Optimized design of an asphalt mixture railway track for vibration attenuation. Study of the dynamic performance

2.1. Vibration mitigation capacity

Considering a viscoelastic behavior, the complex stiffness modulus $E^{*}$ of the asphalt mixtures can be defined as the sum of the real modulus $E^{\text{'}}$ which has into account the elastic component and the imaginary modulus $E^{\mathrm{\text{'}}\mathrm{\text{'}}}$ representing the viscous part:

The quotient of the imaginary and the real component is known as the loss factor $\eta$ and is equal to the tangent of the phase angle $\mathrm{\Phi }$:

The vibration attenuation capacity of a material is given by its damping ratio $\xi$, which is calculated as the loss factor divided by two:

The relation between the phase angle and the damping ratio was studied by Billigri et al. [10] in the abatement of the noise produced in the tire-pavement contact. Since the objective in this case is also to achieve an asphalt mixture with a high damping ratio, different dosages of the mixtures, in which the content and the properties of the aggregates, filler, binder and plastics are varied, are developed determining the phase angle in each case according to the standard UNE-EN 12697 [11] for the determination of the fatigue strength of hot mix asphalts. For this test, the temperature, the excitation frequency and the microdeformations of the specimens must be defined.

The temperature selected was 20°C according to the climate conditions in the experimental stretch location. The excitation frequency was 5 Hz, approximately equal to that of the bogie passage induced frequency of a tram vehicle at low speeds. Finally, five different microdeformation values selected on the basis of the expected values for the infrastructure layers of a tram tack were tested.

Results in Fig. 1 show that the higher values were obtained for the specimens containing a 0.5 % of plastic waste for both asphalt concrete (S20) and stone mastic asphalt (SMA16). Moreover, the phase angle obtained for SMA mixtures was globally higher than these obtained for the S20.

Fig. 1Phase angle values for the different mixtures tested

2.2. Mechanical properties of the mixtures

Besides providing high damping ratio, the bituminous mixture of the new asphalt slab track must fulfill several requirements to ensure the structural stability and durability. These requirements are specified in the PG-3 document of the Spanish Ministry of Development [12] for road works and have been adequately adapted to the needs of the current project.

Within the tests performed to the asphalt mixtures, it should be cited the Marshall stability and flow, fatigue strength and density tests. All the test procedures have been developed in agreement to the standards UNE-EN 12697 [11] for hot mix asphalts.

In Fig. 2, the values obtained for the Young’s modulus are displayed. This parameter is crucial for the design since a high value may cause a reduction in the thickness of the layers, achieving in that manner material cost savings and obtaining the same strength against the loads produced by the vehicles.

Fig. 2Young’s modulus for the different mixtures tested

There does not exist a great difference between the mixtures that obtained the best damping results; the Young’s modulus of the mixture S20-0.5 % is 12200 MPa while this parameter in the case of the SMA16-0.5 % reaches 11800 MPa.

The results of the Marshall stability and flow test, average relative density and voids volume in the mixture are presented in Fig. 3. Although there are differences among the results for the different mixtures tested, in all the cases the minimum specifications of the standards are satisfied: the void volume in the mixture is over 4 % and the Marshall stability higher than 15 kN.

Fig. 3Results for the Marshall stability and flow, average relative density and voids volume test

2.3. Economic appraisal

The economic criteria used for the appraisal of the different asphalt mixtures have only considered the fabrication costs. It is supposed that the rest of the costs (i.e. transportation, compaction, etc.) are similar in all the cases as any of the mixtures requires specific methods different from the conventional ones.

Fig. 4Fabrication cost of the different asphalt mixtures

In Fig. 4, it can be seen how the cost per ton increases with the percentage of plastic in the mixture. In addition, for the same plastic content, the SMA16 mixtures are slightly more expensive than the S20 as a consequence of the higher binder content of the first ones.

In order to ensure that the asphalt mixture chosen is the optimal solution, apart from the logical assessment that has been done in this section the PRESS multicriteria decision making method was performed [13]. Up to six variables were considered in the process with the relative weights shown in Table 1.

As deduced from Table 1, the higher weight has been assigned to the viscous behavior of the mixture. This property is represented by the phase angle and it has been considered of great importance since it determines the vibration mitigation power of the asphalt mixture. The next attribute in importance is the economic cost; the new track final solution will not be just an experimental result but it must be implemented in real tracks and therefore it must be economically viable. Finally, there are considered the structural behavior represented by the Young’s modulus and the stability, flow and voids results obtained from the Marshall tests.

The multicriteria decision making method revealed that the mixture SMA16-0.5 % is the optimal solution according to the vibration attenuation, structural strength and economic cost.

3.1. Design criteria

The calculation of the thicknesses of the asphalt mixture layers in the track structure is performed according to fatigue requirements. In Fig. 5, a representative cross section of the track is presented. It can be seen two different layers of SMA16-0.5 % (surface and intermediate); the gradded aggregate that supports the intermediate layer and the sandy natural ground.

Fig. 5Cross section of the new asphalt slab track

The mechanical properties of the different materials in the track are summarized in Table 2. The Young’s modulus of the sand is marked with an asterisk because it is a priori unknown. It has been assigned a low value in order to ensure that the calculated dimensions of the asphalt mixture are larger than the minimums required in reality. It is a secure method to guarantee the adequate structural behavior of the track against the stresses induced by the vehicles.

Constructing a finite elements model in which the thicknesses of the bituminous layers are variable, the strains produced in the different materials can be calculated. These strains are caused by the passage of the operating trains. The following strains must be checked in the studied track:

• Maximum horizontal tensile strain in the bottom fiber of the intermediate asphalt layer ${\epsilon }_{hSMA}$.

• Maximum vertical compressive strain in the upper fiber of the graded aggregate layer ${\epsilon }_{vGA}$.

• Maximum vertical compressive strain in the upper fiber of the natural ground ${\epsilon }_{vSoil}$.

The fatigue equations for each of these materials have been calculated during the lab tests. These equations link the strain $\epsilon$ produced in each load cycle $N$ with the number of cycles that can be produced without collapsing the material and are presented in the following equations for the mixture SMA16-0.5 % Eq. (4); the graded aggregate Eq. (5) and the sand Eq. (6):

From the information previously presented, the design process is as follows: given an asphalt mixture thickness, the different strains in the defined checkpoints are calculated using a finite elements model. These obtained strains are introduced into the fatigue equations, checking that the number of load cycles $N_i$ is higher than the critic number of cycles $N_{crit}$ estimated for a life span of 50 years and a potential traffic level for each one of the materials. The minimum thickness of the SMA16-0.5 % mixture that satisfies this requirement is chosen as the optimal design. In this case, the optimal thickness resulted of 45.5 cm divided into the surface layer (14.5 cm) and the intermediate layer (31 cm) as depicted in Fig. 5. These results have been calculated considering that the vehicles operating in this case are Vossloh 4100 and Bombardier Flexity Outlook.

The design iterative process is outlined in Fig. 6.

Fig. 6Diagram of the asphalt layer thickness optimization process

3.2. Construction of the stretch of track

After determining the dosage of the mixture and the optimal dimensions of the cross section, a stretch of the new asphalt slab track is constructed in a real operating line. The line chosen was finally in the Alicante (Spain) TRAM network, and the specific location is near the Poble Espanyol station.

Fig. 7a) Compaction of the graded aggregates and b) rail alignment previous to the elastomer pouring

a)

b)

It is a straight stretch at the end of the station, where a 20 m stretch of the former ballasted track was replaced by the new slab track. To do so, the rail, sleepers and ballast layer were completely removed, as well as the rest of granular layers until the distance from the rail head was –65.5 cm, matching the top of the sand stratum in Fig. 5. Then, the 20 cm layer of graded aggregate was placed and compacted, applying a tack coat on the surface to improve the adherence between the aggregates and the asphalt mixture.

The intermediate layer was compacted in two stages because of its high thickness while the surface layer was directly compacted after the placement. The channel that contains the rail was excavated using a trencher machine.

Once the rail channel was completed, the rail was placed using topographic equipments ensuring the longitudinal and transversal alignment and the tops were welded to the existing track. The elastomer used to fill the rail channel was the system Edilon Corkelast^®, in which, the elastomeric material is poured in liquid state providing a total coating of the rail. The construction process of the new stretch of track is shown in Fig. 7.

4.1. Finite elements model

Previous to the calculation of the dynamic response of the slab track, it is necessary to assemble the finite elements model. The cross section depicted in Fig. 5 has been schematically represented, assigning to the different materials in the track the mechanical properties in Table 2.

The dimensions of the model have been chosen so as to study accelerations in the range 2-50 Hz [14]. The symmetric half of the model is represented in Fig. 9 as appears in the software ANSYS Multiphysics/LS-DYNA V.14.

Since in any case it is considered a flawless track, the main mechanism of vibration generation is the 50 kN quasi-static load. This load is induced by the passage of a vehicle Vossloh 4100 which operated on the track stretch during the data acquisition campaign.

4.2. Calibration

As explained in Section 3, the Young’s modulus of the sand in Table 2 has been supposed to design safely the track but the real value of this parameter may differ from 50 MPa. Moreover, the global Rayleigh damping coefficient $\beta$ which represents the contribution of the stiffness matrix to the vibration damping of the system is an unknown input.

Fig. 9Representation of the symmetric half of the stretch of track in the model

With the aim of determining the approximate value of these two inputs, a calibration process is performed. The calibration of a model can be done on the basis of results from experimental modal analyses as in the case of Ribeiro et al. [15] or from real acceleration registers as in this case.

The procedure followed is an iterative method in which pairs of values for the Young’s modulus of the sand and the global Rayleigh damping coefficient $\beta$ are proposed. Then, the different vibration responses are obtained from the finite element model. These solutions are compared with the real acceleration data sets and the combination that yields the closer results to the real registers will be chosen as the correct. The overlapping of the real and the calculated accelerations is shown in Fig. 10, calculated with a combination of $E_{sand}=$144 MPa and $\beta =$ 0.001 in the point located at 0.2 m from the outer side of the rail.

Fig. 10Calibration. Real (black) and calculated (gray) accelerations

4.3. Validation

The real and the calculated responses must be compared in a different point from that used in the calibration in order to validate the model. This point is located at a distance of 0.7 m from the outer side of the rail since real acceleration data sets are available at this point.

The magnitude of the peaks calculated with the model and the time distribution match the records registered by the accelerometer. In addition, the tail times are mostly overlapped in both cases, giving an a idea about the time elapsed between the beginning of the excitation perception and the moment in which the wheel that produces it passes through the section in which the accelerometer is placed producing the peak. These validation criteria based on morphological aspects have been also employed by Costa et al. [16], comparing vibration velocities calculated and measured on a sleeper.

A numerical model able to reproduce accurately the dynamic behavior of the studied track is available. From this model, the dynamic response of the track in different scenarios can be calculated in the next subsection.

Fig. 11Validation. Real (black) and calculated (gray) accelerations

4.4. Dynamic behavior of the new asphalt slab track with different surface layers

One of the advantages of the new track is that the surface layer can be made of different materials without affecting the vibration attenuation power of the whole track. In this manner, a better environmental integration can be achieved in the different locations of the track. It is possible because the most part of the excitation induced by the train is in vertical direction and reaches the infrastructure through the rail foot that lies directly on the intermediate layer as depicted in Fig. 5. Consequently, the influence of the materials located over the rail foot plane is not significant on the overall mitigation power of the track.

To prove that, the SMA16-0.5 % surface layer will be replaced in the previously developed model by other materials which are often used in tram tracks: concrete, cobblestones and a conventional asphalt mixture. The mechanical properties of these materials are shown in Table 3.

The surface layer is represented in the FEM model in Fig. 12 in orange color. The mechanical properties of the elements of this layer will be modified according to Table 3 to represent the different materials in the surface layer and subsequently analyze the dynamic behavior.

The graphs in Fig. 13 (Appendix 1) show how the absolute values of the acceleration decrease and the accelerogram shape blurs as the measuring point moves away from the excitation source. While at the points located at 0.7 m from the rail the effect of each train bogie is manifest, in the farther points the peaks become flat resulting in compact accelerograms with lower values as observed by Galvín and Domínguez [17] in high speed lines. In this manner, the damping capacity of the different materials that the waves traverse is evidenced.

On the other hand, responses slightly differ at 0.7 m from the outer side of the rail for the different materials but are almost identical in the point located at 5 m from the rail. It is because at the nearby points the accelerations have been obtained on the different materials of the surface layer. Their different mechanical properties produce such variations on the vibration responses obtained at these points. However, at a distance of 5 m from the rail the surface material is the same in the three cases and therefore, the results calculated at these points very similar.

Fig. 12Detail of the surface layer elements in orange

The similar responses obtained for different materials of the surface layer ensure the integration capacity of the new asphalt slab track in the different urban environments. Thus, it is an effective, environmental friendly and versatile solution as the new asphalt mixture with plastic waste presents an excellent behavior against vibrations induced by railway vehicles and can be also adapted to different scenarios varying the materials of the surface layer.