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The advanced method requires more information about the site than the base method, especially in relation with the stratigraphic and geotechnical site characteristics. In case of lack of information the user may prefer to use the base method.

The advanced method includes the following steps:

Assessment of seismic hazard on rock, with probability of exceedance of 10% in 50 years (i.e. return period: 475 years) for Class 1 structures (according to the Italian Code, see Decree Sept. 14, 2005) or with probability of exceedance of 10% in 50 years (i.e. return period: 975 years) for Class 2 structures, by accessing a remote database of pre-performed off-line analyses carried out throughout the Italian territory;
Evaluation of local site amplification effects by accessing a remote database of pre-performed off-line amplification analyses carried out for different soil types and columns heights. This information is then combined with the hazard on rock in a probabilistically correct way, by means of a convolution procedure, in order to obtain the hazard at the ground surface;
Evaluation of the expected damage on the given structure typology starting from the capacity and the fragility curves. The inelastic spectral displacement at various frequencies is convoluted with the corresponding fragility curves in order to obtain the unconditioned probability to exceed a predefined damage level within a given period of time (e.g. 30 years).

Seismic Hazard
By selecting the advanced method the seismic hazard at the site is first established by querying a database containing the results of about 20000 analyses performed throughout the entire Italian territory. The results include both peak ground acceleration values and spectral acceleration values computed at different oscillation frequencies. In this way an elastic response spectrum is defined, so that structural damage can be assessed by considering the spectral acceleration estimated at the structure's fundamental frequency.

The following figure depicts the procedure adopted to generate the seismic hazard database used by the system.

Creation of the Seismic Hazard Database

Site Amplification
The advanced method performs the site amplification assessment in a different way than the base method, by accessing a database containing results of many amplification analyses performed off-line for different soil types and column heights. Each analysis was carried out using as input over 50 different acceleration time histories recorded in rock (Pelli et al., 2006a,2006b). The system, according to the information provided by the user, selects the most likely amplification function and, through a convolution procedure, computes the surface acceleration at different frequencies.

The detailed approach couples conventional Probabilistic Seismic Hazard Analysis (PSHA) (Cornell, 1968), with non-linear dynamic analyses of the soil column at the site under consideration subject to real rock ground motions. The dynamic analyses were carried out using a modified version of the computer program SUMDES (Li et al., 1992; 1998), which is a finite element code for analysis of the dynamic response of horizontally layered sites. Each soil layer can be individually modeled using non-linear inelastic constitutive relationships (Dafalias, 1986; Wang and Dafalias, 1990). Although both shear and compression waves can be applied simultaneously, for simplicity only one horizontal acceleration time history was applied in the analyses.
In this approach, the uncertainty in the soil characteristics (and statistical correlation among properties in different layers) can be incorporated by randomization of the soil properties in each analysis, but this option was not used in this study. The non-linear effect of the soil layers on the intensity of the ground motion at the surface is captured by a site-specific, frequency-dependent amplification function, AF(f), where f is a generic oscillator frequency. AF(f), which varies with the intensity of the bedrock motion, is defined as the ratio of the spectral acceleration at the surface to the spectral acceleration at the bedrock, both computed at the same frequency f (Bazzurro and Cornell, 2004a; 2004b):

where S_a^s(f) and S_a^r(f) are the spectral accelerations at the ground surface and at the bedrock, respectively, at the oscillator frequency f, a, b and c are regression constants, σ_lnAF(f) is the standard deviation of the AF(f) - S_a^r(f) relationship (i.e., the standard error of estimation from the statistical regression), and ε_lnAF(f) is a standard normal variate. The relationship between AF(f) and Sar(f) is shown in the figure for an oscillator frequency of 3.5Hz where the results of the 51 ground response analyses are also reported.
The procedure above provides the median AF(f) and its uncertainty, where the latter accounts for record-to-record variability. This information can be coupled via convolution with the site-specific bedrock hazard to obtain the desired surface ground motion hazard for the site.

The new approach provides relationships from which the median values of the regression parameters a, b, c (see Eqn. above) and of the standard deviation can be obtained for each oscillator frequency, given an estimate of the predominant soil type, its plasticity characteristics (non plastic, low, medium and high plasticity), bedrock shear wave velocity (comprised between 800 and 2500m/s) and elastic fundamental frequency of the soil column.

As for the base method the acceleration spectra both on rock and at the ground surface are provided as results.

Structural Damage
The structural damage is estimated starting from the so called "capacity curves". Building capacity (push-over) curves provide simple and reasonably accurate means of predicting inelastic building displacement response for damage estimation purposes.

Through these curves it is possible to estimate, for the building typology under examination, the inelastic spectral displacement.

At this point the fragility curves come into play. They allow to estimate the probability of exceedance of a pre-defined damage level induced by a given spectral displacement. The fragility curves are specific for building typology and age. The probability of being in or exceeding a given damage state is modeled as a cumulative lognormal distribution. For structural damage, given the spectral displacement, Sd, the probability of being in or exceeding a damage state, ds, is modeled as:

where:
S_d,ds is the median value of spectral displacement at which the building reaches the threshold of the damage state, ds,
β_ds is the standard deviation of the natural logarithm of spectral displacement of damage state, ds, and
Φ is the standard normal cumulative distribution function.

Through the fragility curves, for the computed acceleration level, the probability of exceedance of a given structural damage for the structure under examination is established. Four structural damage levels are defined: slight, moderate, extensive and complete. As an example the four damage levels for the typology "Concrete Moment Frame" are defined as follows:

Slight Structural Damage: Flexural or shear type hairline cracks in some beams and columns near joints or within joints.

Moderate Structural Damage: Most beams and columns exhibit hairline cracks. In ductile frames some of the frame elements have reached yield capacity indicated by larger flexural cracks and some concrete spalling. Non ductile frames may exhibit larger shear cracks and spalling.

Extensive Structural Damage: Some of the frame elements have reached their ultimate capacity indicated in ductile frames by large flexural cracks, spalled concrete and buckled main reinforcement; non ductile frame elements may have suffered shear failures or bond failures at reinforcement splices, or broken ties or buckled main reinforcement in columns which may result in partial collapse.

Complete Structural Damage: Structure is collapsed or in imminent danger of collapse due to brittle failure of non ductile frame elements or loss of frame stability. Approximately 20%(low-rise), 15%(mid-rise) or 10%(high-rise) of the total area of C1 buildings with Complete damage is expected to be collapsed.

Similarly, there are fragility curves corresponding to these damage definitions to be applied to all other structural typologies included in the system.

The main reference adopted for the typological classification is the EMS-98 (European Macroseismic Scale, Grunthal, 1998), that provides a detailed description of the most common structural typologies in the european context. In particular, it must be noticed that the EMS-98 scale analyses in depth the masonry buildings as they are often most vulnerable, especially in the Mediterranean area. This basic classification of masonry buildings was integrated based on the work by Giovinazzi e Lagomarsino (2001), whereas the information provided by FEMA 178 (BSSC, 1992) e 310 (ASCE, 1998) was applied for steel and reinforced concrete structures. The latter data refer to the American design and construction practice and therefore they are not completely satisfactory when applied to other countries. Possible improvements in this area are currently under investigation.
The inelastic spectral displacement at various frequencies is convoluted with the corresponding fragility curves in order to obtain the unconditioned probability to exceed one of the four damage levels (slight, moderate, extensive and complete) within a given period of time, like for instance 30 years (see the following figure):

Bibliography

ASCE, 1998. FEMA 310: Handbook for the Seismic Evaluation of Buildings — A Pre-standard. Prepared by the American Society of Civil Engineers for the Federal Emergency Management Agency, Washington D.C.

BSSC, 1992. FEMA 178: NEHRP Handbook for the Seismic Evaluation of Existing Buildings. Prepared by the Building Seismic Safety Council for the Federal Emergency Management Agency, Washington D.C.

Bazzurro, P., and C. A. Cornell (2004a), Ground-motion amplification in nonlinear soil sites with uncertain properties, Bull. Seism. Soc. Am. 94, no. 6, 2090–2109.

Bazzurro, P., and C. A. Cornell (2004b), Nonlinear soil-site effects in probabilistic seismic-hazard analysis, Bull. Seism. Soc. Am. 96, 2110–2123.

Cornell, C.A. (1968), Engineering Seismic Risk Analysis, Bullettin of Seismological Society of America, Vol. 58, No. 5.

Dafalias Y. F. (1986). Bounding Surface Plasticity, I. Mathematical Foundation and the concept of Hypoplasticity, Journal of Engineering Mechanics, ASCE, Vol. 112, No, 9.

Giovinazzi, S., Lagomarsino, S. 2001. Una metodologia per l’analisi di vulnerabilità sismica del costruito. Atti del 10° Convegno Nazionale ANIDIS: L’ingegneria Sismica in Italia, Potenza, Italia.

Grunthal, G. 1998. European Macroseismic Scale 1998. Chaiers du Centre Europèèn de Géodynamique et de Séismologie, Volume 15, Luxembourg.

Li X.S., Wang, Z.L. and Shen C.K. (1992), SUMDES - A nonlinear procedure for response analysis of horizontally-layered sites subjected to multi-directional earthquake loading, University of California at Davis.

Li X.S., Shen, C.K. and Wang Z.L. (1998), Fully coupled inelastic site response analysis for 1986 Lotung Earthquake, J. Geotech. and Geoenvir. Engrg., ASCE, Vol. 124, No. 7, pp. 560-573.

Pelli F., Mangini M., Bazzurro P., Eva C., Spallarossa D., Barani S., (2006a), “Psha in northern italy accounting for non-linear soil behaviour and epistemic uncertainty”, First European Conference on Earthquake Engineering and Seismology (1st ECEES).

Pelli F., Mangini M., Bazzurro P. (2006b), “A simplified approach for site amplification assessment in non-linear soil deposits”, Third International Symposium on the Effects of Surface Geology on Seismic Motion, Grenoble, France.

Wang Z. and Dafalias Y. F. (1990). Bounding Surface Hypoplasticity model for sands, Journal of Engineering Mechanics, ASCE, Vol. 116, No, 5.