# Economic and Technical Viability of Using Shotcrete with Coarse Recycled Concrete Aggregates in Deep Tunnels

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions, the total amount of construction and demolition waste (CDW) represents a third of all waste generated in the European Union. However, there are barriers to its reuse, one of the main of which lies in the lack of trust in the quality of CDW [1].

- -
- Higher water absorption capacity of the RA, leading to concrete mixes with lower workability and effective water/cement ratio;
- -
- Lower compactness and thus lower resistance to crushing, lower modulus of elasticity and higher short- and long-term deformability.

## 2. Experimental Program

#### 2.1. Tests

#### 2.2. Materials

#### 2.3. Mixes Design

## 3. Mechanical Properties

## 4. Technical Viability

#### 4.1. Case Study

_{c}, is equal to 200 mm for CNA shotcrete.

#### 4.2. Elastic Radial Stiffness Criterion, K_{s}

_{s}, is equal to 636 MPa/m (t

_{c}= 200 mm for CNA shotcrete).

#### 4.3. Maximum Pressure Criterion, ${p}_{s}^{m\mathrm{\xe1}x}$

_{c}= 200 mm for CNA shotcrete). Table 7 quantifies the differences in stiffness and equivalent thickness. For IR20, the equivalent thickness increases 12% (24 mm), which can be considered acceptable, while IR50 and IR100 require thickness increments over 28% (more than 50 mm).

## 5. Economic Viability

^{3}, of the different shotcrete scenarios, assuming three possible costs for CRCA to assess its impact:

- Scenario 1 (50% CNA)—the recycled aggregates’ cost is taken as equal to 50% of the natural aggregates (7.5 €/m
^{3}); - Scenario 2 (NULL) —the recycled aggregates’ cost is zero (taking into account that CDW producers are ready to pay to get rid of it);
- Scenario 3 (SUB) —there is a subsidy equal to 7.5 €/m
^{3}to promote recycled aggregates’ use. Because the cost of CRCA is smaller than that of CNA, the unit cost of shotcrete with incorporation of CRCA is smaller.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. The Convergence-Confinement Method

**Figure A1.**Convergence confinement method: (

**a**) evolution of tunnel convergence with face advance; (

**b**) ground reaction curve and support reaction curve (adapted from Orestes [13]).

_{i}, and the radial displacement, u

_{r}, are constant in the tunnel walls.

_{0}. Equations (A1) and (A2) present the elastic and plastic portions of the curve, respectively.

_{r}

^{el}is the elastic radial displacement of the massif, S

_{o}the uniform tension around the tunnel, p

_{i}the pressure of the walls at the tunnel, and G

_{rm}the shear modulus of the rock massif.

_{ψ}is the dilatancy coefficient, P

_{i}

^{cr}the critical pressure, related with the transition of an elastic to plastic behavior of the tunnel walls, and R

_{pl}the radius of the failed region, developed when p

_{i}< P

_{i}

^{cr}.

_{s}, and maximum pressure, p

_{s,max}. Equations (A3)–(A5) describe the support behavior [28].

_{s}is the pressure in the support, f

_{cd}the design compressive strength of the shotcrete, u

_{r}the radial displacement of the support, ν

_{c}the Poisson’s coefficient of the shotcrete, E

_{c}the modulus of elasticity of the shotcrete, R the radius of the shotcrete ring and t

_{c}representing its thickness.

## References

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**Figure 2.**Cost of shotcrete for each composition, assuming different cost scenarios of the recycled aggregates.

**Figure 3.**Variation of lining’s cost per unit length of tunnel for three different costs of Coarse Recycled Concrete Aggregates.

Age [Days] | Number of Specimens | Standard | |
---|---|---|---|

Bond Strength (by Pull-off) | 40 | 3–5 | EN 1542 [19] |

Compression Strength | 7 | 3 | EN 12,390-3 [20] |

28 | 5 | ||

56 | 3 | ||

Splitting Tensile Strength | 28 | 3 | EN 12,390-6 [21] |

Modulus of Elasticity | 28 | 3 | LNEC E-397 [22] |

Abrasion Resistance | 91 | 3 | DIN 52,108 [23] |

Ultra-Sound Pulse Velocity | 28 | 5 | EN 12,504-4 [24] |

Oven-Dry Particles Density (kg/m^{3}) | Water Absorption (%) | Bulk Density (kg/m^{3}) | Shape Index (%) | Los Angeles Wear (%) | |
---|---|---|---|---|---|

Gravel 1 | 2624 | 1.65 | 1406 | 27 | 25 |

Granule | 2634 | 1.02 | 1409 | 22 | 25 |

Coarse Sand | 2574 | 0.71 | 1544 | - | - |

Fine Sand | 2548 | 0.59 | 1557 | - | - |

RA | 2370 | 4.55 | 1287 | 45 | 36 |

RC | C20 | C50 | C100 | ||
---|---|---|---|---|---|

Coarse Natural Aggregates | 0.331 | 0.264 | 0.164 | 0.000 | |

Coarse Recycled Aggregates | 0.000 | 0.066 | 0.164 | 0.327 | |

Fine (Natural) Aggregates | 0.354 | 0.352 | 0.350 | 0.348 | |

Total Aggregates | 0.685 | 0.681 | 0.678 | 0.674 | |

Type I 42.5 R Cements | 0.115 | 0.115 | 0.115 | 0.115 | |

Water | 0.175 | 0.179 | 0.182 | 0.186 | |

Voids | 0.025 | 0.025 | 0.025 | 0.025 | |

Total | 1.000 | 1.000 | 1.000 | 1.000 | |

w/c Ratios | 0.46 | 0.47 | 0.50 | 0.50 |

**Table 4.**Mechanical properties of shotcrete mixes (adapted from Duarte et al. [25]).

RC | C20 | C50 | C100 | |||
---|---|---|---|---|---|---|

Pull-off bond [MPa] | 1.11 | 0.8 | 1.11 | 1.14 | ||

−2.91% | −0.15% | +2.45 | ||||

Compressive strength [MPa] | 7-day | 18.27 | 17.72 | 15.99 | 14.09 | |

−3.01% | −12.48% | −22.88% | ||||

28-day | 37.18 | 33.83 | 30.35 | 27.25 | ||

−9.01% | −18.37% | −26.71% | ||||

56-day | 43.24 | 36.58 | 35.77 | 31.91 | ||

−15.40% | −17.28% | −26.20% | ||||

Splitting tensile strength [MPa] | 3.33 | 3.1 | 3.01 | 2.84 | ||

−6.84% | −9.61% | −14.77% | ||||

Ultrasound pulse velocity [km/s] | 4.82 | 4.79 | 4.54 | 4.48 | ||

−0.45% | −5.66% | −6.97% | ||||

Modulus of elasticity [GPa] | 26.14 | 25.41 | 24.34 | 18.08 | ||

−2.79% | −6.89% | −30.83% | ||||

Abrasion resistance [%] | 8.13 | 7.49 | 7.73 | 7.06 | ||

−7.87% | −4.92% | −13.16% |

IR0 | IR20 | IR50 | IR100 | |
---|---|---|---|---|

f_{cd} [MPa] | 22.1 | 19.9 | 17.6 | 15.5 |

(Δf_{cd,IR0} [%]) | (-) | (−10%) | (−21%) | (−30%) |

E_{c} [GPa] | 26.1 | 25.4 | 24.3 | 18.1 |

(ΔE_{c,IR0} [%]) | (-) | (−3%) | (−7%) | (−31%) |

**Table 6.**Variation of yield stress and equivalent thickness when a similar stiffness criterion is adopted.

IR0 | IR20 | IR50 | IR100 | |
---|---|---|---|---|

Yield Stress: ${p}_{s}^{m\mathrm{\xe1}x}$ [MPa] | 1.43 | 1.32 | 1.21 | 1.39 |

(Δ${p}_{s}^{m\mathrm{\xe1}x}$ [%]) | (-) | (−8%) | (−15%) | (−2%) |

Equivalent Thickness: e [mm] | 200 | 206 | 214 | 283 |

(Δe [%]) | (-) | (3%) | (7%) | (42%) |

IR0 | IR20 | IR50 | IR100 | |
---|---|---|---|---|

K_{s} [MPa/m] | 636 | 697 | 766 | 653 |

(ΔK_{s} [%]) | (-) | (10%) | (20%) | (3%) |

Equivalent Thickness: e [mm] | 200 | 224 | 255 | 290 |

(Δe [%]) | (-) | (12%) | (28%) | (45%) |

Cost Range [€/m ^{3}] | Cost Adopted | |||
---|---|---|---|---|

[€/m^{3}] | [%] | |||

Equipment | 16 to 20 | 18 | 13 | |

Cement and Fly Ash | 45 to 50 | 47.5 | 34 | |

Labour | 30 to 40 | 35 | 25 | |

Additives | 17 to 23 | 20 | 14 | |

Plasticizers | 4 to 5 | 4,5 | 3 | |

Natural Aggregates | 13 to 17 | 15 | 11 | |

Total | 140 | 100 |

CRCA Incorporation Ratio [%] | Thickness [mm] | Theoretical Volume [m^{3}/m] | Estimated Volume with Rebound Losses [m^{3}/m] | Shotcrete Cost Per Unit Volume [€/m^{3}] | Lining’s Cost Per Unit Length [€/m] | Variation [€/m] |
---|---|---|---|---|---|---|

Case 1—Similar stiffness criterion | ||||||

0 | 200 | 3.64 | 4.86 | 140.00 | 680.26 | - |

20 | 206 | 3.75 | 5.00 | 139.20 | 695.94 | +15.68 (2.3%) |

50 | 214 | 3.89 | 5.19 | 138.05 | 716.00 | +35.74 (5.3%) |

100 | 283 | 5.08 | 6.78 | 136.19 | 922.98 | +242.7 (35.7%) |

Case 2—Similar yield stress criterion | ||||||

0 | 200 | 3.64 | 4.86 | 140.00 | 680.26 | - |

20 | 224 | 4.06 | 5.42 | 139.20 | 754.40 | +74.14 (10.9%) |

50 | 255 | 4.60 | 6.14 | 138.05 | 847.13 | +166.87 (24.5%) |

100 | 290 | 5.20 | 6.94 | 136.19 | 944.66 | +264.40 (38.9%) |

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**MDPI and ACS Style**

Duarte, G.; Carrilho Gomes, R.C.; de Brito, J.d.; Bravo, M.; Nobre, J.
Economic and Technical Viability of Using Shotcrete with Coarse Recycled Concrete Aggregates in Deep Tunnels. *Appl. Sci.* **2020**, *10*, 2697.
https://doi.org/10.3390/app10082697

**AMA Style**

Duarte G, Carrilho Gomes RC, de Brito Jd, Bravo M, Nobre J.
Economic and Technical Viability of Using Shotcrete with Coarse Recycled Concrete Aggregates in Deep Tunnels. *Applied Sciences*. 2020; 10(8):2697.
https://doi.org/10.3390/app10082697

**Chicago/Turabian Style**

Duarte, Gonçalo, Rui Carrilho Carrilho Gomes, Jorge de de Brito, Miguel Bravo, and José Nobre.
2020. "Economic and Technical Viability of Using Shotcrete with Coarse Recycled Concrete Aggregates in Deep Tunnels" *Applied Sciences* 10, no. 8: 2697.
https://doi.org/10.3390/app10082697