Roof Snow Loads Research Articles

Simulation of roof snow loads based on a multi-layer snowmelt model: Impact of building heat transfer

Simulation of roof snow loads based on a multi-layer snowmelt model: Impact of building heat transfer

Extreme snowfalls and atmospheric circulation patterns in the Cantabrian Mountains (NW Spain)

This research examines the atmospheric patterns associated with damages caused by extreme snowfalls during a 115-year period, using newspapers as the source to document the events and performing then a synthetic damage index. Between 1900 and 2015 there was 180 days with personal and material damages due to snowfalls (without considering associated hazards as snow avalanches or landslides): Apart from the numerous material damages recorded, 60 people were killed and 254 injured. Advections from the north represented a 30% of damaging days (followed by cyclonic and northeastern) accumulating the greatest number of days in the highest deciles of damage, although cyclonic days were the most damaging ones on average. The analysis of data from five weather stations in the area, allowed to relate weather types with temperature and precipitation extremes, showing that northern and cyclonic types led to the lowest temperature and the highest precipitation. Both the number of events and the damage index decreased throughout the study period, with the most serious events (those that caused deaths and injuries) highly concentrated in the first half of the 20th century. This decrease trend is parallel to that observed in the frequency of two of the most damaging advections, northern and northeastern (responsible for a 46.7% of damage), which have gone from representing 7.3% of days before 1930 to 5.8% after 1990. Futhermore, the relationship between the NAO phases and the days of damage has been examined, noting that damages are less frequent and les intense during the NAO's positive phase. Finally, non-atmospheric drivers such as land-use intensity decline in rural areas and Spanish regulations on roof snow loads standards (initiated in the 1960s and refined subsequently, thus mitigating roof collapses and associated casualties), could have partially contributed to the decline in snowfall damage in the area.

Simulation and statistical analysis of ground snow loads based on a multi-layer snow accumulation and melt model

Ground snow loads, the study of which relies on the snowpack data from historical records of meteorological stations, are the basis of calculating the roof snow loads. In the absence of observation data, the snow accumulation and melt model, also called the snowmelt model, can be used to simulate the annual extreme samples of ground snow loads in each locality, and then the ground snow loads under a given recurrence interval can be obtained through probability analysis. In this paper, a multi-layer snowmelt model is used to input meteorological data such as precipitation, air temperature, wind speed, and relative humidity to obtain detailed information on the long-term snowpack, including snow density, snow depth, and snow water equivalent (SWE), which overcomes the problem of insufficient sample data for observed snow loads. Firstly, the precision of multi-layer snowmelt is checked through data of snow depth and SWE. Then, based on the model, meteorological stations in thirty-seven localities of six Chinese regions are selected to simulate the ground snow loads for nearly 60 years. Subsequently, the maximum snow depth and its occurrence time are compared, and the relationship between snow depth, snow density, and SWE in each region is analyzed. Finally, a variety of probabilistic models are used to calculate the ground snow loads at 50-year recurrence intervals. The goodness of fit of each probabilistic model for the snow loads sample is examined, and the calculated values of ground snow loads are compared with recommended values by the Chinese code. The results indicate that the snowmelt model can accurately reproduce the detailed process of ground snow events, which can be used to obtain the samples of ground snow load extreme. Due to gravity compaction, ground snow loads corresponding to the maximum depth in a certain year differ from the maximum ground snow loads in that year, which requires more attention. The goodness of fit is higher and the results are larger than the values of the code when generalized extreme distribution and logarithmic normal distribution are adopted to estimate extreme ground snow loads.

Numerical simulation of snowdrift on an air-supported membrane structure and response analysis under snow loads

The air supported membrane structure is a typical nonlinear flexible long-span space structure, the wind-induced drift and the resulting accumulation and distribution of snow particles on the structure may be the primary design concern among all loads in heavy-snowfall region. Thus, an accurate prediction of snow distribution on membrane surface is vital to structural design. A numerical simulation method is used to estimate snowdrift in this paper. Based on Euler-Euler method in multi-phase flow theory, this numerical model adopted Mixture model and combined with the snow deposition and erosion model, the snowdrift on an air-supported membrane coal shed is simulated, the distribution factor for roof snow load is given under different wind speed and different directions to estimate the worst load case, snow load on the air-supported membrane structure is significantly affected by snowdrift which causes significant non-uniform snow load. Furthermore, the response analysis of the air-supported membrane structure under snow load is studied, for comparison, uniform snow load case, non-uniform snow load case, and simulated snow load case under 0° wind direction are all considered. The results show that non-uniform snow load caused by snow drifting is more dangerous and should be considered.

Probabilistic study of snow loads on flat roofs considering the effects of wind at representative sites in China

Based on meteorological data, this paper simulates the evolution of ground and roof snow loads over time in winter. The snowmelt model is used to simulate the ground snow load, and the snow transport model is employed in cooperation with the snowmelt model to simulate the flat roof snow load. Through the simulations, samples of annual maximum ground snow loads, annual maximum roof snow loads, and ground-to-roof conversion factors for at least 60 years at 50 representative snowy sites in China are obtained. First, the statistical characteristics of the above samples are analysed. Then, the probabilistic models with different parameter estimation methods are used to fit the samples, and each model's goodness of fit is evaluated by using K-S test, Akaike information criterion (AIC), and Q-Q plot. The results show that the Generalized Extreme Value (GEV) distribution based on Maximum Likelihood Estimation (MLE) of parameters is the preferred probabilistic model for snow loads both on the ground and roofs. However, none of the models selected in this paper can accurately describe the ground-to-roof conversion factor. Therefore, this paper recommends using the R-year ground and roof snow loads obtained by the probabilistic model for calculating the ground-to-roof conversion factor. Finally, the ground-to-roof conversion factor is found to be quite scattered for the most of the studied sites, thus it could be more reasonable to use site-specific values estimated by the method proposed in this paper rather than a uniform value in consideration of safety and economy of the structure.

Physical-based model for exposure coefficient and its validation towards the second generation of Eurocode EN 1991-1-3 for roof snow loads

In standards for structural design, models for snow loads on flat roofs generally provide the basis for determination of snow loads on any roof shapes. They are typically derived from ground snow loads and the predicted effects of exposure of flat roofs primarily due to wind, often conveyed through the exposure coefficient. The paper provides background information on the revision of the model for exposure coefficient in the second generation of the Eurocode on snow loads on structures, prEN 1991-1-3:2020. With the aim to provide an easy-to-use procedure with a minimum amount of input data, but to cover the main physical phenomena, a new formulation is proposed in prEN reflecting up-to-date scientific findings and the model provided in ISO 4355:2013. The prEN model corrects the main deficiency of the model in EN 1991-1-3:2003 where no account for wind velocities expected at the site during a snow season is taken. The prEN formulation additionally requires information on mean wind velocity for the coldest month at the site, that is commonly easily accessible.The contribution starts off by introducing the prEN model. To validate the new model, a parametric study is presented, considering plausible ranges of the main parameters influencing the determination of exposure coefficient in Europe. The outcomes of the new simplified prEN formulation are then compared with an advanced theoretical model. The prEN model is further applied considering detailed meteorological data representative for various climates. The results obtained by the prEN provisions are critically compared with those based on the advanced theoretical model and meteorological data, and with the estimates of the models in ISO 4355:2013 and in the JCSS Probabilistic Model Code.The presented validation demonstrates that the prEN model reflects well typical European snow and wind climates. The model captures a clear decreasing tendency of exposure coefficient with an increasing mean wind velocity. Mean wind velocity in the coldest month of 4.5 m/s appears to provide a reasonable threshold to make distinction between normal and exposed conditions.

On extreme ground snow depth and ground snow load at Canadian sites

The roof snow load in the National Building Code of Canada (NBCC) is expressed as the sum of the snow and rain components. A probabilistic analysis of the components was carried out by using the recorded historical meteorological data. Probabilistic characterizations of the annual maximum ground snow depth SA, ground snow load SL, and snowpack bulk density were given. By considering the commonly adopted probabilistic models for SA, it was found that the use of the lognormal distribution, Gumbel distribution, and generalized extreme value distribution (GEVD) for SA is preferred for 46%, 35%, and 19% of the considered meteorological stations. A similar observation was made for SL. Snow hazard maps in terms of return period values of SA and SL were developed. Also, the hazard maps of (winter) rain load, SR, were developed. It was found that the correlation coefficient between SA and SR is negligible; the implication of this is discussed.

Field measurements of snowdrift characteristics on reduced scale building roofs based on the size effect study

Unbalanced snow distribution, which leads to an excessive snow load in a local area, is one of the main reasons for building collapses. The formation of uneven snowdrifts is closely related to the shape of the building as it seriously affects the turbulent structure and drifting snow process. Unfortunately, the design codes of different countries for applying snow load on building structures cannot give a clear explanation because of the discrepancies between them. Therefore, a series of reduced scale field measurements of snowdrifts on roofs were conducted to clarify such discrepancies. Firstly, the size effect of model scaling was investigated by observing snowdrifts around two models with a scale ratio of 1/2. The results show that the size effect has little influence on the snowdrift pattern on the premise of satisfying the similarity criterion. Thereafter, the snowdrift characteristics of two-level roofed and gable roofed buildings were explored and analyzed through the comparison with different national load codes and collapsed building cases. Overall, the provisions of the Chinese load code differ from the measurement results, which leads to an underestimation of roof snow load. ISO 4355 and Canadian NBC codes could give a better prediction of the snow load by comparison.

Probabilistic Assessment of Roof Snow Load and the Calibration of Shape Coefficients in the Eurocodes

In modern structural codes, the reference value of the snow load on roofs is commonly given as the product of the characteristic value of the ground snow load at the construction site multiplied by the shape coefficient. The shape coefficient is a conversion factor which depends on the roof geometry, its wind exposure, and its thermal properties. In the Eurocodes, the characteristic roof snow load is either defined as the value corresponding to an annual probability of exceedance of 0.02 or as a nominal value. In this paper, an improved methodology to evaluate the roof snow load characterized by a given probability of exceedance (e.g., p=0.02 in one year) is presented based on appropriate probability density functions for ground snow loads and shape coefficients, duly taking into account the influence of the roof’s geometry and its exposure to wind. In that context, the curves for the design values of the shape coefficients are provided as a function of the coefficient of variation (COVg) of the yearly maxima of the snow load on the ground expected at a given site, considering three relevant wind exposure conditions: sheltered or non-exposed, semi-sheltered or normal, and windswept or exposed. The design shape coefficients for flat and pitched roofs, obtained considering roof snow load measurements collected in Europe during the European Snow Load Research Project (ESLRP) and in Norway, are finally compared with the roof snow load provisions given in the relevant existing Eurocode EN1991-1-3:2003 and in the new version being developed (prEN1991-1-3:2020) for the “second generation” of the Eurocodes.

A novel snow transport model for analytically investigating effects of wind exposure on flat roof snow load due to saltation

This paper introduces a novel snow transport model for the analytical simulation of wind-induced snow transport on flat roofs. In the novel model, the differences between precipitation and deposited snow particles on roofs, including the differences in threshold friction velocity and fetch distance for saturated drifting state, are considered. Thus, snow drifting on a roof is divided into drifting without and during snowfall. The effects of terrain category and roof height are also considered using the friction velocity on roofs to compute snow transport rate instead of directly using the wind speed data reported by weather stations. Parametric analysis and case study are conducted to explain the novel model in detail and compare the results with those obtained from the model developed by O’Rourke et al. (2005). The estimated fetch distance for saturated snow drifting by the proposed approach in this study ranges from zero to thousands of meters, which is consistent with field measurement results and more reasonable than the use of constant values. Results of the case study indicate that the proposed snow transport model might be more reasonable because the effects of more factors are considered.

観測用建物モデルを用いた屋根雪荷重の実測 －その1: 計測概要と推定値との比較－

観測用建物モデルを用いた屋根雪荷重の実測 －その1: 計測概要と推定値との比較－

観測用建物モデルを用いた屋根雪荷重の実測 －その2 : 常時微動測定による振動特性の評価－

観測用建物モデルを用いた屋根雪荷重の実測 －その2 : 常時微動測定による振動特性の評価－

Optimising Monitoring: Standards, Reliability Basis and Application to Assessment of Roof Snow Load Risks

This paper addresses the optimisation of monitoring and decision-making criteria regarding the future use of structures. The current state of practice in standards and reliability framework are initially summarised. A general methodology for obtaining cost-optimal decisions is then presented on the basis of limit state design, probabilistic reliability analysis and cost estimates. The implementation of the risk-based approach is illustrated in a case study dealing with the roof of a stadium located in northern Italy. As the roof fails to comply with the requirements of the Eurocodes, the installation of a permanent monitoring system is recommended to allow for a real-time reliability assessment. The results demonstrate the potential of monitoring systems and probabilistic reliability analysis for supporting decisions regarding safety measures such as snow removal or temporary closure of the stadium, as well as reflecting the need to implement the discussed procedures in future standards.

積雪後の降雨に配慮した屋根雪荷重の評価に関する研究 －その5 特殊形状屋根の屋外実験－

積雪後の降雨に配慮した屋根雪荷重の評価に関する研究 －その5 特殊形状屋根の屋外実験－

積雪後の降雨に配慮した屋根雪荷重の評価に関する研究 －その６ 小型模型実験による軒どい排水性能と積雪後の雨荷重との関係について－

積雪後の降雨に配慮した屋根雪荷重の評価に関する研究 －その６ 小型模型実験による軒どい排水性能と積雪後の雨荷重との関係について－

積雪後の降雨に配慮した屋根雪荷重の評価に関する研究 －その７ 特殊形状屋根の室内実験－

積雪後の降雨に配慮した屋根雪荷重の評価に関する研究 －その７ 特殊形状屋根の室内実験－

積雪後の降雨に配慮した屋根雪荷重の評価に関する研究 －その８ 降雨による割増し荷重の建築基準への適用－

積雪後の降雨に配慮した屋根雪荷重の評価に関する研究 －その８ 降雨による割増し荷重の建築基準への適用－

Model for Snow Loading on Gable Roofs

AbstractA particularly large database containing simultaneous measurements of roof and ground snow loads were analyzed for the purpose of establishing a simple empirical model for gable roof snow loads. Due to the nature of the database, the model was developed specifically for unheated structures with nonslippery roof surfaces. As such, it is expected to provide conservative load estimates for heated structures and structures with slippery roof surfaces. The model results are compared to corresponding provisions for balanced and unbalanced snow loads in various United States and European codes and load standards.

熱・氷・水分・空気収支法による屋根雪荷重モデル

熱・氷・水分・空気収支法による屋根雪荷重モデル

Effects of wind exposure on roof snow loads

This paper presents results from an investigation of the suitability of the exposure coefficient as defined in ISO 4355 “Bases for design of structures—Determination of snow loads on roofs”, based on thorough analyses of weather data from 389 weather stations in Norway for the reference 30-year period 1961–1990. First, the background of the exposure coefficient is examined. Historical field investigations of snow loads on roofs are also evaluated. Next, values for the exposure coefficients in Norway are calculated according to ISO 4355. Finally, possible approaches aiming at improving calculations of wind exposure on roof snow loads are suggested. It is shown that the exposure coefficient as defined in ISO 4355 does not reflect the actual effects of wind exposure on roof snow loads in Norway, the main reasons being oversimplifications in the definition of the coefficient and the extreme variations of the climate in Norway. The definition is based on coarse simplifications of snow transport theories, and must be revised and improved to serve as an applicable tool for calculations of design snow loads on roofs in Norway.