Life-Cycle Performance and Cost Analysis of Sand Mitigation Measures: Toward a Hybrid Experimental-Computational Approach | Journal of Structural Engineering | Vol 148, No 7

AbstractWindblown sand action affects civil structures and infrastructures in sandy environments, such as deserts and coasts. The wind interacts with human built structures of any kind leading to harmful effects, endangering their serviceability and users’ safety. To counter it, a number of sand mitigation measures (SMM) have been proposed, primarily through the trial-and-error empirical approach. As such, innovative approaches to properly quantify windblown sand action and to design SMM are needed in the current state-of-art and practice. In this study, the authors propose a novel hybrid approach to derive the life-cycle performance of SMM based on the combination of reliable wind-sand tunnel tests and innovative wind-sand computational simulations. Wind-sand tunnel tests are carried out to characterize the incoming sand flux in open field conditions. In a hybrid approach perspective, wind-sand tunnel measurements allow to properly tuned cheaper wind-sand computational simulations of the full-scale SMM performance. A probabilistic approach for determining windblown sand action and frequencies of sand removal maintenance is applied to a case study on a desert railway. Finally, a life-cycle cost analysis is carried out to assess extra-costs and savings derived from the implementation of the SMM. The proposed approach paves the way toward a comprehensive hybrid approach to the performance assessment of SMM.IntroductionWindblown sand hazard affects several civil structures and infrastructures in sandy desert and coastal environments, such as single buildings, farms, towns, solar plants, pipelines, industrial facilities, roads, and railways (Bruno et al. 2018b). On one hand, coastal regions are experiencing the increased frequency of windstorms induced by climate change, giving rise to sand transport events from sandy coasts to built-up areas. On the other hand, desert regions are increasingly hosting human activities and built structures. Within this framework, railway infrastructures are particularly affected given their specific sensitivity to windblown sand and the increasing number of projects currently ongoing and planned in sandy regions across North Africa, Middle East, and Southeast Asia. This allows civil and structural engineering to familiarize with emerging challenging design issues, analogously to other design problems born from other application fields but resulting in key issues in structural engineering (e.g., Ribeiro et al. 2011; Harris et al. 2015).Windblown sand interacts with surface-mounted human built obstacles of any kind inducing sand erosion and sedimentation around them. From a structural design perspective, windblown sand effects have been categorized into sand limit states (SLS) (Raffaele and Bruno 2019). Sand ultimate limit states (SULS) are defined as the threshold performance level beyond which structures are no longer safe, while attaining sand serviceability limit states implies their loss of functionality. Some examples are shown in Fig. 1: (1) passive lateral sand pressure on a wall and vertical load on a gable roof undermining safety; (2) indoor sand infiltration precluding serviceability; (3) railway full sand coverage compromising train passengers’ safety; and (4) permanent rail deformation affecting serviceability, induced by increased stiffness and decreased damping of contaminated ballast bed.To cope with the effects above, the demand for the development of innovative approaches to properly quantify the so-called windblown sand action (Raffaele and Bruno 2020) and for the design and performance assessment of design solutions to reduce windblown sand induced effects, i.e., sand mitigation measures (SMMs) (Bruno et al. 2018b), has gained momentum in the structural and wind engineering literature.Windblown sand action has been recently defined as an environmental action in analogy to snow (Raffaele and Bruno 2019). Such an analogy results from their phenomenological and modeling resemblance, but also from the comparable detrimental effects they induce on engineering structures and infrastructures (O’Rourke et al. 2005; Tominaga 2018). On one hand, windblown sand action primarily translates into sand accumulation, giving rise to variable, fixed, static loads directly applied to the affected structure. Remarkably, the Algerian snow and wind code is the sole standard defining global and local distributed vertical sand loads for flat and multispan roofs and providing the sand zone mapping of the country (D.T.R. C 2-4.7 2013). On the other hand, windblown sand translates into indirect actions undermining the performance of the built structure/infrastructure and resulting in periodic maintenance operations.Once more in analogy to windblown snow, several design solutions to mitigate windblown sand effects have been proposed so far (see e.g., Alghamdi and Al-Kahtani 2005; Sañudo-Fontaneda et al. 2011; Basnet et al. 2014). SMMs aim to prevent sand from reaching the protected structure/infrastructure. Most of them are located between the sand source and the protected structure, and they are intended to trap incoming sand by promoting sedimentation [Fig. 2(a)]. As a result, the rigorous design shall be performed by considering both the SMM sand-trapping performance and the environmental loads induced by wind and sand. Such a kind of SMMs usually translates into berms and ditches realized through earthworks [Fig. 2(b)], reinforced concrete porous barriers [Fig. 2(c)], solid barriers [Fig. 2(d)], or a combination of them (Bruno et al. 2018b).However, with some remarkable exceptions, the rigorous assessment of windblown sand action, and the design and performance assessment of SMMs remain at their early stage in the structural engineering literature, whereas they are mostly based on trial-and-error approaches in the technical practice. According to the authors, this is due to the multidisciplinary and multiphysic nature of the phenomenon coupling fluid dynamics and aeolian processes. As a result, to fill this gap of knowledge, research should benefit from studies in disciplines adjacent and partially overlapping structural engineering (such as wind engineering, applied mathematics, and aeolian geomorphology), and from experimental and numerical approaches.Physical experiments usually translate into wind tunnel scale tests. wind-sand tunnel (WST) tests have been carried out both on flat ground conditions and around surface-mounted obstacles since the nineteen sixties (White 1996). WST tests allow to reproduce and measure with high accuracy and in a controlled setup the spatial and temporal evolution of wind and sand state variables. Nevertheless, WST tests show some deficiencies related to: (1) the technical difficulty of measuring wind shear stress and sand flux close to the sand bed, and (2) the experimental distortion arising from similarity mismatching related to the impossibility of jointly satisfying all multiphase/multiscale geometric and kinematic similarity requirements when scale models are tested (Raffaele et al. 2021).Numerical simulations of multiphase flows of relevance to structural engineering applications have dramatically increased in the last several decades, particularly as regards wind-driven rain and windblown snow (see e.g., Kubilay et al. 2013; Tominaga 2018). The numerical simulation of windblown sand flow, herein called erosion-transport-deposition (ETD) simulation, is primarily carried out through the resolution of Eulerian–Lagrangian or fully Eulerian models coupling wind-flow aerodynamics and aeolian processes accounting for the morphodynamic evolution of the sand bed, as reviewed in Lo Giudice et al. (2019). Among them, Eulerian ETD simulations are emerging because they adapt well to the engineering needs of modeling large-scale processes and cutting costs with respect to WST tests. However, they shall be carefully adopted only after their calibration on physical experiments.In this study, the authors pave the way towards a novel hybrid approach (Meroney 2016) to derive the life-cycle performance (LCP) of SMMs based on the combination of highly reliable WST tests on flat ground conditions, and innovative ETD simulations of the full-scale SMM behavior to overcome the limitations of the standalone methodologies. WST tests are carried out on a flat sand bed to characterize the incoming sand flux in open field conditions. Within a hybrid approach perspective, WST measurements allow to tune cheaper ETD simulations. ETD simulations are carried out by adopting an Eulerian multiphase first order computational fluid dynamics (CFD) model coupling wind flow aerodynamics and sand erosion, transport, sedimentation, and avalanching (Lo Giudice and Preziosi 2020). LCP is assessed through ETD simulations by taking into account the progressive loss of performance of the SMM caused by the gradual accumulation of sand around it. Then, the probabilistic approach to assess windblown sand action and plan sand removal maintenance operations proposed in Raffaele and Bruno (2019) is applied. This allows accounting for multiple uncertainties in environmental in-field conditions, i.e., wind speed, wind direction and threshold velocity for sand erosion, and for their propagation to the resulting windblown sand action. Finally, a life-cycle cost analysis (LCCA) is carried out. The LCCA is increasingly being adopted in the structural engineering domain to evaluate the monetary impact in a performance-based engineering framework (see e.g., Ierimonti et al. 2018; Le and Caracoglia 2019). LCCA allows to assess extra-costs and savings derived from the adoption of the SMM with respect to the unmitigated design scenario. The technical feasibility of the approach is demonstrated by discussing its application to a topical case study dealing with an endangered desert railway.The paper is organized into four further sections. First, the experimental-computational techniques adopted within the hybrid approach and the modeling framework to assess the life-cycle performance and cost are introduced. The tested case study is introduced, and WST and ETD setups are outlined. Finally, results are discussed and conclusions and perspectives are outlined.Hybrid ApproachThe adopted wind tunnel experimental facility, multiphase computational fluid dynamics model, and probabilistic framework to assess the life-cycle performance and cost analysis are introduced in the following.Wind Tunnel FacilityThe wind tunnel test is carried out in the wind tunnel L-1B of von Karman Institute for Fluid Dynamics. The facility is a closed-circuit wind tunnel with a test section length of about 20 m, and a cross section of height hwt=2  m and width wwt=3  m [Fig. 3(a)].A low-roughness boundary layer is reproduced to simulate open terrain conditions typical for sand desert. To characterize the clean wind boundary layer, avoiding interference of scattered light from flying sand particles with measuring equipment, a flat wooden board of length c=4.9  m, width e=0.3  m, and thickness 1.8×10−2  m with sand grains glued on it was set-up in the rectangular test section [Fig. 3(b)]. A ramp with gentle slope approximately equal to 3° is installed to smooth the transition between wind tunnel floor and the wooden board. The downwind edge is located at the distance a=8hwt from the inlet of the test section. The reference wind velocity U is measured just upwind of the ramp through Prandtl pitot tube at 0.57 m from the wind tunnel floor. Some initial exploratory tests with a sand bed have been performed to ascertain the threshold velocity Ut, defined as the minimum value of the wind speed at which quasisteady sand transport occurs at position d3. Three increasing wind speeds, respectively, equal to U={1.3Ut,1.5Ut,2Ut}, are tested.The mean velocity profile u(z) and mean turbulence intensity profile Iu(z) at the distances d2=3 and d3=4.5  m from the upwind edge of the wooden board are measured along the test section centerline through particle image velocimetry (PIV) technique adopting a smoke generator to seed the flow with oil particles ranging from 1×10−3–5×10−3  mm. Each measurement is taken along the test section centerline to avoid the influence of the boundary layer developed on the lateral sides of the wind tunnel. A 200 mJ Nd:YAG laser source pulsating at 10 Hz is located far downwind of the measuring section. A laser sheet is generated along the test section centerline and perpendicular to the floor. Its width inevitably varies along the fetch length resulting equal to 8.6, 7.2, and 5.4 mm, respectively, at positions d1=1.5, d2=3, and d3=4.5  m. Two CMOS cameras with resolution 2,360×1,776 pixels and a 50 mm objective are located outside the test section to acquire the wind flow field with field of views (FoVs) equal to 18×14  cm. The measured profiles at d2 and d3 results are almost unchanged. Fig. 3(c) shows the measured profiles at d3. The wind speed measurements are fitted with the log-law u(z)=u*/κ·ln(z/z0), being u* the wind shear velocity, κ=0.41 the von Karman constant, and z0 the aerodynamic roughness, leading to u*={0.25,0.33,0.37,0.51} m/s and z0=6.5e−5  m. The corresponding profile of the streamwise turbulence intensity Iu(z) are included in Fig. 3(c), whereas the related streamwise integral length scales measured at pitot location are Lu={0.17,0.22,0.25,0.36} m.Computational ModelThe wind flow is modeled as an unsteady incompressible turbulent flow through Unsteady Reynolds Average Navier Stokes (URANS) equations. URANS equations are chosen because we are primarily interested in the long-term behavior of the sand transport which induces sand erosion and accumulation around SMMs and which takes place on a much larger time scale than turbulence. The SST k−ω turbulence model is adopted because of its proven accuracy in simulating wind flow separation around bluff bodies (Menter et al. 2003), such as SMMs. The same CFD model has been validated in Bruno and Fransos (2015) and adopted in Bruno et al. (2018a), Horvat et al. (2020), and Horvat et al. (2021) on the same class of problems, i.e., nominal 2D bluff bodies immersed in a turbulent atmospheric boundary layer. The set of governing equations reads: (1) ∂ui∂xi=0,∂ui∂t+uj∂ui∂xj=−1ρ∂p∂xi+∂∂xj[ν(∂ui∂xj+∂uj∂xi)]−∂∂xj(u¯i′uj′),∂k∂t+ui∂k∂xi=∂∂xi[(σkνt+ν)∂k∂xi]+P˜k−β*kω,∂ω∂t+ui∂ω∂xi=∂∂xi[(σωνt+ν)∂ω∂xi]+αωkPk−βω2+(1−F1)2σωω∂k∂xi∂ω∂xiwhere t = time; ρ = air density; p = average pressure; ν = air kinematic viscosity; νt = so-called turbulent kinematic viscosity; k = turbulent kinetic energy; and ω = its specific dissipation rate. The kinetic energy production term P˜k is modeled by introducing a production limiter to prevent the build-up of turbulence in stagnation regions, i.e., P˜k=min(Pk,10β*kω), where Pk≈2νtDij(∂ui/∂xj) and Dij = strain-rate tensor. The standard blending function F1 and model constants β*=0.09, σk=0.85, σω=0.65, α=0.31, and β=0.075 are obtained from Menter et al. (2003).Sand-grain roughness wall functions are complemented by SST k-ω turbulence model because of their wide use in computational wind engineering (Blocken et al. 2007) and their proven adequacy from past simulations on the same class of problem (e.g., Liu et al. 2011; Bruno and Fransos 2015). Standard wall functions (Launder and Spalding 1974) with roughness modification (Cebeci and Bradshaw 1977) are applied. The equivalent sand-grain roughness height is determined equal to ks=9.793z0/Cs, where Cs=0.5 is the roughness constant.The sand phase is considered as a passive scalar and modeled through the conservation equation of sand volume fraction ϕs: (2) where the sand flux qi is given by the combination of advection by wind, sedimentation effects due to gravity, and diffusive flux. In particular: (3) qi=us,iϕs+usedϕs+veffϕs∂ϕs∂xiwhere us,i = transport velocity of the sand particles by wind taken proportional to ui, used = vertical sedimentation velocity, and νeff takes into account the mixing-diffusive contribution resulting from the combination of νt and the viscous effect due to random collisions at the sand surface νs=A(2IIDij)B, being A and B model parameters to calibrate the concentration profile, and IIDij the second invariant of Dij (Preziosi et al. 2015).The morphodynamic evolution of the sand surface is accounted for by imposing the continuity of sand flux through the wind-sand interface and the triggering of sand sliding when the sand slope exceeds the critical angle of repose ψcr, i.e., the steepest slope angle sand grains can pile up. This leads to the modified Exner equation (Lo Giudice and Preziosi 2020): (4) ∂h∂t=vav∂∂xi[(|∂h∂xi|−tanψcr)+1+|∂h∂xi|2∂h∂xi|∂h∂xi|]+vΣ,iEDwhere h = height of the wind-sand interface defined on sandy patches only; νav = diffusion coefficient controlling the sliding speed; (·)+ stands for positive part, vΣ,iED=−[1/(ϕcp−ϕs)]qini = velocity of the wind-sand interface due to erosion or sedimentation; ϕcp = sand close-packing volume ratio; and ni = direction normal to the surface.Within the framework of this study: (1) steady-state simulations have been carried out on the WST setup to tune the model free parameters, and (2) unsteady simulations have been carried out on the full-scale SMM to assess its LCP. The adopted boundary conditions (b.c.) and 2D computational domains are schematically shown in Fig. 4. Null ϕs initial conditions are imposed in the whole domains. No-slip b.c. are imposed at the solid walls. At the inlet, Neumann zero-gradient b.c. is imposed for p and ϕs, whereas Dirichlet b.c. is imposed on u, k, ω. At the outlet, Neumann zero-gradient b.c. is imposed for all flow variables, except for Dirichlet b.c. for p. Concerning the WST domain, the inlet profile of u is prescribed using the power law u(z)=U[2z/hwt]1/n for turbulent boundary layer, whereas the inlet profile of k and ω are set constant and equal to k=3/2(UIu)2 and ω=k/(0.090.25Lu). Concerning the full-scale SMM domain, a log-law inlet u profile is set, whereas the profiles of k and ω are set in accordance to Richards and Norris (2011) to replicate a neutral atmospheric boundary layer, and symmetry b.c. is imposed at the top. Finally, a Dirichlet sand erosion b.c. is set to properly model erosion on sandy surfaces, whereas a Neumann b.c. is imposed on nonerodible surfaces. In particular, erosion occurs when the wind shear velocity u* is higher than the threshold one u*t (Kok et al. 2012). According to Ho et al. (2011): (5) −veffϕs∂ϕs∂xini=AHρd¯g(u*2−u^*t2)+where AH = model parameter depending on the physical properties of the sand; d¯ = mean sand diameter; g = acceleration due to gravity, and u^*t directly follows from u*t and takes into account the local effect due to inclined slopes; and u^*t2=u*t2(cosψ+sinψ/tanψcr) being ψ the ground slope angle (Iversen and Rasmussen 1994).Space discretization follows a predominantly structured grid of hexahedral control volumes. The mesh is refined close to the ground, so that the height nw of the wall-adjacent cell: (1) provides a sufficiently high mesh resolution along the normal direction to the surface to adequately resolve the gradients of wind-sand state variables, and (2) complies with the wall function requirement on dimensionless wall unit 30VR,i]=∫VR,i+∞fVi(x,t)dx=1−FVi(VR,i,t)where fVi and FVi = probability density and cumulative distribution functions of Vi, respectively. As a result, the characteristic time of failure Tk,i is given by: (9) Tk,i=pfi−1(pf,k)=inf{t≥0:FVi(t)(VR,i)≤1−pf,k}where pf,k = characteristic probability of failure. Fig. 5(b) sketches the generic trend of the time-variant sand action through its density fVi(t), the mean value μVi(t), and the increasing trend of the probability of failure pfi(t).Finally, LCCA (Fabrycky and Blanchard 1991) can be carried out based on Tk,i, considering the cost of SMM design and construction cd, and sand maintenance related costs associated with the ith obstacle cs,i: (10) c(tL)=∑t=1tL[cd/Td+∑i=1Ncs,i/Tk,i(1+r)t]with  cd=0  if  t>Td  and  cs,i=0  if  t≤Tdwhere c(tL) = cumulated life-cycle cost at time tL; Td = time required for SMM design and construction; N = the number of infrastructure components inducing Vi; and r = the discount rate.Setup of the StudyStudy LayoutThe proposed hybrid approach is applied to a case study railway segment located near Al Ain along the Ethiad Rail line in the United Arab Emirates. The chosen site is threatened by the sand of Rub’ al-Khali desert. The examined railway segment develops along the NE-SW direction. The local sand granulometry is composed of fine grained, moderately well-sorted sand with mean diameter d¯=0.16  mm (Edgell 2006). The probability density function of u*t is derived from Raffaele et al. (2016) as a function of d¯. Conversely, the probability density functions of u* is derived from an anemometric station in proximity of Al Ain. The employed dataset of the 10 min average wind velocity U10 at 10 m from the ground refers to 10 years, from January 2008 to December 2017. The time sampling corresponds to 1 h, whereas the yaw angle discretization is equal to 10°. The aerodynamic roughness length is set equal to z0=3e−3  m, according to the recommendations given in EN 1991-1-4 (CEN 2005).Fig. 6 shows the windblown sand action modeling framework and the related state variables for a single side of the railway infrastructure. The same scheme is mirrored for the opposite side. Such a scheme directly results from the general one in Fig. 5, by putting in series three successive obstacles, i.e., the SMM (i=1), the embankment (i=2), and track (i=3). The berm and ditch is a well-known SMM for desert railway applications [see e.g., Phillips (2011)]. Here, we investigate a generalization of it. The tested SMM results from the combination of a hb=3  m high lb=20  m long berm, followed by a hd=1  m deep ld=20  m long ditch. The berm follows the sinusoidal profile z=hb/2sin[2π/lb(x−lb/4))]+hb/2. The ditch side walls are inclined with 1/3 slope gradient. The height of the embankment is set equal to he=2.5  m. A double-track railway is considered, with a hr=0.25  m deep ballast bed and a 5 m wide line-side access track.The LCP of the SMM is obtained through the proposed hybrid approach. The LCP of the embankment is derived from WST tests in Hotta and Horikawa (1990), whereas the LCP of the railway track is conjectured maximum and constant up to the filling of ballast voids and then linearly decreasing until it reaches its full capacity Vf, in analogy to Raffaele and Bruno (2020). VR,1 and VR,2 are set equal to the volume corresponding to 80% and 50% of the initial value of ei, respectively. Conversely, VR,3 is set equal to the volume giving rise to the SULS at full rail coverage.The LCCA spans the whole service life of the infrastructure, set equal to tL=100  years. The railway construction time is set equal to Td=6  years. The costs retained in the LCCA comprehend: (1) SMM design and construction cd=$790/m, (2) removal and disposal of accumulated sand around the SMM cs,1=$7/m3 and embankment cs,2=$7.7/m3, (3) railway ballast cleaning cs,3=$56/m. For the sake of generality, the discount rate is set equal to r=5%, whereas costs induced by land expropriation due to SMM construction and by loss of capacity due to sand maintenance operations are not considered in the present study. Indeed, they go beyond the single analyzed railway segment and highly depend on the specific features of the whole railway network and country economic system.Wind-Sand Tunnel Test SetupA flat sand bed of length b=4.9  m, width w=1.8  m, and thickness 1.8×10−2  m has been set up in the wind tunnel test section replacing the wooden board [Fig. 7(a)]. The sand bed is confined by wooden slats and fillet to the wind tunnel floor through the upwind ramp in analogy with the setup proposed by Tominaga et al. (2018).The particle size distribution of the tested sand has been obtained through microscopic imaging technique and is plotted in Fig. 7(b) through its cumulative distribution F(d). The mean grain diameter is equal to d¯=0.147  mm, very close to the one on site. The threshold shear velocity obtained through preliminary wind tunnel tests results equals to u*t=0.245  m/s (corresponding to Ut=5.54  m/s). Such a value of u*t agrees with past wind tunnel measurements on sand samples with same d¯ (see e.g., Raffaele et al. 2016).Three tests have been performed by progressively increasing the incoming wind speed U={1.3Ut,1.5Ut,2Ut}. Each test started from the same initial condition, a perfectly flat uniform sand bed, and lasted T=300  s to ensure reaching a quasisteady sand transport. To ensure repeatability, each test has been performed twice. The similarity of the saltation layer with respect to open field condition is taken into account by: (1) assuring that the wind flow is fully rough, i.e., the friction Reynolds number satisfies the criterion Re*≈u*3/2gν=[53,454]>30 (Anno 1984), (2) avoiding disturbance in streamwise pressure by satisfying the Froude number criterion, i.e., Fr=U2/hwtg=[1.24,5.27]<20 (White 1996), and (3) adopting a long sand fetch equal to b=4.9  m to ease sand transport saturation and let the wind flow adjust to the sand z0 (Kok et al. 2012).The installed measuring equipment allows for the detection of the instantaneous sand particles concentration ϕ(z,t) and velocity us(z,t) over the flat sand bed through particle tracking velocimetry (PTV). The laser source pulsates at 2 Hz. The two CMOS cameras are moved along the sand fetch to acquire PTV pictures in d1, d2, and d3. The acquired FoVs are sketched in Fig. 7(c). The velocity and concentration fields of sand particles are detected with 55×40  cm2 FoVs for each position, with a 35 mm objective.Wind-Sand Computational Simulations: Incoming Wind Flow and Sand FeaturesThe incoming wind flow features differ as a function of the computational domain. On the one hand, the incoming wind flow of the WST scale simulation reflects the experimental conditions. The ground aerodynamic roughness length is set equal to z0=6.5×10−5  m, according to the boundary layer PIV measurements. The free parameter of the inlet wind speed power law is set to reproduce the wind speed profiles measured at d2 and d3, resulting in n=10. On the other hand, the incoming wind flow of the SMM full-scale simulations reflects actual desert conditions. The ground aerodynamic roughness length is set equal to z0=3e−3  m. The incoming wind shear velocity is set equal to u*=2u*t=0.49  m/s to exceed u*t and induce windblown sand transport upwind from the SMM. During sand transport events, the lower bound (u*=u*t) of the reference wind speed at the top of the berm is equal to uhB=4.21  m/s, and the corresponding Reynolds number is RehB=8.5×105. In the case of nominally 2D sinusoidal berms, such a value suggests that the flow triggering windblown sand transport is predominantly within the Reynolds supercritical regime (Ferreira et al. 1995). As such, significant Reynolds effects are not expected to take place for u*>u*t.For both computational domains, the adopted sand diameter is set equal to the mean value of the tested sand, i.e., d¯=0.147  mm. The corresponding mean values of threshold shear velocity and sedimentation velocity are respectively set equal to u*t=0.245  m/s, in accordance to wind tunnel PIV measurements, and to used=0.782  m/s, according to the statistical characterization proposed in Raffaele et al. (2020). Finally, the remaining model constants are set equal to νav=0.1  m2/s, ψcr=32°, and ϕcp=0.6.The adopted time step in unsteady ETD simulations is set equal to Δts=1e−3  s, giving rise to a maximum Courant number C≈0.4. Given the time demanding unsteady multiphase simulations, the whole problem is decomposed into shorter simulations to assess the discrete piece-wise LCP. For each tested sand level: (1) an unsteady ETD simulation is carried out up to reaching of quasisteady sand transport conditions by assuring the convergence of incoming and outgoing sand transport rates, (2) LCP is assessed, (3) a new geometry corresponding to a new extrapolated sand level is obtained by shifting the wind-sand interface proportionally to the local value of the erosion-deposition velocity vΣED, and (4) a new mesh is built on the obtained geometry. The above steps are repeated systematically to describe the trend of LCP, up to reaching null SMM performance, i.e., sand flux at inflow equal to sand flux at outflow. The shifting Δh of the wind-sand interface is done manually relying on vΣEDΔt, being Δt an arbitrarily chosen time interval. As such, the convergence of sand transport shall be assured for each extrapolated sand level.ResultsIn the following, the tuned steady ETD simulations are compared with WST measurements, then SMM life-cycle performance is assessed through unsteady ETD simulations. Finally, the time-varying windblown sand action is quantified on the considered case study and life-cycle cost analysis is applied. The proposed hybrid approach can be applied to any kind of structure/infrastructure as long as the LCP of any affected obstacle is available. At the time being, scarce laboratory measurements and even more scarce computational simulations only allow for the quantification of the LCP in the railway infrastructure domain.Comparison between WST Measurements and ETD ResultsSteady-state ETD simulations are tuned on WST measurements by setting the value of free parameters in Eqs. (3) and (5). In this section, the comparison between time-averaged WST measurements and ETD results is provided. In particular, Fig. 8 collects the vertical profiles of the sand volume fraction ϕs(z), streamwise component of the sand velocity us(z), and flux q(z) at positions d1 (a,d,g), d2 (b,e,h), and d3 (c,f,i), providing the mean value μ and standard deviation σ.The sand volume fraction follows the typical exponentially decreasing law μϕs(z)=γe−z/λ (Ho et al. 2011). For a given position, the rate of decay of ϕs(z) is almost the same for u*/u*t=1.3 and u*/u*t=1.5, whereas it sensibly varies for u*/u*t=2. Conversely, for a given wind speed, ϕs(z=0) increases streamwise. According to the authors, the lower than expected μϕs(z) and high σϕs(z) in d1 for u*/u*t=1.3 are caused by the experienced intermittent unsteady sand transport induced by u* still close to the threshold and the short fetch length. Indeed, the adopted first order ETD model is not able to capture such out-of-equilibrium erosion conditions. Discrepancies in ϕs between WST and ETD fade out with the increasing of sand fetch.The sand velocity profiles can be divided into two layers resulting from strong variation of ϕs (Valance et al. 2015). Within the near-wall region where ϕs(z) is high (z/hwt<0.01), us(z) is weakly sensitive to u* and linearly increasing with z. Conversely, where ϕs(z) is low (z/hwt>0.01), us(z) is highly sensitive to u* and follows a logarithmic-like increasing trend. Despite the overall promising matching of profiles for a first order model, ETD simulations are not able to reproduce us≠0 at the ground, and particularly overestimates us close to the ground (0

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