Verification Analysis of Spread Footing

Transcription

1 Vrifiation manual o. Upat 03/016 Vrifiation Analysis of Spra Footing Program: Fil: Spra Footing Dmo_vm_n_0.gpa In this vrifiation manual you will fin a han-ma vrifiation analysis of aring apaity of a spra footing for rain onitions in a prmannt sign situation. sults of th han-ma alulations ar ompar with th rsults from th EO5 Spra Footing program. Trms of frn: In Figur 1, an xampl of a ntri spra footing is shown. Th spra footing has a with h m, a lngth l. 0 m an a hight t m. Th footing ottom is in a pth 1. 0 m. Th arth oy is form of silty san (SM) an its trrain is ajust in a 7 inlination. Th proprtis of soil (fftiv valus) ar shown in Tal 1. In Figur, a loa ating on th spra footing is shown an its valus ar in Tal. Th spra footing is ovr with soil of unit wight 3 z 0.00 k/ m aftr th ralization. Th spra footing is ma from rinfor onrt with unit 3 wight 3.00k/ m. Th imnsions of th olumn on th spra footing ar x m an y m. Th aring apaity is alulat using th stanar approah. Th vrifiation mthoology is on aoring to EC 1997 with sign approah rution of ations an rsistans. In this xampl th slf-wight in favour 1.00 an isfavour 1.35 is alulat. Figur 1 Top viw an ross-stion in x of spra footing 1

2 Soil Unit wight [k/m 3 ] Saturat unit wight [k/m 3 ] sat Angl of intrnal frition [ ] f Cohsion of soil [] f Poisson s ration [-] SM Tal 1 Soil proprtis haratristi fftiv valus Figur Loa on th spra footing Dsign valu k H x k H y k km M x km Ys Tal Valus of th loa M y 1. Th Calulation with Slf-Wight ating Favouraly Calulation of th fftiv ara of th spra footing. An ntri loa ats on th spra footing. Thrfor, th fftiv ara of th spra footing has to alulat. Charatristi wight of th spra footing: h t k

3 Charatristi wight of th ovrurn: ( t) h ( t) ( ) ( ) Z x y z Z k Calulation of th loa ntriity at th footing ottom 1.00 : M x H y t y m Z In th program, ntriity is alulat as a ratio. l y y, ratio 0.11 Vrifiation of th loa ntriity: x, ratio alw - max. ntriity in irtion of th as lngth y, ratio alw - max. ntriity in irtion of th as with t, ratio x. ratio y, ratio - max. ovrall ntriity t, ratio alw Th ntriity of th loa is SATISFACTOY. sult from th EO5 Spra Footing program: x, ratio alw y, ratio alw t, ratio alw, SATISFACTOY Calulation of th fftiv ara of th spra footing (a rtangular shap of th fftiv ara is assum): ff m l ff l m A ff ff l ff m Calulation of th vrtial aring apaity. 3

4 A stanar analysis propos y J. Brinh Hansn is us. Coffiints of aring apaity: tg 45 tg( ) tg tg(31.5) ( 1) ot g( ) ( ) ot g(31.5) ( 1) tg( ) 1,5 ( ) tg(31.5) Coffiints of th shap of th founation: Du to th ntriity, th following situation ourr: l ff wr us. s sin( ) 1 sin( 31.5) l lff ff. Thrfor, lff an s l s l Coffiints of influn of th founation pth: sin( ) sin( 31.5) Coffiints of influn of th slop loa: - angl of viation of th rsultant for from th vrtial irtion H y 10 artg artg 6. Z i i i (1 tg( )) (1 tg(6.794)) Coffiints of slop of th footing ottom: - slop of th footing ottom (1 tg( )) (1 0 tg(31.5))

5 (1 ) (1 1) tg( ) 1 tg(31.5) Coffiints of influn of th slop of th trrain: - slop of th trrain g g tg( ) 1 0.5tg(7.0) g Euivalnt uniform loa aounting for th influn of th founation pth: Calulation of th vrtial aring apaity an its rution y offiint : s i g 0 s i g s V i g V sult from th EO5 Spra Footing program: Extrm ontat strss at th footing ottom: Z A ff sult from th EO5 Spra Footing program: Usag: 5

6 V u %, SATISFACTOY sult from th EO5 Spra Footing program: V 85.8 %, SATISFACTOY u Calulation of th horizontal aring apaity. Th arth rsistan is takn as prssur at rst. Coffiint of arth prssur at rst in a rain soil: K 1 sin( ) 1 sin( 31.5) Prssur at rst in th axis on th uppr an lowr g of th spra footing: t) K ( ) ( 0 z K Valu of arth rsistan: 1 1 S p 0 01 t 01 t sultant vrtial for on th footing ottom: Q V Z k k Horizontal aring apaity an its rution y offiint : a A ff - is xlu for rain onitions (aoring to EC 1997) H h Q tg( ) a H A ff S p Q tg( ) S p tg(31.5) h k 1.10 H sult from th EO5 Spra Footing program: h Usag: V u H h %, SATISFACTOY sult from th EO5 Spra Footing program: V 1. %, SATISFACTOY u 6

7 . Th Calulation with Slf-Wight Ating Unfavouraly Calulation of th fftiv ara. Th haratristi wights of th spra footing an th ovrurn ar th sam as in th alulation with slf-wight in favor. Charatristi wight of th spra footing: k Charatristi wight of th ovrurn: Z k Calulation of th loa ntriity at th footing ottom 1.35 : M x H y t y m Z In th program, ntriity is alulat as a ratio. l y y, pom Vrifiation of th loa ntriity: x, pom alw - max. ntriity in irtion of th as lngth y, pom alw - max. ntriity in irtion of th as with t, pom x. pom y, pom - max. ovrall ntriity t, pom alw Th ntriity of th loa is SATISFACTOY. sult from th EO5 Spra Footing program: Th EO5 Spra Footing program shows th vrifiation of a loa that auss gratr ntriity. In this as a loa with slf-wight in favour is vrifi. Calulation of th fftiv ara of th spra footing (a rtangular shap of th fftiv ara is assum): ff m l ff l m A ff ff l ff m 7

8 Calulation of th vrtial aring apaity. Coffiints of aring apaity: tg 45 tg( ) tg tg(31.5) ( 1) ot g( ) ( ) ot g(31.5) ( 1) tg( ) 1.5 ( ) tg(31.5) Coffiints of th shap of th founation: Du to th ntriity, th following situation ourr: l ff wr us. s sin( ) 1 sin( 31.5) l lff ff. Thrfor, lff an s l s l Coffiints of influn of th founation pth: sin( ) sin( 31.5) Coffiints of influn of th slop of th loa: - angl of viation of th rsultant for from th vrtial irtion H y 10 artg artg 6. Z i i i (1 tg( )) (1 tg(6.574)) Coffiints of th slop of th footing ottom: -slop of th footing ottom

9 (1 tg( )) (1 0tg(31.5)) (1 ) (1 1) tg( ) 1 tg(31.5) Coffiints of influn of th slop of th trrain: - slop of th trrain g g tg( ) 1 0.5tg(7.0) g Euivalnt uniform loa aounting for th influn of th founation pth: Calulation of th vrtial aring apaity an its rution y offiint : s i g 0 s i g s V i g V sult from th EO5 Spra Footing program: Extrm ontat strss at th footing ottom: Z A ff 9

10 sult from th EO5 Spra Footing program: Usag: V u %, SATISFACTOY Calulation of th paramtrs of a slip surfa low th founation. Th paramtrs of a slip surfa ar alulat aoring to Prantl s thory. Dpth of th slip surfa: ar( ) ar(31.5) os( ) tg( ) 1.80 os(31.5) tg(31.5) 4 4 zsp m 31.5 os 45 os 45 sult from th EO5 Spra Footing program: z sp m Lngth of th slip surfa: tg( ) tg(31.5) lsp 1 tg 45 1 tg m sult from th EO5 Spra Footing program: z sp m 10