Dedicated to Professor Charles Fairhurst. His early work on clarifying rock blasting mechanics continues to inspire everyone interested in this illusive topic.
ABSTRACT: The conventional approach of analyzing blast-induced ground vibration contains basic assumptions that have long been questioned. Smooth predictors cannot adequately describe local random fluctuations of ground vibration. The spatially dependent nature of the data makes the regionalized variable approach suitable. Variograms of peak particle velocity (ppv) and of its associated frequency were developed using a blast vibration data set as an example. Predicted values of these ground vibration parameters were obtained using ordinary kriging. Indicator variograms were generated for a given ppv vibration threshold. The probability of exceeding this value at any point within the domain was estimated by indicator kriging. The approach of regionalized variables lends itself naturally to this class of problem. In addition to providing solutions to the problem at hand, it addresses the heretofore difficult question of determining the probability that a given vibration limit is exceeded.
1 INTRODUCTION
Ground motion generated by blasts poses a risk to the surrounding environment. Damage potential to nearby structures as well as annoyance of people, frequently the most important limitation, are related to the particle velocity and the frequency of vibration (e.g. Siskind, 1980). Acceleration and/or displacement are commonly used in relation with earthquake ground motion. Displacement is sometimes used in characterizing ground motion generated by blasting, for example in sensitive structures such as the proposed Superconducting Super Collider high energy particle accelerator (SSC Central Design Group, 1986).
The conventional approach of choosing the peak ground vibration from time-history data is not fully satisfactory because its associated frequency may not be the one that carries the most destructive energy to the structure. In fact, it is difficult to incorporate frequency in such an analysis (e.g. Dowding, 1985, Ch. 6). Plotting ground vibration as a function of distance (or scaled distance) assumes that ground vibration attenuation is the same in all directions. The assumption that attenuation is strictly distance dependent has been questioned (e.g. Reil et al, 1985). Regression does not take into account the local variation or random component of ground vibration and considers only its deterministic part, resulting in models that are smooth and appear precisely defined.
Figure 1. Plan view of blast vibration test site (from Nicholls et al. 1971). Monitoring points are located along the gage lines. (available in full paper)
2 REGIONALIZED VARIABLE APPRAOCH: A CASE STUDY
Ground vibration often exhibits random spatial fluctuations that cannot be described by smooth functions. It follows from basic (theoretical) wave mechanics that for a blast in a given rock type, particle velocities recorded at two points comparable in distance from the blast are more similar than those monitored at two locations with different distances from blast source. This spatially dependent nature of the data can be accounted for by the theory of regionalized variables. Variability and spatial correlation of the ground vibration data can be captured by the variogram function.
