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摘要: 为揭示水泥路面接缝传力杆周围混凝土的受力特性与损伤机理，基于ABAQUS有限元软件，介绍了混凝土损伤塑性(CDP)模型及其参数确定方法，应用CDP模型模拟了混凝土试件单轴拉伸和压缩试验，通过对比模型试验结果验证了CDP模型参数的准确性；在此基础上，建立了接缝设置传力杆的水泥路面三维有限元模型，分析了在不同轴载作用下水泥路面接缝传力杆周围混凝土的塑性应变、损伤因子和等效应力的分布和发展规律，对比了采用CDP模型与混凝土弹性模型时传力杆周围混凝土的应力差异。分析结果表明：对于混凝土单轴拉伸、压缩试件，基于CDP模型的应力-变形全曲线模拟结果均与试验结果一致，说明CDP模型及其参数确定方法准确；对于接缝设传力杆的水泥路面，当荷载作用在接缝传力杆黏结端上方板边时，传力杆黏结端混凝土的受力最为不利；随着轴载的增大，传力杆黏结端底部混凝土率先发生损伤塑性，等效应力逐渐减小；当轴载从100 kN增大至250 kN时，传力杆周围混凝土塑性区范围从底部135°~225°扩展至60°~300°，底部150°~210°范围内混凝土发生完全损伤塑性而退出工作，等效应力趋于0，应力重分布导致更多的荷载由传力杆两侧和上部混凝土承担；若传力杆周围混凝土采用弹性模型，传力杆底部混凝土等效应力将不断增大而超过极限强度，因此，分析传力杆周围混凝土应力集中问题建议采用CDP模型。Abstract: To reveal the mechanical characteristics and damage mechanism of concrete around the dowel bars at the joints in cement pavement, the concrete damaged plasticity (CDP) model and the method for determining its parameters were introduced on the basis of the finite element software ABAQUS. The uniaxial tension and compression tests of concrete specimens were simulated by the CDP model, and the accuracies of the CDP model parameters were verified by the comparison of model test results. On this basis, a three-dimensional finite element model of cement pavement with dowel bars at joints was built to analyze the distribution and development laws of the plastic strain, damage factor, and equivalent stress of concrete around the dowel bars at the joints subjected to different axle loads. Under the CDP model and elastic model of concrete, the difference between the two models in the stress of concrete around the dowel bars was compared. Analysis results show that for the uniaxial tension and compression specimens of concrete, the entire stress-deformation curves achieved by the simulation with the CDP model are consistent with the test results, indicating that the CDP model and its parameters are accurate. For the cement pavement with dowel bars at joints, when the load is applied at the edge of upper slab of the bonded end of a dowel bar, the stress in the concrete around the bonded end of the dowel bar is most disadvantageous. With the increase in the axle loads, the damaged plasticity is encountered first in the concrete at the bottom of bonded end of the dowel bar, and the equivalent stress reduces gradually. When the axle load raises from 100 kN to 250 kN, the range of plastic zone extends from 135°-225° at the bottom to 60°-300° for the concrete around the dowel bar. The concrete in the range of 150°-210° at the bottom is subjected to failure due to the complete damaged plasticity, and the equivalent stress becomes zero. More loads are borne by the concrete on both sides and at the top of the dowel bar due to the stress redistribution. If the elastic model is adopted for the concrete around the dowel bar, the equivalent stress of the concrete at the bottom of the dowel bar will be on the rise to exceed the ultimate strength. Therefore, the CDP model is recommended to analyze the stress concentration of concrete around the dowel bars.
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Key words:
- pavement engineering /
- cement pavement /
- concrete damaged plasticity /
- joint /
- dowel bar
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图 1 混凝土单轴受力状态下的应力-应变曲线
Figure 1. Stress-strain curves of concrete under uniaxial force
图 2 混凝土试件应力-非弹性应变和损伤因子-非弹性应变曲线
Figure 2. Stress-inelastic stain and damage factor-inelastic stain curves of concrete specimens
图 3 数值模拟与试验应力-变形曲线
Figure 3. Stress-deformation curves of numerical simulation and tests
图 13 混凝土为弹性时传力杆周围混凝土的应力
Figure 13. Stresses of concrete around dowel bar as concrete is elastic
表 1 混凝土基本力学性质参数
Table 1. Fundamental mechanical property parameters of concrete
力学性质参数 计算公式 参数值 弯拉强度fr/MPa 5.5 立方体抗压强度fcu/MPa fcu=1.1(fr/0.438)3/2 48.947 轴心抗拉强度ft/MPa ft=0.24fcu2/3 3.211 峰值拉应变εtr/10-3 εtr=6.7×10-5ft1/2 0.120 轴心抗压强度fc/MPa fc=0.4fcu7/6 37.446 峰值压应变εcr/10-3 εcr=5.2×10-4fc1/3 1.738 初始弹性模量E0/MPa E0=ft/εtr 26 700 
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表 2 混凝土单轴拉伸损伤塑性参数
Table 2. Damaged plastic parameters of concrete under uniaxial tension
σt εt/10-3 εti/10-3 dt 3.211 0.120 0.000 0.000 2.923 0.144 0.035 0.038 2.519 0.168 0.074 0.120 2.171 0.192 0.111 0.213 1.895 0.216 0.145 0.300 1.678 0.240 0.177 0.377 1.506 0.264 0.208 0.445 1.367 0.288 0.237 0.502 1.158 0.336 0.293 0.594 0.950 0.408 0.373 0.691 0.743 0.528 0.500 0.789 0.564 0.720 0.699 0.869 0.495 0.840 0.822 0.897 0.371 1.200 1.186 0.941 0.303 1.560 1.548 0.962 0.259 1.919 1.910 0.973 0.228 2.279 2.270 0.979 0.205 2.638 2.630 0.984 0.187 2.997 2.990 0.987
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表 3 混凝土单轴压缩损伤塑性参数
Table 3. Damaged plastic parameters of concrete under uniaxial compression
σc εc/10-3 εci/10-3 dc 33.265 1.241 0.000 0.000 35.330 1.391 0.070 0.005 36.930 1.564 0.184 0.022 37.446 1.738 0.336 0.047 34.184 2.085 0.807 0.122 28.117 2.433 1.381 0.218 22.626 2.780 1.934 0.316 18.392 3.127 2.439 0.406 15.239 3.473 2.904 0.483 12.878 3.820 3.339 0.548 9.678 4.513 4.151 0.648 6.929 5.552 5.293 0.747 4.964 6.935 6.749 0.825 3.638 8.661 8.525 0.881 2.863 10.384 10.277 0.914 2.358 12.104 12.016 0.934
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表 4 试件力学性质参数
Table 4. Mechanical property parameters of specimens
力学性质参数 参数值 轴心抗拉强度ft/MPa 3.2 峰值拉应变εtr/10-3 0.107 轴心抗压强度fc/MPa 46.5 峰值压应变εcr/10-3 1.830 初始弹性模量E0/MPa 30 000
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表 5 路面结构尺寸和材料参数
Table 5. Structural dimensions and material parameters of pavement
结构 长(m)×宽(m)×厚(m) 模量/MPa 泊松比 面层 4.0×3.6×0.26 26 700 0.20 基层 9.0×4.6×0.2 2 500 0.20 底基层 9.0×4.6×0.2 250 0.25 路基 9.0×4.6×6.0 80 0.35
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表 6 荷载参数
Table 6. Loading parameters
轴载/kN 接地压强/MPa 轮印宽/cm 轮印长/cm 50 0.44 22 12.91 100 0.57 22 19.94 150 0.71 24 22.01 200 0.85 24 24.51 250 0.97 24 26.85
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