A Study on Calculation of Rutting Depth of Pavement Asphalt Concrete Layer In Under Vietnam Conditions

Transcription

1 A Study on alculation of Rutting Deth of Pavement Ashalt oncrete Layer In Under Vietnam onditions ao-thang Pham Le-Qui-Don Tecnical University, Vietnam. Hoang-Long Nguyen University of Transort Technology, Vietnam. Nam-Hung Tran Le-Qui-Don Tecnical University, Vietnam. Trung-Hieu Vu University of Transort Technology, Vietnam. Abstract In this aer, we resent the basis of the theoretical calculation of rutting deth of ashalt concrete avement and its alication in calculating the rutting deth of different kinds of ashalt concrete under conditions in of Vietnam. Keywords: Soil-cement dee mixing method, cement-soil iles,cement content, soft soil imrovement. - oulomb element with a static flow limitation σ.tgφ which is arallel to the lunger with the Newton viscocity nonlinear coefficient, also known as the visco-lastic coefficient, and its value varies and deends on velocity distortion [3]. INTRODUTION There are many factors that affect the formation and develoment of lastic deformation of ashalt avement such as comosition of material aggregate, content and shae of skeleton, bitumen and additives, the quality of construction, the magnitude and density of axle as well as the environmental conditions of the construction area. Therefore, the need to study the method of redicting ashalt concrete lastic deformation, and thereby to calculate and select the materials to meet exloitation requirements is very necessary, esecially for troical climate countries as Vietnam. In this aer, the author resent theoretically the basis for calculation of rutting deth of ashalt avement deformation and aly them in Vietnam climate condition. PHYSIAL AND MEHANIAL PROPERTIES OF STUDIED WEAK SOFT SOILS AND EXPERIMENTAL MATERIALS alculate lastic deformation ashalt concrete Under the effect of wheel dynamic load, the mechanical model describing the behavior of the ashalt concrete material can be selected from three successive grous of elements (Figure 1). Grou I characterizes the elastic roerties of the material which is modeled by a sring element with the stiffness G0. Grou II reresents its viscoelastic roerties and the linear deformation which is denoted by a sring element with the stiffness G1 welded arallel to the lunger element with the viscosity coefficient η1. The third element grou characterizes the viscosity and lasticity of the ashalt concrete that consists of a Sanvenant Figure 1. Mechanical model of ashalt concrete material is subjected to dynamic load The nonlinear viscosity coefficient η is determined by the formula: tg (1) where and σ are the shear and normal stresses resectively at the calculated section, MPa; tgφ- coefficient of internal friction of ashalt concrete; γ - deformation velocity, 1/s. With resect to small affected load, the shear stress is smaller than the static flow of the material ( σtgφ), and thus in the material there exists only the elastic deformation of the element grou I and the viscoelastic deformation of the element grou II. When the shear stress exceeds the limit value σtgφ, the visco-lastic strain occurs which is the lastic flow deformation of the ashalt concrete layer. In order to calculate and evaluate lastic ashalt concrete deformation, it is now common ractice to use MEPDG [1] and theoretical methods. With the aim of alying the exerimental mechanical method to the calculation lastic deformation under Vietnamese conditions, it is necessary to conduct a field study to determine the exerimental coefficients in the formula to accord to the Vietnamese 545

2 conditions. Using the theoretical calculation method, only the hysical roerties of the samle of the material should be tested to include in the calculation formula. We resent below the theoretical method that can be used in resent conditions of Vietnam. The ashalt concrete layer in the avement can be subjected to the vertical forces of the wheel track or with additional horizontal force due to braking or horizontal inertia force when the vehicle is running on the horizontal curve. These loads result in normal and shear stresses in the ashalt concrete layer. When the stresses are sufficiently large, lastic deformation can occur in the ashalt concrete layer on the lanes that creats ruttings along the wheel track (see Figure 1). In the case of the lastic deformation of the ashalt concrete layer only, considering an element just under the load center, the normal stress causes volumetric strain and the shear stress causes deviatory strain. In fact, when the ashalt concrete layer has been comacted to ensure the required tightness, the amount of volumetric strain is very small, so it could be ignored in calculation. The deviatory strain is distributed equally to both sides. The general aearance of the rutting attern is shown in Figure. Figure : Tyical rutting on the ashalt avement In Figure 1, LD distance is the deth of the rutting and the straight line IJ '= L is the distance between the two eaks of the rutting so-called the rutting width while h is the deth of the lastic deformation of the ashalt layer. In this article, the method of calculating the lastic deformation of ashalt avement due to both vertical loading and horizontal force and braking will be theoretically resent. Based on the material model shown in Figure 1, ashalt concrete is a material that has visco-elastic roerties, the shear deformation of the ashalt concrete is calculated from elastic, viscoelastic and viscolastic deformations of the three element grous as follows: t( tg). ( t) () G o whichwhere : γ lastic deformation of the ashalt concrete layer; τ shear stress in the ashalt concrete layer, MPa; ψ(t) the rheology function that characterizes the visco-elastic roertises of the material, MPa-1: t 1ex( ) () t E where t - the duration of the load, s, t = D/V, where D,V are the equivalent diameter of the wheel track and the seed of the vehicle resectively; σ vertical stress in the ashalt concrete layer, MPa; θ delay duration of the deformation of the ashalt concrete, s; E- Young modulus of the material, MPa; tgφ coefficient of internal friction of the material; η - viscolastic coefficient of the ashalt concrete, MPa.s. In the right hand side of equation (), the two first terms reresent the values of the elastic and viscoelastic deformations of the ashalt concrete which will disaear when unloaded, so they will be egnored in considering the lastic deformation. At the lastic deformation stage, there exists only the third term with the visco-lastic coefficient η determined by equation (1). Substituting the visco-lastic coefficient into () and neglecting the elastic and viscoelastic deformations, we have the lastic deformation after one time of load action: t. (3) where γ is deformation velocity of the ashalt concrete at calculated temerature of the avement,1/s. As the ashalt material exhibits the rheology roerty, the deformation velocity deends on the seed of the loading rocess and the environment temerature. According to studies conducted by the Russian Road Research Institute [3], the value of the lastic deformation velocity at the calculated temerature can be determined by the one at the temerature of samle testing and it is usually taken at 50o. Under static load and at low temerature, the ashalt concrete exhibits elastic roerties and its shear strength deends only on the adhesion and the internal friction angle φ of the material. However, when the ashalt concrete subjected to dynamic load and at high temerature, it exhibits rheological and visco-lastic roerties, so the shear resistance of the ashalt concrete deends not only on the adhesion and the internal friction angle φ but also some other rheological arameters of the material. In order to consider the rheological characteristics of the ashalt concrete, the Russian Road Research Institute has roosed the lasticity coefficient (m) and the visco-lastic deformation energy (U) that characterizes the behavior of the rheological material under the dynamic load and the behavior of the ashalt concrete at high temeratures resectively. We can calculate the deformation rate T 0 at the calculated temerature through the deformation seed at 50o ( by the following relationshi: 0 ) max tg 1/ m 0 ( ). kt ( ) (4)

3 where m is the lastic coefficient of the ashalt concrete which can be determined by laboratory tests on the samles; τmax is the maximum shear stress due to the vertical and braking loads, MPa; k(t) is the adjustment coefficient that converts the deformation velocity from the exerimental temerature to the calculated temerature and it can be determined by following formula: U 1 1 kt ( ) ex ( ) o o R 73,15 Ttt 73,15 Ttn where R is gas constant and is taken 0,008304kJ/ article gram; U- visco-lasticity deformation energy that characterizes the behavior of ashalt concrete at high temeratures which is determined on the ashalt concrete samles in the laboratory, kj/article gram; T - calculated temerature of the ashalt concrete layer, o o ; T - tn exerimental temerature of the samles (it is normally taken 50 o ); - the cohesion of the concrete determined at the exerimental temerature, T 0. tn Substituting Eq. (4) into Eq. (3) one obtains the lastic deformation of one time of the loading as the relationshi below:. ( max tg ) 1/ m. ( ) t 0 k T (5) 50 Eq. (5) only considers lastic deformation due to the effect of the load for one time. In order to calculate the total lastic deformation during the avement exloitation eriod, one has to take into account the effect of the total axle flow and the variation frequency of the calculated temerature in the ashalt concrete layer during the exloitation eriod from minimum to maximum temeratures as well as considering the robability of overla of the wheel through a calculated section along the width of the lane. In order to determine the total axial flow resulting in lastic deformation, one uses the following formula: Ntt Nqđ. k (6) where Nqđ the total equivalent axial flow during the exloitation term; k robably of the wheel moving ass one oint on the considered lane that is determined by the ractice servey. The temerature in the ashalt concrete layer is variable throughout the exloitation eriod from Tmin Tmax (o). At each temerature level, one obtains one value of the deformation of the ashalt concrete. For the urose of considering this change, the frequency of occurrence of each temerature level during the exloitation eriod should be taken into account that is determined through the observed data during the calculated eriod of the highway. This frequency of calculated temerature is determined by the relationshi below: o tt 0 t( T ) PT ( ) (7) t kt where: t(t0)- the working time of avement at T 0, h; tkttotal avement exloitation time, h. Substituting Eqs. (6) and (7) into Eq. (5) one has total lastic deformation following horizontal direction of the ashalt concrete layer of the exloitation duration as follows: Tmax max tg 1/ m tt. 0 ( ). ( ).. ( ). 50 Tmin N t P T k T dt (8) where T is the variation of calculated temerature from T min to T max. The formula of lastic deformation (8) devotes calculating and selecting the ashalt concrete in accordance with the exloitation requirements. The calculated distortion value γ needs to be less than the one of ermissible deformation that deends on the grade of road. The lastic deformation arameters in formula (8) are comletely determined by the samle test in laboratory and they deend on the tye of ashalt concrete used. Using the distortion value obtained by the formula (8), one can comutes the rutting deth of the ashalt concrete layer. In Figure 1, if it is assumed that only the distortion deformation results in the rutting of the ashalt avement, the volume of the deformation area er unit length with the bottom of the cross section KD, will be equal to the one of the conventional horizontal shear deformation with the bottom of the cross section MN. It can be see that the area of KD is equal to the one of MN and they are assumed triangles, and thereby one has: K. KD N. M (9) where N- the deth of the lastic deformation of the ashalt concrete (in Figure 1, it is denoted h); M- the conventional horizontal dislacement of the ashalt concrete layer The relationshi below is deduced from Eq (9): M K. KD l. KD (10) N N h It can be shown from Figure 1 that, the values of l, L, KD, LD are geometrical dimensions of the rutting obtained from the field measurements. From these actual measurements, it is ossible to accet following aroximate values: l =L/3; KD=.LD/3, and then from Eq (10) on has:. LD. L.. L (11) 9h 9h where δ- rutting deth (δ =LD in Figure 1); L- the width of the rutting, cm; h- the deth of the lastic deformation region of the ashalt concrete, cm. 5454

4 Eq. (9) gives us the relationshi for comuting the rutting (Rutting Deth RD = δ) as follows: 9.. RD h (1). L where γ is calculated by Eq. (8). The exloitation condition is only ensured when the calculated deformation arccoding to Eq. (8) or the rutting comuted from Eq. (1) must not exceed the ermissive value. The ermissive value in the exloitation is regulated corresonding to each grade of the avement. In the formulas (11) and (1), to determine the deformation values γ or the rutting deth RD, it is necessary to know the deth of the lastic deformation h in the ashalt concrete layer. The value of h can be obtained by calculating or surveing the actual samles that deends on the discharge of the traffic, vehicle axle load (magnitude, tire ressure) and tye of the avement. For the highway avement, eg. grade I and II, the deth of rutting takes the value from 5 to 7cm, and in calculation one can choses h = 6cm. INVESTIGATE THE DEGRE OF TEMPERATURE- DEPENDENE PLASTI DEFORMATIONS OF THE ASPHALT ONRETE UNDER ONDITIONS IN VIETNAM Inut data - Temerature calculation: As secified in [,3], the maximum temerature Tmax, which serves ashalt concrete deformation calculation, is determined at deth of cm from the avemnet surface. In order to calculate the temerature at this osition that is caused by air temerature and solar radiation, in the calculation we recommend the exerimental formula of the Ashalt oncrete Institute as follows: T 0,9545( T 0, 00618Lat cm kk,max 0, 89Lat 4, ) 17, 78 (13) where T kk, max the highest temerature of average 7 days er year, 0 ; Lat the latitude of calculated region. For examle, for the region of Hanoi at the northern latitude of 1, the air temerature Tkk, max = From Eq. (13) we can determine the temerature at deth of cm from the avement surface that is equal to The lowest temerature Tmin, according to determined by the equation below: T min kk, min [,3], is 0,856 T 1,7 (14) With resect to Hanoi region, the lowest air temerature is 4 0, hence we obtain Tmin=5,1 0. We consider an examle with the arameters as follows: - Pavement structure of grade I consisting of 3 layers of ashalt concrete with the thickness of 0cm that lies on a base layer of 35cm thickness and a subase of 50cm thickness comosed from gravel aggregate tye I and II resectively. The subgrade has the Young module of 45MPa. - The highway of grade A has exected exloitation term of 15 years, and the ermissive exloitation seed of 10km/h. - The total equivalent time of the alied load at 1 oint for redicting lastic deformation during the exloitation eriod taking the high level exloitation discharge [3] is 4.8 hours and the magnitude of load is 10T corresonding to tyre ressure q = 0.6MPa. - In this examle, we investiage two kinds of ashalt concrete in which the first one is ordinary ashalt concrete which is used commonly in the Vietnam currently. The material arameters are chosen as follows: the cohesion at 50 0 is equal to = 0.3 MPa [3]; the internal friction coefficient tgφ = 0.9; the visco-lasticity deformation energy U = 315 kj /molecule gram; lasticity coefficient m = The second tye is stone matrix ashalt concrete (SMA) with the arameters: the cohesion at 50 0 is equal to =0.5 MPa; the internal friction coefficient tgφ = 0.94; the visco-lasticity deformation energy U = 35 kj /molecule gram; lasticity coefficient m = RESULTS AND DISUSSION The calculation results of deformation and rutting deth based on the formulas (8) and (1) of the two tyes of ashalt concrete are shown in Table 1. In order to determine the deformation and rutting deth, we use the numerical integration method for the temerature levels corresonding to their different frenquencies during the exloitation term of the road. The integral ste in the calculation, ΔT 0, is chosen by 1 0. In table 1: T 0 Temerature at the oint at deth of cm from the avement surface, 0 ; P(T) Frequency of temerature T 0 during the exloitation eriod; γ Plastic deformation of ashalt concrete at the temerature T 0 during the exloitation eriod; RD the rutting deth of ashalt concrete,cm. The results show that the total deformation after 15 years of oeration of ashalt concrete tye 1 reaches γ = and the rutting deth RD = 0.81cm which exceeds the allowable value RD limit = 0.4cm for the velocity of 10km/h according to Russian standard [3]. Therefore, it could be conclude that the ashalt concrete layer does not meet the the requiement of resistance criterion on rutting. With regard to the second tye of ashalt concrete, the total deformation γ = 0.048, and RD = 0.077cm that is minor to the allowable one (0.4cm). Hence, this ashalt concrete satisfies the resistance requirements the the requiement of resistance criterion on rutting. 5455

5 Table 1. alculated results of lastic deformation of the ashalt concrete layer T 0 P(T) Plastic Deformation of ashalt concrete, γ Kind 1 Kind E-1 4.6E E E E-11.53E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-0.46E E E E-0 3.9E E E E E E E E E E E E-0 6.6E-03 Sum γ 1,0000 0,5050 0,0480 RD,cm - 0,810 0,077 Figure 3 shows the results of the relationshi between the degree of lastic deformation of ashalt concrete corresonding to the frequency of different temerature levels calculated for cases of normal ashalt (BTN) and stone matrix ashalt (SMA) concretes during the exloitation eriod. A (=0,3MPa; tgφ=0,9; m=0,11; U=315), SMA (=0,5MPa; tgφ=0,94; m=0,139; U=35). Figure 3. The relationshi between the lastic deformation and the different temerure levels during the exloitation eriod It is seen in figure 3 that at the temerature from 6 to 63 0, the relative line tends to descend. This is exlained that in this temerature range the occurrence frequency of temerature is lower than the other temerature regions (see column P(T) Table 1), so the distortion obtained at these temeratures are lower than at the other. Also from the diagram, when the temerature in the ashalt concrete layer is less than 50 0, the lastic deformation value is very small, i.e. it can be negleable. However, at 50 0 or above the lastic deformation begins to increase strongly. The calculated temerature deending on the geograhic location, for examle in the area of Hanoi (Vietnam) it takes corresonds to the air temerature of about 3 0. At this temerature, as resented above the lastic deformation of the ashalt concrete layer begins to increase raidly. Therefore, in order to avoid the occurrence of high deformation in ashalt concrete, it is recommended to reduce the exloitation discharge or to limit the vehicle load in hot sunlight hours (usually from 11am to 17m on sunny days in the summer) when the air temerature exceeds 3 0. ONLUSIONS AND REOMMENDATIONS By the theoretical calculations, we established the formula of lastic deformation and rutting deth of the ashalt concrete avement under the effect of vertical wheel load and brake force according to horizontal direction. By calculating method resented above, we can the choice the suitable ashalt concrete to meet the requirements of each secific route in ractice. In the calculations, the influence of temerature factors on deformation of different ashalt concrete materials was investigated. In the area of Hanoi, when the air temerature reached over 30 the ashalt concrete begins to occur lastic deformation. This is imortant to managing and exloiting the road to avoid the occurrence of rutting deth of the ashalt avement. 5456

6 REFERENES [1] Imlementation of The NHRP 1-37A Design Guide, Evaluation of Mechanistic -Emirical Design Procedure. Mariland 007. [] Suerave Perfomance graded Ashalt Binder- Secification and Testing/Ashalt Institute Suerave [3] СТП тандарт предприятия метод испытания асфальтобетона на устойчивость к колееобразованию- M