Conceptualization and Prototype of an Anti-Erosion Sensing Revetment for Levee Monitoring: Experimental Tests and Numerical Modeling

water

Article Conceptualization and Prototype of an Anti-Erosion Sensing Revetment for Levee Monitoring: Experimental Tests and Numerical Modeling

Manuel Bertulessi 1,* , Daniele F. Bignami 2, Ilaria Boschini 1 , Andrea Chiarini 3, Maddalena Ferrario 4, Nicola Mazzon 5, Giovanni Menduni 1, Jacopo Morosi 4 and Federica Zambrini 1

1 Civil and Environmental Engineering Department, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy; [email protected] (I.B.); [email protected] (G.M.); [email protected] (F.Z.) 2 Fondazione Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy; [email protected] 3 Studio di Ingegneria Civile e Ambientale ChiariniAssociati, Via Galileo Ferraris, 63, 52100 Arezzo, Italy; [email protected] 4 Cohaerentia Srl, Via Pinturicchio 5, 20131 Milano, Italy; [email protected] (M.F.); [email protected] (J.M.) 5 Maccaferri Innovation Center, Via Ipazia, 2, 39100 Bolzano, Italy; [email protected] * Correspondence: [email protected]

Received: 28 September 2020; Accepted: 26 October 2020; Published: 28 October 2020

Abstract: The problem of levee embankment control during high flows is crucial for flood risk management in floodplains. Levee defense lines are often hundreds of kilometers long and surveys during emergencies are not easy tasks. For these reasons, levees monitored with in situ sensors and a suitable Information Technology (IT) real-time data communication and integration infrastructure, so-called “smart levees”, are gaining increasing interest as a crucial protection technology in floodplains. The paper presents the conceptualization of a prototype of a levee smart revetment, based on the integration of an optical fiber (OF) cable into a steel double-twisted wire mesh. In this paper the feasibility of this kind of revetment is firstly assessed. The flow pattern of overtopping water on the embankment is discussed, thus producing a raw estimation of the shear stress acting on the revetment in the field. A sample case is then analyzed in both numerical and laboratory tests. For this purpose, a numerical Finite Element Model (FEM) to describe the mechanical behavior of a double-twisted wire mesh when loaded along its own plane is presented. Numerical results indicate that the related strain, relatively low as compared to the steel wire yield stress, can be fully detected by the optical fiber continuous Brillouin sensor. This has been validated by the experimental activity performed and a digital twin of the prototype of the smart revetment, suitable for virtually testing the product under any load and constraint conditions and tailoring the production process, has been created.

Keywords: smart levee; distributed ﬁber optic sensors; structure health monitoring; ﬂood risk reduction; emergency management; embankment failure symptoms; erosion control; real-time strain detection; reinforced geomat

1. Introduction Levee monitoring and surveillance during flood events are fundamental activities for flood risk management in lowland areas. This is particularly true for the inland floodplains which are often protected from river floods by thousands and thousands of kilometers of earth embankments [1].

Water 2020, 12, 3025; doi:10.3390/w12113025 www.mdpi.com/journal/water Water 2020, 12, 3025 2 of 16

Nevertheless, these issues affect also coastal embankments which have to protect the coast from storm surges. Scientific research and studies on the stability and design of these kinds of levees are important since the catastrophic consequences of Hurricane Katrina in August 2005 [2]. In this work, riverine embankments are taken into account. Embankment issues, such as overflow or piping, often lead very quickly to a breach, which is notoriously a disastrous event that causes significant damage to neighboring settlements and economies and, in the worst-case scenarios, the loss of human lives [3,4]. Levees, on the other hand, are structures that are almost impossible to test under conditions similar to those of service (as e.g., happens for dams). Despite that, levees, as green or natural/nature-based infrastructures, in most cases, have many conservation functions (e.g., ecosystem services, landscape preservation), avoiding replacement with gray or built infrastructures, not only for financial reasons. Levees play a role as Eco-DRR (Ecosystem-based Disaster Risk Reduction) components of a desirable strategy mixing gray and green options [5]. Their state of health is revealed only when they are recruited to carry out their task, i.e., during river high flows. These are earth structures, exposed to the elements and to an infinite number of possible problems derived from the action of man, or of burrowing animals, or other natural issues such as those due to earthquakes. Therefore, they prove to be intrinsically vulnerable, much more than other riverine structures. The design of levees is often performed taking into account a number of uncertain factors such as hydraulic, hydrologic, structural, and economic uncertainties [6]. The backup for the inherent residual risk [7] is provided by surveillance and monitoring activity, both during ordinary and high flows. Though a number of problems can be assessed during periodic inspection or maintenance (e.g., animal burrows or embankment landslides), other issues remains strongly connected with the hydraulic conditions in the river, such as subsoil failures as a result of piping [8] or overtopping [9]. Trained levee patrollers are usually deployed during high flows in order to recognize the symptoms of failure and communicate relevant findings to the authorities in good time so that they can then issue further directions or initiate procedures to take corrective measures [10]. Recognizing the symptoms of failure requires a deep understanding of the underlying physical mechanisms and a ready and proper team communication. Nonconformities in procedures are unfortunately often observed, both in phenomena understanding and in late communication. A quick localization of failure trigger points along the defense line is fundamental to issue an early warning and activate the related procedures. Although surveillance and monitoring are therefore crucial in disaster prevention, monitoring teams often have to manage hundreds of kilometers in a short time on both sides of the river. A failure symptom can occur in river sections that have not yet been monitored or, worse, just after the team has passed. A systematic improvement in the quality and in the frequency of the structural health information chain would radically increase the safety of the embankments. An accurate and real-time localization of any issue such as the formation of an overflowing water stream could save operational resources, costs, and precious time during emergencies, where every single minute saved is able to make the difference in the consequences of the event. Levees monitored with in situ sensors and a suitable IT real-time data communication and integration infrastructure, so-called smart levees, are gaining increasing interest as a crucial protection technology in floodplains. A smart levee provides continuous information about its conditions to end users who can make informed decisions to maintain the demanded flood protection levels [11]. The smartness refers to the knowledge of the health of the structure and the potential failure mechanisms that could affect it based on the analysis of data collected by the sensors integrated in the levee. The smart levee concept was born and developed in central northern Europe in the 2000’s; among the several research projects promoted, an important contribution has been given by the Dutch IJKdijk [12] and the Polish ISMOP [13]. In both projects, an experimental levee was built and sensorized in order to study levee failure mechanisms. Different type of sensors have been installed both externally and internally on the embankment to measure and monitor the parameters controlling slope stability and seepage phenomena. Among them, OF sensors are frequently used to detect both earth displacements Water 2020, 12, 3025x FOR PEER REVIEW 3 of 16 frequently used to detect both earth displacements and internal temperature variations. Moreover, theyand internalare linear temperature and distributed variations. sensors Moreover, suitable for they monitoring are linear large and areas distributed as in the sensors case of suitable levees. for monitoringDue to largethese areas important as in the and case promising of levees. features, these type of sensors have been taken into accountDue in to the these present important work. and A strain promising and temperatur features, thesee sensing type of anti-erosion sensors have revetment been taken to into be used account as onein the of presentthe components work. A of strain a smart and levee temperature equipment sensing is here anti-erosion proposed. The revetment sensing tocomponent be used as is onegiven of bythe a components continuous OF of a cable smart woven levee equipmenttogether with is here a double-twisted proposed. The steel sensing wire componentmesh (DTWM) is given which by is a stretchedcontinuous out OF on cable the woven embankment together as with an a anti-erosion double-twisted device steel wire[14]. meshThe installation (DTWM) which of this is stretched sensing revetmentout on the in embankment correspondence as an with anti-erosion the most device critical [14 river]. The sections installation would of create this sensing a permanent revetment “levee in sentinel”,correspondence capable with of providing the most critical valuable river information sections would on the create state a permanentof the embankment “levee sentinel”, before, during, capable andof providing after the valuableflood events. information This product on the stateis conceive of the embankmentd to be a native-sensing before, during, structure, and after that the is, flood the structuralevents. This part product is coupled is conceived with the to besensing a native-sensing one in the structure,production that process: is, the structuralthe OF cable part is coupleddirectly wovenwith the into sensing the double-twisted one in the production sections process: of the wire the OFmesh. cable is directly woven into the double-twisted sectionsThe ofpresent the wire paper mesh. provides the first steps towards the conceptualization of this sensing erosion controlThe revetment. present paper In particular, provides the firstfocus steps is on towards the feasibility the conceptualization of the integration of thisprocess sensing and erosionon the capacitycontrol revetment. of the OF to In correctly particular, detect the focusthe mechanical is on the feasibilitybehavior of of the the wire integration mesh solicited process in and its onplane. the Thiscapacity has been of the performed OF to correctly by carrying detect theout mechanicaltwo activities behavior in parallel: of the experimental wire mesh solicitedtests and in numerical its plane. modeling.This has been The performed former was by fundamental carrying out twoto verify activities the integrability in parallel: experimental of the fiber optic tests andwith numerical the wire meshmodeling. and to The collect former a dataset was fundamental for the modeling to verify acti thevity. integrability The latter was of the performed fiber optic using with FEM the wire software mesh and pursuing to collect atwo dataset specific for purposes the modeling: reproduce activity. the The experimental latter wasperformed setup and, usingas a consequence, FEM software create and apursuing digital twin two suitable specific purposes:for virtually reproduce testing the the pr experimentaloduct under any setup load and, and as constraint a consequence, conditions create to a tailordigital the twin production suitable for process. virtually testing the product under any load and constraint conditions to tailor the productionThe first results process. obtained returned a positive feedback on the feasibility of the product concept and clarifiedThe first its results mechanical obtained behavior returned in the a positive application feedback context on theoutlined. feasibility of the product concept and clarified its mechanical behavior in the application context outlined. 2. Materials and Methods 2. Materials and Methods The concept upon which the sensing revetment is conceived is based on an innovative patented technologyThe concept developed upon whichby Officine the sensing Maccaferri revetment Spa (Italy), is conceived which is allows based onthe anproduction innovative of patented double twistedtechnology steel developed wire meshes by Offi withcine Maccaferriadditional Spaelemen (Italy),ts interwoven which allows in the the production double torsions’ of double sections twisted (Figuresteel wire 1). meshes with additional elements interwoven in the double torsions’ sections (Figure1).

Figure 1. DetailDetail ofof OF OF cable cable woven woven into into the the wire wire mesh: mesh: the cablethe cable is directly is directly inserted inserted into double-twisted into double- twistedsections sections during theduring weaving the weaving process. process.

The additional element can act as a reinforcing element of the net, especiallyespecially against actions orthogonal toto itsits plane.plane. ThisThis happens, happens, e.g., e.g., with with steel steel ropes ropes in in rockfall rockfall barriers. barriers. In theIn the present present work, work, this thistechnology technology is applied is applied for the for ﬁrst the time first with time OF with cables, OF combining cables, combining in a single productin a single the protectionproduct the of protectionthe embankment of the againstembankment erosion, against the continuous erosion, monitoringthe continuous of most monitoring of its structural of most health of its [15 structural], and the healthongoing [15], interactions and the ongoing between interactions the levee system between and the environment,levee system and allowing the environment, a one-step advancement allowing a one-stepin Technology advancement Readiness in Level Technology (TRL): fromReadiness a level Leve 4 (technologyl (TRL): from validated a level in 4 the(technology laboratory validated by Oﬃcine in theMaccaferri laboratory Spa) by to aOfficine level 5 (TechnologyMaccaferri Spa) validated to a inlevel an industrially5 (Technology relevant validated environment in an industrially in the case relevant environment in the case of key enabling technologies) [16]. The advantage of this type of

Water 2020, 12,, 3025x FOR PEER REVIEW 4 of 16 wire mesh, compared to the classic simple hexagonal mesh (and this explains its diffusion and success),of key enabling lies in the technologies) fact that it can [16]. be The seen advantage as a “failsafe” of this [17]: type the of effects wire mesh, of the compared local failure to of the a classicsingle steelsimple wire hexagonal remain mesh confined (and thisto its explains surroundings, its diffusion without and success), spreading lies into thelarge fact areas that itof can the be system seen as structure.a “failsafe” [17]: the effects of the local failure of a single steel wire remain confined to its surroundings, withoutThe spreadingsensing revetment to large areas working of the principle system structure.is the following: (i) in the case of levee overtopping, the waterThesensing flowing revetment on the outer working levee side principle exerts is athe shear following: stress on (i) the in embankment the case of levee slope overtopping, and generally the waterproduces flowing a decrease on the in outer local levee temperature; side exerts any a shear change stress in onthe theshape embankment of the outward slope andface generallydue to a landslideproduces aor decrease any movement in local temperature; of the earthen any material change on in thethe shapeembankment of the outward will result face duein a tomodification a landslide ofor the any stress movement system of on the the earthen slope materialsurface; on(ii) thethese embankment stresses are will directly result reported in a modification to the revetment of the stress that itsystem is stressed on the along slope its surface; own plane; (ii) these (iii) hexagonal stresses are me directlyshes react reported to this to stress the revetment by closing that their it isgeometry stressed (Figurealong its 2); own (iv) plane;the OF (iii) cable, hexagonal being coupled meshes with react the to thiswire stress mesh, by detects closing this their behavior geometry by deforming (Figure2); itself.(iv) the OF cable, being coupled with the wire mesh, detects this behavior by deforming itself.

Figure 2. SketchSketch of of the the working working principle principle of the the sensing sensing revetment: the the OF OF cable cable (blue (blue line) detects the closure of the meshes by deforming itself.

It should be noted that the single steel wire, during these stress cases, is generally far from its It should be noted that the single steel wire, during these stress cases, is generally far from its structural limit, and the deformation affects mostly the overall geometry of the mesh. This aspect will structural limit, and the deformation affects mostly the overall geometry of the mesh. This aspect will be discussed in the following sections of this paper. be discussed in the following sections of this paper. 2.1. Stress Analysis 2.1. Stress Analysis The dynamics of overflowing water on the top and on the outward face of an embankment have The dynamics of overflowing water on the top and on the outward face of an embankment have been widely studied in literature in the past [18–20]. Moreover, a complete and detailed numerical and been widely studied in literature in the past [18–20]. Moreover, a complete and detailed numerical experimental analysis of the fluid dynamic process of wave overtopping flow at seadikes is reported and experimental analysis of the fluid dynamic process of wave overtopping flow at seadikes is in [21], and a complete review is presented in a recent book [22]. reported in [21], and a complete review is presented in a recent book [22]. The present work considers the case of the beginning of the overtopping flow in a riverine internal The present work considers the case of the beginning of the overtopping flow in a riverine environment. The fluid exerts a shear stress on the levee surface given by: internal environment. The fluid exerts a shear stress on the levee surface given by: = Sh (1) 𝜏 =𝛾𝑆ℎτo γ (1)

where 𝜏 is the bed shear stress (N m2 −2), 𝛾 the specific weight of the fluid (N3 m–3), 𝑆 the friction where τois the bed shear stress (N m− ), γ the specific weight of the fluid (N m− ), S the friction slope slope(–), and (–),h andthe waterℎ the depth water(m). depth (m). The overtopping overtopping flow flow occurs occurs once once the the level level in inthe the river river exceeds exceeds the theembankment embankment top plane. top plane. The flowTheflow overover the top the is top initially is initially subcritical subcritical and genera and generallylly becomes becomes supercritical supercritical after aftera short a short distance. distance. The flowThe flowis then is then accelerated accelerated due due to the to the action action of ofgravity gravity starting starting as as a alaminar laminar boundary boundary layer layer and becoming turbulent as soon as the Reynolds number exceeds the critical threshold. This fact is easily observed byby thethe change change in in shape shape and and color color of the of nappethe nappe with airwith entrainment air entrainment due to fluctuatingdue to fluctuating velocity velocitycomponents components in a direction in a direction normal tonormal the flow. to the flow. As the flow accelerates the shear stress also increases until resistance to flow (proportional to the square of flow velocity) balances the action of gravity. This of course happens if the slope is long

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As the flow accelerates the shear stress also increases until resistance to flow (proportional to the square of flow velocity) balances the action of gravity. This of course happens if the slope is long enough. At this point the two-phase flow (a mixture of water and air) becomes uniform and a maximum value is reached in the bed shear stress that will not be exceeded until at the downstream end, where a hydraulic jump takes place due to the sudden change in slope. This specific flow pattern has been studied in the last century [23,24]. Both papers agree on a functional relationship that univocally links the slope angle and the average air concentration in the uniform flow. For usual embankments, the layout slope angle ranges between 25 and 35 degrees, corresponding to an air concentration ranging between 35% and 50%. The paper by Wood also proposes equations for velocity distribution and flow resistance; the latter in the following form: ! 8g sin θd d f = φ , c (2) U2 k

2 where f (–) is the usual Darcy-Weisbach friction factor, g (m s− ) is the acceleration due to gravity, θ (–) 1 is the slope angle, U (m s− ) is the velocity of the uniform flow, d (m) is the two-phase flow depth, and φ is a function of relative roughness (k (m) is the homogenous equivalent surface roughness) and equilibrium air concentration c (–). With this formula, applied to Straub and Anderson’s experimental results, the author showed that no significant influence of air entrapment on the friction factor was observed for air concentration lower than 30%. In the present case a maximum reduction in the friction factor can be expected at 30%. However, it should be noted that outward facing slopes are particularly moderate, closer to the lower extreme of the above discussed angle range, while highest values are usually experienced on the internal face. For this reason, the correction has been neglected in the present work. To determine the order of magnitude of the average stress on the revetment, one may imagine the first stage of the overtopping, with a water head in the river d0 in the following range:

d = 0.05 0.15 (m). (3) 0 ÷ above the embankment top. In this case, assuming broad-crested weir behavior for the sake of 2 1 simplicity, the discharge for levee unit length (m s− ) is given by the usual formula:

p 3/2 2 1 q = 0.385 2gd = 0.019 0.034 m s− (4) 0 ÷ By assuming a value of the homogenous equivalent roughness

k = 0.070 (m) (5) suitable for this kind of revetment [25], a maximum value for the average shear stress is obtained:

2 τo = 58 156 N m− (6) ÷ This stress range has been implemented both in numerical models and in experiments to test the ability of the OF cable to measure such a relatively low stress on the mesh structure.

2.2. Methodological Objectives of the Work The conceptualization of the anti-erosion sensing revetment requires the achievement of three fundamental goals for which the product will be designed and developed. The first one is to verify the possibility of coupling the OF cable with the DTWM, accounting also for any possible issues related to the manufacturing process. As concerns the wire mesh, a 0.08 0.10 m double-twisted hexagonal mesh with a 2.2 mm steel × wire diameter has been selected for the realization of the sensorized net. This kind of material is Water 2020, 12, 3025 6 of 16 commonly used as a revetment in earthen structures (often coupled with a three-dimensional matrix polymeric geomat) in order to prevent erosion phenomena caused by factors such as heavy rainfall, surface runoff, and burrowing animals’ activity. OF technology allows instead a distributed strain and temperature sensing along a single cable, suitable for structural health monitoring of civil infrastructures and offering several advantages in terms of installation and logistic issues [26]. At least two fiber optics within the cable are required, one tight for the strain and the other caged in a loose tube in order to adjust strain results with temperature. To achieve a native sensing revetment, the OF cable must feature high resistance to survive the weaving industrial process and withstand rodent attacks and environmental agents, while at the same time it should guarantee a high strain sensitivity to detect the slightest levee movements. Moreover, from an industrialization perspective, the OF cost must ensure an affordable sensing revetment for in-field applications. The BRUsens DSS 7.2mm V3 grip, produced by Solifos AG, is the market item that met most of the requirements listed. It is an OF cable with a diameter compliant with the weaving machine requirement, with a strength member made of 24 steel wires, and an enhanced grip outer jacket to ensure rodent and abrasion protection. Concerning the interrogation system technology to be used together with the sensing revetment, this represents a further fundamental part of the proposed monitoring solution. Indeed, strain and temperature Brillouin-distributed monitoring provides unique performance in terms of distance, spatial resolution, and accuracy. Most distributed systems rely on Brillouin Optical Time-Domain Analysis (BOTDA) techniques, based on pulsed optical pump signals which guarantee spatial resolution generally limited to one meter [27]. An alternative approach is Brillouin Optical Correlation-Domain Analysis (BOCDA), based on the simultaneous phase modulation of both pump and probe waves [28]. By following this approach, efficient amplification occurs only in a confined fiber section, called a “correlation peak” where the Brillouin phase-matching condition is fully satisfied. The correlation peak width can be made as narrow as needed and its position along the sensing fiber can be set by properly tuning the phase modulation rate. BOCDA sensors can thus guarantee high flexibility in measurement configuration with spatial resolution that can reach even a sub-centimetric scale, making it particularly suitable for preliminary laboratory diagnostic tests on scaled structures [29]. As shown in the previous section, the absolute value of shear stress due to water flow is relatively low compared to the one leading to yield stress in the steel wire. The OF sensor challenge, in this case, is not to be able to monitor deformations close to breaking in the material (as happens, e.g., in mesh punch tests) but, on the contrary, to detect minimal deformations such those caused by the onset of the overflow on the embankment. In order to allow the sensorized net to correctly transmit the deformations to the OF, the double twisting process must be strong enough to tightly anchor the cable to the net twisted steel wires. On the other hand, this implies the use of steel armored OF cables to protect the sensor during the production process, that might make the fiber less sensitive to the deformations induced on the net. Therefore, the second aim of this work is to study the mechanical behavior of the mesh stressed in its plane in order to understand the behavior of coupled DTWM-optical fiber system, the internal interactions between the two components, and the strain sensibility required by the interrogation system to monitor strain in the design range. Several works concerning wire mesh modeling can be found in the scientific literature, but they almost all deal with rockfall net systems [30]. As concerns numerical models, two main categories can be distinguished: Finite Element Method (FEM) or Discrete Element Method (DEM) models. In FEM models, the DTWM is discretized in a mesh of interconnected finite elements which can be monodimensional (truss or beam elements), shell finite elements or special purpose elements [31]. This numerical method is suited for non-linear geometries and complex mechanical behaviors. DEM models represent a good alternative when the wire mesh failure has to be considered. In this case the material is described by a series of rigid particles which can overlap during collision. Water 2020, 12, 3025 7 of 16

The hexagonal double-twisted wire mesh is represented by a discrete number of spherical particles, placed at the physical nodes of the mesh. Remote interaction laws are then implemented to represent connections that join the particles [32]. In the present work a micromechanical numerical model of the wire mesh by using FEM has been implemented. Our research on shear stress effects along the mesh plane is actually quite different from that on rockfall barriers where (i) the entity of the actions exerted on the wire mesh are definitely higher and close (or even greater than) to wire yield stress; (ii) the out of plane displacement component of the mesh nodes (negligible in our case) is the main research target; (iii) the high value of stresses and deformations does not require us to consider the contribution of the bending stiffness of the steel wire that, on the contrary, is studied in the present case. As far as the mesh is used as an erosion control mat against shear flow, the problem becomes quite complex. The shear stress exerted by the overflowing stream is adsorbed by the continuous grass turf which, through its root apparatus, transmits it to the sensing revetment due to the polymeric mat to which both the roots and the steel mesh are firmly anchored. This transfer mechanism is quite complex and requires specific laboratory and in situ studies in order to determine the effective stress range on the mesh. Experimental studies have been performed in the last century, e.g., at Colorado state University [33] in order to assess critical shear stress of DTWM in structures against erosion, particularly for mattresses. These are specifically empirical approaches in order to assess a critical value for velocity or shear stresses, mainly for design purposes. Our approach, on the contrary, is mainly focused on understanding the behavior of the smart DTWM in order to assess its effective sensing capability and its production by an industrial weaving machine. However, this transfer mechanism is surely a task for further development. Finally, the third goal of the work is the development of a digital twin (i.e., a structural numerical model) of the sensing revetment. The availability of such a tool is in fact strategic because it can support and improve the technological validation and the subsequent design phase of the final product: known the acting forces and the constraints applied to the revetment, the model returns the expected deformations of the system, allowing us to understand which phenomena and which extent of displacements can actually be detected by the sensing OF.

2.3. Experimental Tests The performed experimental activity consists of two distinct sessions in which OF cable sensitivity in detecting the deformation behavior of the wire mesh has been tested. The activity was performed at “POLICOM” and “Gaudenzio Fantoli” laboratories of the Politecnico di Milano. In both sessions and for each load applied the resulting longitudinal mean deformation of each sensorized mesh was measured. During the first experimental session a standard telecommunication cable (SMF-28, coating 250 µm) was used to detect the mesh deformation and collect a first dataset for the calibration of the numerical model. The OF cable was glued at the double-twisted sections with an epoxy resin. The experimental setup adopted is sketched in Figure3: a DTWM 8 10 cm 2.7 mm wire diameter × square sample, one meter on each side, was bonded along its upper edge to a frame by means of cable ties. The OF cable installed was positioned as the blue line in the scheme: only the central four meshes have been sensorized. In-plane forces are applied through loads of a known mass hooked at the lower edge of the sample, as shown by the red arrow. Some details of the experimental setup are shown in Figure4. This setup remained substantially unchanged even during the second experimental session, where a first prototype of the sensing revetment was tested. The OF cable selected was integrated during the weaving process along the entire length of the DTWM sample. Hence, a total of eight meshes were sensorized. The weaving process required in this case a smaller wire diameter to work correctly: a DTWM 8 10 cm with a 2.2 mm diameter was used. Loads were equally distributed on two nodes at × the same distance from the cable (Figure5), in order to solicit more uniformly the OF cable. Water 2020, 12, x FOR PEER REVIEW 7 of 16 of stresses and deformations does not require us to consider the contribution of the bending stiffness of the steel wire that, on the contrary, is studied in the present case. As far as the mesh is used as an erosion control mat against shear flow, the problem becomes quite complex. The shear stress exerted by the overflowing stream is adsorbed by the continuous grass turf which, through its root apparatus, transmits it to the sensing revetment due to the polymeric mat to which both the roots and the steel mesh are firmly anchored. This transfer mechanism is quite complex and requires specific laboratory and in situ studies in order to determine the effective stress range on the mesh. Experimental studies have been performed in the last century, e.g., at Colorado state University [33] in order to assess critical shear stress of DTWM in structures against erosion, particularly for mattresses. These are specifically empirical approaches in order to assess a critical value for velocity or shear stresses, mainly for design purposes. Our approach, on the contrary, is mainly focused on understanding the behavior of the smart DTWM in order to assess its effective sensing capability and its production by an industrial weaving machine. However, this transfer mechanism is surely a task for further development. Finally, the third goal of the work is the development of a digital twin (i.e., a structural numerical model) of the sensing revetment. The availability of such a tool is in fact strategic because it can support and improve the technological validation and the subsequent design phase of the final product: known the acting forces and the constraints applied to the revetment, the model returns the expected deformations of the system, allowing us to understand which phenomena and which extent of displacements can actually be detected by the sensing OF.

Wateredge2020 of the, 12 ,sample, 3025 as shown by the red arrow. Some details of the experimental setup are shown8 of in 16 Figure 4.

Water 2020, 12, x FOR PEER REVIEW 8 of 16

Water 2020Figure, 12, x 3. FOR Experimental PEER REVIEW test setup—first setup—ﬁrst session: the OF cable is glued at double-twisted sections. 8 of 16

(a) (b)

Figure 4. Details of the experimental setup: (a) OF glued at the double-twisted sections; (b) constraints applied to the DTWM.

This setup remained substantially unchanged even during the second experimental session, where a first prototype of the sensing revetment was tested. The OF cable selected was integrated during the weaving process along the entire length of the DTWM sample. Hence, a total of eight meshes were sensorized. The weaving process required in this case a smaller wire diameter to work (a) (b) correctly: a DTWM 8 × 10 cm with a 2.2 mm diameter was used. Loads were equally distributed on two FigurenodesFigure 4.at4. DetailsDetailsthe same ofof thethe distance experimentalexperimental from setup:thesetup: cable ((aa)) OFOF (Figure gluedglued atat5), thethe in double-twisteddouble-twistedorder to solicit sections;sections; more (uniformly(bb)) constraintsconstraints the OF cable.appliedapplied toto thethe DTWM.DTWM.

This setup remained substantially unchanged even during the second experimental session, where a first prototype of the sensing revetment was tested. The OF cable selected was integrated during the weaving process along the entire length of the DTWM sample. Hence, a total of eight meshes were sensorized. The weaving process required in this case a smaller wire diameter to work correctly: a DTWM 8 × 10 cm with a 2.2 mm diameter was used. Loads were equally distributed on two nodes at the same distance from the cable (Figure 5), in order to solicit more uniformly the OF cable.

Figure 5. Experimental test setup—second session: the OF cable is integrated in the DTWM. Figure 5. Experimental test setup—second session: the OF cable is integrated in the DTWM.

The model was implemented using the FEM software MasterSap, provided by AMV s.r.l., an Italian software house. The characteristics and the geometry of DTWM samples used during experimental activity have been accurately simulated in the model. In this regard, the non-perfect planarity of the wire mesh sample, which is inherent to this kind of revetment due to the typical production process and storage conditions, has been studied. This aspect was considered in the model by giving an out of plane coordinate to the mesh nodes following the usual sample curvature and considering geometric non-linearities. Furthermore, the wire mesh sample, once tied to the

Water 2020, 12, 3025 9 of 16

2.4. Numerical Model The model was implemented using the FEM software MasterSap, provided by AMV s.r.l., an Italian software house. The characteristics and the geometry of DTWM samples used during experimental activity have been accurately simulated in the model. In this regard, the non-perfect planarity of the wire mesh sample, which is inherent to this kind of revetment due to the typical production process Waterand 2020 storage, 12, x conditions,FOR PEER REVIEW hasbeen studied. This aspect was considered in the model by giving9 of an16 out of plane coordinate to the mesh nodes following the usual sample curvature and considering testinggeometric frame non-linearities. and subject to Furthermore,several load cycles, the wire tend meshs to gradually sample, once stretch, tied ch toanging the testing its out frame of plane and shape.subject This to several problem load cycles,is inherent tends to to graduallythe specific stretch, type changing of material its out and of planerecurs shape. regularly This problemduring installationis inherent toin thethe specific field. It type was of overcome material and during recurs modeling regularly by during approximating installation inthe the out field. of plane It was configurationovercome during via modelingparametric by sinusoidal approximating and parabolic the out of functions. plane configuration The results via were parametric then compared sinusoidal withand parabolicthe 2D model, functions. i.e., considering The results the were wire then mesh compared perfectly with planar, the 2D in model,order to i.e., obtain considering a more general the wire solution.mesh perfectly planar, in order to obtain a more general solution. EachEach element element of of the the wire wire mesh mesh is is represented represented by by beam beam finite finite elements, elements, according according to to the the 2-node 2-node Euler-BernoulliEuler-Bernoulli scheme,scheme, thatthat is, is, one-dimensional one-dimensional elements elements capable capable of transmitting of transmitting axial actions,axial actions, cutting, cutting,and bending and bending moments. moments. Due to the Due relatively to the highrelative slendernessly high slenderness of the elements, of the the elements, shear deformability the shear deformabilityof the elements of wasthe elements not considered. was not According considered. to theAccording varying to transversal the varying characteristic transversal sectionscharacteristic of the sectionsdifferent of parts the different that form parts the mesh,that form three the groups mesh, ofthree circular groups section of circular beam section elements beam have elements been created: have beensingle created: wire elements, single wire edge elements, wire elements, edge andwire double-twistedelements, and wiredouble-twisted elements. Aswire regards elements. the latter As regardsgroup, itthe is latter important group, to it observe is important thatthe to observe two wires that that the maketwo wires up the that double-twisted make up the double-twisted section change sectiontheir relative change position their relative along position the element along axis the (Figure element6) and,axis consequently,(Figure 6) and, the consequently, moment of inertiathe moment of the oftwo inertia wires of also the varies.two wires also varies.

Figure 6. The moment of inertia of the twisted wires change according to their relative position: Figure 6. The moment of inertia of the twisted wires change according to their relative position: considering the horizontal axis, the minimum value is obtained in (a), while the maximum one in (c). considering the horizontal axis, the minimum value is obtained in (a), while the maximum one in (c). The configuration shown in (b) returns the average value. The configuration shown in (b) returns the average value. Hence, for the sake of simplicity, a diameter able to produce the average value of momentum amongHence, the possiblefor the sake configurations of simplicity, was a assigneddiameter to able this to group produce of elements. the average value of momentum amongThe the material possible assigned configurations to each element was assigned has an elastic-linearto this group behavior, of elements. and the mechanical parameters are thoseThe material typical ofassigned steel: E =to 150each GPa, elementυ = 0.3. has Young’s an elastic-linear modulus wasbehavior, calibrated and usingthe mechanical the results parametersobtained from are thethose first typica experimentall of steel: E session. = 150 GPa, υ = 0.3. Young’s modulus was calibrated using the resultsOnce obtained the steel from wire the parametersfirst experimental have been session. defined, a focus on the modeling of the mechanical behaviorOnce ofthe the steel meshes wire asparameters a whole was have performed. been defined, As alreadya focus stated,on the whenmodeling a load of isthe applied mechanical in the behaviornet plane, of thethe meshmeshes reacts as a bywhole closing was itsperformed. geometry As (Figure already7); stated, this mechanism when a load is achievedis applied by in twothe net plane, the mesh reacts by closing its geometry (Figure 7); this mechanism is achieved by two different actions: (i) reduction of the mesh opening, equal to 90◦ at rest, due to the presence of a differentmutual interlocking actions: (i) constraintreduction withof the finite mesh sti ffopening,ness; (ii) flexuralequal to deformation 90° at rest, ofdue the to wires the bypresence the residual of a mutualtransmitted interlocking moment. constraint with finite stiffness; (ii) flexural deformation of the wires by the residual transmitted moment.

Figure 7. Sketch of the geometrical closure of the generic mesh when a load is applied in its plane; the closure is given both by a reduction of the vertices openings and the bending of the wires.

Water 2020, 12, x FOR PEER REVIEW 9 of 16

testing frame and subject to several load cycles, tends to gradually stretch, changing its out of plane shape. This problem is inherent to the specific type of material and recurs regularly during installation in the field. It was overcome during modeling by approximating the out of plane configuration via parametric sinusoidal and parabolic functions. The results were then compared with the 2D model, i.e., considering the wire mesh perfectly planar, in order to obtain a more general solution. Each element of the wire mesh is represented by beam finite elements, according to the 2-node Euler-Bernoulli scheme, that is, one-dimensional elements capable of transmitting axial actions, cutting, and bending moments. Due to the relatively high slenderness of the elements, the shear deformability of the elements was not considered. According to the varying transversal characteristic sections of the different parts that form the mesh, three groups of circular section beam elements have been created: single wire elements, edge wire elements, and double-twisted wire elements. As regards the latter group, it is important to observe that the two wires that make up the double-twisted section change their relative position along the element axis (Figure 6) and, consequently, the moment of inertia of the two wires also varies.

Figure 6. The moment of inertia of the twisted wires change according to their relative position: considering the horizontal axis, the minimum value is obtained in (a), while the maximum one in (c). The configuration shown in (b) returns the average value.

Hence, for the sake of simplicity, a diameter able to produce the average value of momentum among the possible configurations was assigned to this group of elements. The material assigned to each element has an elastic-linear behavior, and the mechanical parameters are those typical of steel: E = 150 GPa, υ = 0.3. Young’s modulus was calibrated using the results obtained from the first experimental session. Once the steel wire parameters have been defined, a focus on the modeling of the mechanical behavior of the meshes as a whole was performed. As already stated, when a load is applied in the net plane, the mesh reacts by closing its geometry (Figure 7); this mechanism is achieved by two different actions: (i) reduction of the mesh opening, equal to 90° at rest, due to the presence of a

Watermutual2020 , 12interlocking, 3025 constraint with finite stiffness; (ii) flexural deformation of the wires 10by of the 16 residual transmitted moment.

FigureFigure 7. 7.Sketch Sketch of of the the geometrical geometrical closure closure of of the the generic generic mesh mesh when when a a load load is is applied applied in in its its plane; plane; the the closureclosure is is given given both both by by a a reduction reduction of of the the vertices vertices openings openings and and the the bending bending of of the the wires. wires. A specific calibration of the rotational stiffness assigned to the meshes nodes was performed by progressively reducing the degree of connection Φ of the elements at the nodes of the meshes, starting from the perfect connection (Φ = 100%). In the element definition, the degree of connection and the degree of stiffness are linked by the following formula

K η = a = 1 φ (7) Kg + Ka − where Kg is the joint stiffness and Ka is the beam stiffness, both expressed in (N/m). The implementation of the numerical model is completed with the definition of the boundary and load conditions compliant with those adopted during experimental tests, i.e., the sample fixed to a frame along the upper edge using nylon cable ties. This condition was modeled by using carriage constraints along the upper edge of the mesh sample. Moreover, a hinge constraint was applied to the central node of this edge, in order to avoid model lability in the mesh plane. Carriage constraints also have a constant stiffness along the vertical direction so as to simulate the elastic behavior of the nylon ties. Load conditions are applied according to experimental tests. Finally, the OF cable was represented with beam elements having a circular section, a diameter equal to 7.2 mm and an elastic modulus obtained from tensile tests performed in laboratory. The double twisted sections in which the OF cable is inserted have been modeled considering the two wires twisted and the cable as three beam elements working in parallel.

3. Results Calibration of steel wire Young’s modulus E and the connection degree Φ of the elements to the nodes was performed comparing observed and simulated deformations at the mesh vertexes (Figure8). The model returns the nodal displacements, and the OF elongation ∆l can be computed as follows: q ∆l = ∆x2 + ∆y2 (8) where ∆x and ∆y are the respective diﬀerences in the translations of the nodes in the x and y directions, i.e., the two axes that in the model lie in the net plane when the load is applied. Then, it is possible to obtain the deformation of the OF by dividing its elongation by the longitudinal length of the mesh at rest. The wire mesh, both in the experimental test and numerical model, is stressed in its plane progressively with the loads reported in Table1. This range has been selected in order to study the mechanical behavior of the wire mesh when it is subjected to low-entity actions, as happens with an incipient overﬂowing stream. Water 2020, 12, x FOR PEER REVIEW 10 of 16

A specific calibration of the rotational stiffness assigned to the meshes nodes was performed by progressively reducing the degree of connection Φ of the elements at the nodes of the meshes, starting from the perfect connection (𝛷 = 100%). In the element definition, the degree of connection and the degree of stiffness are linked by the following formula

𝐾 𝜂= =1−𝜙 (7) 𝐾 𝐾 where 𝐾 is the joint stiffness and 𝐾 is the beam stiffness, both expressed in (N/m). The implementation of the numerical model is completed with the definition of the boundary and load conditions compliant with those adopted during experimental tests, i.e., the sample fixed to a frame along the upper edge using nylon cable ties. This condition was modeled by using carriage constraints along the upper edge of the mesh sample. Moreover, a hinge constraint was applied to the central node of this edge, in order to avoid model lability in the mesh plane. Carriage constraints also have a constant stiffness along the vertical direction so as to simulate the elastic behavior of the nylon ties. Load conditions are applied according to experimental tests. Finally, the OF cable was represented with beam elements having a circular section, a diameter equal to 7.2 mm and an elastic modulus obtained from tensile tests performed in laboratory. The double twisted sections in which the OF cable is inserted have been modeled considering the two wires twisted and the cable as three beam elements working in parallel.

3. Results Calibration of steel wire Young’s modulus E and the connection degree Φ of the elements to the nodesWater 2020 was, 12 performed, 3025 comparing observed and simulated deformations at the mesh vertexes (Figure11 of 16 8).

WaterFigureFigure 2020, 128. 8., MeshesxMeshes FOR PEER sensorized sensorized REVIEW during during the the first first experiment experimentalal session. session. Each Each mesh mesh has has been been labelled labelled with with 11 of 16 thethe number number shown shown in in the the image. image. Table 1. Loads applied to the wire mesh both in experimental and numerical activity-first test sessions TheTable(standard model 1. Loads gravity returns applied g assumed the to thenodal wireequal displa mesh to 10 bothcements, m/s2 in). experimental and the OF and elongation numerical activity-first Δ𝑙 can be test computed sessions as (standard gravity g assumed equal to 10 m/s2). follows: Loading Step Load (N) LoadingΔ𝑙 Step1 = ∆𝑥 ∆𝑦 Load10 (N) (8) 12 20 10 where ∆x and ∆y are the respective differences23 in the translations40 20 of the nodes in the x and y directions, i.e., the two axes that in the model3 4lie in the net 80plane 40 when the load is applied. Then, it is possible to obtain the deformation of the OF4 by5 dividing its160 80 elongation by the longitudinal length of the mesh at rest. 5 160 TheIn thiswire step, mesh, as bothregards in thethe experimentalnumerical model, test anda planar numerical geometry model, of theis stressed DTWM inand its aplane linear progressivelysolutionIn this were step, with considered. as the regards loads theAs reported numericalfar as Young’sin Table model, modulus1. a Th planaris range is geometry concerned, has been of the selectedthe DTWM calibration in and order aprocess linear to study solution returns the mechanicalwerethe best considered. value behavior that As corresponds of far the as wire Young’s mesh to the modulus when lower it edge is is su concerned, bjectedof the variability to thelow-entity calibration range acti indicatedons, process as happens by returns the producer, with the best an incipientvalue150 GPa. that overflowing correspondsFor the connection stream. to the lower degree edge instead, of the variability the value range that indicatedminimizes by the the difference producer, 150between GPa. Forexperimental the connection and numerical degree instead, values the in value the total that datase minimizest is chosen. the diff Thiserence value between is finally experimental equal to 85%. and numericalThe result values obtained in the for total mesh dataset 4 is plotted is chosen. in Figure This value 9. The is finallyblue line equal connects to 85%. the The numerical result obtained results, forwhile mesh the 4 experimental is plotted in Figure ones are9. The represented blue line by connects the light the blue numerical triangles. results, while the experimental ones are represented by the light blue triangles.

Mesh 4 9000 8000 7000 )

ԑ 6000 μ 5000 4000 3000 Strain ( 2000 1000 0 0 20406080100120140160180 Load (N) Experimental data E=150 GPa, Ф=85%

Figure 9. Experimental vs. numerical results—mesh 4. Looking at the graph,Figure it can 9. be Experimental seen that the vs. linear numeri modelcal results—mesh fits the experimental 4. data quite well: the mean difference between experimental and numerical results is equal to 215 µε. The fitting with Looking at the graph, it can be seen that the linear model fits the experimental data quite well: the mean difference between experimental and numerical results is equal to 215 με. The fitting with experimental data remains good even in mesh 3 and mesh 2, whereas in mesh 1 the numerical solution underestimates the experimental one. This could be explained by the fact that mesh 1 is the nearest to the boundary conditions of the model and so it could be influenced by them due to the small dimensions of the sample. Another possible explanation can be found as an effect of the geometric non-linearities. As mentioned, in experimental reality the wire mesh sample is not perfectly planar. When a load is applied to the wire mesh, this tends to stretch, causing non-negligible out of plane displacements that can be taken into consideration by activating geometric non- linearities. Therefore, this hypothesis was investigated by changing from a 2D to a 3D model. The results obtained showed a slight improvement of the fitting as concerns mesh 1 with respect the 2D solution. However, at the same time, the fitting with experimental data worsened for mesh 4. Once the calibration process was concluded, the numerical model was used to study the internal actions that arise in the DTWM when it is solicited in its plane. Indeed, for the conceptualization of the sensing revetment it is important to understand the mechanical behavior of the wire mesh, i.e., how the load propagates in the meshes and if the material remains, for the load range considered,

Water 2020, 12, 3025 12 of 16 experimental data remains good even in mesh 3 and mesh 2, whereas in mesh 1 the numerical solution underestimates the experimental one. This could be explained by the fact that mesh 1 is the nearest to the boundary conditions of the model and so it could be influenced by them due to the small dimensions of the sample. Another possible explanation can be found as an effect of the geometric non-linearities. As mentioned, in experimental reality the wire mesh sample is not perfectly planar. When a load is applied to the wire mesh, this tends to stretch, causing non-negligible out of plane displacements that can be taken into consideration by activating geometric non-linearities. Therefore, this hypothesis was investigated by changing from a 2D to a 3D model. The results obtained showed a slight improvement of the fitting as concerns mesh 1 with respect the 2D solution. However, at the same time, the fitting with experimental data worsened for mesh 4. Once the calibration process was concluded, the numerical model was used to study the internal actions that arise in the DTWM when it is solicited in its plane. Indeed, for the conceptualization of the sensingWater revetment 2020, 12, itx FOR is important PEER REVIEW to understand the mechanical behavior of the wire mesh, i.e., how 12 of 16 the load propagates in the meshes and if the material remains, for the load range considered, within within the elastic domain. Figure 10 shows the deformed configuration of the wire mesh when a the elastic domain. Figure 10 shows the deformed configuration of the wire mesh when a concentrated concentrated load is applied at the lower edge of the sample, as done during experimental tests. load is applied at the lower edge of the sample, as done during experimental tests. Carriage constraints Carriage constraints allow the horizontal shift of the lateral edges towards the central part, whereas allow the horizontal shift of the lateral edges towards the central part, whereas at the same time the at the same time the wire mesh stretches in its plane non uniformly. wire mesh stretches in its plane non uniformly.

Figure 10.FigureAmpliﬁed 10. Amplified deformed conﬁgurationdeformed configuration of the DTWM of caused the DTWM by the application caused by of athe concentrated application of a load of 160concentrated N. load of 160 N.

The load,The from load, the from application the application point, migrates,point, migrates determining, determining a V-shaped a V-shaped area, inside area, whichinside thewhich the meshesmeshes close their close geometry. their geometry. This migration This migration path is path also confirmedis also confirmed by the distributionby the distribution of the internalof the internal actionsactions given by given the model,by the model, in particular in particular axial action axial andaction bending and bending moments. moments. Analyzing Analyzing the entity the ofentity of these actions,these actions, it has beenit has observed been observed that within that within the tested the loadtested range load allrange the elementsall the elements are below are thebelow the materialmaterial yielding yielding point. point. DuringDuring the second the second experimental experimental session, session, as already as alre mentioned,ady mentioned, the OF the cable OF was cable integrated was integrated for for the firstthe time first in time the DTWM.in the DTWM. The cable The has cable a non-negligible has a non-neglig stiffibleness stiffness with respect with respect to that to of that the wireof the wire mesh samplemesh sample and so and it has so it been has adequatelybeen adequately simulated simula evented even in the in numericalthe numerical model. model. During During tests, tests, the the loadload set set reported reported in Table in Table2 was 2 was applied applied to the to DTWM,the DTWM, following following the setup the setup previously previously illustrated. illustrated. During the test, the OF cable detected the mean deformation with a sampling resolution of 2 cm. Therefore,Table for 2. Loads each samplingapplied to positionthe wire mesh the slope both ofin expe the linearrimental regression and numerical line and activities—second the correlation test coefficient ofsession the relation (g assumed between equal to the 10 load m/s2). applied and the resulting deformation were calculated. Figure 11 shows the trend of the two variables along the cable. Loading Step Load (N) 1 50 2 80 3 100 4 120

During the test, the OF cable detected the mean deformation with a sampling resolution of 2 cm. Therefore, for each sampling position the slope of the linear regression line and the correlation coefficient of the relation between the load applied and the resulting deformation were calculated. Figure 11 shows the trend of the two variables along the cable.

Water 2020, 12, 3025 13 of 16

Table 2. Loads applied to the wire mesh both in experimental and numerical activities—second test session (g assumed equal to 10 m/s2).

Loading Step Load (N) 1 50 2 80 3 100 Water 2020, 12, x FOR PEER REVIEW 13 of 16 4 120

10.00 1.00

8.00 0.98

6.00 0.96 /N) με

( 4.00 0.94

2.00 0.92 Linear regression line slope 0.00 0.90 Linear correlation coefficient 0.2 0.4 0.6 0.8 1 Position (m)

Figure 11. Linear regression slope and linear correlation coefficient obtained along the OF cable Figure 11. Linear regression slope and linear correlation coefficient obtained along the OF cable integrated in the DTWM. integrated in the DTWM. The results indicate that the OF cable, and therefore the wire mesh, deforms linearly: the correlation The results indicate that the OF cable, and therefore the wire mesh, deforms linearly: the coefficient varies between 0.95 and 0.99. This confirms the results achieved at the end of the calibration correlation coefficient varies between 0.95 and 0.99. This confirms the results achieved at the end of process: the wire mesh, if solicited in its plane, maintains a linear deformation behavior even with the the calibration process: the wire mesh, if solicited in its plane, maintains a linear deformation OF cable integrated. behavior even with the OF cable integrated. Promising results are also obtained from the comparison with the numerical solution: always Promising results are also obtained from the comparison with the numerical solution: always considering a planar geometry and a linear solution, the fitting confirmed the modeling hypothesis considering a planar geometry and a linear solution, the fitting confirmed the modeling hypothesis assumed both for the wire mesh and the OF cable. assumed both for the wire mesh and the OF cable. As concerns the performance of the OF cable selected, measurements showed a halving of the As concerns the performance of the OF cable selected, measurements showed a halving of the strain sensitivity coefficient with respect to the bare fiber case. This reduction could be expected due strain sensitivity coefficient with respect to the bare fiber case. This reduction could be expected due to the presence of several layers in the OF cable. Nevertheless, the resulting sensitivity proved to be to the presence of several layers in the OF cable. Nevertheless, the resulting sensitivity proved to be adequate to detect the DTWM deformation in the range tested. Further measurements are still ongoing adequate to detect the DTWM deformation in the range tested. Further measurements are still in order to verify the presence of a possible relative sliding between the OF and the outer coating and ongoing in order to verify the presence of a possible relative sliding between the OF and the outer to then quantify the exact strain transfer of the OF cable. coating and to then quantify the exact strain transfer of the OF cable. 4. Discussion 4. Discussion The problem of levee embankment control during high flows is crucial for flood risk reduction in floodplains.The problem Levee of levee defense embankment lines are often control hundreds during ofhigh kilometers flows is crucial long and for surveysflood risk during reduction an emergencyin floodplains. are not Levee an easy defense task. lines The conceptare often of hundreds a smart levee of kilometers is gaining long increasing and surveys attention during in the an literatureemergency as aare tool not to an help easy monitor task. andThe increaseconcept of safety a sm againstart levee floods. is gaining increasing attention in the literatureThe paper as a presentstool to help the conceptualizationmonitor and increase and safety the testing against of a floods. prototype of a levee smart revetment based uponThe paper the technology presents ofthe a reinforcedconceptualization geomat obtainedand theby testing a polymer of a madeprototype of a three-dimensional of a levee smart matrixrevetment extruded based onto upon a double the technology twisted steel of a reinforced mesh. The geomat first applied obtained use ofby this a polymer innovative made technology of a three- patenteddimensional by O ffimatrixcine Maccaferri extruded allowedonto a andouble OF cable twisted to be steel embedded mesh. inThe a doublefirst applied twisted use steel of wire this mesh,innovative thus obtaining technology a continuous patented by strain Officine sensor Maccaferri along the revetmentallowed an with OF acable given to space be embedded step. in a doubleIn this twisted paper steel the feasibilitywire mesh, of thus this obtaining kind of a a smart continuous revetment strain is firstsensor assessed. along the A samplerevetment case with is thena given analyzed space instep. both numerical and laboratory tests. For this purpose, an FEM numerical model to describeIn thethis mechanicalpaper the feasibility behavior ofof DTWMthis kind when of a loadedsmart revetment along its own is first plane assessed. is presented. A sample The case flow is then analyzed in both numerical and laboratory tests. For this purpose, an FEM numerical model to describe the mechanical behavior of DTWM when loaded along its own plane is presented. The flow pattern of overtopping water on the embankment is also discussed, thus producing a raw estimation of the shear stress on the revetment. The result of the numerical model of the mesh indicates that the related strain, relatively low as compared to the steel wire yield stress, can be fully detected by the optical fiber continuous Brillouin sensor. Laboratory tests confirm these results: the smart revetment is able to detect the strain of the same order of magnitude of that produced by water flow on the outer embankment face. In principle, this allows long embankment line reaches to be monitored for overtopping. Furthermore, the results

Water 2020, 12, 3025 14 of 16 pattern of overtopping water on the embankment is also discussed, thus producing a raw estimation of the shear stress on the revetment. The result of the numerical model of the mesh indicates that the related strain, relatively low as compared to the steel wire yield stress, can be fully detected by the optical fiber continuous Brillouin sensor. Laboratory tests confirm these results: the smart revetment is able to detect the strain of the same order of magnitude of that produced by water flow on the outer embankment face. In principle, this allows long embankment line reaches to be monitored for overtopping. Furthermore, the results allow us to presume that any significant deformation of the embankment surface (due, e.g., to a landslide) can also be detected by the optical fiber sensor. Important outcomes are also achieved as concerns the study of the deformational behavior of the wire mesh: if the DTWM is solicited in its plane with the load range adopted, its meshes deform almost linearly. This behavior has been correctly simulated in the FEM model implemented, even considering a planar geometry of the DTWM sample. From the modeling activity the “digital twin” of the prototype of the smart material conceived has been obtained. This is a strategic tool that will be used to adequately test and design the revetment. Furthermore, it should also be noted that the revetment itself acts as an excellent erosion control device, and the DTWM preserves the embankment against the action of rodents. Regarding this, it is important to note that the OF cable protection against crushing during manufacturing allows an equally good defense of the fiber core against the action of burrowing animals. Nevertheless, this aspect could reduce the strain sensitivity of the cable without affecting the correct detection of the in-field strain range for which the revetment has been conceived. Next steps of the work will include, firstly, tests of planar multi-load actions (perhaps including terrain friction actions), as a simulation step under field operational conditions in order to provide a first relevant demonstration of the possibilities of the technology, and subsequently, a deployment of a prototype along a selected watercourse will be scheduled.

Author Contributions: Conceptualization, M.B., I.B., G.M. and F.Z.; methodology, M.B., A.C. and G.M.; investigation, M.B., I.B., M.F, J.M., F.Z.; validation, M.B., I.B., A.C., M.F., G.M., J.M. and F.Z.; writing-original draft preparation, M.B., G.M., M.F.; writing-review and editing, G.M., M.F. and D.F.B.; supervision, G.M., N.M. and D.F.B.; project administration, D.F.B.; funding acquisition, G.M. and D.F.B.; N.M., representing Maccaferri Innovation Center srl (employed by this company), contributed to the research, supervising the activities and manufacturing the tested prototype products. A patent on the tested products has been granted (patent applicant: Officine Maccaferri Spa; name of inventor: Francesco Ferraiolo; application number: IT 102018000004022-28.03.2018; status of application: patent granted; specific aspects of manuscripts covered in the patent application: tested samples and their components). Officine Maccaferri Spa is the sole controlling company of Maccaferri Innovation Center srl. All authors have read and agreed to the published version of the manuscript. Funding: This research was partially funded by Maccaferri Innovation Center Srl. Acknowledgments: The authors would like to thank Maccaferri Innovation Center Srl for supporting this research activity. Conflicts of Interest: The authors declare no conflict of interest.

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