The sticking problem caused by the collapse of fractured zone in geothermal drilling will bring great challenges to safe drilling. The traditional prediction of collapse pressure assumes that the surrounding rock is continuous medium, leading to a conservative result. But in fact, cracks are developed tremendously in fracture zone, and the deformation between cracks and rock mass is incompatible. Based on this, this paper uses the non-Euclidean parameters of rock to characterize the joint or fracture characteristics of the wall rock, establishing the stress distribution around the borehole considering the incompatible deformation. At the same time, combining with Mohr-Coulomb failure criterion, a new prediction model of collapse pressure is established. Eventually we analysis the influence of Euclidean parameter (??) and fracture geometry parameters on collapse pressure. The smaller the non-Euclidean parameter (??) is, the larger the equivalent drilling mud density of collapse pressure is; and the larger the area is where the hot dry rock stratum is damaged. This model is capable of giving a reasonable interpretation on why the sticking problem is severe in fractured zone, which makes it a more feasible approach. In addition it provides certain instructions to cooperate the construction.

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