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Chapter 26 GROUND VIBRATION Source of Seismic Wares. When an explosive detonates is a~ borehole, it generates an intense stress wave in the surrounding ~ This crushes the rock around the borehole up to about one boreh~. radius and permanently distorts and cracks it to several boreholtl~ diameters. A schematic diagram of this process is shown in Figtt~. 26-A. ', When the intensity of the stress waves is reduced so that there ig np~. permanent deformation of the rock, the stress wave propageter, through the rock in an elastic manner, that is, in such a manner that' the rock particles are returned to their original position following fh!' passage of the stress wave. ~~± Kinds of Seismic Waves. Theoretical considerations have shown that for an explosion in a spherical or infinitely long cylindrical borehole only compressional waves aze possible in an ideal material without ~ ~ - ~ ~ i~ ` l 1 / 1 ~ ~ \ Explosion Cavity ~ ` and Original r ~ ~\l Drlll Hol ~ / ~•--Blasl- CCU QP --~-- , Fractured `~ ~~' ~_Zone ~ 1 Crushed Zone ~ \~~ / Elastic ~ ` 1 4 i ~ Zone ~ .,. r figure 2g-A. Schematic of the lreoturin9 end tleformet{on emund an exploeton in rock. 424 Vibration and Air Blast poundaries. In nonidea] materials and for cylindrical charges of finite ton¢th, however, shear waves can also be directly produced from axY,~~.,,..... Compressional and shear waves are known as body waves. The compressional waves travel through the rock by alternately compres- aing and dilating the particles of rock through which they pass. These waves travel in the same direction as the particles they push together and pull apart. Their propagation velocity in rock typically exceeds 15,000 feet-par-second or more. Compressional waves can pass through solids, liquids, or gases. The shear waves travel through the earth by causing rock particles W vibrate sideways or at right angles to the forward direction in which the wave travels. Shear waves travel at about two-thirds of the velocity of compressional waves. However, unlike compressional waves, shear waves cannot pass through liquids or gases because these materials have no shear resistance. t-tfien curved compressional and shear waves impinge upon inter- faces, such as the earth's surface, a very complicated process takes place which gives rise to surface waves. The most common of the surface waves is called the Raleigh wave. Because the surface waves dfverge in only two dimensions in contrast to the three-dimensional divergence of body waves, they decay more slowly with distance and frequently dominate the ground motion at distances of several hundred yards or more. In addition to divergence nonelastic processes caused by the friction of particles upon one another cause seismic waves to decrease in intensity with distance. Scientific studies have shown that high- frequency seismic energy is absorbed more readily than low-frequency energy so that the energy content of seismic waves at large distances is concentrated at low frequencies. Duration of the Naves. Because the various kinds of seismic waves travel at dif'Cerent speeds and interact in a complicated manner with themselves and the material in which they travel, a blast which may finish detonating in a few hundred milliseconds or less can produce ground motion Cor several seconds at locations several hundred yazds away. The lengthening of ground motion with distance is enhanced by a process known as dispersion whereby the different frequencies com- posing the various surface waves travel at different velocities. Prediction of Vibration Levels. A simple power law formula has been found useful in relating the weight of the explosive chazge and its distance to the particle displacement, velocity, and acceleration. The form of this equation to determine peak particle velocity is: V = KW"'R-" • V is the peak particle velocity (how fast the ground moves). • K is the ground transmission constant, which is empirically deter- 425 • r