The integration of site effects into Probabilistic Seismic Hazard Assessment (PSHA) is still an open issue within the seismic hazard community. Several approaches have been proposed varying from deterministic to fully probabilistic, through hybrid (probabilistic-deterministic) approaches. The present study compares the hazard curves that have been obtained for a thick, soft non-linear site with two different fully probabilistic, site-specific seismic hazard methods: (1) The analytical approximation of the full convolution method (AM) proposed by Bazzurro and Cornell 2004a,b and (2) what we call the Full Probabilistic Stochastic Method (SM). The AM computes the site-specific hazard curve on soil,
, by convolving for each oscillator frequency the bedrock hazard curve,
, with a simplified representation of the probability distribution of the amplification function,
, at the considered site The SM hazard curve is built from stochastic time histories on soil or rock corresponding to a representative, long enough synthetic catalog of seismic events. This comparison is performed for the example case of the Euroseistest site near Thessaloniki (Greece). For this purpose, we generate a long synthetic earthquake catalog, we calculate synthetic time histories on rock with the stochastic point source approach, and then scale them using an adhoc frequency-dependent correction factor to fit the specific rock target hazard. We then propagate the rock stochastic time histories, from depth to surface using two different one-dimensional (1D) numerical site response analyses, while using an equivalent-linear (EL) and a non-linear (NL) code to account for code-to-code variability. Lastly, we compute the probability distribution of the non-linear site amplification function,
, for both site response analyses, and derive the site-specific hazard curve with both AM and SM methods, to account for method-to-method variability. The code-to-code variability (EL and NL) is found to be significant, providing a much larger contribution to the uncertainty in hazard estimates, than the method-to-method variability: AM and SM results are found comparable whenever simultaneously applicable. However, the AM method is also shown to exhibit severe limitations in the case of strong non-linearity, leading to ground motion “saturation”, so that finally the SM method is to be preferred, despite its much higher computational price. Finally, we encourage the use of ground-motion simulations to integrate site effects into PSHA, since models with different levels of complexity can be included (e.g., point source, extended source, 1D, two-dimensional (2D), and three-dimensional (3D) site response analysis, kappa effect, hard rock …), and the corresponding variability of the site response can be quantified.