Underground projects are often designed with a flat roof, mainly due to the geological surroundings. More specifically, this can be appropriate in the case of a sedimentary formation characterised by horizontal layering such as limestone or sandstone. Also, metamorphic environment can be characterised similarly by structural layering of the minerals such as shcists or marble. In these cases, continuum mechanics is inappropriate for the design.
The theory of the voussoir beam analogue is the most appropriate for flat roofed underground excavations in bedded formations. Among the methodologies that exist, there is one that explicitly requires the existence of multiple cross-joints to be present. In this paper, that methodology is selected to study the design for specific real cases based on selected published works of mining and civil engineering.
A brief description of the theoretical basis is given. Then the predictions of the multi-jointed voussoir beam theory are presented for the specific cases that have been selected. The results are compared to the design that was actually selected as well as to the theoretical predictions. It is seen that the multi-jointed voussoir beam theory can provide in a very simple manner the requirements for the bolting system characteristics for flat roof openings in hard rock.
Hard rock sedimentary or metamorphic formations are often the mining environment for the extraction of certain metals and mineral deposits. They are also often chosen for the construction of caverns for civil uses such as storage or hydropower plants. In these cases, contrary to common practice, a flat roof is preferred as opposed to an arched roof, since the pre-existing planes of weakness create a particular deformation field after the excavation. Typically, the layers of the sediments or metamorphose direction contain few or multiple cross-joints that create a final appearance of brick-laid roof.
Morphologically, at a single outcrop, three joint systems are found ordinarily. Of these, one is near horizontal and corresponds to some lithological factor. The other two are near vertical, conjugate to each other in the sense that they form an angle of 70-90 degrees between them and uncorrelated to lithology as the cut clear across lithological elements such as pebbles and sedimentary units. Further, outcrops very near to each other (within a few kilometers) usually show subparallel joint orientations. Outcrops within a region of 10-20 km radius also show commonly, if treated together, definite, preferential non-lithological joint orientations, but only 20% agrees within 20-30 degrees. These regional joint systems usually change their orientations insignificantly over vast distances until some evident boundary is reached where the orientation boundary changes abruptly. Thanks to these observations it has been generally deduced that the origin of most hard rock joints is that they are shearing fractures or represent shear planes in the triaxial neotectonic field stress (Scheidegger, 1995).