# 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

In PFS and FS stages, it is acceptable to estimate the dynamic response of the ground by means of scalar amplification factors. The model by Stewart et al.45 (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 $$var[\varepsilon]\approx \left(σ^2+σ_{\mathrm{ln}\,Sa}^2 b^2\right)$$

In the feasibility design stages, 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.46 according to an empirical three-component model dependent on Vs30. $\mathrm{ln}\,AF(V_{s30},T)= F_V+F_{760}+F_{nl}+\varepsilon$ 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..47 If the reference condition is set to $$V_{s30}=760 \mathrm{m/s}$$, the $$F_{760}$$ term is dropped.

## Results

For preliminary design purposes, it has been assumed for all foundation scenarios, shear-wave velocities for the top 30 m $$(V_{s.30})$$ 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 amplification factor of the PGA for a 10,000 year event and a class “C” site resulted in $$AF\approx$$ 1.862, considering the median plus a standard deviation term of the model error (84th percentile). For other geotechnical conditions and service levels, the amplification factor is reported in Table 4

 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 1.403 1.441 1.492 1.530 1.567 1.6088 C 2.079 2.024 1.955 1.907 1.862 1.8134 D 2.688 2.588 2.467 2.382 2.304 2.2198

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).↩︎