# Deterministic hazard assessment

## Methodology

A Deterministic Seismic Hazard Assessment (DSHA) involves the development of a particular seismic scenario upon which a ground-motion hazard evaluation is based.48 The scenario involves the postulated occurrence of an earthquake of a specified size occurring at a specified location that produces a ground-motion estimated from a specified empirical model. The controlling scenario from all possible seismic scenarios defines a Maximum Credible Earthquake (MCE) in terms of magnitude, source-to-site distances, and ground-motion intensity.

For a given source, the choice of a specific ground-motion model and the definition of the hazard level defines an earthquake scenario. The source with the magnitude, source-to-site distance and ground-motion models combination which gives the largest ground-motion intensity at the site will be the controlling scenario. The controlling scenario from all possible seismic scenarios defines the maximum credible earthquake in terms of magnitude and source-to-site distances.

The ground-motion hazard level should be established based on the uncertainty in the seismic hazard characterisation, the critical nature of the project, and the consequences of underperformance.

The following steps will be required for a DSHA:

Step 1: Identify all seismic sources that can generate strong ground shaking at the site, and characterise each seismic source in terms of location, geometry, sense of slip, maximum size of rupture area, and earthquake occurrence rates for all magnitudes relevant to the site hazard.

Step 2: From historical and instrumental seismicity, identify the maximum probable earthquake (MPE) that occurred at the site and the maximum credible earthquakes (MCEs) for each source.

Step 3: Select ground-motion models appropriate for the seismic sources, seismotectonic setting and site conditions.

Step 4: Estimate the different source-to-site distances required for each ground-motion model. For finite fault type sources, estimate the source-to-site distances based on the MCEs.

Step 5: Identify the controlling scenario in terms of M-R pairs and define the ranges of representative magnitudes and distances for the records selection stage.

The above parameters determines a large number of different rupture plane combinations, which keep the size of the rupture area, the hypocentral depth and the epicentral distance to the project site invariant. Using a simple numerical simulation algorithm, the intensities $$S_a(T_n)$$ can be obtained for all periodos of interest and all ground-motion models. Assuming a log-normal distribution, the first and second order moments of the probability density function of the seismic intensity can be obtained and therefore, the hazard spectra for all periods.

## Results

#### Controlling scenario

The scenario controlling the seismic hazard is given by the MS fault. For this scenario, the finite-fault metrics were obtained assuming an hypocentre depth between 5 and 35 km and a dip angle of $$\delta=90^\circ$$. Given the site position relative to the fault, the Joyner-Boore distance $$R_{JB}$$ and $$R_X$$ are equal to the epicentral distance $$R_{EPI}=38\,\mathrm{km}$$ for the present scenario. The hypocentral distance ranges between 38 to 52 km and the top edge of rupture $$Z_{TOR}$$ reaches the surface for the minimum hypocentre and a maximum depth of 24 km.

#### Peak Ground Accelerations (PGA)

Peak Ground Accelerations (PGA) is defined as the maximum ground acceleration that occurred during earthquake shaking at a location and represents the amplitude of the largest absolute acceleration recorded on an accelerogram at a site during a particular earthquake. PGA values (84%) in rock reported by the different ground-motion models selected for Simandou, assuming a maximum credible event of $$M_w=6.8$$ and different distances to the source are shown in Figure 10. The bold line represents the weighted-average model obtained from the logic-tree adopted before.

Spectral ordinate values for each model represent the median plus a deviation term of the (unweighted) PGA intensities for a target magnitude equal to the maximum credible magnitude defined for the source $$(M_w=6.8)$$. Figure 11 shows weighted-average PGA values (84%) in rock for different source-to-site distances assuming a maximum credible event of $$M_w=6.8$$

Table ?? summarises the unweighted peak-ground accelerations (PGA) of the different seismic motion prediction models used in this study and the resultant weighted-average obtained from the logic-tree adopted for the region. The maximum credible earthquake assumed for the controlling scenario results in $$PGA\approx$$ 0.18 $$\mathrm{g}$$

For a target scenario with dense soils to soft rocks with shear wave velocities ranging between 400 and 800 m/s (site class “C”), the maximum credible earthquake reported $$PGA\approx$$ 0.248 $$\mathrm{g}$$ (84%)

#### Hazard Spectra

The seismic shaking intensities resulting from the linear response of an SDOF oscillator at different fundamental periods $$T_n$$ define the response spectrum $$S_a(T_n)$$ of each GM model in rock, for a scenario given by the source size $$M_w$$, the closest distance to the source $$R$$ and others source rupture area parameters. Figure 12 shows the spectral ordiantes reported from different ground-motion models for the 84% quantile

The weighted-average ground-motion model for $$M_w=6.8$$ and $$R\approx \ 38 \ km$$ determines the design earthquakes $$S_a(T_n)$$ for rock at the project site. Figure 13 shows the weighted-average spectral ordinates $$S_a(T_n)$$ for different quantiles

Spectral ordinates for other site conditions than rock are shown in Figure 14 (84%)

1. S. Kramer, Geotechnical Earthquake Engineering (Prentice Hall Upper Saddle River, NJ, 1998).↩︎