﻿ 层间接触条件下粘弹性铺装层蠕变分析 Creep Analysis of Viscoelastic Pavement under Interlayer Contact Condition

International Journal of Mechanics Research
Vol. 09  No. 01 ( 2020 ), Article ID: 34118 , 9 pages
10.12677/IJM.2020.91001

Creep Analysis of Viscoelastic Pavement under Interlayer Contact Condition

Xiang Chen, Hu Wang, Ya Wang

School of Science, Chang’an University, Xi’an Shaanxi

Received: Jan. 15th, 2020; accepted: Jan. 30th, 2020; published: Feb. 6th, 2020

ABSTRACT

In order to analyze the creep response of the viscoelastic pavement layer during interlayer contact, a finite element analysis model was established by simplifying the upper structure of the bridge, and the creep law of the pavement layer was analyzed under different load forms, different temperatures and different contact cohesion. The results show that the settlement displacement of asphalt layer under impact load is basically the same as that under vertical load, but it will produce large vertical uplift displacement, and its creep deformation is more complicated. The larger of the influence of loading time on creep of asphalt surface layer, and the higher the temperature, the greater the deformation, the faster the creep stability period; the temperature mainly affects the vertical ridge displacement of the surface layer, and the vertical bulge displacement increases with the increase of temperature, i.e. when the temperature is high, the unstable rut is more likely to occur; under the long-term loading of the impact load, when the cohesive force is 0.01 MPa, local slip occurs between the layers; when the cohesive force is greater than 0.01 MPa, the creep response of the asphalt surface layer remains the same.

Keywords:Bridge Deck Pavement, Interlayer Contact, Viscoelasticity, Creep, Finite Element Analysis

1. 引言

2. 沥青的粘弹性模型

2.1. 基本理论

Burgers模型的本构方程可写为

$\sigma +{p}_{1}\stackrel{˙}{\sigma }+{p}_{2}\stackrel{¨}{\sigma }={q}_{1}\stackrel{˙}{\epsilon }+{q}_{2}\stackrel{¨}{\epsilon }$ (1)

Figure 1. Burgers model

Table 1. Parameters of Burgers model of asphalt materials

2.2. 参数转换

Burgers模型参数不能直接作为prony级数的输入量，需要将其转化为prony级数的剪切模量表达式中所对应的参数。由prony级数来表征粘弹性材料的属性时，其基本形式如下：

$G\left(t\right)={G}_{\infty }+\underset{i=1}{\overset{n}{\sum }}{G}_{i}\mathrm{exp}\left(-\frac{t}{{\tau }_{i}}\right)$ (2)

${\alpha }_{i}=\frac{{G}_{i}}{{G}_{0}}$ (3)

${G}_{1}=\frac{{E}_{1}}{2\left(1+{\mu }_{1}\right)},\text{}{G}_{2}=\frac{{E}_{2}}{2\left(1+{\mu }_{2}\right)},\text{}{n}_{1}=\frac{{\eta }_{1}}{2\left(1+{\mu }_{1}\right)},\text{}{n}_{2}=\frac{{\eta }_{2}}{2\left(1+{\mu }_{2}\right)},\text{}{\mu }_{1}={\mu }_{2}$ (4)

${p}_{1}=\frac{{n}_{1}}{{G}_{1}}+\frac{{n}_{1}+{n}_{2}}{{G}_{2}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{p}_{2}=\frac{{n}_{1}{n}_{2}}{{G}_{1}{G}_{2}},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{q}_{1}=2{n}_{1},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{q}_{2}=\frac{2{n}_{1}{n}_{2}}{{G}_{2}}$ (5)

$\begin{array}{c}G\left(t\right)=\frac{{G}_{1}}{\alpha -\beta }\left[\left(\frac{{G}_{2}}{{n}_{2}}-\beta \right)\cdot \mathrm{exp}\left(-\beta t\right)+\left(\alpha -\frac{{G}_{2}}{{n}_{2}}\right)\cdot \mathrm{exp}\left(-\alpha t\right)\right]\\ ={G}_{0}\left[{\alpha }_{\infty }+{\alpha }_{1}\mathrm{exp}\left(-\frac{t}{{\tau }_{1}}\right)+{\alpha }_{2}\mathrm{exp}\left(-\frac{t}{{\tau }_{2}}\right)\right]\end{array}$ (6)

${G}_{0}={G}_{1},\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\alpha }_{\infty }=0,\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\alpha }_{1}=\frac{1}{\alpha -\beta }\left(\frac{{G}_{2}}{{n}_{2}}-\beta \right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\tau }_{1}=\frac{1}{\beta },\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\alpha }_{2}=\frac{1}{\alpha -\beta }\left(\alpha -\frac{{G}_{2}}{{n}_{2}}\right),\text{\hspace{0.17em}}\text{\hspace{0.17em}}{\tau }_{2}=\frac{1}{\alpha }$

Table 2. Prony series parameters for asphalt materials

3. 有限元模型建立

3.1. 层间接触设置

${\tau }_{\mathrm{lim}}=\mu P+b$ (7)

$|\tau |\le {\tau }_{\mathrm{lim}}$ (8)

3.2. 模型参数及荷载布置

3.2.1. 模型参数

Table 3. Material parameters of waterproof adhesive layer

3.2.2. 荷载布置

$F=0.5G$ (9)

Figure 2. Finite element model

4. 铺装层蠕变规律分析

4.1. 沥青面层在不同荷载下的变化响应

Figure 3. Time history curve of extreme point displacement under different loads

4.2. 沥青层蠕变随时间变化

4.3. 沥青层蠕变随温度变化

Figure 4. Time history curve of bulged displacement of asphalt surface layer

Figure 5. Settlement displacement time history curve of asphalt surface layer

Figure 6. Lateral joint displacement at different temperatures

Figure 7. Displacement of longitudinal joints at different temperatures

4.4. 沥青层蠕变随层间粘聚力变化

Table 4. Creep response under different cohesion forces

5. 结论

1) 在冲击荷载与竖直荷载的长时间作用下，沥青层的蠕变变形略有不同，冲击荷载下会使得沥青层剪应力过大而产生较大的竖向隆起位移，其产生的变形更为复杂。

2) 加载时间的长短对沥青面层蠕变影响较大，沥青面层经受长时间荷载累积后，便会产生永久性变形；温度越高，产生的蠕变变形越大，进入蠕变稳定期更快，更易产生永久变形。

3) 在冲击荷载作用下，会在荷载作用区的行车方向周围产生较大竖向位移，且温度对其的影响较大，即高温时更易出现失稳型车辙。

4) 当黏聚力为0.01 MPa时，在冲击荷载的长时间加载下，层间出现部分滑移；当黏聚力大于0.01 MPa时，其力学响应保持不变。

Creep Analysis of Viscoelastic Pavement under Interlayer Contact Condition[J]. 力学研究, 2020, 09(01): 1-9. https://doi.org/10.12677/IJM.2020.91001

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