# Numerical Analysis of the Mechanical Responses and Transition Section Design of Pavement Structures in the Entrance and Exit Sections of Highway Tunnel

Authors: Xueying Zhao; Aiqin Shen; Baofu Ma
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

The entrance and exit sections of a tunnel are subject to different environments, pavements, and traffic conditions, which is quite different from the average highway, and it should be considered differentially, when designing pavement structures. However, there are no clear regulations on it in Chinese specifications. Over the years, a lot of studies were carried on the entrance and exit sections of a tunnel, but there are few ones on the pavement design and its mechanical response characteristics. In this paper, the Huangjiayu tunnel and the Yangkou tunnel in Shandong province were taken as case study engineerings and their pavement structures in the entrance and exit sections are referred to as Str-1 and Str-2, respectively. In Str-1, asphalt pavement was applied inside and outside the tunnel and a transition section was applied. In Str-2, asphalt pavement was applied outside the tunnel and concrete pavement was applied inside the tunnel when it was built in 2004 and a transition section was not applied. Meanwhile, 7 alternative pavement structures (referred to as Str-1a∼Str-1g), in which the lengths of transition sections were different, were proposed, simulated, and analyzed through FE program ANSYS. Through the analysis of maximum shear stresses in asphalt courses and tensile stresses at the bottom of base courses, it was found that setting a transition structure is essential, and it can ensure the continuity of pavements and significantly reduce the sudden change of shear stress of asphalt layer and thus prevent premature pavement distresses. Hence, Str-1 is more reasonable compared with Str-2. Besides, it was also found that when the asphalt surface outside the tunnel is designed to be three layers, it is more appropriate to use Str-1, in which the concrete slab in the transition structure has variable cross section, and the length of the concrete slab is 4.5 m. When the asphalt surface outside the tunnel is designed to be two layers, Str-1b is more reasonable and the length of the concrete slab is also 4.5 m.


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## Body

## 1. Introduction

With the development of the economy and society, tunnels are more and more widely used in China’s roads. According to statistics published by the Ministry of Transport of China, the number of highway tunnels in China has exceeded 20000, reaching 21316, and the total length has exceeded 20 million meters, reaching 21.999 million meters at the end of 2020. The entrance and exit sections of a tunnel are the transition parts. It is subject to different environments, pavements, and traffic conditions inside and outside the tunnel, which is quite different from the average highway in all aspects. Due to the semiclosed characteristics of tunnels, vehicles would obviously decelerate and accelerate in the process of driving towards and away from tunnels, which may cause pushing effects on the pavement structures. Moreover, according to the traffic survey, at present, the phenomenon of overloading is still serious. When the vehicle loads increase, the number of equivalent axle loads increases exponentially instead of proportionally, which will cause a serious burden on the pavement. Hence, the entrance and exit sections should be considered differentially, when designing the pavement structures.At present, scholars have carried out a lot of research on the entrance and exit sections of tunnels, which can be mainly divided into the following categories: pavement temperature fields [1–3], linear setting [4–7], brightness design [8–13], and operation safety [14–18]. Despite these studies, there are few ones on the mechanical response characteristics of the pavement structures in these sections. Traditionally, concrete pavement is used inside the tunnel and asphalt pavement is used outside the tunnel in China, due to many reasons, such as the need for fire prevention. Hence, the concrete pavement inside the tunnel is directly connected with the asphalt pavement outside the tunnel. However, under the application of traffic loads, the shear stress at the junction of the two structures exceeds 28.37% of the asphalt pavement in the average section [19], which is very prone to shear failure. Meanwhile, distress investigation shows that such pavement structure design, that is, “concrete pavement inside tunnels + asphalt pavement outside tunnels,” will cause frequent cracks in the entrance and exit sections after being used for a short period of time, which will be described in detail in Part 3. In this case, in recent years, there is a trend that asphalt pavement is also applied inside tunnels and a transition structure is set in the middle of pavements inside and outside the tunnel. However, due to the lack of mechanical response analysis, the design of the transition structure is usually based on experience and lack of mechanical guidance. Besides, due to the short paving time, relevant distresses investigation of the transition pavement structure is insufficient, whether it could avoid distresses is still not clear.Therefore, to guide the pavement design in tunnel entrance and exit sections, it is of vital importance to study the mechanical response of the pavement structure specifically in these sections. In this paper, the Yangkou tunnel of Qingdao Binhai Highway and the Huangjiayu tunnel of Qingdao-Lanzhou Highway in Shandong province were taken as case study engineering. Meanwhile, 7 other alternative pavement structures were selected and their mechanical responses were simulated and analyzed through the FE program (ANSYS). The flowchart of this paper is shown in Figure1.Figure 1
Flowchart of this paper.This paper is organized as follows:(1)
Analysis of working conditions inside and outside the tunnels, which have great differences and effects on the behavior of the pavement structures(2)
Investigation into the pavement distresses in the tunnel entrance and exit sections(3)
Proposed FE models and mechanical boundary conditions for pavements(4)
Mechanical responses of the pavement structures in entrance and exit sections of the Yangkou Tunnel and the Huangjiayu Tunnel subjected to traffic loads(5)
Proposed 7 alternative pavement structures and their mechanical responses subjected to traffic loads(6)
Conclusions and suggestions for the future pavement design for the tunnel entrance and exit sections


## 2. Analysis of Working Conditions inside and outside the Tunnels

There are great differences in working conditions inside and outside the tunnels, including environmental conditions (temperature, ventilation, and lighting), pavement structure (structural foundation and width transition), and traffic conditions (frequent braking and channelization). In this part, different pavement structure and traffic conditions will be analyzed specifically since this paper mainly discusses the mechanical response of the tunnel entrance and exit sections under the application of traffic loads. Environmental conditions will be discussed in another paper.


### 2.1. Pavement Structure

#### 2.1.1. Pavement Foundation inside and outside the Tunnels

The pavement structures inside and outside the tunnels have obvious differences. For the pavement outside a tunnel, the pavement structure is built on the subgrade and its resilience modulus is usually 40∼70 MPa. However, for the pavement inside a tunnel, whether invert is set or not, the base course is usually plain concrete, and the whole pavement structure is paved on the bedrock, so that the strength of the bearing layer is much higher than that of the pavement structure outside the tunnel.If the transition part of the pavement structures inside and outside the tunnel cannot be designed well, a huge stress concentration will be generated at the junction of the two pavement structures, which will seriously affect the service life and reduce the driving quality.


#### 2.1.2. Pavement Width

Highway outside the tunnel is usually two-way traffic, and the cross section is composed of central separation belt, carriageway, hard shoulder, and earth shoulder, while the highway inside the tunnel is one-way traffic, and the cross section is narrowed due to the lack of earth shoulder, shown in Figure2. Therefore, the transition design of tunnel pavement width is also an important part of the design of tunnel entrance and exit transition section.Figure 2
The narrowed cross section.


### 2.2. Traffic Conditions

#### 2.2.1. Frequent Acceleration and Deceleration

The design speed outside a tunnel is usually 80∼120 km/h, while that inside a tunnel is only 60∼80 km/h. The design speed of some special tunnels is even as low as 40 km/h. The difference of design speed makes the driver slow down when entering the tunnel and accelerate when leaving the tunnel. In addition, the “black hole,” “black frame,” “white hole,” and “white frame” effects produced by visual shock led to the need for drivers to slow down when driving near the portal to ensure driving safety. Therefore, acceleration and deceleration in these sections are quite serious.


#### 2.2.2. Traffic Channelization inside Tunnels

The tunnel is a semiclosed structure, and the wall rock on both sides will seriously affect drivers, so that they will unconsciously drive close to the marking line in the middle of the road after entering the tunnel, which is easy to cause traffic channelization. In addition, for safety reasons, overtaking is not allowed in a tunnel, which makes vehicles often drive from the entrance to the exit in a certain line, further aggravating the channelization phenomenon.


## 2.1. Pavement Structure

### 2.1.1. Pavement Foundation inside and outside the Tunnels

The pavement structures inside and outside the tunnels have obvious differences. For the pavement outside a tunnel, the pavement structure is built on the subgrade and its resilience modulus is usually 40∼70 MPa. However, for the pavement inside a tunnel, whether invert is set or not, the base course is usually plain concrete, and the whole pavement structure is paved on the bedrock, so that the strength of the bearing layer is much higher than that of the pavement structure outside the tunnel.If the transition part of the pavement structures inside and outside the tunnel cannot be designed well, a huge stress concentration will be generated at the junction of the two pavement structures, which will seriously affect the service life and reduce the driving quality.


### 2.1.2. Pavement Width

Highway outside the tunnel is usually two-way traffic, and the cross section is composed of central separation belt, carriageway, hard shoulder, and earth shoulder, while the highway inside the tunnel is one-way traffic, and the cross section is narrowed due to the lack of earth shoulder, shown in Figure2. Therefore, the transition design of tunnel pavement width is also an important part of the design of tunnel entrance and exit transition section.Figure 2
The narrowed cross section.


## 2.1.1. Pavement Foundation inside and outside the Tunnels

The pavement structures inside and outside the tunnels have obvious differences. For the pavement outside a tunnel, the pavement structure is built on the subgrade and its resilience modulus is usually 40∼70 MPa. However, for the pavement inside a tunnel, whether invert is set or not, the base course is usually plain concrete, and the whole pavement structure is paved on the bedrock, so that the strength of the bearing layer is much higher than that of the pavement structure outside the tunnel.If the transition part of the pavement structures inside and outside the tunnel cannot be designed well, a huge stress concentration will be generated at the junction of the two pavement structures, which will seriously affect the service life and reduce the driving quality.


## 2.1.2. Pavement Width

Highway outside the tunnel is usually two-way traffic, and the cross section is composed of central separation belt, carriageway, hard shoulder, and earth shoulder, while the highway inside the tunnel is one-way traffic, and the cross section is narrowed due to the lack of earth shoulder, shown in Figure2. Therefore, the transition design of tunnel pavement width is also an important part of the design of tunnel entrance and exit transition section.Figure 2
The narrowed cross section.


## 2.2. Traffic Conditions

### 2.2.1. Frequent Acceleration and Deceleration

The design speed outside a tunnel is usually 80∼120 km/h, while that inside a tunnel is only 60∼80 km/h. The design speed of some special tunnels is even as low as 40 km/h. The difference of design speed makes the driver slow down when entering the tunnel and accelerate when leaving the tunnel. In addition, the “black hole,” “black frame,” “white hole,” and “white frame” effects produced by visual shock led to the need for drivers to slow down when driving near the portal to ensure driving safety. Therefore, acceleration and deceleration in these sections are quite serious.


### 2.2.2. Traffic Channelization inside Tunnels

The tunnel is a semiclosed structure, and the wall rock on both sides will seriously affect drivers, so that they will unconsciously drive close to the marking line in the middle of the road after entering the tunnel, which is easy to cause traffic channelization. In addition, for safety reasons, overtaking is not allowed in a tunnel, which makes vehicles often drive from the entrance to the exit in a certain line, further aggravating the channelization phenomenon.


## 2.2.1. Frequent Acceleration and Deceleration

The design speed outside a tunnel is usually 80∼120 km/h, while that inside a tunnel is only 60∼80 km/h. The design speed of some special tunnels is even as low as 40 km/h. The difference of design speed makes the driver slow down when entering the tunnel and accelerate when leaving the tunnel. In addition, the “black hole,” “black frame,” “white hole,” and “white frame” effects produced by visual shock led to the need for drivers to slow down when driving near the portal to ensure driving safety. Therefore, acceleration and deceleration in these sections are quite serious.


## 2.2.2. Traffic Channelization inside Tunnels

The tunnel is a semiclosed structure, and the wall rock on both sides will seriously affect drivers, so that they will unconsciously drive close to the marking line in the middle of the road after entering the tunnel, which is easy to cause traffic channelization. In addition, for safety reasons, overtaking is not allowed in a tunnel, which makes vehicles often drive from the entrance to the exit in a certain line, further aggravating the channelization phenomenon.


## 3. Investigation into Pavement Distress in the Tunnel Entrance and Exit Sections

As the connection part, the entrance and exit sections have experienced great differences in the pavement structures and traffic conditions. Distresses often occur in the early stage of service. In this part, distresses in the entrance and exit sections of the Yangkou tunnel of Qingdao Binhai Highway are investigated.Yangkou tunnel is the first long tunnel in Jiaodong Peninsula, and its position is shown in Figure3. It was opened to traffic at the end of 2006. After several years of use, the pavement surface performance has been declining. The distresses in the sections of tunnel entrance and exit since it was open were investigated, and results are shown in Table 1 and the detection lane areas are shown in Figure 4.Figure 3
Location of Yangkou tunnel and Huangjiayu tunnel [20].Table 1
Distress investigation results of Yangkou tunnel.
Detection laneStake numberInternational roughness index (IRI) (m/km)20082009201120122013Left (up)K62 + 0001.511.630.991.021.13K61 + 0001.430.990.660.871.03K60 + 0001.591.480.630.961.25K59 + 0001.671.160.570.971.16K58 + 0002.001.270.841.281.48Right (down)K57 + 0002.061.741.381.361.42K58 + 0001.791.400.681.031.14K59 + 0001.601.450.851.231.03K60 + 0001.421.210.620.891.14K61 + 0001.391.370.740.901.19Detection laneStake numberRutting depth (mm)20082009201120122013Left (up)K62 + 0005.06.04.09.012.0K61 + 0004.07.04.012.011.0K60 + 0005.07.03.013.011.0K59 + 0005.07.04.012.011.0K58 + 0006.06.03.010.011.0Right (down)K57 + 0007.05.03.012.015.0K58 + 0005.04.04.010.013.0K59 + 0004.05.03.08.014.0K60 + 0005.05.04.07.014.0K61 + 0005.05.04.011.013.0Detection laneStake numberFriction coefficient20082009201120122013Left (up)K62 + 00069.272.050.062.548.6K61 + 00069.670.753.959.740.9K60 + 00067.065.855.557.344.1K59 + 00059.886.958.357.644.1K58 + 00054.667.153.756.647.4Right (down)K57 + 00065.633.474.463.642.9K58 + 00060.833.365.263.447.6K59 + 00061.535.673.461.749.4K60 + 00060.838.677.959.747.2K61 + 00058.934.979.759.342.1Figure 4
The detection lane areas.Concrete pavement was applied inside the Yangkou tunnel and asphalt pavement was applied outside the tunnel when it was first designed in 2004. It can be seen from Table1 that the skid resistance of the pavement in the entrance and exit sections decreases continuously in the process of use. According to a large number of studies on tunnel traffic accidents [21, 22], the decrease of pavement adhesion coefficient is an important reason of traffic accidents near the tunnel entrance and exit sections. In addition, there are also a small number of cracks and pits in the pavement in these sections. Cracks including transverse cracks and longitudinal cracks (shown in Figure 5, red lines) are mainly concentrated in the surface layer and hardly develop into the base course.Figure 5
Transverse and longitudinal cracks on the surface of the pavement in the entrance section of the Yangkou tunnel.Therefore, in August 2013, the Yangkou tunnel was rehabilitated and the picture after rehabilitation is shown in Figure6. The original concrete pavement inside tunnel was milled and a new asphalt course was paved on it (shown in Figure 7), which helps to improve driving comfort, increase the antisliding ability, and ensure driving safety. However, the base course inside the tunnel is still directly connected with the pavement outside the tunnel and has the possibility of shear failure.Figure 6
The Yangkou tunnel after rehabilitation.Figure 7
Paving new asphalt course.


## 4. Pavement Structure and FE Model

### 4.1. Pavement Structure

The pavement structure in the entrance and exit sections of the Huangjiayu tunnel is shown in Figure8 (all acronyms in Figures 8 and 9 are explained in Table 2), and it was referred to as Str-1. A concrete slab is set at the junction part, which can reduce the adverse impact on the structure caused by the large strength gap between the bearing layer and the underlying layer inside and outside the tunnel to a certain extent.Figure 8
Pavement structures in the entrance and exit sections of the Huangjiayu tunnel (Str-1).Figure 9
The original pavement structures in the entrance and exit sections of the Yangkou tunnel (Str-2).Table 2
Explaination of acronyms in Figures8 and 9.
SMA-13Stone mastic asphalt, its nominal maximum aggregate size is 13.2 mm.AC-16CAsphalt concrete, its nominal maximum aggregate size is 16 mm. C means course and its void ratio is 4%∼10%.AC-20CAsphalt concrete, its nominal maximum aggregate size is 19.2 mm. C means course and its void ratio is 4%∼10%.AC-25CAsphalt concrete, its nominal maximum aggregate size is 26.5 mm. C means course and its void ratio is 4%∼10%.AK-13Asphalt antisliding surface, its nominal maximum aggregate size is 13.2 mm.C15Concrete, its standard value of cube compressive strength is 15 MPa.C30Concrete, its standard value of cube compressive strength is 30 MPa.The original pavement structure in the entrance and exit sections of the Yangkou tunnel before rehabilitation is shown in Figure9, and it was referred to as Str-2. The asphalt pavement outside the tunnel is directly connected with the concrete pavement inside the tunnel without any treatment on load-bearing transition.


### 4.2. Pavement FE Model

In this study, FE program ANSYS was used. The FE model is shown in Figure10. The dimensions of the FE model are 4 m × 5 m × (5 m + the length of the transition section + 5 m) (x × y × z). The direction of transverse is x-direction, and the dimension is 4 m. The direction of the pavement depth is y-direction, and the dimension is 5 m. The direction of traffic is z-direction, and the dimension is (5 m + length of the transition section + 5 m), in which the length of the tunnel pavement (Section A, shown in Figure 8) is 5 m and the length of average pavement (Section C, shown in Figure 8) is 5 m. SOLID 185 was used to simulate asphalt layers and SOLID 65 was used to simulate the concrete layer.Figure 10
The FE model in this study.The Tire-Pavement contact area was simplified to rectangle, which is 0.18 m × 0.20 m (x × z). The mesh sizes were different in different areas. In the area where the traffic loads were applied, it was 0.045 m × 0.02 m × 0.05 m (x × y × z) in the asphalt layer and 0.045 m × 0.05 m × 0.05 m (x ×  y × z) in the cement treated layer and concrete layer. It was 0.167 m × 0.13 m × 0.4 m (x × y × z) in other areas.


### 4.3. Mechanical Boundary Condition and Traffic Loads

In this paper, Dongfeng EQ-140 was selected as the representative vehicle and its technical parameters are shown in Li’s research [23]. The tire load was simplified as the uniformly distributed rectangular load.


#### 4.3.1. Vertical Traffic Loads

In this paper, to simplify the calculation and simulation, traffic loads could be estimated using the haversine function as the following equation [24]:(1)Pt=PmaxsinπtT,(2)Pmax=PDAF,where Pmax (MPa) is the peak value of the vibrating load, T (s) is the period of traffic loads, t (s) is the time, P (MPa) is the uniformly distributed traffic loads, P = 0.7 MPa in China, and DAF is the dynamic amplification factor.(3)DAF=1+aV,where V (km/h) is the speed; in this study, V = 60 and 70 km/h, and a is the riding quality evaluation factor, correlated with IRI, and in this study, a=0.035 [25].T could be calculated using the following formula:(4)T=12Rv,where R (m) is the equivalent radius of single wheel load, R=3L/2, and L is the length of the uniformly distributed rectangular load; in this study, L = 0.20 m, and v (m/s) is the speed. Hence, calculation results of the period of traffic loads (T), the dynamic amplification factor (DAF), and the peak value of the vibrating load (Pmax) under different traffic speeds are shown in Table 3.Table 3
Calculation results ofT, DAF, and Pmax under different traffic speeds.
Speed (km/h)6080100120T (s)0.0770.0580.0460.038DAF1.2711.3131.3501.383Pmax (MPa)0.8900.9190.9450.968


#### 4.3.2. Horizontal Traffic Loads

(1) Longitudinal Friction Stresses. The longitudinal tangential stresses are affected by many factors, such as texture depth of the pavement surface, humidity, driving speed, and textures of tires. According to reference [26], the friction coefficient of the asphalt pavement under different driving speeds was measured through the sideways-force coefficient routine investigation machine (SCRIM), and the relationship between the friction coefficient and the driving speed was shown as follows:(5)μ=−0.00695V+0.87495,where μ is the friction coefficient of the asphalt pavement and V is the driving speed (km/h).(2) Transverse Tangential Stresses. In addition to the vertical pressure and the longitudinal friction stresses, vehicles would also cause transverse tangential stresses [27], shown in Figure 11.Figure 11
Contact stresses (vertical, transverse, and longitudinal).AL-Qadi et al. [28] measured the three-dimensional contact stress caused by the tire on the pavement and found that the transverse tangential stresses are about 0.183 times of the vertical stresses. Therefore, in this paper, the transverse tangential stress is taken as 0.183 times of the vertical stress.


### 4.4. Mechanical Parameters

The mechanical parameters are listed in Table4 [29, 30], based on the Chinese Specifications for Design of Highway Asphalt Pavement (JTG D50-2017). The dynamic modulus of asphalt mixture in Table 4 is that under 20°C and 10 Hz.Table 4
Mechanical parameters of pavement materials.
MaterialAK-13SMA-13AC-16AC-20AC-25Dynamic modulusE∗ (MPa)680070009000950010000Poisson’s ratioμ0.250.250.250.250.25Densityρ (kg/m3)24002400245024802505MaterialCement-treated sand gravelGraded macadamSubgradeC15C30Dynamic modulusE∗ (MPa)16000150652000030000Poisson’s ratioμ0.250.350.400.20.2Densityρ(kg/m3)23002250170024502500


### 4.5. Verification of FE Simulation Results

To verify the finite element simulation results in this paper, taking the pavement in Section C in Str-1 as an example, the mechanical responses calculated by the finite element method and the elastic multilayer theory assumption are compared and analyzed.The elastic multilayer theory assumption is the standard method in the Chinese Specifications for Design of Highway Asphalt Pavement (JTG D50-2017) to calculate the mechanical responses. It takes the maximum value of PointA, B, C, and D (shown in Figure 12) as the calculation result in this cross section, and the tire load was simplified as the uniformly distributed double circular load.Figure 12
Mechanical response calculation points in the elastic multilayer theory assumption.
(a)(b)The calculation results of the tensile strain at the bottom of the asphalt layer along the driving direction and the tensile stress at the bottom of the cement treated layer along the driving direction under the application of the standard axle load BZZ-100(100 kN) are shown in Figure13.Figure 13
The calculation results of two methods. (a) The calculation results of the tensile strain at the bottom of the asphalt layer along the driving direction. (b) The calculation results of tensile stress at the bottom of the cement treated layer along the driving direction.
(a)(b)If the calculation results of the finite element method are completely consistent with the calculation results of the elastic multilayer theory assumption, the calculation results shall be distributed along the dotted line in Figure13. It can be seen from Figure 13 that although the calculation results of the two methods are not completely consistent, there is a significant linear relationship between them in general, which can be expressed by the followingequations:(6)asphaltlayer:EL=1.1290×FE+0.2458R2=0.9891,(7)cementtreatedlayer:EL=1.1182×FE+0.00125R2=0.9861,where FE is the calculation results of the finite element method and EL is the calculation results of the elastic multilayer theory assumption.Therefore, the reliability of finite element calculation results can be guaranteed.


## 4.1. Pavement Structure

The pavement structure in the entrance and exit sections of the Huangjiayu tunnel is shown in Figure8 (all acronyms in Figures 8 and 9 are explained in Table 2), and it was referred to as Str-1. A concrete slab is set at the junction part, which can reduce the adverse impact on the structure caused by the large strength gap between the bearing layer and the underlying layer inside and outside the tunnel to a certain extent.Figure 8
Pavement structures in the entrance and exit sections of the Huangjiayu tunnel (Str-1).Figure 9
The original pavement structures in the entrance and exit sections of the Yangkou tunnel (Str-2).Table 2
Explaination of acronyms in Figures8 and 9.
SMA-13Stone mastic asphalt, its nominal maximum aggregate size is 13.2 mm.AC-16CAsphalt concrete, its nominal maximum aggregate size is 16 mm. C means course and its void ratio is 4%∼10%.AC-20CAsphalt concrete, its nominal maximum aggregate size is 19.2 mm. C means course and its void ratio is 4%∼10%.AC-25CAsphalt concrete, its nominal maximum aggregate size is 26.5 mm. C means course and its void ratio is 4%∼10%.AK-13Asphalt antisliding surface, its nominal maximum aggregate size is 13.2 mm.C15Concrete, its standard value of cube compressive strength is 15 MPa.C30Concrete, its standard value of cube compressive strength is 30 MPa.The original pavement structure in the entrance and exit sections of the Yangkou tunnel before rehabilitation is shown in Figure9, and it was referred to as Str-2. The asphalt pavement outside the tunnel is directly connected with the concrete pavement inside the tunnel without any treatment on load-bearing transition.


## 4.2. Pavement FE Model

In this study, FE program ANSYS was used. The FE model is shown in Figure10. The dimensions of the FE model are 4 m × 5 m × (5 m + the length of the transition section + 5 m) (x × y × z). The direction of transverse is x-direction, and the dimension is 4 m. The direction of the pavement depth is y-direction, and the dimension is 5 m. The direction of traffic is z-direction, and the dimension is (5 m + length of the transition section + 5 m), in which the length of the tunnel pavement (Section A, shown in Figure 8) is 5 m and the length of average pavement (Section C, shown in Figure 8) is 5 m. SOLID 185 was used to simulate asphalt layers and SOLID 65 was used to simulate the concrete layer.Figure 10
The FE model in this study.The Tire-Pavement contact area was simplified to rectangle, which is 0.18 m × 0.20 m (x × z). The mesh sizes were different in different areas. In the area where the traffic loads were applied, it was 0.045 m × 0.02 m × 0.05 m (x × y × z) in the asphalt layer and 0.045 m × 0.05 m × 0.05 m (x ×  y × z) in the cement treated layer and concrete layer. It was 0.167 m × 0.13 m × 0.4 m (x × y × z) in other areas.


## 4.3. Mechanical Boundary Condition and Traffic Loads

In this paper, Dongfeng EQ-140 was selected as the representative vehicle and its technical parameters are shown in Li’s research [23]. The tire load was simplified as the uniformly distributed rectangular load.


### 4.3.1. Vertical Traffic Loads

In this paper, to simplify the calculation and simulation, traffic loads could be estimated using the haversine function as the following equation [24]:(1)Pt=PmaxsinπtT,(2)Pmax=PDAF,where Pmax (MPa) is the peak value of the vibrating load, T (s) is the period of traffic loads, t (s) is the time, P (MPa) is the uniformly distributed traffic loads, P = 0.7 MPa in China, and DAF is the dynamic amplification factor.(3)DAF=1+aV,where V (km/h) is the speed; in this study, V = 60 and 70 km/h, and a is the riding quality evaluation factor, correlated with IRI, and in this study, a=0.035 [25].T could be calculated using the following formula:(4)T=12Rv,where R (m) is the equivalent radius of single wheel load, R=3L/2, and L is the length of the uniformly distributed rectangular load; in this study, L = 0.20 m, and v (m/s) is the speed. Hence, calculation results of the period of traffic loads (T), the dynamic amplification factor (DAF), and the peak value of the vibrating load (Pmax) under different traffic speeds are shown in Table 3.Table 3
Calculation results ofT, DAF, and Pmax under different traffic speeds.
Speed (km/h)6080100120T (s)0.0770.0580.0460.038DAF1.2711.3131.3501.383Pmax (MPa)0.8900.9190.9450.968


### 4.3.2. Horizontal Traffic Loads

(1) Longitudinal Friction Stresses. The longitudinal tangential stresses are affected by many factors, such as texture depth of the pavement surface, humidity, driving speed, and textures of tires. According to reference [26], the friction coefficient of the asphalt pavement under different driving speeds was measured through the sideways-force coefficient routine investigation machine (SCRIM), and the relationship between the friction coefficient and the driving speed was shown as follows:(5)μ=−0.00695V+0.87495,where μ is the friction coefficient of the asphalt pavement and V is the driving speed (km/h).(2) Transverse Tangential Stresses. In addition to the vertical pressure and the longitudinal friction stresses, vehicles would also cause transverse tangential stresses [27], shown in Figure 11.Figure 11
Contact stresses (vertical, transverse, and longitudinal).AL-Qadi et al. [28] measured the three-dimensional contact stress caused by the tire on the pavement and found that the transverse tangential stresses are about 0.183 times of the vertical stresses. Therefore, in this paper, the transverse tangential stress is taken as 0.183 times of the vertical stress.


## 4.3.1. Vertical Traffic Loads

In this paper, to simplify the calculation and simulation, traffic loads could be estimated using the haversine function as the following equation [24]:(1)Pt=PmaxsinπtT,(2)Pmax=PDAF,where Pmax (MPa) is the peak value of the vibrating load, T (s) is the period of traffic loads, t (s) is the time, P (MPa) is the uniformly distributed traffic loads, P = 0.7 MPa in China, and DAF is the dynamic amplification factor.(3)DAF=1+aV,where V (km/h) is the speed; in this study, V = 60 and 70 km/h, and a is the riding quality evaluation factor, correlated with IRI, and in this study, a=0.035 [25].T could be calculated using the following formula:(4)T=12Rv,where R (m) is the equivalent radius of single wheel load, R=3L/2, and L is the length of the uniformly distributed rectangular load; in this study, L = 0.20 m, and v (m/s) is the speed. Hence, calculation results of the period of traffic loads (T), the dynamic amplification factor (DAF), and the peak value of the vibrating load (Pmax) under different traffic speeds are shown in Table 3.Table 3
Calculation results ofT, DAF, and Pmax under different traffic speeds.
Speed (km/h)6080100120T (s)0.0770.0580.0460.038DAF1.2711.3131.3501.383Pmax (MPa)0.8900.9190.9450.968


## 4.3.2. Horizontal Traffic Loads

(1) Longitudinal Friction Stresses. The longitudinal tangential stresses are affected by many factors, such as texture depth of the pavement surface, humidity, driving speed, and textures of tires. According to reference [26], the friction coefficient of the asphalt pavement under different driving speeds was measured through the sideways-force coefficient routine investigation machine (SCRIM), and the relationship between the friction coefficient and the driving speed was shown as follows:(5)μ=−0.00695V+0.87495,where μ is the friction coefficient of the asphalt pavement and V is the driving speed (km/h).(2) Transverse Tangential Stresses. In addition to the vertical pressure and the longitudinal friction stresses, vehicles would also cause transverse tangential stresses [27], shown in Figure 11.Figure 11
Contact stresses (vertical, transverse, and longitudinal).AL-Qadi et al. [28] measured the three-dimensional contact stress caused by the tire on the pavement and found that the transverse tangential stresses are about 0.183 times of the vertical stresses. Therefore, in this paper, the transverse tangential stress is taken as 0.183 times of the vertical stress.


## 4.4. Mechanical Parameters

The mechanical parameters are listed in Table4 [29, 30], based on the Chinese Specifications for Design of Highway Asphalt Pavement (JTG D50-2017). The dynamic modulus of asphalt mixture in Table 4 is that under 20°C and 10 Hz.Table 4
Mechanical parameters of pavement materials.
MaterialAK-13SMA-13AC-16AC-20AC-25Dynamic modulusE∗ (MPa)680070009000950010000Poisson’s ratioμ0.250.250.250.250.25Densityρ (kg/m3)24002400245024802505MaterialCement-treated sand gravelGraded macadamSubgradeC15C30Dynamic modulusE∗ (MPa)16000150652000030000Poisson’s ratioμ0.250.350.400.20.2Densityρ(kg/m3)23002250170024502500


## 4.5. Verification of FE Simulation Results

To verify the finite element simulation results in this paper, taking the pavement in Section C in Str-1 as an example, the mechanical responses calculated by the finite element method and the elastic multilayer theory assumption are compared and analyzed.The elastic multilayer theory assumption is the standard method in the Chinese Specifications for Design of Highway Asphalt Pavement (JTG D50-2017) to calculate the mechanical responses. It takes the maximum value of PointA, B, C, and D (shown in Figure 12) as the calculation result in this cross section, and the tire load was simplified as the uniformly distributed double circular load.Figure 12
Mechanical response calculation points in the elastic multilayer theory assumption.
(a)(b)The calculation results of the tensile strain at the bottom of the asphalt layer along the driving direction and the tensile stress at the bottom of the cement treated layer along the driving direction under the application of the standard axle load BZZ-100(100 kN) are shown in Figure13.Figure 13
The calculation results of two methods. (a) The calculation results of the tensile strain at the bottom of the asphalt layer along the driving direction. (b) The calculation results of tensile stress at the bottom of the cement treated layer along the driving direction.
(a)(b)If the calculation results of the finite element method are completely consistent with the calculation results of the elastic multilayer theory assumption, the calculation results shall be distributed along the dotted line in Figure13. It can be seen from Figure 13 that although the calculation results of the two methods are not completely consistent, there is a significant linear relationship between them in general, which can be expressed by the followingequations:(6)asphaltlayer:EL=1.1290×FE+0.2458R2=0.9891,(7)cementtreatedlayer:EL=1.1182×FE+0.00125R2=0.9861,where FE is the calculation results of the finite element method and EL is the calculation results of the elastic multilayer theory assumption.Therefore, the reliability of finite element calculation results can be guaranteed.


## 5. Analysis and Discussion of Mechanical Responses of Transition Structure

### 5.1. Analysis and Discussion of the Influence of Transition Structures

To make a comparison between the mechanical responses of the Yangkou tunnel and the Huangjiayu tunnel, traffic loads of 60 km/h and acceleration of −0.16 m/s2 [31] were applied, to simulate the process of driving into a tunnel. A transition structure was designed in the junction part in the Huangjiayu tunnel (shown in Figure 8), and there is no transition structure in the entrance and exit sections of the Yangkou tunnel (shown in Figure 9).In Part 5.1, the necessity of setting a transition section would be analyzed. Moving loads were applied on the structure and the load step 5 was exactly applied on the interfaces, which was Position ① in Str-1 and Str-2 (shown in Figures8 and 9), respectively. In addition, the simulation result of load step 1 was discarded because there is a large difference between the simulation result of load step 1 and other steps.


#### 5.1.1. Influence of Transition Structure on Asphalt Courses

The discontinuity of the structural layer will have a great impact on the shear performance, and therefore the shear stress response of the asphalt pavement outside the tunnel was firstly analyzed, as shown in Figure14.Figure 14
Shear stress response of the asphalt pavement outside the tunnel. (a) Maximum shear stress outside tunnel in Str-1. (b) Maximum shear stress outside tunnel in Str-2.
(a)(b)It is shown in Figure14 clearly that when the loads pass through the transition section, whether to set the transition structure will have a great impact on the mechanical responses of the asphalt pavement in this section. Specifically, there is a significant difference in the shear stress of the asphalt layer between Str-1 and Str-2.It can be seen from Figure14(a) that when driving through Position ① of Str-1, the maximum shear stress of asphalt course suddenly changes at load step 5. The shear stresses of the SMA-13 layer and the AC-16 layer almost do not change, while shear stress of the AC-20 layer suddenly decreases. It is possibly when the lower layer of asphalt changes into cement concrete, it would result in poor continuity of pavement structure and sudden change of stress. Besides, in spite of this, the shear stresses of each structural layer are still within the allowable range.In contrast to Figure14(b), for load step 5 on Str-2, the asphalt surface layer outside the tunnel is subject to a large stress mutation, which is far more than that of Str-1, which is very unfavorable. Taking the shear stress of the asphalt surface outside the tunnel as an example, the shear stress of the AC-20 layer of Str-1 decreases suddenly, and the variation range of shear stress is 6.43%. For Str-2, not only the shear stresses of the three asphalt layers increase suddenly but also the variation range is huge. The variation range of the AK-13 layer is 16.93% and that of the AC-20 layer and the AC-25 layer is 30.08% and 38.02%, respectively.In addition, it can be seen from Figure14 that the shear stresses of the upper layer of the two structures are greater than those of the middle layer. For average highway, the maximum shear stress of the asphalt layer is about 5-6 cm below the road surface, while for tunnel entrances and exits, the maximum value is obtained from the upper layer, which may be due to the high horizontal stress on the pavement surface caused by frequent braking of vehicles, resulting in the upward movement of the position of the maximum shear stress of the asphalt layer.Therefore, based on the above analysis, it is considered that setting transition structure is essential. There are great differences in the pavement structure inside and outside the tunnel. If the structural differentiation design cannot be carried out, the pavement will be damaged prematurely and cause economic losses.


#### 5.1.2. Influence of Transition Structure on Base Course

Tensile stresses at the bottom of the base course outside the tunnel of Str-1 and Str-2 are shown in Figure15.Figure 15
Tensile stress at the bottom of base course outside the tunnel. (a) Tensile stress at the bottom of base course in Str-1. (b) Tensile stress at the bottom of base course in Str-2.
(a)(b)It can be seen from Figure15 that due to the transition structure, there is a significant difference of tensile stress at the bottom of base course outside tunnel between Str-1 and Str-2, in the process of driving through the structural change.It can be seen from Figure15(a) that for the cement-treated gravel layer of Str-1, the tensile stress at the bottom of the layer decreases with the load moving forward after load step 3. For the concrete layer in transition structure, the tensile stress at the bottom of base course reaches the peak at load step 5. In addition, the tensile stress at the bottom of the cement-treated gravel layer exceeds that of the concrete layer at first. However, this is reversed afterwards. It is possibly because of the change of base course thickness. With the increase of the thickness of the concrete layer, its bearing proportion increases and gradually exceeds that of the cement-treated gravel layer. Hence, the tensile stress at the bottom changes.Since the interface of Str-2 is located at the portal, load steps 2∼4 were directly applied on the pavement outside the tunnel and load steps 6∼9 were applied on the pavement inside the tunnel. To ensure reasonableness of the tensile stress extracted, the tensile stress outside the tunnel was extracted from the bottom of the base course, and the tensile stress at the same depth was extracted for pavement inside the tunnel, as shown in Figure15(b).Figure15(b) shows that in the process of entering the tunnel, the tensile stress will suddenly change at load step 5, and the tensile stress at the bottom of the base course outside the tunnel exceeds that inside the tunnel. It is probably because load step 5 was applied on the interface between pavements inside and outside the tunnel, causing tensile stress at the bottom of the base course increase sharply. At the same time, because the concrete surface layer is used inside the tunnel and its bearing capacity is higher than that of the asphalt surface layer outside the tunnel, the tensile stress at the bottom of the base course in the tunnel is quite small.Comparing the stress of the base course in Figures15(a) and 15(b), the maximum tensile stress at the bottom of the upper base course and the lower base course of Str-2 is higher than that of the corresponding structure in Str-1. Therefore, transition structure can significantly improve performance of pavement structure in the entrance and exit sections, which is conducive to the realization of differentiated structure design.


#### 5.1.3. Influence of Overloading

To evaluate the influence of overloading on the mechanical responses of the pavement structure in the entrance and exit sections, the tensile stress at the bottom of the cement treated gravel layer inside and outside the tunnel is analyzed, and the simulation results are shown in Figure16.Figure 16
Maximum tensile stress at the bottom of the base course under the application of different overloading. (a) Maximum tensile stress in Str-1. (b) Maximum tensile stress in Str-2.
(a)(b)From Figure16, it is found that the tendency of the maximum tensile stress at the bottom of the base course of Str-1 and Str-2 is same, when the traffic loads increase and move forward. Therefore, with the increase of traffic loads, the stress of pavement structure will become more and more unfavorable. When the standard axle load increases to 20% and 50% overloading, respectively, the maximum tensile stress of Str-1 increases by 20.16% and 47.79%, respectively, while that of Str-2 increases by 23.58% and 51.47%, respectively.Based on all the analysis in this section, it is considered that for the asphalt pavement in the entrance and exit sections, ensuring the structural continuity, carrying out differential design, and reasonably setting the transition structure will significantly decrease the stress of the pavement and reduce the probability of cracks and other distresses. Therefore, Str-1 is more reasonable.


### 5.2. Analysis and Discussion of Transition Structures of Seven Alternative Pavements

Based on the analysis of Part 5.1, Str-1 is superior to Str-2 considering tensile stress at the bottom of the base course and shear stress of the asphalt course. Therefore, in this section, Str-1 will be studied further. First, Str-1 and its 7 alternative pavements were proposed. Then, their mechanical responses under the application of traffic loads were analyzed.


#### 5.2.1. Seven Alternative Pavements

Although Str-1 is superior to Str-2 due to the transition structure, however, this transition part was determined by experience without mechanical simulation, and there are no regulations on transition structure design in the Chinese Specifications for Design of Highway Tunnels (JTG 3370.1-2018) and Chinese Specifications for Design of Highway Asphalt Pavement (JTG D50-2017). Hence, 7 alternative pavements were proposed based on Str-1 and are shown in Figures17(b)–17(h), and Figure 17(a) shows Str-1, to propose a more reasonable transition structure.Figure 17
Str-1 and 7 alternative pavement structures. (a) Str-1. (b) Str-1a. (c) Str-1b. (d) Str-1c. (e) Str-1d. (f) Str-1e. (g) Str-1f. (h) Str-1g.
(a)(b)(c)(d)(e)(f)(g)(h)Among them, in Figure17(b), the asphalt pavement is used both inside and outside the tunnel, which reflects pavement of the Yangkou tunnel after rehabilitation. In Figures 17(c) and 17(d), a concrete slab is inserted into the pavement outside the tunnel and the lower asphalt layer and the upper base course transit into concrete slab simultaneously. The length of the concrete slab is 4.5 m and 6 m, respectively. In Figures 17(e)–17(h), the inserted concrete slab has variable cross section. Also, the cross section of inserted concrete slab in Str-1 is variable. The length of the concrete slab in Figures 17(e) and Figures 17(f) and 17(h) is 4.5 m and 6 m, respectively.In addition, according to the Chinese specifications, the length of the pavement concrete slab shall not exceed 6 m and 4∼6 m should be adopted. Therefore, the length of the concrete slab in the pavement structures shown in Figure17 is set to be 4.5 m and 6 m, respectively.


#### 5.2.2. Analysis and Discussion

9 load steps of 70 km/h and −0.16 m/s2 were applied. The load step 5 was exactly applied on the marking place of 8 pavements, and the marking place is shown in Figures 17(a)–17(h) in blue. The simulation results are shown in Table 5.Table 5
Simulation results of 8 pavement structures under the application of traffic loads (MPa).
StructureMarking placePavement outsidePavement insideMaximum shear stress in asphalt courseTensile stress at the bottom of base courseMaximum shear stress in asphalt courseTensile stress at the bottom of base courseSMA-13AC-16AC-20Concrete slabCement treated gravelSMA-13AC-16Concrete pavementStr-1①0.25160.21910.20640.02880.06800.02530.04430.1203②0.24450.21620.18090.01980.09740.01700.03190.0883Str-1a—0.26580.22990.2343—0.02350.24430.21850.0697Str-1b—0.24470.21320.20510.08060.09660.01710.03230.0894Str-1c—0.24510.21340.20560.04640.09330.00870.01700.0477Str-1d①0.24710.21660.20090.02560.09160.02410.04410.1304②0.24460.21630.18090.01990.09730.01720.03240.0961Str-1e①0.25150.21900.20630.02880.06830.02500.04370.1288②0.24500.21640.18120.01770.09440.00820.01620.0482Str-1f①0.24720.21660.20100.02530.09110.023590.04300.1274②0.24500.21650.18120.01780.09430.00850.01670.0498Str-1g①0.24670.21640.20020.02330.09360.01660.03120.0925②0.24500.21650.18120.01790.09410.00860.01690.0503Note. The tensile stress at the bottom of the base course in Table 5 takes the larger value of the tensile stress along the driving direction and perpendicular to the driving direction.From Table5, it can be found that compared with Str-1a, Str-1 and Str-1b∼ Str-1g with transition structure can significantly reduce the maximum shear stress in the asphalt course inside and outside the tunnel. Therefore, concrete slab at the connection part can effectively help pavement transition.It is also shown that compared with Str-1b and Str-1c, when the length of a concrete slab is 4.5 m (Str-1b), the shear stress of each layer is relatively small. Therefore, when the lower asphalt layer and the upper base course transit into the concrete slab simultaneously, it is more reasonable to set the concrete slab at 4.5 m. It can also be understood that when the asphalt surface inside and outside the tunnel is designed to be two layers, it is more reasonable to use Str-1b.To make a comparison among Str-1and Str-1d∼Str-1g and determine the reasonable length of the concrete slab, simulation results when traffic loads were applied on position ② are extracted and shown in Figure18.Figure 18
Maximum shear stress in the asphalt course of Str-1and Str-1d∼Str-1g. (a) Maximum shear stress in the upper and middle asphalt layers. (b) Maximum shear stress in the lower asphalt layer.
(a)(b)It can be seen from Figure18 that the maximum shear stress in asphalt surface outside the tunnel increases with the increase of the length of a concrete slab. When the length of a concrete slab is 4.5 m (Str-1 and Str-1d), the maximum shear stress in the surface is the lowest. Therefore, it can be preliminarily concluded that whether the lower asphalt layer and the upper base course transit into concrete slab simultaneously or not, when the length of the concrete slab is 4.5 m, the maximum shear stress in the asphalt layer of the pavement outside the tunnel is the lowest, which may be due to the fact that when the concrete slab is longer (>4.5 m), it exceeds the appropriate length, making the pavement outside the tunnel indirectly become the asphalt pavement with rigid base, resulting in the increase of the maximum shear stress in the asphalt layer.Since the length of the concrete slab set in Str-1, Str-1b, and Str-1d is 4.5 m, therefore the three pavement structures are further compared. Firstly, Str-1 and Str-1d are compared. Since the stress has been analyzed when the moving loads were applied at position ②, the stress when the moving loads were applied at position ① would be analyzed in this part. When the moving load was applied on position ①, the maximum shear stress in the asphalt layer and the tensile stress at the bottom of the base course of Str-1 are less than those of Str-1d (shown in Table4). Hence, Str-1 is better. It can also be understood that when the asphalt surface outside the tunnel is designed to be three layers and the asphalt surface inside the tunnel is designed to be two layers, the Str-1 is more reasonable.To sum up, it can be concluded that when the asphalt surface outside the tunnel is designed to be three layers, it is more appropriate to use Str-1 as the tunnel transition pavement. When the asphalt surface outside the tunnel is designed to be two layers, Str-1b is more reasonable.


## 5.1. Analysis and Discussion of the Influence of Transition Structures

To make a comparison between the mechanical responses of the Yangkou tunnel and the Huangjiayu tunnel, traffic loads of 60 km/h and acceleration of −0.16 m/s2 [31] were applied, to simulate the process of driving into a tunnel. A transition structure was designed in the junction part in the Huangjiayu tunnel (shown in Figure 8), and there is no transition structure in the entrance and exit sections of the Yangkou tunnel (shown in Figure 9).In Part 5.1, the necessity of setting a transition section would be analyzed. Moving loads were applied on the structure and the load step 5 was exactly applied on the interfaces, which was Position ① in Str-1 and Str-2 (shown in Figures8 and 9), respectively. In addition, the simulation result of load step 1 was discarded because there is a large difference between the simulation result of load step 1 and other steps.


### 5.1.1. Influence of Transition Structure on Asphalt Courses

The discontinuity of the structural layer will have a great impact on the shear performance, and therefore the shear stress response of the asphalt pavement outside the tunnel was firstly analyzed, as shown in Figure14.Figure 14
Shear stress response of the asphalt pavement outside the tunnel. (a) Maximum shear stress outside tunnel in Str-1. (b) Maximum shear stress outside tunnel in Str-2.
(a)(b)It is shown in Figure14 clearly that when the loads pass through the transition section, whether to set the transition structure will have a great impact on the mechanical responses of the asphalt pavement in this section. Specifically, there is a significant difference in the shear stress of the asphalt layer between Str-1 and Str-2.It can be seen from Figure14(a) that when driving through Position ① of Str-1, the maximum shear stress of asphalt course suddenly changes at load step 5. The shear stresses of the SMA-13 layer and the AC-16 layer almost do not change, while shear stress of the AC-20 layer suddenly decreases. It is possibly when the lower layer of asphalt changes into cement concrete, it would result in poor continuity of pavement structure and sudden change of stress. Besides, in spite of this, the shear stresses of each structural layer are still within the allowable range.In contrast to Figure14(b), for load step 5 on Str-2, the asphalt surface layer outside the tunnel is subject to a large stress mutation, which is far more than that of Str-1, which is very unfavorable. Taking the shear stress of the asphalt surface outside the tunnel as an example, the shear stress of the AC-20 layer of Str-1 decreases suddenly, and the variation range of shear stress is 6.43%. For Str-2, not only the shear stresses of the three asphalt layers increase suddenly but also the variation range is huge. The variation range of the AK-13 layer is 16.93% and that of the AC-20 layer and the AC-25 layer is 30.08% and 38.02%, respectively.In addition, it can be seen from Figure14 that the shear stresses of the upper layer of the two structures are greater than those of the middle layer. For average highway, the maximum shear stress of the asphalt layer is about 5-6 cm below the road surface, while for tunnel entrances and exits, the maximum value is obtained from the upper layer, which may be due to the high horizontal stress on the pavement surface caused by frequent braking of vehicles, resulting in the upward movement of the position of the maximum shear stress of the asphalt layer.Therefore, based on the above analysis, it is considered that setting transition structure is essential. There are great differences in the pavement structure inside and outside the tunnel. If the structural differentiation design cannot be carried out, the pavement will be damaged prematurely and cause economic losses.


### 5.1.2. Influence of Transition Structure on Base Course

Tensile stresses at the bottom of the base course outside the tunnel of Str-1 and Str-2 are shown in Figure15.Figure 15
Tensile stress at the bottom of base course outside the tunnel. (a) Tensile stress at the bottom of base course in Str-1. (b) Tensile stress at the bottom of base course in Str-2.
(a)(b)It can be seen from Figure15 that due to the transition structure, there is a significant difference of tensile stress at the bottom of base course outside tunnel between Str-1 and Str-2, in the process of driving through the structural change.It can be seen from Figure15(a) that for the cement-treated gravel layer of Str-1, the tensile stress at the bottom of the layer decreases with the load moving forward after load step 3. For the concrete layer in transition structure, the tensile stress at the bottom of base course reaches the peak at load step 5. In addition, the tensile stress at the bottom of the cement-treated gravel layer exceeds that of the concrete layer at first. However, this is reversed afterwards. It is possibly because of the change of base course thickness. With the increase of the thickness of the concrete layer, its bearing proportion increases and gradually exceeds that of the cement-treated gravel layer. Hence, the tensile stress at the bottom changes.Since the interface of Str-2 is located at the portal, load steps 2∼4 were directly applied on the pavement outside the tunnel and load steps 6∼9 were applied on the pavement inside the tunnel. To ensure reasonableness of the tensile stress extracted, the tensile stress outside the tunnel was extracted from the bottom of the base course, and the tensile stress at the same depth was extracted for pavement inside the tunnel, as shown in Figure15(b).Figure15(b) shows that in the process of entering the tunnel, the tensile stress will suddenly change at load step 5, and the tensile stress at the bottom of the base course outside the tunnel exceeds that inside the tunnel. It is probably because load step 5 was applied on the interface between pavements inside and outside the tunnel, causing tensile stress at the bottom of the base course increase sharply. At the same time, because the concrete surface layer is used inside the tunnel and its bearing capacity is higher than that of the asphalt surface layer outside the tunnel, the tensile stress at the bottom of the base course in the tunnel is quite small.Comparing the stress of the base course in Figures15(a) and 15(b), the maximum tensile stress at the bottom of the upper base course and the lower base course of Str-2 is higher than that of the corresponding structure in Str-1. Therefore, transition structure can significantly improve performance of pavement structure in the entrance and exit sections, which is conducive to the realization of differentiated structure design.


### 5.1.3. Influence of Overloading

To evaluate the influence of overloading on the mechanical responses of the pavement structure in the entrance and exit sections, the tensile stress at the bottom of the cement treated gravel layer inside and outside the tunnel is analyzed, and the simulation results are shown in Figure16.Figure 16
Maximum tensile stress at the bottom of the base course under the application of different overloading. (a) Maximum tensile stress in Str-1. (b) Maximum tensile stress in Str-2.
(a)(b)From Figure16, it is found that the tendency of the maximum tensile stress at the bottom of the base course of Str-1 and Str-2 is same, when the traffic loads increase and move forward. Therefore, with the increase of traffic loads, the stress of pavement structure will become more and more unfavorable. When the standard axle load increases to 20% and 50% overloading, respectively, the maximum tensile stress of Str-1 increases by 20.16% and 47.79%, respectively, while that of Str-2 increases by 23.58% and 51.47%, respectively.Based on all the analysis in this section, it is considered that for the asphalt pavement in the entrance and exit sections, ensuring the structural continuity, carrying out differential design, and reasonably setting the transition structure will significantly decrease the stress of the pavement and reduce the probability of cracks and other distresses. Therefore, Str-1 is more reasonable.


## 5.1.1. Influence of Transition Structure on Asphalt Courses

The discontinuity of the structural layer will have a great impact on the shear performance, and therefore the shear stress response of the asphalt pavement outside the tunnel was firstly analyzed, as shown in Figure14.Figure 14
Shear stress response of the asphalt pavement outside the tunnel. (a) Maximum shear stress outside tunnel in Str-1. (b) Maximum shear stress outside tunnel in Str-2.
(a)(b)It is shown in Figure14 clearly that when the loads pass through the transition section, whether to set the transition structure will have a great impact on the mechanical responses of the asphalt pavement in this section. Specifically, there is a significant difference in the shear stress of the asphalt layer between Str-1 and Str-2.It can be seen from Figure14(a) that when driving through Position ① of Str-1, the maximum shear stress of asphalt course suddenly changes at load step 5. The shear stresses of the SMA-13 layer and the AC-16 layer almost do not change, while shear stress of the AC-20 layer suddenly decreases. It is possibly when the lower layer of asphalt changes into cement concrete, it would result in poor continuity of pavement structure and sudden change of stress. Besides, in spite of this, the shear stresses of each structural layer are still within the allowable range.In contrast to Figure14(b), for load step 5 on Str-2, the asphalt surface layer outside the tunnel is subject to a large stress mutation, which is far more than that of Str-1, which is very unfavorable. Taking the shear stress of the asphalt surface outside the tunnel as an example, the shear stress of the AC-20 layer of Str-1 decreases suddenly, and the variation range of shear stress is 6.43%. For Str-2, not only the shear stresses of the three asphalt layers increase suddenly but also the variation range is huge. The variation range of the AK-13 layer is 16.93% and that of the AC-20 layer and the AC-25 layer is 30.08% and 38.02%, respectively.In addition, it can be seen from Figure14 that the shear stresses of the upper layer of the two structures are greater than those of the middle layer. For average highway, the maximum shear stress of the asphalt layer is about 5-6 cm below the road surface, while for tunnel entrances and exits, the maximum value is obtained from the upper layer, which may be due to the high horizontal stress on the pavement surface caused by frequent braking of vehicles, resulting in the upward movement of the position of the maximum shear stress of the asphalt layer.Therefore, based on the above analysis, it is considered that setting transition structure is essential. There are great differences in the pavement structure inside and outside the tunnel. If the structural differentiation design cannot be carried out, the pavement will be damaged prematurely and cause economic losses.


## 5.1.2. Influence of Transition Structure on Base Course

Tensile stresses at the bottom of the base course outside the tunnel of Str-1 and Str-2 are shown in Figure15.Figure 15
Tensile stress at the bottom of base course outside the tunnel. (a) Tensile stress at the bottom of base course in Str-1. (b) Tensile stress at the bottom of base course in Str-2.
(a)(b)It can be seen from Figure15 that due to the transition structure, there is a significant difference of tensile stress at the bottom of base course outside tunnel between Str-1 and Str-2, in the process of driving through the structural change.It can be seen from Figure15(a) that for the cement-treated gravel layer of Str-1, the tensile stress at the bottom of the layer decreases with the load moving forward after load step 3. For the concrete layer in transition structure, the tensile stress at the bottom of base course reaches the peak at load step 5. In addition, the tensile stress at the bottom of the cement-treated gravel layer exceeds that of the concrete layer at first. However, this is reversed afterwards. It is possibly because of the change of base course thickness. With the increase of the thickness of the concrete layer, its bearing proportion increases and gradually exceeds that of the cement-treated gravel layer. Hence, the tensile stress at the bottom changes.Since the interface of Str-2 is located at the portal, load steps 2∼4 were directly applied on the pavement outside the tunnel and load steps 6∼9 were applied on the pavement inside the tunnel. To ensure reasonableness of the tensile stress extracted, the tensile stress outside the tunnel was extracted from the bottom of the base course, and the tensile stress at the same depth was extracted for pavement inside the tunnel, as shown in Figure15(b).Figure15(b) shows that in the process of entering the tunnel, the tensile stress will suddenly change at load step 5, and the tensile stress at the bottom of the base course outside the tunnel exceeds that inside the tunnel. It is probably because load step 5 was applied on the interface between pavements inside and outside the tunnel, causing tensile stress at the bottom of the base course increase sharply. At the same time, because the concrete surface layer is used inside the tunnel and its bearing capacity is higher than that of the asphalt surface layer outside the tunnel, the tensile stress at the bottom of the base course in the tunnel is quite small.Comparing the stress of the base course in Figures15(a) and 15(b), the maximum tensile stress at the bottom of the upper base course and the lower base course of Str-2 is higher than that of the corresponding structure in Str-1. Therefore, transition structure can significantly improve performance of pavement structure in the entrance and exit sections, which is conducive to the realization of differentiated structure design.


## 5.1.3. Influence of Overloading

To evaluate the influence of overloading on the mechanical responses of the pavement structure in the entrance and exit sections, the tensile stress at the bottom of the cement treated gravel layer inside and outside the tunnel is analyzed, and the simulation results are shown in Figure16.Figure 16
Maximum tensile stress at the bottom of the base course under the application of different overloading. (a) Maximum tensile stress in Str-1. (b) Maximum tensile stress in Str-2.
(a)(b)From Figure16, it is found that the tendency of the maximum tensile stress at the bottom of the base course of Str-1 and Str-2 is same, when the traffic loads increase and move forward. Therefore, with the increase of traffic loads, the stress of pavement structure will become more and more unfavorable. When the standard axle load increases to 20% and 50% overloading, respectively, the maximum tensile stress of Str-1 increases by 20.16% and 47.79%, respectively, while that of Str-2 increases by 23.58% and 51.47%, respectively.Based on all the analysis in this section, it is considered that for the asphalt pavement in the entrance and exit sections, ensuring the structural continuity, carrying out differential design, and reasonably setting the transition structure will significantly decrease the stress of the pavement and reduce the probability of cracks and other distresses. Therefore, Str-1 is more reasonable.


## 5.2. Analysis and Discussion of Transition Structures of Seven Alternative Pavements

Based on the analysis of Part 5.1, Str-1 is superior to Str-2 considering tensile stress at the bottom of the base course and shear stress of the asphalt course. Therefore, in this section, Str-1 will be studied further. First, Str-1 and its 7 alternative pavements were proposed. Then, their mechanical responses under the application of traffic loads were analyzed.


### 5.2.1. Seven Alternative Pavements

Although Str-1 is superior to Str-2 due to the transition structure, however, this transition part was determined by experience without mechanical simulation, and there are no regulations on transition structure design in the Chinese Specifications for Design of Highway Tunnels (JTG 3370.1-2018) and Chinese Specifications for Design of Highway Asphalt Pavement (JTG D50-2017). Hence, 7 alternative pavements were proposed based on Str-1 and are shown in Figures17(b)–17(h), and Figure 17(a) shows Str-1, to propose a more reasonable transition structure.Figure 17
Str-1 and 7 alternative pavement structures. (a) Str-1. (b) Str-1a. (c) Str-1b. (d) Str-1c. (e) Str-1d. (f) Str-1e. (g) Str-1f. (h) Str-1g.
(a)(b)(c)(d)(e)(f)(g)(h)Among them, in Figure17(b), the asphalt pavement is used both inside and outside the tunnel, which reflects pavement of the Yangkou tunnel after rehabilitation. In Figures 17(c) and 17(d), a concrete slab is inserted into the pavement outside the tunnel and the lower asphalt layer and the upper base course transit into concrete slab simultaneously. The length of the concrete slab is 4.5 m and 6 m, respectively. In Figures 17(e)–17(h), the inserted concrete slab has variable cross section. Also, the cross section of inserted concrete slab in Str-1 is variable. The length of the concrete slab in Figures 17(e) and Figures 17(f) and 17(h) is 4.5 m and 6 m, respectively.In addition, according to the Chinese specifications, the length of the pavement concrete slab shall not exceed 6 m and 4∼6 m should be adopted. Therefore, the length of the concrete slab in the pavement structures shown in Figure17 is set to be 4.5 m and 6 m, respectively.


### 5.2.2. Analysis and Discussion

9 load steps of 70 km/h and −0.16 m/s2 were applied. The load step 5 was exactly applied on the marking place of 8 pavements, and the marking place is shown in Figures 17(a)–17(h) in blue. The simulation results are shown in Table 5.Table 5
Simulation results of 8 pavement structures under the application of traffic loads (MPa).
StructureMarking placePavement outsidePavement insideMaximum shear stress in asphalt courseTensile stress at the bottom of base courseMaximum shear stress in asphalt courseTensile stress at the bottom of base courseSMA-13AC-16AC-20Concrete slabCement treated gravelSMA-13AC-16Concrete pavementStr-1①0.25160.21910.20640.02880.06800.02530.04430.1203②0.24450.21620.18090.01980.09740.01700.03190.0883Str-1a—0.26580.22990.2343—0.02350.24430.21850.0697Str-1b—0.24470.21320.20510.08060.09660.01710.03230.0894Str-1c—0.24510.21340.20560.04640.09330.00870.01700.0477Str-1d①0.24710.21660.20090.02560.09160.02410.04410.1304②0.24460.21630.18090.01990.09730.01720.03240.0961Str-1e①0.25150.21900.20630.02880.06830.02500.04370.1288②0.24500.21640.18120.01770.09440.00820.01620.0482Str-1f①0.24720.21660.20100.02530.09110.023590.04300.1274②0.24500.21650.18120.01780.09430.00850.01670.0498Str-1g①0.24670.21640.20020.02330.09360.01660.03120.0925②0.24500.21650.18120.01790.09410.00860.01690.0503Note. The tensile stress at the bottom of the base course in Table 5 takes the larger value of the tensile stress along the driving direction and perpendicular to the driving direction.From Table5, it can be found that compared with Str-1a, Str-1 and Str-1b∼ Str-1g with transition structure can significantly reduce the maximum shear stress in the asphalt course inside and outside the tunnel. Therefore, concrete slab at the connection part can effectively help pavement transition.It is also shown that compared with Str-1b and Str-1c, when the length of a concrete slab is 4.5 m (Str-1b), the shear stress of each layer is relatively small. Therefore, when the lower asphalt layer and the upper base course transit into the concrete slab simultaneously, it is more reasonable to set the concrete slab at 4.5 m. It can also be understood that when the asphalt surface inside and outside the tunnel is designed to be two layers, it is more reasonable to use Str-1b.To make a comparison among Str-1and Str-1d∼Str-1g and determine the reasonable length of the concrete slab, simulation results when traffic loads were applied on position ② are extracted and shown in Figure18.Figure 18
Maximum shear stress in the asphalt course of Str-1and Str-1d∼Str-1g. (a) Maximum shear stress in the upper and middle asphalt layers. (b) Maximum shear stress in the lower asphalt layer.
(a)(b)It can be seen from Figure18 that the maximum shear stress in asphalt surface outside the tunnel increases with the increase of the length of a concrete slab. When the length of a concrete slab is 4.5 m (Str-1 and Str-1d), the maximum shear stress in the surface is the lowest. Therefore, it can be preliminarily concluded that whether the lower asphalt layer and the upper base course transit into concrete slab simultaneously or not, when the length of the concrete slab is 4.5 m, the maximum shear stress in the asphalt layer of the pavement outside the tunnel is the lowest, which may be due to the fact that when the concrete slab is longer (>4.5 m), it exceeds the appropriate length, making the pavement outside the tunnel indirectly become the asphalt pavement with rigid base, resulting in the increase of the maximum shear stress in the asphalt layer.Since the length of the concrete slab set in Str-1, Str-1b, and Str-1d is 4.5 m, therefore the three pavement structures are further compared. Firstly, Str-1 and Str-1d are compared. Since the stress has been analyzed when the moving loads were applied at position ②, the stress when the moving loads were applied at position ① would be analyzed in this part. When the moving load was applied on position ①, the maximum shear stress in the asphalt layer and the tensile stress at the bottom of the base course of Str-1 are less than those of Str-1d (shown in Table4). Hence, Str-1 is better. It can also be understood that when the asphalt surface outside the tunnel is designed to be three layers and the asphalt surface inside the tunnel is designed to be two layers, the Str-1 is more reasonable.To sum up, it can be concluded that when the asphalt surface outside the tunnel is designed to be three layers, it is more appropriate to use Str-1 as the tunnel transition pavement. When the asphalt surface outside the tunnel is designed to be two layers, Str-1b is more reasonable.


## 5.2.1. Seven Alternative Pavements

Although Str-1 is superior to Str-2 due to the transition structure, however, this transition part was determined by experience without mechanical simulation, and there are no regulations on transition structure design in the Chinese Specifications for Design of Highway Tunnels (JTG 3370.1-2018) and Chinese Specifications for Design of Highway Asphalt Pavement (JTG D50-2017). Hence, 7 alternative pavements were proposed based on Str-1 and are shown in Figures17(b)–17(h), and Figure 17(a) shows Str-1, to propose a more reasonable transition structure.Figure 17
Str-1 and 7 alternative pavement structures. (a) Str-1. (b) Str-1a. (c) Str-1b. (d) Str-1c. (e) Str-1d. (f) Str-1e. (g) Str-1f. (h) Str-1g.
(a)(b)(c)(d)(e)(f)(g)(h)Among them, in Figure17(b), the asphalt pavement is used both inside and outside the tunnel, which reflects pavement of the Yangkou tunnel after rehabilitation. In Figures 17(c) and 17(d), a concrete slab is inserted into the pavement outside the tunnel and the lower asphalt layer and the upper base course transit into concrete slab simultaneously. The length of the concrete slab is 4.5 m and 6 m, respectively. In Figures 17(e)–17(h), the inserted concrete slab has variable cross section. Also, the cross section of inserted concrete slab in Str-1 is variable. The length of the concrete slab in Figures 17(e) and Figures 17(f) and 17(h) is 4.5 m and 6 m, respectively.In addition, according to the Chinese specifications, the length of the pavement concrete slab shall not exceed 6 m and 4∼6 m should be adopted. Therefore, the length of the concrete slab in the pavement structures shown in Figure17 is set to be 4.5 m and 6 m, respectively.


## 5.2.2. Analysis and Discussion

9 load steps of 70 km/h and −0.16 m/s2 were applied. The load step 5 was exactly applied on the marking place of 8 pavements, and the marking place is shown in Figures 17(a)–17(h) in blue. The simulation results are shown in Table 5.Table 5
Simulation results of 8 pavement structures under the application of traffic loads (MPa).
StructureMarking placePavement outsidePavement insideMaximum shear stress in asphalt courseTensile stress at the bottom of base courseMaximum shear stress in asphalt courseTensile stress at the bottom of base courseSMA-13AC-16AC-20Concrete slabCement treated gravelSMA-13AC-16Concrete pavementStr-1①0.25160.21910.20640.02880.06800.02530.04430.1203②0.24450.21620.18090.01980.09740.01700.03190.0883Str-1a—0.26580.22990.2343—0.02350.24430.21850.0697Str-1b—0.24470.21320.20510.08060.09660.01710.03230.0894Str-1c—0.24510.21340.20560.04640.09330.00870.01700.0477Str-1d①0.24710.21660.20090.02560.09160.02410.04410.1304②0.24460.21630.18090.01990.09730.01720.03240.0961Str-1e①0.25150.21900.20630.02880.06830.02500.04370.1288②0.24500.21640.18120.01770.09440.00820.01620.0482Str-1f①0.24720.21660.20100.02530.09110.023590.04300.1274②0.24500.21650.18120.01780.09430.00850.01670.0498Str-1g①0.24670.21640.20020.02330.09360.01660.03120.0925②0.24500.21650.18120.01790.09410.00860.01690.0503Note. The tensile stress at the bottom of the base course in Table 5 takes the larger value of the tensile stress along the driving direction and perpendicular to the driving direction.From Table5, it can be found that compared with Str-1a, Str-1 and Str-1b∼ Str-1g with transition structure can significantly reduce the maximum shear stress in the asphalt course inside and outside the tunnel. Therefore, concrete slab at the connection part can effectively help pavement transition.It is also shown that compared with Str-1b and Str-1c, when the length of a concrete slab is 4.5 m (Str-1b), the shear stress of each layer is relatively small. Therefore, when the lower asphalt layer and the upper base course transit into the concrete slab simultaneously, it is more reasonable to set the concrete slab at 4.5 m. It can also be understood that when the asphalt surface inside and outside the tunnel is designed to be two layers, it is more reasonable to use Str-1b.To make a comparison among Str-1and Str-1d∼Str-1g and determine the reasonable length of the concrete slab, simulation results when traffic loads were applied on position ② are extracted and shown in Figure18.Figure 18
Maximum shear stress in the asphalt course of Str-1and Str-1d∼Str-1g. (a) Maximum shear stress in the upper and middle asphalt layers. (b) Maximum shear stress in the lower asphalt layer.
(a)(b)It can be seen from Figure18 that the maximum shear stress in asphalt surface outside the tunnel increases with the increase of the length of a concrete slab. When the length of a concrete slab is 4.5 m (Str-1 and Str-1d), the maximum shear stress in the surface is the lowest. Therefore, it can be preliminarily concluded that whether the lower asphalt layer and the upper base course transit into concrete slab simultaneously or not, when the length of the concrete slab is 4.5 m, the maximum shear stress in the asphalt layer of the pavement outside the tunnel is the lowest, which may be due to the fact that when the concrete slab is longer (>4.5 m), it exceeds the appropriate length, making the pavement outside the tunnel indirectly become the asphalt pavement with rigid base, resulting in the increase of the maximum shear stress in the asphalt layer.Since the length of the concrete slab set in Str-1, Str-1b, and Str-1d is 4.5 m, therefore the three pavement structures are further compared. Firstly, Str-1 and Str-1d are compared. Since the stress has been analyzed when the moving loads were applied at position ②, the stress when the moving loads were applied at position ① would be analyzed in this part. When the moving load was applied on position ①, the maximum shear stress in the asphalt layer and the tensile stress at the bottom of the base course of Str-1 are less than those of Str-1d (shown in Table4). Hence, Str-1 is better. It can also be understood that when the asphalt surface outside the tunnel is designed to be three layers and the asphalt surface inside the tunnel is designed to be two layers, the Str-1 is more reasonable.To sum up, it can be concluded that when the asphalt surface outside the tunnel is designed to be three layers, it is more appropriate to use Str-1 as the tunnel transition pavement. When the asphalt surface outside the tunnel is designed to be two layers, Str-1b is more reasonable.


## 6. Conclusion

The entrance and exit sections of a tunnel are subject to different environments, pavements, and traffic conditions, which is quite different from the ordinary highway section, and it should be considered differentially, when designing the pavement structures. Although a lot of studies were carried on the entrance and exit sections of a tunnel, there are few ones on the mechanical response characteristics of the pavement structures. In this paper, the Huangjiayu tunnel of Qingdao-Lanzhou Highway and the Yangkou tunnel of Qingdao Binhai Highway in Shandong province were taken as case study engineering. Meanwhile, 7 other alternative pavement structures were proposed, simulated, and analyzed through ANSYS. It can be concluded that(1)
Setting transition structure is essential and it can ensure the continuity of the pavement and significantly reduce the sudden change of shear stress of the asphalt layer and thus prevent premature pavement damaged.(2)
For the asphalt pavement in the entrance and exit sections, ensuring the structural continuity, carrying out differential design, and reasonably setting the transition structure will significantly decrease the stress of the pavement and reduce the probability of cracks and other distresses. Hence, Str-1 is more reasonable compared with Str-2.(3)
As Yangkou tunnel, even if the concrete course was milled and an asphalt course was paved, its pavement structure is still quite different from that of Str-1 in the structural continuity. Hence, it is recommended that when a pavement structure like this was rehabilitated, applying a transition structure would be necessary.(4)
When the asphalt course outside the tunnel is designed to be three layers, it is more appropriate to use Str-1 as the tunnel transition pavement, whose concrete slab has variable cross section, and the length of the concrete slab is 4.5 m. When the asphalt surface outside the tunnel is designed to be two layers, Str-1b is more reasonable and the length of the concrete slab is also 4.5 m.



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*Source: 8058525-2022-10-03.xml*