Verification Analysis of the Slope Stability

Transcription

1 Verifiction nul no. 3 Updte 04/016 Verifiction Anlysis of the Slope Stbility Progr: File: Slope Stbility Deo_v_en_03.gst In this verifiction nul you will find hnd-de verifiction nlysis of the stbility of slope nd nchored slope in pernent design sitution. The results of the hnd-de clcultions re copred with the results fro the GEO5 Slope Stbility progr. Ters of Reference: In Figure 1, n exple of slope is shown. The slope hs height H nd is djusted in 1:1.5 inclintion. At the top of the slope is lod f 0 kn/. The erth body is fored of sndy cly (CS). The properties of soil (effective vlues) re shown in Tble 1. The clcultion is divided into two stges. In the 1 st stge the stbility of the slope is clculted nd in the nd stge the stbility of n nchored slope is clculted. The slope stbility is clculted using Fellenius/Petterson ethod nd Bishop s siplified ethod (the circulr slip surfce). The verifiction ethodology of the slope stbility is done ccording to sfety fctors. Figure 1 Slope - diensions Soil Unit weight kn/ 3 Sturted unit weight st kn/ 3 Angle of internl friction ef Cohesion of soil kp c ef CS Tble 1 Soil properties effective vlues 1

2 1. Fellenius/Petterson ethod Verifiction of the Stbility of the Slope The slip surfce ws deterined. In this cse the slip surfce is deterined by circle with its centre t point O x, z ; nd rdius R Points Z sp nd K sp indicte the beginning nd end of the slip surfce. The slope ws divided into verticl blocks of width b i In Figure, slope divided into 0 blocks is shown. Figure Slope verticl blocks Figure 3 Sttic schee of the block Clcultion of the weight of the individul blocks of the slope. The weight of the blocks of the erth body bounded by the slip surfce re clculted. The overll clcultion is shown in Tble. An exple of the clcultion for block nuber 13 is done.

3 Deterintion of the re bove the ground wter tble (the re A ) nd under the ground wter tble (the re B ): A B Weight of the individul prts of the block: A W A kn/, BW, 13 B13 st kn/ Weight force of the block: W AW,13 BW, kn/ 13 Clcultion for ll blocks: Are of the prt A i [ ] B i [ ] Width of the block b i [ ] Weight of one prt A W, i [ kn/ ] B W, i [ kn/ ] Weight of the block W i [ kn/ ] Lod f i [ kn/ ] , Tble Weight nd forces of the lod 3

4 Deterintion of the inclintion of the slip surfce of the individul blocks nd clcultion of the pore pressure. To siplify the hnd-de clcultion the circle slip surfces of the individul blocks hve been replced by lines. The inclintion of the slip surfce is deterined by the ngle between the slip surfce nd the horizontl plne. The height of the ground wter tble ust be deterined for the clcultion of the pore pressure. The height of the ground wter tble h i is considered to the xis of the block. The unit weight of wter is w kn /. The heights of the ground wter tble on the left nd right side of the block ust be deterined for the clcultion of the horizontl forces of the pore pressure. The overll clcultion is shown in Tble 3. An exple of the clcultion for block nuber 13 is done. Inclintion of the slip surfce: Length of the slip surfce: b l cos( 13 ) cos(7.719) Inclintion of the ground wter tble: w, Height of the ground wter tble: h Clcultion of the reduced height of the ground wter tble: hr, 13 h13 cos( w,13) cos(5.0169) Clcultion of the pore pressure: u w hr, kp 13 Clcultion of the horizontl forces of the pore pressure: U U h L,13 w,13) w cos(5.0169) cos( 10 HL, 13 h P,13 w,13) w cos(5.0169) cos( 10 HP, kn/ 7.7 kn/ - left side - right side Clcultion for ll blocks: Inclintion of the slip surfce i [ ] Length of the slip surfce l i [ ] Inclintion of the ground wter tble w,i [ ] Ground wter tble Height of the ground wter tble h i [ ] Reduced height of the ground wter tble h r, i [ ] Pore pressure i u [ kp ] 4

5 Tble 3 Inclintions nd lengths of the slip surfces nd pore pressures Left side of the block h L, i [ ] U HL, i [ kn/ ] Right side of the block h R, i [ ] U HR, i [ kn/ ]

6 Tble 4 Horizontl forces of the pore pressure Clcultion of the sliding oent. The weight of the individul blocks including forces of the lod ct on the horizontl r fro xis of the block to the centre of the circulr slip surfce (to the point O). The rs of the forces re clculted fro the beginning of the slip surfce x, z 8.00; 5.00 ). The overll clcultion is in Tble 5. An exple of the clcultion for block ( Z sp nuber 13 is done. Clcultion of the oent r: b 1.0 r, 13 X zsp X O i b Clcultion of the sliding oent: W f r ( ) kn, ,13 / Clcultion for ll blocks: r, i [ ] Sliding oent, i [ kn/ ] r, i [ ] Sliding oent, i [ kn/ ] Tble 5 Sliding oents Resultnt sliding oent: 0 i1, i kn / Result fro the GEO5 Slope Stbility progr: kn / 6

7 Resultnt ctive force: 0, i i F kn/ R Result fro the GEO5 Slope Stbility progr: F kn/ Clcultion of the resisting oent. Norl forces N i of the individul blocks ust be clculted. The norl force cts upright to the slip surfce. The overll clcultion is shown in Tble 6. An exple of the clcultion for block 13 is done. Clcultion of the sfety fctor : p Clcultion of the norl force: N ( W13 f13) cos( 13) u13 l13 ( U HL,13 U HR,13) sin( 13) 13 N13 ( ) cos(7.719) ( ) sin( 7.719) Clcultion of the resisting oent: c l N tn( ) R tn(7.00) kn / p, kn/ Clcultion for ll blocks: Norl force N i [ kn/ ] Resisting oent p, i [ kn/ ] Norl force N i [ kn/ ] Resisting oent p, i [ kn/ ] Tble 6 Norl forces nd resisting oents 7

8 Resultnt resisting oent: 0 p p, i kn / i1 Result fro the GEO5 Slope Stbility progr: p kn / Resultnt pssive force: 0 p, i i Fp kn/ R Result fro the GEO5 Slope Stbility progr: F p kn/ Clcultion of the sfety fctor: p , NOT OK Result fro the GEO5 Slope Stbility progr: 1. 43, NOT OK Verifiction of the Stbility of Anchored Slope In Figure 4, n exple of nchored slope in the nd stge is shown. The nchor force is F A knnd the spcing is b A. 00. The position of the nchor hed is x, z 16.00; 9.00 H nchor. The nchor hed is on block nuber 9. Figure 4 Anchored slope - diensions 8

9 Clcultion of the sliding oent. The nchor cts s pssive eleent, which ens tht ctive oents will be the se s in the 1 st stge. Resultnt sliding oent: 0 i1, i kn / Result fro the GEO5 Slope Stbility progr: kn / Resultnt ctive force: 0, i i F kn/ R Result fro the GEO5 Slope Stbility progr: F kn/ Clcultion of the resisting oent. The norl forces N i of the individul blocks ust be clculted. The norl force cts perpendiculr to the slip surfce. Norl force on block nuber 9 is influenced by the nchor force. The overll clcultion is shown in Tble 7. An exple of the clcultion for block 13 is done. Anchor force t 1 : ' FA F kn b.00 A / A Clcultion of the r of the nchor force: ra Z O Z nchor Resisting oent of the nchor: ' p, A FA ra kn/ Clcultion of the sfety fctor : p Clcultion of the norl force: N 13 ( W13 f13) cos( 13) u13 l13 ( U HL,13 U HR,13) sin( 13) N13 ( ) cos(7.719) ( ) sin( 7.719) Clcultion of the effect of the nchor force (block nuber 9): N A, 9 F' Asin( 9 ) sin( ) kn/ kn/ Clcultion of the resisting oent: 9

10 c l N tn( ) R tn(7.00) kn / p, Clcultion for ll blocks: Norl force N i [ kn/ ] Resisting oent p, i [ kn/ ] Norl force N i [ kn/ ] Resisting oent p, i [ kn/ ] Tble 7 Norl forces nd resisting oents Resultnt resisting oent: 0 p p, i p, A kn / i1 Result fro the GEO5 Slope Stbility progr: p kn / Resultnt pssive force: 0 p, i p, A i Fp kn/ R Result fro the GEO5 Slope Stbility progr: F p kn/ Clcultion of the sfety fctor: p , SATISFACTORY Result fro the GEO5 Slope Stbility progr: 1. 54, SATISFACTORY 10

11 . Bishop s Siplified ethod Verifiction of the Stbility of the Slope The slip surfce is the se s in the first clcultion using the Fellenius/Petterson ethod (Figure ). The clcultion of the weight of the individul blocks is shown in Tble. Deterintion of the inclintion of the slip surfce of the individul blocks nd clcultion of the pore pressure. To siplify the hnd-de clcultion the circulr slip surfces of the individul blocks hve been replced by lines. The inclintion of the slip surfce is deterined by the ngle between the slip surfce nd the horizontl plne. The height of the ground wter tble ust be deterined for the clcultion of the pore pressure. The height of the ground wter tble h i is considered to the xis of the block. The unit weight of wter is w kn /. The resultnt effect of the horizontl forces of the pore pressure is not significnt nd hd been neglected. The overll clcultion is in Tble 8. An exple of the clcultion for block 13 is done. Inclintion of the slip surfce: Inclintion of the ground wter tble: w, Height of the ground wter tble: h Clcultion of the reduced height of the ground wter tble: hr, 13 h13 cos( w,13) cos(5.0169) Clcultion of the pore pressure: u w hr, kp 13 Clcultion for ll blocks: Inclintion of the slip surfce i Inclintion of the ground wter tble w,i Ground wter tble Height of the ground wter tble h i [ ] Reduced height of the ground wter tble h r, i Pore pressure u i [ kp ] [ ] [ ] [ ]

12 Tble 8 Inclintions of the slip surfces nd pore pressures Clcultion of the sliding oent. The weight of the individul blocks including forces of the lod ct on the horizontl r fro the xis of the block to the centre of the circle slip surfce (to the point O). The rs of the forces re clculted fro the edge of the slip surfce x, z 8.00; 5.00 ). The overll clcultion is shown in Tble 9. An exple of the clcultion for ( Z sp block 13 is done. Clcultion of the r of the force: b 1.0 r, 13 X zsp X O i b Clcultion of the sliding oent: W f r ( ) kn, ,13 / Clcultion for ll blocks: r, i [ ] Sliding oent, i [ kn/ ] r, i [ ] Sliding oent, i [ kn/ ] Tble 9 Sliding oents 1

13 Resultnt sliding oent: 0 i1, i kn / Result fro the GEO5 Slope Stbility progr: kn / Resultnt ctive force: 0, i i F kn/ R Result fro the GEO5 Slope Stbility progr: F kn/ Clcultion of the resisting oent. The clcultion of the resisting oents is itertive becuse the clcultion of the resisting oents ccording to Bishop s ethod depends on the sfety fctor. In the 1 st itertion the sfety fctor is considered. Five itertions re done in the hnd-de clcultion. The overll clcultion is shown in Tble 10. An exple of the clcultion for block 13 is done. Clcultion of the sfety fctor in the individul itertions: p Clcultion of the resisting oent, : c b13 ( W13 f13 u13 b13 ) tn( ) p,13 R tn( ) sin( 13 ) cos( 13 ) ( ) tn(7.00) tn(7.00) sin( ) cos(7.719 ) p, result of the 1 st itertion Clcultion of the resisting oent, : ( ) tn(7.00) tn(7.00) sin( ) cos(7.719 ) p, result of the nd itertion Clcultion of the resisting oent, : ( ) tn(7.00) tn(7.00) sin( ) cos(7.719 ) p, kn / kn / kn / 13

14 result of the 3 rd itertion Clcultion of the resisting oent, : ( ) tn(7.00) tn(7.00) sin( ) cos(7.719 ) p, result of the 4 th itertion Clcultion of the resisting oent, : ( ) tn(7.00) tn(7.00) sin( ) cos(7.719 ) p, result of the 5 th itertion Clcultion for ll blocks: kn / kn / 1 st itertion nd itertion 3 rd itertion 4 th itertion 5 th itertion p, i 1.546, p i p i p i p i [ kn/ ] [ kn/ ] [ kn/ ] [ kn/ ] [ kn/ ] TOTAL , Tble 10 Resisting oents nd sfety fctors, 1.554,

15 Resultnt resisting oent in 5 th itertion: 0 p p, i kn / i1 Result fro the GEO5 Slope Stbility progr: p kn / Resultnt pssive force: 0 p, i i Fp kn/ R Result fro the GEO5 Slope Stbility progr: F p kn/ Clcultion of the sfety fctor in 5 th itertion: p , SATISFACTORY Result fro the GEO5 Slope Stbility progr: 1. 56, SATISFACTORY Verifiction of the Stbility of Anchored Slope In Figure 4, n exple of nchored slope in nd stge is shown. The nchor force is F A knnd the spcing is b A. 00. The position of the nchor hed is x, z 16.00; 9.00 H nchor. Clcultion of the sliding oent. The nchor cts s pssive eleent, which ens tht ctive oents will be the se s in the 1 st stge. Resultnt sliding oent: 0 i1, i kn / Result fro the GEO5 Slope Stbility progr: kn / Resultnt ctive force: 0, i i F kn/ R Result fro the GEO5 Slope Stbility progr: F kn/ 15

16 Clcultion of the resisting oent. The nchor force enters the clcultion of the resisting oents. The clcultion of the resisting oents is itertive becuse the clcultion of the resisting oents using the Bishop s ethod depends on the sfety fctor. In the 1 st itertion the sfety fctor is Five itertions re done in the hnd-de clcultion. The overll clcultion is shown in Tble 11. An exple of the clcultion for block 13 is done. Anchor force t 1 : ' FA F kn b.00 A / A Clcultion of the r of the nchor force: ra Z O Z nchor Resisting oent of the nchor: ' p, A FA ra kn/ Clcultion of the sfety fctor in the individul itertions: p Clcultion of the resisting oent, : p,13 c b13 ( W cos( f13 u13 b13 ) tn( ) R tn( ) sin( 13 ) ) ( ,00) tn( 7.00) tn( 7.00) sin( ) cos(7.719 ) p, result of the 1 st itertion Clcultion of the resisting oent, : ( ) tn(7.00) tn(7.00) sin( ) cos(7.719 ) result of the nd itertion p, Clcultion of the resisting oent, : ( ) tn(7.00) tn(7.00) sin( ) cos(7.719 ) 1.66 p, result of the 3 rd itertion kn / kn / kn / 16

17 Clcultion of the resisting oent, : ( ) tn(7.00) tn(7.00) sin( ) cos(7.719 ) p, result of the 4 th itertion Clcultion of the resisting oent, : ( ) tn(7.00) tn(7.00) sin( ) cos(7.719 ) p, result of the 5 th itertion Clcultion for ll blocks: kn / kn / 1 st itertion nd itertion 3 rd itertion 4 th itertion 5 th itertion p, i 1.641, p i p i p i p i [ kn/ ] [ kn/ ] [ kn/ ] [ kn/ ] [ kn/ ] Anchor TOTAL , Tble 11 Resisting oents nd sfety fctors, 1.665,

18 Resultnt resisting oent in 5 th itertion: 0 p p, i p, A kn / i1 Result fro the GEO5 Slope Stbility progr: p kn / Resultnt pssive force: 0 p, i p, A i Fp kn/ R Result fro the GEO5 Slope Stbility progr: F p kn/ Clcultion of the sfety fctor in 5 th itertion: p , SATISFACTORY Result fro the GEO5 Slope Stbility progr: 1. 67, SATISFACTORY 18