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Abstract. With reference to the rockfall risk estimation and the planning of rockfall protection devices, one of the most critical and most discussed problems is the correct definition of the design block by taking into account its return period. In this paper, a methodology for the assessment of the design block linked with its return time is proposed and discussed, following a statistical approach. The procedure is based on the survey of the blocks that were already detached from the slope and had accumulated at the foot of the slope in addition to the available historical data.

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A wide range of heterogeneous geological units composed of strong rock blocks enclosed in a bonded matrix of fine texture exists worldwide. Such geomaterials belong to geotechnically complex formations and are often referred to as bimrocks (block-in-matrix rocks) or bimsoils (block-in-matrix soils), as a function of their matrix characteristics and the interface strength between the matrix and blocks. Stability problems occurring in such complex geomaterials have been analysed almost exclusively by means of deterministic approaches and with the aim of investigating the effects of variable block contents on their mechanical behaviour. However, bimrocks and bimsoils can present very different internal block-in-matrix arrangements and properties according to their forming process and, consequently, significantly dissimilar mechanical behaviours. Therefore, the aim of this paper was to statistically investigate and compare the stability of theoretical slopes in the most widespread bimrock formations, i.e. sedimentary and tectonic melanges. These formations are characterised by substantial differences in their rock inclusion geometry. To this aim, a great number of 2D slope models were generated to enclose blocks with variable shapes, dimensions, arrangements, inclinations and contents. To obtain statistically based results, fifteen configurations were analysed for each block content and geometrical configuration considered. The results obtained indicate that block shapes and orientations significantly affect the stability of slopes in bimrocks only when the block contents are greater than 40%. Moreover, it is demonstrated that blocks inclined 0° to the horizontal provide the most tortuous and irregular failure surfaces and, consequently, the highest safety factors.

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