Eurocode 7 designs for water pressures and review of survey

BP201.1BP198.1EC7 Workshop, Pavia, April 2010Water pressuresBrian Simpson, Arup Geotechnicswith assistance from:Andrew Bond, Norbert Vogt, Adriaan Seters1

Three simple (????) problems• Concentrating here on safetyrelated to water pressure.• Other issues complicate mattersfurther:• DA’s, materials, resistances,calculations models2

3Extracts from EN1997-1

4Extracts from EN1997-1

Extracts from EN1997-1• DA2* - or DA1* ??5

• Method 1 – γ dst (>1) and γ stb (

Allo owable cha aracteristic FDensity of the block• Method 1 – γ dst and γ stb• W * γ +U * γ ≥ U * γ +F* γ• W γ G;stb + U stb γ G;stb ≥ U dst γ G;dst + F γ Q;dst• Method 2 – γ stb and γ stb• (W - ΔU) * γ G;stb ≥ F * γ Q;dst (buoyant weight method)• Method 3 – γ dst and γ dst• W * γ G;stb – ΔU* γ G;dst ≥ F * γ Q;dst• relative water pressure method - “single source”9

Factoring water pressures.Observation: Method 3 may be better, but still factoring the density of water.• Method 1 – γ dst and γ stb• W * γ +U * γ ≥ U * γ +F* γ• W γ G;stb + U stb γ G;stb ≥ U dst γ G;dst + F γ Q;dst• Method 2 – γ stb and γ stb• (W - ΔU) * γ G;stb ≥ F * γ Q;dst (buoyant weight method)• Method 3 – γ dst and γ dst• W * γ G;stb – ΔU* γ G;dst ≥ F * γ Q;dst• relative water pressure method - “single source”10

• Which limit states are relevant?• Sliding – GEO• Bearing capacity – GEO• Internal strength – STR• EQU? Toppling?14

WU• Do we factor water pressure?• “Single source”? Same factors on horizontal andvertical at a point?• Effect of factoring buoyant weight? γ stb (W k -U k )15

H/Bγ cct / γ w16

• Two combinations (DA1)• Same water pressures for all calculations.• Not “single source” (in any of the plots)• For all methods, results very dependent on factor values, includingmaterial or resistance factors for BC.17

• Different water pressures for each limit state?• No water pressures less than characteristic• Not simply using the most critical?18

• γ G lower for water pressure?• Water pressure less than characteristic considered• This one is “single source”.19

Example 3• How many piles?• How to computedesign BM?RWU20

ΔhW k x γ GDh kU k x γ UR k /γ Rγ G = γ F,inf or γ F,stbγ U = γ Fsup F,sup or γ dst21

ΔhW k x γ GDh kU k x γ UR k /γ R• Water head ratio• Weight ratio• Anchorage ratioh k /DW k /(vol x γ w ) nR k /W k• How much water pressure • How heavy is the building • How much anchorage22

Example 3 – Characteristic situationn Ra,k / Wkhorage ratio,AncCharacteristicweight ratio = 0,1weight ratio = 0.250.8 weight ihratio = 0.5 05weight ratio = 0.75weight ratio = 1weight ratio = 20.60.40.200 0.2 0.4 0.6 0.8Water head ratio, hk / D• Anchorage rationR k /W k• How much anchorage• Water head ratioh k /D• How much water pressure• Weight ratioW k /(vol x γ w )• How heavy is the building23

Weight ratio 0.25. Δh=0.ratio, n Ra,k/ WkAnchorage0.80.60.40.2Design with omega_W = 0.25, delta_h = 0UPL method 1, 0.9nRkUPL method 2GEO DA1-1GEO DA1-2GEO DA1-1*GEO DA2CharacteristicUPLUPLDA1-1DA1-2DA1-1*DA2*• For high water heads, allmethods give somesafety.• How much is needed?• Near the balance point,safety is only providedby increasing the waterpressure.00 0.1 0.2 0.3 0.4Water head ratio, h_k / D24

Weight ratio =0.25. Δh=0.1An nchorage rati io, n Ra,k / Wk0.80.60.40.2Design with omega _ W = 0.25, delta_h = 0.1UPL method 1UPL method 2GEO DA1-1GEO DA1-2GEO DA1-1*GEO DA2Characteristic00 0.1 0.2 0.3 0.4Water head ratio, h_k / D• Increasing the headby Δh provides asafety margin.• But would this beused in addition toother safety factors?, 0.9nRkUPLUPLDA1-1DA1-2DA1-1*DA2*25

Weight ratio = 0.75 (heavy building). Δh=0.1.A nchorage rati io, n Ra,k / Wk0.80.60.40.2Design with omega _ W = 0.75, delta_h = 0.1UPL method 1UPL method 2GEO DA1-1GEO DA1-2GEO DA1-1*GEO DA2Characteristic00.5 0.6 0.7 0.8 0.9Water head ratio, h_k / D• Similar pattern.• Factoring waterpressures starting todominate effect ofΔh., 0.9nRkUPLUPLDA1-1DA1-2DA1-1*DA2*26

Weight ratio = 0.75 - my preferenceΔh=0 0.1or γ*, 0.9nRkAn nchorage rati io, n Ra,k / Wk0.80.60.40.2Design with omega_W = 0.75, delta_h = 0.10.9 Wk, 1.0 Uk, nRk/1.60.9 Wk, 1.0 Uk0.9 Wk, 1.0 Uk, nRk/1.6, no dh0.9 Wk, 1.0 Uk, no dh1.0 Wk, 1.35 Uk, nRk/1.0, no dh1.0 Wk, 1.35 Uk, nRk/1.01.0 Wk, 1.35 Uk, nRk/1.0, no dh1.0 Wk, 1.35 Uk, nRk/1.6, no dhCharacteristic00.5 0.6 0.7 0.8 0.9Water head ratio, h_k / D• DA1-1* becomescritical for bendingmoment.0.9 Wk, 1.0 Uk, nRk/1.60.9 Wk, 1.0 Uk, 0.9nRk0.9 Wk, 1.0 Uk, nRk/1.6, no dh0.9 Wk, 1.0 Uk, no dh1.0 Wk, 1.35 Uk, nRk/1.0, no dh1.0 Wk, 1.35 1.0 Uk, nRk/1.6 nRk/1.01.0 Wk, 1.35 Uk, nRk/1.0, no dh1.0 Wk, 1.35 Uk, nRk/1.6, no dhCharacteristicUPLUPLUPLUPLDA1-1DA1-2DA1-1*DA2*27

Some thoughts• Avoid factoring water pressures – always??• Margins better than factors.• Perhaps factor differential water pressure.• Single source?• Can we retain physical reason?• Apply a lot of common sense.28