求：Estimating the intensity of rock discontinuities,我的邮箱：
hsky189@126.com作者：Lianyang Zhang and H. H. Einstein
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Copyright © 2000 Elsevier Science Ltd. All rights reserved.
Estimating the intensity of rock discontinuities
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Lianyang Zhang and H. H. Einstein,
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Accepted 15 March 2000 Available online 3 July 2000.
Abstract
This paper presents an approach for estimating the intensity of discontinuities and formulating intensity and orientation as a fracture tensor. Specifically the size distribution and the number of discontinuities are estimated first, from which the fracture tensor is then derived. Discontinuity size distribution is inferred from the trace data sampled in circular windows by using a general stereological relationship between the true trace length distribution and the discontinuity diameter distribution assuming circular shaped discontinuities. Because the measured trace lengths are biased, a method is proposed to estimate the true trace length distribution for circular window sampling. Circular window sampling has the advantage of automatically eliminating the orientation bias when estimating the true trace lengths. A method is then presented with which the total number of discontinuities in an objective volume can be estimated from the number of discontinuities observed in normal-size boreholes and using the inferred discontinuity diameter from the circular window sampling on the rock surface. With the derived size distribution and number of discontinuities, the intensity of discontinuities, which is the total surface area of discontinuities per unit volume, can then be calculated and included in a new definition of a fracture tensor. An application of the approach to analyze simulated discontinuities produces satisfactory results.
Article Outline
1. Introduction
2. Basic assumptions
2.1. Planar discontinuities
2.2. Circular discontinuities
2.3. Discontinuities randomly distributed in space
2.4. Discontinuity sizes independent of position
3. Inference of discontinuity size distribution
3.1. Estimation of true trace length distribution f(l)
3.1.1. Mean μl of f(l)
3.1.2. Standard deviation σl of f(l)
3.1.3. Distribution form of f(l)
3.2. Inference of g(D) from f(l)
4. Number of discontinuities
4.1. Probability of intersection
4.2. Number of discontinuities in the objective volume
4.3. Discussion
5. Fracture tensor for describing discontinuity intensity
6. Application to the simulated data by FracMan
6.1. Estimation of true trace length distribution f(l)
6.1.1. Analysis of measured trace lengths
6.1.2. True trace length distribution f(l)
6.2. Inference of discontinuity size distribution
6.3. Number of discontinuities in the objective volume
6.4. Fracture tensor
7. Summary and conclusions
Acknowledgements
References
