Factor of Safety

RocSupport determines Factor of Safety as the ratio of maximum support pressure to the support pressure required for equilibrium. An equilibrium condition is achieved when convergence of the tunnel and support system are equal.

When the Ground Reaction Curve (GRC) intersects the Support Reaction Curve (SRC) in the elastic portion of the SRC, the equilibrium condition is defined as their intersection point. The factor of safety is always greater than or equal to 1 in this case, as shown in Figure 1.

Figure 1. Definition of factor of safety greater than or equal to 1 in RocSupport. SRC intersects GRC before yielding.

In the case when SRC yields before intersecting GRC, the equilibrium condition is not achieved and the factor of safety is less than 1. To calculate a factor of safety, RocSupport finds an "apparent" equilibrium pressure, by projecting the elastic part of the SRC until it intersects the GRC, then divides the maximum support pressure by this "apparent" equilibrium pressure. This is illustrated in Figure 2.

Figure 2. Definition of factor of safety less than 1 in RocSupport. SRC yields before intersecting with GRC.