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Article(id=1244340207072429036, tenantId=1146029695717560320, journalId=1244295746212642849, issueId=1244340201636610993, articleNumber=null, orderNo=null, doi=10.11776/j.issn.1000-4939.2025.06.009, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1683820800000, receivedDateStr=2023-05-12, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774603424088, onlineDateStr=2026-03-27, pubDate=1765728000000, pubDateStr=2025-12-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774603424088, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774603424088, creator=13701087609, updateTime=1774603424088, updator=13701087609, issue=Issue{id=1244340201636610993, tenantId=1146029695717560320, journalId=1244295746212642849, year='2025', volume='42', issue='6', pageStart='1207', pageEnd='1446', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774603422792, creator=13701087609, updateTime=1774603751062, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244341578555306992, tenantId=1146029695717560320, journalId=1244295746212642849, issueId=1244340201636610993, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244341578555306993, tenantId=1146029695717560320, journalId=1244295746212642849, issueId=1244340201636610993, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1292, endPage=1300, ext={EN=ArticleExt(id=1244340210021023798, articleId=1244340207072429036, tenantId=1146029695717560320, journalId=1244295746212642849, language=EN, title=Mesoscale study on the influence of aggregate irregularity on uniaxial compressive properties of concrete, columnId=1244340205327593820, journalTitle=Chinese Journal of Applied Mechanics, columnName=Solid Mechanics, runingTitle=null, highlight=null, articleAbstract=

In order to determine the influence of aggregate irregularity on the mechanical properties and failure morphology of concrete, Python programs were developed to generate randomly distributed aggregate models with different sharpness in ABAQUS, and the 0-thickness cohesive element and variable-thickness solid interface transition zone（ITZ）were established respectively. First, the reliability of model was determined by changing mesh size and friction coefficient between the loading pad and concrete compared with the experiment. Then, the quality of two ITZ modeling methods was analyzed. Finally, the uniaxial compression mechanical behavior of the three-dimensional meso-concrete model was analyzed from the aspects of stress-strain curve, fracture propagation, and energy dissipation. The simulation results show that the 0 thickness cohesive ITZ and the solid thickness ITZ model can predict the compressive strength of concrete, and the stress-strain curve and failure morphology of the ITZ model with solid thickness are more consistent with the experiment. The fracture propagation of concrete is obviously affected by the shape parameters of aggregate. The interior and surface of the spherical aggregate model are penetrating cracks. The strain energy of polyhedral aggregate model is larger, and there are many micro-cracks in the concrete, the possibility being compressed and destroyed into more fragments is higher. With the increase of aggregate irregularity, the compressive strength of concrete increases slightly, but the peak strain is not affected.

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为了在细观层面上研究骨料不规则程度对混凝土力学性能及破坏形态的影响，采用Python程序二次开发了ABAQUS生成尖锐程度不同的随机分布骨料模型，分别建立零厚度cohesive单元与可变厚度的实体界面过渡区（interface transition zone，ITZ）。首先通过改变网格尺寸和加载垫块与混凝土间的摩擦系数确定合适的参数，并与实验对比验证模型的可靠性，随后分析2种ITZ建模方式的优劣，最后对三维细观混凝土模型进行单轴受压模拟，从应力-应变曲线、破坏形态、能量耗散方面进行分析。结果表明：零厚度cohesive ITZ与实体厚度ITZ模型都可预测混凝土抗压强度，具有实体厚度的ITZ模型的应力-应变曲线及破坏形态与实验更加贴合；混凝土破坏形态受骨料形状参数影响明显，球形骨料模型内部与表面均为贯穿式裂缝，多面体骨料模型应变能较大，混凝土内部微裂缝较多，容易受压破坏成更多的碎块；随着骨料不规则程度的增加，混凝土抗压强度略有提高但峰值应变不受影响。

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徐志洪，教授。E-mail:
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label=Tab.1, caption=

Standard grading of concrete[23]

, figureFileSmall=null, figureFileBig=null, tableContent=
筛孔尺寸/mm累计通过率/%累计保留率/%
2.361000
4.757426
9.502377
12.700100
), ArticleFig(id=1244340232137589573, tenantId=1146029695717560320, journalId=1244295746212642849, articleId=1244340207072429036, language=CN, label=表1, caption=

混凝土标准级配[23]

, figureFileSmall=null, figureFileBig=null, tableContent=
筛孔尺寸/mm累计通过率/%累计保留率/%
2.361000
4.757426
9.502377
12.700100
), ArticleFig(id=1244340232280195921, tenantId=1146029695717560320, journalId=1244295746212642849, articleId=1244340207072429036, language=EN, label=Tab.2, caption=

Material parameters

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参数骨料ITZ（cohesive）砂浆ITZ（CDP）
密度/（kg•m-3）2 8002 0002 0002 000
弹性模量/GPa70—2522
泊松比0.2—0.20.2
cohesive黏聚力刚度/（MPa•mm-1）—106——
名义主/切应力/MPa—2.6/10——
法/切向断裂能/（N•mm-1）—0.025/0.062 5——
), ArticleFig(id=1244340232426996573, tenantId=1146029695717560320, journalId=1244295746212642849, articleId=1244340207072429036, language=CN, label=表2, caption=

材料参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数骨料ITZ（cohesive）砂浆ITZ（CDP）
密度/（kg•m-3）2 8002 0002 0002 000
弹性模量/GPa70—2522
泊松比0.2—0.20.2
cohesive黏聚力刚度/（MPa•mm-1）—106——
名义主/切应力/MPa—2.6/10——
法/切向断裂能/（N•mm-1）—0.025/0.062 5——
), ArticleFig(id=1244340232527659879, tenantId=1146029695717560320, journalId=1244295746212642849, articleId=1244340207072429036, language=EN, label=Tab.3, caption=

Comparison of the calculation costs between two ITZ models

, figureFileSmall=null, figureFileBig=null, tableContent=
参数cohesive ITZ模型0.5 mm ITZ模型
ITZ单元数量/万6.527.4
总单元数量/万119.8159.6
计算时长/h2127
), ArticleFig(id=1244340232636711791, tenantId=1146029695717560320, journalId=1244295746212642849, articleId=1244340207072429036, language=CN, label=表3, caption=

2种ITZ模型计算成本对比

, figureFileSmall=null, figureFileBig=null, tableContent=
参数cohesive ITZ模型0.5 mm ITZ模型
ITZ单元数量/万6.527.4
总单元数量/万119.8159.6
计算时长/h2127
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骨料不规则程度对混凝土单轴受压性能影响的数值研究
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周冠韬 , 徐志洪 , 刘聪
应用力学学报 | 固体力学 2025,42(6): 1292-1300
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应用力学学报 | 固体力学 2025, 42(6): 1292-1300
骨料不规则程度对混凝土单轴受压性能影响的数值研究
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周冠韬, 徐志洪 , 刘聪
作者信息
  • 南京理工大学理学院，210094　南京

通讯作者:

徐志洪，教授。E-mail:
Mesoscale study on the influence of aggregate irregularity on uniaxial compressive properties of concrete
Guantao ZHOU, Zhihong XU , Cong LIU
Affiliations
  • School of Science, Nanjing University of Science and Technology, 210094 Nanjing, China
出版时间: 2025-12-15 doi: 10.11776/j.issn.1000-4939.2025.06.009
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摘要
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为了在细观层面上研究骨料不规则程度对混凝土力学性能及破坏形态的影响，采用Python程序二次开发了ABAQUS生成尖锐程度不同的随机分布骨料模型，分别建立零厚度cohesive单元与可变厚度的实体界面过渡区（interface transition zone，ITZ）。首先通过改变网格尺寸和加载垫块与混凝土间的摩擦系数确定合适的参数，并与实验对比验证模型的可靠性，随后分析2种ITZ建模方式的优劣，最后对三维细观混凝土模型进行单轴受压模拟，从应力-应变曲线、破坏形态、能量耗散方面进行分析。结果表明：零厚度cohesive ITZ与实体厚度ITZ模型都可预测混凝土抗压强度，具有实体厚度的ITZ模型的应力-应变曲线及破坏形态与实验更加贴合；混凝土破坏形态受骨料形状参数影响明显，球形骨料模型内部与表面均为贯穿式裂缝，多面体骨料模型应变能较大，混凝土内部微裂缝较多，容易受压破坏成更多的碎块；随着骨料不规则程度的增加，混凝土抗压强度略有提高但峰值应变不受影响。

三维细观混凝土  /  骨料  /  黏聚力单元  /  数值模拟  /  裂纹扩展

In order to determine the influence of aggregate irregularity on the mechanical properties and failure morphology of concrete, Python programs were developed to generate randomly distributed aggregate models with different sharpness in ABAQUS, and the 0-thickness cohesive element and variable-thickness solid interface transition zone（ITZ）were established respectively. First, the reliability of model was determined by changing mesh size and friction coefficient between the loading pad and concrete compared with the experiment. Then, the quality of two ITZ modeling methods was analyzed. Finally, the uniaxial compression mechanical behavior of the three-dimensional meso-concrete model was analyzed from the aspects of stress-strain curve, fracture propagation, and energy dissipation. The simulation results show that the 0 thickness cohesive ITZ and the solid thickness ITZ model can predict the compressive strength of concrete, and the stress-strain curve and failure morphology of the ITZ model with solid thickness are more consistent with the experiment. The fracture propagation of concrete is obviously affected by the shape parameters of aggregate. The interior and surface of the spherical aggregate model are penetrating cracks. The strain energy of polyhedral aggregate model is larger, and there are many micro-cracks in the concrete, the possibility being compressed and destroyed into more fragments is higher. With the increase of aggregate irregularity, the compressive strength of concrete increases slightly, but the peak strain is not affected.

3D mesoscale concrete  /  aggregate  /  cohesive element  /  numerical simulation  /  crack propagation
周冠韬, 徐志洪, 刘聪. 骨料不规则程度对混凝土单轴受压性能影响的数值研究. 应用力学学报, 2025 , 42 (6) : 1292 -1300 . DOI: 10.11776/j.issn.1000-4939.2025.06.009
Guantao ZHOU, Zhihong XU, Cong LIU. Mesoscale study on the influence of aggregate irregularity on uniaxial compressive properties of concrete[J]. Chinese Journal of Applied Mechanics, 2025 , 42 (6) : 1292 -1300 . DOI: 10.11776/j.issn.1000-4939.2025.06.009
正文
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混凝土本身是一种非均质材料，内部存在骨料、孔隙、砂浆和界面过渡区（interfacial transition zone，ITZ）等，所以在受力过程中的破坏形式具有很大的随机性，其中骨料的随机分布导致混凝土破坏机理难以通过常规实验进行分析。目前对于混凝土的数值模拟尺度主要分为宏观、细观和微观[1-3]。细观模型通过对骨料、砂浆和界面过渡区分别建模，能够较好地模拟混凝土的力学性能和破坏机理[4]。WITTMANN[5]认为借助更低一层次尺度下的结构特征可以来解释某一尺度下材料的力学性能，对混凝土除了从宏观角度进行研究外，更关键的是从细观尺度出发以研究混凝土内部结构与宏观特性之间的联系。
骨料的建模方法主要有CT扫描与“生成-投放”两大类。REN等[6]通过CT扫描混凝土断层对骨料与孔隙进行了二维细观分析。JIN等[7]对沥青断层进行CT扫描建立三维骨料离散元模型。HUANG等[8]通过X-CT扫描混凝土试块得到骨料三维信息后进行建模，并分析骨料弹性模量对混凝土抗拉性能的影响。NITKA等[9]利用X-ray和CT扫描带缺口的混凝土梁，并建立颗粒离散元模型验证此三维模型可良好地预测混凝土断裂。田梦云等[10]通过编程生成二维随机骨料模型以探究界面层与孔隙率对混凝土宏观力学响应的影响。黄灵芝等[11]建立三维离散元模型对冻融循环下的混凝土单轴受压破坏模式进行分析。刘利宝等[12]对生成的随机骨料表面插设cohesive单元并研究骨料弹性模型与体积率对混凝土力学性能的影响。在建模阶段，使用球形与多面体骨料进行建模较为常见，尽管多面体骨料更接近真实的碎石形状，但球形与多面体骨料在混凝土及细观分析中的具体区别需进一步研究。
许多研究表明，骨料与砂浆的界面过渡区是影响混凝土宏观力学性能的重要因素[13-15]。ITZ位于骨料与砂浆交界处，由较多的孔隙和水泥组成，其厚度约为0.01~0.05 mm，可以通过缩放或扩大骨料直径再进行布尔差集进行实际建模，但这么薄的实体在划分网格时具有很大的难度，所以通常将界面过渡区建模厚度增加到0.1~1 mm之间[16-17]。目前主要通过2种方式来处理界面过渡区，即有厚度的实体建模并对其赋予劣化的砂浆材料属性[18]，或在骨料与砂浆之间插入0厚度的cohesive单元代替实体界面过渡区[19-20]。作为对混凝土性能影响较大的因素，在细观模型中ITZ使用何种建模方式至关重要。
本研究通过Python编程对球形与不规则多面体骨料进行随机分布建模，并分别建立0厚度cohesive与实体可变厚度界面过渡区，对多组模型进行单轴受压模拟，随后通过测试得出合理的网格密度及加载垫块与混凝土间的摩擦系数，并与实验数据和混凝土压坏形态对比；最后从力学响应、破坏形态、能量耗散及裂缝体积分数等方面对ITZ厚度与骨料不规则程度对混凝土的影响进行分析。
1　模型的建立与材料参数
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1.1　随机骨料生成与级配
WANG等[21]通过利用X-ray批量扫描混凝土内部骨料的三维特征并建立数据库，从而实现异构骨料建模。但此方法由于不能建立较薄的ITZ，难以控制骨料的不规则程度且成本较高，所以本研究使用“生成-投放”法进行建模。不论是球形骨料还是多面体骨料，建模算法步骤是类似的。多面体骨料在建模过程中，需要在已经生成的球面上选取一定数量的顶点再进行平面干涉判断，将这些顶点连接生成平面即组成一个多面体骨料，多面体骨料建模流程如图1所示。
判断各多面体骨料互不干涉的方式基本与球形相同，即令2个多面体外接球球心距离大于其半径之和，但此种算法生成的骨料分布不够均匀。本研究使用一种应用在判断纤维之间干涉的算法[22]，首先在生成多面体顶点时存储顶点坐标数据，其次判断2个骨料中心距离大于一定数值防止小粒径骨料出现在大骨料内部，最后将2个骨料上所有顶点进行距离计算。
式中：da为两骨料上各顶点间最小距离；d为两骨料上各顶点间距离；为骨料p上的一个顶点坐标；为骨料q上的一个顶点坐标；n为多面体骨料上的顶点数量；N为多面体骨料数量；lp为控制各骨料顶点间距的人为给定数值。如图2所示，理论上若多面体顶点数量足够多且lp=0，则各个顶点均不接触，但为了确定各骨料之间不干涉，可适当将lp的数值增大。
表1给出标准级配，包括直径为2.36~4.75 mm的小粒径骨料，直径为4.75~9.5 mm的中粒径骨料，直径为9.5~12.7 mm的大粒径骨料。在建模时将三级配骨料进行数量等效化处理，在生成实体界面过渡区模型时需要比真正骨料粒径更大的空间，并考虑多个模型的计算成本，所以将所有模型的骨料体积率控制在25%，虽然略低于实际中的混凝土，但满足本研究需要。
1.2　ITZ的生成
界面过渡区主要有2种建模方式，在骨料与砂浆单元之间插入0厚度的cohesive单元或者通过布尔操作实现实体厚度ITZ。插入cohesive单元示意图如图3所示，骨料和砂浆都使用C3D4单元类型进行划分，在其间形成COH3D6类型单元。需要说明的是，本研究中的基础单元都为C3D4，并未使用C3D8等六面体单元，虽然六面体单元会大大减少总体单元数量，但在如此不规则的模型中使用六面体单元只能形成体素网格，不适宜模拟混凝土内部各个组分之间的力学性能及裂纹扩展。
对于有厚度的实体ITZ，首先使用python算法生成满足条件的多面体形心坐标并存储各顶点坐标，接着使用数学方法将各顶点在原先基础上进行偏移，然后将新生成的顶点进行连接。为避免出现各面交叉和凹陷的现象，需要再次判断各面之间的关系，最后判断多面体形心、骨料顶点和对应新生成顶点是否在用一条直线上。若满足上述要求，则在ABAQUS中生成模型后使用布尔差集生成多面体实体界面过渡区。图4给出了0.5 mm厚度实体ITZ模型。
1.3　本构关系与材料参数
关于cohesive单元的各项法则和属性定义方式在ABAQUS手册[24]中有详细说明，在CTZ模型中cohesive单元的密度设置与砂浆相同，黏聚力刚度如果取值很大将会出现畸变或者增加计算难度等问题，CABALLERO等[25]建议在混凝土细观分析中选取105~109MPa/mm之间，经过测试后本研究选取106MPa/mm作为黏聚力刚度。对于损伤演化中的法向、切向应力和断裂能则参考NADERI等[26]的研究。
砂浆基体及实体ITZ均使用混凝土塑性损伤模型（CDP），因为ITZ强度一般为砂浆的30%~70%[27-28]，所以ITZ的强度取为砂浆的一半。ABAQUS手册中详细介绍了CDP模型的使用方法，此处不再赘述。CDP模型用以模拟混凝土在受压和受拉过程中的塑性变形和损伤，本研究使用《混凝土结构设计标准》（GB/T 50010—2010）[29]中的压缩应变硬化和软化曲线公式进行模拟。混凝土其余参数如下:标准抗压强度45 MPa，抗拉强度4 MPa，断裂能0.06 J，膨胀角35°，塑性偏心距0.1，双轴与单轴抗压强度之比1.16，混凝土屈服形态参数0.667，黏性参数0.000 5[30-31]。骨料属性定义为不受损伤的弹性体，所有材料属性见表2。
2　模型合理性分析
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2.1　网格密度
如图5所示，三维细观混凝土模型为50 mm×50 mm×50 mm的立方体试块，在Y轴设置2个垫块，下方垫块完全固定，对上方垫块施加向下的竖向位移。
此外，为了得到足够的应力应变响应，设置位移加载达到0.25 mm时停止计算。考虑到准静态细观模拟的计算精度和时间成本，对网格密度、垫块与试块之间的摩擦等参数进行分析，并将计算结果与实验值进行对比以验证数值模拟的可靠性。
不论是静力学还是动力学分析，单元尺寸都对计算精度和分析结果有着不可忽略的影响。过小的单元尺寸会产生巨大的单元数量，并且会增加不必要的计算时间；过大的单元尺寸可能会导致计算结果难以收敛，在混凝土细观分析中也难以精确表现出裂纹扩展状态。为了得到良好的宏观应力-应变曲线和混凝土细观破坏形态，需要经过测试得到一个可以同时满足计算精度与计算速度的网格密度。
以20顶点多面体骨料结合0.25 mm厚度ITZ模型为例，对其划分2、1.5、1、0.8、0.7 mm大小的单元，单元数量分别为2.9×105、5.2×105、1.76×106、2.11×106、2.43×106。图6给出了不同网格密度下的宏观应力-应变曲线，可以看出随着单元尺寸的减小，混凝土应力-应变曲线逐渐趋于稳定，单元尺寸小于1 mm后曲线基本不受网格密度的影响。随着网格密度的增加，计算时间从8 h增加到39 h，同时考虑到此参数对混凝土破坏形态的影响，本研究将所有模型的砂浆单元尺寸划分为1 mm，实体ITZ单元尺寸划分为0.8 mm。
2.2　加载垫块与混凝土间摩擦系数
准静态数值模拟需要依靠能量来评估模型的计算是否合理，一般认为变形材料的总动能不能超过总内能的10%[32]。在准静态分析中模型产生的总动能主要受到位移加载速率的影响，如果加载速率较大则会产生较大的动能。FENG等[33]认为加载速率会影响混凝土应力-应变曲线。为了得到良好的计算结果，本研究参考章毅等[34]的测试数据。
当垫块与混凝土之间摩擦较大时，混凝土横向变形受摩擦力约束形成三维应力状态，并使混凝土抗压强度提高。为确定混凝土单轴受压实验中钢板与混凝土试块间的摩擦系数大小，对20顶点多面体骨料结合0厚度cohesive ITZ模型展开库伦摩擦系数分别为0.01、0.1和0.3的模拟。由图7可以看出，随着摩擦系数的增加，混凝土抗压强度逐渐提高；当摩擦系数为0.1时，峰值应力与LOWES[35]的实验值基本相同。图7同时给出了NADERI等[26]的模拟数据。
由图8可知，模拟的混凝土截面破坏形态与不同摩擦系数下的实验破坏形态[36]类似，从力学响应与破坏形态角度证明本模拟的可靠性，因此所有模型中垫块与混凝土间库仑摩擦系数设置为0.1。
3　ITZ类型的影响
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为确定ITZ类型对混凝土性能的影响，本节对0厚度cohesive单元组成的ITZ模型和0.5 mm厚度实体ITZ模型从破坏形态、力学响应方面进行对比分析。为减少骨料形状及空间分布随机性引起的误差，所有模型中的骨料形态参数及中心位置坐标完全相同，并对其赋予相同的砂浆属性（CDP），仅在ITZ的材料属性上有所差异。
图9给出ITZ厚度不同的20顶点多面体骨料模型在单轴受压情况下的应力-应变曲线。由图9可知，在弹性阶段二者几乎重合，峰值应力仅相差0.38 MPa，即混凝土弹性模量和抗压强度基本不受ITZ类型影响；但在峰值应力后的软化阶段有较大差别，0.5 mm厚度实体ITZ模型下降速率大于cohesive ITZ模型。这是由于cohesive单元在模型中的能量达到一定程度时便会失效，在基体破坏阶段不再参与工作；但有实体厚度的ITZ在峰值应变后才逐渐开始大面积损伤，其弱于砂浆的材料属性在混凝土裂缝快速发展阶段得到体现。
图10展示了2种模型在峰值应变和极限应变时刻的ITZ损伤和砂浆损伤带（保留SDEG>0.9），并统计损伤前后的ITZ单元数量比率来对比2种模型的区别。
由图10可知，应变达到0.001 3时，cohesive ITZ基本完全损伤，受损单元占98.2%，实际中混凝土达到极限应变时ITZ并未大面积损伤；此时实体ITZ仅在大粒径骨料附近出现损伤，小粒径骨料基本还未参与工作，有1.7%单元受损。应变达到0.005时，大骨料附近ITZ基本全部失效，主要裂纹扩展区域的小骨料ITZ失效，受损单元占42.3%，与实际情况类似。从细观角度来看，混凝土受压时薄弱界面过渡区先损伤，随后裂纹扩展至砂浆，其中裂纹蔓延方向主要受大粒径骨料的空间位置分布影响。
表3给出2种ITZ模型的单元数量与计算时长，可以看到cohesive ITZ模型网格数量较少且计算速度略快。但考虑到在砂浆和骨料之间插入0厚度cohesive单元也需要一定的时间，二者在计算成本上无明显优劣。除此之外，实体ITZ模型在细观破坏的模拟中表现较好，更加贴合实验结果，并且cohesive单元的材料参数难以测定，难以保证模拟的精确性。
4　骨料不规则程度的影响
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本节从混凝土单轴受压下的宏观应力-应变响应、破坏形态和相应能量耗散方面来分析骨料形状参数的影响。如图11所示，多面体顶点的减少会使其形状更加尖锐，所以分别建立球形、25顶点多面体、20顶点多面体模型进行数值模拟，界面过渡区均为0.5 mm的实体ITZ。为降低骨料分布随机性引起的误差，分别建立计算5组模型并取其均值进行力学分析。
如图12所示，20顶点多面体骨料模型应力峰值大于25顶点多面体和球形骨料模型，最大相差0.71 MPa，从宏观应力-应变角度来看，骨料形状对混凝土抗压强度影响较小，在相同体积率下混凝土弹性模量受骨料形状影响不大。
较尖锐的多面体骨料可能增加混凝土的抗压强度，裂缝快速发展至临界点后，多面体骨料模型曲线斜率增大，由于其存在较多不规则棱角，在砂浆中传递力更加分散，并且不规则形状骨料之间的咬合力更强，混凝土破坏时需要更高的能量即应变能更大。与球形骨料相比，不规则形状骨料之间更容易出现连锁效应，从而提高混凝土抗压强度和断裂韧性。
图13给出不同形状骨料的宏观破坏形态和细观裂纹走向，并体现各模型的裂缝体积率。从宏观角度来看大多是由贯穿混凝土的剪切斜裂缝或受拉裂缝引起，各骨料模型均出现明显的三角压裂区。球形骨料混凝土破坏多为贯穿裂缝，多面体骨料混凝土呈现出较短但多数量的裂纹，不同形状骨料对宏观破坏形态有一定的影响。由于随着骨料顶点的减少，骨料整体变得愈加尖锐，在棱角处越容易出现应力集中现象。从细观角度来看，随着骨料形状尖锐程度的增加，砂浆中的裂纹走向更多，较球形骨料模型的沙漏状压溃区更加明显。
在外荷载作用下混凝土中的界面过渡区最先失效出现微裂缝，进而裂缝蔓延进入砂浆基质；当遇到强度偏高的骨料后选择避让，所以裂纹扩展路径表现出一定的曲折性。相比多面体骨料，球形骨料在混凝土受到荷载时将力较稳定地传递到砂浆或其余骨料中，而多面体骨料上存在很多棱角，力在其中传递较为分散，这就导致在受压过程中更尖锐的骨料模型会破坏成更多碎块。
为体现破坏后各模型中的裂纹数量和能量消耗，提取出模型损伤后的裂缝体积与初始模型的比值，并输出所有模型中的ALLMD（损伤耗散能）和ALLPD（塑性应变耗散能）之和作为总能量损失进行比较，因为能量曲线均随应变递增，所以取应变最终时刻的能量最大值作为参考（图14a）。如图14（b）所示，随骨料尖锐程度的增加，混凝土在单轴受压下产生的裂缝体积分数增大，能量耗散也更高，这表明骨料形状不规则程度的增加会使得混凝土的损伤体积更大。
5　结论
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本研究通过编写Python程序在ABAQUS中实现球形及多面体骨料的随机分布，并分别在骨料与砂浆中插设0厚度cohesive单元与可变厚度实体单元模拟薄弱界面过渡区，通过控制多面体骨料的顶点数与ITZ厚度，分析骨料不规则程度与ITZ类型对混凝土力学性能及破坏形式的影响，主要结论如下。
1）实体厚度ITZ模型在软化阶段应力下降速度与细观破坏形态更贴合实际情况，适合进行细观破坏与裂纹扩展分析；0厚度cohesive ITZ模型在受压过程中难以真实地模拟薄弱界面过渡区的损伤状态，但单元数量及计算时长较少，两者在预测混凝土受压弹性阶段与峰值应力前皆可应用。
2）混凝土破坏形态受骨料形状参数影响明显，由于多面体骨料棱角处容易出现应力集中现象，裂纹在此处萌生，随着其形状尖锐程度的增加，受力传递更加分散，破坏过程中能量耗散较大，混凝土容易受压破坏成更多的碎块。球形骨料模型破坏主要形成贯穿式裂缝，不适合针对混凝土内部的裂纹萌生与扩展进行分析，而且平滑的骨料形状也与实际工程情况不符。
3）混凝土抗压强度受骨料形状参数影响较小，相同体积率情况下，多面体骨料不规则程度越高，相互之间咬合力更强，模拟混凝土受压峰值应力略高于球形骨料模型，但球形骨料模型网格数量较低，更节省计算成本。
基金
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  • 国家自然科学基金资助项目(11802132)
文献
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2025年第42卷第6期
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doi: 10.11776/j.issn.1000-4939.2025.06.009
  • 接收时间：2023-05-12
  • 首发时间：2026-03-27
  • 出版时间：2025-12-15
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  • 收稿日期：2023-05-12
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国家自然科学基金资助项目(11802132)
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    南京理工大学理学院，210094　南京

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徐志洪，教授。E-mail:
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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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