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2nd Workshop on Four Point Bending, Pais (ed.), © 2009. University of Minho. ISBN 978-972-8692-42-1
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1 INTRODUCTION The European standard EN 13108-0 prescribes the loading frequency to be used in fatigue bend-ing tests to f = 30 Hz. This paper discusses the influence of this test parameter in terms of meet-ing real loading conditions, technical problems in laboratory tests as well as its impact on test results.
In chapter 2, strain measured in a test road is used to evaluate the real loading conditions as-phalt concrete layers are subjected under traffic loading. In chapter 3 the impact of loading fre-quency on laboratory fatigue tests are discussed. The problems related to moving masses are il-lustrated. Further, the fatigue lives measured at varied loading frequencies are discussed. By applying alternative test evaluation principles it is tried to diminish the impact of loading fre-quency on the fatigue test result. Conclusively, a proposal for the conducting of future fatigue tests is drawn.
2 IN-SITU LOADING CONDITION
2.1 Full scale pavement test facility at Bundesanstalt fuer Strassenwesen (BASt) The full scale indoor pavement test facility at BASt consists of a 38 m long, 7.5 m wide and 3.5 m deep concrete trough. For the current project, eight different asphalt pavement construc-tions according to the German pavement design guideline RStO 01 were built in. The test track under construction and after completion is shown in Figure 1.
Loading Frequency and Fatigue: In situ conditions & Impact on Test Results
K. Mollenhauer & M. Wistuba Braunschweig Pavement Engineering Centre (ISBS), Technische Universität Braunschweig, Germany
R. Rabe Bundesanstalt für Straßenwesen, Section Dimensioning and maintenance of roads Bergisch Gladbach, Germany
ABSTRACT: 4PB test according EN 12697-24 are used for evaluating the fatigue resistance of asphalt. For type testing of asphalt concrete (EN 13108-20) these tests have to be performed at a temperature of 20°C and a frequency of 30 Hz which demands extensive test machinery. Results gained on uniaxial cyclic tensile stress tests indicate that the impact of test frequency could be neglected if the interpretation techniques of fatigue test results are changed. The variation of traffic speed induces various loading rates in different types of asphalt pave-ments. Asphalt strain measurements in a full scale test track under real heavy vehicle loading are used to derive realistic frequencies for the application in laboratory tests. In order to elabo-rate the impact of frequency on results of 4PB tests fatigue tests these parameters are varied in an ongoing research study. The results of these tests are presented in the proposed paper.
262
Figure 1. Test track at BASt under construction and after completion
The pavement surface is at the same level as the surrounding floor so that truck overruns can
be conducted over two lanes, each with four different sections. The pavement constructions represent three different construction classes (SV, III, V) which are designed for certain amount of equivalent 10t-axle loads for a design period of 30 years. Following ranges of 10t-ESALs are assigned to the construction classes chosen for the test track:
o SV: > 32 mio. 10t-ESALs o III: > 3 mio. < 10 mio. 10t-ESALs o V: > 0.1 mio. < 0.3 mio. 10t-ESALs
The layout and geometry of the test track with all eight sections and construction classes is
shown in figure 2.
Figure 2. Layout and geometry of the test track with sections and construction classes
Subgrade, granular layers and asphalt base course were built in and compacted manually with
light compaction machinery. Due to the confined conditions the use of paver and rollers was not possible for building these layers. Asphalt binder and wearing course were laid with a paver and compacted with vibration rollers. Material test and control checks according to German technic-al standards were conducted for each layer.
Figure 3 shows the cross sections of the two lanes, each with four pavement constructions. Static plate load test were conducted on top of each granular course. The Ev2 values (mean value of five tests per section) for all granular layers are also shown in figure 3.
On the granular layers all required Ev2 moduli were met. The asphalt base course compaction values in two sections were slightly lower than the required ones, mainly due to the manual compaction. With regard the confined boundary conditions these values were accepted for the test track.
765 8
1 432section
constructionclass SV
constructionclass SV
constructionclass SV
constructionclass V
constructionclass III
constructionclass III
constructionclass III
constructionclass V
7,5 m
38 m
9,5 m 9,5 m 9,5 m 9,5 m
I I
II II
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Figure 3. Cross-sections I and II of pavement constructions at BASt test track
Each test section was equipped with asphalt strain gauges, soil pressure cells and temperature sensors. The principal location of the sensors (example: section 3) is shown in Figure 4.
Figure 4. Location of measuring gauges inside the pavement structure
2.2 Measured pavement response
2.2.1 Boundary situations for high and low stress level Four different truck/trailer and truck/semitrailer combinations were selected for the overruns. The gross weight was varied for each vehicle from empty vehicle (~15 t) up to 52 t for a 6 axle truck/semitrailer combination. The speed was varied in four steps from 2, 7.5, 15 and 30 km/h.
direction of travel
temperature T
thermocouple
strain εx ; εy
asphalt strain gauge
soil pressure cell
stress σx ; σy
48
20
48
22
48
48
1418
2015
wearing course 0/8 binder course 0/16 S
base course 0/22 CS
cementboundsand
leanconcrete
sand/gravel0/32
sand 0/2sand/gravel
0/32
section 1 section 2 section 3 section 4410
45
13
45
45
99
20 15crushedstone base
section 5 section 6 section 7 section 8
wearing course 0/8 binder course 0/16 Sbase course 0/22 CS
sand/gravel0/32
sand/gravel0/32
97 MPa
100 MPa
126 MPa
96 MPa
126 MPa 126 MPa
93 MPa
136 MPa
104 MPa
114 MPa
144 MPa
128 MPa
99 MPa
126 MPa
158 MPa135 MPa
104 MPa
116 MPa
105 MPa
264
2500 overruns were conducted with variation of gross weight, speed, lateral wander and tyre pressure.
Due to the amount of varied parameters and the number of different pavement test sections the following selected parameter combinations shown in Figure 5 and Figure 6 give an overview of the possible range of mechanical stress levels which occurred within the boundary conditions of the test series.
o Low stress situation: low asphalt-temperature (7 °C), high speed (30.5 km/h) and low gross weight (18.1 t) (Figure 5),
o High stress/strain situation: high asphalt-temperature (16.7 °C), low speed (2.7 km/h) and high gross weight (40.1 t) (Figure 6).
Each figure compares asphalt strain induced by truck overruns measured in two comparable pavement construction types of the strongest construction class SV (34 cm asphalt on 0/32 sand/gravel) and the weakest construction class V (12 cm asphalt on 0/32 sand/gravel).
-150
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-50
0
50
100
150
200
250
0 500 1000 1500 2000 2500 3000 3500
long
itudi
nal s
train
[µm
/m]
time [ms]
asphalt base course: low stress situation - construction class SV and V
section 3 (34 cm asphalt), construction class SVsection 4 (12 cm asphalt), construction class V
gross weight: 18.1 tspeed: 30.5 km/hasphalt-temperature: 7.0 C
5.4
4.42.3
4.3 3.9
tension/compression ratio:
Figure 5. Longitudinal strain asphalt base course - low stress situation
-150
-100
-50
0
50
100
150
200
250
5000 10000 15000 20000 25000 30000
long
itudi
nal s
train
[µm
/m]
time [ms]
asphalt base course: high stress situation - construction class SV and V
section 3 (34 cm asphalt), construction class SVsection 4 (12 cm asphalt), construction class V gross weight: 40.1 t
speed: 2.7 km/hasphalt-temperature: 16.7 C
3.12.7 2.3
1.7 2.1
tension/compression ratio:
Figure 6. Longitudinal strain asphalt base course - high stress situation
Following observations can be verified and derived from the measured data within the range of parameters of the entire test program:
265
o Asphalt strains between 10 µm/m and 220 µm/m were measured in the test sections. Higher strains are expected to occur in real service pavement constructions, especial-ly due to higher temperatures.
o Temperature and vehicle speed are decisive factors for the influence on stress and strain level in both, asphalt and granular layer.
o Superposition of stress in asphalt and in granular layers occur under wheel bases of 1.30 m or less
o Due to the alternating compression and tension zones in the asphalt base course su-perposition of adjacent wheels of a triple axle aggregate results in a lower maximum of strain under the mid-wheel of a triple axle aggregate (Figure 6)
o The influence interval of a wheel is determined by the flexural stiffness of the asphalt layer-package
o Absolute compression/tension strain peak ratios of 0.7 at the bottom of thin asphalt packages (12 cm) were observed.
o Tension/compression strain ratios at the bottom of the asphalt layers vary. Most deci-sive factors are temperature, axle configuration, speed and layer thickness.
2.2.2 Influence of the static wheel load To describe the influence of the static wheel load on the pavement response, the peak values of longitudinal asphalt strain and vertical granular stress under the wheel of the 1st trailer single-tired axle of a 2-axle articulated truck with 3-axle trailer were examined. The overruns with four different load stages were all conducted within a range of average asphalt temperatures from 11.0 °C to 14.0 °C. To describe the function using a linear regression analysis, the peak values (average of peak values of three vehicle passes) of each load stage were shifted linear to a refer-ence temperature of 12.5 °C.
Due to the low vehicle speed between 2.4 km/h and 3.0 km/h and the good evenness of the pavement surface the dynamic vertical wheel forces were considered negligible.
The regression functions validate section 8 as the weakest (14 cm asphalt on granular base) and section 1 as the strongest (30 cm asphalt on 20 cm cement stabilized layer). A precise dis-tinction line can be drawn between sections of the weakest construction class V (section 4 and 8), sections of class III (section 5, 6 and 7) and sections of the strongest class SV (section 1, 2 and 3).
Considering the slope of each function as indicator for the stiffness of the construction, the stiffness of the strongest section 1 (slope = 0.008) is 7 times higher than the stiffness of section 8 (slope = 0.0558) for the asphalt strain.
Figure 7 shows the influence of static wheel load on the longitudinal asphalt strain.
y = 0,0080xR² = 0,9944
y = 0,0107xR² = 0,9976
y = 0,0155xR² = 0,9990
y = 0,0484xR² = 0,9222
y = 0,0372xR² = 0,9799
y = 0,0312xR² = 0,9975
y = 0,0309xR² = 0,8619
y = 0,0558xR² = 0,9247
0
50
100
150
200
250
300
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
long
itudi
nal s
train
[µm
/m]
static wheel load FR [kg]
longitudinal asphalt strain L23 axle 3 v = 2,4-3,0 km/h T = 12,5°C
section 1section 2section 3section 4section 5section 6section 7section 8
slope ratio = 7section 8 : section 1
SV
III
V
Figure 7. Longitudinal asphalt strain versus static wheel load - all sections
266
2.2.3 Frequency in asphalt layers of sections with different layer thickness Full friction between the asphalt layers result in a transformation of shear forces. Thus, the as-phalt package acts like a slab under bending with additional vertical stress induces by the tran-sient wheel. The stiffness and therefore the deformation shape of a slab under bending are de-termined by the material stiffness and the overall thickness of the entire package.
A comparison of the longitudinal strains at the bottom of the asphalt base course in three dif-ferent sections (section 3: 34 cm asphalt, section 7: 22 cm asphalt and section 8: 14 cm asphalt) reveals the influence of the asphalt package thickness on the time and length of the compression and tension zones of the asphalt fibres. The geometrical length of the tension zone at the bottom of the asphalt base course is calculated from the sampling rate (1000 Hz) and the average meas-ured vehicle speed. Figure 8 shows the compression and tension zones under a transient steering axle wheel in three different pavement constructions. It can be seen, that the influence area of a wheel and the length of tension and compression zones increase with increasing asphalt thick-ness which means higher flexural stiffness.
-40
-20
0
20
40
60
80
100
2000 2500 3000 3500 4000 4500
long
itudi
nal s
trai
n ε x
[µm
/m]
time [ms]
asphalt strain base course, static wheel load: 7075 kg, v = 7,5-7,7 km/h
section 3 (34 cm asphalt)section 7 (22 cm asphalt)section 8 (14 cm asphalt)
0,47 m
34 cm
22 cm
section 3 section 7
14 cm
section 8
0,96 m
0,60 m
Figure 8. Length of asphalt base course tension zone depending on layer thickness
With increasing asphalt thickness the ratio between tension and compression strain peaks be-
fore, directly under and behind the wheel increases. That means that with increasing asphalt thickness the bottom fibre is subjected to more tension than compression strain. Table 1 shows examples of calculated tension/compression ratios observed in three different pavement con-structions.
Table 1. In situ tension/compression strain ratios depending on layer thickness test road section
asphalt thickness [cm]
min. compression strain [µm/m]
max. tension strain [µm/m]
tension / compres-sion ratio [-]
3 34 7,8 46,4 5,9 7 22 14,1 67,3 4,8 8 14 26,5 93,0 3,5
2.2.4 Vehicle speed and corresponding frequency in asphalt layers The analysis of the strain peak values due to vehicle passes at various speeds confirm the de-creasing of asphalt strain with increasing speed due to the increase of dynamic stiffness. The evaluation also reveals the decrease of tension and compression periods under the transient wheel with increasing speed. The frequency of an equivalent sinusoidal function can be derived from the length of the tension and compression periods.
average asphalt temperature: 12,5 °C
267
Figure 9 shows the measured longitudinal strain shapes at the bottom of an 18 cm asphalt layer and the length of the tension periods. It can also clearly be seen that the peak values de-crease with increasing speed.
-40-30-20-10
0102030405060708090
100110120130
2000 2500 3000 3500 4000 4500 5000
stra
in ε
x[µ
m/m
]
time [ms]
tension zone asphalt strain base course, static wheel load: 3500 kg
2,9 km/h7,9 km/h16,2 km/h31,4 km/h
section 5
18 cm
Figure 9. In situ asphalt strain versus time - tension/compression zones at varying vehicle speed
Table 2 shows the length of the tension periods and the calculated frequencies for the meas-ured vehicle speeds up to 31.4 km/h. An extrapolation for 60 km/h and 80 km/h was done by us-ing a regression analysis.
Figure 10 shows the functions of vehicle speed on the asphalt tension zone and the derived frequency.
Table 2. Length of asphalt tension zone and corresponding frequency - extrapolated verified extrapolated speed [km/h] 2,9 7,9 16,2 31,4 60 80 max. tension zone [ms] 661 257 129 70 38 29 frequency [Hz] 0,8 1,9 3,9 7,1 13,2 17,3
y = 1.804,957x-0,944
R² = 1,000
0
100
200
300
400
500
600
700
0 10 20 30 40 50 60 70 80 90
max
. ten
sion
zone
[ms]
speed [km/h]
length of tension zone - speed
y = 0,277x0,944
R² = 1,00002468
101214161820
0 10 20 30 40 50 60 70 80 90
frequ
ency
[Hz]
speed [km/h]
frequency asphalt strain - speed
Figure 10. Influence of vehicle speed on asphalt strain tension zone and corresponding frequency
In laboratory cyclic tests a sinusoidal load signal is applied. To show the difference between cyclic loading in standard bending tests and in-situ-loading, the strain signal applied in cyclic tests at 2 frequencies are added to the measured strain signals of the test sections (Figure 11). Whereas the actual measured bending strain in the test roads show tension This shows the dif-ference between real measured strains under real loading compared to the induced force shape in the four point bending test where the tension/compression ratio is 1.The time-dependent
661 ms
70 ms
decreasing strain peaks
268
course of horizontal flexural strain in a four point bending specimen corresponds with the ap-plied vertical force and the measured vertical displacement in the middle of the beam. Focussing on the shape, the frequency and the tension and compression periods Figure 11 compares the asphalt strain from in-situ measurements with the applied vertical force measured in a four point bending test of asphalt concrete 0/11 with bitumen 50/70 and with frequencies of 1.0 Hz and 2.0 Hz. The corresponding length of the tension (or the corresponding compression zone) is also shown. It can be seen that the loading frequency of 1.0 Hz corresponds to a frequency of asphalt strain induced by a passing wheel at ~7.6 km/h at the bottom of a 34 cm asphalt layer. The load-ing frequency of 2.0 Hz corresponds to an asphalt strain frequency at the bottom of a 14 cm as-phalt layer.
shape comparison between asphalt strain base course and 4 PB force
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0
50
100
150
2500 3000 3500 4000
time [ms]
long
itudi
nal s
trai
n εx
[µm
/m] -
4PB
forc
e [N
]
section 3 (34 cm asphalt)section 7 (22 cm asphalt)section 8 (14 cm asphalt)F-4PB-1,0 HzF-4PB-2,0 Hz
34 22
section 7
14
section 3 section 8
Figure 11. Comparison between in situ strain shape and four point bending force shape
To compare the tension/compression periods depending on time in a four point bending test
specimen applying a frequency sweep for stiffness determination the relation between the ten-sion zone/tension period and the corresponding frequency the relationships were evaluated and shown in table 3.
Table 3. Frequency and corresponding tension zone period in four point bending test
Sinusoidal force/displacement function: 4 point bending tests frequency [Hz] 0.1 0.2 0.5 1 2 5 10 20 30tension zone [ms] 5000 2500 1000 500 250 100 50 25 16.7
To summarize the results found before, it can be stated from the full scale in-situ measure-
ments of longitudinal strain that vehicle speed and asphalt thickness have a decisive influence on the shape and the frequency of asphalt strain. Extrapolated to a realistic travelling speed on in-service pavements asphalt strain frequencies may vary from 4 Hz to up to more that 20 Hz, depending on the tension/compression function. This means that the corresponding dynamic stiffness may also vary due to the wide range of observed frequencies.
269
Figure 12 shows the asphalt strain periods and corresponding frequencies in different pave-ment structures depending on vehicle speed.
y = 0,09x0,88
R² = 1,00
y = 0,12x0,90
R² = 1,00
y = 0,18x0,90
R² = 1,00
0
2
4
6
8
10
12
0 20 40 60 80 100
freq
uenc
y [H
z]
normalized speed [km/h]
frequency versus speed interval 2 - 6 axle 1
section 3 (34 cm asphalt)section 7 (22 cm asphalt)section 8 (14 cm asphalt)
verified
extrapolated
y = 0,19x0,88
R² = 1,00
y = 0,27x0,88
R² = 1,00
y = 0,36x0,93
R² = 1,00
0
5
10
15
20
25
0 20 40 60 80 100
freq
uenc
y [H
z]
normalized speed [km/h]
frequency versus speed interval 3 - 5 axle 1
section 3 (34 cm asphalt)section 7 (22 cm asphalt)section 8 (14 cm asphalt)
verified
extrapolated
maximum of influence interval of vertical stress on bottom layer
influence interval 1-7
long
itudi
nal s
trai
n [µ
m/m
]
-+ compression
tension
Figure 12. Asphalt tension strain periods and corresponding frequencies in different pavement construc-tions at varying vehicle speed
These results lead to lower loading frequencies than calculated from test road measurements
in Cheneviére et al. (2005). If the shape of the strain peak is used for fitting a sinusoidal strain function as shown in Figure 13, the frequency - traffic speed relationship gained at temperatures of 20°C and 30 °C results in similar correlation (Cheneviére et al. 2005).
Figure 13. Fitting technique for deriving a comparable loading frequency from strain measurements and resulting traffic speed – loading frequency interrelation (Cheneviére et al. 2005)
2.3 Conclusions of in-situ measurements for asphalt laboratory tests
The analysis of measured asphalt strain response in various pavement constructions induced by real vehicles with a wide range of vehicle parameters show the wide range of stress level and strain frequency that occurs at the bottom of asphalt pavement constructions. The analysis of the peak values and tension and compression zones induced by vehicle specific axle configurations provide important information for the boundary conditions and the assessment of asphalt labora-tory tests for stiffness and fatigue. Following principles with regard to the boundary conditions for four point bending tests have been found:
270
o At temperatures between 7 °C and 17 °C horizontal strain levels between 11 µm/m and 220 µm/m could be measured in the various pavements constructions and varied loading vehicles.
o The full scale tests confirm the decreasing of asphalt strain level with increasing speed. Higher loading speeds result in higher frequencies of as well as lower strain reaction which results in an increase in the stiffness modulus.
o The ratio between the maximum observed tension and compression strain varies de-pending on asphalt stiffness, layer thickness and loading conditions. The ratio rises with the thickness of the asphalt pavement. Especially for pavements of high thick-ness as used in motorways in Germany, the maximum tension strain reaches a value 6 times the value of the maximum compression strain. For this reason, loading condi-tions for dynamic asphalt tests should be thought over.
o The loading speed occurring of asphalt strain depends on layer thickness and varies along the cross-section. At the bottom of thin asphalt layers higher loading speeds occur than at the bottom of thick asphalt structures. For a traffic speed of 80 km/h and depending of the structure thickness, the derived frequencies vary between 8 Hz and 22 Hz if the tension zone duration is applied for fitting the sinusoidal function and between 4 Hz and 9 Hz if the duration between the maximum compression peaks is applied. These values are smaller than frequencies earlier evaluated at test roads subjected to higher temperatures.
o A more detailed analysis of all observed in-situ measurements may serve as a basis to adapt loading conditions to archive more realistic stiffness and fatigue determination in four point bending tests.
3 LOADING FREQUENCY IN LABORATORY FATIGUE TESTS
3.1 Impact of loading frequency on fatigue resistance Due to various traffic speeds, the loading speed of in situ loading of asphalt courses varies con-siderably. In cyclic tests the loading speed is simulated by the test frequency.
Saal & Pell (1960) analysed the influence of frequency by varying the loading speed in cyclic of force-controlled bending tests. The fatigue live (number of load cycles) at a test frequency of 13 Hz was found significantly lower than at a frequency of 50 Hz.
Neifar et al. (2003) used uniaxial tests to analyse the permanent deformation in cyclic tests by applying compressive and tensile haversine force-controlled loading. At tensile loading with rest periods at a temperature of +25°C and varied loading frequencies they found that the per-manent deformation after a number of applied load cycles at 1 Hz exceeds the deformation at 10 Hz. If the deformation courses are plotted versus the testing time the slow loading of 1 Hz still results in higher permanent strain than the faster loading at 10 Hz.
Using a viscoelastic continuum damage model for interpretation of fatigue tests on asphalt material, Daniel & Kim (2002) found unique pseudo stiffness failure functions for cyclic tests at varied frequencies and even monotonic tests. The used interpretation procedure is based on the implementation of testing time into the failure model.
In Mollenhauer (2008) the influence of varied testing frequencies on force-controlled Uniaxi-al Cyclic Tensile Stress Tests (UCTST) was analysed. As also shown in Mollenhauer & Lorenzl (2008) the number of load cycles until specimen cracking increased with increasing frequency (Figure 14). But if the test duration until the cracking is used as fatigue criterion, the fatigue lives obtained at varied test frequencies result in the same Wöhler function. This observation could also been made for further fatigue criterions, e.g. stiffness reduction as shown in Figure 15. The left side shows the stiffness moduli measured during UCTST at three varied frequencies versus the number of load cycles. On the left side the figure shows the same values drawn ver-sus the test duration. To consider the frequency-dependent stiffness modulus the measured val-ues are referred to their initial values at the beginning of the test. By this analysis the stiffness measurements result in similar courses which inhibit on their quasi-linear section the same slope d(Smix/Smix,0) / dt.
271
y = 577822x-3,4897
R2 = 0,9895
y = 268163x-3,103
R2 = 0,973
y = 139621x-2,8267
R2 = 0,9019100
1000
10000
100000
1000000
0 0,5 1 1,5 2 2,5
stress difference Δσ [MPa]
Num
ber o
f loa
d cy
cles
unt
il m
akro
cra
ck N
Mak
ro
-10°C; 10 Hz
-10°C; 5 Hz
-10°C; 3 Hzy = 52690x-3,1578
R2 = 0,9515100
1000
10000
100000
0 0,5 1 1,5 2 2,5
stress difference Δσ [MPa]
Test
dur
atio
n un
til m
akro
cra
ck t(
NM
akro
) [s]
-10°C; 10 Hz
-10°C; 5 Hz
-10°C; 3 Hz
-10°C, all f
Figure 14. Results of UCTST at varied loading frequencies (Mollenhauer & Lorenzl 2008)
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
0 20,000 40,000 60,000 80,000
number of load cycle N [-]
stiff
ness
mod
ulus
|E| [
MPa
]
10 Hz5 Hz3 Hz
T = +5°CΔσ = 1,3 MPa
0
0.2
0.4
0.6
0.8
1
1.2
0 2,000 4,000 6,000 8,000
duration of fatigue test t [s]
rela
tive
stiff
ness
mod
ulus
|E|/|
E 0|
[-]
10 Hz5 Hz3 Hz
T = +5°CΔσ = 1,3 MPa
Figure 15. Course of the stiffness modulus |E| versus the number of load cycles N (left) and course of the relative stiffness modulus |E|/|E0| versus test duration t [s] (right)
3.2 4PB-test program
3.2.1 Tested material In the framework of this study a hot mix asphalt material AC 11, as often used as a wearing course material in Europe, was subjected to uniaxial cyclic tensile stress tests (UCTST). Main compositional characteristics of this material are summarised in Table 4.
272
Table 4. Material properties of the hot mix asphalt AC 11 investigated in this study maximum aggregate density [kg/m³] 2,698 Grading
0,25 0,71 2 5 11,28 160,090
10
20
30
40
50
60
70
80
90
100
Sieve [mm]
pass
ing
[%]
grading [mass-%]
< 0.09 mm 9.5 %> 0,09 mm & < 2.0 mm 37.5 %> 2.0 mm 53.0 %
content of crushed aggregate C90/1binder type 50/70softening point Ring & Ball [°C] 52binder content [mass-%] 6.0maximum density [kg/m³] 2,476mean void content of specimens [vol-%] 2.8
3.2.2 Test device The 4PB tests were conducted in a hydraulic test device capable to induce cyclic loads of up to ±50 kN with a frequency of maximum 30 Hz. A test frame was constructed to enable 4PB tests at specimens of various sizes from 40 x 40 x 240 mm³ up to 100 x 100 x mm³. The frame inhi-bits bearings which allow the rotation of the inner and outer clamps. Slide bearings allow the translation at the outer clamps. To reduce the moving masses sliding bearings were avoided at the inner clamps. Furthermore, the upper load frame was constructed using aluminum whereas the bottom (fixed) part of the load frame is made of stainless steel.
The force is measured using a load cell which is located outside of the temperature chamber. The deflection is recorded using a LVDT (± 5 mm) positioned in the centre of the asphalt beam (xs = 0,5·L0).
Figure 16. Test frame for conducting 4PB test positioned in a hydraulic test device
Before conducting the tests the device was calibrated against three aluminium reference
beams of the nominal size 40 x 40 x 280 mm³ with nominal stiffness moduli of 94430, 90880 and 83070 MPa. To reach these values the deflection value was corrected using Equation 1 to consider the bearing play as well as the stiffness of the bending frame elements. Further the ca-libration measurements showed a device-induced time lag between the measured fore and def-lection signal which could not be explained by the moving masses only. As shown in Figure 17 the measured time lag is dependent of the applied test frequency and rises from 3 ° at slow load-ing with f = 1 Hz up to values of 20° at high frequencies of f = 20 Hz. When calculating the ef-fective time lag which produces this phase angle by Equation 2 it can be observed that it reaches a constant value of about tϕ = 2,8 ms at frequencies higher than 5 Hz (Figure 17, right). At lower frequencies the impact of the device time lag is decreasing as the duration of the loading cycles
273
is much higher. Because of this the effective resulting time lag which reaches values of 14 ms at very low frequencies can be neglected.
Consequently, in the following study, the measured time lags were corrected by using Equa-tion 3.
Z(X)korr = Z(X) – (4,53241 · 10-8 + F0 · 2,0616 · 10-5) (1)
f360t
⋅ϕ
=ϕ (2)
ϕcor = ϕmeasured - f · 360 · 0,0028 s (3)
0
5
10
15
20
25
30
0 5 10 15 20 25Frequency f [Hz]
Mea
sure
d P
hase
Lag
ϕ [°
]
Beam IIIBeam IIBeam I
0
0,002
0,004
0,006
0,008
0,01
0,012
0,014
0,016
0 5 10 15 20 25Frequency f [Hz]
Res
ultin
g tim
e la
g t ϕ
[s]
Beam IIIBeam IIBeam I
Figure 17. Device-Induced Phase lag
3.2.3 Moving masses In cyclic tests a specimen is loaded sinusoidally. In 4-Point-Bending tests a comparatively long prismatic specimen is clamped in supports near of its edges whereas two inner clamps are moved sinusoidally in vertical direction. By this loading, horizontal bending strain ε is induced, which is constant between the inner clamps according to bending theory. The bending strain ε can be calculated by using Equation 4 from the vertical deflection z(t) and the geometrical con-stant K(xS). In the following tests are evaluated which were conducted on asphalt specimens with an effective length L0 of 240 mm and a cross section B x H = 40 mm x 40 mm. The dis-tance between inner and outer clamps A is 80 mm. The deflection is measured in the middle of the asphalt beam directly (xS = 120 mm) by means of a LVDT. Thus the geometrical constant K(xS) reaches a value of 0,033 1/mm.
Cyclic test to derive stiffness modulus SMix are usually conducted using a strain amplitude εa of 50 µm/m. According Equation 1 this implies a deflection amplitude of za = 15,3 µm. Typical strain values applied during cyclic fatigue tests are εa = 200 µm/m which is provoked by a def-lection amplitude of za = 61,3 µm. Equation 2 represents the function of the deflection versus time.
6ss 10)x(Z)x(K ⋅⋅=ε (4)
( )zam tf2sinzz)t(z ϕ+⋅⋅π⋅⋅+= (5)
Besides the two inner clamps, also the upper load frame as well as the loading bar moves ac-cording Equation 5. The used bending device results in an equivalent mass Mäq of 15 kg. This moving mass induces a cyclic force function according Equation 6.
)tsin(zM)t(zM)t(aM)t(F 2aäqäqäqm ω⋅ω⋅⋅−=⋅=⋅= && (6)
274
For evaluating the impact of this force, the forces during 4-Point-Bending tests are calculated from the stiffness modulus of an AC 11 for the two deflection amplitudes representing loading conditions during a stiffness and a fatigue test. Further, the left figure contains the resulting forces due to moving masses. As seen on the right figure, the force ratio rises at high test fre-quencies (60 Hz) up to a value of 20 %.
The reduction of the test frequency would limit the described impact of moving masses on the measured forces. To limit this influences suppliers of bending devices introduced an accelation measurement system to correct the measured force during the test. Only by these means force-controlled bending tests at frequencies higher than 10 Hz are possible.
0
100
200
300
400
500
600
700
0,1 1 10 100Frequency f [Hz]
Forc
e F
[N]
Beam Force (50 µm/m)Beam Force (200 µm/m)Mass Force (50 µm/m)Mass Force (200 µm/m)
0
4
8
12
16
20
24
0,1 1 10 100Frequency f [Hz]
Forc
e-R
atio
F(M
ass)
/ F(
Beam
) [%
]
0
2000
4000
6000
8000
10000
12000
Stif
fnes
s M
odul
us S
Mix [M
Pa]
F(Mass) / F (Beam)
Stiffness Modulus SMix
Figure 18 Exemplar calculation of the impact of moving masses on the force measured during 4PB: Left: Bending force resulting from beam stiffness modulus & force induced by moving masses; Right: Force ratio versus frequency and stiffness modulus
3.2.4 Test results 4PB The 4-point-bending tests were analysed according EN 12697-24 by plotting the applied strain amplitude εa versus the number of load cycles NF/50 until the traditional failure criterion is reached (Figure 19). It can be observed that the asphalt endures more loading cycles when loaded by a frequency of 10 Hz rather than 30 Hz. This contradicts the observation made with uniaxial cyclic tensile stress test as shown in Figure 14 where a lower loading frequency results in a decrease of endured load cycle number. This discrepancy can be explained by the different-ly applied mode of loading. Whereas the UCTST were conducted in force-controlled mode, the 4PB tests were conducted deflection controlled. Due to the frequency-dependent stiffness mod-ulus and phase angle raising the frequency results in higher stiffness and thus for same strain amplitudes in higher induces bending stresses.
y = 5617,1x-0,2923
R2 = 0,9492 y = 6850,1x-0,2823
R2 = 0,9368
100
1.000
1.000 10.000 100.000 1.000.000 10.000.000NF/50 [-]
Stra
in a
mpl
itude
εa [
µm/m
]
10 Hz
30 HzAC 11
T = 20°C
Figure 19. Results of 4PB tests at varied frequency
275
By applying the approach introduced by van Dijk (1975) according Equation 7 this observa-tion can be explained by the differences in energy dissipation per load cycle. Due to the higher stress level, the value of dissipated energy per load cycle is higher for the high frequency load-ing compared to the lower frequency. In terms of force-controlled loading as applied at UCTST, the higher stiffness modulus at high loading frequency result for a given applied stress in lower strain amplitudes and thus in lower dissipated energy compared with slower loading.
ϕ⋅π⋅ε⋅σ= sin)N()N()N(W aadis (7)
To validate this assumption, the dissipated energy was calculated for each load cycle during the 4PB tests and summarized. In Figure 20 this accumulated energy dissipation is plotted with the course of stiffness modulus during a fatigue test. From the beginning of the test the stiffness modulus decreases whereas the phase angle rises. Both changes result in a nearly constant ener-gy dissipation during each load cycle and a quasi-linear rising accumulated energy curve. This observation that the changes of stiffness modulus and phase angle result in a nearly constant dissipation rate can be observed during all tests.
At the end of the test, characterized by an accelerating decrease of stiffness modulus, the energy dissipated during each load cycle decreases and the accumulated energy reaches an asymptote-like plateau. This plateau value can be interpreted as the total energy dissipated ΣWdis,tot during the fatigue test until failure of the specimen.
Following an approach of Spiegl (2008) ΣWdis,tot is plotted versus the number of load cycles until conventional failure criterion Nf/50 in Figure 21. Compared to Figure 19 the resulting curves are moved closer to each other.
0
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
0 5.000 10.000 15.000 20.000load cycle N [-]
Stif
fnes
s M
odul
us S
Mix [M
Pa]
0
10
20
30
40
50
60
70
80
90
Phas
e An
gle
ϕ [°
]
SMix
ϕ
Nf/50
0
2.000.000
4.000.000
6.000.000
8.000.000
10.000.000
12.000.000
14.000.000
16.000.000
0 5.000 10.000 15.000 20.000load cycle N [-]
accu
mul
ated
dis
sipa
ted
ener
gy
Σ W
dis [
kJ/m
³]
0
200
400
600
800
1.000
1.200
1.400
1.600
Dis
sipa
ted
Ene
rgy
Wdi
s(N) [
kJ/m
³]
Wdis (N)
ΣWdis
Σwdis,tot
Figure 20. Course of stiffness decrease SMix, phase angle ϕ and dissipated energy ΣWdis during 4PB fati-gue test (T = 20°C, f = 30 Hz)
1.000.000
10.000.000
100.000.000
1.000.000.000
1.000 10.000 100.000 1.000.000 10.000.000NF/50 [-]
accu
mul
ated
dis
sipa
ted
ener
gy
ΣWdi
s,to
t [kJ
/m³] 10 Hz
30 Hz
AC 11T = 20°C
Figure 21. Total accumulated dissipated energy ΣWdis,tot versus number of load cycles until conventional failure criterion Nf/50
276
4 CONCLUSION
The structure of an asphalt pavement and the traffic speed result in varying loading conditions. In cyclic laboratory tests this impact can be analysed by varying the loading frequency.
The horizontal bending strain at the bottom of asphalt structures of varied thickness by varied loading conditions could be measured for deriving loading rates occurring in real pavements. These results show that the loading conditions as applied in cyclic fatigue tests doesn’t meet real loading conditions necessarily. According to these results especially the loading frequency as applied in fatigue tests should be reduced to a value considerably lower than the prescribed fre-quency of 30 Hz.
The application of a lower loading frequency would simplify the demands on the test equip-ment as high loading frequencies result in high inertia-induced forces by moving masses. In def-lection-controlled tests the results of 4-point bending tests can be corrected by the known equa-tions. But as the force value induced by mass can reach at high loading frequencies considerable proportions of the total force applied, the conduction of force-controlled 4-point-bending tests demands high efforts to the test equipment as further acceleration measurement devices.
The varying of the loading frequency has an important impact on the results of fatigue tests. According to results gained at UCTST as well as 4PB there is a distinction between the loading mode. While higher loading frequencies lead to higher load cycles numbers in controlled-force loading, the life time is reduced considerably in controlled deflection tests. In both cases the dis-sipated energy can be used for the interpretation of this phenomenon.
5 REFERENCES
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Mollenhauer, K. & Wistuba, M. 2009. Fatigue effects in uniaxial cyclic tensile stress test: The link be-tween stiffness decrease and accumulation of irreversible strain. 7th International RILEM Symposium on Advanced Testing and Characterization of Bituminous Materials (ATCBM09), 27-29 May 2009, Rhodes, Greece
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Rabe, R. 2008. Pavements under permanent stress – A closer look into a structure. Paper and presenta-tion at the 3rd International Conference On Accelerated Pavement Testing APT 08, Madrid
Saal, R. & Pell, P. 1960. Fatigue of bituminous mixes. Kolloid-Zeitschrift Band 171. 1/1990. pp. 61-71 Spiegl, M. 2008. Tieftemperaturverhalten von bituminösen Baustoffen. Mitteilungen des Instituts für
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