Spatial correlation of along-wind fluctuating wind loads on rectangular high-rise buildings
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摘要:
为探讨建筑深宽比和来流湍流特性对矩形高层建筑顺风向脉动风荷载空间相关性的影响，对深宽比为1/9～9的矩形高层建筑在4种风场中进行了同步测压风洞试验。基于试验结果，分析建筑深宽比、湍流强度和湍流积分尺度对顺风向脉动风荷载竖向相关系数和相干函数的影响；通过非线性最小二乘法，拟合得到了适用于深宽比为1/9～9的矩形高层建筑竖向相关性数学模型。结果表明：顺风向脉动风荷载相关系数同时受到建筑深宽比和测点层高差影响，相关系数随测点层高差增大呈指数衰减；顺风向脉动相干函数随频率增大呈指数衰减，且衰减速率与高差和平均风速的比值大致成正比；对于不同深宽比建筑，湍流积分尺度和湍流强度对顺风向脉动风荷载相关性的影响不同；本文针对不同风场提出的矩形高层建筑顺风向脉动风荷载相关系数和相干函数公式和试验结果吻合良好，可为建筑结构设计及荷载规范修订提供参考。
Abstract:To investigate the effects of side ratio and turbulent characteristics on the spatial correlation of along-wind fluctuating wind loads on rectangular tall buildings, synchronization pressure wind tunnel tests for rectangular tall buildings with side ratios ranging from 1/9～9 were carried out in four wind fields. Based on the experimental findings, the coherence function and vertical correlation coefficient of along-wind fluctuating wind loads were examined in relation to the effects of side ratio, turbulence intensity, and turbulence integral scale. The mathematical model of vertical correlation of rectangular high-rise buildings with a side ratio of 1/9～9 was obtained by the nonlinear least square method. The results show that the correlation coefficient of along-wind fluctuating wind load is affected by both the side ratio and separation distance, and decreases exponentially with the increase of separation distance. The along-wind fluctuating coherence function decays exponentially with the increase of frequency, and the decay rate of the coherence function is roughly positively related to the ratio of separation distance to average wind speed. The effects of turbulence integral scale and turbulence intensity on the correlation of along-wind fluctuating wind loads are different for buildings with different side ratios. It can serve as a guide for structural design and load code revision since the coherence functions and correlation coefficients of along-wind fluctuating wind loads on rectangular high-rise buildings suggested in this work correspond well with the experimental data.
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图 5 O1风场下顺风向脉动风荷载相关系数
Figure 5. Correlation coefficients of along-wind fluctuating wind loads in O1 wind field
图 6 湍流特性对顺风向脉动风荷载相关系数的影响
Figure 6. Effect of turbulence characteristics on correlation coefficients of along-wind fluctuating wind loads
图 7 O1风场下顺风向脉动风荷载相干函数
Figure 7. Coherence functions of along-wind fluctuating wind loads in O1 wind field
图 8 不同风场下顺风向脉动风荷载相干函数
Figure 8. Coherence functions of along-wind fluctuating wind loads in different wind fields
图 9 O1风场下顺风向脉动风荷载相关系数公式拟合参数与计算值比较
Figure 9. Comparison between fitting and calculated values of correlation coefficient formula parameters in O1 wind field
图 10 O1风场下顺风向脉动风荷载相关系数拟合值与试验值比较
Figure 10. Comparison of fitting and experimental value of along-wind fluctuating wind loads in O1 wind field
图 11 O1风场下部分顺风向脉动风荷载相干函数拟合结果
Figure 11. Some coherence function fitting results of along-wind fluctuating wind loads in O1 wind field
图 12 O1风场下顺风向脉动风荷载相干函数衰减系数随建筑深宽比的变化规律
Figure 12. Variation of attenuation coefficient of coherence function with side ratio of building in O1 wind field
图 13 参数p1和p2随$ {\Delta } {{\textit{z}}/}\overline{\textit{z}} $变化规律
Figure 13. Variation law of parameters p1 and p2 with $ {\Delta }{{\textit{z}}/}\overline{\textit{z}} $
表 1 试验模型参数
Table 1. Parameters of experiment models
工况 风场类型 深宽比 拼接方式(从左至右) 测压点个数 1 O1 1/9，9 段1，段3，段5，段7，段9，段11，段12，段10，段8，段6，段4，段2 616 2 O1，O2，S1，S2 1/8，8 段1，段3，段5，段7，段9，段11，段10，段8，段6，段4，段2 588 3 O1 1/7，7 段1，段3，段5，段7，段9，段10，段8，段6，段4，段2 560 4 O1 1/6，6 段1，段3，段5，段7，段10，段8，段6，段4，段2 532 5 O1，O2，S1，S2 1/5，5 段1，段3，段5，段7，段8，段6，段4，段2 504 6 O1 1/4，4 段1，段3，段5，段7，段6，段4，段2 420 7 O1，O2，S1，S2 1/3，3 段1，段3，段5，段6，段4，段2 336 8 O1 1/2.5，2.5 段1，段3，段5，段4，段2 294 9 O1，O2，S1，S2 1/2，2 段1，段3，段5，段2 252 10 O1 1/1.5，1.5 段1，段4，段2 210 11 O1，O2，S1，S2 1 段1，段2 168 
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表 2 典型顺风向相干函数经验公式
Table 2. Empirical formula of typical along-wind coherence function
顺风向相干函数公式 参数取法 $ \text{coh(}{{\textit{z}}}_{i},{{\textit{z}}}_{j},f)=\exp \left(\begin{aligned}-{c}_{{\textit{z}}}\dfrac{f\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{\overline{U}}\end{aligned}\right) $ $ {c}_{{\textit{z}}}=7, \overline{U}=({\overline{U}}_{i}+{\overline{U}}_{j})/2 $ $ \text{coh(}{{\textit{z}}}_{i},{{\textit{z}}}_{j})=\exp \left(\begin{aligned}-\dfrac{\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{{L}_{u{\textit{z}}}}\end{aligned}\right) $ $ {L}_{u{\textit{z}}}=60 $ $ \text{coh(}{{\textit{z}}}_{i},{{\textit{z}}}_{j})=\exp \left(-\dfrac{\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{{L}_{u{\textit{z}}}}\right) $ $ {L}_{u{\textit{z}}}=\sqrt{37\overline{{\textit{z}}}}, \overline{{\textit{z}}}=({{\textit{z}}}_{i}+{{\textit{z}}}_{j})/2 $ $ \text{coh(}{{\textit{z}}}_{i},{{\textit{z}}}_{j},f)=\left(1-\dfrac{{c}_{{\textit{z}}}{f}^{*}\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{2\overline{U}}\right)\exp \left(-{c}_{{\textit{z}}}\dfrac{{f}^{*}\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{\overline{U}}\right) $ $ {f}^{*}=\sqrt{{f}^{2}+\left(\dfrac{\overline{U}}{2 \text{π} L}\right)}^{2}, L=1.34{L}_{u} $ $ \text{coh(}{{\textit{z}}}_{i},{{\textit{z}}}_{j},f)=\exp \left(-{c}_{{\textit{z}}}\dfrac{f\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{\overline{U}}\right) $ $ {c}_{{\textit{z}}}=-2.3\dfrac{\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{\overline{{\textit{z}}}}+5.1 $ $ \text{coh(}{{\textit{z}}}_{i},{{\textit{z}}}_{j},f)=A\exp \left(-{c}_{{\textit{z}}}\dfrac{f\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{\overline{U}}\right) $ $ \begin{array}{l}A = {\left\{ 1.0 + 27.4{\left[\left(\dfrac{{\left| {{{\textit{z}}_i} - {{\textit{z}}_j}} \right|}}{{{H_r}}}\right)\bigg/{\left(\dfrac{{\bar {\textit{z}}}}{{{H_r}}}\right)^{1.5}}\right]^{1.64}}\right\} ^{ - 0.253}}\\{c_{\textit{z}}} = 4.22\exp \left( - 1.22{{\left| {{{\textit{z}}_i} - {{\textit{z}}_j}} \right|} / {{H_r}}}\right) + 3.57\exp \left( - 33.9{{\left| {{{\textit{z}}_i} - {{\textit{z}}_j}} \right|} / {{H_r}}}\right)\end{array} $
Hr为梯度风高度$ \text{coh(}{{\textit{z}}}_{i},{{\textit{z}}}_{j},f)=\left(1-\dfrac{\eta \beta (s){f}^{*}\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{\overline{U}}\right)\exp \left(-\beta (s)\dfrac{{f}^{*}\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{\overline{U}}\right) $ $ {f}^{*}=\sqrt{{f}^{2}+\left(\dfrac{\overline{U}}{2 \text{π} L}\right)}^{2}, L=1.34{L}_{u} $
$ s=\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| {B}^{\alpha /2}/{H}^{1+\alpha /2} $, α为风速剖面指数
β(s)=as2+bs+c, a=−66.26, b=27.39, c=2.354, η=1/3$ \text{coh(}{{\textit{z}}}_{i},{{\textit{z}}}_{j},f)=\exp \left(\begin{aligned}-{c}_{1}\dfrac{f\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{\overline{U}}+{c}_{2}\dfrac{\left| {{\textit{z}}}_{i}-{{\textit{z}}}_{j}\right| }{\overline{{\textit{z}}}}\end{aligned}\right) $ $ {c}_{1}=1.750,{c}_{2}=2.152 $ ${\rm{coh(}}k',\delta ,s) = [1 - \eta \delta \alpha (s)k']\exp [ - \alpha (s)\delta k'] $ $ k' = {{\sqrt {{f^2} + \left(\dfrac{{\overline U}}{{2 \text{π} L}}\right)} ^2}}\bigg/{{\overline U}},L = [{{\varGamma ({1 / 3})} / {\sqrt {\text{π}} }}({5 / 6})]{L_{ux}} $
$\delta = {{{\left| {{{\textit{z}}_i} - {{\textit{z}}_j}} \right|\bar {\textit{z}}} / {B({B / L})}}^{0.6}} $, $\alpha (s) = a{s^2} + bs + c $
a, b, c, η取值和建筑深宽比有关
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