Verification Analysis of the Redi Rock Wall

Transcription

1 Verifiction Mnul no. Updte 06/06 Verifiction Anlysis of the Redi Rock Wll Progr File Redi Rock Wll Deo_v_etric_en_0.grr In this verifiction nul you will find hnd-de verifiction nlysis of the Redi Rock Wll in pernent design sitution. The results of the hnd-de clcultions re copred with results fro the GEO Redi Rock Wll progr. Ters of Reference In Figure, n exple of wll is shown. Wll is constructed of the 7 blocks RediRock. etbcks of the blocks re. Hoogenous soil (silty snd -F) is considered t the both sides of the wll. Footing fro the crushed stone hs thickness 0.0 nd it is plced below the wll. The properties of soil nd footing (effective vlues) re shown in Tble. Verifiction nlysis of the wll is perfored with the help of sfety fctors. The bering cpcity of foundtion soil is clculted by NCMA stndrd. Figure Construction of the Redi Rock Wll diensions oil Unit weight [kn/ ] Angle of internl friction [ ] ef Cohesion of soil c [kp] ef Angle of friction struc.-soil [ ] -F Crushed stone Tble oil properties effective vlues

2 Verifiction of the Whole Wll Clcultion of the weight nd the centroid of the wll. The wll is divided into 8 blocks (7 blocks of RediRock nd footing), which re shown in Figure. Tble shows the diensions of the blocks, their weights nd centroids. Block Type of block Height h i [] Width w i [] Are A i [ ] Unit weight i [kn/ ] Weight W i [kn/] Point of ction x i [] z i [] W i xi W i zi Footing Totl Tble Diensions, weights nd centroids of the individul blocks Centroid of the construction Wi xi 6.69 x t Wi Wi zi 7.79 z t Wi Clcultion of the front fce resistnce. The depth of the soil in front of the wll is 0.6. Pressure t rest is considered. Coefficient of erth pressure t rest (For non-cohesive soils the Jky forul for coputing of the coefficient of erth pressure t rest K 0 is used) K sin sin( 8.00) 0. 0 Verticl norl effective stress z in the footing botto z h kp

3 Pressure t rest in the footing botto 0 z K kp Resultnt force of stress t rest 0 (Resultnt force 0 cts only in horizontl direction, therefore 0 0 h kn/ Point of ction of the resultnt force x z0 h x 0 nd 0z 0 ) Clcultion of the weight nd the centroid of the soil wedges. In figure, two soil wedges re shown. oil wedges re considered bove setbcks nd t the bck side of the wll. The geoetry of both wedges is given by the inclintion. s Figure oil wedges - geoetry Clcultion of the ngle i is obtined fro the itertive forul sin( ) cos( ) sin( ) cos( ) sin i i ( ) rcsin i tn( ) cos( ) i tn( ) cos( i ) inclintion of terrin i estite st itertion sin( ) cos( ) i rcsin. tn(8.00) cos( )

4 nd itertion sin( ) cos(. 8.00) i rcsin tn(8.00) cos(. 0.00) rd itertion sin( ) cos( ) i rcsin. 0 tn(8.00) cos( ) th itertion sin( ) cos( ) i rcsin tn(8.00) cos( ) th itertion sin( ) cos( ) i rcsin. 00 tn(8.00) cos( ) 6 th itertion sin( ) cos( ) i rcsin. 00 tn(8.00) cos( ) Inclintion of the wedge s s i oil wedge, is coposed fro two prts (prt A nd prt B) W A ( 0. ( )) kn/ W B ( ) 0.7 tn(9.00) kn/ Points of ction of the prts A nd B ( ) x A z A x B z B Totl weight nd centroid of the soil wedge W W W.0..9 kn A B / W x x W x A A B B W.9.008

5 z W z W z.0 (.0). (.96) A A B B W.9 Totl weight nd centroid of the soil wedge 0.7 rctn w' ( ) 0. tn(8.869) tn(9.000) h' tn(8.869) tn(9.000) W kn/ tn(8.869) tn(9.000).7 (0. cos(8.869)) x z Clcultion of the ctive pressure. The construction is divided into four levels, in ech is clculted ctive erth pressure nd resultnt forces. Resultnt forces of the ctive pressure re shown in Figure. The ctive erth pressure is clculted using Coulob s theory. Figure Active erth pressure resultnt forces

6 Coefficient of ctive erth pressure in ll levels - bck fce inclintion of the structure 0 - inclintion of terrin Effective vlues fro the Tble re used in clcultion. K - coefficient of ctive erth pressure K i cos ( i ) sin( i ) sin( ) cos ( ) cos( ) i i i cos( ) cos( ) i i i Clcultion of the st level K cos (8.0.0) sin( ) sin( ) cos (.0) cos(.0 8.0) cos(.0 8.0) cos(.0 0.0) Clcultion of the nd level 0.07 rctn ( ) K cos (8.0.) sin( ) sin( ) cos (.) cos(. 8.) cos(. 8.) cos(. 0.0) 0.70 Clcultion of the rd level K cos (8.0.0) sin( ) sin( ) cos (.0) cos(.0 8.0) cos(.0 8.0) cos(.0 0.0) Clcultion of the th level

7 K cos ( ) cos (0.0) cos(0.0 8.) Verticl norl effective stress z in ll levels z kp z h kp z z h kp z z h kp z z h kp Active erth pressure in ll levels, z 0 K kp, b z K kp, z K kp, b z K kp, z K kp, b z K kp, z K kp, b z K kp sin( ) sin( ) cos(0.0 8.) cos( ) 0. Resultnt forces of ctive erth pressure i nd horizontl nd verticl coponents, b h kn/, x cos( ).80 cos(.0 8.0) 0.7 kn/, z sin( ).80 sin(.0 8.0).8 kn/ (, b, ) h, h (..) kn/ cos( ). cos(. 8.0) 0.89 kn, x /, z sin( ). sin(. 8.0).70 kn/ 7

8 8 kn h h b / ) (6. ) (,,, kn x / ) cos(.0. ) cos(, kn z / ) sin(.0. sin( ), kn h h b / ) (. ) (,,, kn x /.68 8.) cos(0.0. cos( ), kn z /.0 8.) sin( 0.0. sin( ), Points of ction of resultnt forces x 9. tn(9.0) z x..6.) (..6. tn(8.869) 6.6.) (. tn(8.869).6. tn(8.869) z ) ( ) ( x ) ( tn(9.0) 6 7.6) (6. tn(9.0) z ) ( ,6) ( x 680. z ) ( ) (. 0,

9 Totl resultnt force of ctive erth pressure x, x, x, x, x kn/ z, z, z, z, z kn/ x z kn/ Point of ction of totl resultnt force i, z xi x i, z i, x zi z i, x Checking for overturning stbility. The oents clculted in the nlysis rotte bout the origin of the coordinte syste (left botto corner of the structure, Figure ). Resisting oent M res nd overturning oent M ovr re clculted for verifiction. Results re copred with results fro the GEO Redi Rock Wll progr. Clcultion of resisting oent M res M W x z W x W x res t 0 0 z x M res kn / Result fro the GEO Redi Rock Wll progr M res kn / Clcultion of overturning oent M ovr M z kn ovr x / Result fro the GEO Redi Rock Wll progr M ovr.0 kn / fety fctor M res F M.68 ovr.6 >.0, ATIFACTORY Result fro the GEO Redi Rock Wll progr F.6 >. 0, ATIFACTORY Checking for slip. lip in the footing botto is checked. Norl force in the footing botto N W W W z kn/ 9

10 Eccentricity of the lod (width of the footing d. 680 ) d M res M ovr e 0.9 N In the progr, eccentricity is clculted s rtio. e 0.9 e po 0.0 d.680 e lw 0. e 0.0, ATIFACTORY po Clcultion of resisting horizontl force H res N tn( ) c ( d e) tn(8.00) ( ) 8.69 kn/ Result fro the GEO Redi Rock Wll progr H res 8.0 kn/ Clcultion of cting horizontl force H kn ct x 0 / Result fro the GEO Redi Rock Wll progr H ct. kn/ fety fctor H res 8.69 F.66 H. ct >.0, ATIFACTORY Result fro the GEO Redi Rock Wll progr F.66 >. 0, ATIFACTORY Bering Cpcity of the Foundtion oil tress in the footing botto N d e kp Result fro the GEO Redi Rock Wll progr 88. kp Clcultion of the bering cpcity. The length of the wll is 0.0. Therefore the effective width of the footing controls the bering cpcity. Effective width of the footing b eff b e Bering cpcity fctors re deterined fro tbles (NCMA nul) N.70 q N c.800 N

11 Bering cpcity of the foundtion soil d foundtion depth R d c N c R d. 9 d N kp q b eff N Result fro the GEO Redi Rock Wll progr R d. kp fety fctor Rd.9 F >.00, ATIFACTORY Result fro the GEO Redi Rock Wll progr F.6 >. 00, ATIFACTORY Diensioning - Anlysis of ections Anlysis of the joint between the block nd the footing Joint between the block nd the footing is nlysed. The joint (in the level of the xis x) is shown in Figure. Figure Diensioning joint between the block nd the footing Clcultion of the weight nd the centroid of the wll. Tble shows the diensions of the blocks, their weights nd centroids. Block Type of block Height h i [] Width w i [] Are A i [ ] Bulk weight i [kn/ ] Weight force W i [kn/] Point of ction x i [] z i [] W i xi W i zi

12 Totl Tble Diensions, weights nd centroids of the individul blocks Centroid of the construction Wi xi.689 x t Wi Wi zi 9.9 z t Wi Clcultion of the front fce resistnce. Depth of the soil in front of the wll is 0.6. Pressure t rest is considered. Coefficient of erth pressure t rest (For non-cohesive soils the Jky forul for coputing of the coefficient of erth pressure t rest K 0 is used) K sin sin( 8.00) 0. 0 Verticl norl effective stress z t the level of the joint z h kp Pressure t rest 0 z K kp Resultnt force of pressure t rest 0 (Resultnt force 0 cts only in horizontl direction, therefore 0 r h kn/ Point of ction of resultnt force 0 0x 0 nd 0z 0 )

13 x z0 h Clcultion of the weight nd the centroid of the soil wedges. The soil wedges re the se s in the verifiction nlysis of the whole wll (Figure ). The centroids of the both soil wedges ust be reclculted. Weight of soil wedges W.9 kn/ W.88 kn/ Centroids of soil wedges x z x z Clcultion of ctive erth pressure. The construction is divided into four levels. In the first three levels, the ctive erth pressure nd the resultnt forces re the se s in the verifiction nlysis of the whole wll. Centroids of the ll resultnt forces ust be reclculted. Verticl norl stress in the th level z z h kp Active erth pressure in the th level, z K kp, b z K kp Resultnt force of the ctive erth pressure nd horizontl nd verticl coponents (, b, ) h, h ( ) cos( ) 8. cos(0.0 8.) 7.8 kn, x / kn/, z sin( ) 8. sin( ).88 kn/ Points of ction of ll resultnt forces of the ctive erth pressure x z x

14 z x z x ( ) 0.7 z 6 0. ( ) Totl resultnt force of the ctive erth pressure x, x, x, x, x kn/ z, z, z, z, z kn/ x z kN/ Point of ction of the totl resultnt force i, z xi x..9 i, z i, x zi z i, x Checking for overturning stbility. The oents clculted in the nlysis rotte bout the origin of the coordinte syste (left botto corner of the block, Figure ). Resisting oent M res nd overturning oent M ovr re clculted for verifiction. Results re copred with results fro the GEO Redi Rock Wll progr. Clcultion of resisting oent M res M W x z W x W x res t 0 0 z x M res kn / Result fro the GEO Redi Rock Wll progr M res 8. kn / Clcultion of overturning oent M ovr M z kn ovr x / Result fro the GEO Redi Rock Wll progr M ovr.66 kn /

15 fety fctor M res 8.7 F.6 M.6 ovr >.0, ATIFACTORY Result fro the GEO Redi Rock Wll progr F.6 >. 0, ATIFACTORY Checking for slip. lip in the joint between the block nd footing is checked. Norl force N W W W z kn/ Eccentricity of the lod (width of the footing d. ) d M res M ovr e 0. N In the progr, eccentricity is clculted s rtio. e 0. e po 0. d. e lw 0. e 0., ATIFACTORY po Clcultion of resisting horizontl force Reduction of the contct between the block nd the footing is not considered H res N tn( ) c ( d e) tn(0.00) (. 0.) 8.07 kn/ Result fro the GEO Redi Rock Wll progr H res 8.08 kn/ Clcultion of cting horizontl force H kn ct x 0 / Result fro the GEO Redi Rock Wll progr H ct 0. kn/ fety fctor H res 8.07 F H 0.9 ct.70 >.0, ATIFACTORY Result fro the GEO Redi Rock Wll progr F.70 >. 0, ATIFACTORY Anlysis of the joint between the block nd the block. Joint between the block nd the block is nlysed. The joint (in the level of the xis x) is shown in Figure.

16 Figure Diensioning joint between the block nd the block Clcultion of the weight nd the centroid of the wll. Tble shows the diensions of the blocks, their weights nd centroids. Block Type of block Height h i [] Width w i [] Are A i [ ] Bulk weight i [kn/ ] Weight force W i [kn/] Point of ction x i [] z i [] W i xi W i zi Totl Tble Diensions, weights nd centroids of the individul blocks Centroid of the construction 6

17 Wi xi.6 x t Wi Wi zi 68.0 z t. 8. Wi Clcultion of the weight nd the centroid of the soil wedge. Only weight of the wedge hs effect. The centroid of the edge ust be reclculted. Weight of the soil wedge W.9 kn/ Centroid of the soil wedge x z Clcultion of ctive erth pressure. The construction is divided into two levels. In the first level, the ctive erth pressure nd the resultnt force re the se s in the verifiction nlysis of the whole wll. Centroids of the ll resultnt forces ust be reclculted. Verticl norl effective stress in the nd level z z h (.6 ). 70 kp Active erth pressure in the nd level, z K kp, b z K kp Resultnt force of the ctive erth pressure nd horizontl nd verticl coponents (, b, ) h, h (.0.) cos( ) 0.0 cos(.0 8.) 9.86 kn, x /, z sin( ) 0.0 sin(.0 8.).9 kn/ kn/ Points of ction of resultnt forces of the ctive erth pressure x z

18 ..86 (.0.).86 tn(8.869) 6 tn(8.869) x (.0.) (.0.).86 z (.0.) Totl resultnt force of ctive erth pressure kn x, x, x / z, z, z kn/ x z kn/ Point of ction of the totl resultnt force i, z xi x i, z i, x zi z i, x Checking for overturning stbility. The oents clculted in the nlysis rotte bout the origin of the coordinte syste (left botto corner of the block, Figure ). Resisting oent M res nd overturning oent M ovr re clculted for verifiction. Results re copred with results fro the GEO Redi Rock Wll progr. Clcultion of resisting oent M res M W x W x x res t z M res kn / Result fro the GEO Redi Rock Wll progr M res 0.6 kn / Clcultion of overturning oent M ovr M z kn ovr x / Result fro the GEO Redi Rock Wll progr M ovr 8.80 kn / 8

19 fety fctor M res 0.80 F M 8.79 ovr. >.0, ATIFACTORY Result fro the GEO Redi Rock Wll progr F. >. 0, ATIFACTORY Checking for slip. lip in the joint of the block nd the block is checked. Norl force N W W z kn/ Eccentricity of the lod (width of the footing d. 09 ) d M res M ovr e 0.67 N 6.8 In the progr, eccentricity is clculted s rtio. e 0.67 e po 0.6 d.09 e lw 0. e 0.6, ATIFACTORY po Clcultion of resisting horizontl force Properties of the block F MAX. kn/ - xil sher cpcity H res N tn( ) c ( d e) 6.8 tn(7.00) (. 0.) 0.86 kn/ H res 0.86 FMAX.0 kn/ H res.0 kn/ ' Result fro the GEO Redi Rock Wll progr H res. kn/ Clcultion of cting horizontl force H 0.97 kn ct x / Result fro the GEO Redi Rock Wll progr H ct 0. kn/ fety fctor H res.0 F H 0.97 ct 6.7 >.0, ATIFACTORY Result fro the GEO Redi Rock Wll progr F 6.7 >. 0, ATIFACTORY 9