J. Shanghai Jiaotong Univ. (Sci.), 2008, 13(2): 206–210 DOI: 10.1007/s12204-008-0206-5
Mechanical Properties of Asphalt Pavement Structure in Highway Tunnel SHI Chun-xiang1∗ (石春香), GUO Zhong-yin2 (郭忠印) (1. Shanghai Institute of Technology, Shanghai 200233, China; 2. Tongji University, Shanghai 200092, China)
Abstract: A linear full 3D finite element method (FEM) was performed in order to present the key design parameters of highway tunnel asphalt pavement under double-wheel load on rectangular loaded area considering horizontal contact stress induced by the acceleration/deceleration of vehicles. The key design parameters are the maximum horizontal tensile stresses at the surface of the asphalt layer, the maximum horizontal tensile stresses at the bottom of the asphalt layer and the maximum vertical shear stresses at the surface of the asphalt layer were calculated. The influencing factors such as double-wheel weight; asphalt layer thickness; base course stiffness modulus and thickness; and the contact conditions among the structure layers on these key design parameters were also examined separately to propose construction procedures of highway tunnel asphalt pavement. Key words: tunnel asphalt pavement structure; three-dimensional finite element method; horizontal force; horizontal tensile stress; vertical shear stress CLC number: U 452.2 Document code: A
Introduction Almost all mechanistic flexible pavement design procedures determine the fatigue life of pavements by considering the tensile stress or strain at the bottom of the asphalt layers. They implicitly assume that fatigue cracks originate at the bottom of the asphalt layers and propagate upwards towards the surface of the pavement. Assuming a uniform normal contact pressure distributed over a circular contact area between the tyre and the pavement surface, layered elastic theory predicts that the maximum horizontal tensile stress (strain) occurs at the bottom of bound layers directly under the load, and the maximum horizontal compressive stress (strain) occurs at the surface of the pavement directly under the load[1] . However, observations from cracked roads in the UK[2] , the US[3−5] , Japan[6] and in Northwest area of China[7] have shown that the cracking originated from the surface of the pavement rather than at the base, particularly for thick flexible constructions. More recently, researchers have hypothesized that the surface cracking phenomenon may be related to the highly non-uniform three dimensional contact stress distribution measured between the tyre and the pavement, inducing large horizontal tensile stresses (strains) in the top section of the pavement structure[8] . Measurements from free-rolling car and truck tyres have Received date: 2007-05-28 Foundation item: Western Traffic (No. 2002-318-000-23) ∗E-mail:
[email protected]
Technology
Funds
shown that, in addition to the normal contact pressure, there can be large transverse and longitudinal shear stresses acting in the contact area. Traditional layered elastic models of a pavement structure typically assume that the load is applied as a uniform vertical contact pressure distributed over a circular contact area. Under these conditions the maximum horizontal tensile stress and strains are usually predicted at the bottom of the asphalt layers, due to the bending stresses induced by the loading. However, on the tunnel asphalt pavements, it should be noted that horizontal tensile stresses at the surface away from the loaded area (due to the negative curvature of the surface). The elastic stiffness modulus of highway tunnel bedrocks is high; the deterioration of well-constructed pavement is not structural. Furthermore, when vehicles enter the tunnels, drivers will decelerate vehicles because of weak light and narrow space, and accelerate vehicles when leaving the tunnels. There exist high horizontal stresses (in the direction of travel) between the tyre and the pavement surface. The objective of this paper is to use a linear elastic full 3D finite element (FE) program to present the key design parameters of highway tunnel asphalt pavement under double-wheel loads considering horizontal contact stress induced by the acceleration/deceleration of vehicles. The following key design parameters were to be calculated: ➀ the maximum horizontal tensile stresses σmax at the surface of the asphalt layer; ➁ the σmax at the bottom of the asphalt layer; ➂ the maximum vertical shear stresses τmax at the surface of the
J. Shanghai Jiaotong Univ. (Sci.), 2008, 13(2): 206–210
207
asphalt layer. The influencing factors such as double-wheel weight; asphalt layer thickness; base course stiffness modulus and thickness; and the contact situation among the structure layers on these key design parameters were also examined separately in order to propose significant construction problems should be considered in the design procedure of the tunnel asphalt pavement.
y-direction is fixed on the front and back planes; the surface is the free plane. Contact conditions among pavement layers are also considered particular layer is characterized by thickness (hi ), elastic stiffness modulus (Ei ) and Poisson’s ration (vi ). Following variants of tunnel pavement structures were given in the table 2.
1 Traffic Loading Form Traditional layered elastic models of a pavement structure typically assume that the load is applied as a uniform vertical contact pressure distributed over a circular contact area. The FEM in this paper, on the other hand, the loading conditions were simplified using a uniform vertical considering horizontal contact pressures distributed over a rectangular contact area which is close to the true contact area between the tyre and pavement. The numeric values of tyre print and tyre pressure are given in the Table 1. Spacing interval between tyres is 34 cm. Tyre contact stresses have been related to double-wheel weight and tyre internal pressure using an empirical formula of form[10] : p = 0.004 2P + 0.29pi + 0.145,
The full three-dimensional finite element model z Loaded area
Tyre print and tyre pressure
Base course Bedrock
Fig. 2
[12]
P /kN
pi /MPa
p/MPa
width/cm
length/cm
20
0.6
0.40
22
11.3
Schematic representation of the pavement analysis problem
Table 2 Layer
40
0.7
0.52
22
17.6
Asphalt layer
50
0.75
0.573
22
19.8
Base course
60
0.8
0.63
22
21.7
Bedrock
80
0.9
0.74
24
22.5
100
1.0
0.855
24
24.4
In general, the horizontal contact stress is defined as 30% of the vertical contact stress, so defined in this paper for calculating.
2 Description of the Full 3D FEM and Pavement Structure Variants Tunnel asphalt pavements generally include asphalt layers, base course and bedrock. The full 3D FEM developed for the pavement structure is shown in Fig. 1. The width along x-direction and y-direction is 3.0 m. The depth along z-direction is varied at the pavement structure thickness. 8-node element is adopted in the model. The schematic representation with boundary conditions of the pavement analysis problem is shown in Fig. 2. z-direction is fixed on the bottom of the model; x-direction is fixed on the left and right planes;
y x
Asphalt layer
(1)
where, p is the tyre contact stress; P is the doublewheel weight; pi is the tyre internal pressure. Table 1
Fig. 1
Pavement structure variants hi /cm
Ei /GPa
vi
8,10,12,14,16,20
1.5
0.35
0,10,15,25,30
2.0,0.5
0.2
250
5.0,0.5
0.2
3 Analysis of Calculated Pavement Responses 3.1
Effect of Double-wheel Weight on Pavement Responses Pavement responses at various double-wheel weights were to be considered. Contact conditions among layers are completely sticking. Following variants of the tunnel pavement structure were given in the table 3. Table 3 Layer
Pavement structure variants-A hi /cm
Ei /GPa
vi
Asphalt layer
14
1.5
0.35
Base course
15
2.0
0.2
250
5.0
0.2
Bedrock
Figures 3–5 present results of the asphalt layer at various double-wheel weights w considering and not considering the horizontal stresses.
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J. Shanghai Jiaotong Univ. (Sci.), 2008, 13(2): 206–210 0.5 0.4 0.3
Fig. 3
20
50 60 w/kN
80
100
σmax at the pavement surface
0.6
0.35 0.25 0.15
Not considering horizontal stress Considering horizontal stress
0.5 τmax/MPa
40
σmax, τmax/MPa
0.1
Fig. 6
8
10
12 14 h1/cm
16
20
Effect of asphalt layer thickness on pavement stresses on the semi-rigid base course
0.4 0.3 0.2 0.1
Fig. 4
20
40
50 60 w/kN
80
100
τmax at the pavement surface
0.6
Not considering horizontal stress Considering horizontal stress
0.5 σmax/MPa
σmax (surface) σmax (bottom) τmax (surface)
0.45 0.2
0.4 0.3 0.2 0.1
Fig. 5
20
40
50 60 w/kN
80
100
σmax at the bottom of the asphalt layer
As can be seen, the stresses of the asphalt layer increase with increasing double-wheel weight level. The effect of horizontal forces on the σmax at the bottom of the asphalt layer is less than that on the σmax and vertical shear stresses τ at the surface of the asphalt layer. These figures indicate that horizontal stresses between the tyre and the pavement surface accelerate the deterioration of the pavement surface. 3.2 Effect of Asphalt Layer Thickness on Pavement Responses Pavement responses at various asphalt layer thicknesses h1 set on the different stiffness modulus base course were to be considered. Contact conditions among layers are completely sticking. Following variants of the tunnel pavement structure were given in the table 4. Table 4
Pavement structure variants-B
Layer
hi /cm
Ei /GPa
vi
Asphalt layer
8,10,12,14,16,20
1.5
0.35
Base course
15
2.0,0.5
0.2
Bedrock
250
5.0
0.2
w/kN
50
As can be seen: (1) When asphalt layer thickness is set 8–10 cm, the σmax and τmax at the surface of the asphalt layer due to the negative curvature at the wheel interspaces surface are higher in magnitude compared to those at the bottom of the asphalt layer. (2) The σmax at the surface of the asphalt layer decrease with increasing asphalt layer thickness level, but the rate of decay decreases when asphalt layer thickness is more than 14 cm. (3) The τmax at the surface of the asphalt layer increase with increasing asphalt layer thickness level, which indicates that increasing asphalt layer thickness level is not favorable for preventing the damage induced by the vertical shear stress. (4) The recommended optimal asphalt layer thickness is 14cm on the semi-rigid base course. Figure 7 presents results of the asphalt layer at various asphalt layer thickness on the flexible base course with E = 500 MPa. 1.2 1.0 σmax, τmax/MPa
σmax/MPa
Figure 6 shows the results of the asphalt layer at various asphalt layer thickness set on the semi-rigid base course with E = 2 GPa.
Not considering horizontal stress Considering horizontal stress
0.6 0.4 0.2
Fig. 7
σmax (surface) σmax (bottom) τmax (surface)
0.8
8
10
12 14 h1/cm
16
20
Effect of asphalt layer thickness on pavement stresses on the flexible base course
As can be seen: (1) The maximum stresses of the asphalt layer decrease with increasing asphalt layer thickness level. (2) The magnitude of stresses is more than that on the semi-rigid base course, so semi-rigid base courses with higher stiffness modulus should be set in the design procedures of tunnels asphalt pavement structure.
J. Shanghai Jiaotong Univ. (Sci.), 2008, 13(2): 206–210
3.3
Effect of Base Course Thickness on Pavement Responses Pavement responses at various base course thicknesses h2 with the different bedrock stiffness modulus were to be considered. CCAL are completely sticking. Following variants of the tunnel pavement structure were given in the table 5. Table 5
Pavement structure variants-C hi /cm
Layer
Ei /GPa
vi
Asphalt layer
14
1.5
0.35
Base course
0,10,15,25,30
2.0
0.2
Bedrock
250
5.0,0.5
0.2
w/kN
50
209
3.4
Effect of Contact Conditions on Pavement Responses Influence of different CCAL on pavement responses were to be considered. No. 1 stands for completely sticking among layers; No. 2 for completely sticking between the asphalt layer and the base course while completely sliding between the base course and the bedrock; No. 3 for completely sliding between the asphalt layer and the base course while completely sticking between the base course and the bedrock; No. 4 for completely sliding among layers. Following variants of the tunnel pavement structure were given in the table 6. Table 6
Figure 8 shows results of the asphalt layer at various base course thicknesses on the rigid bedrock with E = 5 GPa. As can be seen, the change in parameters due to the effects of base course thickness is minute. If the tunnel bedrock stiffness modulus is high, base course should not be set or the base course thickness needs not to be set too thick when assuring the construction smoothness.
0.3 σmax (surface) σmax (bottom) τmax (surface)
0.2
0.1
Fig. 8
0
10
15 h2/cm
25
Figure 9 presents results of the asphalt layer at various base course thicknesses on the flexible bedrock with E = 500 MPa. As can be seen, the change in the σmax at the bottom of the asphalt layer due to the effects of base course thickness is significant, so base course should be set and the recommended optimal base course thickness is 15 cm on the flexible bedrock.
Ei /GPa
vi
Asphalt layer
14
1.5
0.35
Base course
15
2.0
0.2
Bedrock
250
5.0
0.2
w/kN
50
Figure 10 shows results of the asphalt layer at different CCAL. As can be seen, the change in the σmax at the bottom of the asphalt layer due to the effects of CCAL is significant. The most advantageous situation is completely sticking among layers; the most disadvantageous situation is completely sliding among layers, so strengthening the bound among pavement layers especially between the asphalt layer and the base course can effectively control cracking at the bottom of the asphalt layer.
30
Effect of base course thickness on pavement stresses on the rigid bedrock
hi /cm
Layer
σmax, τmax/MPa
σmax, τmax/MPa
0.4
Pavement structure variants-D
0.8 0.7 0.5 0.3 0.1
Fig. 10
σmax (surface) σmax (bottom) τmax (surface)
1
2 CCAL
3
4
Effect of CCAL on the pavement stresses
4 Conclusion σmax, τmax/MPa
1.0
0.6 0.4 0.2 0
Fig. 9
σmax (surface) σmax (bottom) τmax (surface)
0.8
0
10
15 h2/cm
25
30
Effect of base course thickness on pavement stresses on the flexible bedrock
The mechanic analysis has been performed in order to present the key design parameters and propose construction procedures of highway tunnel asphalt pavement as follows: (1) Inclusion of the horizontal stress between the tyre and the pavement surface has been shown to produce higher local values of horizontal tensile stress and vertical shear stress inducing the surface damaging on the pavement surface, at the same time, the magnitude of the horizontal tensile stress at the bottom of the pavement is high. So the key design parameters are the σmax
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at the surface of the asphalt layer, the σmax at the bottom of the asphalt layer and the τmax at the surface of the asphalt layer. (2) Semi-rigid base courses with higher stiffness modulus should be set, and its thickness should be adjusted according to the bedrock stiffness. (3) Increasing asphalt layer thickness level on the semi-rigid base courses is not favorable for preventing the damage induced by the vertical shear stress. The optimal asphalt layer thickness is recommended 14 cm on the semi-rigid base course. (4) Strengthening bounding among pavement layers especially between the asphalt layer and the base course has been shown can effectively control the σmax at the bottom of the asphalt layer.
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