The influence of crumb-rubber on the mechanical properties of Portland cement concrete (PCC) is studied by experimental tests and numerical simulations. The main hypothesis of the study is that replacing part of the stone aggregate with crumb-rubber in the mix modifies the energy dissipation during the cracking process and affects the concrete behaviour under monotonically increasing loads. The experimental research program characterizes the mechanical properties of PCC for three different types of concrete with a variable content of crumb-rubber. The experimental results showed that fracture energy and other properties are directly related to the rubber fineness used in the mixture. The material properties derived for these laboratory tests are used to study, by numerical models, its response through its damage evolution. The numerical model used to simulate the damage evolution of the concrete is the Embedded Discontinuity Method (EDM). One characteristic of the EDM is that it does not need to modify the mesh topology to propagate the damage through the continuum solid. For this study, the Disk-Shaped Compact Tension specimen geometry, normed by the D7313-13 of the ASTM, is used. Results showed that the numerical methods provide good approximation of the experimental curve in the elastic and softening branches.
Even though concrete is the most common material used in infrastructure construction, like roads, it does not always fulfil requirements like low weight, high strength, and ductility, under working-load conditions. Numerous studies have been conducted to improve the mechanical properties of concrete by replacing part of the aggregate with rubber obtained from discarded tires [
Compared with the use of crumb-rubber in asphalt paving mixtures, its use in PCC material is limited [
During the last two decades, studies have investigated possible uses of crumb-rubber from scrap tires [
Khatib and Bayomy [
To attenuate the effects of this issue, Papakonstantinou and Tobolski [
These researchers and others [
In addition to the evaluation of the mechanical properties previously described, understanding the fracture process of rubberized concrete is essential. During the fracture evolution in concrete, there is a release of energy [
Typical load-displacement curve [
Due to the nature of rubber, bonding between this and cement paste is weak, resulting in a reduction of compressive and tensile strength of PCC [
The idea of modelling the damage process in quasi-brittle materials by lumping strain concentration along a crack has motivated the development of formulations of finite elements with embedded discontinuities and their applications to quasi-static problems. This type of finite elements provides a realistic and direct way to implement constitutive models of cohesive cracks in a continuum setting. Following the pioneering work of Ortiz et al. [
The formulation of these elements implies two requirements in the crack zone which must be satisfied: (
The application of the Embedded Discontinuity Method (EDM) to study the damage in solids covers different types of materials. In the context of asphalt concrete, in 2005, Wagoner et al. [
In the present paper, the capabilities of the EDM are shown for modelling the damage process in disk-shaped compact specimens, built of concrete mixtures with different amounts of tire rubber aggregate, based in the EDM formulated by Retama and Ayala [
For this study, three types of concrete were studied: concrete with fine crumb-rubber (CFR), concrete with coarse crumb-rubber (CCR), and, as comparison material, Portland cement concrete (PCC), without crumb-rubber.
To fabricate the concrete mix, conventional Portland cement combined with a coarse aggregate (crushed basalt rock) with a maximum size of 20 mm and fine aggregate (river sand) with a maximum diameter of 5 mm was used.
The crumb-rubber was incorporated into the concrete mix to replace the stone aggregate (fine or coarse depending on the case) in a proportion of 2.5% per weight. The mix proportions for the three types of concrete are shown in Table
Concrete mix design.
Material | Dosage ( |
||
---|---|---|---|
CFR | CCR | PCC | |
Portland cement | 350 | 350 | 350 |
River sand | 770.2 | 790 | 790 |
Crushed basalt | 1000 | 975 | 1000 |
Crushed rubber | 19.8 | 25 | 0 |
Water | 205 | 205 | 205 |
A total of 30 concrete cylinders with diameters of 15 cm and heights of 15 cm (10 cylinders for each type of concrete) were cut with a saw to obtain the Disk-Compact Tension test (DCT). In Figure
DCT specimen geometry.
Characteristic dimensions of the specimen are shown in Figure
A total of 10 specimens were tested for each concrete, that is, concrete with fine crumb-rubber, concrete with coarse crumb-rubber, and concrete without crumb-rubber.
During the DCT test, a servohydraulic press was used to apply the load along with a pair of LVDTs to measure the specimen crack mouth opening displacement (CMOD); see Figure
Specimen mounted in the machine test.
The execution speed of the test was ten times slower than that specified by the ASTM D7313 standard (0.017 mm/s) because, in contrast with an asphalt mix, concrete exhibits a brittle failure, which makes it difficult to collect information from a load—CMOD curve at a fast speed. Several additional tests were performed at a speed of 0.00017 mm/s (one hundred times slower than that specified in the ASTM D7313 standard). The results obtained were unsatisfactory because an elastic recovery phenomenon occurred in the concrete. All specimens were tested at 10°C ± 0.2°C.
The EDM addressed in this paper, for modelling the kinematic behaviour of a finite element crossed by a cohesive crack, that is, crack line in which all damage process zone is lumped and characterized in the form of a traction–displacement law which exhibits softening, corresponds to that developed by Retama and Ayala [
In this method, the two parts in which a finite element is divided by a cohesive crack, referred to in this paper as a discontinuity, are assumed to undergo rigid body motions with respect to the kinematics of the discontinuity as it is shown in Figure
Finite element with internal crack.
To illustrate the method, Figure
The standard kinematics of the finite element is enriched at elemental level, by introducing an internal node where displacements jump
The elastic displacement part is a smooth function defined in the element domain
In (
For modelling the evolution of material damage where mode–I type failure is dominant, altogether with the EDM, a cohesive crack type model is used [
Cohesive crack model.
In this model, the inelastic response is governed by two key material parameters: tensile strength,
Following the work of Retama and Ayala [
Tractions on the discontinuity surface are functions of the normal displacement jump, through
This equation implies that the residual traction has the same direction as the jump displacement, that is, monotonic loading state. Furthermore, (
To complete the constitutive relation for the material in the crack zone, it is necessary to define the tangent constitute tensor
The aim of this section is to show the ability of the EDM to reproduce experimental results under quasi-static loading conditions, showing its numerical and theoretical consistency. Since no shear stresses are allowed along the crack, damage is simulated considering only the mode–I of failure.
The EDM, presented in Section
The specimen geometry used corresponds to that described in Section
The geometry of the specimen includes a notch symmetrically located between the two holes where displacements are imposed. This notch is to guarantee that damage initiates at its tip and the plastic zone around is minimum.
To simulate the test conditions of the specimen, a plane stress state was considered. The used supports are shown in Figure
Finite element model, (a) supports, and (b) mesh.
Elastic and fracture energy properties, used in the numerical simulation, are given in Sections
This section presents results derived from the experimental and numerical studies, for the three concrete mixes, pointing out in the curve load versus CMOD and the energy dissipation in the damage evolution process.
Additional specimen to those used to obtain the fracture energy were tested according to the ASTM standards: for elastic modulus, C469 [
Elastic properties.
Specimen | Compressive strength | Tensile strength | Elastic modulus | |||
---|---|---|---|---|---|---|
MPa | Std. dev. | MPa | Std. dev. | GPa | Std. dev. | |
CFR | 24.51 | 4.21 | 3.23 | 2.45 | 20.51 | 0.50 |
CCR | 24.90 | 4.89 | 2.94 | 3.62 | 19.99 | 0.59 |
PCC | 25.06 | 3.14 | 3.53 | 2.58 | 26.50 | 0.61 |
The average properties taken for the numerical simulation, described in Section
It is observed that the size of crumb-rubber modifies the elastic properties of the concrete. The elastic modulus of concrete CCR is less than those for CFR and PCC; this means that the material undergoes more deformation before the yield strength is reached, that is, increasing the ductility of the material, but its tensile strength is reduced in 16.7% with respect to PCC.
This behaviour of CFR is attributed to the capability of crumb-rubber to deform and its lack of adherence with the cement past.
Results of experimental tests for the three concrete mixes are reported in this section. The measured fracture energy is associated with the mode–I of failure, dominant in this series of tests. Curves of load versus CMOD for CFR, CCR, and PCC concrete are shown in Figures
Fracture energy for CFR.
Fracture energy for CCR.
Fracture energy for PCC.
Values of peak load, maximum CMOD, and fracture energy for the ten specimens, for each concrete type, are shown in Tables
Fracture energy for specimens of CFR.
Specimen |
|
|
|
---|---|---|---|
(kN) | (mm) | (N/m) | |
CFR-1 | 1.470 | 1.459 | 151.943 |
CFR-2 | 1.455 | 1.477 | 143.380 |
CFR-3 | 1.576 | 1.558 | 153.387 |
CFR-4 | 1.585 | 1.417 | 135.700 |
CFR-5 | 1.470 | 1.531 | 124.708 |
CFR-6 | 1.577 | 1.509 | 133.638 |
CFR-7 | 1.555 | 1.490 | 136.615 |
CFR-8 | 1.577 | 1.418 | 130.827 |
CFR-9 | 1.500 | 1.472 | 129.524 |
CFR-10 | 1.492 | 1.540 | 142.878 |
|
|||
|
1.526 | 1.487 | 138.260 |
|
0.052 | 0.048 | 9.483 |
Fracture energy for specimens of CCR.
Specimen |
|
|
|
---|---|---|---|
(kN) | (mm) | (N/m) | |
CCR-1 | 1.463 | 1.923 | 169.504 |
CCR-2 | 1.555 | 2.045 | 178.631 |
CCR-3 | 1.455 | 1.991 | 167.883 |
CCR-4 | 1.504 | 2.050 | 186.118 |
CCR-5 | 1.519 | 2.032 | 180.508 |
CCR-6 | 1.534 | 2.077 | 176.017 |
CCR-7 | 1.565 | 2.072 | 185.607 |
CCR-8 | 1.461 | 2.067 | 182.898 |
CCR-9 | 1.511 | 2.063 | 157.560 |
CCR-10 | 1.495 | 2.007 | 171.737 |
|
|||
|
1.506 | 2.033 | 175.646 |
|
0.039 | 0.048 | 9.034 |
Fracture energy for specimens of PCC.
Specimen |
|
|
|
---|---|---|---|
(kN) | (mm) | (N/m) | |
PCC-1 | 1.641 | 2.361 | 299.241 |
PCC-2 | 1.861 | 2.346 | 291.418 |
PCC-3 | 1.691 | 2.310 | 299.868 |
PCC-4 | 1.666 | 2.411 | 305.065 |
PCC-5 | 1.672 | 2.263 | 303.327 |
PCC-6 | 1.687 | 2.242 | 289.008 |
PCC-7 | 1.677 | 2.356 | 316.717 |
PCC-8 | 1.733 | 2.375 | 282.523 |
PCC-9 | 1.738 | 2.505 | 292.963 |
PCC-10 | 1.687 | 2.285 | 290.294 |
|
|||
|
1.705 | 2.345 | 297.042 |
|
0.062 | 0.077 | 9.848 |
Comparing results of specimens with the two crumb-rubber sizes, we may observe reductions in the maximum load peak and CMOD for the concrete CFR, which is reflected in a reduced total fracture energy value; that is, the fine rubber creates more imperfections in the concrete that increases its brittleness. In the concrete with coarse rubber, imperfections occur but to a lesser extent because rubber is less dispersed throughout the mix.
In this section the results obtained from the numerical simulation are compared with those obtained from experimental tests, pointing out in the characteristics of the softening curve for each concrete mix.
Once the damage propagates, as is shown in Figure
Principal stress
The numerical responses represented by the load versus CMOD curves for the three types of materials, that is, CFR, CCR, and PCC, are shown in Figures
CFR concrete.
CCR concrete.
PCC concrete.
From these curves, it is observed that the ascending branch, for all three materials, is well reproduced by the numerical simulation, that is, Embedded Discontinuity Method. Regarding the softening branch, the best numerical approximation to the experimental data is for the concrete without crumb-rubber PCC. This was not the case for the concrete with crumb-rubber, a fact that may be explained by the influence of the high heterogeneity, present in these types of concrete, on a numerical formulation assuming homogeneous material. Nevertheless, as it is observed in the softening curve for each modified concrete, the highest difference of the numerical results with the experimental curve corresponds to the concrete CCR, Figure
In general, the difference in numerical and experimental curves may be related to fact that concrete materials, modified or not, are highly heterogeneous and their characterization is difficult.
A series of experimental tests for two types of Portland cement concrete, modified with crumb-rubber, and those without crumb-rubber, were conducted to obtain elastic properties and fracture energy for mode–I of failure. Additional numerical studies, based on the Embedded Discontinuity Method, were used to simulate the mechanical behaviour of the material. Some important conclusions may be addressed in the influence of crumb-rubber and the performance of the presented numerical method. The size of the crumb-rubber influences the elastic modulus of the concrete, reducing it for the CFR material and enhancing its ductility. Another effect due to the use of coarse crumb-rubber is that it causes a reduction of 16.7% of the tensile strength. From curves load-CMOD, it may be observed that the concrete with coarse crumb-rubber presents a better behaviour in the softening branch of the curve, since it deforms almost the same as the PCC concrete but with a reduction of the peak load. The difference between results for CFR and CCR may be attributed to the capability of coarse crumb-rubber to deform and its lack of adherence with the cement paste. With respect to the performance of the numerical method to simulate the damage evolution, it is important to point out that, unlike fracture mechanics, it does not require the medication of the mesh topology to accommodate the crack in the solid, once it propagates. The presented Embedded Discontinuity Method reproduces the experimental curve with a good approximation, as well as the correct dissipation of energy according to the physical phenomena. Other sources of variation of numerical results with those experimental ones may be attributed to the characterization of concrete as a homogenous material.
The authors of this paper declare that there are no conflicts of interest regarding its publication.
This research was developed with the support of the “Dirección de Asuntos del Personal Académico (DGAPA)” of the National Autonomous University of Mexico, through the project Análisis No-Lineal de Vigas con Zonas de Plastificación y Funciones Spline, PAPIIT TA101317.