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摘要: 采用弹性地基板理论分析了道面板应力的主要影响因素, 修正了公路标准轴载下路面板的应力计算公式, 得到了飞机荷载下道面板的应力计算公式形式。采用正交设计法对道面结构参数进行安排, 计算了不同道面结构在各种类型飞机荷载下道面板的应力。采用非线性回归方法对应力计算值和飞机荷载参数与道面结构参数进行分析, 得到了单轮飞机荷载下水泥混凝土道面板的应力计算公式。对单轮飞机荷载应力计算公式引入荷载圆半径修正系数, 并采用多元非线性回归方法, 得到了双轮和双轴双轮飞机荷载下道面板的应力计算公式。利用荷载叠加原理得到多轴多轮飞机荷载下道面板应力计算公式。误差分析结果表明: 回归应力计算值与有限元应力计算值相对误差不超过2%, 应力计算公式具有较好的精度。Abstract: With elastic base theory, the main influence factors of stress for pavement slab under plane loads were analyzed, the calculating formula form of stress was deduced by modifying the stress formula of highway pavement under standard axis load.Pavement's structural parameters were organized by orthogonal design method, and the stresses under different combinations of plane loads and pavement structures were calculated by FEM.The stresses and parameters were analyzed by nonlinear regression method, and the calculating formulae of stress under single wheel plane load were got.By introducing the modifying coefficient of load radius, the calculating formulae of stress under dual-wheel and dual-wheel-dual-axes plane loads were deduced by nonlinear regression method.The calculating formulae of stress under multi-wheel-multi-axes loads were deduced by combined load theory.Error analysis result indicates that the relative errors between the calculating results by nonlinear regression method and FEM are less than 2%, so the stress formulae have high precision.
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图 3 单轮飞机荷载下随h变化的公式计算值与FEM计算值
Figure 3. Comparison of calculation values by formula and FEM with change of h under single wheel plane load
图 4 单轮飞机荷载下随Ec/Et变化的公式计算值与FEM计算值
Figure 4. Comparison of calculation values by formula and FEM while Ec/Et changing under single wheel plane load
图 5 单轮飞机荷载下随tdx变化的公式计算值与FEM计算值
Figure 5. Comparison of calculation values by formula and FEM when tdx changing under single wheel plane load
图 6 双轮飞机荷载下随h变化的公式计算值与FEM计算值
Figure 6. Comparison of calculation values by formula and FEM when h changing under dual-wheel plane load
图 7 双轮飞机荷载下随Ec/Et变化的公式计算值与FEM计算值
Figure 7. Comparison of calculation values by formula and FEM when Ec/Et changing under dual-wheel plane load
图 8 双轮双轴飞机荷载下随h变化的公式计算值与FEM计算值
Figure 8. Comparison of calculation values by formula and FEM when h changing under dual-wheel-dual-axes plane load
图 9 双轮双轴飞机荷载下随Ec/Et变化的公式计算值与FEM计算值
Figure 9. Comparison of calculation values by formula and FEM when Ec/Et changing under dual-whee-dual-axes plane load
表 1 道面结构参数水平
Table 1. Levels of pavement's structural parameters
水平 因素 h/m td Ec/GPa Et/MPa 1 0.20 0.55 32 165 2 0.27 0.70 34 210 3 0.34 0.80 36 265 4 0.40 0.90 38 315 
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表 2 正交设计
Table 2. Orthogonal design
计算号 因素水平 h td Ec Et 1 1 1 2 4 2 1 2 3 3 3 1 3 4 2 4 1 4 1 1 5 2 1 2 3 6 2 2 3 2 7 2 3 4 1 8 2 4 1 4 9 3 1 2 2 10 3 2 3 1 11 3 3 4 4 12 3 4 1 3 13 4 1 2 1 14 4 2 3 4 15 4 3 4 3 16 4 4 1 2
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表 3 单轮飞机荷载下纵缝位置部分点应力计算值
Table 3. Part stress values at longitudinal joint under single wheel plane load
FEM计算值 回归公式(3)计算值 相对误差/% 3.107 3.085 0.71 2.992 2.970 0.83 2.876 2.858 0.63 2.819 2.807 0.43 2.628 2.580 1.85 2.525 2.492 1.32 2.414 2.401 0.53 2.246 2.213 1.46
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表 4 单轮飞机荷载下横缝位置部分点应力计算值
Table 4. Part stress values at transverse joint under single wheel plane load
FEM计算值 回归公式(4)计算值 相对误差/% 2.804 2.795 0.30 2.296 2.295 0.03 3.201 3.213 0.36 2.579 2.591 0.47 2.126 2.143 0.80 1.980 2.019 1.95 2.152 2.148 0.20 1.924 1.912 0.62
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表 5 表 5σpd与Krd的计算结果
Table 5. Calculating results ofσpdand Krd
h/m Ec/GPa Et/MPa σpd/MPa Krd 0.20 35 315 3.88 1.084 0.22 36 265 3.52 1.096 0.24 37 210 3.22 1.104 0.28 36 265 2.60 1.115 0.32 35 315 2.16 1.122 0.26 38 165 2.96 1.109 0.30 37 210 2.42 1.117 0.34 36 265 2.02 1.121 0.36 37 210 1.89 1.120 0.38 38 165 1.79 1.117
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表 6 双轮飞机荷载下纵缝位置部分点应力计算值
Table 6. Part stress values at longitudinal joint under dual-wheel plane load
FEM计算值 回归公式(5)计算值 相对误差/% 2.587 2.551 1.39 2.141 2.117 1.12 2.946 2.907 1.32 2.400 2.372 1.17 1.995 1.983 0.60 1.872 1.873 0.05 1.761 1.777 0.91 4.332 4.317 0.35 3.871 3.862 0.23 3.534 3.507 0.76 2.855 2.819 1.26
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表 7 双轮双轴飞机荷载下纵缝位置部分点应力计算值
Table 7. Part stress values at longitudinal joint under dual-wheel-dual-axes plane load
FEM计算值 回归公式计算值 相对误差/% 2.949 3.006 1.93 2.642 2.689 1.78 2.406 2.440 1.41 1.948 1.964 0.82 1.626 1.631 0.31 2.215 2.236 0.95 1.819 1.825 0.33 1.529 1.526 0.20 1.450 1.440 0.69 1.381 1.365 1.16
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表 8 双轮双轴飞机荷载下横缝位置部分点应力计算值
Table 8. Part stress values at transverse joint under dual-wheel-dual-axes plane load
FEM计算值 回归公式计算值 相对误差/% 1.871 1.883 0.64 1.592 1.607 0.94 1.521 1.538 1.12 1.457 1.478 1.44 5.093 4.970 2.42 4.551 4.474 1.69 4.129 4.090 0.94 3.324 3.318 0.18 2.760 2.777 0.62 1.871 1.883 0.64
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