Rock Mass Rating values: frequency distribution histogram of the Rock Mass Rating; different colours represent diverse lithologies. 

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... fi fth parameter of the RMR classi fi cation takes into account the occurrence of water along discontinuities; different values have been assigned on the basis of general moisture conditions of the rock mass, which can be: completely dry (observed in 64% of surveyed sites), damp (24%), wet (11%), dripping (never) or fl owing (1%). The sum of these fi ve parameters leads to the Rock Mass Rating value, which describes the global quality index of the rock mass. From the collected data, some general considerations can be outlined, with the aim to describe analogies and differences in the investigated rock masses, especially about their quality. The examined rock masses, belonging to Tambò and Suretta basement units, show a similar behaviour. Joint orientations and properties are quite similar, and the small variability in lithological characteristics does not signi fi cantly control the discrepancy in rock mass quality [44]. Rock masses of the meta-sedimentary cover, the Spluga Syncline, show a general greater state of deformation. However, for all the lithological and structural units, some common properties have been observed: the water is mostly absent, discontinuities are slightly weathered, without in fi llings and with a medium persistency. The other parameters, i.e. JCS, JRC, aperture, spacing, Jv and consequently RQD, show a great variability, which does not seem to be directly related to the lithology. Indeed, in spite of this lithological variability should obviously be responsible for variations in rock mass quality; it is worth noting that all RMR values are contained in only two classes, irrespective of the lithology (Fig. 5): they range from 45 to 77, half of them belong to the “ fair quality ” class (41 o RMR o 60), while the other half belong to the “ good quality ” class (61 o RMR o 80); most RMR values are included between 50 and 70. It can be stated that in the study area the geomechanical quality of rock masses (expressed by the RMR) mainly depends on the geometrical features which show greater variability, i.e. spacing and correlated values of Jv and RQD [45], JCS and conditions of discontinuities (with particular reference to aperture and roughness). These properties, which are related to tectonic actions, could be considered as regionalized variables, as RMR. Actually, the RMR depends on the geological and structural history of the rock mass, but it describes the quality of the rock mass nowadays, resulting from all the involved geological events. The RMR is a global property of rock masses, depending on all its fractures, despite of their formation mechanism. Therefore the statistical population of RMR is represented from all the rock masses outcropping in the San Giacomo Valley. The homogeneity of the data samples has been guaranteed, because the same support (a scanline 20 m long) has been used in all the geomechanical surveys, with a surveyed height of about 2 m. Geostatistics allows estimating the values of regionalized variables in un-sampled points, capturing the spatial correlation among data, based on the fact that the data sourced from closer locations tend to be more similar than those far apart. Geostatistics provides an unbiased estimation, with uncertain quanti fi cation. Geostatistical approach has been already used several times in rock mass characterization [7 – 31]. In this paper, geostatistical analysis has been performed in order to reconstruct the values of RMR in an area with an extent of approximately 200 km 2 , from super fi cial fi eld data. The geostatistical study has been performed with the RMR index as regionalized variable and has been developed by the following phases: exploratory spatial data analysis, variography, prediction and fi nally validation. First of all, the statistical parameters of RMR have been computed. The RMR index has been evaluated in 55 different locations, along the San Giacomo Valley. RMR values range from 45 to 77, the mean is 60.6, with a standard deviation of 6. The frequency distribution seems to be Gaussian, indeed it is clearly a unimodal distribution, without a signi fi cant asymmetry (Fig. 6a), being both skewness and kurtosis close to zero. Since many geostatistical techniques are more reliable if the variable of interest has a standard Gaussian distribution, it is necessary to verify if the variable has a normal distribution and if not the transformation of data into a standard Gaussian one is essential. It is rare in the modern geostatistics to consider untransformed data. The use of Gaussian technique requires a prior Gaussian transformation of data and the reconstruction of semivariogram model on these transformed data. This transformation has some important advantages: the difference between extreme values is dampened and the theoretical sill should be close to the unit [46]. Furthermore systematic trends should be removed from the variable prior to transformation and semivariogram calculation. The problem is that the most common statistical tests, used to verify if the univariate distribution of the data is Gaussian, are designed on the assumption that the observations are independent and identically distributed. In geostatistical applications, however, this is not usually the case: if the covariance structure has a range greater than the minimum distance between observations, the data are correlated and the standard tests cannot be applied to the probability density function (pdf) or cumulative probability function (cdf) estimated directly from the data. The problem with correlated data arises not from the correlation per se, but from cases in which correlated data are clustered rather than being located on a regular grid [47]. When preferential sampling occurs, observations that are close together provide partially redundant information that must be taken into account in calculating pdf or cdf. Actually, it is dif fi cult and often impossible to sample geological data using a regular grid; therefore the occurrence of preferential sampling is very frequent. For instance, in this case study, the sampling locations are dependent on the outcrop positions and their accessibility; hence they are not disposed on a regular grid. The preferential sampling could lead to the presence of spatial clusters, and subsequent biases. When the sampling is clustered, unbiased estimates of pdf or cdf must fi rst be obtained, by de- clustering, then normality tests can be applied. In this case study, the analysis of the spatial disposition of 55 considered data locations has been performed through the nearest neighbour index, which uses the distance between ...