随机特性在地震动反应谱与强震地面运动模拟中的研究
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摘要
摘要
现阶段抗震设计规范中的设计反应谱是代表实际地震动反应谱两水平方向
的统计平均结果，隐含了两水平向反应谱特征周期相同的假定，其值由场地类别
和设计地震分组确定；而地震影响系数最大值则根据烈度确定。对于垂直方向设
计反应谱，规范中规定为水平向各周期点设计谱的 2/3 倍，一般认为其特征周期
与水平向相同。这种统计平均反应谱实际上包含了许多随机因素，三方向反应谱
之间的关系非常复杂,故仅用一条平均谱来代表是不能反映其真实性态的。本文
基于对大量美国西部地震记录的研究,分析了三方向反应谱在特征周期、谱值比
例、地震影响系数最大值和动力系数最大值等参数方面的差异,以及这些参数与
场地类别、震级和震中距的关系，对规范反应谱的改进提出一些参考的依据，使
结构抗震设计结果更趋于合理。
最后介绍了一种基于随机过程理论的强震地面运动模拟方法－随机方法,分
析表明该方法模拟的地震动加速度时程是合理的,可以应用于实际结构的抗震设
计。
The design response spectra in current Chinese seismic design code are defined
to represent an statistically average result of many horizontal ground acceleration
response spectra, therefore the characteristic periods of two horizontal ground
acceleration response spectra are assumed to be equal, the value is determined by site
category and seismic environment grouping, and the maximum horizontal seismic
effect coefficient is determined by design intensity indicated in seismic zonation.
Whereas the corresponding vertical design response spectra are usually assumed that
the horizontal design response spectra times 2/3,the characteristic period of vertical
design response spectra is taken same as that of horizontal component. However
actually an statistically average ground acceleration response spectra involve a set of
random factors, the relation among three components of the ground motion are
significantly complex, therefore the real state of three components cannot be
reasonably well represented by only one direction design response spectra. Based on
abundant acceleration records in western America, a study on difference among three
components is analyzed. Several parameters among three components are compared
including characteristic period, ratio of vertical ground acceleration response spectra
to the corresponding horizontal component, maximum seismic effect coefficient and
dynamic coefficient. In addition, effects of several factors such as seismic
magnitude,epicentral distance and local site conditions on these parameters are
discussed. Some conclusions are proposed to be used in modification of current
design response spectra. The results would be a means to improve seismic design of
structure.
Moreover, a stochastic method is introduced for simulating strong ground motion.
This method is based on the random process theory. Results of analyses indicate that
artificial acceleration time history obtained by stochastic method are adapted to be
used in engineering practice.
现阶段抗震设计规范中的设计反应谱是代表实际地震动反应谱两水平方向
的统计平均结果，隐含了两水平向反应谱特征周期相同的假定，其值由场地类别
和设计地震分组确定；而地震影响系数最大值则根据烈度确定。对于垂直方向设
计反应谱，规范中规定为水平向各周期点设计谱的 2/3 倍，一般认为其特征周期
与水平向相同。这种统计平均反应谱实际上包含了许多随机因素，三方向反应谱
之间的关系非常复杂,故仅用一条平均谱来代表是不能反映其真实性态的。本文
基于对大量美国西部地震记录的研究,分析了三方向反应谱在特征周期、谱值比
例、地震影响系数最大值和动力系数最大值等参数方面的差异,以及这些参数与
场地类别、震级和震中距的关系，对规范反应谱的改进提出一些参考的依据，使
结构抗震设计结果更趋于合理。
最后介绍了一种基于随机过程理论的强震地面运动模拟方法－随机方法,分
析表明该方法模拟的地震动加速度时程是合理的,可以应用于实际结构的抗震设
计。
The design response spectra in current Chinese seismic design code are defined
to represent an statistically average result of many horizontal ground acceleration
response spectra, therefore the characteristic periods of two horizontal ground
acceleration response spectra are assumed to be equal, the value is determined by site
category and seismic environment grouping, and the maximum horizontal seismic
effect coefficient is determined by design intensity indicated in seismic zonation.
Whereas the corresponding vertical design response spectra are usually assumed that
the horizontal design response spectra times 2/3,the characteristic period of vertical
design response spectra is taken same as that of horizontal component. However
actually an statistically average ground acceleration response spectra involve a set of
random factors, the relation among three components of the ground motion are
significantly complex, therefore the real state of three components cannot be
reasonably well represented by only one direction design response spectra. Based on
abundant acceleration records in western America, a study on difference among three
components is analyzed. Several parameters among three components are compared
including characteristic period, ratio of vertical ground acceleration response spectra
to the corresponding horizontal component, maximum seismic effect coefficient and
dynamic coefficient. In addition, effects of several factors such as seismic
magnitude,epicentral distance and local site conditions on these parameters are
discussed. Some conclusions are proposed to be used in modification of current
design response spectra. The results would be a means to improve seismic design of
structure.
Moreover, a stochastic method is introduced for simulating strong ground motion.
This method is based on the random process theory. Results of analyses indicate that
artificial acceleration time history obtained by stochastic method are adapted to be
used in engineering practice.
引文
1 周锡元，吴育才. 工程抗震的新发展. 清华大学出版社，暨南大学出版社，2002：
40~44
2 曹资，朱志达. 建筑抗震理论与设计方法.北京工业大学出版社，1997：56～
105
3 中华人民共和国国家标准，建筑抗震设计规范（GBJ50011-2001）.中国建筑工
业出版社，2001：7～29
4 胡聿贤. 地震工程学. 地震出版社，1988：614
5 周锡元,樊水荣,苏经宇. 场地分类和设计反应谱的特征周期－《建筑抗震设计规
范》修订简介（八）.工程抗震. 1999（4）：4~5
6 孙平善，杨柏坡等. 场地分类和地震动参数调整研究. 第五届全国地震工程会
议论文集（I）.中国建筑学会抗震防灾研究会，中国地震学会地震工程专业委
员会.1998.
7 薄景山. 场地分类和设计反应谱调整方法研究. 中国地震局工程力学研究所博
士后出站报告. 1998：45～53
8 周锡元，王广军，苏经宇. 场地.地基.设计地震. 地震出版社，1990：148～152
9 冶金工业部建筑研究总院工程抗震研究室编. 九国抗震设计规范汇编. 地震出
版社，1982：146～147
10 H.B.Seed,C.Ugas, J.Lysmer. Site Dependent Spectra for Earthquake Resistant
Design . Bull.Seis.Soc.Am. 1976，66：221～244
11 R.D.Borcherd. Estimates of Site-Dependent Response Spectra for Design
Methodology and Justification. Earthquake Spectra. 1994,10（4）:617-653
12 Geoffrey R.Martin, Ricardo Dobry. Earthquake Site Response and Seismic
Code Provisions. NCEER. 1994,8(4)
13 FEMA,NEHRP Recommended Provisions for Seismic Regullation for New
Building. 1994 Edition. Federal Emergency Management Agency. Washington
D.C.，1995
14 沈聚敏, 周锡元, 高小旺, 刘晶波. 抗震工程学. 中国建筑工业出版社，2000：
76～77
15 王广军，苏经宇. 国外抗震规范中设计反应谱的应用及进展. 建筑科学.1985
（5）
16 International Association for Earthquake Engineering(IAEE). Regulations for
Seismic Design. A World List,1996
- 62 -
参考文献
17 M.D.Trifunac，Anderson.J.G.. Preliminary Empirical Models for Scaling Absolute
Acceleration Spectra. Report No.CE 77-03. Department of Civil Engineering.
Univ.of Southern California.
18 Katayama,T.,Iwasaki.,T., Saeki,M. Statistical Analysis of Earthquake Acceleration
Response Spectra.Proc.JSCE.1978（275）
19 周雍年,震级,震中距和场地条件对地面运动反应谱的影响,地震工程与工程振
动. 1984，4（4）：14～21
20 王国权. 921 台湾集集地震近断层地面运动特征. 中国地震局地质研究所博士
学位论文. 2001：112
21 G.W.Housner. Characteristics of Strong Motion of Earthquakes. Bull.Seis.Soc.Am.
1947，37（1）：19～31
22 康仲远. 中外大城市灾例对比研究系列报告（四）－墨西哥地震和洛山矶北
岭地震. 灾害学. 1997，12(1)：64
23 大崎顺彦. 地震动的谱分析入门. 吕敏申,谢礼立. 地震出版社，1980：111
24 IBC2000(International Building Code). International Code Council,ICC.2000
25 周锡元，王国权，杨润林，高晓安. 1999 年 9 月 21 日台湾集集地震中不同场
地上峰值加速度的衰减特征. 大型复杂结构的关键科学问题及设计理论研究
论文集. 2001：407～413
26 周锡元，王广军，苏经宇. 多层场地土分类与抗震设计反应谱，建筑科学研
究报告. 中国建筑科学研究院. 1983（16）：35～37
27 中华人民共和国国家标准，建筑抗震设计规范（GBJ11-89）.现行建筑结构规
范大全（修订缩印本）. 中国建筑工业出版社，1994：983
28 伍平，于建华. 结构抗震设计中地震动输入的若干问题. 西南交通大学学报.
2002，37（增刊）：44～49
29 杜修力，胡晓，陈厚群. 强震地运动随机过程模拟. 地震学报.1995，17
（1）:104～109
30 D.M.Boore，G.M.Atkinson. Stochastic Prediction of Ground Motion and Spectral
Response Parameters at Hard-rock Sites in eastern North America. Bull.Seism.
Soc.Am.1987,77：440～467
31 Boore,D.M., W.B.Joyner, L.Wennerberg. Fitting the Stochastic ω2 Source Model
to Observed Response Spectra in western North America:trade-offs between ?σ
and k. Bull.Seism.Soc.Am.1992,82：1956～1963
32 Aki,K. Scaling Law of Seismic Spectrum. J.Geophys.Res.1967,72：1217～1231
33 Boore,D.M. Stochastic Simulation of High-frequency Ground Motions based on
Seismological Models of the Radiated Spectra. Bull.Seism.Soc.Am.1983,73：1865
～1894
- 63 -
北京工业大学工学硕士学位论文
34 Atkinson,G.M.，D.M.Boore. Ground Motion Relations for eastern North America.
Bull.Seism.Soc.Am.1995,85：17～30
35 Boatwright,J.，G..Choy. Acceleration Source Spectra Anticipated for Large
Earthquakes in northeastern North America. Bull.Seism.Soc.Am.1992，82：660～
682
36 Haddon,R. Earthquake Source Spectra in eastern North America. Bull.Seism.Soc.
Am.1996,86：1300～1313
37 Atkinson,G.M.，W.Sliva. Stochastic Modeling of California Ground Motions.
Bull.Seism.Soc.Am.2000,90：255～274
38 Hanks,T.C. b values and w-r Seismic Source Models:Implications for Tectonic
Stress Variations along Active Crustal Fault Zones and the Estimation of
High-frequency Strong Ground Motion. J.Geophys.Res.1979,84：2235～2242
39 McGuire,R.K.，T.C.Hanks. RMS Accelerations and Spectral Amplitudes of Strong
Ground Motion during the San Fernando,California,earthquake. Bull.Seism.Soc.
Am.1980,70：1907～1919
40 Hanks,T.C.，R.K.McGuire. The Character of High-frequency Strong Ground
Motion.Bull.Seism.Soc.Am.1981,71：2071～2095
41 David M.Boore. Simulation of Ground Motion using Stochastic Method. 2001：2～
18
42 杜修力, 陈厚群. 地震动随机模拟及其参数确定方法. 地震工程与工程振动.
1994,14(4):1~5
43 Boore.D.M. SMSIM-Fortan Programs for Simulating Ground Motions from
Earthquakes:version2.0-A Revision of OFR 96-80-A. U.S.Geol.Surv.Open-File
Rept.OF 00-509,55PP.2000: 40
44 Boore,D.M., W.B.Joyner, T.E.Fumal. Equations for Estimating Horizontal
Response Spectra and Peak Acceleration from western North American
Earthquakes:a summary of recent work. Seism.Res.Lett.1997,68:128~153
中 国 地 震 局 工 程 力 学 研 究 所 强 震 及 工 程 震 害 资 料 基 础 数 据 库 －
http://www.smsd-iem.net/
40~44
2 曹资，朱志达. 建筑抗震理论与设计方法.北京工业大学出版社，1997：56～
105
3 中华人民共和国国家标准，建筑抗震设计规范（GBJ50011-2001）.中国建筑工
业出版社，2001：7～29
4 胡聿贤. 地震工程学. 地震出版社，1988：614
5 周锡元,樊水荣,苏经宇. 场地分类和设计反应谱的特征周期－《建筑抗震设计规
范》修订简介（八）.工程抗震. 1999（4）：4~5
6 孙平善，杨柏坡等. 场地分类和地震动参数调整研究. 第五届全国地震工程会
议论文集（I）.中国建筑学会抗震防灾研究会，中国地震学会地震工程专业委
员会.1998.
7 薄景山. 场地分类和设计反应谱调整方法研究. 中国地震局工程力学研究所博
士后出站报告. 1998：45～53
8 周锡元，王广军，苏经宇. 场地.地基.设计地震. 地震出版社，1990：148～152
9 冶金工业部建筑研究总院工程抗震研究室编. 九国抗震设计规范汇编. 地震出
版社，1982：146～147
10 H.B.Seed,C.Ugas, J.Lysmer. Site Dependent Spectra for Earthquake Resistant
Design . Bull.Seis.Soc.Am. 1976，66：221～244
11 R.D.Borcherd. Estimates of Site-Dependent Response Spectra for Design
Methodology and Justification. Earthquake Spectra. 1994,10（4）:617-653
12 Geoffrey R.Martin, Ricardo Dobry. Earthquake Site Response and Seismic
Code Provisions. NCEER. 1994,8(4)
13 FEMA,NEHRP Recommended Provisions for Seismic Regullation for New
Building. 1994 Edition. Federal Emergency Management Agency. Washington
D.C.，1995
14 沈聚敏, 周锡元, 高小旺, 刘晶波. 抗震工程学. 中国建筑工业出版社，2000：
76～77
15 王广军，苏经宇. 国外抗震规范中设计反应谱的应用及进展. 建筑科学.1985
（5）
16 International Association for Earthquake Engineering(IAEE). Regulations for
Seismic Design. A World List,1996
- 62 -
参考文献
17 M.D.Trifunac，Anderson.J.G.. Preliminary Empirical Models for Scaling Absolute
Acceleration Spectra. Report No.CE 77-03. Department of Civil Engineering.
Univ.of Southern California.
18 Katayama,T.,Iwasaki.,T., Saeki,M. Statistical Analysis of Earthquake Acceleration
Response Spectra.Proc.JSCE.1978（275）
19 周雍年,震级,震中距和场地条件对地面运动反应谱的影响,地震工程与工程振
动. 1984，4（4）：14～21
20 王国权. 921 台湾集集地震近断层地面运动特征. 中国地震局地质研究所博士
学位论文. 2001：112
21 G.W.Housner. Characteristics of Strong Motion of Earthquakes. Bull.Seis.Soc.Am.
1947，37（1）：19～31
22 康仲远. 中外大城市灾例对比研究系列报告（四）－墨西哥地震和洛山矶北
岭地震. 灾害学. 1997，12(1)：64
23 大崎顺彦. 地震动的谱分析入门. 吕敏申,谢礼立. 地震出版社，1980：111
24 IBC2000(International Building Code). International Code Council,ICC.2000
25 周锡元，王国权，杨润林，高晓安. 1999 年 9 月 21 日台湾集集地震中不同场
地上峰值加速度的衰减特征. 大型复杂结构的关键科学问题及设计理论研究
论文集. 2001：407～413
26 周锡元，王广军，苏经宇. 多层场地土分类与抗震设计反应谱，建筑科学研
究报告. 中国建筑科学研究院. 1983（16）：35～37
27 中华人民共和国国家标准，建筑抗震设计规范（GBJ11-89）.现行建筑结构规
范大全（修订缩印本）. 中国建筑工业出版社，1994：983
28 伍平，于建华. 结构抗震设计中地震动输入的若干问题. 西南交通大学学报.
2002，37（增刊）：44～49
29 杜修力，胡晓，陈厚群. 强震地运动随机过程模拟. 地震学报.1995，17
（1）:104～109
30 D.M.Boore，G.M.Atkinson. Stochastic Prediction of Ground Motion and Spectral
Response Parameters at Hard-rock Sites in eastern North America. Bull.Seism.
Soc.Am.1987,77：440～467
31 Boore,D.M., W.B.Joyner, L.Wennerberg. Fitting the Stochastic ω2 Source Model
to Observed Response Spectra in western North America:trade-offs between ?σ
and k. Bull.Seism.Soc.Am.1992,82：1956～1963
32 Aki,K. Scaling Law of Seismic Spectrum. J.Geophys.Res.1967,72：1217～1231
33 Boore,D.M. Stochastic Simulation of High-frequency Ground Motions based on
Seismological Models of the Radiated Spectra. Bull.Seism.Soc.Am.1983,73：1865
～1894
- 63 -
北京工业大学工学硕士学位论文
34 Atkinson,G.M.，D.M.Boore. Ground Motion Relations for eastern North America.
Bull.Seism.Soc.Am.1995,85：17～30
35 Boatwright,J.，G..Choy. Acceleration Source Spectra Anticipated for Large
Earthquakes in northeastern North America. Bull.Seism.Soc.Am.1992，82：660～
682
36 Haddon,R. Earthquake Source Spectra in eastern North America. Bull.Seism.Soc.
Am.1996,86：1300～1313
37 Atkinson,G.M.，W.Sliva. Stochastic Modeling of California Ground Motions.
Bull.Seism.Soc.Am.2000,90：255～274
38 Hanks,T.C. b values and w-r Seismic Source Models:Implications for Tectonic
Stress Variations along Active Crustal Fault Zones and the Estimation of
High-frequency Strong Ground Motion. J.Geophys.Res.1979,84：2235～2242
39 McGuire,R.K.，T.C.Hanks. RMS Accelerations and Spectral Amplitudes of Strong
Ground Motion during the San Fernando,California,earthquake. Bull.Seism.Soc.
Am.1980,70：1907～1919
40 Hanks,T.C.，R.K.McGuire. The Character of High-frequency Strong Ground
Motion.Bull.Seism.Soc.Am.1981,71：2071～2095
41 David M.Boore. Simulation of Ground Motion using Stochastic Method. 2001：2～
18
42 杜修力, 陈厚群. 地震动随机模拟及其参数确定方法. 地震工程与工程振动.
1994,14(4):1~5
43 Boore.D.M. SMSIM-Fortan Programs for Simulating Ground Motions from
Earthquakes:version2.0-A Revision of OFR 96-80-A. U.S.Geol.Surv.Open-File
Rept.OF 00-509,55PP.2000: 40
44 Boore,D.M., W.B.Joyner, T.E.Fumal. Equations for Estimating Horizontal
Response Spectra and Peak Acceleration from western North American
Earthquakes:a summary of recent work. Seism.Res.Lett.1997,68:128~153
中 国 地 震 局 工 程 力 学 研 究 所 强 震 及 工 程 震 害 资 料 基 础 数 据 库 －
http://www.smsd-iem.net/
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