吉林大学学报(工学版) ›› 2019, Vol. 49 ›› Issue (4): 1144-1152.doi: 10.13229/j.cnki.jdxbgxb20180020

• • 上一篇    

聚丙烯纤维增强混凝土断裂韧度及软化本构曲线确定

梁宁慧1,2(),缪庆旭1,2,刘新荣1,2,代继飞3,钟祖良1,2   

  1. 1. 重庆大学 土木工程学院, 重庆 400045
    2. 库区环境地质灾害防治国家地方联合工程研究中心, 重庆 400045
    3. 中国建设基础设施有限公司, 北京 100044
  • 收稿日期:2018-01-08 出版日期:2019-07-01 发布日期:2019-07-16
  • 作者简介:梁宁慧(1971?),女,副教授,博士研究生. 研究方向:边坡工程,纤维混凝土在土木工程中的应用. E?mail: liangninghui0705@163.com
  • 基金资助:
    重庆市研究生科研创新项目(CYS17040);国家自然科学基金项目(41372356);重庆市基础与前沿研究计划项目(cstc2013jcyjA30005)

Determination of fracture toughness and softening traction⁃separation law of polypropylene fiber reinforced concrete

Ning⁃hui LIANG1,2(),Qing⁃xu MIAO1,2,Xin⁃rong LIU1,2,Ji⁃fei DAI3,Zu⁃liang ZHONG1,2   

  1. 1. School of Civil Engineering, Chongqing University, Chongqing 400045, China
    2. National Joint Engineering Research Center of Geohazards Prevention in the Reservoir Areas, Chongqing 400045, China
    3. China Construction Infrastructure Co, Ltd, Beijing 100044, China
  • Received:2018-01-08 Online:2019-07-01 Published:2019-07-16

摘要:

对粗、细聚丙烯(Polypropylene, PP)纤维不同混掺情况下的混凝土切口梁试件进行三点弯曲试验,基于双K断裂理论探讨了不同尺寸PP纤维混掺方式对试件断裂韧度的影响及其破坏机理,并通过起裂、失稳、黏聚韧度3者之间的定量关系得到实测黏聚韧度、起裂韧度增量和桥接韧度。借鉴3种普通混凝土的双线性软化本构曲线计算得到理论黏聚韧度,并将其与实测黏聚韧度对比,确定适合于不同纤维掺入情况下PP纤维增强混凝土(Polypropylene fiber reinforced concrete, PFRC)的双线性软化本构曲线。研究结果表明,PFRC相对素混凝土有较高的起裂韧度、失稳韧度和断裂能;2或3种尺寸PP纤维混掺时,其桥接应力对桥接韧度的增强效果非常显著;3种尺寸PP纤维在裂缝扩展的不同阶段发挥桥接作用,体现了良好的混掺增强、增韧效应;徐世烺和Reinhardt改进的双线性软化本构曲线,取校正系数λ为6时,可较好地适用于PFRC。

关键词: 土木工程, 聚丙烯纤维增强混凝土, 双K断裂理论, 双线性软化本构曲线

Abstract:

The three?point bending test was carried out on concrete notched beams with different amount of coarse and fine polypropylene(PP) fibers. Based on the double?K fracture theory, the influence of mixing method of PP fibers with different sizes on the fracture toughness and failure mechanism were discussed.The real cohesive toughness, the increment of initiation toughness and the bridge connection toughness were gained by the quantitative relationship between the initiation toughness, the unstable toughness and the cohesive toughness. In addition, The theoretical cohesive toughness was calculated from three kinds of ordinary concrete bilinear softening constitutive curves, which was compared with the real cohesive toughness to determine the bilinear softening traction?separation law of PFRC, which was suitable for different PP fiber incorporation conditions. The results show that PFRC has higher initiation toughness, unstable toughness and fracture energy compared with plain concrete. The enhancement effect of bridge connection toughness from bridging stress is very significant when 2 or 3 sizes of PP fibers are mixed. The 3 sizes of PP fibers play the role of bridging at different stages of crack propagation, and it serves a well function of toughening and strengthening. The bilinear softening traction?separation law proposed by Xu and Reinhardt is well applicable for PFRC when the correction coefficient is 6.

Key words: civil engineering, polypropylene fiber reinforced concrete, double?K fracture model, bilinear softening traction?separation law

中图分类号: 

  • TU528

图1

临界失稳状态下虚拟裂缝区内黏聚应力的分布图"

图2

双线性软化本构曲线"

表1

聚丙烯纤维的物理力学指标"

参 数 FF1 FF2 CF1
直径/mm 0.026 0.100 0.800
长度/mm 19 19 50
抗拉强度/MPa 641 322 706
弹性模量/GPa 4.5 4.9 7.4
断裂伸长率/% 40 15 10
密度/(g·cm-3) 0.91 0.91 0.95
推荐掺量/(kg·m-3) 0.9 0.9 6.0

表2

不同试件的纤维掺量"

试件编号 纤维种类 纤维掺量/(kg·m-3)
A0 0
A1 FF1 0.9
A2 FF2 0.9
A3 CF1 6.0
A4 FF1+CF1 0.6+5.4
A5 FF1+CF1 0.9+5.1
A6 FF1+CF1 1.2+4.8
A7 FF2+CF1 0.6+5.4
A8 FF2+CF1 0.9+5.1
A9 FF2+CF1 1.2+4.8
A10 FF1+FF2+CF1 0.45+0.45+5.1
A11 FF1+FF2+CF1 0.6+0.6+4.8

图3

切口梁试件及其三点弯曲试验装置"

表3

双K断裂韧度及断裂能的计算结果"

试件

编号

CMOD c/μm C T O D c /μm P inl/N

K I c i n i

/(MPa·m1/2)

P m a x /N a c/mm

K I c u n

/(MPa·m1/2)

G f

/(N·m-1)

A0 39.9 10 1665 0.561 2017 57 0.869 104.7
A1 48.1 13 1943 0.654 2441 59 1.133 147.6
A2 42.5 12 1503 0.506 1929 61 0.960 113.3
A3 51.1 15 1807 0.608 2265 61 1.132 403.1
A4 51.2 16 1727 0.582 2243 62 1.120 537.9
A5 58.8 21 1850 0.623 2457 63 1.336 562.0
A6 54.7 18 1752 0.590 2276 64 1.285 535.0
A7 54.8 18 1797 0.605 2351 63 1.287 480.7
A8 56.5 19 1755 0.591 2284 64 1.282 544.2
A9 47.2 16 1627 0.548 2177 64 1.272 433.6
A10 44.9 18 1983 0.670 2552 63 1.356 537.7
A11 57.3 20 1930 0.650 2580 64 1.454 608.8

表4

PFRC的 Δ K I c i n i s 和 K I c c s 值"

试件编号 K I c c s Δ K I c i n i s
A0 0 0
A1 0.171 0.093
A2 0.146 -0.055
A3 0.216 0.047
A4 0.230 0.021
A5 0.405 0.062
A6 0.387 0.029
A7 0.374 0.044
A8 0.383 0.030
A9 0.416 -0.013
A10 0.378 0.109
A11 0.496 0.089

表5

实测黏结韧度与理论黏聚韧度的比较"

试件编号 K I c , T c K I c , E c (Petersson) K I c , E c (CEB?FIP Model Code 1990) K I c , E c (徐世烺和Reinhardt)
λ=5 λ=6 λ=7 λ=8 λ=9 λ=10
i = 1 11 η i 0.601 0.594 0.274 0.149 0.161 0.220 0.279 0.305
A0?1 0.287 0.479 0.344 0.328 0.299 0.283 0.272 0.265 0.260
A0?2 0.335 0.510 0.366 0.348 0.317 0.299 0.288 0.280 0.274
A0?3 0.304 0.415 0.298 0.283 0.259 0.245 0.236 0.230 0.225
η 0 0.08 0.004 0.002 0.0025 0.005 0.007 0.009 0.010
A1?1 0.489 0.525 0.523 0.494 0.445 0.442 0.431 0.419 0.411
A1?2 0.523 0.622 0.620 0.587 0.532 0.529 0.508 0.493 0.483
A1?3 0.424 0.538 0.536 0.506 0.460 0.458 0.441 0.429 0.420
η 1 0.024 0.023 0.011 0.003 0.003 0.0038 0.006 0.008
A2?1 0.588 0.730 0.725 0.692 0.624 0.619 0.594 0.577 0.564
A2?2 0.419 0.630 0.627 0.596 0.540 0.536 0.515 0.501 0.490
A2?3 0.355 0.555 0.552 0.524 0.475 0.474 0.456 0.443 0.434
η 2 0.105 0.101 0.07 0.031 0.029 0.02 0.015 0.012
A3?1 0.493 0.547 0.546 0.509 0.461 0.458 0.441 0.428 0.419
A3?2 0.549 0.837 0.836 0.773 0.692 0.689 0.653 0.631 0.616
A3?3 0.526 0.678 0.677 0.630 0.568 0.563 0.539 0.523 0.512
η 3 0.109 0.108 0.06 0.023 0.02 0.013 0.011 0.01
A4?1 0.517 0.617 0.616 0.571 0.516 0.512 0.491 0.476 0.466
A4?2 0.931 1.06 1.05 0.972 0.863 0.848 0.807 0.779 0.759
A4?3 0.405 0.632 0.632 0.585 0.527 0.523 0.501 0.486 0.475
η 4 0.077 0.051 0.037 0.019 0.021 0.025 0.031 0.037
A5?1 0.791 0.803 0.802 0.743 0.667 0.658 0.630 0.610 0.595
A5?2 0.628 0.771 0.770 0.712 0.639 0.632 0.604 0.586 0.571
A5?3 - - - - - - - - -
η 5 0.020 0.020 0.009 0.015 0.017 0.026 0.031 0.041
A6?1 0.649 0.759 0.757 0.701 0.630 0.623 0.596 0.578 0.564
A6?2 0.740 0.893 0.892 0.823 0.735 0.724 0.691 0.668 0.651
A6?3 0.695 0.845 0.843 0.781 0.699 0.689 0.659 0.638 0.622
η 6 0.058 0.057 0.017 0.0004 0.0001 0.006 0.013 0.02
A7?1 0.713 0.828 0.828 0.763 0.683 0.673 0.644 0.623 0.607
A7?2 0.836 0.960 0.958 0.885 0.788 0.776 0.740 0.715 0.697
A7?3 0.681 0.783 0.781 0.726 0.652 0.644 0.616 0.598 0.583
η 7 0.040 0.038 0.007 0.004 0.007 0.018 0.03 0.04
A8?1 0.805 1.038 1.037 0.952 0.846 0.831 0.791 0.764 0.744
A8?2 0.628 0.741 0.739 0.687 0.617 0.611 0.585 0.567 0.553
A8?3 0.691 0.833 0.832 0.768 0.687 0.678 0.648 0.627 0.612
η 8 0.087 0.086 0.031 0.002 0.001 0.004 0.009 0.016
A9?1 0.541 0.677 0.676 0.630 0.568 0.563 0.540 0.523 0.512
A9?2 0.794 0.943 0.942 0.868 0.773 0.761 0.726 0.701 0.683
A9?3 0.724 0.880 0.879 0.811 0.725 0.715 0.682 0.660 0.643
η 9 0.065 0.064 0.021 0.001 0.0016 0.006 0.013 0.019
A10?1 0.716 0.767 0.766 0.708 0.635 0.628 0.610 0.582 0.568
A10?2 0.783 0.864 0.863 0.797 0.713 0.703 0.671 0.650 0.633
A10?3 0.688 0.755 0.754 0.699 0.627 0.621 0.594 0.576 0.562
η 10 0.014 0.013 0.0004 0.015 0.019 0.034 0.048 0.06
A11?1 0.789 0.774 0.773 0.716 0.643 0.635 0.608 0.589 0.575
A11?2 0.806 0.848 0.847 0.781 0.699 0.689 0.659 0.637 0.621
A11?3 - - - - - - - - -
η 11 0.002 0.002 0.006 0.032 0.037 0.054 0.068 0.080
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