# Bearing Strength of Crumb Rubber Concrete under Partial Area Loading

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emission [2], as a result, burdening the environment. Therefore, the reuse and recycling of the tire rubber in an environmentally friendly way is a hot research issue. In the early 1990s, researchers started to use the recycled rubber particles as aggregates in concrete and studied the applicability of this type of concrete for potential structural applications [3,4,5]. Now, it is believed that the development and application of rubberized concrete is beneficial to the diversified development of concrete material and is of great significance for reducing carbon emissions and achieving green gross domestic product (GDP) [6,7,8].

## 2. Bearing Strength of Concrete

_{b}(F/A

_{b}), which is concentrated under the loading plate, gradually spreads down to a uniformly distributed stress σ

_{l}(F/A

_{l}), as shown in Figure 2. Part of the concrete under the loading plate is under tri-axial compression, while there is a region below this compressive region where the transverse tensile stress is large [20]. The results of a large number of tests show that the bearing strength of concrete is determined by the failure of these two regions [14,20,27,28]. When the compressive region fails, σ

_{b}can reach several times the uni-axial concrete compressive strength owing to the confinement provided by the surrounding concrete. According to the tri-axial failure criterion of concrete, the state of confining stresses determines the failure stress of the compressive region. The greater the confining stresses, the higher the failure stress. The tensile region fails when the tensile stress reaches the tri-axial tensile strength of concrete, which attributes to that the tensile region is under tri-axial tension. It is worth noting that the tensile strength of concrete should be less than its uniaxial tensile strength.

_{cb}is bearing strength of concrete; f

_{c}is the compressive strength of concrete; f

_{ct}is the tensile strength of concrete; A

_{l}is the block gross area; A

_{b}is the loaded area; and θ is the half of the apex angle of the pyramid, which is (45° − φ/2), as shown in Figure 2. The formula successfully predicts the key parameters affecting the bearing strength of concrete, including tensile strength and compressive strength, φ, as well as load concentration ratio (A

_{b}/A

_{l}). In most current standards (e.g., Eurocode 2 [32], ACI 318 [33]), the design equations for the bearing strength of concrete take the load concentration ratio as the main parameter following the “square root equation” proposed by Hawkins [31], which can be expressed as Equation (3).

## 3. Experiment Description

#### 3.1. Test Specimens

_{vr}) refers to the rubber replacement by equal volume of mineral aggregates. As known, the compressive strength of concrete decreases with the increase in rubber content, hence the relatively higher cement quantity was used in CRC to compromise the loss in compressive strength upon the addition of rubber, thus reaching a similar compressive strength as that of NC. Although the usage of cement in CRC cases is relatively higher than that in the NC case, the total CO

_{2}emission of CRC cases is still expected to be lower owing to the reuse of waste rubber, which will be discussed later in Section 3.2.

^{3}kg/m

^{3}. The photos of aggregates are presented in Figure 3.

#### 3.2. Testing Procedure

## 4. Experimental Results

#### 4.1. Fully-Loaded Specimens

#### 4.2. Environment Footprint

_{2}emission of all raw ingredients in concrete, which comes from the whole process of production, delivery, and disposal, was calculated.

_{2}emissions of concrete, the inventory data of ingredients come from the Chinese life cycle database (CLSD) [35], and are listed in Table 3. Among the ingredients in concrete, as shown in Figure 7, the original sources of coarse aggregate and sand are the exploitation of mine, and then they will be fabricated to the desired size at the plant site. The crumb rubber used in this study comes from the grinding of waste rubber, which produces CO

_{2}emission; however, as a waste material, reuse of crumb rubber can avoid the CO

_{2}emission during its disposal process, hence it should subtract the CO

_{2}emission during disposing waste rubber when conducting the calculation.

_{2}emission of concrete. It could be found from Table 4 that the amount of CO

_{2}emission decreases as the rubber contents increase. Compared with NC, the reuse of waste rubber in CRC5 and CRC10 significantly reduced CO

_{2}emission by 60% and 70%, respectively. This is because that the amount of CO

_{2}emission during the process of disposing waste rubber occupies quite a high percentage of concrete, as shown in Figure 8. In summary, the above findings indicate the reuse of rubber in concrete allow it to be more environmentally friendly, albeit with relatively higher cement usage for improving the compressive strength of concrete.

#### 4.3. Partially-Loaded Specimens

#### 4.3.1. Failure Modes

#### 4.3.2. Strain Results

_{l}, as shown in Figure 2. Therefore, the measured compressive strain could represent overall deformation of the loading contact area on specimens, as shown in Figure 2c. Prior to failure, the compressive strain increased rapidly as the applied load increased, which could be attributed to the formation of cracks on specimens.

#### 4.3.3. Displacement Results

#### 4.3.4. Bearing Strength

_{c}is the ratio of bearing strength to compressive strength; β

_{L}is the square root function of the ratio of supporting area (A

_{l}) to area of the bearing plate (A

_{b}); and a and b are the side lengths of the loading plate and concrete block, respectively. Then, Equation (3) can be written as

_{u}is the ultimate load. The ratio β

_{c}was calculated. Figure 14 plots the results of each group and compares them with the curve based on Equation (6). β

_{c}increased almost linearly with β

_{L}, and Equation (6) can give a good prediction. Moreover, there was not much difference between NC and CRC specimens tested at the same curing age in term of β

_{c}. Thus, the current standards for NC could be applied on CRC. Regarding the effect of the curing age, β

_{c}for CRC with a rubber replacement ratio of 5% at 14 curing days was slightly higher than that at 28 days. Equation (6) gives the conservative estimation for β

_{c}.

_{c}. The reason was not clear yet, and further study was carried out by the subsequent finite element analysis.

## 5. Finite Element Analysis

#### 5.1. General

#### 5.2. Material Models

#### 5.2.1. Yield Function

_{2}is the second invariant of the stress deviator; I

_{1}is the first invariant of stress; σ

_{max}is the algebraically maximum principle stress; and α, β, and γ are dimensionless constants as follows:

_{b0}and f

_{c0}are the initial equibiaxial and uniaxial compressive yield stresses, respectively; f

_{t0}is the initial uniaxial tensile yield stress; and K

_{c}is a constant that determines the shape of yield surface on concrete in the deviatoric plane. The failure wedge of concrete was under tri-axial compression. The compressive meridian when is concrete under tri-axial compression should be paid attention to, which can be derived from Equation (8) as follows:

_{b0}and K

_{c}should be obtained from equibiaxial and multiaxial compression tests on concrete. Experimental values of (f

_{b0}/f

_{c0}) for NC are in the range of 1.10 and 1.16. A value of K

_{c}= 0.667 is typical for NC [24]. However, the experimental data on CRC are rare, and the effect of rubber content on these parameters has not been studied yet. Gholampour et al. [21] conducted the first experimental study on the axial compressive behavior of rubberized concrete with rubber replacement ratios of 0%, 6%, 12%, and 18% (RC0, RC6, RC12, and RC18, respectively) under active confinement. The experimental data were plotted in Figure 16, where the abscissa is the ratio of the hydrostatic pressure f

_{l}to f

_{c}and the ordinate is the ratio of tri-axial compressive strength f

_{cc}to f

_{c}. The conclusion was drawn that the axial strength and strain of rubberized concrete increase with confining pressure, following a similar trend to that in NC. This indicates that it is reasonable to use the same parameters as NC for CRC in the yield function.

_{c}= 0.667 was suggested by many researchers when modeling CRC [18,23,25]. Here, the rationality of the value was evaluated by test data reported by Gholampour et al. [21]. Figure 16 plots the curves for Equation (12) when the values of K

_{c}were taken as 1.0 and 0.667. Under small hydrostatic pressures, the value of 0.667 predicted the test data well, while under high hydrostatic pressures, a larger K

_{c}value was appropriate. Therefore, it is necessary to choose an appropriate K

_{c}value for accurately predicting bearing strength.

#### 5.2.2. Flow Rule

_{t0}is the uniaxial tensile stress at failure; and φ is the dilation angle. The eccentricity parameter was taken as 0.1 for all of the models in this study. The dilation angle varies with the type of concrete and concrete stress states. φ was taken as 45° by Han et al. [23] when modeling the headed stud shear connectors in CRC. For the finite element analysis of CRC beam–column members, the sensitivity study carried out by Xu et al. [25] showed that φ affected the load capacity and stiffness of the member, and good simulation results were obtained when the value of φ = 30° was chosen. Duarte et al. [18] believed that the φ value for CRC was lower than that for NC, because of the ability of rubber particles to prevent crack propagation and their incompressible behavior. In their finite element models for short steel tubes filled with rubberized concrete, a lower φ value was used for CRC with a higher content of rubber. In view of the existing inconsistency in the φ value for CRC, the effect of φ on the bearing strength was discussed later.

#### 5.2.3. Uniaxial Stress–Strain Curves

_{cr}is the compressive strength of rubberized concrete; ρ

_{vr}is the rubber replacement ratio; f

_{c0}is the compressive strength of concrete without rubber content; and λ is the function of the replaced mineral aggregate size:

_{g}is the replaced aggregate size and d

_{g,max}is the maximum mineral aggregate size.

_{ctr}and E

_{cr}are the tensile strength and elastic modulus of rubberized concrete, respectively.

_{cr1,1}and ε

_{cr0,1}are the crushing strain of rubberized concrete and normal concrete, respectively.

_{max,r}and w

_{max,0}are the maximum crack width of rubberized concrete and normal concrete, respectively. The calculated compressive strain–strain curve for each group is shown in Figure 6, and the main parameters were calculated by adopting the measured compressive strength.

_{RuC}and v

_{NC}are the Poisson’s ratio of rubberized concrete and normal concrete, respectively; v

_{rubber}is the Poisson’s ratio of rubber particles; and V

_{concrete}and V

_{rubber}are the volumetric fraction of concrete matrix and rubber particles in rubberized concrete mixes, respectively. For CRC5 and CRC10 groups in this study, the values of V

_{rubber}were 7% and 14%, respectively. By assuming that v

_{NC}equals 0.16, the values of v

_{RuC}for CRC5 and CRC10 groups were calculated to be 0.18 and 0.21, respectively.

#### 5.3. Model Calibration and Verification

_{b0}/f

_{c0}), K

_{c}, and φ. The initial values of these parameters were taken as their commonly used values, which were 0.3, 0.16, 1.16, 0.667, and 30°, respectively. When one of the parameters was calibrated, the initial values were taken for the other parameters. As shown in Figure 17a, when u is greater than 0.1, its influence on the calculation results can be ignored, so the value of 0.3 was used for NC models. As shown in Figure 17b,c, the influences of Poisson’s ratio and (f

_{b0}/f

_{c0}) were also small, so the initial values were taken. The calculation results in Figure 17d show that β

_{c}decreases with the increase of the value of K

_{c}. The trend is more obvious when β

_{L}is larger, because the confining stresses in the compressive region increase with β

_{L}, and K

_{c}has a greater impact on the concrete failure strength when concrete is under a larger confining pressure, as shown in Figure 16. Considering that the maximum value of β

_{L}in this study was 3.0, the commonly used 0.667 was adopted for simplicity. Figure 17e shows that β

_{c}increases with the increase of φ, which agrees with the trend predicted by Hawkin’s formula [31]. In view of the measured values of φ for the failure wedges in NC specimens, φ was taken as 50°.

_{c}calculated by the NC-75 and NC-50 models were 2.00 and 3.01, respectively, which were close to the mean values of test results of 1.88 and 3.21, respectively. On the basis of the comparison, it was known that the modeling method can be adopted to analyze the bearing strength of CRC.

#### 5.4. Effect of Rubber Content on Bearing Strength

_{b0}/f

_{c0}), and K

_{c}were not changed in finite element models for CRC specimens. Moreover, v

_{RuC}was taken as the same value as v

_{NC}, because the parametric analysis had shown that it had little effect on bearing strength. In addition, because the measured values of φ for CRC specimens were close to that of NC specimens, the value of φ was also not modified. It can be seen from Figure 17e that the difference in the calculation results when 30° and 50° were taken for φ was within 10%. Figure 21 shows the calculated results for CRC5 and CRC10 groups. It is clear that the rubber content has a negligible effect on the bearing strength, which was consistent with the conclusion obtained from the experimental results.

_{c}fluctuated with ρ

_{vr}when β

_{L}was 5.0, the influence of rubber concrete on β

_{c}was very limited. This indicates that, when the compressive strength of CRC is determined, its bearing strength is not affected by the rubber contents. Thus, the reason the results of the three groups of specimens in the experiment differed slightly is that their difference in compressive strength was small.

_{c}increased notably.

## 6. Discussion

_{ct}/f

_{c}) is one of the key factors determining the bearing strength. A new equation including the ratio (f

_{ct}/f

_{c}) as a parameter was proposed for the prediction of the bearing strength based on a Mohr failure criterion [28]:

_{ct}/f

_{c}) [28]. The significant influence of this ratio on the bearing strength can be also derived from the experimental results reported by Zhao [37], who completed axial compression tests on four groups of 48 reactive powder concrete (RPC) prism specimens. The test results show that, with the addition of steel fibers, the increase in the tensile strength of concrete was more notable than that in compressive strength. As a result, the ratio (f

_{ct}/f

_{c}) increased in RPC with steel fibers and β

_{c}was larger than that of RPC without steel fibers.

_{c}increases as the ratio (f

_{ct}/f

_{c}) increases. However, for CRC of the same compressive strength with NC, the influence of rubber contents on the ratio (f

_{ct}/f

_{c}) is small [8], and the tensile strength (f

_{ct}) of both CRC and NC was calculated according to Equation (16). As a result, the rubber content does not have an important effect on the bearing strength of CRC, which has been confirmed by experimental results. However, when the compressive strength of CRC is smaller than that of NC, the ratio (f

_{ct}/f

_{c}) is larger, as indicated by Equation (22), which was obtained by dividing both sides of Equation (16) by f

_{cr}. Then, the bearing strength of CRC would be larger than that of NC.

## 7. Conclusions

- From experimental observation, the CRC and NC specimens show similar failure modes and deformation properties, which implies that rubber particles have not changed the force transfer and failure mechanism of concrete under partial area loading. At the same time, the measurement results of failure wedge indicate that the difference in the dilation angle of the two types of concrete is not as large as expected.
- Although rubber particles have an effect on some mechanical properties of concrete such as elastic modulus, Poisson’s ratio, and dilation angle, it can be seen through finite element parameter analysis that these parameters have little influence on the bearing strength of concrete. On the other hand, CRC and NC have a small difference in the key mechanical properties that affect bearing strength, such as properties under multi-axial compression, the ratio of tensile strength to compressive strength, and so on. This ultimately leads to the similar bear strength of CRC and NC when their compressive strength is the same.
- The existing formula for calculating the bearing strength of NC can be used to predict that of CRC, including its value at early concrete age, which is very beneficial to the design of CRC structural members.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Partially-loaded concrete block: (

**a**) failure mode; (

**b**) variable description; (

**c**) deformation.

**Figure 5.**Schematic diagram of partial-contact-loading test setup: (

**a**) schematic diagram; (

**b**) photo. LVDT, linear variable displacement transformer.

**Figure 6.**Compressive stress–strain curves of specimens under full contact loading: (

**a**) normal concrete (NC)-150; (

**b**) crumb rubber concrete (CRC)5-150; (

**c**) CRC10-150.

**Figure 9.**Failure modes: (

**a**) NC-75-1; (

**b**) NC-50-2; (

**c**) CRC5-75-3; (

**d**) CRC5-50-1; (

**e**) CRC10-75-2; (

**f**) CRC10-50-1.

**Figure 11.**The load–strain curves of specimens under partial contact loading: (

**a**) NC; (

**b**) CRC5; (

**c**) CRC10.

**Figure 22.**Effect of rubber content on the value of β

_{c}when concrete compressive strength is 25 MPa.

**Figure 23.**Effect of rubber content on the value of β

_{c}when the compressive strength of reference NC is the same: (

**a**) 70 MPa; (

**b**) 50 MPa.

**Table 1.**Mix proportions of the concrete (kg/m

^{3}). NC, normal concrete; CRC, crumb rubber concrete.

Group | Rubber Replacement Ratio | Rubber | Cement | Coarse Aggregate | Sand | Water | Water Reducer | Age /Days |
---|---|---|---|---|---|---|---|---|

NC | 0 | 0 | 298 | 1297 | 610 | 168 | 1.49 | 28 |

CRC5E | 5.0% | 100 | 362 | 1297 | 556 | 168 | 1.81 | 14 |

CRC5 | 5.0% | 100 | 362 | 1297 | 556 | 168 | 1.81 | 28 |

CRC10 | 10.1% | 200 | 598 | 1240 | 414 | 168 | 3.00 | 28 |

Side Length of Loading Plate | 150 mm | 75 mm | 50 mm | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Specimen Number | 1 | 2 | 3 | Mean | 1 | 2 | 3 | Mean | 1 | 2 | 3 | Mean | |

Group | NC | 29.3 | 28.4 | × | 28.9 | 56.7 | 56.4 | 49.4 | 54.2 | 93.6 | 64.0 * | 91.8 | 92.7 |

CRC5E | 18.0 | 18.4 | × | 18.2 | 42.1 | 41.4 | 39.3 | 40.9 | 62.0 | 60.4 | 63.2 | 61.9 | |

CRC5 | 22.5 | 21.7 | 21.1 | 21.8 | 45.0 | 40.9 | 42.5 | 42.8 | 67.6 | 66.8 | 61.6 | 65.3 | |

CRC10 | 20.4 | 19.4 | 21.4 | 20.4 | 37.9 | 39.1 | 30.2 | 35.7 | 54.2 | 68.8 | 58.6 | 60.5 |

Ingredients | Cement | Coarse Aggregate | Sand | Waste Rubber, Grinding | Water Reducer | Waste Rubber, Disposal |
---|---|---|---|---|---|---|

CO_{2} emissions,kg-CO _{2}/kg | 0.98 | 0.00312 | 0.045 | 0.62 | 1.22 | 3.18 |

Mixtures | NC | CRC5 | CRC10 |
---|---|---|---|

CO_{2} emission | 325.35 | 130.03 | 100.20 |

Specimens | NC-75-2 | NC -50-1 | CRC5-75-1 | CRC5-50-3 | CRC10-75-2 | CRC10-50-3 |
---|---|---|---|---|---|---|

a (mm) | 75 | 50 | 75 | 50 | 75 | 50 |

h (mm) | 91 | 87 | 116 | 71 | 74 | 71 |

θ | 22.4° | 16.0° | 17.9° | 19.4° | 26.9° | 19.4° |

φ | 45.2° | 57.9° | 54.2° | 51.2° | 36.3° | 51.2° |

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## Share and Cite

**MDPI and ACS Style**

Xu, X.; Zhang, Z.; Hu, Y.; Wang, X.
Bearing Strength of Crumb Rubber Concrete under Partial Area Loading. *Materials* **2020**, *13*, 2446.
https://doi.org/10.3390/ma13112446

**AMA Style**

Xu X, Zhang Z, Hu Y, Wang X.
Bearing Strength of Crumb Rubber Concrete under Partial Area Loading. *Materials*. 2020; 13(11):2446.
https://doi.org/10.3390/ma13112446

**Chicago/Turabian Style**

Xu, Xiaoqing, Zhigang Zhang, Yangao Hu, and Xin Wang.
2020. "Bearing Strength of Crumb Rubber Concrete under Partial Area Loading" *Materials* 13, no. 11: 2446.
https://doi.org/10.3390/ma13112446