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Article(id=1228048673343472471, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228048667874095618, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.03.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1657555200000, receivedDateStr=2022-07-12, revisedDate=1662998400000, revisedDateStr=2022-09-13, acceptedDate=null, acceptedDateStr=null, onlineDate=1770719219766, onlineDateStr=2026-02-10, pubDate=1711555200000, pubDateStr=2024-03-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770719219766, onlineIssueDateStr=2026-02-10, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770719219766, creator=13701087609, updateTime=1770719219766, updator=13701087609, issue=Issue{id=1228048667874095618, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='3', pageStart='365', pageEnd='538', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770719218462, creator=13701087609, updateTime=1770795476854, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228368518803030940, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228048667874095618, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228368518803030941, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228048667874095618, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=436, endPage=447, ext={EN=ArticleExt(id=1228048673641268062, articleId=1228048673343472471, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Simplified mechanical model and seismic response for isolation tank considering soil-tank-liquid interaction, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to seek a kind of tank structure which can absorb shock and reduce costs，a new structure system of isolation tank is proposed. The restoring force model of rolling isolation is deduced by the principle of balances of forces，and the restoring force model of composite rolling isolation device is obtained. Based on the three-particle model and site soil model，the simplified mechanical model and motion equations of the new isolation tank considering soil-tank-liquid interaction （STLI） are proposed，and the seismic responses of seismic tank and new isolation tank that considered STLI and Non-STLI are studied under different sites. The results show that the new isolation tank can effectively reduce the base shear and overturning moment，but the control of the sloshing wave height is limited. It is suggested that in the high intensity area，under the premise of meeting the shaking wave height，the new isolation tank can be designed to reduce the intensity. After considering the STLI effect，the base shear and overturning moment of seismic tank decrease obviously. The discrepancy rate gradually increases from class Ⅰ site to class Ⅳ site，and the decrease is most significant in soft soil. The seismic responses of the new isolation tank are less affected by the STLI，which can effectively cut off the coupling between the superstructure and the site soil，and weaken the influence of the STLI effect on the superstructure.

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为了寻求一种既能减震又能降低成本的储罐结构，提出一种隔震储罐结构体系，根据力的平衡原则推导了滚动隔震装置恢复力模型，得出了复合滚动隔震装置的恢复力模型。基于三质点模型和场地土模型，提出了考虑土-储罐-液体相互作用（STLI）的隔震储罐的简化力学模型和运动方程，并研究了考虑STLI效应和不考虑STLI效应时抗震储罐和隔震储罐在不同场地的地震响应。结果表明：隔震储罐能够有效地降低其基底剪力及倾覆弯矩，但对晃动波高的控制有限，建议在高烈度区，满足晃动波高的前提下，隔震储罐在设计时可以降低烈度。考虑STLI效应后，抗震储罐的基底剪力和倾覆弯矩明显降低，且从Ⅰ类场地到Ⅳ类场地差异率逐渐增大，软土场地降低最为显著。隔震储罐地震响应受STLI效应的影响较小，可以有效地隔断上部结构与场地土之间的耦联，弱化STLI效应对上部结构的影响。

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孙建刚（1959—），男，博士，教授。电话：（0411）87557350；E-mail：。
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李想（1989—），男，博士研究生，讲师。电话：（0411）87557345；E-mail：。

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李想（1989—），男，博士研究生，讲师。电话：（0411）87557345；E-mail：。

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李想（1989—），男，博士研究生，讲师。电话：（0411）87557345；E-mail：。

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figureFileSmall=lbUxJyfJSqQoLG7TwYXjYQ==, figureFileBig=AAaMUa75vG7jPEslAFqX8A==, tableContent=null), ArticleFig(id=1228048698471547561, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图2, caption=本文提出的隔震储罐结构体系, figureFileSmall=lbUxJyfJSqQoLG7TwYXjYQ==, figureFileBig=AAaMUa75vG7jPEslAFqX8A==, tableContent=null), ArticleFig(id=1228048698563822252, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.3, caption=Composite rolling isolation device, figureFileSmall=HDi477921cmp94GxT0G3Ig==, figureFileBig=CsogV0VEkiXkcZuLmnGaWg==, tableContent=null), ArticleFig(id=1228048698630931119, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图3, caption=复合滚动隔震装置, figureFileSmall=HDi477921cmp94GxT0G3Ig==, figureFileBig=CsogV0VEkiXkcZuLmnGaWg==, tableContent=null), ArticleFig(id=1228048698706428597, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.4, caption=Stress analysis of upper groove, figureFileSmall=aOLQNmYdSweeBr22phmj5w==, figureFileBig=kyo7I2nUKtR2eVDSeUhp3Q==, tableContent=null), ArticleFig(id=1228048698765148857, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图4, caption=上凹槽受力分析图, figureFileSmall=aOLQNmYdSweeBr22phmj5w==, figureFileBig=kyo7I2nUKtR2eVDSeUhp3Q==, tableContent=null), ArticleFig(id=1228048698853229247, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.5, caption=Finite element simulation model, figureFileSmall=mpiKZd3F19RTWxZTCzwAog==, figureFileBig=xigwhNzAU2atimrfdKq/1Q==, tableContent=null), ArticleFig(id=1228048698924532422, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图5, caption=有限元仿真模型, figureFileSmall=mpiKZd3F19RTWxZTCzwAog==, figureFileBig=xigwhNzAU2atimrfdKq/1Q==, tableContent=null), ArticleFig(id=1228048699071333068, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.6, caption=Horizontal displacement excitation, figureFileSmall=VPJY1BmMluFehRacB3lElg==, figureFileBig=4JUjRueUcksF1WiHd9QUEg==, tableContent=null), ArticleFig(id=1228048699159413460, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图6, caption=水平位移激励, figureFileSmall=VPJY1BmMluFehRacB3lElg==, figureFileBig=4JUjRueUcksF1WiHd9QUEg==, tableContent=null), ArticleFig(id=1228048699264271066, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.7, caption=Hysteresis curves of restoring force model and finite element simulation model of rolling isolation device, figureFileSmall=hx/lHAEGzMWkkXtgIT13Jw==, figureFileBig=2vyaP7+a5UfkXI+pfplrFA==, tableContent=null), ArticleFig(id=1228048699364934369, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图7, caption=滚动隔震装置恢复力模型和有限元仿真模型滞回曲线, figureFileSmall=hx/lHAEGzMWkkXtgIT13Jw==, figureFileBig=2vyaP7+a5UfkXI+pfplrFA==, tableContent=null), ArticleFig(id=1228048699461403371, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.8, caption=Soil-structure mechanical model, figureFileSmall=NuV0E3CK3Qt4zhETPM0epQ==, figureFileBig=VU0Dq6k4kJTSjD9KfZqWNQ==, tableContent=null), ArticleFig(id=1228048699566260979, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图8, caption=土-结构力学模型, figureFileSmall=NuV0E3CK3Qt4zhETPM0epQ==, figureFileBig=VU0Dq6k4kJTSjD9KfZqWNQ==, tableContent=null), ArticleFig(id=1228048699633369848, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.9, caption=Mechanical analysis model of isolation tank considering STLI effect, figureFileSmall=ZTtbIgnqbA7GqyQkUUyLUA==, figureFileBig=ut3tMktV7GwSESQYF1TAew==, tableContent=null), ArticleFig(id=1228048699734033148, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图9, caption=考虑STLI效应的隔震储罐力学分析模型, figureFileSmall=ZTtbIgnqbA7GqyQkUUyLUA==, figureFileBig=ut3tMktV7GwSESQYF1TAew==, tableContent=null), ArticleFig(id=1228048699822113537, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.10, caption=Simplified mechanical model of isolation tank considering STLI effect, figureFileSmall=Jp/wfqt6YLILO/UHtn9siQ==, figureFileBig=/45WGzW/cyPQaT2Y0GNYRg==, tableContent=null), ArticleFig(id=1228048699897611014, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图10, caption=考虑STLI效应的隔震储罐简化力学模型, figureFileSmall=Jp/wfqt6YLILO/UHtn9siQ==, figureFileBig=/45WGzW/cyPQaT2Y0GNYRg==, tableContent=null), ArticleFig(id=1228048699973108493, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.11, caption=Finite element simulation model of lead core damper, figureFileSmall=SWYJWLCK4U+TcbwvRRqOjA==, figureFileBig=yOo5X313p30qi1TNLqRudQ==, tableContent=null), ArticleFig(id=1228048700073771796, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图11, caption=铅芯阻尼器有限元仿真模型, figureFileSmall=SWYJWLCK4U+TcbwvRRqOjA==, figureFileBig=yOo5X313p30qi1TNLqRudQ==, tableContent=null), ArticleFig(id=1228048700157657880, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.12, caption=Horizontal displacement excitation, figureFileSmall=mY5gFUr7yAm7fNSdUdU0MQ==, figureFileBig=NdYn1Isad/HVxiGuspXA2w==, tableContent=null), ArticleFig(id=1228048700254126879, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图12, caption=水平位移激励, figureFileSmall=mY5gFUr7yAm7fNSdUdU0MQ==, figureFileBig=NdYn1Isad/HVxiGuspXA2w==, tableContent=null), ArticleFig(id=1228048700354790178, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.13, caption=Hysteresis curves, figureFileSmall=xWnbZbZNKeS6iksd6qxk7g==, figureFileBig=BzhMnYXhOjBjafuKX3PtPA==, tableContent=null), ArticleFig(id=1228048700434481957, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图13, caption=滞回曲线, figureFileSmall=xWnbZbZNKeS6iksd6qxk7g==, figureFileBig=BzhMnYXhOjBjafuKX3PtPA==, tableContent=null), ArticleFig(id=1228048700497396521, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.14, caption=Finite element model of isolation tank considering STLI effect, figureFileSmall=8HLm91fyIeF86RCtYfN3NA==, figureFileBig=08GS3yNeymm32S5sFSzaSw==, tableContent=null), ArticleFig(id=1228048700581282607, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图14, caption=考虑STLI效应的隔震储罐有限元模型, figureFileSmall=8HLm91fyIeF86RCtYfN3NA==, figureFileBig=08GS3yNeymm32S5sFSzaSw==, tableContent=null), ArticleFig(id=1228048700652585781, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.15, caption=Acceleration response spectrum, figureFileSmall=14JEPM5UGkWiAdKkn/Wukw==, figureFileBig=6Zj6iiJR0L4loj47EHjWcg==, tableContent=null), ArticleFig(id=1228048700719694647, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图15, caption=加速度反应谱, figureFileSmall=14JEPM5UGkWiAdKkn/Wukw==, figureFileBig=6Zj6iiJR0L4loj47EHjWcg==, tableContent=null), ArticleFig(id=1228048702103814973, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.16, caption=Seismic response time-history curves, figureFileSmall=EBw0zwBj9PPmcdCcCW5HUQ==, figureFileBig=AxLd8KC48rs3BYmNfsxUAA==, tableContent=null), ArticleFig(id=1228048702162535235, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图16, caption=地震响应时程曲线, figureFileSmall=EBw0zwBj9PPmcdCcCW5HUQ==, figureFileBig=AxLd8KC48rs3BYmNfsxUAA==, tableContent=null), ArticleFig(id=1228048702254809926, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Fig.17, caption=Acceleration response spectrum, figureFileSmall=PFuWBbWRwcqIxZbdJJqN0Q==, figureFileBig=LbGEieTnja8mvY22n36GzA==, tableContent=null), ArticleFig(id=1228048702342890317, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=图17, caption=加速度反应谱, figureFileSmall=PFuWBbWRwcqIxZbdJJqN0Q==, figureFileBig=LbGEieTnja8mvY22n36GzA==, tableContent=null), ArticleFig(id=1228048702443553616, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Tab.1, caption=

Basic parameters of tank

, figureFileSmall=null, figureFileBig=null, tableContent=
储罐半径/m储液高度/m壁厚/m罐壁弹性模量/Pa液体密度/（kg·m-3）泊松比高径比基础半径/m基础埋置深度/m
8.2513.076.11×10-32.06×10111×1030.31.588.51.2
), ArticleFig(id=1228048702628102999, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=表1, caption=

储罐基本参数

, figureFileSmall=null, figureFileBig=null, tableContent=
储罐半径/m储液高度/m壁厚/m罐壁弹性模量/Pa液体密度/（kg·m-3）泊松比高径比基础半径/m基础埋置深度/m
8.2513.076.11×10-32.06×10111×1030.31.588.51.2
), ArticleFig(id=1228048702711989086, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Tab.2, caption=

Parameters of Bouc-Wen model

, figureFileSmall=null, figureFileBig=null, tableContent=
Aiβiγμikl/(N·m-1)α
1.5170017701817327900.003
), ArticleFig(id=1228048702800069479, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=表2, caption=

Bouc-Wen模型参数

, figureFileSmall=null, figureFileBig=null, tableContent=
Aiβiγμikl/(N·m-1)α
1.5170017701817327900.003
), ArticleFig(id=1228048702867178347, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Tab.3, caption=

Physical parameters of soil layer

, figureFileSmall=null, figureFileBig=null, tableContent=
土层覆盖厚度/m密度/(kg·m-3)弹性模量/MPa泊松比内摩擦角/（°）黏聚力/kPa剪切波速/（m·s-1）
素填土2.6160048.440.4128125
淤泥质黏土6159028.040.45108120
粉质黏土5.41840296.520.41620156
粗砂31850577.420.35280265
), ArticleFig(id=1228048702972035952, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=表3, caption=

土层物理参数

, figureFileSmall=null, figureFileBig=null, tableContent=
土层覆盖厚度/m密度/(kg·m-3)弹性模量/MPa泊松比内摩擦角/（°）黏聚力/kPa剪切波速/（m·s-1）
素填土2.6160048.440.4128125
淤泥质黏土6159028.040.45108120
粉质黏土5.41840296.520.41620156
粗砂31850577.420.35280265
), ArticleFig(id=1228048703068504952, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Tab.4, caption=

Seismic response comparison of theoretical model and finite element model

, figureFileSmall=null, figureFileBig=null, tableContent=
TaftPELLWD人工波3平均值平均值差异率/%
基底剪力/(106 N)理论模型1.2481.1961.2691.5261.3104.96
有限元模型1.3411.3781.131.651.375
倾覆弯矩/(107 N·m)理论模型0.9330.9710.9411.1771.00618.82
有限元模型1.0561.1861.191.3471.195
晃动波高/m理论模型0.3270.4450.1370.5440.36317
有限元模型0.3480.5180.1550.6790.425
), ArticleFig(id=1228048703148196733, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=表4, caption=

理论模型和有限元模型地震响应峰值对比

, figureFileSmall=null, figureFileBig=null, tableContent=
TaftPELLWD人工波3平均值平均值差异率/%
基底剪力/(106 N)理论模型1.2481.1961.2691.5261.3104.96
有限元模型1.3411.3781.131.651.375
倾覆弯矩/(107 N·m)理论模型0.9330.9710.9411.1771.00618.82
有限元模型1.0561.1861.191.3471.195
晃动波高/m理论模型0.3270.4450.1370.5440.36317
有限元模型0.3480.5180.1550.6790.425
), ArticleFig(id=1228048703211111296, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Tab.5, caption=

Seismic response comparison of sites Ⅰ，Ⅱ

, figureFileSmall=null, figureFileBig=null, tableContent=
计算内容Ⅰ类场地Ⅱ类场地
QiananGuangzhouTH1TG025人工波1LanzouRH2TH1TG035人工波2
忽略STLI效应基底剪力/(106 N)抗震18.69123.07720.88423.30820.41720.88419.19721.423
隔震1.4081.1121.4911.7451.5562.721.443.035
减震率/%92.4795.1892.8692.5192.3886.9892.585.83
倾覆弯矩/(107 N·m)抗震11.86514.32313.3814.37613.26613.21911.96813.901
隔震1.0181.2811.3081.2441.0711.9671.1952.044
减震率/%91.4291.0690.2291.3591.9385.1290.0285.3
晃动波高/m抗震0.3080.1560.4440.2060.4041.2850.5011.15
隔震0.2940.1550.4310.2240.3271.4110.4971.172
减震率/%4.640.92.93-8.7419.09-9.810.84-1.91
考虑STLI效应基底剪力/(106 N)抗震17.23820.7318.71121.26615.57113.63513.78517.048
隔震1.4071.1261.521.7132.7151.5411.4753.065
减震率/%91.8394.5791.8891.9482.5688.789.382.02
倾覆弯矩/(107 N·m)抗震11.27313.18611.8513.0289.6848.5168.5210.312
隔震1.0121.3661.2891.1972.04311.2012.046
减震率/%91.0289.6489.1290.8178.9188.2685.980.16
晃动波高/m抗震0.3080.1560.4450.2071.2850.4050.5021.151
隔震0.2920.1630.4250.2241.420.3310.4921.176
减震率/%5.08-4.274.46-8.65-10.4418.211.94-2.22
考虑和忽略STLI效应影响的对比分析基底剪力差异率/%抗震7.7710.1710.418.7625.4433.2228.1920.42
隔震0.041.271.951.830.180.972.450.98
倾覆弯矩差异率/%抗震4.997.9411.439.3826.7435.8128.8125.82
隔震0.626.71.453.783.856.60.530.11
晃动波高差异率/%抗震00.060.230.490.030.10.10.06
隔震0.585.171.3900.611.191.030.37
), ArticleFig(id=1228048703286608774, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=表5, caption=

Ⅰ，Ⅱ类场地地震响应对比

, figureFileSmall=null, figureFileBig=null, tableContent=
计算内容Ⅰ类场地Ⅱ类场地
QiananGuangzhouTH1TG025人工波1LanzouRH2TH1TG035人工波2
忽略STLI效应基底剪力/(106 N)抗震18.69123.07720.88423.30820.41720.88419.19721.423
隔震1.4081.1121.4911.7451.5562.721.443.035
减震率/%92.4795.1892.8692.5192.3886.9892.585.83
倾覆弯矩/(107 N·m)抗震11.86514.32313.3814.37613.26613.21911.96813.901
隔震1.0181.2811.3081.2441.0711.9671.1952.044
减震率/%91.4291.0690.2291.3591.9385.1290.0285.3
晃动波高/m抗震0.3080.1560.4440.2060.4041.2850.5011.15
隔震0.2940.1550.4310.2240.3271.4110.4971.172
减震率/%4.640.92.93-8.7419.09-9.810.84-1.91
考虑STLI效应基底剪力/(106 N)抗震17.23820.7318.71121.26615.57113.63513.78517.048
隔震1.4071.1261.521.7132.7151.5411.4753.065
减震率/%91.8394.5791.8891.9482.5688.789.382.02
倾覆弯矩/(107 N·m)抗震11.27313.18611.8513.0289.6848.5168.5210.312
隔震1.0121.3661.2891.1972.04311.2012.046
减震率/%91.0289.6489.1290.8178.9188.2685.980.16
晃动波高/m抗震0.3080.1560.4450.2071.2850.4050.5021.151
隔震0.2920.1630.4250.2241.420.3310.4921.176
减震率/%5.08-4.274.46-8.65-10.4418.211.94-2.22
考虑和忽略STLI效应影响的对比分析基底剪力差异率/%抗震7.7710.1710.418.7625.4433.2228.1920.42
隔震0.041.271.951.830.180.972.450.98
倾覆弯矩差异率/%抗震4.997.9411.439.3826.7435.8128.8125.82
隔震0.626.71.453.783.856.60.530.11
晃动波高差异率/%抗震00.060.230.490.030.10.10.06
隔震0.585.171.3900.611.191.030.37
), ArticleFig(id=1228048703391466379, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=EN, label=Tab.6, caption=

Seismic response comparison of sites Ⅲ，Ⅳ

, figureFileSmall=null, figureFileBig=null, tableContent=
计算内容Ⅲ类场地Ⅳ类场地
TaftPELLWD人工波3PasadenaTH4TH4TG090人工波4
忽略STLI效应基底剪力/(106 N)抗震20.12024.21729.96516.79316.20015.67522.72614.756
隔震2.4262.3761.72433.0764.6242.1363.1787.306
减震率/%87.9490.1994.24581.6871.4686.3786.0250.49
倾覆弯矩/(107 N·m)抗震12.20315.19118.6310.7579.5899.87314.4808.846
隔震1.5151.5691.3372.1952.4141.1712.2453.866
减震率/%87.5989.6792.82579.6074.8388.1484.5056.30
晃动波高/m抗震0.6470.9600.19411.1170.9520.3452.4490.647
隔震0.7140.9450.16121.1940.9090.3821.62171.041
减震率/%-10.361.5616.965-6.914.52-10.7233.77-60.90
考虑STLI效应基底剪力/(106 N)抗震12.5113.5516.68710.7149.6369.11310.61410.669
隔震2.5002.4241.7253.074.772.243.207.42
减震率/%80.0582.1189.66371.3550.4675.4569.8130.41
倾覆弯矩/(107 N·m)抗震7.5658.134610.226.5845.5695.1026.3716.088
隔震1.3571.6661.1562.1712.5011.1762.1823.968
减震率/%82.0679.5388.69167.0355.1076.9565.7534.82
晃动波高/m抗震0.6520.9640.1981.1190.9560.3512.4440.666
隔震0.720.950.1681.2010.9210.3841.6171.065
减震率/%-10.761.5215.2-7.323.67-9.3533.84-60.04
考虑和忽略STLI效应影响的对比分析基底剪力差异率/%抗震37.8244.0444.3136.2040.5241.8653.3027.70
隔震3.052.020.030.213.244.720.831.62
倾覆弯矩差异率/%抗震38.0146.4545.1438.7941.9348.3256.0031.18
隔震10.436.1513.531.093.580.442.802.64
晃动波高差异率/%抗震0.820.421.750.230.461.740.182.89
隔震1.190.423.910.611.350.470.282.33
), ArticleFig(id=1228048703475352465, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228048673343472471, language=CN, label=表6, caption=

Ⅲ，Ⅳ类场地地震响应对比

, figureFileSmall=null, figureFileBig=null, tableContent=
计算内容Ⅲ类场地Ⅳ类场地
TaftPELLWD人工波3PasadenaTH4TH4TG090人工波4
忽略STLI效应基底剪力/(106 N)抗震20.12024.21729.96516.79316.20015.67522.72614.756
隔震2.4262.3761.72433.0764.6242.1363.1787.306
减震率/%87.9490.1994.24581.6871.4686.3786.0250.49
倾覆弯矩/(107 N·m)抗震12.20315.19118.6310.7579.5899.87314.4808.846
隔震1.5151.5691.3372.1952.4141.1712.2453.866
减震率/%87.5989.6792.82579.6074.8388.1484.5056.30
晃动波高/m抗震0.6470.9600.19411.1170.9520.3452.4490.647
隔震0.7140.9450.16121.1940.9090.3821.62171.041
减震率/%-10.361.5616.965-6.914.52-10.7233.77-60.90
考虑STLI效应基底剪力/(106 N)抗震12.5113.5516.68710.7149.6369.11310.61410.669
隔震2.5002.4241.7253.074.772.243.207.42
减震率/%80.0582.1189.66371.3550.4675.4569.8130.41
倾覆弯矩/(107 N·m)抗震7.5658.134610.226.5845.5695.1026.3716.088
隔震1.3571.6661.1562.1712.5011.1762.1823.968
减震率/%82.0679.5388.69167.0355.1076.9565.7534.82
晃动波高/m抗震0.6520.9640.1981.1190.9560.3512.4440.666
隔震0.720.950.1681.2010.9210.3841.6171.065
减震率/%-10.761.5215.2-7.323.67-9.3533.84-60.04
考虑和忽略STLI效应影响的对比分析基底剪力差异率/%抗震37.8244.0444.3136.2040.5241.8653.3027.70
隔震3.052.020.030.213.244.720.831.62
倾覆弯矩差异率/%抗震38.0146.4545.1438.7941.9348.3256.0031.18
隔震10.436.1513.531.093.580.442.802.64
晃动波高差异率/%抗震0.820.421.750.230.461.740.182.89
隔震1.190.423.910.611.350.470.282.33
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考虑土-储罐-液体相互作用的隔震储罐简化力学模型及地震响应研究
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李想 1, 2 , 张书进 1, 3 , 孙建刚 2, 4 , 王尊策 1 , 徐蕾 2 , 崔利富 2 , 吕远 5
振动工程学报 | 2024,37(3): 436-447
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振动工程学报 | 2024, 37(3): 436-447
考虑土-储罐-液体相互作用的隔震储罐简化力学模型及地震响应研究
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李想1, 2 , 张书进1, 3, 孙建刚2, 4 , 王尊策1, 徐蕾2, 崔利富2, 吕远5
作者信息
  • 1东北石油大学机械科学与工程学院,黑龙江　大庆　163318
  • 2大连民族大学土木工程学院,辽宁　大连　116650
  • 3中国石油大庆油田有限责任公司采油工程研究院,黑龙江　大庆　163453
  • 4防灾科技学院土木工程学院,北京　101601
  • 5哈尔滨工业大学土木与环境工程学院,广东　深圳　518055

    • 李想（1989—），男，博士研究生，讲师。电话：（0411）87557345；E-mail：。

通讯作者:

孙建刚（1959—），男，博士，教授。电话：（0411）87557350；E-mail：。
Simplified mechanical model and seismic response for isolation tank considering soil-tank-liquid interaction
Xiang LI1, 2 , Shu-jin ZHANG1, 3, Jian-gang SUN2, 4 , Zun-ce WANG1, Lei XU2, Li-fu CUI2, Yuan LÜ5
Affiliations
  • 1School of Mechanical Science and Engineering, Northeast Petroleum University, Daqing 163318, China
  • 2College of Civil Engineering, Dalian Minzu University, Dalian 116650, China
  • 3Research Institute of Oil Production Engineering, Daqing Oilfield Limited, CNPC, Daqing 163453, China
  • 4School of Civil Engineering, Institute of Disaster Prevention, Beijing 101601, China
  • 5School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, China
出版时间: 2024-03-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.03.008
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摘要
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为了寻求一种既能减震又能降低成本的储罐结构，提出一种隔震储罐结构体系，根据力的平衡原则推导了滚动隔震装置恢复力模型，得出了复合滚动隔震装置的恢复力模型。基于三质点模型和场地土模型，提出了考虑土-储罐-液体相互作用（STLI）的隔震储罐的简化力学模型和运动方程，并研究了考虑STLI效应和不考虑STLI效应时抗震储罐和隔震储罐在不同场地的地震响应。结果表明：隔震储罐能够有效地降低其基底剪力及倾覆弯矩，但对晃动波高的控制有限，建议在高烈度区，满足晃动波高的前提下，隔震储罐在设计时可以降低烈度。考虑STLI效应后，抗震储罐的基底剪力和倾覆弯矩明显降低，且从Ⅰ类场地到Ⅳ类场地差异率逐渐增大，软土场地降低最为显著。隔震储罐地震响应受STLI效应的影响较小，可以有效地隔断上部结构与场地土之间的耦联，弱化STLI效应对上部结构的影响。

土-储罐-液体相互作用  /  隔震储罐  /  复合滚动隔震  /  简化力学模型  /  地震响应

In order to seek a kind of tank structure which can absorb shock and reduce costs，a new structure system of isolation tank is proposed. The restoring force model of rolling isolation is deduced by the principle of balances of forces，and the restoring force model of composite rolling isolation device is obtained. Based on the three-particle model and site soil model，the simplified mechanical model and motion equations of the new isolation tank considering soil-tank-liquid interaction （STLI） are proposed，and the seismic responses of seismic tank and new isolation tank that considered STLI and Non-STLI are studied under different sites. The results show that the new isolation tank can effectively reduce the base shear and overturning moment，but the control of the sloshing wave height is limited. It is suggested that in the high intensity area，under the premise of meeting the shaking wave height，the new isolation tank can be designed to reduce the intensity. After considering the STLI effect，the base shear and overturning moment of seismic tank decrease obviously. The discrepancy rate gradually increases from class Ⅰ site to class Ⅳ site，and the decrease is most significant in soft soil. The seismic responses of the new isolation tank are less affected by the STLI，which can effectively cut off the coupling between the superstructure and the site soil，and weaken the influence of the STLI effect on the superstructure.

soil-tank-liquid interaction  /  isolation tank  /  composite rolling isolation  /  simplified mechanical model  /  seismic response
李想, 张书进, 孙建刚, 王尊策, 徐蕾, 崔利富, 吕远. 考虑土-储罐-液体相互作用的隔震储罐简化力学模型及地震响应研究. 振动工程学报, 2024 , 37 (3) : 436 -447 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.03.008
Xiang LI, Shu-jin ZHANG, Jian-gang SUN, Zun-ce WANG, Lei XU, Li-fu CUI, Yuan LÜ. Simplified mechanical model and seismic response for isolation tank considering soil-tank-liquid interaction[J]. Journal of Vibration Engineering, 2024 , 37 (3) : 436 -447 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.03.008
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引言
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立式石油储罐是石油化工行业重要的存储设施，由于其存储易燃、易爆和有毒介质，一旦发生地震灾害容易引起火灾、爆炸或者造成环境污染等次生灾害，对生态环境和人类生存造成严重的危害。1964年6月16日，日本新潟地震中储油罐破坏后发生大火和爆炸，大火持续15天，烧毁油罐84座，造成严重的经济损失和空气污染［1］。1978年6月12日，日本宫城地震，成品油罐被破坏，造成了陆地和海洋的大面积污染。1976年7月28日，唐山大地震，唐山钢厂和天津化工厂各两座1000 m3的燃料油罐最下层圈壁发生外屈曲，角焊缝开裂，罐内贮油全部泄漏。立式储罐的震害主要表现为罐壁底部的象足式鼓曲，浮顶上部构件损坏，锚固件、罐底板和罐底贴角焊缝的破坏，管接头及其附件的破坏以及地基液化等。由以上储罐震害可知，立式储罐壁薄、容积大，其地震响应主要涉及提离、罐壁应力、罐壁失稳等。为此国内外学者针对储罐结构的特点，从理论、数值仿真以及试验多维度揭示复杂的地震响应机理，从而提高储罐抗震能力，避免其因为地震作用而产生破坏。就当前的研究成果来看，结构控制思想的引入很好地起到了减小地震破坏作用的效果［2-9］。Chalhoub［10］进行了采用基础隔震技术的储罐振动台试验，结果表明，采用橡胶隔震装置的储罐能有效地降低地震响应，但晃动高度略有增加。Shrimali等［11-12］研究了单向和双向地震激励下采用叠层橡胶隔震支座的储罐的地震响应，结果表明该方法可以有效地降低储罐动力响应。Cheng等［13］考虑储罐液-固耦合的影响，研究了采用橡胶隔震支座的矩形钢筋混凝土液体储罐的动态响应。结果表明，由于橡胶隔震支座过滤了外部激励的高频分量，因此储罐不会发生高频共振，当外部激发频率接近液体的一阶频率时，会发生显著的共振。孙建刚［14］从罐壁的柔性和液-固耦合运动出发，建立了隔震三质点控制体系简化分析的力学模型，给出了立式储罐基础隔震控制体系的运动方程。
目前，对储罐隔震问题的研究进展十分迅速［15-16］，然而大多数研究假设储罐基础是刚性的，忽略了土-储罐-液体相互作用对地震响应的影响。近几十年来，国内外学者广泛研究了土-结构相互作用对各种结构体系地震响应的影响［17-22］。由于液体具有流动性，所以SSI效应对储罐的影响正逐渐转化为更为复杂的土-储罐-液体相互作用（STLI）。Haroun等［23］研究了考虑土与储罐相互作用的立式储罐地震响应，研究表明在水平地震作用下，土与结构相互作用能放大储罐的动水压力和倾覆弯矩。孙建刚等［24］采用数值方法研究了考虑土-储罐相互作用的大型立式浮顶储罐的地震响应，研究表明，土壤摆动效应对结构的基底剪力和倾覆弯矩有很大的影响，特别是当场地条件为软土时。
综上所述，隔震对减小储罐地震响应具有很好的效果，而且STLI效应对储罐结构地震响应的影响是不可忽视的。从目前国内外关于储罐隔震体系的研究来看，要实现上述隔震体系，就要使用大量的隔震装置，储罐基础构造也要产生巨大的改变，这必将增加结构体系的建造成本，也使得隔震技术难以大面积推广应用在储罐中。鉴于此，本文在局部改变原结构体系的基础上，提出可以有效降低结构地震响应的隔震储罐结构体系。目前关于土与储罐相互作用的研究仅针对立式储罐，而隔震储罐与立式储罐在结构形式上有很大不同，因此，本文推导了适用于该结构体系的复合滚动隔震装置的恢复力模型，而后提出了基于STLI效应的隔震储罐简化力学模型，研究了考虑STLI效应和忽略STLI效应的隔震储罐和抗震储罐在不同场地的地震响应，探讨了考虑STLI效应的必要性。
1　隔震储罐
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当前的储罐基础隔震体系如图1所示，采用隔震装置将储罐与其基础分隔开。本文所提出的隔震储罐（如图2所示）将罐壁和储罐底板分开，并将储罐底板支撑在砂垫层上，罐壁支撑在复合滚动隔震装置上，采用柔性膜将罐壁和储罐底板连接起来，本文所采用的柔性膜是一种新型弹性体材料，该材料具有韧性高、防水、耐磨、强度高的特性，并具有良好的粘结性，可以保证罐壁在水平方向运动，同时防止储罐内液体泄漏。
该隔震储罐由于罐壁和储罐底板是断开的，并且通过柔性膜连接，所以当发生地震时砂垫层的弓起作用和底板提离作用的作用力传递路径被切断，可以消除弓起破坏和底板提离。由于复合滚动隔震装置的引入能够很好地降低储罐地震响应，而且隔震装置仅作用在罐壁底部，所以能大大减少隔震装置的布置数量，储罐基础结构形式的变化也不大，能有效地降低建造成本，具有良好的经济效益。
2　复合滚动隔震装置
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2.1　复合滚动隔震装置的构成
复合滚动隔震装置由滚动隔震装置和铅芯阻尼器并联而成，如图3所示。滚动隔震装置由带有上、下凹槽的盖板和滚球构成，凹槽设计为圆弧形。将铅芯阻尼器插入橡胶管中，而后将其插入盖板，其中上盖板为贯穿孔，下盖板未贯穿。盖板的开孔需比橡胶管尺寸略小，利用橡胶的挤压受力使铅芯阻尼器固定，其中铅芯阻尼器高度略小于隔震装置的整体高度，以消解滚珠滚动时所引起的复合滚动隔震装置竖向位移，并在铅芯阻尼器顶部布置一根弹簧，用螺栓固定。
2.2　滚动隔震装置恢复力模型
参考文献［25］，通过对滚动隔震装置的恢复力模型进行计算可知，其自振周期和刚度与单摆类似，具体表达式为：
式中　 为上凹槽质心运动轨迹；R为凹槽半径；r为滚球半径；为滚动隔震装置圆频率；m为滚动隔震装置上部质量。
从式（1）和（2）中可以看出，滚动隔震装置的周期和刚度仅与凹槽和滚球的半径有关，而与其相对位移无关。这种方法大大简化了恢复力模型的计算过程，当滚动隔震装置发生较大相对位移时，采用上述方法计算会产生较大误差。本文根据力的平衡原则推导出滚动隔震装置变周期和变刚度恢复力模型。以滚动隔震装置中一个滚动单元为研究对象，其上凹槽受力分析如图4所示。
根据力的平衡原则可得滚球与上凹槽接触面的平衡方程：
式中　 W为上部结构作用于滚动隔震装置的竖向荷载；F为滚动隔震装置的恢复力；T和N分别为上凹槽和滚球接触面的切向摩擦力和法向反力；为转动角度。
切向摩擦力T可表示为［26］：
根据式（3）~（5）可得：
假设滚球中心的运动方程为：
根据式（6）可求得滚动隔震装置恢复力模型为：
式中　 xi为上凹槽的位移；x为滚球中心的位移；为滚球中心的速度。式（8）中第一项为滚动隔震装置弹性恢复力，第二项为滚动隔震装置阻尼力。
滚动隔震装置刚度为：
滚动隔震装置周期为：
由式（10）可知，滚动隔震装置的隔震周期主要与凹槽半径R和滚球半径r及其所处的位置有关。在进行隔震设计时，应首先确定滚球的尺寸大小，而后根据所需隔震周期进行凹槽半径的设计。
2.3　滚动隔震装置恢复力模型验证
为了验证滚动隔震装置恢复力模型的正确性，对比分析滚动隔震装置恢复力模型和有限元仿真模型在水平正弦位移激励下的计算结果。选取凹槽半径R=0.6 m，滚球半径r=0.075 m。将滚动隔震装置简化为二维平面内的运动，采用ADINA有限元软件建立仿真模型，如图5所示。单元材料模型选用双线性的弹塑性模型，材料弹性模量为206 GPa，屈服强度为518 MPa，泊松比为0.3，密度为7850 kg/m3。在模型顶部施加1 N/m的线荷载以及如图6所示的正弦水平位移激励，滚动隔震装置恢复力模型计算结果与有限元仿真模型计算结果如图7所示。
从图7中可以看出，滚动隔震恢复力模型和有限元仿真模型的计算结果十分接近，验证了本文所推导的滚动隔震装置恢复力学模型的准确性。
2.4　复合滚动隔震装置恢复力模型
采用复合滚动隔震装置的隔震储罐在遭遇大风天气或者小幅地震时，滚动隔震装置的起滚力和铅芯阻尼器的初始刚度能保证储罐上部结构不发生大幅振动。当遭遇强震时，滚动隔震装置带动铅芯阻尼器进行水平运动，并在往复运动中耗散地震能量。本文铅芯阻尼器的恢复力模型采用Bouc-Wen光滑型恢复力模型［27］：
式中　 为屈服后与屈服前的水平刚度之比；kl为铅芯的弹性刚度；z为滞变位移。等参数可通过参数识别得到。
根据式（8），可得复合滚动隔震装置恢复力模型为：
式中　 为复合滚动隔震装置的自复位刚度。
3　考虑STLI效应的隔震储罐简化力学模型
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3.1　场地土简化模型
本文将场地土简化为三自由度力学模型［20-22］，分别为平动自由度，摆动自由度和附加自由度，如图8所示。
图8中，ri，e，mf和If分别为结构基础的半径、埋置深度、质量和质量惯性矩；水平平动刚度系数和阻尼系数的计算公式分别为［21-22］：
式中　 为土的密度；为土的泊松比；为场地土的等效剪切波速。
摆动的转动刚度系数和阻尼系数的计算公式分别为［21-22］：
土体附加的自由度包括质量惯性矩和阻尼参数［21-22］，分别表示为：
储罐结构的动响应包括液体晃动和液-固耦合等复杂的动态过程，目前国内外常用Housner［28］和孙建刚等［24］提出的刚性理论和弹性理论力学模型来解决储罐复杂的动响应问题，本文基于上述理论推断，考虑土-结构相互作用的隔震储罐简化力学模型实际上是土壤模型与势流体理论的有机组合。将图8中的场地土模型与隔震储罐结合，构成图9中考虑STLI效应的隔震储罐的力学分析模型。
3.2　隔震储罐简化动力学模型
基于弹性理论的立式储罐水平基础隔震力学模型［28］，将隔震储罐内液体简化为对流质量mc、液固耦合质量mi和刚性质量m0。等效高度分别为hc，hi和h0，储液高度为Hl。液-固耦合质量和对流质量通过等效弹簧刚度kc，ki及阻尼系数cc，ci与罐壁相连，k0为隔震装置等效刚度，Ff为由摩擦力构成的恢复力，Fl为铅芯阻尼器恢复力。地面运动位移、对流晃动位移、液-固耦合位移和隔震装置位移分别为，，和。考虑场地土-储罐-液体相互作用（STLI）的影响，得出考虑STLI效应的隔震储罐简化力学模型，如图10所示。
3.3　运动方程
根据考虑STLI效应的隔震储罐简化动力学模型，利用Hamilton原理得出六自由度体系的运动控制方程：
其中：
式中　 为罐体绕中心的转动惯量；，，表示3个质点的高度。
隔震储罐的基底剪力、倾覆弯矩和晃动波高分别为：
式中　 为储罐半径。
4　简化力学模型验证
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4.1　储罐基本参数及隔震装置设计
本文以3000 m3立式储罐为原型罐设计隔震储罐，其基本参数如表1所示。
设计隔震装置初始隔震周期为Ti=3 s，滚动摩阻系数取为0.005 cm，滚球的半径为r=0.08 m，根据式（10）可算得凹槽半径R=1.2 m。在隔震储罐罐壁底部均匀布置6个复合滚动隔震装置。根据预期隔震层偏移，选定铅芯阻尼器有效高度H=300 mm，直径D=100 mm，建立铅芯阻尼器有限元仿真模型，并对其进行拟静力数值仿真分析，其中模型选用3D Solid单元，材料弹性模量为16.5 GPa，屈服强度为14 MPa，泊松比为0.42。有限元模型如图11所示。
在铅芯阻尼器顶部施加如图12所示的正弦水平位移激励，铅芯阻尼器的滞回曲线如图13所示，通过对数值仿真模型的滞回曲线进行参数识别，获取Bouc-Wen光滑型恢复力模型的参数，如表2所示。
4.2　有限元仿真模型
根据隔震储罐所处位置的实际地质条件，建立考虑场地土影响的有限元仿真模型。其中对于土壤模型，当其直径Di与高度Hi之比大于10时［29］，可基本消除土壤边界对结构的影响。隔震储罐所处位置的土层总高度Hi为17 m，本文选择土壤直径Di为210 m，Di/Hi>10，满足要求。表3为隔震储罐所处位置的土层物理参数。
采用Shell单元模拟储罐罐壁和柔性膜，材料模型分别选用弹塑性模型和超弹性模型。采用3D Fluid单元模拟储罐内液体，液面设置为自由面单元。场地土采用3D Solid单元，材料选用莫尔-库仑材料模型。罐壁底部均匀布置6组复合滚动隔震装置，采用带有高度的线弹簧单元模拟滚动隔震装置，通过对滚动隔震装置恢复力滞回曲线进行参数识别及数据拟合，即可获得表征滚动隔震装置水平方向力学性能的非线性弹簧单元物理参数，铅芯阻尼器采用3D Solid单元模拟，材料模型选用双线性的弹塑性模型。有限元模型如图14所示。
4.3　场地土分类及地震波选择
根据等效剪切波速度和土层覆盖厚度可将场地土分为Ⅰ类、Ⅱ类、Ⅲ类和Ⅳ类。根据规范［30］可计算得出隔震储罐所处位置土层的等效剪切波速和覆盖层厚度分别为146.3 m/s和17 m，属于Ⅲ类场地。因此，所选的地震波必须符合Ⅲ类场地的特点。本文选择3条实际记录的地震波和1条人工合成的地震波作为地震动输入，加速度峰值调整为0.2g，加速度反应谱曲线如图15所示。
4.4　计算结果对比分析
通过计算得出采用有限元模型和理论模型的考虑STLI效应的隔震储罐地震响应，表4为理论模型和有限元模型计算出的地震响应峰值，图16为Taft波作用下考虑STLI效应的隔震储罐基底剪力、倾覆弯矩和晃动波高的时程曲线。
从表4和图16中的数据可以看出，有限元模型和理论模型得出的地震响应峰值非常接近，而且地震响应时程曲线契合较好。同时从表4中可以看出有限元模型计算所得地震响应峰值均大于简化力学模型，且平均差异率均在20%以内，有限元数值仿真结果与简化力学模型计算结果相差不大，两者互为验证，所以本文提出的考虑STLI的隔震储罐简化力学模型是可靠的。
5　算例分析
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参考4.1节储罐基本参数及隔震装置设计进行隔震储罐地震响应研究，储罐基本参数如表1所示，其中e/ri=0.14。
5.1　地震动输入
根据规范［30］要求，本文选择Ⅰ，Ⅱ，Ⅲ，Ⅳ类场地中3条实际记录的地震波和1条人工合成的地震波作为地震动输入。研究考虑STLI效应的隔震储罐地震响应，调整加速度时程曲线峰值为0.4g，四类场地加速度反应谱如图17所示。虽然场地土的类型与土壤的软硬程度和土壤厚度相关［30］，但是场地土简化力学模型只涉及等效剪切波速［21-22］，所以本文以不同剪切波速来表示不同场地土类型。
5.2　地震响应研究
本文采用法，对比分析了不同场地忽略STLI效应和考虑STLI效应的抗震储罐和隔震储罐地震响应，具体计算结果如表5，6所示。
从表5，6数据中可以看出，不同场地地震波作用下，不考虑STLI效应和考虑STLI效应的隔震储罐都可以有效降低储罐的基底剪力和倾覆弯矩，但不能有效控制晃动波高，甚至有放大波高的效应。隔震储罐基底剪力和倾覆弯矩与抗震储罐相比，在坚硬场地土（Ⅰ类场地、Ⅱ类场地、Ⅲ类场地）上的减震效果明显好于在软弱场地土（Ⅳ类场地）上的减震效果，其减震率达67%以上；对于Ⅳ类场地（软土），隔震储罐的基底剪力和倾覆力矩也有明显的减震效果，其减震率也可以达到30%以上。
对于晃动波高的减震效果而言，不同场地地震波作用下，隔震储罐的减震效果差异较大，有时隔震对晃动波高有放大效应。在人工波4（Ⅳ类场地）作用下，隔震储罐较抗震储罐的晃动响应明显增加，隔震后晃动波高较隔震前的晃动波高增加了60%以上，这主要是因为隔震装置会延长结构的自振周期，而晃动波高属于长周期振动，因此隔震储罐对晃动波高的控制并不明显。而在其他地震波作用时，储罐的晃动波高与抗震储罐的晃动波高相比变化不大。
由表5，6数据可知，考虑STLI效应后，抗震储罐的基底剪力和倾覆弯矩明显降低，且从Ⅰ类场地到Ⅳ类场地差异率逐渐增大，坚硬场地差异率最低，其中Ⅰ类场地土Qianan波作用下，考虑STLI效应的抗震储罐基底剪力和倾覆弯矩差异率分别为7.77%和4.99%；软土场地差异率最为显著，其中Ⅳ类场地土Pasadena波作用下，考虑STLI效应的抗震储罐基底剪力和倾覆弯矩差异率分别为40.52%和41.93%；而考虑STLI效应后抗震储罐的晃动波高变化不明显。这主要是因为考虑STLI效应后，相当于在储罐底部植入了柔性层，等效于在抗震储罐底部增加了隔震装置，所以考虑STLI效应后基底剪力和倾覆弯矩逐渐降低，由于液体晃动属于长周期运动，所以考虑STLI效应对晃动波高的影响不明显，而由于Ⅰ类场地接近刚性，土体变形对结构的反应影响很小，所以Ⅰ类场地土地震波作用下，考虑和忽略STLI效应对抗震储罐地震响应差异率明显低于其他类型场地土。隔震储罐地震响应受STLI效应的影响较小，两者基底剪力、倾覆弯矩和晃动波高的差异率最大值为13.53%。这是由于场地土的等效侧向刚度远大于隔震储罐隔震层的水平侧向刚度，因此场地土对隔震储罐的自振周期影响很小。不考虑STLI效应和考虑STLI效应的隔震储罐其自振周期分别为1.962和1.957 s，基本保持一致。说明采用复合滚动隔震装置的隔震储罐可以有效地隔断上部结构与场地土之间的耦联，弱化STLI效应对上部结构的影响。
总之，隔震储罐比传统抗震储罐的基底剪力和倾覆力矩明显降低，由结构抗震知识可知，减震率在75%时，相当于抗震烈度降低2度，减震率在50%时，相当于抗震烈度降低1度。综上分析，建议在高烈度地区，在保证液体晃动波高的要求下，可以采用降烈度设计隔震储罐。
6　结论
收起
（1）根据力的平衡原则推导了滚动隔震装置恢复力模型，并对比分析了滚动隔震恢复力模型和有限元仿真模型在水平正弦位移激励下的计算结果，两者滞回曲线的计算结果十分接近，验证了本文所推导的滚动隔震恢复力学模型的准确性。提出并设计了复合滚动隔震装置，建立了相应的恢复力力学模型。
（2）提出了隔震储罐结构体系，依据速度势理论，考虑土-储罐-液体的相互作用（STLI）的影响，构建了其简化力学模型及相应的运动控制方程。
（3）隔震储罐能够有效地降低储罐的基底剪力及倾覆弯矩，但对储液晃动波高的控制有限。考虑STLI效应后，抗震储罐的基底剪力和倾覆弯矩明显降低，且从Ⅰ类场地到Ⅳ类场地差异率逐渐增大，软土场地降低最为显著。隔震储罐地震响应受STLI效应的影响较小，可以有效地隔断上部结构与场地土之间的耦联，弱化STLI效应对上部结构的影响。
基金
收起
  • 国家自然科学基金资助项目(52178461)
  • 国家自然科学基金资助项目(51878124)
  • 国家自然科学基金资助项目(51478090)
  • 广东省重点领域研发计划项目(2019B111102001)
文献
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2024年第37卷第3期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.03.008
  • 接收时间：2022-07-12
  • 首发时间：2026-02-10
  • 出版时间：2024-03-28
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  • 收稿日期：2022-07-12
  • 修回日期：2022-09-13
基金
国家自然科学基金资助项目(52178461)
国家自然科学基金资助项目(51878124)
国家自然科学基金资助项目(51478090)
广东省重点领域研发计划项目(2019B111102001)
作者信息
    1东北石油大学机械科学与工程学院,黑龙江　大庆　163318
    2大连民族大学土木工程学院,辽宁　大连　116650
    3中国石油大庆油田有限责任公司采油工程研究院,黑龙江　大庆　163453
    4防灾科技学院土木工程学院,北京　101601
    5哈尔滨工业大学土木与环境工程学院,广东　深圳　518055

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孙建刚（1959—），男，博士，教授。电话：（0411）87557350；E-mail：。
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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
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