精度可控地基阻抗力的一种时域差分计算方法
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摘要
将集总参数模型与时域差分递归的滤波器模型相结合,提出了一种可完整考虑基础阻抗函数中奇异项和正则项且精度可控的时域地基阻抗力的计算方法,数值算例表明该方法在感兴趣的频域范围内对频率相关的阻抗函数拟合良好.
Interaction forces between foundation and structure is one of key problems in nonlinear dynamic response analysis of structures accounting for soil-structure dynamic interaction. Currently there are two kinds of methods dealing with it: one is the direct integrity analysis approach, and the other is time-domain substructure approach. Because of far less computational cost comparison to the former, the time-domain substructure approach is very important in engineering. The fact that foundation impedance complexly varies with frequency makes the calculation of time-domain foundation resisting force time-consuming. To simplify the calculation of the time-domain foundation resisting force, many lumped-parameter models have been proposed. Lumped-parameter model reflects the singular component of foundation impedance which is not square integrable and corresponds to simultaneous effect. Nevertheless the regular component can not be reflected accurately, which corresponds to time-delay effect and can be square integrable. The time-domain recursive model proposed by Safak (2006), used for representing the time-domain foundation resisting force, can simulate the regular component of foundation impedance. But the whole essential of foundation impedance can not be reflected in this model because the corresponding filter function has intrinsically limitation at Nyquist frequency. Thus, the time-domain foundation resisting force can not be simulated accurately. Combining the lumped-parameter model and the time-domain difference recursive filter model, a time-domain difference approach of accuracy controllable foundation resisting force is proposed. Numerical results demonstrate that the proposed procedure can perfectly fit the frequency dependent impedance in an interested frequency band.
Interaction forces between foundation and structure is one of key problems in nonlinear dynamic response analysis of structures accounting for soil-structure dynamic interaction. Currently there are two kinds of methods dealing with it: one is the direct integrity analysis approach, and the other is time-domain substructure approach. Because of far less computational cost comparison to the former, the time-domain substructure approach is very important in engineering. The fact that foundation impedance complexly varies with frequency makes the calculation of time-domain foundation resisting force time-consuming. To simplify the calculation of the time-domain foundation resisting force, many lumped-parameter models have been proposed. Lumped-parameter model reflects the singular component of foundation impedance which is not square integrable and corresponds to simultaneous effect. Nevertheless the regular component can not be reflected accurately, which corresponds to time-delay effect and can be square integrable. The time-domain recursive model proposed by Safak (2006), used for representing the time-domain foundation resisting force, can simulate the regular component of foundation impedance. But the whole essential of foundation impedance can not be reflected in this model because the corresponding filter function has intrinsically limitation at Nyquist frequency. Thus, the time-domain foundation resisting force can not be simulated accurately. Combining the lumped-parameter model and the time-domain difference recursive filter model, a time-domain difference approach of accuracy controllable foundation resisting force is proposed. Numerical results demonstrate that the proposed procedure can perfectly fit the frequency dependent impedance in an interested frequency band.
引文
1 Wolf JP. Dynamic Soil-structure Interaction. Prentice-Hall, 1985
2 Lysmer J, Richart FE. Dynamic response of footings to vertical loading. Journal of Engineering Mechanics, ASCE, 1969, 95(4): 65-91
3 Wolf JP. Somaini DR. Approximate dynamic model of embedded foundation in time domain. Earthquake Engineering and Structural Dynamics, 1986, 14(5): 683-703
4 De Barros, Luco JE. Discrete models for vertical vibrations of surface and embedded foundation. Earthquake Engineering and Structural Dynamics, 1990, 19(2): 289-303
5 Jean WY, Ling TW, Penzien J. System parameter of soil foundation for time domain dynamic analysis. Earthquake Engineering and Structural Dynamics, 1990, 19: 541-553
6栾茂田,林皋．地基动力阻抗的双自由度集总参数模型．大连理工大学学报,1996,36(4):477-482(Luan Maotian,Lin Gao．2-DOF lumped-parameter model of dynamic impedances of foundation soils. J of Dalian University of Technology, 1996, 36(4): 477-482 (in Chinese))
7侯兴民,廖振鹏．表面矩形基础阻抗函数的集中参数模型．地震工程与工程振动,1999,19(4):6-13(Hou Xingmin,Liaz,Zhen- peng. Lumped parameter models for impedance matrix of rigid rectangular foundations of the half-space. Earthquake Engineering and Engineering Vibration, 1999, 19(4): 6-13 (in Chinese))
8金峰,张楚汉,王光纶．拱坝-地基动力相互作用的时域模型．土木工程学报,1997,30(1):43~50(Jin Feng,Zhang Chuhan, Wang Guanglun. A time domain model of arch dam-rock foundation interaction. China Civil Engineering Journal, 1997, 30(1): 43-50 (in Chinese))
9 Wu WH, Lee WH. Systematic lumped-parameter models for foundations based on polynomial-fraction approximation. Earthquake Engineering and Structural Dynamics, 2002, 31(7): 1383-1412
10 Wolf JP. Spring-dashpot-mass models for foundation vibrations. Earthquake Engineering and Structural Dynamics, 1997, 26: 931-949
11 Wolf JP, Obernhuber P. Nonlinear soil-structure interaction analysis using dynamic stiffness or flexibility of soil in the time domain. Earthquake Engineering and Structural Dynamics, 1985, 13: 195-212
12 Nakamura N. A practical method to transform frequency dependent impedance to time domain. Earthquake Engineering and Structural Dynamics, 2006, 35(2): 217-231
13 Nakamura N. Improved methods to transform frequency-dependent complex stiffness to time domain. Earthquake Engineering and Structural Dynamics, 2006, 35(8): 1037-1050
14 Yan JY, Zhang CH, Jin F. A coupling procedure of FE and SBFE for soil-structure interaction in time domain. Int J for Numerical Method in Eng, 2004, 59(11): 1453-1471
15 Wolf JP, Motosaka M. Recursive evaluation of interaction forces of unbounded soil in the time domain. Earthquake Engineering and Structural Dynamics, 1989, 18(3): 345-363
16 Wolf JP, Motosaka M. Recursive evaluation of interaction forces of unbounded soil in the time domain from dynamic-stiffness coefficients in the frequency domain. Earthquake Engineering and Structural Dynamics, 1989, 18(3): 365-376
17 Safak E. Time-domain representation of frequency-dependent foundation impedance functions. Soil Dynamics and Earthquake Engineering, 2006, 26(1): 65-70
18 Veletsos AS, Wei YT. Lateral and rocking vibrations of footings. ASCE J Soil Mech Found Div, 1971, 97(SM 9): 1227-1248
19 Luco JE. Impedance functions for a rigid foundations on a layered medium. Nuclear Engineering and Design, 1974, 31: 204-217
20 Makris N, Gazetas G. Dynamic pile-soil-pile interaction PartⅡ: Lateral and seismic response. Earthquake Engineering and Structural Dynamics, 1992, 21(2): 145-162
21 Makris N, Gazetas G. Displacement phase differences in a harmonically oscillating pile. Geotechnique, 1993, 43(1): 135-150
2 Lysmer J, Richart FE. Dynamic response of footings to vertical loading. Journal of Engineering Mechanics, ASCE, 1969, 95(4): 65-91
3 Wolf JP. Somaini DR. Approximate dynamic model of embedded foundation in time domain. Earthquake Engineering and Structural Dynamics, 1986, 14(5): 683-703
4 De Barros, Luco JE. Discrete models for vertical vibrations of surface and embedded foundation. Earthquake Engineering and Structural Dynamics, 1990, 19(2): 289-303
5 Jean WY, Ling TW, Penzien J. System parameter of soil foundation for time domain dynamic analysis. Earthquake Engineering and Structural Dynamics, 1990, 19: 541-553
6栾茂田,林皋．地基动力阻抗的双自由度集总参数模型．大连理工大学学报,1996,36(4):477-482(Luan Maotian,Lin Gao．2-DOF lumped-parameter model of dynamic impedances of foundation soils. J of Dalian University of Technology, 1996, 36(4): 477-482 (in Chinese))
7侯兴民,廖振鹏．表面矩形基础阻抗函数的集中参数模型．地震工程与工程振动,1999,19(4):6-13(Hou Xingmin,Liaz,Zhen- peng. Lumped parameter models for impedance matrix of rigid rectangular foundations of the half-space. Earthquake Engineering and Engineering Vibration, 1999, 19(4): 6-13 (in Chinese))
8金峰,张楚汉,王光纶．拱坝-地基动力相互作用的时域模型．土木工程学报,1997,30(1):43~50(Jin Feng,Zhang Chuhan, Wang Guanglun. A time domain model of arch dam-rock foundation interaction. China Civil Engineering Journal, 1997, 30(1): 43-50 (in Chinese))
9 Wu WH, Lee WH. Systematic lumped-parameter models for foundations based on polynomial-fraction approximation. Earthquake Engineering and Structural Dynamics, 2002, 31(7): 1383-1412
10 Wolf JP. Spring-dashpot-mass models for foundation vibrations. Earthquake Engineering and Structural Dynamics, 1997, 26: 931-949
11 Wolf JP, Obernhuber P. Nonlinear soil-structure interaction analysis using dynamic stiffness or flexibility of soil in the time domain. Earthquake Engineering and Structural Dynamics, 1985, 13: 195-212
12 Nakamura N. A practical method to transform frequency dependent impedance to time domain. Earthquake Engineering and Structural Dynamics, 2006, 35(2): 217-231
13 Nakamura N. Improved methods to transform frequency-dependent complex stiffness to time domain. Earthquake Engineering and Structural Dynamics, 2006, 35(8): 1037-1050
14 Yan JY, Zhang CH, Jin F. A coupling procedure of FE and SBFE for soil-structure interaction in time domain. Int J for Numerical Method in Eng, 2004, 59(11): 1453-1471
15 Wolf JP, Motosaka M. Recursive evaluation of interaction forces of unbounded soil in the time domain. Earthquake Engineering and Structural Dynamics, 1989, 18(3): 345-363
16 Wolf JP, Motosaka M. Recursive evaluation of interaction forces of unbounded soil in the time domain from dynamic-stiffness coefficients in the frequency domain. Earthquake Engineering and Structural Dynamics, 1989, 18(3): 365-376
17 Safak E. Time-domain representation of frequency-dependent foundation impedance functions. Soil Dynamics and Earthquake Engineering, 2006, 26(1): 65-70
18 Veletsos AS, Wei YT. Lateral and rocking vibrations of footings. ASCE J Soil Mech Found Div, 1971, 97(SM 9): 1227-1248
19 Luco JE. Impedance functions for a rigid foundations on a layered medium. Nuclear Engineering and Design, 1974, 31: 204-217
20 Makris N, Gazetas G. Dynamic pile-soil-pile interaction PartⅡ: Lateral and seismic response. Earthquake Engineering and Structural Dynamics, 1992, 21(2): 145-162
21 Makris N, Gazetas G. Displacement phase differences in a harmonically oscillating pile. Geotechnique, 1993, 43(1): 135-150
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