Frequency-dependent equivalent linearization method based on strain interval reduction theory
ZHENG Shan-suo1,2, ZHANG Xiao-yu1,2, LONG Li1,2, CHEN Fang-ge1,2, HE Jun3, LI Ping4
1. School of Civil Engineering, Xi'an University of Architecture and & Technology, Xi'an 710055, China; 2. Key Lab of Structural Engineering and Earthquake Resistance, Ministry of Education, Xi'an, 710055, China; 3. China Qiyuan Engineering Corporation, Xi'an 710055, China; 4. Shaanxi Normal University, Xi'an 710055, China
Abstract：In order to overcome the problem of underestimating the high-frequency Fourier spectrum amplification ratio obtained by the original equivalent linearization method, a frequency-dependent equivalent linearization method considering the effective strain interval reduction is proposed. Based on the traditional equivalent linearization analysis theory, various frequency-dependent equivalent linear methods are combined. The standardized strain spectrum is utilized to characterize the relationship between the equivalent strain and the frequency. The concept of shear strain elastic threshold is introduced to modify the standardized strain spectrum amplitude at the frequency within the elastic strain range. The standardized strain spectrum is fitted by the Gaussian smoothing method, then the piecewise function for the effective strain interval reduction coefficient is established. The ground motion measurement records at vertical stations are utilized to investigate the reliability and applicability of the proposed method. The analysis results of various sites show that the method fully considers the actual situation of the larger shear modulus and smaller damping ratio. Those factors are corresponding to the high-frequency component of the ground motion. The proposed method gives the optimization results of the site seismic response in the high frequency band and provides a basis for the seismic design of the actual projects.
[1] IDRISS I M, SEED H B.Seismic response of horizontal soil layers[J]. Journal of the Soil Mechanics and Foundations Division, 1968, 94(4): 1003-1031. [2] FURUMOTO Y, SUGITO M, YASHIMA A. Frequency- dependent equivalent linearized technique for FEM response analysis of ground[C]// 12th World Conference on Earthquake Engineering, 2002, Auckland. [3] SUGITO M, GODA H, MASUDA T.Frequency dependent equi-linearized technique for seismic response analysis of multi-layered ground[J]. Journal of Geotechnical Engineering, JSCE, 1994, 493(27): 49-58. [4] YOSHIDA N, KOBAYASHI S, SUETOMI I, et al.Equivalent linear method considering frequency dependent characteristics of stiffness and damping[J]. Soil Dynamics and Earthquake Engineering, 2002, 22(3): 205-222. [5] YOSHIDA N, SUETOMI I.DYNEQ: a computer program for dynamic analysis of level ground based on equivalent linear method[R]. Aichi-kon: Engineering Research Institute, Sato Kogyo Co. Ltd. 1996: 61-70. [6] KAUSEL E, ASSIMAKI D.Seismic simulation of inelastic soils via frequency-dependent moduli and damping[J]. Journal of Engineering Mechanics, 2002, 128(1): 34-47. [7] 蒋通, 邢海灵. 水平土层地震反应分析考虑频率相关性的等效线性化方法[J].岩土工程学报, 2007, 29(2): 218-224. (JIANG Tong, XING Hai-ling.An equivalent linear method considering frequency-dependent soil properties for seismic response analysis[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(2): 218-224. (in Chinese)) [8] 王伟, 刘必灯, 周正华, 等. 刚度和阻尼频率相关的等效线性化方法[J]. 岩土力学, 2010, 31(12): 3928-3933. (WANG Wei, LIU Bi-deng, ZHOU Zheng-hua, et al.Equivalent linear method considering frequency dependent stiffness and damping[J]. Rock and Soil Mechanics, 2010, 31(12): 3928-3933. (in Chinese)) [9] 袁晓铭, 李瑞山, 孙锐. 新一代土层地震反应分析方法[J]. 土木工程学报, 2016, 49(10): 95-102, 122.(YUAN Xiao-ming, LI Rui-shan, SUN Rui. A new generation method for earthquake response analysis of soil layers[J]. China Civil Engineering Journal, 2016. 49(10): 95-102, 122. (in Chinese)) [10] KIM D S, STOKOE K H, HUDSON W R.Deformational Characteristics of Soils at Small to Intermediate Strains from Cyclic Tests[M]. Austin: University of Texas at Austin, 1991. [11] OKUR D V, ANSAL A.Stiffness degradation of natural fine grained soils during cyclic loading[J]. Soil Dynamics and Earthquake Engineering, 2007, 27(9): 843-854. [12] VUCETIC M, DOBRY R.Effect of soil plasticity on cyclic response[J]. Journal of Geotechnical Engineering, 1991, 117(1): 89-107. [13] KIM B, HASHASH Y M A. Site response analysis using downhole array recordings during the March 2011 Tohoku-Oki earthquake and the effect of long-duration ground motions[J]. Earthquake Spectra, 2013, 29(S1): 37-54. [14] 侯云亮. 西安地区黄土地基剪切波速与工程特性相关性的研究[D]. 西安: 长安大学, 2007. (HOU Yun-liang.Research on Correlation Between Shear Wave Velocity and Engineering Properties of Soil in Xi'an Area Loss Ground[D]. Xi'an: Chang'an University, 2007. (in Chinese))
