Seismic wave propagation in spatially variable soil continuum can be described by partial differential equations (PDE) with stochastic coefficients. Typical method of analysis in this area is a spectral analysis approach, where time series is presented by a Fourier expansion or a Fourier integral transform. This approach has a limited capability being applicable to the linear problems only.

The novelty of presented method is that it can handle any nonlinear elastic - plastic stochastic constitutive model. The output of the project is the 2D seismic random wave propagation model accounting for the spatial variability of soil properties, described by the linear and nonlinear constitutive models. This model allows accessing the seismic hazard of a region of interest with account of its specific geological and topographic features. Time dependent ground velocities, accelerations, stress components and pressure applied to the walls of an engineering structure (power plant) have been predicted to estimate the seismic lifeline hazard of engineering facilities.

Nonlinear seismic wave propagations are simulated based on a dynamic two dimensional theory of mechanics of continuum with account of nonlinear Hencky-Nadai constitutive models. Boundary conditions relate to the acceleration profile given by accelerometer or seismometer, zero stress components at the ground surface, free surface conditions at the top and non-reflected (absorbed) boundary conditions at distal boundaries.

This model describes heterogeneous spatially distributed ground soil properties, based on a set of nonlinear constitutive equations. Mathematical frame is presented by a coupled set of a nonlinear hyperbolic system of equations, with respect to three components of stress tensor and two components of a velocity vector. Analytical expressions for relating eigenvalues and eigen functions are found using MATLAB symbolic toolbox. The finite volume, characteristically based Total Variation Diminishing (TVD) method used to predict ground motion wave propagations parameters of interest in a time – space domain as a function of a seismic profile, distance, soil properties. Monte-Carlo simulations are used to model the probability of different outcomes in a process of seismic wave propagation.

Library of Congress Subject Headings

Seismic waves--Mathematical models; Seismic waves--Computer simulation; Stochastic models

Publication Date


Document Type


Student Type


Degree Name

Mechanical Engineering (MS)

Department, Program, or Center

Mechanical Engineering (KGCOE)


Alexander Liberson

Advisor/Committee Member

Sarilyn Ivancic

Advisor/Committee Member

Jason Kolodziej


RIT – Main Campus

Plan Codes