Date of Award


Degree Name

Mechanical Engineering


College of Engineering and Computer Sciences

Type of Degree


Document Type


First Advisor

Dr. Mehdi Esmaeilpour, Committee Chairperson

Second Advisor

Dr. Arka Chattopadhyay

Third Advisor

Dr. Andrew Nichols


Underground voids, whether man-made (e.g., mines and tunnels) or naturally occurring (e.g., karst terrain), can cause a variety of threats to surface activity. Therefore, it is important to be able to locate and characterize a potential void in the subsurface so that mitigating measures can be taken. In real-world environments, the subsurface properties and the existence of a void is not known, so the problem is challenging to solve. The numerical analysis conducted in this study takes a step toward understanding the seismic response with and without a void in various types of domains. The Finite Difference Method (FDM) and Finite Element Method (FEM) numerical techniques were used to analyze 1-D and 2-D seismic wave propagation for homogenous domains, layered domains, and with voids in the domain. The outputs of each numerical method were compared via their results and computational efficiency, which has not been completed in the current literature. Additionally, different void shapes were placed in the computational models to analyze each method’s void detection ability.

For 1-D wave propagation, both methods produced identical results at different loading frequencies and Courant numbers. Computationally, both methods have similar run times, while FDM had a simpler implementation than FEM. In a 2-D simulation, COMSOL was used for the FEM, and the staggered-grid technique was used for the FDM. Slight dispersion was observed in all the FDM solutions, where this was attributed to the step size; however, using a smaller step size significantly increased the computational time. For a homogenous model, both methods produced similar vertical particle velocity contours and surface time histories. Computationally, FDM outperformed FEM, and due to its ease of implementation, it was recommended for homogenous wave propagation. A three-layered domain was analyzed that featured a silty clay upper layer, and two lower rock layers. Contours of vertical particle velocity displayed that the majority of the wave remained in the upper third of the domain because of the harsh difference in material properties between the first and second layers. Additionally, a numerical model was created that consisted of the material properties obtained by ultrasonic testing. Reflections were seen in the generated seismograms but were not as visible as the ones seen in the three-layered case because the measured properties are alike and allow the wave to travel easily through the domain. After analyzing the wave propagation in a domain without a void, three void shapes were placed at the center of the domain (ellipse, circle, and square), and the resulting wave propagation was analyzed. There was minimal noise near the interface of rounded shapes in the FDM results, which was attributed to the staircase approximation used to define the shape. The surface time histories displayed reflections due to the void that were not seen in homogeneous cases. The elliptical void produced slightly more pronounced reflections because the length of the shape was larger than the circle and square. The reflections were also more easily seen in the rock domain than in soil. It was difficult locating voids in the three-layer case, but plots that computed the difference between the no-void and void case revealed that the voids did affect wave propagation. The elliptical void had the largest maximum difference of the seismograms, which occurred at the receiver closest to the void. There were differences between the subtracted plots from each method, where this was attributed to the different source incorporation. However, future studies will need to be completed to fully analyze why these plots differed between each method. Reflections from the void were more easily seen in the domain featuring the results from ultrasonic testing because of the similar rock properties that the samples shared. The elliptical void had the most perturbations compared to the square and circular voids. Overall, the FEM had longer computational times than the FDM, but both methods can successfully analyze wave propagation in the studied domains.


Elastic wave propagation – Research.

Finite differences – Research.

Finite element method – Research.

Seismic waves – Research.

Seismic wave propagation – Research.