Abstract
This paper focuses on researching the failure characteristic of damaged rubber concrete under the secondary load. The complete stress-strain curves are obtained from the axial compressive test under the first and the secondary load, and the influence of the incorporation of rubber particles, the particle sizes and the age of rubber concrete on the peak stress, compressive strength, peak strain and limiting strain are discussed, and the difference of the complete stress-strain relationship for the first and the second load is compared. The results show that the damaged rubber concrete still has enough capacity to carry some loads unceasingly, and the better mechanical properties are obtained for damaged rubber concrete with 15% of rubber particles. The deformation values are nearly the same for the rubber concrete under the first and the secondary loads.
Introduction
Rubber concrete (RC) is made by adding some rubber particles into concrete as a partial replacement of natural aggregates, and this method is one of the recycling approaches to reduce the amount of rubber entering landfill [8], and to reduce the amount of natural mineral aggregates in concrete. The reuse of waste tire rubber in concrete could have advantages of both environmental protection and economic viability.
Some experimental studies show that the compressive strength and modulus of elasticity decreased compared to the conventional concrete [7]. Al-Tayeb et al. [1] and Dong et al. [3] reported that with a rise in proportion of crumb rubber content, compressive strength decreases. Wang et al. [9] used the crumb rubber (4.75 mm) at a varying percentage up to 40% with a step size of 10% as a substitute of fine aggregates, and they observed that the compressive strength decreases with increase of the proportion of crumb rubber. However, a special phenomenon can be found, that is the initiation of crack occurs in the specimen when a load is applied to the specimen, but the crack can close if the specimen is unloaded and laid up for some time, and the strength can be improved if the load is again applied to the specimen [4]. For some structures, only the failure on some local nodes leads to the loss of the capacity to bear load for the whole structure, then the local location is reinforced by some methods, and the secondary load is considered to prolong the lifetime of the structures in engineering. Since the usage of crumb rubber as fine aggregates in concrete prolongs setting time and increases the viscosity of concrete [5], the ductility of rubber concrete is better than the conventional concrete. The rubber concrete produces a few cracks after it is loaded, then the crack may be be closed for the self-healing ability of rubber by unloading and laying aside the RC for a few times [2], and it becomes possible that the damaged rubber concrete can bear some loads again. Thus it is significant to research carrying capacity of the damaged rubber concrete with only some micro-cracks under the secondary load.
The experiments are performed for the damaged rubber concrete under the secondary load in this paper, and the changes of the complete stress-strain curve, compressive strength and the deformation of damaged rubber concrete are compared with those from the first load. The novelty of this paper is to illustrate the effect of rubber particles (10 mesh, 40 mesh and 80 mesh) with varying incorporation (0%, 5%, 15%, 25% and 35%) on the mechanical properties of the damaged rubber concrete under the secondary load.
Failure characteristic and crack evolution analysis for rubber concretes
The following were used in the study: Cement brand sea snail PO42.5 R; sand from the river with good grading and density of 2600 kg/m3 and stone from natural gravel with good grading and a density of 2800 kg/m3. Rubber particles (size: 10 mesh, 40 mesh and 80 mesh, density: 1100 kg/m3) were produced by Zhejiang Enxiang Building Materials Corporation, China (Fig. 1). The water used was ordinary tap water.

Rubber particle with different sizes.
Based on the procedure for ordinary concrete mix design (JGJ55-2000), the mechanical properties of RC were studied by adding rubber particles with different sizes and different incorporations into the concrete. The water cement ratio is 0.45, and the test match ratio is shown in Table 1.
Mix ratio of rubber concrete
The first load with the value of 15000 N was applied to the rubber concrete specimen, and a micro-crack was found on the surface of the specimen as shown in Fig. 2(a), then the damaged specimen was unloaded and put aside for three hours. The secondary load was applied to the damaged specimen untill it failed completely. It was found that the crack propagated rapidly from the center to the border of the damaged specimen with the increases of the load, at last some macro-cracks which penetrate through the whole specimen were observed (Fig. 2(b)). The failure characteristic shows an obvious ductile destruction for the damaged rubber concrete.

Failure characteristic for the compression specimen under the first and secondary load.
We took three specimens as a group to do the compressive tests with six groups. The complete stress-strain curves are shown in Fig. 3, in which the strain is the minimum strain of each group, and the stress is the average stress. The influences of the age, the incorporation and the particle size of the rubber concrete on the stress-strain relationship are analyzed. The results show that the stress peak value for rubber concrete is lower than that for the common concrete, but the common concrete specimen fractures quickly after the limited stress is reached, which shows an obvious brittle destruction. For rubber concrete specimen, the tendencies of complete stress-strain curves are similar to each other under the first and secondary load, but the peak stress is higher for RC at the first load than that at the secondary load. The elastic stage, peak-value stage and strain-softening stage is observed on the curves of RC, and the evolution process of deformation localization is described by the curves. For RC with a larger particles and longer ages, the higher peak stress is obtained. The peak stress decreases with the increase of the incorporation of rubber for RC under the action of the first and the secondary load, but the peak stress is the highest for RC under the secondary load while the incorporation of rubber particle is 15%.
Supposing x = 𝜀∕𝜀
c
, y = 𝜎∕f
cp
, (𝜀
c
, is the limiting strain, and f
cp
is the compressive strength of RC) the complete stress-strain curves is fitted by the following equation

Complete stress-strain curves for rubber concrete under the first and secondary load.
As shown in Fig. 4, the compressive strength of damaged rubber concrete under the secondary load decreases compared to that of rubber concrete without damage since the existence of crack at the specimen. For the case of the first load, the compressive strength decreases rapidly with the increase of the incorporation of rubber particles, but the compressive strength nearly has nothing to do with the incorporation of rubber particles for rubber concrete under the secondary load, and a stable compressive strength is obtained for each particles size. The higher compressive strength can be obtained for the longer age and the larger size of the rubber particles. It is also observed from Fig. 4 that the compressive strength at the incorporation of 15% is higher than any one at other incorporation of the rubber particle for rubber concrete under the secondary load, and the result is corresponded to the highest peak stress in the complete stress-strain as shown in Fig. 3, which shows that the mechanical properties are better for damaged rubber concrete with 15% of rubber particle.

Compressive strength for rubber concrete under the first and secondary load.
Table 2 shows the peak strain of the rubber concrete under the first and the second load, which indicates that the peak strain changes a little for the first and the secondary load, and the higher peak strain is obtained for the higher incorporation of rubber particle with larger sizes and longer age.
The peak strain of the rubber concrete under the first and the secondary load unit: × 10−3 mm
The peak strain of the rubber concrete under the first and the secondary load unit: × 10−3 mm
The limiting strain of the rubber concrete under the first and the secondary load unit: × 10−3 mm
Table 3 shows the limiting strain of the rubber concrete under the first and the second load. The results are similar to Table 2, and the limiting strain changes a little for the first and the secondary load, and the higher limiting strain is obtained for the higher incorporation of rubber with larger sizes and longer age. Since the self-healing ability of the rubber materials, some of the surface cracks on the damaged rubber concrete can be closed after it is laid aside a few times, then the deformation capability can further be improved when the damaged rubber concrete is reloaded. It is significant to improve the ductile of concrete by adding the rubber particle into concrete.
In this study, the failure characteristic, the complete stress-strain curves, the compressive strength and the deformation of the damaged rubber concrete under the secondary load are analyzed, and the results are compared with those from the first load. The following conclusions can be drawn:
(1) The damaged rubber concrete can continue to bear some loads before the specimen is destroyed completely, and a typical ductile destruction is observed from the failure surface under the secondary load.
(2) The peak stress and the compressive strength are the highest for the damaged rubber concrete with 15% of the rubber particle, and it is beneficial to improve the mechanical properties by adding 15% of the rubber particles into concrete.
(3) By reloading, the damaged rubber concrete has the capability to resist the same deformation as the rubber concrete without damage for its self-healing ability by laying aside quite a time, and it is significant to improve the brittle of the plain concrete.
Footnotes
Acknowledgements
This work is financially supported by grants from the NSFC (10772047, 11172066), Foshan Science and Innovate Platform for University and Hospital (2016AG100341), Foshan University Free Exploration Fund (2016LGZ06). This work is also partially supported by the Training Plan to Innovation and Enterprise of National University Students, Foshan University.
