Abstract. Rockfalls are a major and essentially unpredictable sources of danger, particularly along transportation routes (roads and railways). Thus, the assessment of their probability of occurrence is a major challenge for risk management. From a qualitative perspective, it is known that rockfalls occur mainly during periods of rain, snowmelt, or freeze-thaw. Nevertheless, from a quantitative perspective, these generally assumed correlations between rockfalls and their possible meteorological triggering events are often difficult to identify because (i) rockfalls are too rare for the use of classical statistical analysis techniques and (ii) not all intensities of triggering factors have the same probability. In this study, we propose a new approach for investigating the correlation of rockfalls with rain, freezing periods, and strong temperature variations. This approach is tested on three French rockfall databases, the first of which exhibits a high frequency of rockfalls (approximately 950 events over 11 years), whereas the other two databases are more typical (approximately 140 events over 11 years). These databases come from (1) national highway RN1 on Réunion, (2) a railway in Burgundy, and (3) a railway in Auvergne. Whereas a basic correlation analysis is only able to highlight an already obvious correlation in the case of the "rich" database, the newly suggested method appears to detect correlations even in the "poor" databases. Indeed, the use of this method confirms the positive correlation between rainfall and rockfalls in the Réunion database. This method highlights a correlation between cumulative rainfall and rockfalls in Burgundy, and it detects a correlation between the daily minimum temperature and rockfalls in the Auvergne database. This new approach is easy to use and also serves to determine the conditional probability of rockfall according to a given meteorological factor. The approach will help to optimize risk management in the studied areas based on their meteorological conditions.

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a faculty of Physical and Mathematical Sciences, department of Mining engineering, university of chile, Santiago, chile; b advanced Mining technology center (aMtc), university of chile, Santiago, chile ABSTRACTThe stability graph method is widely used for open stope mine design. During the development of the method the effect of induced stresses were included by using two-dimensional or limited three-dimensional stress analysis. In this paper, three-dimensional numerical models are used to develop new induced stress curves, and to evaluate the effects on the stability graph method and open stope mine design. Significant differences are identified for the estimated stresses at the wall of the stopes, leading to an increase of the size of the stopes.

A thermodynamic analysis of the synthesis of face-centred cubic (fcc) and body-centred cubic (bcc) solid solutions of Ti-based alloys produced by mechanical alloying was performed. Four Ti-based alloys were analysed: (i) Ti-13Ta-3Sn (at.%), (ii) Ti-30Nb-13Ta (at.%), (iii) Ti-20Nb-30Ta (wt. %) and (iv) Ti-33Nb-4Mn (at.%). The milled powders were characterized by X-ray diffraction, and the crystallite size and microstrain were determined using the Rietveld and Williamson-Hall methods. The Gibbs free energy of mixing for the formation of a solid solution of the three ternary systems (Ti-Ta-Sn, Ti-Nb-Ta and Ti-Nb-Mn) was calculated using an extended Miedema's model, applying the Materials Analysis Applying Thermodynamics (MAAT) software. The values of the activity of each component were determined by MAAT. It was found that increasing the density of crystalline defects, such as dislocations and crystallite boundaries, changed the solubility limit in these ternary systems. Therefore, at longer milling times, the Gibbs free energy increases, so there is a driving force to form solid solutions from elemental powders. Finally, there is agreement between experimental and thermodynamic data confirming the formation of solid solutions.Author Contributions: Conceptualization, C.A. and C.M.; methodology, C.A. and F.S.M.; software, C.A.; validation, I.A.; formal Analysis, C.A., C.M. and S.P.; investigation, C.A., F.S.M. and K.T.; writing-original draft preparation, C.A., S.P. and A.D.; writing-review and editing, S.P., A.D., K.T. and I.A.; visualisation, C.A. and I.A.; project administration, C.A.; funding acquisition, C.A. and K.T. All authors have read and agreed to the published version of the manuscript. Funding:The authors would like to acknowledge the financial support received from the FONDECYT project n 1190797 and FONDEQUIP/EQM project n 140095. Conflicts of Interest:The authors declare no conflict of interest.