# Comparison of Different Solutions for a Seismic and Energy Retrofit of an Auditorium

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}K (hot climate) to 0.26 W/m

^{2}K (cold climate); for basements, from 0.42 W/m

^{2}K to 0.28 W/m

^{2}K; for floors, from 0.32 W/m

^{2}K to 0.22 W/m

^{2}K and 0.80 W/m

^{2}K for partitions. Moreover, in terms of thermal inertia of the opaque envelope, on all sides except north, north-east and north-west, Y

_{IE}must be lower than 0.10 W/(m

^{2}K); for the floors, it must be lower than 0.18 W/(m

^{2}K).

## 2. The Case Study

#### 2.1. Description

^{2}. The “surface-to-volume ratio” (S/V) is equal to 0.65 m

^{−1}, and thus its shape factor indicates high heat gain/loss.

_{p}) are reported according to the standard UNI 10351 [20]. For non-homogenous floors, such as the concrete-brick one, the equivalent thermal resistance (R) has been considered. The proposed standard suggests the most reliable procedure for both research and design when measurements are not available. However, the proposed values have been verified by means of comparison with the materials used for buildings of the same construction period.

#### 2.2. Climatic Zone and Seismic Pericolosity

## 3. Assessment of the Structural Safety of the Auditorium As-Built

#### 3.1. Structural Configuration and In Situ Tests

^{2}), flat beams (section dimensions = 0.40 × 0.32 m

^{2}), and square columns (0.40 × 0.4 m

^{2}); the floors are made of cast-in-place RC and hollow clay bricks as lightening for a total height of 32 cm.

^{2}) supported by circular columns (diameter Φ 80 cm) and a steel-concrete composite floor.

#### 3.2. Numerical Analysis

^{2}was assigned to the floors to take into account the filling and the weight of the flowerbeds. Instead, to simulate the live load, a constant load of 4 kN/m

^{2}was considered.

_{cd}= 20.4/1.35 = 15 MPa and fyd = 306.7 MPa. Furthermore, a partial safety factor for the concrete equal to 1 and 1.5, respectively, for bending and shear stresses was applied. For the masonry, the experimental compressive strength was divided by FC = 1.2 and a partial safety factor of γ

_{M}= 3 in the case of gravity loads and γ

_{M}= 2 in the case of seismic assessment. The verification was carried out according to the provisions of the Italian Building Code [8] that are the same as Eurocode 8 [9].

## 4. Energy Performance Assessment

#### 4.1. Building Plant System Characterization

_{IE}), internal areal heat capacity (χ), decrement factor (f

_{a}), and time lag (ϕ) was calculated according to UNI EN ISO 13786 [26]. The composition of the floors is described in Table 2, Table 3 and Table 4; however, according to the structural assessment for the vertical wall with known thicknesses, the other properties were determined on the basis of the materials’ typology [22]:

- Circular masonry wall: 1. inner lime plaster (thickness 0.02 m, λ = 0.70 W/m K, c
_{p}= 1000 J/kg K); 2. tuff block (thickness 0.70 m, λ = 0.55 W/m K, c_{p}= 1000 J/kg K); 3. outer reinforced plaster (thickness 0.03 m, λ = 0.90 W/m K, c_{p}= 1000 J/kg K); - Plasterboard partitions facing the historic masonry wall: 1. inner lime plaster (thickness 0.02 m, λ = 0.70 W/m K, c
_{p}= 1000 J/kg K); 2. plasterboard (thickness 0.08 m, λ = 0.21 W/m K, c_{p}= 1090 J/kg K).

_{p}= 840 J/kg K); 2. cement mortar (thickness 0.03 m, λ = 1.40 W/m K, c

_{p}= 1000 J/kg K); 3. concrete slab (thickness 0.10 m, λ = 0.33 W/m K, c

_{p}= 1000 J/kg K); 4. preexisting rock (thickness 0.50 m, λ = 1.20 W/m K, c

_{p}= 1000 J/kg K).

^{2}K).

^{2}K: for the basement—0.38 W/m

^{2}K, for the floors—0.32 W/m

^{2}K, and for the partitions—0.80 W/m

^{2}K [5].

#### 4.2. Dynamic Energy Simulation

- Heating Coil

_{min}is the minimum thermal capacitance between water and air, and T

_{w,in}and T

_{air,in}are the temperatures of water and air, respectively, entering in the heat exchanger. Then, the real heat that can be transferred between the fluids (${\dot{\mathrm{Q}}}_{\mathrm{HC}}$) is determined through the efficiency of the coil (ε).

- Cooling Coil

_{pb}is the bypass factor; and h

_{cond}is the enthalpy of the condensed water.

- Cross-Flow Heat Recovery

- Humidifier

_{Sat}) is the crucial parameter to determine the condition of the air at the component outlet.

- Boiler

_{w,set}) selected for the heated water and the system efficiency (η

_{B}). The power necessary to heat up the water is calculated as:

_{p,w}is its heat capacity, and T

_{w,in}is the temperature of the water entering the boiler.

- Air-Cooled Electric Chiller

_{ava}) in the current condition. The available cooling capacity is compared with the required capacity to reach the temperature selected for the chilled water:

_{ch,w,in}and T

_{ch,w,set}are the temperature of the water to be cooled and the set point one, respectively.

^{2}with LED lamps [31].

_{tr,i}) and the total heat losses due to energy transmission (Q

_{tr,tot}) for the winter season were evaluated. Similarly, for the summer period, this ratio was calculated considering the heat gains due to transmission through the opaque and glazed irradiated surfaces and the total heat gains due to energy transmission. The results are reported in Figure 10.

^{2}; this means that there is an important contribution of solar radiation on the opaque envelope, and its utilization is affected by thermal mass.

^{2}, whereas the opaque dispersing surface is 2196 m

^{2}. For this reason, the design of an intervention for the windows is not convenient from an energetic point of view. Similarly, the basement is characterized by very low heat losses during the winter, whereas the negative percentage for the summer period indicates that it contributes to reducing the heat gains and thus helps to reduce the cooling needs. For these reasons, it was not necessary to evaluate the intervention for this component.

^{2}. This result appears to be in good accordance with data reported in [32,33]. In more detail, the sensible energy need during the winter and summer period is, respectively, 17,314 kWh and 5824 kWh. These values are mainly related to the quality of the building envelope and confirm the results of the previous analysis. The refurbishment intervention should be focused mainly on the reduction of the heat losses because the thermal mass assures good summer performance. Moreover, the latent energy need is 4858 kWh and 18,927 kWh, respectively, for the winter and summer energy balance. This contribution is mainly due to the occupation rate, and only an intervention in the air-conditioning system can be decisive in its reduction.

## 5. Integrated Methodology for the Building Upgrading

#### 5.1. Structural Upgrading

- (1)
- Analyze the dynamic response of the building to detect any irregularities;
- (2)
- Define the participation in the seismic resistance of the structure of each structural element;
- (3)
- Define interventions, including the modification of existing elements and the introduction of new structural elements to improve the distribution of seismic actions and optimize the contribution of each element;
- (4)
- Local strengthening of structural elements.

#### 5.2. Energy Upgrading

- -
- Wall insulation: application of 5 cm of wooden fiber insulation (density = 160 kg/m
^{3}; λ = 0.038 W/m K, cp = 2100 J/kg K) on the external side of the tuff masonry wall (TM) and 10 cm on the reinforced concrete wall (RCW); - -
- Floor insulation: application of panels of extruded polystyrene insulation (density = 35 kg/m
^{3}; λ = 0.035 W/m K, cp = 1450 J/kg K) with a thickness of 10.0 cm for floor B (FB) and floor C (FC) and 8.0 cm for floor A (FA); - -
- Partition insulation (PI): installation of brick blocks (30 cm) with integrated insulation (λ = 0.06 W/m K, cp = 1000 J/kg K);
- -
- Heat recovery unit (HR): installation of cross-flow heat recovery unit (efficiency 0.65) that allows heat recovery without any contact, direct or not, between the air fluxes.

_{IE}); the weight of reduction of heat losses for transmission during the winter (∆Q

_{tr,winter}) and summer (∆Q

_{tr,summer}) of the i-component with respect to the global variation of the heat losses for transmission; the total primary energy saving (∆EP); and the reduction in the sensible (∆E

_{s}) balance during summer and winter.

_{tr,winter}and ∆Q

_{tr,summer}must be analyzed. With reference to the winter season, ∆Q

_{tr,winter}is the ratio between the difference of the losses due to thermal transmission on the building component before and after the refurbishment and the difference of the total thermal losses before and after the refurbishment on all elements. Similarly, ∆E

_{S,WINTER}indicates the variation of the sensible heat load compared with the base case. The analysis of Table 8 suggests, once again, that the most important intervention, considering the energy balance, is the floor insulation, since ∆E

_{s}is equal to −47% and −56%, respectively, in the winter and summer season. The insulation of the tuff wall reduced the sensible load by around -6.8% during the winter and −6.0% during the summer. The case of insulated brick blocks on the partition gave different results because it reduced the sensible load during the winter but increased the summer heat load. When the primary energy saving is considered, the contribution of the walls is negligible, whereas with the roof insulation, this reduction was −4.3%.

#### 5.3. Discussion on the Cost-Benefit of the Integrated Approach

^{2}.

^{3}, and the electricity cost is 0.20 EUR/kWh

_{el}.

## 6. Conclusions

- -
- The in situ investigation was finalized to assess the material/structural and the thermal/energy characteristics of the building alongside a complete survey and tests;
- -
- Defining the structural and energy simulation models for studying the weight of the building and plant components on the whole performance;
- -
- Analysis of technical measures for improving both the structural and energy performances step by step, considering the role of the various interventions both in terms of performance improvement and cost and loss aspects.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

ag | ground acceleration |

CE | Cost of Exercise (EUR/y) |

CI | Cost of Investment (EUR) or (EUR/m^{2}) |

C | Thermal Capacitance (kJ/s K) |

COP | Coefficient of Performance (-) |

c_{p} | Specific Heat (kJ/kg K) |

Cu | Usage coefficient |

C/D | capacity/demand ratio |

f_{a} | Decrement factor (-) |

f_{bp} | Bypass factor (-) |

f_{cd} | Compressive concrete strength (MPa) |

FFLP | Fraction of Full Load Power (-) |

f_{yd} | Steel yielding strength (MPa) |

F0 | Maximum amplification factor |

h | Enthalpy (kJ/kg) |

$\dot{\mathrm{m}}$ | Mass flow rate (kg/s) |

M_Ux | Modal participating mass ratio in X direction |

M_Uy | Modal participating mass ratio in Y direction |

M_Uz | Modal participating mass ratio in Z direction |

$\dot{\mathrm{P}}$ | Power (kW) |

PLR | Partial Load Ratio (-) |

$\dot{\mathrm{Q}}$ | Heat transfer or Capacity (kW) |

R | Thermal Resistance (m^{2} K/W) |

T | Temperature (°C) or (K) |

TR | Return period (y) |

U | Thermal transmittance (W/m^{2}K) |

Y_{IE} | Periodic thermal transmittance (W/m^{2}K) |

Greek symbols | |

ΔCE | Reduction of the Exercise Cost (%) |

∆EP | Total Primary Energy Saving (%) |

∆E_{s} | Reduction of the Sensible Load (%) |

∆Q_{tr} | Reduction of Heat Losses for Transmission (%) |

∆U | Variation of the insulation level (%) |

∆Y_{IE} | Variation of thermal inertia (%) |

ε | Efficiency (-) |

η | Efficiency (-) |

λ | Thermal conductivity (W/m K) |

ϕ | Time lag (h) |

χ | Internal areal heat capacity (kJ/m^{2} K) |

ω | Humidity ratio (kg_{vapor}/kg_{air}) |

Subscripts | |

air | Air |

ava | Available |

B | Boiler |

CFHR | Cross-Flow Heat Recovery |

CH | Chiller |

ch | Chilled |

cold | Cold |

cond | Condensed vapor |

cool | Cooling |

el | Electric |

fuel | Of the Fuel |

HC | Heating Coil |

i | i-th element |

in | Inlet |

max | Maximum |

met | Load Met |

min | Minimum |

mix | Mixing condition |

need | Necessary |

out | Outlet |

rej | Rejected |

req | Required |

Sat | Saturation |

set | Set point |

summer | During summer |

tot | Total |

w | Water |

warm | Warm |

wb | Wet Bulb |

winter | During winter |

Acronyms | |

FA | Floor Type A |

FB | Floor Type B |

FC | Floor Type C |

INAF | National Institute of Astrophysics |

PI | Partition Insulation |

RC | Reinforced Concrete |

RCW | Reinforced Concrete walls |

SLV | Life-Safety Limit State |

S/V | Surface-to-Volume ratio |

TM | Tuff Masonry |

ULS | Ultimate Limit State |

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Layer | Thickness (m) | Specific Weight (kN/m^{3}) | Conductivity (W/m K) | Specific Heat (J/kg K) |
---|---|---|---|---|

brick | 0.28 | 8 | R = 0.35 m^{2} K/W | 1000 |

RC joist | 0.28 | 25 | ||

RC slab | 0.04 | 25 | ||

screed | 0.02 | 19 | 0.58 | 1000 |

filling | 0.5 | 18 | 1.41 | 1000 |

tiled floor | 0.02 | 20 | 1.30 | 840 |

Layer | Thickness (m) | Specific Weight (kN/m^{3}) | Conductivity (W/m K) | Specific Heat (J/kg K) |
---|---|---|---|---|

corrugated sheet | 0.0006 | 155 | 460 | |

RC slab | 0.18 | 25 | 1.91 | 1000 |

screed | 0.02 | 19 | 0.58 | 100 |

filling | 0.5 | 18 | 1.41 | 1000 |

tiled floor | 0.02 | 20 | 1.30 | 840 |

Layer | Thickness (m) | Specific Weight (kN/m^{3}) | Conductivity (W/m K) | Specific Heat (J/kg K) |
---|---|---|---|---|

RC slab | 0.20 | 25 | 1.91 | 1000 |

screed | 0.02 | 19 | 0.58 | 1000 |

filling | 0.5 | 18 | 1.41 | 1000 |

tiled floor | 0.02 | 20 | 1.30 | 840 |

Spectrum | ag (m/s^{2}) | F_{0} (-) | T*c (s) | S_{S} (-) | S_{T} (-) | TB (s) | TC (s) | TD (s) |
---|---|---|---|---|---|---|---|---|

Horizontal | 1.88 | 2.41 | 0.34 | 1.20 | 1.20 | 0.15 | 0.46 | 2.37 |

Vertical | 1.88 | 2.41 | 0.34 | 1.00 | 1.20 | 0.05 | 0.15 | 1.00 |

Envelope Components | U (W/m^{2} K) | Y_{IE} (W/m^{2} K) | f_{a} (-) | φ (h) | χ (kJ/m^{2} K) |
---|---|---|---|---|---|

FLOOR A | 1.12 | 0.008 | 0.007 | >24 | 84.0 |

FLOOR B | 1.57 | 0.052 | 0.033 | 19.3 | 97.5 |

FLOOR C | 1.54 | 0.045 | 0.029 | 19.8 | 97.1 |

TUFF MASONRY WALL | 0.66 | 0.003 | 0.005 | >24 | 59.0 |

R.C. WALL | 1.71 | 0.082 | 0.047 | 16.8 | 69.7 |

PARTITION | 1.49 | 1.19 | 0.797 | >24 | 48.5 |

BASEMENT | 0.91 | 0.009 | 0.010 | >24 | 59.4 |

Simulation Models | Type | Library | Main Parameters |
---|---|---|---|

Building | 56 | Standard | As Table 5 |

Heating Coil | 670 | TESS | c_{p,w}: 4.19 kJ/kg K; ε: 0.864 |

Cooling Coil | 508d | TESS | c_{p,w}: 4.19 kJ/kg K;f _{bp}: 0.177 |

Cross-Flow Heat Recovery | 760 | TESS | ε: 0.650 |

Humidifier | 506a | TESS | ε_{Sat}: 0.551 |

Fun | 644 | TESS | ${\dot{\mathrm{m}}}_{\mathrm{air}}$: 2.74 kg/s |

Pump | 110 | Standard | ${\dot{\mathrm{m}}}_{\mathrm{w}}$: 6.5 kg/s (chiller), 1.55 kg/s (boiler) |

Natural Gas Boiler | 700 | TESS | ${\dot{\mathrm{Q}}}_{\mathrm{B}}$ = 75.0 kW η _{B}: 90% |

Air-Cooled Chiller | 655 | TESS | ${\dot{\mathrm{Q}}}_{\mathrm{CH}}$: 137 kW Rated COP: 2.46 |

Structural Upgrading | Period [s] and Partecipating Mass Ratios (%) | Percentage of Base Reaction (%) | C/D Ratio | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

T | M Ux | M Uy | M Rz | r.c. | Masonry | r.c. | Bending | Shear | Masonry | Bending | Shear | ||

Step 1:As-built | 0.120 | 19 | 53 | 20 | X | 40 | 58 | W-A | 0.56 | 0.48 | M1 | 1.99 | 1.12 |

W-B | 1.09 | 0.97 | M2 | 1.92 | 0.33 | ||||||||

W-C | 0.49 | 3.02 | M3 | 4.77 | 0.62 | ||||||||

0.090 | 67 | 25 | - | W-D | 1.08 | 0.49 | M4 | 2.87 | 0.80 | ||||

Y | 37 | 59 | W-E | 0.15 | 0.44 | M5 | 2.63 | 0.45 | |||||

0.050 | 5 | 12 | 60 | M6 | 6.58 | 0.80 | |||||||

M7 | 7.90 | 0.70 | |||||||||||

Step 2: Splitting ofthe E-shape RC wall | 0.130 | 26 | 45 | 20 | X | 35 | 61 | W-A | 0.55 | 0.47 | M1 | 1.73 | 1.52 |

W-B | 1.15 | 1.01 | M2 | 1.86 | 0.73 | ||||||||

W-C | 0.68 | 2.15 | M3 | 2.75 | 1.08 | ||||||||

0.090 | 55 | 35 | - | W-D | 1.27 | 0.42 | M4 | 2.51 | 1.30 | ||||

Y | 39 | 58 | W-E1 | 0.43 | 0.60 | M5 | 5.19 | 0.57 | |||||

W-E2 | 0.61 | 0.61 | M6 | 6.39 | 0.76 | ||||||||

0.050 | 3 | 5 | 21 | W-E3 | 0.54 | 0.71 | M7 | 14.17 | 0.74 | ||||

W-E4 | 1.28 | 0.87 | |||||||||||

Step 3: Addition ofa new RC wall | 0.095 | 85 | - | 4 | X | 38 | 58 | W-A | 1.88 | 1.79 | M1 | 2.42 | 0.98 |

W-B | 1.10 | 0.87 | M2 | 5.01 | 0.70 | ||||||||

W-C | 0.67 | 2.97 | M3 | 2.62 | 0.72 | ||||||||

0.070 | - | 90 | - | W-D | 0.99 | 0.54 | M4 | 2.66 | 0.85 | ||||

Y | 52 | 38 | W-E1 | 0.61 | 0.85 | M5 | 10.94 | 0.80 | |||||

W-E2 | 0.80 | 0.79 | M6 | 7.00 | 0.83 | ||||||||

0.040 | 3 | - | 67 | W-E3 | 0.69 | 0.86 | M7 | 9.88 | 0.59 | ||||

W-E4 | 1.20 | 0.60 | |||||||||||

Step 4: Addition of a new masonry wall made by brick blocks with integrated insulation | 0.076 | 76 | 11 | 2 | X | 34 | 56 | W-A | 2.26 | 1.92 | M1 | 3.53 | 1.28 |

W-B | 1.26 | 1.30 | M2 | 5.39 | 0.79 | ||||||||

W-C | 1.56 | 3.30 | M3 | 2.63 | 0.80 | ||||||||

0.074 | 12 | 70 | - | W-D | 1.64 | 0.89 | M4 | 3.40 | 1.12 | ||||

Y | 52 | 37 | W-E1 | 1.13 | 1.23 | M5 | 11.61 | 1.00 | |||||

W-E2 | 1.33 | 1.14 | M6 | 6.83 | 1.05 | ||||||||

0.05 | 1 | - | 26 | W-E3 | 1.29 | 2.10 | M7 | 17.54 | 0.87 | ||||

W-E4 | 1.57 | 0.75 | |||||||||||

Step 5: Local strenghteningwith FRP and FRCM | 0.076 | 76 | 11 | 2 | X | 34 | 56 | W-A | 2.26 | 1.92 | M1 | 3.53 | 1.98 |

W-B | 1.26 | 1.30 | M2 | 5.39 | 1.33 | ||||||||

W-C | 1.56 | 3.30 | M3 | 2.63 | 1.33 | ||||||||

0.074 | 12 | 70 | - | W-D | 1.64 | 1.28 | M4 | 3.40 | 1.72 | ||||

Y | 52 | 37 | W-E1 | 1.13 | 1.23 | M5 | 11.61 | 1.38 | |||||

W-E2 | 1.33 | 1.14 | M6 | 6.83 | 1.45 | ||||||||

0.050 | 1 | - | 26 | W-E3 | 1.29 | 2.10 | M7 | 17.54 | 1.04 | ||||

W-E4 | 1.57 | 1.03 |

Interventions | ∆U | ∆Y_{IE} | ∆Q_{TR,WINTER} | ∆Q_{TR,SUMMER} | ∆E_{S,WINTER} | ∆E_{S,SUMMER} | ∆EP |
---|---|---|---|---|---|---|---|

TM | −45% | −87% | −7% | −2% | −6.8% | −6.0% | −0.8% |

RCW | −82% | −96% | −2% | −2% | −1.7% | −0.5% | −0.4% |

PI | −88% | −99% | −5% | −7% | −7.1% | +20% | −2.1% |

FA | −71% | −95% | −33% | −34% | −47% | −56% | −4.3% |

FB | −78% | −94% | −33% | −34% | |||

FC | −78% | −96% | −20% | −21% |

Energy | Structure | Integrated | ||||
---|---|---|---|---|---|---|

CI | Total Cost | CI | Total Cost | CI | Total Cost | |

Existing masonry wall | 80 EUR/m^{2} | 22,800 EUR | 230 EUR/m^{2} | 131,250 EUR | 270 EUR/m^{2} | 142,600 EUR |

New masonry wall * | 80 EUR/m^{2} | 22,400 EUR | 68 EUR/m^{2} | 19,070 EUR | 90 EUR/m^{2} | 25,200 EUR |

Roof | 107 EUR/m^{2} | 96,500 EUR | - | - | - | - |

Heat recovery unit | 4500 EUR | 4500 EUR | - | - | - | - |

RC walls | 80 EUR/m^{2} | 3370 EUR | 175 EUR/m^{2} | 1290 EUR | 215 EUR/m^{2} | 3400 EUR |

All | 149,657 EUR | 151,610 EUR | 272,200 EUR |

Interventions | CE (EUR) | ∆CE |
---|---|---|

EXISTING MASONRY AND RC WALLS | 14,421 | −0.82% |

NEW MASONRY WALLS | 14,334 | −1.45% |

ROOF | 14,109 | −3.0% |

HEAT RECOVERY UNIT | 13,790 | −5.20% |

ALL | 12,374 | −15% |

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## Share and Cite

**MDPI and ACS Style**

De Angelis, A.; Tariello, F.; De Masi, R.F.; Pecce, M.R.
Comparison of Different Solutions for a Seismic and Energy Retrofit of an Auditorium. *Sustainability* **2021**, *13*, 8761.
https://doi.org/10.3390/su13168761

**AMA Style**

De Angelis A, Tariello F, De Masi RF, Pecce MR.
Comparison of Different Solutions for a Seismic and Energy Retrofit of an Auditorium. *Sustainability*. 2021; 13(16):8761.
https://doi.org/10.3390/su13168761

**Chicago/Turabian Style**

De Angelis, Alessandra, Francesco Tariello, Rosa Francesca De Masi, and Maria Rosaria Pecce.
2021. "Comparison of Different Solutions for a Seismic and Energy Retrofit of an Auditorium" *Sustainability* 13, no. 16: 8761.
https://doi.org/10.3390/su13168761