A Comparison of Plane and Spherical Transient Voigt Waves with Explosion Generated Waves in Rock Masses

摘要

Plane and spherical waves in a Voigt medium were investigated to compare the calculated wave forms with observed waves generated by large contained HE and NE explosions. Interest is centered on wave forms in what is usually considered to be the elastic region around an explosion. Plane waves do not apply at this distance because of geometry. The plane Voigt wave equation has been previously solved for particle velocity, stress and strain for a unit impulse forcing function. However, solutions for the displacement for a unit impulse and for the four wave parameters for a unit step and a decay exponential involve multipliers in the operational form for which no transform pairs have been published. A method of solution is presented which utilizes a Heaviside expansion of the multipliers in the transform plane which results in products of two infinite series which may be inverted term by term. These may be further resolved as single series with polynomial coefficients for purposes of computation. A similar method of solution of Voigt spherical waves was found for unit impulse, unit step and decay exponential forcing functions for displacement, particle velocity, strain and radial stress. Appropriate recursion formulas make them readily adaptable to computer evaluation. Oscillations occur for a spherical wave whereas for a plane wave they do not. Calculations were performed for particle velocity for three values of the Voigt viscoelastic parameter and comparisons made with pulse forms for waves in granite, tuff and salt. (Author)