The present work shows the application of the Smoothed Particle Hydrodynamics (SPH) on non-Newtonian fluids for simulating the injection of a cementitious material into underground caves to reinforce the soil. In special, it presents two main improvements over the already established SPH formulation: an implicit time integration scheme to overcome the problem of impracticable small time step restriction in highly viscous fluid simulation, and the introduction of air ghost particles (AGP) to fix problems on the free-surface treatment. This project utilizes the Incompressible SPH (ISPH) as a basis for the implementation of such improvements, which guarantees a stable and accurate pressure distribution. We validate the proposed implicit time integration scheme with pipe flow simulations and the free-surface treatment with a simple hydrostatic problem. Also, dam break numerical simulations using the proposed method resulted in very good agreement with experimental data. At last, we demonstrate the potential of this method with the highly viscous vertical jet flow over a horizontal plate validation test, which shows a complex viscous coiling behavior.