Rock Mech. Rock Engng. (2006) 39 (1), 45–57 DOI 10.1007/s00603-005-0050-y Fuzzy and Multiple Regression Modelling for Evaluation of Intact Rock Strength Based on Point Load, Schmidt Hammer and Sonic Velocity By M. Karakus and B. Tutmez Mining Engineering Department, Inonu University, Malatya, Turkey Received May 3, 2004; accepted January 21, 2005 Published online July 19, 2005 # Springer-Verlag 2005 Summary Uniaxial Compressive Strength (UCS), considered to be one of the most useful rock properties for mining and civil engineering applications, has been estimated from some index test results by fuzzy and multiple regression modelling. Laboratory investigations including Uniaxial Compres- sive Strength (UCS), Point Load Index test (PL), Schmidt Hammer Hardness test (SHR) and Sonic velocity (V p ) test have been carried out on nine different rock types yielding to 305 tested specimens in total. Average values along with the standard deviations (Stdev) as well as Coeffi- cients of variation (CoV) have been calculated for each rock type. Having constructed the Mamdani Fuzzy algorithm, UCS of intact rock samples was then predicted using a data driven fuzzy model. The predicted values derived from fuzzy model were compared with multi-linear statistical model. Comparison proved that the best model predictions have been achieved by fuzzy modelling in contrast to multi-linear statistical modelling. As a result, the developed fuzzy model based on point load, Schmidt hammer and sonic velocity can be used as a tool to predict UCS of intact rocks. Keywords: Fuzzy and multiple regression modelling, UCS, P-wave, Schmidt Hammer, Point load. 1. Introduction Recent trend on estimating UCS from simple laboratory index tests has gained accel- eration. Many researchers have been conducting investigations aimed at predicting UCS from non-destructive testing methods such as sound velocity test, porosity, and density. A great number of attempts have been made to predict uniaxial compressive strength of intact rocks (Kahraman, 2001; Katz et al., 2000; Grima and Babuska, 1999; Koncagul and Santi, 1999; Chau and Wong, 1996; Singh and Singh, 1993; Xu et al., 1990; Vallejo et al., 1989). Most of these studies have been dealt with simple models relating UCS to SHR, UCS to V p , UCS to porosity n, UCS to PL and so on. Within