Numerical Investigations of Snow Load Interference Effects on Multiple Arched Roofs Under Wind–Snow Coupled Actions

Abstract

Driven by the intensification of climate change, extreme snow events are becoming more frequent, posing significant risks to the safety of arched-roof structures. The combination of strong winds and heavy snowfall will cause localized snowdrifts that may exceed the safety design values in load codes. Such localized snowdrift phenomena even get worse under the action of mutual interference between buildings. To address this critical safety concern, this study employed a multiphase numerical model to evaluate interference effects on snow accumulation characteristics for grouped arched-roof buildings. Initially, the predictive accuracy of the numerical method was confirmed by comparing the results of a wind tunnel test. On the basis of full validation, a comprehensive numerical investigation was conducted to examine the snow redistribution patterns and aerodynamic interference effects among multiple arch-roofed buildings. Through analysis, the interference effect manifests as additional U-shaped snow accumulation on the windward surface of the disturbed arched roof, and specifically exhibits three distinct evolution stages of snow accumulation in relation to building spacing. Under adverse conditions, the disturbed snow load could increase by up to 1.4~1.5 times the fully exposed load, exceeding values specified in most design codes. Therefore, an amplification factor of 1.4 is recommended for the code-calculated fully exposed snow load to appropriately account for building interference effects.

1. Introduction

Global warming continues to intensify. This leads to more frequent extreme weather events, such as severe blizzards. As a result, engineering disasters are becoming widespread. Many buildings have collapsed under the weight of excessive snow accumulations [1]. For example, in 2008, a large-scale snow disaster in southern China resulted in damage to nearly 2 million buildings. In 2016, a snow disaster in Xinjiang Province destroyed nearly 900 houses. In 2018, heavy snowfall in multiple regions of central and eastern China led to the collapse of nearly 600 houses across five provinces. Among various architectural forms, arched buildings, characterized by curved geometry, face more complex stress conditions under snow loads. Such structures make them highly susceptible to damage from snow accumulations, thus becoming one of the most vulnerable types of structures during snow disasters. Meanwhile, in densely built-up urban environments, aerodynamic interactions between buildings become more significant. The presence of neighboring buildings drastically alters the flow field around a target arched building and further leads to more complex snowdrifts on rooftops, significantly increasing the risk of structural failures across multiple structures. Therefore, it is urgent to delve into the interference effects among arched buildings in urban environments on wind-induced snow drifting, summarize the snow distribution patterns, and enhance the resistance of arched structures to snow disasters.

Owing to the advantages of low cost and fast construction, arched buildings have found widespread applications in various warehouses, commercial establishments, and industrial facilities, etc. However, the vulnerability of arched roofs to snow load resistance has become increasingly pronounced, prompting a surge in scholarly interest aimed at clarifying the snow redistribution characteristics on such structures. Taylor et al. [1,2,3,4] conducted extensive field studies across multiple Canadian sites to record the snow accumulations on arched roofs. A substantial proportion of these observational snowdrift characteristics were incorporated into the modification of the Canadian NBCC load code [5]. Thiis et al. [6] carried out full-scale measurements of the snow distribution on a sports hall with an arch roof located in Oslo, Norway. The resulting measured snowdrift data had been widely utilized as a benchmark for the verification of simulation methods. Furthermore, Paek et al. [7] experimentally investigated the snowdrift patterns on a triple-span arched roof featuring wind-aligned eaves. The results revealed that the snow accumulation was significantly greater at the troughs compared to other locations on the structure. Liu [8] systematically explored the snow accumulation behavior on arched roofs through an examination of varying wind speeds and rise-to-span ratios, revealing that the uneven snow distribution patterns exhibit pronounced sensitivity at a higher wind speed and a large rise–span ratio. Wang et al. [9] employed the Immersed Boundary Method (IBM) to simulate the snow distribution on a simplified arched roof, effectively capturing the dynamic evolution of snow accumulation with time. Sun et al. [10] utilized Fluent software 15.0 to perform simulation analysis on the snow distribution characteristics and mechanical performance of a long-span membrane-structured curved roof at a toll station. Overall, scholars have successively employed field measurements, experimental studies, and simulation methods to conduct in-depth studies on the distribution of snow accumulation on arched roofs, proposing various calculation methods for snow loads on both single-span and multi-span arched roofs. However, existing studies predominantly focus on the distribution characteristics of snow loads on isolated arched-roof buildings in open terrains, overlooking the interferences of surrounding structures on the snow drifting conditions of target arched roofs.

To systematically assess the role of adjacent buildings in snow load redistribution, extensive studies have been conducted from diverse perspectives. Kwok et al. [11] combined field measurements with experimental techniques to characterize the snowdrift formation and mass flux rates in building clusters. Through field measurements of snow accumulation patterns around paired cubic models, Thiis [12] demonstrated that building sheltering effects significantly altered the critical wind velocity required for snow particle entrainment. Tsutsumi [13] gathered data on snow accumulations around a cluster of twelve buildings, which had been widely utilized by researchers to verify the precision of simulation approaches. Beyers et al. [14] applied dynamic mesh technology to simulate the snow drifting phenomena around three buildings, with a particular focus on the effects of interference on snow distributions. In addition to the studies on the influence of building interference on ground snow distributions, a limited number of scholars have turned their attention to the alterations in roof snow loads caused by such interferences. Yin et al. [15] classified four interference-induced snowdrift regimes that substantially affected flat roof snow loading characteristics. Despite thorough investigations into building interference effects on localized ground snow accumulations in recent years, studies examining the influences of surrounding buildings on roof snow distributions remain significantly limited. Actually, the source of roof snow is more easily disturbed by surrounding built-up environments, leading to significant changes in roof snow distribution patterns. However, existing studies primarily concentrate on snow load interference effects for flat roofs, with research focusing on arched roofs being conspicuously underrepresented. Notably, arched roofs exhibit inherent vulnerabilities in resisting unevenly distributed snow loads due to their distinctive structural characteristics, rendering them more sensitive to variations in snow load distribution. Meanwhile, the mutual interference effects among clustered arched structures will exacerbate the uneven distribution of snow.

To address the issue of disturbed snow loads caused by interference effects, various national load codes have introduced exposure coefficients for calculations [5,16,17,18]. However, the determination of disturbed snow load involves multiple influencing factors, such as local meteorological conditions, roof shape, and configuration of surrounding obstacles, etc. [16]. The relevant code provisions explicitly state that these coefficients only reflect the effect of wind-induced snow removal at a roof location without the consideration of the roof shape [16]. Furthermore, due to a lack of data, the determination of the exposure coefficient lacks a rigorous statistical basis, primarily relying on nominal values derived from flat roof scenarios, which greatly limits its accuracy [5,16]. Therefore, current load codes still face challenges, including insufficient foundational data and underdeveloped theoretical models in calculating snow loads of arched roofs under mutual interference. Furthermore, academic attention to disturbed snow loads on arched roofs also remains grossly inadequate, with very few related studies available. Given the weak foundation in the current load codes and academic research regarding the calculation of disturbed snow loads for arched roofs, this study aims to investigate the interference effects on snow loads of arched roofs within building clusters, clarify the influence of diverse building configurations on snow load distribution characteristics, and finally provide an amplification factor for calculating the disturbed snow load.

2. Validation of Simulation Method

2.1. Introduction of Simulation Method

The study of drifting snow in built-up environments primarily relies on three methodologies: field observation, wind tunnel experiment, and numerical simulation [19]. Field observation offers authentic and reliable data by directly measuring wind and snow conditions on roof surfaces. Wind tunnel experiment examines snowdrift patterns by simulating the drifting process on scaled building models, thereby uncovering the underlying transport mechanisms. Numerical simulation, leveraging the advanced computational power of computers, enables high-precision prediction of wind-snow interactions and their effects on roof structures. Field observation and wind tunnel experiment, while established as reliable research methodologies for acquiring practical data, present significant limitations in large-scale parametric investigations, particularly in terms of time, cost, and technology. In comparison, numerical simulation demonstrates distinct advantages, including enhanced flexibility, reduced costs, and superior repeatability, thereby facilitating a more comprehensive analysis of interference mechanisms. Currently, the numerical simulation methods primarily rely on the Euler–Lagrange framework [20,21,22] or the Euler–Euler framework [9,10,23]. In the Euler–Lagrange framework, snow is treated as discrete particles. By conducting a force analysis on these particles, the final snow accumulation distribution is derived. In contrast, the Euler–Euler framework treats the snow as a continuous phase and analyzes its distribution by solving the corresponding governing equations. Compared to the Euler–Lagrange framework, which demands substantial computational resources, the Euler–Euler framework offers lower computational costs, making it more suitable for studying snow load distribution on roofs at the building scale. Consequently, a Euler–Euler framework-based refined multiphase numerical model [15] was employed in this study as the primary investigative approach. The original multiphase model was established in the commercial software ANSYS Fluent 15.0.

The source of roof snow primarily consists of two distinct snow, i.e., free-falling snow due to snowfall and wind-driven drifting snow near roofs [24]. During blizzards, the falling snow, predominantly influenced by drag force and gravity, remains in a state of free motion. Conversely, near the roof surface, the drifting snow is primarily subjected to near-wall shear forces, overcoming both gravitational force and inter-particle cohesion, resulting in a saltation movement along the snow surface. Hence, the numerical model employed in this study incorporated separate governing equations for both the free-falling snow and the drifting snow, enabling a comprehensive simulation of snow distribution patterns on roof surfaces. Specifically, the numerical simulations conceptualized the multiphase flow as three distinct phases, i.e., air (or wind), free-falling snow and surface-transported drifting snow. Here, the air was treated as the primary phase to provide the main driving force, with the two snow types as the secondary phases. The governing equations, including both continuity and momentum conservation, were separately formulated for each phase (Equations (1) and (2)) [15]. The subscript “q” stands for the three distinct phases. Here, “air” represents the air phase, “sky” corresponds to snow particles in free fall, and “surf” refers to drifting snow that is transported along the surface. The parameters, α_q, ρ_q, and u_q, represent the volume fraction, density, and velocity vector of the qth phase, while p signifies the pressure. The symbol g denotes gravitational acceleration. The stress tensor associated with the qth phase is denoted by τ_q.

$${\displaystyle \frac{\partial }{\partial t}}({\alpha }_{\mathrm{q}}{\rho }_{\mathrm{q}})+\nabla \cdot ({\alpha }_{\mathrm{q}}{\rho }_{\mathrm{q}}{\mathbf{u}}_{\mathrm{q}})=0$$

(1)

$${\displaystyle \frac{\partial }{\partial t}}({\alpha }_{\mathrm{q}}{\rho }_{\mathrm{q}}{u}_{\mathrm{q}})+\nabla \cdot ({\alpha }_{\mathrm{q}}{\rho }_{\mathrm{q}}{u}_{\mathrm{q}}{u}_{\mathrm{q}})=-{\alpha }_{\mathrm{q}}\nabla p+\nabla \cdot {\mathbf{\tau }}_{\mathrm{q}}+{\alpha }_{\mathrm{q}}{\rho }_{\mathrm{q}}g+R$$

(2)

R represents the air-snow phase interactions. For different snow phases, R_air,surf and R_air,sky are, respectively, mathematically formulated in Equations (3) and (4) [25]. The coefficients K_air,surf and K_air,sky are utilized to signify the interphase momentum exchange between air and their respective snow phases. These coefficients can be computed using Equations (5) and (6) [25]. The term f denotes the drag function, which can be calculated by Equations (7) and (8) [25]. The Schiller-Naumann model [26] was employed to characterize the aerodynamic drag coefficient C_D, as it is well-suited for simulating snow transport processes, including creep, saltation, and suspension layers [27]. τ_surf and τ_sky signify the respective particulate relaxation times, d_surf and d_sky indicate the corresponding particle sizes. A_surf and A_sky represent the interfacial area concentrations.

$$R_{\mathrm{air},\mathrm{surf}}=K_{\mathrm{air},\mathrm{surf}}\left(u_{\mathrm{air}}-u_{\mathrm{surf}}\right)$$

(3)

$$R_{\mathrm{air},\mathrm{sky}}=K_{\mathrm{air},\mathrm{sky}}\left(u_{\mathrm{air}}-u_{\mathrm{sky}}\right)$$

(4)

$$K_{\mathrm{air},\mathrm{surf}}={\displaystyle \frac{{\rho }_{\mathrm{surf}}f}{6{\mathbf{\tau }}_{\mathrm{surf}}}}{d}_{\mathrm{surf}}{A}_{\mathrm{surf}}$$

(5)

$$K_{\mathrm{air},\mathrm{sky}}={\displaystyle \frac{{\rho }_{\mathrm{sky}}f}{6{\mathbf{\tau }}_{\mathrm{sky}}}}{d}_{\mathrm{sky}}{A}_{\mathrm{sky}}$$

(6)

$$f={\displaystyle \frac{C_{\mathrm{D}}{R}_{\mathrm{e}}}{24}}$$

(7)

$$C_{\mathrm{D}}=\left\{\begin{array}{ll}{\displaystyle \frac{24}{R_{\mathrm{e}}}}\left(1+0.15{R_{\mathrm{e}}}^{0.687}\right)& R_{\mathrm{e}}\le 1000\\ 0.44& R_{\mathrm{e}}>1000\end{array}\right.$$

(8)

During a snowfall, the snow exchange phenomenon, driven by snow erosion and deposition, occurs near the snow surface. Specifically, the erosional process enhances near-surface snow concentration, while deposition causes it to decrease. According to the study by Okaze et al. [24], falling snow particles were assumed to completely deposit, with a particle capture rate of 100%; drifting snow particles, on the other hand, were partially captured by the snow surface and deposited, while the rest continued to drift along the snow surface. The snow exchange process was numerically resolved through additional source terms in the phase-specific continuity equations, as illustrated in Equations (9) and (10) [15].

$${\displaystyle \frac{\partial }{\partial t}}({\alpha }_{\mathrm{surf}}{\rho }_{\mathrm{surf}})+\nabla \cdot ({\alpha }_{\mathrm{surf}}{\rho }_{\mathrm{surf}}{u}_{\mathrm{surf}})=S_{\mathrm{surf}}$$

(9)

$${\displaystyle \frac{\partial }{\partial t}}({\alpha }_{\mathrm{sky}}{\rho }_{\mathrm{sky}})+\nabla \cdot ({\alpha }_{\mathrm{sky}}{\rho }_{\mathrm{sky}}{u}_{\mathrm{sky}})=S_{\mathrm{sky}}$$

(10)

Source terms S_surf (for surface-transported drifting snow) and S_sky (for free-falling snow) are defined in Equations (11) and (12) [15]. q_ero characterizes the flux of snow erosion caused by wind, while q_dep-surf and q_dep-sky describe the deposition fluxes for the corresponding snow, respectively. h_sal represents the height of the saltation layer. These can be calculated using Equations (13)–(15) [15]. By introducing additional parameters, such as constant c_a, friction velocity u^*, threshold friction velocity u^*_t, drifting snow settling velocity w_f, and vertical velocity of free-falling snow u_sky-z, the variation in snow concentration could be accurately calculated. The final snow depth h_s is calculated as detailed in Equation (16), where T denotes the duration of snowfall.

$$S_{\mathrm{surf}}=\left\{\begin{array}{ll}-{\displaystyle \frac{q_{\mathrm{ero}}+q_{\mathrm{dep}-\mathrm{surf}}}{h_{\mathrm{sal}}}}& z\le h_{\mathrm{sal}}\\ 0& z>h_{\mathrm{sal}}\end{array}\right.$$

(11)

$$S_{\mathrm{sky}}=\left\{\begin{array}{ll}-{\displaystyle \frac{q_{\mathrm{dep}-\mathrm{sky}}}{h_{\mathrm{sal}}}}& z\le h_{\mathrm{sal}}\\ 0& z>h_{\mathrm{sal}}\end{array}\right.$$

(12)

$$q_{\mathrm{ero}}=\left\{\begin{array}{ll}-c_{\mathrm{a}}{\rho }_{\mathrm{surf}}{u}^{*}\left(1-{\displaystyle \frac{u_{\mathrm{t}}^{*2}}{u^{*2}}}\right)& u^{*}>u_{\mathrm{t}}^{*}\\ 0& u^{*}\le u_{\mathrm{t}}^{*}\end{array}\right.$$

(13)

$$q_{\mathrm{dep}-\mathrm{surf}}={\alpha }_{\mathrm{surf}}{\rho }_{\mathrm{surf}}{w}_{\mathrm{f}}$$

(14)

$$q_{\mathrm{dep}-\mathrm{sky}}=\left\{\begin{array}{ll}{\alpha }_{\mathrm{sky}}{\rho }_{\mathrm{sky}}{u}_{\mathrm{sky}-z}& u_{\mathrm{sky}-z}>0\\ 0& u_{\mathrm{sky}-z}\le 0\end{array}\right.$$

(15)

$$h_{\mathrm{s}}=\left({\displaystyle \frac{q_{\mathrm{dep}-\mathrm{sky}}}{{\rho }_{\mathrm{sky}}}}+{\displaystyle \frac{q_{\mathrm{dep}-\mathrm{surf}}+q_{\mathrm{ero}}}{{\rho }_{\mathrm{surf}}}}\right)\cdot T$$

(16)

2.2. Experimental Prototype

The accuracy of numerical simulations relies heavily on thorough validations. Full-scale measurement data serves as the most reliable prototype for validating simulation methods. However, the inherent challenges in acquiring comprehensive data elements (such as flow fields, properties of snow particles, and snow distribution, etc.) from field measurements, coupled with their susceptibility to environmental fluctuations (such as the instantaneous acceleration of wind speed and change in wind direction), significantly hinder the analysis of factors affecting prediction accuracy in simulation methods. In contrast, the scaled wind tunnel test has gained broader adoption among scholars for verification and analysis of simulation accuracy owing to its stable experimental environment and superior controllability. To this end, experimental data on snowdrift distribution over an arched roof were employed. The experiment was carried out in the “Simulator of Natural Action of Wind-Rain-Heat-Snow for Space Structures” at Harbin Institute of Technology, as shown in Figure 1. The facility features a refrigerated recirculating wind tunnel with meteorological simulation capabilities, including a snowfall generator for a low-temperature snowfall environment. An arched-roof building (with projected dimensions W₀ × L₀ of 20 m × 20 m, eave height H₀ of 5 m, and a rise-to-span ratio of 1:4) was selected. Based on meteorological records from 1981 to 2010 [28], the reference wind speed U_H at eave height was determined to be 9 m/s, following a power-law profile with an exponent of 0.15. According to the observations of snowfall events in Harbin, the snowfall intensity S_d was set at 9.38 kg/m²·h with a duration T of 5.5 h to represent typical snowfall conditions. To better reflect the movement of natural snow, the snow particles, aged for one month, were sieved and evenly distributed throughout the test section. Through measurements of the falling trajectories of sieved snow particles, the threshold wind speed during drift events, and the geometric shape of accumulated particles, as well as microscopic observation and weighing, the settling velocity, threshold friction velocity, angle of repose, particle size, and density of the experimental particles were sequentially determined. In addition, the primary parameter values for natural snow particles in this study were determined based on the continuous observation of snowfall particles conducted by the author’s team in Harbin from 2011 to 2024, combined with the characteristic parameters of natural snow reported in other previous studies [9,10,29,30,31,32]. The specific physical properties of both the experimental snow and fresh snow in the prototype are listed in

Table 1. Characteristics of both natural snow and experimental sieved snow samples.

Symbol	Parameter	Natural Snow	Sieved Snow
ρs (kg/m3)	Snow density	250 [29,30]	400
Ds (mm)	Snow diameter	0.5	0.3
u*t (m/s)	Threshold friction velocity	0.18 [9,10]	0.25
UTER (m/s)	Settling velocity of falling snow	0.6 [31,32]	0.8
β (°)	Repose angle of snow	50 [9,29]	40

.

Generally, the motion of snow particles is governed by drag force (related to particle size and relative velocity) and gravity (related to particle size and snow density), resulting in different transport regimes such as free falling or near-wall drifting. To accurately reproduce the snow movement on a full-scale arched roof within scaled wind tunnel experiments, appropriate similarity criteria were selected following Zhang’s snowfall-based methodology [33]. This criterion includes the fundamental requirements of geometric similarity, kinematic similarity, and dynamic similarity [34], which primarily focus on the dynamic similarity of falling snow particles under snowfall conditions. Its effectiveness in reproducing the snowdrift patterns on roof surfaces had been rigorously verified. Here, the scaled building model was constructed at a 1:50 scale, resulting in dimensions of 0.4 m lateral width, 0.4 m span, and 0.1 m eave height. Based on the acquired parameters related to the prototype and the experiment,

Table 2. Similarity number comparison between the prototype and scaled model.

No.	Similarity Number	Prototype	Scaled Model
1	${\displaystyle \frac{{\rho }_{\mathrm{a}}}{{\rho }_{\mathrm{s}}}}{\displaystyle \frac{U^2}{g{L}_0}}(1-{\displaystyle \frac{3.5v}{D_{\mathrm{s}}{u}_{\mathrm{t}}^{*}}}{\displaystyle \frac{U_0}{U}})$	0.002	0.002
2	${\displaystyle \frac{S_{\mathrm{d}}}{U_{\mathrm{TER}}}}$	15.6	12.5
3	${\displaystyle \frac{U_{\mathrm{TER}}T}{L_0}}$	0.17	0.20
4	${\displaystyle \frac{{\rho }_{\mathrm{a}}}{{\rho }_{\mathrm{s}}-{\rho }_{\mathrm{a}}}}{\displaystyle \frac{u_{\mathrm{t}}^{*2}}{g{D}_{\mathrm{s}}}}$	3.26 × 10−5	6.53 × 10−5
5	${\displaystyle \frac{u^{*}}{u_{\mathrm{t}}^{*}}}$	1.11	1.04

presents a comprehensive comparison of calculated similarity numbers between the prototype and the scaled model. Here, U₀ and U denote the threshold wind velocity and the wind velocity, respectively; ρ_a and ν are the density and kinematic viscosity of air, respectively; L₀ represents the reference length of the building. Similarity number 1 was employed to characterize the similarity in the trajectories of freely falling snow particles in the air. Similarity numbers 2 and 3 primarily focus on the similarity in total snowfall amount between the prototype and the experiment. Similarity number 4 represents the particulate Froude number, which characterizes the similarity in the transport process of drifting particles near the ground. Similarity number 5, on the other hand, guarantees the snowdrift pattern similarity by maintaining equivalent friction velocities between the prototype and model. Through comparative analysis, the calculated results of each similarity number for the prototype and the scaled model generally exhibit a high degree of agreement. However, it is noteworthy that the fitting result of similarity number 4 is slightly inferior to that of similarity number 1. Given that the aerodynamic interference between buildings primarily acts on the snow particles falling through the air, achieving more precise similarity in the motion of these falling snow particles is essential for thorough investigations into the disturbed snow loads. Through a comprehensive evaluation of these similarity number results, this scaled experiment theoretically demonstrates the capability to simulate realistic snow accumulation behaviors. Based on the calculation results, the experimental conditions were accordingly set: 1.6 m/s eave-height wind speed (index of 0.15 profile exponent), 10 kg/m²·h snowfall intensity, and 6 min duration. Leica MS60 laser scans enabled precise roof snow distribution quantification through coordinate data analysis.

2.3. Comparison of Results

As outlined in Section 2.1, the air-snow multiphase model employed in this study characterizes the spatial distribution of snow by solving separate governing equations for the air and snow phases. Within this air-snow coupled system, the airflow serves as the primary driving force governing snow particle motion. Consequently, accurate simulation of the building’s surrounding flow field is critical for reliable prediction of roof snow accumulation patterns. To ensure the validity of the numerical approach, this section firstly evaluates the predictive accuracy of the adopted turbulence model. The test data of the flow field around an arched-roof building was selected as the validation benchmark [35]. The test was carried out in a wind tunnel with a cross-sectional dimension of 0.5 m (width) × 0.5 m (height). The arched-roof model spanned the entire lateral width of the test section. Furthermore, the building model had an eave height H_e of 0.04 m, an apex height H_p of 0.063 m, and a streamwise span L_p of 0.12 m. A uniform inflow condition was adopted in the test, and the mean wind speed of the incoming flow measured at the eave height U_e was 0.32 m/s, with the turbulence intensity I_s controlled at 0.36%.

The computational domain was configured strictly according to the actual working conditions of the test, with detailed dimensions and boundary configurations illustrated in Figure 2. The building model was installed as a full-width blockage across the test section. Boundary conditions were set as follows: a velocity inlet for the upstream boundary, a pressure outlet for the downstream, and wall boundaries for all other surfaces. A structured grid system was employed for spatial discretization, featuring a minimum grid size of 0.002 m and totaling approximately 1,400,000 cells. Grid independence was verified through sensitivity analysis, demonstrating that further refinement would not significantly affect the solution accuracy. The inflow conditions were set according to the experimentally measured uniform flow parameters. For turbulence modeling, three kinds of models, i.e., the Standard k-ε model, RNG k-ε model, and Realizable k-ε model, were compared to evaluate their predictive performance.

Figure 3 compares the wind velocity profiles at the eave and apex positions along the central axis of the arched-roof model. The results show that the wind velocities predicted by various turbulence models almost coincide at the windward eave and apex positions, and are in consistent agreement with the experimental results. In contrast, near the leeward eave, the wind velocities predicted by the RNG and Standard k-ε models are slightly higher than the experimental values. By comparison, the wind profile calculated by the Realizable k-ε model exhibits better agreement with the experimental results. Figure 4 further compares the turbulent kinetic energy (TKE) profiles obtained by different turbulence models at the leeward eave. Due to the inherent limitations of RANS-based turbulence models, the TKE values predicted by all tested models are higher than the experimental values. However, the Realizable k-ε model demonstrates the smallest deviation from the experimental data, with particularly outstanding performance in the region near the roof. Overall, the Realizable k-ε model shows the best overall performance in reproducing the flow characteristics around the arched roof. Therefore, the Realizable k-ε model was finally selected to solve the flow problems around the multiple arched-roof buildings.

Based on the verified reliability of the turbulence model for flow field prediction, this section further assesses the accuracy of the multiphase model in predicting snow distribution. The numerical simulations were configured to match the scaled experimental conditions as illustrated in Section 2.2. The computational domain was constructed according to the test section dimensions with corresponding boundary conditions, as shown in Figure 5. The inflow boundary condition was configured as a velocity inlet to simulate the inflow of air-snow mixed flow, with the parameters the same as in the experiment. A structural grid system was adopted, featuring a first-layer height of 0.01 m (height of saltation layer [19]) and comprising approximately 600,000 total cells, as shown in Figure 6. Grid sensitivity analysis indicated that the simulation results of snow distribution reached a stable state under the current grid discretization condition. Snow particle properties followed the experimental parameters in Table 1. The validated Realizable k-ε model was employed to solve the turbulent structure around the building.

Figure 7 compares the contours of snow distributions on the arched roof obtained from simulations and experiments. The dimensionless snow depth was defined as h_s/h_s0, where h_s0 represents the snow depth values on open ground. Through comparison, the simulation accurately reproduces both the snow deposition at the windward eave and the extensive snow accumulation on the leeward side observed in experiments. Furthermore, significant snow erosion occurs at the roof apex under the action of high-speed winds. Overall, the numerical result shows good concordance with experimental measurements. Figure 8 offers an additional comparison of the snow depth values along the central vertical cross-section. The results show remarkable consistency between simulation and experiment on the windward side. However, the simulated snow accumulation on the leeward side is relatively less than the experimental result. This discrepancy likely stems from the simulation’s neglect of inter-particle cohesion effects on snow deposition. The cohesive force formed between deposited snow particles significantly restricts their ability to drift downstream and further slide off the roof. Unfortunately, no ideal solution currently exists for modeling cohesive forces between snow particles within the Euler–Euler framework. Despite the localized discrepancy, the simulation well reproduces the total snowdrift amount and peak snow depths on the arched roof, providing enough validation for the scientific validity and effectiveness of the adopted simulation methodology.

3. Interference Mechanisms of Snowdrifts on Arched Roofs

3.1. Fundamental Parameters

Within built environments, arched-roof structures are typically constructed in clustered configurations (paired or multiple units), with standalone structures being uncommon. This arrangement inevitably induces snow load interference effects between adjacent buildings. However, current load codes [5,16,17,18] only address such interferences by multiplying an exposure coefficient to the snow loads on isolated roofs, overlooking their influence on snow load distribution patterns. Consequently, this section systematically investigates the underlying formation mechanisms governing snow accumulations on common multiple-arched roofs under mutual interference conditions.

Here, two full-scale arched-roof buildings positioned in tandem alignment with the wind direction were selected as the targets, as shown in Figure 9. Both structures shared identical planar dimensions of 20 m (L) × 30 m (W) in projection, with a rise-to-span ratio of 1:4. The upstream interfering building featured a 10 m eave height (H₁), while the downstream disturbed building had a reduced eave height of 5 m (H₂). A longitudinal spacing (ΔL) of 10 m was maintained between the trailing edge of the upstream structure and the leading edge of the downstream structure. This configuration creates a sheltered wake region between the two buildings, enabling investigation of wind-snow interaction mechanisms in complex flow fields generated by building interference effects. The computational domain was established with dimensions of 16 L × 11 W × 6 H₁ (based on the building dimensions). To replicate realistic snowfall conditions, the inflow region and the upper boundary of the computational domain were designated as the velocity-inlet boundary conditions. The inflow wind velocity was set to 5 m/s at eave height [36], adopting a power-law exponent of 0.15. The incoming snow volume fraction was determined as 1.3 × 10⁻⁵, corresponding to field measurements from historical snow disaster events in Northeast China [36]. Snow particle properties were parameterized based on the observations in Harbin and previous studies, as discussed above. The falling/drifting snow particles were modeled with a density of 250 kg/m³ [29,30] and a representative diameter of 0.5 mm. The saltation layer was characterized by a particle settling velocity of 0.2 m/s [29] and a threshold friction velocity of 0.18 m/s [9,10]. A structured grid system was employed for spatial discretization, with the first-layer grid height optimized to 0.01 m. Furthermore, the snowdrift simulation on an isolated arched-roof building with an eave height of 5 m was conducted to compare the snow distribution changes before and after flow interferences.

3.2. Analysis of Interference Mechanisms

Considering the significant influence of airflow on roof snow distributions, Figure 10 provides comparative insights into flow behaviors around an isolated arched-roof structure in undisturbed flow conditions, as well as that around two tandem-arranged arched buildings. Here, positive values represent the wind velocity in the downwind direction, while negative values indicate the reverse flow. For the standalone arched-roof building, airflow accelerates progressively as it ascends the roof’s curved surface, reaching peak velocity near the roof apex. Post-apex, decelerating airflow follows the roof’s curvature, generating two separation vortices along both lateral edges. For tandem layouts, the low-speed wake only covers the downstream roof’s windward zone, creating a sheltered low-speed region. Notably, this wake effect diminishes toward the downstream roof’s apex, where flow characteristics revert to patterns comparable with the isolated building from the apex to the rear edge of the downstream roof.

Figure 11 compares the distribution characteristics of dimensionless friction velocities u^*/u^*_t and dimensionless snow depths h_s/h_s0 between an isolated arch-shaped roof and a downstream disturbed arch roof. Both parameters were normalized by the threshold friction velocity and open-ground snow depth, respectively. For the isolated arch-shaped roof, the incoming flow generates an extensive zone of exceeding friction velocities extending from the windward eave to the vicinity of the arch apex, with only localized low-friction-velocity regions persisting near the windward and rear eaves. This pronounced friction velocity gradient leads to a highly uneven snow distribution, manifesting as a characteristic half-span snow load pattern. In the presence of adjacent buildings, the upstream wake flow significantly alters the aerodynamic behavior of the downstream roof. A horseshoe-shaped low-friction-velocity zone forms in the windward region, replacing the high-velocity zone observed on the isolated roof. This flow field reconstruction not only alters the snow erosion pattern but also generates a “U-shaped snow deposition zone” on the downstream windward roof, highlighting the mutual interference effects of adjacent buildings on snowdrifts.

4. Influences of Building Arrangements

4.1. Influence of Height Differences

As discussed, the snow load distribution on an arched roof is primarily determined by its sheltering efficiency within the upstream wake flow. As this aerodynamic sheltering is highly sensitive to surrounding building arrangements, the present analysis systematically examines how variations in neighboring building’ height differences (ΔH) and spacings (ΔL) influence spatial deposition patterns. Regarding height differences, the eave height (H₂) of the downstream arched-roof building was maintained at 5 m for various working cases. Three distinct height differences (ΔH = H₁ – H₂) were examined: 0 m, 5 m, and 10 m, corresponding to the upstream building’s eave heights (H₁) of 5 m, 10 m, and 15 m, respectively. All other computational parameters remained consistent with those outlined in Section 3.1.

Figure 12 provides a comprehensive comparison of horizontal distribution of wind speed at the eave’s height of the disturbed roof, as well as the distributions of friction velocity and snow distribution, under various height difference conditions. Here, both the friction velocity u^* and snow depth h_s underwent normalization processing based on the threshold friction velocity u^*_t and the snow depth h_s0 on open ground, respectively. The aerodynamic influence of upstream buildings on snow deposition patterns over downstream arched roofs mainly manifests in the “U-shaped snow deposition zone” on the windward side of the roof. When the height difference ΔH between buildings is 0 m, the upstream wake fails to shelter the downstream roof, exposing its windward edge to high-speed airflow that accelerates from the eave to the arch apex, creating a half-span snow distribution pattern. Conversely, when the height difference ΔH exceeds 5 m, the upstream wake almost covers the windward half-span of the downstream arched roof, generating a circumferential low-speed zone along roof edges while preserving a localized high-speed zone near the arch apex. As ΔH increases, these high-speed zones contract, causing lateral snow accumulations to progressively extend inward from sidewalls toward the roof center. Furthermore, the normalized total snow loads, derived through integration of all snow depth data across various height difference conditions, show significant increases compared to that on isolated arch roofs, reaching 1.38, 1.46, and 1.40 times the undisturbed state values, respectively. These results clearly indicate that the mutual interference leads to substantial alterations in both the distribution patterns and magnitude of snow loads on arched-roof structures.

4.2. Influence of Building Spacings

To investigate the influence of building spacing, three distinct spacings (ΔL) were examined, i.e., 5 m, 20 m, and 50 m. The experimental configuration maintained an eave height (H₁) of 10 m for the upstream arched-roof building and 5 m (H₂) for the downstream building, resulting in a fixed height difference (ΔH) of 5 m. All other inflow conditions and building dimensions remained consistent with the previous settings.

Figure 13 illustrates the distributions of streamwise wind speeds across a horizontal cross-section at eave height of the disturbed building (upper part), along with the dimensionless friction velocities and snow accumulation patterns on disturbed arched roofs across varying inter-building spacings. As discussed in Section 3.2, the aerodynamic wake generated behind an arched-roof structure features two dominant vortices that extend longitudinally along the lateral edges, complemented by a smaller central vortex region. This distinctive flow promotes accelerated airflow recovery in the central zone, thereby amplifying wind-induced erosion on the roof’s midsection, while the sustained lower-speed flows along the periphery result in diminished snow erosion effects. As the inter-building spacing grows, the central wake region progressively detaches from the downstream roof surface, whereas the lateral vortex systems keep providing aerodynamic sheltering. This flow evolution triggers three phenomena: expansion of the high-speed zone near the roof apex, enhancement of snow particle entrainment, and subsequent leeward deposition along the eaves. The resultant flow modifications drive systematic growth of both the windward erosion zone and leeward peak snow depth, with the transition to a characteristic half-span snowdrift pattern at ΔL = 50 m, demonstrating complete attenuation of building interference effects and convergence toward isolated roof behavior.

5. Disturbed Snow Loads on Arched Roofs

5.1. Analysis of the Disturbed Snow Loads

To systematically examine the aerodynamic interference on snow distribution over arched-roof structures and develop a practical calculation method for structural design, an extended parametric analysis was conducted on snowdrift characteristics under various building arrangements, systematically examining the combined effects of height differences and building spacings. Here, three distinct height differences and seven building spacings were considered, as illustrated in

Table 3. Controlled parametric analysis of height difference (ΔH) and spacing (ΔL) effects on arched roof snow deposition.

Height Difference ΔH (m)	Building Spacing ΔL (m)
0, 2.5, 5	0, 5, 10, 20, 30, 40, 50

. The case where the spacing ΔL was set to zero represented the condition in which the affected building and the interfering building were in direct contact. This configuration was designed to facilitate a comparative analysis of incremental roof snow load variations under the condition of infinitely small spacing. All working cases maintained consistent geometric parameters. All buildings maintained consistent geometric parameters: 30 m lateral width (W), 20 m span (L), and a rise-to-span ratio of 1:4. The downstream building’s eave height (H₂) remained constant at 5 m across all cases, whereas the upstream building height (H₁) varied proportionally to achieve specified height differentials (ΔH). The atmospheric conditions were standardized with an average inflow wind speed of 5 m/s at the 5 m reference height. All other simulation parameters remained unchanged from those specified in Section 4.

Table 4. Normalized average snow depths on the disturbed arched roofs for all working cases.

	Spacing ΔL	0 m	5 m	10 m	20 m	30 m	40 m	50 m
Normalized Average Snow Depth
Windward side	ΔH = 0 m	0.74	0.48	0.44	0.14	0.02	0.01	0.01
	ΔH = 2.5 m	0.94	0.60	0.54	0.47	0.02	0.01	0.01
	ΔH = 5 m	1.07	0.66	0.58	0.53	0.09	0.02	0.01
Leeward side	ΔH = 0 m	1.21	1.23	1.24	1.21	1.22	1.23	1.23
	ΔH = 2.5 m	1.23	1.24	1.27	1.23	1.26	1.24	1.24
	ΔH = 5 m	1.26	1.24	1.27	1.26	1.27	1.26	1.25
Entire roof	ΔH = 0 m	1.00	0.85	0.84	0.68	0.61	0.61	0.61
	ΔH = 2.5 m	1.08	0.88	0.87	0.84	0.61	0.61	0.61
	ΔH = 5 m	1.12	0.91	0.89	0.87	0.63	0.62	0.61

systematically compares the average dimensionless snow depths on disturbed arched roofs under various working cases. Due to the significant differences in snow accumulation patterns observed between the windward and leeward sides of arched roofs, the average snow depth values for the windward half-span, leeward half-span, and the entire roof surface were specifically calculated and presented by averaging the snow depth data in the relevant corresponding regions. Through comparison, the average dimensionless snow depths on the leeward side exhibit high stability, and consistently maintain around 1.24, which are close to the baseline value of 1.23 under undisturbed conditions. This demonstrates the weak sensitivity of leeward snow distribution to disturbed flow fields. In contrast, the snow depths on the windward side show a distinct three-stage evolution process, categorized as the strong interference stage (ΔL < 5 m), platform fluctuation stage (5 m ≤ ΔL ≤ 20 m), and recovery stage (ΔL > 20 m). When the building spacing ΔL approaches zero, the sheltering effect of the upstream building on the downstream roof snow load reaches its maximum intensity. Under this extreme condition, the snow load on the windward side of the downstream roof substantially exceeds that observed at larger spacings. Moreover, as the height difference ΔH increases, the sheltering effect intensifies, with the average snow depth on the windward side rising from 0.74 (ΔH = 0 m) to 1.07 (ΔH = 5 m). In the common spacing range of 5 m~20 m (except for the case of adjacent equal-height buildings with ΔL = 20 m), the snow depth stabilizes around 0.6 with minor fluctuations, forming a pronounced platform stage. As the spacing exceeds from 20 m, the windward snow depth continues to decrease, fully recovering to the fully exposure state when ΔL reaches 30 m. The snow depth variation pattern of the entire roof shows high synchronization with that of the windward side. Its dimensionless snow depth forms a platform stage of 0.9 within the spacing range of 5 m~20 m and reaches the undisturbed critical spacing at ΔL = 30 m. Generally, within the common range of building spacing (ΔL = 5 m~20 m), the total snow load on the disturbed arched roof maintains relative stability. However, as the inter-building spacing decreases further, wind-driven snow particles from the upstream roof progressively accumulate on the windward side of the downstream roof, resulting in increasing snow loads. Consequently, in practical engineering applications, appropriate building spacing can significantly reduce the surcharged snow loads caused by interference effects.

5.2. Calculation Method of Disturbed Snow Loads on Arched Roofs

To account for the impact of interference effects on roof snow loads, load codes in various countries commonly employ an exposure coefficient C_e to modify the snow loads under different exposure conditions (e.g., fully exposure, partial exposure, and shelter). Taking the international load code ISO [16] and American load code ASCE [17] as examples, when normalized against the fully exposed condition (C_e = 0.8 for ISO code and C_e = 0.9 for ASCE code), snow loads under partial exposure conditions require an amplification factor of 1.1 (C_e = 0.9 for ISO code and C_e = 1.0 for ASCE code), while those under sheltered conditions demand a 1.3 factor (C_e = 1.0 for ISO code and C_e = 1.2 for ASCE code). However, current exposure coefficients are primarily determined based on research data of snowdrift removal rates on flat roofs. Given the multi-variable interference effects and the lack of systematic studies, this exposure coefficient system fails to provide accurate calculations for snow loads on irregular roofs such as arched structures. Therefore,

Table 5. Amplification factors for disturbed snow loads on arched roofs for all working cases.

	Spacing ΔL	5 m	10 m	20 m	30 m	40 m	50 m
Normalized Snow Depth
Entire roof	ΔH = 0 m	1.40	1.38	1.12	1.00	1.00	1.00
	ΔH = 2.5 m	1.45	1.42	1.38	1.00	1.00	1.00
	ΔH = 5 m	1.50	1.46	1.43	1.03	1.01	1.00

proposes the amplification factors for disturbed snow loads based on the computational results of snowdrifts on tandem-arranged arched-roof buildings. It should be noted that the cases with zero spacing (ΔL = 0) correspond to the multi-span arched roofs (ΔH = 0) and stepped roofs (ΔH > 0) as defined in the load codes [16,17]. For these standard roof configurations, the snow load can be determined directly using the prescribed shape coefficients in the code, without accounting for upstream interference effects. Consequently, Table 5 only presents the amplification factors for disturbed snow loads with exposure issues (cases with ΔL > 0). Defined as the ratio between the average snow load under each working condition and the undisturbed baseline, this factor corresponds to partially exposed condition in the load codes. Overall, disturbed snow loads on arched roofs can increase to 1.5 times the undisturbed state, stabilizing around 1.4 at the platform fluctuation stage of 5 m~20 m spacing. As the building spacing reaches 30 m, upstream interference effects vanish, and the amplification factor returns to 1.0. Based on these findings, the following design principles are recommended for arched structures. Firstly, determine the interference level of the target building based on the surrounding building spacing. For partial exposed environments with adjacent buildings within 20 m, it is suggested to apply a 1.4 amplification factor to the fully exposed snow load calculated by load codes to rationally consider snow load amplification effects caused by building interferences. Specifically, when the exposure coefficient C_e for fully exposed conditions is defined as 0.8 [16] or 0.9 [17], the corresponding coefficient C_e for partially exposed arched roofs should be amplified by a factor of 1.4. This adjustment yields modified exposure coefficients C_e of 1.12 (0.8 × 1.4) and 1.26 (0.9 × 1.4), respectively. When the distance between surrounding buildings and the target structure exceeds 30 m, environmental interference effects become negligible and can be excluded from engineering analysis.

6. Conclusions

This study examines the snow loading characteristics of multiple arched roofs under mutual interference. The numerical methodology was first validated against experimental data to ensure predictive accuracy. Comprehensive simulations were subsequently performed to investigate snow accumulation behaviors across multiple arched-roof configurations. The analysis revealed the fundamental interference mechanisms governing snow distribution on adjacent arched structures, systematically characterized the disturbed snow load patterns, and developed a calculation approach for determining snow loads on interference-affected arched roofs. The principal findings of this study may be summarized as follows:

• For arched-roof buildings arranged in tandem layouts, the wake vortices generated along the lateral edges of the upstream building establish a horseshoe-shaped low-friction-velocity zone within the originally high-friction-velocity region on the windward surface of the downstream arched roof. This flow modification leaves only a limited high-friction-velocity area near the arch apex. The resulting flow field reconstruction produces a distinctive U-shaped snow accumulation on the windward surface of the downstream roof, clearly demonstrating the significant interference effects between adjacent structures on snowdrift patterns.
• The leeward snow distribution on disturbed arched roofs exhibits remarkable stability, demonstrating strong anti-interference capability to flow field fluctuation. In contrast, windward snowdrifts demonstrate a distinct three-stage evolution with increasing building spacing, i.e., strong interference stage (ΔL < 5 m), platform fluctuation stage (5 m ≤ ΔL ≤ 20 m), and recovery stage (ΔL > 20 m). For the commonly encountered spacing range of 5 m~20 m in urban environments, the disturbed snow loads on arched roofs stabilize at approximately 1.4 times those in undisturbed conditions. Full recovery to the isolated state occurs when the spacing exceeds 30 m. These findings highlight the necessity of incorporating a larger amplification factor for snow load on multiple arched roofs, accounting for interference effects from adjacent structures.

This study has achieved certain results, but it still has the following limitations. In terms of the simulation method, insufficient consideration of the cohesive effects between snow particles led to a rearward shift in the simulated position of peak snow depth on the leeward side of the arched roof. Nevertheless, both the total snow accumulation on the roof and the magnitude of peak snow depth align generally with the prototype test result, indicating that this limitation has an acceptable impact on the core conclusions of this study. Additionally, the scope of this work is limited to investigating snow distribution patterns on two tandem-arranged arched-roof buildings. The snow distribution on roofs under different meteorological conditions (e.g., wind speed, wind direction, etc.) and building layouts (e.g., more adjacent buildings, height-to-spacing ratio, lateral adjacency, etc.) has not been systematically or thoroughly investigated. Future research will further refine the simulation methods and expand the scope of study to more deeply investigate the disturbed snow loads on arched roofs.