Optimizing subgrade design for blowing snow prevention: a CFD-based parametric study

Blowing snow poses a serious threat to highway traffic safety, and appropriate subgrade cross-sectional designs can effectively mitigate the impacts. Systematic studies on how to optimize subgrade structural design to maximize the mitigation of blowing snow disasters are still lacking. To address this, this paper investigates the fundamental parameters of two typical subgrades: embankments and cuttings. To investigate the influence of varying subgrade cross-sectional configurations and slope ratios on the effectiveness of blowing snow control with a focus on single-parameter variations, this study employs CFD (computational fluid dynamics) simulations to analyze velocity contour distributions, snow accumulation patterns, and vertical wind velocity profiles around the models. The results demonstrate that implementing gentle slopes for subgrades (including both embankments and cuttings) or appropriately widening snow accumulation platforms of the cutting can effectively mitigate snow deposition on pavement surfaces. When wind flows through the cutting, the overall wind velocity profile exhibits a W-shaped distribution pattern. Meanwhile, variations in its depth and slope ratio both exhibit positive correlations with road snow accumulation. Furthermore, three embankment models with cross-sectional dimensions identical to those of field conditions but varying heights are established. Through combined field monitoring tests and numerical simulations, wind velocities are systematically measured at ten vertical elevations for all critical locations. Comparative results demonstrate that the flow field distribution patterns and variation trends observed in the field are highly consistent with the numerical simulation results, thereby validating the reliability of the numerical model. This research elucidates the underlying physical mechanisms of how subgrade structural parameters mitigate the impact of snowdrift disasters, providing scientifically validated references for hazard reduction along transportation corridors.

1 Introduction

Blowing snow, defined as an air current carrying substantial amounts of snow particles, is a common natural disaster in the northwest, northeast, and Tibetan Plateau of China (Hu, 1978; Tabler, 2003). As a two-phase flow exhibiting distinct transport dynamics, blowing snow leads to localized deep snow accumulation in affected areas. This phenomenon buries pastures and roadways, disrupts transportation networks, and severely impacts both local livelihoods and economic development (Wang and Zhang, 1999; Michaux et al., 2002; Li, 2021). To develop rational embankment cross-sectional designs for mitigating blowing snow on roadways, in-depth investigations into the influence of various subgrade configurations and their associated parameters on snow control effectiveness are critically needed.

The rational optimization of subgrade configurations, alignment orientations, and embankment heights (or cutting depths) can significantly increase roadway resistance to blowing snow (Okaze et al., 2025; Qiu et al., 2022; Ma et al., 2021) Based on field measurements and engineering practice, Wang (2001) proposed that blowing snow can be effectively mitigated through optimized road alignment selection and subgrade cross-sectional design. Zhu (2007) systematically elaborated on the fundamental principles of highway subgrade cross-sectional design, along with relevant snow disaster prevention techniques and methodologies, thereby providing critical guidance for the development of roadway snow disaster mitigation measures. Schmidt (1980), Schmidt (1981) demonstrated in earlier research that snow particle entrainment is fundamentally governed by interparticle cohesion and collision restitution coefficients. Through a systematic investigation of the relationship between the mean wind velocity profile distribution and drifting snow density, the author established distinct transport-layer wind velocity profile patterns. Gray and Male (2004) analyzed the critical conditions for snow particle motion and the formation processes of snow transport regimes, and demonstrated that the threshold friction velocity for particle entrainment is governed by snow grain size, shape, mass, and interparticle bonding forces. Melo et al. (2024), through measurement data and new physics-based modeling with large-eddy simulation (LES), demonstrated that the transition between the two classically described snow saltation systems—one dominated by aerodynamic entrainment and the other by splash—is governed by the friction velocity.

In recent years, researchers (Beyers and Waechter, 2008; Zhang Z. B. et al., 2024; Li, 2022; Feng et al., 2020; Wang et al., 2020) have employed numerical simulations and wind tunnel experiments to simplify complex scenarios, systematically analyzing the influence of various subgrade configurations and their geometric parameters on blowing snow control effectiveness. Numerical simulations, owing to their time-efficient nature and freedom from constraints such as model scale requirements and similarity ratios, exhibit considerable potential for large-scale experimental studies (Zhou et al., 2019; Zhou and Zhang, 2023; Li et al., 2022a; Alhajraf, 2004). Budd et al. (1966) established theoretical frameworks for blowing snow particle suspensions through homogeneous and heterogeneous turbulent diffusion theories, thereby providing fundamental support for numerical simulations of blowing snow phenomena. Liu et al. (2021a), Liu et al. (2021b) investigated the influence of slope gradients on snow accumulation patterns around embankments through combined field-scale modeling and computational fluid dynamics simulations. Their results demonstrated that windward slope modifications significantly altered snow redistribution, whereas leeward slope variations had negligible effects. Li et al. (2021) established a strong correlation between embankment slope angles and wake flow properties, demonstrating that the extent of the velocity reduction zone downstream is directly proportional to the slope steepness. Ma et al. (2022) employed computational fluid dynamics (CFD) to systematically evaluate the effectiveness of three wind deflector types (vertical, backward, and forward) in mitigating snow accumulation within cuttings. Their analysis focused on resultant flow fields, deposition length, and snow concentration. Tanji (2025) investigated the effect of formed snowdrifts in advance on the turbulent flow and subsequent snowdrift distribution around three types of snow fences in a numerical simulation. Additionally, based on the central-moment lattice Boltzmann method, Watanabe et al. (2024) developed a Lagrangian particle dispersion model coupled with a large-eddy simulation code, which reproduces typical features of drifting snow observed in the field. Fabricus et al. (2025) developed a Stochastic Blowing Snow (SBS) model using Monte Carlo simulation, which integrates the randomness of wind and critical speed to reliably estimate blowing snow probability in both Wyoming and the Alps. Furthermore, Hames et al. (2025) expanded an existing Eulerian–Lagrangian model by incorporating buildings to simulate snowdrifts around complex structures, using advanced saltation physics. This development brings new levels of interaction between snow particles and larger structures, making the simulations more representative of real-world conditions and well-suited for engineering applications. Existing studies have primarily focused on investigating the mechanisms of snow control through parameterized embankment designs, while some researchers have also examined the effects of road cuttings on windbreaks and snow retention (Li et al., 2022b; Li L. Y. et al., 2022). However, systematic investigations into the differential snow control effectiveness of various parameter configurations between embankment and cutting sections remain insufficient, and the accuracy of existing numerical simulations lacks comprehensive validation through field experiments.

To address these identified research gaps, this study employs computational fluid dynamics (CFD) simulations based on the fundamental conservation laws of mass and momentum, with numerical discretization implemented through the finite volume method. The resulting flow phenomena are computationally modeled and visualized, followed by systematic postprocessing and analysis via ANSYS Fluent software. Through systematic analysis of velocity contour distributions, snow accumulation patterns, and vertical wind profiles around the models, this study investigates the influence of varying embankment heights and slope ratios, as well as cutting depths and slope configurations, on blowing snow control effectiveness. This research elucidates the underlying physical mechanisms, providing scientifically validated references for mitigating snowdrift disasters along transportation corridors.

2 Materials and methods

Numerical simulations are generally divided into preprocessing (model building, mesh division, calculation parameter setting), calculation solution, and data postprocessing (the processing software used is CFD-POST, Tecplot360). In this experiment, a two-dimensional model is established via SCDM (Space Claim Direct Modeler), which is a direct modeling tool for CFD pre-processing and geometry operation, offering capabilities for geometry repair, preparation, and optimization. Structured meshing is performed via the ICEM of ANSYS software, and the divided mesh is imported into the ANSYS Fluent module for solver parameter setting and numerical calculation.

2.1 Basic control equation

2.1.1 Mass conservation equation

The mass conservation equation indicates that the increase in mass per unit time in the control volume is equal to the mass of fluid entering the control volume during the same time interval (Zhang Y. et al., 2024), as shown in Equations 1–3:

$\frac{\mathit{\partial }{\mathit{\rho }}_{\mathit{u}}}{\mathit{\partial }\mathit{t}}+\nabla ·\left({\mathit{\rho }}_{\mathit{u}}\overrightarrow{{\mathit{v}}_{\mathit{u}}}\right)=\mathbf{0}(1)$

$\overrightarrow{{\mathit{v}}_{\mathit{u}}}=\frac{{\sum }_{\mathit{j}=\mathbf{1}}^{\mathbf{2}}{\mathit{f}}_{\mathit{j}}{\mathit{\rho }}_{\mathit{j}}\overrightarrow{{\mathit{v}}_{\mathit{j}}}}{{\mathit{\rho }}_{\mathit{u}}}(2)$

${\mathit{\rho }}_{\mathit{u}}={\displaystyle \sum _{\mathit{j}=\mathbf{1}}^{\mathbf{2}}}{\mathit{f}}_{\mathit{j}}{\mathit{\rho }}_{\mathit{j}}(3)$

where ${\rho }_u$, $\overrightarrow{v_u}$ - mixed phase density, mixed phase velocity;

$f_j$, ${\rho }_j$, $\overrightarrow{v_j}$ - phase $j$ volume fraction, $j$ fluid density, $j$ fluid velocity.

2.1.2 Momentum conservation equation

The momentum conservation equation refers to the law of change of fluid momentum in a control volume that is equal to the sum of various forces acting on the control volume (Hazar and Töz, 2024), as shown in Equations 4, 5:

$\frac{\mathit{\partial }\left(\mathit{\rho }{\mathit{u}}_{\mathit{x}}\right)}{\mathit{\partial }\mathit{t}}+\nabla \left(\mathit{\rho }{\mathit{u}}_{\mathit{x}}\mathit{u}\right)=-\frac{\mathit{\partial }\mathit{p}}{\mathit{\partial }\mathit{t}}+\frac{\mathit{\partial }{\mathit{\tau }}_{\mathit{x}\mathit{x}}}{\mathit{\partial }\mathit{x}}+\frac{\mathit{\partial }{\mathit{\tau }}_{\mathit{x}\mathit{y}}}{\mathit{\partial }\mathit{y}}+\mathit{\rho }{\mathit{g}}_{\mathit{x}}(4)$

$\frac{\mathit{\partial }\left(\mathit{\rho }{\mathit{u}}_{\mathit{y}}\right)}{\mathit{\partial }\mathit{t}}+\nabla \left(\mathit{\rho }{\mathit{u}}_{\mathit{y}}\mathit{u}\right)=-\frac{\mathit{\partial }\mathit{p}}{\mathit{\partial }\mathit{y}}+\frac{\mathit{\partial }{\mathit{\tau }}_{\mathit{x}\mathit{y}}}{\mathit{\partial }\mathit{x}}+\frac{\mathit{\partial }{\mathit{\tau }}_{\mathit{y}\mathit{y}}}{\mathit{\partial }\mathit{y}}+\mathit{\rho }{\mathit{g}}_{\mathit{y}}(5)$

where $u_x,u_y$ represents all velocity components in the flow field; $\overline{u}$ represents the velocity vector in the flow field; $\rho$ represents the density of matter in the flow field; $g$ represents the gravitational acceleration in the flow field; $\tau$ represents the component of the viscous force acting on the surface of the micrometric body; and $t$ represents time.

In fluid flow calculations involving heat and energy transfer, the energy equation - essentially an expression of the first law of thermodynamics - must additionally be satisfied. However, since this experiment did not involve thermal energy exchange between control volumes or work done by external forces on the control volume, the energy conservation equation will not be further discussed.

2.2 Model

The wind velocity flow fields of subgrades with different parameters in a blowing snow environment are simulated via Fluent, and a geometrical model is built according to the specific dimensions of the physical work in the blowing snow area. In addition to the dimensions of the model itself, the size of the computational domain also has an important influence on the simulation results. The size of the computational domain was determined with reference to Franke et al. (2007) and Yang et al. (2022). Specifically, the upstream distance between the inlet boundary and the windward toe of the embankment was no less than 5H, while the downstream distance between the outlet boundary and the leeward toe of the embankment was set to a minimum of 15H. Additionally, when the domain height exceeds approximately 5H, the influence of the boundary effects on the near-ground flow structure is significantly reduced, and its impact on the embankment region becomes virtually negligible under these conditions. Therefore, SCDM 2022R2 is used to construct a two-dimensional model, and the length and height of the computational domain of the model are 350 m and 50 m, respectively. The center of the roadbed is 150 m and 200 m away from the entrance and exit of the computational domain, respectively. The computational domain is shown in Figure 1a.

Figure 1

Figure 1. Schematic diagram of the model: (a) the computational domain (b) the mesh generation.

The geometric model was imported into ICEM software for structured meshing, and the meshing was viewed and checked for quality through the ICEM premesh. When the blowing snow occurs in a natural environment, the snow particles basically move against the ground surface, so the mesh is encrypted near the ground surface and on the windward side of the embankment, the road surface, the guardrail, and the leeward side. The rest of the space within a certain height from the surface is not the focus of the test, so a sparser grid is used. The overall grid division is dense at the bottom and sparse at the top, as shown in Figure 1b. In addition, to ensure the accuracy of the computational results, a grid independence test was conducted prior to the numerical simulation, and a grid with relatively high quality and shorter computational time was selected. For boundary layer mesh refinement: within 0.3 m above the ground surface, a grid height of 1 cm is used; between 0.3 m and 1.2 m height, a grid height of 4 cm is adopted; and above 1.2m, the mesh is generated with a grid height of 10 cm.

2.3 Parameter configuration

2.3.1 Turbulence modeling

In ANSYS Fluent, gas-solid two-phase flows are commonly simulated using either the Eulerian-Lagrangian (E-L) discrete particle model or the Eulerian-Eulerian (E-E) two-fluid model. The E-L method treats the gas phase as a continuous fluid and tracks individual snow particles in a Lagrangian frame. This approach is well-suited for dilute particulate flows where particle–particle interactions are negligible. However, for conditions with high particle concentrations, achieving statistical significance requires tracking a prohibitively large number of particles.

In contrast, the E–E two-fluid model treats both phases as interpenetrating continua and solves conservation equations for each. A key assumption is that the local volume cannot be simultaneously occupied by both phases, and therefore the sum of volume fractions equals one. This model is more appropriate for dense drifting-snow conditions, where snow particles exhibit quasi-continuous behavior and interact strongly with the airflow through momentum exchange and turbulence modulation. It should be noted, however, that this approach has inherent limitations. The model’s treatment of the snow phase as a continuum with uniform properties may not fully capture the polydisperse nature of actual snow particles or the dynamic feedback effects of snow deposition and erosion on terrain geometry.

Considering the high particle load and strong aerodynamic feedback observed around the embankment, the Eulerian–Eulerian two-fluid model was adopted in this study. Turbulence was modelled using the standard k–ε model, where k represents the turbulent kinetic energy and ε denotes the dissipation rate. The Eulerian formulation represents the flow velocity field as Equation 6:

$\overrightarrow{\mathit{v}}=\overrightarrow{\mathit{v}}\left(\mathit{x},\mathit{y},\mathit{z},\mathit{t}\right)(6)$

where $x,y,z$ denote the spatial coordinates within the computational domain and $t$ is time.

2.3.2 Material

In the blowing snow two-phase flow calculation, the first phase is the air phase, and the second phase is the snow particle phase. For the air phase properties, the density of the air phase is taken as: $\rho =1.225kg/m^3$, and the dynamic viscosity is taken as $\mu =1.7894\times 10^{-5}kg/m·s$. This study employs an Eulerian multiphase approach coupled with the standard k-ε turbulence model to simulate blowing snow, treating the snow phase as a continuous medium. The governing equation (Tominaga et al., 2011) for snow transport is given by Equation 7:

$\frac{\partial {\rho }_{s}f}{\partial t}+\frac{\partial {\rho }_{s}f{u}_j}{\partial x_j}=\frac{\partial }{\partial x_j}\left[\frac{v_t}{S_c}\left(\frac{\partial {\rho }_{s}f}{\partial x_j}\right)\right]-\frac{\partial {\rho }_{s}f\omega }{\partial x_{\epsilon }}(7)$

where ${\rho }_s$ is the snow density, $f$ is the snow volume fraction, $S_c$ is the Schmidt number (set to 1) (Tominaga and Stathopoulos, 2010), and $\omega$ is the snow particle settling velocity.

Erosion and deposition on the snow surface are governed by the relationship between the friction velocity $u_{*}$ (Zhou et al., 2019) and the threshold friction velocity $u_{*t}$. The friction velocity $u_{*}$ is calculated from the airflow shear stress $\tau$ and the air density ${\rho }_s$ (Equation 8):

$u_{*}=\sqrt{\frac{\tau }{{\rho }_s}}(8)$

Erosion occurs when $u_{*}$ > $u_{*t}$, whereas deposition prevails when $u_{*}$ < $u_{*t}$. The deposition flux $q_{dep}$, erosion flux $q_{ero}$, and total flux $q_{total}$ are respectively defined as Equations 9–11:

$q_{dep}={\rho }_{s}f\omega \frac{{u_{*t}}^2-{u_{*}}^2}{{u_{*t}}^2}(9)$

$q_{ero}=A_{ero}\left({u_{*}}^2-{u_{*t}}^2\right)(10)$

$q_{total}=q_{dep}-q_{ero}(11)$

Here, the snow particle bonding strength is given as $A_{ero}=7\times {10}^{-4}$.

Key physical parameters are derived from field measurements: snow density ${\rho }_s=139kg/m^3$, threshold friction velocity $u_{*t}=0.15m/s$ (calculated from a measured 3 m-height initiation wind speed of 6 m/s based on the logarithmic wind profile model), snow particle settling velocity $\omega =0.1m/s$, and snow particle diameter of 0.2 mm. The gravitational acceleration is set to 9.81 m/s². According to existing studies (Zhou et al., 2024; Zhang et al., 2023; Yin, 2022) and combined with the actual blowing snow conditions in Xinjiang, the volume fraction of snow particles is taken as 0.01.

2.3.3 Boundary condition

The left side of the computational domain is the wind speed inlet boundary. To be more in line with the natural blowing snow environment, the velocity compilation function is used to set the initial wind velocity via a customized wind velocity profile (UDF), and an exponential rate $U_{\left(z\right)}$ is used for the wind velocity profile at the velocity inlet (Equation 12):

${\mathit{U}}_{\left(\mathit{z}\right)}={\mathit{U}}_{\mathbf{2}}\times {\mathit{z}}^{\mathbf{0.15}}(12)$

where: $U_{\left(z\right)}$ represents the wind velocity at height $z$; $U_2$ represents the wind velocity at 2 m, which is 10 m/s, and this wind velocity is the actual measurement of the field test; and $0.15$ represents the ground roughness index for Class B landforms.

The right side of the computational domain is the fluid outlet, and the boundary condition parameter is set to Outflow. Since there is only a single channel, there is no need for additional conditions, and the outlet data are generated automatically after the computational domain is computed. Therefore, there is no effect on the partial fluid flow in front of the outlet boundary. The upper boundary of the computational domain is configured as a symmetry boundary condition. At this boundary, the normal velocity component is set to 0 m/s, while the normal gradient of all flow variables on the symmetry plane is also zero. Implementing the upper wall as a symmetry boundary reduces computational steps and improves simulation efficiency without compromising the accuracy of the numerical results. The lower wall is set as a no-slip wall, and the relative velocity of the fluid in the computational domain is 0 m/s at the lower wall.

2.3.4 Solver

The simulation is set to the 2D fluid domain, and to ensure that the simulation results are close to those of natural blowing snow, the 2D Double Precision option was ticked on the Fluent page. The pressure-based solution model is selected, which is generally suitable for the case of low and incompressible fluid flow. Moreover, the transient calculation is selected, the time step is 1 s, and the time step is 200 s, and the number of individual step iterations is set to 20 times. To improve the simulation calculation process to achieve convergence, the relaxation factor in Fluent is adopted as the software default.

The simulation is configured as a two-dimensional fluid domain. To ensure that the simulation results closely approximate natural wind-driven snow, the “2D Double Precision” option is selected in Fluent. Typically, Fluent offers two solver types: Pressure-Based and Density-Based. The Pressure-Based solver is generally suitable for incompressible flows at low velocities. Based on the actual simulation requirements, the Pressure-Based solver was selected for this case.

The computational modeling of wind-driven snow as a two-phase flow involves highly complex physics, and some numerical error is inevitable in the simulation process. To account for the impact of these errors, both steady-state and transient simulations were performed and their results compared. The analysis revealed that the steady-state approach cannot effectively eliminate accumulating errors. As the iteration count increases, these errors grow progressively, leading to significant deviations of the final results from actual values. In contrast, the transient simulation results align more closely with real-world data. Therefore, the transient method was selected for this study.

2.3.5 Numerical model validation

The Urumqi Western Bypass Expressway project area experiences significant blowing snow, with field-measured snow accumulation profiles along embankment sections illustrated in Figure 2. The junction of the embankment slope and road surface appears perpendicular to the line direction of the ‘snow streamline’, and the direction of the wind movement and embankment line direction perpendicular to the direction of the snow particles will be in the airflow under the role of the hostage around the embankment. According to the survey results of the whole line, the embankments at heights of 1.3 m, 2.5 m, and 3.0 m are selected for onsite measurement tests.

Figure 2

Figure 2. Schematic of field measurement experiment for blowing snow in the study area: (a) the snow streamline, (b) the monitoring stations, (c) the wind velocity measurement, (d) the snow depth measurement.

To verify the accuracy of the numerical simulation, numerical models with the same dimensions as the onsite embankment are established. An analysis of the actual wind velocity of the onsite embankment reveals that the wind velocity varied significantly at the windward toe, the windward shoulder, the center of the road surface, the leeward shoulder, and the leeward toe of the embankment. Consequently, field-measured wind velocities at the windward toe, windward shoulder, roadway centerline, leeward shoulder, and leeward toe are compared with numerical simulation results for embankment heights of 1.3 m, 2.5 m, and 3.0 m. Through combined field monitoring and numerical simulation, wind velocity measurements are obtained at ten vertical heights (1.48 m, 1.36 m, 1.24 m, 1.12 m, 1.00 m, 0.88 m, 0.76 m, 0.64 m, 0.52 m, and 0.40 m) for each critical location, serving as experimental benchmarks. The reliability of the numerical simulation results is further verified by comparing and analyzing the corresponding test values.

The experimental results of the field investigation and numerical simulation indicate a strong correlation between the wind velocities at the five key locations (Figure 3). The wind velocity variation trend at the windward toe is generally consistent, with the wind velocity gradually increasing. However, the increase in the wind velocity at the windward shoulder becomes more pronounced as the embankment height increases. As the airflow traverses the roadway, the wind velocity exhibits sustained acceleration, modulated by guardrail-induced effects that create a bell-shaped acceleration profile - initially increasing then decreasing, with the peak magnitude occurring at the centerline. Notably, the 3 m embankment configuration demonstrates the maximum velocity amplification. When the airflow reaches the leeward toe, the wind velocity decreases to a minimum, forming a certain range of airflow deceleration zones on the leeward side, which easily forms snow in the region.

Figure 3

Figure 3. Numerical simulation validation at key embankment locations: (a) wind velocity at the windward toe, (b) wind velocity at the windward shoulder, (c) wind velocity at roadway centerline, (d) wind velocity at the leeward shoulder, (e) wind velocity at the leeward toe.

Furthermore, a comprehensive quantitative validation was conducted by comparing simulated and field-measured wind velocities across five critical locations around the embankment, totaling 150 data pairs. The mean absolute error (MAE) values were calculated as follows: 0.464 at the windward toe, 0.168 at the windward shoulder, 0.596 at the roadway centerline, 0.413 at the leeward shoulder, and 0.354 at the leeward toe. The overall low MAE values indicate that the simulated wind velocities closely match the field observations, demonstrating good predictive precision across different flow regimes. This consistency confirms the model’s capability in accurately reproducing the wind field for blowing snow studies. Similarly, the simulated snow depths show a high degree of agreement with field measurements across all three embankment heights in both magnitude and spatial distribution, further validating the model’s reliability in predicting snow deposition patterns.

The results of the numerical simulation have some errors with respect to the measured values of the field investigation. The reason is that natural blowing snow is affected by a variety of factors, while the numerical simulation has a certain degree of simplification. The process of establishing the fluid domain and setting the boundary conditions has a certain degree of subjectivity. Although there are some differences between the actual flow field changes and the numerical simulation results, there is a strong correlation between the overall flow field distribution pattern and the change trend. Given the inherent constraints of simulations, a model’s parameterization can be considered reasonable when its predicted flow field distribution and variation trends exhibit strong correlation with field measurements. Therefore, by comparing the numerical simulation results with the measured wind velocity field of the blowing snow, it can be concluded that the numerical simulation parameters are reasonably set and can meet the simulation requirements for different blowing snow conditions.

3 Results

The key factors influencing blowing snow on embankments are primarily the embankment height and slope ratio. Therefore, this study focuses on analyzing the effects of blowing snow accumulation and redistribution under varying embankment heights and slope ratios, which maintain a consistent subgrade width. The numerical simulation test parameters of the embankment are shown in Table 1.

Table 1

Table 1. Design of the embankment test parameters.

Where the variable of snow accumulation in the numerical calculations is represented by the snow deposition-erosion coefficient $R$, with the Equation 13:

$\mathit{R}=\frac{{\mathit{u}}_{\mathit{s}}}{{\mathit{u}}_{\mathit{f}}}(13)$

where: $u_s$ is the initial snow particle volume fraction, with a value of 0.01, and $u_f$ is the volume fraction of snow particles at the end of the calculation, and the occurrence of snow accumulation or snow erosion at that point is determined by whether $R$ is greater than or less than 1.

In the case of the cutting, when the moving airflow passes the windward shoulder of the cutting, the cross section suddenly increases, causing the velocity of the moving airflow to decrease rapidly. At the same time, at the windward toe of the slope, there is an airflow deceleration area or vortex area, and the snow particles in the air are blocked in this area. When wind velocities fall below the critical threshold for sustained snow particle transport, progressive deposition occurs, ultimately resulting in the accumulation of snow that obstructs roadways. The influence of road cuttings on blowing snow dynamics is governed primarily by two key geometric parameters: the cutting depth and slope ratio. This study systematically investigates the distinct effects of varying cutting depths and slope configurations on snowdrift formation patterns, with the principal test cases detailed in Table 2.

Table 2

Table 2. Design of the cutting test parameters.

3.1 Embankment height

Figure 4 shows the wind velocity flow field distribution around the embankment at different embankment heights, where the slope ratio of the embankment is 1:1 and the width of the embankment is 41 m. Specific analyses are carried out based on the distribution of the wind velocity flow field around the embankment at the heights of 0.1 m, 0.5 m, and 2 m from the surface.

Figure 4

Figure 4. Wind velocity contours for embankments at different heights: (a) embankment height: 1 m (b) embankment height: 3 m (c) embankment height: 5 m (d) embankment height: 7 m (e) embankment height: 9 m (f) wind velocity profiles (at the same height).

In the horizontal direction at an embankment height of 1 m, the reduction in the wind velocity from the inlet side to the windward toe at a height of 2 m is 22.2%. In the same case, the increase in the wind velocity from the windward toe to the windward shoulder is 38.8%; the decrease in the wind velocity from the windward shoulder to the center of the road is 33.2%; the decrease in the wind velocity from the leeward shoulder to the leeward toe is 39.2%; and the increase in the wind velocity from the center of the road to the leeward shoulder is lower. In the vertical direction, the wind velocities of embankments of different heights at the same height (2 m from the surface) are compared and analyzed. The calculation reveals that, compared with those at the embankment height of 1 m, the wind velocity of 9 m height embankment at the windward toe, the windward shoulder, the center of the pavement, the leeward shoulder, and the leeward toe decrease by 38.6%, 54.6%, 70.3%, 35.2%, and 34.7%.

With increasing embankment height, the airflow begins to decelerate at a certain distance upstream of the windward side, reaching its minimum velocity at the windward toe. Then, the wind velocity increases to a maximum at the windward shoulder, and the increase in the wind velocity increases with increasing embankment height. The near-surface wind velocity initially decreases before recovery, exhibiting an inverse correlation with embankment height. As the airflow traverses the road surface and reaches the leeward side, the sudden expansion of the flow cross-section induces significant velocity reduction.

When the height of the embankment is less than 5 m, the snow particles carried by the airflow are deposited in large quantities at the windward toe and the road surface (Figure 5). The embankment is easily buried by snow when the height of the embankment is low. When the height of the embankment is greater than 7 m, the snow particles are basically deposited on the windward side, and the accumulation on the road surface is lower, so the damage to the road surface is alleviated. An analysis of the deposition-erosion coefficient of peripheral snow at different embankment heights revealed that the snow distribution on the windward slope of the embankment at different heights is greater. The distribution at the shoulder location decreases, whereas the amount of snow accumulation on the road surface decreases with increasing embankment height. When the heights of the embankment are 3 m, 5 m, 7 m, and 9 m, the average snow particle volume fractions on the road surface decrease by 5.6%, 7.5%, 9.2%, and 11.4%, respectively, compared with those when the height of the embankment is 1 m.

Figure 5

Figure 5. Snow deposition-erosion coefficient for the embankment at different heights.

Consequently, in regions with frequent blowing snow, embankment heights should be designed with adequate elevations above local snow accumulation levels. Field investigations and historical snowfall data should inform site-specific height adjustments to minimize travel lane snow deposition.

Figure 6 shows the wind velocity contours at different embankment heights. Taking Figure 6C as an example, the moving airflow is significantly disturbed by the obstruction of the embankment when it is at a certain distance from the windward side of the embankment. As the airflow gradually approaches the windward side of the embankment, the wind velocity slowly decreases until it reaches a minimum at the toe of the slope, where snow particle deposition occurs. The wind velocity then gradually increases, peaking as it passes over the windward shoulder of the embankment. Owing to the central parapet, the wind velocity decreases and then increases at the road surface, during which snow particles are deposited on the leeward side of the parapet and gradually spread over the entire road surface. As the airflow traverses the leeward side, the wind velocity progressively decelerates, reaching its minimum at the slope toe. Concurrently, the airflow induces vortex formation within a defined recirculation zone, resulting in substantial snow accumulation. Finally, as the airflow moves away from the embankment, the wind velocity gradually increases and reaches the initial value.

Figure 6

Figure 6. Wind velocity contours for embankments at different heights.

3.2 Embankment slope ratio

Considering that the slope ratio of the embankment has a large influence on blowing snow, a numerical simulation is carried out for five different slope ratios of embankments with a height of 5 m and a width of 41 m. According to the distributions of the wind velocity and flow field of embankments with different slope ratios, the moving airflow is most hindered at the windward toe and the leeward toe of the embankment, which is similar to the results of the analyses of the conditions with different embankment heights (Figure 7).

Figure 7

Figure 7. Wind velocity profiles for embankments at different slope ratios: (a) wind velocity profile (slope ratio: 1:1), (b) wind velocity profile (slope ratio: 1:2), (c) wind velocity profile (slope ratio: 1:3), (d) wind velocity profile (slope ratio: 1:4), (e) wind velocity profile (slope ratio: 1:5), (f) wind velocity profile (at the same height).

From the wind velocity flow field distribution in Figure 7, it can be concluded that the velocity flow field around the embankment changes the most at the toe of the slope, especially at the leeward toe of the embankment, where both airflow deceleration and vortex zones appear. While airflow acceleration occurs at the windward shoulder, the airflow decreases and then recovers in wind velocity as it passes through the road surface. As the slope ratio of the embankment increases, the range of near-surface wind velocity changes on the road surface gradually increases. Moreover, the airflow deceleration effect becomes more obvious, and the snow particles are hindered more when passing through the embankment. The computational results reveal that when the embankment slope ratios are 1:1 and 1:2, the wind velocities at the roadway centerline measure 3.24 m/s and 4.23 m/s, representing a 30.5% increase in the wind velocity under the gentler slope condition. Similarly, when the embankment slope ratios are 1:3, 1:4 and 1:5, the wind velocity at the center of the pavement increases by 59.8%, 78.1% and 94.7%, respectively, compared with that at the embankment slope ratio of 1:1. Therefore, as the slope ratio of the embankment decreases, the wind velocity of the airflow moving through the pavement gradually increases, and snow particles are less likely to be deposited.

When the slope ratio is 1:1, the embankment has a greater hindering effect on the movement of airflow, and many snow particles accumulate at the windward toe and the road surface (Figure 8). When the airflow passes the leeward side of the embankment, it enters the vortex region, causing flow reversal and subsequent deposition of wind-driven snow particles in this area. As the slope ratio of the embankment decreases, the disturbance caused by the embankment to the blowing snow gradually decreases, and the snow particles more easily pass through the embankment section, which reduces the snow accumulation on the embankment. Analysis of the snow deposition-erosion coefficient around embankments with varying slope ratios reveals distinct deposition patterns: significant snow particle accumulation occurs at the windward toe and slope face across all configurations, whereas shoulder areas exhibit minimal deposition. Notably, road surface snow accumulation increases proportionally with the embankment slope ratio. When the embankment slope ratios are 1:2, 1:3, 1:4, and 1:5, the average snow particle volume fractions on the road surface are reduced by 4.1%, 5.34%, 5.88%, and 6.97%, respectively, compared with those when the embankment slope ratio is 1:1.

Figure 8

Figure 8. Snow deposition-erosion coefficient for the embankment at different slope ratios.

In practical engineering, the impact of embankments on blowing snow and the amount of work required in the construction of embankments should be considered. Where the height of the embankment is determined, a gentle slope should be used as much as possible.

Figure 9 shows the wind velocity cloud map under different embankment slope ratios. As the embankment slope ratio gradually decreases, the wind velocity at the windward toe of the embankment increases slowly, which indicates that the change in the slope ratio does not have much effect on the wind velocity. However, the increase in the wind velocity at the road surface gradually increases, which leads to a reduction in snow accumulation on the road surface. Moreover, the airflow vortex area on the leeward side of the embankment gradually disappears, resulting in a gradual reduction in snow on the leeward side. Therefore, as the slope ratio of the embankment decreases, snow is less likely to form on the road surface and the leeward side of the embankment.

Figure 9

Figure 9. Wind velocity contours for embankments at different slope ratios.

3.3 Cutting depth

Figure 10 shows the distribution of the wind velocity flow field under different cutting depths, in which the slope ratio of the cuttings is 1:1, and the width is 41 m. An analysis of the wind velocity flow field at five different cutting depths (2 m, 4 m, 6 m, 8 m, and 10 m) reveals that the range of the airflow deceleration zone near the road surface gradually increases with increasing cutting depth. Moreover, the wind velocity decreases gradually.

Figure 10

Figure 10. Wind velocity profiles for cuttings at different depths: (a) wind velocity profile (depth: 2 m), (b) wind velocity profile (depth: 4 m), (c) wind velocity profile (depth: 6 m), (d) wind velocity profile (depth: 8 m), (e) wind velocity profile (depth: 10 m), (f) wind velocity profile (at the same height).

In the horizontal direction at a depth of 2 m, the wind speed decreases by 75.8% from the windward shoulder to the windward toe at a height of 2 m. The wind speed increases by 51.5% after passing through a 5 m wide snow platform. The wind speed increases by 51.5% after the airflow passes through a 5 m wide snow platform and increases by 82.9% until the top of the windward slope of the road embankment. Then, the wind speed starts to decrease and decreases by 12.6% when the airflow passes through the road surface and reaches the leeward shoulder of the embankment, and it decreases by 46.6% at the leeward toe compared with the leeward shoulder. Finally, the wind velocity continues to decrease when the airflow passes through the snow platform on the leeward side and the toe of the slope. However, it continues to increase during the climb along the leeward slope until it reaches a maximum value of 8.92 m/s at the top of the slope, which is an increase in the wind speed of 68.6%. In the vertical direction, when the depth of cutting is 10 m, compared with the depth of 2 m, the changes in the wind velocity at the same height (2 m from the surface height) at the windward shoulder, the windward toe, the foot of the windward slope of the embankment, the center of the pavement, the leeward shoulder of the embankment, the leeward toe, and the leeward shoulder are 48.7%, 30.2%, −1.5%, −86.5%, −78.6%, −95.7%, and −121%, respectively.

Therefore, as the depth of the cutting increases, the wind velocity of the moving airflow decreases to a minimum when it reaches the windward toe of the cutting, and then increases to a maximum at the windward shoulder. The increase in the wind velocity increases with increasing height of the road embankment. The wind velocity at the road surface decreases and then increases, whereas the wind velocity on the leeward side decreases because of the influence of the overflow section.

Snow particles are deposited mainly on the two sides of the snow platform and the road surface. The amount of snow on the leeward side of the snow platform is greater than that on the windward side of the snow platform (Figure 11). Owing to the increase in depth, the snow spreads slowly from the snow platform to the road surface until the center of the road. When the depth is 2 m, the range of the airflow deceleration area at the foot of the slope is limited, and the vortex strength is not large. Therefore, the airflow cannot carry the snow particles that have been deposited to continue moving. The road surface begins to accumulate snow; at this time, the average snow volume fraction of the cutting surface is 1.11. When the depth is 10 m, the average snow volume fraction of the road surface is 1.66, representing a 49.5% increase compared to the scenario with a 2 m cutting depth. As the depth of the cutting increases, the snow accumulation on the road surface becomes increasingly severe.

Figure 11

Figure 11. Snow deposition-erosion coefficient for the cutting at different depths.

Consequently, in regions prone to frequent blowing snow events, optimal cutting depths should be determined through field surveys and local snowfall pattern analysis. For highway construction, while excessive cutting depths should be avoided, appropriately widening snow deposition platforms at given cutting depths can effectively minimize snow particle accumulation in travel lanes.

The snow particles deposited on the surface as the material source of blowing snow will directly affect the amount of snow deposition, and the movement of the airflow as the power source of blowing snow is affected by different forms of cutting, which changes the flow field. Figure 12 presents the wind velocity contour plots under different cutting depths. For a given slope ratio, as the depth increases, the overall dimensions of the subgrade cross-section change. This leads to an expansion of the deceleration zones and vortex zones within the cutting, while the obstructive effect of the cutting on near-surface airflow becomes more pronounced. Therefore, as the depth of the cutting increases, more snow particles are deposited at the cutting slopes and road surface, aggravating the road’s snow hazard.

Figure 12

Figure 12. Wind velocity contours for cuttings at different depths.

3.4 Cutting slope ratio

Figure 13 shows the distribution of the peripheral wind velocity flow field under different cutting slope ratios, in which the depth of the cutting is 6 m and the width of the roadbed is 41 m. An analysis of the velocity flow field under four different cutting slope ratios (1:1, 1:2, 1:3, and 1:4) reveals that with decreasing cutting slope ratio, the snow accumulation on the road surface is relatively reduced, improving driving safety.

Figure 13

Figure 13. Wind velocity profiles for cuttings at different slope ratios: (a) wind velocity profile (slope ratio 1:1), (b) wind velocity profile (slope ratio 1:2), (c) wind velocity profile (slope ratio 1:3), (d) wind velocity profile (slope ratio 1:4), (e) wind velocity profile (at the same height).

When the slope ratio of the cutting is 1:1, the windward side of the cutting produces a wide range of airflow deceleration zones, and the wind velocity flow field of the road surface changes more obviously. The wind speed at a height of 2 m above the roadway centerline is measured as 4.28 m/s. Compared with the inlet wind velocity of 11.14 m/s, the slope ratio of the side of the steeper cutting is more obvious in terms of the deceleration effect of the wind velocity. When the slope ratio of the cuttings is reduced to 1:2, the horizontal wind velocity flow field in the cuttings significantly changes. The wind speed measured at a height of 2 m above the roadway centerline was 6.45 m/s, which is 50.7% higher than that at the 1:1 slope ratio of the cutting. When the slope ratio of the cuttings is reduced to 1:3, the wind velocity at the center of the road surface is 7.97 m/s, which is an increase of 23.1% compared with the slope ratio of 1:2. When the slope ratio of the cuttings is 1:4, the wind velocity at the center of the road surface reaches a maximum value of 8.31 m/s, which is 4.6% higher than when the slope ratio of the cuttings is 1:3.

Analysis of the experimental data reveals that reductions in the cutting slope ratio induce significant modifications to the internal velocity field for a given cutting depth. Concurrently, the influence of the cutting geometry on blowing snow dynamics progressively diminishes, resulting in accelerated near-surface wind velocities that increase snow particle transport efficiency across the roadway.

For different slope ratio, when the slope ratio is 1:1, the locations of the windward side and the leeward toe generate an airflow vortex zone and deceleration zone, which allows many snow particles to diffuse in the air to be deposited on the two sides of the snow accumulation platform (Figure 14). The snow volume fraction of the snow platform on the leeward side reaches 1.76. The snow particles are gradually deposited on the road surface under airflow, making it easy for the road surface snow to accumulate during cutting. When the slope ratio is 1:2, the snow accumulation is similar to that when the slope ratio is 1:1, but the amount of snow on the road surface is relatively low. In contrast, when the slope ratio is 1:4, significant amounts of snow particles are deposited on the windward side of the snow platform due to the snow platform, and the number of snow particles reaching the road surface continues to decrease. Therefore, as the slope ratio decreases, the amount of snow on the road surface during cutting decreases relatively.

Figure 14

Figure 14. Snow deposition-erosion coefficients for the cutting at different slope ratios.

4 Discussion

From a modeling perspective, this study employs the Eulerian-Eulerian two-fluid framework coupled with the standard k-epsilon turbulence model. This approach treats each phase as a continuous medium with distinct and independently resolved physical properties. The incorporation of turbulence effects allows for an improved prediction of vortex flows, thereby enhancing the overall simulation accuracy. The reliability of this model is evidenced by the strong agreement between our findings and established literature. The results collectively demonstrate that an increased embankment slope amplifies flow disturbance and expands the leeward vortex region (Li et al., 2021; Ma et al., 2021), and the effectiveness of gentler slopes in mitigating blowing snow impacts is confirmed (Liu et al., 2021a). Additionally, a suitably increased embankment height alleviates snow accumulation on the road surface (Qiu et al., 2022). Beyond the influence for embankment-related parameters, our results substantiate that the observed mitigating effect of a reduced cutting slope ratio in our study provides further support for the findings of Li (2022). Furthermore, it was found that appropriately reducing the cutting depth, under equivalent engineering constraints, can effectively alleviate snow accumulation on the roadway. In summary, subgrade parameters such as embankment height, cutting depth, and slope ratio indirectly influence the severity of blowing snow disasters by altering the wind field around the structure. For the blowing-snow-prone sections, it is recommended to appropriately increase the embankment height or reduce the cutting depth, combined with the application of gentler slopes. Given the current lack of systematic research on the influence of cutting parameters on blowing snow, the findings of this study provide a scientific basis for future investigations in this area.

While the current model demonstrates stable performance for the scenarios investigated, further in-depth research into model accuracy and applicability remains imperative. In validation-oriented numerical simulations, discrepancies between computational results and field data are inevitable, stemming from the inherent limitations of both modeling methodologies and measurement techniques. In actual blowing snow scenarios, complex terrain interactions and dynamic changes in wind direction and speed often introduce irregular inflection points in wind speed profiles, which may not be fully captured in simulations. Furthermore, the necessary simplifications applied to these complex multiphysics phenomena mean that certain intricate real-world interactions are not fully accounted for. To enhance model fidelity, two primary avenues for improvement are recommended. First, the dynamic feedback from evolving snow topography should be considered. The deposition and erosion of snow particles continuously alter the terrain around the embankment, which in turn modifies the airflow field. Employing dynamic mesh techniques or a multi-step coupling simulation—iteratively predicting snow redistribution, updating the computational geometry, and recalculating the flow—could better replicate the coupled “flow-snow morphology” effects observed in reality. Second, refining the snow phase model is crucial. Adopting a two-way coupling approach, where the airflow influences snow particle trajectory and the particles, in turn, exert momentum and energy feedback on the airflow (via drag and turbulence modulation), would significantly improve the accuracy for high-concentration blowing snow simulations.

5 Conclusion

Systematic investigations into the optimization of subgrade structures for mitigating blowing snow disasters remain limited. In response, this study analyzes the fundamental parameters of two typical subgrade configurations: embankments and cuttings. Numerical simulations are conducted at a reference wind velocity of 10 m/s to analyze the velocity fields and snow deposition patterns around the embankment and cutting models with varying cross-sectional parameters. The key findings are summarized as follows.

• For embankments, the leeward vortex length is positively correlated with height, and the vertical wind profile transitions from an “n”-shape below 20 cm to a height-invariant linear form above it. Higher embankments contribute to a reduction in both slope-specific snow accumulation and overall wind speed. Furthermore, the implementation of a gentler slope increases the wind velocity across the road surface, effectively suppressing snow deposition.

• For cutting structures, airflow develops an extensive deceleration zone featuring a “W”-shaped vertical velocity profile. Increasing the cutting depth from 2 m to 10 m decreases roadway wind velocity by 86.5% and raises the snow volume fraction by 49.5%. Additionally, employing a gentler slope (from 1:1 to 1:4) at a given depth increases wind velocity by 86.3% and reduces snow accumulation by 32.1%. The results demonstrate that adopting shallower depths in combination with gentler slopes constitutes an effective strategy for mitigating blowing snow disasters in cutting design.

• To verify the accuracy of the numerical simulation, numerical models with the same dimensions as the onsite embankment were established. Field monitoring and analysis of wind velocities at critical locations across embankments of heights of 1.3 m, 2.5 m, and 3 m demonstrated strong consistency in flow field distribution patterns and variation trends when compared with the numerical simulation results. The numerical simulation parameters have been demonstrated to be appropriately configured, effectively satisfying the requirements for blowing snow transport modeling.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

JL: Supervision, Investigation, Conceptualization, Writing – review and editing, Resources. ZH: Conceptualization, Writing – original draft, Methodology, Investigation, Formal Analysis. YW: Writing – review and editing, Validation, Resources. FW: Writing – review and editing, Data curation, Methodology. ZY: Writing – review and editing, Project administration.

Funding

The author(s) declared that financial support was received for this work and/or its publication. The research described in this paper was financially supported by the Key Science and Technology Project in Transportation Industry (2022-ZD6-090), the Xinjiang Transportation Science and Technology Project (2122-ZD-006), the 2021 “Unveiling and Commanding” Science and Technology Project of Xinjiang Communications Investment Group (ZKXFWCG2022060004), the Scientific Research Project of Xinjiang Transportation Design Institute (KY2023110701), Xinjiang Transportation Planning Survey and Design Institute Co., Ltd., and China Gezhouba Group Municipal Engineering Co., Ltd. The authors declare that this study received funding from China Gezhouba Group Municipal Engineering Co., Ltd. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article, or the decision to submit it for publication.

Acknowledgements

In completing this project, I would like to express my heartfelt gratitude to all those who have given me support and assistance. I would like to thank my graduate advisors who helped a lot during the data collection and experimental process. Without their assistance, I could not have successfully completed this project. I would also like to express my deep gratitude to my classmates who helped me to complete this article.

Conflict of interest

Authors JL, ZH, FW, and ZY were employed by Xinjiang Transportation Planning Survey and Design Institute Co., Ltd. Author YW was employed by China Gezhouba Group Municipal Engineering Co., Ltd.

The authors declare that this study received funding from Xinjiang Transportation Planning Survey and Design Institute Co., Ltd. The funder had the following involvement in the study: contribution to research design and support of publication activities.

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The author(s) declared that generative AI was not used in the creation of this manuscript.

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