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Article(id=1245390008870355046, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390004252426256, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0315, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1668614400000, receivedDateStr=2022-11-17, revisedDate=1680105600000, revisedDateStr=2023-03-30, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853716342, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853716342, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853716342, creator=13701087609, updateTime=1774853716342, updator=13701087609, issue=Issue{id=1245390004252426256, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='3', pageStart='1', pageEnd='230', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853715241, creator=13701087609, updateTime=1774854338522, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245392618545332491, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390004252426256, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245392618545332492, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245390004252426256, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=157, endPage=163, ext={EN=ArticleExt(id=1245390009201705069, articleId=1245390008870355046, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Experimental studies on soil deformation under seismic loads, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to study the effect of irregular seismic loads on soil deformation characteristics, systematic dynamic triaxial tests were carried out on sand samples in this study. In the test, four irregular seismic stress time histories with different peak values and constant amplitude cyclic sinusoidal loads with 20 cycles were applied to three sand samples with different densities for comparative study. The results show that the strain growth curves of sand samples are significantly different under the input of seismic loads and constant amplitude cyclic loads, and the load type and load waveform are the main factors affecting the strain time history development characteristics of soil elements. The correction coefficient obtained by considering the load irregularity is affected by the load type and the relative compactness of sand, and is not affected by the magnitude of the dynamic stress amplitude of the input loads and the type of sand. Finally, for the calculation of soil element deformation under seismic loads, an estimation method based on conventional constant amplitude triaxial deformation test is given.

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为研究不规则地震荷载对土体变形特性的影响，对砂土试样开展了系统的动三轴试验。试验中分别对3种不同密度砂土试样施加了4条具有不同峰值的不规则地震应力时程及其循环次数为20周的等幅正弦荷载，以便开展对比研究。结果表明：在地震荷载及其等幅循环荷载输入下，砂土试样的应变增长曲线差异显著，荷载类型及荷载波形是影响土单元应变时程发展特征的主要因素。考虑荷载不规则性得到的修正系数受荷载类型和砂土相对密实度的影响，不受输入荷载动应力幅值大小及砂土类型的影响。最后针对地震荷载下土单元变形的计算，给出了以常规的等幅三轴变形试验为依据的估算方法。

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袁晓铭（1963—），男，研究员，博士，主要从事土动力学和岩土工程研究。E-mail：
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孟凡超（1981—），男，副教授，博士，主要从事岩土地震工程研究。E-mail：

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孟凡超（1981—），男，副教授，博士，主要从事岩土地震工程研究。E-mail：

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孟凡超（1981—），男，副教授，博士，主要从事岩土地震工程研究。E-mail：

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label=Fig. 1, caption=Seismic wave input in the tests, figureFileSmall=J9l6Uq71o60z5j74NiZG7Q==, figureFileBig=lbg47qTUmcQEaoFC7M5LKA==, tableContent=null), ArticleFig(id=1245390014478139772, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=CN, label=图1, caption=试验输入地震波, figureFileSmall=J9l6Uq71o60z5j74NiZG7Q==, figureFileBig=lbg47qTUmcQEaoFC7M5LKA==, tableContent=null), ArticleFig(id=1245390014851432849, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=EN, label=Fig. 2, caption=Strain time histories of sand under actual seismic waves and constant-amplitude cyclic loads, figureFileSmall=6E6CBCnBsEX5MLTvYefikA==, figureFileBig=aHUxxffIxVefS56FtMps6A==, tableContent=null), ArticleFig(id=1245390014977261978, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=CN, label=图2, caption=地震荷载与等幅往返荷载输入下砂土试样应变时程, figureFileSmall=6E6CBCnBsEX5MLTvYefikA==, figureFileBig=aHUxxffIxVefS56FtMps6A==, tableContent=null), ArticleFig(id=1245390015094702502, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=EN, label=Fig. 3, caption=Correction coefficient C under different seismic wave, figureFileSmall=TzIT7Zu0WGQktUE6+6o2Vg==, figureFileBig=GCaBE1TMaWq0KmEGLLEN+g==, tableContent=null), ArticleFig(id=1245390015212143024, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=CN, label=图3, caption=不同输入波形影响下的修正系数C, figureFileSmall=TzIT7Zu0WGQktUE6+6o2Vg==, figureFileBig=GCaBE1TMaWq0KmEGLLEN+g==, tableContent=null), ArticleFig(id=1245390015329583541, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=EN, label=Fig. 4, caption=Correction coefficient C under different amplitudes, figureFileSmall=lEM6TAmVu5NM/U2ymJZf3w==, figureFileBig=zJ3febo/PMJ4pJWoRStYEQ==, tableContent=null), ArticleFig(id=1245390015455412670, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=CN, label=图4, caption=不同幅值输入下的修正系数C, figureFileSmall=lEM6TAmVu5NM/U2ymJZf3w==, figureFileBig=zJ3febo/PMJ4pJWoRStYEQ==, tableContent=null), ArticleFig(id=1245390015572853190, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=EN, label=Fig. 5, caption=Correction coefficient C with different densities, figureFileSmall=thmZ9v0eLkfNERc6/dvWMw==, figureFileBig=RzWDd/zCxoawPcM4SH8mWQ==, tableContent=null), ArticleFig(id=1245390015652544970, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=CN, label=图5, caption=不同相对密实度下的修正系数C, figureFileSmall=thmZ9v0eLkfNERc6/dvWMw==, figureFileBig=RzWDd/zCxoawPcM4SH8mWQ==, tableContent=null), ArticleFig(id=1245390015744819665, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=EN, label=Fig. 6, caption=Relationship between correction coefficient C and relative density under different load types, figureFileSmall=+o0G2qKRTPqS472R7zl9JA==, figureFileBig=KU5hsatNEPRH6lvGjyvifA==, tableContent=null), ArticleFig(id=1245390015816122844, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=CN, label=图6, caption=修正系数C与相对密实度在不同荷载类型下的关系, figureFileSmall=+o0G2qKRTPqS472R7zl9JA==, figureFileBig=KU5hsatNEPRH6lvGjyvifA==, tableContent=null), ArticleFig(id=1245390015916786149, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=EN, label=Fig. 7, caption=Relationship between correction coefficient C and relative density, figureFileSmall=UwyAlBRX5MJ6mooUseAg1Q==, figureFileBig=8wbBBeKSxqq2ndlJ0f/JRw==, tableContent=null), ArticleFig(id=1245390016004866545, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=CN, label=图7, caption=修正系数C与相对密实度的关系, figureFileSmall=UwyAlBRX5MJ6mooUseAg1Q==, figureFileBig=8wbBBeKSxqq2ndlJ0f/JRw==, tableContent=null), ArticleFig(id=1245390016097141241, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=EN, label=Table 1, caption=

Physical index of the sands used in tests

, figureFileSmall=null, figureFileBig=null, tableContent=
土类最大干密度/（N/m3）最小干密度/（N/m3）粒径/mm不均匀系数
d10d50d60
哈尔滨砂16.9014.800.260.350.401.54
福建标准砂18.0014.900.250.450.602.40
), ArticleFig(id=1245390016210387461, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=CN, label=表1, caption=

试验用砂的物性指标

, figureFileSmall=null, figureFileBig=null, tableContent=
土类最大干密度/（N/m3）最小干密度/（N/m3）粒径/mm不均匀系数
d10d50d60
哈尔滨砂16.9014.800.260.350.401.54
福建标准砂18.0014.900.250.450.602.40
), ArticleFig(id=1245390016319439375, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=EN, label=Table 2, caption=

Correction coefficient C considering load types

, figureFileSmall=null, figureFileBig=null, tableContent=
荷载类型松砂Dr = 30%中密砂Dr = 50%密砂Dr = 75%
冲击型荷载1.611.080.76
振动型荷载0.460.350.26
), ArticleFig(id=1245390016411714074, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=CN, label=表2, caption=

考虑荷载类型取值的修正系数C

, figureFileSmall=null, figureFileBig=null, tableContent=
荷载类型松砂Dr = 30%中密砂Dr = 50%密砂Dr = 75%
冲击型荷载1.611.080.76
振动型荷载0.460.350.26
), ArticleFig(id=1245390016508183079, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245390008870355046, language=EN, label=Table 3, caption=

Value of correction coefficient C

, figureFileSmall=null, figureFileBig=null, tableContent=
松砂Dr = 30%中密砂Dr = 50%密砂Dr = 75%
1.050.710.51
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修正系数C取值

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松砂Dr = 30%中密砂Dr = 50%密砂Dr = 75%
1.050.710.51
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地震荷载作用下土体变形试验研究
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孟凡超 1, 2 , 袁晓铭 3, 4
地震工程与工程振动 | 2024,44(3): 157-163
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地震工程与工程振动 | 2024, 44(3): 157-163
地震荷载作用下土体变形试验研究
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孟凡超1, 2 , 袁晓铭3, 4
作者信息
  • 1.防灾科技学院，河北 三河 065201
  • 2.河北省地震灾害防御与风险评价重点实验室，河北 三河 065201
  • 3.中国地震局工程力学研究所 地震工程与工程振动重点实验室，黑龙江 哈尔滨 150080
  • 4.地震灾害防治应急管理部重点实验室，黑龙江 哈尔滨 150080

    • 孟凡超（1981—），男，副教授，博士，主要从事岩土地震工程研究。E-mail：

通讯作者:

袁晓铭（1963—），男，研究员，博士，主要从事土动力学和岩土工程研究。E-mail：
Experimental studies on soil deformation under seismic loads
Fanchao MENG1, 2 , Xiaoming YUAN3, 4
Affiliations
  • 1.Institute of Disaster Prevention, Sanhe 065201, China
  • 2.Hebei Key Laboratory of Earthquake Disaster Prevention and Risk Assessment, Sanhe 065201, China
  • 3.Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
  • 4.Key Laboratory of Earthquake Disaster Mitigation, Ministry of Emergency Management, Harbin 150080, China
doi: 10.13197/j.eeed.2024.0315
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摘要
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为研究不规则地震荷载对土体变形特性的影响，对砂土试样开展了系统的动三轴试验。试验中分别对3种不同密度砂土试样施加了4条具有不同峰值的不规则地震应力时程及其循环次数为20周的等幅正弦荷载，以便开展对比研究。结果表明：在地震荷载及其等幅循环荷载输入下，砂土试样的应变增长曲线差异显著，荷载类型及荷载波形是影响土单元应变时程发展特征的主要因素。考虑荷载不规则性得到的修正系数受荷载类型和砂土相对密实度的影响，不受输入荷载动应力幅值大小及砂土类型的影响。最后针对地震荷载下土单元变形的计算，给出了以常规的等幅三轴变形试验为依据的估算方法。

地震荷载  /  变形特性  /  等幅往返荷载  /  修正系数  /  估算方法

In order to study the effect of irregular seismic loads on soil deformation characteristics, systematic dynamic triaxial tests were carried out on sand samples in this study. In the test, four irregular seismic stress time histories with different peak values and constant amplitude cyclic sinusoidal loads with 20 cycles were applied to three sand samples with different densities for comparative study. The results show that the strain growth curves of sand samples are significantly different under the input of seismic loads and constant amplitude cyclic loads, and the load type and load waveform are the main factors affecting the strain time history development characteristics of soil elements. The correction coefficient obtained by considering the load irregularity is affected by the load type and the relative compactness of sand, and is not affected by the magnitude of the dynamic stress amplitude of the input loads and the type of sand. Finally, for the calculation of soil element deformation under seismic loads, an estimation method based on conventional constant amplitude triaxial deformation test is given.

seismic loads  /  deformation feature  /  constant-amplitude cyclic loads  /  correction coefficient  /  estimation method
孟凡超, 袁晓铭. 地震荷载作用下土体变形试验研究. 地震工程与工程振动, 2024 , 44 (3) : 157 -163 . DOI: 10.13197/j.eeed.2024.0315
Fanchao MENG, Xiaoming YUAN. Experimental studies on soil deformation under seismic loads[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (3) : 157 -163 . DOI: 10.13197/j.eeed.2024.0315
正文
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0　引言
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探求土体变形特性在不规则地震荷载作用下的规律性，一直是岩土地震工程研究的主要任务。特别是提出和发展以性态抗震为指导理论以来，控制工程结构的稳定性，土体变形成为首要因素[1-8]。但目前随机地震荷载下土单元变形理论十分不成熟，仍然处于探索阶段，已不能适应现阶段我国工程抗震需求日益发展的现状。
为简化计算，普遍做法是将地震荷载下的土体变形转换为等幅正弦荷载来替代，SEED等[9]是最早提出该等价方法的学者，转换后的等幅应力取0.65倍地震峰值，与其相对应的等幅荷载作用次数，建议以地震震级来确定。大部分科研设计单位都是在这个基础上进行土体变形的研究和应用。但是，这种基于破坏意义上的等效作用次数的分析方法，随着科学研究的不断深入和工程实践要求的提高，在当前我国抗震规范和场地安全性评价中，特别是以烈度或加速度峰值作为基本参数，烈度与震级之间的对应不是很明确的情况下，暴露出了许多问题[10-13]，尤其体现在等效循环作用次数的确定上，使得等价往返次数的确定出现了模糊性和操作性不强的问题。
目前，国内外更倾向于使用固定次数（20周）的正弦荷载来代替地震荷载来开展研究，如袁晓铭等[11]针对黏性土变形问题开展了4组地震波与正弦波输入下的比较研究，其正弦荷载幅值取地震荷载的0.65倍，循环20次，20周等幅荷载下土体变形要大于地震荷载下的变形，对不同地震荷载，二者的比值平均为3.28倍。ISHIHARA等[14]针对饱和砂土液化问题，通过开展一系列动三轴试验进行的研究表明，液化地震剪应力大于等幅20次循环荷载液化剪应力，同时不同波形输入下试样抗液化能力不同，故将地震荷载转换成正弦荷载，循环作用20周，其修正系数C2应按荷载类型确定，对冲击型地震应力时程取1.89，对振动型的地震应力时程取1.64。后期，NAGASE等[15]针对该问题又进一步开展了液化单剪试验，并建议目前日本规范中以20周等幅荷载代替地震荷载确定液化强度时的修正系数C2应考虑砂土密实度的影响，并给出了修正系数。
以定次数等幅往返荷载代替真实地震荷载可避免等价往返作用次数确定上的模糊性，工程实践证明该方法也是可行的。然而，目前的研究主要是针对饱和砂土液化强度而展开，而不规则荷载对土体变形差异影响的研究则较少，有鉴于此，本文利用人工制备的砂土重塑试样开展动三轴测试研究，探讨土体在不规则地震荷载及其定次数循环等幅荷载作用下的变形差异，为进一步改进土体在地震荷载条件下变形的计算打下基础。
1　试验设计
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开展基于地震荷载和等幅往返荷载输入下的动三轴试验，以研究不规则地震荷载作用下的土单元残余应变问题。本研究使用的砂土试样分别取自福建标准砂和哈尔滨砂，试验试样采用湿捣法制作完成，砂样规格为标准大小，直径3.91 cm，高8 cm，其物理性质指标如表1所示。含水量为12%，砂样相对密实度采用Dr = 0.30、Dr = 0.50和Dr = 0.75的砂，分别代表3种状态：稍松、中密和密实。试验时采用偏压固结，施加围压200 kPa，固结比为1.7。
试验中输入的地震荷载，分别为冲击型荷载迁安波、天津波及振动型荷载北岭波、Loma Prieta波，波形如图1所示。地震荷载幅值分别选取160、240、320 kPa，通过调整输入时程曲线纵坐标比例尺的方法获得。输入的等幅正弦荷载峰值取其地震荷载峰值的0.65倍，即正弦荷载峰值分别为104、156、208 kPa，频率取1 Hz。共选取2种试验用砂，3种试样密度，输入5个波形、3组应力幅值，合计90种工况。
2　试验结果
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福建标准砂在相对密实度Dr为50%，输入地震峰值σmax为240 kPa、正弦荷载峰值为156 kPa工况下，试样变形时程的对比如图2所示。由图可知，在地震荷载和等幅正弦荷载输入条件下，砂土试样的应变增长曲线有显著差异。等幅正弦荷载输入下，初期土单元变形增长明显，而后土单元应变逐渐趋于稳定，但在地震荷载影响下，土单元应变时程明显受输入荷载波形控制。在冲击型荷载输入下，由于峰值远大于其他脉冲荷载，其峰值脉冲作用下的应变远大于其他脉冲荷载作用，且峰值前应变占最终应变的90%以上，而峰值后脉冲对土体变形基本没有贡献作用，如图1（a）和（b）所示。在振动型荷载输入下，除峰值外，其幅值较大的部分脉冲对变形的发展也起到了重要作用，但峰值前后同样大小脉冲对土体变形贡献截然不同，位于峰值前脉冲对变形的贡献要远大于峰值后，与冲击型荷载类似，峰值前试样变形占最终残余变形的90%以上，如图1（c）和（d）所示。
3　土单元变形影响因素分析
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将应力幅值等于地震应力峰值0.65倍的等幅循环荷载、20次循环作用的动三轴试验，作为标准测试。定义土单元在标准试验下的残余应变与地震荷载输入下的残余应变之比为应变修正系数C，代表标准试验与不规则地震荷载输入下的相对差别。下面将重点探讨系数C的大小及影响因素。
3.1　荷载类型对修正系数的影响
图3分别给出了4种不同地震荷载输入下修正系数C值的大小，由图可知，荷载波形对修正系数有较大影响，且呈现出一定的规律性。
以福建标准砂变形试验结果为例（图3（a）），在同为冲击型荷载的迁安波及天津波输入下，修正系数C大于1.0，说明等幅正弦荷载下的变形大于地震荷载作用。而在北岭波、Loma Prieta波的振动型荷载作用下，修正系数C小于1.0，说明等幅正弦荷载下的变形小于地震荷载作用。对冲击型荷载，天津波输入下的修正系数大于迁安波作用时的修正系数，不同密实度、不同峰值输入下，二者平均相差35%。而对振动型荷载而言，Loma Prieta波输入下的修正系数略小于北岭波作用下的修正系数，不同密实度、不同峰值输入下，二者平均相差11.6%。但当我们对比不同荷载类型的影响时，发现其修正系数差异较为显著，振动型荷载输入下的应变远大于冲击型荷载输入的应变，平均相差约207%。对比分析哈尔滨砂试验下应变结果，可以得到相同的结论，如图3（b）所示。由此可见，对于修正系数C，荷载类型对修正系数的影响要远大于相同荷载类型不同波形间的差异，而且这种影响规律不受密实度的影响，不受荷载峰值的大小影响，不受砂土的种类影响。
3.2　输入荷载大小对修正系数的影响
输入地震荷载峰值分别为160、240、320 kPa作用下修正系数C的大小，如图4所示。由图可知，在同一地震荷载作用下、相同密实度砂土的修正系数几乎不受输入荷载大小的影响，而基本为定值，同时这种变化规律不受输入荷载类型的影响，不受砂土相对密实度的影响，也不受砂土种类的影响。
以天津波作用下福建标准砂的松砂应变为例，输入地震动应力峰值分别为160、240、360 kPa时，其应变修正系数分别为1.40、1.38、1.41，修正系数平均值为1.40，福建标准砂其他工况及哈尔滨砂的试验结果均表现出相似的变化规律。总体来看，不同地震荷载输入下、相对密实度的砂土试样应变修正系数不同，当输入地震荷载峰值分别为160、240、320 kPa时，其修正系数与其均值的差值最大为22%，最小为0.64%，平均为12%。对于土工试验来说，其不同工况下的这种差异是可以接受的。
3.3　砂土相对密实度对修正系数的影响
砂土相对密实度分别在30%、50%、75%影响下修正系数C的变化，如图5所示。由图可知，相对密实度对修正系数影响较大且具有规律性，修正系数随密实度增大而减小。
由图5还可以观察到，无论是福建标准砂还是哈尔滨砂其应变修正系数明显较为集中分布于上下2个区域内，这主要反映了荷载类型对修正系数的影响，分布于上部的冲击型荷载输入下修正系数要明显高于分布于下部的振动型荷载输入。
3.4　砂土类别对修正系数的影响
由以上分析可知，对福建标准砂和哈尔滨砂而言，地震荷载类型、动应力幅值大小和砂土密实度对修正系数的影响具有相同的变化规律，且在试验工况相同情况下，2种砂土修正系数非常接近，因此可忽略其影响。
4　地震荷载下土体变形的简化估计方法
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综合上述分析可知，以正弦荷载输入下的标准动三轴试验（幅值为地震荷载峰值的0.65倍，循环20周）代替真实不规则地震荷载作用分析土单元的变形，其应变的修正系数C受输入地震荷载类型及砂土相对密实度的影响，不受输入荷载动应力大小及砂土类型的影响。
忽略输入荷载大小、相对密实度的影响，振动型荷载及冲击型荷载作用下不同相对密实度的应变修正系数分布及拟合曲线如图6所示。
根据拟合曲线，修正系数C随着砂土相对密实度的增加而减小，但冲击型荷载作用下的修正系数远大于振动型荷载作用下的修正系数。同时冲击型地震荷载输入下相对密实度小于0.55砂土试样，其变形修正系数大于1.0，即地震荷载作用下土单元的变形小于标准试验得到的变形；修正系数在振动型荷载和相对密实度大于0.55的冲击型荷载输入下都在1.0以下，即地震荷载输入下土单元的变形要大于标准试验得到的变形。
为工程应用方便，略去地震荷载类型的影响，其修正系数的拟合曲线如图7所示。由图可知，当砂土相对密实度小于0.34时，不考虑荷载类型的修正系数大于1.0，标准试验得到的土单元变形将偏大，当砂土相对密实度大于0.34时，如不考虑荷载类型影响，其修正系数小于1.0。
考虑荷载类型的影响时，对应于相对密实度为30%的松砂、50%的中密砂和75%的密砂其修正系数的取值如表2所示。如不考虑荷载类型的影响，其修正系数的取值如表3所示。
综合上述分析，地震荷载下砂土单元变形计算，可采用标准试验法进行简化估计，即以往返作用20次、应力幅值等于0.65倍地震应力峰值的等幅荷载的标准试验为基础，不规则地震荷载输入下土单元的变形等于定次数（循环次数20次）等幅荷载下的残余变形与修正系数之比。
本文给出的以等幅往返三轴变形试验为基础确定地震荷载下土单元变形的估计方法，具有操作方便、概念清晰，能够满足现有试验条件等优点，同时也体现了当今岩土工程抗震研究的发展方向。
5　结论
收起
地震荷载下土单元变形分析一直是岩土地震工程中亟需完善的重要课题，本文通过对砂土试样开展系统的动三轴试验，研究不规则地震荷载对土体变形特性的影响，主要得出以下结论：
1）在地震荷载和等幅正弦荷载输入条件下，砂土试样的应变增长曲线差异显著，地震荷载影响下，土单元应变时程明显受输入荷载波形控制。荷载类型及荷载波形是影响土单元应变时程发展特征的主要因素。
2）考虑荷载不规则性得到的修正系数受荷载类型和砂土相对密实度的影响，不受输入荷载动应力幅值大小及砂土类型的影响，修正系数随砂土相对密实度的增大而减小，冲击型荷载输入下的修正系数要大于振动型荷载输入。
3）针对地震荷载下土单元变形的计算，给出了以常规的等幅三轴变形试验为依据的估算方法。即以正弦荷载输入下的标准动三轴试验（幅值为地震荷载峰值的0.65倍，循环20周）代替真实不规则地震荷载作用分析土单元的变形。
基金
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  • 地震科技星火计划项目(XH204402)
文献
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2024年第44卷第3期
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doi: 10.13197/j.eeed.2024.0315
  • 接收时间：2022-11-17
  • 首发时间：2026-03-30
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  • 收稿日期：2022-11-17
  • 修回日期：2023-03-30
基金
地震科技星火计划项目(XH204402)
作者信息
    1.防灾科技学院，河北 三河 065201
    2.河北省地震灾害防御与风险评价重点实验室，河北 三河 065201
    3.中国地震局工程力学研究所 地震工程与工程振动重点实验室，黑龙江 哈尔滨 150080
    4.地震灾害防治应急管理部重点实验室，黑龙江 哈尔滨 150080

通讯作者:

袁晓铭（1963—），男，研究员，博士，主要从事土动力学和岩土工程研究。E-mail：
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