# Verification: Tests for a Simple Slope in Hoek-Brown Material

Note

To view this project in 3DEC, use the menu command Help ► Examples…. Choose “3DEC/ TheoryAndBackground/ Factor_of_SafetyHoekBrownSlope” and select “HoekBrownSlope.prj” to load. The data file used is shown at the end of this example.

Two verification exercises are performed to validate the factor-of-safety calculation using Hoek- Brown material in 3DEC. The first exercise tests the strength-reduction calculation based upon shear strength, $$\tau$$; the second exercise tests the calculation based upon intact, unconfined compressive strength (see Hoek-Brown Material).

## Factor of Safety with respect to Shear Strength

The factor of safety with respect to Hoek-Brown shear strength is calculated for a simple slope geometry, and compared to results based upon other methods to calculate a safety factor for Hoek- Brown material (i.e., generalized Hoek-Brown, equivalent Mohr-Coulomb, and Bishop and Spencer limit equilibrium methods) reported by Hammah et al. (2005). The rock slope for this comparison calculation has an inclination of 45° and a height of 10 m. The rock is represented as a Hoek-Brown material with the following properties:

 $$E$$ = 5000 MPa $$\nu$$ = 0.3 $$\rho$$ = 2500 kg/m3 $$m_b$$ = 0.067 $$s$$ = 0.000025 $$a$$ = 0.619 $$\sigma_ci$$ = 30 MPa

The 3DEC model mesh used for this test is shown in Figure 1 below. The model contains a horizontal construction joint at the toe of the slope to assist in zoning. The maximum zone width is set to 0.3 m.

By default, when solve fos is executed for a 3DEC model with zone model mhoekbrown, the factor of safety calculation is performed for Hoek-Brown material with respect to shear strength. The calculated factor of safety for this test is 1.16. The failure surface is shown by the displacement magnitude contour plot in Figure 2. The result compares well with the results reported by Hammah et al. (2005). Table 2 summarizes the safety factors reported for this test. Figure 2: Factor of safety and failure surface calculated for simple slope in Hoek-Brown material.

Table 2: Factor of Safety Results for Hoek-Brown Slope
Method Factor of Safety
zone model mhoekbrown with respect to shear strength 1.16
generalized Hoek-Brown strength reduction* 1.15
equivalent Mohr-Coulomb strength reduction* 1.15
Bishop’s simplified limit equilibrium* 1.153
Spencer’s limit equilibrium* 1.152

*from Hammah et al. (2005)

Data File

model new
model large-strain off

;file: HoekBrownSlope.dat
; Hoek-Brown material
;
block create prism &
face-1 12,0,5 22,0,15 36,0,15 36,0,5 &
face-2 12,0.3,5 22,0.3,15 36,0.3,15 36,0.3,5
block create brick 0,36 0,0.3 0,5
block join
block zone generate edgelength 0.3
block zone cmodel assign hoek-brown
block zone property density 2.5e-3 young 5000 poisson 0.3 tension 1e10
block zone property constant-mb 0.067 constant-s 2.5e-5 constant-a 0.619 constant-sci 30
block gridpoint apply vel-x 0 range pos-x 0
block gridpoint apply  vel-x 0 range pos-x 36
block gridpoint apply  vel-y 0 range pos-y 0
block gridpoint apply  vel-y 0 range pos-y 0.3
block gridpoint apply  vel 0 0 0 range pos-z 0

model gravity=0.0,0.0,-10.0

block zone n-m-d on
model factor-of-safety bracket 1.1 1.2 ratio-local 1e-4 filename='HBSlope'