Details
| Original language | English |
|---|---|
| Pages (from-to) | 127-137 |
| Number of pages | 11 |
| Journal | International Journal of Rock Mechanics and Mining Sciences |
| Volume | 72 |
| Publication status | Published - 10 Oct 2014 |
| Externally published | Yes |
Abstract
Fracture size is often estimated from trace length measurements. It is well recognized to be a typical non-unique inverse problem. This paper presents a distribution-free method for estimating the fracture diameter distributions using moments in conjunction with the maximum entropy principle. In this method, moments are used to characterize the statistical nature of the probability distributions. The method involves the inference of the moments of the true trace lengths from the sampled trace data, the explicit expression of moments of fracture diameters using general stereological relationship, and the estimation of fracture diameter distribution using the maximum entropy principle by a given set of moments of fracture diameters. The proposed method makes it possible to achieve a universal form for the fracture diameter distribution without any particular parametric form, and to match the moments of fracture diameters up to the fourth order. The overall behavior of the method is validated by an example, and the results show that it is capable of estimating the fracture diameter distributions.
Keywords
- Fracture diameter, Maximum entropy, Moments, Trace length
ASJC Scopus subject areas
- Earth and Planetary Sciences(all)
- Geotechnical Engineering and Engineering Geology
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In: International Journal of Rock Mechanics and Mining Sciences, Vol. 72, 10.10.2014, p. 127-137.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Estimation of the fracture diameter distributions using the maximum entropy principle
AU - Zhu, Hehua
AU - Zuo, Yulong
AU - Li, Xiaojun
AU - Deng, Jian
AU - Zhuang, Xiaoying
N1 - Funding Information: The authors gratefully acknowledge the financial support of the Natural Science Foundation of China (NSFC 41272289 , 51109162 ), the National Basic Research Program of China ( 973 Program : 2011CB013800 ), and the Science and Technology Plan Project of Ministry of Transport of China ( 2013318J02120 ). The comments of anonymous reviewers greatly improved the original manuscript. Publisher Copyright: © 2014 Elsevier Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2014/10/10
Y1 - 2014/10/10
N2 - Fracture size is often estimated from trace length measurements. It is well recognized to be a typical non-unique inverse problem. This paper presents a distribution-free method for estimating the fracture diameter distributions using moments in conjunction with the maximum entropy principle. In this method, moments are used to characterize the statistical nature of the probability distributions. The method involves the inference of the moments of the true trace lengths from the sampled trace data, the explicit expression of moments of fracture diameters using general stereological relationship, and the estimation of fracture diameter distribution using the maximum entropy principle by a given set of moments of fracture diameters. The proposed method makes it possible to achieve a universal form for the fracture diameter distribution without any particular parametric form, and to match the moments of fracture diameters up to the fourth order. The overall behavior of the method is validated by an example, and the results show that it is capable of estimating the fracture diameter distributions.
AB - Fracture size is often estimated from trace length measurements. It is well recognized to be a typical non-unique inverse problem. This paper presents a distribution-free method for estimating the fracture diameter distributions using moments in conjunction with the maximum entropy principle. In this method, moments are used to characterize the statistical nature of the probability distributions. The method involves the inference of the moments of the true trace lengths from the sampled trace data, the explicit expression of moments of fracture diameters using general stereological relationship, and the estimation of fracture diameter distribution using the maximum entropy principle by a given set of moments of fracture diameters. The proposed method makes it possible to achieve a universal form for the fracture diameter distribution without any particular parametric form, and to match the moments of fracture diameters up to the fourth order. The overall behavior of the method is validated by an example, and the results show that it is capable of estimating the fracture diameter distributions.
KW - Fracture diameter
KW - Maximum entropy
KW - Moments
KW - Trace length
UR - http://www.scopus.com/inward/record.url?scp=84908394304&partnerID=8YFLogxK
U2 - 10.1016/j.ijrmms.2014.09.006
DO - 10.1016/j.ijrmms.2014.09.006
M3 - Article
AN - SCOPUS:84908394304
VL - 72
SP - 127
EP - 137
JO - International Journal of Rock Mechanics and Mining Sciences
JF - International Journal of Rock Mechanics and Mining Sciences
SN - 1365-1609
ER -