# Comparison of Different Intervention Options for Massive Seismic Upgrading of Essential Facilities

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

- the decision matrix
**D**= [x_{ij}] (rectangular n×m, where n is the number of options and m is the number of judgment criteria, in which the generic column represents the performance of the i-th option with respect to the j-th criterion). - the criteria weight vector
**W**, which represents the importance that the decision maker gives to each judgment criterion.

**Step 1**: Construction of the normalized decision matrix

**R**= [r

_{ij}].

_{ij}values in the decision matrix

**D**have to be normalized to form the matrix

**R**= [r

_{ij}]. The normalized value r

_{ij}is calculated as follows:

**Step 2**: Construction of the weighted normalized decision matrix

**V**= [v

_{ij}].

_{j}of the j-th judgement criterion. The weighted normalized value v

_{ij}is calculated as follows:

**Step 3**: Identification ideal solution A

^{*}and negative-ideal solution A

^{−}.

^{*}is determined by considering for each criterion the best performance value among the intervention options. On the other side, the negative-ideal solution A

^{−}is obtained by considering for each criterion the worst performance measure among the options.

**Step 4**: Calculation of the distance of each intervention option A

_{i}from the two “virtual” options A

^{*}and A

^{−}.

**Step 5**: Determination of the relative closeness C

_{i}

^{*}to the ideal solution A

^{*}.

_{i}with respect to A

^{*}is defined as follows:

_{i}

^{*}values, a ranking of the retrofit interventions can be defined. In particular, the optimal intervention is the one with the highest C

_{i}

^{*}value, that is, the intervention option having the shortest distance from the ideal solution and the farthest distance from the negative-ideal solution. Finally, a sensitivity analysis of the results can be carried out to check if the selected solution is also sufficiently stable.

_{1}, C

_{2}, and C

_{3}criteria, which represent the seismic risk mitigation.

_{4}gives a preliminary estimate (US dollar) of the total cost of the considered retrofitting techniques. Furthermore, the demolitions and subsequent renovations costs (partitions, infill panels, doors, etc.) are also considered.

_{5}criterion considers the different aspects related to planning and safety in the construction site operations. For each intervention option, these aspects are assessed according to a Risk Level (RL) defined using Equations (8) and (9).

_{i}) associated with each required activity can be evaluated as follows:

_{6}criterion assesses whether the retrofit intervention involves the removal of students in adjacent classrooms and/or the complete shift of teaching activities in other structures. This criterion aims to avoid costs that are not strictly related to the intervention, such as the costs associated with the movement of occupants in other structures, therefore, a retrofit technique generating less perturbative effects should be preferred. Consequently, the intervention options in which the adjustment works are concentrated in areas that interfere as little as possible with the teaching activities have been preferred.

_{7}criterion estimates the maintenance operations to be performed during the normal life of the structure in the post-intervention phase to preserve the buildings. It describes the exposure to physical and chemical degradation phenomena for each retrofitting technique.

_{8}criterion analyzes the possibility of oversaw the various activities and work processes for each retrofitting technique. Its purpose is to prevent thecorruption and poor execution and management of the work carried out affecting the construction industry. These aspects involve serious irregularities in the execution of the work and in the quantity and quality of the materials used.

_{9}criterion compares the intervention options in terms of aesthetic and functional compatibility (i.e., with the normal activities of the building users). In other words, it evaluates the architectural impact resulting in the installation of the generic retrofit solution. This criterion is very important to ensure the normal activities of the building occupants during the execution of the works.

_{10}criterion considers the different impediments associated with the realization of each intervention option (availability of skilled labor, materials, and technologies) to realize and guarantee a very good final work. In other words, this criterion considers the amount of qualified workforce and skilled technology necessary for the realization of the considered retrofitting techniques. Some techniques require more skilled labor, materials, and technologies than traditional interventions. Generally, these features could be more difficult to find.

_{11}criterion analyzes the production process for each retrofitting technique to maximize the reduction of seismic risk in the areas studied. Retrofit interventions on a considerable number of buildings involve significant industrial needs for real and effective implementation of the mitigation strategies. It is therefore more appropriate to select retrofitting techniques that lend themselves better to their industrial reproducibility to reduce installation times and costs, as well as to guarantee the maximum safety and reliability of the intervention carried out.

## 3. Retrofitting Strategies for School Buildings in Lima

^{2}of extension and a population of about 10 million. Monumental and cultural heritages are widespread and scattered acrossthe city, and the originality of its historic center has earned the award of World Heritage Site by UNESCO in 1988.

- Zone I (S
_{1}) corresponds to hard ground or rock. This area has nolocal amplification. - Zone II (S
_{2}) consists of fine granular soils and colluvial and alluvial clay soils on gravel. This area has moderate amplification effects. - Zone III (S
_{3}) corresponds to sandy soil without the presence of water. The soils in this area are very durable but have important effects of amplification. - Zone IV (S
_{4}) is formed by sandy soil with water. - Zone V (S
_{5}) comprises filler soil.

_{4}and S

_{5}, there are very important amplifications that can even lead to structural instability of buildings due to the liquefaction phenomenon. Fortunately, in S

_{5}there are no schools.

#### 3.1. Buildings Descriptions

_{cm}has been set to 17.50MPa and the mean value of steel yield strength f

_{ym}has been set to 420MPa, while for masonry walls and infill panels, the relevant compressive strength f

_{m}has been assumed equal to 4MPa. Information on amount and detailing of reinforcement in the structural members can be found in Figure 3c.

#### 3.2. Retrofitting Methods

- A
_{1}—Compound walls. - A
_{2}—Steel bracing. - A
_{3}—RC walls. - A
_{4}—Cable bracing system.

_{p}= 0.60) was used as seismic demand.

#### 3.2.1. Intervention A_{1}—Compound Walls

_{1}consists ofcreating opportune confined masonry walls covered on both sides with plaster reinforced with welded wire mesh that jacket each side of the original columns 30 × 45 cm. The jacketing of all these elements creates three compound walls in each of the two longitudinal frames (one for each column 30 × 45 cm). In the upgrading design, the compressive strength of concrete and masonry was assumed equal to 21MPa and 4MPa, respectively, while the yield steel strength was set to 420MPa. This technique allows enhancing the resistance and ductility of the initial structure; obviously with this rehabilitation system, the overall failure of the structure is related to the maximum displacement of the compound walls. Its main advantage is the low cost and ease of construction. Figure 4 shows the schematic view for this intervention.

#### 3.2.2. Intervention A_{2}—Steel Bracing

_{2}consists of placing three steel frames with concentric bracing in each of the two longitudinal frames. The steel frames have cross-section W200 × 135 × 26.6 while the bracings have square hollow section 60 × 60 × 5. The latter are welded to the steel frames, which are connected to the RC frame using shear connectors. All the elements are made of S355 steel. This technique enhances the overall performance of the structure in terms of resistance and ductility, and its failure is related to the flexure failure of RC columns. The main benefit of this reinforcement is the fast installation time, while its disadvantage is the high cost. Figure 5 shows the schematic view for the retrofitting intervention.

#### 3.2.3. Intervention A_{3}—RC Walls

_{3}consists of reinforcing three continues columns in each of the two longitudinal frames, increasing the central column size, and converting the adjacent ones into concrete walls. In designing the reinforced concrete jacketing, the compressive strength of the concrete and the yield strength of reinforcing bars were assumed equal to 21MPa and 420MPa, respectively. This technique requires the reinforcement of the footings for the new walls due to the increase in axial forces during seismic actions [21]. Its main advantage is the great increase in the performance of the structure in terms of stiffness, resistance, and ductility. In addition, it allows to improve the beam-column joints. However, some problems are the need of competent manpower to carry out the reinforcement works, and the time required to perform the intervention. Figure 6 shows the schematic view for the retrofitting intervention.

#### 3.2.4. Intervention A_{4}—Cable Bracing System

_{4}involves the installation of an innovative cable bracing system in each of the two longitudinal frames. In the structural meshes shown in Figure 7, two parallel cables are arranged in diagonal to maintain the openings in the braced fields. They are connected to the RC frame using steel plates in the beam-column joints and steel jackets in the adjacent structural elements.

#### 3.3. Structural Performance Evaluation, Fragility and Vulnerability Curves

_{p}). The latter has been definedby means of the yielding(u

_{y}) and ultimate axial displacement capacity (u

_{u}) of the equivalent truss element (u

_{p}= u

_{u}– u

_{y}), considering a drift yield and ultimate of 1.25‰ and 5‰, respectively. Internal diaphragm constraints have been assigned to all nodes of the same floor to consider the effective stiffness of the floors. In this study, the seismic performances of the foundations are neglected based on the large territorial scale and the available information. Moreover, moment-resisting frames are less sensitive to foundation movement and are often not significantly affected by soil-structure interaction (see for example [26]). Obviously, for planning the interventions, the retrofit cost of the foundation system has been preliminary estimated.

_{si}(slight, moderate, extensive, and complete) have been considered [27], which are coherent with first yielding, immediate occupancy, life safety, and collapse prevention described by existing codes [23,28]. The maximum interstory drift ratio (IDR) has been adopted as engineering demand parameter (EDP). Consequently, each damage state has been evaluated according to the displacement capacity of structural and non-structural elements (Table 2), interpreting the damage states description provided by existing regulations. In Figure 8, 3D models and collapse mechanisms in the longitudinal direction are reported. The obtained capacity curves are reported in Figure 9.

_{i}for a specific level of IM (in this case PGA); $D{F}_{{{\displaystyle ds}}_{i}}$ is the mean damage factor value consequent to the attainment of a given damage state ds

_{i}(Table 4). Conceptually, these damage factor values should be developed based on data collected from studies on specific buildings in Lima. Other values could be applied with great care to avoid gross errors due to the different buildings design practices in other parts of the world, which could be significantly different from those of Lima. Nevertheless, for a first application of the proposed methodology the above assumption was made.

#### 3.4. Seismic Risk Assessments

## 4. Selection of the Optimal Rehabilitation System

**D**= [x

_{ij}] is shown in Table 7.

_{1,}C

_{2}, C

_{3}), the installation cost (C

_{4}), and the functional and architectural compatibility (C

_{9}) have been considered predominant in order to prefer retrofitting intervention having better performance in terms of seismic risk mitigation, costs, and compatibility. As shown in Table 8, the most relevant criteria for the decision about seismic retrofitting are the criteria C

_{1}, C

_{2}, C

_{3}, and C

_{4}(a

_{1k}= a

_{2k}= a

_{3k}= a

_{4k}≥ 1, k = 1,..., 11). They have been judged to be slightly more important than criterion C

_{9}(a

_{19}= a

_{29}= a

_{39}= a

_{49}= 2), and moderately more important than criterion C

_{8}(a

_{18}= a

_{28}= a

_{38}= a

_{48}= 3).Criterion C

_{5}, regarding the safety in construction site operations, has been assumed less important than the others (a

_{5k}≤ 1, k = 1,..., 11) for the reasons above, even if the retrofitting intervention involves a higher level of risk in construction site. This criterion has been considered slightly less important than criterion C

_{7}(a

_{57}= 1/2), and moderately less important than criterion C

_{11}(a

_{28}= 1/3).The criteria concerning the visual inspection (C

_{8}), disruption of use (C

_{6}), and technology level and feasibility (C

_{10}) have been also considered important in the decision-making process, because their lack of consideration would involve additional time, cost, and disruption to be sustained. They have been judged to be between significantly important and significantlymore important (a

_{85}= 6), significantlymore important (a

_{65}= 5), and between significantlyand moderately more important than criterion C

_{2}(a

_{105}= 4), respectively. In Table 9, the criteria weight vector

**W**is presented.

**D**= [x

_{ij}] and the criteria weight vector

**W**, the TOPSIS method has been applied and a ranking of the compared retrofitting interventions has been defined. More specifically, using Equation (1) the normalized decision matrix

**R**= [r

_{ij}] is built (Table 10) and then using Equation (2), the weighted normalized decision matrix

**V**= [v

_{ij}] is defined (Table 11). According this matrix, using Equations (3) and (4) the ideal solution A

^{*}and the negative-ideal solution A

^{−}are obtained (Table 12).

_{i}

^{*}values, the following classification is obtained: A

_{4}> A

_{1}> A

_{2}> A

_{3}; therefore, the fourth retrofitting technique (C

_{i}

^{*}=0.723) is the optimal solution. A sensitivity analysis has been carried out to evaluate the stability of the optimal solution. This analysis consists of varying the weight of each criterion for evaluating whether there is a change in the top of the options ranking. It allows to assess how sensitive is the options ranking to small changes in criteria weights. According to the sensitivity analysis of the results, the optimal solution is also sufficiently stable.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Anelli, A.; Santa-Cruz, S.; Vona, M.; Tarque, N.; Laterza, M. A proactive and resilient seismic risk mitigation strategy for existing school buildings. Struct. Infrastruct. Eng.
**2018**, 15, 137–151. [Google Scholar] [CrossRef] - Liguori, N.; Tarque, N.; Bambarén, C.; Spacone, E.; Viveen, W.; De Filippo, G. Hospital treatment capacity in case of seismic scenario in the Lima Metropolitan area, Peru. Int. J. Disaster Risk Reduct.
**2019**, 38, 101196. [Google Scholar] [CrossRef] - Santa-Cruz, S.; Palomino, J.; Liguori, N.; Vona, M.; Tamayo, R. Seismic Risk Assessment of Hospitals in Lima City Using GIS Tools. In Computational Science and Its Applications—ICCSA 2017; Lecture Notes in Computer Science; Gervasi, O., Murgante, B., Misra, S., Stankova, E., Torre, C.M., Rocha, A.M.A.C., Taniar, D., Apduhan, B.O., Tarantino, E., Ryu, Y., et al., Eds.; Springer: Cham, Switzerland, 2017; Volume 10406, pp. 354–367. [Google Scholar]
- Vona, M.; Anelli, A.; Mastroberti, M.; Murgante, B.; Santa-Cruz, S. Prioritization strategies to reduce the seismic risk of the public and strategic buildings. Disaster Adv.
**2017**, 10, 1–15. [Google Scholar] - Santa-Cruz, S.; Fernandez De Córdova, G.; Rivera Holguin, M.; Vilela, M.; Arana, V.; Palomino, J. Social sustainability dimensions in the seismic risk reduction of public schools: A case study of Lima, Peru. Sustain. Sci. Pr. Policy
**2016**, 12, 34–46. [Google Scholar] [CrossRef] - Ambraseys, N.; Bilham, R. Corruption kills. Nature
**2011**, 469, 153–155. [Google Scholar] [CrossRef] [PubMed] - Bilham, R. The seismic future of cities. Bull. Earthq. Eng.
**2009**, 7, 839–887. [Google Scholar] [CrossRef][Green Version] - Kabir, G.; Sadiq, R.; Tesfamariam, S. A review of multi-criteria decision-making methods for infrastructure management. Struct. Infrastruct. Eng.
**2014**, 10, 1176–1210. [Google Scholar] [CrossRef] - Formisano, A.; Castaldo, C.; Chiumiento, G. Optimal seismic upgrading of a reinforced concrete school building with metal-based devices using an efficient multi-criteria decision-making method. Struct. Infrastruct. Eng.
**2017**, 13, 1373–1389. [Google Scholar] [CrossRef] - Caterino, N.; Cosenza, E. A multi-criteria approach for selecting the seismic retrofit intervention for an existing structure accounting for expected losses and tax incentives in Italy. Eng. Struct.
**2018**, 174, 840–850. [Google Scholar] [CrossRef] - Santa-Cruz, S.; Brioso, X.; Córdova-Arias, C. Selection of seismic reinforcement techniques through a multi-criteria methodology and BIM tools to improve transparency. In Proceedings of the 11th National Conference on Earthquake Engineering 2018 (11NCEE): Integrating Science, Engineering, & Policy, Los Angeles, CA, USA, 25–29 June 2018. [Google Scholar]
- Saaty, T.L. The Analytic Hierarchy Process; McGraw-Hill: New York, NY, USA, 1980. [Google Scholar]
- Saaty, T.L. Decision Making for Leaders: The Analytic Hierarchy Process for Decision in a Complex World; RWS Publications: Pittsburgh, PA, USA, 1999. [Google Scholar]
- Hwang, C.L.; Yoon, K. Multiple Attribute Decision Making. Lecture Notes in Economics and Mathematical Systems; Springer: Berlin, Germany, 1981. [Google Scholar]
- UNI 10942. Building Site–Safety Plans–Guideline for Safety and Coordination Plans; Ente Nazionale Italiano di Unificazione: Milan, Italy, 2001. [Google Scholar]
- Anelli, A.; Santa-Cruz, S.; Vona, M.; Laterza, M. Spatial analysis and ranking for retrofitting of the school network in Lima, Peru. In Computational Science and Its Applications—ICCSA 201; Lecture Notes in Computer Science; Gervasi, O., Murgante, B., Misra, S., Stankova, E., Torre, C.M., Rocha, A.M.A.C., Taniar, D., Apduhan, B.O., Tarantino, E., Ryu, Y., et al., Eds.; Springer International Publishing: Cham, Switzerland, 2017; Volume 10405, pp. 310–325. [Google Scholar]
- Blondet, M.; Dueñas, M.; Loaiza, C.; Flores, R. Seismic Vulnerability of Informal Construction Dwellings in Lima, Peru: Preliminary Diagnosis. In Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, 1–6 August 2004. [Google Scholar]
- Puglia, R.; Vona, M.; Klin, P.; Ladina, C.; Masi, A.; Priolo, E.; Silvestri, F. Analysis of site response and building damage distribution due to the 31 October 2002 earthquake at San Giuliano di Puglia (Italy). Earthq. Spectra.
**2013**, 29, 497–526. [Google Scholar] [CrossRef] - World Bank. Proposed Update of the National Building Regulations to Incorporate the Incremental Reinforcement in Type 780 School Buildings Built Before 1997; World Bank: Lima, Peru, 2016. [Google Scholar]
- Standard E030. Norma Técnica Peruana E.030 Diseño Sismorresistente; Ministerio de Vivienda, Construcción y Saneamiento: Lima, Peru, 2016. (In Spanish) [Google Scholar]
- Loa, G.; Muñoz, A.; Santa-Cruz, S. Seismic evaluation of incremental seismic retrofitting techniques for typical Peruvian schools. In Proceedings of the ASCE Structures Congress 2017, Denver, CO, USA, 6–8 April 2017. [Google Scholar]
- Standard E070. Norma Técnica Peruana E.070 Albañilería; Ministerio de Vivienda, Construcción y Saneamiento: Lima, Peru, 2006. (In Spanish) [Google Scholar]
- CEN. Eurocode 8: Design of Structures for Earthquake Resistance—Part 3: Assessment and Retrofitting of Buildings; European Standard EN 1998-3-2005; European Committee for Standardization: Brussels, Belgium, 2005. [Google Scholar]
- Borzi, B.; Vona, M.; Masi, A.; Pinho, R.; Pola, D. Seismic demand estimation of RC frame buildings based on simplified and nonlinear dynamic analyses. Earthq. Struct.
**2013**, 4, 157–179. [Google Scholar] [CrossRef] - CSI. Computer program SAP2000 (Version 17); CSI Inc.: Walnut Creek, CA, USA, 2014. [Google Scholar]
- FEMA P-58-1. Seismic Performance Assessment of Buildings: Volume 1–Methodology; Applied Technology Council: Redwood City, CA, USA, 2012. [Google Scholar]
- Vona, M.; Manganelli, B.; Tataranna, S.; Anelli, A. An Optimized Procedure to Estimate the Economic Seismic Losses of Existing Reinforced Concrete Buildings due to Seismic Damage. Buildings
**2018**, 8, 144. [Google Scholar] [CrossRef][Green Version] - ASCE/SEI 41-06. Seismic Rehabilitation of Existing Buildings; American Society of Civil Engineers: Reston, VA, USA, 2007. [Google Scholar]
- Rossetto, T.; Gehl, P.; Minas, S.; Galasso, C.; Duffour, P.; Douglas, J.; Cook, O. FRACAS: A capacity spectrum approach for seismic fragility assessment including record-to-record variability. Eng. Struct.
**2016**, 125, 337–348. [Google Scholar] [CrossRef] - Anelli, A.; Mori, F.; Vona, M. Fragility curves of the urban road network based on the debris distributions of interfering buildings. Appl. Sci.
**2020**, 10, 1289. [Google Scholar] [CrossRef][Green Version] - Ordaz, M.; Aguilar, A.; Arboleda, J. CRISIS2007 Ver 7.4. Mexico. 2007. Available online: https://ecapra.org/es/topics/crisis-2007. (accessed on 8 July 2020).
- IGP. Peru and the Mapping of Seismic Hazard; Geophysical Institute of Peru: Lima, Peru, 2012. [Google Scholar]
- Kramer, S.L. Geotechnical earthquake engineering; Prentice Hall International Series in Civil Engineering and Engineering Mechanics: Upper Saddle River, NJ, USA, 1996. [Google Scholar]
- ERN-AL. Site Effects 1.0.0. Evaluación de Riesgos Naturales—America Latina. Ciudad de México, Mexico. 2010. Available online: www.ecapra.org (accessed on 8 July 2020).
- ERN-AL. Comprehensive Approach for Probabilistic Risk Assessment (CAPRA). In Proceedings of the 14th European Conference on Earthquake Engineering, Ohrid, North Macedonia, 30 August–3 September 2010. [Google Scholar]
- Cardona, O.D.; Ordaz, M.; Reinoso, E.; Yamín, L.; Barbat, A. CAPRA—Comprehensive Approach to Probabilistic Risk Assessment: International Initiative for Risk Management Effectiveness. In Proceedings of the 15th World Conference on Earthquake Engineering 2012 (15WCEE), Lisbon, Portugal, 24–28 September 2012. [Google Scholar]

**Figure 8.**3D Finite Element model and collapse mechanisms in the longitudinal direction (weak direction) for the original building type (

**a**,

**b**) and for the retrofitting intervention A

_{1}(

**c**,

**d**), A

_{2}(

**e**,

**f**), A

_{3}(

**g**,

**h**), and A

_{4}(

**i**,

**j**).

**Figure 9.**Capacity curves of the examined structures in the longitudinal direction (weak direction) considering the forces distributions proportional to the first vibration mode (

**a**) and related to the structural masses (

**b**).

**Figure 10.**Fragility curves of the examined structures as built (

**a**), and reinforced by retrofitting intervention A

_{1}(

**b**), A

_{2}(

**c**), A

_{3}(

**d**), and A

_{4}(

**e**).

Judgement Criteria | Type | Associated With | |
---|---|---|---|

C_{1} | Reduction in expected loss for an occasional earthquake | Quantitative | Cost criterion |

C_{2} | Reduction in expected loss for a frequent earthquake | Quantitative | Cost criterion |

C_{3} | Reduction in expected annual loss | Quantitative | Cost criterion |

C_{4} | Installation cost | Quantitative | Cost criterion |

C_{5} | Safety in construction site operations | Quantitative | Cost criterion |

C_{6} | Disruption of use | Qualitative | Cost criterion |

C_{7} | Maintenance | Qualitative | Cost criterion |

C_{8} | Visual inspection | Qualitative | Benefit criterion |

C_{9} | Functional and architectural compatibility | Qualitative | Benefit criterion |

C_{10} | Technology level and feasibility | Qualitative | Benefit criterion |

C_{11} | Massive reproducibility | Qualitative | Benefit criterion |

**Table 2.**Damage States Definition for RC Frames According to the Displacement Capacity of Structural and Non-Structural Elements.

No Damage | Slight Damage | Moderate Damage | Extensive Damage | Complete Damage |
---|---|---|---|---|

SD = None | SD = None | SD = Low | SD = Significant | SD = Near Collapse |

NSD = None | NSD = Weak | NSD = Significant | NSD = Near Collapse | NSD = Collapse |

θ<θ_{y} | θ ≤ θ_{y} | θ_{y}<θ ≤ θ_{y}+0.25θ_{p} | θ_{y}+0.25θp <θ ≤ θ_{y}+0.75θ_{p} | θ_{y}+0.75θ_{p}<θ ≤ θ_{y}+θ_{p} |

v <v_{y} | v <v_{y} | v <v_{y} | v ≤ v_{y} | v ≥ v_{y} |

and | and | and | and | and |

u<u_{y} | u≤ u_{y} | u_{y}< u≤ u_{y}+u_{p} | u>u_{y}+u_{p} | u>u_{y}+u_{p} |

_{y}= yielding chord rotation capacity; θ

_{p}= plastic chord rotation capacity; v = shear displacement; v

_{y}= yielding shear displacement capacity; u = axial displacement; u

_{y}= yielding axial displacement capacity; u

_{p}= plastic axial displacement capacity.

Seismic Record | Local Date | Magnitude | Depth | Epicenter | PGA | Duration |
---|---|---|---|---|---|---|

(Mw) | (Km) | (g) | (Sec) | |||

Angol | 27 February 2010 | 8.8 | 30 | 36.29°S 73.24°W | 0.89 | 180 |

Arequipa | 23 June2001 | 8.4 | 32 | 16.36°S 73.48°W | 0.68 | 75 |

Concepcion | 27 February 2010 | 8.8 | 30 | 36.29°S 73.24°W | 0.51 | 180 |

Huaraz | 31 May 1970 | 7.9 | 45 | 9.40°S 78.90°W | 0.11 | 45 |

Lima | 17 October1966 | 8.1 | 38 | 10.70°S 78.70°W | 0.74 | 45 |

Lima | 3 October 1974 | 8.1 | 36 | 12.25°S 77.52°W | 0.80 | 90 |

Maule | 27February2010 | 8.8 | 30 | 36.29°S 73.24°W | 0.80 | 120 |

Pisco | 15 August2007 | 8.0 | 39 | 13.35°S 76.51°W | 0.57 | 120 |

Tarapaca | 13 June2005 | 7.8 | 116 | 19.99°S 69.20°W | 0.73 | 252 |

Tocopilla | 14 November2007 | 7.7 | 40 | 22.32°S 69.97°W | 0.74 | 60 |

DAMAGE SCALE | ||||
---|---|---|---|---|

Slight | Moderate | Extensive | Complete | |

DAMAGE FACTOR (DF)* | 2% | 10% | 43.5% | 100% |

Structural DF | 0.4% | 1.9% | 9.5% | 18.9% |

Acceleration Sensitive Non-Structural DF | 0.7% | 3.2% | 9.7% | 32.4% |

Drift Sensitive Non-Structural DF | 0.9% | 4.9% | 24.3% | 48.7% |

Total | 2% | 10% | 43.5% | 100% |

Expected Loss for an Occasional Earthquake | Expected Loss for a Frequent Earthquake | Expected Annual Loss | |
---|---|---|---|

($) | ($) | ($) | |

As Built | 142,871,808 | 41,033,804 | 12,849,902 |

Retrofit A_{1}—Compound Walls | 39,057,741 | 12,760,065 | 3,095,984 |

Retrofit A_{2}—Steel bracing | 34,237,128 | 9,956,375 | 2,552,567 |

Retrofit A_{3}—RC walls | 18,807,643 | 4,755,858 | 1,066,880 |

Retrofit A_{4}—Cable Bracing System | 23,309,648 | 4,249,501 | 1,056,047 |

Criterion | Retrofit Technique | A_{1} | A_{2} | A_{3} | A_{4} |
---|---|---|---|---|---|

Disruption of Use | A_{1} | 1 | 1/2 | 1/3 | 3 |

A_{2} | 2 | 1 | 1/2 | 4 | |

A_{3} | 3 | 2 | 1 | 5 | |

A_{4} | 1/3 | 1/4 | 1/5 | 1 | |

Maintenance | A_{1} | 1 | 1/5 | 1 | 1/4 |

A_{2} | 5 | 1 | 5 | 2 | |

A_{3} | 1 | 1/5 | 1 | 1/4 | |

A_{4} | 4 | 1/2 | 4 | 1 | |

Visual Inspection | A_{1} | 1 | 1/7 | 3 | 1/7 |

A_{2} | 7 | 1 | 9 | 1 | |

A_{3} | 1/3 | 1/9 | 1 | 1/9 | |

A_{4} | 7 | 1 | 9 | 1 | |

Functional and Architectural Compatibility | A_{1} | 1 | 2 | 4 | 1/5 |

A_{2} | 1/2 | 1 | 3 | 1/6 | |

A_{3} | 1/4 | 1/3 | 1 | 1/7 | |

A_{4} | 5 | 6 | 7 | 1 | |

Technology Level and Feasibility | A_{1} | 1 | 5 | 3 | 7 |

A_{2} | 1/5 | 1 | 1/4 | 3 | |

A_{3} | 1/3 | 4 | 1 | 5 | |

A_{4} | 1/7 | 1/3 | 1/5 | 1 | |

Massive Reproducibility | A_{1} | 1 | 1/5 | 1 | 1/7 |

A_{2} | 5 | 1 | 5 | 1/3 | |

A_{3} | 1 | 1/5 | 1 | 1/7 | |

A_{4} | 7 | 3 | 7 | 1 |

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | |
---|---|---|---|---|---|---|---|---|---|---|---|

A_{1} | 103,814,067 | 28,273,739 | 9,753,918 | 48,807 | 226 | 0.170 | 0.089 | 0.080 | 0.186 | 0.557 | 0.067 |

A_{2} | 108,634,680 | 31,077,429 | 10,297,335 | 66,322 | 325 | 0.284 | 0.504 | 0.440 | 0.117 | 0.109 | 0.283 |

A_{3} | 124,064,165 | 36,277,946 | 11,783,022 | 67,580 | 159 | 0.473 | 0.089 | 0.040 | 0.056 | 0.281 | 0.067 |

A_{4} | 119,562,160 | 36,784,303 | 11,793,855 | 58,407 | 223 | 0.073 | 0.318 | 0.440 | 0.641 | 0.054 | 0.582 |

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | |
---|---|---|---|---|---|---|---|---|---|---|---|

C_{1} | 1 | 1 | 1 | 1 | 8 | 4 | 7 | 3 | 2 | 5 | 6 |

C_{2} | 1 | 1 | 1 | 1 | 8 | 4 | 7 | 3 | 2 | 5 | 6 |

C_{3} | 1 | 1 | 1 | 1 | 8 | 4 | 7 | 3 | 2 | 5 | 6 |

C_{4} | 1 | 1 | 1 | 1 | 8 | 4 | 7 | 3 | 2 | 5 | 6 |

C_{5} | 1/8 | 1/8 | 1/8 | 1/8 | 1 | 1/5 | 1/2 | 1/6 | 1/7 | 1/4 | 1/3 |

C_{6} | 1/4 | 1/4 | 1/4 | 1/4 | 5 | 1 | 4 | 1/2 | 1/3 | 2 | 3 |

C_{7} | 1/7 | 1/7 | 1/7 | 1/7 | 2 | 1/4 | 1 | 1/5 | 1/6 | 1/3 | 1/2 |

C_{8} | 1/3 | 1/3 | 1/3 | 1/3 | 6 | 2 | 5 | 1 | 1/2 | 3 | 4 |

C_{9} | 1/2 | 1/2 | 1/2 | 1/2 | 7 | 3 | 6 | 2 | 1 | 4 | 5 |

C_{10} | 1/5 | 1/5 | 1/5 | 1/5 | 4 | 1/2 | 3 | 1/3 | 1/4 | 1 | 2 |

C_{11} | 1/6 | 1/6 | 1/6 | 1/6 | 3 | 1/3 | 2 | 1/4 | 1/5 | 1/2 | 1 |

Criterion Weight | ||
---|---|---|

Reduction in Expected Loss for an Occasional Earthquake | w_{C1} | 0.167 |

Reduction in Expected Loss for a Frequent Earthquake | w_{C2} | 0.167 |

Reduction in Expected Annual Loss | w_{C3} | 0.167 |

Installation Cost | w_{C4} | 0.167 |

Safety in Construction Site Operations | w_{C5} | 0.014 |

Disruption of Use | w_{C6} | 0.052 |

Maintenance | w_{C7} | 0.019 |

Visual Inspection | w_{C8} | 0.075 |

Functional and Architectural Compatibility | w_{C9} | 0.109 |

Technology Level and Feasibility | w_{C10} | 0.036 |

Massive Reproducibility | w_{C11} | 0.026 |

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | |
---|---|---|---|---|---|---|---|---|---|---|---|

A_{1} | 0.454 | 0.425 | 0.446 | 0.402 | 0.469 | 0.292 | 0.146 | 0.127 | 0.273 | 0.876 | 0.103 |

A_{2} | 0.475 | 0.467 | 0.470 | 0.546 | 0.675 | 0.489 | 0.827 | 0.700 | 0.172 | 0.171 | 0.432 |

A_{3} | 0.543 | 0.545 | 0.538 | 0.556 | 0.330 | 0.813 | 0.146 | 0.064 | 0.083 | 0.442 | 0.103 |

A_{4} | 0.523 | 0.552 | 0.539 | 0.481 | 0.463 | 0.125 | 0.522 | 0.700 | 0.943 | 0.085 | 0.890 |

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | |
---|---|---|---|---|---|---|---|---|---|---|---|

A_{1} | 0.076 | 0.071 | 0.075 | 0.067 | 0.007 | 0.015 | 0.003 | 0.009 | 0.030 | 0.032 | 0.003 |

A_{2} | 0.079 | 0.078 | 0.079 | 0.091 | 0.010 | 0.025 | 0.016 | 0.052 | 0.019 | 0.006 | 0.011 |

A_{3} | 0.091 | 0.091 | 0.090 | 0.093 | 0.005 | 0.042 | 0.003 | 0.005 | 0.009 | 0.016 | 0.003 |

A_{4} | 0.087 | 0.092 | 0.090 | 0.080 | 0.007 | 0.006 | 0.010 | 0.052 | 0.103 | 0.003 | 0.023 |

C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} | C_{11} | |
---|---|---|---|---|---|---|---|---|---|---|---|

A* | 0.076 | 0.071 | 0.075 | 0.067 | 0.005 | 0.006 | 0.003 | 0.052 | 0.103 | 0.032 | 0.023 |

A^{−} | 0.091 | 0.092 | 0.090 | 0.093 | 0.010 | 0.042 | 0.016 | 0.005 | 0.009 | 0.003 | 0.003 |

Retrofitting Technique | S_{i}^{*} | S_{i}^{-} | C_{i}^{*} |
---|---|---|---|

A_{4} | 0.043 | 0.114 | 0.723 |

A_{1} | 0.087 | 0.061 | 0.413 |

A_{2} | 0.095 | 0.056 | 0.372 |

A_{3} | 0.120 | 0.019 | 0.136 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Anelli, A.; Vona, M.; Santa-Cruz Hidalgo, S. Comparison of Different Intervention Options for Massive Seismic Upgrading of Essential Facilities. *Buildings* **2020**, *10*, 125.
https://doi.org/10.3390/buildings10070125

**AMA Style**

Anelli A, Vona M, Santa-Cruz Hidalgo S. Comparison of Different Intervention Options for Massive Seismic Upgrading of Essential Facilities. *Buildings*. 2020; 10(7):125.
https://doi.org/10.3390/buildings10070125

**Chicago/Turabian Style**

Anelli, Angelo, Marco Vona, and Sandra Santa-Cruz Hidalgo. 2020. "Comparison of Different Intervention Options for Massive Seismic Upgrading of Essential Facilities" *Buildings* 10, no. 7: 125.
https://doi.org/10.3390/buildings10070125