Over the past few decades, earthquake engineering research mainly focused on the effects of strong seismic shaking. After the 1999 earthquakes in Turkey and Taiwan, and thanks to numerous cases where fault rupture caused substantial damage to structures, the importance of faulting-induced deformation has re-emerged. This paper, along with its companion (Part II), exploits parametric results of finite element analyses and centrifuge model testing in developing a four-step semi-analytical approach for analysis of dip-slip (normal and thrust) fault rupture propagation through sand, its emergence on the ground surface, and its interaction with raft foundations. The present paper (Part I) focuses on the effects of faulting in the absence of a structure (i.e., in the free-field). The semi-analytical approach comprises two-steps: the first deals with the rupture path and the estimation of the location of fault outcropping, and the second with the tectonically-induced displacement profile at the ground surface. In both cases, simple mechanical analogues are used to derive simplified semi-analytical expressions. Centrifuge model test data, in combination with parametric results from nonlinear finite element analyses, are utilized for model calibration. The derived semi-analytical expressions are shown to compare reasonably well with more rigorous experimental and theoretical data, thus providing a useful tool for a first estimation of near-fault seismic hazard.