Risk analysis

Background

Why are we doing earthquake risk analysis? Firstly it is motivated by the fact that when earthquake damages are demonstrated people are motivated to take mitigative actions; the second motif is more engineering oriented: when we can quantify damages and losses we can also quantify the cost/benefit ratio of strengthening actions.

When all earthquake disasters are depicted with collapsed homes and structures it is because these collapses are the real killers (not the earthquake shaking alone). The combination of shaking vulnerability and earthquake hazard is called Earthquake Risk. When the vulnerability is expressed as probability of a specified degree of damage from a specified shaking and the hazard is expressed as the probability of the specified shaking, then earthquake risk is expressed as the combined probability. This simple relation provides a mathematical framework for assessing damage and losses from an earthquake quantitatively.

Risk analysis software  - SELENA

NORSAR has recently developed the HAZUS methodology into a stand-alone software that can be applied anywhere in the world, and also includes a logic tree-based weighting of input parameters that allows for the computation of confidence intervals. The new software package from NORSAR is termed SELENA – Seismic Loss Estimation using a Logic Tree Approach.

Much of NORSAR's recent work was concerned with the development of SELENA, which in turn establishes the basis for new research initiatives and applied projects. Since January 2007, SELENA is offered as open source software, which we hope will attract the interest from new users. The SELENA software will now also be more widely used and distributed through research collaboration programs with India, Central America countries, and within different EU projects.

Vulnerability

Probabilistic vulnerability relationships are usually expressed either in matrix form (e.g. as in Woo, 1999), or in terms of probability curves that describe the probabilities that a given structure sustain a certain degree of damage when exposed to a certain ground motion. Such probability curves are often termed vulnerability or fragility functions.

Vulnerability functions are described probabilistic or deterministic. A typical vulnerability curve depicts the cumulative probability of damages (in defined damage states) for a given structure or type of structure.

NORSAR can provide consulting and research into seismic vulnerability, and provide results based on deterministic methods and empirical data.

Click here for more information on vulnerability.

Soil response

The amplification of seismic waves as they propagate through less consolidated sediments and soils is, as already mentioned, a major factor behind earthquake damages. The thick clay deposits in and around Oslo lends this region to such studies. Although Oslo is not a place with a significant seismic activity, a few earthquakes with noticeable intensity have occurred in the past, including a magnitude 5.4 earthquake in the outer Oslofjord in 1904. This earthquake caused masonry building walls to crack as well as chimneys and roof tiles to fall off the houses in the city of Oslo. The observed significant shaking (and the associated damages) was caused by wave amplification through the thick layers of sediments underlying Oslo.

To investigate this phenomenon in more detail we have conducted special studies both in 2004 and 2006, visiting 35 different sites within the city. The technique used insisted in recording ambient seismic noise and to infer the soil response on the basis of such data using the so-called Nakamura technique, based on ambient noise H/V (horizontal-to-vertical) ratios. The results are displayed in the figures below (site 28) and are largely explaining the distribution of damages from the 1904 earthquake. 

Results from Site 28 in the Oslo soil response study, showing recorded data.
Time histories and windows selected for the analysis.




Instrumentation used at site 28.



Statistical analysis of spectral H/V-ratios, median and standard deviations.
The peak at around 6 Hz indicated the main resonant frequency in the soils.

Site characterization

The simple Nakamura technique presented above is complemented by more elaborate methods which have also been tested and used under ICG Project 3, notably an array technique and a technique based on spectral analysis of surface waves (SASW). The former technique has been used in a conceptual study at Sogn Hagekoloni in Oslo, using two different array diameters as shown in the figure below. The data have been analyzed in terms of H/V ratios on individual stations, and a subsurface shear-wave velocity profile was established through joint analysis of the two array geometries. Concordant results were found between the H/V analysis and the array analysis leading to the subsurface shear-wave velocity model.

For the analyzed site, the obtained results indicate a first layer with a thickness of 15.6 m and a Vs of 171 m/s; and a second layer (halfspace) with Vs 955 m/s. Moreover, these values provide a resonance frequency of 2.7 Hz, which is in accordance with the expected value from the initial H/V analysis. 

The SASW method is based on the same principles as the ambient vibration technique, the main difference being that the SASW method uses ground vibrations from active impact sources (sledge hammer, explosives or alike). Due to energy limitations of such sources (in particular the sledge hammer which is often the only option in cities), SASW is mainly suitable for characterizing the shear-wave velocity structure down to about 30-40 m. On the other hand, this method can be designed to provide more accurate information of the shallow subsurface properties.