Bolt-Grout Interactions in Elastoplastic Rock Mass Using Coupled FEM-FDM Techniques

Algorithm 1

Thus, for 𝑡th load step

 𝑖th iteration, do the following:

   For each Gauss (sampling) point of an rock element

      Initialize 𝐃_𝑒𝑝=𝐃

      Find the trial stress Δ𝝈^𝑡_𝑖=𝝈^𝑡_𝑖−1+𝐃_𝑒𝑝Δ𝜺^𝑡_𝑖

      Using trial stresses

      Check if 𝐹>0       (see (3a) and (3b))

      If “No” trial stress is the updated stress

      If “Yes” plastic correction is required (see (5) and (9))

      Determine nodal reaction forces (see (26a) and (26b))

   End For loop

   For each bolt element

      Use FDM procedure to compute displacements

      at each discretized points on the bolt (𝑢_𝑥) (see (18))

      Determine shear force at each discretized point (see (14))

      Transform the shear forces into nodal reaction

      forces for the rock elements having a bolt (see (24))

Add this reaction force to the above reaction force

   End For Loop

 End loop iteration

End loop load step