35 4 Vol.35 No.4 2016 4 Chinese Journal of Rock Mechanics and Engineering April2016 FLAC 3D ( 266590) FLAC 3D CABLE ()() U(i)U max (i) CABLE Fish FLAC 3D (1) (2) () (3) FLAC 3D FLAC 3D CABLE TU 43 A 10006915(2016)04075315 Implementation of bolt broken failure in FLAC 3D and its application LI WeitengYANG NingLI TingchunWANG GangMEI YuchunXUAN Chao (Shandong Provincial Key Laboratory of Civil Engineering Disaster PreventionShandong University of Science and Technology QingdaoShandong 266590China) AbstractIn order to solve the problem that CABLE element in FLAC 3D cannot be broken failurea broken criterion U(i)U max (i) was proposed and a modified mechanical model of CABLE element was established. The broken failure function was added to the modified model and the new model was embedded in the main program of FLAC 3D with the FISH language programming. The broken failure of bolt was realized at the single element leveland the macroscopic broken was finally achieved from parts to whole spontaneously. The tensile tests of bolt bar and the roadway bolt-shotcrete support tests were carried out. The load-displacement curve of the cable bar using the modified model presented the broken failure characteristicwhich was in accordance with the actual mechanical behavior of bolt rodand the quantitative broken effect was achieved and the response was sensitive. When the ground stress exceeded a certain valuethe modified bolts and anchor cables broke in the surrounding rockthe mechanical behavior conformed to the broken failure mechanism of bolt or cable anchor in the practical engineering. The simulation accuracy was improved. The application range of FLAC 3D was expandedand the simulation capability was enhanced. Key wordsgeotechnical engineeringflac 3D boltscable anchorscable elementbrokenmodified model 2015011920150318 (51279096)(BS2015NJ003) (2015RCJJ063) Supported by the National Natural Science Foundation of China(Grant No. 51279096)Foundation for Outstanding Young Scientist in Shandong Province(Grant No. BS2015NJ003) and Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents(Grant No. 2015RCJJ063) (1987)2004 E-maillwteng2007@163.com DOI10.13722/j.cnki.jrme.2015.0060
754 2016 1 () [1-4] ()() [5-11] 1 [81214] () [12-15] () () () FLAC 3D [16-19] CABLE J. Nemcik [4] FLAC 2D [20] FLAC 2D 3.3 FLAC 2D CABLE 2 FLAC 3D CABLE (a) (b) 2.1 CABLE CABLE FLAC 3D 2 [21-22] (c) (d) 1 [81214] Fig.1 Broken cable anchors and bolts [81214] m FLAC 3D CABLE () m m () () 2 CABLE [21-22] Fig2 Basic composition and mechanical model of CABLE element [21-22] CABLE CABLE 2 (Node)
35 4 FLAC 3D 755 (element) 3 [21-22] x x Node 1 Node 2 F tmax F() A EA z u 1 U() O 1 U() Node 1 y x F cmax x u 2 Node 2 u s F() 4 CABLE Fig.4 Mechanical model of CABLE element 3 CABLE [21-22] Fig.3 CableSEL coordinate system and relative shear displacement between cable and rock [21-22] KU ( F Fmax ) F Fmax ( FFmax ) (2) CABLE Node Node CABLE ( 2) u s ( 3) Node 3 CABLE 2 2 u 1 u 2 CABLE FLAC 3D [21] 2.2 CABLE CABLE 4 KU ( F Fmax ) F 0 ( FF ) max (1) U U F F F max CABLE 2 (1) (OA ) CABLE K AE K (3) L K A E L (2) ( A ) CABLE F max ( F tmax F cmax ) K 0 CABLE 4 FLAC 3D F max ()() () 2.3 CABLE FLAC 3D CABLE
756 2016 (1) CABLE (2) (3) 3 CABLE 3.1 CABLE () 0() 0 () FLAC 3D CABLE () Ui () U () i U(i)() max (CABLE element) FLAC 3D U max (i) CABLE 5 3 U() KU ( F F U U ) max max max max max F F ( F F U U ) 0 ( UU ) F tmax U cmax max F() A EA 1 O F cmax B C U() U tmax F() 5 FLAC 3D -CABLE Fig.5 Modified model of CABLE element in FLAC 3D (4) (1) (OA ) (2) (AB ) (3) ( B )() F K ΔF () ()() K 0 () 0 CABLE () 3.2 3.2.1 6 CABLE CID = j CABLE ( CABLE FLAC 3D ) FLAC 3D CABLE FLAC 3D i = i+1 stepi F j K j = 0 F jmax CABLE CABLE K j = 0F tj = 0 U ij (j = 1 n) 6 CABLE Fig.6 Implementation process of CABLE element modification U ij U jmax (1) i (step ii = 123) ( FLAC ) (2) K j 0 K j = 0 i = i+1 K j = 0 CABLE F j F jmax ( 1 0.9)( j CABLE ) i = i+1 F j λf jmax CABLE
35 4 FLAC 3D 757 (3) CABLE CABLE U ij (i j CABLE ) U ij U jmax CABLE K j = 0F j = 0 FLAC 3D CABLE U ij U jmax FLAC 3D CABLE CABLE U ij U ijmax K j = 0F j = 0( 5 B ) CABLE CABLE CABLE (CID) (ID) 3.2.2 FLAC 3D Fish CABLE 1 1 sc_length CABLE Fish U ij () 1 FLAC 3D CABLE Table 1 Some used element variables of CABLE element FLT sc_length(sc_ptr cp) no FLT sc_emod(sc_ptr cp) yes FLT sc_xcarea(sc_ptr cp) yes FLT sc_yten(sc_ptr cp) yes 1 sc_xcarea (SC_PTR cp) sc_emod(sc_ptr cp) sc_yten (SC_PTR cp) FLAC 3D xcarea = 0 emod = 0 yten = 0() () 4 4.1 1 22 mm 2 m 266 kn 25% 7 2.1 m 42 0.05 m (CID) 142 1 (CID1 CID42) 2 m(cid241) CID F 1 2 3 4 39 40 41 42 2m 0.05 m (Node) 7 Fig.7 Diagram of tensile test model of bolt bar 3.8 10 4 m 2 2.0 10 11 Pa 266 kn 2 CABLE ( ) CABLE () U max = 0.05 (1+0.25) = 0.062 5 m 1 10 5 m/step 15 000 8 CID2 9 10 11 15 000 12 CID2 8 2 3
758 2016 300 250 /kn 200 150 100 50 0 0 25 50 75 100 /mm 125 8 Fig.8 Load-displacement curves of bolts 12 (CID = 2) Fig.12 Curves of axial force with length of element CID is 2 9 Fig.9 Curves of element length with steps of some elements on bolts 10 Fig.10 Curves of axial force of some elements on bolts with loading steps 11 Fig.11 Axial force and length of each elements on bolts 40.74 mm 0 0 910 (step 0step 710) 710 CID2 266 kn CID2 4 200 CID2 (62.5 mm) 0( 10) CID2 0 CID2 11 CID2 115.3 mm 131% 266 kn CID2 178.8 mm( 62.5 mm 12) 0 UU max U max 62.5 mm 12 U 62.5 mm 0 4.2 2 1 () ()
35 4 FLAC 3D 759 2 4.2.1 2 12 1 16 CABLE 2 A1A6 CABLE 6 530 MPa 2 Table 2 Numerical experimentation schemes /MPa 1 5 2 10 3 15 4 20 5 25 6 30 A1 5 A2 10 A3 15 A4 20 A5 25 A6 30 13 0.8 m 0.9 m19 / 0.9 m 40 kn 3 1.6 m 2 m 100 kn C15 100 mm 8 mm G1G19 S1S3 4.2.2 40 m 40 m 0.8 m( ) 2.5 m 1.5 m 14(a) 3 2 3 4 100 mm 14(b)(d) 3 13 (mm) Fig.13 Profile of support scheme(unitmm)
760 2016 351 337 352 338 339 LINK 340 341 342 343 344 345 346 347 348 349 350 351 366 352 367 353 368 354 369 355 370 356 371 357 372 358 373 359 374 360 375 (a) (b) (c) CID LINK (d) 14 Fig.14 Numerical model of roadwaysurrounding rock and support of test scheme 3 Table 3 Mechanical parameters of surrounding rock and concrete spray layer E/MPa t /MPa c/mpa /() 2 500 0.27 0.8 1.0 28 25 500 0.20 2.0 3.0 50 50 000 0.25 4 Table 4 Strain softening parameters of mudstone 5 Table 5 Parameters of bolt and cable anchor S/cm 2 F s /kn E/GPa P/kN /% 3.80 700 200 100 5 3.80 266 200 40 20 6 0.9 m 1.4 m 2 m 3.9 m c/mpa /() 0 1.00 28.0 1 10 4 0.95 27.5 2 10 4 0.90 27.0 3 10 4 0.80 26.0 1 0.80 26.0 6 Table 6 Parameters of bolt and cable anchor models / /m / / / 60 0.1 1 39 20 24 0.1 1 14 9 4.2.3 (1) FLAC 3D -CABLE ( 0.4 m) 13 14 5 (2) 24 0.1 m 60 0.1 m ( ) (3) ( 14(c) CID = 337 ) 7 7 Table 7 Anchorage agent parameters /MPa /MPa /() 10 000 10 000 25 0 0 0 20 2 45
35 4 FLAC 3D 761 (4) ( 14(d) ) 3 (5) 7 CABLE LINK LINK LINK 14(b) LINK LINK 14(c) 337360 CID 351375 LINK CID337 LINK351 LINK352 LINK366LINK375 LINK353LINK365 (6) 7 (7) 5 14(d) 100 kn (8) 5 0.1 m U max = 0.12 m U max = 0.105 m 4.2.4 FLAC 3D 1 10 5 8 15 16 () 17 F max 8 Table 8 Statistics of calculation results of deformation and plastic zone volume of each schemes /mm /mm /mm /m 3 1 6.83 7.72 9.3 1.15 2 25.80 31.8 31.5 32.66 3 55.90 72.3 68.2 56.36 4 97.80 134.9 118.2 83.48 5 165.30 227.5 195.9 113.00 6 257.10 352.0 288.2 138.99 A1 6.80 7.7 9.3 1.15 A2 27.50 32.9 31.6 34.23 A3 58.80 75.5 68.6 58.25 A4 108.60 151.1 131.3 91.02 A5 187.70 254.5 209.6 124.07 A6 289.00 409.5 303.8 157.97 /mm 450 400 350 300 250 200 150 100 50 0 0 5 10 15 20 25 30 /MPa 15 Fig.15 Curves of maximum deformation of roadway varied 1.20 1.15 1.10 1.05 with ground stress 1.00 5 10 15 20 25 30 /MPa 16 Fig.16 Curves of modified influence coefficient varied with ground stress 4.2.4.1 (1) 5 MPa
762 2016 5 MPaF max = 484.3 kn (a) 1 10 MPaF max = 447.8 kn (b) 2 15 MPaF max = 468.2 kn (c) 3 5 MPaF max = 484.3 kn (d) A1 10 MPaF max = 251.6 kn (e) A2 15 MPaF max = 266 kn (f) A3 20 MPaF max = 519.8 kn (g) 4 25 MPaF max = 611.5 kn (h) 5 30 MPaF max = 685.5 kn (i) 6 20 MPaF max = 266 kn (j) A4 25 MPaF max = 114.6 kn (k) A5 17 Block State None shear-n shear-p shear-n shear-p tension-p shear-p shear-p tension-p 30 MPaF max = 166.9 kn (l) A6 Fig.17 Deformation shapeplastic zone and axial force diagram of bolt and cable anchor
35 4 FLAC 3D 763 1.0 17(a)(d) (2) 10 MPa 1.0 ( 17) (3) () 15 4.2.4.2 (1) 25 MPa 17(h) 17(k) 0 0 () (2) 17 5 MPa 10 MPa 15 MPa 20 MPa ()25 MPa () (3) 4.2.4.3 5 A5 18 19 5 A5 ( ) G3 CID2 CID19 (CID 1 ) S2 CID2 CID50 (CID 1 ) (a) (b) 18 ( 5) Fig.18 Curves of axial force and length of some CABLE elements varied with steps in the original model scheme 5 (a) (b) 19 ( A5) Fig.19 Curves of axial force and length of some CABLE elements varied with steps in the modified model scheme A5
764 2016 20 220.5 kn 221.9 kn (100 ) 170.6 mm 525.5 kn 150.3 mm 265.8 kn /kn 300 250 200 150 100 50 0 50 0 5 10 15 20 25 CID 20 25 MPa 3 # Fig.20 Axial forces of each elements on bolt #3 when geostress is 25 MPa 1819 (100 ) 211 105 mm 700 kn 0 311 120 mm 266 kn 0 0 309.2 271.9 mm 3.2 81.2 kn 2021 5 A5 G3 2 130.6 141.6 mm 30.6% 41.6% 20% 0 /mm 350 300 250 200 150 100 50 0 0 5 10 15 20 25 CID 21 25 MPa G3 Fig.21 Length of each element on bolt G3 when geoseress is 25 MPa 290.9 mm 120 mm 4.2.4.4 22 A5 ( ) A5 (G17/ G18)S2S1G19G2G4G3(G6/B7) G5G1 22 ( A5) Fig.22 Curves of the axial force of bolts and cable varied with steps in scheme A5 17
35 4 FLAC 3D 765 5 5.1 FLAC 3D CABLE (1) (2) 3 12 (3) (4) +++ () FLAC 3D 5.2 CABLE () 20 CID2 0 (1) 3 1 2 (2) () (3) ()U max U max = U max +ΔU (4) () (5) 18 ( 19) 200 (6)
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