3.1. Compaction Properties
Figure 6 shows the variation in the dry density with the water content obtained by the modified Proctor [
46] test and the vibrating hammer for the slag with the selected PSDs. The same figure also presents information regarding the different slag–rubber mixtures (made with the slag with the selected PSDs) performed with the vibrating hammer. As observed by [
35], in coarse materials with a poor quantity of fines, the compaction curve is not well defined, and it is difficult to evaluate the maximum dry unit weight and optimum water content. The slag dry density is similar with both the vibrating hammer and modified Proctor, although the vibrating hammer allowed for a slightly higher maximum dry unit weight since granular materials compact better with vibration. In all the mixtures, the higher dry density values occured when the material was dry or almost saturated, corroborating the results found by [
47].
While 4% of the water content presented slightly higher dry densities due to particle lubrication, the water contents higher than 4% resulted in drainage during compaction. For this reason, all the specimens for monotonic and cyclic triaxial and CBR tests were moulded with the same water content of 4% to avoid the influence of water content variation on the mixture behaviour. The moulding dry unit weight was the maximum value obtained for each rubber content. For the preparation of the three physical models, the slag on the original PSD mixed with rubber was compacted at an optimum water content of 3% and at a maximum dry density depending on the rubber content (
Figure 7).
Figure 7 shows, for each rubber content, the moulding dry unit weight obtained in the compaction test for each mixture normalised by the moulding dry unit weight of the slag without rubber (
. The normalised dry densities of the slag–rubber mixtures are presented for both the selected PSD and for the original PSD. A clear linear relation was obtained for the data corresponding to both cases. Besides the different PSDs, the normalized dry density followed the same trend with rubber. Although it was expected that the increase in the quantity of rubber would cause a reduction in the dry density due to the lower unit weight of the rubber grains (
Table 3 and
Table 4), such a clear linear relation can be very useful when estimating the mixture dry density, which depends on the rubber content.
In the past, CBR values were one of the most important parameters present in the specifications for granular materials for transport infrastructures. For this reason, this parameter is still in most technical documents, although other parameters, such as the resilient modulus, are gaining importance for design purposes. Comparing the specifications used in different countries, it becomes clear that while Portugal and Brazil have a single CBR limit applicable for sub-base or sub-ballast layers, Australia distinguishes the CBR values depending on the location of the material. Moreover, Australia requires higher CBR values than Portugal and Brazil for the same layer.
Figure 8 presents the CBR values obtained for the slag–rubber mixtures prepared on the selected PSDs. A rapid decrease with the increase in rubber content is observed, indicating that the rubber has a very important influence on the mixture’s mechanical behaviour. A small increase of 2.5% in the rubber content (from 0% to 2.5%) reduced the CBR values to half of the original value. In contrast, for higher rubber contents, the increment of rubber has a smaller impact on the CBR values, as the behaviour is already controlled by the rubber particles instead of the slag grains. This demonstrates that for higher percentages of rubber, there is more rubber–rubber contact, decreasing the strength of the mixture. However, for mixtures with rubber contents less than 7.5%, the CBR values are still within the limits recommended in the Brazilian and Portuguese technical specifications for unbound layers in transport infrastructures.
3.2. Stress–Strain Behaviour
Figure 9 presents the stress–strain curves obtained in monotonic triaxial compression tests for the different slag–rubber mixtures, in terms of the deviatoric stress (q =
) normalised by the mean effective stress (
=
) and axial deformation (ε
a).
Figure 9 shows that the slag–rubber mixtures have a stress–strain behaviour typical of dense granular materials, with a peak strength followed by post-peak softening. However, it is observed that the peak of the stress–strain curve is more pronounced for a smaller quantity of rubber and a lower confining stress. The increase in the rubber content results in a reduction in the peak resistance and higher axial strain at peak, which represents a loss in stiffness. This is expected since the slag is being replaced by a more deformable material. Notwithstanding, a high residual friction angle was obtained even in the specimens with a rubber content of 10%.
To understand the effect of the rubber content on the stress–strain curves, the brittleness index, as proposed by [
50] and described in Equation (2), is presented in
Figure 10, assuming that the residual strength corresponds to the last measured point of the stress–strain curve at around a strain of 14%.
As observed in
Figure 10, the brittleness index, which represents the strain-softening behaviour typical of dense granular materials associated to dilatant behaviour, tends to decrease with the amount of rubber. This may be due to the residual strength that tends to be approximately similar for all rubber contents while the peak strength tends to decrease. This means that with increasing confining pressures and rubber content, the dilation is smaller and so are the brittleness index and peak strength. In granular materials, an increase in the confining pressure corresponds to a reduction in brittleness, since the confining pressure prevents dilation [
51]. This is also visible in the slag–rubber mixtures with confining pressures of 20 and 50 kPa. However, for 70 kPa of confining pressure, this is not so evident.
3.5. Resilient Moduli during Cyclic Loading
The resilient modulus (M
r) is defined as the unloading modulus (see
Figure 13 and Equation (3)) after several cycles of repeated loading.
Given the stress dependency of the resilient modulus in unbound granular materials, many models have been proposed to express
as a function of applied stress [
52]. Trying to represent the increase in the resilient modulus value with increasing confining stress, Biarez [
53] proposed the following equation for uniform sands:
On the other hand, for clayey soils, Moossazadeh and Witczak [
54] identified a greater influence of the deviatoric stress, proposing the following expression:
The most used model [
55,
56,
57], commonly known as K-θ, is a function of the sum of principal stresses (
):
Due to its simplicity, this model and its variations have been widely used in the analysis of material stiffness associated with the stress state, assuming a constant Poisson’s coefficient (usually between 0.2 and 0.3 for granular materials). However, this model considers that the modulus is only a function of the sum of principal stresses, which is not reasonable, since the addition of the deviatoric stress induces more shear deformations.
In Equations (4) to (6), are empirical parameters obtained from the experiments, is the confining stress, θ is the first invariant of stresses in axisymmetric conditions (), and q is the maximum deviatoric stress (q = ).
In
Figure 14, the resilient behaviour of the slag–rubber mixtures is presented (for rubber contents between 0% and 5%) as a function of the confining stress (
Figure 14a), deviatoric stress (
Figure 14b) and first invariant of stresses (
Figure 14c), together with the empirical parameters that show the best adjustment to the experimental data in the basis of the minimum square fit. As expected, this figure shows a decrease in the moduli with an increase in the percentage of rubber. However, it is not the purpose of this study to increase the mechanical properties of the slag by introducing the rubber. Instead, the aim is to identify the possible applications of these mixtures containing two industrial by-products.
It is thus interesting to note that the trend that is typically seen in granular materials of increases in moduli with increasing stress levels is still observed in the slag–rubber mixtures. For this reason, the resilient moduli empirical correlations presented in Equations (4)–(6) were applied to this material. There is a strong correlation with and θ, but less with q, which may be expected as Equation (5) was developed for clays.
Figure 15 shows the dependency of the empirical constants (
k1 and
k2) with rubber content for the first three models. Although the models are different, the empirical constants assume similar values, having a clear relation with rubber content, with exception of
k1 from Equation (4). For
k1 there is a linear decrease with the rubber content (for Equations (5) and (6)), while
k2 tends to increase up to a rubber content of 2.5% and then stabilises.
Table 6 presents the range of resilient modulus values obtained in the cyclic triaxial tests for three rubber contents (0%, 2.5% and 5%). The successive addition of a small quantity of rubber causes a significant reduction in stiffness (approximately 3.2 and 6.6 times, respectively) at low stresses. This reduction is slightly smaller (1.72 and 2.95 times) for the higher stress level, indicating that the effect of the rubber particles’ compressibility is felt mainly under low stress levels. At high stress levels, the particles are already compressed, presenting greater resistance to deformation.
According to Shahu et al. [
58], the resilient modulus values required for a sub-ballast layer are around 60–100 MPa, indicating that the slag rubber mixtures studied herein have resilient moduli values acceptable for sub-ballast layers when the confining pressure is larger than 20 kPa and the rubber content is up to 2.5%.
3.6. Comparison with Previous Studies
Table 7 summarises the results obtained in this study, together with data from other studies. It can be seen that the different research studies show relatively close values among the studied materials. As expected, the addition of rubber causes a decrease in the maximum dry density since rubber is a lighter material than the other aggregates. Moreover, since rubber is a more compressible material [
59], it causes a decrease in the CBR and resilient modulus.
Depending on the rubber content, the values of the resilient modulus range between 20 and 249.6 MPa, while the peak angles of the shearing resistance are always high, between 40 and 71 degrees.
Comparing the results of the slag–rubber mixtures obtained in this work with the granitic aggregate–rubber mixtures found in the literature, it seems that the slag without rubber has greater resilient modulus values than natural aggregates, which is in agreement with previous studies [
1] demonstrating the enhanced mechanical performance of slag particles. However, when the rubber is added, the opposite is verified, which may be associated to the interlocking of slags and rubber. This is more easily analysed when the same stress levels are compared. Hidalgo Signes et al. [
26] obtained resilient modulus values ranging from 92.8 to 249.6 MPa for a confining stress of 34.5 kPa and a deviatoric of 103.4 kPa. In a similar stress state (
= 35 kPa, q = 115 kPa), the mixtures analysed in this paper vary from 53 to 362 MPa for rubber contents of 5% and 0%, respectively. Zhang et al. [
61] obtained resilient modulus values between 150 and 275 MPa with a confining stress of 50 kPa and a deviatoric stress of 200 kPa. For the same stress conditions, the resilient moduli of the mixtures studied in this paper vary between 86 and 529 MPa for rubber contents of 5% and 0%. However, more studies are needed to confirm this trend as it is expected that particle grain size has a major influence on the resilient moduli.