Numerical simulation and theoretical analysis of flexural strengthening of RC beams with high-strength steel strand mesh/ECC
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摘要: 采用有限元模拟与试验相结合的方法，研究了加固层材料用量、加固材料材性、RC梁特征参数等因素对高强钢绞线网/ECC (Engineered cementitious composites)抗弯加固RC (Reinforced concrete)梁受弯性能的影响规律。首先，建立了高强钢绞线网/ECC加固既有无损RC梁有限元分析模型，并与试验结果比较，验证了其准确性和有效性，并采用该模型对关键参数对加固梁受弯性能的影响规律进行系统性分析。结果表明：该加固方法可显著提升RC梁的受弯承载力、刚度、延性，提升幅度分别7.81%~61.84%，6.35%~40.90%，5.92%~50.16%；随着纵向钢绞线配筋率、加固层厚度和开裂应力的增大，承载力的提升幅度增大，而RC梁纵筋配筋率和截面高度增大会降低承载力的提升幅度；加固层厚度与纵向钢绞线配筋率的增大会增加刚度的提升幅度，而RC梁纵筋配筋率、混凝土强度和截面高度的增大会降低对刚度的提升幅度；延性的提升幅度随着混凝土强度的增大而增加。在此基础上结合相关力学理论，提出抗弯加固界限钢绞线用量计算公式及高强钢绞线网/ECC加固RC梁正截面承载力简化计算公式，与试验及数值模拟结果吻合良好。Abstract: Using a combination of finite element simulation and experimentation, the impact of reinforcement layer material quantity, properties of reinforcement materials, and characteristic parameters of RC (Reinforced Concrete) beams on the flexural performance of RC beams strengthened with high-strength steel wire mesh/ECC (Engineered Cementitious Composites) was investigated. Firstly, the finite element (FE) analysis model of existing nondestructive RC beams strengthened with high-strength steel wire mesh/ECC was established, and its effectiveness and accuracy were verified by comparing with the experimental results. The validated FE model was adopted to analyze the influencing factors of flexural performance of strengthened beams systematically. The results indicate that the strengthening method can significantly enhance the flexural bearing capacity, stiffness, and ductility of RC beams, with improvement ranges of 7.81% to 61.84%, 6.35% to 40.90%, and 5.92% to 50.16% respectively. With the increase of longitudinal steel strand reinforcement ratio, thickness and cracking stress of ECC, the promotion range of bearing capacity increases, while the increase of longitudinal steel reinforcement ratio and section height of RC beams decrease the increment of bearing capacity. The increase of the thickness of ECC and the reinforcement ratio of longitudinal steel strand increase the promotion range of stiffness, but the promotion range decreases with the increment of longitudinal reinforcement ratio, concrete strength and section height of RC beams. The increment of ductility only increases with the increase of concrete strength. On this basis, combined with relevant mechanical theories, the calculation formula for the limit amount of steel strands for flexural strengthening and simplified calculation formulas for the normal-section bearing capacity of RC beams reinforced by high-strength steel wire strand mesh-reinforced ECC are proposed, calculation results are in good agreement with experimental and numerical simulation results.
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图 4 各加固RC梁试件弯矩-跨中挠度曲线对比
Figure 4. Comparison of bending moment-midspan deflection curve of strengthened RC beam specimens
图 5 各加固RC梁试件弯矩-跨中混凝土压应变曲线对比
Figure 5. Comparison of bending moment-midspan concrete compression-strain curve of strengthened RC beam specimens
图 6 各加固RC梁试件弯矩-受拉纵筋跨中应变曲线对比
Figure 6. Comparison of bending moment-strain curve of longitudinal reinforcement in tension of strengthened RC beam specimens
图 7 各加固RC梁试件弯矩-钢绞线跨中应变曲线对比
Figure 7. Comparison of bending moment-strain curve of steel strand in midspan of strengthened RC beam specimens
图 8 不同ECC加固层厚度试件荷载-挠度曲线
Figure 8. Load-deflection curves of specimens with different ECC strengthening layer thicknesses
图 9 不同纵向钢绞线配筋率试件荷载-挠度曲线
Figure 9. Load-deflection curves of specimens with different longitudinal steel strand reinforcement ratios
图 10 不同ECC开裂应力试件荷载-挠度曲线
Figure 10. Load-deflection curves of specimens with different ECC cracking stresses
图 11 不同ECC极限抗拉强度试件荷载-挠度曲线
Figure 11. Load-deflection curves of specimens with different ECC ultimate tensile strength
图 12 不同纵筋配筋率试件弯矩-挠度曲线
Figure 12. Bending moment-deflection curves of specimens with different reinforcement ratios
图 13 不同混凝土强度试件荷载-挠度曲线
Figure 13. Load-deflection curves of specimens with different concrete strengths
图 14 不同RC梁高度试件荷载-挠度曲线
Figure 14. Load-deflection curves of specimens with different heights of RC beam
图 15 加固RC梁不同设计参数的评价指标均一化结果
(a) Evaluation metric Mcr; (b) Evaluation metric Ms,y; (c) Evaluation metric Mu; (d) Evaluation metric Be; (e) Evaluation metric Bc; (f) Evaluation metric μΔ ;
Figure 15. Normalized results of evaluation indicators for different design parameters of strengthened RC beams
图 16 加固RC梁截面应变和应力分布
Figure 16. Distribution of cross-section strain and stress of strengthened RC beams
h—Height of the reinforced beam section; hsw—Distance from the steel strand to the top of the compression zone; h0—Effective height of the concrete section；h1—Thickness of the reinforcement layer; εc—Concrete compressive strain; εcu—Ultimate compressive strain value of concrete under non-uniform compression; xn—Height of the compression zone; εsw—Tensile strain in the steel strand; εsw,y—The strain corresponding to the nominal yield stress of the steel strand; εy—Ultimate tensile strain of the reinforcement; εe—Tensile strain of the reinforcement layer; Ts—Tensile force provided by the reinforcement; Tsw—Tensile force provided by the steel strand; TE—Tensile force provided by the reinforcement layer; Cc—Compressive force provided by the concrete
图 17 加固RC梁承载力公式计算值与试验值/模拟值间的离散程度
Figure 17. Dispersion degree between calculated value of bearing capacity formula and test value/simulation value of strengthened RC beams
表 1 试件设计
Table 1. Design of test specimens
Test specimen d/mm ρ/%(n) ECC formula[26] A-2 3.0 0.580 (5) Formula 1 A-3 3.0 0.812 (7) Formula 1 B-1 3.0 0.580 (5) Formula 2 B-2 3.0 0.580 (5) Formula 3 C-1 4.5 0.515 (2) Formula 1 D-1 3.6 0.686 (4) Formula 1 Notes: d—Diameter of steel strand; n—Number of longitudinal steel strands; ρ—Longitudinal steel strand reinforcement ratio. 
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表 2 ECC力学性能指标
Table 2. Mechanical properties of ECC
ECC
formula[26]fe/MPa Ee/GPa σkm/MPa εkm/% σtu/MPa εe,u/% 1 37.3 14.1 1.37 0.025 2.18 1.88 2 46.5 14.6 1.91 0.035 2.81 0.75 3 36.6 14.3 1.86 0.032 2.30 2.47 Notes: fe—Compressive strength of ECC; Ee—Elastic modulus of ECC; σkm—Cracking stress of ECC；εkm—Cracking strain of ECC; σtu—Ultimate tensile strength of ECC; εe,u—Ultimate tensile strain of ECC.
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表 3 高强钢绞线拉伸试验数据
Table 3. High-strength steel strand tensile test data
d/mm A/mm2 Erw/GPa σswu /MPa εu/% 3.0 4.35 139 1919.02 2.96 3.6 6.43 109 1521.21 3.47 4.5 9.65 130 1706.46 3.37 Notes: A—Cross-sectional area of the steel strand; Erw—Elastic modulus of steel strand；σswu—Ultimate tensile strength of the steel strand ; εu—Ultimate tensile strain of the steel strand
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表 4 加固RC梁试件参数设计以及有限元计算结果
Table 4. Parameter design of strengthened RC beam specimens and finite element calculation results
Specimen
Numberρs/% ρrw/% σkm/MPa σtu/MPa FM Mcr/(kN·m) Ms,y/(kN·m) Mu/(kN·m) Be Bc μ△ DB-0 0.936 — — — — 2.73 13.14 15.62 — — 3.21 DB-14 1.283 — — — — 2.77 17.87 20.07 — — 2.23 DB-16 1.686 — — — — 2.81 22.09 23.94 — — 1.56 DB-18 2.148 — — — — 2.86 25.89 27.21 — — 1.15 DB-35 0.936 — — — — 2.84 13.35 15.99 — — 3.33 DB-40 0.936 — — — — 2.97 13.64 16.28 — — 3.42 DB-45 0.936 — — — — 3.07 14.22 16.75 — — 3.59 DB-250 0.936 — — — — 3.97 21.89 25.89 — — 2.97 DB-300 0.936 — — — — 5.61 34.72 39.54 — — 2.52 MLA-20 0.936 0.58 1.5 2.5 CP 3.72 16.32 22.88 1.22 1.17 4.39 MLA-25 0.936 0.58 1.5 2.5 CP 3.86 16.72 23.29 1.28 1.18 4.19 MLA-30 0.936 0.58 1.5 2.5 CP 4.05 17.15 23.44 1.35 1.19 3.91 MLA-35 0.936 0.58 1.5 2.5 CP 4.29 17.34 23.63 1.41 1.2 3.63 MLB-0 0.936 0 1.5 2.5 CP 3.77 15.54 16.84 1.27 1.12 4.82 MLB-3 0.936 0.348 1.5 2.5 CP 3.82 16.17 20.56 1.27 1.15 4.38 MLB-7 0.936 0.812 1.5 2.5 CE 3.99 17.29 24.36 1.28 1.22 3.74 MLB-9 0.936 1.044 1.5 2.5 CE 4.1 17.7 25.28 1.29 1.25 3.4 MLE-1.5 0.936 0.58 1.5 4.5 CP 3.86 16.78 23.59 1.29 1.18 3.97 MLE-2.0 0.936 0.58 2 4.5 CP 4.06 17.18 23.94 1.29 1.2 3.91 MLE-2.5 0.936 0.58 2.5 4.5 CP 4.24 17.56 24.12 1.29 1.21 3.88 MLE-3.0 0.936 0.58 3 4.5 CP 4.42 17.95 24.38 1.29 1.22 3.87 MLF-2.5 0.936 0.58 2.5 2.5 CP 4.24 17.24 23.76 1.29 1.2 4.22 MLF-3.5 0.936 0.58 2.5 3.5 CP 4.24 17.39 24.07 1.29 1.2 4.07 MLF-5.5 0.936 0.58 2.5 5.5 CP 4.24 17.67 24.49 1.29 1.21 3.77 MLG-14 1.283 0.58 1.5 2.5 CP 4 20.31 25.37 1.21 1.13 2.87 MLG-16 1.686 0.58 1.5 2.5 CP 4.12 24.46 28.44 1.17 1.09 1.95 MLG-18 2.148 0.58 1.5 2.5 CE 4.27 28.31 31.49 1.15 1.06 1.42 MLH-35 1.283 0.58 1.5 2.5 CE 3.99 17.03 23.67 1.23 1.15 4.37 MLH-40 1.686 0.58 1.5 2.5 CP 4.13 17.26 24.04 1.2 1.12 4.52 MLH-45 2.148 0.58 1.5 2.5 CP 4.24 17.38 24.41 1.17 1.1 4.65 MLI-250 0.936 0.58 1.5 2.5 R 5.67 27.25 35.71 1.15 1.17 3.86 MLI-300 0.936 0.58 1.5 2.5 CP 7.8 40.08 50.36 1.1 1.13 3.27 Notes: Specimen number (DB—Non-reinforced; ML—simulated RC beam, A-I—The group number；The number after the “-” indicates the value of the varying parameter in that group); ρs—RC beam longitudinal reinforcement ratio; ρrw—Longitudinal steel strand reinforcement ratio in the reinforcement layer; FM—Failure mode; CP—Due to concrete crushing to reach ultimate bearing capacity and concrete crushing occurs after the steel strand reaches nominal yield stress; CE—Due to concrete crushing to reach ultimate bearing capacity and concrete crushing occurs before the steel strand reaches nominal yield stress; R—Due to steel strand breaking to reach ultimate bearing capacity and steel strand breaking occurs before concrete crushing; Mcr—Cracking moment；Ms,y—Yield moment of reinforcement；Mu—Failure load; Be—Stiffness ratio in the elastic stage；Bc—Stiffness ratio during the cracked working stage.
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表 5 高强钢绞线界限用量
Table 5. Limit dosage of high strength steel strand
Specimen
NumberSectional area
of the steel
strand /mm2Relative values of stress and strain
during concrete crushingσs/fy εs/εy σsw/fsw,y εsw/εsw,y MLB-0 0 — — — — MLB-1 4.35 (1) 1 11.98 Tensile rupture Tensile rupture MLB-2 6.70 (2) 1 10.53 1.16 2.05 MLB-3 13.05 (3) 1 9.98 1.14 1.77 MLB-4 17.40 (4) 1 9.46 1.13 1.42 MLB-5 21.75 (5) 1 9.04 1.09 1.33 MLB-6 26.10 (6) 1 8.65 1.04 1.14 MLB-7 30.45 (7) 1 7.23 0.99 0.99 MLB-8 34.80 (8) 1 6.32 0.98 0.95 MLB-9 39.15 (9) 1 3.99 0.96 0.87
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