DOI.779/CJGE48 p p p 5 p 3 p p TU43 A 4548(4)8569 989 E-mal: shagguasq@gmal.com A modfed p- curve method cosderg rotato of sol resstace SHANGGUAN Sh-qg, LIU Hog-ju, PIAO Chu-de 3 (. Collage of Cvl Egeerg, Togj Uverst, Shagha 9, Cha;. Isttute of Evrometal Scece ad Egeerg, Ocea Uverst of Cha, Qgdao 66, Cha; 3. The School of Resource ad Earth Scece, Cha Uverst of Mg ad Techolog, Xuzhou 6, Cha) Abstract: The combed load of momets ad horzotal forces whch are ot coplaar at ple top geerall cause a complex ple deformato. Uder ths crcumstace, aalss s ofte performed b usg the three-dmesoal fte elemet method, whch s ot coveet ad practcal. To smplf the procedure, a modfed p- curve method s proposed 3D space uder the assumpto that sol resstace sprgs ca be rotated o the horzotal plae. A correspodg mathematcal programmg (optmzato) model s establshed for solvg ths method. Based o the prcple of the mmum potetal eerg, the geeralzed potetal eerg equato s selected as the objectve fucto whch the sol sprg actg work s represeted b the tegrated p- curve fuctos, ad the ple deformato compatblt codtos are selected as costrats, formg a olear programmg model. Ths model assumes fve DOFs (degrees of freedom) per ode, ad the p- effect s cosdered. The mathematcal programmg model s valdated through three examples. The results show that the assumptos the proposed method are reasoable, ad the model s feasble. Aalss of the sol resstace rotato o the horzotal plae s carred out uder b-drectoal ueveess bedg, ad the coordato of dsplacemet ad force s preseted effectvel the proposed model. Ke words: p- curve method; horzotal load; p- ; drecto of sol resstace; mathematcal programmg 6 6 [] XYZ XYZ p 476 3 3 *
8. p 57 [] [3] [4] Klar [5] 3 m p Matlock [6] p Reese [7] p [8] p XY [9] XY [] [] p p 5 XY Z 3 X Y plaxs3d embedded ple [] 3 Z p p p p p( ) p p( ) p () ( x,,) x XY p X Y p p( ) x () ( x,,) / p=p( ) p( ) p( ) p( ) p p( ) p( ) p( ) p p p( ) p Y p XOY X Y XOY FLAC 3D Plaxs 3D m p XOY 36
58 4 p p Fg. Geeral vew of phscal model Z ( p (3) l p EI l p p p ( )d (4a) p( )d (4b) ( p A p ( )d Qs l (5) Q s Matlock p A O Nell p A 5 Qs 5 Q p ( p ) EI A p( )d QsQz l (6) z ' + Z. 6 x ( A p( )d QsQz l (7) f ( x, ) x ( ) ( ) x EI EI x l l A p( )d Qs Qz (8) 78 X Y ( ) ( ) ( ) (9) x 9, j () j j
8. p 59 j l () j j () j j j / (3) j Z Z Z z x xj x j z (4) z' Z l z = z z cos ) l (5) x (6) ZOX j (7) ( x l (8) x j j / (9) j x x x x m A p( )d QsQz l () j j s.t. j l j j j j / x l x xj x j j j / j x x x x z z z cos ) l () p p. 4 3Pu 3 8 /3 8Y 5 Y 5 () Pu ( 8 Y5) 6 PY u 5 8 Y 5 p Kz Kz pu pu ( p u ) e e l Kz (3) 3[8]4b 3 p( )d BFGSDFP SPQ 7 Fg. Flow chart for solvg mathematcal model
53 4 MATLAB x l ( ) l+( + 3) l3 ( + ) l l+ + l+ l+ + l+ + l (4) 4 X MATLAB x MATLAB V 5 m Table Effect of amplfed ukow varables (5 uts of m-legth) mm BFGS 6 9 ~ < 9 3 7 ~ < 7 4. 6 5 ~ 5 ~ 4 5. 9 ~.~. XY 3 7 8 / p 7 7 R 7 4 = p 7 ( ) ( ) ( l l l Q ml Q m l Q m l A (5) p( )d m l/l 5 ( ) ( ) EI Qml Qml l l ( ) Qml A p( )d l EI EI [( C) C ] ( C) C l l EI [( C) C] A p( )d l (6) C 6 MATLABLINGO p p [3-4] 3. m l =8. m d =.8 me =.93 4 MPal =. md =.8 m E =.8 4 MPa l 3 =4.8 md 3 =.8 m E 3 =.8 4 MPa m= kn/m 3 F z =9. kn F x =65 kn MATLAB 73 m 43.5% p
8. p 53 Table Results of example [3] [4] 33.949 33.949 33.849 /mm 6.48 6.48 6.395 /mm 76.667 78.4 76.67 /mm / -3 7.568 7.69 7.67 8.54 8.9 8.74 /mm / 3.44.6.387 /knm 6687. 6737. 665 /kn 898. 883.45 p [5] p. Pa 46 m.74.9.35.733 m 4 3 kn/m 3 K 9 kn/m 3.55 4.5 3 p [5] p Table 3 Results of example /m /m /(MN m) /mm /().6 3.98 3.7 7. 3. 49.7 [5] 4 8.5 45 8.7 6 38.9 855 9.7.6 3.98 3.3.69 7. 3. 5..699 4 8.5 45 8.4.695 6 39 855 4.4.79 3 FLAC 3D FLAC 3D [6].6 m m m 7.6 MPa. MPa kpa 5 X X YOZ p p 6.5 cm 3 N p p FLAC 3D FISH p p 3 p MATLAB m p 4 p p b b f ( ) a ' a /( b) (b ) P u FLAC 3D p Fg. 3 P curves recorded ad aalzed FLAC 3D cm 5 FLAC 3D 3 MN m
53 4 p m Table 4 Fuctos of p curves obtaed b mathematcal regresso (upper m) /m a b R. 6.5467.9684 ~4 mm 6.5 6.736.999 ~4 mm 9.58 6.853.994 ~3 mm 3.8 7.993.994 ~3 mm 4.466 7.963.9943 ~ mm 5 5.6 7.87.9984 ~ mm 6 3.33 7.4.998 ~.5 mm 7.47 7.8769.986 ~ mm 8.4 7.8996.993 ~.4 mm 9 4.64 7.97.997 ~.3 mm 4.85 7.9836.998 ~.3 mm m Table 5 Stffess EI of ple (cotuum) obtaed b back aalss..(upper m) /(MN m) X /m.98 / -4 / 4 /( 3 MN m ) /( MN m ).58.63 8.7 3..66.86.3.9 5.8 3.89.75.64 3.33 9.9 3 4.4 4.9.96 3. 4.5 7.6 3 3.9 4.35 3.76 3.44 5.54 5.4 3 3.8 4. 3.99 3.76 6.49 3.6 3 3.8 3.65 3.89 4.8 7.36.88 3 3.7 3.6 3.67 4.44 8.8 8.75 4 3.3.44 3.48 4.84 9.98.7 4.9.86 3.38 5.9.78.9 4.3.36 3.34 5.7 3 X 46 kn X.86 MN/m 45 Fg. 5 Vector drecto of dsplacemet (egatve drecto of sol resstace) alog z drecto FLAC 3D FLAC 3D m 6 8 3 p 6 FLAC 3D 4 FLAC 3D 4 m 7 m Fg. 4 Ple dsplacemet alog z drecto of example FLAC 3D Fg. 6 Vector dagram of dsplacemet b FLAC 3D X
8. p 533 YOZ X 7X YOZ 8 X Y YOZ X Fg. 7 Ifluece of momet load o YOZ plae o X dsplacemet p 5 p p p p( )p 5 p( ) p p FLAC 3D 3 4 BFGS [] JB/T3 [S].. (JB/T3 Wd turbe geerator sstem desg requremets[s].. ( Chese)) [],,. [J]., 98, 3(): 7 4. (ZHANG We-qg, ZHAO X-hog, ZAI J-m. Fte laer aalss for laered ad elastc half-space uder arbtrar force sstem[j]. Chese Joural of Geotechcal Egeerg, 98, 3(): 74. ( Chese)) [3],,. YOZ Fg. 8 Ifluece of momet load o YOZ plae o vector drecto of dsplacemet (egatve drecto of sol resstace) [C]// ( ). 993: 795 8. (HE Guag-m, ZHANG Chog-we, WANG She. Elastc-plastc aalss of ple-sol-cap teracto wth a
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