Article(id=1244316344183799864, tenantId=1146029695717560320, journalId=1244215477623373855, issueId=1244316342938087728, articleNumber=null, orderNo=null, doi=10.16285/j.rsm.2024.1518, pmid=null, cstr=32223.14.j.rsm.2024.1518, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1733760000000, receivedDateStr=2024-12-10, revisedDate=null, revisedDateStr=null, acceptedDate=1737475200000, acceptedDateStr=2025-01-22, onlineDate=1774597734733, onlineDateStr=2026-03-27, pubDate=1763049600000, pubDateStr=2025-11-14, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774597734733, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774597734732, creator=13701087609, updateTime=1774597734732, updator=13701087609, issue=Issue{id=1244316342938087728, tenantId=1146029695717560320, journalId=1244215477623373855, year='2025', volume='46', issue='11', pageStart='3329', pageEnd='3672', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1774597734436, creator=13701087609, updateTime=1774597825220, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244316723801862468, tenantId=1146029695717560320, journalId=1244215477623373855, issueId=1244316342938087728, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244316723806056773, tenantId=1146029695717560320, journalId=1244215477623373855, issueId=1244316342938087728, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=3441, endPage=3450, ext={EN=ArticleExt(id=1244316344875860029, articleId=1244316344183799864, tenantId=1146029695717560320, journalId=1244215477623373855, language=EN, title=Experimental study on threshold strain for pore pressure increase and stiffness degradation in saturated coral sand under complex stress paths, columnId=1244316343936332083, journalTitle=Rock and Soil Mechanics, columnName=Fundamental Theory and Experimental Research, runingTitle=null, highlight=null, articleAbstract=

The accumulation of excess pore water pressure (EPWP) under cyclic loading may induce partial or complete liquefaction of saturated coral sands, posing significant threats to the safety of structures and foundations. In numerical simulations and analyses, accurate prediction of EPWP development is essential, with the determination of threshold strain serving as a critical step. A novel method has been developed to determine the threshold strains (pore pressure threshold strain γtp, stiffness degradation threshold strain γtd, and flow threshold strain γtf) for the EPWP generation and stiffness degradation in saturated coral sands under complex stress paths. This was achieved isotopically consolidated, undrained single-stage and multistage cyclic shear tests, including 90° jumps and continuous rotations of principal stress. The findings indicate that while γtp, γtd, and γtf are relatively insensitive to the cyclic stress, they are significantly influenced by the initial relative density (Dr). Additionally, the gap between γtp and γtd widens as Dr increases. Under varying cyclic loading conditions and initial physical states, γtf corresponds to the EPWP ratio of approximately 0.9, with a corresponding stiffness index of around 0.10. The proposed method for determining γtp, γtd, and γtf can effectively reduce the number of required cyclic tests, making it suitable for use as input values in numerical calculations or analytical methods, and for characterizing soil behavior under stress and strain conditions.

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循环荷载作用下超静孔压的累积可能导致饱和珊瑚砂的局部或完全液化,显著影响建(构)筑物的安全性。在数值模拟与分析中,准确预估超静孔压的增长尤为重要,而阈值应变的确定则是关键环节。通过循环应力主轴90°跳转和连续旋转的均等固结、不排水的单级和分级循环剪切试验,提出了确定复杂应力路径下饱和珊瑚砂超静孔压增长和刚度退化的阈值应变(孔压阈值应变γtp、刚度退化阈值应变γtd和流动阈值应变γtf)的新方法。结果表明,γtpγtdγtf均受循环应力路径的影响较小,但受初始相对密实度Dr的影响显著。此外,随着Dr的增加,γtpγtd之间的差距逐渐扩大。在不同循环加载条件和初始物理状态下,γtf对应的孔压比约为0.9,而其对应的刚度指数约为0.10。确定γtpγtpγtf的新方法的提出可以有效减少室内循环试验的数量,以便于作为数值计算或分析方法的输入值,或用于表征土体在应力和应变条件下的行为特性。

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陈国兴,男,1963年生,博士,教授,主要从事土动力学与岩土地震工程方面的研究工作。E-mail:
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秦悠,男,1994年生,博士,教授,主要从事土动力学方面的研究。E-mail:

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秦悠,男,1994年生,博士,教授,主要从事土动力学方面的研究。E-mail:

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秦悠,男,1994年生,博士,教授,主要从事土动力学方面的研究。E-mail:

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Rock and Soil Mechanics, 2024, 45(11): 3295-3303., articleTitle=Liquefaction flow characteristics of saturated silt under initial shear stress, refAbstract=null), Reference(id=1244316375288758434, tenantId=1146029695717560320, journalId=1244215477623373855, articleId=1244316344183799864, doi=null, pmid=null, pmcid=null, year=2012, volume=34, issue=9, pageStart=1604, pageEnd=1610, url=null, language=null, rfNumber=[33], rfOrder=41, authorNames=王志华, 周恩全, 陈国兴, journalName=岩土工程学报, refType=null, unstructuredReference=王志华, 周恩全, 陈国兴, . 循环荷载下饱和砂土固-液相变特征[J]. 岩土工程学报, 2012, 34(9): 1604-1610., articleTitle=循环荷载下饱和砂土固-液相变特征, refAbstract=null), Reference(id=1244316375402004650, tenantId=1146029695717560320, journalId=1244215477623373855, articleId=1244316344183799864, doi=null, pmid=null, pmcid=null, year=2012, volume=34, issue=9, pageStart=1604, pageEnd=1610, url=null, language=null, rfNumber=[33], rfOrder=42, authorNames=WANG Zhi-hua, ZHOU En-quan, CHEN Guo-xing, journalName=Chinese Journal of Geotechnical Engineering, refType=null, unstructuredReference=WANG Zhi-hua, ZHOU En-quan, CHEN Guo-xing, et al. Characteristics of solid-liquid phase change of saturated sand under cyclic loading[J]. 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注:N为循环次数;G为剪切模量;G0为初始剪切模量。

, figureFileSmall=g6cqsF6ZZhCzZji23EkJ0Q==, figureFileBig=JwtboI7513Bc0RcuXkd1Og==, tableContent=null), ArticleFig(id=1244316360914878979, tenantId=1146029695717560320, journalId=1244215477623373855, articleId=1244316344183799864, language=EN, label=Fig.2, caption=Stress state of a hollow cylindrical specimen, figureFileSmall=lOeiOZ1jTx0+yAJnY5cwhQ==, figureFileBig=WM6YiyUSr09a+DHaWVtdkg==, tableContent=null), ArticleFig(id=1244316361044902410, tenantId=1146029695717560320, journalId=1244215477623373855, articleId=1244316344183799864, language=CN, label=图2, caption=空心圆柱试样受力状态, figureFileSmall=lOeiOZ1jTx0+yAJnY5cwhQ==, figureFileBig=WM6YiyUSr09a+DHaWVtdkg==, tableContent=null), ArticleFig(id=1244316361187508749, tenantId=1146029695717560320, journalId=1244215477623373855, articleId=1244316344183799864, language=EN, label=Fig.3, caption=Grading curve and SEM image of Nansha coral sand, figureFileSmall=fIOSrol23IYYGLbThWkI1w==, figureFileBig=BK30bmww2eaoy+8LkAiIlQ==, tableContent=null), 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articleId=1244316344183799864, language=EN, label=Fig.5, caption=Undrained cycle response characteristics of single-staged and multi-staged tests, figureFileSmall=NNDY3jJ0DVqPH9jhomfH/g==, figureFileBig=Ab4jFvPzMX2ovTzV3uoS8A==, tableContent=null), ArticleFig(id=1244316361720185382, tenantId=1146029695717560320, journalId=1244215477623373855, articleId=1244316344183799864, language=CN, label=图5, caption=单级及分级试验的不排水循环反应特性, figureFileSmall=NNDY3jJ0DVqPH9jhomfH/g==, figureFileBig=Ab4jFvPzMX2ovTzV3uoS8A==, tableContent=null), ArticleFig(id=1244316361858597422, tenantId=1146029695717560320, journalId=1244215477623373855, articleId=1244316344183799864, language=EN, label=Fig.6, caption=Cyclic strain paths of saturated coral sand under various cyclic stress paths, figureFileSmall=1ZJ3vmkGJyjpMs3wQ8sMWg==, figureFileBig=tlaSybXcOLfa9w8uIIK6GA==, tableContent=null), ArticleFig(id=1244316361959260723, tenantId=1146029695717560320, journalId=1244215477623373855, articleId=1244316344183799864, 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tableContent=null), ArticleFig(id=1244316365436338917, tenantId=1146029695717560320, journalId=1244215477623373855, articleId=1244316344183799864, language=CN, label=图14, caption=刚度指数随偏应变幅值的变化, figureFileSmall=l0S94XWg7TpE6GyyjyjY1w==, figureFileBig=2Z6zTVZ6/mWXSSFRTIrvmA==, tableContent=null), ArticleFig(id=1244316365578945261, tenantId=1146029695717560320, journalId=1244215477623373855, articleId=1244316344183799864, language=EN, label=Table 1, caption=

Test protocol for undrained cyclic shear tests with 90° principal stress axis jumps and continuous rotations

, figureFileSmall=null, figureFileBig=null, tableContent=
编号 Dr/% Drc/% ασ/(°) γtp/% γtd/% γtf/%
SS014550.420.01.375
SS024549.7322.51.351
SS034549.6245.01.350
SS044550.1967.51.401
SS054549.8290.01.395
MS013036.080.00.021 60.026 91.063
MS023036.4422.50.022 20.028 81.241
MS033036.5245.00.019 10.025 11.006
MS043036.0467.50.019 60.024 41.110
MS053036.3790.00.018 30.024 21.365
MS064550.620.00.023 00.031 31.347
MS074549.7322.50.027 00.034 81.306
MS084549.1745.00.024 40.032 21.395
MS094550.0867.50.023 90.032 41.374
MS104549.8590.0.0.023 10.033 71.452
MS116063.650.00.029 10.038 71.536
MS126063.3222.50.029 30.041 41.478
MS136063.1945.00.029 80.039 61.465
MS146063.3567.50.031 20.040 51.541
MS156064.0590.00.030 30.040 61.478
MS167074.130.00.032 10.042 91.549
MS177073.9222.50.033 60.043 11.556
MS187074.0045.00.033 80.045 41.538
MS197074.2667.50.034 10.044 61.614
MS207073.9790.00.032 40.042 01.581
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不排水循环剪切试验方案(90°跳转应力路径)

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SS024549.7322.51.351
SS034549.6245.01.350
SS044550.1967.51.401
SS054549.8290.01.395
MS013036.080.00.021 60.026 91.063
MS023036.4422.50.022 20.028 81.241
MS033036.5245.00.019 10.025 11.006
MS043036.0467.50.019 60.024 41.110
MS053036.3790.00.018 30.024 21.365
MS064550.620.00.023 00.031 31.347
MS074549.7322.50.027 00.034 81.306
MS084549.1745.00.024 40.032 21.395
MS094550.0867.50.023 90.032 41.374
MS104549.8590.0.0.023 10.033 71.452
MS116063.650.00.029 10.038 71.536
MS126063.3222.50.029 30.041 41.478
MS136063.1945.00.029 80.039 61.465
MS146063.3567.50.031 20.040 51.541
MS156064.0590.00.030 30.040 61.478
MS167074.130.00.032 10.042 91.549
MS177073.9222.50.033 60.043 11.556
MS187074.0045.00.033 80.045 41.538
MS197074.2667.50.034 10.044 61.614
MS207073.9790.00.032 40.042 01.581
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Test protocol for undrained cyclic shear tests with continuous principal stress direction rotations

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编号 Dr/% Drc/% α σmax/(°) γtp/% γtd/% γtf/%
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SS074549.1045.01.382
SS084551.6167.51.340
SS094549.8790.01.411
MS214550.1122.50.028 40.032 91.354
MS224549.9845.00.028 00.034 21.388
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不排水循环剪切试验方案(连续旋转应力路径)

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SS084551.6167.51.340
SS094549.8790.01.411
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MS224549.9845.00.028 00.034 21.388
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复杂应力路径下饱和珊瑚砂孔压增长与刚度退化的阈值应变试验研究
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秦悠 1 , 龙慧 1 , 吴琪 2 , 庄海洋 3 , 陈国兴 2
岩土力学 | 基础理论与实验研究 2025,46(11): 3441-3450
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岩土力学 | 基础理论与实验研究 2025, 46(11): 3441-3450
复杂应力路径下饱和珊瑚砂孔压增长与刚度退化的阈值应变试验研究
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秦悠1 , 龙慧1, 吴琪2, 庄海洋3, 陈国兴2
作者信息
  • 1.南华大学 土木工程学院,湖南 衡阳 421001
  • 2.南京工业大学 岩土工程研究所,江苏 南京 211816
  • 3.华东交通大学 土木建筑学院,江西 南昌 330013
  • 秦悠,男,1994年生,博士,教授,主要从事土动力学方面的研究。E-mail:

通讯作者:

陈国兴,男,1963年生,博士,教授,主要从事土动力学与岩土地震工程方面的研究工作。E-mail:
Experimental study on threshold strain for pore pressure increase and stiffness degradation in saturated coral sand under complex stress paths
You QIN1 , Hui LONG1, Qi WU2, Hai-yang ZHUANG3, Guo-xing CHEN2
Affiliations
  • 1.School of Civil Engineering, University of South China, Hengyang, Hunan 421001, China
  • 2.Institute of Geotechnical Engineering, Nanjing Tech University, Nanjing, Jiangsu 211816, China
  • 3.School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang, Jiangxi 330013, China
出版时间: 2025-11-14 doi: 10.16285/j.rsm.2024.1518
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循环荷载作用下超静孔压的累积可能导致饱和珊瑚砂的局部或完全液化,显著影响建(构)筑物的安全性。在数值模拟与分析中,准确预估超静孔压的增长尤为重要,而阈值应变的确定则是关键环节。通过循环应力主轴90°跳转和连续旋转的均等固结、不排水的单级和分级循环剪切试验,提出了确定复杂应力路径下饱和珊瑚砂超静孔压增长和刚度退化的阈值应变(孔压阈值应变γtp、刚度退化阈值应变γtd和流动阈值应变γtf)的新方法。结果表明,γtpγtdγtf均受循环应力路径的影响较小,但受初始相对密实度Dr的影响显著。此外,随着Dr的增加,γtpγtd之间的差距逐渐扩大。在不同循环加载条件和初始物理状态下,γtf对应的孔压比约为0.9,而其对应的刚度指数约为0.10。确定γtpγtpγtf的新方法的提出可以有效减少室内循环试验的数量,以便于作为数值计算或分析方法的输入值,或用于表征土体在应力和应变条件下的行为特性。

饱和珊瑚砂  /  复杂应力路径  /  阈值应变  /  孔压增长  /  刚度退化

The accumulation of excess pore water pressure (EPWP) under cyclic loading may induce partial or complete liquefaction of saturated coral sands, posing significant threats to the safety of structures and foundations. In numerical simulations and analyses, accurate prediction of EPWP development is essential, with the determination of threshold strain serving as a critical step. A novel method has been developed to determine the threshold strains (pore pressure threshold strain γtp, stiffness degradation threshold strain γtd, and flow threshold strain γtf) for the EPWP generation and stiffness degradation in saturated coral sands under complex stress paths. This was achieved isotopically consolidated, undrained single-stage and multistage cyclic shear tests, including 90° jumps and continuous rotations of principal stress. The findings indicate that while γtp, γtd, and γtf are relatively insensitive to the cyclic stress, they are significantly influenced by the initial relative density (Dr). Additionally, the gap between γtp and γtd widens as Dr increases. Under varying cyclic loading conditions and initial physical states, γtf corresponds to the EPWP ratio of approximately 0.9, with a corresponding stiffness index of around 0.10. The proposed method for determining γtp, γtd, and γtf can effectively reduce the number of required cyclic tests, making it suitable for use as input values in numerical calculations or analytical methods, and for characterizing soil behavior under stress and strain conditions.

saturated coral sand  /  complex stress path  /  threshold strain  /  excess pore water pressure generation  /  stiffness degradation
秦悠, 龙慧, 吴琪, 庄海洋, 陈国兴. 复杂应力路径下饱和珊瑚砂孔压增长与刚度退化的阈值应变试验研究. 岩土力学, 2025 , 46 (11) : 3441 -3450 . DOI: 10.16285/j.rsm.2024.1518
You QIN, Hui LONG, Qi WU, Hai-yang ZHUANG, Guo-xing CHEN. Experimental study on threshold strain for pore pressure increase and stiffness degradation in saturated coral sand under complex stress paths[J]. Rock and Soil Mechanics, 2025 , 46 (11) : 3441 -3450 . DOI: 10.16285/j.rsm.2024.1518
循环荷载作用下饱和砂土会出现超静孔压ue和不可逆变形的累积,进而导致局部或完全液化,显著影响建(构)筑物的安全[1]。因此,研究ue不仅在岩土地震工程中至关重要,在海洋基础工程中同样有重要作用[2-3]。在设计中,ue可以通过刚度退化系数来解释。然而,由于土体反应和ue的产生与消散之间存在复杂的非线性相互作用,数值模拟的耦合模型通常更为适宜。无论何种情况,循环室内试验结果都是此类计算的必要输入值[4-5]。因此,作为数值计算或分析方法的输入值,并且作为表征土体应变状态变化的重要参数,阈值应变的研究显得尤为重要。
ue的产生本质上是一个应变依赖而非应力依赖的过程。由于土体的循环强度似乎取决于ue的产生,因此,循环强度的降低也是一个应变依赖的过程[6]。在基于应变状态和应力-应变反应所提出的土体行为概念框架基础上[7],Díaz-Rodríguez等[6]进一步总结了各种应变状态和应变阈值。对于饱和土,有4种不同类型的循环阈值应变:线性阈值应变γt1、体积阈值应变γtv、刚度退化阈值应变γtd及流动阈值γtf。这些阈值应变及其划定的应变范围可以通过剪切模量(刚度)退化曲线来表征。
图1所示,线性阈值应变γt1标志着土体从线性弹性到非线性弹性的转变。在该阈值之前,土体的非常小的应变弹性范围表现为几乎恒定的刚度区域,能量耗散最小且不产生ue。对于饱和砂土,γt1通常在5×10−6到6×10−5之间[8]。在小应变区,土体呈现出非线性应力-应变行为和细微的结构变化。体积阈值应变γtv或孔压阈值应变γtp则代表了具有完全可恢复性的小应变区与强度衰退较小的中应变区之间的界限[9-10]。当应变低于这一值时,土体不会产生显著的体应变或ue积累[11-12]。饱和砂的γtvγtp通常在8×10−5到9×10−4之间,并且与砂土类型、初始状态及循环加载条件密切相关[9, 13]
退化阈值应变γtd通常被视为剪切模量(刚度)开始快速下降的标志,区分了可恢复刚度范围与快速刚度退化范围[14-15]。当剪应变幅度超过γtd时,初始结构出现损伤,循环加载过程中表现出较高的能量损失,并且试样中会显著积累ue[16]。此外,流动阈值γtf定义了试样进入黏塑性模式并达到稳态相的转变点[6, 17]。在超过γtf后,应变状态进入残余应变范围[18]。以上这些阈值应变在工程中得到了广泛应用,但由于土体所受应力的复杂性,关于复杂循环应力路径下饱和砂土的阈值应变的研究鲜有报道。
珊瑚岛礁主要分布在南北纬30°之间,表层由未胶结的松散沉积层组成,包含大量由造礁珊瑚、珊瑚藻及其他海洋生物的骨架残骸在原地沉积或近源搬运沉积而成的珊瑚砂[19]。珊瑚砂是南海岛礁及毗邻海域的主要岩土介质,地震引起的珊瑚砂液化是珊瑚岛礁重大地震灾害的主要成因之一[20]。此外,波浪诱发的海床液化灾害也有相关报道。在地震、波浪等复杂往复荷载作用下,地基土中的主应力通常会发生变化[21-22],因此,需要进一步考虑循环应力路径对饱和珊瑚砂阈值应变的影响。本文通过分级和单级应力控制的不排水循环剪切试验,探讨了复杂循环应力路径下饱和珊瑚砂的孔压阈值应变、刚度退化阈值应变和流动阈值。
采用南京工业大学岩土工程研究所采购的空心圆柱扭剪仪(hollow cylindrical torsional shear apparatus,简称HCA)开展不排水循环剪切试验。HCA仪由以下4个主要部分组成:伺服主机系统及压力室(含自行研发增加的内压平衡仓)、压力/体积控制器、数据采集/控制系统以及计算机系统。该设备能够独立动态控制轴力W、扭矩MT、外围压po和内围压pi,HCA仪的技术参数详见Chen等[23]。如图2所示,空心圆柱试样的土单元存在4个应力分量:竖向应力σz、径向应力σr,环向应力σθ和扭剪应力τ,大、中、小主应力(σ1σ2σ3)可通过这些应力分量计算得出。σ1σz的夹角为主应力方向角α
试验材料为取自南沙群岛的珊瑚砂。从图3展示的试验珊瑚砂电镜扫描图可以看出,珊瑚砂颗粒表面粗糙,吸附少量细粒,形状不规则,大多呈次角状或片状,并且富含内孔隙。经测定,试验珊瑚砂的主要成分包括55.5%的文石,41.5%的高镁方解石及3.0%的方解石,其碳酸钙含量约为90.28%。试验珊瑚砂的级配曲线如图3所示,根据规范测得试验珊瑚砂的相对密度Gs为2.80,平均粒径d50为0.31 mm,不均匀系数Cu为4.67,曲率系数Cc为0.86,最大和最小孔隙比分别为emax=1.72,emin=0.99。
试验采用空心圆柱试样,试样高度H=200 mm,内、外直径分别为di=60 mm、do=100 mm。采用干装法制样,控制初始相对密实度Dr分别为30%、45%、60%和70%。将烘干的砂土按照级配对每层所需的颗粒质量单独配制,均分5层倒入承膜筒中,对于松散或中密状态的试样,需要通过轻微振捣严格控制装样时的高度。对于较密实的试样,还需要轻击薄壁桶,并对各层之间进行刮毛处理,以确保试样的均匀性。将试样放置在压力室中后,为使试样达到饱和,先通入15 min的CO2以置换土体中的空气,然后从试样底部通入无气水,直至无气泡排出;再分3步反压饱和至400 kPa。饱和阶段需要对试样进行饱和度Sr测试,依据B值(B为均等固结条件下的孔隙压力系数)随Sr的单调增长关系可知[24],当B值>0.95,Sr非常接近于1。Skempton[25]提出的B值如下所示:
式中:A为偏压或非均等固结条件下的孔隙压力系数;Δσ1和Δσ3分别为大、小主应力的变化值;Δu为孔压变化值。当测得B值≥0.97时,可认为该试样已经饱和。饱和后,对试样进行均等固结,初始平均主应力。通过数据采集系统及计算机控制系统采集并反馈试样的体积变化,依据试样固结前后体积变化量计算固结后相对密实度Drc表1表2列出了Drc的数据,发现相同Dr下试样的Drc的波动范围较小,这表明试样制备的均匀性较好。
为探究复杂应力路径下饱和珊瑚砂的阈值应变,设计了单级和分级应力控制的不排水循环剪切试验。如图4所示,在单级试验中,使用单一应力幅值qa循环加载直至试样液化;而在分级试验中,采用多个不同应力幅值组成,加载过程连续不中断,前10个阶段依次进行5个周期的循环加载,期间qa逐渐增加,直至第11个阶段,qa达到30 kPa,并持续加载至液化。循环应力比CSR(cyclic stress ratio)被定义为qa的比值[26]。对于空心圆柱试样,qa可被表示为[3, 9, 27]
故分级试验的CSR从0.01逐步增加至0.30。单级试验选取较为典型的qa=30 kPa[3, 28],即CSR=0.30。珊瑚砂由于其复杂的赋存条件,在综合考虑地震和波浪荷载的典型频率范围后[9, 29],无论进行分级试验还是单级试验,其循环加载试验的频率均设定为0.1 Hz。此外,不排水循环剪切试验在应力主轴90°跳转和连续旋转的应力路径条件下进行,应力主轴90°跳转应力路径的初始主应力方向角ασ分别为0°、22.5°、45.0°、67.5°和90.0°。连续旋转应力路径的最大循环加载方向角ασmax分别为22.5°、45.0°、67.5°和90.0°。关于循环加载应力路径的详细说明,请参阅文献[23]。试验中采用四向动态加载控制技术,确保在加载过程中的中主应力系数bσ始终保持0.5不变,其中bσ=(σ2σ3)/(σ1σ3)。具体试验方案如表12所示。
图5展示了给定循环应力路径下饱和珊瑚砂试样在单级和分级试验中的不排水循环反应特性,包括超静孔压ue、轴向应变εz、径向应变εr、环向应变εθ、扭剪应变γ及偏应变γqγq=(ε1ε3)/2)随循环次数N的变化,其中,ε1ε3分别为大、小主应变。
从图中可以看出,在单级试验中,循环荷载下ue迅速累积,在前5个循环就已经达到25 kPa,与之相对应的γq(表征试样整体变形)也已经累积到0.25%。而在分级试验中,由于初始循环应力幅值较小,ue与应变的累积相对较为缓慢,尤其是在CSR≤0.10时,分级试验中测得的ue与应变无明显变化。因此,分级试验较单级试验可以测得更宽应变范围的ue,从而有助于更精确地获取相应阈值应变值。
图6为不同循环应力路径下饱和珊瑚砂的循环应变路径[(εzεθ)/2,γ)]发展趋势。循环应变路径上任意一点到原点的距离为偏应变γq。给定循环应力路径下,分级试验与单级试验的循环应变路径发展趋势一致,表明加载模式(单级和分级)不影响循环应变路径的发展。此外,图7展示了不同循环加载模式下饱和珊瑚砂试样的超静孔压比ru随偏应变幅值γqa的变化。ruγqa的关系不受循环加载模式的影响。在半对数坐标系下,单级加载试验测得的应变值较为集中,无法反映较小应变水平下ue的增长特性。相较之下,分级试验测出了小-中-大应变范围内ue的变化。
孔压阈值应变γtp(体积阈值应变γtv)表征了完全可恢复性的小应变区与仅伴随轻微强度衰减的中应变区之前的界限。低于该阈值时,土体中不会出现明显的体应变εv(排水条件)或ue(不排水条件)。由于单级试验中测试方法的局限,如图7所示,第1个循环后量测到的ru已经接近0.1,无法进一步研究孔压产生的阈值(较小应变时的孔压)。在分级试验中,初始施加的应力较小,导致砂土结构仅发生微小变化,试样表现出较低水平的ue和应变累积。将ru=0.001(即ue=0.1 kPa)设为超静孔压产生的阈值,其对应的γqa即为孔压阈值应变γtp图7显示,在Dr=45%的条件下,不同循环应力路径下饱和珊瑚砂的γtp范围为0.023 0%~0.028 4%,不同循环应力路径下γtp的变化较小,局限于一个较窄的范围。对于不同的Dr图8展示了不同循环应力路径下的γtp值,整体来看,γtp值随Dr增加而增大,并且不同Drγtp的范围具有明确界限。该结果与Hus[11-12]及Sliver等[30]的研究结果一致,进一步验证了上述规律的普适性和可靠性。
循环加载过程中刚度随循环次数增加而逐渐降低的阈值应变被称为刚度退化阈值应变γtd。关于这一阈值常有争议。对于黏性土,γtpγtd之间的区别更加明显,甚至有时γtd会小于γtp[14];而对于饱和砂土,γtpγtd之间的区别并不十分显著[13],也有研究报道称两者相等[10]。本文试验数据使用Chen等[31]提出的基于相关函数法的模量计算方法进行处理。该方法在计算小应变时较传统方法具有更高的精度,详细的计算过程详见文献[31]。
图9展示了不同Dr下饱和珊瑚砂试样的刚度Gγqa的变化。从图中可以看出,在小-中应变范围(<10−4)时,不同Dr下的饱和珊瑚砂的G表现出随γqa增加先增后减的趋势,这一现象也被Vucetic[13]、杨铮涛[28]等报道。其机制可解释为砂土颗粒在循环加载过程中接触状态的变化导致颗粒硬化,随后转变为软化(即刚度衰退)。伴随着ue的增加,持续的循环加载会使砂粒间的接触状态进一步改变,颗粒间的接触趋于紧密,接触力增大。然而,产生的ue会导致有效应力降低,从而使砂粒间的接触力减小,宏观上表现为G的循环衰退特征。
表1表2详细展示了不同初始状态和循环加载条件下饱和珊瑚砂的γtpγtd值。如图10所示,γtpγtd之间存在分界线,且两者之间的差距随着Dr的增加而增大。这表明,Dr的增加使得在相同应变水平下砂粒之间的相对位移减少,导致ue积累转变为刚度退化所需的应变水平增加。
流动阈值定义为试样在表现出黏塑性材料特性并达到稳态状态时的应变,此时刚度降至约初始刚度G0的10%(即G/G0约为0.1)。这一概念可解释为强度损失与材料状态转变的临界点。美国土木工程师学会土动力学委员会将“液化”定义为“任何物质转变为液体的行为或过程”,其中的液化触发概念与流动阈值的定义相似。Qin等[17]之前的研究提出了一种基于流体特性的液化触发方法,采用平均流动系数κa来评价循环荷载下饱和砂土的流动性(见图11[32](图中,q为偏应力,qminqmax分别为单周循环内的最小、最大偏应力):
式中:分别为一周循环荷载作用下的最大和最小偏应变率;A为一周循环荷载作用下曲线所围成的面积;为偏应变率;为一周循环荷载作用的平均剪应力。
图12展示了平均流动系数的计算示意图。根据κa的定义可知[33]κa不仅反映了应力–应变率曲线的形状影响,还体现了将饱和砂土作为流体考虑的表观黏度特性。该参数具有明显的物理意义,适合描述循环荷载作用下饱和砂土的流动特性。κa值越大,则该周循环荷载作用下平均偏应力引起的偏应变率越大,表明饱和砂土的流动性越强[17]
图12比较了单级试验与分级试验的流动性曲线(即κaN的关系)。从图中可以看出,分级试验的循环次数明显更多,但两种试验方法测得的流动性曲线具有相似的特征。试样都经历了从无流动性的固态特性逐步转变为有限流动性的固-液过渡状态,最终达到类似液体的强流动性状态,这表明试验方法未改变饱和珊瑚砂的固液相变特性。
图13展示了不同初始状态和循环加载条件下饱和珊瑚砂的平均流动系数梯度Δκa/κa(Δκa为两个循环内的平均流动系数差值)随ru变化的情况,其中Δκa/κa=(κa,i+1κa,i)/κa,iκa,iκa,i+1分别为第i个、i+1循环的平均流动系数。Δκa/κaru的变化呈现出先增后减的趋势,并存在明显的转折点。在循环荷载作用下,饱和珊瑚砂试样的有效应力随ue的积累逐渐降低,导致试样变形急剧积累及宏观结构损伤。梯度表征平均流动系数的变化,尤其是其突然而显著的下降,表明了饱和珊瑚砂变形速率的剧变,标志着流动性的转折。饱和珊瑚砂试样从固态转变为液态的相变过渡状态对应的ru约为0.9,且定义为相变孔压比ruth
此外,图14展示了代表性试验工况下刚度指数δγqa变化的关系,其中δ=GN/G1G1为刚度退化阈值对应的刚度,GN为第N个循环的刚度。研究发现,流动阈值对应的δ值接近0.1,这与流动阈值的定义一致。因此,ruth对应的应变水平可视为复杂循环加载下饱和珊瑚砂的流动阈值。当然需要指出的是,通过流体特性表征饱和砂土流动阈值的可行性还需更多试验验证,以便作为数值分析和计算的输入参数,或用于表征土体在应力和应变条件下的行为特性。后续将进一步开展本文所提出的确定阈值应变的新方法的数值分析应用。
本文通过开展分级试验,测量了复杂循环应力路径下饱和珊瑚砂的超静孔压ue与刚度G的在宽应变范围内的变化,探究了复杂循环应力路径下饱和珊瑚砂的孔压阈值应变、刚度退化阈值应变及流动阈值。得到了以下几点结论:
(1)孔压阈值应变γtp和刚度退化阈值γtd受循环应力路径的影响较小,主要与初始相对密实度Dr有关,且随着Dr的增加而增大。此外,γtdγtp之间的差距也随着Dr的增加而不断扩大。
(2)将液化珊瑚砂视为等效黏性流体,基于平均流动系数梯度随超静孔压比的变化趋势,提出了一种确定流动阈值γtf的新方法,γtf对应刚度指数约为0.1。
(3)要覆盖土体的循环特性,需要进行大量的循环试验,为了减少室内循环试验的次数,提出了确定γtpγtpγtf的新方法,以便于作为数值计算或分析方法的输入值,或用于表征土体在应力和应变条件下的行为特性。
  • 国家自然科学基金(52278503)
  • 湖南省自然科学基金(2024JJ8503)
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2025年第46卷第11期
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doi: 10.16285/j.rsm.2024.1518
  • 接收时间:2024-12-10
  • 首发时间:2026-03-27
  • 出版时间:2025-11-14
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  • 收稿日期:2024-12-10
  • 录用日期:2025-01-22
基金
National Natural Science Foundation of China(52278503)
国家自然科学基金(52278503)
National Science Foundation of Hunan Province(2024JJ8503)
湖南省自然科学基金(2024JJ8503)
作者信息
    1.南华大学 土木工程学院,湖南 衡阳 421001
    2.南京工业大学 岩土工程研究所,江苏 南京 211816
    3.华东交通大学 土木建筑学院,江西 南昌 330013

通讯作者:

陈国兴,男,1963年生,博士,教授,主要从事土动力学与岩土地震工程方面的研究工作。E-mail:
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2种不同金属材料的力学参数

Family
属数
Number of
genus
种数
Number of
species
占总种数比例
Percentage of
total species (%)

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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