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 水利水运工程学报   2019 Issue (3): 76-84.  DOI: 10.16198/j.cnki.1009-640X.2019.03.010 0

### 引用本文 [复制中英文]

[复制中文]
FENG Yunfen, GAO Shufei. Seismic vulnerability analysis of pile-supported wharves based on displacement[J]. Hydro-science and Engineering, 2019(3): 76-84. (in Chinese) DOI: 10.16198/j.cnki.1009-640X.2019.03.010.
[复制英文]

### 文章历史

1 易损性分析方法

 $P\left( {C < D|{I_{\rm{M}}}} \right) = 1 - \mathit{\Phi }\left( {\frac{{\ln {\mu _C} - \ln {\mu _D}}}{{\sqrt {\beta _C^2 + \beta _D^2} }}} \right)$ (1)

1.1 基于云图法的易损性函数

 $D\left( {{I_{\rm{M}}}} \right) = aI_{\rm{M}}^b\varepsilon$ (2)

 $\ln \left[ {D\left( {{I_{\rm{M}}}} \right)} \right] = \ln a + b\ln {I_{\rm{M}}} + \ln \varepsilon$ (3)

 $\ln {\mu _D} = \ln \hat a + \hat b\ln {I_{\rm{M}}}$
 ${\beta _D} = \sqrt {\frac{{\sum\limits_{i = 1}^n {{{\left[ {\ln {D_i} - \ln {\mu _D}} \right]}^2}} }}{{n - 2}}}$

1.2 基于条带法的易损性函数

 $P\left( {D > d|{I_{{\rm{M}}j}}} \right) = 1 - \mathit{\Phi }\left( {\frac{{\ln d - \lambda |{I_{{\rm{M}}j}}}}{{{\beta _{D|{I_{{\rm{Mj}}}}}}}}} \right)$ (4)

 $\lambda |{I_{{\rm{Mj}}}} = \ln {\mu _{D|{I_{{\rm{M}}j}}}} - \frac{1}{2}\beta _{D|{I_{{\rm{M}}j}}}^2$ (5)
 ${\beta _{D|{I_{{\rm{M}}j}}}} = \sqrt {1 + \delta _{D|{I_{{\rm{M}}\mathit{j}}}}^2}$ (6)

 $P\left( {C < D|{I_{{\rm{M}}j}}} \right) = 1 - \mathit{\Phi }\left( {\frac{{\ln {\mu _C} - \ln {\mu _{D|{I_{{\rm{M}}j}}}}}}{{\sqrt {\beta _C^2 + \beta _{D|{I_{{\rm{Mj}}}}}^2} }}} \right)$ (7)
1.3 码头破坏状态的定义

2 高桩码头结构模型和地震动记录 2.1 码头结构模型

 图 1 高桩码头断面(单位：高程，m; 其他，mm) Fig.1 Transverse section of wharf (unit: elevation in m; others in mm)
 图 2 桩与横梁连接构造(单位：高程，m; 其他，mm) Fig.2 Details of pile-beam connection (unit: elevation in m; others in mm)

2.2 地震动记录

 图 3 各地震波震级与断层距之间关系 Fig.3 Relationships between Mw and R
 图 4 各地震波峰值地面加速度与断层距之间关系 Fig.4 Relationships between aPG and R
3 易损性分析结果

 图 5 码头Pushover曲线 Fig.5 Pushover curve for wharf

 ${f_{{\rm{DM}}}} = \sqrt {1 + {{\left[ {0.3\left( {1 + 20{e_0}/{L_l}} \right)} \right]}^2}}$ (8)

 图 6 位移需求的回归分析 Fig.6 Regression analysis for displacement demands

 $\ln \left( {{\mu _D}} \right) = 1.163\ln \left( {{a_{{\rm{PG}}}}} \right) + 2.447\;1$ (9)

 图 7 码头易损性曲线 Fig.7 Vulnerability curves of wharf

 图 8 云图法和条带法计算结果对比 Fig.8 Comparison between results from cloud map method and stripe method

 图 9 βC对易损性曲线的影响 Fig.9 Effects of βC on vulnerability curves

4 结语

(1) 基于码头的总位移建立易损性曲线，可以很好地和基于位移的高桩码头抗震设计方法相结合，从概率角度评估码头的抗震性能。

(2) 由云图法和条带法建立的码头易损性曲线差别不大，考虑到条带法需要的时程分析次数较多，故建议采用云图法建立码头的易损性曲线，但地震动记录的选取应符合一定的准则。

(3) 位移能力的不确定性对码头的易损性曲线有较大影响，在分析中应予以考虑；由于目前对于码头位移能力不确定性的研究较少，位移能力的对数标准差可近似取为0.3，但仅适用于采用Pushover分析确定码头位移能力的情况，而码头位移能力的不确定性则有待进一步深入研究。

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Seismic vulnerability analysis of pile-supported wharves based on displacement
FENG Yunfen , GAO Shufei
School of Architecture and Civil Engineering, Liaocheng University, Liaocheng 252000, China
Abstract: In view of the fact that the total displacement of the wharf is seldom used as a performance index in the seismic vulnerability analysis of the pile-supported wharf at present, a displacement-based vulnerability analysis method is proposed based on the cloud map method and stripe method respectively. The proposed method takes into account the uncertainty of earthquake ground motion and defines the failure status of the pile-supported wharf based on the strain limits of pile material. In order to illustrate this analysis method, 80 earthquake records are used to analyze the vulnerability curves of the pile-supported wharf by using the cloud map method and stripe method respectively. The differences between the vulnerability curves given by two methods are compared, and the influences from the uncertainty of displacement capacity on the vulnerability curves are analyzed. The analysis results show that there is little difference between the vulnerability curves of wharves established by the cloud map method and the stripe method, which can be neglected. However, considering the small amount of calculation of the cloud map method, it is suggested to use the cloud map method in the vulnerability analysis of wharves. The uncertainty of displacement capacity plays an important role in the analysis of the vulnerability curves, and should not be neglected in the analysis and should be taken into account.
Key words: pile-supported wharves    seismic vulnerability analysis    cloud map method    stripe method    displacement capacity uncertainty