An LES-based fragility methodology for low-rise buildings incorporating net wind pressure and debris-induced failures

Abstract

Roof systems in low-rise buildings are particularly vulnerable to wind loads, often sustaining severe damage during typhoons. Consequently, accurate hazard assessments are essential for risk mitigation. This paper presents an engineering-based fragility approach to evaluate typhoon-induced hazards on low-rise buildings. In this approach, peak wind loads are determined through Large Eddy Simulation (LES), thus avoiding inaccuracies associated with empirical formulas. The method also captures the relationship between wind loads and wind damage by incorporating windborne debris, both external and internal wind pressures, and the condition of the openings. A key advantage over existing models is its ability to assess the impact of building location and local construction features—such as eaves, parapets, and storm mitigation devices—on wind damage. As an illustrative example, this paper examines a group of buildings equipped with a typical storm mitigation device (spoiler). The results indicate that, in a regularly arranged building group, spoilers become more effective at reducing roof tile damage as the wind direction angle increases. Under lower wind speeds, spoilers on front-row buildings are the primary factor mitigating roof tile damage, whereas at higher wind speeds, spoilers on rear-row buildings have a larger influence. Additionally, for a regular arrangement, the spoiler’s ability to mitigate wind damage to building envelopes weakens as building density increases.

Keywords

fragility assessment wind damage flying debris low-rise building large eddy simulation

Introduction

Previous studies indicate that the structural components and accessories of low-rise buildings are particularly vulnerable to severe wind conditions. One key factor driving roof damage and failure is the intense suction generated within the separation bubble—formed when wind flow separates around sharp roof elements such as eaves and ridge corners (Lin and Surry, 1998).

Wind-induced loads acting on a building’s roof are profoundly influenced by local construction features, including eaves, parapets, and storm mitigation strategies. For instance, wind tunnel experiments by Li et al. (2018) demonstrated that adding spoilers can reduce local suction near roof corners by up to 90% for the mean value and 80% for the peak value. Kopp (2005) investigated various parapet configurations (e.g., partial or porous parapets, fences, and splitters) and showed that these can significantly alter roof wind pressure distributions. Additionally, Huang (2014) found that in wind tunnel tests comparing eight different eave designs, roof wind pressures varied by as much as 30% among the eave configurations. Beyond these local features, wind loads on low-rise buildings can also be markedly influenced by surrounding structures. Numerous studies report that buildings experience substantial increases or reductions in wind loads due to the Venturi and shielding effects, respectively (Dai, 2015; Li et al., 2017), making the positioning of a building within a group a key factor in its wind load characteristics.

For low-rise buildings, damage to envelope components is not only caused by high wind pressure but also by flying debris (damaged roof tiles) generated from upwind buildings (Lin, 2010). The relationship between wind pressure–induced damage and windborne debris–induced damage for building groups is complex. When doors and windows are damaged by flying debris, the internal pressure of the affected building increases. The higher internal pressure of damaged buildings increases the damage probability of roof tiles and generates more flying debris to impact downwind buildings, constituting a complex cascading effect. Consequently, the role of building location and local construction features in wind-induced damage warrants further exploration.

Recently, the engineering-based wind damage assessment methodologies based on the knowledge of wind–structure interactions and component capacities are proposed and more rigorous than the assessment methodologies based on the historical claims data. These methodologies model the failure of building components by comparing their resistance capacities with the corresponding wind loads. For instance, Yau et al. (2011) developed an integrated risk model to estimate structural damage and economic losses in clusters of residential buildings exposed to hurricane winds, while He et al. (2018) proposed a methodology to predict the progressive failure of low-rise buildings under wind–structure interaction, aiming at cost-effective design. Li et al. (2021) introduced a loss-assessment model for residential building groups under wind hazards by considering interference effects among buildings. However, these methods rely on wind load data derived from statistics or empirical formulas, potentially compromising accuracy and failing to account for construction variability and building location. Ji et al. (2021) develops a database-assisted probabilistic framework based on a simplified progressive damage process, to more realistically assess the wind hazard on a low-rise building with potential multiple openings. This database-assisted probabilistic method takes into account the correlation between roof wind pressures and improves the accuracy of the assessment, but still requires additional wind tunnel tests. Most importantly, this method cannot take into account the effect of wind-induced debris quantity on the damage probability of windows and doors of buildings in downwind areas. As a result, existing wind-damage vulnerability assessment methods are not well suited to evaluating how building location and local construction features affect wind damage severity.

This paper develops an engineering-based fragility approach for the assessment of typhoon-induced hazards on low-rise buildings. In the developed approach, the peak wind loads of the building are obtained by the LES method, thereby avoiding the potential inaccuracies of empirical formulas. Furthermore, the proposed approach captures the interplay between damage caused by wind pressure and debris by incorporating an indicator of the quantity of wind-induced debris. As an illustrative example, a group of buildings equipped with a typical storm mitigation device (a spoiler) is analyzed. The wind pressures and ensuing damage to these buildings under extreme wind events are predicted by accounting for interference effects and cascading failures. The mitigation effects of spoilers on wind pressure and wind-induced damage at different locations within the building group are also investigated.

Framework of wind-induced damage assessment

In this section, an engineering-based wind damage assessment methodology, including the determination of opening condition and peak wind load, and debris damage model, will be presented.

Building model and surrounding conditions

The model building used in this study is a two-story masonry residential structure with a gable roof, measuring 10.5 m in length and 7 m in width, featuring a 30° roof pitch. The eave height is 7 m, and the eave length is 1 m, as shown in Figure 1(a). The spoilers are installed on the eave and gable wall of the building, as shown in Figure 1(b). According to the design recommendation from Li et al. (2018), the width of the spoilers is 0.4 m. The spoiler body is parallel to the building roof, and the distance between the roof and spoiler is 0.4 m. The roof tile on the building is a typical flat tile in China, and its size and density ρ_rt are 0.3 m × 0.328 m and 3000 kg/m³, respectively. According to the design size of a single building, the whole roof of the building can be covered by 2178 roof tiles. In addition, the building model has 15 windows with a size of 1.5 m × 1.8 m and one glass door with a size of 1.5 m × 2 m. The spatial building density CA (hereafter, building density), shown in Figure 2 and defined as equation (1), is equal to 0.3 in this study. Additionally, the values of BB and DD are 5.78 m and 8.67 m, respectively.

C A = \frac{b d}{(b + B) (d + D)}

(1)

Figure 1.

Test model. (a) Sketch of the building (b) Building with spoiler.

Figure 2.

Arrangement of the building group.

Determination of peak wind load

In order to effectively evaluate the wind damage to envelope components, it is necessary to determine the peak wind load and compare them to the wind load resistances for various opening configurations. This study employs the Bernoulli equation to derive internal pressure for various opening scenarios and utilizes an improved Hermite moment model method, as provided by Liu (Liu et al., 2017), to calculate the peak wind load.

External wind pressure

This study employs the Large Eddy Simulation (LES) method to model the external wind pressure on buildings. The wall-adapted local eddy-viscosity model (LES WALE model), introduced by Nicoud and Ducros in 1999, is utilized to compute the subgrid-scale viscosity of the subgrid-scale models. The entire simulation process is conducted using Fluent software. The external wind pressure coefficient of the ith envelope component at time t is defined as

C_{p e, i} (t) = \frac{P_{p e, i} (t)}{0.5 \cdot ρ \cdot {U_{r e f}}^{2}}

(2)

Where ρ is the air density; U_ref is the velocity at the reference height; P_pe,i(t) is the area-average wind pressure for the roof tile, window and door at time t.

Internal wind pressure

The internal pressure within a building is generated by the local external wind pressures acting on its envelope openings. The Bernoulli equation (Oh et al., 2007; Oh and Kopp, 2014) is used to calculate the internal pressure. Assuming that there are M damaged doors and windows, the air motion at the ith (i = 1, 2, …, M) window or glass door can be expressed as

ρ l_{e, i} \ddot{x_{i}} + 0.5 ρ k_{i}^{- 2} \dot{x_{i}} | \dot{x} | = 0.5 ρ {k U}_{r e f}^{2} (C_{p e, i} (t) - C_{p i} (t))

(3)

where l_e,i represents the effective length of the air slug; κ_i is the discharge coefficient compensating for energy losses. The terms

x_{i}

{\dot{x}}_{i}

, and

{\ddot{x}}_{i}

refer to the displacement, velocity, and acceleration of the air motion at the ith window/door, respectively. C_pe,i(t) denotes the external pressure coefficient at the ith window/glass door, while C_pi(t) stands for the internal pressure coefficient. Given that the ratio of the opening area to the wall thickness is typically large, the frictional effects of air movement are neglected. In accordance with the principle of mass conservation, the continuity equation can be formulated as follows:

γ P_{a} \sum_{i = 1}^{M} a_{i} x_{i} = 0.5 ρ U_{r e f}^{2} V C_{p i} (t)

(4)

where P_a is the atmospheric pressure; γ is the ratio of specific heat capacity of air; a_i is the area of the ith window/door; and V is the building volume. By substituting equation (4) into equation (3), the internal pressure coefficient time series can be directly calculated.

Peak net wind pressure

After obtaining the external and internal wind pressure coefficients of the building, the net wind pressure coefficients time history of the ith envelope component can be calculated by

C_{p n, i} (t) = C_{p e, i} (t) - C_{p i} (t)

(5)

The peak net wind pressure coefficient C_npeak,i of the ith envelope component is obtained by the improved Hermite moment model method proved by Liu (Liu et al., 2017) as follows:

C_{n p e a k, i} = C_{n m e a n, i} - g \cdot C_{n r m s, i}

(6)

where C_nmean,i is the mean value of the net wind pressure coefficients C_np,i(t) over the sampling period, C_nrms,i is the standard deviation of C_np,i(t), and g is the peak factor. The peak net wind pressure of the ith envelope component can be expressed as

P_{n p e a k, i} = 0.5 ρ U_{r e f}^{2} \cdot C_{n p e a k, i}

(7)

Roof tile failure modeling

The roof structure of the building is shown in Figure 3. The flat tiles staggered lap each other supported by the rafters. A water-resistant saturated felt underlayment is rolled out between the roof tiles and rafter. Roof tile failure is defined to occur when the peak uplift force L_rt acting on the roof tile exceeds the sum of the roof tile gravity G_t and the resistance R_tp, as shown in Figure 4. Thus, the roof tile failure model can be expressed as

L_{r t} - (R_{t p} + G_{t^{'}}) > 0

(8)

L_{r t} = P_{n p e a k} \cdot a_{r}

(9)

where a_r is the area of the roof tile; G_t' = G_t∙cos α, and G_t is assumed to follow a lognormal distribution with a median of 1273 and a covariance of 0.05 according to Zhang et al. (2014). Furthermore, based on the roof slope and the action areas under the pressure from adjacent roof tiles, R_tp can be denoted as LN (ln (636.5), 0.05). R_tp is equal to zero when the adjacent roof tiles are damaged.

Figure 3.

Roof structure.

Figure 4.

Force analysis of the roof tile.

Window and door failure modeling

The failure of an individual window/glass door is assumed to be caused by either wind pressure loads or windborne debris impacts.

Wind pressure

The model for window/door failure, which is similar to the roof tile failure model, can be expressed as follows:

L_{w} - R_{w} > 0

(10)

where L_w is the peak wind load on the window/door; R_w is the resistance capacity of the window/door.

Windborne debris impacts

The debris risk analysis model proposed by Lin and Vanmarcke (2010) is used to assess debris damage risk to the windows and doors of group buildings. In this risk analysis model, the damaged debris landing positions are assumed to follow a two-dimensional Gaussian distribution, and its probability density function u (x,y) can be expressed as

μ (x, y) = 1 / (2 π σ_{x} σ_{y}) \cdot \exp [1 / 2 {{((x - m_{x}) / σ_{x})}^{2} + {(y / σ_{y})}^{2}}]

(11)

In the coordinate system of this model, x is the along-wind direction, and y is the across-wind direction. In addition, m_x is the mean value of the along-wind flying distance for damaged roof tiles, which is related to the 3-s gust wind speed. Here, σ_x and σ_y are the standard deviations of the along-wind and across-wind flying distances, respectively. Furthermore, σ_x is assumed to be a function of the 3-s gust wind speed, which can be expressed as σ_x = ηm_x, where η is assumed to be 0.35 based on the post-disaster damage survey of Twisdale et al. (1996). In addition, according to the observation of the debris trajectory variation in the along-wind and across-wind directions, see Lin et al. (2006), σ_y is assumed to be equal to σ_x. Then, based on Poisson random measure theory, the mean number of debris hits on windows can be expressed as

α (j_{w}) = \sum_{i = 1}^{I} v_{i} (j_{w}) = \sum_{i = 1}^{I} λ_{i} A_{j} μ_{i} (j) p_{i} (j_{w} | j) Φ_{i} (Z > ζ_{j_{w}} | j_{w})

(12)

where the subscript i is used to identify the properties of a building seen as a debris source and where j is used to identify the properties of a building considered an impact target. A_j denotes the area occupied by house j, and λ_i is the amount of debris generated from building i. Φ_i (Z>ζ_jw|j_w) is the probability of the debris horizontal momentum (Z) exceeding the window resistance (ζ_jw) when the debris object impacts the window. According to the wind speed and building model in this study, the typical debris impact momentum is assumed to be much higher than the window resistance. Thus, the probability Φ_i (Z>ζ_jw|j_w) = 1 for all cases. Here, p_i (j_w|j) is the probability of debris impacting the window, given that the debris impacts the target building.

In this model, the trajectory of all debris generated from all buildings is assumed to be independent, and the total number of debris impacts on window j_w of buidling j follow a Poisson distribution. Thus, the probability P (j_w,n) that j_w suffers a total of n debris hits is

P (j_{w}, n) = \frac{e^{- α (j_{w})} {[α (j_{w})]}^{n}}{n!}

(13)

The probability that there are no impacts on j_w is

P (j_{w}, n = 0) = e^{- α (j_{w})}

(14)

and the probability of debris damage to j_w is then

P_{D} (j_{w}) = 1 - e^{- α (j_{w})}

(15)

Identification of the debris source buildings

For any given building in the group, the potential debris sources under varying wind directions must satisfy two conditions:

(1) Debris only affects adjacent buildings and does not impact non-adjacent downwind structures. This is because, according to Lin’s wind tunnel experiments on debris trajectories (Lin et al., 2006), the specific shape and weight of the roof tiles in this study prevent debris from ascending during flight. Furthermore, all buildings in this case have the same height, meaning debris tends to be blocked by intervening structures and is therefore unlikely to reach non-adjacent ones. For instance, as shown in Figure 2, under a 45° wind direction, Building No. 9 can be impacted by debris from Buildings No. 5, No. 6, and No. 8, but not from Buildings No. 1, No. 2, No. 3, No. 4, or No. 7.

(2) Debris from a source building can only strike a target building if the angle between the wind direction and the vector connecting their geometric centers is less than 90°. This principle follows from Lin’s wind tunnel results (Lin et al., 2006), which indicate that debris primarily lands in a downwind direction. If the angle between the source-to-target vector and the wind direction is greater than or equal to 90°, debris rarely reaches the target building. For example, under a 45° wind direction (Figure 5), the angle between Buildings No. 7 and No. 5 is 78.69°, so debris from Building No. 7 may affect Building No. 5. Conversely, the angle between Buildings No. 3 and No. 5 is 101.31°, so debris from Building No. 3 is excluded. Based on this principle, the debris sources for Building No. 5 are Buildings No. 1, No. 2, No. 4, and No. 7.

Figure 5.

Debris sources around building no. 5 under a 45° wind direction.

Procedure of estimating vulnerability

In this wind-induced hazard assessment model, wind loads on the building are directly obtained through the use of the LES method, while accounting for uncertainties in material properties and flying object trajectories to determine the resistance of envelop components and the probability of flying debris impact, respectively. Thus, the Monte Carlo simulation was used to obtain the vulnerability of the buildings, and the procedure of this method is shown in Figure 6.

(1) Prior to the Monte Carlo simulation, the time history of the external wind pressure coefficients on a group of buildings under a particular wind direction were obtained using LES simulation. And the reference wind speed needs to be determined.

(2) The values of all resistance parameters (R_tp, R_w, G_t) are randomly assigned to the roof tile and windows/doors of each building according to the distribution function.

(3) Based on the wind direction and the spatial arrangement of the buildings (as shown in Figure 2), the buildings were ordered according to the sequence in which they are exposed to the airflow. This ensures that wind-induced debris generated by downwind buildings does not impact those located in the upwind area. For instance, under the 30° wind direction, the buildings were ordered as follows: No.1, No.2, No.4, No.3, No.5, No7, No.6, No.8, No.9.

(4) The buildings are evaluated sequentially according to their position relative to the wind direction. For each building, debris sources are identified using the method detailed in Section 2.4.3, and damage to windows and doors is then calculated using Equations (10) and (15). If windows or doors are damaged, the internal wind pressure coefficients are recalculated using Equations (3) and (4). This process is repeated iteratively until no further damage to windows and doors occurs. Next, peak net wind pressures are determined using equation (7), and roof tile damage is assessed accordingly. Finally, the number of wind-induced debris fragments is counted.

(5) After assessing the damage for each individual building, the total numbers of damaged roof tiles, windows, and doors across the entire building group are tallied, allowing the calculation of the overall damage ratios for each component type (tiles, windows, and doors) for the entire building group.

Figure 6.

Flowchart of the Monte Carlo simulation.

External wind pressure simulation

Computational domain and grid division

The computational domain is illustrated in Figure 7, with a length of 27.5H and a rectangular cross section measuring 15H in width and 8H in height. Here, H represents the scaled building height in the LES model, set to 0.48 m to reflect a 1:20 scale of the actual 9.6 m building height. To maintain a blockage ratio below 3%, the building model is positioned at a distance of 7H from the inlet boundary. For the wind field, the outlet and ground wall are treated with outflow and wall boundary conditions, respectively, while symmetry boundary conditions are imposed on the upper and lateral boundaries.

Figure 7.

Computational domain of simulation.

The hybrid grid method is used in this study to generate the mesh. The computational domain was divided into three parts, namely Flow Field 1, Flow Field 2 and Flow Field 3 shown in Figure 7. The interior flow field (Flow Field 2 and 3) uses an unstructured tetrahedral mesh, and the exterior flow field (Flow Field 1) use a structured hexahedral mesh, which can increase the efficiency of mesh generation. In order to more precisely simulate the wind field around the buildings, the grid density of the Flow Field 3 is increased, and the minimum grid size is set to 0.0002 m shown in Figure 8. The total number of grids in the model is around 8.5 × 10⁶.

Figure 8.

Grid meshing arrangement of the computational domain.

Inflow simulation

Achieving precise outcomes in Large Eddy Simulations (LES) necessitates the creation of a random inflow boundary flow field that adheres to predefined spatial correlations and turbulence features. To facilitate this, the narrowband synthesis random flow generator (NSRFG) introduced by Yu et al. (2018), was integrated as a UDF library in FLUENT software for generating the necessary inflow turbulence. In addition, adjustments were made to the turbulent boundary layer at the center of the model, using both the mean wind speed and turbulence intensity to align with the inflow velocity profiles associated with open country terrain, as detailed in the AIJ Recommendations for Loads on Buildings AIJ (2015). Figure 9(a) presents the longitudinal profiles of mean wind velocity U and turbulence intensity I_u at the center of the computational domain, positioned 7H from the inlet boundary, without a physical model in place. At the 10-m reference height, the observed longitudinal turbulence intensity I_u and reference velocity U_H are approximately 23% and 10.2 m/s, respectively. The measured mean velocity profile follows a power law with an exponent of 0.15. Solid and dashed lines in the figure correspond to the specifications for Terrain Category II (open country terrain) as outlined in the AIJ Recommendations (2015). The CFD simulation results for the turbulent boundary layer (TBL) show strong alignment with these AIJ guidelines.

Figure 9.

Power spectra and inflow profiles. (a) Inflow velocity profiles at the center of model (b) Power spectra in the longitudinal direction (c) Power spectra in the lateral direction (d) Power spectra in the vertical direction.

Figure 9 illustrates the power spectra of velocity fluctuations in the longitudinal, lateral, and vertical directions. In this figure, the variable f represents the frequency, while L_u, L_v and L_w refer to the longitudinal turbulence integral length scales in the respective directions. The black line represents the Karman-type spectrum. The CFD simulation results show lower power spectrum values compared to the Karman-type spectrum at higher reduced frequencies due to filtering effects. Nevertheless, in the lower reduced frequency range, the overall shape of the spectra closely aligns with the Karman-type spectrum, showing good agreement despite some deviations at higher frequencies.

Verification of the CFD simulation method

In this study, the accuracy of CFD simulations was assessed by comparing the simulated roof wind pressure with experimental data from wind tunnel tests (Li et al., 2018). The model dimensions and spoiler configurations, scaled at 1:20, are presented in Figure 1. The wind tunnel experiment simulated an open-terrain wind environment. Longitudinal mean velocity and turbulence intensity profiles, shown in Figure 10(a), were measured around the model. The mean velocity profile followed a power law with an exponent of 0.15. At the reference height of 10 m, the reference velocity U_ref and longitudinal turbulence intensity were approximately 9.3 m/s and 22%, respectively. Figure 10(b) compares the longitudinal wind spectrum at the reference height with the von Karman spectrum, showing strong agreement between the two.

Figure 10.

Wind condition of wind tunnel test. (a) Longitudinal mean velocity and turbulence intensity (b) Longitudinal wind spectrum at 10 m.

The wind pressure on the roof was converted into the dimensionless coefficient C_p = p/0.5ρU_ref², where ρ is the air density and p is the wind pressure. Here, C_p,mean denotes the mean wind pressure coefficient over the simulation duration, and the peak wind pressure coefficient, C_p,peak, was determined using the modified Hermite moment model (Liu et al., 2017). Figure 11 compares the numerically simulated mean wind pressure coefficients on the roof with wind tunnel data (Li et al., 2018), showing that the simulated results generally agree with the experimental measurements. Figure 12 presents a comparison of the simulated and experimentally measured peak wind pressure coefficients. At a 90° wind angle, the simulated peak pressures along the roof ridge and edges are slightly higher than those observed in the wind tunnel tests, which may be attributed to the filtering effect (Ricci et al., 2018) in LES that reduces turbulence energy (see Figure 9).

Figure 11.

The mean wind pressure coefficients on the building roof in the simulation and experiment. (a) Experiment data under 0° wind direction (b) Simulation data under 0° wind direction (c) Experiment data under 90° wind direction (d) Simulation data under 90° wind direction

Figure 12.

The peak wind pressure coefficients on the building roof in the simulation and experiment. (a) Experiment data under 0° wind direction (b) Simulation data under 0° wind direction (c) Experiment data under 90° wind direction (d) Simulation data under 90° wind direction.

To quantitatively evaluate the LES simulations, 20 measurement points were placed along both the eaves and gable walls, each 0.3 m from the roof edge (Figure 13). The peak wind pressures obtained from the LES at these points were compared with wind tunnel measurements, as also shown in Figure 13. The results indicate that for both 0° and 90° wind directions, the LES-calculated peak pressures closely match the wind tunnel data. The only exception appears at the roof corners, where the LES slightly overestimates the maximum peak pressure, but the discrepancy remains under 8%.

Figure 13.

The peak wind pressure coefficients at measurement points. (a) 0° wind direction (b) 90° wind direction.

Further verification of the LES method’s ability to predict peak wind pressures on a group of buildings was conducted using the wind tunnel test database (Aerodynamic Database) from Tokyo Polytechnic University (TPU). The building model and arrangement from the TPU database are illustrated in Figure 14. The test building and its surrounding structures share the same dimensions, and the spatial building density for the scenario is set at CA = 0.3. The experimental atmospheric boundary layer corresponds to Terrain Category III as specified by the AIJ guidelines AIJ (2004). Figure 15 compares the peak wind pressures obtained by LES with those measured in the wind tunnel, revealing that the distribution trends of peak pressures from LES closely follow the wind tunnel data. Moreover, the maximum peak wind pressure values from both methods exhibit strong consistency.

Figure 14.

Building model and Building arrangement of the TPU wind tunnel test. (a) Building model (b) Building arrangement.

Figure 15.

Comparison of the peak wind pressure coefficients on the test building of the building group in the Simulation and Experiment. (a) Experiment data under 0° wind direction (b) Simulation data under 0° wind direction (c) Experiment data under 90° wind direction (d) Simulation data under 90° wind direction.

In summary, despite minor discrepancies, the LES-calculated wind pressure distribution aligns well with experimental results, indicating that the CFD simulation approach employed here provides reliable predictions of wind pressure on the building.

Wind pressure on building group with spoilers

Based on the ASCE-7 standard (ASCE, 2010), the roof of the building model shown in Figure 16 is partitioned into 18 zones. The peak area-averaged wind pressures on these zones are calculated by the improved Hermite moment model method, as provided by Liu (Liu et al., 2017).

Figure 16.

Building roof partitions (δ = 1 m).

Due to the large number of buildings, only the peak area-averaged wind pressure coefficients for selected representative buildings (Buildings No. 1, No. 5, and No. 9) are presented. Figure 17 compares these coefficients for buildings with and without spoilers under wind directions of 0°, 30°, 60°, and 90°. The results clearly indicate that installing spoilers reduces the peak area-averaged wind pressures on these buildings to varying degrees. Specifically, notable reductions occur at the leeward ridge areas (Zones C, I, and O) at wind directions of 0° and 30°, with a maximum decrease of approximately 40% (Zone C of Building No. 1 at 30° wind direction). Additionally, the windward gable zones (Zones A, B, C, D, E, F, and G) exhibit substantial wind pressure reductions under 0° and 30° wind directions, with the maximum reduction reaching 43% at Zone A of Building No. 1 under the 90° wind direction. Taking into account the positioning of the buildings, the mitigation of wind pressure was significantly greater for the front row building (building No.1) than for the back row buildings (building No.5 and No.9), particularly for wind directions of 60° and 90°. It is noteworthy that the wind pressure at the windward roof of all three buildings increased after the installation of spoilers, but the increase was marginal.

Figure 17.

Peak area-averaged wind pressure coefficients for several buildings under change of wind direction (for CA = 0.3). (a) Wind pressure on the buildings under the 0° wind direction (b) Wind pressure on the buildings 30° wind direction (c) Wind pressure on the buildings 60° wind direction (d) Wind pressure on the buildings 90° wind direction.

To reveal the wind pressure variation on the roof of the group building more clearly, the wind pressure difference ΔC_p,peak(θ) is defined as

Δ C_{p, p e a k} (θ) = \bar{C_{p, p e a k} (θ)} - C_{p, p e a k} (θ)

(16)

where C_p,peak(θ) is the wind pressure coefficient on roofs after installing spoilers and

\bar{C_{p, peak} (θ)}

is the wind pressure coefficient on roofs without installing spoilers. When the wind pressure difference ΔC_p,peak(θ) is more than zero, the wind pressure on the roof as affected by the spoiler is higher than the original wind pressure. The wind pressure differences ΔC_p,peak(θ)on the roofs of group buildings under different typical wind directions of θ = 0°, 30°, 60° and 90° are shown in Figure 18. Spoilers significantly affect wind pressures at the roof-edge zones but exert minimal influence on interior roof zones. The mitigation effect strengthens as the wind direction angle increases. Under a 0° wind direction, the wind pressure on the windward eave and leeward roof slightly decreases, whereas interior roof zones experience a minor increase, with differences generally less than 1. At the 30° wind direction, the reduction is most substantial near the ridge zone, reaching a maximum of about 2 on Building No. 3. At a 90° wind direction, the primary reduction region shifts toward the windward gable wall area, with front-row buildings experiencing greater pressure reductions than those in the back rows; the maximum decrease reaches approximately 3.53. It is also noteworthy that, although spoilers slightly increase the wind pressure at the windward roof region, this increase remains modest (less than 0.6) compared to other roof zones (Figure 18). Consequently, the spoilers effectively mitigate peak wind pressures without creating additional areas of high vulnerability.

Figure 18.

Wind pressure difference ΔC_p of the building group with 9 sets of spoilers (CA = 0.3).

Wind damage of group buildings

The influence of mitigation device

The wind-induced damage to the buildings was evaluated under 17 distinct wind speed conditions, ranging from 10 m/s to 50 m/s in increments of 2.5 m/s. To reveal the influence of the spoiler on the envelope components failures of group buildings, the mean damage ratio of roof tiles (CM_RT) and the mean damage ratio of windows and doors (CM_WD) of all Monte Carlo simulations under different typical wind directions of θ = 0°, 30°, 60° and 90° are compared in this section.

The mean damage ratio of roof tiles (CM_RT) of the building group are compared in Figure 19. Results demonstrate that spoilers significantly mitigate roof tile damage, especially within the wind speed range of 20–40 m/s. Furthermore, the effectiveness of spoilers in reducing roof tile damage increases with the wind direction angle due to the stronger wind pressure mitigation effects at higher wind angles, as depicted in Figure 18. Under wind directions of 0°, 30°, 60°, and 90°, the maximum reductions in the roof tile damage ratio are 21%, 25%, 66%, and 62%, respectively. Notably, under a 90° wind direction, the roof tile damage ratio for buildings without spoilers remains nearly unchanged between 30 and 40 m/s, but rises sharply beyond 40 m/s. The reason is as follows: as shown in Figure 17(d), at a 90° wind angle, the peak wind pressure on the upstream building (Building No. 1) is significantly higher than that on the downwind buildings (Buildings No. 5 and No. 9). Consequently, for wind speeds of 0–30 m/s, all damaged roof tiles originate from the upstream building (Figure 20(d)). As the wind speed increases to 30–40 m/s, there is little to no change in the overall root tile damage ratio, because the upstream building’s roof tiles have already been destroyed, while the relatively lower roof pressure on the downwind buildings does not cause additional roof tile failures (also shown in Figure 20(d)). However, once the wind speed exceeds 40 m/s, the roof pressure on the downwind buildings increases, leading to additional roof tile failures there as well. Hence, the overall tile damage ratio for the building group rises sharply from 40 to 50 m/s (Figure 20(d)).

Figure 19.

Mean damage ratio of roof tiles (CM_RT) of the building groups. (a) 0° wind direction (b) 30° wind direction (c) 60° wind direction (d) 90° wind direction.

Figure 20.

The damage ratio of roof tiles (CM_RT) of the building No. 1, No. 5 and No. 9 for Case 1. (a) 0° wind direction (b) 30° wind direction (c) 60° wind direction (d) 90° wind direction.

A detailed comparison of the roof tile damage ratios for buildings in different rows (Building No. 1 in the front row, and Buildings No. 5 and No. 9 in the back rows) is presented in Figure 20. The results indicate that the roof tile damage ratios decreased significantly for both front-row and back-row buildings under wind directions of 0°, 30°, 60°, and 90°. Despite the fact that Figure 18 demonstrates greater wind pressure reductions for the front-row buildings compared to those in the back rows, the spoilers had a similar overall impact on reducing roof tile damage across all rows. Specifically, the maximum reduction in CM_RT of the front building (building No.1) and the back row buildings (building No.5 and No.9) can reach 80% and 85%, respectively. It is noteworthy that the wind speed interval corresponding to the maximum reduction in roof tile damage differs for the front (building No.1) and back row buildings (building No.5 and No.9). For the front-row building (No. 1), significant damage reduction was observed primarily within the 20–40 m/s wind speed range, while for the back-row buildings (No. 5 and No. 9), substantial reductions were observed at higher wind speeds of 30–50 m/s. This difference arises because, even after spoiler installation, the peak wind pressures on the front-row building remained higher than those on the back-row buildings (as shown in Figure 17), leading to earlier roof tile damage at lower wind speeds. Consequently, the spoilers are particularly effective in reducing roof tile damage on the front-row buildings at lower wind speeds and become more influential on the back-row buildings at higher wind speeds. Thus, the overall damage mitigation provided by spoilers is dependent on both building position and wind speed.

The total damage ratios of windows and doors, including the portion specifically caused by windborne debris, are compared in Figure 21. At wind speeds below 30 m/s, debris-induced impacts dominate window and door damage. However, as wind speeds increase beyond this threshold, direct wind pressure gradually becomes more influential. Since spoilers primarily mitigate roof wind pressures rather than wall pressures, their indirect effect on reducing window and door damage primarily arises from the decrease in windborne debris. Figure 21 illustrates a similar trend in the variation of window and door damage compared to roof tiles, although the magnitude of damage reduction is smaller, with a maximum reduction of around 14% occurring at a 30° wind direction.

Figure 21.

Mean damage ratio of windows and doors (CM_WD) of the building group. (a) 0° wind direction (b) 30° wind direction (c) 60° wind direction (d) 90° wind direction.

Figure 22 further explores the debris-induced window and door damage ratios for Buildings No. 1, No. 5, and No. 9. The window and door damage in downstream buildings is notably influenced by tile damage on their upstream neighbors. For instance, under a 0° wind direction, Building No. 1 shows minimal change in roof tile damage before and after spoiler installation, resulting in negligible impacts on window and door damage in Building No. 5. Conversely, when significant reductions in roof tile damage occur in Building No. 5 due to spoiler installation, Building No. 9 correspondingly experiences a substantial reduction in window and door damage. The wind speed range at which these window and door damage reductions occur is also lower for Building No. 5 compared to Building No. 9.

Figure 22.

The damage ratio of windows and doors (CM_WD) of the building No. 1, No. 5 and No. 9. (a) 0° wind direction (b) 30° wind direction (c) 60° wind direction (d) 90° wind direction.

Building group with different spatial building density

To reveal the influence of spoilers on the wind damage of the building groups with different building densities, the frequency distribution histograms of CM_RT and CM_WD under different building densities (CA = 0.1, CA = 0.3, CA = 0.6) are compared in Figure 23. The $\bar{x}$ and σ in the figure are the average value and standard deviation of the damage ratio, respectively. Results indicate that spoiler effectiveness decreases as building density increases. Specifically, the average roof tile damage ratio reductions for CA = 0.1, 0.3, and 0.6 are approximately 14%, 7%, and 5%, respectively. When the building density CA = 0.1, the frequency reduction of the buildings with more than 40% roof tiles loss reach a maximum, which is equal to 8%. However, the change in window and door damage ratio remains minor across different densities, consistently around 1%. Generally, the effects of the spoiler on reducing wind damage of the envelope components become weaker with increasing building density.

Figure 23.

The mean damage ratio of envelope components with different spatial building density. (a) CA=0.1 (b) CA=0.3 (c) CA=0.6.

Conclusion

The current study develops an engineering-based fragility approach for the assessment of typhoon-induced hazards on low-rise buildings considering wind pressure– and windborne debris–induced hazards, internal pressurization, and component failures. A regularly arranged group of nine residential buildings, equipped with storm mitigation devices (spoilers), was selected as the research object. The influence of spoilers on the wind pressure and wind damage of the regular arrangement building group was revealed. The conclusions of the investigation are as follows:

(1) The fragility assessment method proposed in this article can elucidate how local construction features and interference effects among buildings impact the vulnerability of buildings to wind disasters. By comparing the vulnerability calculation outcomes with building wind pressure calculation results, the findings obtained through the proposed vulnerability assessment method are shown to be consistent with established knowledge and rationality.

(2) For the regular arrangement building group, the reduction in roof tile damage ratio provided by spoilers becomes increasingly pronounced with greater wind direction angles, and the maximum reduction in the roof tiles damage ratio can reach 60% for the building group in this study. In addition, the roof tiles damage ratio of building group is mainly affected by the spoilers on the front row buildings under a lower wind speed, and affected by the spoilers on the back row buildings under a higher wind speed.

(3) For the regular arrangement building group, the effects of the spoiler on reducing wind damage of the envelope components become weaker with increasing building density. The reduction of the roof tiles damage ratio increases with decreasing building density, and the change in the windows/doors damage ratio is very small, around 1% under building density of 0.1, 0.3 and 0.6.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Dalian Minzu University Research Start-up Fund (Shi Gan)

ORCID iD

Shi Gan

References

Aerodynamic database for non-isolated low-rise buildings . https://www.wind.arch.t-kougei.ac.jp/_system/eng/contents_/code/tpu

Architectural Institute of Japan (2004) AIJ Recommendations for Loads on Buildings. Japan: Architectural Institute of Japan. (in Japanese).

Architectural Institute of Japan (2015) AIJ Recommendations for Loads on Buildings. Japan: Architectural Institute of Japan.

ASCE 7-10 (2010) Minimum Design Loads for Buildings and Other Structures. Reston, VA: American Society of Civil Engineers: Structural Engineering Institute. (ASCE 7–10).

Dai

Yan

Liu

(2015) Numerical simulation of interference effects of local wind pressures on roof of low-rise buildings. Journal of Natural Disasters 24: 224–233.

Pan

Cai

, et al. (2018) Progressive failure analysis of low-rise timber buildings under extreme wind events using a dad approach. Journal of Wind Engineering and Industrial Aerodynamics 182: 101–114.

Huang

Peng

(2014) Aerodynamic devices to mitigate rooftop suctions on a gable roof building. Journal of Wind Engineering and Industrial Aerodynamics 135: 90–104.

Zhang

, et al. (2021) Fragility assessment of typhoon-induced hazard to roof sheathing panels of low-rise building. Journal of Structural Engineering 147(7): 04021081.

Kopp

Surry

Mans

(2005) Wind effects of parapets on low buildings: Part 1. Basic aerodynamics and local loads. Journal of Wind Engineering and Industrial Aerodynamics 93(11): 817–841.

10.

Gan

, et al. (2017) Wind-induced interference effects on low-rise buildings with gable roof. Journal of Wind Engineering and Industrial Aerodynamics 170: 94-106.

11.

Gan

(2018) Wind pressure mitigation on gable roofs for low-rise buildings using spoilers. Journal of Structural Engineering 144(8): 04018104.

12.

Wang

Yang

, et al. (2021) Loss assessment of wind-induced damage for residential buildings groups based on engineering vulnerability. Journal of Building Engineering 42: 102435.

13.

Lin

Surry

(1998) The variation of peak loads with tributary area near corners on flat low building roofs. Journal of Wind Engineering and Industrial Aerodynamics 77–78(5): 185–196.

14.

Lin

Vanmarcke

(2010) Windborne debris risk analysis Part I. Introduction and methodology. Wind and Structures 13: 191–206.

15.

Lin

Letchford

Holmes

(2006) Investigation of plate-type windborne debris, Part I. Experiments in wind tunnel and full scale. Journal of Wind Engineering and Industrial Aerodynamics 94: 51–76.

16.

Lin

Vanmarcke

Yau

(2010) Windborne debris risk analysis Part II. Application to structural vulnerability modeling. Wind and Structures 13: 207–220.

17.

Liu

Chen

Yang

(2017) Estimation of peak factor of non-Gaussian wind pressures by improved moment-based hermite model. Journal of Engineering Mechanics, ASCE 143(7): 06017006.

18.

Nicoud

Ducros

(1999) Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow, Turbulence and Combustion 62(3): 183–200.

19.

Kopp

(2014) Modelling of spatially and temporally-varying cavity pressures in air-permeable, double-layer roof systems. Building and Environment 82: 135–150.

20.

Kopp

Inculet

(2007) The UWO contribution to the nist aerodynamic database for wind loads on low buildings: part 3. internal pressures. Journal of Wind Engineering and Industrial Aerodynamics 95(8): 755–779.

21.

Ricci

Patruno

Kalkman

, et al. (2018) Towards LES as a design tool: wind loads assessment on a high-rise building. Journal of Wind Engineering and Industrial Aerodynamics 180: 1–18.

22.

Twisdale

Vickery

Steckley

(1996) Analysis of Hurricane Windborne Debris Risk for Residential Structure. Raleigh: Technical report, Applied Research Associates, Inc.

23.

Yau

Ning

Vanmarcke

(2011) Hurricane damage and loss estimation using an integrated vulnerability model. Natural Hazards Review 12(4): 184–189.

24.

Yang

Xie

(2018) A new inflow turbulence generator for large eddy simulation evaluation of wind effects on a standard high-rise building. Building and Environment 138: 300–313.

25.

Zhang

Nishijima

Maruyama

(2014) Reliability-based modeling of typhoon induced wind vulnerability for residential buildings in Japan. Journal of Wind Engineering and Industrial Aerodynamics 124: 68–81.