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-0.3598 Tc 0.6742 Tw (ABSTRACT: A computer analysis of bench stability has been developed to account for multiple occurrences of p) Tj
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( ) Tj
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-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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54 788.25 TD
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/F0 11.625 Tf
0 Tc 0.0938 Tw ( ) Tj
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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
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0 Tc -0.6563 Tw ( ) Tj
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164.25 0 TD 0 Tc 0.0938 Tw ( ) Tj
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201.75 0 TD -0.0221 Tc 0 Tw (s) Tj
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-0.2897 Tc (S) Tj
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121.5 0 TD 0 Tc 0.0938 Tw ( ) Tj
-121.5 -12 TD ( ) Tj
13.5 -12.75 TD ( ) Tj
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0 -12 TD ( ) Tj
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237.75 0 TD -0.0163 Tc 0 Tw (c-) Tj
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0 -12 TD ( ) Tj
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0 -12 TD ( ) Tj
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13.5 -12 TD ( ) Tj
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0 -267 TD ( ) Tj
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0.0607 Tc (T) Tj
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0.1762 Tc -0.2407 Tw ({ ) Tj
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