Influence of gauge length on the measurement of resilient modulus of bituminous mixtures

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 quarter-gauge length, the cumulative vertical deformations at the end of 200 preconditioning load cycles stays within 0.025 mm as stipulated in ASTM D7369-11. In the case of half-gauge 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 quarter-gauge length exhibited better repeatability when compared to half-gauge length.

Introduction

Majority of the Indian highway network is constructed with bituminous materials. As per IRC: 37-2012 design procedures for bituminous pavements, the input material property for bituminous mixtures is resilient modulus. Resilient modulus is a material property which is used for characterising the stiffness of bituminous mixtures for use in mechanistic-empirical pavement design. The basic premise of resilient modulus is that within the linear regime when the applied load is considerably small when compared to the failure load, the material shows recoverable and irrecoverable deformations which are in the steady state (Fig. 1). The corresponding recoverable strain is defined as a resilient strain which is used in the calculation of resilient modulus. In a sense, resilient modulus can be considered as the elastic modulus based on the recoverable strain under repeated loads [1]. The various factors that affect the resilient modulus are diameter and thickness of the specimen, gauge length, temperature, magnitude and duration of loading, type of waveform, and the axis of loading [2].

Fig. 1

Strains under repeated loading [1]

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 Later this ASTM standard was withdrawn in 2003 and replaced with the new ASTM protocol (ASTM D7369-11 [4]) in which both the horizontal and vertical deformations are measured.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 D7369-11 is provided.

Determination of resilient modulus as per ASTM D7369-11

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.

This test can be carried out on cylindrical bituminous mixture samples with two different diameters of 101.6 mm and 152.4 mm and a thickness of 63.5 mm. As per the test protocol, one can use three different gauge lengths for computing resilient modulus value for bituminous mixtures (Fig. 2). The three different gauge lengths in relation to the diameter of the test specimens are ¼ of the diameter (25.4 mm for a 101.6 mm diameter of the specimen or 38.1 mm for a 152.4 mm diameter of the specimen), ½ of the diameter (50.8 mm for a 101.6 mm diameter of the specimen or 76.2 mm for a 152.4 mm diameter of the specimen) and one diameter. It should be noted that both the sides of the samples are fixed with LVDT’s for an identical gauge length.

Fig. 2

Specimens fixed with various gauge lengths. a Full-gauge length, b half-gauge length, c quarter-gauge length

As per test protocol [4], a split cylindrical sample is subjected to vertical compressive haversine loading of 1 Hz frequency at 25 °C. The sample shall be preconditioned along the axis of testing by applying a minimum 100 load cycles in the form of haversine pulse of 0.1 s loading and 0.9 s rest period. The next five cycles after preconditioning period are used for the computation of Poisson’s ratio and resilient modulus. Both the preconditioning cycles and test load cycles constitute one sequence of loading. After one sequence of loading, the sample is rotated 90°, and the sample is again subjected to the same sequence of loading. Thus, one sample is subjected to test at two different orientations, and the deformations are measured along the horizontal and vertical direction using the sensors mounted on the surface of the sample. Using a curve fitting technique specified in the test protocol, the total and instantaneous recoverable horizontal and vertical deformations are determined. The post-processing procedure involves computing Poisson’s ratio (Eq. 1) and the resilient modulus (Eq. 2).

$$ \begin{array}{*{20}c} {\mu = \frac{{I_{4} - I_{1} \times \left( {\frac{{\delta_{v} }}{{\delta_{h} }}} \right)}}{{I_{3} - I_{2} \times \left( {\frac{{\delta_{v} }}{{\delta_{h} }}} \right)}},} \\ \end{array} $$

(1)

$$ \begin{array}{*{20}c} {M_{R} = \frac{{P_{cyclic} }}{{\delta_{h} \times t}}\left( {I_{1} - I_{2} \times \mu } \right).} \\ \end{array} $$

(2)

Here μ is the Poisson’s ratio, M_R is the resilient modulus in MPa, δ_v and δ_h are the measured recoverable vertical deformation and horizontal deformation in mm respectively, t is the thickness of specimen in mm, P_cyclic is the cyclic load applied to the specimen in N, and I₁, I₂, I₃, I₄ are the constants which vary according to the gauge length positions as shown in Table 1.

Table 1 Constant values for $\varvec{M}_{\varvec{R}}$ and μ calculation [4]

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.

Experimental investigation

In this study, bituminous concrete grade-2 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 half-gauge length and quarter-gauge length.

The sample selected for conducting resilient modulus test was marked on both sides along the horizontal and vertical diametric axis. Depending upon the selected gauge length, the gauge points were glued on both sides of the sample surface along the horizontal and vertical axis using an alignment device. Finally, the LVDT’s were mounted on top of the gauge points. The stepwise procedure for LVDT fixing is shown in Fig. 3.

Fig. 3

Stepwise procedure for LVDT fixing. a Axis marking, b alignment device, c guage points, d fixing alignment device, e fixing guage points, f LVCT’s mounted on samples

Before the conduct of resilient modulus test, the indirect tensile test was carried out to determine the indirect tensile failure load. As per the test protocol, one can use 10–20% of the failure load for conducting resilient modulus test. The indirect tensile test was carried out for samples prepared with each binder at 25 °C followed by the procedure outlined in ASTM D6931-17 [5]. The maximum load at which the sample fails is taken as the indirect tensile failure load of the sample. In this investigation, 10% of indirect tensile failure load was used for testing unmodified and modified binders. The indirect tensile failure load at 25 °C and the load level (10%) used for this study is tabulated in Table 2.

Table 2 Indirect Tensile strength load of bituminous samples at 25 °C

Before conducting the resilient modulus test, the sample is placed inside the temperature controlled cabin kept at test temperature for a minimum duration of 6 h for conditioning. Then the sample is placed on the test device for testing in such a way that it is sandwiched between the top and bottom loading strips as shown in Fig. 4. The bottom loading strip is a fixed one while the top one is free to move.

Fig. 4

Alignment of the sample inside the loading strips

Instead of 100 preconditioning cycles as stipulated in ASTM D7369-11, 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 post-processing analysis. The deformations in both horizontal and vertical directions for 0 and 90-degree orientations were measured using the sensors mounted on the surface of the sample and recorded for all the 205 load cycles at every 0.001-s 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.

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, half-gauge length and quarter-gauge length was selected, and the influence of gauge length is discussed below.

Influence of gauge length

From the Fig. 5, it is observed that the cumulative vertical deformation for the VG30 sample at the end of 100 preconditioning cycles using half-gauge length and quarter-gauge length was found to be less than 25 µm. When the sample is subjected to 200 preconditioning cycles with half-gauge length, the cumulative vertical deformation exceeded 25 µm. However, for quarter-gauge length, the cumulative vertical deformation for VG30 sample stayed within 25 µm without much variability between different planes (Fig. 6). Similar observations were seen in the case of modified binder (PMB40 (E)) tested at same load levels and same testing temperature for both the gauge lengths (Figs. 7 and 8).

Fig. 5

VG30 with 200 preconditioning cycles

Fig. 6

VG30 with 200 preconditioning cycles (quarter-gauge length)

Fig. 7

PMB40 (E) with 200 preconditioning cycles

Fig. 8

PMB40 (E) with 200 preconditioning cycles (quarter-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 quarter-gauge 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.

Effect of gauge length on resilient modulus

Tables 3 and 4 shows the computed resilient modulus and Poisson’s ratio corresponding to instantaneous and total recoverable deformations for unmodified and modified binders tested using half and quarter-gauge length at 25 °C.

Table 3 Test results for unmodified binder (VG30) at 25 °C

Table 4 Test results for modified binder (PMB40 (E)) at 25 °C

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 quarter-gauge 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 quarter-gauge length and half-gauge 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 quarter-gauge length.

Conclusions

In this paper, the influence of two different gauge lengths on the measurement of resilient modulus for bituminous mixtures with modified and unmodified binders was studied. This study was carried out as per the ASTM D7369-11 test protocol. The following conclusions derived from this investigation are as follows:

• 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 quarter-gauge length testing. This implies that the test results obtained from quarter-gauge length show more precision when compared to half-gauge length.

• For quarter-gauge 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 half-gauge length was not well established.