根据修正压力场理论(MCFT)^[9-11]可知, RC梁的抗剪承载力V主要由混凝土和箍筋的抗剪承载力贡献(分别记为V_c和V_s)组成。

由于钢筋的空间锈蚀分布具有非均匀性, 导致其薄弱截面在受力状态下往往会产生应力集中, 从而降低钢筋的强度。其中, 根据钢筋的截面锈损率η_sv可以确定锈蚀箍筋的名义屈服强度f_vyc^[12]。

式中:η_sv=(A_v-A_vc)/A_v, A_v和A_vc分别为箍筋锈

蚀前后的截面积; f_vy为箍筋锈蚀前的屈服强度。

钢筋锈蚀会减小纵筋和箍筋的截面积, 从而降低配筋率和配箍率。其中, 纵筋和箍筋发生锈蚀后, 对应的配筋率ρ_sc和配箍率ρ_vc分别为

式中:b为梁的截面宽度; h₀为梁的截面有效高度; s为箍筋间距; A_sc为纵筋锈蚀后的截面积。

此外, 钢筋锈蚀往往会造成混凝土锈胀开裂或剥落, 所以锈蚀RC梁的有效截面宽度b_c需要根据η_sv进行修正^[13]。

式中:c为混凝土保护层厚度; d_sv为箍筋的直径。

对于外荷载P作用下发生剪切破坏的RC梁, 其斜裂缝分布如图 1所示, 从中选取的微元体Ω的应力平衡条件和应力莫尔圆^[11]如图 2所示。根据微元体Ω的应力平衡条件可得

图 1

图 1 RC梁的斜裂缝分布 Fig. 1 Distribution of diagonal crack of RC beam

图 2

图 2 微元体的应力平衡条件与应力莫尔圆 Fig. 2 Stress balance condition and stress mohr circle of microelement

式中:f_x和f_y分别为x和y方向上的总应力; f₁和f₂分别为垂直于和平行于混凝土裂缝方向的平均主拉应力和平均主压应力; $v = \frac{V}{{\left( {{b_{\rm{c}}}{h_{\rm{v}}}} \right)}}$为剪应力, h_v为截面的有效抗剪高度, 通常近似取h_v=max(0.9h₀, 0.72h), h为RC梁的截面高度; f_sx和f_sy分别为纵向钢筋和横向钢筋的拉应力; θ为临界斜裂缝倾角, 其计算模型为^[14]

式中:λ为剪跨比; k_λ=-0.04λ+1.11, 为剪跨比修正系数; k_nsc=1+(nρ_sc)^-1; k_nvc=1+(nρ_vc)^-1; n=E_s/E_c为钢筋和混凝土之间的弹性模量比, E_s和E_c分别为钢筋和混凝土的弹性模量; α₁=v_c/v=V_c/V, 建议值为0.38^[14]; v_c为与混凝土抗剪承载力贡献值V_c对应的剪应力。由于剪应力v=V/(b_ch_v), 所以可以将式(7)变换为

由式(9)可知, 截面剪应力v由斜拉应力f₁和斜压应力f₂抵抗。其中, f₁满足应力-应变关系^[9]

式中:ε_cr为混凝土的开裂应变, 通常取0.5×10^-3[9]; f′_c为混凝土的抗压强度; ε₁为主拉应变。

RC梁的受力情况如图 3所示, 由竖向力平衡条件可得

图 3

图 3 RC梁的主应力和力平衡示意图 Fig. 3 Principal stress and force balance of RC beam

式中:f_vyc为锈蚀箍筋的名义屈服强度。

根据式(9)的第1和第2个等式分别可得$v = \frac{{{f_1} + {f_2}}}{{\left( {{\rm{tan}}\;\theta + {\rm{cot}}\;\theta } \right)}}$和V=vbh_v, 将v代入V=vbh_v可得$V = \frac{{{f_1} + {f_2}}}{{{\rm{tan}}\;\theta + {\rm{cot}}\;\theta }}b{h_{\rm{v}}}$。根据式(11)可得${f_2} = \frac{{{A_{\rm{v}}}{f_{{\rm{vyc}}}}}}{{bs\;{\rm{si}}{{\rm{n}}^2}\theta }} + \frac{{{f_1}{\rm{co}}{{\rm{s}}^2}\theta }}{{{\rm{si}}{{\rm{n}}^2}\theta }}$, 将f₂代入$V = \frac{{{f_1} + {f_2}}}{{{\rm{tan}}\;\theta + {\rm{cot}}\;\theta }}b{h_{\rm{v}}}$可得

结合式(12)和式(10)可知:抗剪承载力V与f₁有关, 而f₁又与ε₁有关。根据MCFT^[9-11]进一步分析可知, ε₁与斜裂缝间距和θ有关, 而θ又与待求的V有关。所以, 式(12)通常需要通过迭代分析才能求解。为了避免迭代分析, 通过引入ε₁与箍筋屈服应变ε_y的关系来简化计算^[15]。

式中: ${\varepsilon _{\rm{y}}} = \frac{{{f_{{\rm{vyc}}}}}}{{{E_{\rm{s}}}}}$为箍筋的屈服应变。

结合式(1)、式(10)、式(12)和式(13), 可以建立锈蚀RC梁的抗剪承载力分析模型

式中:V_c=f₁b_ch_vcot θ和${V_{\rm{s}}} = \frac{{{A_{\rm{v}}}{f_{{\rm{vyc}}}}{h_{\rm{v}}}{\rm{cot}}\;\theta }}{s}$分别为混凝土和箍筋的抗剪承载力贡献。在实际工程中, 可以先根据现场测试^[16-17]或分析模型^[18]确定混凝土中的钢筋锈蚀率, 然后根据文献[16, 19]确定钢筋的平均锈蚀深度或最大锈蚀深度, 进而根据文献[20]来确定钢筋的截面锈损率η_sv, 最后结合式(2)、式(4)和式(14)可以计算锈蚀RC梁的抗剪承载力。

2 对比分析与验证

选取文献[4, 21-29]中的85组试验数据来验证模型的计算精度和适用性, 见表 1。其中, 锈蚀RC梁的抗剪承载力实测值V_t的范围为41.90~155.80 kN, h₀的范围为150~265 mm, b的范围为100~200 mm, 实测f′_c的范围为14.76~89.40 MPa, λ的范围为1.5~3.5, n的范围为5.98~9.63, ρ_s的范围为1.92%~2.79%, s的范围为150~254 mm, ρ_v的范围为0.19%~0.56%, 实测f_vy的范围为275.00~524.00 MPa; η_ss的范围为0.00%~26.84%, η_sv的范围为0.60%~60.10%。基于上述85组试验数据, 选取文献[3-5, 7]中的4种锈蚀RC梁的抗剪承载力分析模型对比验证模型的计算精度。其中, 文献[3]的锈蚀RC梁的抗剪承载力分析模型为

$ \begin{array}{*{20}{c}} {{V_{{\rm{n1}}}} = \varphi \left( {\frac{{0.08}}{{\lambda - 0.3}} + \frac{{100{\rho _{\rm{s}}}}}{{\lambda {{f'}_{\rm{c}}}}}} \right){{f'}_{\rm{c}}}b{h_0} + }\\ {\gamma '\left( {0.4 + 0.3\lambda } \right)\frac{{{A_{\rm{v}}}{f_{{\rm{vy}}}}}}{s}{h_0}} \end{array} $

(15)

式中:φ和γ′分别为考虑钢筋锈蚀对混凝土和箍筋抗剪承载力贡献影响的经验系数; ρ_s为未锈蚀纵筋的配筋率。

文献[4]的锈蚀RC梁抗剪承载力分析模型为

$ \begin{array}{*{20}{c}} {{V_{{\rm{n2}}}} = {P_{\rm{v}}}\left[ {\frac{{b{h_0}}}{{a/{h_0}}}\frac{{{C_{\rm{s}}}}}{{{h_0}}}\left( {1 - 0.5\frac{C_{\rm{s}}}{{{h_0}}}} \right){{f'}_{\rm{c}}}} \right. + }\\ {\left. {0.5{\rho _{\rm{v}}}{f_{{\rm{vy}}}}{{\left( {1 - \frac{{{C_{\rm{s}}}}}{{{h_0}}}} \right)}^2}\left( {\frac{a}{{{h_0}}}} \right)} \right]} \end{array} $

(16)

式中:P_v为考虑箍筋锈蚀影响的经验修正系数; C_s为混凝土的剪压区高度; a为剪跨; ρ_v为未锈蚀箍筋的配箍率。

文献[5]的锈蚀RC梁抗剪承载力分析模型为

$ {V_{{\rm{n3}}}} = \frac{{1.75}}{{1 + \lambda }}{f_{\rm{t}}}{b_{\rm{c}}}{h_{0{\rm{c}}}} + {f_{{\rm{vyc}}}}\frac{{{A_{{\rm{sv}}}}}}{s}{h_{0{\rm{c}}}} $

(17)

式中:f_t为混凝土的抗拉强度; h_0c为RC梁锈蚀后的有效截面高度。

文献[7]的锈蚀RC梁抗剪承载力分析模型为

$ {V_{{\rm{n4}}}} = 0.17\lambda \sqrt {{{f'}_{\rm{c}}}} {b_{\rm{c}}}{h_0} + \frac{{{A_{{\rm{vc}}}}{f_{{\rm{vy}}}}}}{s}{h_0} $

(18)

文献[3-5, 7]中的4种模型与本文模型的计算值(记为V_d)的对比分析见表 1和图 4。此外, 利用式(19)计算各模型的均方根误差δ_c。

$ {\delta _{\rm{c}}} = \sqrt {\frac{1}{{85}}\sum\limits_{i = 1}^{85} {{{\left( {{V_{{\rm{t}}i}} - {V_{{\rm{p}}i}}} \right)}^2}} } $

(18)

表 1

表 1 85组试验数据的设计参数和抗剪承载力测试值 Table 1 Design parameters and tested shear strength of 85 sets of experimental data 编号 文献 年份 n λ b/mm h0/mm ρs/% ρv/% s/mm fvy/MPa f′c/MPa ηss/% ηsv/% Vt/kN 抗剪承载力的模型计算值/kN Vd Vn1 Vn2 Vn3 Vn4 1 [25] 2007 8.71 1.50 100 175 1.94 0.44 150.00 324.00 23.58 19.98 30.81 43.20 39.29 49.71 52.87 23.68 27.07 2 [25] 2007 8.16 2.50 100 175 1.94 0.44 150.00 324.00 26.82 10.48 17.58 42.10 55.70 50.71 48.93 21.47 38.00 3 [25] 2007 9.63 1.50 100 175 1.94 0.44 150.00 324.00 19.29 0.00 28.60 48.70 50.10 59.92 50.16 22.78 26.69 4 [28] 2010 9.47 2.50 100 175 1.94 0.44 200.00 324.00 19.92 0.00 8.25 41.90 52.40 52.44 48.96 20.21 37.92 5 [25] 2007 8.92 2.50 100 175 1.94 0.44 150.00 324.00 22.45 0.00 8.25 41.90 53.69 54.05 51.79 20.75 38.84 6 [28] 2010 9.47 1.50 100 175 1.94 0.44 200.00 324.00 19.92 0.00 23.03 48.70 49.77 61.91 58.13 22.99 28.22 7 [25] 2007 8.52 2.50 100 175 1.94 0.44 150.00 324.00 24.65 9.41 7.05 43.90 53.70 53.28 54.07 21.05 39.91 8 [25] 2007 9.37 2.50 100 175 1.94 0.44 150.00 324.00 20.37 5.44 5.78 46.80 51.90 53.25 49.48 20.22 38.70 9 [28] 2010 9.47 2.50 100 175 1.94 0.44 200.00 324.00 19.92 0.00 7.10 47.30 52.29 52.79 48.96 20.21 38.21 10 [25] 2007 9.17 2.50 100 175 1.94 0.44 150.00 324.00 21.27 0.00 7.10 47.30 52.98 53.65 50.50 20.50 38.70 11 [25] 2007 9.66 1.50 100 175 1.94 0.44 150.00 324.00 19.17 0.00 15.83 52.10 48.61 62.65 65.86 22.74 29.84 12 [28] 2010 9.47 1.50 100 175 1.94 0.44 200.00 324.00 19.92 0.00 15.82 52.10 48.99 63.53 67.28 22.99 30.02 13 [28] 2010 9.47 1.50 100 175 1.94 0.44 200.00 324.00 19.92 0.00 7.98 53.00 48.23 65.29 74.67 22.99 31.97 14 [28] 2010 9.47 2.50 100 175 1.94 0.44 200.00 324.00 19.92 0.00 4.01 50.80 52.47 53.73 48.96 20.21 38.98 15 [25] 2007 9.32 1.50 100 175 1.94 0.44 150.00 324.00 20.59 0.00 7.98 53.00 48.55 66.06 76.02 23.19 32.12 16 [25] 2007 9.12 1.50 100 175 1.94 0.44 150.00 324.00 21.51 6.30 4.24 52.90 48.51 66.76 77.86 23.36 33.26 17 [24] 2004 7.34 2.00 120 200 1.92 0.32 170.00 275.00 33.16 0.00 34.75 47.65 49.13 73.84 52.86 30.01 39.34 18 [25] 2007 8.16 2.50 100 175 1.94 0.44 150.00 324.00 26.84 0.00 4.01 50.80 55.80 58.13 56.18 21.66 41.39 19 [25] 2007 9.15 1.50 100 175 1.94 0.44 100.00 324.00 21.33 3.71 2.99 54.30 48.54 68.06 77.52 23.36 33.53 20 [24] 2004 7.23 2.00 120 200 1.92 0.32 170.00 275.00 34.16 0.00 22.37 50.20 63.68 77.74 73.12 30.32 42.34 21 [24] 2004 7.23 2.00 120 200 1.92 0.32 170.00 275.00 34.16 0.00 31.88 53.50 49.05 75.61 58.15 30.32 40.33 22 [4] 2008 8.47 2.20 150 155 2.26 0.19 150.00 331.52 24.91 26.00 9.20 62.00 59.10 42.27 70.50 22.85 43.18 23 [4] 2008 8.47 2.20 150 155 2.26 0.19 150.00 331.52 24.91 1.50 0.80 60.00 61.43 63.50 70.50 23.23 44.40 24 [28] 2011 6.15 3.00 150 150 2.68 0.19 200.00 441.50 47.33 26.20 32.30 53.69 71.82 46.33 48.29 27.40 67.39 25 [24] 2004 7.34 2.00 120 200 1.92 0.32 170.00 275.00 33.16 0.00 35.26 61.05 49.20 73.72 52.06 30.01 39.23 26 [28] 2011 6.23 3.00 150 150 2.68 0.19 200.00 441.50 46.12 24.80 32.70 55.43 71.64 47.15 47.21 27.19 66.61 27 [24] 2004 7.34 2.00 120 200 1.92 0.32 170.00 275.00 33.16 0.00 24.56 60.00 63.50 76.12 68.66 30.01 41.49 28 [4] 2008 8.47 2.20 150 155 2.26 0.19 150.00 331.52 24.91 19.00 8.30 67.00 60.00 49.03 70.50 22.98 43.31 29 [24] 2004 7.52 2.00 120 200 1.92 0.32 170.00 275.00 31.65 0.00 18.79 60.15 61.80 75.70 75.87 29.53 42.12 30 [28] 2011 6.83 3.00 150 150 2.68 0.19 200.00 441.50 38.29 5.72 21.50 55.20 84.83 63.93 56.93 26.00 63.94 31 [4] 2008 8.47 2.20 150 155 2.26 0.19 150.00 331.52 24.91 2.80 1.70 65.00 61.40 63.35 70.50 23.21 44.27 32 [24] 2004 7.23 2.00 120 200 1.92 0.32 170.00 275.00 34.16 0.00 30.77 63.05 48.91 75.86 59.90 30.32 40.56 33 [4] 2008 8.47 2.20 150 155 2.26 0.19 150.00 331.52 24.91 8.60 5.10 68.00 60.94 59.39 70.50 23.14 43.78 34 [4] 2008 8.47 2.20 150 155 2.26 0.19 150.00 331.52 24.91 4.20 2.70 68.00 61.37 63.19 70.50 23.19 44.12 35 [4] 2008 8.47 2.20 150 155 2.26 0.19 150.00 331.52 24.91 14.00 7.20 70.00 60.53 53.94 70.50 23.06 43.47 36 [4] 2008 8.47 2.20 150 155 2.26 0.19 150.00 331.52 24.91 6.60 4.00 69.00 61.26 61.47 70.50 23.16 43.94 37 [4] 2008 8.47 2.20 150 155 2.26 0.19 150.00 331.52 24.91 11.60 6.30 72.00 60.72 56.36 70.50 23.10 43.60 38 [24] 2004 7.52 2.00 120 200 1.92 0.32 170.00 275.00 31.65 0.00 19.53 67.30 61.90 75.54 74.74 29.53 41.97 39 [28] 2011 5.97 2.00 150 150 2.68 0.25 150.00 441.50 50.24 24.80 25.30 71.69 87.20 69.40 91.11 37.36 53.21 40 [28] 2011 6.44 2.00 150 150 2.68 0.25 150.00 441.50 43.10 15.80 32.10 78.01 69.20 76.33 71.30 35.71 48.96 41 [4] 2008 8.47 3.10 150 155 2.79 0.25 150.00 331.52 24.91 0.00 1.80 80.00 72.66 62.61 59.15 23.23 57.76 42 [4] 2008 8.47 3.10 150 155 2.79 0.25 150.00 331.52 24.91 0.00 0.60 80.00 72.47 62.94 59.15 23.23 58.00 43 [28] 2011 6.36 2.00 150 150 2.68 0.25 150.00 441.50 44.21 6.30 29.50 76.35 88.66 92.28 77.31 36.23 50.03 44 [23] 2010 6.87 2.00 150 175 2.30 0.25 100.00 275.00 37.89 3.17 2.71 75.90 73.35 94.73 111.52 34.07 52.66 45 [22] 2011 8.11 1.50 120 200 2.62 0.48 150.00 321.80 27.15 0.00 54.15 85.20 65.44 98.66 34.03 40.36 31.75 46 [23] 2010 6.87 2.00 150 175 2.30 0.25 100.00 275.00 37.89 2.44 2.61 77.80 73.44 94.75 111.52 34.08 52.68 47 [23] 2010 6.87 2.20 150 175 2.30 0.25 150.00 275.00 37.89 3.14 2.75 79.00 74.52 88.12 99.89 32.68 56.14 48 [28] 2011 6.21 2.00 150 150 2.68 0.25 150.00 441.50 46.32 7.70 21.30 78.17 87.65 94.47 95.60 36.77 52.85 49 [23] 2010 6.87 2.20 150 175 2.30 0.25 100.00 275.00 37.89 3.12 2.71 82.50 74.52 88.12 99.89 32.68 56.15 50 [23] 2010 6.87 2.00 150 175 2.30 0.25 100.00 275.00 37.89 2.04 1.85 83.00 73.37 94.90 111.52 34.09 52.82 51 [4] 2008 8.47 3.10 150 155 2.79 0.25 150.00 331.52 24.91 0.00 4.00 92.00 73.00 62.02 59.15 23.23 57.34 52 [4] 2008 8.47 3.10 150 155 2.79 0.38 254.00 331.52 24.91 0.00 0.70 80.00 81.69 76.14 67.50 29.63 64.22 53 [4] 2008 8.47 3.10 150 155 2.79 0.45 150.00 331.52 24.91 0.00 0.80 76.00 86.91 83.21 72.01 33.07 73.25 54 [4] 2008 8.47 3.10 150 155 2.79 0.38 150.00 331.52 24.91 0.00 3.50 84.00 82.16 74.98 67.50 29.63 63.40 55 [4] 2008 8.47 3.10 150 155 2.79 0.38 203.00 331.52 24.91 0.00 0.40 84.00 81.64 76.26 67.50 29.63 64.31 56 [4] 2008 8.47 3.10 150 155 2.79 0.25 150.00 331.52 24.91 0.00 2.40 96.00 72.75 62.45 59.15 23.23 57.65 57 [4] 2008 8.47 3.10 150 155 2.79 0.45 150.00 331.52 24.91 0.00 3.80 80.00 87.43 81.75 72.01 33.07 72.21 58 [4] 2008 8.47 3.10 150 155 2.79 0.38 254.00 331.52 24.91 0.00 2.20 88.00 81.94 75.52 67.50 29.63 63.78 59 [23] 2010 6.87 1.80 150 175 2.30 0.25 100.00 275.00 37.89 3.41 2.77 96.00 72.19 103.25 127.11 35.66 49.16 60 [4] 2008 8.47 3.10 150 155 2.79 0.45 150.00 331.52 24.91 0.00 3.80 92.00 87.43 81.75 72.01 33.07 72.21 61 [4] 2008 8.47 3.10 150 155 2.79 0.45 150.00 331.52 24.91 0.00 3.70 92.00 87.41 81.80 72.01 33.07 72.24 62 [4] 2008 8.47 3.10 150 155 2.79 0.45 150.00 331.52 24.91 0.00 2.00 96.00 87.11 82.63 72.01 33.07 72.83 63 [4] 2008 8.47 3.10 150 155 2.79 0.38 150.00 331.52 24.91 0.00 4.90 104.00 82.40 74.41 67.50 29.63 62.99 64 [22] 2011 8.11 1.50 120 200 2.62 0.56 150.00 463.90 27.15 0.00 25.74 131.50 102.74 123.98 105.72 55.83 63.73 65 [22] 2011 8.11 1.50 120 200 2.62 0.56 150.00 463.90 27.15 0.00 19.54 128.10 101.38 127.46 120.93 55.83 67.60 66 [22] 2011 8.11 1.50 120 200 2.62 0.56 150.00 463.90 27.15 0.00 11.73 129.00 99.82 131.86 140.09 55.83 72.48 67 [29] 2013 6.62 3.00 200 265 2.15 0.20 150.00 433.00 40.80 12.10 60.10 115.40 147.01 109.54 24.04 73.49 159.04 68 [29] 2013 6.62 3.50 200 265 2.15 0.25 150.00 373.00 40.80 8.10 44.30 109.80 143.48 119.40 64.32 71.81 182.40 69 [29] 2013 6.62 3.00 200 265 2.15 0.20 150.00 373.00 40.80 8.60 46.50 119.80 131.89 120.94 59.05 69.02 161.88 70 [29] 2013 6.62 2.50 200 265 2.15 0.14 200.00 476.00 40.80 2.20 17.60 111.80 129.70 157.26 154.37 71.89 139.72 71 [29] 2013 6.62 3.50 200 265 2.15 0.25 200.00 433.00 40.80 7.60 40.80 111.20 153.59 129.45 78.10 77.66 188.83 72 [29] 2013 5.98 2.50 200 265 2.15 0.14 150.00 339.00 49.95 1.60 13.30 119.80 125.52 166.69 175.61 70.15 144.20 73 [29] 2013 5.98 3.00 200 265 2.15 0.20 150.00 433.00 49.95 8.30 44.10 115.80 146.32 140.69 74.22 78.71 181.36 74 [29] 2013 5.98 3.00 200 265 2.15 0.20 150.00 524.00 49.95 5.40 32.40 109.80 155.37 162.94 115.72 85.93 193.25 75 [29] 2013 5.98 2.00 200 265 2.15 0.19 100.00 476.00 49.95 7.10 51.10 129.20 136.06 196.07 77.94 95.31 115.94 76 [29] 2013 6.62 2.50 200 265 2.15 0.14 150.00 339.00 40.80 0.90 7.60 137.80 115.91 150.81 168.92 64.42 133.86 77 [29] 2013 5.98 3.00 200 265 2.15 0.20 150.00 373.00 49.95 5.30 30.50 125.70 133.02 150.53 110.64 74.18 183.18 78 [29] 2013 5.98 2.50 200 265 2.15 0.14 150.00 458.00 49.95 7.30 51.40 133.50 129.79 153.25 57.36 76.48 138.91 79 [21] 1997 6.62 2.00 200 265 2.15 0.19 150.00 339.00 40.80 7.50 54.20 147.70 113.25 165.50 56.15 78.48 99.24 80 [29] 2013 5.98 3.50 200 265 2.15 0.25 150.00 373.00 49.95 5.20 29.90 121.60 163.24 147.32 110.42 76.43 206.00 81 [29] 2013 6.62 3.50 200 265 2.15 0.25 200.00 524.00 40.80 7.00 40.80 121.30 171.74 140.40 85.09 86.53 195.97 82 [26] 2006 5.98 3.50 200 265 2.15 0.25 150.00 433.00 49.95 7.10 38.90 121.70 159.09 143.59 90.02 82.16 206.41 83 [29] 2013 6.62 2.00 200 265 2.15 0.19 150.00 458.00 40.80 8.10 55.60 151.60 129.80 168.05 52.45 87.22 104.08 84 [29] 2013 5.98 3.50 200 265 2.15 0.25 150.00 524.00 49.95 5.60 33.20 121.70 174.57 162.85 116.42 91.10 217.73 85 [29] 2013 5.98 2.50 200 265 2.15 0.14 150.00 476.00 49.95 5.40 40.70 155.80 127.08 163.84 93.14 77.53 143.34

表 1 85组试验数据的设计参数和抗剪承载力测试值 Table 1 Design parameters and tested shear strength of 85 sets of experimental data

图 4

图 4 抗剪承载力的模型计算值与试验值的对比 Fig. 4 Comparison between tested and calculated shear strength

式中:V_ti和V_pi分别为第i根锈蚀RC梁的抗剪承载力测试值和模型计算值。根据计算结果可知, V_n1、V_n2、V_n3、V_n4和V_d的δ_c分别为18.77、30.09、45.10、35.63和18.21 kN。由此可见, 本文模型的δ_c最小, 说明模型的计算精度更高。

结合图 4和表 1可知, V_t与V_n1的比值的均值(标准差)为0.95(0.20), 说明V_n1具有一定的计算精度, 但是该模型无法揭示锈蚀RC梁的抗剪机理; V_t与V_n2、V_n3和V_n4的比值的均值(标准差)分别为1.16(0.59)、2.27(0.58)和1.32(0.40), 说明这3个模型的计算值总体偏小, 且离散性较大, 原因在于, 上述模型考虑的影响因素不全面且缺乏严密的理论基础; V_t与V_d的比值的均值(标准差)为1.01(0.17), 说明模型的离散性较小, 且计算精度较高, 主要原因在于该模型是基于修正压力场理论推导建立的, 具有较为严密的理论基础, 而且综合考虑了多种重要因素的影响。

3 结论

基于修正压力场理论, 建立了锈蚀RC梁的抗剪承载力分析模型, 并利用85组试验数据开展了对比验证分析。分析结果表明:

1) 该模型的计算值与试验值的比值的均值与1.0比较接近, 且标准差较小, 说明模型的计算精度高、离散性小。

2) 锈蚀RC梁的传统抗剪承载力模型大多属于经验模型, 考虑的影响因素不全面且缺乏严密的理论推导, 导致计算精度有限。

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