The accuracy of the models built using FLAC3D depend on the element/zone size. The zones in FLAC3D have a linear interpolation of displacements therefore the stress and strain inside the zone are constant, to model variation of stresses and strain around excavations a minimum number of zones is required to capture that variation.
The impact on the results of using different zone size is shown with the following simple example:
The points used to compare the results obtained with different zone size and pillar’s width are the following:
An example of the model with 5 elements across the pillar and crown pillar is shown below, note the location of one the control points is in the center of the crossing of the pillar and the crown pillar and coincide with the center of an element, in other words, a refinement of the model does not shift the location of the control points.
To compare the results volumetric strain and deviatoric stress at specific location were used. The following plots shows the results for the 4×6 pillar dimension with less plastic deformation, below the same results for the 4×4 pillar dimension with larger plastic deformation. The independent variable in all of them is the number of elements across the pillars
The results show the following:
- There is an improvement in precision when the number of zones around the excavation is increased.
- For areas with larger plastic strain a larger number of zones is required to achieve the same precision achieved when the plastic strain is not high.
- 7 zones across the span of the excavation seems reasonable to model stresses and strain around openings.
- The number of zones should be increased to 9 or more if large plastic strain is expected around the excavation.
