Seismic Fragility Curves

Reconnaissance studies following recent significant earthquakes have revealed the seismic vulnerability of curved bridges. Curved steel bridges are widely utilized as important components of transportation networks across the United States especially when geometry and curve alignment of a highway requires a curved structure. However, there are a few studies regarding the seismic vulnerability of horizontally curved steel girder bridges as one of the most critical components of transportation networks.
Comprehensive and rational evaluation of seismic vulnerability of transportation networks can be achieved through methodological Seismic Risk Assessment (SRA). Fragility curves which express the conditional probability of reaching or exceeding a predefined damage state are essential as input to any SRA tools such as HAZUS and REDARS for the seismic vulnerability evaluation. This study aims to fill in the gap on
the current state-of-the-knowledge in the seismic response and fragilities of horizontally curved bridges with steel I-girders.

WdZ / ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱ /ŶƚƌŽĚƵĐƚŝŽŶ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱ ϭ͘ϭ ĂĐŬŐƌŽƵŶĚ ŽĨ ƚŚĞ ^ƚƵĚLJ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱ ϭ͘Ϯ ^ƚĂƚĞŵĞŶƚ ŽĨ ƚŚĞ WƌŽďůĞŵ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϳ ϭ͘ϯ KďũĞĐƚŝ|ĞƐ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵ ϭ͘ϰ ^ŝŐŶŝĨŝĐĂŶĐĞ ŽĨ ƚŚĞ ^ƚƵĚLJ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϵ ϭ͘ϱ ^ĐŽƉĞ ĂŶĚ >ŝŵŝƚĂƚŝŽŶ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϬ ϭ͘ϲ ĞĨŝŶŝƚŝŽŶ ŽĨ dĞƌŵƐ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϭ ŚĂƉƚĞƌ // ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϯ ZĞ|ŝĞǁ ŽĨ ZĞůĂƚĞĚ >ŝƚĞƌĂƚƵƌĞ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϯ Ϯ͘ϭ &ŽƌĞŝŐŶ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϯ Ϯ͘Ϯ >ŽĐĂů ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϰ Ϯ͘ϯ &ƌĂŐŝůŝƚLJ Ƶƌ|ĞƐ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϲ Ϯ͘ϰ ƌŝĞĨ ,ŝƐƚŽƌLJͬĂĐŬŐƌŽƵŶĚ ŽĨ ƚŚĞ ^ƚƌƵĐƚƵƌĞ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϳ , WdZ /// ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϵ ŽŶĐĞƉƚƵĂů ĂŶĚ dŚĞŽƌĞƚŝĐĂů &ƌĂŵĞǁŽƌŬ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϵ ϯ͘ϭ ŽŶĐĞƉƚƵĂů &ƌĂŵĞǁŽƌŬ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϭϵ ϯ͘Ϯ dŚĞŽƌĞƚŝĐĂů &ƌĂŵĞǁŽƌŬ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ Ϯϭ , WdZ /s ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϯϬ Dd,KK>K'z͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϯϬ ϰ͘ϭ ŽŶ|ĞŶƚŝŽŶĂů &ƌĂŐŝůŝƚLJ Ƶƌ|Ğ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϯϬ ϰ͘Ϯ hŶĐŽŶ|ĞŶƚŝŽŶĂů &ƌĂŐŝůŝƚLJ Ƶƌ|Ğ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϰϮ , WdZ s ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϰϰ Z^h>d E /^h^^/KE ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϰϰ , WdZ s/ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱϳ KE>h^/KE E ZKDDE d/KE ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱϳ ϲ͘ϭ ŽŶĐůƵƐŝŽŶ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱϳ ϲ͘Ϯ ZĞĐŽŵŵĞŶĚĂƚŝŽŶ ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱϴ />/K'Z W,z ͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘͘ ϱϵ 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.

Response-history nonlinear dynamic analysis is an analytical tool that often sees use in risk-oriented earthquake engineering applications. In the context of performance-based earthquake engineering, dynamic analysis serves to obtain a probabilistic description of seismic structural vulnerability. This typically involves subjecting a nonlinear numerical computer model to a set of ground-motions that represent a sample of possible realizations of base acceleration at the site of interest. The analysis results are then used to calibrate a stochastic model that describes structural response as a function of shaking intensity. The sample size of the ground-motion record set is nowadays usually governed by computation-demand constraints, yet it directly affects the uncertainty in estimation of seismic response. The present study uses analytical and numerical means to investigate the record sample size, n, required to achieve quantifiable levels of mean relative estimation error on seismic risk metrics. Regression-based cloud analysis in the context of Cornell's reliability method and incremen-tal dynamic analysis using various intensity measures were employed to derive a relation of the form Δ= ffiffiffi n p , where Δ is a parameter that depends on both the dispersion of structural responses and the shape of the hazard curve at the site. For the cases examined, n can be kept in the 40 to 100 range and achieve 10% mean relative error. The study can contribute to guide engineers towards an informed a-priori assessment of the number of records needed to achieve a desired value for the coefficient of variation of the estimator of structural seismic risk.

The study presents probabilistic structural fragility assessment of public school buildings in Istanbul, which were constructed based on a standardized/typical project. The typical structure is a four-story, reinforced concrete shear wall building with moment resisting frames. Derivation of fragility functions rely on nonlinear dynamic analyses through Monte Carlo simulations. Nonlinear dynamic analyses are initially performed for a fully deterministic structural model based on the blueprints of the typical school building project. Uncertainties are introduced in different analysis cases following a modified version of the algorithm presented in Smyth et al. (2004) [21], which considers the effect of the random distribution of the parameters using a Monte Carlo approach. Aleatory uncertainties concerning material properties (i.e. compressive strength of concrete, yield strength of reinforcing steel and concrete density), geometrical characteristics (i.e. span lengths and story heights) and cross sectional dimensions of beams, columns and shear walls as well as epistemic uncertainty in the direction of ground motion excitation are considered. Statistical distributions for the parameters considered are obtained from in-situ measurements and material sampling tests. Fragility functions are produced in terms of peak ground acceleration and velocity as well as of the elastic spectral displacement at the first vibration period of the building. Mean damage ratios are calculated from the derived fragility functions. They are further compared to mean damage ratios calculated for similar building typologies provided in HAZUS-MH technical manual and in Istanbul building inventory.

The effects of far distant earthquakes felt in regions with low and moderate seismicity has increased markedly over the last decade. Henceforth fragility curves in this study are to indicate whether buildings are safe to enter or not after an earthquake event occurring more than 300km away. The probability of light, moderate and severe damage states occurring on two and four storey reinforced concrete buildings up to a peak ground acceleration of 0.2g were predicted. The building models were constructed using finite element software based on eight node brick elements with three degrees of freedom at each node. The analysis was carried out using a dynamic response spectrum to calculate the peak inter-storey drift ratios. For the development of fragility curves, the results were collated following a log-normal mean distribution. The results showed that light damage is likely to occur with a probability of over 10% within a 50 year period, while the existing record is unlikely to cause structural damage. The fragility curves were comparable to those for RC moment resisting frames obtained by (Rossetto and Elnashai 2003) at a lower drift limit, with approximately 2% of inter-storey drift ratio.

http://www.sciencedirect.com/science/article/pii/S1877705811013531

Estimation of damage probability of buildings under a future earthquake is an essential issue to ensure the seismic reliability. Fragility curves are useful tools for showing the probability of structural damage due to earthquakes as a function of ground motion indices. The purpose of this study is to compare the damage probability of R/C buildings with low and high level of strength and ductility through fragility analysis. Two different types of sample buildings have been considered which represent the building types mentioned above. The first one was designed according to TEC-2007 and the latter was designed according to TEC-1975. The pushover curves of sample buildings were obtained via pushover analyses. Using 60 ground motion records, nonlinear time-history analyses of equivalent single degree of freedom systems were performed using bilinear hysteretic model and peak-oriented hysteretic model with stiffness -strength deterioration for each scaled elastic spectral displacement. The damage measure is maximum inter-story drift ratio and each performance level considered in this study has an assumed limit value of damage measure. Discrete damage probabilities were calculated using statistical methods for each considered performance level and elastic spectral displacement. Consequently, continuous fragility curves have been constructed based on the lognormal distribution assumption. Furthermore, the effect of hysteresis model parameters on the damage probability is investigated.

This study focuses on the development of a statistical model for buildings with infilled reinforced concrete frames. The cornerstone of this study is the nonlinear numerical model of a school building in Nepal. The model is developed based on the ASCE 14-17 guidelines, and it is extensively validated with field data. Then, it is used in a series of parametric studies conducted to identify the influential material parameters, and in incremental dynamic analyses conducted to provide data for the calibration of the statistical model. The three-staged least square statistical modeling approach is employed to relate the influential material parameters and ground motion intensity measures with important response quantities related to the peak and residual first story drift ratios.

Regional seismic scenarios for Venezuelan school buildings are presented, based on a simplified methodology that develops fragility curves to characterize the seismic vulnerability, assess damages, losses and risk levels. The basic hypothesis is that buildings were designed and built in compliance with the seismic code in force at the time of the construction. Adopting a bilinear capacity curve five damage states were defined. The proposed methodology was calibrated by means of comparing the predicted damage with the observed damaged in an
ensemble of school buildings affected by the 1997 Cariaco earthquake. A computational tool based on GIS to estimate damages and losses associated with a particular seismic event was developed, using modern seismic attenuation relationships. Seismic risk based on seismic hazard maps is also determined, which facilitates the task of prioritization for structural retrofitting decisions. The computational tool was applied to the evaluation of three regional scenarios.

Despite the moderate ground motions observed during the seismic events in Northern Italy, May 2012, reinforced concrete (RC) precast industrial buildings suffered excessive damage, which led to substantial direct and indirect losses. The aim of this paper is to present a seismic fragility model for Italian RC precast buildings, to be used in earthquake loss estimation and seismic risk assessment. An analytical methodology has been used that consists of (1) random sampling of one hundred structures for each building typology, (2) pushover analysis to establish a number of damage limit states, (3) execution of nonlinear dynamic analysis and comparison of the maximum demand with the limit state capacity to allocate the structure in a damage state, and (4) regression analysis on the cumulative percentage of buildings in each damage state for a set of intensity measure levels to derive the statistical parameters of the fragility functions. The building population employed in the analysis was generated considering both material and geometric variability that was obtained from the field surveys of 650 industrial facilities, as well as other information available in the literature. Several aspects of the fragility derivation process were further analysed, such as the correlation between different intensity measure types and damage, the consideration of different collapse mechanisms (e.g. beam-column connection failure) and the differences in the resulting fragility curves when adopting a 2D or a 3D modelling environment. A good agreement with preliminary empirical fragility functions based on field data was also observed.

Seismic fragility of structure is the conditional frequency of its failure for a given value of seismic response parameter, which is generally taken as peak ground acceleration. A method for determining the seismic fragility using deflection based structural analysis (pushover analysis) has been developed. Application of deflection based fragility analysis method is illustrated with an example problem of reinforced concrete frame structures taken from a safety related concrete building of PHWR based nuclear power plant.

Vulnerability assessment of the structure is the most important and wide area of research which requires more input from the engineers and seismologist. The seismic vulnerability assessment of the structure can be evaluated by developing Fragility curves. Fragility curves shows the conditional probability of the structure exceeding the particular performance limit of the given damage state during strong ground motions. Fragility curves can be developed for different parameters like spectral displacement (Sd), spectral acceleration (Sa) Peak ground acceleration (PGA) , Inter storey drift ratio (IDR) etc. This paper describes about the different methods used in deriving the Fragility curves like conventional methods, Nonlinear Dynamic analysis methods and Nonlinear Static analysis methods. Also the fragility analysis of 5 Storied Steel Moment Resisting Frame (SMRF) has been carried out based on the parameters suggested by HAZUS M.H 2.1. Nonlinear static pushover analysis of the frame has been carried out in ETABS2016. Fragility curves are developed based on the pushover analysis results. The damage states defined as per HAZUS are Slight damage (SD), Moderate damage (MD) Extensive damage (ED) and Complete damage (CD). After carrying out the fragility analysis for the steel SMRF, it has been found out that, as the spectral displacement increases probability of failure for the slight damage of the structure is very high and the probability of failure for the complete damage is very low. Hence the probability of failure of the structure reduces from slight damage to complete damage.

Group de recherche en structures, Département des génies civil, géologique et des mines, Polytechnique Montréal, Montréal, Québec, Canada, H3T 1J4 RÉSUMÉ: Cet article présente une méthodologie pratique pour évaluer la performance et l'endommagement sismiques des ponts au Québec. Les étapes de cette approche sont illustrées en l'appliquant à un pont conçu selon le Code canadien sur le calcul des ponts routiers (CSA S6). Une modélisation par éléments de fibres est utilisée pour prédire la réponse sismique non linéaire du pont. Les piles du pont, en béton armé, sont modélisées par des éléments de fibres obéissant à des lois de comportement non linéaires représentant l'acier et le béton constitutifs. Les analyses dynamiques temporelles non linéaires sont effectuées sous l'effet de secousses sismiques sélectionnées pour correspondre à l'aléa sismique du site du pont. Le processus de sélection et d'étalonnage des séismes par rapport au spectre sismique de conception est illustré. L'endommagement de la pile, associé au déplacement latéral de la structure, est relié à l'intensité des secousses sismiques. Les résultats des analyses sont exploités pour obtenir des courbes de fragilité en considérant différents états d'endommagement tels que la fissuration du béton de la pile, l'éclatement de l'enrobage de béton, ou le flambement des armatures est également illustrée. Des analyses sont réalisées pour évaluer la sensibilité des résultats au nombre des séismes sélectionnés et au spectre cible de conception adopté.

In order to inform decision-making regarding measures to mitigate the impact of induced seismicity in the Groningen gas field in the Netherlands, a comprehensive seismic risk model has been developed. Starting with gas production scenarios and the consequent reservoir compaction, the model generates synthetic earthquake catalogues which are deployed in Monte Carlo analyses, predicting ground motions at a buried reference rock horizon that are combined with nonlinear amplification factors to estimate response spectral accelerations at the surface. These motions are combined with fragility functions defined for the exposed buildings throughout the region to estimate damage levels, which in turn are transformed to risk in terms of injury through consequence functions. Several older and potentially vulnerable buildings are located on dwelling mounds that were constructed from soils and organic material as a flood defence. These anthropogenic structures are not included in the soil profi...

The U.S. Geological Survey (USGS) Engineering Risk Assessment Project has developed the Seismic Risk Web Application to combine earthquake hazard and structural fragility information in order to calculate the risk of earthquake damage to structures. Enabling users to incorporate their own hazard and fragility information into the calculations will make it possible to quantify (in near real-time) the risk of additional damage to structures caused by aftershocks following significant earthquakes. Results can quickly be shared with stakeholders to illustrate the impact of elevated ground motion hazard and earthquake-compromised structural integrity on the risk of damage during a short-term, post-earthquake time horizon.

Despite the moderate ground motions observed during the seismic events in Northern Italy, May 2012, reinforced concrete (RC) precast industrial buildings suffered excessive damage, which led to substantial direct and indirect losses. The aim of this paper is to present a seismic fragility model for Italian RC precast buildings, to be used in earthquake loss estimation and seismic risk assessment. An analytical methodology has been used that consists of 1) random sampling of one hundred structures for each building typology, 2) pushover analysis to establish a number of damage limit states, 3) execution of nonlinear dynamic analysis and comparison of the maximum demand with the limit state capacity to allocate the structure in a damage state, and 4) regression analysis on the cumulative percentage of buildings in each damage state for a set of intensity measure levels to derive the statistical parameters of the fragility functions. The building population employed in the analysis was generated considering both material and geometric variability that was obtained from the field surveys of 650 industrial facilities, as well as other information available in the literature. Several aspects of the fragility derivation process were further analysed, such as the correlation between different intensity measure types and damage, the consideration of different collapse mechanisms (e.g. beam-column connection failure) and the differences in the resulting fragility curves when adopting a 2D or a 3D modelling environment. A good agreement with preliminary empirical fragility functions based on field data was also observed.

In this study, a simplified approach for the analytical development of fragility curves of high-rise RC buildings is presented. It is based on an approximate modal decomposition procedure known as the Uncoupled Modal Response History Analysis (UMRHA). Using an example of a 55-story case study building, the fragility relationships are developed using the presented approach. Fifteen earthquake ground motions (categorized into 3 groups corresponding to combinations of small or large magnitude and source-to-site distances) are considered for this example. These ground motion histories are scaled for 3 intensity measures (peak ground acceleration, spectral acceleration at 0.2 sec and spectral acceleration at 1 sec) varying from 0.25g to 2g. The presented approach resulted in a significant reduction of computational time compared to the detailed Nonlinear Response History Analysis (NLRHA) procedure, and can be applied to assess the seismic vulnerability of complex-natured, higher modedominating tall reinforced concrete buildings.

Risk assessment is a useful tool for determining ultimate behavior of structures subjected to highly unpredictable and uncertain dynamic forces produced from earthquakes. Fragility curves are the best representation of risk assessment. In the present study, risk assessment and fragility analysis of asymmetric structures subjected to seismic loading are evaluated. Further, the effects of various eccentricities on seismic risk assessment are also studied. The fragility curves are developed for different cases of eccentricities and various structural configurations of 5 storied RCC bare frame building. The considered buildings are subjected to ground motions of past recorded earthquakes. Incremental Dynamic Analyses carried out to evaluate the responses of the considered buildings subjected to earthquake excitations. Considering various performance levels as per ATC-40, Monte Carlo is the method used to develop fragility curves. It is observed that for immediate occupancy failure criteria, the probability of failure is increased constantly with increasing the percentage of structural eccentricity. Further, very less variation is observed in the probability of failure under life safety and collapse prevention failure stages.

Fragility functions play an essential role in evaluating the seismic vulnerability of structures. To establish the seismic fragility functions of lightly Reinforced Concrete (RC) beam-column joints, the Park-Ang Damage model has been amended to quantify the damage states and the modified Bouc-Wen-Baber-Noori model has been employed and implemented in ABAQUS to predict the structural hysteresis behavior. Following successful calibration of the numerical results of a RC test frame from literature, the proposed model has been utilized to assess the seismic fragility curves of low to mid-rise RC frames in Singapore for 30 scaled ground motions using incremental dynamic analysis approach.