Probabilistic models

a) Probabilistic slip surface
b) Probabilistic wedge


 

a) Probabilistic slip surface

(1) Model geometry and parameters

bsf = dip angle of the slope face [°]
bss = dip angle of the slip surface [°]
do = distance between the slope crest and the slip surface [m] or [ft]
a = width of the rock compartement [m] or [ft]
Smoy = mean surface of the slip surface [m²] or [ft²]
L = mean spacing of the disontinuity set [m] or [ft]
P(do) = probability that the slip surface crosses the rock mass completely at a distance of do [%]

(2) Comments

Limitation for the angles: bsf ³ bss

(3) Results

do and P(do) are computed following JABOYEDOFF ET AL. (1996) :

(4) Example

bsf = 90°
b
ss = 45°
a = 30 m
Smoy = 1000 m²
L = 10 m


do = 16.67 m
P(16.67) = 81.11 %

 

b) Probabilistic wedge

(1) Model geometry and parameters

d1,2 = distances between the slope crest and the slip surfaces º mean spacings of the discontinuties [m] or [ft]
a1,2,sf = dip direction of the slip surfaces 1 and 2, and of the slope face [°]
b1,2,sf = dip angle of the slip surfaces 1 and 2, and of the slope face [°]
h = height of emergence of the intersection line [m] or [ft]

(2) Comments

d1,2 may be computed using a probabiliy threshold

(3) Result

h is computed following JABOYEDOFF ET AL. (1996)

(4) Example 1

d1 = 2 m
d2 = 1 m
a
1 = 018°
b
1 = 70°
a
2 = 052°
b
2 = 47°
a
sf = 045°
b
sf = 65°

h = 1.746 m

(5) Example 2

d1 = 10 m
d2 = 8 m
a
1 = 237°
b
1 = 25°
a
2 = 352°
b
2 = 18°
a
sf = 025°
b
sf = 65°

h = 20.623 m