With more bridge construction projects taking place in mountainous areas in
recent years, the structural engineer faces a difficulty, namely, the characterisation
of the wind environment in mountainous terrain (Zhang et
al., 2008, 2010). Most of the wind characteristics
of plains and coastal areas are analysed according to Class A or B landforms.
Corresponding parameters for the mean wind profile and turbulence characteristics
of these two landforms are given in Chinas Wind-resistant design
specification for highway bridges (Professional Standard
PRC, 2004) (referred to henceforth as the Specification). These parameters
can be directly applied in wind-resistance calculations and wind tunnel tests.
However, mountainous areas present landform and terrain variations and complex
wind-field distributions. The current Specification is only suitable for an
isotropic wind-field over a flat landform. However, the wind characteristics
of mountainous areas, with their complex terrains and landforms, differ greatly
from those in the Specification. Thus it is necessary to modify these parameters
using field measurements and wind tunnel tests while especially investigating
a bridges wind-resistance under a mountainous terrains wind characteristics.
In wind engineering, wind speed is usually considered as comprising two components:
the turbulence that generates gusts or calm winds and the mean wind speed. Of
these components, turbulence exhibits intensive non-linear random fluctuations
in both space and time (Simiu and Scanlan, 1996; Sharma
and Richards, 1999). To study the wind-resistance of a large span bridge,
it is firstly required to more accurately simulate and define the wind characteristics
around the bridge site. Therefore, measurement and statistical analysis were
used as the main approaches to this study (Xian et al.,
2008; Gang, 2012; Zhang et
al., 2006). This study concerned a long-span bridge in the mountainous
area of western China as Fig. 1 shows. Anemometers were installed
up the height of the construction tower on the bridge site. Using the anemometers,
the wind environment characteristics around the bridge site were measured. Site
parameters such as: Wind speed, turbulence intensity, turbulent wind power spectrum
density function, turbulence integral scale, etc., were then analysed.
MEASUREMENT METHODS OF THE WIND CHARACTERISTICS
Measurement instruments: A PH anemometer was used to measure wind characteristics
over the range zero to 60 m sec-1 at a precision of <3 mm sec-1.
Data-logging through a computers serial port allowed for the acquisition
and real-time storage of high frequency data and uninterrupted wind speed observations.
To obtain the distribution characteristics of wind turbulence at the bridge
site and meet the wind field requirements for bridge wind-resistance design
(Andersen and Lovseth, 1995), nine PH anemometers were
installed. They were installed towards the north up the height of the bridge
site (one per 10 m) as Fig. 2 shows. Using these anemometers,
the direction and speed of instantaneous wind and mean wind were measured. Wind
direction was defined by compass bearing (i.e., a northerly blew from 0°).
||Study site for, (a, b) Long-span bridge in the mountainous
||Anemometer installed at 90 m above the arch springing
Principles behind wind turbulence: Studies of the wind characteristics
often assume a neutral boundary layer and do not consider the influence of the
temperature gradient. Generally (Pasquill, 1974), neutral
boundary layers are observed during strong wind weather events with mean wind
speeds above 6 m sec-1. Meanwhile, the study of bridge wind-resistance
mainly considers the effect of turbulent wind. In meteorology, wind above scale
5 is classified as gale force. According to the Beaufort wind scale, the lower
limit of a scale 5 wind is 8 m sec-1. Only wind at, or above, a certain
scale can induce excessive load or vibration to an extent affecting the safety
of a bridge structure (Gu et al., 2002; Ai
and Xing, 2012; Ge et al., 2002; Lin
et al., 2008; Shum et al., 2008).
Typically, in addition to the vortex-induced vibrations of a flexible large-span
bridge are caused by wind speeds of approximately 8 m sec-1 while
other vibrations (including flutter, buffeting and galloping) are caused by
wind speeds above 8 m sec-1. Comprehensive analysis showed that the
low limit of 10 min mean speed of the winds turbulence in this study was
8.0 m sec-1.
Data processing method: Before processing the measurements, original data were pre-treated. Invalid data (those influenced by rainfall, environment and the stability of data acquisition system) were removed: Only valid data exceeding 90% reliability were involved in subsequent calculations.
Turbulence characteristic analysis was based on 10 min intervals. Ten-minute sub-samples were divided according to date and time sequence. Then those valid rates of the sub-samples were re-calculated. Only sub-samples with a valid rate of more than 95% could be used in the analysis of turbulence characteristics. Moreover, in the analysis of integral scale and frequency spectrum, the invalid data points which were deleted should be completed by incorporation at corresponding times and positions. The integrity of time information and consistency of sample length, were thereby ensured.
In wind engineering, the structural scale is smaller than the meteorological scale. The study of wind characteristics mainly concentrates on the wind characteristics of nearby regions and mainly includes. The mean wind speed and direction, turbulence intensity, gust factor, turbulence integral scale and turbulent wind speed power spectrum.
Mean wind speed and direction: It is assumed that the 3-D wind sequence measured by an anemometer is ux(t), uy(t) and uz(t). Using a vector decomposition method, the horizontal mean wind speed U and wind direction angle φ in any 10 min interval can be obtained thus:
Since the vertical wind speed direction aligns with the z-axis in anemometer coordinates, the vertical mean wind speed is obtained from Eq. 3:
are the 3-D mean wind speeds of the sample in a 10 min interval. Based on the
calculation of the mean wind speed above, the formulae for longitudinal turbulent
wind speed ut, transverse turbulent wind speed vt and
vertical turbulent wind speed wt can be obtained thus:
Turbulence intensity: Turbulence intensity reflects the fluctuating
intensity of wind. It is the simplest parameter used to describe atmospheric
turbulence. According to the Specification, turbulence intensity is defined
as the ratio of the mean square root of the turbulent wind speed and the horizontal
mean wind speed in a 10 min interval. Turbulence intensities of longitudinal
turbulence speed u(t), transverse turbulent wind speed v(t) and vertical turbulent
wind speed w(t) can be expressed by Eq. 7-9:
where, σu, σv, σw are the mean square roots of the turbulent wind speed u(t), v(t) and w(t) respectively; U(z) is the mean wind speed at height z above ground.
Gust factor: The turbulence intensity of wind can also be represented
by its gust factor G(tg), defined as the ratio of the maximum mean
wind speed in gust duration time tg (usually, the gust duration in
structural wind engineering is 2-3 sec: tg was chosen as 3 sec for
this study) to the mean wind speed during a basic time interval (Xie
et al., 2009), namely:
are the mean values of the along-wind and cross-wind turbulent wind speed in
time tg respectively.
Turbulence integral scale: The mathematical expression of turbulence integral scale is:
In Eq. 12, R12(x) is the correlation function
of two longitudinal turbulent wind speeds (u1(x1, y1,
z1, t) and u2(x1+x, y1, z1,
t); t is the time; σu is the variance of turbulence speed u
and R(0) = σu2. Assuming that a turbulent vortex
migrates at speed U(z), turbulence speed U(z) can be defined by u(x-x'/U(z),
τ). The integral scale of turbulence can be calculated using the autocorrelation
function in Eq. 13:
Turbulence power spectrum density function: The turbulent wind speed power spectra in different countries specifications differ. The horizontal turbulent wind speed spectrum in the wind-resistant design currently used in China is as follows:
The vertical turbulent wind speed spectrum usually follows Eq. 15:
where, f = nz/U, z is the height from the ground, u* is the friction
speed, u*2 = σu2/β and
β is the friction speed coefficient.
ANALYSIS OF MEASUREMENT RESULTS
Mean wind speed and direction: Figure 3 present the wind-roses during winter and summer: winter mainly saw northeast winds while summer saw prevailing southeast and south winds.
Figure 4 shows the wind speed time history curve measured by sensors at a height of 70 m above the arch springing during certain periods of summer and winter. Since the measurement was only conducted for slightly more than one year, it would be less reliable to calculate the basic 1 in 100 year wind speed for this site using the data obtained. Considering this situation, the cross threshold method (peak over threshold method) that only needed a small number of samples was used in subsequent calculations. Using this method, the weight of the maximum wind speed was reduced. Meanwhile, most of the maximum wind speeds in one year were retained. Thus it became possible to estimate extreme wind speeds using shorter wind speed sequences: The basic wind speed was calculated thus:
where, vs is the wind speed threshold, b and c are scale and shape parameters respectively, μ0 is the annual average incidence of a given wind speed, n(vs) is the average occurrence times of extreme wind speed (the wind speed exceeds threshold vs) and N is the annual average number of times the wind speed exceeded a certain value. Using Eq. 16 the basic 1 in 100 year wind speed for this site was calculated as 26.8 m sec-1.
Turbulence intensity: Figure 5 show the variations
in turbulence intensity at 10 and 90 m, above the arch springing respectively.
In both Figure 5a and b, the turbulence
intensity at 10 m above the arch springing exceeded 40%, with individual points
exceeding 50%; the turbulent intensity at 90 m was above 15%. The results implied
that, in typically mountainous areas, the turbulence intensity was far greater
than recommended values in the Specification. Turbulent wind posed serious problems
and would be a prime cause of bridge buffeting.
Gust factor: According to the measured data, the ratio of the maximum
mean wind speed and horizontal mean wind speed in the gust duration time tg
measured by sensors at different heights was calculated. Using this ratio, the
gust factors in cross- and along-wind directions were obtained. Then the gust
factors were weighted and averaged to acquire the gust factor value for each
||Wind-rose (m sec-1), (a) Winter and (b) Summer
||(a) Field observation data of wind-speed at the bridge site
(summer) and (b) Field observation data of wind-speed at the bridge site
||(a) Turbulence intensity at 10 m above the arch springing
and (b) Turbulence intensity at 90 m above the arch springing
||(a) Time-history curve of the gust factor: Along-wind direction
and (b) Time-history curve of the gust factor: Cross-wind direction
Finally, the variation laws of the gust factors at different heights were
derived, that is, the gust factors time-history curves were obtained.
||Autocorrelation function: Turbulent wind speed, 10 m above
the arch springing
For brevitys sake, only the January time-history curves for the gust
factor at heights: 10, 50 and 90 m above the arch springing are shown as Fig.
6a and b.
For mountainous terrain, in the along-wind direction, the maximum value of the gust factor at 10 m above the arch springing was observed in August, with a value about 1.6 while that at 90 m occurred in January, with a value of about 1.4; in the cross-wind direction, the maximum value of the gust factor at 10 m above the arch springing was observed in January, with a value about 1.15 while that at 90 m above the arch springing occurred in January and March, with a value of around 0.8. On the whole, the down-wind turbulence intensity in mountainous terrain was higher than that on the plains. Turbulent winds can easily cause buffeting of bridge structures.
Turbulence integral scale: Figure 7 shows the autocorrelation function of the turbulent wind speed at a height of 10 m above the arch springing: Only when τ→∞, did the autocorrelation function R(τ) tend to zero. To obtain accurate Tu values, the sampling time should be extended towards infinity. Therefore, as this was impossible, the turbulence integral scale Lxu obtained by autocorrelation function R(τ) was prone to error and a new analysis method was needed.
Therefore, a spectrum fitting technique was used to obtain turbulence
integral scale. The wind speed spectrum curve in Fig. 7 was
compared to the von-Karman spectrum and the formula Lxu
= TuU(z), respectively. When regularisation coordinates were used,
the spectrum shape in Fig. 7 was basically the same as the
von Karman spectrums shape. The wind speed spectrum, as expressed by von-Karman
spectrum and Lxu = TuU(z), provided the relationship
between wind speed spectrum and turbulence integral scale. Therefore, through
iterative fitting of the relationship formula, corresponding turbulence integral
scales could be obtained.
|| Turbulence integral scale
||Vertical turbulent wind speed power spectrum curve
The comparison of the turbulence integral scales obtained by spectrum fitting
method and autocorrelation function indicated that, with increased sampling
time, the results of the two methods became closer.
The turbulence integral scale obtained by analysing the measured data is shown in Fig. 8: The mean value of the turbulence integral scale in the along-wind direction was 48.5 m while that in the cross-wind direction was 42.1 m. These two values were only about 70% of the standard values.
Turbulence power spectrum: To investigate the relationship governing
the variations in the turbulence power spectrum, the horizontal and vertical
turbulent power spectrums of the wind speed at a height of 10 m above the arch
springing were drawn using log-log coordinates, as shown in Fig.
9 where frequency nz/U forms the abscissa and nS(z, n)/σu2
|| Vertical turbulent wind speed power spectrum
For convenience when comparing, Fig. 9 also displays the
von Karman and Simiu, spectra from the Specification.
Figure 10 shows the vertical turbulent wind power spectrum curve at a height of 10 m. For convenience when comparing, Fig. 10 also shows the simulated spectrum represented by Eq. 17 and the Panofsky spectrum from the Specification.
In Fig. 9 and 10, the measured horizontal turbulent wind speed spectrum was relatively close to the von-Karman spectrum, but showed greater differences from the Simiu spectrum; the peak values of the wind speed power spectrum curve shifted towards the higher frequency band; the vertical wind spectrum curve presented larger differences between it and the Panofsky spectrum recommend in the Specification. The relationship between them was fitted using (17), i.e.,:
Vertical turbulent wind speed spectrum:
Test results for one year showed that, due to the larger fluctuations caused by mountainous terrain, the concept of basic wind speed in the Specification was not applicable to this site and its innate complexities; the average wind speed showed complicated variations with height and the wind profile did not fit either logarithmic, or exponential, models commonly used.
The turbulence intensity and gust factor of western mountainous areas were
significantly greater than the reference values in the Specification while the
turbulence integral scale was much smaller than that recommended by the Specification.
The peaks of turbulent wind speed power spectrum shifted to the higher frequency
band. The power spectral model of the turbulent wind speed was possibly able
to be simulated using Eq. 18 and 19.
Horizontal turbulent wind speed spectrum:
Vertical turbulent wind speed spectrum:
In Eq. 18 and 19, f = nz/U, n is the
gust frequency; z is the height above the arch springing and u and w are the
horizontal and vertical turbulent wind speeds respectively.
Based on the measured anemometer data, the characteristics of strong winds on the site of a long-span bridge in mountainous terrian were investigated. The following conclusions were drawn:
||Measurement results showed that the wind speed varied with
height, the wind speed profile of the bridge site did not fully comply with
either logarithmic, or exponential, models
||Concerning mountainous terrain, the turbulence intensity was higher than
that on the plains; the turbulence intensity and gust factor were significantly
higher than their reference values in the Specification. The turbulence
integral scale was lower than the recommended value in the Specification
||Turbulence intensity calculation results suggested that the turbulence
intensity at height of 10 m above the arch springing exceeded 40%: at 90
m it was still as high as 15%. Turbulent wind posed significant problems
and was a major cause of bridge buffeting
The authors would like to gratefully acknowledge the support of this research by National Natural Science Foundation of China (No. 50778185).