#
Case Study of a Heavily Damaged Building during the 2016 M_{W} 7.8 Ecuador Earthquake: Directionality Effects in Seismic Actions and Damage Assessment

^{*}

## Abstract

**:**

_{W}7.8 earthquake, which occurred in Muisne (Ecuador) on 16 April 2016, were analyzed under two perspectives. The first one deals with the influence of these effects on seismic intensity measures (IMs), while the second refers to the assessment of the expected damage of a specific building located in Manta city, Ecuador, as a function of its azimuthal orientation. The records of strong motion in 21 accelerometric stations were used to analyze directionality in seismic actions. At the closest station to the epicenter (R

_{Rup}= 20 km), the peak ground acceleration was 1380 cm/s

^{2}(EW component of the APED station). A detailed study of the response spectra ratifies the importance of directionality and confirms the need to consider these effects in seismic hazard studies. Differences between IMs values that consider the directionality and those obtained from the as-recorded accelerograms are significant and they agree with studies carried out in other regions. Concerning the variation of the expected damage with respect to the building orientation, a reinforced concrete building, which was seriously affected by the earthquake, was taken as a case study. For this analysis, the accelerograms recorded at a nearby station and detailed structural documentation were used. The ETABS software was used for the structural analysis. Modal and pushover analyses were performed, obtaining capacity curves and capacity spectra in the two main axes of the building. Two advanced methods for damage assessment were used to obtain fragility and mean damage state curves. The performance points were obtained through the linear equivalent approximation. This allows estimation and analysis of the expected mean damage state and the probability of complete damage as functions of the building orientation. Results show that the actual probability of complete damage is close to 60%. This fact is mainly due to the greater severity of the seismic action in one of the two main axes of the building. The results are in accordance with the damage produced by the earthquake in the building and confirm the need to consider the directionality effects in damage and seismic risk assessments.

## 1. Introduction

_{W}, 7.8, struck the north-western coast of Ecuador at 6:58 pm. (UTC-5, local time). The epicenter was located near the town of Muisne, 170 km northwest from Quito. Although the epicenter was in a remote rural area, several towns in the coastal provinces were affected due to their high intensity. The earthquake occurred at a 20-km depth as a result of the relative displacement between the Nazca plate and the South American plate, through a subduction process [1]. This process has generated catastrophic events in South America throughout the contact zone between these two plates, repeatedly, affecting Chile, Peru, and Ecuador [2].

## 2. Part I: Directionality in the Seismic Action

#### 2.1. Materials and Methods

_{X}and acc

_{Y}[PGA

_{X}and PGA

_{Y}, see Equations (1) and (2)]. Then, a combination (e.g., geometric mean, PGA

_{GM}) or the larger value (PGA

_{Larger}) of the PGA of the as-recorded components are commonly used as intensity measures in the development of ground motion prediction equations (GMPEs):

_{max}herein. This PGA can also be obtained, in a simplified way, computing the maximum value of the Euclidean norm or the root-sum-of-squares of the as-recorded acceleration components (Equation (7)):

_{max}) is produced is estimated through the following equation:

_{max}occurs.

#### 2.2. Results

_{X}, PGA

_{Y}, PGA

_{Larger}, and PGA

_{max}were computed for the 21 ground-motion records available. Since all the stations are oriented so that the horizontal components coincide with the east-west and north-south directions, the PGA

_{X}and PGA

_{Y}are now called PGA

_{EW}and PGA

_{NS}, respectively. Results are shown in Table 1. Acceleration maps for each measure (Figure 2) were georeferenced and interpolated from values presented in Table 1. In Figure 2a,b, maps with PGA

_{NS}and PGA

_{EW}are presented. Clearly, PGA

_{EW}presents larger values when compared to PGA

_{NS}. Figure 2c,d present the PGA

_{Larger}and PGA

_{max}results, respectively. Both variables show comparable results, but the PGA

_{max}has greater accelerations, as can be seen in Table 1. The maximum as-recorded PGA was produced in the APED station with a value of 1380 cm/s

^{2}. At this station, the true maximum acceleration (PGA

_{max}) was 1397 cm/s

^{2}. Notice that the stations ACH1, ACHN, ALIB, AOTA, and APO1 exhibit differences between PGA

_{max}and PGA

_{Larger}higher than 10%. This fact is interesting since we can underestimate the peak acceleration up to 20% (see station ACH1).

_{W}8.3 Illapel, Chile [13]; 2010 M

_{W}8.8 Maule, Chile [14]). From our perspective, these patterns should be considered in the design of seismic resistant structures. For instance, in near-fault areas, orienting the strong axis of buildings in the direction normal to the fault may reduce the risk of suffering a higher seismic damage due to directionality or directivity effects.

## 3. Part II: Case Study: Damage Assessment of a Heavily Damaged Building

#### 3.1. Materials and Methods

#### 3.1.1. Structural Model

#### 3.1.2. Parametric Model

_{L}).

#### 3.1.3. Park and Ang-Based Damage Index

_{N}is the normalized spectral displacement, I

_{PA}is the new damage index based on the damage index of Park and Ang, K

_{S}is the secant stiffness, and E is the energy dissipated; α is the parameter that distributes the contributions of the stiffness degradation and the dissipation of the energy to the global damage.

_{T}, related to the first derivative of the capacity spectrum [21]. The incorporation of this function into the damage index allows the incorporation of sharp variations in the damage due to sudden drops in stiffness that are not considered well in the secant stiffness function. This improved index is defined by modifying Equation (9) as follows:

_{NLN}), and the energy, E, the secant stiffness, K

_{S}, the tangent stiffness, K

_{T}, functions, and the damage index, I

_{PA}, based on the Park and Ang index. In this same figure, damage state thresholds are also shown. These damage states and thresholds are briefly described below.

#### 3.1.4. Fragility Curves and Mean Damage State

_{PA}. Significant differences are observed, especially for the states of Severe and Complete damage. Although it depends on the shape of the capacity spectrum, in general, the Risk-UE proposal tends to overestimate minor damage and underestimate severe damage.

_{i}(Sd) is the probability of damage state i and F

_{i}(Sd) is the fragility curve of damage state i. It is also useful to have the mean damage state curve (MDS), which is defined by the following equation:

#### 3.2. Results

#### Building–Seismic Action Interaction

_{-Trans.}axis of the building is oriented 144° from the east (counter-clockwise) and therefore the Y

_{-Long.}axis is oriented E54°N (see Figure 14). Figure 15 shows the horizontal as-recorded acceleration components and the particle motion (hodogram). As seen in this figure, the maximum acceleration (PGA

_{max}) occurred at a different angle (see pink arrow and Table 1) from the as-recorded ones (0°—EW and 90°—NS). The maximum intensity occurred close to the transversal axis of the building.

_{Trans.}) and for the longitudinal direction (Y direction, Dir Y

_{Long.}). This figure also indicates the periods of the building in the X and Y axes. Note how the most intense seismic action is given for the X

_{Trans.}direction of the building, which most likely meant an increase in the damage caused by the earthquake on this building.

_{Trans.}direction would be larger due to a higher seismic demand. The PP values obtained are shown in Table 4.

## 4. Discussion and Conclusions

_{Larger}and PGA

_{max}are compared.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Singaucho, J.C.; Aurore, L.; Viracucha, C.; Ruiz, M. Observaciones del sismo del 16 de abril de 2016 de magnitud Mw 7.8. Intensidades y aceleraciones. Inf. Ref. Datos RENAC
**2016**, 1–20. [Google Scholar] - Bilek, S.L. Invited review paper: Seismicity along the South American subduction zone: Review of large earthquakes, tsunamis, and subduction zone complexity. Tectonophysics
**2010**, 495, 2–14. [Google Scholar] [CrossRef] - Pinzón, L.A.; Pujades, L.G.; Macau, A.; Figueras, S. Increased seismic hazard in Barcelona (Spain) due to soil-building resonance effects. Soil Dyn. Earthq. Eng.
**2019**, 117, 245–250. [Google Scholar] [CrossRef] - Pinzón, L.A.; Pujades, L.G.; Diaz, S.A.; Alva, R.E. Do Directionality Effects Influence Expected Damage? A Case Study of the 2017 Central Mexico Earthquake. Bull. Seismol. Soc. Am.
**2018**, 108, 2543–2555. [Google Scholar] [CrossRef][Green Version] - Pinzón, L.A.; Mánica, M.A.; Pujades, L.G.; Alva, R.E. Dynamic soil-structure interaction analyses considering directionality effects. Soil Dyn. Earthq. Eng.
**2020**, 130, 106009. [Google Scholar] [CrossRef] - Pinzón, L.A.; Pujades, L.G.; Hidalgo-Leiva, D.A.; Diaz, S.A. Directionality models from ground motions of Italy. Ing. Sismica
**2018**, 35, 43–63. [Google Scholar] - Pinzón, L.A.; Diaz, S.A.; Pujades, L.G.; Vargas, Y.F. An efficient method for considering the directionality effect of earthquakes on structures. J. Earthq. Eng.
**2019**, 1–30. [Google Scholar] [CrossRef] - Boore, D.M. Orientation-Independent, Nongeometric-Mean Measures of Seismic Intensity from Two Horizontal Components of Motion. Bull. Seismol. Soc. Am.
**2010**, 100, 1830–1835. [Google Scholar] [CrossRef] - Moya-Fernández, A.; Pinzón, L.A.; Schmidt-Díaz, V.; Hidalgo-Leiva, D.A.; Pujades, L.G. A Strong-Motion Database of Costa Rica: 20 Yr of Digital Records. Seismol. Res. Lett.
**2020**, 91, 3407–3416. [Google Scholar] [CrossRef] - Computers and Structures, Inc. ETABS—Integrated Analysis, Design and Drafting of Building; Systems Computers and Structures, Inc.: Walnut Creek, CA, USA, 2019. [Google Scholar]
- Pujades, L.G.; Vargas-Alzate, Y.F.; Barbat, A.H.; González-Drigo, J.R. Parametric model for capacity curves. Bull. Earthq. Eng.
**2015**, 13, 1347–1376. [Google Scholar] [CrossRef][Green Version] - Ye, L.; Kanamori, H.; Avouac, J.P.; Li, L.; Cheung, K.F.; Lay, T. The 16 April 2016, MW 7.8 (MS 7.5) Ecuador earthquake: A quasi-repeat of the 1942 MS 7.5 earthquake and partial re-rupture of the 1906 MS 8.6 Colombia–Ecuador earthquake. Earth Planet. Sci. Lett.
**2016**, 454, 248–258. [Google Scholar] [CrossRef][Green Version] - Shrivastava, M.N.; González, G.; Moreno, M.; Reddy, C.; Salazar, P.; Yáñez, G.; González, J.; de la Llera, J.C.; Báez, J.C. Coseismic and Afterslip of the Mw 8.3 Illapel Earthquake 2015 from Continuous GPS data. Geophys. Res. Lett.
**2016**, 43, 10710–10719. [Google Scholar] [CrossRef][Green Version] - Vigny, C.; Socquet, A.; Peyrat, S.; Ruegg, J.-C.; Métois, M.; Madariaga, R.; Morvan, S.; Lancieri, M.; Lacassin, R.; Campos, J.; et al. The 2010 Mw 8.8 Maule Megathrust Earthquake of Central Chile, Monitored by GPS. Science
**2011**, 330, 1417–1422. [Google Scholar] [CrossRef][Green Version] - Shahi, S.K.; Baker, J.W. NGA-West2 models for ground motion directionality. Earthq. Spectra
**2014**, 30, 1285–1300. [Google Scholar] [CrossRef][Green Version] - Haji-Soltani, A.; Pezeshk, S. Relationships among Various Definitions of Horizontal Spectral Accelerations in Central and Eastern North America. Bull. Seismol. Soc. Am.
**2017**, 108, 409–417. [Google Scholar] [CrossRef] - Boore, D.M.; Kishida, T. Relations Between Some Horizontal-Component Ground-Motion Intensity Measures Used in Practice 1. Bull. Seismol. Soc. Am.
**2016**, 107, 334–343. [Google Scholar] [CrossRef] - FEMA. Prestandard and commentary for the seismic rehabilitation of buildings, FEMA 365. Fed. Emerg. Manag. Agency
**2000**, 518. [Google Scholar] - Park, Y.; Ang, A.H.S.; Wen, Y.K. Seismic damage analysis of reinforced goncrete buildings. J. Struct. Eng.
**1985**, I11, 740–757. [Google Scholar] [CrossRef] - Park, Y.; Ang, A.H.-S. Mechanistic Seismic Damage Model for Reinforced Concrete. J. Struct. Eng.
**1985**, 111, 722–739. [Google Scholar] [CrossRef] - Hidalgo-Leiva, D.A.; Pujades, L.G.; Barbat, A.H.; Diaz, S.A.; Vargas-, Y.; Pinzón, L.A. Damage index for structures with elements of high flexural stiffness and/or brittle behavior. In Proceedings of the 16th European Conference on Earthquake Engineering, Thessaloniki, Greece, 18–21 June 2018; pp. 1–12. [Google Scholar]
- Braga, F.; Dolce, M.; Liberatore, D. A Statistical Study on Damaged Buildings and an Ensuing Review of the MSK-76 Scale. In Proceedings of the Seventh European Conference on Earthquake Engineering, Athens, Greece, 20–25 September 1982; pp. 431–450. [Google Scholar]
- Braga, F.; Dolce, M.; Liberatore, D. Assessment of the relationships between Macroseismic Intensity, Type of Building and Damage, based on the recent Italy Earthquake Data. In Proceedings of the 8th European Conference on Earthquake Engineering, Lisbon, Portugal, 7–12 September 1986; pp. 39–46. [Google Scholar]
- Milutinovic, Z.V.; Trendafiloski, G.S. WP4: Vulnerability of Current Buildings; Institute of Earthquake Engineering and Engineering Seismology (IZIIS): Skopje, North Macedonia, 2003; Volume 111. [Google Scholar]
- Cosenza, E.; Manfredi, G. Damage indices and damage measures. Prog. Struct. Eng. Mater.
**2000**, 2, 50–59. [Google Scholar] [CrossRef] - Vargas-Alzate, Y.F.; Pujades, L.G.; Barbat, A.H.; Hurtado, J.E.; Diaz, S.A.; Hidalgo-Leiva, D.A. Probabilistic seismic damage assessment of reinforced concrete buildings considering direccionality effects. Struct. Infrastruct. Eng.
**2018**, 14, 817–829. [Google Scholar] [CrossRef] - Vargas-Alzate, Y.F. KaIROS Project. Keeping and Increasing Resilience Opportunities and Sustainability of Communities against Earthquakes. European Commission: Brussels, Belgium. Available online: https://cordis.europa.eu/project/rcn/215743/factsheet/en2018 (accessed on 8 February 2021).

**Figure 2.**Peak ground acceleration maps of the as-recorded components (

**a**) N-S and (

**b**) E-W, (

**c**) the larger value of the as-recorded components, and (

**d**) the true peak acceleration (PGA

_{max}).

**Figure 3.**Flow direction of the PGA

_{max}in the horizontal plane during the 2016 Ecuador earthquake.

**Figure 4.**Response spectra of the horizontal as-recorded rotated components and the RotD100 response spectrum for the 2016 Ecuador earthquake ground motion recorded in AMNT station.

**Figure 5.**Comparison of the ratios RotD100/GM and RotD100/Larger obtained with the 2016 Ecuador earthquake motion with the ratios obtained by other researchers.

**Figure 6.**(

**a**) Studied building. (

**b**) In green, the main building used to build up the structural model and in red, the annex that was not considered in the structural model (pictures taken from Google Maps street view).

**Figure 8.**Capacity curve and spectra in the X and Y directions. The points resulting from the pushover analysis, the interpolated curves (int) at a fixed step, and the bilinear forms (Bilinear) are shown.

**Figure 11.**Capacity spectra (

**left**) and damage functions (

**right**) for: X direction and Y direction. Bilinear forms of capacity spectra and thresholds of damage states based on the Risk-UE project (Ds

_{Trh RUE}) and those based on the Park and Ang damage index (Ds

_{Trh IPA}) are shown. See also the explanations in the text.

**Figure 12.**Fragility curves: (

**a**) X-direction, Risk-UE thresholds, (

**b**) X-direction, Park and Ang index thresholds; (

**c**) Y-direction, Risk-UE thresholds, (

**d**) Y-direction, Park and Ang index thresholds.

**Figure 14.**Location and distance between the studied building and the closest accelerometric station, AMNT. The orientation of the building with respect to north is also depicted.

**Figure 15.**2016 M

_{W}7.8 Ecuador earthquake recorded at AMNT station. (

**a**) As-recorded E-W and N-S accelerograms, and (

**b**) acceleration hodogram.

**Figure 16.**The 5% damped response spectra for the accelerograms obtained in the direction defined by the angle θ, from the projection of the as-recorded components EW and NS recorded at AMNT station. This figure is given in period-spectral acceleration (T-Sa) and in spectral displacement-spectral acceleration (Sd-Sa) formats. The fundamental periods of the principal axes of the building (X

_{Trans.}and Y

_{Long.}) are also indicated.

**Figure 17.**Linear-equivalent approximation to estimate the performance point of X

_{Long.}(144° case) and Y

_{Long.}(54° case) axes.

**Figure 18.**Mean damage state and complete damage probability as a function of the rotation angle of the seismic action. The orientation of the principal axes of the building (54° and 144°) is shown.

**Figure 19.**Damage probability matrices for the two main axes of the building (54° and 144° approximately) and for the two hypotheses used to define the damage states’ thresholds.

**Table 1.**Values of

**PGA**ratio, and

_{EW}, PGA_{NS}, PGA_{max}, PGA_{max}/PGA_{Larger}**θ**for the 21 ground motions recorded by the National Accelerographic Network of Ecuador. R

_{PGA(max)}_{epi}: epicentral distance.

Station | R_{epi}(km) | PGA_{EW}(m/s ^{2}) | PGA_{NS}(m/s ^{2}) | PGA_{max}(m/s ^{2}) | $\frac{\mathit{P}\mathit{G}{\mathit{A}}_{\mathit{m}\mathit{a}\mathit{x}}}{\mathit{P}\mathit{G}{\mathit{A}}_{\mathit{L}\mathit{a}\mathit{r}\mathit{g}\mathit{e}\mathit{r}}}\text{}$ | θ_{PGA(max)}Azimuth North |
---|---|---|---|---|---|---|

AMM2 | 235 | 0.25 | 0.35 | 0.35 | 1.00 | 354° |

ACH1 | 407 | 0.25 | 0.24 | 0.30 | 1.20 | 43° |

ACHN | 120 | 3.20 | 3.64 | 4.12 | 1.13 | 210° |

ACUE | 381 | 0.35 | 0.29 | 0.35 | 1.00 | 271° |

AES2 | 76 | 1.51 | 1.08 | 1.52 | 1.00 | 96° |

AGYE | 270 | 0.18 | 0.23 | 0.24 | 1.04 | 340° |

AIB1 | 202 | 0.48 | 0.57 | 0.58 | 1.02 | 166° |

AIB2 | 204 | 0.21 | 0.32 | 0.32 | 1.00 | 357° |

ALAT | 206 | 0.31 | 0.27 | 0.31 | 1.00 | 85° |

ALIB | 308 | 0.41 | 0.39 | 0.46 | 1.12 | 56° |

ALJ1 | 492 | 0.15 | 0.16 | 0.17 | 1.06 | 209° |

ALOR | 159 | 0.26 | 0.26 | 0.26 | 1.00 | 175° |

AMIL | 288 | 0.51 | 0.45 | 0.53 | 1.04 | 244° |

AMNT | 171 | 3.97 | 5.14 | 5.34 | 1.04 | 340° |

AOTA | 188 | 0.42 | 0.34 | 0.48 | 1.14 | 240° |

APED | 36 | 13.80 | 8.13 | 13.97 | 1.01 | 279° |

APO1 | 167 | 3.11 | 3.74 | 4.16 | 1.11 | 226° |

ASDO | 115 | 2.02 | 1.09 | 2.06 | 1.02 | 260° |

ATUL | 251 | 0.16 | 0.21 | 0.21 | 1.00 | 0° |

EPNL | 174 | 0.26 | 0.20 | 0.27 | 1.04 | 260° |

PRAM | 171 | 0.24 | 0.23 | 0.25 | 1.04 | 44° |

**Table 2.**Geometry of the sections and specifications of the materials of the beams and columns of the building studied.

Section Code | fc (kg/cm^{2}) | Dimensions (mm) | Steel Rebar | Rebar |
---|---|---|---|---|

C-1 and C-2 | 180 | 400 × 400 | 8 #5 | A615 Grade 40 |

C-3 | 180 | 450 × 450 | 4 #5 + 4 #6 | A615 Grade 40 |

C-4 and C-5 | 180 | 350 × 350 | 8 #5 | A615 Grade 40 |

C-6 | 180 | 400 × 400 | 4 #5 + 4 #6 | A615 Grade 40 |

C-7 and C-8 | 180 | 300 × 300 | 8 #4 | A615 Grade 40 |

C-9 | 180 | 350 × 350 | 4 #4 + 4 #5 | A615 Grade 40 |

Beam-1 | 170 | 200 × 500 | 2 #3 + 2 #4 | A615 Grade 40 |

Beam-2 | 170 | 200 × 300 | 2 #3 + 2 #4 | A615 Grade 40 |

Beam-3 | 170 | 200 × 600 | 2 #3 + 2 #4 | A615 Grade 40 |

CS | m (g/cm) | Sdu (cm) | Sau (g) | µ (adim) | σ (adim) | ε_{L} (adim) |
---|---|---|---|---|---|---|

X | 0.095 | 11.62 | 0.622 | 0.420 | 0.241 | 7.35 × 10^{−3} |

Y | 0.118 | 10.35 | 0.757 | 0.410 | 0.331 | 1.28 × 10^{−2} |

Axis | Angle | Sa_{pp} (cm/s^{2}) | Sd_{pp} (cm) |
---|---|---|---|

X_{-Trans.} | 144° | 561.8 | 9.3 |

Y_{-Long.} | 54° | 544.2 | 5.6 |

**Table 5.**Mean damage state and complete damage probability in the main axes of the building based on the proposal of the Risk- UE project and, the Park and Ang damage index.

Axis | Angle | Mean Damage State | Complete Damage Probability (%) | ||
---|---|---|---|---|---|

I_{PA} | RUE | I_{PA} | RUE | ||

X_{-Trans.} | 144° | 3.50 | 3.07 | 59.24 | 34.85 |

Y_{-Long.} | 54° | 2.09 | 2.40 | 7.52 | 12.91 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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**

Pinzón, L.A.; Pujades, L.G.; Medranda, I.; Alva, R.E. Case Study of a Heavily Damaged Building during the 2016 *M _{W}* 7.8 Ecuador Earthquake: Directionality Effects in Seismic Actions and Damage Assessment.

*Geosciences*

**2021**,

*11*, 74. https://doi.org/10.3390/geosciences11020074

**AMA Style**

Pinzón LA, Pujades LG, Medranda I, Alva RE. Case Study of a Heavily Damaged Building during the 2016 *M _{W}* 7.8 Ecuador Earthquake: Directionality Effects in Seismic Actions and Damage Assessment.

*Geosciences*. 2021; 11(2):74. https://doi.org/10.3390/geosciences11020074

**Chicago/Turabian Style**

Pinzón, Luis A., Luis G. Pujades, Irving Medranda, and Rodrigo E. Alva. 2021. "Case Study of a Heavily Damaged Building during the 2016 *M _{W}* 7.8 Ecuador Earthquake: Directionality Effects in Seismic Actions and Damage Assessment"

*Geosciences*11, no. 2: 74. https://doi.org/10.3390/geosciences11020074