Characterization of Vertical and Horizontal Propagations of Double Cracks in Asphalt Pavements under Moving Loads
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摘要: 为了研究移动荷载作用下沥青路面的复合开裂的变化规律，基于断裂力学及有限元数值模拟方法，考虑沥青面层材料的粘弹性，分别研究了移动荷载作用下不同双裂纹间距、不同反射裂纹深度对面层top-down（纵向）、基层反射（横向）裂纹应力强度因子的影响，探讨了其开裂扩展特性，评估了不同移动荷载状态下面层top-down裂纹的断裂疲劳寿命.结果表明：移动荷载作用下，面层top-down裂纹以Ⅱ型扩展为主，在单裂纹及双裂纹间距为0时，分别对应其扩展最严重与最轻微情形，但双裂纹间距及反射裂纹深度对其扩展影响较小；对于基层反射裂纹，当双裂纹间距为400 mm时，最易发生Ⅰ、Ⅱ型开裂扩展，随着反射裂纹深度的增加，扩展程度也逐渐增大；不同移动荷载状态下的top-down复合型裂纹断裂疲劳寿命长短顺序为：高速最长，次之静态、低速制动最短，制动情形下的疲劳寿命仅为高速情形下的20.4%.Abstract: The purpose of this research is to analyse the evolution of vertical and horizontal propagations of double cracks in asphalt pavements under moving loads using fracture mechanics and finite-element numerical simulations. In this regard, the effects of cracking space and reflective cracking depth on surface top-down cracking and base layer reflective cracking were studied by considering the viscoelastic behaviour of the surface material. Subsequently, crack propagation was characterized and the fatigue lives due to surface top-down cracking under different moving load levels were evaluated. The results indicated that surface top-down cracking mainly occurred in the type Ⅱ mode. Moreover, the cases of single crack and zero crack spacing corresponded to the conditions of most critical and noncritical propagations, respectively. However, crack spacing and the depth of reflective cracking did not have a significant influence on its propagation. For base layer reflective cracking, the most severe type Ⅰ and Ⅱ propagations occurred within a 400 mm cracking space, and the crack propagation level grew with increasing depth. The fatigue lives due to top-down mixed mode cracking under different moving load levels ranked in descending order as high speed, static state, low speed, and braking state. The fatigue life in the braking state was only 20.4% of that in the high-speed state.
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图 6 不同裂纹间距下top-down裂纹Ⅰ、Ⅱ、Ⅲ型应力强度因子时程曲线
Figure 6. TypeⅠ, Ⅱ, and Ⅲ stress intensity factor-time history curves of a top-down crack for different crack spacings
图 8 不同裂纹间距下反射裂纹应力强度因子时程曲线
Figure 8. Stress intensity-time history curve of a reflective crack for different crack spacings
图 9 不同C2下top-down裂纹Ⅰ、Ⅱ、Ⅲ型应力强度因子时程曲线
Figure 9. TypeⅠ, Ⅱ, and Ⅲ stress intensity factor-time history curves of a top-down crack under different C2
图 10 不同反射裂纹深度下Keff变化规律
Figure 10. Keff variation diagram for different reflection crack depths
图 11 不同反射裂纹深度下反射裂纹应力强度因子时程曲线
Figure 11. Stress intensity factor-time history curves of a reflective crack for different crack depths
表 1 路面结构各层参数
Table 1. Material parameters of different pavement layers
材料 层位 动态模量/MPa 泊松比 密度/
(kg·m-3)沥青混凝土 面层 — 0.25 2 400 水泥稳定碎石 基层 15 000 0.20 2 200 水泥稳定碎石 底基层 13 000 0.20 2 100 土基 土基 100 0.35 1 800 
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表 2 面层Prony级数模型参数
Table 2. Prony parameters of the surface material
参数 瞬态弹性模量E0=18 GPa 松弛时间/s 0.2 2.0 20.0 2×102 2×103 2×104 2×105 2×106 弹性模量/MPa 628.4 1 005.5 5 020.3 6 655.9 2 806.9 719.0 735.5 327.7 注:表中材料参数为-5 ℃条件下的取值.
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表 3 不同计算点位Keff峰值
Table 3. Keff maxima of different calculation points
计算点位 1 2 3 4 5 6 Keff峰值/(kPa·m1/2) 4.646 45.978 45.903 46.061 46.222 54.497
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表 4 不同裂纹间距下反射裂纹Keff峰值
Table 4. Keff maxima for different crack spacings
裂纹间距/mm 0 100 200 300 400 500 Keff/(kPa·m-0.5) 18.075 17.371 16.534 18.202 18.723 17.102
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表 5 不同C2下反射裂纹Keff峰值
Table 5. Keff maxima of a reflective crack under different C2
C2/cm 4 6 8 10 12 Keff/(kPa·m0.5) 10.454 13.199 14.851 18.075 19.003
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表 6 不同荷载状态下Keff-max拟合多项式
Table 6. Keff-max fitting polynomials for different loads
荷载种类 Keff-max拟合多项式 R2 低速(36 km/h) Keff-max=-735.524C3+90.596 06C2-0.763 560 4C+0.357 484 348 0.999 高速(108 km/h) Keff-max=-60.440 5C3-19.949 936 4C2+4.113 761 16C+0.263 089 809 2 0.980 制动(-5 km/h) Keff-max=-420.575C3+48.547 26C2-0.450 745 24C+0.513 707 757 1 0.989 静载 Keff-max=-856.497 5C3+102.035 361C2-0.809 021 737C+0.351 227 799 4 0.997
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表 7 不同荷载状态下top-down裂纹疲劳寿命
Table 7. Top-down crack fatigue life under different loading conditions
荷载种类 低速(36 km/h) 高速(108 km/h) 制动(-5 km/h) 静载 N/次 1.228×108 2.011×108 4.110×107 1.246×108
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