Armor Layer Research Articles

2D water-wave interaction with permeable and impermeable slopes: Dimensional analysis and experimental overview

The main objective of this research is to characterize and quantify the prevalent physical processes in the energy transformation of a regular wave train when it interacts with permeable and impermeable breakwaters. Two sources of experimental data are considered: (a) numerical experiments on an undefined impermeable rigid slope, using the numerical model (IH–2VOF), and (b) physical experiments on a non-overtoppable permeable breakwater with a cube armor layer and a porous core of finite width in a 2D wave flume. A revised dimensional analysis reveals that the relative water depth, h/L, and the incident wave steepness, H/L, at the toe of permeable and impermeable breakwaters are the key factors to define and optimize the experimental space (HI/L, h/L). Moreover, the product of (h/L) (HI/L) can be applied to identify the type of wave breaking and the domains of wave energy transformation, and to quantify the reflected and transmitted energy coefficients and the dissipation rate (KR2,KT2,D∗). Fitting an experimental curve (i.e. a sigmoid function) to the impermeable data, the slope is a plotting parameter. The same conclusion is obtained for a permeable breakwater; in addition the wave energy coefficients depend on the relative breakwater width B*/L, and the relative core grain size and D50,p/L, and armor unit diameter, Da/L. Because the range of the design factors spans several orders of magnitude, a log-transformation provides a well behaved experimental space [ln(h/L), ln(H/L)] which is likely of benefit to verify the wave breaker type and the related dissipation-reflection-transmission on slopes. Finally, this study shows that there is not a biunivocal relationship between the Iribarren number, Ir, and the type of breaker, the reflection and transmission coefficients and the bulk dissipation. Therefore, Iribarren's number is not a sufficient similarity parameter for the analysis of wave breaking, and related flow characteristics on slopes.

Bulk Wave Dissipation in the Armor Layer of Slope Rock and Cube Armored Breakwaters

The objective of this research is to analyze the interaction of the incident wave train with a mound breakwater (specifically, dissipation in the armor layer) and to quantify the performance of the structure built with different types and sizes of armor units. The generalized Π -Buckingham theorem is invoked to choose a complete set of independent variables that govern the principal interaction processes. The analysis is based on two sets of experimental data obtained in the wave flume of IISTA, University of Granada, and in the wave flume of Aalborg University. The bulk dissipation depends on the product of the relative water depth and the incident wave steepness, (h/L)(HI/L), the relative size of the armor diameter, Da/HI, the relative thickness, e/L, the shape and specific placement criterion, the characteristics of the porous core, B*/L, D50,p/L, and the slope angle of the breakwater. For a given breakwater, the product of (h/L)(HI/L) can be used to identify and quantify three hydrodynamic performance regimes: reflective, dissipative and transitional, based on the prevalent interaction processes. Moreover, the dimensional analysis provides a functional relationship between the stability parameter and the bulk dissipation. For two mound breakwaters, one built with cubes of Da=49.6 mm and the other one with rocks of Da=44.0 mm, the bulk dissipation is almost similar over the entire range of (h/L)(HI/L). These results could be useful for the assimilation of data obtained in different wave flumes, the optimization of the breakwater design and to revise the notional permeability parameter.

Numerical study on the axial-torsional response of an unbonded flexible riser with damaged tensile armor wires

The local mechanical response of a 2.5" unbonded flexible riser with damaged wires is studied by a nonlinear finite element (FE) model. Firstly, the riser was supposed to be under pure tension and pure torsion. Stiffness and force distribution of the intact riser predicted by the analytical and numerical models are compared, and deviations between the two solutions are discussed. Then, two up to eight wires in the outer tensile armor layer are assumed to be damaged. Numerical results indicate that uneven deformations caused by the broken wires result in a clear nonlinear force redistribution among the outer wires. The maximum and minimum forces supported by the remaining intact outer wires are closely related to the number of damaged wires, boundary conditions and the load direction. Finally, the effect of internal frictions on the load recovery of damaged wires is studied by increasing the FE model length and applying the pre-pressure. It was found that damaged wires can progressively recover their load-carrying capacities with the increase of internal frictions. In addition to the boundary effects, axial stress of the damaged wire is linear with the length of the riser, which indicates that results obtained from the short model can be employed to estimate the load recovery characteristics of the long model.

Reliability-based design and sensitivity analysis of rock armors for rubble-mound breakwater

Predicting the stability of armor blocks placed on breakwaters is one of the main challenges in coastal and ocean engineering. However, the armor layer’s damage mechanism is very complicated so that there are many uncertainties in the estimation of different parameters in armor design. The inherent uncertainties in these parameters necessitate reliability analysis to ensure the stability of the breakwaters. This study proposed a reliability-based framework for estimating the rock armors weight based on the probabilistic analysis. The effect of different sources of uncertainties in determining effective parameters such as wave height, wave period, water-level changes and armor density was introduced and applied in calculating rock armors weight. Moreover, the correlations between breakwater life span, its probability of failure and stable armor weight were also considered in the analysis. Based on this method, armor weight could be computed according to any desired reliability level and breakwater life span. Results of sensitivity analysis showed that the most critical parameters affecting the reliability of armor weight are wave height and dimensionless damage level. Finally, the presented case study in this article addressed the use of this method in the design of armor weight for a breakwater constructed in the southern part of the Caspian Sea. Results showed that the stable armor weight to maintain a probability of failure equal to 0.005 placed on a breakwater with 50-year life span under a 100-year design storm condition in the Caspian Sea is about 24.28 ton. Moreover, by increasing the breakwater life span from 50 to 100 years, the armor weight increases only by about 10%.

Effect of wave storm representation on damage measurements of breakwaters

In this work, the effects of storm representation on damage measurements of a breakwater are studied in a small-scale physical wave flume. In particular, a two-layer breakwater with cubic armor units randomly placed is considered. A storm recorded in the Mediterranean Sea is the basis to analyze the armor layer damage. Storm sea states are represented in the laboratory using four different methodologies: i) Real storm methodology (RSM, used here as benchmark test) ii) Classical methodology (CM) iii) Equivalent Magnitude Storm with a triangular shape (EMSI) and iv) Equivalent Magnitude Storm with a trapezoidal shape (EMSA). For the four methodologies, the experiments are repeated five times. Considering laboratory occupation times, results suggest that a minimum of five repetitions of CM should be performed to obtain an average damage value that can represent the average damage given by RSM. Although this recommendation is linked to the tested conditions, it provides useful information to set-up experiments dealing with similar breakwater and wave conditions.

Theoretical and numerical methods to predict the behaviour of unbonded flexible riser with composite armour layers subjected to axial tension

Unbonded flexible risers are widely applied to deep-water oil and gas production field, and their complex cross-section mechanical properties have always been a challenging issue in ocean engineering. Over the recent years, the traditional steel tensile armour layers of unbonded flexible risers are replaced by composite materials, owing to their advantages of lightweight and high strength. In this paper, a theoretical deduction based on energy method and a numerical method in consideration of detailed geometric properties are proposed to analyze the behaviour of the unbonded flexible riser with composite armour layers. Both the theoretical and numerical methods take full consideration of the material orientation of composite, and for the numerical model, two local coordinate systems are established to define the material properties of composite armour layers. Based on a 2.5-inches unbonded flexible riser model with eight-layers, some cases from theoretical and numerical methods are presented for validation. Then the effect of the fiber volume fraction of composite on the axial tensile stiffness, as well as the weight of the unbonded flexible riser, is discussed. Furthermore, characteristics analysis of axial stiffness is carried out and the effect of the boundary condition is discussed as well.

Numerical Simulation of Wave Overtopping on Breakwater with an Armor Layer of Accropode Using SWASH Model

In this paper, a new method for predicting wave overtopping discharges of Accropode armored breakwaters using the non-hydrostatic wave model Simulating WAves till SHore (SWASH) is presented. The apparent friction coefficient concept is proposed to allow the bottom shear stress term calculated in the momentum equation to reasonably represent the effect of comprehensive energy dissipation caused by the roughness and seepage during the wave overtopping process. A large number of wave overtopping cases are simulated with a calibrated SWASH model to determine the values of equivalent roughness coefficients so that the apparent friction coefficients can be estimated to achieve the conditions with good agreement between numerical overtopping discharges and those from the EurOtop neural network model. The relative crest freeboard and the wave steepness are found to be the two main factors affecting the equivalent roughness coefficient. A derived empirical formula for the estimation of an equivalent roughness coefficient is presented. The simulated overtopping discharges by the SWASH model using the values of the equivalent roughness coefficient estimated from the empirical formula are compared with the physical model test results. It is found that the mean error rate from the present model predictions is 0.24, which is slightly better than the mean error rate of 0.26 from the EurOtop neural network model.

Influence of irregularities in the rock underlayer on the stability of XblocPlus

Many rubble mound breakwaters are nowadays made with an armour layer consisting of single layer interlocking elements. The stability of these armour layers could well be influenced by the irregularity of the rock underlayer, as that influences the degree of interlocking. Especially for the new types of regularly placed armour, this might be an important factor for the stability. However, this aspect has not been studied widely yet. Therefore, this paper investigates the influence of irregularities in the underlayer on the stability of a type of single layer breakwater elements. Model tests have been conducted in which the irregularities in the underlayer were systematically varied. The irregularities in the underlayer and the orientations of breakwater elements were measured with 3D-scanning. The breakwater armour unit used in the tests is the XblocPlus. A new failure mechanism, not previously observed for breakwater elements, was found to initiate damage. Causing the armour to be pushed outward by a combined effect of the weight of the upper armour and the excessive hydraulic pressure of the remaining water under the armour layer. Especially large-scale convex (i.e. protruding outwards) undulations in the cross-shore direction influenced the stability of the armour layer. This influence has been quantified.

Form friction factor of armored riverbeds

Resistance to flow because of the presence of bed forms over armored riverbeds is of paramount importance, leading to the effective design of water-resources-related projects. Based on the findings over bed armored surfaces, it is shown that the controlling roughness (ks) can be taken as equal to the median diameter of the armor layer. Analytical methodologies for total and grain friction factors have been proposed here that take flow non-uniformity into account using the velocity distribution and friction slope. The percentage composition of form friction factor in the total friction factor was estimated to be 40%. The results were explained in light of the coupling of the sediment threshold problem with the friction factor and coarse-grain rearrangement in armor layer. The computed form friction factor by proposed method was compared with Keulegan’s method and is found to give satisfactory results, showing 80% agreement of all field data sets.

Physical model of scour at the toe of rock armoured structures

Toe structures are a common feature in coastal rock armoured structures, both safeguarding the structure against scour at the toe and providing support to the armour layer. The toe structure itself is often comprised of rocks as well. Hence, generally some form of scour protection, such as a filter layer or a geotextile, is applied underneath the toe structure. Currently, there is a lack of available methods to judge the necessity of these kinds of costly scour protection measures underneath the toe structure. In this paper, a unique data set from physical model tests of scour at the toe of rock armoured structures is presented. The bed level change is measured by a laser scanner across the entirety of the sand bed, including underneath the structure. Additionally, the temporal development of the scour at the glass wall of the flume is measured using an innovative combination of video imagery and a deep learning algorithm. The sand diameter is not varied in the physical model tests. In all tests, scour was observed both in front of the structure and underneath the structure. Two expressions have been derived that give estimates for both kinds of scour, and thus can give insight into the necessity of scour protection underneath the toe structure.

Non-symmetric cyclic bending of helical wires in flexible pipes

Unbonded flexible pipes have superior fatigue performance as the internal armor layers are allowed to move relative to each other, leading to reduced structural loading. The main interactions between the internal layers are the contact forces and the frictional forces. Frictional interaction leads to a complex non-linear response of unbonded flexible pipes making prediction of cyclic bending fatigue a demanding task. Nevertheless, detailed understanding of local armor wire stresses and the related fatigue phenomena is of paramount importance as unbonded flexible risers are often operated close to their mechanical limits. This paper presents a method for calculating the tensile armor wire loading and the hysteresis effect on flexible pipes when subjected to tension, and non-symmetric cyclic bending. The effect of non-symmetric cyclic bending with different tensile armor lay angles, and frictional conditions are studied. The analysis uses an efficient repeated unit cell finite element model, allowing the analysis to be performed on a desktop computer. The study shows that the tensile armor wires gradually translate towards the compression side of the pipe bending plane, when the unbonded flexible pipe is subjected to combined tension and non-symmetric cyclic bending. In the analysis, cyclic bending is applied until steady-state in the bending response is achieved over a full bending cycle. The global bending response of the flexible pipe and the tensile armor wire loading conditions for fully stabilized non-symmetric cyclic bending become symmetric around the frictionless state for the mean cyclic bending curvature. An approximate analytic model for the tensile armor in the stabilized cycle, based on symmetric bending about the geodesic curve corresponding to the mean pipe curvature, is proposed.

Overtopping layer thickness and overtopping flow velocity on mound breakwaters

Mound breakwater design is evolving owing to rising sea levels caused by climate change and social concern regarding the visual impact of coastal structures. The crest freeboard of coastal structures tends to decrease while overtopping hazard increases over time. Pedestrian safety when facing overtopping events on coastal structures has been assessed considering the overtopping layer thickness (OLT) and overtopping flow velocity (OFV). This paper proposes a new method to estimate the OLT and OFV on mound breakwater crests during extreme overtopping events, based on 123 2D small-scale physical tests of conventional low-crested mound breakwaters with a single-layer Cubipod® and double-layer rock and cube armors. The new method to estimate OLT exceeded by 2% of incoming waves is based on formulas given in literature for dikes, but adapted and calibrated for mound breakwaters. The formula to estimate the OFV exceeded by 2% of incoming waves is based on the correlation between the statistics of the OLT and OFV, considering an empirical coefficient calibrated for each type of armor layer. Exponential and Rayleigh distribution functions are proposed for estimating the OLT and OFV with exceedance probabilities under 2%. Although the statistics of OLT and OFV depend on similar variables, contrary to intuition, specific OLT and OFV corresponding to the same overtopping event appear to be independent.

A global-local fretting analysis methodology and design study for the pressure armour layer of dynamic flexible marine risers

In this paper, a global-local fretting design methodology for the pressure armour layer of flexible marine risers is outlined. This includes global dynamic riser analysis, geometrical and analytical sub-models and local nub-groove contact finite element analysis. Furthermore, a fretting test rig is developed and utilised to quantify coefficient of friction and wear coefficient under representative nub-groove loading conditions. The combination of the global-local computational methodology and experimental characterisation of pressure armour wire material allows for the development of running condition fretting maps. This identifies design criteria for critical riser global curvatures that are associated with minimum number of cycles to failure. The design methodology presented in this paper is applied to a realistic riser design study, using extreme sea-state loading conditions. In this case study, the predicted pressure armour fretting fatigue lives are found to be in the same range as the plain fatigue lives of the tensile armour layer.

Wave parameters influence on breakwater stability

This research paper experimentally explored the wave parameters effects on the breakwater armour layer stability. Breakwater stability mainly depends on the armour layer that guards the inner layers against the wave attack and the wave condition affects the breakwater stability. The wave height, length and steepness effect were investigated during the test program. Different formulas were available in the literature to predict the breakwater stability. The laboratory results were thus employed to assess the applicability of existing design equations. Experimental results showed that under normal wave condition (Hs) the breakwater was stable, whereas under storm condition (Hs of 1.2 designed wave height) the roundhead reached the failure state. The results approved the impact of wave parameters on the breakwater stability and damage progression. Results revealed that the existing design formulas underestimate the structure stability.

A review of reliability analysis of offshore scour protections

The R&D project Oracle – offshore risk analysis for climate change adaptation and lifetime extension – is focused on optimising the design of scour protection schemes for the extended lifetime of offshore foundations. This project proposes an optimisation of scour protections by combining reliability-based techniques with the novel concepts of dynamic and wide-graded armour layers. The ultimate goal is to develop a decision support system (DSS) for scour protection design and risk and reliability analysis to be used by professionals and researchers dealing with fixed foundations applied to marine renewable energy projects (e.g. wind, wave and tidal). However, a meaningful implementation of such a DSS implies prior analysis of several knowledge gaps related to scour protection in the offshore environment, which are yet to be fully addressed in the literature. This paper provides a brief review of the scientific and technical challenges in the research field of reliability of offshore scour protection. On the basis of identified challenges, the discussion of future research lines is performed with a particular focus on the aim of the Oracle project. The recent findings related to risk and reliability analysis of offshore scour protection are addressed and framed within the existing knowledge gaps in the literature.

Drone Based Quantification of Channel Response to an Extreme Flood for a Piedmont Stream

The influence of extreme floods on the form and functioning of upland systems has concentrated on the erosive impact of these flows. They are seen to be highly competent with coarse sediment transport rates limited by upstream supply and moderated by the ‘blanketing’ effect of an armour layer. This study investigates the effect of extreme events on the upland sediment cascade subjected to a recent extreme rainfall-induced flood event. The drone-based survey generated orthophotography and a DEM surface, which was compared with historic LiDAR data. This allowed erosion and deposition to be quantified and the surface micro-variation used to characterise stable and mobile sediment. The idealised model of sediment residence time increasing downstream is questioned by the findings of this study as relatively little coarse bedload sediment appears to have been transferred downstream in favour of initial local channel erosion (moderated by legacy large sediment), mid-reach palaeo-channel reactivation, sub-channel infilling and downstream deposition of the majority of mobilised sediment across berm and bar surfaces within the active inset channel margins. Channel margin erosion was largely limited to fine sediment stripping moderated by the re-exposure of post-glacial sediment. Only a weak relationship was found between local channel slope and deposition, with storage linked more to the presence of inset berm and bar areas within the inset active channel. Downstream fining of sediment is apparent as is a strong contrast between coarser active sub-channels and finer bar and berm areas.

Extension of shallow water rock armour stability formulae to nonlinear waves

The present paper presents new formulae for hydraulic stability of the main armour layer on rock armoured conventional rubble mound structures. In the present study, new stability tests were performed covering both mild (1:100) and steep (1:30) foreshores. The tests covered nonbreaking and breaking waves on the foreshore and also waves of very low steepness. The tests with the 1:30 foreshore showed the armour layer to be significantly more stable in the surging domain than predicted with the Van Gent et al. (2004) formulae. This was attributed to nonlinear waves with significantly larger H1/3 than Hm0. New stability formulae are presented and fitted to existing and present stability data. The new formulae provide a significant increase in the reliability for nonlinear waves compared to the Van Gent et al. (2004) formulae.

3-D Scale Model Study of Wave Run-Up, Overtopping and Damage in a Rubble-Mound Breakwater Subject to Oblique Extreme Wave Conditions

A set of scale-model tests carried out to enlarge the range of wave steepness values analysed in run-up, overtopping and armour layer stability studies, focusing on oblique extreme wave conditions and on their effects on a gentler slope breakwater’s trunk armour and roundhead, is presented in this paper. A stretch of a rubble mound breakwater (head and part of the adjoining trunk, with a slope of 1(V):2(H)) was built in a wave basin at the Leibniz University Hannover to assess, under extreme wave conditions (wave steepness of 0.055) with different incident wave angles (from 40º to 90º), the structure behaviour in what concerns wave run-up, wave overtopping and damage progression of the armour layer. Two types of armour elements (rock and Antifer cubes) were tested. Non-intrusive methodologies including a new application of laser scanning technique for the assessment of both armour layer damage and wave run-up and overtopping were used. It is expected that such work will contribute also with data to improve empirical formulas as well as to validate complex numerical model for wave-structure interaction.

Effect of Axial Compression and Wet Collapse Loads on Torsional Response of Flexible Pipe

Flexible pipes connect the two critical systems of the floating production platform and underwater production, which play an important role in the transportation of oil and gas as well as water injection. However, flexible pipes are often subjected to multiple loads that threaten their stability in the service process. In this study, a model of a flexible pipe containing practical cross section in all layers is established to study the effects of axial compression and wet collapse loads on clockwise and anticlockwise torsional responses. The results of calculation show that the axial compression and radial expansion of the flexible pipe are caused by the axial compression load, which reduces clockwise torsional stiffness. The wet collapse load induces the bending deformation of the flexible pipes in clockwise and anticlockwise torsion, where the bending deformation of clockwise torsion is significantly affected by the change in the Young’s modulus of the tensile armor layers. This study shows that clockwise torsional stiffness is small and exhibits a trend of axial compression. Clockwise torsion has poor stability in combination with axial compression and wet collapse loads, respectively. Therefore, to prevent instability in flexible pipes, clockwise torsion load, or which coupled with axial compression and wet collapse load, should be avoided.

Analytical and experimental studies on flexible pipes tensile armors lateral instability in cyclic bending

This paper aims at investigating the flexible pipe armor wires lateral instability mechanism. For a flexible pipe subjected to longitudinal compressive loads associated with cyclic bending, analytical model that depicts the slips of the armor wires in bending and the ultimate state of the armor wires after numerous bending cycles, stable or unstable, is presented. This model is capable of evaluating the equilibrium path of the armor wire after numerous bending cycles in stable conditions, as well as estimating the critical longitudinal compressive load that may eventually cause the lateral instability of the armor layers. The analytical estimation of the armor wires lateral stability limit is compared with existing test data available in the literature, as well as the data of two new tests introduced in the present context, where excellent correlations are demonstrated. In addition, some useful suggestions for improving the design of flexible pipes against the armor wires lateral instability failure are presented.