Modified Pyke's hysteretic model considering damping ratio
LIU Fang-cheng1, YANG Jun2, WU Meng-tao1,3
1.College of Civil Engineering, Hunan University of Technology, Zhuzhou 412007, China; 2.Department of Civil Engineering, the University of Hong Kong, Hong Kong, China; 3.Department of Civil Engineering, Tianjin University, Tianjin 300072, China
Abstract：The damping ratio is a dynamic soil property that indicates the capacity of energy dissipation under cyclic loadings, and it plays an important role in dynamic response analysis of sites and soil-structure systems. Based on the dynamic shear modulus curves and damping ratio curves in the references, the accuracy of damping ratio predicted by Pyke’s model is studied, and it is found that the predicted damping ratio by Pyke’s model largely exceeds the measured damping ratio in the range of large strain amplitude. A modified Pyke’s model for accurate simulation of damping ratio of soils, named as D-Pyke model, is proposed, which combines the damping ratio-based hysteretic curve equations with the unloading-reloading rules of the original Pyke’s model. The new model assumes that the fullness of the hyperbolic hysteresis curve is determined by the shape-factor that is determined from the experimental damping ratio curves according to the shear-strain amplitude of the current hysteretic loading curve. The shear-strain amplitude of the current hysteretic loading curve is calculated from the shear-stress amplitude based on the skeleton curve of soils, and the shear-stress amplitude is determined according to Pyke’s rules. Based on the results of cyclic simple shear tests on a silty clay, it is verified that the D-Pyke model simulates the nonlinear shear modulus and damping ratio properties more reasonably than the original Pyke’s model. The D-Pyke model inherits the advantages of Pyke’s model, i.e., it simulates well the ratcheting effects of soils under cyclic loadings, and it obeys simple unloading/reloading criteria under irregular loadings. The proposed model can provide a more reasonable constitutive simulation method for the analysis of soil response under stochastic loading.
[1] MASING G.Eigenspannungen und verfestigung beim messing[C]// Proceedings of the 2nd International Congress of Applied Mechanics. Zurich, 1926: 332-335. (MASING G.Residual stress and deformation of the brass[C]// Proceedings of the 2nd International Congress of Applied Mechanics. Zurich, 1926: 332-335. (in German)) [2] PHILLIPS C, HASHASH Y M A. Damping formulation for nonlinear 1D site response analyses[J]. Soil Dynamics and Earthquake Engineering, 2009, 29(7): 1143-1158. [3] IWAN W D.On a class of models for the yielding behavior of continuous and composite systems[J]. Journal of Applied Mechanics, 1967, 34: 612-617. [4] 王志良, 王余庆, 韩清宇. 不规则循环剪切荷载作用下土的黏弹塑性模型[J]. 岩土工程学报, 1980, 2(3): 10-19. (WANG Zhi-liang, WANG Yu-qing, HAN Qing-yu.Visco-elastoplastic model for soils under irregular cyclic loading[J]. Chinese Journal of Geotechnical Engineering, 1980, 2(3): 10-19. (in Chinese)) [5] 郑大同, 王天龙. 土的滞回特性及其模型化[C]// 中国土木工程学会第四界土力学及基础工程学术会议论文选集. 北京: 中国建筑工业出版社, 1986: 302-308. (ZHENG Da-tong, WANG Tian-long.Hysteretic properties of soils and its modelization[C]// Proceeding of the 4th Soil Mechanics and Foundation, CCES. Beijing: China Architecture and Building Press, 1986: 302-308. (in Chinese)) [6] 栾茂田, 林皋. 场地地震反应一维非线性计算模型[J]. 工程力学, 1998, 9(1): 94-103. (LUAN Mao-tian, LIN Gao.Ramberg-Osgood constitutive model with variable parameters for dynamic nonlinear analysis of soils[J]. Earthquake Engineering and Engineering Vibration, 1992, 12(2): 69-78. (in Chinese)) [7] MURAVSKII G.On description of hysteretic behaviour of materials[J]. International Journal of Solids and Structures, 2005, 42(9): 2625-2644. [8] 尚守平, 刘方成, 王海东. 基于阻尼的地震循环荷载作用下黏土非线性模型[J]. 土木工程学报, 2007, 40(3): 74-81. (SHANG Shou-ping, LIU Fang-cheng, WANG Hai-dong.Nonlinear model based on damping ratio for clay under seismic c loading[J]. China Civil Engineering Journal, 2007, 40(3): 74-81. (in Chinese)) [9] HASHASH Y, PHILLIPS C, GROHOLSKI D R.Recent advances in non-linear site response analysis[C]// Fifth International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics and Symposium in Honor of Professor I. M. Idriss. San Diego, 2010: 1-22. [10] PYKE R M.Nonlinear soil models for irregular cyclic loadings[J]. Journal of the Geotechnical Engineering Division, 1980, 105(6): 715-726. [11] KOKUSHO T.Cyclic triaxial test of dynamic soil properties for wide strain range[J]. Soils and Foundations, 1980, 20(2): 45-60. [12] SEED H B, WONG R T, IDRISS I M, et al.Moduli and damping factors for dynamic analyses of cohesionless soils[J]. Journal of Geotechnical Engineering, 1986, 112(11): 1016-1032. [13] SUN J I, GOLESORKHI R, SEED H B.Dynamic Moduli and Damping Ratios for Cohesive Soils[R]. Berkeley: University of California, 1988. [14] IDRISS I M, Response of soft soil sites during earthquakes[C]// Proceeding of a Memorial Symposium to Honor Professor Seed H. B. Berkeley: University of California, 1990. [15] VUCETIC M, DOBRY R.Effect of soil plasticity on cyclic response[J]. Journal of Geotechnical Engineering, 1991, 117(1): 89-107. [16] ISHIBASHI I, ZHANG X.Unified dynamic shear moduli and damping ratios of sand and clay[J]. Soils and Foundations, 1993, 33(1): 182-191. [17] DARENDELI M B.Development of a new family of normalized moduli reduction and material damping curves[D]. Austin: University of Texas at Austin, 2001. [18] VUCETIC M.Normalized behavior of clay under irregular cyclic loading[J]. Canadian Geotechnical Journal, 1990, 27(1): 29-46.
