A layered rock in underground works is simplified as a rectangular plate and the mechanical model of a rock plate simply supported on four sides is established based on the deformation and force features of the rock under practical engineering conditions. The mechanical mechanism of collapse of the rock plate under the combined action of in-plane stress, vertical stress and dynamic loads during production disturbance is studied using the catastrophe theory. The total potential function and the bifurcation-set equation are derived for the rock system when it undergoes swallowtail catastrophe. The study shows that the instability collapse of layered rocks in underground works under the combined action of in-plane stress, vertical stress and dynamic loads during production disturbance accords with the swallowtail catastrophe model. Ultimate frequency of catastrophe instability of rock plates is given in the paper, which has certain guiding significance in controlling rock collapse instability.
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