With increasing environmental awareness, the idea of sustainable development has become widespread. It is very important to meet the human socioeconomic needs in the context of maintaining ecological balance. This task is also undertaken by geotechnical engineers, whose work focuses on three broad areas: sustainable improvement/reinforcement of weak subsoil, sustainable foundation design, and sustainable geotechnical design. These activities include, for example: (1) the use of alternative environmentally friendly materials in geotechnical constructions such as embankments, slopes, dams; (2) reuse of waste such as rubber tires, fly ash, natural or artificial fibers for improvement and stabilization; and (3) conscious design and modeling based on geotechnical parameters. For years, these issues have been widely discussed, analyzed, and practiced in geotechnical engineering [22,31,32,48,52], especially in transportation geotechnics [10,51]. Difficult and complicated geotechnical conditions are considered, e.g. when the subsoil contains weak cohesive soils of plastic consistency or shows volume changes (swelling or shrinking) under the influence of changes in water content [25]. In the case of such soils, actions are taken to reduce the weight of the embankments built on them or to reduce their swelling [27]. Rubber waste from car tires can be used for this purpose, according to the rule “end-of-life tires” (ELT). Each such new application requires research [18,24,50]. Among the tests performed, direct shear tests [6,28,45], unconfined compression tests or triaxial tests [1,18,46] dominate. The two basic conclusions presented in the available literature are: (1) regardless of the type of soil, its unit weight when added to rubber waste decreases and reduces the weight of the structure [16] and (2) the mechanical properties of soil–rubber mixtures vary depending on the type of soil, the type of waste rubber used (size/shape [42,43]), and its percentage (weight or volume; [9,46]).
An interesting research problem arises here, the aim of which is the practical use of cohesive soils–rubber waste mixtures in geoengineering as light embankments on weak soils or for the construction of road or railway embankments. This issue finds its solution not only by experiment but also by design.
Nowadays, the basis of the design process is the performance of many numerical analyses that allow the simulation of future processes of impact on the designed object [4]. Based on the performed analyses, it is possible to prove the fulfillment of limit states, both ultimate and serviceability. They allow for the consideration of many cases and variants, which allows for the optimal selection of construction and material solutions to be able to erect a safe and functional facility. In particular, numerical analyses play an important role when using new materials, for which a number of laboratory tests have been carried out, but the application of which has not yet been tested in practical implementations [8].
The first problem is the need to obtain a suitable base for the construction of the road surface. According to polish standards, in road construction, properties in this area are checked in trial load tests with a rigid VSS steel plate [38]. On roads with a higher traffic load, it is required that the value of the secondary deformation modulus
All the issues very important in the design of road embankments and pavement structures presented above were taken into account during the planning and implementation of triaxial tests and numerical analyses, and are discussed in the following sections.
Two cohesive soils from Southern Poland were selected for the tests. One of them of a characteristic red color (hence the usable name—red clay (RC) [29] came from Triassic deposits in Patoka, near Częstochowa. While the other soil, named by us—kaolin (K), came from the Porcelain Factory in Tułowice. According to a classification consistent with the standard PN-EN ISO 14688-2:2006 [34] and the unified soil classification system (USCS) [3], these are respectively:
Swelling (RC)—clay with silt (siCl) [34]/clay with high plasticity (CH) [3]: Nonswelling (K)—clay with silt (siCl) [34]/clay with low plasticity (CL) [3]:
where:
A detailed list of all parameters and a description of the tests from which they were obtained can be found in the works of Jastrzębska [18], Jastrzębska and Tokarz [24].
One tire waste size was used in soil–rubber mixtures: granulate (G) 1–5 mm (Fig. 1). The rubber additive originated from the local shredding companies and contained negligible amounts of textile parts. The parameters characteristic for granulate (according to [24]) indicating their homogeneous nature are as follows:
Granulate (G)—
The specific gravity of rubber was approximately 1.15 g/cm3, which falls within the range of values given by Akbulut et al. [2] and Kalkan [26].
For the purposes of numerical analyses, the following mixtures of pure soil (RC or K) with the addition of 0, 10, and 25% rubber waste (G) in relation to the total mass were prepared:
RC-G-10 (90% red clay with 10% addition of granulate 1–5 mm); RC-G-25 (75% red clay with 25% addition of granulate 1–5 mm); K-G-25 (75% kaolin with 25% addition of granulate 1–5 mm); RC (100% red clay); K (100% kaolin).
The proper specimens from RC and K, and their mixtures with granulate (RC-G and K-G) were prepared by cutting the specimens directly from a block prepared in a Proctor apparatus or by pushing out from the cylindrical forms pressed into Proctor's mold (Fig. 2). A detailed description of the samples preparation was presented in the works of Jastrzębska [18], Jastrzębska and Tokarz [24]. It is worth noting that with the higher content of rubber waste, the density of soil–rubber mixtures decreased accordingly: RC − ρ = 1.85 g/cm3, RC-G-10 − ρ = 1.62 g/cm3, RC-G-25 − ρ = 1.46 g/cm3, K − ρ = 1.94 g/cm3, K-G-25 − ρ = 1.52 g/cm3. This fact is important in the case of loading a weak subsoil with embankments made of soil–rubber mixtures.
The full research program included triaxial tests: cyclic and monotonic CU (consolidated, undrained) and monotonic UU (unconsolidated, undrained) was conducted according to the Standards PN EN ISO 17892-9 [36] and PKN-CEN ISO/TS 17892-8:2009 [33], respectively. Each sample (tests CU) was saturated, initially by flushing with deaerated water, and after by using back pressure procedure (at the end of the back pressure procedure, Skempton parameter was equal to
Numerical analyses were performed by the finite element method using the Z_Soil 2020 program [7]. In the case of the stability analysis, a simplification was used in the form of assuming a plane strain state, which is characteristic for linear objects [5,41,44]. When analyzing the VSS plate test, the assumption of axial symmetry was adopted, which is also correct for a homogeneous substrate (at least to the depth of the test range, which is defined as 2
A common problem when performing numerical analyses is the selection of parameter values used in the computation. The use of advanced constitutive models makes it necessary to specify various parameters that often do not have a simple physical interpretation, which makes it impossible to determine their values on the basis of typical laboratory or field tests. Hence, the great desire to use simple models for which it is possible to precisely determine the values of model parameters [12]. Of course, then it is necessary to perform practical verifications that will confirm the correctness of the performed numerical analyses.
In the stability analysis of the slopes of the embankments, the computations were divided into two stages. The first one is the generation of the state of primary stresses, which arise from the self-weight of the soils forming the road embankment. The current state of the embankment was taken into account—the analysis of the change in the state of stress and the resulting settlements of the subsoil under the embankment during the erection of the earth structure was omitted [23]. The next step is the analysis of the stability by the strength reduction method
As a result of the decrease in the strength parameters, plastic zones, which appear in part of the model, are eliminated in subsequent iterative steps using the phenomenon of stress redistribution. The procedure is carried out until the iterative procedures do not converge, which means that the computation are completed. The results of the analyses are the value of the safety factor
The procedure of estimating the value of the
The basic in situ test used in road construction is a load test of a rigid VSS steel plate with a diameter of 300 mm. In road jargon, it is called a test of the bearing capacity of the subsoil or road pavement structure. This test allows the assessment of the condition of the native soil layer or aggregate layer to a depth of approx. 0.5–0.6 m below the level of the steel plate base. The layers of the communication embankment are assessed in the same way, and a single test allows to visualize the condition of 1–2 layers of the embankment. The test loads are carried out in two stages. The first is the primary load, which in steps of 50 kPa reaches a value of 250–450 kPa depending on the type of the tested element (soil layer, embankment layer, lower or upper layers of the pavement structure). The next stage of the analysis is the secondary loading after unloading. In this stage, repeated pressures of approx. 100 kPa lower than in the first stage are applied. The results of the analyses are the values of the
In addition to the above modules, the result of the analyses is also the value of the strain ratio determined from the relationship (3.3):
The numerical model used for the stability analysis is shown in Fig. 3. A road embankment with a height of 6 m was analyzed. Owing to the symmetry of the problem, half of the model was taken, assuming the axis of symmetry running through the center of the embankment. It should be noted that in order to be able to take into account the above simplification, the shape of the embankment, the course of layers in the subsoil, and the corpus of the embankment, as well as the assumed boundary conditions must be characterized by symmetry. The built numerical model had 2777 finite elements. Generally, the stability of a given slope is determined by the geometric shape and the strength and deformation properties of the materials that build the embankment. In the case of a weaker subsoil, the properties of the subsoil on which the embankment was erected also have a large impact on its stability. Hence, the need to take into account the subsoil to a depth that will ensure no influence of boundary conditions on the obtained analysis results. Similarly, the area of the base of the embankment should be considered. In the built model, a distance of 25 m from the base of the embankment and 20 m into the ground under the embankment was assumed. Standard geotechnical boundary conditions were used, which assume that displacements in both directions are prevented in all nodes on the lower edge of the model and horizontal displacements in nodes on both side edges are not possible. In the stability analyses, the occurrence of exploitation load on the road surface was additionally taken into account, which was assumed as a uniform pressure of 25 kPa exerted on the part of the embankment crown occupied by the surface structure.
With numerical analyses of VSS test load simulations, the dimensions of the geometrical model (Fig. 4) of the analyzed model are correspondingly smaller. They result from the dimensions of the plate used in the tests, the radius of which is: D/2 = 150 mm. The defined model has dimensions of 5
Similar to Das and Singh [9] and Tajdini et al. [46], a random change in the internal friction angle and cohesion is visible (Table 1). The results confirm the opinion that testing the soil–rubber mixture intended for engineering applications is necessary each time. Table 1 summarizes the strength parameters (internal friction angle ϕ and cohesion
The strength parameters obtained from CU/UU triaxial tests.
RC-G-10 | 24 | 61 | 24 | 62 |
RC-G-25 | 15 | 30 | 28 | 22 |
K-G-25 | 9 | 70 | – | – |
RC | – | – | 21 | 167 |
K | 25* | 11* | – | – |
Parameters taken for numerical analyses.
The corpus of the embankment (soil–rubber mixture) | 15.0 | 30 | 15 | 60 |
Subsoil under the embankment | 21.0 | 5 | 30 | 40 |
Pavement structure | 22.0 | Elastic material | 800 |
A total of 3 material zones were adopted. When analyzing the stability of the embankment slopes, the parameters of the elements simulating the behavior of the layers of the pavement structure, as well as the elements being the subsoil, were adopted in such a way that these layers did not affect the obtained analysis results. Therefore, the situation when the slope stability is affected by a weak subsoil was not analyzed. The problem defined in this way will allow to assess the possibility of using the tested material in road construction.
The most important, from the point of view of the issues discussed in the article, are the parameters of the soil–rubber mixture from which the embankment was made. These values were estimated based on mean values obtained in laboratory tests (Table 1, [18,24]). A careful estimation of the parameter values was adopted, which allows us to treat them as derived values (experts) according to the Eurocode 7 standard. The properties of the subsoil under the embankment were assumed in such a way that the subgrade did not determine the obtained results. The results of numerical analyses will make it possible to assess the possibility of using the tested material in road construction from the point of view of the strength and deformation properties and the impact of these properties on the results of acceptance tests, as well as the safety margin due to the stability of the embankment.
The analysis of the slope stability of the road embankment was carried out in three stages. The first one is the generation of the state of primary stresses in the subsoil and the corpus of the embankment, which results from the self-weight of the soils and materials. Next, the operational load of the road surface was set in calculation steps. The third and most important stage was the stability analysis carried out using the
The first stage of the numerical simulation of VSS plate load test tests is also the generation of the primary stress state. Owing to the dimensions of the model, in this case the obtained values are definitely smaller. Next, the load transferred to the steel plate was applied. The path of the primary load was carried out, obtaining the value of 350 kPa. Next the unloading and reloading process to the value of 250 kPa was realized. The obtained values of displacements of the plate center will allow to calculate the values of modules
The results of analyses of the behavior of the road embankment erected with using the analyzed rubber–soil material are presented in Figures 5–9. The first of them (Fig. 5) shows the values of settlements due to operational loads of the road surface structure. The maximum settlement amounts to 5.8 mm and these values are within the requirements of the relevant regulations and standards [37,38,39]. Fig. 6 shows the yield surface at the moment of loss of stability, which corresponds to the value of the safety factor
As part of the numerical analyses performed, the impact of the cohesion and the internal friction angle values on the value of the safety factor was also carried out. The results of these analyses are presented in the figures below. It is easy to see that the cohesion is the decisive factor in the safety margin (Fig. 7a). If a sufficiently high value of cohesion is confirmed, this material will be an excellent component that will guarantee safe use of the communication structure. It is also easy to notice the large influence of the value of the internal friction angle (Fig. 7b).
The results of the second of the performed analyses—simulation of the VSS plate test, on the basis of which the properties of the subsoil and embankment layers in road construction are determined, are shown in Fig. 8. Based on the stress–settlement relationship, from the appropriate load phases, the values of the stiffness modulus and the strain ratio can be determined. The obtained modules for the results presented in the Fig. 8 are equal to:
Based on the considerations carried out, it can be concluded that the numerical model of the analyzed issues presented in this article is the right tool for assessing the properties of objects made from the analyzed material.
The results obtained in the performed numerical analyses indicate that the soil–rubber material, provided that appropriate properties are obtained in laboratory and field tests, can be used in the corpus of communication embankments, as well as in the lower layers of the pavement structure. Very favorable values of cohesion and internal friction angle guarantee obtaining the appropriate stability coefficient, as well as the required results in VSS plate tests, which are the basic tests carried out during road works. In cases of practical use of this type of materials in road construction, numerical analyzes must be preceded by the proper determination of model parameters in laboratory tests.
The results of laboratory tests confirm the necessity of testing soil–rubber mixtures each time before their use in embankments. The observed overall decrease in shear strength and stiffness of the tested material is variable and depends on the type of soil and the content of rubber waste. In some cases, an addition of 5% granulate is more preferable, and in other situations—10%. However, this recommended addition of granulate should not exceed 30% by weight.
An important element of the designing process with the use of soil–rubber mixtures is the performance of numerical analyses, which, based on the results of laboratory tests, will allow to estimate the properties of the obtained layers. In particular, a simulation of the VSS slab load test should be carried out, which is crucial in the implementation of road construction works. In addition, it is extremely important to perform slope stability analyses, especially in the case of high embankments. Stability of slopes is largely determined by the strength properties of the lower layers of embankments, hence numerical analyses allow for realistic estimation of the existing safety margin.
Performed numerical analyses showed that the addition of rubber granulate in the amount of 5–25% allows the use of the material (depending on the road class) for road embankments or lower layers of the pavement structure.