o // r—’ i “rrrlrepoh lr 594
TRANSCRIPT
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“\\ ‘ ‘. r—’I “rRRL Repoh LR 594
TRANSPORT and ROADRESEARCH LABORATORY
Depatiment of the Environment
TRRL REPORT LR 594
THEORETICAL EVALUATION OF THE EFFECT OF TEMPERATUREON THE FATIGUE BEHAVIOUR OF BITUMINOUS ROAD-BASES
by
M.E. Nunn (The Refined Bitumen Association)
Structural Properties DivisionStructures Department
Transport and Road Research LaboratoryCrowthorne, Berkshire
1973
CONTENTS
Abstract
Page
1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Introduction
Assumptions
2.1 Road structure2.2 Elastic properties of the layers
2.3 Calculations ofstress and strain2.4 Temperature conditions
Analysis and discussion of results
3.1 Effect of temperature on the stress and strain levels within thepavement structure
3.2 Application of laboratory fatigue data to the road
3.3 Fatigue behaviour of the road
Sub-base modulus
Thickness of bound layer
Temperature gradients
Comments
Conclusions
Acknowledgements
References
3s C CROWN COPYRIGHT 1973
2
2222
3
334
5
5
5
6
7
8
8
Extracts fmm the text may be reproducedprovided the source is acknowledged
~, .<.- . .
CORRECTIONS TO LR 594
1. Page 4, paragraph 1, line 2, for ‘cases’ read ‘bases’
2. Page 5, section 5, line 5, for ‘temperatures’ read ‘temperature’
3. Page 6, section 7, paragraph 1, 6th line, for ‘strain’ read ‘strains’
4. Page 7, section 8, paragraph 4, line 3, for ‘indetermining’ read ‘in det(;rmining’
5. Fig 3, the temperatures should be listed in the reverse order, ie replace ’55504540
3525 10°C’ with ’102535404550 55°C’.
THEORETICAL EVALUATION OF THE EFFECT OF TEMPERATURE ON THEFATIGUE BEHAVIOUR OF BITUMINOUS ROAD-BASES
ABSTRACT
This Report describes a theoretical investigateion into the fatigue behaviour
of rolled asphalt road-bases when subjected to a range of road temperatures
that occurs in the British climate.
The pavement considered in the analysis conformed to the recom-mendations of R“oad Note 29. The elastic and fatigue behaviour of thematerial was characterised by uniaxial sinusoidal stress tests.
The relative fatigue behaviour of the road is related to that in the testson two bases; (a) the total tensile strain, and (b) the strain produced
directly as a result of the tensile stress. The bottom of the road-base is shownto be most vulnerable to fatigue damage at certain temperatures which depenclupon the modular ratio between the road-base and sub-base. If this modularratio falls below unity the maximum total tensile strain no longer occurs atthe bottom of the road-base but at some point higher in the road structure
where the stresses are wholly compressive.
The effects of varying the thickness of the bound layers, of changingthe sub-base moduli, and the significance of temperature gradients are also
considered.
1. INTRODUCTION
A substantial amount of information exists on the fatigue behaviour, under laboratory conditions, of bitumen-
bound road materials. It is necessary to relate the experimental data obtained from relatively simple laboratorytests to the more complex situation existing in the road. Here the behaviour of the entire pavement structuremust be considered because the possibility of fatigue cracking is not only influenced by the characteristics ofthe bituminous mixture but also by the thickness and characteristics of other components comprising the
pavement structure.
The temperature of a bituminous road layer influences its elastic properties, which in turn affect the
stress and strain distribution and hence the degree of fatigue damage caused by the passage of wheel loads.The sensitivity of the properties of bitumen-bound road materials to variations in temperature poses the questionof whether repetitive loading of such materials in the road is more damaging at high or low temperatures.
This Report uses the results from a multilayer elastic analysis to show how variations in temperature affectthe nominal stress and strain distributions in a typical pavement and hence to decide which depths and tempera-tures are likely to be the most critical for fatigue. The effects of varying the thickness of the bc)und layers,changes in the sub-base moduli, and temperature gradients are also considered. This information is necessaryto promote a better understanding of the fatigue behaviour of the road in service, to aid planning of laboratorytests, and to enable comparisons between the fatigue behaviour of different bituminous mixes to be madeunder appropriate test conditions.
2. ASSUMPTIONS
2.1 Road structure
The road construction considered in this analysis conformed to the recommendations in Road Note291for a road comprising a rolled asphalt road-base and bearing a cumulative total of 60 mfllion commercial
vehicles during its design life. The thicknesses of the various layers are given in Table 1. In Section 5 the
effect of varying the total thickness of the bound layers on the calculated stresses and strains is examined.
2.2 Elastic properties of the layers
Road Note 29 specifies that for roads carrying cumulative traffic in excess of 0.5 million standard aflesthe minimum CBR of the sub-base should be 30% and this value has been assumed. A CBR of 7% was assumedfor the sub-grade. The CBR values were converted to moduli using a rough correlation that has been found to
exist between the dynamic modulus E and field CBR values 2. This correlation indicates that the E value isroughly proportional to the CBR value:-
E ~ CBR x l,04kN/m2 ... ... ... ... ... ... ... ... ... ... (1)
Both the sub-base and sub-grade moduli are assumed to be independent of temperature.
For the base-course and road-base the moduli were taken from measurements made on a rolled asphalt
mix over a range of temperatures in uniaxial tests under continuous sinusoidd loading at 25 HZ3 (whichaccording to Klomp and Niesman4 corresponds to a vehicle speed of approximately 80 km/hr); the modulus of
the wearing course was assumed to be 2Wo greater.
Poisson’s rat io for bituminous mixes is a function of frequency, temperature and strain. Sayegh5 has
reported that it increases from 0.1 for high frequencies, low temperatures and small deformations to 0.5 for
low frequencies, high temperatures and large deformations. For the purposes of these calculations Poisson’s
ratio was assumed to increase linearly with temperature from 0.35 at IO”C up to 0.45 at 4~C and remain
constant thereafter.
The values of elastic modulus and Poisson’s ratio assumed for this analysis are given in Table 1.
2.3 tilculations of stress and strain
The stresses and strains at various levels in the road were calculated assuming that the p~vement surface!was subjected to a wheel load equal to half a standard afle load (41 kN) distributed over a circular area of149 mm radius, giving a surface pressure of 586 kN/m2.
The maximum horizontal stresses and strains at a given depth will occur directly beneath the wheel load.These will be critical in evaluating the effect of fatigue in the road-base. Horizontal and vertical stress and
strain components were calculated at various depths using a computer prugramme for a multi-layer linearelastic analysis”.
The sign convention adopted is positive for tension and negative for compression.
2.4 Temperature conditions
The effects of different temperatures on the stress and strain distributions in the road, assuming the
temperature is uniform throughout the depth of the road, are examined in Sections 3,4 and 5, covering a
range of temperatures from 1&C to 55”C. In Section 6 the effect of a temperature gradient is considered.
2
3. ANALYSIS AND DISCUSSION OF RESULTS
3.1 Effwt of temperature on the stress and strain levels within the p:~vement strutiure
Figs 1, 2 and 3 illustrate how the calculated radial stress, radial strain, and vertical stress components dueto a wheel load vary with changing temperature throughout the base-course and road-base combinations for theroad construction given in Table 1.
3.2 Applimtion of laboratory fatigue data to the road
Before comparisons can be made between the fatigue resistance of pavements at different temperaturesor of different constructions it is necessary to establish a criterion so that the damaging effect of passing wheel
loads may be judged. h laboratory tests under uniaxial constant stress amplitude conditions the initial tensile
strain an be used to predict the fatigue life of the test specimen3’8.
In the simple uniaxial test the tenstie strain is the direct result of a tensile stress. The strain situation ina road is more complex. The longitudinal principal strain in the road is given by:-
Ox – V(OV+ az)
Ex = ... ... ... ... ...
where ‘x =
‘Y =Uz =
v =
E=
L
longitudinal principal stress
transverse principal stress
vertical principal stress
Poisson’s ratio
Young’s modulus
This strain may be sub-divided into two contributions
axc;=— ... ... . .. . .. ... ..!
E
,, v (Uy t Oz)‘x = ... ... . .. . .. .. . ...
E
where e; is the direct strain and e; is the Poisson strain.
...
...
...
...
...
...
...
...
...
...
...
...
... (2)
... (3)
... (4)
Figs 1, 2 and 3 show that as the bound layers we&en due to increasing temperature and the vertical
compressive stress component Uz at a given point in the road increases, the contribution to the horizontaltensile strain from this stress component also increases according to Eq. (2). At the same time the horizontal
stress components decrense and eventually become compressive at high road temperatures. It is, therefore,possible to have a situation in which the road base experiences large horizontal tensile strains while all three
principal stresses are compressive. The total horizontal strain, together with the clirect and Poisson straincontributions at the bottom of the road-base for the road structure considered are shown in Fig. 4 as afunction of temperature.
bboratory fatigue testing is usually conducted under uniaxial or simple flexurd loading conditions
and as such these tests only demonstrate the relationship between an applied direct strain and the fatigue life;no quantitative data are pubtished on the influence of the Poisson strain on the fatigue life.
3
In view of the uncertainties in applying uniaxid test data to the road situation the fatigue behaviour ofthe road has been related to that in the tests on two cases (a) the total tensile strain, and (b) the strain produced
as the direct resdt of a tensile stress. These two relationships can roughly be regarded as limits of tolerance inapplying uniaxid data to the road situation. If the Poisson strain and the direct strain have a simflar effect onthe fatigue life then (a) will be adequate, but if the Poisson strain has a small effect then (b) will suffice.
3.3 Fatigue bhaviour of the road
Uniaxid tests on a hot rolled asphalt under controlled stress conditions show that for a particular tem-perature the data can be represented by a straight line on a log-log plot of initial strain vs cycles to failure3.Tests were carried out at only two temperatures (25 “C and 10°C) and for the present purposes a linear relation-
ship has been assumed to estimate fatigue lives at other temperatures.
The fatigue life N under sinusoidal constant stress amplitude loading for an initial tensile strain e at atemperature TC can be expressed by the following relationship:-
log N = 17.512 t 0.0705T – 5.2 loge ... ... ... ... ... ... ... ... (5)
At all temperatures the road layers experience stress and strain pulses of varying magnitudes due to the
passage of different wheel loads. It is assumed that the same summation law can be used to integrate thedamage over the wheel load spectrum at any temperature. The damage resulting from one wheel load can,therefore, be used to assess the relative amount of damage occurring in the road at different temperatures.
The calculated fatigue life of the bottom of the road base for a road temperature of 25°C was taken as the
datum life and the fatigue lives at other temperatures were calculated relative to this. These relative fatiguelives based on the total and the direct radial strains at the bottom of the road-base are plotted in Fig. 5 as afunction of temperature. Both of these curves demonstrate a temperature level at which the road is most
sensitive to fatigue damage.
Calcdation of the fatigue life of the underside of the road-base based on the total horizontal strainshow that the greatest sensitivity to fatigue damage will occur between 4VC and 45”C. At these temperaturesthe horizontal tensile stress is low and the large tensile strain is almost entirely due to the Poisson’s ratio effectof the increased vertical compressive stress. Fig. 2 shows that at high road temperatures it is not the undersideof the road base which experiences the largest tensile strains; these wi~ occur higher in the road base. Thistype of strain behaviour has been verified experimentally by Dempwolff and Sommer9. If, therefore, the totaltensile strain is the criterion of fatigue distress then more attention should be paid to the fatigue behaviour ofthe material higher in the road structure.
Fig. 5 shows that for a fatigue criterion based only on the direct tensile strain the road base will showthe greatest sensitivity to fatigue damage at a road temperature between 30”C and 35 “C. The fatigue behaviourof the road when the horizontal and vertical stresses become compressive is unknown. There is a real possibility
that cyclic compressive stresses could lead to healing of any damage 1°mused at lower temperatures and could,
therefore, be beneficial to the fatigue resistance of the road.
The degree of fatigue damage caused by the passage of traffic in a road at a particular temperature will bea function of the fatigue sensitivity of the road and the duration of time the road spends at that temperature.
The duration of time layers in a typical En~ish road spent at particular temperatures over the course ofone year are shown in Figs 6a, 6b and 6c. These are averages of results recorded over a five year period!l They
demonstrate that the road spends a considerable portion of its life at a relat ively high temperature; i.e., above20°C for an average of about 115 days per year.
The data represented in Fig. 5 were used to estimate the relative fatigue damage caused to the road-baseat various temperature levels for a road experiencing the temperature spectrum given in Fig. 6c. The durationof time a road spends at a particular temperature together with the estimated relative fatigue life and the
4
fraction of the fatigue damage occuring during that time are shown in Table 2; damage histograms are also
i~ustrated in Fig. 7. The damage histograms for the two distress criteria considered show that the majority
of the fatigue damage occurs when the road base temperature is within the range 15-30°C, the most damaging
temperature interval being 20-25°C.
4. SUB-BASE MODULUS
The fatigue sensitive temperature regions of the pavement mentioned in the last section depend upon themodular ratio between the sub-base and the road-base. The sub-base modulus is independent of temperaturewhilst the moduli of the bound layers are extremely temperature dependent. The effect of temperature
variations is to cause changes in this modular ratio. The values of the total radial strain, direct radial strain
and the radial stress components as a function of this modular ratio for various values of the sub-base modulus
are shown in Figs 8 and 9. A value of 0.35 for Poisson’s ratio was used in these”ciilculations. These show thatthe peak value of the total tensfle strain occurs when the modular ratio is approximately unity and the peak
direct radial tensile strain occurs at a modular ratio of about three. Also the stiffer the sub-base the lowerthe strain in the road-base and hence the more resistant will be the road to fatigue.
Measured moduli of different bituminous mixes at a particular temperature show considerabledifferences. An approximate value of the radial strain or stress at the bottom of the road-base for a given sub-base and road-base modulus for the road construction given in Table 1 can be estimated from these Figures.
5. THICKNESS OF BOUND LAYER
The effect of varying the thickness of the bound layer on the horizontal stress and strain at the underside ofthe road base at various temperatures is shown in Fig. 10. The fatigue resistance of the road wfll, of course,
diminish with a decrease in the layer thickness due to the resultant increase in stress and strain. However,the relative stress and strain values remain approximately the same at the various temperatures for different
thicknesses, and so the temperatures levels at which the road base is Wely to be most critical to fatigue will be
largely independent of the thickness of the bound layer.
6. TEMPERATURE GRADIENTS
The analysis has assumed that all depths in the road are at a constant temperature, whereas temperaturegradients are normally encountered. Any rapid temperature changes occur at the road surface, the road tem-
peratures lower down being relatively stable. A temperature gradient of the type likely to be encountered canbe calcdated by solving the equation for heat flow in one direction, viz:-
where a = the~~ diffusivity
~ = temperature
t = time
(6)
By the use of finite differences this equation can be transformed into a set of simultanec)us equations
suitable for solution.
5
[ , rn,n] [dm,n+l- ‘m,nl,a ‘mtl ,n t~m_l n–24=
(6X)2 &t... . .. ... ... (7)
These equations were solved to determine the temperature gradient in the road two hours after assuminga sudden change had taken place in the surface of a road of uniform temperature. Temperatures within the road
layers were calculated using a value of 0.625 x 10-6 m2 <1 for the thermal diffusivity of the bound road material.
This value was calcdated from the thermal properties of the constituent materials used in the rolled asphalt.
The calculated temperature gradient is shown in Fig. 11.
A temperature difference of 15°C between the road surfam and the bottom of the road-base was assumed;this is as large a temperature gradient as can normally be expected in practice. The effect of this temperaturegradient on the calculated radid strain and stress components is shown in Figs 12 and 13 which also show the
radial stress and strain distributions in a road with no temperature gradient. In the calcdations the bound road
layers were sub-divided, and the mean temperature within each sub-layer was used to determine the values ofits elastic parameters.
From these results it can be concluded that in roads in which a temperature gradient exists the radial stressand strtin, especially in the lower regions of the road-base, are simflar to the stresses and strains in a road ofconstant temperature, provided the temperature at the bottom of the road-base is used in the constant roadtemperature calculation.
7. COMMENTS
In this analysis the influence of temperature on the fatigue behaviour of a heavily trafficked road has beenexamined. The calculated fatigue’behaviour of the road depends on its construction, the elastic and fatigue
data, and the temperature spectrum used in the calculations. The moduli and fatigue data can show considerablevariations for different bituminous mixes. Fig. 8 demonstrates that it is the modular ratio (MR) between the
road-base and the sub-base which determines the temperature at which the total and the direct tensile radial
strain at the bottom of the road base reach a maximum value.
As the road temperature increases the MR decreases. When it has fallen to about 3.0 the direct tensileradial strain is a maximum; a further decrease to about 1.0 will cause the radial stress and hence the directtensile strain to fall to zero. At this temperature the total tensile strain becomes a maximum. A situationwould, therefore, exist when calculations of fatigue life, based on the direct strain, would predict a zerofatigue damage rate whereas calculations based on the total strain would predict that the fatigue damagerate would be at a maximum. In the example considered the temperature at which MR = 1.0 is greater than
4&C, which is outside the temperature range normally experien~-d at the bottom of the road-base of anEn@ish road; consequently, the damage histograms calculated for the two strain criteria (Fig. 7), did notdiffer significantly in shape. If data for a bituminous material with lower moduli values had been used, sothat MR became 1.0 at a temperature which the road achieved for a significant length of time, the twodamage histograms in Fig. 7 would be considerably different. The effect on the calculated stresses andstrains of using different moduli for the road base can be estimated from Figs 8 and 9, and hence if fatiguedata for the road-base material is avaflable the fatigue behaviour can be assessed.
In a three-dimensional stress system interactions between stresses and strains in different directions
are such that the strain and stress components in any direction are not proportional to one another. WhenMR <1.0 the total radial strtin and the radial stress at the bottom of the road-base have opposite signs. The
large tensile strains result from Poisson’s ratio effect of the increased compressive vertical stress. The multi-axial condition is, therefore, different from the uniaxial condition norma~y encountered in laboratory tests;
no quantitative data are published on the effect of Poisson strains on the fatigue behaviour of a bound roadmat erial.
Fig. 2 shows that when MR <1.0 the maximum total tensile strain no longer occurs at the bottom of
the road-base, but at some position higher in the road structure. Here dl three principal stress componentswill be compressive. It appears that if the temperature level at which this occurs falls within the temperature
spectrum experienced by the road-base then some attention should be paid to the bound material higher inthe road structure if the total tensile strain is an adequate fatigue distress criterion.
The maximum direct tensile strain always occurs at the bottom of the roadbase and is always proportionalto the stress in any given direction. The uniaxial test provides information on how a direct strain influences
the fatigue life of a bound material, but gives no information on the effect of a Poisson strain.
In applying a fatigue distress criterion to the road the reservations mentionf;d shodd be kept in mind.Predictions of the relative fatigue behaviour of the road, based on the total and direct tensile strains in theroad base, can show considerable differences, depending on the moduli data used in the calculations. There
is, therefore, a need for a mdti-axial test to identify how interactions between the stresses and strains indifferent directions affects the fatigue life.
8. CONCLUSIONS
1.
2.
3.
4.
5.
6.
7.
The temperature has an important effect on the horizontal stresses and strains in a ro;d-base with
bituminous materials. The important parameter is the modular ratio MR b~:tween the road-base and
the sub-base. As the road temperature increases MR decreases.
The total radial tensile strain at the bottom of the road-base is a maximum when MR x 1.0. At thistemperature the horizontal tensile stresses at the bottom of the road-base are very low and the largetensile strains are produced by the Poisson’s ratio effect of the compressive vertical stress. At highertemperatures the maximum tensile strain no longer occurs at the bottom of the road-ba~~ but at some
point higher in the road structure where the stresses are wholly compressive.
The direct radial tensile strain at the bottom of the road-base is a maximum when MR x 3.0 (i.e. about
1WC below that of the total tensfle strain), and it will reduce to zero when MR ~ 1.0. The greatestdirect radial tensile strains always occur at the bottom of the road-base regardless of temperature.
The example considered in this analysis is most sensitive to fatigue damage at a temperature in therange 30-45°C dependingon whetherthedirectstrain or total strain is the more important parameter
indetermining fatigue performance.
The amount of fatigue damage caused by the passage of wheel-loads at a particular temperature is afunctiGn of the fatigue sensitivity of the road and the duration of time the road spends at this tempera-ture. For the example considered the major part of the damage (about 80:%) is caused during the time
when the road-base is above 15°C and the most damaging temperature interval is 20-25°C.
Under multi-axial conditions interactions between stresses and strains in different directions are suchthat the stress and strain in a given direction are no longer proportional to one another and may not beof the sanle sign. A multi-axial test system is needed to identify the relativt> importance (of direct andindirect strains in determining fatigue performance.
Temperature gradients in the road are relatively unimportant. The calculated horizontal stresses and
strains at the bottom of the road-base for a road in which a temperature gradient exists are simflar tothose calcdated for a constant temperature road, provided the temperature used for the constanttemperature calculation is equal to the temperature close to the bottom of the road-base in thetemperature gradient case.
7
9. ACKNOWLEDGEMENTS
This Report was prepared in the Repeated Loading of Materials Section (Section Uader: Mr K D Raithby) of
the Structural Properties Division as part of a co-operative research program me between the Transport and Road
Research bboratory and the Refined Bitumen Association.
The author acknowledges the work carried out by Mr A B Sterling, of the Transport and Road Research
bboratory and Mr R T.N Goddard, of the Refined Bitumen Association Limited, in providing the data from
laboratory tests which were used in this analysis.
10. REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
TRANSPORT AND ROAD RESEARCH LABORATORY. A guide to the structural design of pavementsfor new roads. Road Note 29, 3rd Edition, 1970, HM Stationery Office.
HEUKELOM, W, and C R FOSTER. Proc. ASCE., 86, No SM 1 (1960), 1.
RAITHBY, K D,and A B STERLING. Some effects of loading history on the fatigue performance ofrolled asphalt. Department of the Environment, TRRL Report LR 496. Crowthorne, 1972 (Transport
and Road Research Laboratory).
KLOMP, A J G,and T W NEISMAN. Observed and calculated strains at various depths in asphalt pave-
ments, Second hternational Conference on the Structural Design of Asphalt Pavements, Ann Arbor,
Michigan, 1967.
SAYEGH, G. Visco-elastic properties of bituminous mixtures, Second International Conference on theStructural Design of Asphalt Pavements, Ann Arbor, Michigan, 1967.
THROWER, EN. Calculations of stresses and displacements in a layered elastic structure. Ministry ofTransport, RRL Report LR 160. Crowthorne, 1968 (Road Research hboratory).
THROWER, EN. Calculations of stresses and displacements in a layered elastic structure, Part 11.Department of the Environment, RRL Report LR 373. Crowthorne, 1971 (Road Research hboratory).
PELL, P S. Fatigue of bituminous materials in flexible pavements, Proc. Inst. CivflEng.,Vol31,July 1965.
DEMPWOLFF, R,and P SOMMER. Comparisons between measured and calculated stresses and strainsin flexible road structures, Third hternationd Conference of the Structural Design of Asphalt Pave-
ments, London, 1972.
BUIN, R and J SAUNIER. Deformability, fatigue and healing properties of asphalt mixes. SecondInternational Conference on the Structural Design of Asphalt Pavements, Ann Arbor, Michigan, 1967.
GALLOWAY, J W. Temperature durations at various depths in bituminous roads. Ministry of Transport,RRL Report LR 138. Crowthorne, 1968 (Road Research Laboratory).
8
— —
“Ew g
—
s.o
G.o
“Ew g
bm0.
m.o
—
‘Ew g
0w0
—
“Ew g
—
“Ew g
—
00.
—
TABLE 2
Fatigue damage occurring in the temperature intervals
Duration of Fatigue behaviour based on total Fatigue behaviour based on directTemperature temperature Fraction of time radial strain radial strain
interval interval in base spent in temperatureTc section (from Ref 1) interval Relative fatigue Fraction of Relative fatigue Fraction of
days/year life damage fife damage
–5 too 2 0.005 8.0 0.002 3.6 0.003
Otots 42 0.115 8.0 0.032 4.0 0.056
+S totlo 84.5 0.232 7.0 0.076 4.6 0.098
tloto+ls 62.5 0.172 4.1 0.094 3.8 0.088
t15tot20 61 0.167 2.5 0.151 2.2 0.149
+20tot25 74 0.203 1.4 0.327 1.2 0.329
+25tot30 33 0.091 0.80 0.255 0.78 0.226
t30tot35 5 0.014 0.55 0.056 0.56 0.047
t35tot40 0.5 0.001 0.36 0.007 0.64 0.004
.,.
0
100
200
300
ISUB-BASE
400600 400 200 0 -200
Rodiol stress (kN /m*)
-400 -600
Fig. 1. RAOIAL STRESS IN THE ROAO AT VARIOUS TEMPERATURES
o
100
200
300
~WEARING COURSE
—. ——
——
SUB-B
——
SE
.— —
I\500c
\——
/
450c 400c
!1/
——
400600 500 400 300 200 100 0 -100
—— —
Radial strain (x 10-6)
Fig. 2, RADIAL STRAIN IN THE ROAD AT VARIOUS TEMPERATURES
o 00
00N
o0m
0u.-
4L
3
00
1
0
-----
/
/
I\
1\\\
I1:1:1:
~9--9,
,/M
4\\\
--:
‘%\\
\\
0
(g-ol x ) U!DJ?S
100.0
10”0
1.0
01
——
—
—
\\
\\
Fatigue life of the roadcalculated from equation 5
based on the total radialtensile strain at theunderside of the road base
Fatigue life based on thedirect tensile strain
\
—
——
/
+
10 15 20 25 30 35 40 45 50 55
Temperature (~)
Fig,5, THE RELATIVE FATIGUE LIFE OF THE ROAO flASE AS A
FUNCTION OF TEMPERATURE
80
60
40
20
0r
a) Between wearing
1 and basecoursecourse
L-lo -5 0 5 10 15 20 25 30 35 40 45 50
Temperature (oC )
80
60
40
20
b) Between basecourseand base
wo 0L
-lo -5 0 5 10 15 20 25 30 35 40 45 50s
80
60
40
20
.
Temperature (oC )
c ) In base
Lo-10 -5 0 5 10 15 20 25 30 35 40 45 50 “
Temperature (°C )
Fig. 6 TEMPERATURE/ TIME HISTOGRAMS AT VARIOUS LAYERS IN THE ROAOAVERAGEO
OVER 5 YEARS
a) Damage histogmm based onusing the total tensile strainto calculate the fatigue life
.
L0 0k -10 -5 0 5 10 15 20 25 30 35 40 45g
c.-
0.4
0.3
0.2
0.1
0
—
Temperature (°C)
-lo -5 0 5 10 15 :
—
1:
b)
—
.
.
Temperature (°C)
Damage histogram based onusing the direct tensile strainto calculate the fatigue life
1-3 35 40 45
Fig. 7 DAMAGE HISTOGRAM FOR MATERM1 AT THE EOTTOM OF THE ROAOEASE
/’
\
o0
I.1II
1
0
-ua
a
a
(9-OLX ) U!DJTS ~l!SUal
800
600
400
200
01 10 1(
Modular rat io
Fig. 9 RADIAL STRESS AT THE UNOERSIOE OF THE ROAOEASE AS A FUNCTIONOF MOOULARRATIO
10200
400c
400c
\- 25°C
-\--
— Stress
— — Strain I
--
--
250 30010
350
Total thickness of bound layers (mm)
Fig. 10 STRESS ANOSTRAIN AT THE UNOERSIOE OF THE ROAOBASLYS PAVEMENT THICKNESS
I—
III
II
IIII
II
I
I
III
I
o 00m
Lu0ua
ROAD SURFACE
WEARING COURSE
——
1
—-
/
/BASE COURSE AND
ROAD BASE
/
I
\
1 4
SUB-BASE
200 150
1/,//‘/.0
-5–2—6 —
100 50 0
——.
I
f I1
2
3
4
5
6
7
—
Constant temperature
Constont temperature
Constant temperature
Surface temperatureBottom of road base
Surface temperatureBottom of road base
Surface temperatureBottom of road base
Surface temperature
Bottom of road base
Radial strain (x10-6mm/mm)
Fig. 12. EFFECT OF A TEMPERATURE GRADIENT ON THE RAOIA1 STRAIN
-50
40”C
25°C
100C
25°C400c
400c
25°C
100C
25°C
25°C
loOc
-100
EE
0 I I
WEARING COURSE——- -—— ——- -—— —. —
100
BASE COURSEAND ROAD BASE
200
—Constant ternpemture 100C
300 —-Surface temperature 25°CBottom of roaci base 100 C
SUB-BASE
400 1:600 400 200 0 -200 -400 -m
Radial stress (k N/m2)
o I IWEARING COURSE
100
BASE COURSEAND ROAD BASE
2004
—Constant temperature 25°C——Surface temperature 10°C
300 ——— “ —~>’ ——— Bottom of roa(~ base 25°C—--Surface temperature 400C
SUB-BASE Bottom of road base 25° C
400 I IBoo m 400 200 0 - 20CI -400 -m
Radial stress (kN/m2)
oWEARING COURSE
——— .—— - -—— ——! —— —- — —
0 ;100 /
BASE COURSE /
AND ROAD BASE
200 /,
300 ‘—— ——— —— —— —.—- .——
— Constant temperature 400CSUB-BA SE ‘-Surface temperature 25*C
Bottom of road base 40 ‘C
400 T 1 [ I800 mo 400 200 0 - 20CI -400 -m
Radial stress (kN/m*)
Fig 13. EFFECT OF A TEMPERATURE GRAOIANT ON THE RAOIA1STRESSDISTRIBUTION
(1851) Dd635221 3,750 10/73 HPLtd., So’ton G1915PRINTED IN ENGLAND
ABSTRACT
Theoreti@l evaluation of the effea of temperature on the fatigue behaviour of bituminousroad-bases: M. E. NUNN: Department of the Environment, TRRL Report LR 594: Crowthorne, 1973(Transport and Road Research hboratory). This Report describes a theoretical investigation into thefatigue behaviour of rolled asphalt road-bases when subjected to a range of road temperatures that occurs
in the British climate.
The pavement considered in the analysis conformed to the recommendations of Road Note 29. Theelastic and fatigue behaviour of the material was characterised by uniatial sinusoidal stress tt?sts.
The relative fatigue behaviour of the road is related to that in the tests on two bases; (a) the total ten-
sfie strain, and (b) the strain produced directly as a resdt of the tensile stress. The bottom c)f the road-baseis shown to be most vulnerable to fatigue damage at certain temperatures which depend upon the modularratio between the road-base and sub-base. If this modular ratio falls below unity the mtimum total tenstie
strain no longer occurs at the bottom of the road-base but at some point higher in the road structure wherethe stresses are wholly compressive.
The effects of varying the thi&ness of the bound layers, of changing the sub-base rnoduli, and thesignificance of temperature gradients are dso considered.
ABSTRACT
Theoretiml evaluation of the effeti of temperature on the fatigue behaviour of bituminousroad-bases: M. E. NUNN: Department of the Environment, TRRL Report LR 594: Crf)wthorne, 1973
(Transport and Road Research bboratory). This Report describes a theoretical investigation into thefatigue behaviour of rolled asphalt road-bases when subjected to a range of road temperatures that occurs
in the British climate.
The pavement considered in the analysis conformed to the recommendations of Road Note 29. Theelastic and fatigue behaviour of the material was characterised by uniatial sinusoidal stress tt~sts.
The relative fatigue behaviour of the road is related to that in the tests on two bases; (:~) the total ten-
We strain, and (b) the strain produced directly as a restit of the tensile stress. The bottom c)f the road-baseis shown to be most vulnerable to fatigue damage at certain temperatures which depend upon the modularratio between the road-base and sub-base. If this modular ratio falls below unity the mtimum total tensfle
strain no longer occurs at the bottom of the road-base but at some point higher in the road structure wherethe stresses are wholly compressive.
The effects of varying the thi&ness of the bound layers, of changing the sub-base moduli, and thesignificance of temperature gradients are dso considered.