考虑脉冲参数随机性的近断层地震动降维建模

张钦; 刘子心; 刘章军

doi:10.11899/zzfy20230305

考虑脉冲参数随机性的近断层地震动降维建模

doi: 10.11899/zzfy20230305

张钦^1,,
刘子心²,
刘章军^1, ,

1.
武汉工程大学，土木工程与建筑学院, 武汉 430074
2.
防灾科技学院, 中国地震局建筑物破坏机理与防御重点实验室, 河北三河 065201

基金项目: 国家自然科学基金项目（51978543、52108444）；湖北省高等学校优秀中青年科技创新团队计划项目（T2020010）

详细信息

作者简介:
张钦，男，生于1998年。硕士研究生。主要从事工程结构抗震方面研究工作。E-mail：784338243@qq.com

通讯作者:
刘章军，男，生于1973年。教授，博士生导师。主要从事工程结构抗灾方面研究工作。E-mail：liuzhangjun73@aliyun.com

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出版历程
- 收稿日期: 2022-06-29
- 刊出日期: 2023-08-31

Dimension Reduction Modeling of Near-fault Ground Motion Considering Randomness of Pulse Parameters

Zhang Qin^1
,,
Liu Zixin²,
Liu Zhangjun^{1
, ,}

1.
School of Civil Engineering and Architecture, Wuhan Institute of Technology, Wuhan 430074, China
2.
Key Laboratory of Building Collapse Mechanism and Disaster Prevention, Institute of Disaster Prevention, China Earthquake Administration, Sanhe 065201, Hebei, China

摘要

摘要: 根据50组近断层脉冲型强震动记录，采用连续小波变换提取最强速度脉冲分量，建立最强速度脉冲峰值时刻的统计模型。对近断层地震动加速度高频分量的演变功率谱模型参数进行识别，并利用谱表示-随机函数方法实现了降维模拟，进而积分得到速度高频分量。对脉冲参数进行随机化处理，并采用改进Gabor小波模型随机模拟速度低频分量。将速度高频分量与低频分量叠加得到近断层地震动速度时程。数值算例表明，近断层地震动加速度代表性时程集合的幅值谱和反应谱均与实测记录拟合一致，验证了降维模拟方法的工程适用性。近断层脉冲型地震动的降维模拟与概率密度演化理论相结合，可实现工程结构的随机地震反应与抗震可靠性精细化分析。
- 近断层地震动 /
- 向前方向效应 /
- 速度脉冲识别 /
- 降维模拟
Abstract: Based on 50 groups of near-fault pulse-like ground motion records, the strongest velocity pulse component was extracted by continuous wavelet transform, and the statistical model of the peak time of strongest velocity pulse was established. At the same time, the parameters of the evolution power spectrum model of the high frequency component of near-fault ground motion acceleration are identified, and its dimension reduction simulation is realized by spectral representation-random function method, and then the high frequency component of velocity is obtained by integrating. Secondly, the pulse parameters are randomized and the improved Gabor wavelet model is used to simulate the low-frequency component of velocity. Finally, the process of near-fault ground motion velocity is obtained by superposing them. Numerical examples show that the amplitude spectrum and response spectrum of the representative time history set of near-fault ground motion acceleration are consistent with the measured records, which verifies the engineering applicability of the proposed method. The combination of dimension reduction simulation of near-fault pulse-like ground motion and probability density evolution theory can realize the subtle analysis of random seismic response and seismic reliability of engineering structures.
- Near-fault ground motion /
- Forward directivity /
- Velocity pulse identification /
- Dimension reduction simulation

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图 1 $ {t_{{\text{pk}}}} $与$ {M_{\text{W}}} $回归模型

Figure 1. Regression model between peak time$ {t_{{\text{pk}}}} $of the strongest velocity pulse and magnitude $ {M_{\text{W}}} $

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图 2 高频能量分布拟合曲线

Figure 2. High frequency energy distribution fitting curve

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图 3 低频脉冲模型参数的经验分布函数

Figure 3. Empirical distribution functions of low- frequency pulse model parameters

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图 4 近断层地震动高、低频分量代表性时程

Figure 4. Representative time-history of high and low frequency components of near-fault ground motions

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图 5 近断层地震动高、低频分量代表性样本集合均值、标准差的目标值与模拟值比较

Figure 5. Comparison of mean, standard deviation of representative time-history set of high and low frequency components upon near-fault ground motions with the target values

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图 6 近断层地震动的代表性时程

Figure 6. The representative time-histories of near-fault ground motions

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图 7 近断层地震动加速度反应谱、幅值谱模拟值与实测值的比较

Figure 7. Comparison of simulated value and measured value of response spectrum and amplitude spectrum of near-fault ground motion acceleration

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表 1 近断层脉冲型地震动记录信息

Table 1. Information of the measured records of near-fault pulse-like ground motions

RSN 编号	矩震级 M_W	断层距 R/km	脉冲周期 T_p/s	脉冲峰值 PGV/（cm·s⁻¹）	脉冲峰值时刻t_pk/s	RSN 编号	矩震级 M_W	断层距 R/km	脉冲周期 T_p/s	脉冲峰值 PGV/（cm·s⁻¹）	脉冲峰值时刻t_pk/s
150	5.7	3.10	1.23	49.60	2.725	1161	7.5	10.90	5.99	53.00	6.100
159	6.5	0.70	2.34	53.50	7.650	1176	7.5	4.80	4.95	90.60	11.750
161	6.5	10.40	4.40	36.70	8.880	4040	6.6	1.70	2.02	124.20	17.860
170	6.5	7.30	4.42	70.80	7.390	4065	6.0	2.90	1.22	35.80	4.915
171	6.5	0.10	3.42	116.40	4.980	4098	6.0	3.00	1.33	51.60	3.220
173	6.5	8.60	4.52	55.20	7.445	4100	6.0	3.00	1.08	57.90	3.185
178	6.5	12.90	4.50	55.80	8.210	4101	6.0	5.50	0.52	31.00	2.720
179	6.5	7.00	4.79	80.80	6.730	4102	6.0	3.60	1.02	43.50	3.115
180	6.5	4.00	4.13	96.50	7.195	4103	6.0	4.20	0.70	38.30	2.970
181	6.5	1.40	3.77	121.60	7.300	4107	6.0	2.50	1.19	81.90	3.445
182	6.5	0.60	4.38	111.90	5.880	4113	6.0	2.90	1.13	27.00	2.930
184	6.5	5.10	6.27	73.50	7.455	4115	6.0	2.60	1.19	56.50	3.120
185	6.5	7.50	4.82	73.40	7.075	4126	6.0	3.80	0.57	43.40	2.305
316	5.9	16.70	4.39	60.80	10.090	6887	7.0	18.10	12.60	59.90	31.130
451	6.2	0.50	1.07	76.80	3.585	6897	7.0	8.50	7.83	65.90	25.460
459	6.2	9.90	1.23	37.30	5.835	6911	7.0	7.30	9.92	106.10	24.840
568	5.8	6.30	0.81	68.30	1.405	6927	7.0	7.10	7.37	116.50	25.270
723	6.5	0.90	2.39	143.90	12.200	6928	7.0	25.70	10.60	30.20	21.590
838	7.3	34.90	9.13	28.80	14.960	6942	7.0	26.80	8.04	56.50	28.090
879	7.3	2.20	5.12	132.30	12.100	6960	7.0	13.60	9.39	63.80	26.220
900	7.3	23.60	7.50	55.80	18.440	6962	7.0	1.50	7.14	85.70	25.390
1106	6.9	1.00	1.09	105.60	7.820	6966	7.0	22.30	8.76	65.70	26.520
1114	6.9	3.30	2.83	103.00	9.850	6969	7.0	20.90	9.35	64.40	27.770
1119	6.9	0.30	1.81	95.60	5.390	6975	7.0	6.10	8.93	74.10	27.480
1120	6.9	1.50	1.55	153.20	6.170	8161	7.2	11.30	8.72	72.60	39.510

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表 2 近断层地震动高频分量模型参数取值

Table 2. Simulation parameters of high-frequency component in near-fault ground motion

参数	取值	参数	取值
频率离散点数N	1 600	地震动峰值加速度${ \overline{A}}_{\mathrm{max}} $	240 cm·s⁻²
截止频率上限$ \omega_{{\rm{u}}} $	50π rad·s⁻¹	峰值因子$ r $	2.6
截止频率下限$ \omega_{1} $	2π rad·s⁻¹	场地土卓越圆频率$ \omega_{{\rm{g}}} $	15.7 rad·s⁻¹
频率离散步长$ \Delta \omega $	0.094 rad·s⁻¹	场地土阻尼比$ \zeta_{{\rm{g}}} $	0.887
高、低频分界限$ f_{{\rm{r}}} $	2π rad·s⁻¹	基岩卓越圆频率$ \omega_{{\rm{f}}} $	1.57 rad·s⁻¹
地震动持时$ T $	30 s	基岩阻尼比$ \zeta_{{\rm{f}}} $	0.887
时间步长$ \Delta t $	0.02 s	样本数量$ n_{{\rm{sel}}} $	1 069

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表 3 近断层地震动低频脉冲成分模型参数取值

Table 3. Simulation parameters of low-frequency component in near-fault ground motion

模型参数	概率分布	概率分布系数
T_N	对数正态分布	M₁=1.028 1，S₁=0.903 4
$ \varphi $	正态分布	M₂=−0.66，S₂=2.80
PGV	广义极值分布	k=0.008 7，Sigma=24.64，M_u=58.47
$T_{\rm{p}} $	威布尔分布	S_c=4.998 4，S_a=1.405 5
注：M₁、S₁分别为对数正态分布的均值和标准差；M₂、S₂分别为正态分布的均值和标准差；Sigma、M_u、k分别为广义极值分布的尺度参数、位置参数和形状参数；S_c和S_a分别为威布尔分布的尺度参数和形状参数。

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