پیش بینی رفتار مکانیکی از گرانیت پورتو با استفاده از تکنیک های داده کاوی

The determination of mechanical properties of granitic rocks has a great importance to solve many engineering problems. Tunnelling, mining and excavations are some examples of these problems. The purpose of this paper is to apply Data Mining (DM) techniques such as multiple regressions (MR), artificial neural networks (ANN) and support vector machines (SVM), to predict the uniaxial compressive strength and the deformation modulus of the Oporto granite. This rock is a light grey, two-mica, medium-grained, hypidiomorphic granite and is located in Oporto (Portugal) and surrounding areas. Begonha (1997) and Begonha and Sequeira Braga (2002) studied this granite in terms of chemical, mineralogical, physical and mechanical properties. Among other things, like the weathering features, those authors applied correlation analysis to investigate the relationships between two properties either physical or mechanical or physical and mechanical. This study took the data published by those authors to build a database containing 55 rock sample records. Each record contains the free porosity (N48), the dry bulk density (d), the ultrasonic velocity (v), the uniaxial compressive strength (σc) and the modulus of elasticity (E). It was concluded that all the models obtained from DM techniques have good performances. Nevertheless, the best forecasting capacity was obtained with the SVM model with N48 and v as input parameters

Uniaxial compressive strength and modulus of elasticity are very important parameters in the analyses of rock masses behavior. These parameters are used to study underground and surface mining, slope stability, drilling and blasting and mechanical rock engineering (Tiryaki, 2008). Furthermore, they assume great importance in analytical and numerical solutions. To take into account the many factors that affect the strength and deformability of rock masses, large scale in situ tests should be performed. Because such tests are very expensive and consume a lot of time, the unconfined compressive lab tests are an alternative to them. However, even the latter tests require a heavy frame and a careful preparation of the rock cores and continue to be more expensive and time consuming than other tests based on index properties. These easier and faster tests have been performed to obtain index properties that can be correlated both with uniaxial compressive strength (σc) and modulus of elasticity (E). Irfan and Dearman (1978) presented correlations for granites between the uniaxial compressive strength and density, the effective porosity and the uniaxial compressive strength, the Young’s modulus and effective porosity and the Young’s modulus and sonic velocity. Christaras, Auger, and Mosse (1994) compared dynamic methods for the determination of modulus of elasticity with direct static methods for different types of French rocks. They used the mechanical resonance frequency and ultrasonic velocity techniques and concluded that these non-destructive methods are suitable for the determination of static modulus of elasticity. Kahraman (2001) presented correlation between uniaxial compressive strength values and the corresponding results of point load, Schmidt hammer, sound velocity and impact strength tests. He presented a nonlinear relationship between sound velocity and uniaxial compressive strength with a coefficient of correlation of 0.83. However he advised that the prediction is more reliable at low strength than at higher strength because the points are more dispersed at higher values. Begonha (1997) and Begonha and Sequeira Braga (2002) studied the mineralogical, chemical and geotechnical features of the granitic residual soils of the Oporto granite, the physical properties of the granitic rock, as well as the weathering effect in the geotechnical and physical properties. Those authors showed that all the properties of the Oporto granite are strongly affected by the weathering process. Arel and Tuğrul (2001) studied the weathering and its relation to geomechanical properties of granitic rocks from Turkey. They present several correlations between point load index, uniaxial compressive strength, slake durability, porosity, loss on ignition, dry and saturated unit weight and water properties. Tuğrul (2004) studied the changes in pore characteristics of different types of rock from Turkey due to weathering and presented relationships between both total and effective porosity and other engineering properties. Sharma and Singh (2007) presented a table with many relationships between P-wave velocity and uniaxial compressive strength reported by several researchers with coefficients of correlation (r) between 0.531 and 0.880. They also presented their own empirical relation for seven types of rocks with a coefficient of correlation of 0.9022. They concluded that P-wave velocity is a reliable method for estimating not only σc but also impact strength index and slake durability index. Kiliç and Teymen (2008) used non-destructive and indirect methods to estimate the mechanical properties of rocks by statistical equations. They tested nineteen different rock types and pointed out satisfactory correlations between shore hardness, point load index, sound velocity, Schmidt hardness and porosity and uniaxial compressive strength, indirect tensile strength and abrasion resistance. They presented nonlinear correlations between σc and Vp (R2 = 0.94) and uniaxial compressive strength and the porosity (R2 = 0.93). However, the authors advertised that equations may not be suitable for rocks with very low porosity (<2%). The use of correlations like those mentioned above, should many times lead to unsatisfactory forecasts. To overcome this problem, artificial intelligent tools such as Data Mining techniques can be useful to build more accurate predictive models. The Data Mining is a step in the overall process of discovering useful knowledge from databases and consists in the application of suitable algorithms or techniques to extract knowledge from data and obtain a pattern or model. Neural networks and support vector machines are examples of DM algorithms. The ANN technique is the most widely used technique in the rock engineering domain. It has been used to build models to identify probable failure on rock masses (Guo, Wu, Zhou, & Yao, 2003), for rock classification (Millar & Hudson, 1994), for prediction of uniaxial compressive strength (Dehghan et al., 2010, Singh et al., 2001 and Zorlu et al., 2008), tensile strength (Singh et al., 2001), modulus of elasticity of rocks (Dehghan et al., 2010, Majdi and Beiki, 2010 and Miranda et al., 2011), the weathering degrees of rocks (Dagdelenler et al., 2011 and Gokceoglu et al., 2009), etc. This technique is based on the functioning of the human nervous system and can handle data with complex relationships that can be strongly nonlinear. Support vector machines are alternative techniques to the ANN but scarce applied in rock engineering. Like the ANN, the SVM has a high degree of complexity. These DM techniques and the traditional multiple regression were used in this study to build models to forecast the σc and E of granitic rocks from Oporto, Portugal. As far as we know, SVM has not yet been applied to predict both σc and E of granitic or other rocks.

Free porosity (N48), dry bulk density (d) and ultrasonic velocity (v) were used as input variables in multiple regression analysis, artificial neural networks and support vector machines in order to predict the uniaxial compressive strength (rc) and the modulus of elasticity (E) of granitic rocks. These DM techniques were used to improve the predictive capacity of E and rc in relation to the equations presented by Begonha (1997) and Begonha and Sequeira Braga (2002) that include only one input variable each time. It was concluded that in general, when the SVM models were used, the results were better than those obtained with the Begonha’s equations and the other models. The best results were obtained using N48 and v as input variables with the SVM model. Both ANN and SVM models have the ability to capture the nonlinear features. However, the advantage of the SVM model over the ANN model is the absence of local minimum in the learning phase. Perhaps this advantage had led to its superiority over the ANN model. It must be emphasize that Begonha’s equations have been built with all the dataset whereas the results obtained with the DM techniques only used part of the dataset. This stress the quality of the results obtained with the DM techniques. Nevertheless, it must be emphasize that the DM techniques demand a great amount of data to extract knowledge. In this study only 45 registers were used in the training phase and 10 registers in the testing phase. Therefore, in spite of the good predictive capacity presented by the DM models, it is necessary to perform more tests to increase the dataset and perform more analyses to have a more consistent conclusion about the best model to apply.