预应力超高性能混凝土矩形梁的抗剪性能及钢纤维增强机理

孙斌; 罗锐; 钟鸣宇; 宋超林; 肖汝诚

预应力超高性能混凝土矩形梁的抗剪性能及钢纤维增强机理

1.
同济大学　土木工程学院, 上海 200092
2.
上海市政工程设计研究总院(集团)有限公司, 上海 200082

基金项目: 国家自然科学基金 (51878494；52378185)

详细信息

通讯作者:
宋超林，博士，博士后，研究方向为不确定性量化与桥梁工程中的设计优化方法　E-mail: songcl@tongji.edu.cn

中图分类号: TU375.1
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出版历程
- 收稿日期: 2024-10-11
- 修回日期: 2024-11-16
- 录用日期: 2024-11-26
- 网络出版日期: 2024-12-09

Shear performance and steel fiber reinforcement mechanism of prestressed ultra-high performance concrete rectangular beams

1.
College of Civil Engineering, Tongji University, Shanghai 200092, China
2.
Shanghai Municipal Engineering Design Institute (Group) Co., Ltd., Shanghai 200082, China)

Funds: National Natural Science Foundation of China (51878494; 52378185)

摘要

摘要:
为研究钢纤维对预应力超高性能混凝土(UHPC)矩形梁抗剪性能的影响，本文以钢纤维的掺量、尺寸和形状为变量，开展了基于四点加载法的矩形梁抗剪试验，重点分析荷载-挠度关系、裂缝扩展规律及破坏模式。采用塑性损伤模型对抗剪行为进行数值模拟，系统探讨了不同设计参数下抗剪承载力对钢纤维掺量的敏感性。通过极限平衡法对抗剪机理进行了分析，并与设计规范进行对比。结果表明，钢纤维能够显著抑制裂缝扩展，掺量从1%提高至2.5%可使抗剪承载力提升10.7%；弯钩型钢纤维能使结构延性较平直型钢纤维提高41.7%。参数分析显示，在较大剪跨比或较低配筋率条件下，钢纤维掺量的增加对抗剪承载力的提升效果更为显著。美国规范和极限平衡法能够以平均误差小于5%的精度较准确地预测抗剪承载力，而法国和德国规范尽管单独考虑了钢纤维的贡献，但预测结果偏于保守。
- 超高性能混凝土梁 /
- 抗剪性能 /
- 钢纤维 /
- 数值模拟 /
- 极限平衡法 /
- 承载力预测
Abstract:
To investigate the effect of steel fibers on the shear performance of prestressed ultra-high performance concrete (UHPC) rectangular beams, four-point loading tests were conducted with variables including fiber content, size, and shape, focusing on load-deflection behavior, crack propagation, and failure modes. The sensitivity of shear capacity to fiber parameters under different design conditions was systematically explored using a plastic damage model by numerical simulations. Results show that the shear capacity improves by 10.7% when the fiber content increases from 1% to 2.5%, and hooked steel fibers can improve the structural ductility by 41.7% compared to straight steel fibers. Parametric analyses indicate that the effect of fiber content is more significant under larger shear span-to-depth ratios or lower reinforcement ratios. The American code and ultimate equilibrium method predict the shear capacity with an average error of less than 5%, while the French and German codes yield conservative estimates, despite accounting for fiber contributions.
- ultra-high performance concrete beam /
- shear performance /
- steel fibers /
- numerical simulation /
- ultimate equilibrium method /
- load-bearing capacity prediction

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图 1 试验用钢纤维

Figure 1. Shapes of steel fibers used in the experiment

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图 2 UHPC单轴拉压试验构件(单位：mm)

Figure 2. Diagram of uniaxial tension and compression test specimens (Unit: mm)

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图 3 试验梁截面(单位：mm)

Figure 3. Cross-section of test beams (Unit: mm)

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图 4 试验梁布置(单位：mm)

Figure 4. Experimental setup (Unit: mm)

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图 5 骨头形轴拉UHPC矩形梁试件应力-应变关系

Figure 5. Stress-strain relationship of bone-shaped axial tension UHPC rectangular beam specimens

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图 6 立方体轴压UHPC矩形梁试件应力-应变关系

Figure 6. Stress-strain relationship of cubic axial compression UHPC rectangular beam specimens

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图 7 预应力UHPC矩形梁荷载-挠度关系

Figure 7. Load-deflection relationship of prestressed UHPC rectangular beams

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图 8 UHPC矩形梁裂缝分布和破坏模式

Figure 8. Crack patterns and failure modes of UHPC rectangular beams

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图 9 试验梁B0荷载-应变关系

Figure 9. Load-strain relationship of test beam B0

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图 10 UHPC矩形梁数值模型本构关系

Figure 10. Constitutive model in numerical simulation of UHPC rectangular beams

E₀ is the initial elastic stiffness of the material; d_c and d_t are the compressive and tensile damage factors, representing the plastic damage of the material, where 0 indicates no damage and 1 indicates complete damage. ${\varepsilon }_{\mathrm{c}}^{\mathrm{i}\mathrm{n}}$ and ${\varepsilon }_{\mathrm{t}}^{\mathrm{c}\mathrm{k}}$ are the crushing strain and cracking strain. ${\varepsilon }_{0\mathrm{c}}^{\mathrm{e}\mathrm{l}}$ and ${\varepsilon }_{0\mathrm{t}}^{\mathrm{e}\mathrm{l}}$ are the initial elastic deformations. ${\varepsilon }_{\mathrm{c}}^{\mathrm{p}\mathrm{l}}$ and ${\varepsilon }_{\mathrm{t}}^{\mathrm{p}\mathrm{l}}$ are the equivalent plastic strains, while ${\varepsilon }_{\mathrm{c}}^{\mathrm{e}\mathrm{l}}$ and ${\varepsilon }_{\mathrm{t}}^{\mathrm{e}\mathrm{l}}$ are the corresponding equivalent elastic deformations

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图 11 UHPC矩形梁数值模型

Figure 11. Numerical model of UHPC rectangular beams

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图 12 UHPC矩形梁数值模拟和试验承载力对比

Figure 12. Comparison of shear capacities between numerically models and test of UHPC rectangular beams

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图 13 L0受拉损伤因子分布

Figure 13. Tensile damage distribution of L0

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图 14 设计参数对UHPC矩形梁极限承载力的影响

Figure 14. Influence of design parameters on shear capacity of UHPC rectangular beams

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图 15 UHPC矩形梁抗剪极限状态隔离体受力分析

Figure 15. Force analysis on isolated segment of flexural-shear section at ultimate state of UHPC rectangular beams

${\sigma }_{\mathrm{c}}$ is the normal stress of concrete; ${\tau }_{\mathrm{c}}$ is the shear stress of concrete; $\xi$ is the ratio of the compression zone height to the effective depth of the cross-section; $b$ is the beam width; $d$ is the effective depth of the cross-section; ${A}_{\mathrm{s}}$ , ${A}_{\mathrm{p}}$ , and ${A}_{\mathrm{v}}$ are the total areas of tensile reinforcement, stirrups, and prestressing tendons, respectively, while ${\sigma }_{\mathrm{s}}$ , ${\sigma }_{\mathrm{p}}$ , and ${\sigma }_{\mathrm{v}}$ denote their corresponding stresses. ${\sigma }_{\mathrm{f}}$ is the fiber bridging stress. ${l}_{\mathrm{w}}$ is the horizontal projection length of the diagonal crack. ${V}_{\mathrm{u}}$ is the shear capacity

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图 16 各计算模型中分项比例

Figure 16. Item proportions in various calculation models

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表 1 UHPC配合比(单位：kg·m⁻³)

Table 1 UHPC mix proportions (Unit: kg·m⁻³)

Cement	Silica fume	Ground filler	Quartz sand	Water	Superplasticizer	Fiber
733	220	220	982	175	12	1%-2.5%

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表 2 试件分组及参数

Table 2 Parameters of test specimens

Tension	Compression	Beams	Fiber			f_t/MPa	f_cu/MPa	Flowability/mm
Tension	Compression	Beams	Content	Shape	Length/diameter	f_t/MPa	f_cu/MPa	Flowability/mm
T-λ-1	C-λ-1	B-λ-1	1%	Straight	14 mm/0.22 mm	9.00	120.97	269
T-λ-1.5	C-λ-1.5	B-λ-1.5	1.5%	Straight	14 mm/0.22 mm	9.31	123.73	260
T0	C0	B0	2%	Straight	14 mm/0.22 mm	9.62	126.00	247
T-λ-2.5	C-λ-2.5	B-λ-2.5	2.5%	Straight	14 mm/0.22 mm	9.94	128.20	236
T-S-T	C-S-T	B-S-T	2%	Twisted	14 mm/0.22 mm	8.52	127.27	230
T-S-H	C-S-H	B-S-H	2%	Hooked	14 mm/0.22 mm	10.38	133.27	232
T-L-6	C-L-6	B-L-6	2%	Straight	6 mm/0.12 mm	9.87	128.22	248
T-L-13	C-L-13	B-L-13	2%	Straight	13 mm/0.32 mm	8.95	128.67	237
Notes: f_t is tensile strength; f_cu is cubic compressive strength; λ is the volume fraction of steel fibers; S is the shape of the steel fibers, and L is the length of the steel fibers. T is the twisted type, and H is the hooked type.

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表 3 UHPC矩形梁裂缝发展及破坏模式

Table 3 Crack development and failure modes of UHPC rectangular beams

Beams	${\mathit{V}}_{\rm{u}}/{{\mathrm{kN}}}$	${\mathit{W}}_{\rm{u}}/{{\mathrm{mm}}}$	$\mathit{N}$	$\mathit{\theta }/\left(^\circ \right)$	Failure mode
B-λ-1	562	Broken	24	39	Diagonal tension
B-λ-1.5	606	5.4	17	40	Shear compression
B0	618	3.5	14	41	Shear compression
B-λ-2.5	644	0.6	12	39	Flexure
B-S-T	611	2.5	18	41	Shear-Flexure
B-S-H	655	1.4	14	40	Shear-Flexure
B-L-6	603	0.8	20	41	Shear-Flexure
B-L-13	620	1.3	16	40	Shear-Flexure
Notes: ${V}_{\rm{u}}$ is the ultimate shear capacity; ${W}_{\rm{u}}$ is the width of the main crack at ${V}_{\mathrm{u}}$ ; N is the number of diagonal cracks with a width exceeding 10 cm at ${V}_{\mathrm{u}}$ ; $\theta$ is the inclination angle of the main diagonal crack.

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表 4 塑性损伤模型(CDP)模型关键参数

Table 4 Key parameters of concrete damage plasticity (CDP) model

Dilation angle/(°)	Eccentricity	f_b0/f_c0	K	Viscosity parameter
30	0.1	1.16	0.667	0.0003
Notes: f_b0/f_c0 is ratio of biaxial compressive strength to uni axial compressive strength. K is yield surface shape factor for stress state adjustments.

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表 5 UHPC矩形梁抗剪承载力计算模型

Table 5 Predictive model of shear capacity of UHPC rectangular beams

Standards	Predictive formulas
NF P18-710^[19]	${V}_{\mathrm{u}}={V}_{\mathrm{c}}+{V}_{\mathrm{s}}+{V}_{\mathrm{f}}$ ${V}_{c}=0.24 k{f}_{\mathrm{c}}^{1/2}b{\textit{z}}$ , $k=1+3{\sigma }_{\mathrm{c}\mathrm{p}}{/f}_{\mathrm{c}\mathrm{k}}$ , ${V}_{\mathrm{f}}={\sigma }_{\mathrm{f}}b{\textit{z}}$ ； ${\sigma }_{\mathrm{f}}=\dfrac{1}{{\varepsilon }_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\varepsilon }_{\mathrm{e}\mathrm{l}}}{\int }_{{\varepsilon }_{\mathrm{e}\mathrm{l}}}^{{\varepsilon }_{\mathrm{m}\mathrm{a}\mathrm{x}}}{\sigma }_{\mathrm{f}}\left(\varepsilon \right)d\varepsilon$ , ${V}_{\mathrm{s}}={A}_{\mathrm{v}}{\textit{z}}{f}_{\mathrm{y}}\mathit{cot}\theta /s$ , ${\textit{z}}=0.9 d$
DAfStb^[20]	${V}_{\mathrm{u}}={V}_{\mathrm{c}}+{V}_{\mathrm{s}}+{V}_{\mathrm{f}}$ ${V}_{\mathrm{c}}=0.15\left(1+\sqrt{200/d}\right)\left(100\cdot {A}_{\mathrm{s}}/\left(b\cdot d\right){f}_{\mathrm{c}}\right){ }^{1/3}+\mathrm{ }0.12\cdot {\sigma }_{\mathrm{c}\mathrm{p}}$ ${V}_{\mathrm{f}}={0.7 f}_{\mathrm{t}}bh$ ${V}_{\mathrm{s}}={A}_{\mathrm{v}}{\textit{z}}{f}_{\mathrm{y}}\mathit{cot}\theta /s$
FHWA-HRT-23^[21]	${V}_{\mathrm{u}}={V}_{\mathrm{c}}+{V}_{\mathrm{s}}$ ${V}_{\mathrm{C}}={f}_{\mathrm{t}}bdcot\theta$ ; ${V}_{\mathrm{s}}={A}_{\mathrm{v}}\mathrm{d}{f}_{\mathrm{y}}cot\mathrm{\theta }/s$
Notes: ${V}_{\mathrm{c}}$ , ${V}_{\mathrm{s}}$ and ${V}_{\mathrm{f}}$ are the shear contributions of concrete, reinforcement, and fibers, respectively. $k$ is the prestress enhancement coefficient. ${f}_{\mathrm{c}}$ is the standard compressive strength. z is the internal lever arm. ${\sigma }_{\mathrm{c}\mathrm{p}}$ is the axial stress induced by prestress. ${\varepsilon }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\varepsilon }_{\mathrm{e}\mathrm{l}}$ are the maximum uniaxial tensile strain and elastic strain. $\theta$ is the angle between the principal compressive stress and the axis, iteratively calculated based on ${\rho }_{\mathrm{s}}$ , ${\rho }_{\mathrm{v}}$ , and the tensile strain-hardening behavior described in FHWA-HRT-23.

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表 6 UHPC矩形梁抗剪承载力计算结果比较

Table 6 Predictive model of shear capacity of UHPC rectangular beams

Beams	Test	NF P18-710			DAfStb			FHWA-HRT-23			LBM
Beams	${V}_{\mathrm{e}\mathrm{x}\mathrm{p}}$	${\sigma }_{\mathrm{f}}$	${V}_{\mathrm{c}\mathrm{a}\mathrm{l}}$	$\delta$	${\sigma }_{\mathrm{f}}$	${V}_{\mathrm{c}\mathrm{a}\mathrm{l}}$	$\delta$	$\theta$	${V}_{\mathrm{c}\mathrm{a}\mathrm{l}}$	$\delta$	${\sigma }_{\mathrm{f}}$	${V}_{\mathrm{c}\mathrm{a}\mathrm{l}}$	$\delta$
B-λ-1	562	6.9	492	−1.3%	6.3	555	−12.5%	41.5	516	−8.1%	6.9	594	5.7%
B-λ-1.5	606	7.2	503	−6.5%	6.5	567	−17.0%	40.2	557	−8.0%	7.2	601	−0.8%
B0	618	9.1	593	−6.3%	6.7	579	−4.1%	38.3	615	−0.5%	9.1	632	2.2%
B-λ-2.5	644	9.3	602	−8.2%	7.0	591	−6.5%	38.3	633	−1.8%	9.3	637	−1.1%
B-S-T	611	7.4	515	−11.8%	6.0	539	−15.7%	38.3	554	−9.3%	7.4	609	−0.4%
B-S-H	655	9.9	626	−7.1%	7.3	609	−4.4%	38.3	657	0.3%	9.9	650	−0.7%
B-L-6	603	9.5	609	−2.4%	6.9	589	1.0%	40.2	586	−2.8%	9.5	639	6.0%
B-L-13	620	8.0	543	−10.4%	6.3	555	−12.4%	38.3	578	−6.8%	8.0	619	−0.1%
Average				−6.7%			−8.9%			−4.6%			1.3%
Notes: ${V}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ is the experimental shear capacity; ${V}_{\mathrm{c}\mathrm{a}\mathrm{l}}$ is the calculated shear capacity; $\delta$ is the relative difference of ${V}_{\mathrm{c}\mathrm{a}\mathrm{l}}$ with respect to ${V}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ .

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长摘要

目的
超高性能混凝土(Ultra-High Performance Concrete, UHPC)因其优异的力学性能和耐久性，在桥梁等基础设施中得到了广泛应用。抗剪性能是UHPC梁设计中的关键控制因素，掺入钢纤维能显著增强其抗剪能力，但增强机理和量化模型仍不完善。本文旨在系统探讨钢纤维掺量、形状及尺寸对预应力UHPC矩形梁抗剪性能的影响，揭示其抗剪机理，并通过试验研究、数值模拟和理论分析为UHPC梁的设计提供科学依据。
方法
设计并开展了8根长3.1 m、高0.35 m的UHPC矩形梁抗剪试验。试验以钢纤维体积掺量(1%、1.5%、2%、2.5%)、形状(平直型、扭曲型、弯钩型)和尺寸(14 mm/0.22 mm、6 mm/0.12 mm、13 mm/0.32 mm)为变量，采用四点加载法，重点分析荷载-挠度关系、裂缝扩展规律及破坏模式。基于混凝土塑性损伤模型(Concrete Damage Plasticity, CDP)开展数值模拟，进一步探讨不同设计参数下抗剪承载力对钢纤维掺量的敏感性。理论分析方面，基于极限平衡法分析抗剪机理构建UHPC梁抗剪承载力预测模型，并与法国NF P18-710、德国DAfStb及美国FHWA-HRT-23规范方法进行对比验证。
结果
试验结果表明，UHPC梁的抗剪过程可分为弹性阶段、带裂缝工作阶段和极限状态阶段。钢纤维通过剪跨区裂缝的桥接作用改善剪压区的应力分布，延缓主裂缝扩展和失稳过程，从而显著提升抗剪能力和延性。掺量从1%提高至2.5%时，抗剪承载力平均提升10.7%；弯钩型钢纤维表现出显著的增韧效果，使延性提升41.7%，并在限制裂缝宽度和数量方面效果最佳。掺量和形状对梁体破坏模式的转变有重要影响。在掺量较小(1%)时，梁体表现出脆性的斜拉破坏；而在较高掺量和复杂纤维形状作用下，梁体逐渐表现出延性的剪压破坏或弯剪破坏，当掺量达到2.5%时表现出弯曲破坏。采用塑性损伤模型的数值模拟能较好地再现试验梁的荷载-挠度曲线和破坏模式，抗剪承载力的平均误差为3%，但对极限状态下变形的预测略低于试验值(误差为-7.7%)。参数分析发现，钢纤维对抗剪性能的增强效果随剪跨比的减小而减弱；在剪跨比为1的条件下，纤维掺量从1%增至2.5%时，抗剪承载力仅提升2.6%。钢纤维与受拉钢筋及箍筋之间存在显著的协同作用，在较高箍筋率条件下，钢纤维的增效作用相对减弱；而纵向受拉钢筋率及预应力的变化对抗剪性能影响较小。理论分析表明，UHPC梁的抗剪承载力由未开裂区域混凝土的压力、钢纤维的拉应力和箍筋等部分共同组成，现有设计标准均考虑了上述贡献。法国和德国规范单独考虑了钢纤维桥接应力的数值，但将其计入抗剪贡献时采用了简化变角桁架模型导致了偏于保守的结果(平均误差分别为-8.9%和-6.7%)。美国FHWA-HRT-23规范基于改进压力场理论推导，计算值与试验结果更为接近(平均误差为-4.6%)，但在低掺量条件下略显不足。极限平衡法预测精度最好，平均误差控制仅1.3%。
结论
系统揭示了钢纤维掺量、形状及尺寸对预应力UHPC矩形梁抗剪性能的影响规律，明确了钢纤维通过桥接裂缝和优化剪压区应力分布显著提升梁体抗剪承载力和延性的作用机理。研究表明，高掺量(≥2%)和复杂形状(弯钩型或长径比大的钢纤维)对抗剪承载力和延性的提升最为显著；钢纤维对剪跨比较大或箍筋率较低梁体的增效作用尤为突出。此外，提出的极限平衡法在预测UHPC梁抗剪承载力时表现出较高的精度，优于现行国际规范。

创新点

超高性能混凝土(UHPC)是一种具有卓越性能的纤维增强水泥基材料，已在桥梁等基础设施中得到了广泛应用。然而，钢纤维在提升UHPC梁抗剪性能方面的具体作用机理和量化模型仍不够完善，现有设计方法在预测精度上存在提升空间。
本文通过抗剪试验和数值模拟系统分析了钢纤维掺量、尺寸及形状复杂度对梁抗剪能力的影响。研究结果显示，钢纤维通过桥接裂缝及优化剪压区的应力分布，显著提高了梁的抗剪强度和延性，并改善了破坏模式。将钢纤维掺量从1%提高至2.5%可使抗剪承载力增加10.7%，该效果在较大剪跨比和低配箍率条件下尤为显著。通过对多种抗剪承载力预测方法的比较，美国规范精度优于法国和德国规范，提出的极限平衡法在预测中的误差控制在6%以内，表现出较高的适用性。
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试验梁裂缝分布和破坏模式
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不同(a)剪跨比和(b)配箍率下钢纤维掺量对抗剪承载力的影响