Worked examples. Dr. Bernd Schuppener German Federal Waterways Engineering and Research Institute, Karlsruhe Past Chairman of CEN TC250/SC 7

Transcription

1 13-14 June 2013, Dublin Worked examples HYD and UPL limit it states Dr. Bernd Schuppener German Federal Waterways Engineering and Research Institute, Karlsruhe Past Chairman of CEN TC250/SC 7

2 Worked example: Verification of uplift of a base slab in an excavation 2

3 Example: verification of failure by uplift UPL H=10 m D=10m 1,0 L SPW =15 m ϕ k ϕ k = 32,5 U k a = 10 m; b = 5 m γ conrete = 24,0 kn/m³ conrete γ = 10 kn/m³ γ Steel d = 2,34 kn/m² Waterpressure: U k =H γ w b a = 5000 kn 3

4 EN : Verification of uplift (1)P Verification for uplift (UPL) shall be carried out by checking that the design value of the combination of destabilising permanent and variable vertical actions (V dst;d )i is less than or equal to the sum of the design value of the stabilising permanent vertical actions (G stb;d) and of the design value of any additional resistance to uplift (R d ): where V dst,d G stb;d + R d (2.8) dst,d stb;d d V dst,d = G dst;d +Q dst;d (2) Additional resistance to uplift may also be treated as a stabilising permanent vertical action (G stb;d ). 4

5 UPL partial factors and model factor Factor type Factor EN German NA and DIN 1054 Permanent unfavourable action Irish NA γ G;dst Permanent favourable action γ G;stb Variable unfavourable action γ Q;dst Angle of shearing resistance γ φ Pile tensile resistance γ s;t Model factor on wall η resistance 5

6 UPL- verification with the weight of the structure only For the verifications the following quantities are needed: Self-weight base-slab: Base-slab: d = 1,0 m, γ concrete = 24,0 kn/m³: Base-area A = a b = 10,0 5,0 = 50,00 m² G concrete = A d γ concrete G concrete = 50 1,0 24,0 = 1200 kn. Self weight sheet-pile-wall: ll d SPW = 003 0,03 m, γ Steel = 78,0 kn/m³ Weight per unit area: g = 78,0 0,03 = 2,34 kn/m², G SPW = L SPW 2 2 (a +b) g g = ,34 34 = 1053 kn Total characteristic weight of the structure: G k = G concrete + G SPW = = 2253 kn 6

7 UPL-verification with the weight of the structure only G Required: V dst,d G stb;d + R d eq. (2.8) V dst,d = U d G d U k γ G,dst G k γ G,stb But: ,00 = 5000 kn > ,90 = 2028 kn Hence UPL requirement not satisfied! U 7

8 UPL-verification including wall frictional resistance R G R U V dst,d G stb;d + R d U d G d + R d U k γ G,dst (G k + R k ) γ Gstb G,stb 8

9 Verification of failure by uplift UPL frictional resistance R The characteristic value of the wall frictional resistance R k will be treated as a stabilising action determined as the vertical component of the characteristic active earth pressure reduced by a model factor of η = 0,80: R k = E ah,k tan δ a η The wall friction angle is assumed to be δ k = 2/3 ϕ k. For horizontal surface area and vertical wall the earth pressure coefficient is K ah,k = 0,25 (from Fig. C 1.1 of EN for ϕ k = 32.5 ) and tan δ a = 0,397. The earth pressure is assumed to act only on the outer surface of the sheet pile wall: E ah,k = 2 (a + b) 0,5 L SPW² γ K ah,k E ah,k = 30 0,5 15² 10 0,25 = 8437 kn R k = E ah,k tan δ k η R k = ,397 0,8 = 2680 kn 9

10 UPL - including wall frictional resistance G R Require: U d G d + R d U k γ Gdst G,dst (G k + R k ) γ Gstb G,stb But: ,00 = 5000 > ( ) 0,90 = 4400 kn Hence UPL requirement is not satisfied U 10

11 Example: Irish verification of uplift failure for UPL Calculation of R d Using ϕ k,inf = 32,5 o, i.e. the inferior characteristic ϕ value, and applying UPL γ ϕ = 1,25 to the tan(ϕ k,inf ) to obtain to ϕ d and δ d, gives a design wall frictional resistance R d value that is slightly greater than the characteristic value R k, which is not acceptable. Hence a superior characteristic value ϕ k,sup is needs to be used. This is obtained, after Bond and Harris (2008), by assuming a normal distribution for ϕ and a standard deviation of 3 o so that ϕ k,sup = 32,5 o ,0 = 42.4 o. Then applying the partial factor of 1.25 as a multiplier to tan(ϕ k,sup ) gives ϕ d,sup = 48.8 o and hence an R d value of 2580 kn with a margin of safety of 1.33 on the characteristic value. 11

12 Example: Irish verification of failure by uplift UPL G R U Require: U d G d + R d U k γ G,dst G k γ G,stb + R k γ G,stb i.e ,00 = 5000 > , = 4608 kn Hence ULP requirement is not satisfied and tensile piles are required 12

13 GEO partial factors and model factor Factor type Factor Irish NA Irish NA German NA DA1.C1 DA1.C2 DA2 + DIN 1054 Permanent unfavourable γ G;dst action, transient situation Permanent favourable γ G;stb action Variable unfavourable action Angle of shearing resistance γ Q;dst γ φ Pile tensile resistance γ s;t Model factor on wall η resistance 13

14 Irish design for GEO verification E d R d G U R As explained previously, R d is obtained using the superior ϕ value so that for: γ φ = 1,0, R d = 3440 kn γ φ = 1,25, R d = 2580 kn E d = U k γ G -G k γ G,inf = 5000 γ G 2253 γ G;inf DA1.C1: E d = , ,0=4497kN 10 > R d = 3440kN DA1.C2: E d = , ,0=2747kN < R d = 2580kN Hence GEO ULS is not satisfied 14

15 Uplift - verification with tension piles EN Piles - ground tensile resistance (3)P For tension piles, two failure mechanisms shall be considered: pull-out of the piles from the ground mass; uplift of the structure and the block of ground containing the piles. 15

16 GEO - verification with tension piles F R Determination of the tensile action F from the structure on the pile using ultimate limit state GEO (DA2) U k L P Rt R t F td t,d = U d (R d + G d ) 16

17 Pile design (GEO) for verification of failure by uplift G R 17 F t,d = U F U k γ G -(G k + R k ) γ G,inf F t,d : design value of the action on the piles γ G = 1.20 for unfavourable actions (according to DIN 1054 for transient situations: construction period) γ G,inf = 1.00 for favourable effects of actions

18 Pile design (GEO) for verification of failure by uplift G R U 18 E 1 E d = U k γ G -(G k + R k ) γ G,inf F t,d = ,20 - ( ) 1,00 F t,d = F t,d = 1067 kn

19 Pile design (GEO) for verification of failure by uplift E d R U Rt,d L Driven piles: L tot = n L, D = 0,5 m, q sk s,k = 35 kn/m² γ P = 1,40 (DIN 1054) R t,d = L tot q s,k π D / γ P 19 R t,d = 39,25 L tot

20 Pile design (GEO) for verification of failure by uplift F t R U k L R t F t,d R t,d eq. (7.12) ,25 L tot L tot 27,2 m 20

21 Pile design (GEO) for verification of failure by uplift x 1,66 m l a =3,33 m l a x x l a =3,33 333m 3,33 m 3,33 m l a =3,33 m 1,66 m 10,0 m 2,50 m 5,0 m 2,50 m Selected: 3 Piles L = 10 m 21

22 Irish pile design for GEO verification of uplift failure E d R d eq. (2.5) U G R t R As explained previously, R d is obtained using the superior ϕ value so that for: γ φ = 1,0, R d = 3440 kn γ φ = 1,25, R d = 2580 kn E d = U k γ G -G k γ G,inf = 5000 γ G 2253 γ G;inf R t,d = R t,k / γ s;t + R d = L tot q s,k π D / γ s;t + R d = L tot 35 π 0.5 / γ s;t + R d = L tot / γ s;t + R d Hence require: L tot γ s;t (5000 γ G 2253 γ G;inf R d ) /

23 Irish pile design for GEO verification of uplift failure DA1.C1 U G R R t L tot 1.25 ( ) /54.98 L tot = 24.0 Hence, for 3 piles, each should be 8 m long 23

24 Irish pile design for verification of GEO uplift failure DA1.C2 U G R R t L tot 1.6 (5000 1, ) / 54,98 = 4.9m, L tot = 4.9m, i.e. for 3 piles, each should be 1.6 m long. Hence design length is 8 m NOTE: DA1.C1 controls o the design not DA1.C2 due to large balancing a forces 24

25 Verification of uplift of structure + ground block containing i the piles G R V dst,d G stb;d + R d (2.8) U d G d + G soil,d + R d U U k γ G,dst (G k + G soil,k+ + R k ) γ G,stb G soil 25

26 Determination of G soil,k according to DIN 1054, G soil,k [ ( )] 2 2 l l L 1/ 3 l + l ϕ η γ = n cot a b a b N: number of piles, L = length of piles l a = 5,0 m greater grid distance piles, l b = 3,3333 m smaller grid distance piles, γ = 10,0 kn/m³ submerged weight soil η = 0,80 model factor for the weight. G soil,k = 3 {5,0 3,33 (10 1/ , 0 + 3, 33 cot 32,5 )} 0,8 10 G soil,k = 2740 kn Model factor: η = 0,80 according to DIN 1054! 26

27 Verification of uplift of structure + ground block containing i the piles G R U U d G d + R d + G soil,d G soil U k γ G,dst (G k + R k + G soil,k ) γ G,stb kn 27

28 Worked example: failure by hydraulic heave HYD 28

29 Verification of failure by heave (1)P When considering a limit state of failure due to heave by seepage of water in the ground (HYD, see 10.3), it shall be verified, for every relevant soil column, that the design value of the destabilising total pore water pressure (u dst;d ) at the bottom of the column, or the design value of the seepage force (S dst;d ) in the column is less than or equal to the stabilising i total t vertical stress (σ stb;d ) at the bottom of the column, or the submerged weight (G stb;d ) of the same column: u dst;d σ stb;d (2.9a) S dst;d d G stb;d (2.9b) 29

30 Verification of safety against hydraulic heave NN - 1,0 m S dst,d G stb,d NN - 4,0 m NN - 5,4 m Medium dense Sand: γ = 10 kn/m³ t NN - 12,0 m 30 b=t/2

31 Verification of safety against hydraulic heave using formula by EAU h = 1,4 m t = 6,60 m h = 4,4 m h r h = r h h t ,4 = 1, , i = h r / t = 0,32 = 2,13 m u = (t + h r ) γ w 31

32 Verification of safety against hydraulic heave NN - 1,0 m Seepage force S k : S k = i γ W V NN - 4,0 m NN - 5,4 m Effective self weight of the soil column G k: G k = γ V G HYD Ulimate limit state: k S k γ dst G k γ G,stb NN - 12,0 m S k 32

33 Verification of safety against hydraulic heave Table A.17 - Partial factors on actions (γ F ) Action Symbol Value permanent unfavourable a γ G;dst favourable b γ G;stb 0.90 variable unfavourable a γ G;stb 1.50 a b destabilising; stabilising 33

34 Verification of safety against hydraulic heave NN - 1,0 m NN - 4,0 m NN ,4 m Seepage force S k : S k = i γ W V k γ W Effective self weight of the soil column G k: G k = γ V NN - 12,0 m G k G k S k HYD Ulimate limit state: S k γ dst G k γ G,stb

35 Safety against hydraulic heave: eq. 2.9b u dst;d σ stb;d NN - 1,0 m NN - 4,0 m NN ,4 mh = 1,4 m t = 6,60 m NN - 12,0 m σ stb;d u dst;d d u k = (t + h r ) γ w h r = 2,13m u k = ( ) 10 u k = 87.3 kn/m² σ stb;k = t (γ +γ w ) σ stb;k = σ stb;k = 132 kn/m² u k γ G,dst σ stb;k γ G,stb

36 13-14 June 2013, Dublin Geotechnical design with worked examples eurocodes.jrc.ec.europa.eu