Fragility Analysis of Pangasinan State University Urdaneta City

Campus Buildings

RUTH ANN D. MANINGDING1,*, JAN NICHOLAS S. BALDO2

1College of Engineering and Architecture,

Pangasinan State University,

Urdaneta City, Pangasinan, 2428,

PHILIPPINES

2College of Engineering and Architecture,

University of Cordilleras,

Baguio City, Benguet, 2600,

PHILIPPINES

*Corresponding Author

Abstract: – The Philippines is a seismically susceptible region because of its unique geographical location within the

Pacific Ring of Fire. Over the years, the Philippines has had several destructive earthquakes that have caused

building collapses and numerous fatalities. Schools are particularly vulnerable to earthquakes because most were

built using outdated building rules that do not comply with current seismic design criteria. The age of PSU buildings,

which ranges from 10 to 40 years, may increase their vulnerability to seismic hazards. Buildings designed with the

old codes might lack the necessary reinforcement and structural elements to withstand the forces generated by an

earthquake, potentially leading to catastrophic failures and endangering the lives of students, faculty, and other

occupants. Moreover, the San Manuel Fault Line near PSU buildings in Urdaneta City, Pangasinan, heightens the

risk of a significant seismic event affecting these structures. Given the critical role that schools play in communities,

both in providing education and serving as essential facilities during and after disasters, assessing their seismic

vulnerability becomes crucial. So far, no research has been conducted to evaluate the PSU building’s vulnerability to

seismic activity in the event of a significant earthquake. In line with this, this study aimed to perform a seismic

fragility analysis of PSU buildings in Urdaneta City, Pangasinan, Philippines, to determine how susceptible they

were to earthquakes. This study applies preliminary assessment using Rapid Visual Screening of FEMA P-154 to

filter out which buildings need further evaluation and detailed assessment using fragility analysis. The screened

buildings are evaluated using fragility curves to assess if the building could endure an earthquake with a 0.4 g PGA

and a 10% probability of exceedance, following the National Structural Code of the Philippines (NSCP)

requirements for seismic zone 4. The structural model of PSU buildings was created using SAP 2000, and the non-

linear static analysis, specifically the ATC40 Capacity Spectrum Method, was performed to determine the data

required to develop the fragility curves. The results demonstrate that the seismic scores of Engineering Buildings 1,

2, and 3 are below the RVS FEMA P-154 standard of 2.0, indicating that further investigation is required to evaluate

their vulnerability thoroughly. Additionally, these buildings were observed to withstand a maximum peak ground

acceleration of 0.60 g PGA at a 10% probability of exceedance based on the developed fragility curves,

corresponding to earthquake intensity up to VIII, indicating "severe shaking.” Furthermore, analysis of the fragility

curves demonstrates that none of the structures exceed the 10% probability of exceedance at 0.4 g PGA, aligning

with NSCP standards for Seismic Zone 4. As a result, these buildings are considered safe for occupancy without

requiring retrofitting measures.

Key-Words: - earthquake, rapid visual survey, seismic vulnerability assessment, fragility analysis, capacity spectrum

method, probability of exceedance.

Received: June 13, 2024. Revised: October 25, 2024. Accepted: November 21, 2024. Published: December 12, 2024.

1 Introduction

1.1 Background of the Study

Earthquakes can occur unexpectedly and without

warning, [1]. When tectonic plates move along a

fault line in the crust of the earth, it can generate

intense shaking of the ground, which is known as an

earthquake, [2]. The Philippines is prone to seismic

activity due to its distinctive geographic position

within the Pacific Ring of Fire. Over time, the

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nation has experienced devastating earthquakes,

resulting in building failures and significant loss of

life, [3].

Schools are particularly vulnerable to

earthquakes because most were built using outdated

building rules that do not comply with current

seismic design criteria, and others were constructed

without seismic design. Despite the inclusion of

seismic provisions in modern construction, older

buildings might still pose risks to occupants due to

their age and deterioration, [4], [5]. The seismic

vulnerability assessment of schools needs special

attention due to its essential role in the community,

both in education and post-earthquake function.

Schools play a valuable additional role in disaster

recovery efforts. When there is an emergency,

schools are usually utilized as evacuation centers,

[6]. The Department of Education in the Philippines

has designated schools as evacuation centers,

ensuring they are readily available during disasters,

[7]. During emergencies, a more secure and resilient

school may save children's lives and help get things

back to normal in the community, [8].

Due to its location close to the San Manuel

Fault Line, PSU buildings will be affected by a

significant seismic event. The San Manuel fault line

is 12.7 kilometers away from the structures,

according to the Phivolcs Fault Finder App, [9].

Moreover, the age range of most PSU buildings is

10 to 40 years old. The age of the structures may

contribute to their susceptibility to earthquake

hazards. The structural reliability and integrity of

the buildings may decrease over time due to normal

wear and tear, environmental conditions, and

structural deterioration, [10]. These structures were

designed and built using outdated building codes

that fail to meet current seismic design standards.

This study analyzed the seismic fragility of

PSU buildings in Urdaneta City, Pangasinan,

Philippines, to determine their susceptibility to

earthquakes. It applied preliminary assessment

using Rapid Visual Screening and detailed

assessment using fragility analysis of the buildings.

Rapid Visual Screening (RVS) of FEMA P-154

provides an initial assessment of the buildings

against earthquake hazards to filter out which

buildings need further evaluation. The seismic

susceptibility of the screened structures is evaluated

using fragility curves, which depict the likelihood of

collapse or damage at different levels of ground

shaking.

One of the primary distinctions of this study is

its specific focus on PSU Urdaneta City Campus

Buildings. By developing fragility models that are

tailored to the unique construction practices,

materials, geological conditions, and environmental

factors of Urdaneta City, this research directly

addresses the specific needs of the region. This

localization means that the findings directly apply to

the city's specific context, making them highly

relevant for local stakeholders, including city

planners, engineers, policymakers, and school

administration. They can use these precise insights

to develop more effective mitigation strategies and

improve the overall seismic resilience of PSU

Urdaneta City Campus buildings and other public

buildings within the region.

1.2 Objectives of the Study

This study was conducted to carry out a fragility

analysis of PSU buildings in Urdaneta City,

Pangasinan, Philippines, to evaluate their

susceptibility to earthquake damage. Specifically:

1. To identify those buildings that need to be

prioritized for further detailed seismic

evaluation based on the cut-off score of FEMA

P-154.

2. To determine the damage level of the selected

PSU buildings when subjected to a peak ground

acceleration of 0.4 g.

3. To obtain the seismic vulnerability of the

selected PSU buildings based on the developed

fragility curves.

4. To determine the maximum possible intensity

that PSU buildings can withstand.

1.3 Conceptual Framework

The conceptual framework for this study applies a

preliminary and detailed assessment of the

buildings, as depicted in Figure 1. Rapid Visual

Screening (RVS) is one of the valuable techniques

for rapidly determining the seismic risk of

significant structures, such as school buildings.

These procedures will initially assess a building's

vulnerability to seismic hazards. The buildings that

have undergone screening with scores less than the

cut-off of RVS FEMA P-154 are assessed for

seismic vulnerability using fragility analysis, which

shows the likelihood of failure or damage at various

intensities of ground shaking.

Fig. 1: Conceptual Framework

Rapid Visual

Screening Fragility

Analysis

Seismic

Vulnerability

Assesment

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1.4 Scope and Delimitation

The study focuses on conducting a fragility analysis

of PSU buildings in Urdaneta City, Pangasinan,

Philippines. The Rapid Visual Screening (RVS)

method from FEMA P-154 prioritizes buildings and

identifies those requiring additional evaluation. The

PSU Urdaneta Campus has eleven (11) buildings

considered for the study, as presented in Table 3.

Actual measurements were conducted to verify the

plans' dimensions, and the rebound hammer test was

performed to assess the on-site compressive strength

of the concrete. Also, to ensure accurate data for

generating the fragility curves, the researchers

conducted additional tests, including a tensile test,

to determine the actual tensile strength of the rebars.

This approach differentiates this study from others

that rely solely on the specifications provided in the

plans. The exposed rebars at the top of columns

were acquired, and a tensile test was done using the

Universal Testing Machine (UTM) on steel bars to

assess the tensile strength of reinforcing bars.

SAP 2000 will create and simulate structure

models subject to earthquakes. The major structural

elements of the building are all included in the

structural modeling, which is limited only by the

concrete works. Microsoft Excel will run the

simulation, analyze the results, and produce the

fragility curves using the data collected. Nonlinear

static "pushover" analysis will be carried out to

generate capacity curves. The pushover parameters

will follow the provisions of the ATC-40 Capacity

Spectrum Method (CSM). The Incorporated

Research Institutions for Seismology (IRIS)

databases were used to collect the ground motion

data (GMD). The structural models were subjected

to seven (7) local earthquakes and five (5)

international earthquakes. The seven (7) earthquakes

that were recorded in the Philippines from 1988 to

2023 are displayed in Table 1 (Appendix). The five

(5) earthquakes that occurred in foreign countries

from 1996 to 2023 are presented in Table 2

(Appendix).

2 Methodology

The descriptive analytical case study method is

selected to align with the necessary methodology,

blending descriptive and analytical approaches to

assess the building's susceptibility to seismic events

thoroughly. A descriptive approach was employed

for the preliminary assessment of the PSU buildings

using Rapid Visual Survey forms. The analytical

component evaluated the building's structural

behavior and response to seismic events. A

computational model of the PSU buildings was

created using SAP 2000 software, and non-linear

static analysis, specifically the ATC40 Capacity

Spectrum Method, was performed to determine the

data required to generate the fragility curves. These

models simulated the building's response to seismic

forces and helped assess its vulnerability and

potential damage.

2.1 Research Design

Figure 2 is an illustration of the proposed procedure.

PSU buildings will undergo a preliminary

assessment utilizing Rapid Visual Screening to

determine whether buildings require additional

investigation. The obtained structural plan will be

modeled using SAP 2000 software, and pushover

analysis and response spectrum analysis will be

carried out using the ground motion data gathered.

Pushover curves and response spectra, in turn,

determine an earthquake's demand and a building's

capacity. These first two components serve as inputs

for the Capacity Spectrum Method used in structural

assessments. Creating a fragility curve includes

statistical analysis of the structural response data.

Fig. 2: Research Design

2.2 Population and Locale of the Study

The PSU Urdaneta City Campus is located along

McArthur Highway in Barangay San Vicente,

Urdaneta City, Pangasinan, Philippines, covering an

area of 25,499 square meters. The city's precise

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geographical position is 15.9835° N latitude and

120.6334° E longitude. Figure 3 depicts the PSU

Urdaneta Campus' site development plan. Eleven

(11) school buildings, including the Graduate

School building, were involved in the case study.

The 11 buildings included in the study are listed in

Table 3.

Fig. 3: PSU Urdaneta City Campus Site

Development Plan

Table 3. Name of buildings in PSU Urdaneta City

Campus

Building Number

Building Name

BLDG 1

Academic Building 1

BLDG 2

Academic Building 2

BLDG 3

Academic Building 2 (extension)

BLDG 4

Engineering Building 1

BLDG 5

Engineering Building 2

BLDG 6

Engineering Building 3

BLDG 7

Educational Building

BLDG 8

General Education Building

BLDG 9

PTBI (Pangasinan Technology

Business Incubator Center)

BLDG 10

School of Advanced Studies

BLDG 11

Student Activity Center

2.3 Data Gathering Procedure

This study aims to create analytical fragility curves

for the buildings at Pangasinan State University

(PSU) Urdaneta Campus using a four-phase

technique indicated in Figure 4.

.

Fig. 4: Flow of Activity

2.3.1 Phase 1: Rapid Visual Screening (RVS)

Rapid Visual Screening (RVS) is an initial filter to

identify buildings with potential seismic

vulnerabilities, allowing for further evaluation and

prioritization of retrofitting efforts. RVS is a simple

yet effective method, [11]. The methodology

employed in the RVS procedure relies on

conducting a walkway inspection of a structure and

completing a Data Collection Survey Form by the

surveyor after visually examining the structure

externally and, when possible, internally, without

engaging in complex computations, [12]. The first

step was research planning, which involved pre-

field planning activities, pre-field data collection,

and preliminary site investigation. The pre-field

planning activities include selecting the data

collection forms, training the screeners to conduct

the RVS, and the review of the acquired data. The

next step is the execution of rapid visual screening.

The final section involves analyzing the collected

data, [13]. Using the FEMA P-154 RVS checklist,

the researchers determine each building's

vulnerability score. Buildings with a score of two or

below are advised to undergo a more thorough

evaluation, [14]. While Rapid Visual Screening

(RVS) may lack the precision of detailed modeling,

it provides a simple and effective approach for

identifying parts of a city prone to earthquake

vulnerability, [15], [16], [17].

2.3.2 Phase 2: Structural Modelling of PSU

Buildings

Acquire architectural and structural plans from the

university's physical plant office and verify

dimensions through on-site measurements. A

rebound hammer test will be used to estimate the

compressive strength of the concrete materials used

in the structures. This involves selecting

Phase 4

Development of Seismic Fragility Curves

Phase 3

The Capacity Spectrum Method as a Structural

Assessment Methodology

Phase 2

Structural Modelling of PSU Buildings

Phase 1

Rapid Visual screening of PSU Buildings

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representative samples of critical exterior columns

and beams, with three test locations chosen for each

beam and column. The Schmidt hammer, commonly

known as a Swiss hammer or rebound hammer, is a

specialized tool to evaluate the rebound or elasticity

of materials like concrete and rock, [18]. Its

primary function lies in determining surface

hardness and resistance to penetration. Acquire

exposed rebars at the top of columns and conduct a

tensile test using a Universal Testing Machine

(UTM) to assess the tensile strength of reinforcing

bars. The following are the procedures for creating a

three-dimensional frame model of the structure in

SAP 2000, [19].

1. Specify the grid system and develop a three-

dimensional frame model of the structure,

including the dimensions, shapes, and

arrangements of various structural elements.

2. Define material and geometric properties for

each structural element, such as material

properties of concrete and rebars, section

properties, and boundary conditions.

3. Define the load pattern and assign a gravity

load.

2.3.3 Phase 3: The Capacity Spectrum Method

The Capacity Spectrum Method (CSM), a

performance-based seismic evaluation approach,

determines a structure's seismic capacity, [20]. This

process involves generating the structure's capacity

curve by performing a pushover analysis. Response

spectra illustrate the demands of the seismic ground

motion, [21]. The intersection of the capacity and

demand curves is known as the performance point.

The capacity curve was derived using pushover

curves employing traditional pushover analysis, and

the demand curve was derived from the inelastic

response spectra of specific ground motion

recordings, [22]. The Capacity Spectrum Method

(CSM) was conducted using the following

methodologies:

1. Perform pushover analysis on the PSU building

structural model using SAP 2000.

2. Acquire ground motion data from the

Incorporated Research Institutions for

Seismology (IRIS). Find the normalized Peak

Ground Acceleration (PGA). The normalized

ground motion data is produced by scaling the

original ground motion data up and down, [23].

Convert normalized PGA into a response

spectrum through SeismoSignal.

PGANormalized=(GMD) 󰇡PGAExcitation

PGAMaximum 󰇢 (1)

where:

GMD = Ground Motion Data

= the level of excitation ranges

from peak ground acceleration (PGA) values,

starting from 0.1 g up to 3.0 g.

=absolute maximum ground

motion data

3. Determine the performance points by analyzing

the intersection of the capacity and response

spectrum curves. Several values of performance

points are obtained by scaling the demand curve

into various excitation levels, ranging from 0.1

g to 3.0 g.

2.3.4 Phase 4: Development of Seismic Fragility

Curves.

Fragility curves show the risk of structural damage

caused by varying levels of ground shaking. An

analytical method was used to produce these

fragility curves, and the following is a thorough

step-by-step procedure, [24], [25].

1. Determine the damage state threshold using

Table 4 and the data (yield displacement and

ultimate displacement) from the pushover curve

to calculate the limits of spectral displacement

for each damage state.

2. Establish the damage ranking by applying the

calculated damage state thresholds.

3. Determine the damage states corresponding to

all displacement performance points obtained

from the capacity curve and response spectrum.

Table 4. Damage State Threshold Values, [26],[27]

Damage

State

Damage

Rank

Spectral Displacement

No Damage

D



Slight

C



Moderate

B



Extensive

A

󰇟󰇛󰇜󰇠

Complete

As



Where:

dy = yield displacement, du = ultimate displacement

4. Count the frequency of occurrence for each

damage state threshold with the performance

points.

5. Compute the damage ratio by obtaining the total

cumulative probability of occurrence. This ratio

is calculated by dividing the number of

occurrences by the total number of records at a

specific Peak Ground Acceleration (PGA) level.

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6. Determine the standard deviation and mean

accordingly. The mean and standard deviation

were obtained for every damage state using

equations (2) and (3). The lognormal values of

PGAs were then multiplied by each frequency

to provide lognormal values for the standard

deviation and mean.

λ=x

N (2)

ξ=(x- λ)2

N-1 (3)

Where:

x = individual ground motion data obtained

N= sample size of ground motion data

λ = mean of the ground motion data

ξ = standard deviation

7. The probability of exceedance (Pr) may be

calculated by applying equation (4).

󰇣󰇝󰇛󰇜󰇞

󰇤 (4)

Where:

Pr=probability of exceedance

x = peak ground acceleration

λ = mean

 = standard deviation

=standard normal deviation

8. Plot the likelihood of exceedance versus the

peak ground acceleration (PGA) excitation level

to create seismic fragility curves for the PSU

buildings.

3 Results and Discussion

3.1 Rapid Visual Screening (RVS) Results

The RVS scores of all 11 school buildings are

displayed in Figure 5. Three of the buildings have

scores below 2.0, which is the FEMA P-154 cutoff

score. Eight of the eleven school buildings had

ratings higher than 2, indicating better seismic

performance. Engineering Buildings 1 (BLDG4),

Engineering Buildings 2 (BLDG5), and Engineering

Buildings 3 (BLDG6) had scores lower than the

cutoff of 2. This suggests that a more thorough

examination of these structures is required to

precisely determine their vulnerability to seismic

risks.

Fig. 5: RVS Score

3.2 Structural Modelling of PSU Buildings

Out of the eleven school buildings, Engineering

Buildings 1 (BLDG4), Engineering Buildings 2

(BLDG5), and Engineering Building 3 (BLDG6)

had scores that were below the cutoff of 2,

indicating the need for a more thorough

investigation using fragility analysis. The structural

model was created based on architectural and

structural plans, and material properties were

incorporated using SAP 2000. All the buildings'

main structural elements are included in the

structural modeling, with the focus of the research

being on the beams, girders, and columns that make

up the structure. Accordingly, the finished structural

models of school buildings are shown in isometric

perspective in Figure 6, Figure 7 and Figure 8.

Fig. 6: Structural Model of Engineering Building 1

Fig. 7: Structural Model of Engineering Building 2

BLD

G 1 BLD

G 2 BLD

G 3 BLD

G 4 BLD

G 5 BLD

G 6 BLD

G 7 BLD

G 8 BLD

G 9 BLD

G 10 BLD

G 11

Σειρά1 2,5 3,4 2,8 0,9 1,5 0,9 3,4 3,4 2,5 2,5 2,5

0

1

2

3

4

RVS SCORE

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Fig. 8: Structural Model of Engineering Building 3

3.2.1 Rebound Hammer Test

The rebound hammer test was conducted on the

school buildings to estimate the on-site compressive

strength of the concrete structures. The procedure

involves pressing the device against the concrete

surface until the hammer impacts the surface a

designated number of times at each test location.

The resulting readings from these impacts are

interpreted using a rebound hammer test chart, and

the average of these readings is used to determine

the compressive strength. A thorough explanation of

the methodologies for performing a rebound

hammer test is available in the American Standards

for Testing and Materials (ASTM C805) journal,

[28]. Tests were carried out for one column and

beam in each building at three locations close to

supports and at midspan. Instead of conducting tests

on each column and beam, a sampling strategy was

implemented. This method focused on selecting a

representative sample of each building's critical

exterior columns and beams. Specifically, three test

locations were carefully chosen for each beam and

column. Ten readings should be taken from each

test area and averaged to determine the compressive

strength. Table 5 (Appendix) summarizes the

compressive strength used for each building

obtained from the rebound hammer test.

3.2.2 Tensile Test

The exposed rebars at the top of columns were

obtained for each building to assess the tensile

strength of reinforcing bars. The sample steel bars

were tested using the Universal Testing Machine at

the authorized materials testing and geotechnical

engineering laboratory facility. During the tensile

test, the material specimen is subjected to a

gradually increasing axial load until it reaches the

point of failure or fracture, as shown in Figure 9.

The yield point and ultimate tensile strength

summary were determined as shown in Table 6

(Appendix) and used in the structural model as

material properties.

Fig. 9: Fractured Specimen of Engineering Building

1

3.3 The Capacity Spectrum Method as a

Structural Assessment Methodology

3.3.1 Pushover Curve

Figure 10, Figure 11 and Figure 12 display the

pushover curves for Engineering Building 2,

Engineering Building 1, and Engineering Building 3

along X- and Y-directions. The graphs depict the

relationship between displacement (x-axis) and base

shear force (y-axis). The peak point on the pushover

curve indicates the structural material's capacity to

withstand maximum lateral loads. In contrast, the

yield point indicates the structure’s boundary within

the elastic range, [29]. By utilizing the yielded

displacement (dy) and ultimate displacement (du)

and inputting these values into the equations

outlined in Table 2 (Appendix), one can calculate

the damage thresholds for each damage state

accordingly. In Engineering Building 2, as depicted

in Figure 10, the yield point was reached in the x-

direction at a base shear force of 3026.783 kN,

corresponding to a displacement of 20.079 mm. The

maximum displacement, on the other hand, was

recorded at 173.476 mm, with the structure enduring

a base shear force of 3402.297 kN. Similarly, in the

y-direction, the yield point was observed at a base

shear force of 1796.186 kN with a displacement of

26.437 mm, while the maximum displacement of

263.273 mm occurred at a base shear force of

2089.338 kN. The maximum base shear force of

3402.297 kN in the x-direction is higher than

2089.338 kN in the y-direction. This result suggests

that Engineering Building 2 can sustain a greater

base shear force in the x-direction, indicating that

this is the building's strongest axis. In contrast,

Engineering Buildings 1 and 3 can tolerate higher

base shear force in the y-direction, as shown in

Figure 11 and Figure 12, respectively, implying that

the y-direction is the strongest axis for these

buildings.

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Fig. 10: Pushover Curve of Engineering Building 2

in the X and Y directions

Fig. 11: Pushover Curve of Engineering Building 1

in the X and Y-direction

Fig. 12: Pushover Curve of Engineering Building 3

long X and Y-direction

3.3.2 Ground Motion Inputs

All ground motion records are obtained from the

Incorporated Research Institutions for Seismology

(IRIS), as shown in Figure 13. For these records, 12

actual local and foreign earthquake events are

considered, as shown in Appendix in Table 1 and

Table 2. Using Microsoft Excel, each ground

motion has been normalized and scaled accordingly

from 0.1g to 3.0g, as shown in Figure 14. There are

720 scaled earthquake recordings when the elastic

response spectra of the East-West and North-South

directions are considered for each event. As seen in

Figure 15, the response spectra are obtained using

SeismoSignal software. The response spectra were

run in SAP 2000 and converted to demand

spectrum.

Fig. 13: Ground Motion Records from Incorporated

Research Institutions for Seismology (IRIS)

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Fig. 14: Normalized Peak Ground Acceleration of

Luzon Earthquake (02-24-1988) of magnitude of 7.2

Fig. 15: Response Spectra based on Luzon

Earthquake (02-24-1988) of magnitude 7.2 with

0.1g PGA along East-West direction using

SeismoSignal Software

3.3.3 Capacity Spectrum Method (CSM)

The capacity spectrum approach defines the

performance point as the intersection of the capacity

and response spectrum curves. Following the ATC-

40 Capacity Spectrum Method (CSM), the capacity

curve obtained from the pushover curve can be

superimposed onto the demand spectrum curve,

[30]. Several performance point values are obtained

by scaling the demand curve into various excitation

levels between 0.1 g and 3.0 g. A total of 1440

performance points were determined for a single

model in the east-west and north-south directions,

corresponding to 12 ground motion records.

Fig. 16: Capacity Curve based on July 16, 1990

Luzon, Philippine’s earthquake with 1.0g PGA

based on magnitude 6.5 in the east-west direction at

X-axis of Engineering Building 2

Figure 16 illustrates the superimposed capacity

curve sample for Engineering Building 2 at 1.0 g

PGA, corresponding to a magnitude 6.5 earthquake

in Luzon, Philippines, on July 16, 1990. A summary

of performance points achieved when the

Engineering Buildings 2 model in SAP 2000 was

exposed to an earthquake of magnitude 6.5 that

occurred on July 16, 1990, in Luzon, Philippines, is

shown in Table 7 (Appendix).

3.4 Development of Seismic Fragility Curves

3.4.1 Damage State Threshold Limits

The spectral displacement for the buildings on both

x and y axes is determined in this study by applying

the approach, shown in Table 4. The data presented

in Table 8 (Appendix) outline the structural damage

state thresholds for both the y-axis and x-axis

directions of each school building. In addition to the

no-damage condition (D), the damage thresholds

used in this study are categorized into four groups:

slight damage (C), moderate damage (B), extensive

damage (A), and complete damage (As).

Table 8 (Appendix) shows that the spectral

displacement values for C and B are small in both

the x and y directions. Damage thresholds with

small values have a higher likelihood of being

exceeded. The damage thresholds for A and As are

comparatively greater than the spectral

displacements for C and B. For example,

Engineering Building 2 displayed a damage

threshold of 173.476 mm for As in the x-direction.

This indicates that to achieve "complete damage,” a

spectral displacement of 173.476mm is required.

This data was then used to determine the damage

rank and generate a set of fragility curves.

3.4.2 Damage Ranking

The provided tabulated data for the damage ranking

was generated utilizing the acquired performance

points and the damage state threshold limits. Table 9

(Appendix) depicts the performance points

associated with scaled peak ground acceleration

values and the corresponding damage rankings for

Engineering Building 2 along the East-West

direction (x-axis), derived from data recorded

during the magnitude 8.0 earthquake near the east

coast of Peru on August 15, 2007. The data

indicates higher damage states correspond to higher

peak ground acceleration values. Specifically, Table

9 (Appendix) shows that Engineering Building 2

sustained complete damage (As) at a peak ground

acceleration of 2.0 g during this seismic event.

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3.4.3 Probability of Occurrence

The Occurrences of earthquakes for each damage

state threshold were tallied using the performance

points. Table 10 (Appendix) summarizes the

occurrence frequency for different damage

conditions observed in Engineering Building 2

along the y-axis in the East-West direction based on

varying levels of peak ground acceleration (PGA)

measured in gravitational units (g). This table

generates a graph showing the probability of

occurrence for each damage situation. The

cumulative damage ratios, representing the

correlation between each damage rank and its

corresponding PGA value, were the basis for

constructing the probability of occurrence graphs.

Figure 17, Figure 18 and Figure 19 illustrate the

percentage of each damage rank associated with the

PGA. These graphs indicate that the damage rank

consistently rises as the PGA increases from 0.1 g to

3.0 g.

For Engineering Building 2, as shown in Figure

17, the graph illustrates the probability of

occurrence of different damage conditions for

Engineering Building 2 along the y-direction as a

function of peak ground acceleration (PGA). At

PGA’s up to 0.4 g, the probability of experiencing

no damage to slight damage (state D) is 100%,

indicating that the building remains mostly intact.

As the PGA increases from 0.5 g to 1.2 g, the

building will experience slight to moderate damage

(states C and B). This range indicates that the

building suffers from minor structural issues that

gradually escalate as the seismic intensity increases.

Fig. 17: Probability of Occurrence for Engineering

Building 2 in the East-West Direction(y-axis).

The building sustains moderate to extensive

damage as we approach 1.3 g-1.9 g (states B and A).

This suggests that at these levels of seismic activity,

the building's structural integrity is compromised to

a greater extent, resulting in substantial damage that

may require significant repairs or lead to partial

structural failure. Finally, the structure will

experience extensive to complete damage in the 2.0

g–3.0 g range (states A and As). This indicates that

the building will likely to experience catastrophic

structural failure, leading to complete damage.

Figure 18 illustrates the probability that

Engineering Building 1 will receive slight to

moderate damage, ranging from 0.5 g to 1.3 g, along

the east-west direction along the y-axis. The

building sustains moderate to extensive damage as

we get closer to 1.4 -2.8g. Finally, the structure will

undergo extensive damage, ultimately leading to

complete damage within the 2.9–3.0g range.

Fig. 18: Probability of Occurrence for Engineering

Building 1 in East-West Direction (Y-axis)

Figure 19 depicts the likelihood of Engineering

Building 3 experiencing slight to moderate damage

between 0.2 g and 1.1 g in the east-west direction

(y-axis). The building sustains moderate to

extensive damage as we approach 1.2-2.6 g.

Finally, the structure will experience extensive to

complete damage in the 2.7–3.0 g range.

Fig. 19: Probability of Occurrence for Engineering

Building 3 in East-West Direction (y-axis)

3.4.4 Fragility Curves

The fragility curves evaluate the likelihood of

reaching or exceeding each damage condition

(slight, moderate, extensive, and complete) over

peak ground accelerations (PGA) from 0.1 g to 3.0

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g. The probabilities (Pr) for each damage condition

were shown on a single graph, resulting in a clear

and interpretable representation in Appendix in

Figure 20, Figure 21 and Figure 22.

In practical terms, the "D" or "No Damage"

condition should be excluded from the fragility

curves, [29]. The figures show the probabilities for

exceeding a damage condition with its associated

scaled peak ground acceleration.

For Engineering Building 2, depicted in Figure

20 (Appendix), the likelihood of surpassing the

specified ground acceleration of 0.4 g is as follows:

in the east-west direction along the X-axis, it's

23.41%, 5.49%, 5.20%, 5.22%, and 5.47% for no

damage (D), slight damage (C), moderate damage

(B), extensive damage (A), and complete damage

(As), respectively. Along the Y-axis, it's 43.30%,

7.50%, 5.61%, 5.20%, and 5.29% for the same

corresponding levels of damage. Likewise, in the

north-south direction along both the X and Y axes,

the probabilities of surpassing a peak ground

acceleration of 0.4 g are as follows: 17.52%, 5.55%,

5.19%, 5.21%, and 5.39% for no damage (D), slight

damage (C), moderate damage (B), extensive

damage (A), and complete damage (As),

respectively. Along the Y-axis, the probabilities are

40.09%, 6.26%, 5.34%, 5.19%, and 5.27% for the

same levels of damage.

As illustrated in Figure 21 (Appendix), the

probabilities of exceeding a peak ground

acceleration of 0.4 g for Engineering Building 1 in

the east-west direction along the X and Y axes are

40.17%, 6.53%, 5.46%, 5.25%, and 5.23%, and

18.89%, 5.35%, 5.32%, 5.19%, and 5.44%,

respectively. These probabilities correspond to

damage levels of no damage (D), slight damage (C),

moderate damage (B), extensive damage (A), and

complete damage (As). Similarly, in the north-south

direction along the X-axis, the probabilities of

exceeding a peak ground acceleration of 0.4g are

39.98% for no damage (D), 6.74% for slight damage

(C), 5.38% for moderate damage (B), 5.19% for

extensive damage (A), and 5.33% for complete

damage (As). Along the Y-axis, the probabilities are

18.15% for no damage (D), 5.31% for slight damage

(C), 5.25% for moderate damage (B), 5.23% for

extensive damage (A), and 0% for complete damage

(As).

As illustrated in Figure 22 (Appendix), the

probabilities of exceeding a peak ground

acceleration of 0.4 g for Engineering Building 3 in

the east-west direction along the X-axis are 55.46%,

21.98%, 8.07%, 5.31%, and 5.24%. Along the Y-

axis, the probabilities are 53.88%, 21.07%, 6.84%,

5.19%, and 5.39%. These values correspond to

damage levels of no damage (D), slight damage (C),

moderate damage (B), extensive damage (A), and

complete damage (As), respectively. Similarly, in

the north-south direction along the X-axis, the

probabilities of exceeding a peak ground

acceleration of 0.4 g for Engineering Building 3 are

53.96% for no damage (D), 18.18% for slight

damage (C), 6.24% for moderate damage (B),

5.22% for extensive damage (A), and 5.24% for

complete damage (As). Along the Y-axis, the

probabilities are 54.23% for no damage (D), 17.62%

for slight damage (C), 6.82% for moderate damage

(B), 5.19% for extensive damage (A), and 5.33% for

complete damage (As). The resulting fragility

curves indicate that as peak ground acceleration

increases, the likelihood of exceeding all damage

states also rises.

The study considered the seismic requirements

outlined in the National Structural Code of the

Philippines (NSCP), focusing on the probability of

exceedance (Pr) for the "complete damage (As)"

state. This assessment involved evaluating the

impact of a 0.4 g PGA earthquake along the east-

west and north-south axes of each building.

According to the NSCP, structures in the Philippines

are designed to endure a peak ground acceleration of

0.4g with a 10% probability of exceedance,[31],

which is also included in the CSIRO handbook

entitled "Designing Resilient”, [32]. An extract

from the book mentioned above is presented in

Figure 23.

Fig. 23: Basic Design PGA

In addition to the NSCP provision, the Structural

Engineers Association of California (SEAOC) has

the following excerpt: “A structure with 30 or more-

year lifespan is not SAFE when subjected to a

seismic event with a 10% probability of exceeding

the collapse or complete damage. The structure,

being more than 50 years old, is vulnerable to large-

magnitude earthquakes”, [33].

Table 11.A (Appendix) shows that under the

condition of complete damage (As), the

probabilities of exceedance for Engineering

Buildings 1, 2, and 3 in the East-West direction

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remain relatively consistent, with maximum values

of approximately 5%. Similarly, as summarized in

Table 11.B (Appendix), the probabilities of

exceedance at 0.4g PGA for complete damage (As)

in the North-South direction are approximately 5%

for Engineering Buildings 2 and 3. However,

Engineering Building 1 demonstrates a 0%

probability of exceedance under the complete

damage (As) condition in the Y-Axis, indicating no

vulnerability to this level of seismic loading for this

building. Furthermore, fragility curve analysis,

which evaluates the likelihood of structural damage

under seismic events, revealed that none of these

three buildings exceeded the 10% probability of

exceedance at 0.4 g PGA under “complete damage

(As).” This analysis conforms to the criteria

established by the National Structural Code of the

Philippines (NSCP) for buildings in Seismic Zone 4,

demonstrating that the structures are safe for

occupancy and do not require retrofitting measures.

The maximum peak ground acceleration (PGA)

values that Engineering Building 1 can withstand

with a 10% likelihood of exceedance are displayed

by the generated fragility curves shown in Table

12.A and Table 12.B in Appendix. In the east-west

direction(x-axis), the building can endure slight

damage of up to 0.50 g, moderate damage of up to

0.53 g, extensive damage of up to 0.55 g, and

collapse damage of up to 0.60 g. Along the y-axis in

the same direction, the building can withstand slight

damage of up to 0.55 g, moderate damage of up to

0.56 g, extensive damage of up to 0.59g, and

collapse damage of up to 0.60g. Similarly, in the

north-south direction along the x-axis, the analysis

revealed that Engineering Building 1 could

withstand the following maximum peak ground

accelerations (PGA) for potential earthquakes: 0.49

g for 'slight damage', 0.54 g for 'moderate damage',

0.58 g for 'extensive damage', and 0.60 g for

'collapse damage. Along the y-axis in the north-

south direction, the building can withstand slight

damage of up to 0.56g, moderate damage of up to

0.57g, and extensive damage of up to 0.58g.

The analysis of Engineering Building 2 indicates

its ability to withstand various levels of peak ground

acceleration (PGA) with a 10% probability of

exceedance. Along the east-west direction (x-axis),

the building can sustain slight damage of up to 0.55

g, moderate damage of up to 0.58 g, extensive

damage of up to 0.58 g, and collapse damage of up

to 0.60g. Along the y-axis in the same direction, it

can endure slight damage of up to 0.46 g, moderate

damage of up to 0.53 g, extensive damage of up to

0.57 g, and collapse damage of up to 0.60g.In the

north-south direction (x-axis), Engineering Building

2 can withstand slight damage of up to 0.55 g,

moderate damage of up to 0.59 g, extensive damage

of up to 0.60 g, and collapse damage of up to 0.60 g.

Along the y-axis in this direction, it can sustain

slight damage of up to 0.50 g, moderate damage of

up to 0.56 g, extensive damage of up to 0.59 g, and

collapse damage of up to 0.60 g.

The seismic fragility curves for Engineering

Building 3 in the east-west orientation show its

ability to withstand various levels of peak ground

acceleration (PGA) with a 10% probability of

exceedance. Along the x-axis, the building can

endure slight damage of up to 0.25 g, moderate

damage of up to 0.43 g, extensive damage of up to

0.56 g, and collapse damage of up to 0.60 g. Along

the y-axis in the same orientation, it can sustain

slight damage of up to 0.25 g, moderate damage of

up to 0.48 g, extensive damage of up to 0.58 g, and

collapse damage of up to 0.60 g. In the north-south

(x-axis), Engineering Building 3 can withstand

slight damage of up to 0.29 g, moderate damage of

up to 0.50 g, extensive damage of up to 0.58 g, and

collapse damage of up to 0.58 g. Along the y-axis in

this direction, it can endure slight damage of up to

0.29 g, moderate damage of up to 0.48g, extensive

damage of up to 0.58 g, and collapse damage of up

to 0.60g.

The maximum peak ground acceleration (PGA)

associated with a 10% probability of exceedance for

every damage condition for all structures is

displayed in Appendix in Table 12.A and Table

12.B. The results indicate that all three buildings

would sustain "complete damage (As)" at a

maximum PGA of 0.60 g. Consequently, it was

determined that these buildings can withstand a

maximum of 0.60 g, which exceeds the Philippine

National Structural Code's (NSCP) minimum

standard of 0.4g. According to the Modified

Mercalli Scale, a PGA of 0.60 g corresponds to

Intensity VIII, characterized as "severe" shaking,

[34]. This level of shaking can cause significant

structural damage and pose serious risks to

occupants and safety. If seismic activity exceeds a

PGA of 0.60 g, the structures will likely sustain

irreparable damage, rendering them unsafe for

occupancy. Additionally, the findings are in

Appendix in Table 12.A and Table 12.B align with

the pushover curve results shown in Figure 10,

Figure 11 and Figure 12, validating the directional

strengths of the buildings and confirming the

accuracy of the pushover analysis. When a structure

can withstand a higher PGA in the x-direction than

the y-direction, it signifies that the structural

integrity, reinforcements, and design along the x-

axis are more robust. This is often observed through

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higher base shear forces and greater peak ground

accelerations in that direction during analysis, [35].

Specifically, for Engineering Building 2, the base

shear force in the x-direction is 3402.297 kN,

significantly higher than the 2089.338 kN in the y-

direction, as shown in Figure 10. This disparity

indicates that Engineering Building 2 can withstand

a greater base shear force in the x-direction,

identifying it as the building's strongest axis. This

conclusion is further supported by consistently

higher peak ground acceleration values for all

damage states in the x-direction compared to the y-

axis, as shown in Appendix in Table 12.A and

Table 12.B. Similarly, for Engineering Buildings 1

and 3, the results show larger peak ground

accelerations in the y-direction than in the x-

direction, demonstrating that the y-direction is the

strong axis, confirming the results obtained from the

pushover curve as shown in Figure 11 and Figure

12.

4 Conclusion

Three buildings, namely Engineering Buildings 1

(BLDG4), Engineering Buildings 2 (BLDG5), and

Engineering Buildings 3 (BLDG6), with seismic

scores below the RVS FEMA P-154 cutoff of 2.0

underscore the importance of conducting further

detailed assessments that go beyond simple RVS

scores. These comprehensive evaluations are crucial

for precisely determining the level of vulnerability

of these buildings to seismic risks using fragility

analysis. By integrating comprehensive evaluation

data, such as detailed structural modeling, site-

specific ground motion characteristics, and

historical earthquake data, the fragility analysis

becomes more robust. This allows for a more

precise determination of the seismic performance of

the buildings, leading to more accurate predictions

of potential damage.

Furthermore, the analysis of the fragility curves

showed that Engineering Building 1, Engineering

Building 2, and Engineering Building 3, under the

condition of "complete damage (As)," demonstrated

a maximum probability of exceedance (Pr) of 5% at

0.40 g PGA. Because no value was more than 10%,

this result fulfills the minimum requirement set by

the National Structural Code of the Philippines

(NSCP) for structures in Seismic Zone 4.

Consequently, these buildings are declared safe for

occupancy and do not require retrofitting measures.

Moreover, the fragility curve analysis indicates

that Engineering Building 1, and Engineering

Building 2 have a low probability, below 10%, of

experiencing any damage from slight to complete

during seismic events. However, Engineering

Building 3 shows a higher likelihood of sustaining

slight damage, with a lower probability of

experiencing moderate to complete damage. This

suggests that while Engineering Building 3 may

suffer minor damage like hairline cracks and non-

structural component failures, it remains safe for

occupancy during most seismic events.

Finally, the results showed that Engineering

Building 1, Engineering Building 2, and

Engineering Building 3 would sustain "complete

damage (As)" at a maximum PGA of 0.60 g PGA.

Consequently, it was discovered that these buildings

can tolerate a maximum of 0.60 g, surpassing the

minimum standard of 0.4 g set by the National

Structural Code of the Philippines . According to the

Modified Mercalli Scale, a peak ground acceleration

(PGA) of 0.60g corresponds to Intensity VIII,

described as "severe" shaking, [36]. As peak ground

acceleration (PGA) increases, the probability of

exceeding each damage rank concurrently rises, as

shown in the resulting fragility curves. The fragility

curve indicates that the structure becomes highly

vulnerable during high PGA events. In the event of

an earthquake with a recorded PGA exceeding

0.60g, the structure has a high probability of

collapsing. Additionally, the analysis reveals that

Engineering Building 2 experienced higher peak

ground acceleration (PGA) along its y-axis. This can

be attributed to the y-axis being structurally

stronger, as confirmed by the results from the

pushover analysis. Therefore, the structural

components along the x-axis of Engineering

Building 2 were deemed more significant. Similarly,

Engineering Buildings 1 and 3 show larger peak

ground accelerations in the y-direction than in the x-

direction, demonstrating that the y-direction is the

strong axis.

Acknowledgement:

The authors would like to thank Pangasinan State

University (PSU) Urdaneta Campus for permitting

them to conduct the study.

Declaration of Generative AI and AI-assisted

Technologies in the Writing Process

During the preparation of this work the authors used

QuillBot in order to improve the readability and

language of the manuscript. After using this tool, the

authors reviewed and edited the content as needed

and take full responsibility for the content of the

publication.

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Development of Analytical Fragility Curves",

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no. 7, pp. 945-954, July 2017, [Online].

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San Fernando, Pampanga, Philippines Using

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(ICOSAT 2017), Jakarta, 2017, pp.140-142.

DOI: 10.2991/icosat-17.2018.30.

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

All authors are equal contributors to this work.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors declare that there are no conflicts of

interest.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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APPENDIX

Table 1. Local Ground Motion Data

Location

Magnitude

Latitude

Longitude

Depth

Date

Luzon, Philippines

Mw 7.2

13.45

124.63

18.02 km

24/02/1988

Luzon, Philippines

Mw 6.5

10.81

126.83

44.4 km

17/07/1990

Mindanao, Philippines

Mw 6.5

8.33

126.52

63.2 km

25/10/1990

Samar, Philippines

Mw 7.1

12.07

125.28

20.7 km

21/04/1995

Samar, Philippines

Mw 7.0

12.63

125.58

5.3 km

05/05/1995

Philippine Islands Region

Mw 7.6

10.81

126.83

44.4 km

31/08/2012

Luzon, Philippines

Mw 7.0

17.55

120.80

46.0 km

27/07/2022

Table 2. Foreign Ground Data Motion

Location

Magnitude

Latitude

Longitude

Depth

Date

Kuril Islands

Mw 7.1

45.26

149.89

36.6 km

07/02/1996

Near the Coast of Peru

Mw 8.0

-13.38

-76.56

41.2 km

15/08/2007

Near East Coast of Japan

Mw 9.1

38.29

142.50

19.7 km

11/03/2011

Near the Coast of Central Chile

Mw 8.3

-31.57

-71.67

22.4 km

16/09/2015

Central California

Mw 7.1

35.77

-117.60

8.0 km

06/07/2019

Table 5. Summary of Compressive Strength Used for Each Building

Location of

Test Area

Part of

Structure

Rebound Reading Number

Average

Rebound

Reading

Correction

Factor

Corrected

Compressive

Strength

(MPa)

A

B

C

D

E

F

G

H

I

J

Engineering

Building 2

Column

1

38.30

37.10

34.00

34.50

36.20

37.50

36.60

41.20

37.40

35.50

36.83

1

17.80

Beam 1

38.10

39.30

31.30

32.70

37.10

32.80

31.20

35.50

37.30

37.80

35.31

1

16.00

Engineering

Building 1

Column

2

34.60

44.10

36.80

39.20

34.90

40.00

39.90

37.00

36.70

40.50

38.37

1

19.10

Beam 2

39.40

43.20

44.40

49.10

42.00

42.90

39.00

40.70

37.10

46.80

42.46

1

21.80

Engineering

Building 3

Column

3

37.20

39.60

41.10

43.90

39.60

42.50

37.50

41.80

40.40

43.10

40.67

1

21.60

Beam 3

41.20

42.80

3480

42.40

37.30

39.60

41.20

40.70

44.20

40.23

1

21.30

Table 6. Summary of the tensile strength used for each building.

Test

Engineering Building 1

Engineering Building 2

Engineering Building 3

Mechanical Properties

Yield point (psi)

53.650

49,300

47,850

Tensile Strength (psi)

72,500

66,700

Elongation, %

20

TS/YS Ratio

1.35

1.47

1.39

Description of fracture

IRR

Bending Properties

Degree bent, 180 degrees

No crack

Physical Properties

Actual Unit Mass, kg/m

1.506

1.522

1.555

Variation in Mass, %

-2.96

-1.93

0.19

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Table 7. Performance Points summary tabulation based on the July 16, 1990, earthquake in Luzon, Philippines

(6.5)

Table 8. Damage State Threshold Limits of each School Building

Building Name

X – Direction

Y – Direction

Spectral Displacement (mm)

D

C

B

A

As

D

C

B

A

As

Engineering Building 1

Engineering Building 2

Engineering Building 3

0

12.892

14.055

33.162

18.417

20.079

47.347

34.585

58.428

103.765

83.088

173.476

272.939

0

11.754

18.506

10.348

16.792

26.437

14.783

33.344

85.646

79.024

83.001

263.273

271.748

PGA

East-West Direction

North-South Direction

X-Axis

Y-Axis

X-Axis

Y-Axis

V(KN)

D(mm)

V(KN)

D(mm)

V(KN)

D(mm)

V(KN)

D(mm)

0.1

161.629

1.013

145.137

1.238

86.033

0.560

116.230

0.846

0.2

323.265

1.981

290.276

3.203

172.059

1.075

232.456

2.420

0.3

484.893

2.948

435.413

5.168

258.092

1.590

348.686

3.994

0.4

646.522

3.916

580.549

7.133

344.124

2.106

464.910

5.567

0.5

808.158

4.884

725.688

9.097

430.157

2.621

581.142

7.141

0.6

969.787

5.852

870.825

11.062

516.183

3.136

697.366

8.714

0.7

1131.422

6.820

1015.964

13.027

602.216

3.651

813.596

10.288

0.8

1285.740

7.770

1161.101

14.992

688.249

4.166

929.820

11.861

0.9

1422.885

8.678

1306.238

16.957

774.275

4.681

1046.052

13.435

1

1559.975

9.585

1439.106

18.833

860.307

5.196

1162.286

15.008

1.1

1696.997

10.492

1538.897

20.454

946.340

5.712

1278.506

16.582

1.2

1833.959

11.399

1636.117

22.033

1032.373

6.227

1394.732

18.155

1.3

1970.866

12.305

1703.246

23.553

1118.399

6.742

1487.995

19.627

1.4

2107.706

13.211

1750.163

25.009

1204.432

7.257

1577.081

21.074

1.5

2244.484

14.117

1795.410

26.413

1285.415

7.768

1665.592

22.512

1.6

2381.208

15.022

1822.421

28.557

1362.316

8.277

1719.107

24.045

1.7

2517.866

15.927

1837.381

31.196

1439.689

8.789

1768.599

25.581

1.8

2654.468

16.831

1852.200

33.810

1517.549

9.304

1806.816

27.254

1.9

2791.004

17.735

1862.637

36.569

1595.897

9.823

1826.522

29.280

2

2914.284

18.581

1873.854

39.112

1674.729

10.345

1839.610

31.589

2.1

2954.486

19.063

1881.266

41.991

1754.063

10.870

1852.621

33.884

2.2

2993.651

19.533

1885.446

45.888

1833.898

11.399

1862.885

36.274

2.3

3027.965

20.153

1887.717

50.417

1914.238

11.931

1871.386

38.603

2.4

3048.454

21.432

1896.816

53.621

1995.082

12.466

1878.564

41.169

2.5

3068.735

22.698

1909.032

56.313

2076.447

13.004

1885.539

46.073

2.6

161.629

1.013

145.137

1.238

2158.331

13.547

1925.582

60.114

2.7

323.265

1.981

290.276

3.203

2240.735

14.092

1927.960

63.099

2.8

484.893

2.948

435.413

5.168

2323.673

14.641

1930.357

66.108

2.9

646.522

3.916

580.549

7.133

2407.149

15.194

1932.774

69.141

3.0

808.158

4.884

725.688

9.097

2491.162

15.750

1935.209

72.199

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Table 9. Sample Performance Points and Damage Ranking for Engineering Building 2 in

East-West Direction (y-direction)

PGA

D (mm)

DST

PGA

D (mm)

DST

0.1

3.773

D

1.6

99.976

A

0.2

8.273

D

1.7

103.798

A

0.3

12.773

D

1.8

107.318

A

0.4

17.273

D

1.9

110.699

A

0.5

21.318

C

2

271.975

As

0.6

25.133

C

2.1

289.502

As

0.7

30.173

B

2.2

302.407

As

0.8

36.878

B

2.3

310.541

As

0.9

44.605

B

2.4

318.423

As

1.0

67.657

B

2.5

326.042

As

1.1

67.657

B

2.6

332.870

As

1.2

81.329

B

2.7

339.473

As

1.3

89.378

A

2.8

345.862

As

1.4

93.742

A

2.9

354.010

As

1.5

96.798

A

3

370.062

As

Table 10. Sample Total Number of Occurrence in the East-West

Direction (y-axis) for Engineering Building 2

PGA (g)

Y - Direction

PGA (g)

Y - Direction

D

C

B

A

As

D

C

B

A

As

0.1

12

0

1.6

2

3

4

0

0.2

12

0

1.7

2

4

0

0.3

12

0

1.8

2

4

0

0.4

12

0

1.9

0

2

6

4

0

0.5

10

2

0

2.0

0

2

6

3

1

0.6

10

2

0

2.1

0

2

5

4

1

0.7

8

2

0

2.2

0

2

3

6

1

0.8

8

2

0

2.3

0

2

3

5

2

0.9

8

2

0

2.4

0

2

3

5

2

1.0

5

4

3

0

2.5

0

2

3

4

3

1.1

4

0

2.6

0

2

4

1.2

4

0

2.7

0

1

3

4

1.3

3

5

3

1

0

2.8

0

4

3

5

1.4

2

5

4

1

0

2.9

0

4

3

5

1.5

2

4

2

0

3.0

0

3

4

5

Table 11.A: Summary of Probability of Exceedance for PSU Buildings at 0.4g Peak Ground Acceleration in the

East-West Direction for Each Damage Rank

Building Name

East – West

X – Axis

Y - Axis

C

B

A

As

C

B

A

As

Engineering Building 1

Engineering Building 2

Engineering Building 3

6.53%

5.49%

21.98%

5.46%

5.20%

8.07%

5.25%

5.22%

5.31%

5.23%

5.47%

5.24%

5.32%

7.50%

21.07%

5.32%

5.61%

6.84%

5.19%

5.20%

5.19%

5.44%

5.29%

5.39%

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Table 11.B: Summary Of Probability of Exceedance for PSU Buildings at 0.4g peak ground acceleration in the

North-South Direction for every damage rank.

Building Name

North - South

X – Axis

Y - Axis

C

B

A

As

C

B

A

As

Engineering Building 1

Engineering Building 2

Engineering Building 3

6.74%

5.55%

18.18%

5.38%

5.19%

6.54%

5.19%

5.21%

5.22%

5.33%

5.39%

5.24%

5.31%

6.26%

17.62%

5.25%

5.34%

6.82%

5.23%

5.34%

5.19%

0%

5.27%

5.33%

Table 12.A: Maximum Peak Ground Acceleration in the East-West Direction with a 10% Probability of

Exceedance

Building Name

East – West

X – Axis

Y - Axis

C

B

A

As

C

B

A

As

Engineering Building 1

Engineering Building 2

Engineering Building 3

0.50 g

0.55 g

0.25 g

0.53 g

0.58 g

0.43 g

0.55 g

0.58 g

056 g

0.60 g

0.55 g

0.46 g

0.25 g

0.56 g

0.53 g

0.48 g

0.59 g

0.57 g

0.58 g

0.60 g

Table 12.B: Maximum Peak Ground Acceleration in the North-South Direction with a 10% Probability of

Exceedance

Building Name

North - South

X – Axis

Y - Axis

C

B

A

As

C

B

A

As

Engineering Building 1

Engineering Building 2

Engineering Building 3

0.49 g

0.55 g

0.29 g

0.54 g

0.59 g

0.50 g

0.58 g

0.60 g

0.58 g

0.60 g

0.58 g

0.56 g

0.50 g

0.29 g

0.57 g

0.56 g

0.48 g

0.58 g

0.59 g

0.58 g

0.60 g

Fig. 20: Seismic Fragility Curves of Engineering Building 2

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Fig. 21: Seismic Fragility Curves of Engineering Building 1

Fig. 22: Seismic Fragility Curves of Engineering Building 3

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