Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

EARTHQUAKE HAZARD AND RISK ASSESSMENT TOOL USING

MONTE-CARLO SIMULATION TECHNIQUES

C. Kaufmann1 and J. Schwarz2

ABSTRACT For the study area of Central Europe, an intensity-based hazard and risk assessment model is developed. The procedures implemented are structured in a modular system. Probabilistic Seismic Hazard Analysis performed using the program PSSAEL (Rosenhauer, 1999), which calculates Earthquake-Libraries on the basis of Extreme-Value statistics and GUMBEL-Parameters (m, τ, σ, Mmax). The HAZARD module enables the Monte-Carlo simulation of earthquake libraries for each intensity level, which are representative for the hazard level under consideration. A set of empirical-statistically derived relationships between macroseismic intensity, distance and source parameters has to be regarded as the key element of the general approach. The parameters of the simulated earthquakes can be directly related to ground motion prediction models. A new method is presented by linking results of site investigations (H/V spectra) with a self-designed strong-motion database including recordings from sites with instrumentally verified subsoil conditions. A cluster analysis is performed, taking H/V spectra from the target site measurements as search and evaluation criterion. Each measurement is providing a target function (H/V spectra) which is the basis for a ranking of the best fitting strong-motion recording sites. The whole procedure can be characterized as a modified "single-station" approach while only records from classified stations with comparable subsoil profiles are finally used for the elaboration of Site-Specific Ground Motion Prediction Equations (SGMPE's). Uncertainties of the modules seismic HAZARD and SITE amplification can be applied to the buildings of the target area. In case of masonry structures the damage grades are predicted for all simulated scenarios on the basis of numerical simulations and further evaluation criteria implemented in the subroutines of the VULNERABILITY evaluation tool.

1Senior Researcher, Earthquake Damage Analysis Center, Bauhaus-University Weimar, Germany christian.kaufmann@uni-weimar.de 2Head, Earthquake Damage Analysis Center, Bauhaus-University Weimar, Germany schwarz@uni-weimar.de Kaufmann C, Schwarz J. Earthquake hazard and risk assessment tool using Monte-Carlo simulation techniques. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

DOI: 10.4231/D35Q4RM70

Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

Earthquake hazard and risk assessment tool using Monte-Carlo

simulation techniques

C. Kaufmann1 and J. Schwarz2

ABSTRACT

For the study area of Central Europe, an intensity-based hazard and risk assessment model is developed. The procedures implemented are structured in a modular system. Probabilistic Seismic Hazard Analysis performed using the program PSSAEL (Rosenhauer, 1999), which calculates Earthquake-Libraries on the basis of Extreme-Value statistics and GUMBEL-Parameters (m, τ, σ, Mmax). The HAZARD module enables the Monte-Carlo simulation of earthquake libraries for each intensity level, which are representative for the hazard level under consideration. A set of empirical-statistically derived relationships between macroseismic intensity, distance and source parameters has to be regarded as the key element of the general approach. The parameters of the simulated earthquakes can be directly related to ground motion prediction models. A new method is presented by linking results of site investigations (H/V spectra) with a self-designed strong-motion database including recordings from sites with instrumentally verified subsoil conditions. A cluster analysis is performed, taking H/V spectra from the target site measurements as search and evaluation criterion. Each measurement is providing a target function (H/V spectra) which is the basis for a ranking of the best fitting strong-motion recording sites. The whole procedure can be characterized as a modified "single-station" approach while only records from classified stations with comparable subsoil profiles are finally used for the elaboration of Site-Specific Ground Motion Prediction Equations (SGMPE's). Uncertainties of the modules seismic HAZARD and SITE amplification can be applied to the buildings of the target area. In case of masonry structures the damage grades are predicted for all simulated scenarios on the basis of numerical simulations and further evaluation criteria implemented in the subroutines of the VULNERABILITY evaluation tool.

Introduction The implementation of seismic risk analysis requires the appropriation of characteristic input parameters and data levels which are usually afflicted by uncertainties. It is still not sufficiently and systematically studied how and in which extent the uncertainties of the individual input parameters affect the results, which are of engineering interest, i.e. the level and local distribution of damage, and their probability of being exceeded due to model uncertainties. 1Senior Researcher, Earthquake Damage Analysis Center, Bauhaus-University Weimar, Germany christian.kaufmann@uni-weimar.de 2Head, Earthquake Damage Analysis Center, Bauhaus-University Weimar, Germany schwarz@uni-weimar.de Kaufmann C, Schwarz J. Earthquake hazard and risk assessment tool using Monte-Carlo simulation techniques. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

The scatter of results is in a so far not adequately quantified. Therefore, the existing modular system is modified and extended by new elements, correlations and definitions that allow a multi-directional treatment of uncertainties. The system is based on the following principles [1]:

- Separate treatment of uncertainties in each module, - Maintaining scatter of interim results within the input for the subsequent modules and - Quantification of influence on the scatter arising from the individual modules

as well as module changes for the interim and the final results. The paper gives preference to a more detailed presentation of the HAZARD module, where different source region models are implemented, and of the SITE module, where a new technique for the self-generation of Site-specific Ground-motion Predictions Equations (SGMPE) has been introduced. These equations are in particular applicable to target regions where instrumentally site measurements are available or can be performed with low effort.

Hazard Probabilistic Seismic Hazard Analysis is performed using the program PSSAEL [2]. For each zoning element (see Fig. 1) of the applied seismicity models AR04, Gru06, and GruDACH [3] [4] [5], the magnitude-exceedance rates are calculated on the basis of Extreme-Value statistics and GUMBEL-Parameters (m, τ, σ, Mmax) using recently elaborated catalogue EKDAG [6] [7]. The intensity exceedance rates for the study area of Albstadt are given by Fig. 2. For practical reasons, damaging intensities are of interest, only.

Figure 1. Map of southwest Germany

including boundaries of seismic zones in the used models.

Figure 2. Intensity exceedance rates for

the different seismic zone models.

a) Cumulative distribution of

distance D. b) Cumulative distribution of

magnitude ML. Figure 3. Deaggregation of seismic hazard for intensities of different mean return periods

exemplary for seismic zone model AR04. Shaking effects (intensities) describe the regional or local hazard. Following the descriptions of EMS-98 slight to moderate structural damage has to be expected by shaking effects between intensity IEMS = 6 and 8. A mean return period of about 100 years can be assigned to the intensity of the September 03, 1978 Albstadt Earthquake (IEMS = 7.25). The PSSAEL tools enable the Monte-Carlo simulation of earthquake libraries. For each intensity level a list of about 2000 successful trials (from several millions generated ones) seems to be representative for the hazard level under consideration. Each data point (earthquake) is described by a magnitude-distance pair and its epicentral coordinates (see Fig. 4) as well as source depths (see Fig. 5). The cumulative distribution of magnitudes and distances are illustrated in Fig. 3a and 3b for the seismic zone model AR04 and mean return periods of 475, 975 and 2475 years. Due to the high seismicity concentration within a rather limited zone including the study area, the differences in the hazard are mainly related to the magnitude ML. The median and 84% fractiles of distance (d50 and d84) remain nearly unchanged in a range from 5 to 8 km, while the magnitude is increasing steadily, i.e. damage and loss scenarios have to consider near-field events, only. The earthquake libraries deliver the condensed information about the uncertainties of the site-dependent hazard estimate. The parameters of the simulated earthquakes can be related to ground motion models (attenuation functions), directly. They have to be regarded as one key element of the procedure predetermining the scatter within spectral amplitudes on the action side and damage grades in case of analytical investigations of individual buildings of the predominant structural system.

Figure 4. Magnitude – distance relation for

mean return periods 475y and 2475y.

Figure 5. Location and depth distribution

for mean return periods 475y and 2475y.

Site

The primary database of classified strong motion recording sites refers to the outcome of a measurement campaign carried out in the spring of 2004 in California. It was done in close cooperation with the United States Geological Survey (USGS). Fig. 6 shows the respective region of California and the strong-motion recording sites between the south coast of San Pablo Bay in the North (north of San Francisco) and Imperial Valley in the South where the measurements were carried out. As a whole, 300 strong-motion sites in the central and southern parts of California were investigated and classified [8]. Within this comprehensive instrumental study, the recording sites are classified with respect to their ground classes considering the characteristics of the uppermost 30 m of the subsoil overlaying the geological depth profile. The initial earthquake database consists of more than 615 strong-motion records of 102 near-field events being recorded at 183 stations at time of the first data elaboration and publication of ground motion prediction equations by Schwarz et al., 2007 [9]. In order to allow a consistent site classification even of those Californian strong-motion sites where detailed information on the geological subsoil conditions is missing, a hybrid procedure based on analytical investigations of model soil profiles and instrumental measurements based on noise records was developed. This allows the classification of a site of interest into site-specific subsoil classes of the German seismic code DIN 4149: 2005 [10] simply by the shape of spectral H/V-ratio on micro-tremor data recorded at the site [11] [8]. In this respect, the main decisive factor is the location of its predominant peak in the spectral domain being characterized by a distinct and well-defined hump (see Fig. 8).

Figure 6. Map of central and southern California with instrumentally observed strong-motion sites.

Instrumental Site Classification of the Target Sites During a series of different measurement campaigns, instrumental micro-tremor recordings were conducted at different locations in and around the municipal area of Albstadt, providing the basis for the target site classification. During a site measurement, ambient noise data is recorded for approximately one hour. The data is used to compute a characteristic H/V spectrum for this particular site, which indicates the transfer characteristics of the site. Long time measurements at many other sites did prove the temporal stability of these spectra. The results of this instrumental site classification are indicating different site conditions for particular areas of the town. Higher elevated areas are dominated by a rock type site assignment (B-R according to DIN 4149: 2005). The majority of the valley sites are soft soil sites (C-S), underlain by thick layers of sediments. Fig. 8 shows the H/V spectra for all investigated sites. The spectra of measurement site AWI is exemplary marked in red. It is surrounded by similar shaped spectra of other sites. These sites build a site cluster with similar transfer characteristics represented by the point color in Fig. 7. Different options are offered by the SITE module. In case of sufficiently detailed information about the geology and depth profile, site response studies can be performed by simulating the uncertainty of input data with a set of about 100 variations for each profile.

Figure 7. Map of Albstadt including the

location of the measurement sites.

Figure 8. H/V spectra for all 25

measurement sites. Cluster Analysis and Selection of Reference Sites The whole procedure can be described by the following steps: (1) Target functions in the form of the Median H/V-spectra (see Fig. 8, red line) are determined as an outcome from instrumental site investigations. Reference functions are available from the measurements at the strong motion recording sites (see Fig. 6). (2) By analogy considerations between the different target functions (from measurement points in Albstadt) and the H/V function of the reference sites (light blue curves in Fig. 9), the most appropriate ones (black curves in Fig. 9) are identified using error minimization routines within a frequency range being variable in selection. (3) The instrumentally determined H/V-spectra from the strong motion stations serve as reference to identify a set of the 10 best matching spectra in comparison to the target site H/V-spectra. Finally for each target function, a list of the top 10 reference (strong motion recording) sites is taken into a scoring list. Steps (2) and (3) are repeated for all target functions. (4) A cluster analysis is performed to separate the target functions into classes. To achieve this goal, a virtual distance is computed for each possible target site pair. If step (3) gives almost the same reference sites for target site A and B, the virtual distance between these target sites is very low. If A and B have completely different reference sites, their virtual distance is high. A cluster algorithm is using this virtual distance as criterion to assign the target sites to classes with similar reference sites. (5) After identification of the clusters the strong motion records provided by all reference sites appearing in the cluster are combined within a cluster site class that is most appropriate for the ground motion prediction.

Figure 9. Pool of reference site H/V spectra

(light blue), target site H/V spectra (red) and 10 best fits (black).

Figure 10. Response spectra calculated

with site cluster specific ground motion prediction equations.

The whole procedure can be characterized as a modified „single-station“ approach while only records from classified reference stations with comparable subsoil profiles (under the assumption of similar site amplification effects) are finally used for the elaboration of Site-Specific Ground Motion Prediction Equations (SGMPEs). The key and linking element of the presented procedure is the instrumental subsoil classification, making the different datasets unique and site-specifically applicable. Data Elaboration and Regression Types Ground Motion Prediction Equation: Generally, two types of regression analyses are elaborated, differing in the applied regression model and in the size of the dataset to rest upon. Regression type I: The dataset is restricted to records in the site classes for which the ground motion prediction is worked out. Since this type of regression is based exactly on that type of data (narrowed dataset) for which a prediction is elaborated, no site coefficients are incorporated. The general form of the regression is given by Eq. 1: log (y) = C1 + C2 M + C3 log (r) + σ P (1) with y the ground motion parameter in g (PGA or Sa), M the magnitude (Mw), r a function of the distance measure (r = √ (R2 + h2), while R is the distance (either epicentral repi or Joyner-Boore distance rJB), h the source depth and P the uncertainty term in the GMPE. Resulting response spectra for this regression type and all site clusters are shown in Fig. 10. Regression type II: Irrespective of the selected site class the regression analysis is based on the entire dataset covering all events recorded at all types of subsoil. Based on pure rock-type soil conditions, coefficients are determined. The regression model to be used is given by Eq. 2. A ground motion prediction for a specific site class (i-j; i-soil class, j-geological class) is performed by setting the respective “Switch” variable Si-j to 1 while all others are set to 0.

log (y) = C1 + C2 M + C3 log (r) + C4 S(B-R) + C5 S(C-R) + C6 S(B-T)+ C7 S(C-T) + C8 S(C-S) + σ P (2) Site-Specific Ground Motion Prediction Equation: In case of the proposed cluster analysis, prediction Eq. 2 has to be replaced by Eq. 3. The site class coefficients (C4 to C8) and corresponding “Switch”-variables Si-j have to be extended by the site-specific class for the site cluster. For Eq. 1 (Regression type I) no modification is needed, because it is solely based on the site-specific cluster. log (y) = C1 + C2 M + C3 log (r) + C4 S(B-R) + C5 S(C-R) + C6 S(B-T)+ C7 S(C-T) + C8 S(C-S) + C9 S(site cluster) + σ P (3) It has to be noticed that recordings contained in the site-specific class have to be removed from their original class. It could happen that all recordings from a certain class move to the site-specific class. In this case the coefficient and “Switch”-variable for that class have to be removed from Eq. 3.

Vulnerability For the typical building representatives (Fig. 11) the response is predicted by quasi-static nonlinear pushover-analysis (Fig. 12) and further evaluation criteria of the BLM-Tool [12] for all simulated scenarios. For model calibration a f–factor is used [13]. The factor is related to the effective level of ground motion in case of unreinforced masonry structures. It account for the observed discrepancy between the outcome of analytical studies and the occurred damage grades at Albstadt September 1978 earthquake statistically investigated by [14].

Figure 11. View and cross section of the example

building.

Figure 12. Example for determining

the performance point of the structural system.

Risk Assessment

The risk analysis for a typical masonry building with wooden floors (Fig. 11) is done by simulation of 1000 scenarios with randomly changing input parameters. Uncertainties of seismic HAZARD (expressed by the earthquake libraries generated for the used seismic zone models) and soil amplification (expressed by SITE specific GMPE) are combined in hazard-consistent,

site-dependent ground motions applied to the structural system. In case of unreinforced masonry structures, uncertainties in the VULNERABILITY are expressed by a simulated range of f–factors taking into account the problems of an adequate modeling and limits of commonly used force-based design principles. Results for the different site clusters and different mean return periods are illustrated by the damage probability curves in Fig. 13 and 14. For the example building a damage grade 3 was reported on a cluster 1 site. As it can be shown, the site-clustering of ground motion prediction equations enables a differentiation of the damage prognosis. Using the proposed simulation technique, damage probability curves can be generated for different site clusters and mean return periods which can be related to performance-based design levels.

Figure 13. Damage probability curves for

the site clusters and a mean return period of 475y.

Figure 14. Damage probability curves for

site cluster 1 and different mean return periods.

Conclusions

For the study area of Central Europe, an intensity-based hazard and risk assessment model has been developed. The modular system enables simulations and statistical simplifications within each of the basic elements as well as the transmission of the results between the linked modules. Making use of the simulated earthquake libraries calculated by the Probabilistic Seismic Hazard Analysis and the implemented empirical-statistically derived relationships between macroseismic intensity, distance and source parameters, risk assessment can be performed in terms of damage prognosis for hazard levels which are of importance for the further promotion of performance-based design concepts.

The parameters of the simulated earthquakes can be directly related to ground motion prediction models. A new method is presented by linking results of site investigations (H/V spectra) with a self-designed strong-motion database including recordings from sites with instrumentally verified subsoil conditions. The paper presents a clustering technique for the self-

generation of Site-specific Ground-motion Predictions Equations (SGMPE) using instrumentally site measurements from representative locations within the target region.

Transferring the seismic action for all simulated events of the earthquake library to

individual building representatives (in our study: unreinforced masonry systems) damage probability curves for different site clusters and hazard levels (mean return periods) can be elaborated. The procedure can be repeated for the whole building typology to come up with a new kind of risk mapping.

References 1. Kaufmann C. Monte-Carlo simulations for seismic risk analysis considering uncertainties of input parameters.

Phd Thesis (in preparation), 2013.

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10. DIN 4149:2005. Buildings in German earthquake regions – design loads, analysis, and structural design of buildings. Deutsche Institut für Normung e.V. (DIN), April 2005, 84 pp.

11. Lang D. Damage potential of seismic ground motion considering local site effects. Scientific technical reports 1 (ISBN 3-86068-227-X). EDAC, Bauhaus-University Weimar, 2004, 293 pp.

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