Evaluation of Fracture Resistance of Asphalt Mixtures Using the Single-Edge Notched Beams

CCCC First Highway Consultants Co., Ltd., Xi’an, Shaanxi 710065, China School of Architecture and Civil Engineering, Xi’an University of Science and Technology, Xi’an, Shaanxi, China Guangxi Key Lab of Road Structure and Materials, Guangxi Transportation Research & Consulting Co., Ltd., Nanning, Guangxi, China Key Laboratory for Special Area Highway Engineering of Ministry of Education, Chang’an University, Xi’an, Shaanxi, China School of Highway, Chang’an University, Xi’an, Shaanxi, China


Introduction
e research on the fracture characteristics of asphalt mixture is one of important topics on the properties of asphalt mixture.e main research methods for analysis and evaluation of the fracture characteristics include the numerical simulation method and fracture test method [1][2][3].
e numerical simulation is usually realized by the finite element method (FEM) and discrete element method (DEM).Two-dimensional (2D) micromechanical models using FEM and DEM have been developed to simulate microscale crack propagation of cemented particulate materials, which obtained well explanations of observed crack failures of the samples [1,2,4,5].e results of FEM simulation and the results of DEM simulation are usually compared to evaluate the similarities and differences.e findings show that the results of FEM simulation and DEM simulation have a fundamental similarity and, at the same time, have some basic differences [4].Furthermore, threedimensional (3D) model development has become a trend for the numerical simulation of fracture analysis.
e fracture test has three typical test methods, namely, the single-edge notched beam (SENB) test, the semicircular bending (SCB) test, and the disk-shaped compact tension (DC(T)) test, which are mainly applied to obtain the fracture characteristics of asphalt concrete [6][7][8][9].
ese three methods have different specimen geometries, application occasions, and fracture models, so the results can hardly be compared directly [8,10].
For asphalt mixtures, one kind of viscoelastic materials, the fracture characteristics are not only related to the initial crack depth but also to the temperature.erefore, the aim of this study was to determine and compare the fracture properties of three typical surface layer asphalt mixtures, namely, two kinds of two continuously graded asphalt mixtures and a stone mastic asphalt (SMA), at di erent conditions of the initial crack depth and the temperature.Considering as the simple and widely used model, the SENB test was applied in this study and the SENB with di erent notched depths were tested at di erent temperatures.

Materials.
ree asphalt mixtures used in this study included two continuously graded asphalt mixtures with nominal maximum aggregate size (NMAS) of 13.2 mm and 16 mm (AC-13 and AC-16) and a gap-graded stone mastic asphalt with NMAS of 13.2 mm (SMA-13).e experimental gradation curves of those three asphalt mixtures are shown in Figure 1.A base asphalt SK90 was used in AC-13 and AC-16, and a styrene-butadiene-styrene-(SBS-) modi ed asphalt binder produced by Shanxi Guolin Huatai Asphaltic Products Co., Ltd. was used in SMA-13.e properties of the base asphalt and the SBS-modi ed asphalt binder are shown in Tables 1 and 2, respectively.e coarse aggregate and ne aggregate used in those three mixtures are basalt, and the properties are listed in Tables 3 and 4.
e mineral ller used in this study is limestone powder, and the properties are listed in Table 5. Besides, lignin bers were used as the stabilizer in SMA mixture.Table 6 lists the properties of bers.Design asphalt contents were 5.0% for AC-13, 4.6% for AC-16, and 6.0% for SMA-13, which had 3.9%, 4.3%, and 4.1% void content, respectively.In addition, 0.3% of ber was used in SMA-13.

Fabrication of Single-Edge Notched Beam.
e slab specimens (300 mm × 300 mm × 50 mm) were fabricated using a rolling wheel compactor.e slab specimens were sawed into beams with the diameters of 250 mm (length) × 35 mm (height) × 30 mm (width).
A notch of designed depth, approximately 4 mm wide, with a square end, was sawed at the middle point of each beam, and single-edge notched beams (SENB) were obtained.A group of single-edge notched beams are shown in Figure 2. A material test system (MTS-810) with an environmental chamber was used to perform the three-point bending tests.e configuration of the three-point bending test on a SENB is shown in Figure 3. e loading span is 200 mm.In a three-point bending test, the load using a constant displacement rate of 0.05 mm/min was directly applied at the point right above the notch on the upper surface.

ree-Point
e midspan displacement δ was recorded at a sampling frequency of 10 Hz during the whole loading process until failure.e load-displacement curve can be drawn to obtain the peak loads.Advances in Materials Science and Engineering

Theoretical Background
3.1.Fracture Toughness.e SENB specimen loaded in a three-point bending con guration and notched at the midpoint, as shown in Figure 3, is under the mode of tension, so the fracture toughness for a SENB specimen is given as follows [11,12]: where a is the notch depth, σ 0 is the applied stress, and Y I is the normalized fracture toughness.e applied stress is given as follows: where P is the applied load, s is the loading span, and h and w are the specimen height and width, respectively, as seen in Figure 3. e normalized fracture toughness, Y I , is given by the following analytical expression [3,[13][14][15]: 3.2.Fracture Energy.Fracture energy, G F , is de ned as the area under the load-displacement curve divided by the ligament area, which could be expressed as follows [16]: where W is the work of fracture for an entire crack propagation period and A lig is the area of the ligament.
Figure 4 shows the work of fracture W for crack propagation, which can be expressed as (5), considering the e ects of the self-weight of the beam [17,18].
where W 0 is the work performed by the external force P for crack propagation and W 1 , W 2 , and W 3 are the additional works caused by the self-weight of the beam.Based on special Figure 4: A load-displacement curve for a stable three-point bend test on a single-edge notched beam.W 0 de nes the area under the loaddisplacement curve if there is no compensation for the energy supplied by the weight of the beam, m is the weight of the beam (between the supports), and g 9.81 m/s 2 [17]. 4 Advances in Materials Science and Engineering hypothetic situation, W 2 and W 3 can be calculated as follows [12,17]: According to (4)-( 6), fracture energy, G F , can be expressed as (7) [16], so that the fracture energy of asphalt mixture could be calculated from a load-displacement curve recorded [19].
where G F the fracture energy (N/m), m m 1 + m 2 (kg), m 1 Ms/L (weight of the beam between the supports), M weight of the specimen, m 2 weight of the part of the loading arrangement which is not attached to the machine but follows the beam until failure, δ 0 the midspan displacement of the specimen at failure (m), δ midspan displacement (m), g 9.81 (m/s 2 ), and A lig area of the ligament.P, s, and L are shown in Figure 3. Advances in Materials Science and Engineering the load-displacement curves of the mixtures present typical three stages.At the rst stage, the load increases linearly with the displacement up to the peak.At the second stage, after the peak, the load decreases largely with the displacement and, at the same time, the fracture develops rapidly.At the third stage, the load decreases steadily until the specimen fracture failure.

Ultimate Load.
e ultimate loads of the three-point bending tests can be obtained through the load-displacement curves.Figure 6 shows the ultimate loads for the SENB specimens of the three mixtures with di erent notch depths at 10 °C.From Figure 6, with the increase of notch depth, the ultimate loads of three kinds of asphalt mixture show a linear downward trend.In addition, under the same conditions of notch depth, the ultimate load of the AC-13 specimen is minimum, AC-16 is moderate, and SMA-13 is maximum among the three asphalt mixtures.It is analyzed that the higher ultimate load of the SMA-13 specimen is attributed to the material composition, which the utilization of the SBSmodi ed asphalt and the ber can contribute to improving the tensile strength and the ultimate load.

Fracture Toughness.
Fracture toughness, K I , for SENB specimens with di erent notch depths can be determined by ( 1)-( 3).e calculations of fracture toughness for di erent notch depths are shown in Figure 7.With the increase of notch depth, for the three asphalt mixtures, the fracture toughness increases moderately.It is notable that the fracture toughness for SMA-13 is largest among the three asphalt mixtures at the same conditions of notch depth.

Fracture Energy.
From load-displacement curves, the fracture energy of mixtures was calculated by using (7).Fracture energy of the three-point bending test on SENB specimens with di erent notch depths is shown in Figure 8. From Figure 8, it can be seen that the notch depth has no signi cant e ects on the fracture energy of AC-13 specimens.For AC-16 and SMA-13, there is no obvious regularity of the notch depth versus the fracture energy.e contents of ne aggregate (less than 2.36 mm) of AC-16 and SMA-13 are relatively small, and the contents of course aggregate are relatively large, which results in increasing the discreteness of the fracture energy of the specimen.

Displacement.
e load-displacement curves were recorded by three-point bending tests.Figure 9 shows the 6 Advances in Materials Science and Engineering load-displacement curves at di erent temperatures.According to Figure 9, AC-13, AC-16, and SMA-13 have similar load-displacement curves at di erent temperatures.At −20 °C, the loads rise rapidly, and there are no peak values until fracture failure which indicates that the SENB specimens are brittle failure in the three-point bending tests at −20 °C.When the temperature increases (from −10 °C to 10 °C), the specimens present a certain toughness, the load of the beam increases rst and then decreases with the displacement.In particular, when the temperature increases to 20 °C, it is obvious that the load-displacement curves at 20 °C are noticeably di erent from the curves at the lower temperatures.At 20 °C, the linearly increase stage of the load reduces and the load rises steadily with the displacement and the load decreases when the fracture grows to a certain extent and the specimen fracture failure occurs until the displacement reaches a relatively large value compared with that at lower temperatures.

Loading.
Figure 10 shows the ultimate loads for the SENB specimens of the three mixtures at di erent temperatures.e ultimate loads increase at rst and then decrease and reach the maximum at 0 °C, which could be resulted in that asphalt mixture is a viscoelastic material that the mechanical properties depend with temperatures.e SENB specimens are brittle fracture at −20 °C, and the ultimate load is small, and toughness of the SENB specimens  Advances in Materials Science and Engineering increases with temperatures which contributes to the ultimate load increase.
e tensile strength of the SENB specimens decreases with temperatures after the critical temperature, and the ultimate load decreases.

Fracture Toughness.
Figure 11 shows the fracture toughness at di erent temperatures for SENB specimens using the three asphalt mixtures.It can be found that the fracture toughness at −20 °C of AC-13 and AC-16 is higher than that of SMA-13.However, it can be seen that SMA-13 has higher fracture toughness than AC-13 or AC-16 has at temperatures from −10 °C to 20 °C, indicating its better resistance to fracture generally.

Fracture Energy.
e fracture energy at di erent temperatures for SENB specimens using the three asphalt mixtures is shown in Figure 12.It can be seen from Figure 12 that the fracture energy increases with temperatures.At the lower temperatures, −20 °C and −10 °C, the asphalt mixtures present relatively notable elasticity and SENB specimens trend to brittle crack, consequently the three asphalt mixtures have similar fracture energy.At the higher temperatures, 0 °C to 20 °C, the asphalt mixtures present relatively notable viscosity especially at moderate temperatures, 10 °C to 20 °C, which the fracture energy greatly di ers among the three asphalt mixtures.From Figure 12, the fracture energy of SMA-13 is signi cantly larger than those of AC-13 and AC-16.

Conclusions
is study adopted the SENB test to evaluate the fracture properties of three typical surface layer asphalt mixtures, AC-13, AC-16, and SMA-13, changing with variations of notched depths and temperatures.e following conclusions can be drawn: (1) e notch depth has no signi cant e ects on the fracture toughness and the fracture energy, but the gradation has relatively obvious e ects on the fracture energy, which the larger contents of course aggregate results to increase the discreteness of the fracture energy of the specimen.(2) e ultimate loads of the SENBs reach the maximum at 0 °C, which could be resulted in that viscoelastic properties of asphalt mixture depend with temperatures.(3) e fracture toughness at −20 °C of continuously graded asphalt mixtures are higher than those of   Advances in Materials Science and Engineering gap-graded asphalt mixtures.On the contrary, the fracture toughness of gap-graded asphalt mixtures is higher at temperatures from −10 °C to 20 °C.(4) Temperature has significant effects on the fracture energy, and the fracture energy increases with temperatures.e fracture energy of SMA-13 is significantly larger than those of AC-13 and AC-16.

Figure 3 :
Figure 3: A schematic illustration of the three-point bending test on a single-edge notched beam.

Table 4 :
Properties of fine aggregate.

Table 5 :
Properties of mineral filler.

Table 6 :
Properties of lignin fibers.

Table 2 :
Properties of SBS-modified asphalt.

Table 3 :
Properties of coarse aggregate.