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-0.0588  Tc 0.0026  Tw (Mapping and analysis of rock discontinuities) Tj
207.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-228 -12  TD /F0 11.625  Tf
( ) Tj
0 -12  TD -0.3069  Tc 1.1506  Tw (Geotechnical data collection methods, such as scan) Tj
228 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.7969  Tc 0.1406  Tw (line ) Tj
-232.5 -12.75  TD -0.386  Tc 0  Tw (\(detail) Tj
27 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.4641  Tc 2.8079  Tw (line\) mapping and fracture) Tj
120 0  TD -0.1211  Tc 0  Tw (-) Tj
3.75 0  TD -0.469  Tc 1.8128  Tw (set mapping \(Miller, ) Tj
-155.25 -12  TD -0.2601  Tc 1.6039  Tw (1983\), provide important i) Tj
119.25 0  TD -0.4586  Tc 1.3023  Tw (nformation on fracture orie) Tj
118.5 0  TD -0.7168  Tc 0  Tw (n-) Tj
-237.75 -12.75  TD -0.4074  Tc 1.144  Tw (tations, spacings, lengths, and roughness.  Typical ma) Tj
237 0  TD 0.0332  Tc 0  Tw (p-) Tj
-237 -12  TD -0.4477  Tc 1.0414  Tw (ping sites in the project vicinity include natural rock ou) Tj
240 0  TD -0.1764  Tc 0  Tw (t-) Tj
-240 -12.75  TD -0.4577  Tc 2.0514  Tw (crops \(if the project is in in) Tj
125.25 0  TD -0.2318  Tc 0  Tw (i) Tj
2.25 0  TD -0.4012  Tc 1.0574  Tw (tial development stages\) or ) Tj
-127.5 -12  TD -0.3522  Tc 0.7272  Tw (available rock slope cuts along roads or accessible min) Tj
242.25 0  TD -0.6615  Tc 0.0052  Tw (e ) Tj
-242.25 -12.75  TD -0.1688  Tc 0  Tw (benches.) Tj
38.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-24.75 -12  TD -0.535  Tc 3.3475  Tw (The first step in analyzing such field data typ) Tj
211.5 0  TD -0.2318  Tc 0  Tw (i) Tj
2.25 0  TD -0.6198  Tc -0.7864  Tw (cally ) Tj
-227.25 -12.75  TD -0.3475  Tc 2.3579  Tw (consists of plotting the poles to fractures on a lower) Tj
243 0  TD -0.1211  Tc 0  Tw (-) Tj
-243 -12  TD -0.3332  Tc 1.7394  Tw (hemisphere stereonet in order to identify fracture sets, ) Tj
0 -12.75  TD -0.2875  Tc 3.7563  Tw (which appear as clusters of poles \(Hoek and Bray) Tj
0  Tc -1.4063  Tw ( ) Tj
0 -12  TD -0.3086  Tc 1.6023  Tw (1978\).  The interaction of the) Tj
135 0  TD -0.3016  Tc 0.8454  Tw ( proposed slope cut with ) Tj
-135 -12.75  TD -0.3763  Tc 0.97  Tw (the orientations of these fracture sets allow the engineer ) Tj
0 -12  TD -0.3979  Tc 0.4083  Tw (to identify potential slope failure modes \(i.e. plane shears ) Tj
T* -0.2962  Tc 3.2024  Tw (and wedges, for our pa) Tj
113.25 0  TD -0.1211  Tc 0  Tw (r) Tj
3.75 0  TD -0.3959  Tc 3.1896  Tw (ticular study\).  It should be) Tj
0  Tc -0.6563  Tw ( ) Tj
-117 -12.75  TD -0.3615  Tc 0.6427  Tw (noted that in any rock) Tj
96 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.4674  Tc 0.5612  Tw (slope stability evaluation, the ge) Tj
137.25 0  TD -0.7168  Tc 0  Tw (n-) Tj
-237.75 -12  TD -0.4101  Tc 0.5038  Tw (eral progression in the enginee) Tj
131.25 0  TD -0.1211  Tc 0  Tw (r) Tj
3.75 0  TD -0.557  Tc 0.6508  Tw (ing analysis is:) Tj
60.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-182.25 -12.75  TD ( ) Tj
0 -12  TD 0.1406  Tc -0.0469  Tw (1. ) Tj
12 0  TD 0  Tc 0.0938  Tw ( ) Tj
6 0  TD -0.2926  Tc 1.8864  Tw (Use fracture) Tj
54.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.0551  Tc 0.1489  Tw (set ) Tj
16.5 -0.75  TD /F2 11.625  Tf
-0.2638  Tc 0  Tw (orientations) Tj
57.75 0.75  TD /F0 11.625  Tf
-0.427  Tc 2.0207  Tw ( to identify pote) Tj
72.75 0  TD -0.7168  Tc 0  Tw (n-) Tj
-206.25 -12.75  TD -0.5033  Tc 0.5971  Tw (tial slope failure modes;) Tj
102 0  TD 0  Tc 0.0938  Tw ( ) Tj
-120 -12  TD 0.1406  Tc -0.0469  Tw (2. ) Tj
12 0  TD 0  Tc 0.0938  Tw ( ) Tj
6 0  TD -0.3606  Tc 0.6687  Tw (For the critically oriented sets, evaluate the likel) Tj
209.25 0  TD -0.9264  Tc 0  Tw (i-) Tj
-209.25 -12.75  TD -0.4959  Tc 0.8896  Tw (hood of having sufficient fracture ) Tj
145.5 -0.75  TD /F2 11.625  Tf
-0.2537  Tc 0  Tw (lengths) Tj
35.25 0.75  TD /F0 11.625  Tf
-0.5239  Tc 0.1176  Tw ( to form ) Tj
-180.75 -12  TD -0.5688  Tc 0.6626  Tw (kinematically viable failure ) Tj
116.25 0  TD -0.3121  Tc 0.4059  Tw (blocks; and) Tj
51 0  TD 0  Tc 0.0938  Tw ( ) Tj
-185.25 -12.75  TD 0.1406  Tc -0.0469  Tw (3. ) Tj
12 0  TD 0  Tc 0.0938  Tw ( ) Tj
6 0  TD -0.3927  Tc 1.6115  Tw (For fracture sets with sufficient lengths, est) Tj
192 0  TD -0.2318  Tc 0  Tw (i) Tj
2.25 0  TD -0.3997  Tc -0.2565  Tw (mate ) Tj
-194.25 -12  TD -0.4852  Tc 0.579  Tw (the ) Tj
16.5 -0.75  TD /F2 11.625  Tf
-0.1306  Tc 0.9744  Tw (shear strength) Tj
70.5 0.75  TD /F0 11.625  Tf
-0.3474  Tc 0.7411  Tw ( so that an engineering stabi) Tj
122.25 0  TD -0.9264  Tc 0  Tw (l-) Tj
-209.25 -12.75  TD -0.4049  Tc 0.4986  Tw (ity analysis can be conducted.) Tj
129.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-147.75 -12  TD ( ) Tj
0 -12.75  TD -0.3927  Tc 1.0115  Tw (In the computer simulation of rock fractures in a set, ) Tj
-13.5 -12  TD -0.3062  Tc 0.5874  Tw (one should strive to preserve the natural spatial depen) Tj
237 0  TD 0.0332  Tc 0  Tw (d-) Tj
-237 -12.75  TD 0.0885  Tc (e) Tj
5.25 0  TD -0.3564  Tc 1.2001  Tw (nce in fracture properties.  Spatial covar) Tj
179.25 0  TD -0.2318  Tc 0  Tw (i) Tj
2.25 0  TD -0.269  Tc 0.3628  Tw (ance or semi) Tj
56.25 0  TD -0.1211  Tc 0  Tw (-) Tj
-243 -12  TD -0.2553  Tc 0.6705  Tw (variograms \(Isaaks and Srivastava 1989\) provide a st) Tj
237.75 0  TD -0.0163  Tc 0  Tw (a-) Tj
-237.75 -12  TD -0.397  Tc 2.3122  Tw (tistical format for describing the spatial dependence in) Tj
0  Tc -1.4063  Tw ( ) Tj
0 -12.75  TD -0.3227  Tc 0.6977  Tw (fracture properties, which has been demonstrated by La ) Tj
0 -12  TD -0.2519  Tc 0.4707  Tw (Pointe \(1980\) and Miller \(1979\).  T) Tj
157.5 0  TD -0.3574  Tc -0.0488  Tw (hus, instead of sim) Tj
80.25 0  TD -0.7168  Tc 0  Tw (u-) Tj
-237.75 -12.75  TD -0.3865  Tc 4.2303  Tw (lating fracture prope) Tj
95.25 0  TD -0.1211  Tc 0  Tw (r) Tj
3.75 0  TD -0.4193  Tc 3.888  Tw (ties independently in space, the) Tj
0  Tc -0.6563  Tw ( ) Tj
-99 -12  TD -0.3958  Tc 2.8646  Tw (measured spatial continuity can be incorporated using) Tj
0  Tc -1.4063  Tw ( ) Tj
0 -12.75  TD -0.12  Tc 0.9637  Tw (methods d) Tj
47.25 0  TD 0.0885  Tc 0  Tw (e) Tj
5.25 0  TD -0.3196  Tc 0.8822  Tw (scribed by Miller \(1985\).  To conduct such ) Tj
-52.5 -12  TD -0.5788  Tc 2.1726  Tw (a fra) Tj
21 0  TD 0.0885  Tc 0  Tw (c) Tj
5.25 0  TD -0.5817  Tc (ture) Tj
16.5 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.4095  Tc 1.4675  Tw (set simulation, each of the particular fracture ) Tj
-47.25 -12.75  TD -0.2812  Tc 1.1249  Tw (properties need) Tj
69 0  TD -0.2268  Tc 0.642  Tw ( to be modeled by an appropriate semi) Tj
174 0  TD -0.1211  Tc 0  Tw (-) Tj
-243 -12  TD -0.5244  Tc 2.3682  Tw (variogram model using the \223sill\224 \(sample var) Tj
200.25 0  TD -0.2318  Tc 0  Tw (i) Tj
2.25 0  TD -0.2811  Tc 0.7499  Tw (ance\), the ) Tj
-202.5 -12.75  TD -0.4755  Tc 1.3193  Tw (\223nugget\224 value \(i.e. the semi) Tj
124.5 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.3755  Tc 1.0317  Tw (variogram value at a sep) Tj
108.75 0  TD -0.0163  Tc 0  Tw (a-) Tj
-237.75 -12  TD -0.4063  Tc 1.0834  Tw (ration distance of zero\), and the spatial \223range\224 of infl) Tj
237.75 0  TD -0.7168  Tc 0  Tw (u-) Tj
-237.75 -12.75  TD -0.406  Tc 1.0623  Tw (ence.  A probability distribution model for each ) Tj
213.75 0  TD -0.3928  Tc -0.2635  Tw (fracture ) Tj
-213.75 -12  TD -0.1998  Tc 0.0435  Tw (property also is needed.) Tj
105.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
ET
q 
321 785.25 5.25 3.75 re h W n 
BT
321 788.25  TD
( ) Tj
ET
Q 
BT
321 775.5  TD
-0.4607  Tc 1.7211  Tw (An essential input for the stability calculations is the ) Tj
-13.5 -12  TD -0.4532  Tc 1.522  Tw (mean length of fractures in a given set.  An e) Tj
202.5 0  TD 0.1875  Tc 0  Tw (x) Tj
5.25 0  TD -0.4743  Tc -0.182  Tw (ponential ) Tj
-207.75 -12.75  TD -0.434  Tc 1.2778  Tw (pdf \(probability density function\) is a) Tj
162.75 0  TD -0.0221  Tc 0  Tw (s) Tj
3.75 0  TD -0.3156  Tc 0.1594  Tw (sumed for fracture ) Tj
-166.5 -12  TD -0.452  Tc 4.1886  Tw (length, then the probability of a fracture being) Tj
222 0  TD -0.6673  Tc 4.5111  Tw ( long) Tj
0  Tc -0.6563  Tw ( ) Tj
-222 -12.75  TD -0.4318  Tc 1.5756  Tw (enough to form a viable failure path through the bench ) Tj
0 -12  TD -0.3946  Tc 0.4883  Tw (can be obtained directly from the exponential probability ) Tj
0 -12.75  TD -0.4957  Tc 2.9644  Tw (distribution.  This pdf is a one) Tj
141.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.3522  Tc 1.5709  Tw (parameter distribution, ) Tj
-146.25 -12  TD -0.3785  Tc 1.0859  Tw (being defined only by the mean value.  See Section 3.1 ) Tj
0 -12.75  TD -0.3446  Tc 0.4384  Tw (below. ) Tj
32.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-18.75 -12  TD ( ) Tj
-13.5 -12.75  TD -0.0938  Tc 0  Tw (2.2) Tj
14.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
7.5 0  TD /F1 11.625  Tf
-0.0621  Tc -0.5941  Tw (Shear streng) Tj
58.5 0  TD 0.3529  Tc 0  Tw (th) Tj
9.75 0  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
-90 -12  TD ( ) Tj
0 -12.75  TD -0.4041  Tc 0.7122  Tw (Shear strength along rock fractures typically is est) Tj
217.5 0  TD -0.2318  Tc 0  Tw (i) Tj
2.25 0  TD -0.2823  Tc 0.376  Tw (mated ) Tj
-219.75 -12  TD -0.5147  Tc 1.037  Tw (in one of two ways:  the JRC) Tj
129 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.1109  Tc -0.3579  Tw (JCS method proposed by ) Tj
-133.5 -12  TD -0.3046  Tc 3.0769  Tw (Barton et al \(1972\), and by using lab) Tj
180.75 0  TD 0.1875  Tc 0  Tw (o) Tj
6 0  TD -0.3942  Tc 2.738  Tw (ratory direct) Tj
55.5 0  TD -0.1211  Tc 0  Tw (-) Tj
-242.25 -12.75  TD -0.2939  Tc 4.9814  Tw (shear test data to describe either a linear Mohr) Tj
242.25 0  TD -0.1211  Tc 0  Tw (-) Tj
-242.25 -12  TD -0.3661  Tc 4.8099  Tw (Coulomb failure envelope or a power) Tj
185.25 0  TD -0.1211  Tc 0  Tw (-) Tj
3.75 0  TD -0.1019  Tc (curv) Tj
19.5 0  TD -0.454  Tc 4.2977  Tw (e model) Tj
0  Tc -0.6563  Tw ( ) Tj
-208.5 -12.75  TD -0.1607  Tc 0.2544  Tw (\(Jaeger 1971\). ) Tj
67.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-54 -12  TD -0.3197  Tc 1.5385  Tw (A general power) Tj
75.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.2846  Tc 0.8784  Tw (curve model has been adopted for ) Tj
-93.75 -12.75  TD -0.3422  Tc 1.9359  Tw (use in the NIOSH bench analysis computer pr) Tj
211.5 0  TD 0.1875  Tc 0  Tw (o) Tj
6 0  TD -0.3446  Tc 0.4384  Tw (grams, ) Tj
-217.5 -12  TD -0.5191  Tc 0.4253  Tw (given by the following expression:) Tj
145.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-132 -12.75  TD ( ) Tj
0 -12.75  TD /F3 11.625  Tf
0.1466  Tc 0  Tw (t) Tj
5.25 0.75  TD /F0 11.625  Tf
-0.234  Tc 0.3277  Tw (  =  a) Tj
23.25 -0.75  TD /F3 11.625  Tf
-0.2599  Tc 0  Tw (s) Tj
6.75 4.5  TD /F0 7.2656  Tf
0.1172  Tc (b) Tj
3.75 -3.75  TD /F0 11.625  Tf
0.141  Tc -0.0473  Tw ( + c) Tj
18 0  TD 0  Tc 0.0938  Tw ( ) Tj
5.25 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD -0.5182  Tc 0.612  Tw (   \(1\)) Tj
21.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-225.75 -12.75  TD ( ) Tj
0 -12  TD -0.2719  Tc 0  Tw (where:) Tj
29.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
9 -0.75  TD /F3 11.625  Tf
0.1466  Tc 0  Tw (t) Tj
5.25 0.75  TD /F0 11.625  Tf
-0.3348  Tc 0.4286  Tw ( = shear strength;) Tj
75.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-119.25 -12.75  TD ( ) Tj
38.25 -0.75  TD /F3 11.625  Tf
-0.2599  Tc 0  Tw (s) Tj
7.5 0.75  TD /F0 11.625  Tf
-0.3751  Tc 0.2189  Tw ( = effective normal stress; and ) Tj
133.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-179.25 -12  TD ( ) Tj
38.25 0  TD -0.1919  Tc 0.1357  Tw (a, b, c = model parameters.) Tj
121.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-159.75 -12.75  TD ( ) Tj
0 -12  TD -0.3192  Tc 2.9442  Tw (This equation describes a power model with a y) Tj
228.75 0  TD -0.1211  Tc 0  Tw (-) Tj
-242.25 -12  TD -0.3505  Tc 1.7397  Tw (intercept.  It reduces to a simple linear model when b ) Tj
0 -12.75  TD -0.3579  Tc 1.2017  Tw (equals 1.0, thus making \223c\224 equal to cohesion, and \223a\224 ) Tj
0 -12  TD -0.4123  Tc 0.3989  Tw (equal to the coefficient of friction \(i.e. tan) Tj
177.75 -0.75  TD /F3 11.625  Tf
-0.0566  Tc 0  Tw (f) Tj
6.75 0.75  TD /F0 11.625  Tf
-0.0137  Tc (\).) Tj
6 0  TD 0  Tc 0.0938  Tw ( ) Tj
-177 -12.75  TD -0.5032  Tc 1.3469  Tw (The variability of) Tj
74.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
3 -0.75  TD /F3 11.625  Tf
0.1466  Tc 0  Tw (t) Tj
4.5 0.75  TD /F0 11.625  Tf
-0.403  Tc 0.2467  Tw (, given a predicted value of ) Tj
120.75 -0.75  TD /F3 11.625  Tf
-0.2599  Tc 0  Tw (s) Tj
7.5 0.75  TD /F0 11.625  Tf
-0.2768  Tc 0.3706  Tw (, also ) Tj
-223.5 -12  TD -0.3969  Tc 0.7719  Tw (is needed in the bench stability analysis.  Cu) Tj
192.75 0  TD -0.1211  Tc 0  Tw (r) Tj
3.75 0  TD -0.5565  Tc 0.6502  Tw (rently in the ) Tj
-196.5 -12.75  TD -0.2976  Tc 2.6414  Tw (NIOSH codes, the shear strength is modeled with a ) Tj
0 -12  TD -0.4028  Tc 0.8299  Tw (gamma pdf with a standard deviation defined by a user) Tj
242.25 0  TD -0.1211  Tc 0  Tw (-) Tj
-242.25 -12.75  TD -0.4728  Tc 0.5666  Tw (specified coefficient of variation \(CV\).  This coeff) Tj
214.5 0  TD -0.5418  Tc 0.6356  Tw (icient is ) Tj
-214.5 -12  TD -0.5859  Tc 0.6797  Tw (given by:) Tj
38.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-24.75 -12.75  TD ( ) Tj
0 -12  TD -0.0564  Tc 0.1502  Tw (CV = s) Tj
33 -3  TD /F3 7.2656  Tf
-0.1896  Tc 0  Tw (t) Tj
3 3  TD /F0 11.625  Tf
-0.138  Tc 0.2318  Tw ( / m) Tj
17.25 -3  TD /F3 7.2656  Tf
-0.1896  Tc 0  Tw (t) Tj
3.75 3  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
5.25 0  TD -0.2352  Tc 0.329  Tw (    or     s) Tj
40.5 -3  TD /F3 7.2656  Tf
-0.1896  Tc 0  Tw (t) Tj
3 3  TD /F0 11.625  Tf
-0.0738  Tc 0.1675  Tw ( = CV\(m) Tj
40.5 -3  TD /F3 7.2656  Tf
-0.1896  Tc 0  Tw (t) Tj
3.75 3  TD /F0 11.625  Tf
-0.1211  Tc (\)) Tj
3 0  TD 0  Tc 0.0938  Tw ( ) Tj
7.5 0  TD ( ) Tj
11.25 0  TD -0.0938  Tw (    ) Tj
11.25 0  TD 0.0938  Tw ( ) Tj
10.5 0  TD ( ) Tj
10.5 0  TD -0.5182  Tc 0.612  Tw (   \(2\)) Tj
21.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-225.75 -12.75  TD ( ) Tj
0 -12  TD -0.2719  Tc 0  Tw (where:) Tj
29.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
9 0  TD -0.0221  Tc 0  Tw (s) Tj
4.5 -3  TD /F3 7.2656  Tf
-0.1896  Tc (t) Tj
3.75 3  TD /F0 11.625  Tf
-0.3322  Tc 0.2759  Tw ( = standard deviation of ) Tj
106.5 -0.75  TD /F3 11.625  Tf
0.1466  Tc 0  Tw (t) Tj
5.25 0.75  TD /F0 11.625  Tf
-0.3171  Tc 0.4108  Tw (; and) Tj
21.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-180 -12.75  TD ( ) Tj
38.25 0  TD -0.0443  Tc 0  Tw (m) Tj
8.25 -2.25  TD /F3 7.2656  Tf
-0.1896  Tc (t) Tj
3.75 2.25  TD /F0 11.625  Tf
-0.4528  Tc 0.3591  Tw ( = mean of ) Tj
50.25 -0.75  TD /F3 11.625  Tf
0.1466  Tc 0  Tw (t) Tj
4.5 0.75  TD /F0 11.625  Tf
-0.3742  Tc 0.4679  Tw ( given by Eq. \(1\).) Tj
76.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-181.5 -12  TD ( ) Tj
0 -12.75  TD -0.2771  Tc 0.2875  Tw (Therefore, as the normal stress increases, so does the ) Tj
-13.5 -12  TD -0.3115  Tc 2.8428  Tw (shear strength and so does the standard deviation of) Tj
0  Tc -0.6563  Tw ( ) Tj
0 -12  TD -0.3698  Tc 0.6135  Tw (shear strength.  Typical values for the shear strength CV ) Tj
0 -12.75  TD -0.2778  Tc 0.8716  Tw (range from 0.15 to 0.35.  Note that for small values of ) Tj
0 -12  TD -0.3118  Tc 2.3556  Tw (CV \(i.e. less than 0.2\), the gamma pdf begins to a) Tj
236.25 0  TD 0.0332  Tc 0  Tw (p-) Tj
-236.25 -12.75  TD -0.4541  Tc 1.5705  Tw (proximate a normal pdf.  The key advantage in using a ) Tj
0 -12  TD -0.3543  Tc 0.4481  Tw (gamma pdf to describe shear strength ) Tj
166.5 0  TD -0.3881  Tc 0.2319  Tw (is that this partic) Tj
70.5 0  TD -0.7168  Tc 0  Tw (u-) Tj
-237 -12.75  TD -0.4551  Tc 1.4488  Tw (lar pdf is defined only for positive values, which means ) Tj
0 -12  TD -0.4219  Tc 0.5156  Tw (that ) Tj
19.5 -0.75  TD /F3 11.625  Tf
0.1466  Tc 0  Tw (t) Tj
5.25 0.75  TD /F0 11.625  Tf
-0.4157  Tc 0.5928  Tw ( in the computer analysis never can take on unrea) Tj
215.25 0  TD -0.9264  Tc 0  Tw (l-) Tj
-240 -12.75  TD -0.5492  Tc 1.393  Tw (istic negative va) Tj
69.75 0  TD -0.2318  Tc 0  Tw (l) Tj
2.25 0  TD -0.4632  Tc 0.4069  Tw (ues for low values of ) Tj
93 -0.75  TD /F3 11.625  Tf
-0.2599  Tc 0  Tw (s) Tj
6.75 0.75  TD /F0 11.625  Tf
-0.3667  Tc 0.3105  Tw (.  Note that small ) Tj
-171.75 -12  TD -0.505  Tc 0.6925  Tw (normal stresses are common when analyzing small failure ) Tj
0 -12.75  TD -0.3109  Tc 0.4047  Tw (masses along bench crests.) Tj
117.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-104.25 -12  TD -0.3437  Tc 1.2946  Tw (In summary, the required geotechnical input needed ) Tj
-13.5 -12.75  TD -0.2965  Tc 1.1402  Tw (for the NIO) Tj
53.25 0  TD -0.372  Tc 0.3407  Tw (SH bench stability programs can be summ) Tj
183.75 0  TD -0.0163  Tc 0  Tw (a-) Tj
-237 -12  TD -0.4353  Tc 0.529  Tw (rized as follows:) Tj
69.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
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54 785.25 5.25 3.75 re h W n 
BT
54 788.25  TD
0 0 0 rg 
/F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
ET
Q 
BT
54 774.75  TD
0 0 0 rg 
/F2 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
0 -12  TD -0.0678  Tc 0  Tw (Bplane.exe) Tj
54.75 0.75  TD /F0 11.625  Tf
0.0332  Tc 0.0606  Tw ( \(2) Tj
12.75 0  TD -0.1211  Tc 0  Tw (-) Tj
3.75 0  TD -0.3284  Tc 0.2347  Tw (d analysis of plane shears\)) Tj
114.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-186 -12.75  TD ( ) Tj
0 -12  TD -0.5042  Tc 0.598  Tw (Bench height \(m\) and width \(m\)) Tj
138.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-138.75 -12.75  TD -0.3106  Tc 3.4043  Tw (Number of back) Tj
78.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.4165  Tc 1.4478  Tw (break cells \(typically set so cells       ) Tj
-96.75 -12  TD 0  Tc 0.0938  Tw ( ) Tj
26.25 0  TD -0.1764  Tc 0.2701  Tw (are about 1) Tj
50.25 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.5441  Tc 0.6378  Tw (m wide\)) Tj
35.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-102.75 -12.75  TD -0.3144  Tc 0.4082  Tw (Bench face angle \(degrees\)) Tj
118.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-118.5 -12  TD -0.4234  Tc 0.5172  Tw (Ground water heig) Tj
81.75 0  TD -0.3504  Tc 0.4442  Tw (ht above bench toe \(m\)) Tj
102 0  TD 0  Tc 0.0938  Tw ( ) Tj
-183.75 -12.75  TD -0.379  Tc 0.2585  Tw (Rock mass unit weight \(tonne/cu.m\):  mean, sd) Tj
204 0  TD 0  Tc 0.0938  Tw ( ) Tj
-204 -12  TD -0.1543  Tc 0  Tw (Fracture) Tj
37.5 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.6059  Tc 0.6996  Tw (set mean length \(m\)) Tj
84.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-126.75 -12.75  TD -0.1543  Tc 0  Tw (Fracture) Tj
37.5 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.4014  Tc 3.9237  Tw (set dip \(deg.\):  mean, sd, nugget value,) Tj
0  Tc -0.6563  Tw ( ) Tj
-55.5 -12  TD 0.0938  Tw ( ) Tj
26.25 0  TD 0.0827  Tc 0  Tw (sp) Tj
10.5 0  TD 0.0885  Tc (a) Tj
4.5 0  TD -0.3919  Tc 0.2981  Tw (tial range \(no. of fractures\)) Tj
115.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-143.25 -12.75  TD -0.1543  Tc 0  Tw (Fracture) Tj
37.5 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.5166  Tc 6.1103  Tw (set spacing \(m\):  mean, nugget value,) Tj
0  Tc -0.6563  Tw ( ) Tj
-55.5 -12  TD 0.0938  Tw ( ) Tj
26.25 0  TD 0.0827  Tc 0  Tw (sp) Tj
10.5 0  TD 0.0885  Tc (a) Tj
4.5 0  TD -0.3462  Tc 0.2524  Tw (tial range \(no. of frac) Tj
90.75 0  TD -0.1617  Tc 0  Tw (tures\)) Tj
24.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-145.5 -12  TD -0.2481  Tc 0  Tw (Fracture) Tj
36.75 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.429  Tc 3.3977  Tw (set waviness \(deg.\):  mean, nugget value,) Tj
0  Tc -0.6563  Tw ( ) Tj
-41.25 -12.75  TD 0.0938  Tw ( ) Tj
15 0  TD -0.3408  Tc 0.4346  Tw (spatial range \(no. of fractures\)) Tj
130.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-145.5 -12  TD -0.4367  Tc 0.5304  Tw (\(Note:  waviness is the average dip minus the ) Tj
198.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
8.25 0  TD -1.2795  Tc 0  Tw (min) Tj
15 0  TD -0.9264  Tc (i-) Tj
-222 -12.75  TD -0.3806  Tc 0.4744  Tw (mum dip of a fracture, and it represents a ) Tj
182.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
3 0  TD -0.4631  Tc 3.5569  Tw (measure of) Tj
0  Tc -1.4063  Tw ( ) Tj
-185.25 -12  TD -0.5977  Tc 0  Tw (large) Tj
21 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.2999  Tc -0.3563  Tw (scale roughness\)) Tj
71.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-96.75 -12.75  TD -0.3574  Tc 0.0761  Tw (Shear strength \(tonne/sq.m\) terms: ) Tj
152.25 0  TD 0.1248  Tc -0.3311  Tw ( a, b, c, CV ) Tj
55.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-207.75 -12  TD ( ) Tj
0 -13.5  TD /F2 11.625  Tf
-0.0788  Tc 0  Tw (Bwedge.exe) Tj
58.5 0.75  TD /F0 11.625  Tf
0.0332  Tc 0.0606  Tw ( \(3) Tj
12.75 0  TD -0.1211  Tc 0  Tw (-) Tj
3.75 0  TD -0.3854  Tc 0.2291  Tw (d analysis of wedges\)) Tj
93.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-168.75 -12  TD ( ) Tj
2.25 -12.75  TD -0.5042  Tc 0.598  Tw (Bench height \(m\) and width \(m\)) Tj
138.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-138.75 -12  TD -0.3106  Tc 3.4043  Tw (Number of back) Tj
78.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.4165  Tc 1.4478  Tw (break cells \(typically set so cells       ) Tj
-96.75 -12.75  TD 0  Tc 0.0938  Tw ( ) Tj
26.25 0  TD -0.1764  Tc 0.2701  Tw (are about 1) Tj
50.25 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.5441  Tc 0.6378  Tw (m wide\)) Tj
35.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-102.75 -12  TD -0.354  Tc 0.4478  Tw (Bench face angle and dip direction \(degrees\)) Tj
195 0  TD 0  Tc 0.0938  Tw ( ) Tj
-195 -12.75  TD -0.3609  Tc 0.4546  Tw (Ground water height above bench toe \(m\)) Tj
183.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-183.75 -12  TD -0.255  Tc -0.0262  Tw (Rock mass ) Tj
51.75 0  TD -0.4766  Tc 0.3203  Tw (mean unit weight \(tonne/cu.m\)) Tj
131.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-183 -12  TD ( ) Tj
0 -12.75  TD -0.4561  Tc 0.4666  Tw (The following input is needed for both the left ) Tj
200.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
4.5 0  TD -0.8012  Tc 0  Tw (fra) Tj
11.25 0  TD -0.0163  Tc (c-) Tj
-229.5 -12  TD -0.3997  Tc 0.3268  Tw (ture set and the right fracture set that form ) Tj
185.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
11.25 0  TD -0.4852  Tc 0.579  Tw (viable ) Tj
-196.5 -12.75  TD -0.1922  Tc 0  Tw (wedges:) Tj
36 0  TD 0  Tc 0.0938  Tw ( ) Tj
-22.5 -12  TD ( ) Tj
0 -12.75  TD -0.1543  Tc 0  Tw (Fracture) Tj
37.5 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.6059  Tc 0.6996  Tw (set mean length \(m\)) Tj
84.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-126.75 -12  TD -0.1543  Tc 0  Tw (Fracture) Tj
37.5 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.3721  Tc 0.4659  Tw (set dip direction \(deg.\):  mean, sd, nug) Tj
167.25 0  TD -0.1211  Tc 0  Tw (-) Tj
3.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
2.25 0  TD -0.2352  Tc 0.329  Tw (get ) Tj
-228.75 -12.75  TD -0.3368  Tc 0.1806  Tw (value, spatial range \(no.) Tj
103.5 0  TD -0.4557  Tc 0.5495  Tw ( of fractures\)) Tj
55.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-145.5 -12  TD -0.1543  Tc 0  Tw (Fracture) Tj
37.5 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.4014  Tc 3.9237  Tw (set dip \(deg.\):  mean, sd, nugget value,) Tj
0  Tc -0.6563  Tw ( ) Tj
-55.5 -12.75  TD 0.0938  Tw ( ) Tj
26.25 0  TD 0.0827  Tc 0  Tw (sp) Tj
10.5 0  TD 0.0885  Tc (a) Tj
4.5 0  TD -0.3919  Tc 0.2981  Tw (tial range \(no. of fractures\)) Tj
115.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-143.25 -12  TD -0.1543  Tc 0  Tw (Fracture) Tj
37.5 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.5166  Tc 6.1103  Tw (set spacing \(m\):  mean, nugget value,) Tj
0  Tc -0.6563  Tw ( ) Tj
-55.5 -12.75  TD 0.0938  Tw ( ) Tj
26.25 0  TD 0.0827  Tc 0  Tw (sp) Tj
10.5 0  TD 0.0885  Tc (a) Tj
4.5 0  TD -0.3919  Tc 0.2981  Tw (tial range \(no. of fractures\)) Tj
115.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-143.25 -12  TD -0.2777  Tc 0.3714  Tw (Shear strength \(tonne/sq.m\) terms:  a, b, c, CV) Tj
205.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-205.5 -12.75  TD ( ) Tj
12.75 0  TD -0.1211  Tc 0  Tw (\() Tj
3.75 -0.75  TD /F3 11.625  Tf
-0.2599  Tc (s) Tj
6.75 0.75  TD /F0 11.625  Tf
-0.0955  Tc 0.1893  Tw ( and ) Tj
22.5 -0.75  TD /F3 11.625  Tf
0.1466  Tc 0  Tw (t) Tj
4.5 0.75  TD /F0 11.625  Tf
-0.3341  Tc 0.4279  Tw ( expressed in tonne/sq.m\)) Tj
112.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-162.75 -12  TD ( ) Tj
-13.5 -12.75  TD 0.1875  Tc 0  Tw (3) Tj
6 0  TD 0  Tc 0.0938  Tw ( ) Tj
7.5 0  TD -0.1348  Tc 0.2285  Tw (STOCHASTIC MODELING ) Tj
137.25 0  TD -0.2096  Tc 0  Tw (CONCEPTS) Tj
59.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-210 -24  TD -0.4278  Tc 1.3549  Tw (The probability of retaining a specified bench width for ) Tj
0 -12.75  TD -0.446  Tc 3.4564  Tw (given failure modes in a bench can be estimated by) Tj
0  Tc -1.4063  Tw ( ) Tj
0 -12  TD -0.4577  Tc 1.1514  Tw (simulating potential failure geometries and cat) Tj
199.5 0  TD 0.0885  Tc 0  Tw (a) Tj
5.25 0  TD -0.6299  Tc 0.7237  Tw (loging the ) Tj
-204.75 -12.75  TD -0.237  Tc 0  Tw (back) Tj
21.75 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.2891  Tc 4.1329  Tw (break position of eac) Tj
103.5 0  TD -0.4074  Tc 3.6262  Tw (h one on the top of the) Tj
0  Tc -0.6563  Tw ( ) Tj
-129.75 -12  TD -0.4316  Tc 1.9182  Tw (bench.  Stability of a given failure geom) Tj
181.5 0  TD 0.0885  Tc 0  Tw (e) Tj
5.25 0  TD -0.2836  Tc 0.8774  Tw (try can occur ) Tj
-186.75 -12.75  TD -0.486  Tc 2.2048  Tw (two ways:  1\) the failure length is not long enough to ) Tj
0 -12  TD -0.452  Tc 0.9208  Tw (pass entirely through the bench, and 2\) the failure length ) Tj
0 -12.75  TD -0.432  Tc 2.6924  Tw (is long enough to pass through the bench, but sliding) Tj
0  Tc -1.4063  Tw ( ) Tj
0 -12  TD -0.0236  Tc 0.8674  Tw (does not) Tj
38.25 0  TD -0.3211  Tc 0.7898  Tw ( occur \(Miller 1983\).  The probability of stabi) Tj
202.5 0  TD -0.9264  Tc 0  Tw (l-) Tj
-240.75 -12.75  TD -0.4414  Tc 1.2851  Tw (ity for each geometry then is given by the sum of these ) Tj
0 -12  TD -0.3997  Tc 0.4934  Tw (two probability values:) Tj
98.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-84.75 -12.75  TD ( ) Tj
-13.5 -12  TD ( ) Tj
ET
q 
321 785.25 5.25 3.75 re h W n 
BT
321 788.25  TD
( ) Tj
ET
Q 
BT
321 775.5  TD
( ) Tj
0 -12  TD 0.2865  Tc 0  Tw (P) Tj
6.75 -3  TD /F0 7.2656  Tf
-0.3012  Tc (stab) Tj
11.25 3  TD /F0 11.625  Tf
-0.424  Tc 0.4106  Tw ( = P\(failure path not long enough\) ) Tj
149.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-167.25 -12.75  TD -0.4778  Tc 0.5247  Tw (         + P\(failure path long enough and no sli) Tj
193.5 0  TD 0.1875  Tc 0  Tw (d) Tj
5.25 0  TD -0.7445  Tc (ing\)) Tj
16.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-215.25 -12  TD ( ) Tj
0 -12.75  TD 0.2865  Tc 0  Tw (P) Tj
6.75 -3  TD /F0 7.2656  Tf
-0.3012  Tc (stab) Tj
11.25 3  TD /F0 11.625  Tf
-0.1634  Tc 0.0071  Tw ( = \(1 ) Tj
24.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD 0.2865  Tc -0.1927  Tw ( P) Tj
9.75 -3  TD /F0 7.2656  Tf
0.0607  Tc 0  Tw (L) Tj
3.75 3  TD /F0 11.625  Tf
0.1196  Tc -0.0259  Tw (\) + P) Tj
22.5 -3  TD /F0 7.2656  Tf
0.0607  Tc 0  Tw (L) Tj
4.5 3  TD /F0 11.625  Tf
0.0332  Tc (\(1) Tj
9.75 0  TD -0.1211  Tc (-) Tj
4.5 0  TD 0.2865  Tc (P) Tj
6 -3  TD /F0 7.2656  Tf
-0.2897  Tc (S) Tj
4.5 3  TD /F0 11.625  Tf
-0.1211  Tc (\)) Tj
3.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
12 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD -0.5182  Tc 0.5049  Tw (       \(3\)) Tj
33 0  TD 0  Tc 0.0938  Tw ( ) Tj
-226.5 -12  TD ( ) Tj
-13.5 -12.75  TD -0.4177  Tc 0.8864  Tw (Thus, the probability of failure length and the pro) Tj
215.25 0  TD 0.1875  Tc 0  Tw (b) Tj
6 0  TD -0.6019  Tc -0.0543  Tw (ability ) Tj
-221.25 -12  TD -0.4233  Tc 2.767  Tw (of sliding must be computed for each pote) Tj
198 0  TD 0.1875  Tc 0  Tw (n) Tj
5.25 0  TD -0.6316  Tc 1.8504  Tw (tial failure ) Tj
-203.25 -12.75  TD -0.394  Tc 0.3378  Tw (mass generated in the bench sim) Tj
140.25 0  TD 0.1875  Tc 0  Tw (u) Tj
4.5 0  TD -0.6626  Tc (lation.) Tj
26.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-157.5 -12  TD ( ) Tj
-13.5 -12.75  TD -0.0938  Tc 0  Tw (3.1) Tj
14.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
7.5 0  TD /F1 11.625  Tf
-0.0509  Tc 0.1447  Tw (Probability of failure length) Tj
129.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-138 -12  TD /F0 11.625  Tf
( ) Tj
-13.5 -12.75  TD -0.4422  Tc 2.786  Tw (The probability that a given simulated fracture) Tj
211.5 0  TD -0.6122  Tc 1.9559  Tw ( is long ) Tj
-211.5 -12  TD -0.3897  Tc 1.5668  Tw (enough to pass entirely through the bench is computed ) Tj
0 -12  TD -0.3204  Tc 2.2892  Tw (as an exceedance probability using an e) Tj
183.75 0  TD 0.1875  Tc 0  Tw (x) Tj
4.5 0  TD -0.397  Tc 0.8658  Tw (ponential pdf ) Tj
-188.25 -12.75  TD -0.3929  Tc 1.9867  Tw (model for the fracture) Tj
98.25 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.4043  Tc 0.9981  Tw (set lengths.  The exponential cdf ) Tj
-102.75 -12  TD -0.532  Tc 1.3758  Tw (\(cumulative distribution function\) is a one) Tj
180.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.2977  Tc 0.3914  Tw (parameter cdf ) Tj
-185.25 -12.75  TD -0.4207  Tc 0.5145  Tw (model given by \(Devore 1) Tj
114 0  TD -0.1081  Tc 0  Tw (995\):) Tj
23.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-123.75 -12  TD ( ) Tj
0 -12.75  TD 0.4577  Tc 0  Tw (F\() Tj
10.5 0  TD /F1 11.625  Tf
0.0885  Tc (x) Tj
5.25 0  TD /F0 11.625  Tf
-0.4999  Tc 0.453  Tw (\) = 0,             if ) Tj
70.5 0  TD /F1 11.625  Tf
0.0885  Tc 0  Tw (x) Tj
6 0  TD /F0 11.625  Tf
0.1905  Tc -0.0968  Tw ( < 0) Tj
18 0  TD 0  Tc 0.0938  Tw ( ) Tj
-110.25 -12  TD ( ) Tj
0 -12.75  TD -0.1845  Tc 0.1282  Tw (        = 1 ) Tj
41.25 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD 0.0885  Tc 0.0052  Tw ( e) Tj
8.25 3.75  TD /F0 7.2656  Tf
-0.1695  Tc 0  Tw (-) Tj
2.25 0  TD /F1 7.2656  Tf
-0.2259  Tc (x) Tj
2.25 0  TD /F0 7.2656  Tf
0.2888  Tc (/m) Tj
8.25 -3.75  TD /F0 11.625  Tf
-0.8364  Tc 0.5551  Tw (,   if ) Tj
19.5 0  TD /F1 11.625  Tf
0.0885  Tc 0  Tw (x) Tj
6 0  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
3 0  TD 0.1935  Tc 0  Tw (>) Tj
ET
416.25 513 6.75 0.75 re f
BT
423 516  TD
-0.5625  Tc 0.6094  Tw ( 0               ) Tj
51.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
6.75 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD -0.5182  Tc 0.612  Tw (   \(4\)) Tj
21.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-225.75 -12  TD -0.486  Tc 0.5798  Tw (where:  m = mean.) Tj
81.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-81.75 -12.75  TD ( ) Tj
0 -12  TD -0.4198  Tc 2.1636  Tw (The length required for a through) Tj
151.5 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.537  Tc 1.3807  Tw (going failure path ) Tj
-169.5 -12.75  TD -0.4607  Tc 0.5544  Tw (for a plane) Tj
46.5 0  TD -0.1211  Tc 0  Tw (-) Tj
3.75 0  TD -0.345  Tc 0.4387  Tw (shear fracture is calculated by:) Tj
132 0  TD 0  Tc 0.0938  Tw ( ) Tj
-168.75 -12  TD ( ) Tj
0 -12.75  TD /F1 11.625  Tf
0.0885  Tc 0  Tw (x) Tj
6 0  TD /F0 11.625  Tf
-0.4503  Tc 0.544  Tw ( = h/sin\(D\)) Tj
47.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
9 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD -0.5182  Tc 0.612  Tw (   \(5\)) Tj
21.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-225.75 -12  TD ( ) Tj
0 -12  TD -0.2719  Tc 0  Tw (where:) Tj
29.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
9 0  TD -0.4425  Tc 0.4425  Tw (h = vertical height of failure mass, as ) Tj
160.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
5.25 0  TD -0.2057  Tc 0  Tw (mea) Tj
18 0  TD -0.0716  Tc (s-) Tj
-235.5 -12.75  TD -0.4533  Tc 0.4533  Tw (ured from the toe of the failure to ) Tj
146.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
6 0  TD -0.3055  Tc 1.1493  Tw (the top of the bench; ) Tj
-152.25 -12  TD -0.5955  Tc 0  Tw (and) Tj
15.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-2.25 -12.75  TD ( ) Tj
38.25 0  TD -0.3896  Tc 2.7333  Tw (D = dip of failure plane \(or wedge inter) Tj
190.5 0  TD -0.1211  Tc 0  Tw (-) Tj
-242.25 -12  TD 0  Tc 0.0938  Tw ( ) Tj
51.75 0  TD 0.0332  Tc 0  Tw (se) Tj
9.75 0  TD 0.0885  Tc (c) Tj
5.25 0  TD -0.4736  Tc 0.5673  Tw (tion line for wedge failures\).) Tj
120.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-174 -12.75  TD ( ) Tj
0 -12  TD -0.3878  Tc 1.8149  Tw (Thus, the probability that fracture length takes on a ) Tj
-13.5 -12.75  TD -0.4104  Tc 0.5041  Tw (value greater th) Tj
66.75 0  TD -0.612  Tc -0.7943  Tw (an ) Tj
12.75 0  TD /F1 11.625  Tf
0.0885  Tc 0  Tw (x) Tj
6 0  TD /F0 11.625  Tf
-0.4941  Tc 0.3379  Tw ( is given by:) Tj
51 0  TD 0  Tc 0.0938  Tw ( ) Tj
-123 -12  TD ( ) Tj
0 -12.75  TD -0.1336  Tc 0.2273  Tw (P\(X > ) Tj
30.75 0  TD /F1 11.625  Tf
0.0885  Tc 0  Tw (x) Tj
5.25 0  TD /F0 11.625  Tf
0.0866  Tc 0.0071  Tw (\) = 1 ) Tj
24.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.2426  Tc -0.0386  Tw ( P\(X ) Tj
24 0  TD 0.1935  Tc 0  Tw (<) Tj
ET
410.25 303 6.75 0.75 re f
BT
417 306  TD
0  Tc 0.0938  Tw ( ) Tj
3 0  TD /F1 11.625  Tf
0.0885  Tc 0  Tw (x) Tj
6 0  TD /F0 11.625  Tf
-0.1634  Tc 0.2571  Tw (\) = 1 ) Tj
24 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD 0.4577  Tc -0.3639  Tw ( F\() Tj
13.5 0  TD /F1 11.625  Tf
0.0885  Tc 0  Tw (x) Tj
5.25 0  TD /F0 11.625  Tf
0.0866  Tc 0.0071  Tw (\) = 1 ) Tj
24.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD 0.0332  Tc 0.0606  Tw ( \(1 ) Tj
15.75 0  TD -0.1211  Tc 0  Tw (-) Tj
3.75 0  TD 0.0885  Tc 0.0052  Tw ( e) Tj
8.25 3.75  TD /F0 7.2656  Tf
-0.1695  Tc 0  Tw (-) Tj
2.25 0  TD /F1 7.2656  Tf
-0.2259  Tc (x) Tj
3 0  TD /F0 7.2656  Tf
0.2888  Tc (/m) Tj
7.5 -3.75  TD /F0 11.625  Tf
-0.1211  Tc (\)) Tj
3.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-225.75 -12  TD ( ) Tj
0 -12.75  TD 0.141  Tc -0.141  Tw (               = e) Tj
58.5 3.75  TD /F0 7.2656  Tf
-0.1695  Tc 0  Tw (-) Tj
1.5 0  TD /F1 7.2656  Tf
-0.2259  Tc (x) Tj
3 0  TD /F0 7.2656  Tf
0.2888  Tc (/m) Tj
8.25 -3.75  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
2.25 0  TD -0.135  Tc 0.2287  Tw ( = P) Tj
18.75 -2.25  TD /F0 7.2656  Tf
0.0607  Tc 0  Tw (L) Tj
4.5 2.25  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
9 0  TD ( ) Tj
3 0  TD ( ) Tj
8.25 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD -0.5182  Tc 0.5049  Tw (       \(6\)) Tj
33 0  TD 0  Tc 0.0938  Tw ( ) Tj
-240 -12  TD ( ) Tj
0 -12.75  TD -0.5008  Tc 0.5946  Tw (Example:  for mean length = 1.6m and  ) Tj
171.75 0  TD /F1 11.625  Tf
0.0885  Tc 0  Tw (x) Tj
6 0  TD /F0 11.625  Tf
-0.2674  Tc -0.0139  Tw ( = 3m,) Tj
29.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-193.5 -12  TD ( ) Tj
0 -12.75  TD -0.117  Tc 0.2107  Tw (P\(X > 3\) = e) Tj
57.75 3.75  TD /F0 7.2656  Tf
-0.1695  Tc 0  Tw (-) Tj
1.5 0  TD 0.2031  Tc (3/1.6) Tj
15.75 -3.75  TD /F0 11.625  Tf
0.0022  Tc 0.0916  Tw ( = 0.153 = P) Tj
57 -2.25  TD /F0 7.2656  Tf
0.0607  Tc 0  Tw (L) Tj
4.5 2.25  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
3 0  TD ( ) Tj
-139.5 -12  TD ( ) Tj
0 -12  TD -0.3011  Tc 1.1449  Tw (In the case of three) Tj
86.25 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.4634  Tc 1.0572  Tw (dimensional wedges, which slide) Tj
142.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-246.75 -12.75  TD -0.4802  Tc 2.4906  Tw (along the line of intersection, the probability of length ) Tj
0 -12  TD -0.6673  Tc 0  Tw (su) Tj
9 0  TD -0.1211  Tc (f) Tj
3 0  TD -0.4702  Tc 2.1389  Tw (ficient for failure is the joint probability that the left ) Tj
-12 -12.75  TD -0.4568  Tc 3.2172  Tw (fracture is long enough and the right fracture is long) Tj
0  Tc -0.6563  Tw ( ) Tj
0 -12  TD -0.5294  Tc 0  Tw (enough:) Tj
33 0  TD 0  Tc 0.0938  Tw ( ) Tj
-19.5 -12.75  TD ( ) Tj
0 -12  TD 0.2865  Tc 0  Tw (P) Tj
6.75 -3  TD /F0 7.2656  Tf
0.0607  Tc (L) Tj
4.5 3  TD /F0 11.625  Tf
-0.2615  Tc -0.0198  Tw (\(wedge\) = P) Tj
54.75 -3  TD /F0 7.2656  Tf
0.0607  Tc 0  Tw (L) Tj
4.5 3  TD /F0 11.625  Tf
-0.4981  Tc 0.5918  Tw (\(left\) ) Tj
23.25 -1.5  TD /F4 9.4453  Tf
-0.2227  Tc 0  Tw (x) Tj
5.25 1.5  TD /F0 11.625  Tf
0.2865  Tc -0.1927  Tw ( P) Tj
9 -3  TD /F0 7.2656  Tf
0.0607  Tc 0  Tw (L) Tj
4.5 3  TD /F0 11.625  Tf
-0.4931  Tc (\(right\)) Tj
26.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD -0.5182  Tc 0.612  Tw (   \(7\)) Tj
21.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-225.75 -12.75  TD ( ) Tj
-13.5 -12  TD -0.5262  Tc 0.245  Tw (After setting the length ) Tj
99.75 0  TD -0.343  Tc 0.3117  Tw (of the wedge intersection equal to ) Tj
-99.75 -12.75  TD /F1 11.625  Tf
0.0885  Tc 0  Tw (x) Tj
5.25 0  TD /F0 11.625  Tf
-0.2693  Tc 0.4881  Tw ( in Eq. \(6\), the corresponding P) Tj
139.5 -2.25  TD /F0 7.2656  Tf
0.0607  Tc 0  Tw (L) Tj
4.5 2.25  TD /F0 11.625  Tf
-0.3738  Tc 0.4676  Tw (\(left\) and P) Tj
48.75 -2.25  TD /F0 7.2656  Tf
0.0607  Tc 0  Tw (L) Tj
4.5 2.25  TD /F0 11.625  Tf
-0.4587  Tc 0.1775  Tw (\(right\) can ) Tj
-202.5 -12  TD -0.4481  Tc 1.5918  Tw (be computed using the mean length for the left fracture ) Tj
0 -12.75  TD -0.3375  Tc 0.3562  Tw (set and the mean length for the right fracture set, respe) Tj
237 0  TD -0.0163  Tc 0  Tw (c-) Tj
-237 -12  TD -0.6626  Tc (tively.) Tj
25.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
ET

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54 785.25 5.25 3.75 re h W n 
BT
54 788.25  TD
0 0 0 rg 
/F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
ET
Q 
BT
40.5 775.5  TD
0 0 0 rg 
/F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
0 -12  TD 0.1563  Tc 0  Tw (3.2) Tj
14.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
7.5 0  TD /F1 11.625  Tf
-0.0706  Tc 0.1644  Tw (Probability of sliding) Tj
98.25 0  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
-120 -12.75  TD ( ) Tj
0 -12  TD -0.1788  Tc 1.7726  Tw (The probab) Tj
53.25 0  TD -0.5407  Tc 1.1345  Tw (ility of sliding for a given slope failure mode ) Tj
-53.25 -12.75  TD -0.251  Tc 0.9876  Tw (can be estimated by Monte Carlo methods a) Tj
199.5 0  TD 0.1875  Tc 0  Tw (p) Tj
6 0  TD -0.3695  Tc 0.4632  Tw (plied to a ) Tj
-205.5 -12  TD -0.8535  Tc 0  Tw (limiting) Tj
30 0  TD -0.1211  Tc (-) Tj
4.5 0  TD -0.4728  Tc 1.3166  Tw (equilibrium analysis, whereby a distribution \(hi) Tj
204 0  TD -0.0716  Tc 0  Tw (s-) Tj
-238.5 -12.75  TD -0.3739  Tc 0.7177  Tw (togram\) of safety factor values is generated by many r) Tj
237.75 0  TD -0.0163  Tc 0  Tw (e-) Tj
-237.75 -12  TD -0.3776  Tc 3.2214  Tw (peated calculations using po) Tj
129.75 0  TD -0.0221  Tc 0  Tw (s) Tj
4.5 0  TD -0.5367  Tc 2.8804  Tw (sible realiza) Tj
52.5 0  TD -0.4954  Tc 1.5892  Tw (tions of input ) Tj
-186.75 -12.75  TD -0.4456  Tc 2.8727  Tw (values. The probability of sliding then is equal to the) Tj
0  Tc -0.6563  Tw ( ) Tj
0 -12  TD -0.3012  Tc 0  Tw (fra) Tj
12 0  TD 0.0885  Tc (c) Tj
4.5 0  TD -0.3419  Tc 3.2689  Tw (tion of safety factors that are less than 1.0. The) Tj
0  Tc -0.6563  Tw ( ) Tj
-16.5 -12.75  TD -0.3692  Tc 0.9402  Tw (safety factor is defined as the ratio of resisting forces to ) Tj
0 -12  TD -0.4099  Tc 0.837  Tw (driving forces, and a value of 1.0 indicates limiting equ) Tj
240.75 0  TD -0.9264  Tc 0  Tw (i-) Tj
-240.75 -12.75  TD -0.8245  Tc 1.6682  Tw (librium \(i.) Tj
41.25 0  TD -0.4208  Tc 0.7396  Tw (e. the potential failure mass is just on the verge ) Tj
-41.25 -12  TD -0.556  Tc 0.6497  Tw (of sliding\).) Tj
45 0  TD 0  Tc 0.0938  Tw ( ) Tj
-31.5 -12  TD -0.353  Tc 4.8218  Tw (However, even after completing a Monte Carlo) Tj
0  Tc -0.6563  Tw ( ) Tj
-13.5 -12.75  TD -0.4375  Tc 0.5313  Tw (simulation study using several thousand iterations, the r) Tj
237.75 0  TD -0.0163  Tc 0  Tw (e-) Tj
-237.75 -12  TD -0.4232  Tc 2.2045  Tw (sulting histogram of safety factors represents only one ) Tj
0 -12.75  TD -0.4084  Tc 2.5647  Tw (possible realization of the actua) Tj
144.75 0  TD -0.4249  Tc 2.0186  Tw (l safety factor pdf.  A ) Tj
-144.75 -12  TD -0.5658  Tc 1.4095  Tw (slightly different distribution will r) Tj
145.5 0  TD 0.0885  Tc 0  Tw (e) Tj
5.25 0  TD -0.6287  Tc 1.0225  Tw (sult if the simulation is ) Tj
-150.75 -12.75  TD -0.4018  Tc 2.2456  Tw (repeated using a different random seed starting value.  ) Tj
0 -12  TD -0.4019  Tc 0.9644  Tw (Thus, questions always arise regarding the number of i) Tj
240 0  TD -0.1764  Tc 0  Tw (t-) Tj
-240 -12.75  TD -0.3367  Tc 0.3234  Tw (erations to use and the repeatability of results.) Tj
199.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-186 -12  TD -0.5588  Tc 0  Tw (Fourie) Tj
28.5 0  TD -0.3663  Tc 3.7101  Tw (r analysis provides an alternative to Monte) Tj
0  Tc -0.6563  Tw ( ) Tj
-42 -12.75  TD -0.4577  Tc 1.0515  Tw (Carlo simulation in estimating the probability distr) Tj
218.25 0  TD -0.2318  Tc 0  Tw (i) Tj
2.25 0  TD -0.5773  Tc -0.829  Tw (bution ) Tj
-220.5 -12  TD -0.3238  Tc 0.5009  Tw (of the safety factor, provided that the safety factor equ) Tj
237.75 0  TD -0.0163  Tc 0  Tw (a-) Tj
-237.75 -12.75  TD -0.4548  Tc 1.1111  Tw (tion can be written as the sum of ind) Tj
162.75 0  TD 0.0885  Tc 0  Tw (e) Tj
5.25 0  TD -0.321  Tc 0.7897  Tw (pendent pdf\222s.  A ) Tj
-168 -12  TD -0.4603  Tc 1.679  Tw (computationally efficient way to estim) Tj
168.75 0  TD -0.3345  Tc 0.8032  Tw (ate the actual pdf ) Tj
-168.75 -12.75  TD -0.3489  Tc 1.6093  Tw (of the safety factor relies on discrete Fourier methods, ) Tj
0 -12  TD -0.3951  Tc 0.6388  Tw (which take advantage of the computing speed of the fast ) Tj
T* -0.3457  Tc 0.4394  Tw (Fourier transform \(Miller 1982\).  As presented by Feller ) Tj
0 -12.75  TD -0.3435  Tc 2.9685  Tw (\(1966\), the sum of independent pdf\222s in the \223space\224) Tj
0  Tc -1.4063  Tw ( ) Tj
0 -12  TD -0.543  Tc 4.0117  Tw (domain is analo) Tj
75 0  TD -0.3897  Tc 3.7334  Tw (gous to the product of their Fourier) Tj
0  Tc -0.6563  Tw ( ) Tj
-75 -12.75  TD -0.4864  Tc 0.5801  Tw (transforms in the \223frequency\224 domain.) Tj
164.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-150.75 -12  TD -0.3304  Tc 0.7992  Tw (For our case, if fracture shear strength is assumed to ) Tj
-13.5 -12.75  TD -0.3655  Tc 1.303  Tw (have a gamma pdf and fracture waviness is a) Tj
201.75 0  TD -0.0221  Tc 0  Tw (s) Tj
4.5 0  TD -0.3782  Tc 0.4719  Tw (sumed to ) Tj
-206.25 -12  TD -0.438  Tc 2.1  Tw (have an exponential pdf \(which is a special form of a ) Tj
0 -12.75  TD -0.3787  Tc 1.7225  Tw (gamma pdf\), then th) Tj
92.25 0  TD -0.3185  Tc 1.5373  Tw (e output safety factor pdf  can be ) Tj
-92.25 -12  TD -0.1978  Tc 1.7916  Tw (described as a gamma pdf.  The pro) Tj
171.75 0  TD 0.1875  Tc 0  Tw (b) Tj
5.25 0  TD -0.6439  Tc 1.2376  Tw (ability of sliding ) Tj
-177 -12.75  TD -0.2923  Tc 0  Tw (\(P) Tj
10.5 -2.25  TD /F0 7.2656  Tf
-0.2897  Tc (S) Tj
3.75 2.25  TD /F0 11.625  Tf
-0.4506  Tc 1.2006  Tw (\) is computed by numerically integrating the area u) Tj
223.5 0  TD -0.7168  Tc 0  Tw (n-) Tj
-237.75 -12  TD -0.377  Tc 1.1582  Tw (der the discretized pdf of the safety factor to the left of ) Tj
0 -12.75  TD -0.2743  Tc 0.243  Tw (safety factor = 1.0.  That is,) Tj
121.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-121.5 -12  TD ( ) Tj
13.5 -12.75  TD ( ) Tj
8.25 0  TD 0.2865  Tc 0  Tw (P) Tj
6.75 -2.25  TD /F0 7.2656  Tf
-0.2897  Tc (S) Tj
4.5 2.25  TD /F0 11.625  Tf
-0.1136  Tc 0.2074  Tw ( = P\(SF ) Tj
38.25 0  TD 0.1935  Tc 0  Tw (<) Tj
ET
111.75 253.5 6.75 0.75 re f
BT
118.5 256.5  TD
-0.1006  Tc 0.1943  Tw ( 1.0\) ) Tj
24 0  TD 0  Tc 0.0938  Tw ( ) Tj
6.75 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD -0.0182  Tc 0.0049  Tw (       \(8\)) Tj
33.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-240.75 -12  TD ( ) Tj
13.5 -12.75  TD -0.5086  Tc 6.0024  Tw (Additional information on this analytical method) Tj
0  Tc -0.6563  Tw ( ) Tj
-13.5 -12  TD -0.3249  Tc 1.0854  Tw (based on Fourier convolution of pdf\222s was reported by ) Tj
0 -12  TD -0.2855  Tc 0.3792  Tw (Miller \(1982\).) Tj
61.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-48 -12.75  TD ( ) Tj
0 -12  TD ( ) Tj
-13.5 -12.75  TD 0.1875  Tc 0  Tw (4) Tj
6 0  TD 0  Tc 0.0938  Tw ( ) Tj
7.5 0  TD -0.2769  Tc 0.3707  Tw (BENCH STABILITY ANAL) Tj
132.75 0  TD -0.2978  Tc 0  Tw (YSIS) Tj
24.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-171 -24.75  TD -0.2677  Tc 1.8615  Tw (The concept of bench back) Tj
126 0  TD -0.1211  Tc 0  Tw (-) Tj
3.75 0  TD -0.457  Tc 1.4508  Tw (break cells is illustrated in ) Tj
-129.75 -12  TD -0.3844  Tc 0.6924  Tw (Figures 1 and 2.  For the plane) Tj
136.5 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.4154  Tc (she) Tj
14.25 0  TD -0.3697  Tc 0.3135  Tw (ar analysis \(Fig. 1\), a ) Tj
-155.25 -12.75  TD -0.3501  Tc 0.7438  Tw (random starting point is selected near the bench toe and ) Tj
0 -12  TD -0.4002  Tc 2.7439  Tw (then fracture locations up the bench are simulated by) Tj
0  Tc -1.4063  Tw ( ) Tj
0 -12.75  TD -0.3557  Tc 1.4495  Tw (generating spatially dependent fracture spacings.  Fra) Tj
237.75 0  TD -0.0163  Tc 0  Tw (c-) Tj
-237.75 -12  TD -0.3339  Tc 1.1777  Tw (ture dips and waviness values also are generated using ) Tj
0 -12.75  TD -0.2889  Tc 1.8827  Tw (spatial dep) Tj
48.75 0  TD -0.3978  Tc 1.4916  Tw (endence and assigned to individual fractures ) Tj
-48.75 -12  TD -0.3761  Tc 0.4699  Tw (previously located on the slope face.) Tj
159 0  TD 0  Tc 0.0938  Tw ( ) Tj
ET
q 
321 785.25 5.25 3.75 re h W n 
BT
321 788.25  TD
( ) Tj
ET
Q 
BT
321 775.5  TD
( ) Tj
0 -12  TD ( ) Tj
0 -12.75  TD ( ) Tj
0 -12  TD ( ) Tj
0 -12.75  TD ( ) Tj
0 -12  TD ( ) Tj
-13.5 -12.75  TD ( ) Tj
13.5 -12  TD ( ) Tj
0 -12.75  TD ( ) Tj
0 -12  TD ( ) Tj
0 -12.75  TD ( ) Tj
0 -12  TD ( ) Tj
0 -12.75  TD ( ) Tj
0 -12  TD ( ) Tj
T* ( ) Tj
-13.5 -12.75  TD ( ) Tj
13.5 -12  TD ( ) Tj
0 -12.75  TD -0.3699  Tc 0.4636  Tw (Figure 1.  Simulated plane shears \(Miller 1983\).) Tj
209.25 0  TD 0  Tc 0.0938  Tw ( ) Tj
-209.25 -12  TD ( ) Tj
0 -267  TD ( ) Tj
0 -12  TD -0.4047  Tc 0.4985  Tw (Figure 2.  Simulated 3) Tj
96.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.3068  Tc 0.4006  Tw (d wedges \(Miller 1983\).) Tj
106.5 0  TD 0  Tc 0.0938  Tw ( ) Tj
-221.25 -12.75  TD ( ) Tj
13.5 -12  TD -0.5101  Tc 3.1351  Tw (By simulating many realizations of a given bench, ) Tj
-13.5 -12.75  TD -0.0742  Tc 0  Tw (each) Tj
20.25 0  TD -0.4139  Tc 1.2577  Tw ( of which contains multiple occurrences of the pa) Tj
218.25 0  TD -0.1211  Tc 0  Tw (r-) Tj
-238.5 -12  TD -0.475  Tc 2.1521  Tw (ticular failure mode, the probability of stability for any ) Tj
0 -12.75  TD -0.3011  Tc 2.6448  Tw (specified back) Tj
65.25 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.4148  Tc 1.9014  Tw (failure cell can be estimated as follows ) Tj
-69.75 -12  TD -0.3682  Tc 0.4619  Tw (\(Miller 1983\):) Tj
60.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-60.75 -12.75  TD ( ) Tj
13.5 -12  TD 0.0019  Tw (                                                 ) Tj
142.5 -1.5  TD /F0 8.7187  Tf
0.4067  Tc -0.4614  Tw (N      J) Tj
23.25 -1.5  TD /F0 7.2656  Tf
0.2302  Tc 0  Tw (i) Tj
2.25 3  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
-168 -12.75  TD 0.2865  Tc 0  Tw (P) Tj
6.75 -2.25  TD /F0 7.2656  Tf
0.4321  Tc (CS) Tj
9 2.25  TD /F0 11.625  Tf
-0.423  Tc 0.5167  Tw ( =  [\(N) Tj
31.5 -2.25  TD /F0 7.2656  Tf
0.0607  Tc 0  Tw (T) Tj
5.25 2.25  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
3 0  TD -0.1211  Tc 0  Tw (-) Tj
3.75 0  TD 0.6178  Tc -0.5241  Tw ( N\)) Tj
15.75 0  TD -0.1875  Tc 0  Tw (/N) Tj
11.25 -2.25  TD /F0 7.2656  Tf
0.0607  Tc (T) Tj
5.25 2.25  TD /F0 11.625  Tf
-0.0394  Tc -0.2419  Tw (] + \(1/N) Tj
36.75 -2.25  TD /F0 7.2656  Tf
0.0607  Tc 0  Tw (T) Tj
5.25 2.25  TD /F0 11.625  Tf
-0.1211  Tc 0.2149  Tw (\) ) Tj
6.75 -0.75  TD /F3 13.8047  Tf
0.0776  Tc 0  Tw (S) Tj
9 0.75  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
2.25 -0.75  TD /F0 15.2578  Tf
0.1762  Tc -0.2407  Tw ({ ) Tj
11.25 0  TD /F3 11.625  Tf
0.072  Tc 0  Tw (P) Tj
9.75 0.75  TD /F0 11.625  Tf
-0.0182  Tc -0.263  Tw ( [\(1 ) Tj
18.75 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD -0.4635  Tc -0.1927  Tw ( P) Tj
9 -2.25  TD /F0 7.2656  Tf
0.1454  Tc 0  Tw (Lj) Tj
6.75 2.25  TD /F0 11.625  Tf
-0.3227  Tc 0.0415  Tw (\) | s) Tj
15.75 -2.25  TD /F0 7.2656  Tf
0.2302  Tc 0  Tw (i) Tj
2.25 2.25  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
-229.5 -12  TD 0  Tw (                                                ) Tj
139.5 -1.5  TD /F0 7.9922  Tf
0.0498  Tc 0.0521  Tw (i=1     j=1) Tj
33 0  TD 0  Tc 0.252  Tw ( ) Tj
-172.5 -12  TD ( ) Tj
0 -11.25  TD /F0 11.625  Tf
0.0938  Tw ( ) Tj
8.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD ( ) Tj
10.5 0  TD ( ) Tj
11.25 0  TD -0.0134  Tw (       ) Tj
20.25 0  TD 0.0938  Tw ( ) Tj
1.5 0  TD 0.24  Tc -0.3963  Tw ( +  P) Tj
21.75 -3  TD /F0 7.2656  Tf
0.1454  Tc 0  Tw (Lj) Tj
6.75 3  TD /F0 11.625  Tf
-0.3418  Tc -0.3144  Tw (\(1 ) Tj
12 0  TD -0.1211  Tc 0  Tw (-) Tj
4.5 0  TD 0.2865  Tc -0.1927  Tw ( P) Tj
9.75 -3  TD /F0 7.2656  Tf
-0.4048  Tc 0  Tw (Sj) Tj
6 3  TD /F0 11.625  Tf
-0.0727  Tc 0.1665  Tw (\) | s) Tj
16.5 -3  TD /F0 7.2656  Tf
0.2302  Tc 0  Tw (i) Tj
2.25 3  TD /F0 11.625  Tf
0  Tc 0.0938  Tw ( ) Tj
2.25 -1.5  TD /F0 13.8047  Tf
0.1237  Tc 0.1751  Tw (}   ) Tj
18 1.5  TD /F0 11.625  Tf
-0.5182  Tc 0  Tw (\(9\)) Tj
12.75 0  TD 0  Tc 0.0938  Tw ( ) Tj
-229.5 -12  TD ( ) Tj
-13.5 -12.75  TD ( ) Tj
0 -12  TD ( ) Tj
0 -12.75  TD ( ) Tj
0 -12  TD ( ) Tj
ET
q 
193.5 0 0 172.5 338.25 591 cm 
/im1 Do

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