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Article(id=1241791690369995630, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241791680479822062, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2025.0202, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1713715200000, receivedDateStr=2024-04-22, revisedDate=1716912000000, revisedDateStr=2024-05-29, acceptedDate=null, acceptedDateStr=null, onlineDate=1773995810357, onlineDateStr=2026-03-20, pubDate=1745424000000, pubDateStr=2025-04-24, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773995810357, onlineIssueDateStr=2026-03-20, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773995810357, creator=13701087609, updateTime=1773995810357, updator=13701087609, issue=Issue{id=1241791680479822062, tenantId=1146029695717560320, journalId=1241701559352995854, year='2025', volume='45', issue='2', pageStart='1', pageEnd='237', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773995807999, creator=13701087609, updateTime=1773996976041, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241796579670163949, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241791680479822062, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241796579670163950, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1241791680479822062, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=14, endPage=21, ext={EN=ArticleExt(id=1241791692848829353, articleId=1241791690369995630, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Simplified analysis of seismic performance of rectangular single-span underground structures based on the restraint effect of nonlinear spring, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

This paper proposes a nonlinear spring restraint structure to overcome the limitations of the static thrust test method in evaluating underground structure systems. Considering the difficulties of soil-structure interaction, high costs, and limited observability of test phenomena, the proposed approach integrates basic principle of the reaction displacement method for underground structures. It recognizes that the traditional elastic spring fails to capture soil state changes during loading, thus prompting the introduction of a more dynamic spring-structure system. It suggests using nonlinear springs instead of soils for analyzing seismic performance. Through Pushover analysis on a single-span underground structure model, the influence of factors such as the axial compression ratio and spring-structure interaction on mechanical performance is investigated. Comparing bending moment capacity curves of key sections shows that the static thrust overlay model for spring-underground structures is suitable for seismic analysis of underground structures. Up to an inter-story displacement angle of 1/200, both the linear and nonlinear spring models are highly accurate, but beyond this threshold, the nonlinear spring model is significantly superior. The simplified analysis method for seismic performance of nonlinear spring-underground structure systems provides insights into the complex force behaviors of underground structures.

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为了弥补考虑土-结构相互作用的地下结构体系静力推覆试验方法耗资、耗时、试验现象不易观察等缺点，结合地下结构反应位移法基本原理，基于弹性弹簧仅代表加载过程某一特殊时刻的状态，无法表述土体在加载过程中的状态变化对结构的影响，提出了基于非线性弹簧代替周围约束土体的地下结构抗震性能静力推覆分析方法。以某单跨地下结构为例，开展土-地下结构模型的Pushover分析，基于非线性弹簧-地下结构体系，分析了轴压比、弹簧与结构间的相互作用关系对结构受力性能的影响。对比分析关键断面弯矩能力曲线，结果表明弹簧-地下结构体系静力推覆模型可应用于地下结构抗震研究中，在层间位移角达到1/200前，线性弹簧模型与非线性弹簧模型均有较高的精度，层间位移角超过1/200后，非线性弹簧模型的精度明显高于线性弹簧模型。非线性弹簧-地下结构体系抗震性能简化分析方法为研究地下结构复杂的受力特性提供参考。

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许成顺（1977—），女，教授，博士，主要从事岩土地震工程研究。E-mail：
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刘洪涛（1986—），男，副教授，博士，主要从事装配式地下结构抗震性能研究。E-mail：

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刘洪涛（1986—），男，副教授，博士，主要从事装配式地下结构抗震性能研究。E-mail：

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刘洪涛（1986—），男，副教授，博士，主要从事装配式地下结构抗震性能研究。E-mail：

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Spring stiffness distribution

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编号底部弹簧刚度/（kN/m）侧墙弹簧弹簧刚度/（kN/m）
111610022300
25860012000
3481007600
4441006400
5427007700
64330010100
74610030600
853700—
957300—
10116100—
), ArticleFig(id=1241802913274724775, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791690369995630, language=CN, label=表1, caption=

弹簧刚度分布表

, figureFileSmall=null, figureFileBig=null, tableContent=
编号底部弹簧刚度/（kN/m）侧墙弹簧弹簧刚度/（kN/m）
111610022300
25860012000
3481007600
4441006400
5427007700
64330010100
74610030600
853700—
957300—
10116100—
), ArticleFig(id=1241802913446691263, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791690369995630, language=EN, label=Table 2, caption=

Comparison of calculation results

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性能状态层间位移角限值θPushover/（kN•m）线性弹簧/（kN•m）非线性弹簧/（kN•m）线性弹簧与Pushover结果误差/%非线性弹簧与Pushover结果误差/%
断面B断面D断面B断面D断面B断面D断面B断面D断面B断面D
基本完好1/1000283.39-376.51300.21-328.01301.65-297.434.207.834.5612.77
轻度损伤1/500284.07-207.39251.99-260.53239.99-284.488.0011.8011.0017.13
中度损伤1/300209.49-124.13213.86-199.96217.85-150.621.3420.672.567.22
严重损伤1/200197.70-39.95246.52-155.88204.00-192.4215.5341.012.0053.93
), ArticleFig(id=1241802913614463434, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1241791690369995630, language=CN, label=表2, caption=

计算结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
性能状态层间位移角限值θPushover/（kN•m）线性弹簧/（kN•m）非线性弹簧/（kN•m）线性弹簧与Pushover结果误差/%非线性弹簧与Pushover结果误差/%
断面B断面D断面B断面D断面B断面D断面B断面D断面B断面D
基本完好1/1000283.39-376.51300.21-328.01301.65-297.434.207.834.5612.77
轻度损伤1/500284.07-207.39251.99-260.53239.99-284.488.0011.8011.0017.13
中度损伤1/300209.49-124.13213.86-199.96217.85-150.621.3420.672.567.22
严重损伤1/200197.70-39.95246.52-155.88204.00-192.4215.5341.012.0053.93
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基于非线性弹簧约束作用的矩形单跨地下结构抗震性能简化分析研究
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刘洪涛 1 , 胡炳麟 1 , 韩润波 2 , 许成顺 3 , 杜修力 3
地震工程与工程振动 | 2025,45(2): 14-21
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地震工程与工程振动 | 2025, 45(2): 14-21
基于非线性弹簧约束作用的矩形单跨地下结构抗震性能简化分析研究
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刘洪涛1 , 胡炳麟1, 韩润波2, 许成顺3 , 杜修力3
作者信息
  • 1.北京建筑大学 土木与交通工程学院，北京 100044
  • 2.赤峰学院 资源环境与建筑工程学院，内蒙古 赤峰 024000
  • 3.北京工业大学 城市与工程安全减灾教育部重点实验室，北京 100124

    • 刘洪涛（1986—），男，副教授，博士，主要从事装配式地下结构抗震性能研究。E-mail：

通讯作者:

许成顺（1977—），女，教授，博士，主要从事岩土地震工程研究。E-mail：
Simplified analysis of seismic performance of rectangular single-span underground structures based on the restraint effect of nonlinear spring
Hongtao LIU1 , Binglin HU1, Runbo HAN2, Chengshun XU3 , Xiuli DU3
Affiliations
  • 1.School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
  • 2.School of Resources, Environment and Architectural Engineering, Chifeng University, Chifeng 024000, China
  • 3.Key Laboratory of Urban Security and Disaster Engineering of the Ministry of Education, Beijing University of Technology, Beijing 100124, China
出版时间: 2025-04-24 doi: 10.13197/j.eeed.2025.0202
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摘要
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为了弥补考虑土-结构相互作用的地下结构体系静力推覆试验方法耗资、耗时、试验现象不易观察等缺点，结合地下结构反应位移法基本原理，基于弹性弹簧仅代表加载过程某一特殊时刻的状态，无法表述土体在加载过程中的状态变化对结构的影响，提出了基于非线性弹簧代替周围约束土体的地下结构抗震性能静力推覆分析方法。以某单跨地下结构为例，开展土-地下结构模型的Pushover分析，基于非线性弹簧-地下结构体系，分析了轴压比、弹簧与结构间的相互作用关系对结构受力性能的影响。对比分析关键断面弯矩能力曲线，结果表明弹簧-地下结构体系静力推覆模型可应用于地下结构抗震研究中，在层间位移角达到1/200前，线性弹簧模型与非线性弹簧模型均有较高的精度，层间位移角超过1/200后，非线性弹簧模型的精度明显高于线性弹簧模型。非线性弹簧-地下结构体系抗震性能简化分析方法为研究地下结构复杂的受力特性提供参考。

地下结构  /  Pushover分析方法  /  弹簧-地下结构体系  /  土-结构相互作用  /  抗震性能

This paper proposes a nonlinear spring restraint structure to overcome the limitations of the static thrust test method in evaluating underground structure systems. Considering the difficulties of soil-structure interaction, high costs, and limited observability of test phenomena, the proposed approach integrates basic principle of the reaction displacement method for underground structures. It recognizes that the traditional elastic spring fails to capture soil state changes during loading, thus prompting the introduction of a more dynamic spring-structure system. It suggests using nonlinear springs instead of soils for analyzing seismic performance. Through Pushover analysis on a single-span underground structure model, the influence of factors such as the axial compression ratio and spring-structure interaction on mechanical performance is investigated. Comparing bending moment capacity curves of key sections shows that the static thrust overlay model for spring-underground structures is suitable for seismic analysis of underground structures. Up to an inter-story displacement angle of 1/200, both the linear and nonlinear spring models are highly accurate, but beyond this threshold, the nonlinear spring model is significantly superior. The simplified analysis method for seismic performance of nonlinear spring-underground structure systems provides insights into the complex force behaviors of underground structures.

underground structure  /  Pushover analysis method  /  spring-underground structure system  /  soil-structure interaction  /  seismic performance
刘洪涛, 胡炳麟, 韩润波, 许成顺, 杜修力. 基于非线性弹簧约束作用的矩形单跨地下结构抗震性能简化分析研究. 地震工程与工程振动, 2025 , 45 (2) : 14 -21 . DOI: 10.13197/j.eeed.2025.0202
Hongtao LIU, Binglin HU, Runbo HAN, Chengshun XU, Xiuli DU. Simplified analysis of seismic performance of rectangular single-span underground structures based on the restraint effect of nonlinear spring[J]. Earthquake Engineering and Engineering Dynamics, 2025 , 45 (2) : 14 -21 . DOI: 10.13197/j.eeed.2025.0202
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0　引言
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近年来，随着城市化进程的推进，各国对地下空间的开发及应用速度显著提升[1-3]。长期以来，人们普遍认为，地下结构受周围土体的约束作用，且受地震动随深度增加而衰减特性的影响，其抗震性能明显优于地上结构[4-5]。然而，阪神大地震中大量地铁车站出现震害现象，尤其是大开车站发生完全塌毁[6-7]，引起了学术界和工程界对地下结构抗震问题的广泛关注。
模型试验是研究地下结构抗震性能的重要方法，常用的试验方法分为动力试验[8]和拟静力试验[9]。其中动力试验又可分为离心机振动台试验和普通振动台试验，前者受限于空间和重力特性无法开展大比例的模型试验，而后者仅能开展1 g重力作用下的试验[10-13]。地下结构与地上结构明显区别是地下结构受周围土体的约束作用，其变形主要取决于周围土体变形，自振特性并不明显，因此，拟静力试验可适用于地下结构的抗震性能分析。拟静力试验可分为构件层面的试验[9，14-15]和结构层面的试验。构件层面的拟静力试验存在难以反映地下结构整体抗震性能的问题。结构层面的试验主要是以整个结构作为对象，研究结构整体的地震响应。孔令俊等[16]采用试验和数值模拟分析了结构的薄弱部位、耗能能力和承载能力等情况，并建议合理的加腋宽度及坡度。陈之毅等[17]以某多层地铁车站为研究对象开展了结构层面的单向推覆试验，采用倒三角形的推覆加载模式，研究了车站的破坏模式及塑性铰出现顺序。上述研究可以直观地观察结构整体的抗震性能，但不能考虑土-结构间相互作用。徐琨鹏[10]研发了可开展单向拟静力推覆试验的大型地下结构模型箱并在该模型箱中进行了土体自由场拟静力推覆试验，得到了土体水平基床系数沿深度和变形的变化规律。
陈晋男等[18]将层间位移角作为装配式地铁车站的损伤指标，并基于动力增量分析方法建立了不同类别场地内装配式地铁车站结构的易损性曲线，对不同性能状态的损伤概率进行了评估。杜修力等[19]对不同橡胶支座类型的减震效果及支座实体受力状态进行对比研究，通过理论分析和数值模拟，探讨了橡胶支座在地铁车站结构中的减震机理。韩润波等[20-21]使用弹簧近似考虑土体约束作用，研究了弹簧-结构整体抗震性能、结构薄弱位置及破坏形态。CHEN等[22]开展了弹簧约束下的两层三跨预制地铁车站拟静力推覆试验，通过与时程分析法得到的结果对比，验证了弹簧-结构系统的有效性，证实了所研制的装置能够对装配式地铁车站等大型地下复杂结构进行抗震试验。
本文在已有研究基础上[18-22]，开展了非线性弹簧-地下结构体系单向推覆模型的数值分析，介绍了弹簧刚度的取值方法。在验证非线性弹簧在弹簧-地下结构体系中的适用性及准确性的基础上，进一步分析了轴压比、弹簧与结构间相互作用关系对结构受力特性的影响，为研究地下结构的抗震性能及试验简化方法提供参考。
1　地下结构Pushover分析
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刘晶波等[23]借鉴地上结构抗震分析中的Pushover分析方法，发展了适用于地下结构的Pushover分析方法。该方法能够给出变形全过程与关键断面内力能力曲线，与传统的地下结构抗震分析方法相比，具有实施方便、计算工作量小及计算精度高等优点[24]。因此，以地下结构Pushover分析方法计算得到的结果为参考，用以验证弹簧-地下结构模型的适用性及准确性。
1.1　地下结构Pushover分析模型的建立
采用有限元分析软件ABAQUS建立二维平面应变模型，如图1所示。该模型宽度为36 m，高度为28 m，结构上覆土层厚度为4 m。模型侧边界设置MPC绑定约束。地下结构宽9 m，高8 m，底板厚度为1 m，侧墙及顶板厚度为0.8 m，侧墙配筋率为1.2%，顶板及底板的配筋率为0.8%。结构顶底板与侧墙连接位置标记A、B、C、D这4个关键断面，如图2所示。
模型土体为均质黏性土，选用弹塑性本构模型，简化为各向同性硬化规律，使用摩尔-库伦屈服准则；土体剪切波速为300 m/s，密度为2000 kg/m3，泊松比取0.3，土体网格尺寸1 m×1 m，与结构接触的土体网格适当加密，尺寸为0.5 m×1.0 m。结构模型混凝土强度等级为C40，使用塑性损伤本构模型；钢筋型号选用HRB335，选用理想弹塑性本构模型，钢筋内置于结构中。假定位移连续，不考虑土体与结构之间的相对滑移。
1.2　地下结构Pushover分析过程
地下结构Pushover分析方法由柱状土自由体模型及土-结构模型2个模型组成。首先，将自由土体模型底部及侧面节点水平向位移固定，完成地应力平衡。然后，读取侧面各节点水平向反力及竖向位移，并作为土-地下结构模型的侧边界条件，对模型施加倒三角形水平惯性加速度至矩形地下结构层间位移角达到1/102[25]，记录每一增量的土与结构的非线性反应数据，即可得到地下结构完整的能力曲线。
2　弹簧-地下结构模型的推覆分析
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2.1　弹簧-地下结构模型的建立
弹簧-地下结构模型见图3，混凝土及钢筋的材料属性与土-地下结构模型保持一致。在地下结构两侧布置限位器，为侧墙弹簧提供支点，同时，限制地下结构底部节点水平向位移。
使用弹簧单元代替土体对地下结构的约束，地下结构模型侧面和底部布置弹簧。由于土体剪切模量随着剪应变的增加而减小[20]，为充分考虑土体自加载至结构发生破坏的全过程约束作用，提取地下结构Pushover分析模型变形过程中增加的法向力，将其作为地震过程中土体对结构的支撑力。从上述Pushover分析方法土-结构模型的模拟结果中提取相应数据计算弹簧-地下结构模型的弹簧刚度。底部弹簧刚度参考反应位移法弹簧刚度的计算原理，将地下结构破坏时刻土体沿Y轴方向的位移施加至土体模型，如图4所示。提取分析结果节点Y轴方向的反力，通过式（1）即可计算得到对应节点影响范围内的地基系数。
式中：K为地基系数；u为地下结构破坏时刻的位移；F为对土体模型施加位移后得到的节点反力；S为节点影响范围内的土体面积。
侧墙弹簧刚度的计算方法与底部弹簧刚度的计算方法相比，不同点是提取X轴方向的位移施加到土体模型上，提取对应节点X轴方向的反力。结合计算所得到的节点地基系数、结构尺寸以及实际需求选择合适的弹簧数量，取每个弹簧所代替的土体节点地基系数的平均值，可求得每个弹簧的刚度。
弹簧-地下结构模型侧墙弹簧7个，底部弹簧10个。侧墙弹簧按照从上到下的顺序编号，底部弹簧按照从左到右的顺序编号如图3所示。各弹簧刚度取值如表1所示。
弹簧刚度的取值直接受其所等效土体的面积及沿纵深布置弹簧的数量影响，模型使用的是足尺二维平面应变模型，所以弹簧刚度取值较大。考虑到经济性及试验场地限制等因素，地下结构试验通常使用缩尺模型，因此，在实际试验过程中弹簧刚度取值要远小于本文的弹簧刚度。在弹簧刚度满足试验要求的前提下，保证极限位移下弹簧未进入塑性状态即可，该方法对弹簧的材料、强度和硬度等力学特性无其他要求。
2.2　弹簧-地下结构模型的有效性验证
对比土-地下结构模型与弹簧-地下结构模型中结构的受拉损伤云图，可以发现2个模型的损伤位置基本一致，如图5所示。模型中使用线性弹簧近似考虑土体对结构的约束作用，然而，在实际地震过程中随着土体剪应变的增加，土体的剪切模量是逐渐减小的，这将显著影响在地震过程中土与结构之间的相互作用。显然，使用弹簧代替土体，仅能半定量的考虑土体的约束作用[21]。因此，该模型重点关注断面B和断面D的抗震性能弯矩能力曲线，模拟结果与Pushover模型对比结果如图6所示。由图可知，2种方法的抗震性能曲线在层间位移角达1/200之前吻合较好。随着加载土体侧墙基床系数的逐渐降低，从而导致弹簧-地下结构模型能力曲线逐渐降低。综上，弹簧-地下结构体系可应用于单跨矩形地下结构抗震性能研究。
3　非线性弹簧-地下结构体系的适用性分析
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土体水平基床系数随着推覆水平的增大而减小[26]。在弹簧-地下结构体系中弹簧的刚度始终恒定，这与实际情况有所差别，为此可引入非线性弹簧，研究非线性弹簧在弹簧-地下结构体系中的适用性及准确性。
3.1　非线性弹簧的实现
非线性弹簧可通过连接器输入位移-荷载曲线的方法实现，基于侧墙弹簧的布置数量，确定连接器的位移-荷载曲线。由于弹簧-地下结构模型与土-地下结构模型边界条件及加载方式的不同，导致两者变形形式有所差别，如图7所示。为了使得到的位移-荷载曲线能够应用到弹簧-地下结构体系中，将土-地下结构模型底部位移视为平移，即截取提取到的位移-荷载曲线后半段定义非线性弹簧，如图8所示。
3.2　结果分析
非线性弹簧与线性弹簧能力曲线的对比结果如图9所示。从断面B弯矩能力曲线可以看出，在层间位移角达到1/200之前，线性弹簧模型和非线性弹簧模型的能力曲线与Pushover能力曲线吻合效果均较好；当层间位移角超过1/200后，线性弹簧模型的能力曲线精度显著下降，而非线性弹簧模型曲线仍保持较高的精度。其原因可能是随着层间位移的增加，土体的刚度逐渐降低，而线性弹簧的刚度保持不变，从而导致其精度逐渐降低。从断面D弯矩能力曲线可以看出，线性弹簧模型和非线性弹簧模型的能力曲线差别不大。层间位移角达到1/200之前两者吻合较好，随着层间位移的增加，线性弹簧模型与非线性弹簧模型的吻合程度均有所降低，其原因是断面D处于结构底部，弹簧-地下结构模型底部位移较小，难以体现出弹簧的非线性，因此，导致非线性弹簧模型与线性弹簧模型的吻合程度差异较小。
依据BAO等[25]对地下结构抗震性能等级的划分，对比分析了弹簧-地下结构体系及非线性弹簧-地下结构体系可满足的性能指标等级，如表2所示。可以发现线性弹簧-地下结构体系可基本满足中度损伤性能指标分析，而非线性弹簧-地下结构体系除严重破坏阶段的底部截面外可满足全过程性能指标分析。
4　能力曲线敏感性分析
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通过以上分析表明非线性弹簧-地下结构体系应用于单跨地下结构抗震性能研究的有效性。但是，对于影响非线性弹簧-地下结构静力推覆试验方法准确性的因素及其敏感性仍有待研究。因此，将从轴压比和弹簧与结构间的相互作用分析影响该模型准确性的因素并给出合理的建议，为弹簧地下结构体系发展提供参考。
4.1　轴压比
埋深是影响地下结构地震响应的重要因素[27]，在不足以形成土拱效应的前提下，不同的埋置深度将导致结构所受到的上覆荷载不同[28]。在浅埋情况下，随着埋置深度的增加势必会造成地下结构顶部的轴向力增大。
设置轴压比u为0.07、0.14、0.28的模型，与地下结构Pushover分析方法的结果对比如图10所示。
由图10可知，轴压比对关键断面的最大弯矩有显著影响，随着轴压比的增大，关键断面B、D的最大弯矩也随之增大，最大弯矩对应的层间位移也随着轴压比的增大而增大，其原因可能是轴压比的增大导致顶板与侧墙间的整体性增强，侧墙与顶板在推覆过程中更倾向于同步移动；关键断面D远离加载点，因此上述现象较为明显。轴压比对能力曲线影响较大，建议在使用该方法进行地下结构抗震性能研究时应重点考虑轴压比的影响。
4.2　弹簧与结构间的接触性能
从结构设计角度上看，接触面上的摩擦因数并非影响地下结构抗震计算的关键因素[29]。但是，对于非线性弹簧-地下结构体系来说，弹簧与结构间的相互作用关系对能力曲线的影响还有待研究。弹簧连接钢板与地下结构接触面设置摩擦，法向设置硬接触，切向摩擦系数μ分别为0.3、0.5、0.7，并与不考虑摩擦的结果进行对比，如图11所示。
荷载沿结构水平向加载，结构的切向位移较小，所以摩擦系数的大小对能力曲线影响较小。这与已有研究结论相符[6，30]，即土-地下结构界面摩擦系数取0.2~0.8时，对结构的内力、变形和土压力等地震反应影响相对有限。从断面D的能力曲线来看，设置摩擦时截面的峰值弯矩提高了17.1%，同时达到弯矩对应的层间位移更大。断面B距离加载点较近，现象并不明显。
5　结论
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本文借鉴我国现行规范中传统反应位移法的基本原理和理论，以地下结构Pushover分析方法结果作为精确解，验证了弹簧-地下结构体系单向推覆模型在单跨矩形地下结构中的适用性。在此基础上，引入了非线性弹簧并分析了轴压比和弹簧与结构间相互作用的影响，得到以下结论：
1）对比土-地下结构Pushover分析模型与弹簧-地下结构体系单向推覆模型得到的抗震性能曲线及结构损伤云图，表明弹簧-地下结构体系单向推覆模型可应用于单跨地下结构抗震性能分析。
2）非线性弹簧的引入可以有效提高弹簧-地下结构体系的精度，为弹簧-地下结构单向推覆体系的应用奠定了基础。
3）地下结构侧墙的轴压比以及是否考虑弹簧与地下结构间的摩擦，对非线性弹簧-地下结构的能力曲线影响显著。建议在设置轴压比及弹簧与结构间的接触关系时，结合实际情况重点考虑。
基金
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  • 国家自然科学基金项目(52478488)
  • 内蒙古自治区自然科学基金项目(2023QN05012)
文献
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2025年第45卷第2期
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doi: 10.13197/j.eeed.2025.0202
  • 接收时间：2024-04-22
  • 首发时间：2026-03-20
  • 出版时间：2025-04-24
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  • 收稿日期：2024-04-22
  • 修回日期：2024-05-29
基金
国家自然科学基金项目(52478488)
内蒙古自治区自然科学基金项目(2023QN05012)
作者信息
    1.北京建筑大学 土木与交通工程学院，北京 100044
    2.赤峰学院 资源环境与建筑工程学院，内蒙古 赤峰 024000
    3.北京工业大学 城市与工程安全减灾教育部重点实验室，北京 100124

通讯作者:

许成顺（1977—），女，教授，博士，主要从事岩土地震工程研究。E-mail：
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https://castjournals.cast.org.cn/joweb/dzgcygczd/CN/10.13197/j.eeed.2025.0202
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
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
栓菌属 Trametes 5 2.39
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