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Combined Probabilites of Peak Wind and Snow Load Events

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RESILIENT INFRASTRUCTURE
June 14, 2016
NDM-552-1
COMBINED PROBABILITIES OF PEAK WIND AND SNOW LOAD
EVENTS
Jill V. Bond
Rowan Williams Davies and Irwin (RWDI), Canada
Albert J. Brooks
Rowan Williams Davies and Irwin (RWDI), Canada
Scott L. Gamble
Rowan Williams Davies and Irwin (RWDI), Canada
Jan C. Dale
Rowan Williams Davies and Irwin (RWDI), Canada
ABSTRACT
structural design. Appropriate combination factors are provided based on the probability of failure due to the
simultaneous occurrence of the specified loads. Load Combination Cases 3 and 4 of Table 4.1.3.2.A include the
combination of wind and snow loads, which are transient in nature. The recommended combination factors are
intended to provide a uniform degree of reliability for design. However, in reality, the probability of the
simultaneous loading due to wind and snow depends on the local meteorological climate. This probability can be
more accurately simulated through the Finite Area Element (FAE) process, which studies the hour-by-hour
accumulation and depletion of snow based on historical meteorological records. It takes into account variables such
as wind speed and direction, temperature, humidity, water retention in a snow pack and many others. In the present
work, the accumulation and depletion of snow on a modelled ground patch and the corresponding wind speeds were
computed on an hourly basis to determine the correlation of wind and snow loads. Using this process, this paper
investigates the interaction between wind and snow loads for 25 distinct regions in Canada, for both ground and roof
1. INTRODUCTION
structural design. These factors are provided based on the probability of failure due to the simultaneous occurrence
of the specified loads, and are intended to be conservative enough to reliably encompass a variety of loading
scenarios that are expected to be encountered in practise. Load Combination Cases 3 and 4 of Table 4.1.3.2.A
include the combination of wind and snow loads, which are transient in nature and depend on the regional
meteorological climate. The load combination factors themselves, however, are the same across all regions.
This paper investigates the possibility that the simultaneous loading of wind and snow would depend on the local
meteorological climate and the wind exposure of the surface carrying the loads. This is done through the use of
sophisticated snow and wind load simulation tools, which are used to model climate-specific loads for various
loading scenarios on a building. Typically wind and snow loads are calculated independently, but by modelling them
simultaneously, it is expected that a great deal of refinement in the predicted loads can be provided to create a more
efficient and reliable structure.
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2. METHODOLOGY
Estimates of the snow loads for 25 locations across Canada were determined using the Finite Area Element (FAE)
method, and were combined with the hourly wind data as measured at local meteorological stations. The FAE
method simulates the hour-by-hour deposition, drifting, and melting of snow and absorption of rain and melt water
into a snow pack within a grid system that divides the roof into a large number of finite areas. Entire winters are
simulated on an hour-by-hour basis, including the cumulative effects of successive storms, drifting events and
melting periods. Specific methodology and applications of the FAE method are described in: Irwin and Gamble
1988 and Gamble et al. 1992. Both ground snow loads and roof snow loads for a generic building were modelled
using this method, and then analysed alongside the wind pressures for the same areas. These techniques are
described below.
2.1 Ground Snow Simulation
First, an isolated patch of ground for each region was simulated by using a single grid element with the FAE
method. To do this, the FAE simulation requires detailed hourly and daily meteorological data including wind speed
and direction, dry bulb temperature, rainfall, snowfall and cloud cover. The resulting time series of hour by hour
accumulation and depletion of snow was recorded for the entire period of record, which encompassed between 30
and 60 years of data, depending on the availability of data for each meteorological station. The peak annual snow
load maxima were plotted, and a Fisher-Tippet Type 1 fit was used to determine the 1 in 50 year mean recurrence
In addition to simulating ground snow, the effect of snow loading on a typical commercial building with large upper
and lower roofs and a step height of 3 metres was parametrically assessed. A 1:300 scale model of this building was
tested within a boundary layer wind tunnel using a standard suburban wind and turbulence profile to determine wind
velocities at various points on the building surface for drifting purposes. The orientation of the building was
evaluated for 16 equally incremented compass directions. This allowed for the investigation into the effects of local
climate, wind directionality and step orientations on snow accumulation and depletion. Further descriptions of this
parametric roof step model can be found in: Dale et al, 2014, Dale et al, 2015. The geometry and intent of this
model is similar to the scale model building used by Tsuchiya et al, 2002 for review of snow modelling tools on a
generic building roof step.
The FAE simulation method was then used to determine the area averaged snow loads on the upper roof and the step
region of the lower roof on an hour-by-hour basis, as well as the peak 1 in 50 year mean recurrence snow load value
as determined using the peak annual maxima and a Fisher-Tippet Type 1 fit. One building orientation was selected
for each meteorological station, which corresponded to the roof’s maximum sensitivity to the region’s prevailing
winds and climate. This was selected based on the ratio of upper roof area averaged snow load to the lower roof area
averaged snow load; a larger ratio indicates that the upper roof is generally more scoured of snow compared to the
lower roof. This also tends to result in a more significant lower roof accumulation.
Figure 1 Plan and elevation views of the parametric model building. Dimensions are given in full-scale
millimeters. Wind tunnel sensor locations indicated by the dark blue circles.
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2.3 Wind Pressure
Hourly wind speed records from each of the 25 meteorological sites within Canada were analyzed to determine the
expected 1 in 50 year mean recurrence wind speed using a Fisher-Tippet Type III fit. The hourly records and the 1 in
50 year wind speed were converted to equivalent wind pressures using Equation 1, where P is pressure, ρ is the
density of air, and V is the wind speed.
[1] P = ½ρV2
For the purposes of comparison, the wind loads on the building roofs were considered the same as those at the
ground for ease of analysis and to highlight the effects of variable snow load effects. Future work will include
specific roof wind loads for the geometry of the reference building.
2.4 Combining the Data
For each of the ground, upper roof and step region scenarios, the hourly snow loads were normalized to the scenario-
specific 1 in 50 year snow load value and the hourly wind pressures were normalized to the site-specific 1 in 50 year
wind load value. Thus, the hour by hour normalized snow loads and wind pressures can be plotted against each other
referenced to an equivalent return period.
3. COMBINED WIND AND SNOW LOAD FACTORS
3.1 Ground Snow Simulation All Meteorological Stations
Figure 2 presents the normalized snow loads versus normalized wind pressures including data for all 25 unique
meteorological sites within Canada. Each data point within the plot corresponds to the simulated wind and snow
load at one hour within the time series, for a total of 1227 years and 10 748 520 hours.
To allow for the direct comparison of wind and snow loads, the combination factors recommended within the NBCC
were factored from the ultimate limit state design (Equation 2 and 3) to a limit state value equivalent to 1 in 50 year
mean recurrence interval (Equations 4 and 5):
[2] Ultimate State Design: 1.5 S+0.4W
[3] Ultimate State Design: 1.4 W+0.5S
[4] Limit State Design: 1.0S +0.285W
[5] Limit State Design: 1.0W +0.33S
Each of these loading combination factors have been overlaid on Figure 2. As can be seen, a number of data points
for both wind and snow loads lie beyond a value of 1, indicating a mean recurrence interval beyond the 1 in 50 year
return period. This is expected for a data set consisting of a long period of record with some events above the
desired return period. Noting that the plot in Figure 2 contains in excess of ten million points, the data reveals that
only a small number of simulated events fall outside the point recommendations provided by the NBCC. This
implies that the code provides a reliable, conservative estimate of the joint probabilities, as one would expect from a
code intended for use by the engineering community at large.
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This time series approach to tracking the snow accumulation with a corresponding wind load allows us to see how
these variables interplay. For example, one may assume that the point of greatest interest is the largest value within
the desired return period. However, this may not necessarily be the case, as the net load effect on an actual structure
of these coincident factors depends on a multitude of variables such as wind direction, geometry of the building and
the distribution of snow which is the result of the preceding meteorological events. Thus, a load combination
maximizing a particular load effect could be any combination of wind and snow within a range appropriately
described by a function that encompasses data points corresponding to the desired return period. Determining this
function is challenging, but may be notionally described by a function that encompasses all but say 2% of the data
points within the normalized return period, thus corresponding to approximately the 50 year mean recurrence period.
Future work is recommended to further refine the interpretation of this data to a more usable generalized format over
the time series approach currently used by the authors.
3.2 Meteorological Climate and Load Case Specific Combinations
Hourly time series of load combinations are presented for three cities within Canada: Halifax, Toronto and
Vancouver. These cities were selected because they have different meteorological climates which produced different
trends in the presented data.
3.2.1 Combined Load Factors - Halifax Meteorological Climate
Normalized ground snow loads and coincident normalized wind loads using meteorological data recorded at
Shearwater Airport in Halifax from 1953 through 2006 can be seen in Figure 3. Each data point corresponds to a
single hour of time within the period of record. The corresponding peak annual maxima and Fisher-Tippet Type 1
fit can be seen in Figure 4, which was used to calculate the 1 in 50 year snow load. As can be seen within the data,
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the peak snow loads typically occur in April, however many of the peak wind loads that occurred simultaneously
with moderately high snow loads occur early to mid-winter. In fact, some of the highest wind load events occurred
during the winter in January and February. Review of the distribution of the data within Figure 3 indicates that the
general trends in the data are similar to those presented in Figure 2.
A dramatic shift in the simulated wind and snow load values becomes evident when values are derived on a building
geometry and load case specific basis using the parametric building model previously described. Figure 5 presents
data from the exposed upper roof of the building, and as a result is generally well exposed to wind and subsequent
snow scour. Figure 6 presents data from the lower roof of the building including the roof step region, where snow
from the upper roof is typically redistributed.
The comparison between the exposed and sheltered roof steps indicates a significant shift in combined wind and
snow factors, in addition to a shift in time as to when they typically occur. For example, combined factors typically
peak in February and March on the exposed roof step. This is evident by the lack of peak snow load events later in
spring as is commonly seen within Canada, and due to the extreme event that is beyond the 1 in 50 year mean
recurrence interval that appears in the extreme value fit (right image in Figure 5) that is not present within the
ground snow simulation, nor within the sheltered roof scenario. This indicates that the Halifax region is susceptible
to significant single snowfall events.
In the sheltered scenario, accumulations typically build over a prolonged period of time and peak late in the winter,
typically in March and April. As snow is present for a longer period of time there is a greater probability of a
coincident high wind speed event, leading to a significantly higher shift in the combined wind and snow load factors
when compared to the exposed roof scenario.
Figure 3 Normalized snow load vs. normalized wind load as recorded at Shearwater Airport in Halifax from 1953
through 2006.
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Figure 4 Annual ground snow load maxima for Shearwater Airport from 1953 through 2006 using a Fisher-Tippet
Type 1 fit.
Figure 5 Hour-by-hour area averaged roof snow loads for an exposed roof (left) and corresponding annual maxima
for Shearwater Airport from 1953 through 2006 using a Fisher-Tippet Type 1 fit (right).
Figure 6 Hour-by-hour area averaged snow loads for a sheltered roof (left) and corresponding annual maxima for
Shearwater Airport from 1953 through 2006 using a Fisher-Tippet Type 1 fit (right).
###-7
3.2.2 Combined Load Factors - Toronto Meteorological Climate
Load combination factors simulated using 62 years of meteorological data (1953 through 2015) from Pearson
International Airport in Toronto illustrate a trend observed within the larger data set of locations analyzed. As seen
in the Halifax data, a distinct shift in the data is seen between the ground snow, and the exposed and sheltered roof
loading scenarios. Unlike within the Halifax dataset, the seasonal distribution of peak snow load and wind data
points are more uniformly distributed. This indicates that the Toronto meteorological climate may be less prone to
significant single event snow accumulations, or there is less wind and resulting snow scour, indicating a lower
exposure factor on upper roof surfaces or a combination of both.
Similar to the data presented in Figure 6, the data plotted within Figure 8 indicates a greater frequency of significant
snow accumulation present on the lower sheltered roof throughout the winter as there is an upward shift in the
coincident wind load data compared to the exposed roof.
Figure 7 Normalized snow load vs. normalized wind load as recorded at Pearson International Airport in Toronto
from 1953 through 2015.
Figure 8 Simulated area averaged exposed roof snow load (left) and sheltered roof snow load (right).
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3.2.3 Combined Load Factors - Vancouver Meteorological Climate
Review of data from Vancouver International Airport from 1953 through 2012 indicates that load combination
factors within the NBCC may contain a great deal of conservatism. The trends in these figures are the result of the
meteorological climate of Vancouver where peak snow loads are often the result of a single snowfall event. The
limited difference between the distribution of wind and snow load data points in the exposed and sheltered roof
cases indicates that this climate is not as conducive to snow drifting and redistribution as those previously described.
This is the result of the warmer, wet climate of Vancouver leading to snowfall which is less susceptible to drifting,
and due to cyclical ambient air temperature that tend to melt accumulations relatively soon after the precipitation
event. These typical meteorological characteristics will limit the probability that a wind event of significance will
occur when snow is present. In these scenarios, significant reductions in the load combination factors recommended
by the NBCC are possible.
Figure 9 Normalized snow load vs. normalized wind load as recorded at Vancouver International Airport from
1953 through 2012.
Figure 10 Simulated area averaged exposed roof snow load (left) and sheltered roof snow load (right).
###-9
4. SUMMARY OF FINDINGS
As described within this paper, the simulation of the hour by hour accumulation and depletion of snow load on a
ground snow patch and roof allows for the detailed analysis of combined snow and wind load probabilities. The
conclusions drawn from this work include:
1. The combined probabilites of a peak snow and wind load are dependent on the meteorological climate of a site as
evidenced by the wide range of snow and wind load data points between simulations illustrated for Halifax,
Toronto and Vancouver meteorological data sets.
2. Wind and snow load combination factors are influenced by the building geometry. Differences in these factors are
the result of building specific variables such as geometry, but also the interaction of these variables to the
meteorological climate and are therefore not considered mutually independent. As seen when comparing the
Halifax and Toronto meterological data sets, combination factors for the exposed upper roof are a funciton of
the climate, as some loading scenarios become more sensitive to specific climatic conditions, such as large
3. The NBCC recommended load combination factors are likely conservative for some meteorological climates such
as Vancouver.
4. In addition, the NBCC recommended load combination factors may be conservative for a number of building load
cases, such as on exposed roof surfaces. Additional investigation into the load effect of the combined wind and
snow loads may be required to investigate the reliability of the combination factors for load cases where snow is
present over greater periods of time.
5. Advances analysis techniques, such as what were used within this paper can be used to better understand the
interconnected relationships between the variables of snow load, wind loads, building geometry and
meteorological climate.
5. RECOMMENDATIONS FOR FUTURE WORK
Determining the net effect of coincident wind and snow loads for generic or building and site specific application is
not a simple process. Future work by the authors and by the engineering community should be undertaken to further
investigate these combination factors. Topics of investigation include:
1. Simulation and statistical models for snow and wind load combination functions to better reflect the wide range
of load design scenarios that can occur. This should include further research into assigning appropirate
probabilities to the data, including methods for reconciling the differences between a peak annual snow load
and an hourly event wind load, for example.
2. Develop climate-specific snow load combination factors for use along with the current ground snow and wind
load values presented within the NBCC.
3. Develop generic building applicable refinements to the snow and wind load combination factors by investigating
varaiables such as wind exposure and roof size/geometry.
4. To provide refinements to building load case specific wind loads, specific wind loads should be determined and
applied, as the wind loads presented within have been simplistically modelled for the purposes of comparison of
trends.
6. REFERENCES
Dale J.C., Gamble S.L., and Brooks A.J. 2014. Design snow load refinement using modelling and analysis
techniques. Canadian Society of Civil Engineers. CSCE2014 4th International Structural Specialty Conference.
Halifax, NS.
Dale J.C., Gamble S.L., and Brooks A.J. 2015. Proposed refinements to design snow load derivation. American
Society of Structural Engineers 2015 Structures Congress.
F.M. Bartlett, H.P. Hong, and W. Zhou. 2003. Load factor calibration for the proposed 2005 edition of the National
###-10
F.M. Bartlett, H.P. Hong, and W. Zhou. 2003. Load factor calibration for the proposed 2005 edition of the National
448.
Gamble, S.L., Kochanski, W.W., and Irwin, P.A.. 1992. Finite Area Element Snow Loading Prediction
Applications and Advancements. Journal of Wind Engineering and Industrial Aerodynamics, 41
Irwin, P.A., Gamble, S.L., and Taylor, D.A.. 1995. Effects of Roof Size, Heat Transfer, and Climate on Snow
Loads: Studies for the 1995 NBC. Canadian Journal of Civil Engineering, 22
National Building Code. (2010). National Research Council of Canada, Ottawa, ON. Vol.2 Section 4.1.6.
Tsuchiyaa, M., Tomabechib T., Hongoa T., and Uedac H. 2002. Wind effects on snowdrift on stepped flat roofs.
Journal of Wind Engineering and Industrial Aerodynamics, 90 18811892.
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