Subgroup A - Appendix B

Appendix B of the Subgroup A report Failure mode design equations and related partial safety factors. J. Dalsgaard Sørensen and H. F. Burcharth For explanation and derivation of the safety factors see the subgroup D report. Table B1. Partial safety factors for sliding failure of vertical wall caissons. Design equation 1 ˆ G = G ( γ H Hˆ ST L , ρˆ c , Uˆ Hor . Force , Uˆ Ver . Force , ξˆ , f , B) γZ

1 ˆ ˆ f − U Hor . Force FˆH = ( FˆG − Uˆ Ver. Force FˆU ) γZ In calculation of FˆU and FˆH apply as wave height γ H Hˆ STL . Deep water. Design without model tests.

Deep water. Wave load determined by model tests.

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

γH 1.4 1.3 1.3 1.2 1.1

γZ 1.7 1.4 1.2 1.2 1.0

γH 1.5 1.4 1.4 1.3 1.1

γZ 1.7 1.4 1.3 1.2 1.1

Shallow water. Design without model tests.

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

γH 1.3 1.2 1.2 1.1 1.0

γZ 1.9 1.6 1.4 1.3 1.2

γH 1.4 1.3 1.3 1.2 1.0

γZ 1.9 1.6 1.4 1.3 1.2

γZ 1.5 1.4 1.2 1.2 1.2

γH 1.4 1.3 1.3 1.2 1.1

γZ 1.5 1.4 1.2 1.2 1.0

Shallow water. Wave load determined by model tests.

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

γH 1.3 1.2 1.2 1.1 1.0

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

γH 1.2 1.1 1.1 1.1 1.0

γZ 1.6 1.5 1.3 1.2 1.1

γH 1.3 1.2 1.2 1.1 1.0

γZ 1.6 1.5 1.3 1.2 1.1

Hˆ STL TL B Uˆ Hor. Force

significant wave height with return period TL structure lifetime width of caisson 0.90, bias factor to be applied to the Goda horizontal wave force

Uˆ Ver. Force

0.77, bias factor to be applied to the Goda vertical wave force

Uˆ Hor. Moment

0.81, bias factor to be applied to the moment from the Goda horizontal wave forces around the shoreward heel of the base plate

Uˆ Ver. Moment

ρc FG FH

0.72, bias factor to be applied to the moment from the Goda vertical wave forces around the shoreward heel of the base plate mass density of caisson buoyancy reduced weight of caisson horizontal wave force calculated by the Goda Formula

FU

wave induced uplift force calculated by the Goda formula

f

friction coefficient

B1

Table B2. Partial safety factors for overturning failure of vertical wall caissons. Design equation G = G ( γ H Hˆ STL , ρˆ c ,Uˆ Hor . Moment ,Uˆ Ver . Moment , ξˆ , B ) = ( Mˆ G − Uˆ Ver. Moment M U ) − Uˆ Hor . Moment M H In calculation of Mˆ U and Mˆ H apply as wave height γ H Hˆ STL . Design without model tests.

Wave load determined by model tests.

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

γH 2.7 2.0 1.6 1.2

γH 2.5 1.7 1.2

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

γH 2.1 1.7 1.4 1.3 1.1

γH 2.3 1.9 1.6 1.4 1.2

Hˆ STL TL

significant wave height with return period TL structure lifetime

B

width of caisson

Uˆ Hor. Force

0.90, bias factor to be applied to the Goda horizontal wave force

Uˆ Ver. Force

0.77, bias factor to be applied to the Goda vertical wave force

Uˆ Hor. Moment

0.81, bias factor to be applied to the moment from the Goda horizontal wave forces around the shoreward heel of the base plate

Uˆ Ver. Moment

0.72, bias factor to be applied to the moment from the Goda vertical wave forces around the shoreward heel of the base plate

ρc

mass density of caisson

MG

moment of FG around heel of caisson

MH

moment of FH around heel of caisson

MU

moment of FU around heel of caisson

FG

buoyancy reduced weight of caisson

FH

horizontal wave force calculated by the Goda Formula

FU

Wave induced uplift force calculated by the Goda formula

B1

Table B3. Partial safety factors for foundation failure of vertical wall caissons – Sand subsoil. Design equation parameters G = G ( γ H Hˆ STL , ρˆ c ,Uˆ Hor . Force ,Uˆ Ver . Force ,Uˆ Hor . Moment ,Uˆ Ver . Moment , 1 1 ζˆ , taˆn ϕ d1 , taˆn ϕ d 2 , B ) γZ γZ Design equations are presented in Appendix A of the Subgroup A report Deep water. Design without model tests. γZ is used for both rubble mound and sand subsoil.

Deep water. Wave load determined by model tests. γZ is used for both rubble mound and sand subsoil.

σ ' FH S = 0.05 σ ' FH S = 0.2

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

γH 1.4 1.3 1.2 1.1 1.1

γZ 1.3 1.2 1.2 1.1 1.0

γH 1.4 1.3 1.2 1.1 1.1

γZ 1.3 1.2 1.2 1.2 1.0

Shallow water. Design without model tests. γZ is used for both rubble mound and sand subsoil.

Pf 0.01 0.05 0.10 0.20 0.40

γH 1.3 1.2 1.2 1.1 1.1

Hˆ STL TL B

Uˆ Hor. Force Uˆ Ver . Force

Uˆ Hor. Moment Uˆ Ver. Moment

ϕd

γZ 1.4 1.3 1.2 1.1 1.0

γH 1.3 1.3 1.2 1.1 1.1

γZ 1.4 1.3 1.2 1.2 1.0

γZ 1.2 1.1 1.1 1.1 1.0

γH 1.4 1.4 1.3 1.1 1.1

γZ 1.2 1.1 1.1 1.1 1.0

Shallow water. Wave load determined by model tests. γZ is used for both rubble mound and sand subsoil.

σ ' FH S = 0.05 σ ' FH S = 0.2

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

γH 1.3 1.3 1.2 1.1 1.1

Pf 0.01 0.05 0.10 0.20 0.40

γH 1.3 1.3 1.2 1.1 1.1

γZ 1.2 1.1 1.1 1.1 1.0

γH 1.4 1.4 1.3 1.1 1.1

γZ 1.2 1.1 1.1 1.1 1.0

significant wave height with return period TL structure lifetime width of caisson 0.90, bias factor to be applied to the Goda horizontal wave force 0.77, bias factor to be applied to the Goda vertical wave force 0.81, bias factor to be applied to the moment from the Goda horizontal wave forces around the shoreward heel of the base plate 0.72, bias factor to be applied to the moment from the Goda vertical wave forces around the shoreward heel of the base plate

sin ϕ' cos ψ 1 − sin ϕ' sin ψ

ϕ'

effective friction angle of friction material (sand or rubble stone)

ψ

dilation angle of friction material (sand or rubble stone)

ρc

mass density of caisson

B2

Table B4. Partial safety factors for foundation failure of vertical wall caissons –Clay subsoil. Design equation parameters G = G( γ H Hˆ ST L , ρˆ c , Uˆ Hor . Force , Uˆ Ver . Force , Uˆ Hor . Moment , Uˆ Ver . Moment , 1 1 taˆ n ϕ d 1 , cˆ u , B ) ζˆ , γZ γc Design equations are presented in Appendix A of the Subgroup A report

Deep water. Design without model tests. γZ is used for rubble mound and γc for clay subsoil.

Pf 0.01 0.05 0.10 0.20 0.40

σ ' FH S = 0.05

σ ' FH S = 0.2

γH 1.3 1.2 1.1 1.0 1.0

γH 1.4 1.3 1.2 1.0 1.0

γZ 1.5 1.4 1.3 1.3 1.1

γC 1.6 1.5 1.5 1.4 1.1

γZ 1.5 1.4 1.3 1.3 1.1

γC 1.6 1.5 1.5 1.5 1.2

Deep water. Wave load determined by model tests. γZ is used for rubble mound and γc for clay subsoil.

Pf 0.01 0.05 0.10 0.20 0.40

σ ' FH S = 0.05

σ ' FH S = 0.2

γH 1.2 1.1 1.0 1.0 1.0

γH 1.3 1.2 1.1 1.0 1.0

γZ 1.5 1.3 1.3 1.2 1.1

γC 1.6 1.5 1.5 1.3 1.1

γZ 15. 1.3 1.3 1.3 1.1

γC 1.6 1.5 1.4 1.3 1.1

Shallow water. Design without model tests. γZ is used for rubble mound and γc for clay subsoil.

Pf 0.01 0.05 0.10 0.20 0.40

σ ' FH S = 0.05

σ ' FH S = 0.2

γH 1.2 1.1 1.1 1.0 1.0

γH 1.3 1.2 1.2 1.1 1.1

γZ 1.5 1.4 1.3 1.3 1.1

γC 1.6 1.5 1.3 1.3 1.1

γZ 1.5 1.4 1.3 1.2 1.1

γC 1.6 1.5 1.3 1.3 1.1

Shallow water. Wave load determined by model tests. γZ is used for rubble mound and γc for clay subsoil.

Pf 0.01 0.05 0.10 0.20 0.40

σ ' FH S = 0.05

σ ' FH S = 0.2

γH 1.2 1.1 1.1 1.0 1.0

γH 1.3 1.2 1.1 1.1 1.1

γZ 1.3 1.2 1.2 1.1 1.0

γC 1.4 1.4 1.3 1.3 1.0

B3

γZ 1.3 1.2 1.2 1.1 1.0

γC 1.4 1.4 1.3 1.2 1.0

Hˆ STL TL

significant wave height with return period T structure lifetime

B

width of caisson

Uˆ Hor. Force

0.90, bias factor to be applied to the Goda horizontal wave force

Uˆ Ver. Force

0.77, bias factor to be applied to the Goda vertical wave force

Uˆ Hor . Moment

0.81, bias factor to be applied to the moment from the Goda horizontal wave forces around the shoreward heel of the base plate

Uˆ Ver . Moment

0.72, bias factor to be applied to the moment from the Goda vertical wave forces around the shoreward heel of the base plate

ϕd

sin ϕ' cos ψ 1 − sin ϕ' sin ψ

ϕ'

effective friction angle of friction material (sand or rubble stone)

ψ ρc cu

dilation angle of friction material (sand or rubble stone) mass density of caisson undrained shear strength of clay

B4

Table B5. Partial safety factors for toe-berm rock armour failure in front of vertical wall caissons (Madrigal and Valdés 1995). Design without model tests. Design equation G=

hˆ 1 ˆ ˆ ∆ Dn 50 (5.8 b − 0.60) N od0.19 − γ H Hˆ STL γZ hˆs

Deep water.

Shallow water.

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

γH 1.6 1.4 1.3 1.2 1.1

γZ 1.3 1.2 1.2 1.1 1.0

xˆ

γH 1.7 1.5 1.4 1.3 1.2

γZ 1.3 1.2 1.2 1.1 1.0

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

γH 1.5 1.3 1.2 1.1 1.1

γZ 1.5 1.3 1.2 1.2 1.0

γH 1.6 1.4 1.3 1.2 1.2

γZ 1.5 1.3 1.2 1.2 1.0

mean values of x equivalent cube side length of medium rock size significant wave height with return period TL equal to structure lifetime water depth on top of toe berm water depth in front of toe berm number of displaced units within a strip of width Dn

Dn50

H sTL hb hs Nod

Table B6. Partial safety factors for scour at circular vertical wall roundheads (Sumer and Fredsøe 1997). Design without model tests. Design equation G=

1 γZ

Sˆ T − 0.5(1 − exp( −0.175( Kˆ C ( γ H Hˆ S L ) − 1))) ˆ B

where KC =

U mT p

B In calculation of Um apply as wave height γ H Hˆ STL . Deep and shallow water. σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40 xˆ B

H sTL S Tp Um

γH 2.0 2.0 2.0 2.0 2.0

γZ 2.4 2.0 1.8 1.5 1.2

γH 2.0 2.0 2.0 2.0 2.0

γZ 2.4 2.0 1.8 1.5 1.2

mean values of x diameter of vertical wall roundhead significant wave height with return period TL equal to structure lifetime scour depth wave peak period max wave generated velocity of water particles at the undisturbed sea bed

B5

Table B7. Partial safety factors for hydraulic stability failure of Dolosse (Burcharth and Liu 1992). Design without model tests. Design equation 1 ˆ ˆ G= ∆ Dn ( 47 − 72rˆ)ϕˆ Dˆ 1 / 3 Nˆ Z−0.1 − γ H Hˆ STL γZ σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40 xˆ

γH 2.1 1.7 1.5 1.3 1.0

γZ 1.08 1.00 1.00 1.00 1.10

γH 2.4 1.7 1.6 1.3 1.1

γZ 1.02 1.08 1.00 1.04 1.02

mean values of x equivalent cube side length of armour unit = (Volume)1/3 relative number of units displaced significant wave height with return period TL equal to structure lifetime number of waves packing density ρs/ρw – 1 mass density of armour units mass density of water

Dn D

H sTL Nz φ ∆ ρs ρw

Table B8. Partial safety factors for hydraulic stability failure of Tetrapods (Van der Meer 1988). Design without model tests. Design equation G=

Nˆ 0.5 1 − 0.1 ˆ ˆ (3.75 0od.25 + 0.85) sˆom ∆Dn − γ H Hˆ STL ˆ γZ Nz σ ' FH S = 0.05 σ ' FH S = 0.2

Pf 0.01 0.05 0.10 0.20 0.40 xˆ Dn

H sTL Nz Nod som ∆ ρs ρw

γH 1.7 1.4 1.3 1.2 1.0

γZ 1.02 1.06 1.04 1.02 1.08

γH 1.9 1.5 1.4 1.3 1.1

γZ 1.04 1.08 1.04 1.00 1.00

mean values of x equivalent cube side length of armour unit = (Volume)1/3 significant wave height with return period TL equal to structure lifetime number of waves number of displaced units within a strip of width Dn wave steepness, Hs/Lom ρs/ρw – 1 mass density of armour units mass density of water

B6

Table B9. Partial safety factors for trunk Dolos breakage (Burcharth et al 1995). Design without model tests. Design equation G=

1 B − C 0 Mˆ C1 Sˆ C2 ( γ H Hˆ STL ) C3 γZ

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

xˆ

γH 1.9 1.5 1.4 1.2 1.1

γZ 1.00 1.04 1.00 1.10 1.00

γH 2.1 1.6 1.5 1.3 1.1

γZ 1.00 1.10 1.00 1.00 1.02

C0 C1 Dolos waist ratio 0.325 0.00973 -0.749 0.37 0.00546 -0.782 0.42 0.01306 -0.507

C2 -2.584 -1.221 -1.743

C3 4.143 3.147 2.871

mean values of x relative number of broken units significant wave height with return period TL equal to structure lifetime mass of unit in ton concrete tensile strength in M Pa

B

H sTL M S

Table B10. Partial safety factors for trunk Tetrapod breakage (Burcharth et al 1995). Design without model tests. Design equation G=

1 B − 3.3910 −3 Mˆ −0.79 Sˆ −2.73 ( γ H Hˆ STL ) 3.84 γZ

σ ' FH S = 0.05 σ ' FH S = 0.2 Pf 0.01 0.05 0.10 0.20 0.40

xˆ B

H sTL M S

γH 1.9 1.6 1.4 1.2 1.1

γZ 1.10 1.00 1.04 1.10 1.00

γH 2.1 1.7 1.5 1.3 1.1

γZ 1.06 1.00 1.04 1.06 1.04

mean values of x relative number of broken units significant wave height with return period TL equal to structure lifetime mass of unit in ton concrete tensile strength in M Pa

B7

B8