STUDY ON SHAKING TABLE TEST OF FREESTANDING STONE CAVE DWELLING
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摘要: 根据现场调研，以山西省静乐县典型三连拱独立式石箍窑洞为研究对象，设计制作了缩尺比例为1∶4的模型结构，并对其进行了地震模拟振动台试验，分析了模型结构的自振频率、阻尼比、加速度放大系数、最大相对位移、位移角、底部剪力与耗能等。结果表明：独立式石箍窑洞结构在地震作用下的薄弱部位为边洞洞口处拱顶与中窑腿；随着输入地震波峰值加速度的增大，模型结构自振频率下降，阻尼比上升；模型结构各部位的动力放大系数随着输入峰值加速度的增加变化不大， x向动力放大系数最大处为拱顶，y向动力放大系数最大处为窑顶；输入加速度峰值为70 gal(小震)、200 gal(中震)、440 gal(大震)时，结构最大侧移角均出现在拱顶，分别为1/1618、1/491、1/255，输入峰值加速度为600 gal时，最大侧移角出现在窑顶，为1/102；输入峰值加速度为800 gal时，结构的最大扭转角为0.0037 rad；底部剪力和累积滞回耗能均随着输入地震波峰值加速度的增大而增大。研究结果可为石箍窑洞这一西北传统民居的妥善保护和传承提供科学依据。Abstract: According to the on-site investigation, taking the typical three-arch freestanding stone cave dwelling in Jingle County, Shanxi Province as the research object, the paper designed and manufactured a 1/4 model, and then carried out a shaking table test for it. The natural vibration frequency, damping ratio, acceleration amplification factor, maximum relative displacement, lateral displacement angle, base shear force and structural energy dissipation were analyzed. Test results show that the weak parts under the earthquake action are the dome and the middle kiln leg at the entrance of the side cave. With the increase of the peak acceleration of input seismic wave, the natural vibration frequency of the model decreases and the damping ratio increases. The dynamic amplification coefficients of the model changes little with the increase of the input peak acceleration. The largest dynamic amplification coefficient in the x-direction and y-direction occurs at the arch roof and kiln roof, respectively. When the input peak acceleration is 70 gal (frequent earthquakes), 200 gal (fortification earthquakes) and 440 gal (rare earthquakes), the maximum lateral displacement angle of the model occurs in the arch roof, which is 1/1618, 1/491 and 1/255, respectively. When the input peak acceleration is 600 gal, the maximum lateral displacement angle occurs in the kiln roof, which is 1/102. When the input peak acceleration is 800 gal, the maximum torsion angle of the model is 0.0037 rad. The bottom shear force and energy dissipation of the model increase with the increase of the peak acceleration of input seismic wave.
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图 5 三条地震波影响系数曲线对比
Figure 5. Comparison of influence coefficient of three seismic waves
图 9 x向不同峰值加速度下动力放大系数
Figure 9. Dynamic amplification factor under different peak acceleration in x direction
图 10 y向不同峰值加速度下动力放大系数
Figure 10. Dynamic amplification factor under different peak accelerations in y direction
图 11 不同工况下位移时程曲线
Figure 11. Displacement time history curves under different working conditions
图 12 不同地震波作用下的位移包络图
Figure 12. Displacement envelope diagram under different seismic waves
图 13 不同地震波作用下最大位移角
Figure 13. Maximum displacement angle under different seismic waves
图 17 结构累计滞回耗能曲线
Figure 17. Cumulative hysteretic energy consumption curve of structure
表 1 模型参数相似关系
Table 1. Similarity of model parameters
物理量 相似关系 物理量 相似关系 长度 1/4 质量 1/32 位移 1/4 时间 ${\text{1}}:2\sqrt 2 $ 应力 1 加速度 2 弹性模量 1 频率 $2\sqrt 2 :1$ 密度 2 阻尼 $1:16\sqrt 2 $ 
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表 2 黄土的动力特性
Table 2. Dynamic properties of loess
密度
ρ/(g/cm3)干密度
ρd/(g/cm3)含水率
ω/(%)初始动弹性模量
Ed0/(kg/cm2)阻尼比
ξ固结应力比
Kc破坏振次
Nf围压
σ3/kPa破坏动应力
σdf/kPa动粘聚力
Cd/kPa动摩擦角
φ/(º)1.78 1.63 11.6 2358.41 0.087~0.131 4.5 10 90 373.46 88.42 40.69 100 393.99 110 410.95 20 90 373.17 88.12 100 393.12 110 409.93 30 90 372.57 87.94 100 392.25 110 408.91
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表 3 试验加载工况
Table 3. Testing loading cases
序号 工况编号 输入峰值加速度${a_{pg}}/g$ 地震
水准x向 y向 z向 1 B1 − − − − 2/3/4 Ex1/Lx1/Rx1 0.07 − − 7度
多遇5/6/7 Exy1/Lxy1/Rxy1 0.07 0.060 − 8/9/10 Exyz1/Lxyz1/Rxyz1 0.07 0.060 0.046 11 B2 − − − − 12/13/14 Ex2/Lx2/Rx2 0.14 − − 8度
多遇15/16/17 Exy2/Lxy2/Rxy2 0.14 0.119 − 18/19/20 Exyz2/Lxyz2/Rxyz2 0.14 0.119 0.091 21 B3 − − − − 22/23/24 Ex3/Lx3/Rx3 0.20 − − 7度
设防25/26/27 Exy3/Lxy3/Rxy3 0.20 0.170 − 28/29/30 Exyz3/Lxyz3/Rxyz3 0.20 0.170 0.130 31 B4 − − − − 32/33/34 Ex4/Lx4/Rx4 0.44 − − 7度
罕遇35/36/37 Exy4/Lxy4/Rxy4 0.44 0.370 − 38/39/40 Exyz4/Lxyz4/Rxyz4 0.44 0.370 0.290 41 B5 − − − − 42/43/44 Ex5/Lx5/Rx5 0.60 − − 8度
(0.3 g)
设防45/46/47 Exy5/Lxy5/Rxy5 0.60 0.510 − 48/49/50 Exyz5/Lxyz5/Rxyz5 0.60 0.510 0.390 51 B6 − − − − 52/53/54 Ex6/Lx6/Rx6 0.80 − − 9度
设防55/56/57 Exy6/Lxy6/Rxy6 0.80 0.680 − 58/59/60 Exyz6/Lxyz6/Rxyz6 0.80 0.680 0.520 61 B7 − − − − 62 Ex7 1.00 − − − 63 Exy7 1.00 0.850 − 64 Exyz7 1.00 0.850 0.650 65 B8 − − − − 66 Ex8 1.24 − − 9度
罕遇67 Exy8 1.24 1.050 − 68 Exyz8 1.24 1.050 0.810 69 B9 − − − − 注：x向为平行于窑脸方向；y向为沿窑洞进深方向。
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表 4 模型结构自振频率与阻尼比
Table 4. Frequency and damping ratio of model structure
加载阶段 x向 y向 频率/Hz 阻尼比/(%) 频率/Hz 阻尼比/(%) 震前(B1) 18.36 1.34 15.04 4.97 输入0.07 g(B2) 17.97 1.44 14.84 7.32 输入0.14 g(B3) 17.96 1.64 14.55 7.69 输入0.28 g(B4) 16.99 1.75 14.00 8.45 输入0.44 g(B5) 15.53 2.60 13.96 9.77 输入0.60 g(B6) 14.45 2.73 13.96 9.80 输入0.80 g(B7) 12.01 4.30 12.69 9.22 输入1.00 g(B8) 9.08 6.30 10.54 9.34
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表 5 台面加速度和基础顶面加速度对比
Table 5. Comparison of acceleration between platform and foundation
输入加速度峰值/g x向(m/s2) y向(m/s2) 台面 基础顶面 比值 台面 基础顶面 比值 0.07 0.672 0.673 0.999 0.583 0.585 0.997 0.14 1.375 1.373 1.001 1.163 1.166 0.997 0.28 2.752 2.755 0.999 2.335 2.334 1.000 0.44 4.321 4.326 0.999 3.668 3.669 1.000 0.60 5.789 5.788 1.000 4.994 4.996 1.000 0.80 7.852 7.852 1.000 6.669 6.667 1.000 1.00 9.796 9.801 0.999 8.336 8.339 1.000
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