Appendix B Pushover Curve

!" #" $ % " & # '

( )

" )

*

!

!"#$ % "

! & ' & ( )*! &

" "*)+,-!

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TABLE OF CONTENTS /d/KE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϯ 'DEd͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϰ ,WdZ/͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱ /ŶƚƌŽĚƵĐƚŝŽŶ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱ ϭ͘ϭĂĐŬŐƌŽƵŶĚŽĨƚŚĞ^ƚƵĚǇ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱ ϭ͘Ϯ^ƚĂƚĞŵĞŶƚŽĨƚŚĞWƌŽďůĞŵ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϳ ϭ͘ϯKďũĞĐƚŝǀĞƐ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϵ ϭ͘ϰ^ŝŐŶŝĨŝĐĂŶĐĞŽĨƚŚĞ^ƚƵĚǇ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϵ ϭ͘ϱ^ĐŽƉĞĂŶĚ>ŝŵŝƚĂƚŝŽŶ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϬ ϭ͘ϲĞĨŝŶŝƚŝŽŶŽĨdĞƌŵƐ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϭ ŚĂƉƚĞƌ//͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯ ZĞǀŝĞǁŽĨZĞůĂƚĞĚ>ŝƚĞƌĂƚƵƌĞ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯ Ϯ͘ϭ&ŽƌĞŝŐŶ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϯ Ϯ͘Ϯ>ŽĐĂů͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϰ Ϯ͘ϯ&ƌĂŐŝůŝƚǇƵƌǀĞƐ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϲ Ϯ͘ϰƌŝĞĨ,ŝƐƚŽƌǇͬĂĐŬŐƌŽƵŶĚŽĨƚŚĞ^ƚƌƵĐƚƵƌĞ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϳ ,WdZ///͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϵ ŽŶĐĞƉƚƵĂůĂŶĚdŚĞŽƌĞƚŝĐĂů&ƌĂŵĞǁŽƌŬ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϵ ϯ͘ϭŽŶĐĞƉƚƵĂů&ƌĂŵĞǁŽƌŬ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϭϵ ϯ͘ϮdŚĞŽƌĞƚŝĐĂů&ƌĂŵĞǁŽƌŬ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘Ϯϭ ,WdZ/s͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϯϬ Dd,KK>K'z͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϯϬ ϰ͘ϭŽŶǀĞŶƚŝŽŶĂů&ƌĂŐŝůŝƚǇƵƌǀĞ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϯϬ ϰ͘ϮhŶĐŽŶǀĞŶƚŝŽŶĂů&ƌĂŐŝůŝƚǇƵƌǀĞ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϰϮ ,WdZs͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϰϰ Z^h>dE/^h^^/KE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϰϰ ,WdZs/͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϳ KE>h^/KEEZKDDEd/KE͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϳ ϲ͘ϭŽŶĐůƵƐŝŽŶ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϳ ϲ͘ϮZĞĐŽŵŵĞŶĚĂƚŝŽŶ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϴ />/K'ZW,z͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ϱϵ

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2

DEDICATION

This scholarly work is dedicated to my mother, Mrs. Zenaida Joaquin Bautista – Baylon and to my father, Mr. Isabelo Buan Baylon, who both helped me in sending to school and who selflessly found ways to provide me financial support as long as they can.

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ACKNOWLEDGMENT

This book will not possible without the valuable contribution of the following: To my publisher, Lambert Academic Publishing, Incorporated, for giving me this great opportunity to share to the world the fruits of my half-a-decade research works, specifically in the seismic assessments using fragility curves. To my brothers and sisters, who are always there to help me and always motivate me to pursue my career as an academician and practicing civil engineer. To my co-faculty members in Adamson University, University of the East – Caloocan & Manila campuses, Far Eastern University – East Asia College (now Institute of Technology), Malayan Colleges of Laguna, First Asia Institute of Technology and Humanities, Christian College of Tanauan, Pamantasan ng Lungsod ng Maynila (University of the City of Manila), and Manuel Luis Quezon University, who will always there to inspire me and teach me to love my profession as a teacher, mentor, quizzer coach, student organization adviser, and a family member away from my true home. To my former professors in Tanauan South Central School, De La Salle Lipa, De La Salle University – Manila, University of the Philippines – Diliman, who would never be tired in giving all their best to educate me and be who I am now, as a fellow educator. To my former, current, and future students who patiently attend my classes, pass what I have required them to accomplish, knowing that, in the near future, these will be useful in their chosen endeavor. To my former research advisees, who tirelessly followed and unfollowed my advises to make their research work valuable in their immediate community, and be a responsible researcher in the future. To my research mentors, DR. LESSANDRO ESTELITO O. GARCIANO, and DR. ANDRES WINSTON C. ORETA, of De La Salle University – Manila, who opened my youthful and vigorous mind in the vast area of knowledge through writing publishable research works, and never stopped inspiring, motivating, and inviting me to write more invaluable papers in local and international conferences, conventions, and journal papers. Dr. Garciano is very instrumental in the author’s development of interval analysis application to seismic fragility curves, to whom the author is indebted.

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CHAPTER I Introduction

1.1 Background of the Study

The specific geographic location of the Philippines make it vulnerable to a lot of tectonic activities. The country lies on the pacific ring of fire, making it prone to earthquakes. The ring of fire is an area in the basin of the Pacific Ocean where a large number of earthquakes occur. Thus this is the reason why the Philippines experience a lot of earthquake and in fact almost every week, low magnitude earthquake occur that an average person can take for granted. But regardless of their magnitudes, it may affect the integrity of many structures when accumulated. The country is susceptible to seismic hazards and it is essential for the people to know the threat that it will cause. Due to its vulnerability, there was a need to institutionalize systems and programs that would improve the disaster resilience of local communities (Aquino IV, 2015). Transportation lifelines was not an exception to this kind of phenomenon. This lifelines are used to transport manpower in businesses and commercial establishment. If affected, economic breakdown might arise due to lose of millions of pesos. Hence, the government should make their move regarding to this problem. The safety of the citizens and the integrity of the structure of this lifelines is at stake if a more destructive earthquake occur. Like the 2013 Bohol earthquake that generates a magnitude of 7.2 that cost a total of 2.25 billion worth of damage to public buildings, roads, bridges, and

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flood controls, in which more than 73,000 structures were damaged and more than 14,500 of that were totally destroyed (NDRRMC, 2013) . And the 1968 Casiguran earthquake which has a magnitude of 7.3, that damage a number of buildings beyond repair like the Ruby Tower. As follows, the need for seismic analysis for this structures emerge. To mitigate the effects of such temblor, retrofitting the structure that might collapse is the best choice. Earthquake hazards was cheaper than rebuilding (Palafox Jr., 2015). To date, it is impossible to predict when earthquake will strike even with the current technology the world has to offer. But based on historical records, the next West Valley Fault “Big One” might happen within this lifetime. In the last 1,400 years, the West Valley Fault only moved four times and has an interval of 400 years. The last major earthquake from the West Valley Fault happened in 1658 (Solidum Jr., 2015). Analyzing the records, the West Valley Fault is due on this modern days. A large earthquake from the West Valley Fault can significantly affect the metro manila. The sensational West Valley Fault runs through Bulacan, Rizal, Quezon City, Marikina City, Makati City, Pasig City, Taguig City and Muntinlupa City down to Laguna and Cavite (Solidum Jr., 2015). It is predicted to generate a magnitude 7.2 earthquake that may cause an estimated 12.7 percent heavy and 25.6 percent partly damage in residential building while heavy damage is estimated around 8-10 percent and partly damage is 20-25 percent for public buildings. Given Manila's population of 9,932,560 it is estimated to have a 33,500 or 0.3 percent fatalities. And a total of 113,600 or 1.1 percent of the population may also be injured. Since the magnitude 7.2 may also cause fire an additional count of deaths by fire of 18,000 people (PHIVOLCS, 2014).But being aware

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of the structural soundness of these lifelines and other buildings will most likely lessen the casualties. The West Valley Fault is approximately 10 kilometers away from the Monumento station of LRT line 1, which will be the focus of this research. This research will study and provide a seismic analysis on the piers of the LRT 1 between the Monumento station and 5th Avenue station. It has been 30 years since the construction of the LRT line 1. Since then, many disaster the line withstand like the Rizal day bombing, earthquakes, and floods that may cause deterioration to the piers and foundation. Doing research would be essential as the threat of this “Big One” arises.

1.2 Statement of the Problem The susceptibility of the Philippines to earthquakes is very high. The piers in LRT line 1, 5th avenue station- Monumento is at risk. Thus taking a research on this transportation lifeline on how vulnerable it is, must be taken into a momentous consideration. That is why this research will endeavor on how the LRT Line 1, 5th Avenue to Monumento Station behaves when subjected into a certain peak ground acceleration motion, followed by this question: What is the probability of exceedance of every category in damage rank of LRT line 1 Monumento to 5th Avenue station and carriageway piers under shear failure when subjected to ground motion level 1,2 and 3? As prescribed by seismic design of railroad bridges (Mathews, 2002). •

Level 1 Ground motion represents that during the life of the structure it has an occasional event with a reasonable probability of being exceeded.

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•

Level 2 Ground motion represents that during the life line of the structure it has a rare event with a low probability of being exceeded.

•

Level 3 Ground motion represents that during the lifeline of the structure it has a very rare or maximum credible event with a very low probability of being exceeded.

“These levels are defined in terms of peak ground acceleration with a given average return period”. (Mathews, 2002)

Table 1: Level 1, Level 2 and Level 3 Ground motion level Earthquake Magnitude 0.0-4.99 5.0-5.99 6.0-6.99 6.0-6.99 >7.0

Ground motion Level 1 1 2&3 2&3

Distance From Epicenter Action California & Baja Remainder of N.A. n/a n/a none 50 100 Restricted speed 150 300 Restricted speed 100 200 Stop & inspect As directed, but not less than for lower magnitude

(Source: Seismic design of railroad bridge,2002)

In the Philippines there is a limited study concerning seismic assessment of transportation lifeline. And based on the results of those studies, it come up with a certain probability that the structure will be damaged, hence, there will be a certain cost for repair and rehabilitation.

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1.3 Objectives This research aims to establish conventional and unconventional seismic fragility curves of the LRT carriageway pier. Specifically, •

To accurately assess the seismic performance of LRT pier.

•

To come up with an upper bound and lower bound fragility curve using Interval Uncertainty Analysis.

1.4 Significance of the Study Nowadays, earthquake trends in the Philippines because of the study made by the MMEIRS that the west valley fault will crack within this time period. This study will provide not only data that will assess the structure from earthquake, but also for other professionals to understand the result of a certain earthquake into the structure. This study can be used by the government for creating efficient solution in dealing with seismic forces. This research is relatively new in the Philippines, this means that the Philippines is not yet ready for this kind of catastrophic phenomenon. This research also emphasize to give precautionary measures that can assist to mitigate the hazard that may happen to the structure when exposed to earthquake. Assessing the piers in LRT line 1 can save thousands of life. Informing the public on the result of the lifeline when it fails into earthquakes that was used in this study can

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minimize casualties when the said disaster happens. The safety of those people who uses the said facility can be ensured. In addition, the LRT is located over the Rizal Avenue Extension road; with this, the Rizal Avenue Extension road will be unpassable if the lifeline will fall into the critical damage category and for that, two transportation lifelines will be inaccessible. This study will be beneficial to the government, people within the vicinity and daily passengers of the LRT. And also this study can be used by the government for creating efficient solution in dealing with seismic forces.

1.5 Scope and Limitation This study is made to assess the capability of piers of LRT to resist shear failure when subjected to a certain Ground motion level. But the main scope of this research is to investigate one pier in 5th avenue station to monument station. There are two types of analysis that will be applied; the nonlinear static analysis (Pushover analysis) and nonlinear dynamic analysis (Time history analysis), to obtain the yield stiffness of the structure. The study is only limited to seismic forces. The investigation will only focus on the behavior of the pier and its capacity to resist shear failure.

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1.6 Definition of Terms

Assessment. The act of making a judgement about something. Fragility Curves.

It is define as the probabilities of damage for specified damage

states at various levels of ground acceleration. Intensity. Describes the perceived surface ground shaking and damage caused by an earthquake. Pushover Analysis. It is a static, nonlinear procedure using simplified nonlinear technique

to

estimate

seismic

structural

deformations.

It

is

an

incremental

static analysis used to determine the force-displacement relationship, or the capacity curve, for a structure or structural element. Time-History Analysis.

Time-history analysis provides for linear or nonlinear

evaluation of dynamic structural response under loading which may vary according to the specified time function.

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Ductility Factor. The ratio of the total deformation at maximum load to the elastic-limit deformation. Yield Energy. Energy that comes from something. Damage Index. A Damage index is thus defined as the ratio between the initial and the reduced resistance capacity of a structure, evaluated by using an evolution equation for the yield strength in which the structural damageability is included. The ability of this index to model different damage situations is demonstrated. Peak Ground Acceleration. It is a measure of earthquake acceleration on the ground and an important input parameter for earthquake engineering, also known as the design basis earthquake ground motion (DBEGM). Pier. A solid support designed to sustain vertical pressure, in particular.

Magnitude of an Earthquake. It is a number assigned by the Richter magnitude scale to quantify the energy released by an earthquake. Pacific Ring of Fire. It is an arc around the Pacific Ocean where many volcanoes and earthquakes are formed. West Valley Fault. One of the two major fault segments of the Valley Fault System which runs through the cities of Marikina, Pasig and Muntinlupa and is capable of producing large scale earthquakes on its active phases with a magnitude of 7 or higher. Retrofit.

To furnish with new or modified parts or equipment not available or

considered necessary at the time of manufacture.

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Chapter II Review of Related Literature

The review of related literature for this chapter will be incorporating considerable topics as backdrop for the proposed research. Topics included are: Seismic Assessment of Built Structures for both foreign and local study, Fragility Curves, and Brief History of LRT line 1.

2.1 Foreign Extensive seismic accident during the past few decades have continued to demonstrate the destructive power of earthquake, with failures to structures such as bridges, as well as giving rise to great economic losses. Economic losses for bridges very often surpass the cost of damage and should therefore be taken into account in selecting seismic design performance objectives (Girard, Légeron, & Roy, 2012). Highway bridge network has a compelling contribution towards the economic welfare of a country and thus earthquake induced damage to bridge structures can cause potential economic catastrophe to the country (Siddiquee, 2015) .Thus, seismic analysis would be more constructive before the said earthquake to happen. One of the most popular mean in evaluating the seismic performance of existing and newly construct building is by the use of nonlinear static pushover analysis. The expectation is that the pushover analysis will provide adequate information on seismic demands imposed by the design ground motion on the structural system and its components (Shetty et.al n.d.). Nonlinear static (pushover analysis) is one of four

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analysis procedures embodied in FEMA 356 / ASCE 41 and commonly used in performance-based design approaches (Dutta, n.d.). By several researchers (Banerjee & Shinozuka, 2007; Mander, 1999; Mander & Basoz, 1999; Shinozuka et al., 2000); it is performed on bridge components to estimate their capacity whereas component demand is calculated from response spectrum analysis. Later, seismic capacity and demand are plotted together against increasing spectral acceleration. Probabilities of reaching any certain damage states are calculated from the intersection between these two plots. Although this method captures the nonlinear response of structure, lack of ability to consider the hysteresis damping of the structure makes it less attractive. Nonlinear dynamic time history analysis is considered as the most effective method for fragility analysis and used widely by several researchers (Billah and Alam, 2013; Choi, 2002; Karim and Yamazaki, 2003; Nielson, 2005; Padgett, 2007). Its ability to capture the dynamic response of structure by considering geometric nonlinearity and material inelasticity allows producing reliable fragility curves. Unlike other methods fragility analyses using nonlinear time history analysis necessitates a large amount of ground motion time history data that also results in high computational costs. This particular study adopted nonlinear time history analysis to generate seismic fragility curves for wall pier bridge type (Siddiquee, 2015).

2.2 Local It was the Luzon earthquake of July 1990 that researchers start the collaborative study about the seismic hazard analysis in the Philippines. The seismic hazard in the Philippines was evaluated from historical earthquake data using a new computer program called the Seismic Hazard Mapping Program (H-Map). The seismic hazard is

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given in terms of the expected peak ground acceleration and expected acceleration response spectrum. Regions including Central Luzon which suffered heavy damage during the 16th of July 1990 earthquakes were identified. The design level of seismic force of the Philippines was then compared with those of Japan and is found to be considerably lower. Long period structures are found to be more vulnerable to damage. The collection of strong ground motion records from Philippine earthquakes is necessary for more realistic design levels for the Philippines. From the seismic hazard maps, a seismic zoning map based on the expected maximum accelerations is proposed (Yamazaki, F.; Molas, G. L; Tomatsu, Y.;, 1992). Another study conducted due to the collaborative effort of Japan International Cooperation Agency (JICA), Metropolitan Manila Development Authority (MMDA), and Philippine Institute of Volcanology and Seismology (PHIVOLCS) was the “Study for Earthquake Impact Reduction for Metropolitan Manila in the Republic of the Philippines (MMEIRS)”. This study was conducted from August of 2002 to March of 2004 and covered the entire Metropolitan Manila, with an area of 636 km2. This study aims to achieve “A Safer Metropolitan Manila from Earthquake Impact” and proposed its goals and main objectives listed as follows; 1) To develop a national system resistant to earthquake impact, 2) To improve Metropolitan Manila’s urban structure resistant to earthquake, 3) To enhance effective risk management system, 4) To increase community resilience, 5) To formulate reconstruction systems, 6) To promote research and technology development for earthquake impact reduction measures (MMEIRS, 2004) .

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The study began by analyzing the past historically recorded earthquakes and instrumentally recorded earthquakes, a total of 18 earthquakes were selected as scenario earthquakes, which have potential damaging effect to Metropolitan Manila: also earthquake ground motion, liquefaction potential, slope stability and tsunami height are estimated. Finally three models (namely, model 08 (West Valley Faults M.7.2), Model 13 (Manila Trench M.7.9), Model 18 (1863 Manila Bay M.6.5)), were selected for detail damage analysis because these scenario earthquakes show typical and severe damages to Metropolitan Manila. Given the previous models the MMEIRS study estimated the damage of the potential rupture of West Valley Fault, approximately 40% of the total number of residential buildings within Metropolitan Manila will collapse or be affected. This building collapse directly affects large numbers of people, since it is estimated to cause 34,000 deaths and 114,000 injuries. Moreover, additional 18,000 deaths are anticipated by the fire spreading after the earthquake event. This human loss, together with properties and economy losses of Metropolitan Manila will be a national crisis (MMEIRS, 2004).

2.3 Fragility Curves Bridges, railway bridges, are one of the most susceptible highway structures when it comes in seismic damages. The method often used in assessing the capability of specific structure to an earthquake is seismic fragility curve (Shinozuka, et.al 2001). Fragility curve is a conditional probability of a structure of attaining or exceeding a given damage when subjected to seismic loads (Zhong et.al 2010). Basically, it is the most commonly used method in assessing structures under the occurrence of an earthquake, to come up with evaluating seismic risks as well as for decision-making process.

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Seismic fragility curve analysis has a huge role in seismic risk assessment; yet some fragility models of structures focus on the condition of the structure assuming that it is newly build, yet the service life of the structure have the chance of ignoring the fact that it will face multiple earthquakes during the its lifetime (Yan, 2013).The output of fragility curve can be used by researchers, reliability experts, administrators, and design engineers to evaluate and improve the structural and non-structural seismic capability of structures (Requiso, 2013). .There is no particular applicable best method for calculating fragility curves (Shinozuka et al, 2000).Different methods such as non-linear static and non-linear dynamic may be used. Both linear and nonlinear are used for structural analysis of structures. In nonlinear analysis, behavior of material beyond linear elastic limit, nonlinearity, are taken into account, this method uses ground motion data to be executed. The seismic fragility curves assess the vulnerability of a structure for each damage state namely; slight, moderate, extensive and complete damage. The probability of exceeding in percent of a particular damage is plotted with the ground motion intensity which expressed in PGA (Peak Ground Acceleration) .

2.4 Brief History/Background of the Structure The project which aims to raise the public transport to a higher level was initiated in October of 1981. It is said that in the 1980s the number of automobiles in Metro Manila’s streets has grown by an average of 10.82% annually and at the same time it also has the 39.26% of the nation’s total number of vehicles, at this point public

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transport was nearing its “saturation point” but was still barely able to meet the demand, it was then the former First Lady Imelda R. Marcos, who happened to be the Governor of Metro Manila, wanted her “City of Man” to be on par with other world capital. She noted that the NCR (National Capital Region) lacked an operating rail-based transport network. The result was the elevated ‘no frills’ basic transport line now known as the LRT (Light Rail Transit), or Metrorail (Satre, 1998). The construction of the LRT line 1 was divided into three phases – the first phase started at Taft Avenue between EDSA and Libertad (Phase 1A) the second phase was the construction of the Rizal line (Phase 1B) and the third phase was the construction of the Pasig River Bridge which then connect the north and south sections. The project which was almost taken 5 years to be finished was put into service on May 12, 1985 (LRTA, 2014). Since its completion no seismic assessment of its piers had ever been conducted and only maintenance keep its piers intact, as early as 1990 the LRT was showing premature aging due mostly to its poor maintenance and overloading (Satre, 1998). In relation with the issue of the “Big One”, will these piers stand against the destructive force of this earthquake? “In the West Valley Fault earthquake scenario, many structures in the Metro Manila will be destroyed and approximately 37 000 lives will be lost” (Solidum, Jr., 2014)

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CHAPTER III Conceptual and Theoretical Framework

3.1 Conceptual Framework Structural Model and Ground motion Data Nonlinear Static Analysis (Pushover Analysis)

Failure: Mode of Shear

Nonlinear Dynamic Analysis (Time History Analysis)

Interval Uncertainty Analysis (IUA)

Parameters for Damage Index Damage Indices

IUA Seismic Fragility Curves

Plot of Difference of IUA Seismic Fragility Curves vs Conventional Fragility Curves = INPUT

= PROCESS

= OUTPUT

Figure 3. 1 Conceptual Framework of the research (Source: Baylon, 2015)

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Figure 3.1 illustrates the Conceptual Framework of the Study. First, work on the Structural Model and the Normalized Ground Motion Data gathered. The architectural and the structural plans of the LRT Line 1 obtained from the office of Light Railway Transit Authority will be the basis of the structural model. The mode of failure used is shear. Using Non-Linear Static (Pushover Analysis) and Non-linear Dynamic (Timehistory Analysis), the conventional seismic fragility curves has been developed with the assistance of the SAP2000. The outputs of the given two nonlinear analyses are the parameters for the damage index formula. These parameters were calculated to get the lower bound, upper bound, and mean value of the damage indices using the Interval Uncertainty Analysis for every ground motion data’s peak ground accelerations (PGA) from 0.2g to 2.0g. Each damage index corresponds to a certain damage rank by Hazus (2003). These damage ranks were counted as frequencies to compute the probabilities of occurrence for different values of the Peak Ground Acceleration (PGA). The probabilities of occurrence were used to compute the mean and standard deviations that will be used in the lognormal equation for the analysis of fragility curve for every level of damage. Then the seismic fragility curve was created by plotting the cumulative lognormal probability versus the peak ground acceleration for every levels of damage. By comparing these fragility curves to the conventional seismic fragility curves creates another plot of the difference of Interval Uncertainty Analysis’ (IUA) Fragility curves to that of conventional fragility curves.

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3.2 3.2.1

Theoretical Framework PGA Normalization

To obtain the IUA fragility curves and conventional fragility curves, the structural model of LRT line 1 station is subjected to both nonlinear static analysis and nonlinear dynamic analysis. In this study, the ground motion records should be multiplied to the ratio of normalized peak ground acceleration and the original peak ground acceleration as shown in equation 1 (Requiso, 2013). The Normalized Ground Motion data is scaled up or down from the original ground motion data. § PGANormalized (GroundMoti on )¨ ¨ PGA Original ©

3.2.2

· ¸ ¸ ¹

ሺͳሻ

Pushover Analysis (Nonlinear Static Analysis)

Push over analysis is just one type of Nonlinear Static Analysis which is primarily used for estimating the strength and drift capacity of a structure when subjected into a certain earthquake (Estella, Gamit, Liolio, & Reyes, 2015). It is performed by subjecting a structure to a monotonically increasing pattern of lateral loads, representing the inertial forces which would be experienced by the structure when subjected to ground shaking. Under incrementally increasing loads various structural elements may yield sequentially. Consequently, at each event, the structure experiences a loss in stiffness. The expectation is that the pushover analysis will provide adequate information on seismic demands imposed by the design ground motion on the structural system and its

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components (Govind, Shetty, & Hegde, n.d.). In other words, a pushover curve is used to identify the yield stiffness of the structure. The pushover analysis has two types, the force controlled pushover and displacement controlled pushover. In force controlled pushover the structure is pushed until it reach a certain force. While the displacement controlled pushover the structure is pushed until it reach a specified displacement (Estella, Gamit, Liolio, & Reyes, 2015). In this study, the researchers only used the displacement controlled type of pushover analysis. Also in this analysis, the relationship between force and displacement is shown.

3.2.3

Time History Analysis (Nonlinear Dynamic Analysis)

It utilizes the combination of ground motion records with a detailed structural model, therefore is capable of producing results with relatively low uncertainty (Estella, Gamit, Liolio, & Reyes, 2015). Nonlinear dynamic analysis or the time history analysis is considered as the most effective method for fragility analysis and used widely by several researchers. Its ability to capture the dynamic response of structure by considering geometric nonlinearity and material inelasticity allows producing reliable fragility curves. To perform the dynamic response analysis, the pier was modelled as a single-degree-of freedom (SDOF) system using a bilinear model (Priestley et al. 1996). The time history analysis have 3 types namely, bilinear model, peak-oriented model and pinching model. When the model is based on the standard bilinear hysteretic rules with kinematic strain hardening it is bilinear model. When For the bilinear model, this model is based on the standard bilinear hysteretic rules with kinematic strain hardening. When the model keeps the basic hysterical rules (proposed by Clough and Johnston in 1966),

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it is peak-oriented model. And when the model is similar to peak-oriented model but has two parts: which are the maximum permanent deformation and maximum load experienced in the direction of loading then it is pinching model (Estella, Gamit, Liolio, & Reyes, 2015).

3.2.4

Ductility Factors

The software used can directly perform the nonlinear static analysis (pushover analysis) and the nonlinear dynamic analysis (time history analysis) to come up with the ductility factors. The ductility factors such as the displacement ductility (d), ultimate ductility (u), and the hysteretic energy ductility (h) were obtained in order to further assess the damage of the bridge pier. To come up with conventional seismic fragility curves, ductility factors are needed (Karim & Yamazaki, 2001).

Ɋୢ ൌ

ߜ௠௔௫ ሺ݀‫ܿ݅݉ܽ݊ݕ‬ሻ ሺʹሻ ߜ௬

Ɋ୳ ൌ

ߜ௠௔௫ ሺ‫ܿ݅ݐܽݐݏ‬ሻ ሺ͵ሻ ߜ௬

Ɋ୦ ൌ

‫ܧ‬௛ ሺͶሻ ‫ܧ‬௘

Where: ߜ௠௔௫ ሺ‫ܿ݅ݐܽݐݏ‬ሻ= displacement at maximum reaction at the push over curve (static)

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ߜ௠௔௫ ሺ݀‫ܿ݅݉ܽ݊ݕ‬ሻ= maximum displacement at the hysteresis model (dynamic) ߜ௬ = yield displacement from the push-over curve (static) ‫ܧ‬௛ = hysteretic energy, i.e., area under the hysteresis model ‫ܧ‬௘ = yield energy, i.e., area under the push-over curve (static) but until yield point only 3.2.5

Damage Index Calculation

With the use of ductility factors, the damage indices of the pier can now be computed using equation 5.

‫ܫ‬஽ ൌ

Ɋୢ ൅ ߚɊ୦ ሺͷሻ Ɋ୳

Where ߚ is the cyclic loading factor taken as 0.15 for bridges.

3.2.6

Damage Rank by Hazus

By using Table 3.1, the damage rank (DR) for each damage index (‫ܫ‬஽ ) can be identified (Requiso, 2013). Table 3. 1 Relationship between the damage index (DI) and damage rank (DR) Damage index (ࡵࡰ ) 0.00 < ୈ 0.14 0.14 < ୈ 0.40 0.40 < ୈ 0.60 0.60 < ୈ 1.00 1.00 ࡵࡰ Source: HAZUS, 2003

Damage rank (DR) D C B A As

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Definition No damage Slight damage Moderate damage Extensive damage Complete damage

3.2.7 Interval Arithmetic Operations

In computing for intervals, the key point is it is like computing with sets (Moore et.al, 2009). In both axes, X and Y, the basic arithmetic operations presented are given by upper and lower bound. ܺ෨ ൌ ൣܺܺ൧ܻ෨ ൌ ൣܻܻ൧ By definition then, the sum of two intervals X and Y is the set ܺ෨ ൅ ܻ෨ ൌ ൣܺ ൅ ܻܺ ൅ ܻ൧ሺ͸ሻ The difference of two intervals X and Y is the set ܺ෨ െ ܻ෨ ൌ ൣܺ െ ܻܺ െ ܻ൧ሺ͹ሻ The product of X and Y is given by ܺ෨ܻ෨ ൌ ሾ݉݅݊ܵ݉ܽ‫ܵݔ‬ሿሺͺሻ Where: ܵ ൌ ൣܻܻܻܻܺܺܺܺ൧ In Division, it can be done via multiplication by the reciprocal of the second operand ܺ෨ Ȁܻ෨ ൌ ܺ෨ሾͳȀܻ෨ሿሺͻሻ Where: ͳȀܻ෨ ൌ ൣͳȀܻͳȀܻ൧

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This assumes 0 ‫ ב‬Y

3.2.8 Interval Uncertainty Analysis

In this study, the researchers not only tend to come up with the conventional fragility curves but also to construct the IUA fragility curves to deal with the uncertainties of this research. The importance of IUA fragility curves is to give a boundary to the conventional fragility curves. The assumption of the researchers is that all the results of Nonlinear Static Analysis and Nonlinear Dynamic Analysis are in Normal Distribution function.

Figure 3. 2 Concept of Interval Uncertainty Analysis in Setting a Value of Interval Based from a Normal Distribution (Source: Baylon, 2015) ෩ is the interval, μ−σ is the lower bound, and μ+σ is the upper bound Where ܺ To get the lower and upper bound

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ߪ ‫ܥ‬Ǥ ܱǤ ܸǤ ൌ ሺͳͲሻ ߤ The value of the Coefficient of Variation may vary between 1%, 5%, 10%, and 20% depending on the outcome of the fragility curve. There is an optimum C.O.V. in every damage ranks. ܺ ൌ ሾሺͳ െ ‫ܸܱܥ‬ሻߤሺͳ ൅ ‫ܸܱܥ‬ሻߤሿሺͳͳሻ

Input intervals in equations 2-5 to get Interval Uncertainty Analysis (IUA). To come up with the values of the damage indices intervals, the outputs of the software are the parameters. These parameters were calculated to get the lower bound, upper bound, and mean value of the damage indices using the Interval Uncertainty Analysis for every ground motion data’s peak ground accelerations (PGA) (Baylon, 2015).

ߤ෤ௗ ൌ

ߜሚ௠௔௫ ሺ݀‫ܿ݅݉ܽ݊ݕ‬ሻ ሺʹሻ ߜሚ௬

ߤ෤௨ ൌ

ߜሚ௠௔௫ ሺ‫ܿ݅ݐܽݐݏ‬ሻ ሺ͵ሻ ߜሚ௬

Ɋ෤୦ ൌ

‫ܫ‬ሚ஽ ൌ

‫ܧ‬෨௛ ሺͶሻ ‫ܧ‬෨௘

Ɋ෤ୢ ൅ ߚɊ෤୦ ሺͷሻ Ɋ෤୳

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3.2.9 Probability of Exceedance

After knowing the damage rank, the damage ratio can be calculated. The damage ratio is defined as the number of occurrence of each damage rank (no, slight, moderate, extensive, and complete) divided by the total number of records (Requiso, 2013). Once acquired, the damage ratio was plotted with the ln (PGA) on a lognormal probability paper to obtain the necessary parameters (mean and standard deviation) to construct the fragility curves. After getting the mean and standard deviation, the probability of exceedance (PR) can now be computed. Where Φ is the standard normal distribution, X is the peak ground acceleration, is the mean and is the standard deviation. ܲோ ൌ ) ቆ

ሺܺሻ െ ɉ ቇ ሺͳʹሻ Ƀ

෨ ෩ ቆሺܺሻ െ ɉቇ ሺͳʹሻ ෪ோ ൌ ) ܲ Ƀ෨ The Following equations (1-5 and 12) were adapted from Karim and Yamazaki (2001)

3.2.10 Fragility Analysis

Then by plotting the acquired cumulative probability vs the peak ground acceleration (PGA normalized to different excitation), the Seismic fragility curve can be obtained (Karim & Yamazaki, 2001).

28

3.2.11 Comparison of Conventional to IUA Fragility Curves

Finally, make fragility curves using the acquired cumulative probability from “Interval Uncertainty Analysis”. Then compare these fragility curves to conventional fragility curves creates the plot of difference of IUA’s Fragility curves to that of conventional fragility curves.

29

CHAPTER IV METHODOLOGY

The primary goal of this research is for the researchers to construct a reliable

conventional seismic fragility curves and IUA seismic fragility curves of the LRT line 1, 5th Avenue to Monumento carriageway pier. The research will primarily use the two known methods namely nonlinear static analysis and nonlinear dynamic analysis for the construction of the conventional seismic fragility curves and IUA seismic fragility curves to account for the shear failure of the railway piers when subjected to different ground motions using SAP 2000. This research adopted the method used by Habibullah & Pyle (1998) for the nonlinear static analysis and the method by Karim & Yamazaki (2001) for the nonlinear dynamic analysis. To explain further, the nonlinear static analysis is use to obtain the yield and maximum displacement of the structure from the generated push over curve as well as the yield energy. On the other hand the nonlinear dynamic analysis is use to determine the maximum displacement and the hysteretic energy of the hysteresis model, the output of the two analyses are the necessary parameters in constructing the conventional seismic fragility curves as well as the IUA seismic fragility curves. This procedure is possible by using the SAP 2000.

4.1 Conventional Fragility Curve The following are the step by step procedure for the nonlinear static analysis by Habibullah & Pyle (1998):

30

ϭ͘ Model the whole system using SAP 2000 and define the necessary section

properties in the usual manner. The graphical interface of the structural computer programs makes this task quick and easy. See figures

Figure 4. 1 Structure Model

(a)

(b)

Figure 4.2 Section Properties (a) Lower Section (b) Upper Section

Ϯ͘ Define properties and acceptance criteria for the pushover hinges. The two

programs includes several built-in default hinge properties that are based on average values from ATC-40 for concrete members and average values from FEMA-273 for steel members. These built in properties can be useful for

31

preliminary analyses, but user defined properties are recommended for final analyses. ϯ͘ Locate the pushover hinges on the model by selecting one or more frame

members and assigning them one or more hinge properties.

(a)

32

(b) Figure 4.3 (a) Hinge Assignment (b) Auto Hinge Properties

33

ϰ͘ Define the pushover load cases.

(a)

(b) Figure 4.4 (a) Push Over Case Properties (b) Load Cases

34

ϱ͘ Run the basic static analysis as well as the static nonlinear pushover analysis. ϲ͘ Display the pushover curve.

Figure 4.5 Push Over Curve

35

The sample generated pushover curve shown in Fig. 4.6 will now provide the yield and maximum displacement of the system. The area under the yield displacement is defined as the Energy at yield. These values will be used later on once the nonlinear dynamic analysis has been finished

(a)

(b) Figure 4.6 (a) Push Over (b) Yield Point of Push Over Curve

For the nonlinear dynamic analysis, the researchers will use the selected ground motion data obtained from past historical earthquakes. The steps for this method of analysis by Karim and Yamazaki (2001) are as follows: 1. Select the earthquake ground motion records. 2. Normalize PGA of the selected records to different excitation levels. 3. Create the basic computer model of the system using SAP 2000.

36

4. Input the earthquake ground motion data in SAP2000 by defining the time history function.

Figure 4.7 Time History Definition

37

5. Define the time history load case which is a nonlinear modal function.

Figure 4.8 Time History Case Properties

38

6. Run the non-linear dynamic response analysis using the selected records.

Figure 4.9 Load Cases (Time history)

7. The program will now display the plot function known as the hysteretic model for the nonlinear dynamic response analysis which will provide the hysteretic energy and the maximum displacements. A sample hysteresis model is shown in Fig. 4.2.

Figure 4.10 Hysteresis

39

For the construction of the conventional seismic fragility curve an analytical approach will be adopted to construct the fragility curves of the system (Karim and Yamzaki, 2001). The steps in constructing the seismic fragility curves are as follows: ϭ͘ Obtain the ductility factors. The maximum displacement and hysteretic energy

obtained from Time history analysis along with the obtain maximum displacement, displacement at yield and yield energy from the pushover analysis were accounted to solve for the ductility factors known as displacement ductility, ultimate ductility and hysteretic energy ductility using equations 2a, 3a and 4a respectively. Ɋୢ ൌ

ߜ௠௔௫ ሺ݀‫ܿ݅݉ܽ݊ݕ‬ሻ ͲǤͳͲͳ ൌ ൌ ͻǤͺͳ ͲǤͲͳͲ͵ ߜ௬

Ɋ୳ ൌ

ߜ௠௔௫ ሺ‫ܿ݅ݐܽݐݏ‬ሻ ͲǤʹ͵ ൌ ൌ ʹʹǤ͵͵ ͲǤͲͳͲ͵ ߜ௬

Ɋ୦ ൌ

‫ܧ‬௛ ͹ʹǤͷͷ ൌ ൌ ʹǤʹ͵ ‫ܧ‬௘ ͵ʹǤ͸Ͳ͵

Ϯ͘ Obtain the damage indices of the structure in each excitation level using equation

5a. ‫ܫ‬஽ ൌ

Ɋୢ ൅ ߚɊ୦ ͻǤͺͳ ൅ ሺͲǤͳͷሻሺʹʹǤ͵͵ሻ ൌ ൌ ͲǤͶͷͶ ʹʹǤ͵͵ Ɋ୳

ϯ͘ Calibrate the damage indices for each damage rank. In this study the

researchers will use Table 2 which shows the relationship between the damage

40

index and damage rank, this step will be repeated prior to the other selected ground motion data. (HAZUS, 2013).

Table 4 Kobe-Takatori (X-direction) ϰ͘ Obtain the number of occurrences of each damage rank in each excitation level

and get the damage ratio. In this step the number of occurrence of each damage rank at their respective ground excitation level is counted. A sample table for number of occurrence is shown in Fig. 4.9.2.

ϭϬϬй ϴϬй ϲϬй ϰϬй ϮϬй Ϭй

Ϭ͘ϮŐ

EŽĂŵĂŐĞ;Ϳ

Ϭ͘ϰŐ

Ϭ͘ϲŐ

^ůŝŐŚƚĂŵĂŐĞ;Ϳ

Ϭ͘ϴŐ

ϭ͘ϬŐ

ϭ͘ϮŐ

DŽĚĞƌĂƚĞĂŵĂŐĞ;Ϳ

ϭ͘ϰŐ

ϭ͘ϲŐ

ǆƚĞŶƐŝǀĞĂŵĂŐĞ;Ϳ

ϭ͘ϴŐ

Ϯ͘ϬŐ

ŽŵƉůĞƚĞĂŵĂŐĞ;ƐͿ

Figure 4.11 Probability of Occurrence

ϱ͘ Construct the fragility curves for each damage rank using log normal distribution.

Obtain the mean and standard deviation for each damage rank, the cumulative probability of exceedance (PR) of the damage equal or higher than the damage

41

rank can be computed using equation 12a. Then by simply plotting acquired cumulative probability with the peak ground acceleration (PGA normalized to different excitation), the fragility curve can now be obtained.

4.2 Unconventional Fragility Curve For the construction of the Interval Uncertainty Analysis (IUA) Seismic fragility curves, the parameters obtained from the two methods of analysis will be used. In this study, the researchers use Interval application namely Octave to obtain the parameters for IUA. The steps in this method of research are as follows (Baylon, 2015). 1. Compute for the intervals using the basic arithmetic operations, equations 6-9 shows the basic arithmetic operations use to compute for the intervals. 2. Input the intervals in equations 2b, 3b, 4b and 5b to get the Interval Uncertainty Analysis (IUA). Use the outputs of the software as the parameters to obtain the values of the damage indices intervals.

3. Get the lower bound, upper bound, and mean value of the damage indices using the Interval Uncertainty Analysis for every ground motion data’s peak ground accelerations (PGA). See Appendices D.2 and D.3. 4. Compute for the probability of occurrence for IUA using equation 12b. 5. Using the acquired cumulative probability from “Interval Uncertainty Analysis” the IUA seismic fragility curves can now be construct.

42

6. Finally, evaluate the probability of exceedance difference. By comparing the

fragility curves derived by using IUA to the conventional seismic fragility curves creates another plot of the difference of IUA mean probabilities to that of conventional probabilities versus Peak Ground Acceleration.

43

CHAPTER V RESULT AND DISCUSSION

By following strictly the methodology and with the aid of the materials used in this research, the researchers was able to come up with the following results. The conventional fragility curve shows the different amount of damages to pier in LRT line 1 located between the 5th Avenue to Monumento Station when subjected to different peak ground acceleration with shear being the mode of failure. Lifelines in the Philippines such as the LRT are designed to withstand a peak ground acceleration of 0.4g according to the Department of Public Works and Highways – Bureau of Design (DPWH-BoD). The conventional fragility curve for Y-direction in figure 5.1 shows the plot of the probability of exceedance versus the peak ground acceleration, analyzing this plot, it can be seen that the probability of exceedance are 11.62%, 6.66%, 6.18%, and 6.16% for slight damage (C), moderate damage (B), extensive damage (A) and complete damage (As) respectively.

44

&ƌĂŐŝůŝƚǇƵƌǀĞƐ;ŽŶǀĞŶƚŝŽŶĂůͿzŝƌĞĐƚŝŽŶ WƌŽďĂďŝůŝƚǇŽĨǆĐĞĞĚĂŶĐĞ;ŝŶйͿ

ϭϬϬй ϵϬй ϴϬй ϳϬй ϲϬй ϱϬй ϰϬй ϯϬй ϮϬй ϭϬй Ϭй Ϭ

Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ ;ĐͿ

;ĐͿ

;ĐͿ

Ɛ;ĐͿ

Figure 5.1 Fragility Curves (Conventional) Y Direction

Referring to the figure 5.2, the conventional seismic fragility curves for the x direction of the asset, as the plot shows, it can be seen that the probability of exceedance in this direction are 10.96%, 6.56%, 6.15%, and 6.23% for slight damage (C), moderate damage (B), extensive damage (A) and complete damage (As) respectively.

45

&ƌĂŐŝůŝƚǇƵƌǀĞƐ;ŽŶǀĞŶƚŝŽŶĂůͿyŝƌĞĐƚŝŽŶ WƌŽďĂďŝůŝƚǇŽĨǆĐĞĞĚĂŶĐĞ;ŝŶйͿ


Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ ;ĐͿ

;ĐͿ

;ĐͿ

Ɛ;ĐͿ

Figure 5.2 Fragility Curves (Conventional) X Direction

Now, the concept of the Interval Uncertainty Analysis has been applied and the plot shown is the IUA – Mean for Y-direction shown in figure 5.3, the plot shows the following probabilities of exceedance, for the slight damage (C) a probability of exceedance of 17.04% can be observed, 6.59% for moderate damage (B), 6.34% for extensive damage (A) and 6.24% for complete damage (As).

46

&ƌĂŐŝůŝƚǇƵƌǀĞƐ;/hͲDĞĂŶͿzŝƌĞĐƚŝŽŶ ϭϬϬй WƌŽďĂďŝůŝƚǇŽĨǆĐĞĞĚĂŶĐĞ;ŝŶйͿ

ϵϬй ϴϬй ϳϬй ϲϬй ϱϬй ϰϬй ϯϬй ϮϬй ϭϬй Ϭй

Ϭ

Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ ;/hͲDͿ

;/hͲDͿ

;/hͲDͿ

Ɛ;/hͲDͿ

Figure 5.3 Fragility Curves (IUA-Mean) Y Direction

The IUA – Mean seismic fragility curve for X-direction in figure 5.4 shows the following probabilities of exceedance, for slight damage (C) its probability of exceedance is found to be 12.93%, for moderate damage (B) it is 6.81%, 6.31% for extensive damage (A), and 6.27% for the complete damage (As).

47

&ƌĂŐŝůŝƚǇƵƌǀĞƐ;/hͲDĞĂŶͿyŝƌĞĐƚŝŽŶ ϭϬϬй WƌŽďĂďŝůŝƚǇŽĨǆĐĞĞĚĂŶĐĞ;ŝŶйͿ

ϵϬй ϴϬй ϳϬй ϲϬй ϱϬй ϰϬй ϯϬй ϮϬй ϭϬй Ϭй Ϭ

Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ ;/hͲDͿ

;/hͲDͿ

;/hͲDͿ

Ɛ;/hͲDͿ

Figure 5.4 Fragility Curves (IUA-Mean) X Direction

Using the mean seismic fragility curves for both X and Y directions, the researchers was able to come up with the so-called “bounded” fragility curve for each damage rank, the purpose of this fragility curve is to eliminate the uncertainties in this research (aleatoric and epistemic uncertainties), moreover, this seismic fragility curve is also useful for the cost analysis of the possible retrofitting process for the asset. In figure 5.5, the bounded fragility curve for slight damage (C) in the Y-direction, can be observed that at 0.4g, the upper and lower boundaries are 26.67% and 7.42% respectively, therefore a range of 19.25% is given to determine the cost of retrofitting.

48

ŽƵŶĚĞĚ&ƌĂŐŝůŝƚǇƵƌǀĞƐ͕ZсΗΗ WƌŽďĂďŝůŝƚǇŽĨǆĐĞĞĚĂŶĐĞ;ŝŶйͿ


Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ ;ĐͿ

;>Ϳ

;hͿ

Figure 5.5 Bounded Fragility Curves, DR="C"

For the moderate damage (B) in Y-direction, the bounded fragility curve shows that the upper boundary is 7.02% and a lower boundary is 6.16%, therefore a 0.86% of range is given to determine the cost of retrofitting in this damage category, in figure 5.6 at 0.4g

49



Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ ;ĐͿ

;>Ϳ

;hͿ

Figure 5.6 Bounded Fragility Curves, DR="B"

For the extensive damage (A) in Y-direction, the plot of the bounded fragility curve in figure 5.7 shows that at 0.4g, an upper boundary of 6.52% and a lower boundary of 6.17% has been found, therefore a 0.35% of range is given to determine the cost of retrofitting in this damage category.

50



Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ ;ĐͿ

;>Ϳ

;hͿ

Figure 5.7 Bounded Fragility Curves, DR="A"

Lastly, for the bounded fragility curve with a damage rank of As (complete damage) in the Y-direction in figure 5.8, the plot shows a relatively small probability of exceedance. Analyzing this plot, it can be found out that the probability of exceedance of the upper boundary of this fragility curve is found to be 6.14% and that of the lower boundary is 6.34%, this only means that retrofitting in at this stage is not applicable anymore.

51

ŽƵŶĚĞĚ&ƌĂŐŝůŝƚǇƵƌǀĞƐ͕ZсΗƐΗ WƌŽďĂďŝůŝƚǇŽĨǆĐĞĞĚĂŶĐĞ;ŝŶйͿ


Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ Ɛ;ĐͿ

Ɛ;>Ϳ

Ɛ;hͿ

Figure 5.8 Bounded Fragility Curves, DR="As"

From the figure 5.9, the bounded fragility curve for slight damage (C) in the Xdirection, shows that the upper and lower boundaries are 18.72% and 7.15% respectively at 0.4g, therefore a range of 11.57% is given to determine the cost of retrofitting.

52



Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ ;ĐͿ

;>Ϳ

;hͿ

Figure 5.9 Bounded Fragility Curves, DR="C"

For the moderate damage (B) in X-direction, the bounded fragility curve shows that the upper boundary is 7.41% and a lower boundary is 6.20%, therefore a 1.21% of range is given to determine the cost of retrofitting in this damage category, in figure 5.10 at 0.4g

53



Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ ;ĐͿ

;>Ϳ

;hͿ

Figure 5.10 Bounded Fragility Curves, DR="B"

For the extensive damage (A) in X-direction, the plot of the bounded fragility curve in figure 5.11 shows that at 0.4g, an upper boundary of 6.27% and a lower boundary of 6.34% has been found, it can be seen that the upper boundary yields a much smaller probability of exceedance than the lower boundary, it can be simply explained that at this category, retrofitting is not applicable.

54



Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ ;ĐͿ

;>Ϳ

;hͿ

Figure 5.11 Bounded Fragility Curves, DR="A"

Lastly, for the bounded fragility curve with a damage rank of As (complete damage) in the X-direction in figure 5.12, this plot shows a relatively small probability of exceedance. Analyzing this plot, it can be found out that the probability of exceedance of the upper boundary of this fragility curve is found to be 6.20% and that of the lower boundary is 6.34%, this only means that retrofitting at this stage is not applicable anymore.

55

ŽƵŶĚĞĚ&ƌĂŐŝůŝƚǇƵƌǀĞƐ͕ZсΗƐΗ WƌŽďĂďŝůŝƚǇŽĨǆĐĞĞĚĂŶĐĞ;ŝŶйͿ


Ϭ͕Ϯ

Ϭ͕ϰ

Ϭ͕ϲ

Ϭ͕ϴ

ϭ

ϭ͕Ϯ

ϭ͕ϰ

ϭ͕ϲ

ϭ͕ϴ

Ϯ

W';ŝŶŐͿ Ɛ;ĐͿ

Ɛ;>Ϳ

Ɛ;hͿ

Figure 5.11 Bounded Fragility Curves, DR="As"

Comparing the probability of exceedance of X and Y fragility curves at 0.4g peak ground acceleration. The Y fragility curve yields a much higher probability than X. The reason behind this is that either the Y-direction of the structure is the weak axis or the ground motions are prominent in Y-direction than that of the X-direction.

56

CHAPTER VI CONCLUSION AND RECOMMENDATION

6.1 Conclusion It is known that Philippine structures were designed to withstand a 0.4g earthquake, referring to the table 6.1, a 0.4g earthquake can caused a moderate to heavy damage in the structure. Checking the validity of the constructed fragility curve, at 0.4g (PGA) the plot shows a relatively small percentage of probability of exceedance. It is also known thru the use of constructed fragility curve that the structure will have a high percentage of probability of exceedance, that the structure will have an extensive damage at 2.0g (PGA). Which is acceptable since it is only an approximation. We conclude that the structure can tolerate an earthquake that most likely to occur in the Philippines, hence the structure is relatively safe and strong.

W'ŝŶƌĞůĂƚŝŽŶǁŝƚŚŝŶƚĞŶƐŝƚǇ ;^ŽƵƌĐĞ͗^ĞŝƐŵŝĐƐƐĞƐƐŵĞŶƚŽĨ>Zd>ŝŶĞϭ^ŽƵƚŚǆƚĞŶƐŝŽŶWŝĞƌǇĞůĂƌŵĞŶĞƚůͿ

57

6.2 Recommendation For the future researchers of Seismic Fragility Curve of LRT. The researchers recommend to assess a pier which is slender than the pier in Monumento and 5th Avenue Station for comparison such as the pier in Monumento to Balintawak Station. As an addition, the researchers would also recommend to make a fragility curve for confinement failure to understand more about the behavior of LRT pier. In part of modelling, the researchers recommend to study a method or another approach in dealing with the whole system of LRT for a much greater results. Also the researchers would like to suggest to model and assess the asset (structure) using finite element method. In application of the IUA, the researchers suggest to apply the Interval Arithmetic Operation on the Pushover Curve and the Hysteresis Model for more accurate result of the interval. Also, to use more earthquake datum occurring specifically in the Asia. The use of another software would also be recommended such as Seismostruct and CSI Bridge.

58

BIBLIOGRAPHY Aquino IV, P. B. (2015). Calling for a Study on the Authorities. http://newsinfo.inquirer.net/. Baylon, M. B. (2015). Reliability analysis of bridge pier using interval uncertainty analysis. a graduate thesis. EARTHQUAKE ENGINEERING. Dutta, A. (n.d.). Estella, V. A., Gamit, J. D., Liolio, R. L., & Reyes, J. V. (2015). Seismic Assessment of Lambingan Bridge. Girard, Légeron, & Roy. (2012). A Model for Seismic Performance Assessment, n.p. Karim, K. R., & Yamazaki, F. (2001). Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation. EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS. LRTA. (2014). Mathews, R. (2002). Design of Railroad Bridge. MMEIRS. (2004). 1. NDRRMC. (2013). National Disaster Risk Reduction and Management Council. Palafox Jr., F. (2015). Are We Ready For The "Big One". PHIVOLCS. (2014). Philippine Institute of Volcanology and Seismology. Requiso, D. (2013). Seismic Fragility of Transportation Lifeline Piers in the Philippines, under Shear Failure, Relationship between the damage index (DI) and the damage rank (DR). Earthquake Engineering, 20, 38. Satre, G. L. (1998). The Metro Manila LRT System - A Historical Perspective. New Urban Transit Systems, 36.

59

Siddiquee, K. N. (2015). SEISMIC VULNERABILITY ASSESSMENT OF WALL PIER HIGHWAY BRIDGES IN BRITISH COLUMBIA, n.p. Solidum Jr., R. (2015). Earthquake Hazards and Risk Scenario for Metro Manila and Vicinity: the Need for Whole of Society Preparedness. Yamazaki, F.; Molas, G. L; Tomatsu, Y.;. (1992). Seismic hazard analysis in the Philippines using earthquake occurence data. Earthquake Engineering, 1.

60

Appendix A Computation of Dead Load

61

ĞĂĚ>ŽĂĚŽŵƉƵƚĂƚŝŽŶ

62

Appendix B Pushover Curve

63

APPENDIX B: PUSHOVER CURVE

64

Appendix C Hysteresis Models

65

Appendix C.1 Hysteresis Models (Shear X)

66

Appendix C.1: Hysteresis Models (Shear X) SHEAR X – BOHOL SHEAR X (BOHOL) – 1.0g

SHEAR X (BOHOL) – 0.2g SHEAR X (BOHOL) – 0.4g

SHEAR X (BOHOL) – 0.6g SHEAR X (BOHOL) – 0.8g

67

SHEAR X (BOHOL) – 1.2g





68

SHEAR X – KOBE-HIK

SHEAR X (KOBE-HIK) – 0.2g


SHEAR X (KOBE-HIK) – 0.6g SHEAR X (KOBE-HIK) – 0.4g

69






70


SHEAR X – KOBE-KAKOGAWA

SHEAR X (KOBE-KAKOGAWA) – 1.0g


SHEAR X (KOBE-KAKOGAWA) – 0.6g SHEAR X (KOBE-KAKOGAWA) – 0.4g

71






72


SHEAR X – KOBE-KJM

SHEAR X (KOBE-KJM) – 0.2g


SHEAR X (KOBE-KJM) – 0.6g SHEAR X (KOBE-KJM) – 0.4g

73






74


SHEAR X – KOBE-NISHI AKASHI

SHEAR X (KOBE-NISHI AKASHI) – 0.2g




75






76


SHEAR X – KOBE-SHIN OSAKA SHEAR X (KOBE-SHIN OSAKA) – 0.6g

SHEAR X (KOBE-SHIN OSAKA) – 0.2g SHEAR X (KOBE-SHIN OSAKA) – 1.0g

77

SHEAR X (KOBE-SHIN OSAKA) – 0.4g





78



SHEAR X – KOBE-TAKARAZU

SHEAR X (KOBE-TAKARAZU) – 0.2g


79







80



SHEAR X – KOBE-TAKATORI

SHEAR X (KOBE-TAKATORI) – 0.2g


81







82



SHEAR X – MINDORO-MRK

SHEAR X (MINDORO-MRK) – 0.2g


83





SHEAR X (MINDORO-MRK) – 1.8g SHEAR X (MINDORO-MRK) – 0.8g

84



SHEAR X – MINDORO-PHV

SHEAR X (MINDORO-PHV) – 0.2g


85







86



SHEAR X – MINDORO-SKB

SHEAR X (MINDORO-SKB) – 0.2g


87







88



SHEAR X – TOHOKU-AIC SHEAR X (TOHOKU-AIC) – 0.2g

89

SHEAR X (TOHOKU-AIC) – 0.6g






90




SHEAR X – TOHOKU-FKS

91

SHEAR X (TOHOKU-FKS) – 0.2g






92





93

SHEAR X – TOHOKU-HYG

SHEAR X (TOHOKU-HYG) – 0.2g






94





95

SHEAR X – TOHOKU-SIT

SHEAR X (TOHOKU-SIT) – 0.2g






96





97

Appendix C.2 Hysteresis Models (Shear Y)

98

Appendix C.2: Hysteresis Models (Shear Y) SHEAR Y – BOHOL

SHEAR Y (BOHOL) – 0.2g






99





100

SHEAR Y – KOBE-HIK

SHEAR Y (KOBE-HIK) – 0.2g






101





102

SHEAR Y – KOBE-KAKOGAWA

SHEAR Y (KOBE-KAKOGAWA) – 0.2g






103





104

SHEAR Y – KOBE-KJM

SHEAR Y (KOBE-KJM) – 0.2g






105





106

SHEAR Y – KOBE-NISHI AKASHI

SHEAR Y (KOBE-NISHI AKASHI) – 0.2g






107





108

SHEAR Y – KOBE-SHIN OSAKA

SHEAR Y (KOBE-SHIN OSAKA) – 0.2g






109





110

SHEAR Y – KOBE-TAKARAZU

SHEAR Y (KOBE-TAKARAZU) – 0.2g






111





112

SHEAR Y – KOBE-TAKATORI

SHEAR Y (KOBE-TAKATORI) – 0.2g






113





114

SHEAR Y – MINDORO-MRK

SHEAR Y (MINDORO-MRK) – 0.2g






115





116

SHEAR Y – MINDORO-PHV

SHEAR Y (MINDORO-PHV) – 0.2g






117





118

SHEAR Y – MINDORO-SKB

SHEAR Y (MINDORO-SKB) – 0.2g






119





120

SHEAR Y – TOHOKU-AIC

SHEAR Y (TOHOKU-AIC) – 0.2g






121





122

SHEAR Y – TOHOKU-FKS

SHEAR Y (TOHOKU-FKS) – 0.2g






123





124

SHEAR Y – TOHOKU-HYG

SHEAR Y (TOHOKU-HYG) – 0.2g






125





126

SHEAR Y – TOHOKU-SIT

SHEAR Y (TOHOKU-SIT) – 0.2g






127





128

46

Appendix C.3 Maximum Displacement from Hysteresis Model

129

Appendix C.3.: Maximum Displacement from Hysteresis Model

Dy/DhD/^W>DEd&ZKD,z^dZ^/^DK>;^,ZyͿ D/EKZK W'ŝŶƚĞƌŵƐŽĨŐ K,K> DZ;^,ZyͿ dK,KDEd&ZKD,z^dZ^/^DK>;^,ZyͿ DEd&ZKD,z^dZ^/^DK>;^,ZzͿ ;^,ZyͿ D/EKZK K,K> DZ;^,ZyͿ ;^,ZzͿ D/EKZK W'ŝŶƚĞƌŵƐŽĨŐ K,K> DZ/dzK&yEKEsEd/KE>;^,ZyͿ KhEd W' Ɛ Ϭ͘ϮŐ Ϭ͘ϭϵϭϵϭϮ Ϭ͘ϬϭϯϬϴϲ Ϭ͘ϬϬϴϱϭϮ Ϭ͘ϬϭϬϮϱϴ Ϭ͘ϬϭϮϵϮϵ Ϭ͘ϰŐ Ϭ͘ϰϯϵϮϯϳ Ϭ͘ϭϬϵϲϰϲ Ϭ͘Ϭϲϱϱϴϯ Ϭ͘Ϭϲϭϰϱ Ϭ͘ϬϲϮϮϵϲ Ϭ͘ϲŐ Ϭ͘ϲϬϱϮϵϲ Ϭ͘ϮϱϵϬϲϱ Ϭ͘ϭϱϵϰϱϲ Ϭ͘ϭϯϳϴϳϳ Ϭ͘ϭϮϵϬϵϲ Ϭ͘ϴŐ Ϭ͘ϳϭϯϵϴϰ Ϭ͘ϰϬϳϴϭϲ Ϭ͘Ϯϲϯϰϭϵ Ϭ͘ϮϮϭϬϱϰ Ϭ͘ϭϵϵϱϰϳ ϭ͘ϬŐ Ϭ͘ϳϴϳϬϰϭ Ϭ͘ϱϯϰϳϱϲ Ϭ͘ϯϲϮϵϰ Ϭ͘ϯϬϭϳϮϳ Ϭ͘ϮϲϳϱϯϮ ϭ͘ϮŐ Ϭ͘ϴϯϳϲϵϵ Ϭ͘ϲϯϲϰϲ Ϭ͘ϰϱϮϮϯϲ Ϭ͘ϯϳϲϬϲϱ Ϭ͘ϯϯϬϲϰϲ ϭ͘ϰŐ Ϭ͘ϴϳϯϴϯϳ Ϭ͘ϳϭϱϳϳϵ Ϭ͘ϱϮϵϴϳϰ Ϭ͘ϰϰϮϴϳϱ Ϭ͘ϯϴϴϭϲϭ ϭ͘ϲŐ Ϭ͘ϵϬϬϮϱϵ Ϭ͘ϳϳϲϵϵϯ Ϭ͘ϱϵϲϯϮϰ Ϭ͘ϱϬϮϭϲϵ Ϭ͘ϰϰϬϭϬϲ ϭ͘ϴŐ Ϭ͘ϵϭϵϵϵϰ Ϭ͘ϴϮϰϭϮϰ Ϭ͘ϲϱϮϳϳϭ Ϭ͘ϱϱϰϰϳϯ Ϭ͘ϰϴϲϴϮϵ Ϯ͘ϬŐ Ϭ͘ϵϯϱϬϬϴ Ϭ͘ϴϲϬϰϳϵ Ϭ͘ϳϬϬϱϴϭ Ϭ͘ϲϬϬϰϵϳ Ϭ͘ϱϮϴϳϵϴ

WZK/>/dzK&yEKEsEd/KE>;^,ZzͿ KhEd W' Ɛ Ϭ͘ϮŐ Ϭ͘Ϯϯϱϲϭϵ Ϭ͘ϬϭϰϮϰ Ϭ͘ϬϬϴϰϰϰ Ϭ͘ϬϬϵϲϵϭ Ϭ͘ϬϭϭϲϮϱ Ϭ͘ϰŐ Ϭ͘ϰϳϵϵϴϱ Ϭ͘ϭϭϲϮϯϭ Ϭ͘Ϭϲϲϱϴϲ Ϭ͘Ϭϲϭϳϲϱ Ϭ͘ϬϲϭϲϬϳ Ϭ͘ϲŐ Ϭ͘ϲϯϯϳϴϱ Ϭ͘ϮϳϬϱϳϮ Ϭ͘ϭϲϮϵ Ϭ͘ϭϰϭϱϱϴ Ϭ͘ϭϯϮϮϴϴ Ϭ͘ϴŐ Ϭ͘ϳϯϮϯϵϵ Ϭ͘ϰϮϭϳϯ Ϭ͘Ϯϲϵϱϭ Ϭ͘ϮϮϴϵϵϲ Ϭ͘ϮϬϳϵϱϰ ϭ͘ϬŐ Ϭ͘ϳϵϴϯϴϰ Ϭ͘ϱϰϵϬϴϳ Ϭ͘ϯϳϭϮϮϱ Ϭ͘ϯϭϯϳϰϯ Ϭ͘ϮϴϭϮϮϮ ϭ͘ϮŐ Ϭ͘ϴϰϰϮϳϭ Ϭ͘ϲϱϬϬϲϮ Ϭ͘ϰϲϮϬϴϮ Ϭ͘ϯϵϭϱϭϰ Ϭ͘ϯϰϵϬϵϴ ϭ͘ϰŐ Ϭ͘ϴϳϳϮϮϲ Ϭ͘ϳϮϴϭϭϯ Ϭ͘ϱϰϬϲϴϳ Ϭ͘ϰϲϭϬϬϭ Ϭ͘ϰϭϬϲϰϲ ϭ͘ϲŐ Ϭ͘ϵϬϭϱϯϳ Ϭ͘ϳϴϳϴϴϰ Ϭ͘ϲϬϳϲϮ Ϭ͘ϱϮϮϮϱϱ Ϭ͘ϰϲϱϴϲϵ ϭ͘ϴŐ Ϭ͘ϵϭϵϴϳϴ Ϭ͘ϴϯϯϱϴϵ Ϭ͘ϲϲϰϭϴϲ Ϭ͘ϱϳϱϴϵϳ Ϭ͘ϱϭϱϭϲϳ Ϯ͘ϬŐ Ϭ͘ϵϯϯϵϴϰ Ϭ͘ϴϲϴϲϮϳ Ϭ͘ϳϭϭϴϱϯ Ϭ͘ϲϮϮϳϰϳ Ϭ͘ϱϱϵϬϵϮ

168

Appendix G.2 Tabulated Probability of Exceedance (IUA Lower Bound)

169

Appendix G.2: Tabulated Probability of Exceedance (IUA Lower Bound)

WZK/>/dzK&yE>KtZKhE;^,ZyͿ KhEd Ɛ Ϭ͘ϮŐ Ϭ͘ϭϱϲϱϮϰ Ϭ͘ϬϬϴϰϱϳ Ϭ͘ϬϭϮϰϭϯ Ϭ͘Ϭϭϰϰϲϱ Ϭ͘Ϭϭϰϰϲϱ Ϭ͘ϰŐ Ϭ͘ϰϬϭϳϭ Ϭ͘ϬϳϭϱϬϲ Ϭ͘Ϭϲϭϵϴϱ Ϭ͘Ϭϲϯϯϵϳ Ϭ͘Ϭϲϯϯϵϳ Ϭ͘ϲŐ Ϭ͘ϱϳϳϱϯϵ Ϭ͘ϭϳϳϲϴϲ Ϭ͘ϭϯϬϭϵϳ Ϭ͘ϭϮϲϲϴϱ Ϭ͘ϭϮϲϲϴϱ Ϭ͘ϴŐ Ϭ͘ϲϵϱϯϮϰ Ϭ͘Ϯϵϰϯϯϯ Ϭ͘ϮϬϮϱϱϰ Ϭ͘ϭϵϮϯϰϳ Ϭ͘ϭϵϮϯϰϳ ϭ͘ϬŐ Ϭ͘ϳϳϱϬϲϳ Ϭ͘ϰϬϯϴϳ Ϭ͘ϮϳϮϰϴϯ Ϭ͘ϮϱϱϰϬϮ Ϭ͘ϮϱϱϰϬϮ ϭ͘ϮŐ Ϭ͘ϴϯϬϯϰϰ Ϭ͘ϰϵϵϴϲϵ Ϭ͘ϯϯϳϯϲϮ Ϭ͘ϯϭϯϵϳϰ Ϭ͘ϯϭϯϵϳϰ ϭ͘ϰŐ Ϭ͘ϴϲϵϲϬϱ Ϭ͘ϱϴϭϮϲϴ Ϭ͘ϯϵϲϯϴϳ Ϭ͘ϯϲϳϱϰ Ϭ͘ϯϲϳϱϰ ϭ͘ϲŐ Ϭ͘ϴϵϴϭϮϮ Ϭ͘ϲϰϵϭϴϱ Ϭ͘ϰϰϵϱϳϭ Ϭ͘ϰϭϲϭϳϮ Ϭ͘ϰϭϲϭϳϮ ϭ͘ϴŐ Ϭ͘ϵϭϵϮϱϭ Ϭ͘ϳϬϱϰϰϭ Ϭ͘ϰϵϳϮϴϮ Ϭ͘ϰϲϬϭϵ Ϭ͘ϰϲϬϭϵ Ϯ͘ϬŐ Ϭ͘ϵϯϱϭϴϱ Ϭ͘ϳϱϭϵϮϭ Ϭ͘ϱϰϬϬϭϰ Ϭ͘ϱ Ϭ͘ϱ W'

WZK/>/dzK&yE>KtZKhE;^,ZzͿ KhEd W' Ɛ Ϭ͘ϮŐ Ϭ͘ϭϳϱϳϵϳ Ϭ͘ϬϬϴϱϵϰ Ϭ͘ϬϬϵϵϭϰ Ϭ͘Ϭϭϭϳϱϱ Ϭ͘Ϭϭϰϰϲϱ Ϭ͘ϰŐ Ϭ͘ϰϮϮϳϰϰ Ϭ͘Ϭϳϰϭϳϴ Ϭ͘Ϭϲϭϱϵϴ Ϭ͘Ϭϲϭϲϱϵ Ϭ͘Ϭϲϯϯϵϳ Ϭ͘ϲŐ Ϭ͘ϱϵϯϮϵϭ Ϭ͘ϭϴϰϴϯϵ Ϭ͘ϭϯϵϵϱϵ Ϭ͘ϭϯϭϵϬϭ Ϭ͘ϭϮϲϲϴϱ Ϭ͘ϴŐ Ϭ͘ϳϬϲϬϬϯ Ϭ͘ϯϬϱϳϬϱ Ϭ͘ϮϮϱϱϵϵ Ϭ͘ϮϬϲϵϴϭ Ϭ͘ϭϵϮϯϰϳ ϭ͘ϬŐ Ϭ͘ϳϴϭϵϳϲ Ϭ͘ϰϭϴϮϳϮ Ϭ͘ϯϬϴϲϯϳ Ϭ͘Ϯϳϵϲϲϭ Ϭ͘ϮϱϱϰϬϮ ϭ͘ϮŐ Ϭ͘ϴϯϰϲϯϰ Ϭ͘ϱϭϲϬϰϰ Ϭ͘ϯϴϰϵϴϭ Ϭ͘ϯϰϳϬϭϯ Ϭ͘ϯϭϯϵϳϰ ϭ͘ϰŐ Ϭ͘ϴϳϮϭϭϴ Ϭ͘ϱϵϴϭϵϰ Ϭ͘ϰϱϯϯϲϲ Ϭ͘ϰϬϴϭϮϰ Ϭ͘ϯϲϳϱϰ ϭ͘ϲŐ Ϭ͘ϴϵϵϰϰ Ϭ͘ϲϲϲϭϮϲ Ϭ͘ϱϭϯϴϮϰ Ϭ͘ϰϲϮϵϵϲ Ϭ͘ϰϭϲϭϳϮ ϭ͘ϴŐ Ϭ͘ϵϭϵϳϳϮ Ϭ͘ϳϮϭϵϬϲ Ϭ͘ϱϲϲϵϯϯ Ϭ͘ϱϭϮϬϮϰ Ϭ͘ϰϲϬϭϵ Ϯ͘ϬŐ Ϭ͘ϵϯϱϭϳϴ Ϭ͘ϳϲϳϲϬϲ Ϭ͘ϲϭϯϰϲϱ Ϭ͘ϱϱϱϳϱ Ϭ͘ϱ

170

Appendix G.3 Tabulated Probability of Exceedance (IUA Upper Bound)

171

Appendix G.3: Tabulated Probability of Exceedance (IUA Upper Bound)

WZK/>/dzK&yEhWWZKhE;^,ZyͿ KhEd W' Ɛ Ϭ͘ϮŐ Ϭ͘ϮϯϴϲϮϳ Ϭ͘Ϭϯϭϴϵϳ Ϭ͘ϬϬϴϱϵϮ Ϭ͘ϬϬϵϬϳϮ Ϭ͘ϬϭϮϰϬϲ Ϭ͘ϰŐ Ϭ͘ϰϴϮϲϬϵ Ϭ͘ϭϴϳϭϱϳ Ϭ͘Ϭϳϰϭϰϯ Ϭ͘ϬϲϮϳϯϮ Ϭ͘Ϭϲϭϵϴϭ Ϭ͘ϲŐ Ϭ͘ϲϯϱϱϲϲ Ϭ͘ϯϳϯϬϯϳ Ϭ͘ϭϴϰϳϰϵ Ϭ͘ϭϰϳϲϳϭ Ϭ͘ϭϯϬϮϭϮ Ϭ͘ϴŐ Ϭ͘ϳϯϯϱϮϲ Ϭ͘ϱϯϬϱϵϳ Ϭ͘ϯϬϱϱϲϱ Ϭ͘Ϯϰϭϯϵϱ Ϭ͘ϮϬϮϱϵϲ ϭ͘ϬŐ Ϭ͘ϳϵϵϬϲϮ Ϭ͘ϲϱϬϴϬϰ Ϭ͘ϰϭϴϬϵϲ Ϭ͘ϯϯϭϵϲϳ Ϭ͘ϮϳϮϱϱϮ ϭ͘ϮŐ Ϭ͘ϴϰϰϲϰϵ Ϭ͘ϳϯϵϯϱϵ Ϭ͘ϱϭϱϴϰϴ Ϭ͘ϰϭϰϰϳ Ϭ͘ϯϯϳϰϱϰ ϭ͘ϰŐ Ϭ͘ϴϳϳϰϬϱ Ϭ͘ϴϬϰϬϬϳ Ϭ͘ϱϵϳϵϵϭ Ϭ͘ϰϴϳϰϴϮ Ϭ͘ϯϵϲϰϵϵ ϭ͘ϲŐ Ϭ͘ϵϬϭϱϴϰ Ϭ͘ϴϱϭϮϴϱ Ϭ͘ϲϲϱϵϮϰ Ϭ͘ϱϱϭϭϲ Ϭ͘ϰϰϵϳϬϭ ϭ͘ϴŐ Ϭ͘ϵϭϵϴϯϵ Ϭ͘ϴϴϲϬϴϲ Ϭ͘ϳϮϭϳϭϭ Ϭ͘ϲϬϲϯϬϱ Ϭ͘ϰϵϳϰϮϰ Ϯ͘ϬŐ Ϭ͘ϵϯϯϴϴϵ Ϭ͘ϵϭϭϵϮϭ Ϭ͘ϳϲϳϰϮϭ Ϭ͘ϲϱϯϵϮ Ϭ͘ϱϰϬϭϲϲ

WZK/>/dzK&yEhWWZKhE;^,ZzͿ KhEd W' Ɛ Ϭ͘ϮŐ Ϭ͘Ϯϰϭϴϴϳ Ϭ͘ϬϲϰϮϭϭ Ϭ͘ϬϬϴϰϭϱ Ϭ͘ϬϬϴϱϰϳ Ϭ͘ϬϭϬϲϲϳ Ϭ͘ϰŐ Ϭ͘ϰϴϱϰϮϵ Ϭ͘Ϯϲϲϲϱϵ Ϭ͘ϬϳϬϭϲϮ Ϭ͘ϬϲϱϮϭ Ϭ͘Ϭϲϭϯϵϵ Ϭ͘ϲŐ Ϭ͘ϲϯϳϰϳϱ Ϭ͘ϰϲϬϵϲϴ Ϭ͘ϭϳϯϴϵϱ Ϭ͘ϭϱϴϭϭϲ Ϭ͘ϭϯϱϴϯϵ Ϭ͘ϴŐ Ϭ͘ϳϯϰϳϯϭ Ϭ͘ϲϬϴϭϯϱ Ϭ͘Ϯϴϴϭϱϭ Ϭ͘ϮϲϭϬϭϯ Ϭ͘ϮϭϲϰϱϮ ϭ͘ϬŐ Ϭ͘ϳϵϵϳϴϱ Ϭ͘ϳϭϯϰϬϳ Ϭ͘ϯϵϱϴϵϵ Ϭ͘ϯϱϵϲϯϱ Ϭ͘ϮϵϰϲϮϲ ϭ͘ϮŐ Ϭ͘ϴϰϱϬϱ Ϭ͘ϳϴϳϵϳϱ Ϭ͘ϰϵϬϳϴϵ Ϭ͘ϰϰϴϮϳϵ Ϭ͘ϯϲϲϴϭϰ ϭ͘ϰŐ Ϭ͘ϴϳϳϱϵϯ Ϭ͘ϴϰϭϭ Ϭ͘ϱϳϭϲϰϵ Ϭ͘ϱϮϱϱϬϭ Ϭ͘ϰϯϭϵϬϰ ϭ͘ϲŐ Ϭ͘ϵϬϭϲϯϭ Ϭ͘ϴϳϵϯϳϲ Ϭ͘ϲϯϵϰϱϯ Ϭ͘ϱϵϭϳϮϵ Ϭ͘ϰϴϵϴϵϲ ϭ͘ϴŐ Ϭ͘ϵϭϵϳϵϯ Ϭ͘ϵϬϳϯϬϵ Ϭ͘ϲϵϱϴϴϵ Ϭ͘ϲϰϴϭϬϰ Ϭ͘ϱϰϭϮϲϳ Ϯ͘ϬŐ Ϭ͘ϵϯϯϳϴϮ Ϭ͘ϵϮϳϵϲϭ Ϭ͘ϳϰϮϳϰϭ Ϭ͘ϲϵϱϵϱ Ϭ͘ϱϴϲϲϲϴ

172

Appendix H Definition of Terms

173

Appendix H: Definition of Terms Assessment The act of making a judgment about something. Fragility Curves It is define as the probabilities of damage for specified damage states at various levels of ground acceleration. Intensity Describes the perceived surface ground shaking and damage caused by an earthquake. Pushover Analysis It is a static, nonlinear procedure using simplified nonlinear technique to estimate seismic structural deformations. It is an incremental static analysis used to determine the force-displacement relationship, or the capacity curve, for a structure or structural element.

Time-History Analysis Time-history analysis provides for linear or nonlinear evaluation of dynamic structural

response

under

loading

specified time function. Ductility Factor

174

which may vary

according

to

the

The ratio of the total deformation at maximum load to the elastic-limit deformation. Yield Energy Energy that comes from something. Damage Index A Damage index is thus defined as the ratio between the initial and the reduced resistance capacity of a structure, evaluated by using an evolution equation for the yield strength in which the structural damageability is included. The ability of this index to model different damage situations is demonstrated. Peak Ground Acceleration It is a measure of earthquake acceleration on the ground and an important input parameter for earthquake engineering, also known as the design basis earthquake ground motion (DBEGM). Pier A solid support designed to sustain vertical pressure, in particular.

Magnitude of an Earthquake It is a number assigned by the Richter magnitude scale to quantify the energy released by an earthquake. Pacific Ring of Fire

175

It is an arc around the Pacific Ocean where many volcanoes and earthquakes are formed. West Valley Fault One of the two major fault segments of the Valley Fault System which runs through the cities of Marikina, Pasig and Muntinlupa and is capable of producing large scale earthquakes on its active phases with a magnitude of 7 or higher. Retrofit To furnish with new or modified parts or equipment not available or considered necessary at the time of manufacture.

176

Appendix I Bibliography

177

Appendix I: Bibliography ƋƵŝŶŽ/s͕W͘͘;ϮϬϭϱͿ͘ĂůůŝŶŐĨŽƌĂ^ƚƵĚǇŽŶƚŚĞƵƚŚŽƌŝƚŝĞƐ͘ŚƚƚƉ͗ͬͬŶĞǁƐŝŶĨŽ͘ŝŶƋƵŝƌĞƌ͘ŶĞƚͬ͘ ĂǇůŽŶ͕D͘͘;ϮϬϭϱͿ͘ZĞůŝĂďŝůŝƚǇĂŶĂůǇƐŝƐŽĨďƌŝĚŐĞƉŝĞƌƵƐŝŶŐŝŶƚĞƌǀĂůƵŶĐĞƌƚĂŝŶƚǇĂŶĂůǇƐŝƐ͘ĂŐƌĂĚƵĂƚĞ ƚŚĞƐŝƐ͘Zd,YhĠŐĞƌŽŶ͕ΘZŽǇ͘;ϮϬϭϮͿ͘DŽĚĞůĨŽƌ^ĞŝƐŵŝĐWĞƌĨŽƌŵĂŶĐĞƐƐĞƐƐŵĞŶƚ͕Ŷ͘Ɖ͘ ^͘;ϮϬϭϰͿ͘WŚŝůŝƉƉŝŶĞ/ŶƐƚŝƚƵƚĞŽĨsŽůĐĂŶŽůŽŐǇĂŶĚ^ĞŝƐŵŽůŽŐǇ͘ ZĞƋƵŝƐŽ͕͘;ϮϬϭϯͿ͘^ĞŝƐŵŝĐ&ƌĂŐŝůŝƚǇŽĨdƌĂŶƐƉŽƌƚĂƚŝŽŶ>ŝĨĞůŝŶĞWŝĞƌƐŝŶƚŚĞWŚŝůŝƉƉŝŶĞƐ͕ƵŶĚĞƌ^ŚĞĂƌ &ĂŝůƵƌĞ͕ZĞůĂƚŝŽŶƐŚŝƉďĞƚǁĞĞŶƚŚĞĚĂŵĂŐĞŝŶĚĞǆ;/ͿĂŶĚƚŚĞĚĂŵĂŐĞƌĂŶŬ;ZͿ͘ĂƌƚŚƋƵĂŬĞ ŶŐŝŶĞĞƌŝŶŐ͕ϮϬ͕ϯϴ͘ ^ĂƚƌĞ͕'͘>͘;ϭϵϵϴͿ͘dŚĞDĞƚƌŽDĂŶŝůĂ>Zd^ǇƐƚĞŵͲ,ŝƐƚŽƌŝĐĂůWĞƌƐƉĞĐƚŝǀĞ͘EĞǁhƌďĂŶdƌĂŶƐŝƚ^ǇƐƚĞŵƐ͕ ϯϲ͘ ^ŝĚĚŝƋƵĞĞ͕EZ/>/dz^^^^DEdK&t>>W/Z,/',tzZ/'^/E Z/d/^,K>hD/͕Ŷ͘Ɖ͘ ^ŽůŝĚƵŵ:ƌ͕͘Z͘;ϮϬϭϱͿ͘ĂƌƚŚƋƵĂŬĞ,ĂǌĂƌĚƐĂŶĚZŝƐŬ^ĐĞŶĂƌŝŽĨŽƌDĞƚƌŽDĂŶŝůĂĂŶĚsŝĐŝŶŝƚǇ͗ƚŚĞEĞĞĚĨŽƌ tŚŽůĞŽĨ^ŽĐŝĞƚǇWƌĞƉĂƌĞĚŶĞƐƐ͘ zĂŵĂǌĂŬŝ͕&͖͘DŽůĂƐ͕'͘>͖dŽŵĂƚƐƵ͕z͖͘͘;ϭϵϵϮͿ͘^ĞŝƐŵŝĐŚĂǌĂƌĚĂŶĂůǇƐŝƐŝŶƚŚĞWŚŝůŝƉƉŝŶĞƐƵƐŝŶŐ ĞĂƌƚŚƋƵĂŬĞŽĐĐƵƌĞŶĐĞĚĂƚĂ͘ĂƌƚŚƋƵĂŬĞŶŐŝŶĞĞƌŝŶŐ͕ϭ͘

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