The polar spectrum
The polar spectrum is a new tool describing the seismic spectra demand in each horizontal directions by means of graduated color maps. In particular, it represents the projection on the horizontal plan of the spectral surface obtained by evaluating the spectra in each horizontal direction by considering the ground accelerations time histories just in these directions.
Each radius of the polar spectrum represents, thus, the response evaluated in that direction and each circumference, instead, represents the spectral demand for a fixed period in each directions. In the following figures, are represented for example the polar spectrum and the Spectral Surface for the Erzincan event (1992). The periods 0.5, 1.0 and 1.5 are marked by black thin circumference, the origin corresponds to 0 sec. period.
Seismic action in α direction
Spectral Surface for the Erzincan seismic event
Polar spectrum in terms of Pseudo – Accelerations for the Erzincan seismic event
By analyzing the result it is possible to observe that the response spectra evaluated along the main directions NS and EW do not always represent the highest seismic demand and. The polar spectrum leads to obtain, instead, a really fascinating description of the spatial features of the seismic demand, leading to well understanding the dynamic features of the seismic events.
EXAMPLE 1: L’AQUILA 2009 EVENT
On Monday April 6, 2009 at 3:32 a.m. local time, an Mw 6.3 earthquake with shallow focal depth (10 km) struck central Italy in the vicinity of L’Aquila, a city of about 73,000 people that is the capital of the Abruzzo region. The earthquake killed 305 people, injured 1500, destroyed or damaged an estimated 10000-15000 buildings, prompted the temporary evacuation of 70000-80000 residents, and left more than 24000 homeless.
Record AM043-station AQK
Spectra evaluated every 9° for serveral direction in the horizontal plane
Circular ring placed in polar spectra from inside to outside
at 0.5,1.0 and 1.5 sec. vibration periods, 0° corresponds to the South
For the registration station AQK the largest demand is generally attained along the NW-SE direction with the highest value around 1.5 sec. for PSV and SD. Instead, PSA presents peaks around 0.2 sec and high values until 1.5 sec..
EXAMPE 2: EMILIA ROMAGNA 2012 EVENT
On 20 May 2012 at 04:03 local time (02:03 UTC) an earthquake registering magnitude 5.9 struck in the Emilia-Romagna region, about 36 kilometres (22 mi) north of the city of Bologna.
20th May event – Station MRN
Spectra evaluated every 9° for serveral direction in the horizontal plane
Circular ring placed in polar spectra from inside to outside
at 0.5,1.0 and 1.5 sec. vibration periods, 0° corresponds to the South
Results show that in the case of recording station MRN, for the Emilia Romagna 20th May event, spectral responses are generally characterized by the highest values in the NNW-SSE direction. More complex appears the seismic demand in terms of PSA in the range 0.3÷0.7 sec: for lower and higher period the maximum response is attained in the NNW-SSE direction, in medium period in the E-W direction
NORME E BIBLIOGRAFIA
- L. Petti, A. Lodato “Preliminary comparison between response spectra evaluated for Emilia Romagna earthquakes and elastic demand spectra according to the new Seismic Italian Code“ RELUIS, Rete dei Laboratori Universitari di Ingegneria Sismica, 2012
- L. Petti, I. Marino“Preliminary comparison between response spectra evaluated at close source for L’Aquila earthquake and elastic demand spectra according to the new Seismic Italian Code” RELUIS, Rete dei Laboratori Universitari di Ingegneria Sismica, 2009
- L. Petti, I. Marino “The polar spectrum: a new spatial representation of seismic demand”, 14 ECEE European Conference on Earthquake Engineering, Horid 2010
- L. Petti, I. Marino, L. Cuoco “Seismic response analysis of 3d structures through simplified non-linear procedures” Proceedings of the 14th World Conference on Earthquake Engineering (14WCEE), Beijing, 12-17 October 2008
- EERI Special Earthquake Report “The Mw 6.3 Abruzzo, Italy, Earthquake of April 6, 2009”, June 2009
- ITACA, Italian Accelerometric Archive
- RAN – National Accelerometric Network – DPC Dipartimento di Protezione Civile
- NTC2008, Norme tecniche per le costruzioni, D.M. 14 Gennaio 2008