Estimation of joint trace length probability distribution function in igneous, sedimentary, and metamorphic rocks
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ORIGINAL PAPER
Estimation of joint trace length probability distribution function in igneous, sedimentary, and metamorphic rocks Jamal Zadhesh & Seyed-Mohammad Esmaeil Jalali & Ahmad Ramezanzadeh
Received: 6 March 2012 / Accepted: 25 January 2013 # Saudi Society for Geosciences 2013
Abstract To predict the behavior of structures in and on jointed rock masses, it is necessary to characterize the geomechanical properties of joints and intact rock. Among geometry properties of joints, trace length has a vital importance, because it affects rock mass strength and controls the stability of the rock structures in jointed rock masses. Since joint length has a range of values, it is useful to have an understanding of the distribution of these values in order to predict how the extreme values may be compared to the values obtained from a small sample. For this purpose, three datasets of joint systems from nine exposures of igneous, metamorphic, and sedimentary rocks are studied. Joint trace length is one of the most difficult properties to measure accurately, but it may be possible to record other geometrical properties of exposed joints accurately; thereby, support vector machine (SVM) model is used to predict the joint trace length. SVM is a novel machine learning method, which is a powerful tool used to solve the problem characterized by small sample and non-linearity with a good generalization performance. Consequently, goodness-of-fit (GOF) tests were applied on these data. According to these GOF tests, the lognormal distribution was found to be the best probability distribution function for representing a joint trace length distribution. Keywords Jointed rock masses . Joint trace length . Distribution function . Support vector machine . Goodness-of-fit tests (GOF) . Lognormal distribution
Introduction From an engineering point of view, knowledge on the type and intensity of the rock defects may be much more important J. Zadhesh (*) : S.-M. E. Jalali : A. Ramezanzadeh Faculty of Mining, Petroleum and Geophysics, Shahrood University of Technology, Shahrood, Iran e-mail: [email protected]
than on the types of rock which will be encountered (Terzaghi 1946). The engineering properties of rock masses are controlled by the characteristics of the discontinuities and intact rocks. Discontinuity is the general term used in rock mechanics for any mechanical weak plane in a rock mass having zero or low tensile strength (Palmstrom 1995). To predict the behavior of structures in and on such jointed rock masses, it is necessary to characterize the joint geometry, the geomechanical properties of the joints, and the geomechanical properties of the intact rock. Joint is a discontinuity plane of natural origin along where it has been no visible displacement (Hudson & Harrison 1997) which is found in all component rocks within about 1 km of the Earth’s surface, at all orientation and at sizes ranging from a few millimeters to several hundred meters (Priest 1993). The length of a joint describes the length of the potential failure
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