Unbound granular materials used in this study were dolomitic in nature and extracted from a quarry near the town of Villena (Spain) which is located approximately 120 km from the laboratory facilities. Several tests were conducted on these materials, including granulometric, density, and water absorption (see Table 1). Figure 2 depicts their corresponding granulometric curves. Based on this data, the material collected was found to comply with the general characteristics of a sub-ballast material (27–30).

Rubber shreds were obtained from scrap tyres and supplied by the Spanish recycling company RMD^®. For configuring the sub-ballast mixes, the rubber particles were sized between 8 and 18 mm with a low percentage of fibres. Steel wires (always presented in rubber tyres) were removed to avoid the introduction of any metallic element in the tested mixes. Similar to the unbound granular materials, tests such as granulometric, density, and water absorption were undertaken on the rubber shreds to fully characterise this component (see Table 1).

The tested specimens consisted of compacted samples of granular materials and mixes of granular materials with rubber shreds placed in transparent and hollow PVC tubes with an external diameter of 110 mm, a thickness of 2.2 mm, and a length of 1120 mm. Four quantities of rubber shreds introduced in the granular soil were studied: 1%, 2.5%, 5% and 10% over the granular soil weight. Selected dimensions of the specimens took into account various factors, including: heterogeneity of the samples; size of granular soil particles (tube diameter was set at more than five times the maximum soil size); workability conditions; and the need to ensure sufficient slenderness to facilitate the flexural behaviour of the specimens so as to obtain representative values of vibration damping. According to the material supplier, the PVC tubes had a density of 1.36 g/cm³ and water absorption of 0.5%, with an elastic modulus of 3040 MPa. These characteristics ensured that the tubes selected did not have a significant influence on the dynamic response of specimens, and were sufficiently stiff and strong to hold the compacted sample.

Unbound granular materials obtained from the quarry were firstly dried to remove any residual water content. Since each specimen needed more than 20 kg of sample material, homogeneity was achieved by creating 15 subsamples. In each subsample, the granular material was mixed with rubber shreds, and thereafter, the optimum water content for compaction was added. Each subsample was independently and adequately stored in the laboratory. Before compaction, the moisture and dry density of every sample was measured, and a standard Proctor modified test was also performed (31, 32).

Compaction of the samples in the PVC tube was conducted by using a vibrating compaction hammer (Kango 900 model) equipped with a tamping foot (100 mm in diameter) capable of exercising an energy blow of 16.4 J with a frequency of about 33 Hz. The total weight of this equipment was nearly 35 kg. Although the thickness of the PVC tube was expected to be able to bear the compaction stresses, nylon clamps were fitted to the tube during compaction of the samples to improve mechanical performance during this process. The compaction operation was carried out in 15 layers with a rate of 10 s of vibration per layer. This procedure, which was determined after carrying out a series of preliminary trial and error tests, ensured that nearly 100% of the dry density of the sample was reached.

Once compaction was finished, the tube ends were closed using polyurethane plates and adhesive tape to avoid any loss of material during the manipulation and testing of the specimens. Specimens were stored in a climatic chamber with a constant temperature and relative humidity of 20 ºC and 95% respectively. The specimen preparation process is summarised in Figure 3.

As indicated in Table 2, specimens were named SUB_X, with X equal to REF for the reference case, i.e. traditional soil-only sub-ballast (no rubber shred), and equal to MIXp when testing the proposed mix of granular soil and rubber shreds, being p the percentage of rubber introduced over the granular soil weight. Average values for dry density and moisture in each of the tested specimens are also referred to in Table 2. It can be seen that maximum dry density significantly decreases with the amount of rubber introduced in the soil. Similarly, a slight decrease in the optimum moisture is observed. The reduction found in dry density and optimum moisture is approximately proportional to the rubber shred content.

To study the capacity of the proposed mixes to attenuate vibrations, specimens were submitted to a hammer impact test according to (33). Tests were carried out in the Geotechnical Laboratory of the Universitat Politècnica de València.

Specimens were placed horizontally and subjected to two structural configurations as depicted in Figures 4 and 5: (i) simply supported on steel rollers (referred hereafter as the ‘S’ configuration); and (ii) uniformly supported on highly damping polyurethane (PU) foam (referred hereafter as the ‘U’ configuration).

The excitation impact was applied at a distance of 50 mm from one of the ends of the specimen by an impulse hammer with a force sensor and tips (0–100 lbf, PCB 086C01 model). A piezoelectric accelerometer (MEF KS76C100) with a sensitivity of 100 mV/g, a frequency range of between 0.13 Hz to 24 kHz, and an acceleration range of up to 6 g, was used for registering the vibrations induced by the hammer. A sampling frequency of 200 Hz was selected, and a signal conditioner (MEF M32 model) with an IEPE exit signal, was used to improve the signal received by the data acquisition system. For each structural configuration mentioned (S and U), two tests were conducted by alternatively placing the accelerometer in two positions (see Figures 4 and 5): (1) at the mid-span section; and (2) at a distance of 50 mm from the opposite end to where the impact was applied. A flow chart of the specimen preparation and testing can be seen in Figure 6.

A series of hammer impact tests were carried out on the compacted samples of granular soil and mixes of granular soil with rubber shred specimens. The values of the vibration amplitudes induced in the specimens by the hammer and its consequent and progressive diminution over time were registered. Figure 7 shows the registered excitation over time, as well as the correspondent spectra for specimens SUB_REF, SUB_MIX2.5 and SUB_MIX10 under the ‘S’ structural configuration (simply supported) and for the accelerometer placed at the opposite end to where the impact is applied with the hammer (configuration 2).

As can be seen, in the time domain there are no significant differences between these three tests at first sight and the specimens with and without rubber shreds behave similarly. Conversely, the three spectra show a similar pattern in the frequency domain, but the spectra for specimens with rubber shreds is slightly shifted to lower frequencies, which means they have a lower natural frequency.

It was assumed that the natural frequency of the specimens relates to the first of the peaks. The presence of the second peak, very close to the first, might be put down to the existence of some spurious modes which are present in the studied signal due to different sources of noise. It should be noted that the specimens tested are very heterogeneous, since no cementitious material is present, and are composed of granular soil, shredded rubber, water, and the PVC tube. Besides, a hammer impact test introduces a punctual and sudden excitation in the samples. Even though these aspects may have interfered in the registered signals, such events are normal in dynamic testing, and so the results obtained can be considered completely useful.

The potential attenuation that the inclusion of rubber shreds may cause in a compacted granular soil was studied by obtaining the damping ratio, ζ, in each specimen tested. This parameter can be found (26) in both the time domain of the signal and the frequency domain. In the time domain, the damping ratio can be derived from the logarithmic decrement in the signal, i.e. the natural log of the ratio of the amplitudes of any two successive peaks using Eq. [1]:

where δ is the logarithmic decrement, which can be obtained using Eq. [2]:

being A₁ and A₂, two amplitudes (with A₁ > A₂) separated n successive peaks.

The bandwidth method was used for the frequency domain. On this method, once the spectrum of the given signal is computed, the damping ratio is easily obtained according to Eq. [3]:

where ω_n is the natural frequency of the system, and Δω the distance between the two frequencies located in the same peak as ω_n, but for a spectral amplitude value equal to that registered for ω_n and divided by √2.

For the case of the specimens study, both aforementioned procedures were applied for computing the value of the damping ratio, ζ. Results are summarised in Table 3, in which in addition to the value of ζ for each specimen, the values are listed for the maximum amplitude (A_max) registered during tests, as well as natural frequencies (ω_n). Moreover, for every series of specimens, average values are also shown.

An analysis of the results reveals that the values obtained for the damping ratio for both approaches differ significantly. In the case of the time domain, the damping value ratios are almost identical in all the tests carried out. This gives rise to the idea that using the logarithmic decrement method in the time domain is not an optimal approach with unbound granular materials, due to the diverse sources of noise that might be present in the signals and which may produce no significance for the results.

However, the values of the damping ratio extracted by using the bandwidth method show that the addition of rubber shreds to the unbound granular materials considerably increases this parameter as expected, and consequently the capacity of the sub-ballast to absorb and attenuate vibrations. Hence, the frequency domain shows to be a suitable approach to study this kind of materials; likely, that can be explain because of own the nature of the use of the frequency domain, which makes signals be clearer.

A noticeable dispersion of results in the frequency domain is observed in some specimens though, probably due to the aforementioned noise issues, as well as the own heterogeneity of the tested samples. As Figure 8 depicts, an increment in the damping ratio is more evident when using the ‘U’ structural configuration, i.e. when the specimens are laying on PU foam; in these cases, increments of between the 105% and the 191% are observed. In contrast, the simply supported structural configuration (‘S’) gives more scattered values, ranging from increments of around 100% to cases of very low (30%) increments or even no increments. The scattering observed in the ‘S’ configuration may have been the consequence of the reduced elastic modulus of specimens (i.e. of the mixes of granular materials and rubber shreds), as well as the absence of cohesion in the specimens (it is important to remember that specimens were ‘only’ compacted, but any kind of bound material was used). This may have caused a small disturbance in the wave transmission when specimens were excited with the hammer. Given the less scattered results, the use of the uniform PU layer support (‘U’ configuration) appears to mitigate this aspect.

As reported in previous research (25), the addition of rubber shreds to granular soil tends to decrease degradation of the materials (a reduction in the values of both Los Angeles and Micro-Deval tests is observed), and this enables the use of unbound granular materials that cannot otherwise fulfil sub-ballast specifications. However, as the rubber content increases, a lower bearing capacity (CBR) is registered. Furthermore, as shown above, the maximum dry density attained by the soil, as well as its optimum water content, are also dependent on the rubber shred content added – and both parameters tend to decrease as rubber content increases.

Conversely, the obtained results show no evidence that a greater amount of rubber shred will cause an increase in the damping ratio. Therefore, at least for the percentages of rubber shreds used in this study (less than 10% by weight), there is no optimum amount of rubber in terms of attenuation capacity. Instead, the results show that an average increase in the damping ratio of around the 95% can be expected once rubber is added to a granular soil. Hence, the amount of rubber to be added will should be determined based on other issues like those previously related.