).

Due to the phenomena complexity, an approach combining physical and numerical modelling with prototype measurements shall be used [8] . Composite modelling allows taking advantage of the strengths of each approach while trying to avoid their limitations. Because prototype data is usually scarce, efforts should be done to perform systematic data collections.

Well-designed small-scale physical models of port and offshore terminals are a valuable tool to study the response of moored ships to different environmental conditions and design parameters. In fact, despite being a simplified reproduction of the reality, physical models can reproduce the phenomena with more influence on the behaviour of moored ships in harbours under wind, current and wave forcing, including the non-linear effects related to the mooring system and to the propagation of waves to shallower waters and their interaction with coastal structures.

Numerical models evolved significantly and gained much importance in recent years, but still cannot replace entirely physical modelling. Turbulence, viscous and higher order effects rely on tuning in calculation models, Van der Molen (2006[9]). Physical modelling is one of the most reliable tools for studying the behaviour of moored ships in ports [10][11], finding application in the design of port facilities, study of downtime and mooring problems [12] [13] and calibration of numerical models.

In the study of the response of ships moored in a port, as in other coastal engineering domains, inertial forces acting on the flow are balanced primarily by forces resulting from the action of gravity. Thus, Froude similitude is applied to ensure that the correct relationship is maintained between those forces when the prototype is scaled down to model dimensions.

Scale definition is a key issue in any physical model study. In harbour models subjected to the action of short period waves, a compromise should be establish between the idea of building a sufficiently large model to minimize any potential scale effect and the need to reproduce in the facility on a proper undistorted scale the entire area of interest. The cost of the study is proportional to the geometric scale, which also determines the duration of the test plan. Operational issues should also be considered: the displacement of a 100 000 dwt full loaded oil tanker is around 120 kg in a 1/100 scaled-model and about 960 kg in a 1/50 scaled-model. A very small scale may create problems related to the accuracy measurements are carried out.

In short, the model geometrical scale shall be defined in accordance with the experimental facility dimensions, the size of the coastal area of interest, expected quality of the results (i.e. scale effects), as well as operational and economic criteria. Usual scales range between 1:80 and 1:120, [1].
Sea states are usually reproduced by multi-element wave generation systems, preferably equipped with dynamic wave absorption systems and set-down compensation. In fact, being normally shallow water studies, a theoretical set-down compensation need to be introduced in the form of a second order-driving signal to ensure, in real time, that bound long waves propagate realistically in the model and without being contaminated by spurious second order effects (this applies to machines designed to reproduce only first order waves). Correct reproduction of wave conditions is of vital importance; hence, second-order wavemaker theory for the generation of multidirectional waves is recommended.

Bound-long waves in short crested seas are expected to have magnitudes that are about half the size of the set-down in long crested seas, even with a narrow directional spread of wave energy. Arguments for using long crested random waves in physical models of harbours may be: swell frequently presents relatively long crests; wave refraction ensures that directional spreading is reduced in coastal waters; to obtain conservative results. If long period effects are expected to be important that approach may no longer be justified, as spreading of wave energy in depths typical of harbour entrances may be sufficient to lead to lower set-downs and consequently less ship movement and long wave excitation.

Harbour breakwaters, berthing structures and beaches need to be reproduced in the model to create realistic wave conditions near the berths. Dissipative beaches shall be carefully installed to minimize the importance of unwanted reflections from the basin side walls or other boundaries. The test duration and the temporal sequence of incident waves are expected to influence moored ship's response. Test duration must be large enough so that the different wave groups are reproduced in the model and the response of the ship to those groups is recorded. In addition, there is no advantage in carrying out very long tests if the temporal sequence of incident waves consists of the repetition of a base random sequence of waves. Irregular long and short crested waves generated by filtered white noise techniques are normally used. Short and long period wave conditions need to be calibrated in the facility.

Experimental equipment may consists of wave gauges to measure the water free surface elevation, cantilever force transducers (with built-in strain gauges) to measure the loads applied on mooring lines and fenders and a motion capture system. This system shall measure the motions of moored ships, in its six degrees of freedom (surge, sway, heave, roll, pitch and yaw), without contact with the model.

Floating bodies (ships) have to be accurately reproduced on a geometrically undistorted scale and care should be taken when reproducing the mass distribution of the full-scale ship for the selected loading conditions. Hence, ship models are ballasted prior to testing to obtain the required hydrostatic and hydrodynamic characteristics; selected weights are placed inside the ship hull to reproduce the ship displacement, centre of gravity position, draft, metacentric heights and natural periods of oscillation.

Scale factors for elastic forces and weight of the mooring lines should ideally be equal. Compatibility between the two scales becomes particularly difficult when it comes to mooring lines with a nonlinear force-extension relationship. Even when mooring lines have linear characteristics, it is seldom possible to find a material that allows simultaneous verification of both scales. Therefore, only the forces more important for the behaviour of the model are reproduced properly. For normal mooring conditions, the weight of ship mooring ropes is inferior to 1.0% of its maximum breaking load. Therefore, the load-elongation characteristics of mooring lines are reproduced by elastic elements (e.g. coil springs) in combination with force transducers. Inelastic strings (e.g. kevlar) are used to connect the ship to the mooring points on the berth. This technique allows overcoming the difficulties related to selecting a suitable material to reproduce elasticity of mooring lines and enables simulation of nonlinear force-elongation relationships.

Mooring lines with the same orientation are often reproduced by an equivalent cable (double mooring line). Pretension loads applied to mooring lines need to be verified before each test to ensure that results for different test conditions can be compared. The (non-linear) load-elongation curves of fenders and mooring lines may be simulated by a set of coil springs. Sometimes it is satisfactory to linearize their non-linear behaviour: thus, each mooring element is reproduced by an equivalent linear mooring line (or fender) with a constant stiffness (that does not depend on elongation) and the same energy absorption capacity of the non-linear element up to its maximum elongation (or deflection).

Most scale effects result from the incorrect reproduction of the fluid viscosity in the physical model, due to the practical incompatibility of Froude and Reynolds similarity criterion [14]. Indeed, in current cases, fluid viscosity takes roughly the same values in the model and the prototype. Those scale effects may be controlled by ensuring that flow has turbulent characteristics, i.e., the Reynolds number does not falls below reference values, which depend on the phenomena being analysed.

With respect to short-wave propagation, the incorrect reproduction of fluid viscosity can result in higher energy losses by bottom or internal friction. These effects may be controlled by preventing waves travelling long distances in the physical model or by correcting expected energy losses in the wavemaker specifying bigger wave heights. Viscous and surface tension forces may affect reflection, transmission across porous structures or by overtopping, and waves breaking.

Moored floating structures may have large amplitude motions in response to low-frequency excitations that are limited essentially by the damping forces. Improper reproduction of the fluid viscosity tend to increase viscous damping in the model (compared to prototype) leading to an underestimation of the response of those structures [14]. The influence of fluid viscosity may be felt, for instances, in the viscous damping of roll oscillations. Indeed, as roll radiation damping is usually small, viscous damping (eddy shedding and skin friction) may represent a significant part of the overall roll damping. While the flow around the hull is fully turbulent in the prototype, the boundary layer in small-scale models will have probably laminar characteristics. Losses in the boundary layer will not be properly reproduced, leading to enhanced roll damping. However, eddy shedding represents often the main contribution to viscous damping and appears to scale for all but the smallest of models. Thus, as long as a proper geometric scale is selected, small-scale physical models are not expected to overestimate significantly viscous roll damping.

Friction forces developed at the interface ship-fenders may represent the main component of roll damping, especially when high pretension forces are applied on mooring lines, high friction fenders are installed on the berth or the wind blows the ship onto the fenders. Under these conditions, viscous damping loses importance.

Stability of Geotextile Encapsulated Sand-Systems

This research focused on

  1. the stability of geotextile encapsulated sand-systems against scour and beach lowering;
  2. the cross-shore component of sediment transport to study the response of a dune-beach system under conditions of erosion, accretion, persistent erosion and conditions alternating between periods of erosion and accretion; and
  3. the comparison of four different coastal protection schemes against each other, and against a reference case.

In total five models, corresponding to three erosion control systems with two configurations, one nearshore detached submerged breakwater with four configurations, and one non-protected dune-beach system as reference, were studied. Model characteristics were derived from a prototype dune beach system from the NW coast of Portugal.

The overall performance of each coastal protection scheme was evaluated against its hydraulic stability under wave loading and on its efficiency in maintaining a beach and in protecting the shoreline, based on the measurement of wave-induced morphodynamic changes over shorter and longer time-scales. As detailed bellow, five perspectives were considered in this assessment:

  • Stability of geotextile encapsulated sand-systems under wave-loading;
  • Scour-depth development and scour-and-deposition patterns over the cross-shore length of the model; observations of erosion and backfilling during a test duration;
  • Dependency between scour-depth and the non-dimensional variables;
  • Storm response: changes in cross-shore beach-profile when exposed to storm conditions lasting for 30 minutes; beach levels drawdown at the structure and beach lowering;
  • Recovery between storms: response to the changing forcing conditions; build up during swell conditions, followed by beach levels drawdown during storm conditions; volumetric changes due to seasonal variability;
  • Coastal evolution: beach-profile change under persistent erosional conditions.

The geometric scale, NL, was selected as the largest model possible to obtain results of highest possible accuracy. For the 2D-experiments the selected model scale was based on considerations of the size of the prototype dune-beach system, the size of the available facility, grain size diameter of available sediments, and controlling factors with respect to the limiting values of the period and height of the model waves.

The experiments were conducted only for irregular waves. The use of regular waves with height and period equal to those of significant wave can give inconsistent or erroneous results in the analysis of wave transformation and action of waves, Goda (2000[15]).

The following procedures were taken forward while selecting the scaling criteria and scale ratios of the models employed:

  • Geometrically undistorted model;
  • The nearshore hydrodynamics and sediment parameters were modelled according to Froude similarity;
  • The movable-bed model was composed of sand material;
  • The considered dominant mode of transport was suspended load transport;
  • The movable-bed model was built as large as possible so that the character of the wave breaking process is properly simulated, i.e., so that viscous and surface tension effects are negligible.

Three types of geosystems were used in the model tests; sand-filled containers, and sand wrapped around geotextile sheets made both from commercially available non-woven geotextile filters, and geotextile tubes of different sizes made from commercially available woven geotextile filters.

Although the geosystems used in the model tests were made from commercially available geotextile materials, they are not obviously suitable for use in the prototype. Taken into account the information about the materials and scaling relationships, the following scaling aspects would require some consideration while scaling down the material properties: stiffness and tensile strength of the geotextile during wave experiments; stiffness and tensile strength of the geotextile during filling; and sand tightness.

The proper scaling of several of the former aspects is not possible to fulfil, so a compromise is deemed necessary. Here it is assumed that geotextiles in the model are relatively too strong (about 1:1 to 1:3 of the prototype); yet, since they are not loaded to rupture it can be neglected. In regard to filling, the strength had only to ensure no damage to the geotextile during handling. Flexibility is warrant by a thinner geotextile. The hydraulic permeability of a GSC-structure depends mainly on the size between neighbouring containers (Recio, 2007[16]), thus so long the geometry is properly scaled the model represents adequately the permeability in the prototype. This means that aspects such as dimensions, placement and shape, also related to filling percentage and geotextile stiffness, have to be taken forward into the model. Both aspects, filling percentage and stiffness, may not be neglected in model, as failure to address them properly may result in a too large permeability in model compared to prototype by lower adaptation curvatures of the containers to the adjacent ones.

The characteristics of sediment transport dynamics in the nearshore region were sought to be prevalent and thus, the dimensionless fall speed parameter was used to determine the length scale of the geometrically undistorted model, which was scaled to Froude similarity ([math]\lambda=1/12[/math]).

In order to minimize scale effects produced by non-satisfied similarity, the model length scale was set to the maximum size that could be accommodated by the facilities at FEUP Laboratory of Hydraulics having in consideration the prototype characteristics, the sediment scale parameters, and controlling factors with respect to wave conditions. As the influence of surface tension is most significant for periods smaller than 0.35s, and for water-depths less than 2cm [1] it is anticipated that the scale effects due to non-satisfied Weber similarity are negligible. Moreover, the turbulent characteristics of the nearshore dynamics makes it safe to assume that the spurious effects of viscosity are not underestimated in the model. Sediment transport mechanisms along the cross-shore profile, namely the suspension by wave breaking and the sheet flow conditions in the swash zone, appear to be correctly reproduced in the model.

In regard to the scaling down of the geotextile properties some simplifications were introduced. It was assumed that the geotextiles in the model were relatively too strong but since they were not loaded to rupture it is negligible. In regard to filling, the strength had only to ensure no damage to the geotextile during handling. Flexibility was warrant by a thinner geotextile. The hydraulic permeability of a GSC-structure depends mainly on the size between neighbouring containers (Recio, 2007[16]) and thus, so long the geometry is properly scaled the model should represent adequately the permeability in the prototype (i.e., so long the dimensions, placement and shape, also related to filling percentage, are scaled down correctly). At last, requirements as regard to geotextile sand tightness were considered.

In regard to laboratory effects the following potential sources of error were examined:

  1. wave generation;
  2. resonant oscillations forced across the boundaries of the test section;
  3. absorption of reflected waves;
  4. blockage effects;
  5. compaction of sediments in the bed; and
  6. accuracy of the instruments.

Resonant oscillations across the boundaries of the test section, and absorption of reflected waves have been examined. In addition, the evaluation of generated wave conditions based on the wave-data recorded during the experiments assured that the different models have been set-up to run on similar hydrodynamic conditions and thus that the comparison applied to the wave-induced morphodynamic change was possible and reliable. Representative sea-states were chosen from the prototype; in addition, the use of irregular wave trains also avoids the model effects of regular wave generation in coastal sediment models.

Blockage effects around the structures were minimal, as only the array of four wave probes were at the flow section during the experiments. The pore-pressure sensors were buried into the sand at sufficient depth so that they would not emerge due to bottom erosion.

For each wave run-segment with plane beach, the bed conditions were thoroughly checked before the experiment and the bed was carefully levelled to the desired gradient. To minimize the effects caused by the initial bed profile, the sand bed was repeatedly levelled until the measured beach-profile was within a minimum tolerance range based on the ideal conditions. To prevent disturbances and to assure that the level of sand saturation was roughly the same for each wave-run segment with plane beach, the water during levelling was kept to SWL. Above it, the beach-profile was slowly wet so as to reduce air entrainment.

Coastal Sediment Transport

A medium to long-term coastline evolution numerical model was developed that may be of important usage, namely, for the test and comparison of interventions to control erosion. The model assumes that long-shore transport is the most relevant governing process and incorporates a bottom updating scheme, based on pre-defined rules for cross-shore profile development. The critical analysis of its performance both in generic tests and in applications to real situations showed the need to improve the numerical description cross profile development.

Furthermore, to increase the confidence in its results, physically meaningful ranges should be established for morphodynamic parameters used in calibration (underwater limit of measurable bottom changes, wave run-up limit, and beach face slope). Coherent sets of field data would be needed (topo-hydrographic, hydrodynamic and sedimentary), but these are frequently insufficient, unavailable or exceptionally expensive, especially for the high energetic coastal zones of the Portuguese west coast.

A physical model study was conducted with the primary purpose of improving the numerical description of erosional and depositional beach profile when submitted to persistent long-shore transport induced by irregular wave conditions. A three-dimensional movable-bed long-shore transport model was designed and implemented at the Hydraulics Laboratory of the Hydraulics, Water Resources and Environmental Division of the Civil Engineering Department of the Faculty of Engineering of University of Porto (SHRHA-DEC-FEUP). It was conceived to reproduce the active part of a small stretch of the Portuguese west coast undergoing a persistent erosion situation, modelling on typical hydrodynamic and morpho-sedimentary characteristics.

A small-scale physical model of a beach, which is intended to derive quantitative results for the prototype, it is extremely difficult to define and operate, making them rare. Indeed, the difficulties found were many, starting with the selection of the laws of similarity to adopt, the need for geometric distortion, the discontinuities imposed by the borders, the laboratory and scale effects. In addition to the complexity inherent to short-wave hydrodynamics there are also the problems of reproducing sediment transport processes (related with the sediments’ grain size, bedforms and dominant mode of sediment transport).

These problems would be smaller at larger scales, only possible in very large facilities, but with higher difficulties of operation and involved costs. Because the design approaches for these small-scale models are not clearly established in the literature of this, theoretical approaches together with critical analysis of results from a few previously conducted research programs were the basis for the design of the implemented model. To reproduce a beach stretch with sufficient long-shore extension and still be able to measure significant bottom change, the model had to be geometrically distorted.

It was primarily a short wave hydrodynamic model following Froude’s scaling laws, in which the characteristic wave length scale was associated with the geometric vertical scale, thus ensuring the adequate reproduction of the wave shoaling and refraction. Long-shore sediment transport was considered the most relevant process to reproduce. Since it is significant inside the surf zone, where high turbulence levels occur, the mode of sediment transport considered dominant was suspension and Vellinga’s scaling laws were adopted.

These are recommended for distorted models and were drawn from a large number of multi-scaling physical model tests, only possible in large scale facilities. The selected scaling laws defined the relation between horizontal, vertical and sediments’ grain size scales. Sand was search for a grain size, minimizing distortion and vertical scale. The specific grain size found defined the relation between horizontal and vertical scales. The selection of the horizontal scale ([math]N_x=37[/math]) set the vertical scale ([math]N_z=74[/math]) and the model geometric distortion ([math]\Omega=2[/math]).

Important scale effects in hydrodynamics were essentially due to model distortion: incorrect reproduction of diffraction, transition in breaking type, reflection enhancement and exaggerated wave run-up. In sediment transport processes scale effects were mainly related to the viscous effects in the bottom boundary layer and to the grain size of the sand. Identified effects were: the incorrect reproduction of bed forms, confirmed by the presence of ripples having dimensions characteristic of the prototype, eventually lower transport rates and higher percolation. The higher percolation combined with the reflection enhancement and the exaggerated wave run-up would eventually result in steeper beaches. In spite of the uncertainty level inherent, the experimental results were articulated with simulations of the referred numerical model making use of the morphological time scale, calculated from the long-shore transport rates measured in the physical model. Nevertheless, small-scale three-dimensional surf-zone physical models are more easily useful for the derivation of qualitative results as the comparison of the local effects of different coastal defence interventions. Higher accuracy in quantitative results is largely dependent on the improvement of the knowledge of the processes. This can only be achieved in the Nature laboratory.

Although the wave generation system is quite recent, incorporating state-of-the-art techniques for the compensation of known laboratory effects, re-reflection in the wave paddles was noticed during the experiments. The improvement of reflection absorption and spurious long-waves compensation are still required. The bottom profiler system was touch-sensitive, thus intrusive for the model. Besides that, because it is mounted on a beam, it is not so practical to move. Also its moving along the beam is quite sensible to dust particles, unavoidable in movable-bed models. Alternative, less intrusive apparatus for surf-zone bottom surveying should be investigated.

Related articles

How to apply models
Modelling coastal hydrodynamics
Sand-filled geosystems in coastal engineering


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The main author of this article is Taveira Pinto, Francisco
With contributions by: Paulo Rosa-Santos, Luciana das Neves, Raquel Silva