A predictive model on equivalent number of strain cycles for earthquake loads
GAO Guang-yun, SHI Chao, CHEN Qing-sheng
1. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China; 2. Department of Civil and Environmental Engineering, National University of Singapore, Singapore 117576
Abstract：The equivalent number of strain cycles plays an important role in seismic response analyses. The existing calculation methods for the equivalent number of strain cycles are mostly based on accumulated damage theories. However, the time history of an earthquake load is required in the prediction using these methods, which is complicated in the equivalent conversion. In order to address these issues, 296 records of horizontal seismic time-history records, which cover different kinds of the epicenter distance and magnitude, are used in this study. The equivalent number of strain cycles is calculated for the sand with a relative density of 45% subjected to the selected earthquake load. Based on the statistical analysis using the nonlinear mixed-effects model, a predictive model for the equivalent number of strain cycles is proposed for both unidirectional and bi-directional earthquake loads. By examining the p-value and the residual distribution, the results show that the predictive values are reasonable. The proposed predictive model is validated by the measured data.
高广运, 石超, 陈青生. 地震荷载等效循环周数的预测模型[J]. 岩土工程学报, 2015, 37(11): 2040-2044.
GAO Guang-yun, SHI Chao, CHEN Qing-sheng. A predictive model on equivalent number of strain cycles for earthquake loads. Chinese J. Geot. Eng., 2015, 37(11): 2040-2044.
[1] CHEN Q S, GAO G Y, YANG J. Dynamic response of deep soft soil deposits under multidirectional earthquake loading[J]. Engineering Geology, 2011, 121(1/2): 55-65. [2] 陈青生, 高广运, 何俊锋. 地震荷载不规则性对砂土震陷的影响[J]. 岩土力学, 2011, 32(12): 3713-3720. (CHEN Qing-sheng, GAO Guang-yun, HE Jun-feng. Effect of irregularity of earthquake loading on seismic compression of sand[J]. Rock and Soil Mechanics, 2011, 32(12): 3713-3720. (in Chinese)) [3] 陈青生, 熊 浩, 高广运. 地震荷载特征及其对砂土震陷影响试验研究[J]. 岩土工程学报,2014,36(8): 1483-1489. (CHEN Qing-sheng, XIONG Hao, GAO Guang-yun. Experimental study on properties of seismic loading and their influence on seismic compression in sands[J]. Chinese Journal Geotechnical Engineering, 2014, 36(8): 1483-1489. (in Chinese)) [4] MARTIN G R, FINN L W D, SEED H B. Fundamentals of liquefaction under cyclic loading[J]. Journal of the Geotechnical Engineering Division (ASCE), 1977, 103(GT6): 549-64. [5] YOUD T L, IDRISS I M. Liquefaction resistance of soil: summary report from the 1996 NCEER and 1998 Geoenvironmental Eng (ASCE) 2001, 127(4): 297-313. [6] 孟凡超, 袁晓铭, 孙 锐. 不规则荷载下土体动力响应研究综述[J]. 世界地震工程, 2011, 27(2): 154-8. (MENG Fan-chao, YUAN Xiao-ming, SUN Rui. Review on soil dynamic response under irregular loads[J]. World Earthquake Engineering. 2011, 27(2): 154-8. (in Chinese)) [7] SEED H B. Representation of irregular stress time histories by equivalent uniform stress series in liquefaction analyses[R]. California: Earthquake Engineering Research Center, College of Engineering, University of California, 1975. [8] GREEN R A, TERRI G A. Number of equivalent cycles concept for liquefaction evaluations: revisited[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2005, 131(4): 477-88. [9] 陈青生, 熊 浩, 高广运. 基于R_N 非线性疲劳损伤累积模型的砂土震陷计算方法[J]. 岩土工程学报, 2013, 35(12): 2203-2211. (CHEN Qing-sheng, XIONG Hao, GAO Guang-yun. Procedure for evaluating seismic compression in sands based on R-N cumulative damage fatigue nonlinear model[J]. Chinese Journal Geotechnical Engineering, 2013, 35(12): 2203-2211. (in Chinese)) [10] LIU A H, STEWART J P, ABRAHAMSON N A, et al. Equivalent number of uniform stress cycles for soil liquefaction analysis[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2001, 127(12): 1017-26. [11] 李春明. 混合效应模型在森林生长模型中的应用[J]. 林业科学, 2009, 45(4): 131-8. (LI Chun-ming. Application of mixed effects models in forest growth model[J]. Scientia Silvae Sinicae, 2009, 45(4): 131-8. (in Chinese)) [12] MCGUIRE R K, SILVA W J, COSTANTINO C J. Technical basis for revision of regulatory guidance on design ground motions: Hazard-and risk-consistent ground motion spectra guidelines[C]// US Nuclear Regulatory Commission, Washington D C, 2001. [13] 陈青生, 高广运, GREEN R A, 等. 砂土震陷分析中多维地震荷载等效循环周数计算[J]. 世界地震工程, 2010, 26: 6-12. (CHEN Qing-sheng, GAO Guang-yun, GREEN R A. Computation of equivalent number of uniform strain cycles for seismic compression of sand subjected to multi- directional earthquake loading[J]. World Earthquake Engineering, 2010, 26: 6-12. (in Chinese)) [14] Program-R (version 2.5.0). “A language and environment for statistical computing and graphics[CP/OL]. 2012. http:// www.r- project.org/.” [15] STAFFORD P J, BOMMER J J. Empirical equations for the prediction of the equivalent number of cycles of earthquake ground motion[J]. Soil Dynamics and Earthquake Engineering, 2009, 29: 1425-1436.
