# Improved Serviceability and Environmental Performance of One-Way Slabs through the Use of Layered Natural and Recycled Aggregate Concrete

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## Abstract

**:**

## 1. Introduction

## 2. Parametric Study of Layered One-Way Slab Deflections

#### 2.1. OpenSees Modeling of Time-Dependent Behavior

#### 2.2. Concrete Types and Constitutive Relations

_{c}at peak strain ε

_{c0}, determined by f

_{c}and the tangent modulus of elasticity E

_{c}. After the peak, stress decreases linearly to the residual strength f

_{cu}at the ultimate strain ε

_{cu}. In this study, considering concrete strength classes defined in the fib Model Code 2010 [21], the mean compressive strength f

_{cm}was adopted for f

_{c}, concrete modulus E

_{cm}for E

_{c}and a strain of 3.5‰ for ε

_{cu}. In the post-cracking tensile region, TDConcreteMC10NL follows the relation proposed by Tamai et al. (1988) as:

_{ct}and ε

_{ct0}are the axial tensile strength and strain at cracking, respectively, ε

_{ct}and σ

_{ct}are the tensile strain and corresponding stress, respectively, and b

_{ts}is a tension-softening parameter (originally proposed as 0.4 by Tamai et al., 1988). In the current study, the mean axial tensile strength f

_{ctm}was adopted for f

_{ct}, according to the corresponding strength class [21], whereas the tension softening parameter b

_{ts}was adopted as 0.8 for NAC and 0.9 for RAC50 and RAC100, according to a calibration performed on a database of experimental results, previously reported by Tošić and Kurama [6].

_{ctm}was calculated as a function of the compressive strength using the expression from the fib Model Code 2010 [21] as:

_{ck}is the characteristic strength of concrete, i.e., the 5%-fractile of compressive strength as per the fib Model Code 2010 [21]. Previous research has shown that the relationship between the compressive and tensile strengths for RCA is similar to that for NAC [26]. Therefore, Equation (2) was used for all of the concrete types in the study. However, the modulus of elasticity E

_{cm}is highly affected by RCA [2], and thus an expression proposed by Tošić et al. [5] was used to calculate E

_{cm}by adjusting the equation provided in the fib Model Code 2010 [21] as:

_{cm}is the mean compressive strength (= f

_{ck}+ 8 MPa).

_{cs,RAC}is the total RAC shrinkage strain, ε

_{cs}is the total shrinkage strain (basic + drying) calculated according to the fib Model Code 2010, φ

_{RAC}is the total RAC creep coefficient, and φ is the total creep coefficient (basic + drying) calculated according to the fib Model Code 2010.

_{tot}is the total strain, ε

_{m}is the mechanical strain, ε

_{cbc}and ε

_{cdc}are the basic and drying creep strains, respectively, ε

_{cbs}and ε

_{cds}are the basic and drying shrinkage strains, respectively, t is the current time, t

_{s}is the age of concrete at the start of drying, and t

_{0}is the age of concrete at loading. This strain is then used to check the equilibrium in each cross-section, determine the internal forces and check the convergence of the unbalanced force vector in the global analysis [17]. Thermal strains are not included in the formulation for TDConcreteMC10NL.

#### 2.3. Formulation of the Parametric Study and Modeling

_{1}= 30 mm from the nearest concrete top/bottom face, i.e., the effective depth to the tension reinforcement was d = 170 mm, and concrete cover was assumed equal for all concrete types. This decision was based on a review of several studies that showed that, when RAC is produced with equal compressive strength as NAC, its carbonation resistance is similar or negligibly lower [27,28,29].

_{sw}= 5 kN/m

^{2}, additional (superimposed) dead load, Δg = 3.0 kN/m

^{2}, and live load, q = 3 kN/m

^{2}. This means that the total ULS design load was q

_{Ed}= 15.3 kN/m

^{2}(1.35·g

_{sw}+ 1.35·Δg + 1.50·q).

_{s,ULS}was adopted with no excess reinforcement, checking also for the minimum reinforcement ratio according to Eurocode 2 [31] (~0.013%). In the case of simply supported slabs, the reinforcement ratio, ρ, was assumed to be constant along the entire span. For the continuous slabs, the top (tension) reinforcement over the interior support was adopted over a length of 0.3·L on each side of the support, whereas the bottom reinforcement in the spans was adopted constant over the entire length in each span. Reinforcement was modeled with a bi-linear stress–strain relationship using the Steel01 material model in OpenSees, with a yield strength of 500 MPa, modulus of elasticity of 200 GPa and post-yield hardening modulus of 20 GPa.

_{2}= 0.0 and 0.6. This resulted in quasi-permanent loads of 8.0 and 9.8 kN/m

^{2}, and quasi-permanent-to-design load ratios, q

_{qp}/q

_{Ed}, of 0.52 and 0.64, respectively. For all combinations, the characteristic load (g

_{sw}+ Δg + q) was equal to 11 kN/m

^{2}.

#### 2.4. Parametric Analysis Results

#### 2.4.1. Simply Supported One-Way Slabs

_{lim}, which represents the ratio of the maximum slab deflection to the limit (i.e., allowable) deflection for quasi-permanent load, equal to L/250 [21]. Importantly, deflections that remain below the allowable value would not have practical implications (i.e., they would not alter the design). The normalized deflection is plotted against the L/d ratio; and, once a/a

_{lim}exceeds 1, the deflection limit is not satisfied. It can be seen from the figure that this generally happened for L/d ratios ranging between 22 and 25, i.e., for spans of 3.74 to 4.25 m.

_{lim}ratio increase in the same order. This is of course explained by the lower modulus of elasticity and tension stiffening and higher creep and shrinkage with increased amounts of RCA. The influence of creep and shrinkage is dominant as the differences are more pronounced for RH = 50%, for which both are larger than for RH = 80%. The effect of concrete strength is not significant, whereas the effect of the quasi-permanent-to-design load ratio can be noticed in a slight increase of differences between NAC, RAC50 and RAC100.

_{qp}/q

_{Ed}= 0.64 and RH = 50%). The top fiber strains ε

_{c,1}are seen to be equal in both concretes because the top fibers in both are NAC. However, a stark difference exists for the bottom fiber strains ε

_{c,2}, which are NAC and RAC100 in the NAC and L-RAC100 slabs, respectively, due to the much higher shrinkage in the bottom half of the L-RAC100 slab.

_{qp}/q

_{Ed}= 0.52 and RH = 80%, simply supported slabs can be used up to L/d approximately 27.0, 26.5 and 26.0 utilizing NAC, RAC50 and RAC100, respectively. Even though these differences exist, they are not large, and the maximum L/d values are already high for simply supported slabs when considering code recommendations [31]. More importantly, though, the results provide a strong argument for the use of layered RAC as a way of achieving satisfactory ULS and SLS behavior (equal to or even superior to NAC), and at the same time a not insignificant utilization of RCA (equal to the amount used in RAC50, but with better deflection behavior).

#### 2.4.2. Continuous One-Way Slabs

_{lim}and L/d are the same as those for the simply supported slabs. As expected, deflections are satisfied up to higher L/d ratios, approximately 27–32, for the continuous slabs as compared with the simply supported slabs. As with the simply supported slabs, for homogenous concretes, the deflections increase in the order from NAC, RAC50 and RAC100, and the significance of the parameters remains similar: i.e., negligible influence of concrete class (for the two classes considered), small influence of load level and larger influence of relative humidity.

_{qp}/q

_{Ed}= 0.52 and RH = 80%. The moment diagrams for the two slabs are shown at 180 days (after only quasi-permanent load is left) and at the end of the analysis (25 years). Differences in the moment diagrams of the two slabs at 180 days are a consequence of increased shrinkage and cracking in the L-RAC100 slab, since the bottom half of the section is RAC100 with lower tension stiffening. It can be seen that between 180 days and 25 years, there is very little change in moment (i.e., moment redistribution) in the NAC slab, while a much larger decrease of negative moment above the support and increase of positive moment within the span occur for the L-RAC100 slab.

_{lim}> 1. Hence, this effect can be considered to have little consequence for practical applications.

## 3. LCA of Homogeneous and Layered One-Way Slabs

#### 3.1. LCA Model

^{2}of slab with a height equal to 0.2 m. All three alternatives had the same strength and service life, but different deflections per FU, as shown in Figure 4 and Figure 6. Therefore, the obtained LCA results are interpreted considering their different deflection behaviors.

_{eff}for the selected mixtures are presented in Table 1 (in the case of RAC, (w/c)

_{eff}refers to the water-cement ratio disregarding the water needed for RCA to achieve a saturated surface dry condition that is satisfied either by mixing in additional batch water or by pre-soaking the RCA; in the case of NAC, (w/c)

_{eff}is equal to the apparent w/c ratio). For the C25/30 strength class, the RAC50 and RAC100 mixtures had slightly larger average cement contents (i.e., lower average (w/c)

_{eff}) than the NAC mixtures), but this difference was not evident for the C30/37 strength class. A larger variation was observed for the cement content than for the (w/c)

_{eff}ratio (except for RAC50, C25/30); however, the greater variability for the cement content in the NAC mix designs was not expected.

^{3}for diesel, hard coal, soft coal and natural gas, respectively. The LCI and Life Cycle Impact Assessment (LCIA) calculations for each selected mixture were performed using an Excel-based software. A statistical analysis was performed on the impact indicators level.

#### 3.2. LCIA Results

^{3}) will cause a large scatter of impact values.

## 4. Conclusions

- Within the considered parametric study, the largest influence on the time-dependent service-load deflection behavior of one-way slabs was exerted by relative humidity, as its decrease significantly increased creep and shrinkage; the quasi-permanent-to-design load ratio had a moderate effect on the results, whereas the change in concrete strength class from C25/30 to C30/37 did not have a significant effect.
- For both simply supported and continuous homogeneous one-way slabs, the deflections increased in the order of NAC, RAC50 and RAC100, which was expected due to the increased creep and shrinkage with increased amounts of RCA. However, the layered L-RAC100 slab exhibited a deflection behavior practically equal to NAC. This was explained by the differential shrinkage between the bottom RAC100 and the top NAC layer; analyzing cross-sectional strains and curvatures, it was shown that the larger shrinkage of the bottom RAC100 layer compensated for part of the load-induced deflections.
- The “cradle-to-gate” LCA showed that the RAC50 and L-RAC100 slabs have an equal or better environmental performance than the NAC slab. This means that, considering both structural and environmental assessments, L-RAC100 slabs can be viewed as an improved solution, compared with NAC slabs.

## Supplementary Materials

## Author Contributions

## Funding

`ł`odowska-Curie grant agreement no. 836270 and from the United States Department of State through the Fulbright Visiting Scholar Grant “Optimization of Stratified Recycled Concrete Structures Based on Numerical Analyses and Life Cycle Assessment.” Any opinions, findings, conclusions, and/or recommendations in the paper are those of the authors and do not necessarily represent the views of the funding organizations.

## Conflicts of Interest

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**Figure 3.**Statical systems considered in the parametric study and cross-section discretization: (

**a**) simply supported one-way slab, (

**b**) continuous one-way slab, (

**c**) discretization of slab cross-section into fibers.

**Figure 5.**Top (top) and bottom (bottom) fiber strains for NAC (left) and L-RAC100 (right) simply supported slabs with L/d = 20, C25/30, q

_{qp}/q

_{Ed}= 0.64 and RH = 50%.

**Figure 7.**Redistribution of bending moments over time for NAC and L-RAC100 continuous one-way slabs with L/d = 35, C25/30, q

_{qp}/q

_{Ed}= 0.52 and RH = 80%.

**Figure 9.**Environmental impact indicators of RAC50 and L-RAC100 slabs relative to NAC slab, with C25/30 (mean values).

**Figure 10.**Environmental impact indicators of RAC50 and L-RAC100 slabs relative to NAC slab, with C30/37 (mean values).

**Table 1.**Mean values and standard deviations of constituent materials and effective water-cement ratio for considered concrete mixes.

Concrete Class | Concrete Type | Cement (kg/m ^{3}) | Fine Aggregate (kg/m ^{3}) | Coarse Aggregate (kg/m ^{3}) | (w/c)_{eff} | |
---|---|---|---|---|---|---|

NA | RCA | |||||

C25/30 | NAC | 340 (42) | 744 (112) | 1077 (107) | / | 0.55 (0.04) |

RAC50 | 359 (24) | 743 (114) | 523 (56) | 501 (69) | 0.50 (0.06) | |

RAC100 | 364 (36) | 717 (113) | / | 1012 (117) | 0.51 (0.04) | |

C30/37 | NAC | 374 (44) | 730 (70) | 1050 (72) | / | 0.49 (0.04) |

RAC50 | 381 (35) | 728 (60) | 521 (41) | 484 (47) | 0.49 (0.04) | |

RAC100 | 380 (29) | 743 (116) | / | 947 (122) | 0.48 (0.04) |

_{eff}—effective water-cement ratio.

Type of Data | Source (File Name in Ecoinvent V2.0) | Geography |
---|---|---|

Energy | ||

Coal mining and distribution | Ecoinvent [89] (hard coal, at regional storage/kg/EEU) | EU average |

Diesel production, distribution, and usage | Ecoinvent [89] (diesel, at regional storage/kg/RER) (diesel, burned in building machine/MJ/GLO) | EU average |

Natural gas production, distribution, and usage | Ecoinvent [89] (natural gas, high pressure, at consumer/MJ/RER) (natural gas, burned in industrial furnace >100 kW/MJ/RER) | EU average |

Electricity | Ecoinvent [89] (production mix RER/kWh/RER) | EU average |

Concrete components | ||

Cement production | CEMBUREAU (the European Cement Association) EPDs for CEMI, CEMII and CEMIII [94,95] | EU average |

NA production | Ecoinvent [90] (gravel, round, at mine/kg/CH) (gravel, crushed, at mine/kg/CH) | estimated as EU average |

RCA production | Industry (Marinković et al., 2008) [92] | Serbia |

Concrete | ||

Concrete production | Kellenberger et al. (2007) [90] | estimated as EU average |

Transportation of concrete components | ||

Road and river | Ecoinvent [91] (transport, lorry 16–32 t, EURO5/tkm/RER) (transport, barge/tkm/RER) | EU average |

Material | Route | Transport Distance (km) | Transport Type | |
---|---|---|---|---|

From | To | |||

River NA | Place of extraction | Concrete plant | 100 × 2 | Barge 10,000 t |

Crushed NA | Place of extraction | Concrete plant | 100 × 2 | Truck 16–32 t |

Recycled aggregate | Recycling plant^{1} | Concrete plant | 20 × 2 | Truck 16–32 t |

Mobile recycling plant ^{2} | Demolition site | 50 × 2 | Truck 16–32 t | |

Cement | Cement factory | Concrete plant | 100 × 2 | Truck 16–32 t |

^{1}Recycling is performed in a mobile plant at demolition site;

^{2}For each campaign of 2500 t, mobile plant (20 t) is transported along 50 km.

NAC | RAC50 | L-RAC100 | |||
---|---|---|---|---|---|

GWP (g CO _{2}-eq.) | C25/30 | mean | 68.5 | 69.6 | 69.2 |

CoV (%) | 14.7 | 10.7 | 13.1 | ||

C30/37 | mean | 74.7 | 74.6 | 72.9 | |

CoV (%) | 11.0 | 8.0 | 10.0 | ||

EP (g PO _{4}^{3−}-eq.) | C25/30 | mean | 25.0 | 23.2 | 23.6 |

CoV (%) | 10.8 | 8.9 | 11.7 | ||

C30/37 | mean | 26.4 | 24.6 | 24.5 | |

CoV (%) | 7.1 | 5.9 | 10.3 | ||

AP (g SO _{2}-eq.) | C25/30 | mean | 155.8 | 148.6 | 149.7 |

CoV (%) | 12.3 | 9.3 | 11.9 | ||

C30/37 | mean | 166.7 | 158.1 | 156.4 | |

CoV (%) | 7.7 | 6.5 | 9.8 | ||

POCP (g C _{2}H_{4}-eq.) | C25/30 | mean | 15.7 | 14.7 | 14.9 |

CoV (%) | 13.3 | 9.4 | 12.8 | ||

C30/37 | mean | 16.7 | 15.7 | 15.5 | |

CoV (%) | 7.8 | 6.4 | 10.3 | ||

ADPFF (MJ) | C25/30 | mean | 405.2 | 373.3 | 376.3 |

CoV (%) | 17.3 | 10.5 | 16.5 | ||

C30/37 | mean | 431.4 | 399.6 | 392.0 | |

CoV (%) | 8.2 | 6.7 | 12.6 |

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**MDPI and ACS Style**

Tošić, N.; Marinković, S.; Kurama, Y. Improved Serviceability and Environmental Performance of One-Way Slabs through the Use of Layered Natural and Recycled Aggregate Concrete. *Sustainability* **2020**, *12*, 10278.
https://doi.org/10.3390/su122410278

**AMA Style**

Tošić N, Marinković S, Kurama Y. Improved Serviceability and Environmental Performance of One-Way Slabs through the Use of Layered Natural and Recycled Aggregate Concrete. *Sustainability*. 2020; 12(24):10278.
https://doi.org/10.3390/su122410278

**Chicago/Turabian Style**

Tošić, Nikola, Snežana Marinković, and Yahya Kurama. 2020. "Improved Serviceability and Environmental Performance of One-Way Slabs through the Use of Layered Natural and Recycled Aggregate Concrete" *Sustainability* 12, no. 24: 10278.
https://doi.org/10.3390/su122410278