Method for Rock Fissure Hazard Analysis
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A stochastic rock fissure hazard model is presented based on geological characterization of the occurrence and propagation of fissures. The hazard model is developed in two steps: (1) fissure propagation model and (2) fissure occurrence model. For the fissure propagation model, the initiation point, length, azimuth and depth of fissures are described as random variables that define the spatial distribution, direction and extent of fissure propagation in a specified volume. From this model probabilities of a fissure crossing an underground waste repository can be estimated given that a fissure has been initiated. Fissure occurrences are represented as a Poisson stochastic process. The fissure occurrence and fissure propagation models are combined to obtain the probability of fissures crossing a waste repository as a function of time. In particular, probabilities of at least one fissure crossing the repository at a site during the life of a repository can be estimated with the proposed model. In order to demonstrate the usefulness and applicability of this model, the rock fissure hazard is estimated at a site in the Krafla region in northeastern Iceland. This location is selected purely because long fissures have been identified, these been studied extensively and data was available to estimate the various model parameters. The data from the Krafla region was used to estimate the parameters for the probability distributions of fissure initiation location, length, azimuth and depth. Fissure initiating location is modeled as a joint normal and uniform distribution in the plane overlying the waste repository. Fissure length and azimuth direction are represented through lognormal and normal distributions, respectively. Data for fissure depth was not available, thus the probabilities of fissure depth are determined assuming a uniform distribution based on several observations which indicate that fissure depths cannot be larger than their lengths and very long and shallow fissures are unlikely to occur. These distributions are combined to develop probability distribution of fissures extending over the volume of an underground waste repository. Fissure occurrences are assumed to be independent in time and equally likely in space and are described by a Poisson stochastic process. These assumptions are rather simplistic, however, they represent a first attempt at modeling fissure occurrences. The advantage of using the Poisson model is that only one parameter is needed and the specific pattern on fissure initiation does not need to be specified. Fissure initiation patterns are difficult to obtain in general and the assumption that fissures occur with equal likelihood along a line appears to be reasonable. To specify the Poisson model, past observations on fissure occurrences over time are used to estimate the annual rate of fissure initiating locations. With this model, the probability of one or more fissures initiating in the vicinity of the repository are obtained. These probabilities are combined with the fissure propagation model to determine the probability of at least one fissure crossing an underground waste repository over a specified future time period. Similarly, annual probabilities of at least one fissure crossing the repository and probabilities of one fissure crossing the repository can be evaluated. The rock fissure hazard at a site estimated by the proposed model reflects the geological characteristics of fissure propagation and the fissure occurrences in time. It is recognized, however, that the characteristics of fissure propagation and fissure occurrence patterns strongly depend on the material properties and the time-dependent stress conditions of the rock. Thus future studies should concentrate on modeling the specific pattern of the occurrences and propagation of fissures in rock. It is expected that these characteristics of fissures will change depending on the specific region making it particularly difficult to develop a generic model.
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