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Title: Mathematical model for describing stress wave propagation in a jointed rock mass
Authors: United States. Army. Office of the Chief of Engineers.
Drake, James L.
Keywords: Ground shock
Jointed rock
Mathematical models
Stress waves
Wave propagation
Publisher: Weapons Effects Laboratory (U.S.)
Engineer Research and Development Center (U.S.)
Series/Report no.: Technical report (U.S. Army Engineer Waterways Experiment Station) ; N-73-7.
Description: Technical report
Abstract: A mathematical model that describes the effects of joints and fractures on the propagation of energy in a jointed rock mass was developed and verified with experimental evidence from seismic and nuclear tests. The model demonstrated that the average arrival time in a jointed medium is reduced from that in an unfractured rock by an amount related to the average number of joints encountered by the wave. It was also demonstrated that the mean-square fluctuations in the arrival times are directly related to the mean-square fluctuations in the joint density. Because the travel time and joint density statistics are directly related by the model developed in this study, carefully planned seismic tests can be used for exploration of the jointing. It is suggested that seismic surveys can be used to determine the competency of rock. An average time history of a propagating disturbance was calculated which includes the effects of jointing on an arbitrary pulse. Joints were shown to control the rise times to peak particle velocity, hence peak accelerations, for large, contained explosions. Rise time parameters determined from seismic surveys correlated well with rise time parameters determined from nuclear and high-explosive tests in salt and granite. A ground shock prediction formula was developed which includes the effect of joints on waves generated by contained explosions. Scaling laws were proposed for nuclear explosions that, when combined with the ground shock prediction, collapsed test data from six nuclear explosions in various rock types onto one curve. Test data fell within, 37 percent of the predicted peak particle velocity and 34 percent of predicted peak particle accelerations (percentages indicate one standard deviation). Salient features of the predicted time history were in good agreement with measurements.
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