Rock mechanics modeling based on soft granulation theory

This paper describes application of information granulation theory, on the design of rock engineering flowcharts. Firstly, an overall flowchart, based on information granulation theory has been highlighted. Information granulation theory, in crisp (non-fuzzy) or fuzzy format, can take into account engineering experiences (especially in fuzzy shape-incomplete information or superfluous), or engineering judgments, in each step of designing procedure, while the suitable instruments modeling are employed. In this manner and to extension of soft modeling instruments, using three combinations of Self Organizing Map (SOM), Neuro-Fuzzy Inference System (NFIS), and Rough Set Theory (RST) crisp and fuzzy granules, from monitored data sets are obtained. The main underlined core of our algorithms are balancing of crisp(rough or non-fuzzy) granules and sub fuzzy granules, within non fuzzy information (initial granulation) upon the “open-close iterations”. Using different criteria on balancing best granules (information pockets), are obtained. Validations of our proposed methods, on the data set of in-situ permeability in rock masses in Shivashan dam, Iran have been highlighted. general network are affected from the several parameters, concluded in “granulation level” factor. In this paper, we interest to tack in to account soft granulation in rock system. Upon this, by focusing in two categories C-1 and C-2, in figure1, we develop different soft granulation methods based on intelligent systems and approximate reasoning methods. Added to this, the bridging between hard and soft granulation is abstracted. The most main distinguished facets of the soft granules are: set theory, interval analysis, fuzzy set, rough set. Each of these theories considers part of uncertainty of information (data, words, pictures...). Due to association of uncertainty and vagueness with the monitored data set, particularly, resulted from the in-situ tests (such lugeon test), accounting relevant approaches such probability, Fuzzy Set Theory (FST) and Rough Set Theory (RST) to knowledge acquisition, extraction of rules and prediction of unknown cases, more than the past have been distinguished. Zadeh has emphasized the role of FST in geosciences will be increased during future years [3]. The RST introduced by Pawlak has often proved to be an excellent mathematical tool for the analysis of a vague description of object [4], [5]. The adjective vague, referring to the quality of information, means inconsistency, or ambiguity which follows from information granulation. The rough set philosophy is based on the assumption that with every object of the universe, is associated a certain amount of information, expressed by means of some attributes used for object description. The indiscernibility relation (similarity), which is a mathematical basis of the rough set theory, induces a partition of the universe in to blocks of indiscernible objects, called elementary sets, which can be used to build knowledge about a real or abstract world. Precise condition rules can be extracted from a discernibility matrix. Application of RST in different fields of the applied sciences has been reported [6], [7], but developing of such system (based on approximate analysis) in rock engineering have not been outstanding, relatively. Figure 2 shows a general procedure, in which the IGT accompanies by a predefined project based rock engineering design. After determination of constraints and the associated rock engineering considerations, the initial granulation of information as well as numerical (data base) or in linguistic formats is accomplished. Improvement of modeling instruments based upon IGs, whether in independent or affiliated shape with hard computing methods (such fuzzy finite element, fuzzy boundary element, stochastic finite element...) are new challenges in the current discussion. In this study, under “modeling instruments” box, we propose three algorithms; namely successive elicitation of crisp (non-fuzzy), fuzzy and rough granulations: Self Organizing Neuro-Fuzzy Inference System (Random and Regular neuron growth), in an abbreviated manner: SONFIS-R, SONFIS-AR; and Self Organizing Rough Set Theory (SORST). Fig.1. one of the last general flowcharts to rock engineering design [2] In figure 3, we have concluded a summary of current overall granulation in a rock project that leads to the formation of fuzzy granules on the attributes (properties) of joints. Figure4 show how one usually employs granulation procedure to permeability analysis in a dam site, instinctively. The rest of paper has been organized as section 2: preliminaries on some soft granulation methods, i.e. SOM, NFIS, and RST in next section, we propose three main algorithms and part 4 covers a practical instance, describes how the soft granules ensue a relatively complete analysis on the permeability of Shivashan dam site, in Iran.