CFRP网格-聚合物水泥砂浆加固RC梁抗剪承载力计算方法

王博; 王媛媛; 王征鹏; 张军雷; 王天松

doi:10.13801/j.cnki.fhclxb.20220419.004

CFRP网格-聚合物水泥砂浆加固RC梁抗剪承载力计算方法

doi: 10.13801/j.cnki.fhclxb.20220419.004

1.
长安大学　建筑工程学院，西安 710061
2.
日本東京都立大学　都市基盤環境学域，东京 192-0397

基金项目: 陕西省青年科技新星项目(2021KJXX-17)

详细信息

通讯作者:
王博，博士，教授，博士生导师，研究方向为工程抗震与韧性提升　E-mail: chnwangbo@chd.edu.cn

中图分类号: TU
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出版历程
- 收稿日期: 2022-01-20
- 修回日期: 2022-04-11
- 录用日期: 2022-04-12
- 网络出版日期: 2022-04-20
- 刊出日期: 2023-02-15

Study on calculation method of RC beam's shear bearing capacity of CFRP grid-polymer cement mortar

1.
School of Civil Engineering, Chang’an University, Xi’an 710061, China
2.
Department of Civil and Environmental Engineering, Tokyo Metropolitan University, Tokyo 192-0397, Japan

Funds: Shaanxi Province Youth Science and Technology Nova Project (2021KJXX-17)

摘要

摘要: 为揭示碳纤维增强树脂复合材料(Carbon fiber reinforced polymer，CFRP)网格-聚合物水泥砂浆(Polymer cement mortar，PCM)抗剪加固钢筋混凝土(RC)梁的受剪机制并建立其承载力计算方法，对RC梁进行了四点弯曲试验和有限元模拟，重点分析了CFRP网格对RC加固梁的抗剪贡献，建立了基于改进的桁架拱模型的抗剪承载力计算方法。结果表明：RC梁侧粘贴CFRP网格-PCM加固层不仅可以抑制斜裂缝的发展，而且还提高了抗剪承载力；CFRP网格与钢筋之间具有良好的协同工作性能，其中，横向CFRP网格筋分担了约16%的箍筋应变；回归分析指出纵向CFRP网格筋的应变约为横向CFRP网格筋应变的0.29倍；综合考虑纵向CFRP网格的销栓作用和横向CFRP网格分担的箍筋应变，提出了基于改进桁架-拱模型的承载力计算方法，具有更好的适用性和准确性，能够满足设计要求。
- CFRP网格-PCM抗剪加固RC梁 /
- 四点弯曲试验 /
- 有限元分析 /
- 改进的桁架-拱模型 /
- 承载力计算方法
Abstract: In order to reveal the shear mechanism of the carbon fiber reinforced polymer (CFRP) grid-polymer cement mortar (PCM) shear reinforced reinforced concrete (RC) beam and establish its bearing capacity calculation method, four-point bending tests and finite element simulation were conducted on the RC beams. The shear contribution of the CFRP grid to the RC reinforced RC beam was analyzed, and the shear bearing capacity calculation method was established based on the improved truss arch model. The results show that the CFRP grid-PCM reinforcement layer can not only inhibit the development of inclined cracks, but also improve the shear bearing capacity. CFRP grid and reinforcement have good cooperative working performance, where the horizontal CFRP grid shares about 16% of the stirrup strain. Regression analysis indicates that the strain of the vertical CFRP grid is about 0.29 times than that of the horizontal CFRP grid. Comprehensively considering the dowel action of the longitudinal CFRP grid and the stirrup strain shared by the horizontal CFRP grid, the bearing capacity calculation method is presented based on the improved truss-arch model, which has better applicability and accuracy to meet the design requirements.
- CFRP grid-PCM shear-reinforced RC beam /
- four-point bending test /
- finite element analysis /
- improved truss-arch model /
- bearing capacity calculation method

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图 1 试件尺寸及配筋图

Figure 1. Drawing of specimen size and reinforcement

P—Load

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图 2 试验加载示意图

Figure 2. Schematic diagram of experimental loading

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图 3 位移计和应变片布置位置

C-1-C-6—Surface strain gauge of specimen; D1-D8—Displacement sensor; S-1-S-7—Reinforcement strain gauge of BS and BGS

Figure 3. Position of displacement gauge and strain gauge

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图 4 CFRP网格-PCM加固钢筋混凝土(RC)梁有限元模型

RP—Reinforced polymer

Figure 4. CFRP grid-PCM reinforced concrete (RC) beam finite element model

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图 5 试验梁BGS剪切破坏裂缝分布

Figure 5. Distribution of shear failure cracks in BGS specimen

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图 6 CFRP网格-PCM加固RC梁试验与有限元模拟破坏形态对比

Figure 6. Comparison of failure modes between the test of CFRP grid-PCM shear-reinforced RC beams and finite element simulation

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图 7 CFRP网格-PCM加固RC梁荷载-位移曲线对比

Figure 7. Comparison of load-displacement curves of CFRP grid-PCM shear-reinforced RC beams

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图 8 试件BS和BGS的荷载-钢筋应变曲线

Figure 8. Load-steel strain curves of BS and BGS specimens

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图 9 荷载-CFRP网格应变曲线

G1, G2, G11, G13, G18, G20, G21, G24, G28, G29, G36, G40—Strain gauges

Figure 9. Load-CFRP grids strain curves

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图 10 纵向和横向CFRP网格与箍筋之间的相互作用

Figure 10. Interactions between the vertical and horizontal CFRP grids and the stirrups

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图 11 纵向和横向CFRP网格筋应变的关系曲线

λ—Shear span ratio; f_c—Compressive strength of the concrete; ρ_g—CFRP grid reinforcement rate; E_g—Elastic modulus of the CFRP grid; ε_u—Effective strain of the FRP grid bars

Figure 11. Strain curves of CFRP grid in horizontal and vertical directions

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图 12 改进的桁架拱模型

Figure 12. Improved truss arch model

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图 13 基于不同FRP网格抗剪加固RC梁承载力计算方法的计算结果比较

Figure 13. Comparison of calculation results of calculation methods for the bearing capacity of RC beams strengthened with different FRP grids

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表 1 试件设计

Table 1. Specimen design

Specimen	Existing steel bars			FRP grid	Shear span λ	PCM thickness/ mm	Existing vertical reinforcement ratio/%	Anti-shear reinforcement ratio/%
Specimen	Tensile reinforcement	Handling reinforcement	Stirrup	FRP grid	Shear span λ	PCM thickness/ mm	Existing vertical reinforcement ratio/%	Anti-shear reinforcement ratio/%
BS	D32-SD345	D10-SD345	D10-SD345@200	—	2.63	—	5.8	0.36
BG	D32-SD345	—	—	CR8-100×100		20	5.6	0.22
BGS	D32-SD345	D10-SD345	D6-SD345@200	CR8-100×100		20	5.8	0.35
Notes: B—Reinforced concrete beam; S—Beam is equipped with stirrup; G—Stick carbon fiber reinforced polymer (CFRP) grid-polymer cement mortar (PCM) reinforcement layer on both sides; BS—Reinforced concrete beams provided with stirrups; BG—Reinforced concrete beam with only CFRP-PCM reinforced layer without stirrup; BGS—Reinforced concrete beams with stirrups and CFRP-PCM reinforcement layer; D—Diameter; SD—Reinforcement strength grade; CR8—CFRP grid of 8 mm in diameter; FRP—Fiber reinforced polymer.

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表 2 混凝土配合比

Table 2. Concrete mix proportion

Maximum grain size/mm	Colony/ mm	Water cement ratio/%	Air ratio/%	Measurement unit/(kg·m^–3)
Maximum grain size/mm	Colony/ mm	Water cement ratio/%	Air ratio/%	Water	Cement	Fine aggregate	Coarse aggregate	Admixture
20	120	55.6	4.5	158	284	792	1126	1.3

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表 3 混凝土和聚合物水泥砂浆(PCM)材料性能

Table 3. Properties of concrete and polymer cement mortar (PCM) materials

Material	Compression strength/MPa	Tensile strength/MPa	Modulus of elasticity/GPa
Concrete	34.1	2.92	31.9
PCM	36.7	2.87	30.1

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表 4 钢筋与碳纤维增强树脂复合材料(CFRP)网格的力学性能

Table 4. Mechanical properties of steel and carbon fiber reinforced polymer (CFRP) grids

Material	Type	Cross-sectional area/mm²	Yield strength /MPa	Modulus of elasticity/GPa	Tensile strength /MPa
Concrete iron	D32	794.2	389	200	587
	D10	71.3	413	200	561
	D6	31.7	417	200	570
CFRP grid	CR8	26.4	—	100	1400

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表 5 混凝土塑性损伤模型参数取值

Table 5. Parameters of plastic damage model for concrete

Type	Expansion angle ψ	Offset ε	$ {\sigma _{{\text{b0}}}}/{\sigma _{{\text{c0}}}} $	K_c	Coefficient of viscosity μ
Value	38	0.1	1.16	0.6667	0.0005
Notes: $ {\sigma _{{\text{b0}}}}/{\sigma _{{\text{c0}}}} $—Ratio of biaxial and uniaxial compression limit strength; K_c—Ratio of stretching and the second stress invariant on the compression meridian.

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表 6 CFRP网格-PCM加固RC梁试验结果汇总

Table 6. Summary of test results for CFRP grid-PCM shear-reinforced RC beams

Specimen	Peak load P/kN		$ {P_{\text{t}}}/{P_{\text{c}}} $	Cross-mid deflection D/mm		$ {D_{\text{t}}}/{D_{\text{c}}} $	Shear cracking load P_s/kN		$ {P_{{\text{st}}}}/{P_{{\text{sc}}}} $
Specimen	Test value P_t/kN	Simulation value P_c/kN	$ {P_{\text{t}}}/{P_{\text{c}}} $	Test value D_t/mm	Simulation value D_c/mm	$ {D_{\text{t}}}/{D_{\text{c}}} $	Test value P_st/kN	Simulation value P_sc/kN	$ {P_{{\text{st}}}}/{P_{{\text{sc}}}} $
BS	690	614	1.12	8.35	8.07	1.03	210	172	1.22
BG	617	601	1.03	7.09	6.77	1.05	225	188	1.19
BGS	757	722	1.05	7.40	7.39	1.00	320	256	1.25

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表 7 RGS试件参数信息

Table 7. Parameter information of RGS specimens

Specimen	Stirrup	Stirrup ratio /%	Grid type-spacing: Vertical and horizontal /(mm×mm)	Reinforcement ratio /%	Ultimate load /kN
RGS-S200	D6-SD345@200	0.16	CR8-100×100	0.22	722.2
RGS-S150	D6-SD345@150	0.21			737.7
RGS-S100	D6-SD345@100	0.32			746.4
RGS-H100 V150	D6-SD345@200	0.16	CR8-100×150	0.15	711.9
RGS-H100 V100			CR8-100×100	0.22	722.2
RGS-H100 V50			CR8-100×50	0.44	774.2
Notes: RGS—Reinforced concrete (RC) beam with stirrup and CFRP-PCM reinforcement layer; S200—Stirrup spacing is 200 mm; H—Horizontal grid spacing; V—Vertical grid spacing.

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表 8 CFRP网格-PCM加固RC梁试件与未加固试件参数信息

Table 8. Parameter information of CFRP grid-PCM shear-reinforced RC beam specimens and unreinforced specimens

Type of specimen	Specimen number	Vertical reinforcement		Stirrup	CFRP grid	PCM thickness /mm	Horizontal grid ratio/%
Type of specimen	Specimen number	Tensile reinforcement	Compressive reinforcement	Stirrup	CFRP grid	PCM thickness /mm	Horizontal grid ratio/%
First group	NRS-50	6-D32-SD345	2-D10-SD345	D6-SD345@200	—	—	—
First group	RGS-50				CR8@50	20	0.44
Second group	NRS-100				—	—	—
Second group	RGS-100				CR8@100	20	0.22
Third group	NRS-150				—	—	—
Third group	RGS-150				CR8@150	20	0.15
Notes: NRS-50—Reinforced concrete (RC) beam with no CFRP-PCM reinforcement layer but with stirrup in 50 mm spacing (NRS-100 and NRS-150 are in the same manner); RGS-50—Reinforced concrete (RC) beam with CFRP-PCM reinforcement layer and stirrup in 50 mm spacing (RGS-100 and RGS-150 are in the same manner).

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表 9 纵向和横向CFRP网格应变信息汇总

Table 9. Summary of grid strain information for horizontal and vertical CFRP

Specimen	Shear span λ	Concrete strength/MPa		CFRP grid type	Ratio $ {\rho _{\text{g}}} $/%	PCM thickness/ mm	Vertical grid strain $ {\varepsilon _{{\text{ver}}}} $/$ {10^{ - 6}} $	Horizontal grid strain $ {\varepsilon _{{\text{hor}}}} $/$ {10^{ - 6}} $
Specimen	Shear span λ	Tensile strength $ {f_{\text{t}}} $	Compression strength $ {f_{\text{c}}} $	CFRP grid type	Ratio $ {\rho _{\text{g}}} $/%	PCM thickness/ mm
RGS1	2.6	2.92	34.1	CR8@50	0.44	20	2853.17	367.52
							2993.50	511.91
							2919.94	548.94
RGS2	2.6	2.92	34.1	CR8@100	0.22		2581.23	551.82
							2837.57	1003.05
							2599.29	920.19
RGS3	2.6	2.92	34.1	CR8@150	0.15		2029.87	825.87
							3905.37	1088.63
							3461.74	988.99
RGS4	1.8	2.92	34.1	CR8@100	0.22		3735.11	913.96
							3564.48	1299.26
							3570.80	1245.58
RGS5	2.2	2.92	34.1	CR8@100	0.22		3625.54	1150.78
							3141.04	1094.90
							3260.70	1078.79
RGS6	2.6	2.20	26.6	CR8@100	0.22		2337.90	571.62
							2200.77	770.38
							2289.55	794.90
RGS7	2.6	2.64	38.0	CR8@100	0.22		2494.30	704.24
							3012.34	1069.08
							2389.03	834.12

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表 10 不同FRP网格抗剪加固RC梁抗剪承载力计算值与试验值比较

Table 10. Comparison of calculated and experimental values of shear capacity of RCbeams strengthened with different FRP grids

Data sources	Specimen	$ {P_{{\text{exp}}}} /{\rm{kN}}$	$ {P_{{\text{cal}}}} $^[5]/kN	$ {P_{{\text{cal}}}}/{\rm{kN}} $	$ {P_{{\text{exp}}}}/{P_{{\text{cal}}}} $^[5]	$ {P_{{\text{exp}}}}/{P_{{\text{cal}}}} $	$ {P_{{\text{exp}}}}/{P_{{\text{cal}}}} $ analysis		$ {P_{{\text{exp}}}}/{P_{{\text{cal}}}} $^[5] analysis
Data sources	Specimen	$ {P_{{\text{exp}}}} /{\rm{kN}}$	$ {P_{{\text{cal}}}} $^[5]/kN	$ {P_{{\text{cal}}}}/{\rm{kN}} $	$ {P_{{\text{exp}}}}/{P_{{\text{cal}}}} $^[5]	$ {P_{{\text{exp}}}}/{P_{{\text{cal}}}} $	Mean value	Variable coefficient	Mean value	Variable coefficient
Text	BG	617	330	466	1.87	1.32	1.22	0.16	1.85	0.32
Text	BGS	757	414	562	1.83	1.35
[5]	RCF4	881	768	625	1.15	1.41
	RCF6	949	887	704	1.07	1.35
	RCF8	943	939	769	1.00	1.23
	RCF4’	950	810	721	1.17	1.32
	RCF64	860	823	704	1.04	1.22
[6]	PGB	352	105	290	3.35	1.21
[11]	S150-CGM	677	449	458	1.51	1.48
[11]	S250-CGM	571	248	428	2.30	1.33
[12]	L3	373	186	385	2.00	0.97
[12]	L4	511	253	385	2.01	1.33
[21]	NO.2	588	320	408	1.84	1.44
[21]	NO.4	631	332	498	1.90	1.27
[22]	SB1	376	245	304	1.53	1.24
	SB2	449	230	446	1.95	1.01
	SB3	471	190	601	2.48	0.78
[23]	SB2-3	449	229	441	1.96	1.02
[24]	D	195	122	255	1.60	0.76
[25]	C35 S3-M2-G2	674	261	472	2.58	1.43
[25]	C40 S0-M2-G2 bc	484	181	395	2.67	1.22
Notes: $ {P_{{\text{cal}}}} $—Shear bearing capacity of the FRP grid reinforced RC beam which is calculated based on the proposed method; $ {P_{{\text{exp}}}} $—Shear bearing capacity of the FRP grid reinforced RC beam which is calculated based on the corresponding test; RCF4, RCF6 and RCF8—Reinforced by CR4 CFRP, CR6 CFRP and CR8 CFRP grid whose vertical reinforcement interval was 50 mm compared with 150 mm of other specimens (CR4, CR6 and CR8 are the type of the CFRP grid in ABAQUS); RCF4'—Reinforced by CR4 CFRP grid whose vertical reinforcement interval was 50 mm compared with 50 mm of other specimens; RCF64—Reinforced by CR6&4 CFRP grid whose horizontal grid was CR4 and vertical grid was CR6; PGB—Beam was strengthened with high strength PCM and high strength carbon fiber-reinforced plastics (CFRP) gride bars; S150-CGM and S250-CGM—Beam with CFRP grid embedded in mortar (CGM), and the beam with 6 mm stirrups @150 mm c/c and @250 mm c/c; L3—Fiber grid and polymer mortar reinforced concrete beams (FRP GRID&NC-RC); L4—Fiber grid and engineered cementitous composite (ECC) reinforced concrete beams (FRP GRID&ECC-RC); NO.2 and NO.4—Beam with 2 row and 4 row of CFRP grid; SB1, SB2, SB3—FRP grid used in the ultra high toughness cementitious composite (UHTCC) layer (Measured thickness: 1 mm, 3 mm and 5 mm respectively); SB2-3—A 3 mm BFRP grid reinforced ECC composite SB2 reinforced concrete beam; D—RC beam strengthened with FRP grid; C35 S3-M2-G2—Beam C35 S3 with stirrup was strengthed by the use of mortar 2 and grid M; C40 S0-M2-G2 bc—Beam C40 S0 without stirrup but was strengthed by the use of mortar 2 and grid M; c/c—Center/Center; BFRP—Boron fiber reinforced plastic.

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