# Micromechanical Multiscale Modeling of ITZ-Driven Failure of Recycled Concrete: Effects of Composition and Maturity on the Material Strength

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## Abstract

**:**

## 1. Introduction

## 2. Model Development

#### 2.1. Micromechanical Representation of Recycled Concrete

- A considerable fraction of the recycled aggregates are either completely free of attached mortar or cement paste covers only a negligible part of their surfaces. Recycled aggregates that exhibit such a morphology are herein labeled as class I aggregates.
- A considerable fraction of the recycled aggregates are old mortar particles where none of the many small aggregates inside the mortar exhibits a dominant size, labeled herein as class II aggregates.
- A considerable fraction of the recycled aggregates are single stone aggregates, whereby the majority of the aggregate surface is covered by cement paste, labeled herein as class III aggregates.

#### 2.2. Modeling of Hydrate Failure in Critical ITZs

- the ITZ between the new natural aggregates and the new cement paste matrix, herein labeled as ${\mathcal{I}}_{na}^{ncp}$, associated with ${\mathcal{I}}_{na}^{ncp}$ failure as sketched in Figure 4a;
- the ITZ between the old plain aggregates and the new cement paste matrix, associated with ${\mathcal{I}}_{opa}^{ncp}$ failure as sketched in Figure 4b;
- the ITZ between the old mortar aggregates and the new cement paste matrix, associated with ${\mathcal{I}}_{oma}^{ncp}$ failure as sketched in Figure 4c;
- the ITZ between the old embedded aggregates and the old cement paste matrix inside the old mortar aggregates, associated with ${\mathcal{I}}_{oea}^{ocp}$ failure as sketched in Figure 4d;
- the ITZ between the old covered aggregates and the old cement paste cover, associated with ${\mathcal{I}}_{oca}^{ocp}$ failure as sketched in Figure 4e;
- the ITZ between the old cement paste cover and the new cement paste matrix, associated with ${\mathcal{I}}_{ocpc}^{ncp}$ failure as sketched in Figure 4f.

#### 2.3. Stress Downscaling to Hydrates via ITZs

#### 2.4. Upscaling of Hydrate Failure to Failure of Recycled Concrete

#### 2.5. Material Phase Properties

## 3. Model Predictions

#### 3.1. Sensitivity Study Regarding the w/c-Ratio of New and Old Paste and the Age of New Paste

#### 3.2. Sensitivity Study Regarding the ITZ Porosity

#### 3.3. Sensitivity Study Regarding the Recycled Aggregate Morphology

- The volume fraction of old plain aggregates (class I) amounts to 65%, allowing for maintaining 35% of old cement paste (according to composition of the benchmark concrete), which is then attributed to old mortar aggregates (class II), i.e., the class volume fractions read as ${f}_{\mathrm{I}}=0.65$, ${f}_{\mathrm{II}}=0.35$, ${f}_{\mathrm{III}}=0$.
- All aggregates are considered to be old mortar aggregates (class II), i.e., ${f}_{\mathrm{I}}=0$, ${f}_{\mathrm{II}}=1$, ${f}_{\mathrm{III}}=0$.
- All aggregates are considered to be old covered (class III), i.e., ${f}_{\mathrm{I}}=0$, ${f}_{\mathrm{II}}=0$, ${f}_{\mathrm{III}}=1$.

#### 3.4. Sensitivity Study Regarding the Old Cement Paste Content

#### 3.5. Sensitivity Study Regarding the Aggregate Replacement Ratio

## 4. Discussion

## 5. Conclusions

- The extent of the strength reduction for recycled concrete compared to conventional concrete is determined by the ITZ, where failure is induced, and thus most importantly by the mutual stiffness contrasts between old cement paste, new cement paste, and aggregates.
- Old concretes with high $w/c$ ratios do not qualify as source of recycled aggregates if high-strength recycled concretes are targeted, since the aggregate-old cement paste ITZ will trigger macroscopic failure and the potential of a high-quality new cement paste cannot be exploited. Ideally, the $w/c$-ratios of old and new cement paste match, resulting in less pronounced stress concentration and consequently an optimized use of cement. This calls for careful selection of the parent concrete.
- Modeling the commonly observed weakness of ITZs between old and new cement paste, resulting from water migration or chemical reactions, by means of increasing the porosity of the ITZ shows that the early-age strength significantly reduces with increasing ITZ porosity. For mature pastes, however, weak ITZs between old and new paste do not significantly alter the uniaxial compressive strength.
- The strength of recycled concrete does generally decrease with increasing content of old cement paste in the recycled aggregates, whereby the decrease is less pronounced at early ages.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Appendix A. Mathematical Expressions for Stiffness Homogenization and Stress Concentration

## Appendix B. Covered Aggregate Inclusion

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**Figure 1.**Multiscale micromechanical representation of recycled concrete; two-dimensional sketches refer to three-dimensional representative volume elements (RVEs).

**Figure 2.**Visual classification of typical coarse recycled aggregates (see Bendimerad et al. [32] for more details on the aggregates).

**Figure 4.**Schematic representation of ITZ-driven failure (cracking) in recycled concrete under uniaxial compressive loading in vertical direction.

**Figure 5.**Definition of coordinate systems, position angle, and orientation angles: (

**a**) Cartesian base frame $\underline{e}{}_{x},\underline{e}{}_{y},\underline{e}{}_{z}$ as well as polar angle $\psi $ describing the position along the aggregate surface; (

**b**) spherical base frame $\underline{e}{}_{r},\underline{e}{}_{\vartheta},\underline{e}{}_{\phi}$ as well as azimuth angle $\phi $ and polar angle $\vartheta $ describing the orientation of the hydrate needle.

**Figure 6.**Uniaxial compressive strength evolution with respect to the hydration degree of the new cement paste matrix ${\xi}_{ncp}$: (

**a**) for an old cement paste-related $w/c$-ratio amounting to ${(w/c)}_{ocp}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}0.5$ and different new cement paste-related $w/c$-ratios, whereby solid lines refer to concrete containing recycled aggregates only (${f}_{ra}^{a}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}1$) and dashed lines refer to conventional concretes without recycled aggregates (${f}_{ra}^{a}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}0$); (

**b**) for different old and new cement paste-related $w/c$-ratios ${(w/c)}_{ocp}\in \{0.2,0.35,0.5,0.7\}$ and ${(w/c)}_{ncp}\in \{0.2,0.35,0.5,0.7\}$.

**Figure 7.**Uniaxial compressive strength of the benchmark recycled concrete as function of the ITZ porosity factor ${F}_{por}$ for different hydration degrees: (

**a**) for ${(w/c)}_{ncp}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}0.35$, and (

**b**) for ${(w/c)}_{ncp}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}0.5$. The solid lines represent the material strength, and the dashed lines represent the theoretical strength in case of ${\mathcal{I}}_{opa}^{ncp}$-failure only.

**Figure 8.**Uniaxial compressive strength evolution of the benchmark recycled concrete for (

**a**) one dominating recycled aggregate morphology and (

**b**) for the three limit cases of recycled aggregate morphology, and for different new cement paste-related $w/c$-ratios.

**Figure 9.**Dimensionless uniaxial compressive strength of recycled concrete (normalized with respect to the strength of the benchmark composition with ${f}_{ocp}^{ra}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}0.35$) as function of the recycled aggregate-related old cement paste volume fraction: (

**a**) for ${(w/c)}_{ncp}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}0.35$, and (

**b**) for ${(w/c)}_{ncp}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}0.5$.

**Figure 10.**Dimensionless uniaxial compressive strength of recycled concrete (normalized with respect to the strength of conventional with ${f}_{ra}^{a}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}0$) as function of the recycled aggregate-related old cement paste volume fraction: (

**a**) for ${(w/c)}_{ncp}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}0.35$, and (

**b**) for ${(w/c)}_{ncp}\phantom{\rule{-0.166667em}{0ex}}=\phantom{\rule{-0.166667em}{0ex}}0.5$.

**Table 1.**Non-zero isotropic elasticity constants of material phases according to [21].

Bulk Modulus | Shear Modulus | |||
---|---|---|---|---|

k [GPa] | $\mathit{\mu}$ [GPa] | |||

clinker | ${k}_{clin}$ | 116.58 | ${\mu}_{clin}$ | 53.81 |

hydrates | ${k}_{hyd}$ | 18.69 | ${\mu}_{hyd}$ | 11.76 |

aggregates (old and new) | ${k}_{agg}$ | 35.35 | ${\mu}_{agg}$ | 29.91 |

hydrates | ${k}_{por}$ | 0.00 | ${\mu}_{por}$ | 0.00 |

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**MDPI and ACS Style**

Königsberger, M.; Staquet, S.
Micromechanical Multiscale Modeling of ITZ-Driven Failure of Recycled Concrete: Effects of Composition and Maturity on the Material Strength. *Appl. Sci.* **2018**, *8*, 976.
https://doi.org/10.3390/app8060976

**AMA Style**

Königsberger M, Staquet S.
Micromechanical Multiscale Modeling of ITZ-Driven Failure of Recycled Concrete: Effects of Composition and Maturity on the Material Strength. *Applied Sciences*. 2018; 8(6):976.
https://doi.org/10.3390/app8060976

**Chicago/Turabian Style**

Königsberger, Markus, and Stéphanie Staquet.
2018. "Micromechanical Multiscale Modeling of ITZ-Driven Failure of Recycled Concrete: Effects of Composition and Maturity on the Material Strength" *Applied Sciences* 8, no. 6: 976.
https://doi.org/10.3390/app8060976