9. Seismic Design of RETAINING STRUCTURES GRAVITY WALLS

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1 9. Seismic Design of RETAINING STRUCTURES Part A: GRAVITY WALLS G. BOUCKOVALAS Professor of NTUA October 009 CONTENTS 9.1 DYNAMIC EARTH PRESSURES for DRY SOIL 9. HYDRO-DYNAMIC PRESSURES 9.3. DYNAMIC PRESSURES for SATURATED SOILS 9.4 PSEUDO STATIC DESIGN 9.5 DISPLACEMENT based DESIGN (performance based design) Sggested Reading Steven Kramer: Capter 11 GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.1

HYDRO-DYNAMIC PRESSURES 9.3. DYNAMIC PRESSURES for SATURATED SOILS 9.4 PSEUDO STATIC DESIGN 9.

2 9.1 DYNAMIC EARTH PRESSURES for DRY SOIL Te metod of ΜΟΝΟΝΟΒΕ - ΟΚΑΒΕ GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.

3 GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.3

4 9. HYDRO-DYNAMIC PRESSURES WESTERGAARD (1933) Hydro-STATIC pressures p (x) =γ x ws H application point: w 1 P = p (x)dx = γ H ws ws w 0 Η/3 from base Hydro-DYNAMIC pressures ± p wd (x) = kγwh x/h 8 ± P = k γ H =. k P 1 application point: ( 11 ) wd w ws 0.40Η from base ATTENTION! Te excess pore pressures are positive in front of te wall and negative beind it. Tus te total ydro-dynamic pressure acting on a submerged wall is twice tat given by te Westergard solution! REMARKS: Westergaard teory applies under te following assumptions: free water (no backfill) vertical wall face very large (teoretically infinite) extent of water basin GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.4

Te excess pore pressures are positive in front of te wall and negative beind it.

5 Effect of of tank tank widt ± p wd (x) = CnkγwH x / H 8 ± Pwd = CnkγwH 1 n ( = 11. C k P ) n ws όπου 4 L/H C n = < L/H (C = 100. για L / H > 0. ) application point: 0.40Η from te base Effect of of wall wall inclination Zangar (1953) & Cwang (198) x x x x ± p wd (x, α ) = C m( α) k γwη ( ) + ( ) H H H H ή, or, προσε approximately γγιστικά ± p wd (x, α ) = C m( α) kγwη 8 x H Westergaard GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.5

40Η from te base Effect of of wall wall inclination Zangar (1953) & Cwang (198) x x x x ± p wd (x, α ) = C m( α) k

6 Effect of of wall wall inclination ± p wd (x, α ) = Cmk γwη 8 x H και and ± Pwd = Cmk γwη 1 ( = 11. C k P ) m ws όπου were ο α C m 001. α( ) 0. π ( rad) application point: 0.40Η απότηνβάση GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.6

7 9.3 DYNAMIC PRESSURES for SATURATED FILL ± p wd (x,e,..) = CekγwH x / H 8 ± P wd (e,..) = CekγwH 1 ( 11. C k P ) ό were που C.. tan log με wit e ws πnγwh e EwkT n =πορ porosity ώδες γ w w = ειδικ unit weigt ό βάρος of νερού water Η = βάθος water νερού dept Ε =Bulk =Μέτρο modulus συμπ. of νερού water (( kpa) k = συντελεστής permeability διαπερατότητας coefficient Τ = δεσπόζουσα predominant περίοδος period of δόνησης saking 6 WATER Pysical analog (Matsuzawa et al. 1985) + FILL in oter words. Correction factor C e expresses te portion of pore water wic vibrates FREELY, i.e. independently from te soil skeleton. soil skeleton free water trapped water, wic vibrates togeter wit te soil skeleton Hence, Hence, dynamic eart eart pressures are are exerted by by te te soil soil skeleton AND ANDte trapped water water and and consequently (you (you may may prove prove it it easily) easily) te te Mononobe-Okabe relationsips apply apply for for :: γ* γ* * = γ ΞΗΡΟ C ΞΗΡΟ e +γ e +γ ΚΟΡ.(1-C ΚΟΡ e ) e ) GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.

of νερού water (( 10 10 6 kpa) k = συντελεστής permeability διαπερατότητας coefficient Τ = δεσπόζουσα predominant περίοδος period of δόνησης saking 6 WATER Pysical analog (Matsuzawa et al.

8 EXAMPLE: n=40%, γ w =10 kn/m 3 E w = 106 kpa, T=0.30 sec H C e = tanlog k Fill Material well graded gravel gravel coarse sand C e > 0.80 p wd Westergaard C e = p wd Ce Westergaard fine sand silt Clayey sand & gravel C e < 0.0 p wd 0 EXAMPLE: n=40%, γ w =10 kn/m 3 E w = 106 kpa, T=0.30 sec H C e = tanlog k Permeable fill: Cobbles, gravel, Coarse sand (Η<0m) Semi-permeable» fill: coarse sand (Η > 0m), fine sand (H < 0m) Impermeable fill: silt, clay, clayey or silty sand and gravel GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.8

0 p wd 0 EXAMPLE: n=40%, γ w =10 kn/m 3 E w = 106 kpa, T=0.30 sec H C e = 05.

9 SUMMARY of Hydrodynamic Pressures Hydrodynamic pressures on te sea-side of te wall p wd (x) = CmCnkγwΗ x / H 8 Pwd = CmCnkγwH 1 ( = 11. C C k P ) m n ws C m = effect of inclined wall C n = effect of water basin lengt Hydrodynamic pressures on te fill-side of te wall p wd (x) = CmCnCekγwH x / H 8 Pwd = CmCnCekγwH 1 ( = 11. C C C k P ) m C e = effect of filll n e ws application point: 0.40Η from base GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.9

C C k P ) m n ws C m = effect of inclined wall C n = effect of water basin lengt Hydrodynamic pressures on te

10 9.4 PSEUDO STATIC DESIGN Genera Case... P a = ενεργητική active eart ώθηση pressure γαιών = k a (( γγ ΚΟΡ SA T - γ W )H 1 PW = γwh Δ P = P = ΔP W Wd ΑΕ =dynamic = δυναμικές eart ωθήσεις pressures γαιών = ( k ) γ * Η με γ * = C γ + ( 1 C ) γ wit γ* = Ce e ΞΗΡΟ γ DRY υδροδυναμικές ydrodynamic ωθήσεις pressures (κατά τα προηγού μενα) + (1-Ce)γ e SAT ΚΟΡ ATTENTION! P a computation requires (γ κορ -γ w ) wile Ρ ΑΕ computation requires γ*. Tus, wen it is necessary to compute bot P a and Ρ ΑΕ wit a common unit weigt (e.g. ΕΑΚ 00) you must use: te buoyant unit wegt (γ κορ -γ w ) a modified seismic coefficient k * = k γ κορ γ * γ w P a = ενεργητική active eart ώθηση pressure γαιών = k a (( γγ ΚΟΡ SA T - γ W )H 1 PW = γwh Δ P = P = ΔP W Wd ΑΕ =dynamic = δυναμικές eart ωθήσεις pressures γαιών = ( k ) γ * Η με γ * = C γ + ( 1 C ) γ wit γ* = Ce e ΞΗΡΟ γ DRY υδροδυναμικές ydrodynamic ωθήσεις pressures (κατά τα προηγού μενα) + (1-Ce)γ e SAT ΚΟΡ GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.10

) γ wit γ* = Ce e ΞΗΡΟ γ DRY υδροδυναμικές ydrodynamic ωθήσεις pressures (κατά τα προηγού μενα) + (1-Ce)γ e SAT ΚΟΡ 1 1 3 4 ATTENTION!

11 Special Special case: case «IMPERMEABLE» fill fill P a = ενεργητική active eart ώθηση pressure γαιών = k a (( γγ ΚΟΡ SA T - γ W )H 1 PW = γwh Δ P = P = ΔP W Wd υδροδυναμικές ydrodynamic ωθήσεις pressures (κατά τα προηγού μενα) ΑΕ =dynamic = δυναμικές eart ωθήσεις pressures γαιών = ( k ) γ * Η με γ * = C γ + ((Ce=0) 1 C ) γ wit γ* = e γξηρο SAT e ΚΟΡ Clayey sand Clayey silt Silty sand Clayey or silty gravel Special Special case: case «IMPERMEABLE» fill fill Δ P = P = ΔP ήor W Wd = υδροδυναμικές ydrodynamic ωθήσεις pressures = = ΑΕ = dynamic δυναμικές eart ωθήσεις pressures γαιών = ( k ) γ 4 γ ΚΟΡ ΔP ΑΕ = = (k )( γ γ ) Η ΚΟΡ W 8 γ γ ΚΟΡ W 3 0 ΚΟΡ Η k *. k Clayey sand Clayey silt Silty sand Clayey or silty gravel GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.11

sand Clayey or silty gravel Special Special case: case «IMPERMEABLE» fill fill Δ P = P = ΔP ήor W Wd = υδροδυναμικές ydrodynamic ωθήσεις pressures = = 0 1 3 ΑΕ = dynamic δυναμικές eart ωθήσεις

12 Special Special case: case «PERMEABLE» fill fill 1 P a = ενεργητική active eart ώθηση pressure γαιών = k a ( γ γ )H ΚΟΡ W 1 PW = γwh Δ P = P = ydrodynamic υδροδυναμικές pressure ωθήσεις 0 ΔP W Wd ΑΕ = δυναμικές dynamic eart ωθήσεις pressure γαιών = ( k ) γ* Η γ * = γ wit γ* = ΞΗΡ γ DRY. με (C = 1) e sand sand & gravel cobbles ballast Special Special case: case «PERMEABLE» fill fill Δ P = P = ΔP ήor W Wd = ydrodynamic υδροδυναμικές pressure ωθήσεις ΑΕ = dynamic δυναμικές eart ωθήσεις pressure γαιών = ( k ) γ 4 γ ΞΗΡ ΔP ΑΕ = = (k )( γ γ ) Η ΚΟΡ W 8 γ γ ΚΟΡ W 3 ΞΗΡ Η k * 1.6 k sand sand & gravel cobbles ballast GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.1

με (C = 1) e sand sand & gravel cobbles ballast Special Special case: case «PERMEABLE» fill fill Δ P = P = ΔP ήor W Wd = ydrodynamic υδροδυναμικές pressure ωθήσεις 0 1 3 ΑΕ =

13 EXAMPLE: Wat do I do wen I am not sure about te permeability of te fill material? Vertical & smoot wall Basin of infinite lengt C m = C n = 0 Fill: γ ΞΗΡΟ =16 kn/m 3 γ ΚΟΡ. = 0 kn/m 3 C e = Δ PW = PWd = kγwh * ΔP ΑΕ = ( k )( γκορ γw) Η 4 C eγ + ( 1 C e) γ ΞΗΡΟ με k * = γ γ κορ w ΚΟΡ k Total Total orizontal trust: ΣF ΣF d = d Ρ Ρ ΑΕ +Ρ ΑΕ +Ρ wd +C wd +C e P e wd wd impermeable fill permeable fill Total Total overturning moment: ΣΜ ΣΜ d =0.60H d Ρ Ρ ΑΕ +0.40Η ΑΕ (1+C (1+C e ) e ) Ρ wd wd GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.13

0 Δ PW = PWd = kγwh 1 1 3 * ΔP ΑΕ = ( k )( γκορ γw) Η 4 C eγ + ( 1 C e) γ ΞΗΡΟ με k * = γ γ κορ w ΚΟΡ k Total Total orizontal trust: ΣF ΣF d = d

14 9.5 DISPLACEMENT based DESIGN (or performance based design ) RICHARDS-ELMS METHOD δ: friction angle between wall side and fill φ ο : friction angle between wall base and ground Performance based design: o o ( AE A ) N = W+ Δ P + P tanδ F= Ntanϕο ολ Ntanϕ F.S. = P P P P k W ο o o A +Δ AE + w +Δ w + Even toug F.S. oλ < 1.0 (sliding failure) tere is no collapse of te wall (!!), but development of limited displacements, wic may be tolerable.. SLIDING FAILURE OF GRAVITY WALLS α cr =Ng : critical seismic acceleration leading to F.S. oλ =1.00 GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.14

= P P P P k W ο o o A +Δ AE + w +Δ w + Even toug F.S. oλ < 1.0 (sliding failure) tere is no collapse of te wall (!

15 Εναλλακτικά: δ= f t με: α cr Νg = α 115. V 1 αcr α 630. έδαφος f = 50. βράχος α ( 1 α ) cr cr Computation of Relative Sliding. NEWMARK (1965) (1965)... V ( 1 acr) δ = 0.50 a acr δ 0.50 a acr V 1 RICHARDS & ELMS ELMS (199) (199) V 1 δ 008. a a 4 CR E.M.Π. (1990) (1990) V (1 a CR ) δ t 1 acr a GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 acr 9A.15

50 a acr δ 0.50 a acr V 1 RICHARDS & ELMS ELMS (199) (199) V 1 δ 008. a a 4 CR E.M.Π.

16 Comparison wit numerical predictions for actual eartquakes by Franklin & Cang (19).... PERMANENT DISPLACEMENT (in) άνω άνωόριο για γιαδιάφορα Μ Newmark - I (1965) Newmark II (1965) Ricards & Elms (199) Ε.Μ.Π. (1990) a CR /a Seismic failure & downslope sliding Relative Velocity Relative Sliding δ d 4 V a 0.08 a a CR = min V a 0.50 a a CR GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.16

17 for EXAMPLE PEAK SEISMIC ACCELERATION a = 0.50g PEAK SEISMIC VELOCITY V = 1.00 m/s (T e 0.80 sec) CRITICAL or YIELD ACCELERATION a CR = 0.33g (=/3 a ) Relative Sliding δ d 4 V a 0.08 a a CR = min V a 0.50 a a CR 9 cm! THUS,if we can tolerate some small down-slope displacements, te pseudo static analysis is NOT performed for te peak seismic acceleration a, but for te.... EFFECTIVE seismic acceleration a E = ( ) a New design pilosopy: * 4 V k δ= 008. k DISPLACEMENT BASED DESIGN (or performance based design) α * * α V k = = k g αδ 14 / Instead of designing te wall for k =a /g,i coose a lower k * (< k ) wic is a function of te allowable wall displacement δ. In tat case, te required factor of safety is F.S.=1.00 alternatively: k k * = qw με: q = 1 w / 14 V α δ GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.1

... EFFECTIVE seismic acceleration a E = (0.50 0.80) a New design pilosopy: * 4 V k δ= 008. k DISPLACEMENT BASED DESIGN (or performance based design) α * * α V k = = k 0.

18 In accordance wit tis design pilosopy, ΕΑΚ requests tat: k α= = α α γ q w g n k k * = qw γ n =importance coefficient.00 δ(mm)=300a 1.50 δ(mm)=00a q w = 1.5 δ(mm)=100a (τοίχοι από Ο.Σ.) 1.00 ancored flexible walls 0.5 basement walls, etc GEORGE BOUCKOVALAS, National Tecnical University of Ates, Greece, 011 9A.18

5 δ(mm)=100a (τοίχοι από Ο.Σ.) 1.00 ancored flexible walls 0.

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