José Muralha

Response by the Authors to S. R. Hencher’s Discussion of the Paper “Comparison of Different Techniques of Tilt Testing and Basic Friction Angle Variability Assessment

In a recent publication (Alejano et al. 2012), some issues concerning the evaluation of the basic friction angle /b of saw-cut rock surfaces were addressed. In his discussion, S.R. Hencher provides a series of useful references with some low values for the basic friction angle, refers to the variability of this parameter and puts forward a series of comments regarding the paper. The authors would like to acknowledge S.R. Hencher’s interest in the paper and thank him for extending the scope of the research and for providing the opportunity to present these additional comments, clarify some aspects of the work and highlight some of the main conclusions. The main aim of the author’s work was to facilitate the laboratory estimate of /b to input a reliable value in the formulation of Barton’s peak shear strength criterion. As stated in the first paragraph of the introduction to the paper, it is important to note that this criterion applies to natural unfilled rough rock joints. A priori it therefore does not apply to filled discontinuities or to those that have suffered previous shear (typically mismatched), where polished or slicken-sided surfaces appear and where flour rock or fill can be encountered. Concerning the variability of /b, it is important to note that the tilt tests presented in the paper were performed using samples from the same rock types. Moreover, tilt tests were performed using the lateral surfaces of prismatic samples cut from the same rock block. So, the standard deviation values presented in the paper only take into account the intrinsic variability of this kind of test. Tilt tests for the evaluation of /b and the remaining index tests for the characterization of rock joint shear strength proposed by Barton (1999) are very simple and straightforward. As a consequence, inexperienced designers may overlook the variability in the resulting basic friction angles and this, in turn, may lead to hazardous safety assessments. It should also be stressed that the dispersion of the empirical equations that support Barton’s peak shear strength criterion has always been mentioned, from the earliest works to present days (Barton and Choubey 1977; Barton 2011). The paper presents results of tilt tests that rendered low basic friction values. Such low values of /b are generally provided by unweathered rocks with high compressive strength (e.g., in excess of 150 MPa). These low friction values should be anticipated, as saw-cut surfaces and cores of these rocks often show very smooth and sometimes polished surfaces. In the particular case of porphyritic granite, the values displayed in Fig. 1 of the paper refer to all tilt tests repetitions performed with all possible combinations of the lateral faces (120 mm long and 45 mm wide) of two prismatic blocks, resulting in 384 values corresponding to 3 repetitions 9 (8 9 8 combinations) 9 2 tilting directions. To address the issue of the low /b values, it is preferable to study just the result of each tilt test, considering this as the median of the three repetitions. These values, presented in Fig. 1, show clearly that around 50 % of the values are below 20 . In fact, the median is exactly 19 , the mean (arithmetic) of the friction angles is 19.2 and the standard deviation is 4.46 . L. R. Alejano (&) J. González Department of Natural Resources and Environmental Engineering, University of Vigo, Vigo, Spain e-mail: alejano@uvigo.es

The influence of mechanical and geometrical variability in rock mass deformability

Abstract A probabilistic analysis regarding the deformability of rock masses is presented. The studied case considers a 2D analysis of a strip footing on a rock mass with a single joint set parallel to the surface. The geometrical and mechanical modelling will be considered with increasing complexity: from a model with constant spacing to a model that incorporates exponential distributions for the joint spacing and inverse of a normal distribution for the normal stiffness of the joint set. The probabilistic analysis is accomplished using a Monte Carlo simulation procedure based on the results of a commercially available numerical code. The following results and conclusions are presented: analysis of the performance of the simulation; relations between the settlement and the number of discontinuities, the depth of the first discontinuity under the footing and the number of discontinuities within 5 and 10 m of the surface; statistical description of the settlement for different joint spacings; a linear relation fits well the relation between the settlement and the number of joints; the settlement dispersion only increases slightly when the mechanical variability is introduced; the mean settlement and its standard deviation increase linearly with the joint set intensity.