Simulation of contact mechanics in fractured media is of paramount important in the scope of computational mechanics. In this work, a preconditioned mixed-finite element scheme with Lagrange multipliers is proposed in the framework of constrained variational principle, which has the capability to handle frictional contact mechanics of the multi-crossing fractures. The slippage, opening and contact traction on fractures are calculated by the resulted saddle-point algebraic system. A novel treatment is devised to guarantee physical solutions at the intersected position of crossing fractures. A preconditioning technique is introduced to re-scale the resulting saddle-point algebraic system, to preserve the robustness of the system. An iteration strategy, namely monolithic-updated contact algorithm, is then designed to update the two primary unknowns (displacement and Lagrange multiplier) in one algebraic block. A series of numerical tests is conducted to study the contact mechanics of single- and multi-crossing fractures. Benchmark study is presented to verify the presented numerical method. Two tests with crossing fractures are studied, in which the slippage and opening can be calculated. The effects of crossing fractures on the deformation field can be observed in the calculated results, in which the variation of slippage/opening is analyzed by different loading conditions.
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