Engineering Rock Mechanics

330 Design of surface excavations

418.8 A rock slope with a face angle of Sf is cut into a rock mass
containing a single set of fractures dipping into the slope at an
angle B. The strength of the fractures is purely frictional. Assume
that tan& Qf and /3 can all be considered as normally distributed
variables with the following parameters:

Variable tan4 Sf B

Mean 0.55 50° 60°

Standard deviation 0.1 5 5O 1 Oo

Investigate the variability of the factor of safety due to interlayer

slip for this slope, using either standard normal random values ob-

tained from statistical tables, or values produced by your computer/

calculator. Perform as many trials as you have the patience for (but

at least 35).

A18.8 A straightforward way of solving this is to use a computer

spreadsheet. We start by entering standard random variables into three

columns (one column for each of the random parameters) and then using

these to compute random values of the parameters using the relation

random variable = (standard random variable x standard deviation) + mean.

Each triplet of the random values is then used to compute a factor of

safety. The table will look like the one below.

Mean: 0.55 50" 60"

Standard deviation: 0.15 5" lo"

Standard normal random Random values Factor of safety

-0.258

-0.514

1.282

0.394

0.547

0.926

0.283

0.350

-0.919

-1.381

-0.424

-1.854

0.507

-0.153

-0.795

-0.611

-1.495

2.059

0.911

0.322

0.997

1.431

-0.172

-0.083

2.382

-2.004

1.054

0.097

0.972

-0.360

-0.768

-1.761

-1.133

0.731

0.784

-0.516

-0.319

-0.055

1.601

-0.842

-0.805

-0.371

-0.018

0.147

0.167

1.903

-0.103

2.006

-0.529

-1.315

0.067

• 1.085
  -0.283
  -2.011
  0.903
  1.050
  0.541
  -2.065
  -0.854
  1.328
  -2.569
  0.448
  0.546
  -0.276
  -1.502
  -0.133
  0.340
  -1.072
  0.366

0.51

0.47

0.74

0.61

0.41

0.63

0.34

0.69

0.59

0.60

0.49

0.27

0.63

0.53

0.43

0.46

0.33

0.86

0.69

0.60

0.40

0.76

0.52

48.7

47.4

56.4

52.0

45.4

52.7

43.1

54.6

51.4

51.8

47.9

40.7

52.5

49.2

46.0

46.9

42.5

60.3

54.6

51.6

45.0

57.2

49.1

57.4 1.77

54.9 2.17

72.8 0.91

63.9 1.25

50.8 3.78

65.5 1.18

69.3 1.03

62.8 1.32

63.5 1.28

55.8 2.00

41.5 -1.98

65.1 1.20

58.5 1.65

52.1 3.04

53.9 2.39

80.6 0.70

69.1 1.03

63.2 1.29

50.0 4.54

74.3 0.87

58.3 1.67

46.2 -27.47

45.1 -7.69