A spray concrete support system of an underground structure is a coating placed on a surface of the mine opening with compressed air; compared with other types of support systems it has the following advantages [i]: high strength; small volume of the opening taken up by the support system, which reduces the necessary breakage volume; good cohesion with the rocks; potential for complete mechanization of support building; easy maintenance and support reinforcement; and reduced consumption of materials.The principal feature of the static work of a spray concrete support system is the fact that concrete sprayed onto rocks is in contact with the rock over its entire surface and forms a common deformable system with the rock; this allows a full utilization of the rocks bearing capacity, which is also increased by the solidified layer of rocks around the opening created as spray concrete seeps into cracks.On the other hand, the spray concrete support structure mimics the shape of the opening, i.e., it has uneven elements commensurable with an opening thickness, which is likely to lead to stress concentrations and support failures.These features of spray concrete support systems are not fully taken into consideration in estimations and designs of such systems.For example, in [2,3] spray concrete supports are viewed as rectangular plates working in flexure at a uniform loading, defined in advance. In [4][5][6] calculations are done on the basis of a solution of a contact problem of interaction of a two-layer ring modeling the support system and the consolidated rock layer with a linearly deformable bed, but neither the influence of uneven elements nor the design shape of the transverse cross section of the tunnel are considered (the ring is assumed to be round); in [7, 8] the influence of uneven elements of the surface on the bearing capacity of the support is estimated, but the support is viewed as an envelope circular in the design cross section and experiencing uniform exterior pressure outside the rock bed. The uneven elements of the tunnel surface are taken into account also in [9, I0], where solutions of two-dimensional problems of elasticity theory are applied to circular [9] openings and openings of an arbitrary shape with a common symmetry axis [i0], and the uneven elements are approximated by an hypotrochoidal curve in a medium with a weight, but the openings are regarded as unsupported, i.e., the model disregards the fact that spray concrete coating has different deformational characteristics than does the rock bed itself. A solution of the contact problem for a noncircular ring with uneven elements supporting the opening in a medium with weight has been derived for calculating the characteristics of spray concrete supports in [ii] and also in [6], but the layer of concrete-consolidated rock was disregarded.For a more detailed analysis of the deformation process of sprayed concrete support, this paper describes a calculation method based on the solution of a two-dimensional contact problem of the elasticity ...
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