钢纤维-橡胶/混凝土单轴受压全曲线试验及本构模型

赵秋红; 董硕; 朱涵

doi:10.13801/j.cnki.fhclxb.20200916.001

钢纤维-橡胶/混凝土单轴受压全曲线试验及本构模型

doi: 10.13801/j.cnki.fhclxb.20200916.001

赵秋红^{1, 2, ,},
董硕¹,
朱涵^{1, 2}

1.
天津大学　建筑工程学院，天津 300072
2.
天津大学　滨海土木工程结构与安全教育部重点实验室，天津 300350

基金项目: 国家自然科学基金(51678406；51878447；51378340)；天津市研究生科研创新项目(2019YJSB162)

详细信息

通讯作者:
赵秋红，博士，教授，博士生导师，研究方向为高层抗震、桥梁抗震、高性能结构及材料　E-mail：qzhao@tju.edu.cn

中图分类号: TB332
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出版历程
- 收稿日期: 2020-08-03
- 录用日期: 2020-09-01
- 网络出版日期: 2020-09-16
- 刊出日期: 2021-07-15

Experiment on stress-strain behavior and constitutive model of steel fiber-rubber/ concrete subjected to uniaxial compression

ZHAO Qiuhong^{1, 2
, ,},
DONG Shuo¹,
ZHU Han^{1, 2}

1.
School of Civil Engineering, Tianjin University, Tianjin 300072, China
2.
Key Laboratory of Coastal Civil Structure and Safety of China Ministry of Education, Tianjin University, Tianjin 300350, China

摘要

摘要: 将钢纤维(SF)掺入橡胶混凝土中，能够改善由于橡胶颗粒掺入导致的强度降低，并进一步增加延性。为研究SF-橡胶/混凝土的抗压性能，配制得到SF体积分数分别为0vol%、0.5vol%、1.0vol%和1.5vol%及橡胶颗粒等体积替换砂率为0%、10%和20%的10组SF-橡胶/混凝土试件，并进行单轴受压全曲线试验。结果表明：SF的桥联作用及其与橡胶颗粒的协同作用可改善混凝土的抗压性能，试件破坏呈明显延性特征。随SF掺量的增加，SF-橡胶/混凝土试件的抗压强度及弹性模量均明显增大，其相应峰值应力的应变及全曲线峰值后延性也相应增加；随橡胶颗粒掺量的增加，SF-橡胶/混凝土试件相应峰值应力的应变及全曲线峰值后延性增加，而抗压强度及弹性模量有所减小。在已有研究基础上，通过曲线拟合试验数据，提出适用于SF-橡胶/混凝土的单轴受压应力-应变全曲线数学表达式，模型与试验结果吻合较好，为此类混凝土的结构分析设计提供了理论基础。
- 钢纤维-橡胶/混凝土 /
- 单轴受压应力-应变全曲线试验 /
- 钢纤维掺量 /
- 橡胶掺量 /
- 本构模型
Abstract: Adding steel fiber (SF) into rubber concrete can improve the strength reduction caused by the incorporation of rubber particles, and further increase the ductility. Ten groups of SF-rubber/concrete under uniaxial compression were conducted in order to study the compressive properties. The crumb rubber particles were incorporated at different percentages of 0%, 10% and 20% by volume substation of sand, and SF with volume fraction of 0vol%, 0.5vol%, 1.0vol%, and 1.5vol% were added to the concrete mixture. The results show that the bridging action of SF and its positive synergy with rubber particles in SF-rubber/concrete can improve the compressive behavior of concrete. The failure process of SF-rubber/concrete specimens is mild and slow, and the failure mode is obviously ductile. After adding SF, the compressive strength and elastic modulus of the SF-rubber/concrete increase obviously, and the strains at the peak stress and the post-peak ductility increase. With the increase of rubber particles, the strain at the peak stress and the post-peak ductility of SF-rubber/concrete further increase. But the compressive strength and elastic modulus of SF-rubber/concrete are reduced by adding rubber particles. Based on the test data and the literature of stress-strain curve expression, a more suitable analytical model was proposed to generate the stress-strain curve of SF-rubber/concrete, which can be applied in the analysis and design of SF-rubber/concrete structural members.
- steel fiber-rubber/concrete /
- stress-strain curve test under uniaxial compression /
- volume fraction of steel fiber /
- volume substation of rubber particles /
- constitutive model

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图 1 单轴受压应力-应变全曲线试验加载装置

Figure 1. Test setup of uniaxial compressive stress-strain curves

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图 2 钢纤维(SF)-橡胶/混凝土试件受压破坏过程示意图

Figure 2. Schematic diagrams of compressive process of steel fiber (SF)-rubber/concrete specimens

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图 3 SF-橡胶/混凝土试件的受压破坏形态

Figure 3. Compressive failure modes of SF-rubber/concrete specimens

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图 4 SF-橡胶/混凝土试件单轴受压应力-应变全曲线

Figure 4. Uniaxial compressive stress-strain curves of SF-rubber/concrete specimens

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图 5 PC、橡胶/混凝土、SF/混凝土试件单轴受压应力-应变曲线理论模型与试验曲线比较

Figure 5. Comparison between theoretical and experimental curves of PC, rubber/concrete, SF/concrete specimens

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图 6 SF-橡胶/混凝土形状参数${\alpha _{\rm{c}}}$拟合效果对比

Figure 6. Comparison of shape parameters ${\alpha _{\rm{c}}}$ between experimental and predicted results of SF-rubber/concrete

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图 7 SF-橡胶/混凝土单轴受压应力-应变曲线理论模型与试验曲线对比

Figure 7. Comparison between theoretical and experimental uniaxial compressive stress-strain curves of SF-rubber/concrete

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表 1 试验混凝土配比

Table 1. Mixture proportions of test concretes

Type	Specimen denotation	Water-binder mass ratio	Volume fraction of steel fiber/vol%	Volume substitution ratio of rubber particles/%	Water/ kg	Cement/ kg	Fine aggregate/ kg	Coarse aggregate/ kg	Mass fraction of super plasticizer/ wt%
PC	R-0-F-0.0	0.34	0	0	160	470	820	960	1
Rubber/ concrete	R-10-F-0.0	0.34	0	10	160	470	738	960	1
Rubber/ concrete	R-20-F-0.0	0.34	0	20	160	470	656	960	1
SF/ concrete	R-0-F-0.5	0.34	0.5	0	160	470	820	960	1
	R-0-F-1.0	0.34	1.0	0	160	470	820	960	1
	R-0-F-1.5	0.34	1.5	0	160	470	820	960	1
SF-rubber/ concrete	R-10-F-0.5	0.34	0.5	10	160	470	738	960	1
	R-10-F-1.0	0.34	1.0	10	160	470	738	960	1
	R-10-F-1.5	0.34	1.5	10	160	470	738	960	1
	R-20-F-1.0	0.34	1.0	20	160	470	656	960	1
Notes: PC—Plain concrete; SF—Steel fiber; R—Rubber particles; R-0, R-10, R-20—Rubber volume substitution ratios of 0%, 10% and 20%, respectively; F—Steel fiber; F-0.0, F-0.5, F-1.0, F-1.5—Steel fiber volume fractions of 0vol%, 0.5vol%, 1.0vol% and 1.5vol%, respectively.

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表 2 SF-橡胶/混凝土试件单轴受压试验及计算结果

Table 2. Uniaxial compressive tests and calculation results of SF-rubber/concrete specimens

Specimen type	Specimen denotation	${f_{{\rm{cu}}}}$/MPa	${f_{{\rm{c,t}}}}$/MPa	${f_{{\rm{c,c}}}}$/MPa	$\dfrac{{{f_{{\rm{c,t}}}}}}{{{f_{{\rm{c,c}}}}}}$	${\varepsilon _{{\rm{c,t}}}}$/10⁻³	${\varepsilon _{{\rm{c,c}}}}$/10⁻³	$\dfrac{{{\varepsilon _{{\rm{c,t}}}}}}{{{\varepsilon _{{\rm{c,c}}}}}}$	${E_{{\rm{c,t}}}}$/10⁴	${E_{{\rm{c,c}}}}$/10⁴	$\dfrac{{{E_{{\rm{c,t}}}}}}{{{E_{{\rm{c,c}}}}}}$
PC	R-0-F-0.0	68.7	48.9	48.9	1.00	1.95	1.90	1.02	3.81	3.70	1.03
Rubber/concrete	R-10-F-0.0	58.5	41.3	40.4	1.02	2.11	2.11	1.00	3.36	3.39	0.99
Rubber/concrete	R-20-F-0.0	46.5	32.0	32.0	1.00	2.40	2.40	1.00	3.09	3.03	1.02
SF/concrete	R-0-F-0.5	72.1	51.1	51.0	1.00	2.06	2.07	1.00	3.99	3.98	1.00
	R-0-F-1.0	74.7	53.1	53.1	1.00	2.25	2.23	1.00	4.25	4.26	1.00
	R-0-F-1.5	78.9	56.4	55.1	1.02	2.43	2.42	1.00	4.53	4.55	1.00
SF-rubber/ concrete	R-10-F-0.5	60.2	42.7	42.5	1.00	2.31	2.26	1.02	3.55	3.65	0.97
	R-10-F-1.0	61.4	42.2	44.6	0.95	2.52	2.39	1.06	3.82	3.91	0.98
	R-10-F-1.5	65.7	46.1	46.7	0.99	2.60	2.59	1.00	4.17	4.21	0.99
	R-20-F-1.0	48.9	34.1	36.1	0.94	2.73	2.70	1.01	3.70	3.53	1.05
Notes: ${f_{{\rm{cu}}}}$—Cube compressive strength; ${f_{{\rm{c,t}}}}$—Experimental axial compressive strength; ${f_{{\rm{c,c}}}}$—Calculated axial compressive strength; ${\varepsilon _{{\rm{c,t}}}}$—Experimental strain at peak stress point; ${\varepsilon _{{\rm{c,c}}}}$—Calculated strain at peak stress point; ${E_{{\rm{c,t}}}}$—Experimental elastic modulus; ${E_{{\rm{c,c}}}}$—Calculated elastic modulus.

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表 3 国内外常用普通混凝土(PC)、橡胶/混凝土和SF/混凝土受压应力-应变曲线模型

Table 3. Theoretical stress-strain models of plain concrete (PC), rubber/concrete and SF/concrete under compression in literatures

	References	${f_{\rm{c}}}$/MPa	Admixture	Constitutive models and parameter
PC	Carreia-Chu et al^[8]	—	—	$\sigma = \dfrac{{{f_{\rm{c}}}\beta (\varepsilon/{\varepsilon _{\rm{c}}})}}{{\beta - 1 + {{(\varepsilon/{\varepsilon _{\rm{c}}})}^\beta }}}$; $\beta = {\left( {\dfrac{{{f_{\rm{c}}}}}{{32.4}}} \right)^3} + 1.55$; ${\varepsilon _{\rm{c}}} = 700{({f_{\rm{c}}})^{0.25}} \times {10^{ - 6}}$
	Guo^[9]	—	—	$x = \dfrac{\varepsilon }{{{\varepsilon _{\rm{c}}}}}$; $y = \dfrac{\sigma }{{{f_{\rm{c}}}}}$; $y = \left\{ \begin{array}{l} ax + (3 - 2a){x^2} + (a - 2){x^3}\mathop {}\limits_{} (0 < x \leqslant 1) \\ \dfrac{x}{{b{{(x - 1)}^2} + x}}\mathop {}\limits_{} (x > 1) \\\end{array} \right.$ $a = 2.4 - 0.0125{f_{\rm{c}}};\;b = 0.157{f_{\rm{c}}}^{0.795} - 0.905$
	GB 50010—2010^[10]	—	—	$\sigma = (1 - {d_{\rm{c}}}){E_{\rm{c}}}\varepsilon $; ${d_{\rm{c}}} = \left\{ \begin{array}{l} 1 - \dfrac{{{\rho _{\rm{c}}}n}}{{n - 1 + {x^n}}}\mathop {}\nolimits_{} (\varepsilon \leqslant {\varepsilon _{\rm{c}}}) \\ 1 - \dfrac{{{\rho _{\rm{c}}}n}}{{{\alpha _{\rm{c}}}{{(x - 1)}^2} + x}}\mathop {}\nolimits_{} (\varepsilon > {\varepsilon _{\rm{c}}}) \\\end{array} \right.$;${\rho _{\rm{c}}} = \dfrac{{{f_{\rm{c}}}}}{{{E_{\rm{c}}}{\varepsilon _{\rm{c}}}}}$; $n = \dfrac{{{E_{\rm{c}}}{\varepsilon _{\rm{c}}}}}{{{E_{\rm{c}}}{\varepsilon _{\rm{c}}} - {f_{\rm{c}}}}}$; $x = \dfrac{\varepsilon }{{{\varepsilon _{\rm{c}}}}}$; ${\alpha _{\rm{c}}} = 0.157f_{\rm{c}}^{0.785} - 0.905$ ${\varepsilon _{\rm{c}}} = 700 + 172\sqrt {{f_{\rm{c}}}} \times {10^{ - 6}}$
Rubber/ concrete	Feng et al^[16]	50–80	Amount: 0–37.8 kg∙m⁻³ Size: 0.198–8 mm	${a_1} = 2.4 - 0.01{f_{{\rm{cu}}}}$; $a = {a_1}(1 - 0.0529{\rho _{\rm{r}}}d_{\rm{r}}^{ - 0.0347})$${a_2} = 0.132f_{{\rm{cu}}}^{0.785} - 0.905$; $b = {a_2}(1 + 0.046{\rho _{\rm{r}}}d_{\rm{r}}^{ - 0.135})$${f_{{\rm{c}},{\rm{r}}}} = {f_{\rm{c}}} \times {{\rm{e}}^{\left( {\frac{{ - 0.0251{\rho _{\rm{r}}}{d_{\rm{r}}}}}{{ - 0.1058 + {d_{\rm{r}}}}}} \right)}}$; ${\varepsilon _{{\rm{c}},{\rm{r}}}} = (3\;666.7 - 105.8\sqrt {{f_{{\rm{c}},{\rm{r}}}}} ) \times {10^6}$
	Li et al^[17]	30–50	Amount: 0–50.92 kg∙m⁻³ Size: 0.173–4 mm	$a = (2.4 - 0.0125{f_{\rm{c}}}) \times \exp \left(0.107{\rm{ln}}{d_{\rm{r}}} + \dfrac{{0.006\rho _{\rm{r}}^{1.0169}{d_{\rm{r}}}}}{{{d_{\rm{r}}} - 0.1287}}\right)$; $b = (0.157{f_{\rm{c}}}^{0.785} - 0.905) \times \exp \left(0.0617{\rm{ln}}{d_{\rm{r}}} - \dfrac{{0.283\rho _{\rm{r}}^{0.3322}{d_{\rm{r}}}}}{{{d_{\rm{r}}} + 0.0018}}\right)$; ${f_{{\rm{c}},{\rm{r}}}} = {f_{\rm{c}}} \times \exp \left( {\dfrac{{ - 0.0734{\rho _{\rm{r}}}^{0.4947}{k^{ - 3.2634}}{d_{\rm{r}}}}}{{{d_{\rm{r}}} - 0.0737}}} \right)$; ${\varepsilon _{{\rm{c}},{\rm{r}}}} = (938.0584 + 158.1626\sqrt {{f_{{\rm{c}},{\rm{r}}}}} ) \times {10^6}$
	Li et al^[18]	35–50	Amount: 0–40.5 kg∙m⁻³ Size: 1.18 mm, 2.36 mm	$\beta = \left\{ \begin{array}{l} {\left[ {1.02 - 1.17/({E_{\rm{p}}}/{E_{{\rm{c}},{\rm{r}}}})} \right]^{ - 0.74}}\mathop {}\nolimits_{} (\varepsilon \leqslant {\varepsilon _{{\rm{c}},{\rm{r}}}}) \\ {\left[ {1.02 - 1.17/({E_{\rm{p}}}/{E_{{\rm{c}},{\rm{r}}}})} \right]^{ - 0.74}} + (\gamma + \mu )\mathop {}\nolimits_{} (\varepsilon > {\varepsilon _{{\rm{c}},{\rm{r}}}}) \\ \end{array} \right.$ $\gamma = {(135.16 - 0.1744{f_{{\rm{c}},{\rm{r}}}})^{ - 0.46}}$; $\mu = 0.35\exp ( - 9.11/{f_{{\rm{c}},{\rm{r}}}})$${E_{\rm{p}}} = {f_{{\rm{c}},{\rm{r}}}}/{\varepsilon _{{\rm{c}},{\rm{r}}}}$; ${\varepsilon _{{\rm{c}},{\rm{r}}}} = ({f_{{\rm{c}},{\rm{r}}}}/{E_{{\rm{c}},{\rm{r}}}})\left[ {\upsilon/(\upsilon - 1)} \right]$; $\upsilon = {f_{{\rm{c}},{\rm{r}}}}/17 + 0.8$;
SF/concrete	Nataraja^[19]	30–50	Type: Corrugated ${l_{\rm{f}}}/{d_{\rm{f}}}$: 55, 82; ${V_{\rm{f}}}$: 0vol%, 0.5vol%, 0.75vol%, 1.0vol%	$\beta = 0.5811 + 1.93\lambda _{\rm{f}}^{ - 0.7406}$${f_{{\rm{c}},{\rm{f}}}} = {f_{\rm{c}}} + 2.1604{\lambda _{\rm{f}}}$;${\varepsilon _{{\rm{c}},{\rm{f}}}} = {\varepsilon _{\rm{c}}} + 0.0006{\lambda _{\rm{f}}}$
	Gao^[23]	20–30	Type: Shear-wave ${l_{\rm{f}}}/{d_{\rm{f}}}$: 46; ${V_{\rm{f}}}$: 0vol%, 0.5vol%, 1.5vol%, 2.0vol%	$a = {E_{{\rm{c}},{\rm{f}}}}(1.3 + 0.014{f_{{\rm{c}},{\rm{f}}}} + 0.96{\lambda _{\rm{f}}})/{f_{{\rm{c}},{\rm{f}}}} \times {10^3}$$b = (1.4 + 0.012{f_{{\rm{c}},{\rm{f}}}}^{1.45})(1 - 0.8{\lambda _{\rm{f}}}^{0.295})$, $1.5 \leqslant a < 3.0$
	Zhang^[24]	40–50
	Lv et al^[25]	50–90	Type: Hooked-end ${l_{\rm{f}}}/{d_{\rm{f}}}$: 62.5; ${V_{\rm{f}}}$: 0vol%, 1.0vol%, 1.5vol%, 2.0vol%	${\alpha _{{\rm{c}},{\rm{f}}}} = (0.157f_{\rm{c}}^{0.785} - 0.905)\left[ {1 - 0.0192({l_{\rm{f}}}/{d_{\rm{f}}}){V_{\rm{f}}}^{0.08}} \right]$${\varepsilon _{{\rm{c}},{\rm{f}}}} = (700 + 172\sqrt {{f_{\rm{c}}}} )(1.0 + 0.189{\lambda _{\rm{f}}}) \times {10^{ - 6}}$${E_{ {\rm{c} },{\rm{f} } } } = \dfrac{ { { {10}^5} } }{ {2.2 + \left({ {34.7} }/{ { {f_{ {\rm{cu} },{\rm{k} } } } } }\right)} }(1 - 0.0006{\lambda _{\rm{f} } })$
Notes: ${f_{\rm{c}}}$—Axial compressive strength of PC; ${\varepsilon _{\rm{c}}}$—strain at peak stress point of PC; ${\varepsilon _{\rm{u}}}$—Ultimate strain of PC; ${d_{\rm{c}}}$—Damage evolution parameters of PC; ${f_{{\rm{c}},{\rm{r}}}}$—Peak stress of Rubber/Concrete; ${\varepsilon _{{\rm{c}},{\rm{r}}}}$—Strain at peak stress point of Rubber/Concrete; $E{}_{{\rm{c}},{\rm{r}}}$—Elastic modulus of Rubber/Concrete;${f_{{\rm{c}},{\rm{f}}}}$—Peak stress of SF/Concrete; ${\varepsilon _{{\rm{c}},{\rm{f}}}}$—Strain at peak stress point of SF/Concrete; $E{}_{{\rm{c}},{\rm{f}}}$—Elastic modulus of SF/Concrete; V_f—Volume fraction of steel fiber; l_f/d_f—Length to diameter ratio of SF.

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