Coupled thermo‐mechanical algorithm for fractured rock mass by the composite element method

Abstract

SummaryTo assess the influence of thermal stress on fracture deformation, a composite element algorithm of thermo‐mechanical coupling for fractured rock mass is developed based on the composite element method (CEM). This study aims to investigate coupled processes associated with the (i) effect of temperature on mechanical deformation and (ii) effect of fracture aperture on heat transfer. The composite element contains fracture segments exhibiting arbitrary shapes with variables that can be interpolated from their mapped nodal variables; the mapped variables can be determined using the governing equations derived from the variational principle or virtual work principle. The proposed coupling algorithm can simulate the discontinuity of fractures, with consideration of the heat transfer of rock blocks and fractures, together with heat exchange among fractures and the adjacent rock mass. A computational mesh is generated without restrictions by explicitly embedding the fractures into the mapped composite elements, substantially simplifying the pre‐process work. Analytic solutions to the transient temperature problem are examined to verify the proposed CEM algorithm. Two three‐dimensional numerical models are developed to perform thermo‐mechanical coupling analyses. These analyses are used to prove the advantage of the mesh handler and the reliability of the proposed algorithm. During coupling with the CEM model, the computational mesh requires no modification regardless of changes in fracture aperture. Results indicate that an increase in temperature leads to rock expansion, causing fracture deformation, which affects the general temperature of the fractured rock mass.