PERIOD-DEPENDENT NONLINEAR CHARACTERISTICS OF SURFACE/BOREHOLE SPECTRAL ACCELERATION RATIOS

doi:10.3969/j.issn.0253-4967.2024.06.010

Abstract

Abstract:

Weak overburden layers at shallow surfaces would substantially affect the ground motion characteristic parameters of ground motion, such as spectral accelerations, and these influences regularly showed obvious nonlinearity with the increase of ground motion strength. Despite the differences between motions down the borehole and ground motions on bedrock, the surface/borehole spectral ratios could reflect the seismic site effect to some extent and overcome the shortcomings of the lack of reference bedrock stations in the standard spectral ratio method and the assumption of seismic point source in the generalized inversion method. In recent years, more and more scholars have studied the nonlinear dynamic characteristics of the soil body and its change trend based on the strong motion data by comparing the surface/borehole spectral acceleration ratios under different motion strengths. However, the research conclusions, especially the quantitative characterization of the nonlinear characteristics, still need to be improved due to the insufficient statistical sample size.

It was found that the surface/borehole spectral acceleration ratio curves at the same station exhibited high similarity under different motion strengths. However, these spectral acceleration ratios significantly decreased as motion strength increased and shifted towards longer periods at certain period ranges. The surface/borehole spectral acceleration ratios at different motion strengths corresponding to the same period point cannot adequately reflect their nonlinear characteristics. It is more reasonable to characterize these features by the corresponding relationships between the points on the surface/borehole spectral acceleration ratio curve shapes at different motion intensities. Although some scholars have proposed methods for correcting the dominant frequency offset, there remains a lack of effective methods for fixing the period shift of the surface/borehole spectral acceleration ratio across the wholeentire period range, as well as for the quantitative characterization of nonlinear characteristic parameters throughout the wholeentire period range. Dynamic Time Warping(DTW)algorithm is a nonlinear alignment method that combines time alignment and measurement matching. The core idea of the Dynamic Time Warping(DTW)algorithm is to find the optimal mapping between two-time series by calculating the distance between their respective discrete points and identifying the best path connecting them. This process enables point-to-point matching between the two-time series, and the DTW distance(sum of distances along the best path)can be utilized to assess their similarity.

In this study, we selected 166 700 strong-motion records from 180 stations in Japan's KiK-net network them. We grouped them by ground motion intensity to obtain the surface/borehole spectral acceleration ratios and their average values for each station under different intensity levels. A dynamic time warping algorithm was employed to effectively correct long-period shifts in the spectral acceleration ratio curves, which allowed for the precise extraction of both the period shift and amplitude attenuation values at various period points for each seismic station. Subsequently, a detailed statistical analysis was conducted to assess how these values varied about different levels of ground motion intensity. In addition, nonlinear characteristic parameter curves, dependent on both the period and seismic intensity changes, were derived for different site categories, accompanied by the establishment of corresponding empirical relationships. Furthermore, a novel method was proposed to predict the surface-to-borehole spectral ratio under conditions of strong seismic motion, utilizing the spectral acceleration ratio data obtained from weaker ground motion intensity scenarios. This approach is intended to offer more precise and detailed data support for adjusting nonlinear site effects in China's seismic design codes and seismic hazard zoning maps. Ultimately, the goal is to provide a more refined and comprehensive basis for enhancing the nonlinear site response adjustments in China's seismic design specifications and seismic motion parameter zoning maps.

The quantitative analysis of period offset characteristics of the surface/borehole spectral acceleration ratios indicated that the period offsets were more significant under larger motion strength. Meanwhile the period offsets at different periods were not consistent, and the relative period offsets at the same period exhibited linear relationships with motion strength under the double-logarithmic coordinates. The relative period offsets could be reliably expressed by the period offset coefficient defined empirically. The period offset coefficients obtained at each station and on each site class (Ⅰ, Ⅱ, Ⅲ, and Ⅳ) of Chinese standards were all related to the period, which showed a trend of initially increasing and subsequently decreasing with the increase of the period. Furthermore, the period offset coefficients increased with the thickness and softness of the overburden layers, which indicated more significant period offsets on sites of thick and soft overburden layers. The quantitative analysis of the amplitude decay characteristics of the surface/borehole spectral acceleration ratios indicated that the spectral ratio amplitude was lower under more considerable motion strength. Meanwhile, the amplitude rates at different periods were not consistent, and the spectral ratio amplitude at the same period exhibited fine linear relationships with motion strength under the semi-logarithmic coordinates. The amplitude decay rate could be reliably expressed by the amplitude decay coefficient defined empirically. The amplitude decay coefficients obtained at each station and on each site class (Ⅰ, Ⅱ, Ⅲ, and Ⅳ) of Chinese standards were all related to the period. They approximately conformed to a Gaussian function under the semi-logarithmic coordinates, indicating that the amplitude decay rates were lower in the middle period range(the platform segment of spectral accelerations)compared to the shorter or longer period ranges. Moreover, the amplitude decay coefficients (<0) decreased with the thickness and softness of the overburden layers, which indicated faster amplitude decay rates on sites of thick and soft overburden layers. Despite the differences between surface/borehole spectral acceleration ratios and soil surface/bedrock surface spectral acceleration ratios, the period offset coefficients and amplitude decay coefficients derived statistically could reflect the nonlinear characteristics of seismic site effects to some extent. According to the empirical relationships for relative period offsets and amplitude decay rates of surface/borehole spectral acceleration ratios on different site classes (Ⅰ, Ⅱ, Ⅲ and Ⅳ) of Chinese standards, the surface/borehole spectral acceleration ratios under stronger motions could be predicted reliably by surface/borehole spectral acceleration ratios under weaker motion.

Key words: ground motion, engineering geological condition, local site effect, surface/borehole spectral acceleration ratio, dynamic time warping algorithm

摘要：

浅地表软弱覆盖土层会显著影响加速度反应谱等地震动特性表征参数, 且其影响程度随地震动强度增加呈现显著的非线性特征。文中基于日本KiK-net台网180个台站的166 700组强震动记录, 采用动态时间规整(DTW)算法对地表/井下反应谱谱比曲线的周期偏移进行修正, 定量分析了地表/井下反应谱谱比随地震动强度的周期偏移与幅值衰减特性, 发现相对周期偏移量与谱比幅值均与地震动强度在对数或半对数坐标系下呈线性关系, 且不同周期点的相对周期偏移与幅值衰减速率并不相同。统计获得了各台站及Ⅰ、 Ⅱ、 Ⅲ、 Ⅳ类场地上的周期偏移系数和幅值衰减系数, 发现其均随周期增加呈现先增大后减小的趋势, 表明在地震动能量丰富的加速度反应谱平台段, 地表/井下反应谱谱比曲线的周期偏移更为显著, 但幅值衰减则相对较慢。尽管地表/井下反应谱谱比与土层地表/基岩地表反应谱谱比之间存在差异, 统计得到的周期偏移系数和幅值衰减系数仍可在一定程度上反映地震动场地效应的非线性特征。

关键词: 地震动, 工程地质条件, 局部场地效应, 地表/井下反应谱谱比, 动态时间规整算法

WANG Lin, WANG Yu-shi, LI Xiao-jun, LIU Yan-qiong, DING Yi. PERIOD-DEPENDENT NONLINEAR CHARACTERISTICS OF SURFACE/BOREHOLE SPECTRAL ACCELERATION RATIOS[J]. SEISMOLOGY AND GEOLOGY, 2024, 46(6): 1391-1407.

王琳, 王玉石, 李小军, 刘艳琼, 丁毅. 地表/井下加速度反应谱谱比的周期相关非线性特征[J]. 地震地质, 2024, 46(6): 1391-1407.

Figures/Tables 10

Fig. 1 Distribution of magnitude, epicenter distance and borehole peak acceleration for selected records.

Fig. 2 Surface/ borehole spectral acceleration ratios under different strong-motion strengths at Station FKSH19.

Fig. 3 Schematic diagram of DTW algorithm regularization path for surface/borehole spectral acceleration ratios.

Fig. 4 Optimal mapping and period offset correction results of DTW algorithm regularization at Station FKSH19.

Fig. 5 Relative period offsets under different motion strengths and periods at Station FKSH19.

Fig. 6 Period offset coefficient α related to period on site class Ⅰ, Ⅱ, Ⅲ and Ⅳ.

Fig. 7 Surface/borehole spectral acceleration ratio after period offset correction and normalized surface/ borehole spectral acceleration ratio at Station FKSH19.

Fig. 8 Normalized surface/ borehole spectral acceleration ratio under different motion strengths and periods at Station FKSH19.

Fig. 9 Amplitude decay coefficient β related to period on site class Ⅰ, Ⅱ, Ⅲ and Ⅳ.

Table1 Regression coefficients between nonlinear characteristic parameters and periodicity for site Class Ⅰ, Ⅱ, Ⅲ and Ⅳ

非线性特征参数	回归系数	场地类别
非线性特征参数	回归系数	Ⅰ	Ⅱ	Ⅲ	Ⅳ
周期偏移系数 $α$	a	0.196	0.276	0.243	0.555
	b	0.06	0.07	0.09	0.13
	c	1.10	1.09	1.21	2.15
	d	0	0	0	-0.258
幅值衰减系数 $β$	$a_{1}$	0.069	0.124	0.141	0.102
	$b_{1}$	0.35	0.42	0.9	0.58
	$c_{1}$	0.593	0.581	0.176	1.08
	$a_{2}$	0.008	0.027	0.012	0.0075
	$b_{2}$	0.132	0.240	0.220	0.242

Table1 Regression coefficients between nonlinear characteristic parameters and periodicity for site Class Ⅰ, Ⅱ, Ⅲ and Ⅳ

非线性特征参数	回归系数	场地类别
非线性特征参数	回归系数	Ⅰ	Ⅱ	Ⅲ	Ⅳ
周期偏移系数 $α$	a	0.196	0.276	0.243	0.555
	b	0.06	0.07	0.09	0.13
	c	1.10	1.09	1.21	2.15
	d	0	0	0	-0.258
幅值衰减系数 $β$	$a_{1}$	0.069	0.124	0.141	0.102
	$b_{1}$	0.35	0.42	0.9	0.58
	$c_{1}$	0.593	0.581	0.176	1.08
	$a_{2}$	0.008	0.027	0.012	0.0075
	$b_{2}$	0.132	0.240	0.220	0.242

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