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Article(id=1245389865248994148, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245389858412282468, articleNumber=null, orderNo=null, doi=10.13197/j.eeed.2024.0217, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1656691200000, receivedDateStr=2022-07-02, revisedDate=1662134400000, revisedDateStr=2022-09-03, acceptedDate=null, acceptedDateStr=null, onlineDate=1774853682099, onlineDateStr=2026-03-30, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774853682099, onlineIssueDateStr=2026-03-30, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774853682099, creator=13701087609, updateTime=1774853682099, updator=13701087609, issue=Issue{id=1245389858412282468, tenantId=1146029695717560320, journalId=1241701559352995854, year='2024', volume='44', issue='2', pageStart='1', pageEnd='232', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774853680470, creator=13701087609, updateTime=1774854277127, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1245392361031840387, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245389858412282468, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1245392361031840388, tenantId=1146029695717560320, journalId=1241701559352995854, issueId=1245389858412282468, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=160, endPage=168, ext={EN=ArticleExt(id=1245389865597121389, articleId=1245389865248994148, tenantId=1146029695717560320, journalId=1241701559352995854, language=EN, title=Vibration response of saturated foundation caused by train operation under irregular track conditions, columnId=null, journalTitle=Earthquake Engineering and Engineering Dynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

In order to study the vibration response of saturated foundation caused by train moving load under irregular track conditions, and further improve the vibration propagation and attenuation law of saturated foundation, the track irregularity load is introduced into the saturated foundation 2.5D finite element in this paper. The track irregularity load is transformed into frequency domain-wave number domain through Fourier transform, and the vibration response caused by the quasi-static load is compared and analyzed. The results indicate that when the vehicle speed is low, the vibration difference caused by the following two conditions is very small. As the vehicle speed increases, track irregularity significantly increases the amplitude of acceleration and displacement of saturated foundation, and the time-history curves show stronger fluctuation. Track irregularity has little influence on the acceleration spectrum at the center of the track. When the train runs at low speed and high speed, the frequency spectrum rules of the two loads are basically the same, and the main frequency distribution is basically the same. Under the condition of track irregularity, only the acceleration in each frequency band increases slightly. In addition, the pore water pressure of saturated foundation caused by high-speed railway will be greatly increased by track irregularity, and the pore water pressure decreases rapidly with the increase of depth.

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为研究轨道不平顺条件下列车运行引起的饱和地基振动响应，进一步完善饱和地基的振动传播和衰减规律，将轨道不平顺引入饱和地基2.5D有限元，通过Fourier变换得到频域-波数域表达式，对比分析准静态荷载与不平顺条件下高铁列车运行对饱和地基加速度、位移和孔隙水压力的影响规律。研究结果表明：列车速度较低时，2种条件下列车引起的饱和地基振动相差不大，随着列车速度提高，轨道不平顺使饱和地基的加速度幅值和位移幅值显著增大，且在时程曲线规律上呈现更强的波动性；轨道不平顺对轨道中心加速度频谱影响较小，列车在低速和高速运行时，2种荷载的频谱规律均基本一致，主频分布也基本相同，轨道不平顺条件下仅各频段加速度大小略有增加；轨道不平顺会大幅增加高速列车运行引起的饱和地基孔隙水压力，且随着深度增加孔压迅速衰减。

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刘森（1999—），男，硕士研究生，主要从事岩土动力学方面的研究。E-mail：
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高盟（1974—），男，副教授，博士，主要从事土动力学及环境岩土工程研究。E-mail：

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高盟（1974—），男，副教授，博士，主要从事土动力学及环境岩土工程研究。E-mail：

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高盟（1974—），男，副教授，博士，主要从事土动力学及环境岩土工程研究。E-mail：

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Parameters of CRH3 ‘Harmony’ vehicle group

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参数名称编组形式/节头车长度/m全长/m同车转向架中心/m转向架轴重/t中间车长度/m固定轴距/m邻车转向架中心/m
数值825.675201.80017.3751524.7752.5007.500
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CRH3型“和谐号”车组参数

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参数名称编组形式/节头车长度/m全长/m同车转向架中心/m转向架轴重/t中间车长度/m固定轴距/m邻车转向架中心/m
数值825.675201.80017.3751524.7752.5007.500
), ArticleFig(id=1245389879648039460, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389865248994148, language=EN, label=Table 2, caption=

Typical values of track irregularity under different control conditions

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控制条件波长/m正矢/mm
行车平稳性5016
209
105
作用到线路上的动力附加动载52.500
20.600
10.300
波形磨耗0.5000.100
0.0500.005
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不同控制条件下轨道不平顺典型值

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控制条件波长/m正矢/mm
行车平稳性5016
209
105
作用到线路上的动力附加动载52.500
20.600
10.300
波形磨耗0.5000.100
0.0500.005
), ArticleFig(id=1245389880092635704, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389865248994148, language=EN, label=Table 3, caption=

Parameters of saturated soil verification

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参数名称数值参数名称数值
泊松比0.3333孔隙率0.3
剪切模量/（×109 N/m2）3流体体积模量/（×109 Pa）1.5
土骨架密度/（kg/m3）2500动力渗透系数/（×10-6 m/s）1.0
孔隙流体密度/（kg/m3）1000——
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饱和土体验证参数取值

, figureFileSmall=null, figureFileBig=null, tableContent=
参数名称数值参数名称数值
泊松比0.3333孔隙率0.3
剪切模量/（×109 N/m2）3流体体积模量/（×109 Pa）1.5
土骨架密度/（kg/m3）2500动力渗透系数/（×10-6 m/s）1.0
孔隙流体密度/（kg/m3）1000——
), ArticleFig(id=1245389880323322438, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389865248994148, language=EN, label=Table 4, caption=

Computational mechanical parameters of saturated soil

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参数名称数值参数名称数值
土骨架密度/（kg/m3）1850土体剪切模量/（×107 Pa）1.85
孔隙流体密度/（kg/m3）1000流体体积模量/（×109 Pa）2
土体剪切波速/（m/s）100动力渗透系数/（×10-7 m/s）1
材料阻尼0.05泊松比0.40
孔隙率0.47——
), ArticleFig(id=1245389880432374349, tenantId=1146029695717560320, journalId=1241701559352995854, articleId=1245389865248994148, language=CN, label=表4, caption=

饱和土体计算力学参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数名称数值参数名称数值
土骨架密度/（kg/m3）1850土体剪切模量/（×107 Pa）1.85
孔隙流体密度/（kg/m3）1000流体体积模量/（×109 Pa）2
土体剪切波速/（m/s）100动力渗透系数/（×10-7 m/s）1
材料阻尼0.05泊松比0.40
孔隙率0.47——
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轨道不平顺条件下列车运行引起的饱和地基振动响应
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高盟 1, 2 , 刘森 1, 2 , 李丹阳 1, 2
地震工程与工程振动 | 2024,44(2): 160-168
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地震工程与工程振动 | 2024, 44(2): 160-168
轨道不平顺条件下列车运行引起的饱和地基振动响应
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高盟1, 2 , 刘森1, 2 , 李丹阳1, 2
作者信息
  • 1.山东科技大学 山东省土木工程防灾减灾重点实验室，山东 青岛 266590
  • 2.山东科技大学 土木工程与建筑学院，山东 青岛 266590

    • 高盟（1974—），男，副教授，博士，主要从事土动力学及环境岩土工程研究。E-mail：

通讯作者:

刘森（1999—），男，硕士研究生，主要从事岩土动力学方面的研究。E-mail：
Vibration response of saturated foundation caused by train operation under irregular track conditions
Meng GAO1, 2 , Sen LIU1, 2 , Danyang LI1, 2
Affiliations
  • 1.Shandong Province Key Laboratory of Civil Engineering & Disaster Prevention and Mitigation, Shandong University of Science and Technology, Qingdao 266590, China
  • 2.College of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao 266590, China
doi: 10.13197/j.eeed.2024.0217
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摘要
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为研究轨道不平顺条件下列车运行引起的饱和地基振动响应，进一步完善饱和地基的振动传播和衰减规律，将轨道不平顺引入饱和地基2.5D有限元，通过Fourier变换得到频域-波数域表达式，对比分析准静态荷载与不平顺条件下高铁列车运行对饱和地基加速度、位移和孔隙水压力的影响规律。研究结果表明：列车速度较低时，2种条件下列车引起的饱和地基振动相差不大，随着列车速度提高，轨道不平顺使饱和地基的加速度幅值和位移幅值显著增大，且在时程曲线规律上呈现更强的波动性；轨道不平顺对轨道中心加速度频谱影响较小，列车在低速和高速运行时，2种荷载的频谱规律均基本一致，主频分布也基本相同，轨道不平顺条件下仅各频段加速度大小略有增加；轨道不平顺会大幅增加高速列车运行引起的饱和地基孔隙水压力，且随着深度增加孔压迅速衰减。

轨道不平顺  /  移动荷载  /  饱和地基  /  2.5D有限元  /  高速铁路

In order to study the vibration response of saturated foundation caused by train moving load under irregular track conditions, and further improve the vibration propagation and attenuation law of saturated foundation, the track irregularity load is introduced into the saturated foundation 2.5D finite element in this paper. The track irregularity load is transformed into frequency domain-wave number domain through Fourier transform, and the vibration response caused by the quasi-static load is compared and analyzed. The results indicate that when the vehicle speed is low, the vibration difference caused by the following two conditions is very small. As the vehicle speed increases, track irregularity significantly increases the amplitude of acceleration and displacement of saturated foundation, and the time-history curves show stronger fluctuation. Track irregularity has little influence on the acceleration spectrum at the center of the track. When the train runs at low speed and high speed, the frequency spectrum rules of the two loads are basically the same, and the main frequency distribution is basically the same. Under the condition of track irregularity, only the acceleration in each frequency band increases slightly. In addition, the pore water pressure of saturated foundation caused by high-speed railway will be greatly increased by track irregularity, and the pore water pressure decreases rapidly with the increase of depth.

track irregularity  /  moving load  /  saturated foundation  /  2.5D finite element  /  high-speed railway
高盟, 刘森, 李丹阳. 轨道不平顺条件下列车运行引起的饱和地基振动响应. 地震工程与工程振动, 2024 , 44 (2) : 160 -168 . DOI: 10.13197/j.eeed.2024.0217
Meng GAO, Sen LIU, Danyang LI. Vibration response of saturated foundation caused by train operation under irregular track conditions[J]. Earthquake Engineering and Engineering Dynamics, 2024 , 44 (2) : 160 -168 . DOI: 10.13197/j.eeed.2024.0217
正文
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0　引言
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随着中国高速铁路的发展和列车运行速度的提高，高铁运行引起的环境振动问题愈发突出。同时，随着高铁运营时间增加而产生的路基不均匀沉降，以及轮轨间磨耗、各部件间隙等原因都将导致列车轨道出现不平顺，从而影响列车正常运行。因此，研究轨道不平顺条件下高铁列车运行引起的饱和地基振动规律以控制其产生的环境振动显得尤为重要。
已有研究对移动荷载作用下饱和地基的振动响应问题进行了各种有益探索。CAI等[1-2]基于Biot多孔弹性理论，对不同车速引起的轨道和路基动力响应进行了研究。高广运等[3-5]基于Biot控制方程将2.5D有限元法推广至饱和土模型，建立了列车-轨道-地基耦合的2.5D饱和地基模型，对比了弹性地基与饱和地基振动响应差异。YAO等[6]建立了多孔弹性半空间中的车辆-轨道-地面耦合模型，对高速列车作用下路基的动力响应进行了评估。曹志刚等[7-8]将地基模拟为饱和多孔弹性半空间，将列车移动荷载简化为轴荷载，用半解析方法研究了列车加速或减速时的地面振动和超孔隙水压力。钱建固等[9]将列车移动荷载简化为矩形分布荷载，解析研究了饱和多孔介质中不同荷载速度及频率引起的饱和地基振动放大效应。
然而，现有对饱和地基的研究多将列车移动荷载简化成点荷载、简谐荷载和准静态荷载等，未考虑轨道不平顺的影响，不能较好地表征真实列车荷载。蔡袁强等[10-11]、王玉[12]将车辆和轨道-地面子系统耦合在一起，钢轨表面的竖向不平顺采用Jenkins给出的形式进行简化，半解析研究了饱和多孔介质中列车动态荷载由于轨道不平顺产生的地基振动。陈瑶等[13]采用正弦曲线表示不平顺路面，研究了不平顺路面对交通荷载引起的饱和地基振动影响。胡静[14]将轨道不平顺简化为单个余弦不平顺，分析了高速铁路引起的饱和软土地基动力响应。巴振宁等[15]采用半解析方法，运用Jenkins给出的荷载形式模拟钢轨表面的竖向不平顺，研究了层状饱和地基的动力响应问题。周仁义等[16]利用列车的准静态荷载与道路不平顺引起的附加动荷载两部分来模拟轨道交通，对饱和地基中交通荷载产生的动应力展开了解析理论研究。
事实上，对于轨道不平顺作用下饱和地基的振动响应研究还非常匮乏，且这些研究多将轨道不平顺简化成Z（x）= Aei（2π/λ）x的形式，仅考虑了列车的自重恒载和轨道不平顺引起的附加动荷载两部分，不能真实地反映列车运行特征。针对现有研究的不足，本文在饱和地基2.5D有限元基础上，同时考虑轨道不平顺、附加动荷载和轨面波形磨耗效应，修正列车荷载表达式，进一步研究轨道不平顺作用下饱和地基振动响应，完善饱和地基的振动传播和衰减规律。在工程应用中，本文提供的方法能够更真实地表征列车实际运行状态，可为高速铁路的安全性评估及地基振动响应预测提供重要参考。
1　有限元模型
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1.1　有限元模型的建立
在高广运等[3-5]推导的饱和多孔介质基本理论基础上，采用2.5D有限元方法建立图1所示模型。模型边界条件采用文献[3]推导的黏弹性动力人工边界。采用FORTRAN语言编程，实现黏弹性动力人工边界的设置，以及准静态列车移动荷载、不平顺列车移动荷载的施加。
采用四节点单元对轨道、路基和地基进行离散。二维网格中每个节点均含有3个自由度，包含一个沿列车移动方向的自由度，以此模拟列车运行引起的三维振动响应。其中计算域的半宽为60 m、深度为30 m，网格尺寸划分为0.5、1.0、2.0 m三级，在宽度方向设置为0.5、1.0、2.0 m，在深度方向设置为0.5、1.0 m，有限元网格划分示意图如图2所示。
1.2　准静态列车移动荷载
列车参数选取CRH3型“和谐号”的相关数据，列车编组为4M+4T，车组参数如表1所示。
列车荷载模型示意图如图3所示，图中为列车的4节编组。选用秦沈客运专线的相关数据[17]作为轨道参数，钢轨和轨枕质量m =540 kg/m，钢轨弯曲刚度EI =13.254 MN•m2，轨道板宽度为3 m。
将高铁列车荷载模拟为一系列轮重荷载组成，准静态列车荷载表达式[18]在时域和空间域表示为
对坐标x和时间t进行Fourier变换可得
式中：D为列车车厢数；c为列车沿x坐标移动速度；ω0为自振频率；P0为列车轮对静载；LS为车厢总长度；LD为列车荷载到观察点之间的距离；an，bn分别为前后轴之间的距离；δ为Dirac函数。
1.3　不平顺列车移动荷载
根据梁波等[19]提出的列车荷载模拟方法，采用一个激励力函数同时反映轨道不平顺、附加动荷载和轨面波形磨耗效应，并考虑叠加组合与钢轨、轨枕的分散传递因素，以此表征真实列车运行情况。将修正列车移动荷载表示为
其中：
式中：k1为列车轮对力在线路上的叠加系数；k2为钢轨及轨枕的分散系数；分别对应行车平稳性、作用到线路上的动力附加动载和波形磨耗这3种控制条件中振动荷载的典型值，如表2所示；M0为簧下质量；ωj =2πc/Lj为振动圆频率，Lj为几何不平顺曲线波长；Aj为几何不平顺矢高。
对式（6）作Fourier变换，得到不平顺列车移动荷载在频域-波数域内的表达式为
式中，当ω>0时为“+”，当ω<0时为“-”。的表达式为
2　饱和土2.5D有限元验证
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为了验证本文饱和土2.5D有限元计算模型的准确性，现将本文模型计算结果与LU等[20]研究的移动荷载作用下饱和土多孔介质半空间的半解析解结果进行对比，采取与LU相同的荷载施加方法，将移动荷载直接施加在饱和土体上，忽略轨道系统的影响。模型验证选取相同的饱和土体参数和荷载数值。饱和多孔介质验证参数取值如表3所示。
竖向点荷载沿x坐标方向在地表运行，移动荷载速度分别取c1 =0.1cs、c2 = 0.5cs、c3 = 0.9cs。其中，剪切波速，G为剪切模量。归一化位移U∗=UG/F和归一化孔压p∗=p/F在3种移动荷载速度下，坐标（0.0，1.0，-1.0）位置处本文解与文献[20]解的对比，如图4（a）和（b）所示。
由图4可知，当列车速度为0.1cs和0.5cs时，位移和孔压的振动响应较小，但当列车速度接近cs时，振动明显增大。从整体来看，本文计算结果与LU的半解析解结果基本吻合，图中车速为0.9cs时计算结果略大于文献结果，是由于2.5D有限元计算方法不同，以及本文结构模型细化带来的差异。说明利用本文计算模型研究轨道不平顺条件下列车运行引起的饱和地基振动响应是准确可靠的。
3　饱和地基振动响应分析
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3.1　饱和地基加速度响应
根据所建模型，列车选取CRH3型“和谐号”，对不平顺条件下高铁运行引起的动力响应进行研究。参考目前国内“和谐号”列车运行速度，将列车分为：低速列车（30 m/s）、高速列车（100 m/s）。轨道不平顺参数k1取1.538，k2取0.7；几何不平顺曲线波长取L1 =10 m，L2 =2 m，L3 =0.5 m；几何不平顺矢高A1 =3.5 mm，A2 =0.4 mm，A3 =0.08 mm。饱和土体的计算力学参数如表4所示，计算模型长为120 m、深度为30 m。傅里叶反变换点取4096，时间间隔为0.0025 s。
取距离轨道中心5、10、15、20 m处4个监测点，绘制距轨道中心不同距离处的加速度时程曲线如图5所示。由图可知，当车速为30 m/s时，饱和地基上加速度幅值衰减很快，准静态荷载作用下5、10、15、20 m处4个监测点的加速度幅值分别为8.193、0.818、0.135、0.025 mm/s2，而不平顺条件下各监测点处加速度幅值与准静态基本相同，且不同监测点处加速度时程规律十分接近。当车速为100 m/s时，由于此时车速达到土体的剪切波速，地基中产生共振现象，振动幅值和振动波形均出现明显变化[21]，故加速度幅值显著增加，且地基各点衰减变慢，准静态荷载作用下5、10、15、20 m处4个监测点的加速度幅值分别为0.694、0.132、0.025、0.013 mm/s2，而不平顺荷载作用下各监测点处加速度幅值分别为3.200、0.550、0.179、0.077 mm/s2，可以看出列车高速运行情况下，轨道不平顺对饱和地基加速度幅值有显著影响，且各监测点处加速度幅值曲线呈现明显的不平顺波动性。
轨道中心处地面加速度频谱曲线如图6所示。由图可知，轨道不平顺对轨道中心加速度频谱影响较小，列车在低速和高速运行时，2种荷载的频谱规律均基本一致，主频分布也基本相同，轨道不平顺条件下仅各频段加速度大小略有增加。图中还可以看出，随着车速提高，轨道中心频率由中低频变为中高频，且主频显著提高。
3.2　饱和地基位移响应
距轨道中心不同距离处的竖向位移时程曲线如图7所示。列车以30 m/s的速度在准静态条件下运行时，距轨道中心5 m处的监测点仍能观测到轮轨分布，且只存在向下的竖向位移，随着距离继续增大，地表竖向位移表现为向上的波动性，且轮轨分布不再明显。此时，轨道不平顺条件下地表的竖向位移传播衰减规律与准静态荷载基本相同。当车速为100 m/s时，饱和地基表面竖向位移幅值明显增加，且各监测点衰减变慢，距轨道中心10 m处仍能观测到较明显的轮轨分布，且位移时程曲线形状更加复杂，还存在向上的竖向位移；与列车低速运行不同的是，此时考虑轨道不平顺的地表竖向位移幅值明显大于准静态荷载，且位移时程的波动性更强，说明列车高速运行时，由于轨道的不平顺，地表的位移响应将更加剧烈。
距轨道中心不同距离处的水平位移时程曲线如图8所示。当车速为30 m/s时，准静态荷载的水平位移变化趋势和变化规律与不平顺条件下基本相同，这是因为列车速度较低时，地基变形的来源是列车轴重，其动力变形比例较小。当车速为100 m/s时，不平顺荷载引起的饱和地基5 m处监测点水平位移幅值为0.361 mm，远高于准静态荷载的0.159 mm，这是由于轨道不平顺包含了列车随机激振的主要组分，列车速度的提高显著影响了荷载的振动圆频率，因此列车高速运行时地基水平位移幅值明显高于准静态荷载，并且在时程曲线规律上具有更强的波动性。
3.3　饱和地基孔隙水压力
列车低速和高速运作时轨道中心下不同深度处的孔隙水压力时程曲线如图9所示，其中只列出了2、4、6、10 m深度的情况。由图可知，当列车荷载为准静态时，随着列车速度提高孔隙水压力略有增加，列车速度为30 m/s时，孔压最大值接近5 kPa，列车速度为100 m/s时，孔压峰值为5.8 kPa，列车运行引起的孔压相对较小，并随着深度的增加衰减很快。当考虑轨道不平顺条件时，随着列车速度提高孔隙水压力显著增加，在深度2 m监测点处，列车速度为30 m/s时，孔压最大值接近6.5 kPa，而列车速度100 m/s时，孔压峰值为14.3 kPa，可见轨道不平顺会大幅增加高速列车引起的饱和地基孔隙水压力，这是因为当车速达到土体剪切波速时，列车共振会使地基产生较大的孔隙水压力[3]，而轨道不平顺条件下这种共振效应被放大。因此，为确保列车运行的安全性，考虑轨道不平顺具有十分重要的意义。
4　结论
收起
考虑轨道不平顺的影响，对饱和地基上的准静态列车移动荷载进行修正，对比分析了准静态荷载与不平顺条件下高铁列车运行引起的饱和地基动力响应。主要结论如下：
1）列车速度为30 m/s时，轨道不平顺对饱和地基影响较小，列车速度提高到100 m/s（即达到土体剪切波速）时，不平顺条件下饱和地基动力响应显著大于准静态荷载，且波动性增大。
2）列车速度较低时，不平顺条件下饱和地基加速度幅值与准静态基本相同；随着列车速度提高，轨道不平顺对饱和地基加速度幅值产生显著影响，加速度幅值明显增加，地基各点衰减变慢，且加速度幅值曲线呈现明显的不平顺波动性。轨道不平顺对轨道中心加速度频谱影响较小，列车在低速和高速运行时，2种荷载的频谱规律均基本一致，主频分布也基本相同，轨道不平顺条件下仅各频段加速度大小略有增加。但随着车速提高，轨道中心频率由中低频变为中高频，且主频显著提高。
3）列车高速运行时，考虑轨道不平顺的饱和地基竖向位移幅值和水平位移幅值均明显大于准静态荷载，且在时程曲线规律上具有更强的波动性。
4）当列车荷载为准静态时，随着列车速度提高孔隙水压力略有增加；当考虑轨道不平顺时，高速列车引起的饱和地基孔隙水压力大幅增加，且随深度增加孔压迅速衰减。
基金
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  • 山东省自然科学基金项目(ZR2021ME144)
文献
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2024年第44卷第2期
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doi: 10.13197/j.eeed.2024.0217
  • 接收时间：2022-07-02
  • 首发时间：2026-03-30
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  • 收稿日期：2022-07-02
  • 修回日期：2022-09-03
基金
山东省自然科学基金项目(ZR2021ME144)
作者信息
    1.山东科技大学 山东省土木工程防灾减灾重点实验室，山东 青岛 266590
    2.山东科技大学 土木工程与建筑学院，山东 青岛 266590

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刘森（1999—），男，硕士研究生，主要从事岩土动力学方面的研究。E-mail：
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2种不同金属材料的力学参数
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species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
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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
栓菌属 Trametes 5 2.39
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