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钢纤维混凝土多轴损伤比强度准则

丁发兴 吴霞 向平 余志武 聂磊鑫

丁发兴, 吴霞, 向平, 余志武, 聂磊鑫. 钢纤维混凝土多轴损伤比强度准则[J]. 工程力学, 2022, 39(9): 123-132. doi: 10.6052/j.issn.1000-4750.2021.05.0372
引用本文: 丁发兴, 吴霞, 向平, 余志武, 聂磊鑫. 钢纤维混凝土多轴损伤比强度准则[J]. 工程力学, 2022, 39(9): 123-132. doi: 10.6052/j.issn.1000-4750.2021.05.0372
DING Fa-xing, WU Xia, XIANG Ping, YU Zhi-wu, NIE Lei-xin. DAMAGE RATIO STRENGTH CRITERION FOR STEEL FIBER REINFORCED CONCRETE UNDER MULTIAXIAL STRESSES[J]. Engineering Mechanics, 2022, 39(9): 123-132. doi: 10.6052/j.issn.1000-4750.2021.05.0372
Citation: DING Fa-xing, WU Xia, XIANG Ping, YU Zhi-wu, NIE Lei-xin. DAMAGE RATIO STRENGTH CRITERION FOR STEEL FIBER REINFORCED CONCRETE UNDER MULTIAXIAL STRESSES[J]. Engineering Mechanics, 2022, 39(9): 123-132. doi: 10.6052/j.issn.1000-4750.2021.05.0372

钢纤维混凝土多轴损伤比强度准则

doi: 10.6052/j.issn.1000-4750.2021.05.0372
基金项目: 国家自然科学基金面上项目(51978664);湖南省自然科学杰出青年基金项目(2019JJ20029)
详细信息
    作者简介:

    丁发兴(1979−),男,浙江人,教授,工学博士,博导,主要从事工程材料强度理论、钢-混凝土组合结构研究(E-mail: dinfaxin@csu.edu.cn)

    向 平(1982−),男,湖南人,教授,工学博士,博导,主要从事混凝土结构抗震及计算力学研究(E-mail: pxiang@csu.edu.cn)

    余志武(1955−),男,湖南人,教授,工学硕士,博导,主要从事结构工程、桥梁工程与防灾工程研究(E-mail: zhwyu@csu.edu.cn)

    聂磊鑫(1995−),男,河南人,博士生,主要从事工程结构抗震研究(E-mail: csunlx@csu.edu.cn)

    通讯作者:

    吴 霞(1996−),女,四川人,博士生,主要从事工程材料强度理论研究(E-mail: wuxia1@csu.edu.cn)

  • 中图分类号: TU501

DAMAGE RATIO STRENGTH CRITERION FOR STEEL FIBER REINFORCED CONCRETE UNDER MULTIAXIAL STRESSES

  • 摘要: 以损伤比强度理论为基础,建立了钢纤维混凝土真三轴损伤比强度准则,并根据钢纤维混凝土试验资料,推荐了钢纤维混凝土损伤比变量表达式中的6个经验参数。利用钢纤维混凝土在单轴、双轴和三轴受力状态下的应力-应变曲线试验结果验证了损伤比取值合理性,对比了单轴受拉、单轴受压和双轴等压等典型受力状态下钢纤维混凝土和普通混凝土损伤比变量取值的差异。通过与国内外共104组钢纤维体积率为0.5%~2.5%的钢纤维混凝土三轴强度试验资料的比较,表明六经验参数钢纤维混凝土损伤比强度准则的三维破坏包络面接近已有认识;通过与国内外强度准则比较,表明损伤比强度准则与钢纤维混凝土三轴试验数据有较高的吻合度。对于围压三轴受力状态,提出简化的钢纤维混凝土常规三轴强度准则,并与已有常规三轴强度准则进行比较分析。此外,对于材料处于二轴受力,推荐了简化的损伤比二轴强度准则中的经验参数取值。
  • 图  1  应变计算模型

    Figure  1.  Calculation model of strain

    图  2  钢纤维混凝土在偏平面上的强度规律

    Figure  2.  The strength rules of SFRC on the deviatoric plane

    图  3  典型应力状态下钢纤维混凝土损伤比变量验证

    Figure  3.  Verification of damage ratio variable for SFRC in typical stress states

    图  4  拉压子午线与试验数据比较

    Figure  4.  The comparison of the predicted strength on the tensile and compressive meridians with test data

    图  5  偏平面与试验数据比较

    Figure  5.  Comparison of the predicted traces in the deviatoric panes with test data

    图  6  钢纤维混凝土各强度准则对应拉压子午线

    Figure  6.  Comparisons of the predicted strength on the tensile and compressive meridians of SFRC strength criteria with experimental data

    图  7  钢纤维混凝土强度准则对应的偏平面比较

    Figure  7.  Comparisons of the traces in the deviatoric plane of SFRC strength criteria with experimental data

    图  8  围压强度理论值与试验值比较

    Figure  8.  Comparison of the theoretical confining compression results with test data

    图  9  不同常规三轴强度准则下围压强度预测值与实测值的比较

    Figure  9.  Comparison of the predicted results of SFRC confining triaxial strength criteria with test data

    图  10  钢纤维混凝土二轴破坏曲线

    Figure  10.  Failure curves of SFRC under states of biaxial stress

    图  11  钢纤维混凝土和普通混凝土简化二轴强度准则破坏曲线

    Figure  11.  Failure curves of damage ratio strength criterion for SFRC and plain concrete under biaxial stress states

    表  1  真三轴损伤比强度准则主应力表达式

    Table  1.   Principal stress expressions of true triaxial damage ratio strength criterion

    应力状态主应力形式
    三轴受拉$\sigma _1^2 + \sigma _2^2 + \sigma _3^2 - 2{v_{D,{\rm t}} }({\sigma _1}{\sigma _2} + {\sigma _2}{\sigma _3} + {\sigma _1}{\sigma _3}) = f_{\text{t} }^{\text{2} }$
    一轴受压二轴受拉$\dfrac{ {\sigma _1^2} }{ {f_{\text{t} }^{\text{2} } } } + \dfrac{ {\sigma _2^2} }{ {f_{\text{t} }^{\text{2} } } } + \dfrac{ {\sigma _3^2} }{ {f_{\text{c} }^{\text{2} } } } - \left[2{v_{D,{\rm t} } }\dfrac{ { {\sigma _1}{\sigma _2} } }{ {f_{\text{t} }^{\text{2} } } } + ({v_{D,{\rm c} } } + {v_{D,{\rm t} } })\dfrac{ { {\sigma _1}{\sigma _3} } }{ { {f_{\text{t} } }{f_{\text{c} } } } } + ({v_{D,{\rm c} } } + {v_{D,{\rm t} } })\dfrac{ { {\sigma _2}{\sigma _3} } }{ { {f_{\text{t} } }{f_{\text{c} } } } }\right] = 1$
    二轴受压一轴受拉$\dfrac{ {\sigma _1^2} }{ {f_{\text{t} }^{\text{2} } } } + \dfrac{ {\sigma _2^2} }{ {f_{\text{c} }^{\text{2} } } } + \dfrac{ {\sigma _3^2} }{ {f_{\text{c} }^{\text{2} } } } - \left[({v_{D,{\rm c} } } + {v_{D,{\rm t} } })\dfrac{ { {\sigma _1}{\sigma _2} } }{ { {f_{\text{t} } }{f_{\text{c} } } } } + 2{v_{D,{\rm c} } }\dfrac{ { {\sigma _2}{\sigma _3} } }{ {f_{\text{c} }^{\text{2} } } } + ({v_{D,{\rm c} } } + {v_{D,{\rm t} } })\dfrac{ { {\sigma _1}{\sigma _3} } }{ { {f_{\text{t} } }{f_{\text{c} } } } }\right] = 1$
    三轴受压$\sigma _1^2 + \sigma _2^2 + \sigma _3^2 - 2{v_{D,{\rm c}} }({\sigma _1}{\sigma _2} + {\sigma _2}{\sigma _3} + {\sigma _1}{\sigma _3}) = f_{\text{c} }^{\text{2} }$
    下载: 导出CSV

    表  2  钢纤维混凝土三轴试验样本信息

    Table  2.   Information on SFRC triaxial experimental specimens

    文献[10][11][12][16][17]
    纤维类型熔抽钢纤维端钩型钢纤维短直钢纤维剪切型钢纤维端钩型钢纤维
    ρf/(%)0.5、1.0、1.5、2.0、2.51.01.0、2.01.0、2.01.0、2.0
    尺寸/mm长度25;等效直径0.5长度30;直径0.5长度13;直径0.1750.4×0.5×25/
    l/d50607455.644
    下载: 导出CSV

    表  3  典型应力状态下损伤比取值

    Table  3.   The damage ratio value for typical stress states

    材料类型$单轴受拉 {v_{D,{\text{t}}}} $$ 单轴受压v_{D,{\rm{c}}}^{\text{u}} $$ 双轴等压v_{D,{\rm{c}}}^{\text{b}} $
    普通混凝土0.151.090.694
    钢纤维混凝土0.151.190.730
    下载: 导出CSV

    表  4  钢纤维混凝土损伤比强度准则与钢纤维混凝土试验结果比较

    Table  4.   The comparison of damage ratio strength criterion for SFRC between predicted results and experimental data

    钢纤维体积率0.5%
    (10组)
    1.0%
    (51组)
    1.5%
    (8组)
    2.0%
    (27组)
    2.5%
    (8组)
    0.5%~2.5%
    (104组)
    均值1.0061.0350.9831.0530.9511.026
    离散系数0.0600.1090.0570.0690.1090.097
    下载: 导出CSV

    表  5  钢纤维混凝土强度准则与试验数据比较

    Table  5.   Comparison of SFRC criteria between calculated data and test results

    应力状态
    准则(体积率)/(%)三轴受压三轴拉压全部三轴受力
    均值离散系数均值离散系数均值离散系数
    笔者(0.5~2.5)1.0400.0770.9900.1341.0260.097
    宋玉普等[10]0.51.0420.1661.1530.1291.0860.159
    1.01.2320.1901.2770.3171.2440.234
    1.50.9430.1940.8260.0130.8990.173
    2.01.1600.1920.8360.0571.1240.208
    2.50.9110.1760.7130.1310.8120.203
    下载: 导出CSV

    表  6  各准则与钢纤维混凝土围压试验比较

    Table  6.   Comparison of different strength criteria for SFRC between theoretical data and confining pressure test data

    准则均值离散系数
    本文真三轴1.0980.136
    简化常规三轴1.0400.123
    Lu 等[11]Mohr-Coulomb1.0100.129
    Willam-Warnke0.9810.116
    Noori等[12]Mohr-Coulomb0.8560.192
    Willam-Warnke1.1470.356
    幂律准则1.0550.204
    下载: 导出CSV

    表  7  准则二轴形式与简化

    Table  7.   Form and simplification of criterion under states of biaxial loads

    应力
    状态
    一般形式简化形式
    二轴
    拉伸
    $\dfrac{ {\sigma _1^2} }{ {f_{\text{t} }^{\text{2} } } } + \dfrac{ {\sigma _2^2} }{ {f_{\text{t} }^{\text{2} } } } - 2{v_{D,{\rm t}} }\dfrac{ { {\sigma _1}{\sigma _2} } }{ {f_{\text{t} }^{\text{2} } } } = 1$$ \dfrac{{\sigma _1^2}}{{f_{\text{t}}^{\text{2}}}} + \dfrac{{\sigma _2^2}}{{f_{\text{t}}^{\text{2}}}} - {c_1}\dfrac{{{\sigma _1}{\sigma _2}}}{{f_{\text{t}}^{\text{2}}}} = 1 $
    二轴
    拉压
    $\dfrac{ {\sigma _1^2} }{ {f_{\text{t} }^{\text{2} } } } + \dfrac{ {\sigma _3^2} }{ {f_{\text{c} }^{\text{2} } } } - ({v_{D,{\rm c}} } + {v_{D,{\rm t}} })\dfrac{ { {\sigma _1}{\sigma _3} } }{ { {f_{\text{t} } }{f_{\text{c} } } }} = 1$$ \dfrac{{\sigma _1^2}}{{f_{\text{t}}^{\text{2}}}} + \dfrac{{\sigma _3^2}}{{f_{\text{c}}^{\text{2}}}} - {c_2}\dfrac{{{\sigma _1}{\sigma _3}}}{{{f_{\text{t}}}{f_{\text{c}}}}} = 1 $
    二轴
    压缩
    $\dfrac{ {\sigma _2^2} }{ {f_{\text{c} }^{\text{2} } } } + \dfrac{ {\sigma _3^2} }{ {f_{\text{c} }^{\text{2} } } } - 2{v_{D,{\rm c}} }\dfrac{ { {\sigma _2}{\sigma _3} } }{ {f_{\text{c} }^{\text{2} } } } = 1$$ \dfrac{{\sigma _2^2}}{{f_{\text{c}}^{\text{2}}}} + \dfrac{{\sigma _3^2}}{{f_{\text{c}}^{\text{2}}}} - \left[{c_3} + {c_4}{\left(\dfrac{{{\sigma _2} - {\sigma _3}}}{{{\sigma _2} + {\sigma _3}}}\right)^2}\right]\dfrac{{{\sigma _2}{\sigma _3}}}{{f_{\text{c}}^{\text{2}}}} = 1 $
    下载: 导出CSV

    表  8  简化二轴损伤比强度准则中各经验参数取值

    Table  8.   The values of the empirical parameters in the simplified biaxial damage ratio strength criterion

    材料类型c1c2c3c4
    普通混凝土0.31.151.3880.79
    钢纤维混凝土0.31.341.4600.92
    下载: 导出CSV

    表  9  钢纤维混凝土二轴试验样本信息

    Table  9.   Information on SFRC biaxial experimental specimens

    文献[18][19][20][21][22]
    纤维类型直钢纤维端钩型钢纤维端钩型钢纤维熔抽钢纤维端钩型钢纤维
    ρf /(%)1.0、2.02.00.5、1.00.5、1.0、1.51.0、1.5、2.00.5、1.0、1.5
    尺寸/mm长度35;等效直径0.54长度30;直径0.55长度35;等效直径0.6
    l/d45、595965555860
    下载: 导出CSV
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  • 收稿日期:  2021-05-18
  • 修回日期:  2021-08-04
  • 网络出版日期:  2021-08-27
  • 刊出日期:  2022-09-01

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