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地震作用下二維場地模態疊加等效線性化方法

李雪菊 潘旦光 石樹中

李雪菊, 潘旦光, 石樹中. 地震作用下二維場地模態疊加等效線性化方法[J]. 工程力學, 2023, 40(10): 179-189. doi: 10.6052/j.issn.1000-4750.2022.01.0105
引用本文: 李雪菊, 潘旦光, 石樹中. 地震作用下二維場地模態疊加等效線性化方法[J]. 工程力學, 2023, 40(10): 179-189. doi: 10.6052/j.issn.1000-4750.2022.01.0105
LI Xue-ju, PAN Dan-guang, SHI Shu-zhong. A MODAL-SUPERPOSITION-BASED EQUIVALENT LINEARIZATION METHOD FOR SEISMIC RESPONSE ANALYSIS OF TWO-DIMENSIONAL SITES[J]. Engineering Mechanics, 2023, 40(10): 179-189. doi: 10.6052/j.issn.1000-4750.2022.01.0105
Citation: LI Xue-ju, PAN Dan-guang, SHI Shu-zhong. A MODAL-SUPERPOSITION-BASED EQUIVALENT LINEARIZATION METHOD FOR SEISMIC RESPONSE ANALYSIS OF TWO-DIMENSIONAL SITES[J]. Engineering Mechanics, 2023, 40(10): 179-189. doi: 10.6052/j.issn.1000-4750.2022.01.0105

地震作用下二維場地模態疊加等效線性化方法

doi: 10.6052/j.issn.1000-4750.2022.01.0105
基金項目: 土木工程防災國家重點實驗室開放基金項目(SLDRCE15-01);浙江省地震局“地震災害風險評估技術應用研究”創新團隊項目
詳細信息
    作者簡介:

    李雪菊(1995?),女,寧夏人,博士生,主要從事工程結構抗震研究(E-mail: lixueju1995@126.com)

    石樹中(1968?),男,湖南人,高工,博士,主要從事地震工程研究(E-mail: Shisz68@163.com)

    通訊作者:

    潘旦光(1974?),男,浙江人,教授,博士,博導,主要從事防災減災工程及防護工程研究(E-mail: pdg@ustb.edu.cn)

  • 中圖分類號: TU435

A MODAL-SUPERPOSITION-BASED EQUIVALENT LINEARIZATION METHOD FOR SEISMIC RESPONSE ANALYSIS OF TWO-DIMENSIONAL SITES

  • 摘要: 為快速進行多維場地地震反應分析,將模態攝動法和模態疊加法相結合,提出了一種非比例滯后阻尼二維場地的模態疊加等效線性化計算方法。在該方法中,根據原系統的模態分析結果,利用模態攝動法得到迭代剛度修正后新系統的模態,然后,采用模態疊加法實現非比例復阻尼體系運動方程中矩陣維數的降階,形成廣義坐標耦合和解耦的模態疊加等效線性化法,在此基礎上,進一步討論了阻尼矩陣耦合系數的影響。隨后,以杭州某一工程場地為例,研究不同輸入地震動幅值下,場地水平加速度動力放大系數隨地震動幅值的變化規律,并與二維頻域等效線性化計算結果比較,驗證所提算法的精度和有效性。計算結果表明:采用廣義坐標耦合的模態疊加法,不同地震動輸入幅值下,計算誤差均小于5%;廣義坐標解耦方法所得地表加速度放大系數的計算誤差隨耦合因子的增大而增大;當地震動幅值小于0.1 g時,可采用強制解耦方法計算場地地震反應。從計算效率看,模態疊加等效線性化法和二維頻域等效線性化法的迭代次數基本相同,但計算時間約為頻域等效線性化法的一半。
  • 圖  1  CMSEL算法計算流程圖

    Figure  1.  The flow chart of CMSEL

    圖  2  各類土的G/Gmax、λγd關系曲線

    Figure  2.  G/Gmax-γd、λ-γd relation curves of soil

    圖  3  有限元模型

    Figure  3.  Finite element model

    圖  4  輸入波加速度時程及Fourier譜

    Figure  4.  Ground acceleration histories and Fourier spectra

    圖  5  βh的相對誤差隨振型截止頻率的變化

    Figure  5.  The relative errors of βhvarying with mode cut-off frequency

    圖  6  ${e_{{\beta _{\rm{h}}}}}$-耦合因子α

    Figure  6.  The ${e_{{\beta _{\rm{h}}}}}$ varying with α

    圖  7  地表加速度反應譜

    Figure  7.  The ground acceleration response spectra

    表  1  鉆孔地質參數

    Table  1.   Parameters of boreholes

    層號土層類型深度/m剪切波速/(m·s?1)密度/(kg·m?3)泊松比
    鉆孔1鉆孔2鉆孔1鉆孔2鉆孔1鉆孔2
    1 雜填土 0.825 1.105 119 121 1800 0.32
    2 素填土 1.650 2.210 125 132 1800 0.30
    3 砂質粉土 4.800 6.000 137 144 1900 0.32
    4 砂質粉土夾粉砂 8.300 9.000 138 159 1930 0.33
    5 砂質粉土 12.400 11.000 159 167 1930 0.32
    6 粉砂 16.200 18.200 189 187 1980 0.35
    7 砂質粉土夾淤泥質土 18.500 18.410 252 174 1900 0.33
    8 淤泥質粉質粘土 26.300 27.000 155 164 1800 0.34
    9 粉質粘土 29.750 27.900 257 240 2000 0.32
    10 粉質粘土 粘土 30.800 31.000 257 258 1820 0.32
    11 粉礫 31.200 33.000 289 275 2050 0.32
    12 粉礫 含砂粉質粘土 32.900 37.700 289 321 2000 0.32
    11 圓礫 40.640 40.640 360 346 2100 0.32
    下載: 導出CSV

    表  2  地震波

    Table  2.   Earthquake ground motions

    編號地震波時間/(年/月/日)監測臺站地震臺站震中距/km
    E1 Far-sfern 1971.09.02 Isabella Dam San Fernando 130.00
    E2 Far-chichi 1999.09.20 KAU082 Chi-Chi Taiwan 168.72
    E3 Mid-chichi 1999.09.20 TTNO25 Chi-Chi Taiwan 65.79
    E4 Mid-lomap 1989.10.18 Point Bonita Loma Prieta 83.37
    E5 Near-lomap 1989.10.18 Belmont-Envirotech Loma Prieta 43.94
    E6 Near-sfern 1971.09.02 Pasadena-Old Seismo Lab San Fernando 21.50
    下載: 導出CSV

    表  3  土體部分模態及截斷指標值

    Table  3.   Partial frequencies and modal truncation indexes

    模態頻率/Hz振型參與
    系數γ
    累積振型加速度
    貢獻系數A1
    累積振型加速度
    貢獻系數A2
    11.0535.192×10337.55436.602
    374.2031.064×10372.10171.780
    715.848?888.20693.62392.972
    796.117?544.67296.46694.476
    806.2152.6901796.93296.479
    下載: 導出CSV

    表  4  ZD-1地表βh的相對誤差

    Table  4.   The relative errors of βh for ZD-1 /(%)

    地震波0.035 g0.1 g0.2 g
    CMSELE10.4520.1990.825
    E20.0930.0540.697
    E30.0540.0410.323
    E40.0680.0860.521
    E50.7051.5750.676
    E61.2650.6650.013
    平均值0.4400.4370.509
    DMSELE14.4537.2216.407
    E24.1177.9809.067
    E32.6858.7936.863
    E43.5544.8339.465
    E50.3833.2542.689
    E60.1927.6248.422
    平均值2.5646.6187.152
    下載: 導出CSV

    表  5  ZD-2地表βh的相對誤差

    Table  5.   The relative errors of βh for ZD-2 /(%)

    地震波0.035 g0.1 g0.2 g
    CMSELE10.2310.431.107
    E20.0820.0690.411
    E30.0940.0330.056
    E40.1660.0850.457
    E50.60.9480.261
    E60.7830.5671.720
    平均值0.3260.3550.669
    DMSELE11.1614.0993.863
    E20.0824.4946.423
    E35.5727.6897.203
    E41.7135.9689.842
    E50.3470.9432.042
    E64.5925.9897.532
    平均值2.2454.8646.151
    下載: 導出CSV

    表  6  阻尼矩陣耦合因子α

    Table  6.   The coupling factor of damping matrix

    PGA/gE1E2E3E4E5E6平均值
    0.0350.2300.3440.3030.2210.2280.3070.272
    0.1000.3200.3380.3470.2720.2990.3110.315
    0.2000.2800.3710.3300.3490.3180.3460.332
    下載: 導出CSV

    表  7  兩種方法的計算概況

    Table  7.   The calculation profile of two methods

    地震波迭代次數運行時間比
    NFNCNDTC/TFTD/TF
    E17.678.008.170.5350.462
    E28.337.808.170.5200.414
    E37.336.806.830.4660.336
    E47.676.606.830.6330.448
    E56.676.256.330.7120.511
    E67.837.337.830.5590.502
    注:NF、NCND分別為FDEL、CMSEL和DMSEL法的平均迭代次數;TF、TCTD分別為FDEL、CMSEL和DMSEL法計算耗時。
    下載: 導出CSV

    黑人大屌丝逼逼
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  • 收稿日期:  2022-01-21
  • 修回日期:  2022-04-18
  • 網絡出版日期:  2022-04-23
  • 刊出日期:  2023-10-10

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