Influence of gauge length on the measurement of resilient modulus of bituminous mixtures
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Abstract
This paper investigates the influence of gauge length on the measurement of resilient modulus of bituminous mixtures with modified and unmodified binders tested at 25 °C. From this investigation, it is clear that for the tests carried out using a quartergauge length, the cumulative vertical deformations at the end of 200 preconditioning load cycles stays within 0.025 mm as stipulated in ASTM D736911. In the case of halfgauge length, the cumulative vertical deformation exceeds 0.025 mm after the application of 200 preconditioning load cycles. It was seen that the resilient modulus and Poisson’s ratio computed from the deformations measured using quartergauge length exhibited better repeatability when compared to halfgauge length.
Keywords
Resilient modulus Gauge length Preconditioning Poisson’s ratio1 Introduction
Earlier resilient modulus testing was carried out using ASTM test protocol [3] in which deformation is measured only in the horizontal direction, and the Poisson’s ratio is assumed for finding the modulus value. Later this ASTM standard was withdrawn in 2003 and replaced with the new ASTM protocol (ASTM D736911 [4]) in which both the horizontal and vertical deformations are measured. In a heterogeneous material such as asphalt mixture, the gauge length plays a critical role in the measurement of deformations. At this point, no clarity exists on the influence of gauge length on the computed resilient modulus. The present study is mainly focused on the influence of gauge length on the computation of resilient modulus values for unmodified and modified bituminous mixtures. In the following, a brief outline of the ASTM D736911 is provided.
2 Determination of resilient modulus as per ASTM D736911
The first step in the test procedure for estimating the resilient modulus value of bituminous mixtures is to compute the indirect tensile strength value of the specimen. Based on the indirect tensile strength value, the load to be applied to the specimen is selected for conducting the resilient modulus test. The load level selected for the test is limited to 10–20% of indirect tensile strength value of the specimen for any given temperature.
Constant values for \( \varvec{M}_{\varvec{R}} \) and μ calculation [4]
Gauge length as a fraction of diameter of specimen  I _{1}  I _{2}  I _{3}  I _{4} 

0.25  0.144357  − 0.450802  0.155789  − 0.488592 
0.50  0.233936  − 0.780056  0.307445  − 1.069463 
As per the test protocol [4], one needs to test a minimum of 3 samples from each type for checking the repeatability of resilient modulus values within the laboratory, and the allowable standard deviation is stipulated as 7%. Therefore, after testing one type of sample, one thus has 24 resilient modulus values (3 trials × 2 orientation × 2 planes × 2 deformations) and the required standard deviation is computed from such data set.
3 Experimental investigation
In this study, bituminous concrete grade2 with median grading and a binder content of 5% was used. This investigation was carried out using one unmodified binder (VG30) which confirms to IS 73 (2013) and a modified binder (PMB40 (E)) which confirms to IS 15462 (2004). Samples with 150 mm diameter and 160 mm height were prepared using gyratory compactor, with 205 gyrations for the compaction process. The gyratory compacted samples were sliced into small cylindrical samples of 150 mm diameter and 63.5 mm thickness, and the sliced samples with an air void of 4 ± 0.5% were used for this investigation. All the tests were carried out at 25 ± 0.5 °C with halfgauge length and quartergauge length.
Indirect Tensile strength load of bituminous samples at 25 °C
Binder  IDT failure load (kN)  Load level used for testing (10%) 

VG30  24.32  2.432 
PMB40 (E)  21.10  2.110 
Instead of 100 preconditioning cycles as stipulated in ASTM D736911, 200 preconditioning load cycles were applied such that the sample exhibits a constant strain rate [6]. After 200 preconditioning cycles, the next five cycles were used for the postprocessing analysis. The deformations in both horizontal and vertical directions for 0 and 90degree orientations were measured using the sensors mounted on the surface of the sample and recorded for all the 205 load cycles at every 0.001s interval using UTS 003 software [7]. The deformation was analysed to calculate the total horizontal recoverable deformation and total vertical recoverable deformations for each cycle following the curve fitting procedure mentioned in the test protocol [4]. Using the total horizontal and vertical recoverable deformations, both Poisson’s ratio and the resilient modulus values were computed.
4 Results and discussion
As per test protocol [4], one can conduct the test for all the three different gauge lengths before selecting the resilient modulus value. In this investigation, halfgauge length and quartergauge length was selected, and the influence of gauge length is discussed below.
4.1 Influence of gauge length
The preconditioning load cycles are provided to ensure that the sample reaches a steady state. If the sample deformation exhibits steady state, the variability in the computed resilient modulus values can be reduced. From observing the above test results, if one uses a quartergauge length, the number of preconditioning cycles required is 200, and steady state can be reached. However, in the case of samples tested using half–gauge length, with 200 preconditioning cycles, it is difficult to reach steady state.
4.2 Effect of gauge length on resilient modulus
Test results for unmodified binder (VG30) at 25 °C
Plane  Quartergauge length  Halfgauge length  

Instantaneous  Total  Instantaneous  Total  
μ  M _{ R}  μ  M _{ R}  μ  M _{ R}  μ  M _{ R}  
0°  
1  0.22  10,637  0.21  7510  0.36  11,565  0.35  7282 
2  0.24  11,110  0.26  8729  0.42  11,892  0.30  7948 
90°  
1  0.23  11,410  0.24  8231  0.25  10,054  0.35  6574 
2  0.25  10,726  0.27  8272  0.27  11,010  0.26  7040 
Test results for modified binder (PMB40 (E)) at 25 °C
Plane  Quartergauge length  Halfgauge length  

Instantaneous  Total  Instantaneous  Total  
μ  M _{ R}  μ  M _{ R}  μ  M _{ R}  μ  M _{ R}  
0°  
1  0.29  8777  0.30  5958  0.33  9668  0.30  6363 
2  0.30  8908  0.32  6379  0.31  9818  0.25  7081 
90°  
1  0.30  9082  0.33  6981  0.40  9358  0.35  6512 
2  0.26  8645  0.27  6137  0.24  8987  0.13  6179 
From the above data, it is seen that the resilient modulus values computed using instantaneous recoverable deformations are high when compared to the resilient modulus computed using total recoverable deformations. If one compares the resilient modulus values estimated using quartergauge length, unmodified binder shows higher modulus value than the modified binder at 25 °C. In the case of half gauge length, it is difficult to point out the variation in the resilient modulus values between unmodified and modified binders. Analyzing the test results from the perspective of gauge length, the variation in the estimated resilient modulus values are less for the quartergauge length and halfgauge length. However, the variability in the estimated values for Poisson’s ratio and resilient modulus between different planes and orientation were observed as less (standard deviation is less than 7%) for quartergauge length.
5 Conclusions

It is possible to achieve steady state for a sample tested with ¼ th diameter of the specimen as gauge length (quarter) when subjected to 200 preconditioning cycles. In the case of gauge length, the sample may reach a steady state when subjected to more number of preconditioning cycles.

Since the sample reaches a steady state when subjected to 200 preconditioning cycles, the variability was found to be less in the computed resilient modulus and Poisson’s ratio for quartergauge length testing. This implies that the test results obtained from quartergauge length show more precision when compared to halfgauge length.

For quartergauge length, the computed instantaneous and total resilient modulus value for unmodified binder was higher than the modified binder. Since the variability in the test results is more, comparison of the resilient modulus values for different binders with halfgauge length was not well established.
Notes
Acknowledgements
The authors thank Department of Science and Technology, Govt. of India [Grant number DST/TSG/STS/2011/46] for the funding and IPC Global, Australia for the technical support provided during the experimental investigation.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no competing interests.
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