Prediction of the Rock Brittleness Index Using Nonlinear Multivariable Regression and the CART Regression Tree

From 1960s several attempts have been made to measuring the rock brittleness index BI. Schwartz (1964) using results of a series of triaxial tests on rock samples, stated that the rock’s behavior from frangibility to ductility happens in 4.3 ratios of principal stresses. Altindag (2002; 2003) introduced a new method for prediction of the BI by the division of the uniaxial compressive strength (UCS) of the rock to Brazilian tensile strength (BTS). In the late 1960s punch penetration test (PPT) introduced by Handewith (1971) to measure some physical properties of rock sample related to hardness and toughness of rock. Yagiz (2006) stated that the PPT’s results for measuring the BI have a very high correlation with TBM penetration rate. Although the PPT has very delightful results, application of this test is very expensive and needs much time as well.
Since 2002, researchers have made some efforts to predict the BI results acquired by PPT. Yagiz (2009) using 48 sets of 30 different tunnel rock’s PPT test data, introduced a new linear multivariable equation for prediction of the BI. In that equation, 3 major rock’s physical properties as UCS, BTS and unit weight were used. Also, Yagiz (2010) introduced a new nonlinear multivariable equation and improved the accuracy of prediction from R2=0.88 to R2=0.89. As well Khandewal et al (2016) developed a new equation using Genetic Programming (GP) based on Yagiz (2009) data with R2=0.90, but none of these equations include the type of rock as a major factor that influences the BI. In the present study, the BI will be investigated by considering the rock type (or texture) as an important parameter, and a new nonlinear multivariable equation will be introduced. As well using a classification and regression tree (CART) a new attempt will be made to predict the PPT’s result for the BI.