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    Title: DESIGN OF GRANULAR PAVEMENT LAYERSCONSIDERING CLIMATIC CONDITIONS

    Authors: Sabine Werkmeister, Dresden University of Technology

    Professur fr Straenbau,Technische Universitt Dresden,

    Mommsenstrae 13, 01069 Dresden, GermanyE-mail: [email protected]

    Tel +49 351 4633 5334 Fax +49 351 4633 7705

    Ralf Numrich, Dresden University of Technology

    Professur fr Straenbau,Technische Universitt Dresden,

    Mommsenstrae 13, 01069 Dresden, GermanyE-mail: [email protected]

    Tel +49 351 4633 5334 Fax +49 351 4633 7705

    Andrew R Dawson, University of Nottingham

    Nottingham Centre of Pavement Engineering,University Park, Nottingham, NG7 2RD, UK

    E-mail: [email protected]

    Tel +44 115 951 3902 Fax +44 115 951 3898

    Frohmut Wellner, Dresden University of Technology

    Professur fr Straenbau,Technische Universitt Dresden,

    Mommsenstrae 13, 01069 Dresden, GermanyE-mail: : [email protected]

    Tel +49 351 4633 2817 Fax +49 351 4633 7705

    Transportation Research Board,82th Annual MeetingJanuary 12-16, 2003

    Washington D.C.

    Length of text: 3687 words

    Number of figures and tables: 15 (3750 word equivalents)

    TOTAL 7437 word/word equivalents

    TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal.

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    Werkmeister, Numrich, Dawson, Wellner 1

    DESIGN OF GRANULAR PAVEMENT LAYERS CONSIDERING CLIMATIC

    CONDITIONS

    Werkmeister S1, Numrich R1 Dawson A R2 and Wellner F1

    Abstract. A new simple design approach will be described that utilizes test results from the Repeated Load Triaxial

    Apparatus to establish the risk level of permanent deformations in the unbound granular layers (UGL) in pavement

    constructions under consideration of the seasonal effects. From this data a serviceability limit line (plastic

    shakedown limit) stress boundary for the unbound granular materials (UGM) was defined for different moisture

    contents. Below this line the material will have stable behavior. The serviceability limit line was applied in a finite-

    element (FE)-program FENLAP to predict whether or not stable behavior occurs in the UGM. To calculate the stressin the UGL, a nonlinear elastic model (Dresden Model), which is described in the paper, was implemented into the

    FE-program. The effects of changing moisture content during Spring-thaw period and asphalt temperature onpavement structural response were investigated. Additionally, permanent deformation calculations for the UGL were

    performed taking the stress history into consideration. The results clearly demonstrate that, for pavement

    constructions with thick asphalt layers, there is no risk of rutting in the granular base, even at high number of load

    repetitions. The study showed that the proposed design approach is a very satisfactory simple method to assess therisk against rutting in the UGL, even without the calculation of the exact permanent deformation of the pavement

    construction.

    1Dresden University of Technology, Germany

    2University of Nottingham, UK

    TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal.

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    Werkmeister, Numrich, Dawson, Wellner 2

    INTRODUCTION

    In order to determine the most economical combination of layer thickness and material types for a pavement, it isnecessary to develop analytical pavement design methods on the basis of finite-element (FE)-calculations as

    opposed to empirical design methods. Furthermore analytical design methods would need to take into account the

    properties of the soil foundation and the traffic to be carried during the service life of the road.

    A pre-requisite for any successful analytical design methodology is the acquisition of reliable measurements fromrepresentative experimental investigations followed by appropriate mathematical characterization of the deformation

    behavior of both the bound and unbound materials used in pavement construction.

    When collecting the data, it is necessary to take into account climatic conditions. In particular, the climatic

    conditions should include variations in the moisture content of the Unbound Granular Layers (UGL) and asphalt

    temperatures throughout the year. Using the principle of superposition, it is also possible to combine the various axleloads into a cumulative design traffic loading.

    RESEARCH PROJECT AND TESTING PROCEDURE

    This paper reports on two research projects at the chair of pavement engineering, Dresden University of

    Technology, which are aimed at developing a model to describe the resilient and permanent deformation behavior of

    Unbound Granular Materials (UGM) in pavement constructions. A serviceability based design method (analyticalapproach) will be described that utilizes test results from the Repeated Load Triaxial (RLT) apparatus to establish

    the risk level of permanent deformations in the UGL. This research on the deformation behavior of UGM is aprerequisite for an analytical design program for flexible pavements, which is under development at the Dresden

    University of Technology.

    The RLT apparatus used in the project has been developed at the University of Nottingham, and can simulate

    dynamic pavement loadings. A Granodiorite with a maximum grain size of 32mm was tested (1). The tests wereconducted at 4% moisture content (assumed natural water content) and 5% moisture content (assumed water content

    during the Spring-thaw period). For these tests the constant confining pressure levels were set at 40, 70, 140 and210kPa. For each test, once the confining pressure was achieved, an additional dynamic vertical stress (deviator

    stress) was applied at a frequency of 5 Hz. The triaxial tests were carried out using dynamic axial stresses with stress

    ratios (D/3) in the range 0.5 to 11.

    MODELING OF THE DEFORMATION BEHAVIOUR

    Shakedown Analysis of Pavement Constructions

    The essence of a shakedown analysis is to determine the critical shakedown load for a given pavement. Pavementsoperating above the critical shakedown load are predicted to exhibit increased accumulation of permanent strains

    under long term repeated loading conditions that eventually lead to incremental collapse (e.g. rutting). Those

    pavements operating at load levels below this critical shakedown load may exhibit some distress, but should settle

    down and reach an equilibrium state in which no further mechanical deterioration occurs (1). Traditional pavement

    design methods (e.g. German pavement design guidelines, (12)) assume that the pavement deteriorates indefinitely.

    However, there is ample field evidence that this is not always true and that steadystate conditions are frequently

    achieved.

    Unbound Granular Layers

    The shakedown approach can be used to characterize the deformation behavior of UGM in pavement constructions.The application of the shakedown concept to UGM as used in pavement construction is possible, although

    adaptations have to be made to allow for the particular response of UGM to repeated loading. Behavior can be

    categorized into 3 possible Ranges A, B or C (Figure 1) (1). If the UGLs behave in a manner corresponding toRange A, the pavement will shake down. After post-compaction deformations, no further permanent strains

    develop and the material subsequently responds elastically. Thus Range A is permitted in a pavement, provided that

    the accumulated strain before the development of fully resilient behavior is sufficiently small. The material in Range

    B does not shake down, rather it will achieve failure at a very high number of load repetitions. In that case theresilient strains are no longer constant and will increase slowly (decrease of stiffness). Range C behavior -

    incremental collapse or failure - should not be allowed to occur in a pavement (2). Shakedown limit calculations

    (critical shakedown load) can be used to predict whether or not stable behavior occurs in the UGL of the pavement

    TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal.

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    Werkmeister, Numrich, Dawson, Wellner 3

    construction (1). The shakedown analysis of Repeated Load Triaxial Test (RLTT) results can be used for rankingmaterials as a performance specification method to determine the resistance against rutting of UGMs (15). Of course

    the shakedown limits of the UGL are also strongly dependent on seasonal effects (mainly moisture content). The

    moisture content has been identified as the factor having the largest influence on the mechanical properties of UGM

    (e.g. (15)) and this aspect is particularly addressed in this paper.

    Analysis of the results from many permanent deformation RLT tests revealed an exponential relationship (Equation

    1) between the applied stresses (1max/3) and the boundaries of the various deformation responses (i.e. betweenRanges A, B and C as shown in Figure 1)

    =

    3

    max11

    (1)

    where:

    1max [kPa] peak axial stress;3 [kPa] cell pressure; [kPa] material parameter; [-] material parameter (3).With this equation it is possible to deduce the shakedown limit even at small stress ratios (Figure 2).

    As a practical method of defining the range boundaries (which define the stress conditions at which the type of

    permanent strain response changes) and, hence, the material parameters for Equation 1, RLT tests are performed on

    a series of specimens (or in a multi-stage test on one specimen) at increasing 1max/3 ratios. When the plastic axialstrain accumulated from 3,000 to 5,000 load applications is 0.045 * 10

    -3strain, the range A-B boundary (the

    Shakedown Limit) is reached. When this strain equals 0.3 * 10-3

    strain, the range B-C boundary (the Plastic

    Creep Limit) is reached. As there is an associated change in resilient behavior for materials operating in the

    various ranges (20), it is recommended that the observed response Ranges A, B and C should form the basis formodeling permanent and resilient deformation behavior. Thus material laws have to be developed for each separaterange.

    Range A is the most important range because stable behavior will be the predominant requirement for UGLs in high

    trafficked pavement constructions. Hence, in this paper, the permanent and resilient deformation behavior are

    modeled only for Range A.

    Dresden Model (Resilient deformation behavior)

    Investigations of the non-linear elastic stress-strain-behavior of UGM have been carried out for the past 10 years atDresden University of Technology. In this section only a short overview on the modeling of the UGM can be given.

    Further details are available elsewhere (4), (5), (7), (18), (19).

    Modified plate-bearings tests with cyclic loadings (5) were carried out on UGLs. Heaving was observed at a

    distance range of 4501200mm from the load axis (Figure 3). At all measured stress-levels the same behavior was

    observed. Linear elastic analysis did not predict this heaving and therefore RLTT on the same UGM as used for the

    plate-bearings tests were conducted to investigate the non-linear behavior. As a result of the data from the RLT

    testing a new material law the Dresden Model was developed (4). This non-linear elastic model is expressed in

    terms of modulus of elasticity E and Poissons ratio as follows:

    DCQEQ

    III

    Q

    I ++=21 (2)

    BARI

    III ++=

    (3)

    (0 < < 0.5)where:

    I [kPa] minor principal stress (absolute value);III [kPa] major principal stress (absolute value);D [kPa] constant term of modulus of elasticity;

    Q, C, Q1, Q2, R, A, B model parameters, determined with RLT.

    The model includes a stress independent stiffness of 38kPa for crushed aggregates and 30kPa for sand and gravel(parameter D) consequent upon the residual confining stress in-situ. The residual stress has the effect of reducing the

    strains at small stress levels and could be assumed by examining modified plate-bearing test results carried out by

    TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal.

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    Werkmeister, Numrich, Dawson, Wellner 4

    Klemt (11). The parameter D is mainly influenced by macroscopic parameters like the degree of compaction of theUGM, content of fines, shape of the grains and water content. The RLT results do not allow determination of the

    parameter D because the residual stress needs some time to develop in a real pavement construction. To obtain the

    model parameters the RLT apparatus at the Nottingham University was used.

    To check the validity of the Dresden Model the surface deflection induced by plate bearing tests was predicted(Figure 3) using the FE-program FENLAP (7). A comparison was carried out to assess the accuracy of other

    material laws (e.g. Mayhew, Boyce and K-

    Model) by comparing the results of calculated deflections from all the

    models against the measured values. The best approximation is given by the Dresden-Model. The maximum

    deflection under the load agrees with the measured value. In addition heaving beneath the loading plate could be

    found with this model.In this research the resilient deformation behavior of a Granodiorite was investigated at moisture contents of 4, 5 , 6

    and 7%. These seem to be small steps of moisture variation, but the RLT samples can be prepared with a very good

    accuracy ( 0.1%). For RLT results with a moisture content of 6 and 7% it was not possible to determine the

    material parameters. During RLT at 7% (= w opt) water was draining out of the sample during the test, which means

    there will be inhomogeneous conditions during testing. However, the RLT results at moisture contents of 4 and 5%were taken into account for modeling. Figure 4 clearly shows a high dependency of the resilient deformation

    behavior and, hence, the model parameters (Table 1) on the moisture content. Increasing the water content resultedin a significant reduction in the stiffness, a result also observed by others (20, 22, 23, 24, 25, 26, 27).

    Dresden Model (Permanent deformation behavior)

    The available models of permanent deformation behavior of UGM are much less developed than those of resilientdeformation behavior. In modeling the long-term behavior of pavements, it is essential for the analysis to take into

    account the gradual accumulation of permanent strain with the number of load repetitions and the important role

    played by stresses. Hence the main objective of research into long term behavior should be to establish a constitutive

    model which predicts the amount of permanent strain at any number of load repetitions at a given stress level.

    Ideally it should take into consideration the different deformation behavior in the Ranges A, B and C.

    A material law for the permanent deformation behavior in Range A has been developed. The stress-dependentHuurman model serves as basis for the new model (8). The first part of the model describes the deformation

    behavior in Range A - a linear increase ofp1 in log(p)-log(N) space, where A gives p1 at N = 1,000 and B givesthe slope ofp1 with log(N). Using the second part of the Huurman-Model we are able to describe the behavior alsoin Ranges B and C (collapse) with an exponential increase ofp1 with N.

    ( )

    +

    = 1C1000

    AN 1000D

    B

    1

    N

    pe

    N (4)

    where:

    p1 [10-3] vertical permanent strains;A, B, C, D [-] model coefficients;

    N [-] number of load repetitions.

    The model coefficients A, B are defined:

    53

    421aa

    III

    a

    IaaA ++= (5)

    5

    3

    421bb

    I

    b

    I

    III bbB

    +

    += (6)

    (such that for 3 = 0, A = B = 0) where:a1-5, b1-5 [-] model parameters, determined by the RLT.

    However, it is necessary to determine different parameters for the different ranges. The parameters given in Table 1for Equation 5 and 6 are only valid for Range A. Further study is necessary to define parameters C and D.

    Asphalt layer (Resilient deformation behavior)

    The asphalt layers were assumed to be linear elastic (= 0.35). The asphalt stiffness is mainly influenced by theasphalt mixture composition, the frequency of loading and the climatic conditions (temperature). The moduli of

    elasticity of the asphalt layers were calculated using the method of Franken and Verstraeten (9) which was applied

    to a typical German mix composition:

    TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal.

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    Werkmeister, Numrich, Dawson, Wellner 5

    = ERE (7)

    Va

    b

    ge

    V

    VE 0458.0

    55.0

    410436.1

    = (8)

    where:E [MN/m2] modulus of elasticity

    E [MN/m2] glass modulus

    R [-] parameter dependent on frequency, softening point ring and ball temperature, needle

    penetration - Table 3 (nomogram in (9));

    Vg [Vol.-%] void content in the asphalt mixture;

    Vb [Vol.-%] binder volume in the asphalt mixture;

    Va [Vol.-%] volume of the mineral aggregate in the asphalt mixture.The average climatic conditions for Germany were analyzed to estimate the different asphalt surface temperatures

    during the year (Figure 5). The temperature gradient was determined for each of these temperatures (FIGURE 6) andtwelve temperature ranges defined. Each asphalt layer was separated into two centimeter thick sub-layer and allotted

    one of these temperatures (10).

    DESIGN PROCESS

    Granular base and asphalt rutting are a common form of flexible pavement distress. In a flexible pavement, asphalt

    rutting can be controlled by proper material selection and mix design. Granular base rutting can be controlled by

    using a better granular material for the UGL. Also, increasing the thickness of the asphalt pavement reduces thestresses in the UGL and, hence, reduces rutting in the granular base (Equations 1, 4, 5 and 6).

    In fact, granular base rutting can be avoided by limiting stress in the UGL. For this reason a critical stress level

    (shakedown analysis) needs to be defined for the UGL to Range A behavior (Figure 1). This critical stress level can

    be used as a simple design method to avoid granular base rutting in pavement constructions (1). The design process

    proposed is a check as to whether or not stabilizing behavior will occur in the UGL under consideration of different

    climatic conditions. The following shows that the Springthaw period is the critical period each year, through which

    the pavement must survive without incurring excessive surface rutting or other distress. As already shown, the

    moisture effects and the influence of the asphalt temperature must be taken into consideration in the design process.Should the plastic shakedown limit be exceeded, then a risk of high permanent deformation in the UGL exists.

    Nevertheless, it may be possible to accept Range B behavior in the UGL for Low Volume Roads.

    FINITE ELEMENT CALCULATIONS

    Estimation of the risk against rutting in the UGL

    All the results described in the previous sections were used to analyze the behavior of a number of pavement typesas provided in the empirical German pavement design guideline RStO 01 (12). For different constructions there

    are seven different categories available, depending on the number of equivalent 10 t-axle load cycles. Several design

    checks for structures with several asphalt pavements were examined in this paper (Table 2) using the FE-program

    FENLAP (13). Relations were also developed relating the thickness of the asphalt layer to the tensile stresses at the

    bottom of the asphalt layer and the maximum stresses at the top of the UGL respectively.

    The subgrade was modeled as linearly elastic ( E = 45MPa, = 0.49), which is acceptable as stresses in the subgradeare much more the result of dead weight stresses than of traffic loading. A circular load with a constant tire pressure

    of 0.81 N/mm (corresponding to an axle load of 11.5 tonnes) was assumed.To take into consideration the effect of Spring-thaw on pavement response, the thaw period was assumed to last for3 weeks at a moisture content of 5% compared to 4% moisture content during the rest of the year Figure 5.

    The tensile stress at the bottom of the asphalt layer was calculated for different temperatures and moisture contents

    and used as input with an asphalt fatigue relation to predict the fatigue lives of the pavement layer (14).

    The stress ratios 1max/3 were calculated using the vertical and horizontal stress at the top of the UGL, the differenttemperatures (FIGURE 6) and moisture contents.. The stresses were used as input for the shakedown analysis

    (Figure 8) to predict the risk of rutting in the UGL. FIGURE 7 shows a comparison of the stresses imposed and the

    plastic shakedown limits of a Granodiorite. The stresses developed at different pavement surface temperatures were

    TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal.

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    Werkmeister, Numrich, Dawson, Wellner 6

    highly dependent on the stiffness of the asphalt layer. As the illustration reveals, the stress ratios calculated byFENLAP (13) for the constructions with 220mm or more asphalt cover were found to be within Range A (stable

    behavior). Thus there is no danger of large permanent deformations in the UGL. At 5% UGL moisture content

    (Spring-thaw), higher stresses were observed (but the increase was insignificant) and the range A/B boundary

    reduces significantly. Fortunately, only pavements experiencing high temperatures during Spring-thaw - a rarecombination - have UGL rutting problems indicated. This design chart allows an assessment of the risk of rutting in

    the UGL to be carried out even without calculation of permanent deformations.

    Determination of the Permanent Deformations of the UGL

    However, to calculate the exact permanent deformations of the UGL, equations 4, 5 and 6 can be used. Furthermore

    the climatic conditions and the effect of stress history need to be taken into account. To obtain information about theeffect of stress history, multi-stage triaxial tests were conducted and compared with current permanent deformation

    tests (3). Figure 9 shows that the permanent strain rate depends on the accumulated permanent strain 1p. In fact,the post compaction period at each stress level should not be considered during calculation of the accumulated

    permanent strains 1p. The calculation starts with the lowest stress level at zero strains. The next step is todetermine the permanent strains 1p at the higher stress level after consideration of the accumulated permanentstrains from the lower stress level 1p (Figure 10).A pavement construction with an asphalt pavement of 340mm (UGL: Granodiorite at 4% water content) was

    investigated. This pavement construction is recommended in the German pavement design guidelines (12) for

    highways with a service live of 30 years and more than 32,000,000 10t-axle load cycles. On the basis of the 1 and3 obtained from the earlier analysis (Figure 8), the permanent strains under traffic loading based on the appropriate1p-model were calculated for each year of the service life of the road and for all temperature ranges FIGURE 6.Figure 11 shows the development of the permanent strains under traffic loading of the UGL as a function of the

    service life of the road. The figure shows clearly the decrease of permanent strains with increasing depth.

    Furthermore the annual increment of the permanent strains is decreasing. Figure 12 shows the rut depth at the

    surface of the UGL as a function of N. It can be seen that even at a high number of load repetitions the permanent

    deformations were very small (rut depth = 0.18mm after 100,000,000 cycles of 11.5t-axle loads).

    DISCUSSION AND CONCLUSIONS

    The objective of this study was to take into account the influence of climatic conditions and thickness of the asphalt

    pavement on the stress distribution within the UGL in pavement constructions. A general procedure was proposed to

    evaluate the risk against rutting in the UGL.

    Two different pavement constructions (340mm and 220mm asphalt layer thicknesses) were investigated. Themoisture effect (increase of moisture content in the UGLs in the Spring-thaw period) and the influence of the asphalt

    temperature was taken into consideration in the design process. The Springthaw period is often the critical periodeach year, which the pavement must survive without incurring excessive surface rutting or other distress if the

    moisture content in the UGL is high, because the stiffness of UGM is strongly affected by changes in moistureconditions.

    The calculated stresses distribution by FENLAP showed that almost all the stresses were below the critical stress

    level no risk of rutting in the UGL (Figure 2), but at 47.5C the stresses at the top of the UGL with a 220mm

    asphalt pavement were close to the plastic shakedown limit at normal UGM moisture levels. It seems that a 220mmasphalt pavement provides little margin against rutting failure for high trafficked roads. This thickness of asphalt

    pavements is currently recommended for high trafficked roads in the German design guidelines (3,000,000 10 t-axle

    load cycles).

    The influence of a small change in moisture content (1%) on the deformation behavior of the unbound granular

    materials and the shakedown limits is significant. The increase of stresses with increasing moisture content from 4 to5% is insignificant, but the shakedown limits decrease considerably. Perhaps higher moisture contents than 5% will

    occur during the Spring-thaw period, so future research should be focused on collecting field data of moisturecontents in the UGL throughout the year. RLT testing should be carried out on UGM with moisture contents

    occurring in the field. However, at higher water contents, it is probable that the plastic shakedown limit and the

    stiffness may decrease further, which means at a high moisture content there can be a high risk of rutting in the UGL

    (17). For this reason, the UGM used in pavement construction should be not very sensitive to water, a good drainage

    system is indicated and adequate water permeability of the UGL is important.

    TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal.

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    Werkmeister, Numrich, Dawson, Wellner 7

    FE calculations have shown that even at a high number of load repetitions the permanent deformations of the UGLare negligible, provided the stresses in the UGL are sufficiently small. For this reason, an exact determination of the

    permanent deformation of the UGM is not necessary, if the stresses are within the stable range (A).

    The design process recommended, is a simple design method to assess the risk against rutting in the UGL, which

    does not require the determination of an exact permanent deformation of the UGL. This design method is suitablefor high trafficked roads, where the stresses are within the stable range.

    In the UGL of Low Volume Roads much higher stresses will occur probably in the Range B because the thicknessof the asphalt pavement is much lower compared to highly trafficked roads. For constructions with thin asphalt

    pavements there is a risk of rutting at high number of load repetitions (6). In this case, determination of the amount

    of permanent deformation is necessary to determine the number of load applications that the pavement can survive

    without incurring excessive surface rutting. Prerequisite is the development of elastic and plastic models to describe

    the deformation behavior of UGM in the Range B.

    ACKNOWLEDGEMENTS

    The following organizations are gratefully acknowledged for financially supporting this research into deformation

    behavior of UGMs DFG, Central Public Funding Organization for Academic Research in Germany (Deutsche

    Forschungsgemeinschaft) and BASt, Federal Highway Research Institute of Germany.The authors also gratefullyacknowledge the suggestions provided by Dr. Salah Zoorob of the University of Nottingham, UK.

    REFERENCES

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    17. Gidel, G.,Breysse, D., Denis, A. & Hornych, P., Modeling Unbound Granular materials Response from

    Laboratory and field measurements. InBearing Capacity of Roads, Railways and Airfields. Proceedings of the6th international Symposium on the Bearing Capacity of Roads and Airfields (BCRA), Lisbon, Balkema 2002,

    pp. 1001-1012.18. Wellner, F. & Gleitz, T., Stress-Strain Behaviour of Granular Materials. In Unbound Granular Materials.

    Proceedings of an International Workshop on Modeling and advanced Testing for Unbound Granular Materials,

    Lisbon, Balkema 1999, pp. 177-186.

    19. Wellner, F., Influence of the stress dependent strain behaviour of unbound road bases on the stress of

    superposinited top layers. in Flexible Pavements, [Proceedings of the Euroflex Symposium, 1993, Lisbon], ed.

    A. Gomes Correia, Balkema, Rotterdam, 1996, pp. 311-318.20. Dawson A.R., Paute, J.L. & Thom, N.H., Mechanical characteristics of unbound granular materials as a

    function of condition, in Flexible Pavements, [Proceedings of the Euroflex Symposium, 1993, Lisbon], ed. A.

    Gomes Correia, Balkema, Rotterdam, 1996, pp. 35-45.

    21. Werkmeister, S., Dawson, A.R. & Wellner, F., Permanent deformation behavior of granular materials and the

    shakedown concept,Int. Jnl. Road Materials & Pavement Design (in press for 2003).

    22. Barksdale, R.D. & Itani, S.Y., Influence of aggregate shape on base behaviour. Transp. Res. Rec. 1227,

    Transportation Research Board, Washington, D.C., 1989, 173182.

    23. Hicks, R.G. & Monismith, C.L., Factors influencing the resilient properties of granular materials.Hwy. Res.Rec. 345, 1971, pp. 1531.

    24. Heydinger, A.G., Xie, Q.L., Randolph, B.W. & Gupta, J.D., Analysis of resilient modulus of dense and open-

    graded aggregates. Transp. Res. Rec. 1547, Transportation Research Board, Washington, D.C., 1996, pp. 16.

    25. Smith, W.S., and Nair, K.,Development of procedures for characterization of untreated granular base coarse

    and asphalt-treated base course materials. Rep. No. FHWA-RD-74-61, Federal Highway Ad-ministration,

    Washington, D.C., 1973.

    26. Raad, L., Minassian, G. & Gartin, S., Characterization of sat-urated granular bases under repeated loads.Transp. Res. Rec. 1369, Transportation Research Board, Washington, D.C., 1992, pp.7382.

    27. Vuong, B., Influence of density and moisture content on dynamic stress-strain behaviour of a low plasticitycrushed rock.Rd. and Transp. Res., 1(2), 1992, pp. 88100.

    28. Haynes, J.G. & Yoder, E.J., Effects of repeated loading on gravel and crushed stone base course materials used

    in the AASHO Road Test.Hwy. Res. Rec., 39, 1963.

    TRB 2003 Annual Meeting CD-ROM Paper revised from original submittal.

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    List of Tables and Figures

    TABLE 1 Parameter for the elastic and plastic Dresden-Model, Range A - density = 2.26 g/cm3

    (10) (3)

    TABLE 2 Investigated constructions index 1, line 1, RStO 01 (12)

    TABLE 3 Determination of the modulus of elasticity for the different asphalt layers (10)

    FIGURE 1 Indicative permanent strain behavior (1)

    FIGURE 2 Stress ratio versus vertical stress, Granodiorite at 4% water content (3)

    FIGURE 3 Comparison of measured and calculated resilient surface deflections (7)

    FIGURE 4 Vertical resilient strain versus confining pressure at different moisture contents ( 1 max/3 = 2) (10)

    FIGURE 5 Averaged frequencys of the asphalt surface temperatures in Germany during the year (16)

    FIGURE 6 Temperature regime within the asphalt layer (10)

    FIGURE 7 Stresses at the top of the UGL on the load axis (3), (10)

    FIGURE 8 Stresses in the UGL for different asphalt surface temperatures on the load axis, 340mm asphalt pavement

    (10)

    FIGURE 9 Influence of the stress history on the permanent deformation

    FIGURE 10 Consideration of stress history on modeling permanent deformation

    FIGURE 11 Progress of the permanent vertical strains in the UGL for 340mm asphalt pavement during the service

    life of the road

    FIGURE 12 Rut depth at surface of the UGL as function of N (11.5t axle load), asphalt pavement 340mm

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    TABLE 1 Parameter for the elastic and plastic Dresden-Model, Range A - density = 2.26 g/cm3 (10) (3)

    Parameter Moisture content

    Elastic Dresden-Model 4% 5%

    Q [kPa]1-Q2 5,386.1 10772.2

    C [kPa]1-Q1-Q2

    2315.6 599.1

    Q1 [-] 0.593 0.690Q2 [-] 0.333 0.333R [-] 0.017 0.037

    A [kPa]-1

    -0.0024 -0.0012

    B [-] 0.352 0.320

    Plastic Dresden-Model

    a1 [-] 0.1929 E-02a2 [-] -0.2228 E-15a3 [-] 7.8614

    a4 [-] 0.1116 E-04

    a5 [-] 1.9496

    b1 [-] 0.8914b2 [-] -0.89658

    b3 [-] -0.1319b4 [-] 0.3060 E-02

    b5 [-] 0.6757

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    TABLE 2 Investigated constructions index 1, line 1, RStO 01 (12)

    Category

    asphalt layer on granular base SV III

    asphalt surface course

    asphalt intermediate course

    asphalt course

    granular base (UGL)

    Equivalent 10 t-axle load

    cycles[mil.]

    4

    8

    22

    120

    45

    4

    4

    14

    53

    120

    45

    > 32 > 0.8 3

    thickness [cm]; Ev2 minimum value

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    TABLE 3 Determination of the modulus of elasticity for the different asphalt layers (10)

    Category SV III

    asphalt surface courseSMA 0/11 S AC 0/11

    asphalt cement[-]

    PmB 45 70/100

    needle penetration [1/10mm] 35 70

    softening point R&B [C] 65 49

    bulk density [g/cm3] 2,33 2,35

    maximum density [g/cm3] 2,43 2,41

    density asphalt cement [g/cm3] 1,02 1,02

    asphalt cement content [M.-%] 6,8 6,6

    asphalt intermediate course 0/16 S 0/16

    asphalt cement [-] PmB 45 50/70

    needle penetration [1/10mm] 35 50softening point R&B [C] 65 56

    bulk density [g/cm3] 2,35 2,38

    maximum density [g/cm3] 2,51 2,5

    density asphalt cement [g/cm3] 1,02 1,02

    asphalt cement content [M.-%] 4,5 4,7

    asphalt base 0/22 CS 0/22 CS

    asphalt cement [-] 50/70 50/70

    needle penetration [1/10mm] 50 50

    softening point R&B [C] 56 56

    bulk density [g/cm3] 2,38 2,38

    maximum density [g/cm3

    ] 2,55 2,55density asphalt cement [g/cm

    3] 1,02 1,02

    asphalt cement content [M.-%] 4,2 4,2

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    FIGURE 1 Indicative permanent strain behavior (1)

    permanent

    strain

    Range A

    Range B

    Range C

    Number of load cycles

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    FIGURE 2 Stress ratio versus peak axial stress, Granodiorite at 4% water content (3)

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    FIGURE 3 Comparison of measured and calculated resilient surface deflections (7)

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    FIGURE 4 Vertical resilient strain versus confining pressure at different moisture contents (1 max/3 = 2) (10)

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    0

    5

    10

    15

    20

    25

    -12.5

    -7.5-2.5

    2.5

    7.5

    12.5

    17.5

    22.5

    27.5

    32.5

    37.5

    42.5

    47.5

    Temperature [C]

    Frequency

    [%]

    Spring-thaw period

    2.8 %2.8 %

    FIGURE 5 Averaged frequencys of the asphalt surface temperatures in Germany during the year (16)

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    FIGURE 6 Temperature regime within the asphalt layer (10)

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    FIGURE 7 Stresses at the top of the UGL on the load axis (3), (10)

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    FIGURE 8 Stresses in the UGL for different asphalt surface temperatures on the load axis, 340mm asphalt

    pavement (10)

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    FIGURE 9 Influence of the stress history on the permanent deformation behavior

    (Key G = Granodiorite, 3 _D (both in kPa) MSt multi stage tests) (3)

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    FIGURE 10 Consideration of stress history on modeling permanent deformation behavior

    Number of load c cles

    Permanent

    strain

    N1

    N2

    p1

    p2

    p

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    FIGURE 11 Progress of the permanent vertical strains in the UGL for 340mm asphalt pavement during the

    service life of the road

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    FIGURE 12 Rut depth at surface of the UGL as function of N (11.5t axle load), asphalt pavement 340mm


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