Date of Award


Embargo Period


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Civil and Environmental Engineering


Jacobo Bielak


This dissertation presents a numerical scheme based upon the finite element framework for the numerical modeling of earthquake-induced ground motion in the presence of realistic topographic variations of the earths crust. We show that by adopting a non-conforming meshing scheme for the numerical representation of the surficial topography we can obtain very accurate representations of earthquake induced ground motion in mountainous regions. From the computational point of view, our methodology proves to be accurate, efficient, and more importantly, it allows us to preserve the salient features of multi-resolution cubic finite elements. We implemented the non-conforming scheme for the treatment of realistic topographies into Hercules, the octree-based finite-element earthquake simulator developed by the Quake Group at Carnegie Mellon University. We tested the benefits of the strategy by benchmarking its results against reference examples, and by means of convergence analyses. Our qualitative and quantitative comparisons showed an excellent agreement between results. Moreover, this agreement was obtained using the same mesh refinement as in traditional flat-free simulations.

Our approach was tested under realistic conditions by conducting a comprehensive set of deterministic 3D ground motion numerical simulations in an earthquake-prone region exhibiting moderate-to-strong surficial irregularities known as the Aburra Valley in Antioquia - Colombia. We proposed a 50 x 50 x 25 km3 volume to perform our simulations, and four Mw = 5 rupture scenarios along a segment of the Romeral fault, a significant source of seismic activity of Colombia. We created and used the Initial Velocity Model of the Aburra Valley region (IVM-AbV) which takes geology as a proxy for shear-wave velocity. Each earthquake model was simulated using three different models: (i) realistic 3D structure with realistic topography; (ii) realistic 3D structure without topography; and (iii) homogeneous half space with realistic topography. Our results show how realistic topography greatly modifies the ground response. In particular, they highlight the importance of the combined interaction between source-effects, focusing, soft-soil conditions, and 3D topography. We provide quantitative evidence of this interaction and show that topographic amplification factors at some locations can be as high as 500 percent, while some other areas experience reductions. These are smaller than the amplifications, on the order of up to 100 percent.