# Tests and Simulation of the Bond-Slip between Steel and Concrete with Recycled Aggregates from CDW

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Campaign

#### 2.1. Materials

#### 2.2. Experimental Procedures

_{b}is the bond length (100 mm).

## 3. Experimental Results and Discussion

#### 3.1. Strength and Stiffness

_{cm}

_{,28}) and 56 days (f

_{cm}

_{,56}), splitting tensile strength at 28 days (f

_{ctm}

_{,28}) and Young’s modulus at 28 days (E

_{cm}

_{,28}) of the concrete mixes. In Table 7 and the following tables, the labelling of the concrete mixes is as follows: (i) “RC” stands for reference concrete and for concrete mixes with RA from CDW; (ii) the first “C” stands for concrete; (iii) the two or three digit number that follows is the percentage replacement of NA with RA from CDW (10, 50 or 100%); (iv) “C” or “F” stand, respectively for coarse or fine fraction (of aggregates replaced); and (v) the last three letters are an abbreviation (“Val”—Valnor, “Vim”—Vimajas, “Amb”—Ambilei and “Ret”—Retria) of the recycling plant from which the RA were collected.

#### 3.2. Bond-Slip

_{max}) obtained for each concrete mix. Additionally, Figure 1a shows the bond stress vs. slip curves (τ vs. s) of the RC, C100C-Val, C100C-Ret, C100F-Vim and C100F-Amb in which these curves were obtained. Both Table 8 and Figure 1a show that, as the content of RA from CDW increases, the bond strength between steel and concrete decreases. It should be referred that, shortly after the maximum bond stress occurred in the specimens, they failed by splitting, as shown in Figure 1b, since no confinement was applied. This justifies the absence of the majority of the descending branches of the τ vs. s curves depicted in Figure 1a.

_{max}by means of the compressive strength of concrete. Kim and Yun [44] also refer that the prediction of the bond strength by means of the compressive strength of concrete is more appropriate than by means of the tensile strength. Given this, the analytical expressions proposed by Orangun et al. [45] (Equation (2)), Darwin et al. [46] (Equation (3)) and CEB-FIP [47] (Equations (4) and (5)), which were developed for the prediction of bond strengths by means of the compressive strength for natural aggregate concrete, were plotted superimposed with the experimental results obtained in this work in Figure 3, in particular, regarding CEB-FIP [47]. Expressions for both good confinement (Equation (4)) and poor confinement (Equation (5)) are shown,

_{cm}’ is the equivalent compressive strength of concrete obtained in cylindrical specimens, which can be estimated from their cubic counterparts by multiplying these values by 0.80 [48].

## 4. Description of the Numerical Model

#### 4.1. Geometry and Mesh

#### 4.2. Materials

_{s}= 210 GPa [50] (CEN, 2010b) and ν

_{s}= 0.30 [50] (CEN, 2010b) were adopted. As for concrete, the experimental values of the Young’s modulus measured for each concrete mix, E

_{cm}(Table 7) were used and a common value for the Poisson’s ratio of ν

_{c}= 0.20 [48] (CEN, 2010a) was used for all concrete mixes. It is recognized that the Young’s modulus at 28 days used herein is an approximation, since such property at 56 days (when the pull-out tests were conducted) was not determined. Furthermore, the value of Poisson’s ratio for all concrete mixes is also a simplified, but deemed adequate, approximation.

#### 4.3. Bond-Slip

_{max}the maximum bond stress (bond strength) and τ

_{f}= 0.15 τ

_{max}the minimum bond stress, α is the power of the curve defining the ascending branch of the bond-slip law, which can assume values between 0 (the bond-slip law starts with a constant value of τ

_{max}) and 1 (the bond-slip law presents a linear ascending branch), and s

_{1}, s

_{2}and s

_{3}are, respectively, the slips at the end of the ascending branch, at the beginning of the descending branch and at the end of the descending branch. The FIB Model Code [47] suggests that α = 0.4 and that τ

_{max}= 2.0√f

_{cm}’ are used for good bond conditions (e.g., ribbed rebars, as used in this work) and unconfined concrete (failure occurs by concrete splitting, as observed experimentally). Indeed, in the previous section, it was shown that the correlation between compressive strength and bond strength fell between 2.0√f

_{cm}’ and 2.5√f

_{cm}’. However, since the failure of specimens was by splitting, a factor of 2.0 was considered to be the most appropriate, as recommended by FIB Model Code [47]. It is recalled that in 2.0√f

_{cm}’, f

_{cm}’ is the equivalent compressive strength of concrete in cylindrical specimens, obtained by multiplying the cubic compressive strength by 0.80 [48]. As seen ahead, both these options (regarding α and estimation of τ

_{max}) yield good agreement between numerical and experimental results. The FIB Model Code [47] also proposes that s

_{1}= s

_{2}= 0.60 mm and that s

_{3}= 1.0 mm. The latter was adopted and revealed to be irrelevant for the analyses since all specimens failed by splitting before reaching it. However, the adoption of s

_{1}= s

_{2}= 0.60 mm did not lead to good results, as also shown ahead. Hence, s

_{1}and s

_{2}were calibrated by curve fitting and by the values suggested by the bond-slip curves available (RC, C100C-Val, C100C-Ret, C100F-Vim and C100F-Amb). Additionally, as seen above, two distinct behaviors were observed experimentally: in the RC and in mixes with CRA from CDW, the bond-slip curves presented a descending branch shortly after the peak stress was reached, whereas mixes with FRA showed a portion of the curves similar to that of a plateau before the descending branch occurred. This was accounted for in the numerical models by bringing s

_{1}and s

_{2}closer to each other in the former cases and making them more apart in the latter (see also Table 9).

_{τ}) as well as damage initiation and evolution of the bond properties. The bond-slip behavior was assumed, in all cases, to be linear elastic up to a slip of s = 0.01 mm and since, in such conditions, τ = K

_{τ}× s, K

_{τ}was determined by dividing the value of τ for s = 0.01 mm by s = 0.01 mm. For slips higher than s = 0.01 mm, the bond-slip curves were implemented by the transformation of the FIB Model Code [47] bond-slip law along with the experimental properties of the concretes into a damage-slip curve, as required by Abaqus [49] in which the damage parameter (D) for each value of slip is obtained in the usual way by D = 1 − τ/(K

_{τ}× s). Table 9 shows the properties adopted for the bond-slip curves of each concrete mix used in the simulations.

#### 4.4. Boundary Conditions, Loading and Analysis Procedure

## 5. Numerical Results and Discussion

#### 5.1. Verification of the Numerical Model

_{max}= 2.0√f

_{cm}‘, as suggested by the FIB Model Code [47], seems suitable to model the bond-slip behavior between steel and the concrete mixes studied.

_{1}and s

_{2}, they also seem to have been correctly estimated based on the experimental results. Figure 6a shows the influence of different values of α and Figure 6b the influence of adopting s

_{1}= s

_{2}= 0.60 for the RC, as suggested by the FIB Model Code [47] (CEB-FIP, 1990). As seen there, with respect to the value of α, in fact the one leading to the best agreement between numerical and experimental results, is α = 0.4, i.e., that suggested by the FIB Model Code [47] (CEB-FIP, 1990). However, regarding the influence of the slips, it is possible to observe that, when the values of slip proposed by the FIB Model Code [47] (CEB-FIP, 1990) are used, s

_{1}= s

_{2}= 0.60, the numerical and experimental curves show a poor qualitative agreement. Furthermore, the difference between numerical and experimental bond strengths for RC increases from 10% to 14%. This allows us to conclude that the values of s

_{1}and s

_{2}are key parameters to be estimated if the simulation of the bond-slip behavior between steel and concrete is sought for rather than only the prediction of the bond strength.

_{XX}= 2.7 MPa < 4.0 MPa, for RC and σ

_{XX}= 1.9 MPa < 2.6 MPa, for C100F-Vim) and the compressive stresses (with Z-axis direction) are lower than the corresponding compressive strengths (σ

_{ZZ}= 15.2 MPa << 61.1 MPa, for RC and σ

_{ZZ}= 10.8 MPa << 30.6 MPa, for C100F-Vim). This means that, up to the maximum bond stress, neither tensile cracking nor compressive crushing would be predicted by the models in the concrete parts and therefore the adoption of the elastic properties of the concrete mixes seems sufficient to model their bond-slip behavior. It is also interesting to observe, in both cases and with respect to the tensile stress fields, an area (in red) corresponding to maximum tensile stresses visible near the right-hand side of the models. Such an area would be the location where cracking would occur, leading to tensile splitting of the specimens, as observed experimentally. It is naturally understood, however, that the tensile stresses that arise in the model are only due to Poisson’s effect rather than from the summed effect of the former and of rib mobilization and surface roughness, which would increase tensile stresses in the post-peak stage of the response.

#### 5.2. Prediction of the Bond-Slip Behaviour of Concrete with Recycled Aggregates from Construction and Demolition Waste

_{max}= 2.0√f

_{cm}’ were also adopted. Hence, only s

_{1}and s

_{2}, which were identified as key parameters to be determined, were required to be estimated. To do so, the simplest approach was taken, which was to perform a linear interpolation (between the RC and the concrete mixes with 100% of replacement of NA with RA from CDW) to determine the values of s

_{1}and s

_{2}as shown in Figure 8. Figure 8a,b shows, respectively, the variation of s

_{1}and s

_{2}with the percentage of replacement of NA with RA from CDW. Additionally, for each variation set of points, a linear regression was adopted in order to be able to interpolate the values of s

_{1}and s

_{2}for mixes with different contents of RA from CDW.

_{1}and s

_{2}read,

_{1}and k

_{2}are coefficients that account for the fraction of aggregates replaced, which are the slopes of the linear regressions presented before in Figure 8: (i) for fine aggregates, k

_{1}= 0.0020 and k

_{2}= 0.0055 and (ii) for coarse aggregates, k

_{1}= 0.0005 and k

_{2}= 0.0010. As can be seen, the values of k

_{1}and k

_{2}are much smaller in the case of coarse aggregates than in the case of fine aggregates, as the former were observed to have a lower influence on the bond-slip curves than the latter.

_{max,Num}) of all concrete mixes as well as their comparison with the experimental values (τ

_{max,Num}/τ

_{max,Exp}), obtained using the numerical model developed and the simplified approach described before. As seen there, with the approach proposed (estimation of slips based on percentage and fraction of aggregates replaced), it is possible to obtain good predictions of the bond strengths. The average ratio between numerical and experimental bond strengths is 0.95 and the maximum difference is 14%. Indeed, it was shown before (Figure 6b) that the values of s

_{1}and s

_{2}influence not only the aspect of the bond-slip curves but also the value of the bond strength.

## 6. Conclusions

- -
- The high roughness and clay content of RA from CDW leads to a need to increase the effective water/binder ratio to obtain the workability constant in all concrete mixes (fixed parameter). This, together with the high porosity of RA, leads to recycled aggregate concrete with lower strength and stiffness by circa 5% and 4%, respectively, compared to the reference concrete per each 10% increase of NA replaced with RA from CDW.
- -
- Given the typical correlation between both properties, the influence of the increase of RA from CDW on bond strength is similar to that on compressive strength: per each 10% of NA replaced with RA from CDW, bond strength tends to decrease by about 5%. Furthermore, it is concluded that the increase in the content of RA from CDW results in an increase in the slip for maximum bond stress, especially when fine RA are used. Although anchorage length was not assessed in this work, the use of concrete with RA from CDW seems feasible in reinforced concrete members and similar anchorage lengths may be expected (for a given concrete strength) as the correlation between bond strength and compressive strength is similar to that found for natural aggregate concrete.
- -
- The use of FIB Model Code equations for unconfined concrete and good bond conditions are found to provide good estimates of bond strength for concrete with RA from CDW. When the full set of equations prescribed in this standard is used, in the finite element model developed, the bond-slip behavior (bond stress vs. slip curves) between steel and concrete with RA from CDW can also be accurately predicted: the average ratio between numerical and experimental bond strengths is 0.97. Given this and since the results presented are only dependent on the compressive strength of concrete and on size and content of RA from CDW, it can be stated that the outcomes presented have general validity and may be used as a benchmark in future investigations.
- -
- Besides the knowledge of the compressive strength of concrete with RA from CDW, it is shown that numerical modeling of the bond-slip behavior requires estimating the values of the slips associated with the end of the ascending branch and onset of the descending branch of the bond-slip equations of the FIB Model Code, which are different from those proposed. A first attempt to propose an additional equation that accounts for the fraction and percentage of NA replaced with RA from CDW is made and proven to yield good results.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Numerical vs. experimental bond-slip curves of (

**a**) RC, (

**b**) C100C-Val, (

**c**) C100C-Ret, (

**d**) C100F-Vim, (

**e**) C100F-Amb and (

**f**) influence of mesh discretization on the bond-slip behavior of RC.

**Figure 6.**Influence of (

**a**) the value of α and (

**b**) the adoption of s

_{1}= s

_{2}= 0.60 in the numerical bond-slip curve of RC.

**Figure 7.**Numerical (

**a**) tensile and (

**b**) compressive stress fields of RC and (

**c**) tensile and (

**d**) compressive stress fields of C100F-Vim at the corresponding instants of maximum bond stress (stress values in MPa).

**Figure 9.**Numerical bond vs. slip curves of concrete mixes with (

**a**) CRA from Valnor and (

**b**) FRA from Vimajas.

Composition (%) | CRA Valnor | CRA Retria | FRA Vimajas | FRA Ambilei |
---|---|---|---|---|

Concrete, mortar and natural stone | 70.8 | 69.1 | 75.2 | 83.7 |

Masonry—clay materials | 28.6 | 28.6 | 11.6 | 0.9 |

Glass | 0.5 | 2.1 | 1.0 | 15.4 |

Bituminous materials | 0.0 | 0.0 | 10.5 | 0.0 |

Others | 0.1 | 0.2 | 1.7 | 0.0 |

Total | 100.0 | 100.0 | 100.0 | 100.0 |

Physical Tests | CL 3 * | CL 2 * | CL 1 * | CRA Valnor | CRA Retria |
---|---|---|---|---|---|

Oven-dry particles density (kg/m^{3}) | 2599 | 2609 | 2522 | 2091 | 2137 |

Water absorption (%) | 1.5 | 1.3 | 2.7 | 8.6 | 8.4 |

Bulk density (kg/m^{3}) | 1360 | 1350 | 1348 | 1095 | 1236 |

Shape index (%) | 15 | 17 | 18 | 24 | 24 |

Los Angeles wear (%) | 26 | 28 | - | 52 | 46 |

Physical Tests | Fine Sand | Coarse Sand | FRA Vimajas | FRA Ambilei |
---|---|---|---|---|

Oven-dry particle density (kg/m^{3}) | 2583 | 2581 | 2070 | 2112 |

Water absorption (%) | 0.3 | 0.7 | 10.1 | 12.9 |

Bulk density (kg/m^{3}) | 1530 | 1540 | 1332 | 1435 |

Chemical Tests | CRA Valnor | CRA Retria | FRA Vimajas | FRA Ambilei | Threshold |
---|---|---|---|---|---|

Water-soluble chloride content | <0.010 | <0.010 | 0.016 | <0.010 | 0.010 ^{1} |

Water-soluble sulphate content | 0.04 | 0.04 | 0.18 | 0.11 | 0.20 ^{1} |

Acid-soluble sulphate content | 0.2 | 0.3 | 0.8 | 0.2 | 0.8 ^{1} |

Sulphur global content | 0.1 | 0.1 | 0.3 | 0.1 | 1.0 ^{1} |

Light contaminants content | 1.5 | <0.1 | 1.7 | 1.8 | 0.5 ^{1} |

Humus content | Negative | Negative | Negative | Negative | Negative |

Water solubility | 1.0 | 1.2 | 2.1 | 0.5 | 10.0 ^{2} |

^{1}According to EN 12620 (2008);

^{2}According to EN 1744 (2009).

Cement | 0.115 | |
---|---|---|

Fine aggregates | 0–0.063 | 0.000 |

0.063–0.125 | 0.016 | |

0.125–0.25 | 0.044 | |

0.25–0.5 | 0.050 | |

0.5–1 | 0.057 | |

1–2 | 0.066 | |

2–4 | 0.076 | |

Coarse aggregates | 4–5.6 | 0.041 |

5.6–8 | 0.046 | |

8–11.2 | 0.047 | |

11.2–16 | 0.121 | |

16–22.4 | 0.122 | |

Water | 0.182 | |

Voids | 0.017 | |

Total | 1.000 |

Recycled Aggregates | 0 | 10 | 50 | 100 | ||||
---|---|---|---|---|---|---|---|---|

Slump (mm) | w/c Ratio | Slump (mm) | w/c Ratio | Slump (mm) | w/c Ratio | Slump (mm) | w/c Ratio | |

CRA Valnor | 114 | 0.51 | 126 | 0.52 | 120 | 0.53 | 120 | 0.53 |

CRA Retria | 118 | 0.52 | 125 | 0.53 | 121 | 0.53 | ||

FRA Vimajas | 119 | 0.53 | 124 | 0.58 | 121 | 0.64 | ||

FRA Ambilei | 140 | 0.52 | 140 | 0.53 | 135 | 0.55 |

**Table 7.**Mechanical properties of the concrete mixes with RA from CDW and their variation (∆) with respect to the RC.

Concrete Mix | f_{cm}_{,28}(MPa) | ∆ (%) | f_{cm}_{,56}(MPa) | ∆ (%) | f_{ctm}_{,28}(MPa) | ∆ (%) | E_{cm}_{,28}(GPa) | ∆ (%) |
---|---|---|---|---|---|---|---|---|

RC | 53.9 ± 1.8 | - | 61.1 ± 1.6 | - | 4.0 ± 0.0 | - | 40.5 ± 0.2 | - |

C10C-Val | 54.1 ± 2.2 | 0.2 | 58.8 ± 1.9 | −3.8 | 3.7 ± 0.3 | −8.3 | 39.1 ± 0.4 | −3.5 |

C50C-Val | 46.2 ± 2.7 | −14.3 | 50.1 ± 2.1 | −18.1 | 3.2 ± 0.0 | −19.5 | 29.2 ± 0.9 | −27.9 |

C100C-Val | 35.3 ± 1.4 | −34.5 | 43.2 ± 1.5 | −29.4 | 3.1 ± 0.1 | −24.3 | 21.1 ± 0.5 | −47.9 |

C10C-Ret | 48.3 ± 2.3 | −10.4 | 53.4 ± 0.9 | −12.6 | 4.0 ± 0.4 | −0.4 | 37.7 ± 0.0 | −6.9 |

C50C-Ret | 44.9 ± 1.4 | −16.8 | 42.7 ± 1.8 | −30.2 | 3.2 ± 0.3 | −20.6 | 31.5 ± 0.2 | −22.3 |

C100C-Ret | 40.1 ± 1.1 | −25.6 | 33.9 ± 2.6 | −44.5 | 2.7 ± 0.2 | −32.1 | 26.3 ± 0.0 | −35.1 |

C10F-Vim | 49.2 ± 1.1 | −8.7 | 52.8 ± 1.9 | −13.7 | 3.9 ± 0.1 | −7.2 | 40.8 ± 0.6 | −4.7 |

C50F-Vim | 37.6 ± 1.3 | −30.2 | 40.5 ± 0.1 | −33.7 | 3.7 ± 0.3 | −26.2 | 34.8 ± 0.3 | −21.2 |

C100F-Vim | 30.2 ± 0.5 | −44.1 | 30.6 ± 0.9 | −50.0 | 2.9 ± 0.0 | −34.6 | 26.7 ± 0.4 | −42.5 |

C10F-Amb | 51.6 ± 1.0 | −4.3 | 52.3 ± 0.4 | −14.5 | 3.4 ± 0.1 | −14.9 | 40.3 ± 0.3 | −0.5 |

C50F-Amb | 46.8 ± 1.2 | −13.3 | 48.1 ± 0.9 | −21.3 | 3.4 ± 0.3 | −14.6 | 37.4 ± 0.4 | −7.7 |

C100F-Amb | 38.4 ± 1.2 | −28.8 | 40.3 ± 0.1 | −34.0 | 3.2 ± 0.1 | −20.7 | 32.5 ± 0.6 | −19.8 |

Concrete Mix | τ_{max}(MPa) | ∆ (%) |
---|---|---|

RC | 16.3 ± 1.4 | - |

C10C-Val | 14.4 ± 1.1 | −11.5 |

C50C-Val | 13.5 ± 1.7 | −17.1 |

C100C-Val | 12.7 ± 1.1 | −22.1 |

C10C-Ret | 15.9 ± 1.9 | −2.7 |

C50C-Ret | 14.8 ± 1.1 | −9.3 |

C100C-Ret | 13.4 ± 1.0 | −18.0 |

C10F-Vim | 14.5 ± 0.4 | −11.2 |

C50F-Vim | 11.3 ± 0.9 | −30.9 |

C100F-Vim | 9.5 ± 0.8 | −41.9 |

C10F-Amb | 14.7 ± 1.0 | −9.9 |

C50F-Amb | 14.1 ± 0.6 | −13.4 |

C100F-Amb | 13.1 ± 0.6 | −19.6 |

Concrete Mix | K_{τ} (MPa/mm) | τ_{max} (MPa) | τ_{f} (MPa) | s_{1} (mm) | s_{2} (mm) | s_{3} (mm) |
---|---|---|---|---|---|---|

RC | 421.96 | 13.99 | 2.10 | 0.20 | 0.25 | 1.00 |

C100C-Val | 324.63 | 11.76 | 1.76 | 0.20 | 0.35 | 1.00 |

C100C-Ret | 317.23 | 11.50 | 1.72 | 0.25 | 0.35 | 1.00 |

C100F-Vim | 226.35 | 9.90 | 1.48 | 0.40 | 0.80 | 1.00 |

C100F-Amb | 259.50 | 11.35 | 1.70 | 0.40 | 0.80 | 1.00 |

Concrete Mix | τ_{max,Num}(MPa) | τ_{max,Num}/τ_{max,Exp}(-) |
---|---|---|

RC | 14.6 | 0.90 |

C10C-Val | 14.3 | 0.99 |

C50C-Val | 13.3 | 0.99 |

C100C-Val | 12.3 | 0.97 |

C10C-Ret | 13.7 | 0.86 |

C50C-Ret | 12.7 | 0.86 |

C100C-Ret | 12.0 | 0.90 |

C10F-Vim | 13.7 | 0.94 |

C50F-Vim | 12.6 | 1.12 |

C100F-Vim | 10.2 | 1.07 |

C10F-Amb | 13.7 | 0.93 |

C50F-Amb | 13.7 | 0.97 |

C100F-Amb | 11.7 | 0.89 |

Average | 0.95 | |

Standard deviation | 0.07 |

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## Share and Cite

**MDPI and ACS Style**

Bravo, M.; Duarte, A.P.C.; de Brito, J.; Evangelista, L.
Tests and Simulation of the Bond-Slip between Steel and Concrete with Recycled Aggregates from CDW. *Buildings* **2021**, *11*, 40.
https://doi.org/10.3390/buildings11020040

**AMA Style**

Bravo M, Duarte APC, de Brito J, Evangelista L.
Tests and Simulation of the Bond-Slip between Steel and Concrete with Recycled Aggregates from CDW. *Buildings*. 2021; 11(2):40.
https://doi.org/10.3390/buildings11020040

**Chicago/Turabian Style**

Bravo, Miguel, António P. C. Duarte, Jorge de Brito, and Luís Evangelista.
2021. "Tests and Simulation of the Bond-Slip between Steel and Concrete with Recycled Aggregates from CDW" *Buildings* 11, no. 2: 40.
https://doi.org/10.3390/buildings11020040