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When bench stability ) Tj 0 -12.75 TD -0.4497 Tc 2.3247 Tw (is controlled primarily by rock failures that slide along) Tj 0 Tc -1.4063 Tw ( ) Tj 0 -12 TD -0.3237 Tc 2.2388 Tw (natural fractures \(such as plane shears and tetrahedral) Tj 0 Tc -1.4063 Tw ( ) Tj 0 -12.75 TD -0.3202 Tc 0.9972 Tw (wedges\), a stochastic computer analysis can be used to ) Tj 0 -12 TD -0.3809 Tc 4.2247 Tw (evaluate the) Tj 56.25 0 TD 0.0846 Tc 3.7591 Tw ( pro) Tj 22.5 0 TD 0.1875 Tc 0 Tw (b) Tj 5.25 0 TD -0.4287 Tc 4.085 Tw (ability of retaining specified catch) Tj 159 0 TD -0.1211 Tc 0 Tw (-) Tj -243 -12.75 TD -0.4508 Tc 1.9696 Tw (bench widths. If the original slope geometry plan and ) Tj 0 -12 TD -0.3543 Tc 0.448 Tw (blasting layout are intended to produce catch benches of ) Tj 0 -12.75 TD -0.5466 Tc 1.0494 Tw (a certain width, it is unlikely that such width actually will ) Tj 0 -12 TD -0.3604 Tc 0.6042 Tw (be retained after blasting and excavatio) Tj 172.5 0 TD -0.5165 Tc 0.6102 Tw (n when kinemat) Tj 68.25 0 TD -0.9264 Tc 0 Tw (i-) Tj -240.75 -12.75 TD -0.3781 Tc 4.8781 Tw (cally viable rock failure modes are present in the) Tj 0 Tc -0.6563 Tw ( ) Tj 0 -12 TD -0.3235 Tc 0.5244 Tw (benches. Consequently, rockfall hazard assessment and ) Tj 0 -12.75 TD -0.3591 Tc 3.2029 Tw (related slope stability safety issues must co) Tj 202.5 0 TD 0.1875 Tc 0 Tw (n) Tj 5.25 0 TD -0.3818 Tc 1.2256 Tw (sider the ) Tj -207.75 -12 TD -0.2305 Tc 3.6992 Tw (predicted, operational catch) Tj 129 0 TD -0.1211 Tc 0 Tw (-) Tj 3.75 0 TD -0.3713 Tc 3.465 Tw (bench geom) Tj 56.25 0 TD 0.0885 Tc 0 Tw (e) Tj 5.25 0 TD -0.451 Tc 3.5447 Tw (try and not) Tj 0 Tc -0.6563 Tw ( ) Tj -194.25 -12 TD -0.4806 Tc 0.1993 Tw (the originally d) Tj 63 0 TD 0.0885 Tc 0 Tw (e) Tj 5.25 0 TD -0.5337 Tc 0.6275 Tw (signed, id) Tj 41.25 0 TD -0.4057 Tc 0.4995 Tw (eal geometry.) Tj 59.25 0 TD 0 Tc 0.0938 Tw ( ) Tj -168.75 -12.75 TD ( ) Tj 11.25 0 TD -0.3011 Tc 1.3323 Tw ( In fractured rock masses, bench failures most co) Tj 223.5 0 TD -0.8327 Tc 0 Tw (m-) Tj -234.75 -12 TD -0.3486 Tc 0.8923 Tw (monly occur in the upper portion of the bench, because ) Tj 0 -12.75 TD -0.3618 Tc 0.9806 Tw (the fracture lengths required for failure are shorter here. ) Tj 0 -12 TD -0.3813 Tc 0.475 Tw (That is, small plane shears or wedges typically break out ) Tj 0 -12.75 TD -0.2891 Tc 1.1328 Tw (along the crest o) Tj 74.25 0 TD -0.3851 Tc 0.7601 Tw (f a bench, due to the higher probability ) Tj -74.25 -12 TD -0.4291 Tc 1.7229 Tw (that natural fractures will be long enough here to form ) Tj 0 -12.75 TD -0.5324 Tc 1.3761 Tw (kinematically viable fai) Tj 99 0 TD -0.2318 Tc 0 Tw (l) Tj 2.25 0 TD -0.3535 Tc 0.6972 Tw (ure modes. This characteristic is ) Tj -101.25 -12 TD -0.4086 Tc 1.2524 Tw (observed in mine benches, and it should be reflected in ) Tj 0 -12.75 TD -0.307 Tc 1.9007 Tw (the probabili) Tj 57 0 TD -0.0221 Tc 0 Tw (s) Tj 3.75 0 TD -0.3524 Tc 2.3962 Tw (tic outcome of a bench stabil) Tj 135.75 0 TD -0.574 Tc 1.1678 Tw (ity analysis. ) Tj -196.5 -12 TD -0.517 Tc 3.6108 Tw (Thus, the probability of retaining a full width on the) Tj 0 Tc -0.6563 Tw ( ) Tj 0 -12.75 TD -0.4209 Tc 1.2647 Tw (bench is not as high as the probability of retaining, say, ) Tj 0 -12 TD -0.407 Tc 0.8341 Tw (80% of the original bench width. Probabilities of retai) Tj 237.75 0 TD -0.7168 Tc 0 Tw (n-) Tj -237.75 -12.75 TD -0.346 Tc 2.4085 Tw (ing bench widths increase as the specified widths d) Tj 237.75 0 TD -0.0163 Tc 0 Tw (e-) Tj -237.75 -12 TD -0.0995 Tc 0.1932 Tw (crease. Only occa) Tj 83.25 0 TD -0.4085 Tc 0.5022 Tw (sionally do longer fractures o) Tj 126 0 TD 0.0885 Tc 0 Tw (c) Tj 5.25 0 TD -0.3969 Tc 0.1157 Tw (cur and ) Tj -214.5 -12.75 TD -0.4624 Tc 0.9653 Tw (allow for larger failures to affect much of the bench face ) Tj 0 -12 TD -0.4801 Tc 0.5738 Tw (and severely diminish the catch width.) Tj 164.25 0 TD 0 Tc 0.0938 Tw ( ) Tj -150.75 -12 TD -0.4095 Tc 1.7533 Tw (Minor bench instabilities and rockfalls adversely i) Tj 221.25 0 TD -0.8327 Tc 0 Tw (m-) Tj -234.75 -12.75 TD -0.3809 Tc 2.9496 Tw (pact mine safety in two key areas. First, as fai) Tj 226.5 0 TD -0.2318 Tc 0 Tw (l) Tj 2.25 0 TD -0.3418 Tc -0.3144 Tw (ures ) Tj 38.25 444.75 TD 0.1071 Tc 1.1116 Tw (break back a) Tj 60.75 0 TD -0.2399 Tc 1.4051 Tw (long the top of a bench, storage c) Tj 154.5 0 TD 0.0885 Tc 0 Tw (a) Tj 5.25 0 TD -0.3602 Tc -0.296 Tw (pacity ) Tj -220.5 -12.75 TD -0.4599 Tc 2.3037 Tw (for holding rockfall debris is significantly r) Tj 191.25 0 TD 0.0885 Tc 0 Tw (e) Tj 5.25 0 TD -0.1892 Tc 1.033 Tw (duced, and ) Tj -196.5 -12 TD -0.382 Tc 0.9258 Tw (falling rock from above may not be caught and retained ) Tj 0 -12 TD -0.2133 Tc 0.9321 Tw (on the bench. Second, as roc) Tj 135 0 TD 0.1875 Tc 0 Tw (k) Tj 6 0 TD -0.4819 Tc 0.8757 Tw (fall debris spills onto the ) Tj -141 -12.75 TD -0.331 Tc 3.4247 Tw (bench below, it reduces the storage capacit) Tj 206.25 0 TD -0.4191 Tc 2.0128 Tw (y of that ) Tj -206.25 -12 TD -0.5338 Tc 4.6775 Tw (bench and may even trigger multiple) Tj 176.25 0 TD -0.1211 Tc 0 Tw (-) Tj 4.5 0 TD -0.395 Tc 1.4888 Tw (bench failures. ) Tj -180.75 -12.75 TD -0.3722 Tc 1.591 Tw (Thus, the capability to pr) Tj 113.25 0 TD 0.0885 Tc 0 Tw (e) Tj 5.25 0 TD -0.4818 Tc 1.2006 Tw (dict the size of bench failures ) Tj -118.5 -12 TD -0.4078 Tc 1.4015 Tw (and their impact on the catch width would provide key ) Tj 0 -12.75 TD -0.4201 Tc 0.6805 Tw (input to designing the bench geometry \(i.e. bench height, ) Tj 0 -12 TD -0.399 Tc 0.2427 Tw (face angle, and width\)) Tj 95.25 0 TD 0.0938 Tc 0 Tw (.) Tj 3 0 TD 0 Tc 0.0938 Tw ( ) Tj -84.75 -12.75 TD -0.392 Tc 2.5215 Tw (The National Institute for Occupational Safety and ) Tj -13.5 -12 TD -0.2379 Tc 4.2317 Tw (Health \(NIOSH\) Spokane Research Laboratory ) Tj 3.6289 Tc 0 Tw (f) Tj 236.25 0 TD 0.0332 Tc (o-) Tj -236.25 -12.75 TD -0.4241 Tc 1.2678 Tw (cuses on safety and health issues in the mining i) Tj 211.5 0 TD 0.1875 Tc 0 Tw (n) Tj 5.25 0 TD -0.2813 Tc 0.375 Tw (dustry. ) Tj -216.75 -12 TD -0.384 Tc 1.8111 Tw (A project began several years ago aimed at mitigating ) Tj 0 -12.75 TD -0.3476 Tc 2.4414 Tw (rockfall hazards in open) Tj 110.25 0 TD -0.1211 Tc 0 Tw (-) Tj 4.5 0 TD -0.4321 Tc 2.7758 Tw (pit mines and quarri) Tj 92.25 0 TD -0.2012 Tc 1.2949 Tw (es. One ) Tj -207 -12 TD -0.3575 Tc 1.6179 Tw (aspect of this project has involved the development of ) Tj 0 -12.75 TD -0.39 Tc 1.3409 Tw (computer software to analyze bench stability and back) Tj 242.25 0 TD -0.1211 Tc 0 Tw (-) Tj -242.25 -12 TD -0.2263 Tc 5.5701 Tw (break characteri) Tj 76.5 0 TD -0.0221 Tc 0 Tw (s) Tj 4.5 0 TD -0.391 Tc 5.9848 Tw (tics in a hazard) Tj 81.75 0 TD -0.1211 Tc 0 Tw (-) Tj 3.75 0 TD -0.2016 Tc 5.5453 Tw (based, stochastic) Tj 0 Tc 0.0938 Tw ( ) Tj -166.5 -12 TD -0.2984 Tc 3.3922 Tw (framework. One computer pr) Tj 143.25 0 TD 0.1875 Tc 0 Tw (o) Tj 6 0 TD -0.5644 Tc 3.6581 Tw (gram analyzes plane) Tj 93 0 TD -0.1211 Tc 0 Tw (-) Tj -242.25 -12.75 TD -0.4507 Tc 1.1445 Tw (shear failure modes in a two) Tj 125.25 0 TD -0.1211 Tc 0 Tw (-) Tj 4.5 0 TD -0.549 Tc (dimension) Tj 43.5 0 TD -0.3282 Tc 0.422 Tw (al framework by ) Tj -173.25 -12 TD -0.6515 Tc 2.9952 Tw (simulating plane) Tj 70.5 0 TD -0.1211 Tc 0 Tw (-) Tj 3.75 0 TD -0.3632 Tc 2.1712 Tw (shear fractures in the bench and then ) Tj -74.25 -12.75 TD -0.4243 Tc 2.393 Tw (calculating the pro) Tj 83.25 0 TD 0.1875 Tc 0 Tw (b) Tj 6 0 TD -0.3901 Tc 1.9838 Tw (ability of stability for each one, as ) Tj -89.25 -12 TD -0.371 Tc 0.4647 Tw (well as identifying the corresponding backbreak distance ) Tj 0 -12.75 TD -0.5032 Tc 2.0219 Tw (on the bench. By repeating the simulation many times ) Tj 0 -12 TD -0.5573 Tc 3.1511 Tw (for a given benc) Tj 77.25 0 TD -0.4465 Tc 2.2903 Tw (h, the probability of retaining various ) Tj -77.25 -12.75 TD -0.3145 Tc 0.5958 Tw (bench widths can be estimated. Another computer pr) Tj 236.25 0 TD 0.0332 Tc 0 Tw (o-) Tj -236.25 -12 TD -0.406 Tc 2.3748 Tw (gram analyzes three) Tj 90 0 TD -0.1211 Tc 0 Tw (-) Tj 4.5 0 TD -0.5229 Tc 1.9292 Tw (dimensional wedges by simulating ) Tj -94.5 -12.75 TD -0.4017 Tc 0.7455 Tw (fractures from two fracture sets and conducting a similar ) Tj 0 -12 TD -0.0495 Tc 0 Tw (back) Tj 21.75 0 TD -0.1211 Tc (-) Tj 3.75 0 TD -0.2808 Tc 0.3745 Tw (break analysis. ) Tj 68.25 0 TD 0 Tc 0.0938 Tw ( ) Tj -80.25 -12.75 TD -0.2962 Tc 2.8899 Tw (A stochastic \(or probabilistic\)) Tj 138 0 TD -0.1895 Tc 1.7832 Tw ( approach is needed ) Tj -151.5 -12 TD -0.3251 Tc 2.3355 Tw (because rock fractures in a bench face are numerous ) Tj 0 -12.75 TD -0.4739 Tc 2.2343 Tw (and too difficult to analyze individually. For the co) Tj 234.75 0 TD -1.5827 Tc 0 Tw (m-) Tj -234.75 -12 TD -0.3087 Tc 2.2775 Tw (puter model to generate realistic fracture pa) Tj 202.5 0 TD -0.2318 Tc 0 Tw (t) Tj 3 0 TD -0.3294 Tc 1.1732 Tw (terns and ) Tj -205.5 -12.75 TD -0.3405 Tc 3.3092 Tw (subsequent slope failure modes, representative ge) Tj 236.25 0 TD 0.0332 Tc 0 Tw (o-) Tj -236.25 -12 TD -0.5255 Tc 2.8693 Tw (technical input inform) Tj 96 0 TD -0.3311 Tc 1.9248 Tw (ation must be available. This i) Tj 141 0 TD -0.7168 Tc 0 Tw (n-) Tj -237 -12 TD -0.4076 Tc 0.7513 Tw (formation often can be obtained readily from a thorough ) Tj 0 -12.75 TD -0.4707 Tc 0.1895 Tw (geotechnical site investigation.) Tj 129.75 0 TD 0 Tc 0.0938 Tw ( ) Tj -396.75 726.75 TD /F0 17.4375 Tf -0.0252 Tc -0.1069 Tw (Computer modeling of catch benches to mitigate rockfall hazards in open ) Tj 0 -20.25 TD -0.009 Tc 0.1496 Tw (pit mines) Tj 63 0 TD 0 Tc 0.1406 Tw ( ) Tj -63 -34.5 TD /F0 13.8047 Tf -0.46 Tc 0.3838 Tw (Stanley M. Miller) Tj 92.25 0 TD 0 Tc 0.2988 Tw ( ) Tj -92.25 -11.25 TD /F1 11.625 Tf -0.0219 Tc 0.0085 Tw (Geological Engineering Program, University of Idaho, Moscow, Idaho) Tj 329.25 0 TD 0 Tc 0.0938 Tw ( ) Tj -329.25 -21.75 TD /F0 13.8047 Tf -0.3609 Tc 0.6597 Tw (Jami M. Girard) Tj 81.75 0 TD 0 Tc 0.2988 Tw ( ) Tj -81.75 -11.25 TD /F1 11.625 Tf -0.027 Tc 0.1207 Tw (NIOSH Spokane Research Laboratory, Spokane, Washington) Tj 284.25 0 TD 0 Tc 0.0938 Tw ( ) Tj -284.25 -21 TD /F0 13.8047 Tf -0.2924 Tc 0.5912 Tw (Edward McHugh) Tj 93 0 TD 0 Tc 0.2988 Tw ( ) Tj -93 -12 TD /F1 11.625 Tf -0.0948 Tc 0 Tw (NIOSH) Tj 33.75 0 TD -0.0193 Tc 0.113 Tw ( Spokane Research Laboratory, Spokane, Washington) Tj 250.5 0 TD 0 Tc 0.0938 Tw ( ) Tj -284.25 -21 TD /F0 13.8047 Tf 0.2988 Tw ( ) Tj 0 -15 TD ( ) Tj 0 -11.25 TD /F1 11.625 Tf 0.0938 Tw ( ) Tj ET q 40.5 585 504 12 re h W n BT 40.5 588 TD /F0 11.625 Tf -0.3598 Tc 0.6742 Tw (ABSTRACT: A computer analysis of bench stability has been developed to account for multiple occurrences of p) Tj ET Q q 543.75 585 10.5 12 re h W n BT 543.75 588 TD /F0 11.625 Tf 0.0332 Tc 0 Tw (o-) Tj ET Q BT 40.5 576 TD /F0 11.625 Tf -0.4044 Tc 1.2482 Tw (tential slope) Tj 52.5 0 TD -0.1211 Tc 0 Tw (-) Tj 4.5 0 TD -0.9617 Tc (failu) Tj 17.25 0 TD -0.3281 Tc 0.6361 Tw (re modes in discontinuous rock masses. Bench) Tj 208.5 0 TD -0.1211 Tc 0 Tw (-) Tj 4.5 0 TD -0.2993 Tc 0.2859 Tw (scale plane shears and tetrahedral wedges are sim) Tj 216.75 0 TD -0.7168 Tc 0 Tw (u-) Tj -504 -12.75 TD -0.3925 Tc 0.5545 Tw (lated and stochastically analyzed to estimate the probability of retaining specified catch) Tj 376.5 0 TD -0.1211 Tc 0 Tw (-) Tj 4.5 0 TD -0.3669 Tc 0.2732 Tw (bench widths. This geotechn) Tj 126 0 TD -0.9264 Tc 0 Tw (i-) Tj -507 -12 TD -0.5869 Tc 2.8056 Tw (cal information is useful in designing ) Tj 2.4375 Tc 0 Tw (b) Tj 176.25 0 TD -0.4474 Tc 1.8536 Tw (ench configurations to improve pit) Tj 153.75 0 TD -0.1211 Tc 0 Tw (-) Tj 4.5 0 TD -0.4435 Tc 1.5372 Tw (slope stability and help alleviate rockfall ) Tj -334.5 -12.75 TD -0.2074 Tc 0 Tw (hazards.) Tj 36.75 0 TD 0 Tc 0.0938 Tw ( ) Tj ET endstream endobj 9 0 obj 13100 endobj 10 0 obj<> endobj 11 0 obj<> endobj 12 0 obj<>/ProcSet 2 0 R>>>> endobj 13 0 obj<>stream q 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 0.1875 Tc 0 Tw (2) Tj 6 0 TD 0 Tc 0.0938 Tw ( ) Tj 7.5 0 TD -0.2342 Tc 0.3279 Tw (GEOTECHNICAL INPUT) Tj 123.75 0 TD 0 Tc 0.0938 Tw ( ) Tj -137.25 -24.75 TD -0.4283 Tc 0.7363 Tw (Stability analysis of rock failure modes requires inform) Tj 237.75 0 TD -0.0163 Tc 0 Tw (a-) Tj -237.75 -12.75 TD -0.3641 Tc 2.4936 Tw (tion on the slope geometry, the physical pro) Tj 204.75 0 TD 0.1875 Tc 0 Tw (p) Tj 6 0 TD -0.4204 Tc 0.5142 Tw (erties of ) Tj -210.75 -12 TD -0.1211 Tc 0 Tw (r) Tj 3.75 0 TD -0.3665 Tc 0.929 Tw (ock discontinuities that define the modes, and local e) Tj 234 0 TD -0.7168 Tc 0 Tw (n-) Tj -237.75 -12.75 TD -0.3368 Tc 0.3234 Tw (vironmental conditions \(such as ground water pore pre) Tj 238.5 0 TD -0.0716 Tc 0 Tw (s-) Tj -238.5 -12 TD -0.3867 Tc 3.5742 Tw (sure\). Slope geometry is specified by the engineer,) Tj 0 Tc -0.6563 Tw ( ) Tj 0 -12.75 TD -0.2714 Tc 0.2969 Tw (based on actual field conditions or on a proposed slope ) Tj 0 -12 TD -0.4125 Tc 1.5063 Tw (design plan. Other input data usuall) Tj 162 0 TD -0.3956 Tc 0.8643 Tw (y must be obtained ) Tj -162 -12.75 TD -0.3809 Tc 0.4746 Tw (by geotechnical site investigation procedures.) Tj 196.5 0 TD 0 Tc 0.0938 Tw ( ) Tj -196.5 -12 TD ( ) Tj 0 -12.75 TD -0.0938 Tc 0.1875 Tw (2.1 ) Tj 20.25 0 TD /F1 11.625 Tf -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 ET endstream endobj 14 0 obj 18240 endobj 15 0 obj<> endobj 16 0 obj<> endobj 17 0 obj<> endobj 18 0 obj<> endobj 19 0 obj<>/ProcSet 2 0 R>>>> endobj 20 0 obj<>stream q 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 endstream endobj 21 0 obj 19745 endobj 22 0 obj<> endobj 23 0 obj<> endobj 24 0 obj<>/XObject<>/ProcSet 2 0 R>>>> endobj 25 0 obj<>stream q 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 endstream endobj 26 0 obj 12081 endobj 27 0 obj<>stream ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿþª?ÿÿÿÿ?ÿÿÿ?ÿúúÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ? ¹ú²ú¾«Æ·¾Ã¾Ã¾Ã¾Ã¾ÃÒ»¼¶Ã«Æ¬