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Criteria for controlling rutting of asphalt concrete materials in sloped pavement
Construction and Building Materials 35 (2012) 330–339
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Criteria for controlling rutting of asphalt concrete materials in sloped pavement Li Chang ⇑, Li Linglin Dept. of Highway and Railway Engineering, Univ. of Southeast, Jiangsu 210096, China
h i g h l i g h t s " Specimen in rutting test and actual pavement are modeled. " Long-term rutting depth of actual pavement is predicted. " Material criteria are put forward with traffic volume and gradient of slope. " A method is provided for controlling long-term rutting depth.
a r t i c l e
i n f o
Article history: Received 9 November 2011 Received in revised form 12 April 2012 Accepted 16 April 2012
Keywords: Asphalt pavements Rutting Control Finite element method (FEM) Slopes
a b s t r a c t The development of rutting is one of the most common distresses in asphalt pavement. Especially at road sections with longitudinal slope, the problem is more serious than sections with no slope. This is because the slope decreases the average speed of vehicles running upward, so the total loading time increases dramatically. In China, dynamic stability (DS) in rutting test is used as the main experimental criteria to control the asphalt concrete (AC) materials before construction. It is supposed that the larger the DS index is means the material has better capability of retarding the ruts’ development after constructed. Fixed DS criteria are set for diverse road situations. These differences in situations exhibit in structure and materials, traffic volume, climate condition and the gradient of sloped pavement. This paper aims at establishing a new control approach of AC material for dealing with rutting problem. Finite element method (FEM) is used to simulate two objects: specimen in rutting test and typical actual pavement with slope. In these simulations, the constitutive model of AC is the common basis. Through the model, specimen in rutting test and actual pavement are connected. It provides a possible way to control pavement rutting by computing and providing detailed criteria for specific project with special situations. These criteria change with actual service circumstances of pavement. Compared with fixed criteria, they are more flexible, accurate and feasible for using in rutting control practice. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Rutting computation method The rutting of asphalt pavement derives from the non-linear, viscous and plastic properties of asphalt concrete (AC). It includes the viscoelastic and viscoplastic characteristics of asphalt and the plastic properties of gravel and soil. Rutting can be described as the unrecoverable vertical deformation. Establishing suitable constitutive model for AC is very important to analyze pavement structure and predict its response during usage. It is true for rutting prediction too. The former researchers [1–3] have drawn the conclusion that model should represent the deformation rule of AC pavement under high temperature and heavy load.
⇑ Corresponding author. Tel.: +86 13851514929. E-mail address: [email protected] (C. Li). 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.04.003
Archilla and Medanat [4] considered finite element method (FEM) provides a convenient approach to attain valid analyzing results from actual engineering structures. Especially in terms of considering viscoelastic property of AC, FEM can provide a practical and precise approach. This method can be used widely. It has become one of the most promising methods to investigate rutting problem of AC pavement [5]. Since 1990s, with the development of computer technology, FEM has become more and more popular. Now, the rutting prediction researches evolve from linear viscoelastic theory to non-linear viscoelastoplasticity theory. Corresponding studies in China are a little tardier. In 1990s, rutting researches were mainly based on high temperature performance experiments. Some prediction models were developed. It can be conclude that, the trend of rutting research is changing from elastic theory to viscoelastic and plastic theory, from linear theory to non-linear theory. FEM can deal with more than one kind of constitutive relations in one computed body. It can be used to simulate complex structures.
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Using FEM to analyze rutting problem is a numeric, simple and realistic way to attain reasonable results. At present, many researchers use FE software to solve rutting problems. This paper uses ABAQUS to analyze and decide the requirements for AC material in order to control pavement rutting, especially pavement at longitudinal slope sections.
‘‘allowable SPT,’’ an assessment can be performed on the mix to determine whether it is acceptable or not, as shown in Table 2. These typical tests and indicators shown above are realistic methods used for AC material control. However, they have not being closely connected to the performance of AC placed on road yet. 1.3. Problems at present
1.2. Material control for reducing rutting Under actual service circumstances of pavement, for retarding the development of rutting, the only way is to modulate the structure and material properties of pavement. It includes adding rutting-resistance layer and choosing AC materials with better hightemperature performance. Rutting is very sensitive to heavy load and its loading time. At road sections with longitudinal slope, average vehicles’ speed decreases when running upward. It results in more serious rutting distress at these sections. Special attention should be focused on this problem. This research tries to develop a series of material controlling criteria for road sections, which have different vehicle volumes and longitudinal slopes. In the mid 1980’s the Georgia loaded-wheel tester (GLWT) was developed. In 1996, Pavement Technology Inc. manufactured the first asphalt pavement analyzer (APA). This device is a modification of the GLWT and also can be used for rutting susceptibility of HMA pavements. The mix verification tester (MVT) is a device developed for testing rut susceptibility of field mixes. It uses the same standards as the APA, but is only capable of testing two gyratory or one beam compacted specimen at the same time. The MVT was developed to be used in a field laboratory because of its smaller size and weight [6]. But until recently, there is no criterion to directly measure rut susceptibility of HMA mix being placed on the roadway during production, not to mention the criteria of AC materials used at longitudinal slopes. Rutting test is used broadly in China. Dynamic stability (DS) index is used commonly to evaluate rutting susceptibility of AC. This test is carried out at 60 °C as required in Chinese specification [7]. Three AC layer systems are the most frequently used pavement structure. There are two kinds of criteria for different types of asphalt. As to AC using modified asphalt, depending on the average high temperature in July, the criterion is from 800 to 3000 (1/ mm). As for AC using regular asphalt, it is from 400 to 800. These criteria are used for the two upper layers of the three AC layers pavement. For bottom layer, it is lower, as listed in Table 1 [8]. The simple performance test (SPT) criteria are used to help select the most appropriate mix and structure combination during both the HMA mix and flexible pavement design process. In NCHRP report 580 [9], a simple example of how these SPT criteria would be implemented is presented in Table 2. This table shows that for a given mix and structure combination, at a given set of environmental and traffic level conditions, a minimum (allowable) SPT value would be required to limit a given pavement distress to a userdefined maximum desired value. This would be identical to selecting the maximum rut depth desired in the HMA pavement. When a laboratory or in situ measured mix SPT value is compared to this
Although rutting researches have lasted for years, and many achievements have been made, there are still some core problems left unresolved. Especially for road sections with longitudinal slopes: (1) The special driving condition of vehicles on slope is usually not considered, but it definitely influences the rutting situation of AC layers. (2) The gradients of slopes are usually not considered. (3) The relationship between laboratory experiment and actual performance of pavement has not been investigated thoroughly, so there is no detailed and corresponding standard that can be used for the rutting control of AC materials at sloped road sections. As generally known, rutting of AC pavement results from the properties of AC materials. It is critical to establish a method, which can provide effective, flexible and feasible material control criteria for specific road sections, especially at sloped sections. This is the focus of this research. 2. Objectives and method 2.1. Objectives As mentioned above, for controlling the rutting of AC pavement, there are some AC material control tests and criteria. However, these criteria are fixed or have nothing to do with the actual circumstances of pavement in service period. They do not change with different traffic volumes, temperature conditions and pavement structures. In other words, there are no practical criteria established at all. It results in poor pavement performance, distress or potential waste of material capability. This paper intends to establish a series of rutting control criteria. Numerical simulation is used to investigate the developing rule of rutting in laboratory and field. They are connected by the properties of AC materials. These properties are represented by parameters of AC used in constitutive model of FEM. Based on this connection between specimen and actual pavement, experimental control criteria of AC materials can be established to meet specific rutting control requirement of pavement. This is especially useful to control the material properties used at sloped sections. When the gradient and length of the slope grow, vehicles pass this section with a lower speed in upward direction. It results in the increasing in loading time. As a result, rutting is much more severe than horizontal sections. DS is used as a regular experimental indicator for detailed material control. Based on the vehicles, temperature and structure conditions, different DS requirements are put forward as criteria to limit the long-term rutting depth below a reasonable value. 2.2. Method Rutting influences the smoothness and safety of driving. It becomes worse mostly in the hottest days in a year, typically July or August. Increments of several millimeters can be observed in a few days.
Table 1 DS criteria in rutting test for AC material selection (1/mm). Asphalt type
AC (using regular asphalt) AC (using modified asphalt)
Layer position
Upper and middle layers Bottom layer Upper and middle layers
Average daily highest temperature in July (°C) Higher than 30
20–30
Lower than 20
800 500 1500–3000
600 400 1000–2000
400 300 800
Notes: 1. AC using modified asphalt seldom used for bottom layer; 2. For AC using modified asphalt, except the average daily highest temperature in July, the lowest temperature in winter is used for sub-zone zone too, and different criteria are used for different sub-zones, the given range is the lowest and highest criteria for all sub-zones.
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Table 2 General SPT criteria example using any test for any distress. Specimen ID
Actual SPT value measured in the laboratory or at the project site
Minimum allowable SPT value calculated for project conditions
Decision: yes or no?
A
150,000 units
200,000 units
B
225,000
Not acceptable Acceptable
4cm AC-13 6cm AC-20 8cm AC-25 10cm ATB-30 (Optional) 40cm Cement stabilized gravel 20cm Lime stabilized soil Subgrade
When investigating the rutting problem, a three-dimension (3D) object is selected. It has dimensions: 3.5 m length, 1.5 m width, and 1.78 m height (see Fig. 2a). As for the height, it includes 18 cm AC layer, 40 cm cement stabilized base, 20 cm lime stabilized subbase, and 100 cm subgrade. When considering the structure with ATB, the height is 1.88 m. The ‘‘C3D20R’’ element in ABAQUS is used in computation, it is a 3D solid element with 20 nodes and second order (quadratic) reduced integration element. When meshing, the dimensions of elements depend on its layer thickness. For better analysis, the dimensions of divisions in X and Z directions are not equal. The main principle used is that smaller size elements are set near to the loading area and the surface of pavement. Detailed dimensions and mesh used for FE computation are shown in Fig. 2. Pavement object is parted into eight equal divisions in Y direction, 20 divisions in X direction and 25 divisions in Z direction. The total number of elements is 4000. Boundary conditions are simple supports on the four vertical edge planes and the bottom plane.
Fig. 1. Pavement structure for analyzing.
3.2. Hypotheses of load and temperature Actually, temperature, traffic volume and gradient of slope are all critical influence factors of rutting. A series of criteria should be established to meet different situations, such as different traffic volumes, and gradients. Time hardening form of power-law model is selected as basic constitutive relation of AC to compute the rutting. Its parameters can be attained from experiments. According to existed standards, a suitable RD limitation is decided as long-term rutting control target. Based on model parameters, the long-term rutting depth can be calculated. Then it can be compared with the control target. If exceeded, the increment is divided into three AC layers. The next step is to modulate the parameters of timehardening model to meet the decreasing requirements of each layer in pavement. There are three parameters in time-hardening model of AC. Some of them is very stable for ordinary AC, and can be assumed as constant. There is no direct approach to control these parameters. It is more practical to control AC materials through some experiment and corresponding indicator and criteria. Rutting test is selected and numeric simulation is carried out. Parameters in the model are the bridge to connect the two objects: actual pavement and rutting test specimen. On the contrary, the DS index can be set separately for each AC layer and different road conditions to meet the requirement of long-term rutting depth. Three traffic volume levels are set, and 15 combinations of traffic level and gradient are established. Through computation, two of them need special DS control to meet long-term rutting depth limit. By this way, a new approach is established to limit the long-term rutting depth of sloped pavement by controlling the experimental indicator of AC materials. This paper is a preliminary study to establish a series of material control criteria for pavement rutting control. Using them, rutting on AC pavement at sloped sections can be controlled more subtly, according to their circumstances. They are traffic volumes, structure detail, and temperature field.
The rutting of AC pavement is the consequence of many factors, but the most important external factor is the load and high temperature. 3.2.1. Load Based on the analysis of vehicles driving on Chinese highway, a typical truck is selected for calculating the driving rule on the sloped pavement. The truck is called Dongfong EQ140. It has a single rear axle with four tires; its fully loaded weight is 10 tons on rear axle. In rutting computation, there are two levels of load: single time load and repeated load. The latter is based on the former, and finally used in computation. It has two important factors: contact stresses and loading time.
3. Structure, hypotheses, model and parameters
3.2.1.1. Contact stresses and its areas. When vehicle runs on sloped pavement, there are two main differences from running on horizontal surface: the speed of typical truck is slower and its weight can be decomposed to two forces in two directions (parallel and perpendicular to surface plane of pavement). The contact stress is assumed as constant, 0.7 MPa. ‘‘Two rectangle shapes’’ are selected in this research. The length of each contact rectangle is defined as L. It is parallel to the driving direction. The width is defined as B. Suppose the contact stress is uniform within the area, it has relationship with load P
3.1. Numerical model
P ¼ nw pBL
A typical pavement structure is selected as reference at first. It includes three AC layers (the total thickness is 18 cm), cement stabilized base course (40 cm) and lime stabilized subbase layer (20 cm), as shown in Fig. 1. For evaluating the effectiveness of asphalt treated base (ATB), two structures are compared, they are with or without 10 cm ATB layer. The AC-13, AC-20 and AC-25 are three types of AC most frequently used in China. Nominal maximum particle size (NMPS) is used to distinguish them. For instance, AC-13 has a NMPS of 13 mm, which is corresponding to the square-opening sieve size of 13.2 mm. The other two types are corresponding to 19.5 mm and 26.5 mm respectively. Their gradations are provided by Chinese specification of asphalt pavement construction. For investigating the influence of different gradients of sloped pavement, 4%, 5%, 6% and 7% are selected as four typical conditions. They are the tangent of slope angles. The slope with 0% gradient is used as comparison.
ð1Þ
where P is the weight of vehicle’s rear axle, N; nw is the tire number on rear axle, it is 4 for EQ140; p is the contact stress of the tire, Pa; L and B are the length and width of each contact rectangle, m. According to the tire on EQ140, its width B is set to 18.6 cm, and the distance between two adjacent tire center points is set to 31.4 cm, as shown in Fig. 3. 3.2.1.2. Loading time. During each tire passing, a pulse load is loaded. Its value, shape and time change with tire load, speed and so on. It can be assumed as a haversine or trigonometric function. Stress equivalence rule is used in this research, and the load is assumed as haversine shape, then further converted to static continuous load. For one time load,
Z 0
t0
r sin
pt t0
dt ¼ r0 t 0
ð2Þ
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(a) Dimensions of numerical model
(b) Meshes of numerical model
L
Fig. 2. Dimensions and meshes of three-dimension pavement structure.
Fig. 3. Contact area shape of two tires (cm).
It can be solved
2
r0 ¼ r p
ð3Þ
where r is the peak value of haversine load, Pa; r0 is the equivalent static load, Pa; t0 is the tire contact time for a loading period, s. When the contact stress and length are fixed, based on vehicle speed v, the time of every loading t0 is
t0 ¼
L
v
¼
P nw pBv
ð4Þ
So, when the loading times is N, the accumulated loading time t is
t ¼ N t0
ð5Þ
Bring the Eqs. (4) into (5)
t¼
NP 0:36nw pBv
typical truck EQ140, the speed on different slopes is computed and listed in Table 3. The vehicle distribution in transverse direction is very important when coupled with high temperatures. A typical distribution is selected in this research. It is assumed as the same in each day. This traffic distribution of a typical two-direction and fourlane highway in one typical day is surveyed and listed in Fig. 4. It can be seen in Fig. 4 that, traffic volume mainly distributes in day time, and it has two peak values at 10:00AM and 6:00PM. The shape of the curve likes a saddle. Based on surveyed traffic data, the daily traffic volume is calculated. The annual average daily traffic (AADT) is about 11,000 per day. Referring to Chinese specification [10], lane factor is g = 0.45. AADT of one lane is N = 11,000 0.45 = 4950 times/d. It can be used for computation of loading time. According to Fig. 4, the traffic volume and its corresponding time can be distributed into every hour of a single day. The result is shown in Table 4.
ð6Þ
where N is the loading times; P is the weight of axle, for simplifying purpose, it is assumed as the weight when the vehicle is fully loaded, kN; nw is the tire number of axle; p is the contact stress of tire, MPa; B is the width of contact rectangle, cm; v is the vehicle speed, km/h. It can be seen in Eq. (6) that, the vehicle speed shows obvious influence on the creation of rutting. For actual pavement, low speed (in other words, long loading time) vehicles under high temperature are the worst conditions for rutting development. For
3.2.2. Temperature Temperature influences rutting of AC pavement greatly. Previous researches show that, rutting increases obviously in the hottest
Table 3 The stable speed for EQ140 (full loaded) on different slope gradients (km/h). Slope gradient i (%) Stable speed (km/h)
4 60
5 55
6 50
7 40
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C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339
qðtÞ ¼ a expðððt bÞ=cÞ2 Þ
Fig. 4. Traffic volume distribution ratio by hours in single typical day.
several days of summer period. So, the temperature field must be considered, coupled with traffic volume. The base to consider long-term rutting is the increment of rutting in 1 day. Because the complexity of AC material and its time dependent characteristics, it is very hard to simulate a long-term rutting procedure. This research developed a simplified method to compute long-term rutting depth on the basis of daily rutting computation result. There are some parameters needed for the computing purpose, they are shown in Table 5. The computed data can be compared with the investigated data. Model and its parameters can be verified and modulated. At a specific point in pavement, the daily temperature changing curve can be assumed as Gaussian distribution. It can be represented by the following formula
ð7Þ
where q(t) is the solar radiation intensity; a, b, c are undetermined coefficients, and they are shown in Table 6. The data used for regression come from field investigating data of an actual pavement section within the hottest 7 days in 1 year. Then, the discrete temperature data are converted to a continuous curve. Using the user subroutine DFLUX, the temperature changing in vertical direction can be represented, and the whole temperature field can be decided. When computing, a steady state analysis should be constituted at first. This is used to decide the initial temperature field. Initial temperature is set to 20 °C. Then, transient state analyzing steps are set. They are used to simulate the temperature changing in seven hottest days. Seven analyzing steps are used, and each step represents 1 day. The comparison between predicted temperature and surveyed data in 1 day is shown in Fig. 5. This predicted temperature field is set as the typical temperature situations, and then coupled with the influence of load in the computations after.
3.3. Constitutive model and parameters Rutting is mainly an external expression of the creeping property of AC materials. For rutting analysis, the constitutive model should be able to represent the creeping effect. There are several kinds of models that can be used in ABAQUS. One of them is time hardening model. It is simple and its parameters can be regressed from experimental data. Triaxial creep experiment is selected and implemented to get creep parameters.
Table 4 Loading time of one lane in every hour within single typical day. Time
Loading time (s)
Time
Loading time (s)
Time
Loading time (s)
24:00–1:00
Gradient
4 5 6 7
0.72 0.78 0.86 1.07
8:00–9:00
Gradient
4 5 6 7
3.61 3.94 4.32 5.39
16:00–17:00
Gradient
4 5 6 7
3.52 3.83 4.21 5.25
1:00–2:00
Gradient
4 5 6 7
0.64 0.69 0.76 0.95
9:00–10:00
Gradient
4 5 6 7
3.68 4.01 4.41 5.50
17:00–18:00
Gradient
4 5 6 7
3.80 4.14 4.54 5.67
2:00–3:00
Gradient
4 5 6 7
0.61 0.66 0.73 0.91
10:00–11:00
Gradient
4 5 6 7
3.55 3.86 4.24 5.29
18:00–19:00
Gradient
4 5 6 7
3.54 3.86 4.24 5.28
3:00–4:00
Gradient
4 5 6 7
0.64 0.69 0.76 0.95
11:00–12:00
Gradient
4 5 6 7
3.29 3.58 3.94 4.91
19:00–20:00
Gradient
4 5 6 7
2.56 2.79 3.06 3.82
4:00–5:00
Gradient
4 5 6 7
0.76 0.83 0.91 1.14
12:00–13:00
Gradient
4 5 6 7
2.62 2.86 3.14 3.91
20:00–21:00
Gradient
4 5 6 7
1.94 2.11 2.32 2.89
5:00–6:00
Gradient
4 5 6 7
1.09 1.18 1.30 1.62
13:00–14:00
Gradient
4 5 6 7
2.63 2.87 3.15 3.93
21:00–22:00
Gradient
4 5 6 7
1.59 1.74 1.91 2.38
6:00–7:00
Gradient
4 5 6 7
1.86 2.02 2.22 2.77
14:00–15:00
Gradient
4 5 6 7
3.13 3.41 3.75 4.67
22:00–23:00
Gradient
4 5 6 7
1.24 1.36 1.49 1.86
7:00–8:00
Gradient
4 5 6 7
3.34 3.64 3.99 4.98
15:00–16:00
Gradient
4 5 6 7
3.36 3.65 4.01 5.01
23:00–24:00
Gradient
4 5 6 7
0.98 1.06 1.17 1.46
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C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339 Table 5 Parameters used for pavement temperature field analysis. Parameter
AC layers
Thermal conductivity k (J/m h °C) Density q (kg/m3) Specific heat capacity c (J/kg°C) Solar absorptance as Pavement surface emissivity e Absolute zero temperature TZ (°C) Stefan–Boltzmann constant r (J/(m2 h K4))
AC-13
AC-20
AC-25
7380 2100 1168.0
4500 2400 894.0
4176 2600 921.1
Cement stabilized base course
Lime stabilized subbase
Subgrade
3960 2077 810.0 0.87 0.81 273 2.041092 104
5148 2100 942.9
5616 1800 1040.0
Table 6 Undetermined coefficients and their coefficients of determination. Time
a (106)
a (95%, confidence interval) (106)
b
b (95%, confidence interval)
c
c (95%, confidence interval)
R2
1 2 3 4 5 6 7
2.920 2.230 2.453 2.643 2.424 2.327 2.187
(2.759, (2.121, (2.266, (2.562, (2.302, (2.171, (2.046,
10.08 11.46 12.48 11.67 12.10 12.17 11.70
(9.95, 10.22) (11.34, 11.59) (12.31, 12.65) (11.59, 11.76) (11.94, 12.25) (12.00, 12.35) (11.52, 11.88)
2.979 3.134 2.688 3.377 3.793 3.218 3.384
(2.789, (2.957, (2.451, (3.256, (3.573, (2.968, (3.132,
0.9857 0.9883 0.9728 0.9952 0.9865 0.9777 0.9791
3.081) 2.339) 2.640) 2.725) 2.545) 2.484) 2.327)
3.168) 3.312) 2.924) 3.497) 4.013) 3.467) 3.636)
So
e_ cr ¼ Aqn tm
ð12Þ
The function above is the basic constitutive equation of time hardening model in ABAQUS, where A, n and m are model parameters, generally, A and n > 0; 1 < m 6 0.
Fig. 5. Temperature investigating data and its regression curve in 1 day.
3.3.1. Constitutive model In time hardening model, the creep deformation of material can be represented by function of temperature T, time t and stress q
ecr ¼ f ðT; q; tÞ
ð8Þ
If complying with Bailey–Norton rule, the function becomes C2 C3
ecr ¼ C 1 q t
4. Computation results
ð9Þ
where q and t are deviatoric stress and loading time; C1, C2 and C3 are undetermined coefficients, which depend on the temperature and material type, and can be decided through test data. Generally, C2 P 0, C3 6 1. Suppose q does not change with time t
e_ cr ¼
@ ecr decr ¼ ¼ C 1 C 3 qC 2 t C3 1 @t dt
ð10Þ
Let
A ¼ C1C3 n ¼ C2 m ¼ C3 1
3.3.2. Parameters The specimens are produced by superpave gyratory compactor (SGC) under the pressure of 0.6 MPa. Universal test machine (UTM) is used in this experiment. Loading curve is haversine. Each loading cycle lasts 1 s, 0.1 s for loading and 0.9 s for rest. The peak loads are 0.7 MPa, 0.8 MPa and 0.9 MPa. Five temperature levels are selected. They are 20 °C, 30 °C, 40 °C, 50 °C and 60 °C. As for tensile parameters, uniaxial compression test is selected to measure the resilient modulus, and MTS-810 is used. Detailed experimental conditions are listed in Table 7. Multiple linear regressions can be done. Then the parameters (A, n and m) in ABAQUS can be computed, typical AC materials are attained and shown in Table 8. The resilient modulus of AC materials can be measured by MTS810 equipment, and the results are listed in Table 8 too. Base course, subbase and subgrade are assumed as elastic materials, and their elastic parameters are listed in Table 9.
ð11Þ
4.1. RD under different traffic volume For understanding the relationship of RD and corresponding traffic volume, different traffic volumes are selected. They are 1000, 5000, 10,000, 15,000 and 200,000 times per day. If the other conditions keep the same, the total loading time can be computed by the method above, and the RD results in one hottest day are shown in Fig. 6a. It can be seen from Fig. 6a, the relationship of traffic volume and RD is nearly linear when using the time hardening model. It means the RD increases with traffic volume before material failure. For investigating the source of deformation, along the depth direction, creep deformations ratio (deformation per centimeter) at different depths are calculated and shown in Fig. 6b.
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C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339 Table 7 Experimental conditions. Experiment type
Triaxial creep test
Resilient modulus
Specimen dimension Loading model Load level Temperature level (°C)
150 mm (diameter) 150 mm (height) Haversine curve (0.1 s loading, 0.9 s rest) 0.7 MPa, 0.8 MPa, 1.0 MPa 20, 30, 40, 50, 60
150 mm (diameter) 150 mm (height) Repeated loading and unloading 0.1P, 0.2P, 0.3P, . . . , 0.7P 20, 30, 40, 50, 60
Table 8 Creep and elastic parameters of typical AC materials. AC type
Temperature (°C)
A
n
m
Ra dj
14
2
Resilient modulus E (MPa)
Poisson’s ratio l
SMA-13
20 30 40 50 60 20 30
3.27 10 1.66 1013 1.45 1012 6.95 109 7.32 108 2.29 1014 1.73 1013
1.562 1.437 1.320 0.690 0.561 1.574 1.326
0.592 0.587 0.577 0.525 0.502 0.596 0.585
0.9326 0.9458 0.9420 0.9244 0.9048 0.9264 0.9225
1400 1000 700 530 450 1200 850
0.25 0.30 0.35 0.40 0.45 0.25 0.30
AC-20
40 50 60 20 30
3.67 1012 2.40 108 3.89 107 2.30 1014 1.71 1013
1.288 0.992 0.639 1.536 1.431
0.570 0.532 0.441 0.581 0.576
0.9364 0.8493 0.9103 0.9364 0.9207
600 440 380 1000 900
0.35 0.40 0.45 0.25 0.30
AC-25
40 50 60
1.96 1012 1.80 108 1.88 107
1.384 0.536 0.449
0.562 0.522 0.418
0.9062 0.8015 0.8992
710 500 400
0.35 0.40 0.45
Notes: The creep parameters are regressed from test data, E is attained from test data, l is selected according to temperatures.
5. Long-term rutting depth prediction
Table 9 Elastic parameters of base course, subbase and subgrade layers. Material
Resilient modulus E (MPa)
Poisson ration l
Cement stabilized gravel Lime stabilized soil (lime and flyash stabilized soil) Subgrade
1600 550
0.25 0.30
35
0.35
It can be seen that, the traffic volume influences mainly the rutting of middle and bottom layers of AC pavement, especially the middle layer (with depth between 0.04 and 0.10 m). With the increasing of traffic volume, the middle layer produces more rutting deformation than other layers. 4.2. With or without ATB layer Different pavement structures have different rutting resistance capabilities. ATB is an important layer which is used to reduce the rutting of general pavement structure with three AC layers. For understanding the effectiveness of ATB, the computing results of rutting with and without ATB layer are compared, and rutting deformation of each sub-layer is shown in Fig. 7. As shown in Fig. 7, after adding the ATB layer under three AC layers, the thickness of pavement increases, but the RD value decreases. When the total thickness of asphalt layers is larger than 18 cm, RD will not increase too much as the thickness increases. ATB is a special asphalt mixture, which has high performance of anti-shear. When it is added to pavement structure, the upper layers of AC have better stress condition when loaded. The rutting of ATB is very small. On the whole, the RD of pavement with ATB is less than that without ATB. It can also be seen from Fig. 7 that, the middle layer of the three AC layers are influenced heavily. The changing tendency of rutting deformation keeps the same when the gradient changes.
As mentioned above, a short-term (such as 1 day) RD computation method is established. The long-term rutting analysis is very complicated. A simplified method should be investigated to attain reasonable predicting result. The first step is to analyze the parameters used in constitutive model. This provides clues for simplification.
5.1. Parameter sensitivity analysis In this section, the three parameters of the constitutive model: A, n and m are analyzed for their influence on sensitivity of RD. There are four AC layers (including ATB) in the pavement. They are continuous and locate at the top of the pavement structure. Further computation results show the parameters of ATB have little influence on the total RD. Therefore, the parameters of the three AC layers are the main analyzing objects. For simplifying, elastic parameters are assumed constant. For each AC layer, there are three parameters: A, n and m. The method is: suppose two of the parameters are constant; then, for three layers, changing the third parameter simultaneously with the same ratio. Therefore, the sensitivity of RD can be compared. For the convenience of comparing with rutting test simulation result, 60 °C is selected as the standard temperature condition. The loading time is set to 5 s. Referring to test data, under different temperatures, the possible limits of each parameter are decided: A/ A60°C changes from 0.1 to 1.0; n/n60°C changes from 1.0 to 1.6; m/ m60°C changes from 0.4 to 1.0 (at 60 °C, the three parameters are represented by A60°C, n60°C and m60°C). The changing ratio is set to 10%. The computation results of RD are shown in Fig. 8. The ‘‘parameters ratio to 60 °C’’ means the ratio of some parameter at any temperature divided by its value at 60 °C. Through this method, the relative sensitivity can be compared, and the absolute value of each parameter is neglected.
C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339
For convenience of further analysis, the curve of n near 60 °C is regressed by linear type formula
3.5 y = 7E-05x + 1.5795 2 R = 0.993
3
RD ¼ 2:526
2.5
RD (mm)
337
2 1.5
n 2:150; R2 ¼ 0:988 n6 0
ð13Þ
5.2. Long-term RD computation and control standard
1 0.5 0 0
5000
10000
15000
20000
AADT (times/day)
(a) Rutting depth under different traffic volumes RD per centimeter (mm/cm) -0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0
Depth (m)
0.05 0.1 1000 0.15
5000
0.2
10000
0.25
15000 20000
0.3
(b) RD produced at different depths under different traffic volumes Fig. 6. Rutting depth under different traffic volumes.
RD per centimeter (mm/cm)
Depth (m)
0
0.02
0.04
0.06
0.08
0.1
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0.12
0.14
Without ATB With ATB
(a) 0% gradient
RD per centimeter (mm/cm) 0
0.05
0.1
0.15
0.2
For controlling the rutting resistance of AC mixtures, a RD controlling standard should be established for pavement. When RD is still very small, it does not influence the ride comfort. But when it increases, the situation changes. Rain in the rut decreases the friction between vehicle and road surface, meantime it has the possibility to penetrate into pavement materials, and this lowers down the strength of these materials. A typical phenomenon is stripping of asphalt and loosening of mixture. These become worse on rutted pavement. On the other hand, the deep rut menaces the safety of driving, especially when vehicle changes lane. A RD control criterion should be put forward. For example, Britain takes 10 mm as the critical criterion of RD; when it reaches 20 mm, the pavement is considered as failed. In the design method of AI, the critical criterion of rutting depth is 13 mm. The critical PSI value is 2.5 in the pavement design guide of AASHTO, and its corresponding RD value is 15 mm. The critical RD value is 10 mm for freeway in the asphalt pavement design manual of Shell Company. Based on the actual quality control level in China, the critical RD value is set to 10 mm for freeway, and the material control goal is to keep RD at sloped pavement lower than 10 mm in 5 years. This criterion is established as a maintenance standard for pavement and used in further computations. Some researches show, rut comes into being mainly in May– September. Therefore, the rutting accumulated in these 5 months is used to represent the rutting in the whole year. The long-term RD computation steps are: (1) Based on the climate data of the 5 months, the temperature field is simulated, which provides the temperature condition for further computation. (2) Compute the converted time in one typical day as the time used for creep analysis, and attain the rutting depth result in 1 day. (3) Based on the linear changing principle of AC mixture within stable creep period, coupled with different temperature situation, the time-RD regression relation can be attained, and furthermore, the monthly rutting curve can be attained. (4) Summing up all the months (five in 1 year), the approximate RD in 5 year is attained.
Depth (m)
0
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
The monthly regression formulas are listed in Table 10, with two variables: the gradient of slope and the specific month.
Without ATB With ATB
(b) 6% gradient Fig. 7. Influence of ATB to RD of three AC layers.
It can be seen from Fig. 8 that, m has very little influence on RD. For common materials, it can be neglected when compared with the other two parameters: A and n. A has a nearly linear influence tendency. Considering that the possible changing range of A is very large, two points are added: 0.01 and 0.001.
Fig. 8. Rutting sensitivity for the material parameters in time-hardening model.
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Based on Table 10, following steps above, the 5-year prediction results are computed and listed in Table 11.
Table 11 Total RD in 5 years.
5.3. Creep parameter control It is obvious that the changing of parameters of time-hardening model results in the changing of RD computation value. In other words, long-term RD can be controlled by modulating the parameters of time-hardening model: A, n and m. It provides a clue of material control for actual pavement. Through previous computations, it shows that the rutting deformation ratio of each AC layer is decided mainly by structure and layer thickness. They have little correlation with load type and time. According to previous computation data, the rutting deformation of the top three AC layers (called: upper layer, middle layer and bottom layer) is 95% or more of the total deformation (RD). Furthermore, the upper, middle and bottom layers are nearly 30%, 50% and 20% of the total deformation of all three AC layers. The exceeding rutting deformation are divided with this ratio to each AC layer. Then, the parameters of time-hardening model: A, n and m are modulated to lower down the total RD to 10 mm. Through analysis of mathematical software, it shows that, for general AC types, A and n have a very good power function correlation. They are listed in Table 12. It is mentioned above, m can be assumed as constant, so the long-term RD can be easily modulated by a single parameter A (or n). For material control, the next step is to find the relationship between this single parameter and experimental parameter, such as dynamic stability (DS). This can be attained through rutting test simulation.
Gradient (%)
RD (mm)
0 4 5 6 7
5.86 7.19 7.61 8.09 8.93
Notes: The bold numbers are larger than 10 mm. There are totally nine kinds of situations.
Table 12 Repression formulas of A and n for general AC layers. Material
Repression formula 10
AC-13 AC-20 AC-25
10.06
9
A = 2.508 10 n + 4.559 10 A = 4.770 1011 n11.37 + 7.990 109 10 7.34 A = 3.985 10 n + 6.521 109
R2
R2adj
0.9995 0.9980 0.9990
0.9990 0.9961 0.9998
6. Material criterion for rutting controlling of AC Fig. 9. Numerical model for the simulation of rutting test.
A, n and m are viscous parameters of AC materials. They can be computed from test data, but cannot be attained from experiment directly. So, it is difficult to control materials by using these parameters. Rutting test is a regular experiment, and it is used broadly. In this experiment, viscous characteristic of single type AC material is represented by the RD on specimen. The result of this experiment is represented by single indicator: DS. For the convenience of controlling AC materials, the simulation of rutting test is done and the DS criterion is established to meet the pavement RD limitation requirement. According to the rutting test, the dimensions of the specimen are 300 mm in length, 300 mm in width and 50 mm in height. The contact stress of rubber tire is 0.7 MPa, the passing distance is 230 mm, and the width of tire is 50 mm. So, vertical uniform pressure is distributed in an area of 230 mm 50 mm. The object is shown in Fig. 9. According to the experiment requirements of rutting test, the effective area of loading tire is: Atire = N/p = 700 N/ 0.7 MPa = 0.001 m2. The loading area on the specimen can be calculated by multiplying moving distance with width of the tire:
Table 13 Traffic volume grades. Traffic volume level
BZZ-100 kN AADT Ne (104 times per lane)
Medium Heavy Ultra heavy
300–1200 1200–2500 2500–4000
A = 230 mm 50 mm = 0.0115 m2. Therefore, for point within the loading area on the specimen, the effective loading time ratio is k = 0.001 m2/0.0115 m2 = 0.087. At 45 min and 60 min, the effective loading time are T45min = 45 min 0.087 = 234.8 s, and T60min = 60 min 0.087 = 313.2 s. The same element is used in this computation. Specimen object is parted into five equal divisions in direction 3 (height), and 18 divisions in direction 1 and 2. The total number of elements is 1620. Boundary conditions are simple supports on the four vertical edge planes and the bottom plane.
Table 10 Prediction formula of RD in 5 years. Gradient (%)
0 4 5 6 7
Month 5
6
7
8
9
y = 0.001x + 0.18015 y = 0.001x + 0.22215 y = 0.001x + 0.21815 y = 0.001x + 0.22215 y = 0.001x + 0.23115
y = 0.003x + 0.39203 y = 0.001x + 0.52503 y = 0.001x + 0.52703 y = 0.001x + 0.55503 y = 0.001x + 0.59303
y = 0.008x + 1.10363 y = 0.005x + 1.41663 y = 0.005x + 1.48863 y = 0.005x + 1.51863 y = 0.004x + 1.61863
y = 0.007x + 0.91047 y = 0.004x + 1.16547 y = 0.004x + 1.22447 y = 0.004x + 1.27147 y = 0.004x + 1.31447
y = 0.002x + 0.33579 y = 0.001x + 0.43779 y = 0.001x + 0.42979 y = 0.001x + 0.44679 y = 0.001x + 0.49279
Notes: The ‘‘x’’ in table means the total loading time, its unit is second, ‘‘y’’ means the total RD for 5 years, its unit is millimeter.
C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339 Table 14 Two situations exceeding the long-term RD limitation and its modulated DS standard. Situations
1
2
Gradient (%) Traffic level (104 times per lane) DS requirement (1/mm)
6 4000 2269 2800 2858
7 4000 4244 4653 4790
Upper Middle Bottom
Notes: Under different situations, if the three AC layers of pavement structure can meet the DS standard listed in table above, the RD in 5 years will less than 10 mm.
For typical three-layer AC pavement above, when the computed long-term RD exceeding 10 mm target, the exceeding RD is divided into three AC layers with fixed ratio. A (or n) of each layer should be modulated to reduce the RD to the required value. Then, modulated A (or n) should be brought into rutting test simulation. The required DS value of AC material of each layer can be calculated. Using this method, more comprehensive DS criteria are established. These criteria are decided by two factors: traffic volumes (three grades, the traffic volume grades are divided as Table 13) and gradients of sloped pavement (five grades: 0%, 4%, 5%, 6%, 7%). If the computed long-term RD value exceeds 10 mm in 5 years, the material criteria are provided for all the three AC layers. For asphalt material used on freeway, DS limitation is set to 2000 (1/mm) in China. If the computed criteria are lower than this, it should not be included in the final control criteria table. If higher than this, its detailed conditions are listed. There are totally 15 combinations of traffic volume and slope gradient, and two of them need criteria higher than 2000. They are listed in Table 14. 7. Conclusion RD control is a difficult job for asphalt pavement, especially for the asphalt pavement with longitudinal slope gradient. Through the RD computation of actual pavement structure and the simulation of rutting test, a new approach is established to carry out RD control on the level of AC material control. Through the investigation above, some conclusions can be drawn: (1) For time-hardening model, the RD increases with the traffic volume; before the failure of the material, their relationship is close to linear curve.
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(2) To the pavement with three AC layers, the influence of traffic volume is mainly on the middle and bottom AC layer. (3) Adding ATB layer can effectively reduce RD; this effect is more significant when the gradient of sloped pavement increases. (4) Through analyzing parameters used in time-hardening model, it can be found that, m has less influence than other two parameters; A and n have some correlation with each other. If they are controlled and modulated, the RD can be controlled effectively. The long-term rutting controlling requirement can be met. (5) According to approach above, combinations of conditions are put forward as basic service situations, and the DS criteria of AC materials in different layers are established. If these material requirements can be met, the long-term RD limitation target can be realized. It provides a flexible and feasible way to control the rut on sloped AC pavement.
References [1] Miller Tyler, Ksaibati Khaled, Farrar Mike. Using Georgia loaded-wheel tester to predict rutting. TRB 1995;1473:17–24. [2] Ramsamooj DV, Ramadan J, Lin GS. Model prediction of rutting in asphalt concrete. J Transport Eng 1998;24(5):448–56. [3] Fwa TF, Tan SA, Zhu LY. Rutting prediction of asphalt pavement layer using C-u model. USA J Transport Eng ASCE 2004(9/10):675–83. [4] Archilla AR, Medanat S. Development of asphalt pavement rutting mold from experimental data. In: 79th Annual TBR meeting, Washington DC, National Research Council; 2000. [5] Haider Syed Waqar, Chatti Karim, Emin Kutay M, Eason James, Redelius. Effect of design and site factors on structural rutting of flexible pavements in the LTPP SPS-1 experiment. In: Association of asphalt paving technologistsproceedings of the technical sessions, association of asphalt paving technologists -proceedings of the technical sessions 2006 annual meeting; 2006. p 425–56. [6] Moore Jason R, Prowell Brian D. Evaluation of the mixture verification tester for determining the rutting susceptibility of hot-mix asphalt, NCAT report 06-07, vol. 1, Final report; February 2006. [7] Ministry of Transport of People’s Republic of China. Standard test methods of bitumen and bituminous mixtures for highway engineering. JTG E20-2011; December 2011. [8] Ministry of Transport of People’s Republic of China. Technical specification for construction of highway asphalt pavements. JTG F40-2004; January 2005. [9] Witczak MW. Specification criteria for simple performance tests for rutting, NCHRP REPORT 580, volume I: dynamic modulus (E), volume II: flow number and flow time, Washington, DC; 2007. [10] Ministry of Transport of People’s Republic of China. Specifications for design of highway asphalt pavement. JTG D50-2006; January 2007.
Contents lists available at SciVerse ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Criteria for controlling rutting of asphalt concrete materials in sloped pavement Li Chang ⇑, Li Linglin Dept. of Highway and Railway Engineering, Univ. of Southeast, Jiangsu 210096, China
h i g h l i g h t s " Specimen in rutting test and actual pavement are modeled. " Long-term rutting depth of actual pavement is predicted. " Material criteria are put forward with traffic volume and gradient of slope. " A method is provided for controlling long-term rutting depth.
a r t i c l e
i n f o
Article history: Received 9 November 2011 Received in revised form 12 April 2012 Accepted 16 April 2012
Keywords: Asphalt pavements Rutting Control Finite element method (FEM) Slopes
a b s t r a c t The development of rutting is one of the most common distresses in asphalt pavement. Especially at road sections with longitudinal slope, the problem is more serious than sections with no slope. This is because the slope decreases the average speed of vehicles running upward, so the total loading time increases dramatically. In China, dynamic stability (DS) in rutting test is used as the main experimental criteria to control the asphalt concrete (AC) materials before construction. It is supposed that the larger the DS index is means the material has better capability of retarding the ruts’ development after constructed. Fixed DS criteria are set for diverse road situations. These differences in situations exhibit in structure and materials, traffic volume, climate condition and the gradient of sloped pavement. This paper aims at establishing a new control approach of AC material for dealing with rutting problem. Finite element method (FEM) is used to simulate two objects: specimen in rutting test and typical actual pavement with slope. In these simulations, the constitutive model of AC is the common basis. Through the model, specimen in rutting test and actual pavement are connected. It provides a possible way to control pavement rutting by computing and providing detailed criteria for specific project with special situations. These criteria change with actual service circumstances of pavement. Compared with fixed criteria, they are more flexible, accurate and feasible for using in rutting control practice. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Rutting computation method The rutting of asphalt pavement derives from the non-linear, viscous and plastic properties of asphalt concrete (AC). It includes the viscoelastic and viscoplastic characteristics of asphalt and the plastic properties of gravel and soil. Rutting can be described as the unrecoverable vertical deformation. Establishing suitable constitutive model for AC is very important to analyze pavement structure and predict its response during usage. It is true for rutting prediction too. The former researchers [1–3] have drawn the conclusion that model should represent the deformation rule of AC pavement under high temperature and heavy load.
⇑ Corresponding author. Tel.: +86 13851514929. E-mail address: [email protected] (C. Li). 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.04.003
Archilla and Medanat [4] considered finite element method (FEM) provides a convenient approach to attain valid analyzing results from actual engineering structures. Especially in terms of considering viscoelastic property of AC, FEM can provide a practical and precise approach. This method can be used widely. It has become one of the most promising methods to investigate rutting problem of AC pavement [5]. Since 1990s, with the development of computer technology, FEM has become more and more popular. Now, the rutting prediction researches evolve from linear viscoelastic theory to non-linear viscoelastoplasticity theory. Corresponding studies in China are a little tardier. In 1990s, rutting researches were mainly based on high temperature performance experiments. Some prediction models were developed. It can be conclude that, the trend of rutting research is changing from elastic theory to viscoelastic and plastic theory, from linear theory to non-linear theory. FEM can deal with more than one kind of constitutive relations in one computed body. It can be used to simulate complex structures.
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Using FEM to analyze rutting problem is a numeric, simple and realistic way to attain reasonable results. At present, many researchers use FE software to solve rutting problems. This paper uses ABAQUS to analyze and decide the requirements for AC material in order to control pavement rutting, especially pavement at longitudinal slope sections.
‘‘allowable SPT,’’ an assessment can be performed on the mix to determine whether it is acceptable or not, as shown in Table 2. These typical tests and indicators shown above are realistic methods used for AC material control. However, they have not being closely connected to the performance of AC placed on road yet. 1.3. Problems at present
1.2. Material control for reducing rutting Under actual service circumstances of pavement, for retarding the development of rutting, the only way is to modulate the structure and material properties of pavement. It includes adding rutting-resistance layer and choosing AC materials with better hightemperature performance. Rutting is very sensitive to heavy load and its loading time. At road sections with longitudinal slope, average vehicles’ speed decreases when running upward. It results in more serious rutting distress at these sections. Special attention should be focused on this problem. This research tries to develop a series of material controlling criteria for road sections, which have different vehicle volumes and longitudinal slopes. In the mid 1980’s the Georgia loaded-wheel tester (GLWT) was developed. In 1996, Pavement Technology Inc. manufactured the first asphalt pavement analyzer (APA). This device is a modification of the GLWT and also can be used for rutting susceptibility of HMA pavements. The mix verification tester (MVT) is a device developed for testing rut susceptibility of field mixes. It uses the same standards as the APA, but is only capable of testing two gyratory or one beam compacted specimen at the same time. The MVT was developed to be used in a field laboratory because of its smaller size and weight [6]. But until recently, there is no criterion to directly measure rut susceptibility of HMA mix being placed on the roadway during production, not to mention the criteria of AC materials used at longitudinal slopes. Rutting test is used broadly in China. Dynamic stability (DS) index is used commonly to evaluate rutting susceptibility of AC. This test is carried out at 60 °C as required in Chinese specification [7]. Three AC layer systems are the most frequently used pavement structure. There are two kinds of criteria for different types of asphalt. As to AC using modified asphalt, depending on the average high temperature in July, the criterion is from 800 to 3000 (1/ mm). As for AC using regular asphalt, it is from 400 to 800. These criteria are used for the two upper layers of the three AC layers pavement. For bottom layer, it is lower, as listed in Table 1 [8]. The simple performance test (SPT) criteria are used to help select the most appropriate mix and structure combination during both the HMA mix and flexible pavement design process. In NCHRP report 580 [9], a simple example of how these SPT criteria would be implemented is presented in Table 2. This table shows that for a given mix and structure combination, at a given set of environmental and traffic level conditions, a minimum (allowable) SPT value would be required to limit a given pavement distress to a userdefined maximum desired value. This would be identical to selecting the maximum rut depth desired in the HMA pavement. When a laboratory or in situ measured mix SPT value is compared to this
Although rutting researches have lasted for years, and many achievements have been made, there are still some core problems left unresolved. Especially for road sections with longitudinal slopes: (1) The special driving condition of vehicles on slope is usually not considered, but it definitely influences the rutting situation of AC layers. (2) The gradients of slopes are usually not considered. (3) The relationship between laboratory experiment and actual performance of pavement has not been investigated thoroughly, so there is no detailed and corresponding standard that can be used for the rutting control of AC materials at sloped road sections. As generally known, rutting of AC pavement results from the properties of AC materials. It is critical to establish a method, which can provide effective, flexible and feasible material control criteria for specific road sections, especially at sloped sections. This is the focus of this research. 2. Objectives and method 2.1. Objectives As mentioned above, for controlling the rutting of AC pavement, there are some AC material control tests and criteria. However, these criteria are fixed or have nothing to do with the actual circumstances of pavement in service period. They do not change with different traffic volumes, temperature conditions and pavement structures. In other words, there are no practical criteria established at all. It results in poor pavement performance, distress or potential waste of material capability. This paper intends to establish a series of rutting control criteria. Numerical simulation is used to investigate the developing rule of rutting in laboratory and field. They are connected by the properties of AC materials. These properties are represented by parameters of AC used in constitutive model of FEM. Based on this connection between specimen and actual pavement, experimental control criteria of AC materials can be established to meet specific rutting control requirement of pavement. This is especially useful to control the material properties used at sloped sections. When the gradient and length of the slope grow, vehicles pass this section with a lower speed in upward direction. It results in the increasing in loading time. As a result, rutting is much more severe than horizontal sections. DS is used as a regular experimental indicator for detailed material control. Based on the vehicles, temperature and structure conditions, different DS requirements are put forward as criteria to limit the long-term rutting depth below a reasonable value. 2.2. Method Rutting influences the smoothness and safety of driving. It becomes worse mostly in the hottest days in a year, typically July or August. Increments of several millimeters can be observed in a few days.
Table 1 DS criteria in rutting test for AC material selection (1/mm). Asphalt type
AC (using regular asphalt) AC (using modified asphalt)
Layer position
Upper and middle layers Bottom layer Upper and middle layers
Average daily highest temperature in July (°C) Higher than 30
20–30
Lower than 20
800 500 1500–3000
600 400 1000–2000
400 300 800
Notes: 1. AC using modified asphalt seldom used for bottom layer; 2. For AC using modified asphalt, except the average daily highest temperature in July, the lowest temperature in winter is used for sub-zone zone too, and different criteria are used for different sub-zones, the given range is the lowest and highest criteria for all sub-zones.
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Table 2 General SPT criteria example using any test for any distress. Specimen ID
Actual SPT value measured in the laboratory or at the project site
Minimum allowable SPT value calculated for project conditions
Decision: yes or no?
A
150,000 units
200,000 units
B
225,000
Not acceptable Acceptable
4cm AC-13 6cm AC-20 8cm AC-25 10cm ATB-30 (Optional) 40cm Cement stabilized gravel 20cm Lime stabilized soil Subgrade
When investigating the rutting problem, a three-dimension (3D) object is selected. It has dimensions: 3.5 m length, 1.5 m width, and 1.78 m height (see Fig. 2a). As for the height, it includes 18 cm AC layer, 40 cm cement stabilized base, 20 cm lime stabilized subbase, and 100 cm subgrade. When considering the structure with ATB, the height is 1.88 m. The ‘‘C3D20R’’ element in ABAQUS is used in computation, it is a 3D solid element with 20 nodes and second order (quadratic) reduced integration element. When meshing, the dimensions of elements depend on its layer thickness. For better analysis, the dimensions of divisions in X and Z directions are not equal. The main principle used is that smaller size elements are set near to the loading area and the surface of pavement. Detailed dimensions and mesh used for FE computation are shown in Fig. 2. Pavement object is parted into eight equal divisions in Y direction, 20 divisions in X direction and 25 divisions in Z direction. The total number of elements is 4000. Boundary conditions are simple supports on the four vertical edge planes and the bottom plane.
Fig. 1. Pavement structure for analyzing.
3.2. Hypotheses of load and temperature Actually, temperature, traffic volume and gradient of slope are all critical influence factors of rutting. A series of criteria should be established to meet different situations, such as different traffic volumes, and gradients. Time hardening form of power-law model is selected as basic constitutive relation of AC to compute the rutting. Its parameters can be attained from experiments. According to existed standards, a suitable RD limitation is decided as long-term rutting control target. Based on model parameters, the long-term rutting depth can be calculated. Then it can be compared with the control target. If exceeded, the increment is divided into three AC layers. The next step is to modulate the parameters of timehardening model to meet the decreasing requirements of each layer in pavement. There are three parameters in time-hardening model of AC. Some of them is very stable for ordinary AC, and can be assumed as constant. There is no direct approach to control these parameters. It is more practical to control AC materials through some experiment and corresponding indicator and criteria. Rutting test is selected and numeric simulation is carried out. Parameters in the model are the bridge to connect the two objects: actual pavement and rutting test specimen. On the contrary, the DS index can be set separately for each AC layer and different road conditions to meet the requirement of long-term rutting depth. Three traffic volume levels are set, and 15 combinations of traffic level and gradient are established. Through computation, two of them need special DS control to meet long-term rutting depth limit. By this way, a new approach is established to limit the long-term rutting depth of sloped pavement by controlling the experimental indicator of AC materials. This paper is a preliminary study to establish a series of material control criteria for pavement rutting control. Using them, rutting on AC pavement at sloped sections can be controlled more subtly, according to their circumstances. They are traffic volumes, structure detail, and temperature field.
The rutting of AC pavement is the consequence of many factors, but the most important external factor is the load and high temperature. 3.2.1. Load Based on the analysis of vehicles driving on Chinese highway, a typical truck is selected for calculating the driving rule on the sloped pavement. The truck is called Dongfong EQ140. It has a single rear axle with four tires; its fully loaded weight is 10 tons on rear axle. In rutting computation, there are two levels of load: single time load and repeated load. The latter is based on the former, and finally used in computation. It has two important factors: contact stresses and loading time.
3. Structure, hypotheses, model and parameters
3.2.1.1. Contact stresses and its areas. When vehicle runs on sloped pavement, there are two main differences from running on horizontal surface: the speed of typical truck is slower and its weight can be decomposed to two forces in two directions (parallel and perpendicular to surface plane of pavement). The contact stress is assumed as constant, 0.7 MPa. ‘‘Two rectangle shapes’’ are selected in this research. The length of each contact rectangle is defined as L. It is parallel to the driving direction. The width is defined as B. Suppose the contact stress is uniform within the area, it has relationship with load P
3.1. Numerical model
P ¼ nw pBL
A typical pavement structure is selected as reference at first. It includes three AC layers (the total thickness is 18 cm), cement stabilized base course (40 cm) and lime stabilized subbase layer (20 cm), as shown in Fig. 1. For evaluating the effectiveness of asphalt treated base (ATB), two structures are compared, they are with or without 10 cm ATB layer. The AC-13, AC-20 and AC-25 are three types of AC most frequently used in China. Nominal maximum particle size (NMPS) is used to distinguish them. For instance, AC-13 has a NMPS of 13 mm, which is corresponding to the square-opening sieve size of 13.2 mm. The other two types are corresponding to 19.5 mm and 26.5 mm respectively. Their gradations are provided by Chinese specification of asphalt pavement construction. For investigating the influence of different gradients of sloped pavement, 4%, 5%, 6% and 7% are selected as four typical conditions. They are the tangent of slope angles. The slope with 0% gradient is used as comparison.
ð1Þ
where P is the weight of vehicle’s rear axle, N; nw is the tire number on rear axle, it is 4 for EQ140; p is the contact stress of the tire, Pa; L and B are the length and width of each contact rectangle, m. According to the tire on EQ140, its width B is set to 18.6 cm, and the distance between two adjacent tire center points is set to 31.4 cm, as shown in Fig. 3. 3.2.1.2. Loading time. During each tire passing, a pulse load is loaded. Its value, shape and time change with tire load, speed and so on. It can be assumed as a haversine or trigonometric function. Stress equivalence rule is used in this research, and the load is assumed as haversine shape, then further converted to static continuous load. For one time load,
Z 0
t0
r sin
pt t0
dt ¼ r0 t 0
ð2Þ
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C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339
(a) Dimensions of numerical model
(b) Meshes of numerical model
L
Fig. 2. Dimensions and meshes of three-dimension pavement structure.
Fig. 3. Contact area shape of two tires (cm).
It can be solved
2
r0 ¼ r p
ð3Þ
where r is the peak value of haversine load, Pa; r0 is the equivalent static load, Pa; t0 is the tire contact time for a loading period, s. When the contact stress and length are fixed, based on vehicle speed v, the time of every loading t0 is
t0 ¼
L
v
¼
P nw pBv
ð4Þ
So, when the loading times is N, the accumulated loading time t is
t ¼ N t0
ð5Þ
Bring the Eqs. (4) into (5)
t¼
NP 0:36nw pBv
typical truck EQ140, the speed on different slopes is computed and listed in Table 3. The vehicle distribution in transverse direction is very important when coupled with high temperatures. A typical distribution is selected in this research. It is assumed as the same in each day. This traffic distribution of a typical two-direction and fourlane highway in one typical day is surveyed and listed in Fig. 4. It can be seen in Fig. 4 that, traffic volume mainly distributes in day time, and it has two peak values at 10:00AM and 6:00PM. The shape of the curve likes a saddle. Based on surveyed traffic data, the daily traffic volume is calculated. The annual average daily traffic (AADT) is about 11,000 per day. Referring to Chinese specification [10], lane factor is g = 0.45. AADT of one lane is N = 11,000 0.45 = 4950 times/d. It can be used for computation of loading time. According to Fig. 4, the traffic volume and its corresponding time can be distributed into every hour of a single day. The result is shown in Table 4.
ð6Þ
where N is the loading times; P is the weight of axle, for simplifying purpose, it is assumed as the weight when the vehicle is fully loaded, kN; nw is the tire number of axle; p is the contact stress of tire, MPa; B is the width of contact rectangle, cm; v is the vehicle speed, km/h. It can be seen in Eq. (6) that, the vehicle speed shows obvious influence on the creation of rutting. For actual pavement, low speed (in other words, long loading time) vehicles under high temperature are the worst conditions for rutting development. For
3.2.2. Temperature Temperature influences rutting of AC pavement greatly. Previous researches show that, rutting increases obviously in the hottest
Table 3 The stable speed for EQ140 (full loaded) on different slope gradients (km/h). Slope gradient i (%) Stable speed (km/h)
4 60
5 55
6 50
7 40
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C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339
qðtÞ ¼ a expðððt bÞ=cÞ2 Þ
Fig. 4. Traffic volume distribution ratio by hours in single typical day.
several days of summer period. So, the temperature field must be considered, coupled with traffic volume. The base to consider long-term rutting is the increment of rutting in 1 day. Because the complexity of AC material and its time dependent characteristics, it is very hard to simulate a long-term rutting procedure. This research developed a simplified method to compute long-term rutting depth on the basis of daily rutting computation result. There are some parameters needed for the computing purpose, they are shown in Table 5. The computed data can be compared with the investigated data. Model and its parameters can be verified and modulated. At a specific point in pavement, the daily temperature changing curve can be assumed as Gaussian distribution. It can be represented by the following formula
ð7Þ
where q(t) is the solar radiation intensity; a, b, c are undetermined coefficients, and they are shown in Table 6. The data used for regression come from field investigating data of an actual pavement section within the hottest 7 days in 1 year. Then, the discrete temperature data are converted to a continuous curve. Using the user subroutine DFLUX, the temperature changing in vertical direction can be represented, and the whole temperature field can be decided. When computing, a steady state analysis should be constituted at first. This is used to decide the initial temperature field. Initial temperature is set to 20 °C. Then, transient state analyzing steps are set. They are used to simulate the temperature changing in seven hottest days. Seven analyzing steps are used, and each step represents 1 day. The comparison between predicted temperature and surveyed data in 1 day is shown in Fig. 5. This predicted temperature field is set as the typical temperature situations, and then coupled with the influence of load in the computations after.
3.3. Constitutive model and parameters Rutting is mainly an external expression of the creeping property of AC materials. For rutting analysis, the constitutive model should be able to represent the creeping effect. There are several kinds of models that can be used in ABAQUS. One of them is time hardening model. It is simple and its parameters can be regressed from experimental data. Triaxial creep experiment is selected and implemented to get creep parameters.
Table 4 Loading time of one lane in every hour within single typical day. Time
Loading time (s)
Time
Loading time (s)
Time
Loading time (s)
24:00–1:00
Gradient
4 5 6 7
0.72 0.78 0.86 1.07
8:00–9:00
Gradient
4 5 6 7
3.61 3.94 4.32 5.39
16:00–17:00
Gradient
4 5 6 7
3.52 3.83 4.21 5.25
1:00–2:00
Gradient
4 5 6 7
0.64 0.69 0.76 0.95
9:00–10:00
Gradient
4 5 6 7
3.68 4.01 4.41 5.50
17:00–18:00
Gradient
4 5 6 7
3.80 4.14 4.54 5.67
2:00–3:00
Gradient
4 5 6 7
0.61 0.66 0.73 0.91
10:00–11:00
Gradient
4 5 6 7
3.55 3.86 4.24 5.29
18:00–19:00
Gradient
4 5 6 7
3.54 3.86 4.24 5.28
3:00–4:00
Gradient
4 5 6 7
0.64 0.69 0.76 0.95
11:00–12:00
Gradient
4 5 6 7
3.29 3.58 3.94 4.91
19:00–20:00
Gradient
4 5 6 7
2.56 2.79 3.06 3.82
4:00–5:00
Gradient
4 5 6 7
0.76 0.83 0.91 1.14
12:00–13:00
Gradient
4 5 6 7
2.62 2.86 3.14 3.91
20:00–21:00
Gradient
4 5 6 7
1.94 2.11 2.32 2.89
5:00–6:00
Gradient
4 5 6 7
1.09 1.18 1.30 1.62
13:00–14:00
Gradient
4 5 6 7
2.63 2.87 3.15 3.93
21:00–22:00
Gradient
4 5 6 7
1.59 1.74 1.91 2.38
6:00–7:00
Gradient
4 5 6 7
1.86 2.02 2.22 2.77
14:00–15:00
Gradient
4 5 6 7
3.13 3.41 3.75 4.67
22:00–23:00
Gradient
4 5 6 7
1.24 1.36 1.49 1.86
7:00–8:00
Gradient
4 5 6 7
3.34 3.64 3.99 4.98
15:00–16:00
Gradient
4 5 6 7
3.36 3.65 4.01 5.01
23:00–24:00
Gradient
4 5 6 7
0.98 1.06 1.17 1.46
335
C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339 Table 5 Parameters used for pavement temperature field analysis. Parameter
AC layers
Thermal conductivity k (J/m h °C) Density q (kg/m3) Specific heat capacity c (J/kg°C) Solar absorptance as Pavement surface emissivity e Absolute zero temperature TZ (°C) Stefan–Boltzmann constant r (J/(m2 h K4))
AC-13
AC-20
AC-25
7380 2100 1168.0
4500 2400 894.0
4176 2600 921.1
Cement stabilized base course
Lime stabilized subbase
Subgrade
3960 2077 810.0 0.87 0.81 273 2.041092 104
5148 2100 942.9
5616 1800 1040.0
Table 6 Undetermined coefficients and their coefficients of determination. Time
a (106)
a (95%, confidence interval) (106)
b
b (95%, confidence interval)
c
c (95%, confidence interval)
R2
1 2 3 4 5 6 7
2.920 2.230 2.453 2.643 2.424 2.327 2.187
(2.759, (2.121, (2.266, (2.562, (2.302, (2.171, (2.046,
10.08 11.46 12.48 11.67 12.10 12.17 11.70
(9.95, 10.22) (11.34, 11.59) (12.31, 12.65) (11.59, 11.76) (11.94, 12.25) (12.00, 12.35) (11.52, 11.88)
2.979 3.134 2.688 3.377 3.793 3.218 3.384
(2.789, (2.957, (2.451, (3.256, (3.573, (2.968, (3.132,
0.9857 0.9883 0.9728 0.9952 0.9865 0.9777 0.9791
3.081) 2.339) 2.640) 2.725) 2.545) 2.484) 2.327)
3.168) 3.312) 2.924) 3.497) 4.013) 3.467) 3.636)
So
e_ cr ¼ Aqn tm
ð12Þ
The function above is the basic constitutive equation of time hardening model in ABAQUS, where A, n and m are model parameters, generally, A and n > 0; 1 < m 6 0.
Fig. 5. Temperature investigating data and its regression curve in 1 day.
3.3.1. Constitutive model In time hardening model, the creep deformation of material can be represented by function of temperature T, time t and stress q
ecr ¼ f ðT; q; tÞ
ð8Þ
If complying with Bailey–Norton rule, the function becomes C2 C3
ecr ¼ C 1 q t
4. Computation results
ð9Þ
where q and t are deviatoric stress and loading time; C1, C2 and C3 are undetermined coefficients, which depend on the temperature and material type, and can be decided through test data. Generally, C2 P 0, C3 6 1. Suppose q does not change with time t
e_ cr ¼
@ ecr decr ¼ ¼ C 1 C 3 qC 2 t C3 1 @t dt
ð10Þ
Let
A ¼ C1C3 n ¼ C2 m ¼ C3 1
3.3.2. Parameters The specimens are produced by superpave gyratory compactor (SGC) under the pressure of 0.6 MPa. Universal test machine (UTM) is used in this experiment. Loading curve is haversine. Each loading cycle lasts 1 s, 0.1 s for loading and 0.9 s for rest. The peak loads are 0.7 MPa, 0.8 MPa and 0.9 MPa. Five temperature levels are selected. They are 20 °C, 30 °C, 40 °C, 50 °C and 60 °C. As for tensile parameters, uniaxial compression test is selected to measure the resilient modulus, and MTS-810 is used. Detailed experimental conditions are listed in Table 7. Multiple linear regressions can be done. Then the parameters (A, n and m) in ABAQUS can be computed, typical AC materials are attained and shown in Table 8. The resilient modulus of AC materials can be measured by MTS810 equipment, and the results are listed in Table 8 too. Base course, subbase and subgrade are assumed as elastic materials, and their elastic parameters are listed in Table 9.
ð11Þ
4.1. RD under different traffic volume For understanding the relationship of RD and corresponding traffic volume, different traffic volumes are selected. They are 1000, 5000, 10,000, 15,000 and 200,000 times per day. If the other conditions keep the same, the total loading time can be computed by the method above, and the RD results in one hottest day are shown in Fig. 6a. It can be seen from Fig. 6a, the relationship of traffic volume and RD is nearly linear when using the time hardening model. It means the RD increases with traffic volume before material failure. For investigating the source of deformation, along the depth direction, creep deformations ratio (deformation per centimeter) at different depths are calculated and shown in Fig. 6b.
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C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339 Table 7 Experimental conditions. Experiment type
Triaxial creep test
Resilient modulus
Specimen dimension Loading model Load level Temperature level (°C)
150 mm (diameter) 150 mm (height) Haversine curve (0.1 s loading, 0.9 s rest) 0.7 MPa, 0.8 MPa, 1.0 MPa 20, 30, 40, 50, 60
150 mm (diameter) 150 mm (height) Repeated loading and unloading 0.1P, 0.2P, 0.3P, . . . , 0.7P 20, 30, 40, 50, 60
Table 8 Creep and elastic parameters of typical AC materials. AC type
Temperature (°C)
A
n
m
Ra dj
14
2
Resilient modulus E (MPa)
Poisson’s ratio l
SMA-13
20 30 40 50 60 20 30
3.27 10 1.66 1013 1.45 1012 6.95 109 7.32 108 2.29 1014 1.73 1013
1.562 1.437 1.320 0.690 0.561 1.574 1.326
0.592 0.587 0.577 0.525 0.502 0.596 0.585
0.9326 0.9458 0.9420 0.9244 0.9048 0.9264 0.9225
1400 1000 700 530 450 1200 850
0.25 0.30 0.35 0.40 0.45 0.25 0.30
AC-20
40 50 60 20 30
3.67 1012 2.40 108 3.89 107 2.30 1014 1.71 1013
1.288 0.992 0.639 1.536 1.431
0.570 0.532 0.441 0.581 0.576
0.9364 0.8493 0.9103 0.9364 0.9207
600 440 380 1000 900
0.35 0.40 0.45 0.25 0.30
AC-25
40 50 60
1.96 1012 1.80 108 1.88 107
1.384 0.536 0.449
0.562 0.522 0.418
0.9062 0.8015 0.8992
710 500 400
0.35 0.40 0.45
Notes: The creep parameters are regressed from test data, E is attained from test data, l is selected according to temperatures.
5. Long-term rutting depth prediction
Table 9 Elastic parameters of base course, subbase and subgrade layers. Material
Resilient modulus E (MPa)
Poisson ration l
Cement stabilized gravel Lime stabilized soil (lime and flyash stabilized soil) Subgrade
1600 550
0.25 0.30
35
0.35
It can be seen that, the traffic volume influences mainly the rutting of middle and bottom layers of AC pavement, especially the middle layer (with depth between 0.04 and 0.10 m). With the increasing of traffic volume, the middle layer produces more rutting deformation than other layers. 4.2. With or without ATB layer Different pavement structures have different rutting resistance capabilities. ATB is an important layer which is used to reduce the rutting of general pavement structure with three AC layers. For understanding the effectiveness of ATB, the computing results of rutting with and without ATB layer are compared, and rutting deformation of each sub-layer is shown in Fig. 7. As shown in Fig. 7, after adding the ATB layer under three AC layers, the thickness of pavement increases, but the RD value decreases. When the total thickness of asphalt layers is larger than 18 cm, RD will not increase too much as the thickness increases. ATB is a special asphalt mixture, which has high performance of anti-shear. When it is added to pavement structure, the upper layers of AC have better stress condition when loaded. The rutting of ATB is very small. On the whole, the RD of pavement with ATB is less than that without ATB. It can also be seen from Fig. 7 that, the middle layer of the three AC layers are influenced heavily. The changing tendency of rutting deformation keeps the same when the gradient changes.
As mentioned above, a short-term (such as 1 day) RD computation method is established. The long-term rutting analysis is very complicated. A simplified method should be investigated to attain reasonable predicting result. The first step is to analyze the parameters used in constitutive model. This provides clues for simplification.
5.1. Parameter sensitivity analysis In this section, the three parameters of the constitutive model: A, n and m are analyzed for their influence on sensitivity of RD. There are four AC layers (including ATB) in the pavement. They are continuous and locate at the top of the pavement structure. Further computation results show the parameters of ATB have little influence on the total RD. Therefore, the parameters of the three AC layers are the main analyzing objects. For simplifying, elastic parameters are assumed constant. For each AC layer, there are three parameters: A, n and m. The method is: suppose two of the parameters are constant; then, for three layers, changing the third parameter simultaneously with the same ratio. Therefore, the sensitivity of RD can be compared. For the convenience of comparing with rutting test simulation result, 60 °C is selected as the standard temperature condition. The loading time is set to 5 s. Referring to test data, under different temperatures, the possible limits of each parameter are decided: A/ A60°C changes from 0.1 to 1.0; n/n60°C changes from 1.0 to 1.6; m/ m60°C changes from 0.4 to 1.0 (at 60 °C, the three parameters are represented by A60°C, n60°C and m60°C). The changing ratio is set to 10%. The computation results of RD are shown in Fig. 8. The ‘‘parameters ratio to 60 °C’’ means the ratio of some parameter at any temperature divided by its value at 60 °C. Through this method, the relative sensitivity can be compared, and the absolute value of each parameter is neglected.
C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339
For convenience of further analysis, the curve of n near 60 °C is regressed by linear type formula
3.5 y = 7E-05x + 1.5795 2 R = 0.993
3
RD ¼ 2:526
2.5
RD (mm)
337
2 1.5
n 2:150; R2 ¼ 0:988 n6 0
ð13Þ
5.2. Long-term RD computation and control standard
1 0.5 0 0
5000
10000
15000
20000
AADT (times/day)
(a) Rutting depth under different traffic volumes RD per centimeter (mm/cm) -0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0
Depth (m)
0.05 0.1 1000 0.15
5000
0.2
10000
0.25
15000 20000
0.3
(b) RD produced at different depths under different traffic volumes Fig. 6. Rutting depth under different traffic volumes.
RD per centimeter (mm/cm)
Depth (m)
0
0.02
0.04
0.06
0.08
0.1
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0.12
0.14
Without ATB With ATB
(a) 0% gradient
RD per centimeter (mm/cm) 0
0.05
0.1
0.15
0.2
For controlling the rutting resistance of AC mixtures, a RD controlling standard should be established for pavement. When RD is still very small, it does not influence the ride comfort. But when it increases, the situation changes. Rain in the rut decreases the friction between vehicle and road surface, meantime it has the possibility to penetrate into pavement materials, and this lowers down the strength of these materials. A typical phenomenon is stripping of asphalt and loosening of mixture. These become worse on rutted pavement. On the other hand, the deep rut menaces the safety of driving, especially when vehicle changes lane. A RD control criterion should be put forward. For example, Britain takes 10 mm as the critical criterion of RD; when it reaches 20 mm, the pavement is considered as failed. In the design method of AI, the critical criterion of rutting depth is 13 mm. The critical PSI value is 2.5 in the pavement design guide of AASHTO, and its corresponding RD value is 15 mm. The critical RD value is 10 mm for freeway in the asphalt pavement design manual of Shell Company. Based on the actual quality control level in China, the critical RD value is set to 10 mm for freeway, and the material control goal is to keep RD at sloped pavement lower than 10 mm in 5 years. This criterion is established as a maintenance standard for pavement and used in further computations. Some researches show, rut comes into being mainly in May– September. Therefore, the rutting accumulated in these 5 months is used to represent the rutting in the whole year. The long-term RD computation steps are: (1) Based on the climate data of the 5 months, the temperature field is simulated, which provides the temperature condition for further computation. (2) Compute the converted time in one typical day as the time used for creep analysis, and attain the rutting depth result in 1 day. (3) Based on the linear changing principle of AC mixture within stable creep period, coupled with different temperature situation, the time-RD regression relation can be attained, and furthermore, the monthly rutting curve can be attained. (4) Summing up all the months (five in 1 year), the approximate RD in 5 year is attained.
Depth (m)
0
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
The monthly regression formulas are listed in Table 10, with two variables: the gradient of slope and the specific month.
Without ATB With ATB
(b) 6% gradient Fig. 7. Influence of ATB to RD of three AC layers.
It can be seen from Fig. 8 that, m has very little influence on RD. For common materials, it can be neglected when compared with the other two parameters: A and n. A has a nearly linear influence tendency. Considering that the possible changing range of A is very large, two points are added: 0.01 and 0.001.
Fig. 8. Rutting sensitivity for the material parameters in time-hardening model.
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C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339
Based on Table 10, following steps above, the 5-year prediction results are computed and listed in Table 11.
Table 11 Total RD in 5 years.
5.3. Creep parameter control It is obvious that the changing of parameters of time-hardening model results in the changing of RD computation value. In other words, long-term RD can be controlled by modulating the parameters of time-hardening model: A, n and m. It provides a clue of material control for actual pavement. Through previous computations, it shows that the rutting deformation ratio of each AC layer is decided mainly by structure and layer thickness. They have little correlation with load type and time. According to previous computation data, the rutting deformation of the top three AC layers (called: upper layer, middle layer and bottom layer) is 95% or more of the total deformation (RD). Furthermore, the upper, middle and bottom layers are nearly 30%, 50% and 20% of the total deformation of all three AC layers. The exceeding rutting deformation are divided with this ratio to each AC layer. Then, the parameters of time-hardening model: A, n and m are modulated to lower down the total RD to 10 mm. Through analysis of mathematical software, it shows that, for general AC types, A and n have a very good power function correlation. They are listed in Table 12. It is mentioned above, m can be assumed as constant, so the long-term RD can be easily modulated by a single parameter A (or n). For material control, the next step is to find the relationship between this single parameter and experimental parameter, such as dynamic stability (DS). This can be attained through rutting test simulation.
Gradient (%)
RD (mm)
0 4 5 6 7
5.86 7.19 7.61 8.09 8.93
Notes: The bold numbers are larger than 10 mm. There are totally nine kinds of situations.
Table 12 Repression formulas of A and n for general AC layers. Material
Repression formula 10
AC-13 AC-20 AC-25
10.06
9
A = 2.508 10 n + 4.559 10 A = 4.770 1011 n11.37 + 7.990 109 10 7.34 A = 3.985 10 n + 6.521 109
R2
R2adj
0.9995 0.9980 0.9990
0.9990 0.9961 0.9998
6. Material criterion for rutting controlling of AC Fig. 9. Numerical model for the simulation of rutting test.
A, n and m are viscous parameters of AC materials. They can be computed from test data, but cannot be attained from experiment directly. So, it is difficult to control materials by using these parameters. Rutting test is a regular experiment, and it is used broadly. In this experiment, viscous characteristic of single type AC material is represented by the RD on specimen. The result of this experiment is represented by single indicator: DS. For the convenience of controlling AC materials, the simulation of rutting test is done and the DS criterion is established to meet the pavement RD limitation requirement. According to the rutting test, the dimensions of the specimen are 300 mm in length, 300 mm in width and 50 mm in height. The contact stress of rubber tire is 0.7 MPa, the passing distance is 230 mm, and the width of tire is 50 mm. So, vertical uniform pressure is distributed in an area of 230 mm 50 mm. The object is shown in Fig. 9. According to the experiment requirements of rutting test, the effective area of loading tire is: Atire = N/p = 700 N/ 0.7 MPa = 0.001 m2. The loading area on the specimen can be calculated by multiplying moving distance with width of the tire:
Table 13 Traffic volume grades. Traffic volume level
BZZ-100 kN AADT Ne (104 times per lane)
Medium Heavy Ultra heavy
300–1200 1200–2500 2500–4000
A = 230 mm 50 mm = 0.0115 m2. Therefore, for point within the loading area on the specimen, the effective loading time ratio is k = 0.001 m2/0.0115 m2 = 0.087. At 45 min and 60 min, the effective loading time are T45min = 45 min 0.087 = 234.8 s, and T60min = 60 min 0.087 = 313.2 s. The same element is used in this computation. Specimen object is parted into five equal divisions in direction 3 (height), and 18 divisions in direction 1 and 2. The total number of elements is 1620. Boundary conditions are simple supports on the four vertical edge planes and the bottom plane.
Table 10 Prediction formula of RD in 5 years. Gradient (%)
0 4 5 6 7
Month 5
6
7
8
9
y = 0.001x + 0.18015 y = 0.001x + 0.22215 y = 0.001x + 0.21815 y = 0.001x + 0.22215 y = 0.001x + 0.23115
y = 0.003x + 0.39203 y = 0.001x + 0.52503 y = 0.001x + 0.52703 y = 0.001x + 0.55503 y = 0.001x + 0.59303
y = 0.008x + 1.10363 y = 0.005x + 1.41663 y = 0.005x + 1.48863 y = 0.005x + 1.51863 y = 0.004x + 1.61863
y = 0.007x + 0.91047 y = 0.004x + 1.16547 y = 0.004x + 1.22447 y = 0.004x + 1.27147 y = 0.004x + 1.31447
y = 0.002x + 0.33579 y = 0.001x + 0.43779 y = 0.001x + 0.42979 y = 0.001x + 0.44679 y = 0.001x + 0.49279
Notes: The ‘‘x’’ in table means the total loading time, its unit is second, ‘‘y’’ means the total RD for 5 years, its unit is millimeter.
C. Li, L. Li / Construction and Building Materials 35 (2012) 330–339 Table 14 Two situations exceeding the long-term RD limitation and its modulated DS standard. Situations
1
2
Gradient (%) Traffic level (104 times per lane) DS requirement (1/mm)
6 4000 2269 2800 2858
7 4000 4244 4653 4790
Upper Middle Bottom
Notes: Under different situations, if the three AC layers of pavement structure can meet the DS standard listed in table above, the RD in 5 years will less than 10 mm.
For typical three-layer AC pavement above, when the computed long-term RD exceeding 10 mm target, the exceeding RD is divided into three AC layers with fixed ratio. A (or n) of each layer should be modulated to reduce the RD to the required value. Then, modulated A (or n) should be brought into rutting test simulation. The required DS value of AC material of each layer can be calculated. Using this method, more comprehensive DS criteria are established. These criteria are decided by two factors: traffic volumes (three grades, the traffic volume grades are divided as Table 13) and gradients of sloped pavement (five grades: 0%, 4%, 5%, 6%, 7%). If the computed long-term RD value exceeds 10 mm in 5 years, the material criteria are provided for all the three AC layers. For asphalt material used on freeway, DS limitation is set to 2000 (1/mm) in China. If the computed criteria are lower than this, it should not be included in the final control criteria table. If higher than this, its detailed conditions are listed. There are totally 15 combinations of traffic volume and slope gradient, and two of them need criteria higher than 2000. They are listed in Table 14. 7. Conclusion RD control is a difficult job for asphalt pavement, especially for the asphalt pavement with longitudinal slope gradient. Through the RD computation of actual pavement structure and the simulation of rutting test, a new approach is established to carry out RD control on the level of AC material control. Through the investigation above, some conclusions can be drawn: (1) For time-hardening model, the RD increases with the traffic volume; before the failure of the material, their relationship is close to linear curve.
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(2) To the pavement with three AC layers, the influence of traffic volume is mainly on the middle and bottom AC layer. (3) Adding ATB layer can effectively reduce RD; this effect is more significant when the gradient of sloped pavement increases. (4) Through analyzing parameters used in time-hardening model, it can be found that, m has less influence than other two parameters; A and n have some correlation with each other. If they are controlled and modulated, the RD can be controlled effectively. The long-term rutting controlling requirement can be met. (5) According to approach above, combinations of conditions are put forward as basic service situations, and the DS criteria of AC materials in different layers are established. If these material requirements can be met, the long-term RD limitation target can be realized. It provides a flexible and feasible way to control the rut on sloped AC pavement.
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