Flexural damage assessment for UHPC panels under blast loadings
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摘要: 为构建爆炸荷载作用下超高性能混凝土（UHPC）板弯曲损伤等级评估的p-I（压力-冲量）曲线：采用条带法进行截面分析，建立了考虑UHPC材料拉/压软化和塑性铰影响的UHPC简支单向板的非线性抗力方程和等效单自由度（ESDOF）理论模型；通过与六炮次爆炸实验中UHPC板的挠度时程，以及UFC 3-340-02和FHWA规范推荐方法的计算结果对比，验证了本文理论模型的可靠性；基于验证的ESDOF模型，构建了评估UHPC板的不同弯曲损伤等级的p-I曲线并开展了参数影响分析，提出并验证了UHPC板弯曲损伤评估的p-I曲线经验公式。结果表明：提高混凝土强度等级和钢筋屈服强度、增加受拉钢筋配筋率和板厚，以及减小净跨均可提升UHPC板的抗爆性能。Abstract: To establish the p-I (pressure-impulse) diagram for flexural damage assessment of ultra-high performance concrete (UHPC) panels under blast loadings, cross-sectional analysis using the strip method was performed to establish the moment curvature relationship for simply supported one-way UHPC panels. This process involved considering the tensile/compressive softening of UHPC through the utilization of material constitutive models with softening properties and describing the strain rate effect of UHPC and reinforcement with the dynamic increase factor (DIF) that varies according to different strip layers. Subsequently, the nonlinear resistance function considering the effect of plastic hinge was developed, based on the moment curvature relationship and a simplified half-span symmetric beam model. Then, an equivalent single degree of freedom (ESDOF) theoretical model, adopting the nonlinear resistance function, was established and employed to predict the deflection-time histories of UHPC panels under explosions. The reliability of the above theoretical model was verified by comparing the predicted results with the deflection time histories of test UHPC panels in six shots of explosion tests. Additionally, the superiority of the proposed ESDOF model was proved by comparing with the corresponding calculation results obtained from the recommended methods using bilinear ideal elastic-plastic resistance functions based on the UFC 3-340-02 and FHWA codes. Furthermore, based on the verified ESDOF model, p-I diagrams for evaluating the flexural damage level of UHPC panels were established and parametric analysis was carried out. The results indicate that increasing the concrete strength grade, yield strength of reinforcement, tensile reinforcement ratio, and panel thickness, while reducing the clear span, are beneficial for the blast-resistant performance of UHPC panels. Finally, empirical formulae for p-I diagrams, taking into consideration the abovementioned influencing factors, were proposed and verified for assessing the flexural damage of UHPC panels. These formulae can serve as a valuable reference for evaluating blast-induced damage in UHPC panels.
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图 6 非线性抗力方程的建立及荷载-质量转换系数与挠度关系
Figure 6. Nonlinear resistance function and the relationship between KLM and deflection
图 8 UHPC板的预测挠度时程与实验/数值模拟结果对比
Figure 8. Comparisons of predicted deflection-time histories and experimental/simulated results of UHPC panels
图 9 UHPC-D4的预测挠度时程与实验结果的对比
Figure 9. Comparisons of predicted and experimental deflection-time histories of UHPC-D4
图 10 UHPC板的ESDOF模型预测挠度时程与实验结果对比
Figure 10. Comparisons of ESDOF model predicted deflection time histories and experimental results of UHPC panels
图 12 不同混凝土强度等级UHPC板的p-I曲线
Figure 12. p-I diagrams for UHPC panels with different concrete strength grades
图 13 不同钢筋屈服强度UHPC板的p-I曲线
Figure 13. p-I diagrams for UHPC panels with different yield strengths of reinforcement
图 14 不同纵筋配筋率UHPC板的p-I曲线
Figure 14. p-I diagrams for UHPC panels with different longitudinal reinforcement ratios
图 15 不同厚度UHPC板的p-I曲线
Figure 15. p-I diagrams for UHPC panels with different thicknesses
图 16 不同净跨UHPC板的p-I曲线
Figure 16. p-I diagrams for UHPC panels with different clear spans
图 17 基于ESDOF模型分析生成的p-I曲线与经验公式预测结果对比
Figure 17. Comapriosns between p-I diagrams from ESDOF model ananlysis and empirical formulae
表 2 UHPC板的尺寸、配筋及材料特性参数
Table 2. Dimensions, reinforcement and material properties parameters of UHPC panels
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表 3 ESDOF模型预测峰值挠度与实验/数值模拟结果对比
Table 3. Comparisons of ESDOF model predicted and experimental/simulated maximum deflections
实验 试件 实验值/mm 模拟值/mm UFC 3-340-02 FHWA 本文 预测值/mm 误差/% 预测值/mm 误差/% 预测值/mm 误差/% Su等[1] UHPC-1 27.86 27.44 27.73 −0.5 17.39 −37.6 26.42 −5.2 UHPC-2 − 38.90 41.89 7.6 24.92 −35.9 37.25 −4.2 UHPC-3 − 48.13 55.98 16.3 32.56 −32.3 47.67 −1.0 Li等[2] UHPC-D4 72 − 123.99 72.2 49.95 −30.6 73.11 1.5 Mao等[3] A 110 − 113.24 2.9 88.24 −19.8 111.44 1.3 B 210 − 193.32 −7.9 145.24 −30.8 213.46 1.6
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表 4 UHPC板弯曲损伤
$p{\text{-}}I $ 曲线经验公式相关参数Table 4. Parameters of the empirical formulae of flexural damage p-I diagrams for UHPC panels
影响因素 参数 表达式 θ=2° θ=5° 基准板 pb0 106 127 Ib0 1214 2228 βb 1.634 1.642 100≤fc/MPa≤250 $ {\eta _{{f_{\text{c}}}}} $ 0.717 + 0.325 (fc/150) − 0.042 (fc/150)2 0.251 + 1.065 (fc/150) − 0.319 (fc/150)2 $ {\lambda _{{f_{\text{c}}}}} $ 0.839 + 0.187 (fc/150) − 0.025 (fc/150)2 0.614 + 0.550 (fc/150) − 0.167 (fc/150)2 $ {\alpha _{{f_{\text{c}}}}} $ 0.951 + 0.065 (fc/150) − 0.013 (fc/150)2 0.993 + 0.002 (fc/150) + 0.005 (fc/150)2 300≤fy/MPa≤600 $ {\eta _{{f_{\text{y}}}}} $ 0.293 + 1.061 (fy/500) − 0.354 (fy/500)2 0.191 + 1.106 (fy/500) − 0.295 (fy/500)2 $ {\lambda _{{f_{\text{y}}}}} $ 0.635 + 0.571 (fy/500) − 0.206 (fy/500)2 0.534 + 0.700 (fy/500) − 0.233 (fy/500)2 $ {\alpha _{{f_{\text{y}}}}} $ 1.034 − 0.081 (fy/500) + 0.047 (fy/500)2 0.999 − 0.017 (fy/500) + 0.017 (fy/500)2 0.393A0/Ac≤ρt/%
≤1.728A0/Ac$ {\eta _{{\rho _{\text{t}}}}} $ 0.292 + 0.791 (ρtAc/0.864A0) − 0.087 (ρtAc/0.864A0)2 0.159 + 0.947 (ρtAc/0.864A0) − 0.123 (ρtAc/0.864A0)2 $ {\lambda _{{\rho _{\text{t}}}}} $ 0.619 + 0.448 (ρtAc/0.864A0) − 0.071 (ρtAc/0.864A0)2 0.524 + 0.572 (ρtAc/0.864A0) − 0.107 (ρtAc/0.864A0)2 $ {\alpha _{{\rho _{\text{t}}}}} $ 0.998 − 0.001 (ρtAc/0.864A0) + 0.005 (ρtAc/0.864A0)2 0.973 + 0.032 (ρtAc/0.864A0) − 0.005 (ρtAc/0.864A0)2 100≤h/mm≤250 ηh −0.294 + 0.928 (h/100) + 0.377 (h/100)2 −0.603 + 1.536 (h/100) + 0.071 (h/100)2 λh −0.452 + 1.353 (h/100) + 0.101 (h/100)2 −0.438 + 1.376 (h/100) + 0.062 (h/100)2 αh 0.834 + 0.211 (h/100) − 0.045 (h/100)2 0.928 + 0.090 (h/100) − 0.018 (h/100)2 1000≤L/mm≤4000 ηL 0.187 − 28.977 0.029L/2000 0.218 − 23.259 0.034L/2000 λL 0.492 − 2.586 0.200L/2000 0.533 − 2.265 0.210L/2000 αL 1.201 − 0.213 (L/2000) + 0.022 (L/2000)2 1.185 − 0.203 (L/2000) + 0.021 (L/2000)2
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表 5 验证板的参数取值
Table 5. Parameter values for the validation panels
板编号 fc/MPa fy/MPa ρt/% h/mm L/mm 1 100 300 0.393 100 4000 2 200 300 0.864 200 3000 3 120 550 1.047 150 2500
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