# Site effects

## Methodology

Ground motion prediction models are based on regression models of acceleration records obtained at seismological stations founded on solid ground (BC) or rock (A,B). In order to define design earthquakes for arbitrary geotechnical conditions on site, it is necessary to estimate the dynamic response of the site for different ground motions and site conditions

For low intensity seismic hazard scenarios it is acceptable to estimate the dynamic response of the ground by means of scalar amplification factors. The model by Stewart et al.80 (used in the American standard ASCE 7-16 and other building codes), defines the site amplification relative to a rock site class condition (NEHRP site class A). In this approach, the ground motions (spectral ordinates) expected on arbitrary site conditions $$S_a^{*}(T_n)$$ can be obtained from the ground motions obtained for rock site conditions $$S_a^{o}(T_n)$$ through an amplification factor $$AF$$ defined as $$AF=S_a^{*}(T_n)/S_a^{o}(T_n)$$. According to this approach, the amplification factor $$AF$$ can be obtained from

$\mathrm{ln} AF(T_n) = a+b\,\mathrm{ln}⁡\,S_a(T_n) + \varepsilon$ where $$a(T_n), b(T_n)$$ are model parameters and $$\varepsilon$$ is a log-normal random variable, with mean $$E[\varepsilon]\approx 0$$ and variance $$var[\varepsilon]\approx \sigma^2$$ In the SRK approach, the spectral ordinates of the rock accelerations are defined probabilistically by a log-normal random variable with mean $$E[Sa]\approx \mu_{lnSa}$$ and variance $$var[Sa]\approx \sigma_{lnSa}^2$$ and the uncertainty of the seismic hazard assessment is included in AF error term $$var[\varepsilon]\approx \left(σ^2+σ_{\mathrm{ln}\,Sa}^2 b^2\right)$$

When the geotechnical properties of different strata are known from MASW, CPT or SPT data, it is possible to estimate an amplification factor from shear wave velocities $$V_{s30}$$. For these scenarios, the amplification factor can be estimated by the model of Stewart et al.81 according to an empirical three-component model dependent on $$V_{s30}$$. $\mathrm{ln}\,AF(V_{s30},T)= F_V+F_{760}+F_{nl}+\varepsilon$ In this expression, $$F_V$$ is a scaling term relative to $$V_{s30}=760 \mathrm{m/s}$$, $$F_{760}$$ is amplification at $$V_{s30}=760 \mathrm{m/s}$$ relative to $$V_s=3000 \mathrm{m/s}$$ and $$F_{nl}$$ is a factor that considers non-linear effects, which has strong influence in soft-soil conditions. The error term $$\varepsilon$$ is a log-normal random variable, with mean $$E[\varepsilon]\approx 0$$ and variance

$\mathrm{Var}[\varepsilon]\approx \sigma_V^2+\sigma_{760}^2+\sigma_{nl}^2$ The non-linear components are discussed in Hashash et al..82 If the reference condition is set to $$V_{s30}=760 \mathrm{m/s}$$, the $$F_{760}$$ term is dropped.

## Geotechnical information

The GGM TSF site extends across 230 ha, located in the geological region of Yamarna Terrane greenstone. The terrain slopes moderately to the northeast of the site and a surface water drainage was located along the eastern side of the site, where alluvial materials have been deposited. Several geotechnical campaigns were carried out comprising: 20 geotechnical drills with depths up to 21 m, more than 60 test pits up to 3.0 m and 16 DCP up to 1.0 m. Two geotechnical shallow foundation typical profiles can be distinguished across the TSF site area (SRK 2021):

Profile 1: a 0.20m thick topsoil of silty sand/sandy silt (SM/ML) followed by highly weathered or highly fractured basalt observed as gravel with sand and fines in the upper ~2m and as highly fractured core thereafter. Below the highly fractured basalt, fresh rock occurs from 4.5-20m depths.

Profile 2: a 0.20m thick topsoil of silty sand/sandy silt (SM/ML) followed by ~2.0m of alluvial material (CL-CI, SM-SC), extremely weathered basalt observed as silt/ silty sand followed by highly weathered basalt at depths ranging from a minimum depth of 1.0 m observed as gravel with sand and fines.

For site soils materials, Kokusho and Hardin & Richart correlations can be evaluated to estimate a shear modulus and calculate a mean value. The formula is common and the parameters change according to the soil type, $$G=A {p^{\prime}}^{n} \left( (C_e-e)^2/(1+e) \right)$$, where $$A$$ is a material strength constant, $$e$$ is the void ratio, $$C_e=2.17$$ is a material state constant and $$p^{\prime}$$ is the effective mean stress.83

## Results

The average shear-wave velocity of the top 30 m resulted in $$V_{s30}≈655 ± 70\,\mathrm{m/s}$$ for Profile 1 and $$V_{s30}≈620 ± 60 \mathrm{m/s}$$ for Profile 2, both ranging between 400 and 800 m/s, corresponding to class “C” sites according to the Uniform Building Code, ASCE 7-16 and NEHRP. This class is representative of dense soils to soft rocks.

The mean and 84th percentile amplification factor of the PGA for a 10,000 year event and a class “C” are $$AF\approx$$ 1.194 and $$AF\approx$$ 1.78. For geotechnical conditions of reference, corresponding to site classes according to the Uniform Building Code, ASCE 7-16 and NEHRP, Table 7 and Table 8 report the mean and 84th percentile amplification factor for different service levels.

 Site Amplification AF(PGA) - (mean) NEHRP TR=500 TR=1000 TR=2500 TR=5000 TR=10000 MCE AB 1.000 1.000 1.000 1.000 1.000 1.0000 B 1.015 1.044 1.081 1.108 1.132 1.1415 C 1.333 1.295 1.251 1.221 1.194 1.1846 D 1.677 1.611 1.534 1.483 1.438 1.4219
 Site Amplification AF(PGA) - (+84%) NEHRP TR=500 TR=1000 TR=2500 TR=5000 TR=10000 MCE AB 1.000 1.000 1.000 1.000 1.000 1.0000 B 1.469 1.511 1.566 1.604 1.640 1.6529 C 1.986 1.930 1.864 1.819 1.780 1.7653 D 2.521 2.423 2.306 2.230 2.162 2.1380

1. “Amplification Factors for Spectral Acceleration in Tectonically Active Regions,” Bull. Seismol. Soc. Am. 93 (2003).↩︎

2. “Expert Panel Recommendations for Ergodic Site Amplification in Central and Eastern North America” (PEER Report, 4., 2017).↩︎

3. “Recommendations for Ergodic Nonlinear Site Amplification in Central and Eastern North America” (PEER Report, 5., 2017).↩︎

4. James K. Mitchell and Kenichi Soga, Fundamentals of Soil Behavior (New Jersey: John Wiley & Sons,INC., 2005).↩︎