example: geogrid reinforced wall - congreso · pdf filedin 1054:2010-12 . supplementary rules...

Geotechnik im Bauwesen Geotechnical Engineering Univ.- Prof. Dr.-Ing. Martin Ziegler

1 Educational session Geosynthetics in reinforced soil structures Example: Geogrid reinforced wall

Example: Geogrid reinforced wall



1. Introduction to safety concept

Example: Geogrid reinforced wall

2. Determination of characteristic soil parameters

3. Design as rigid block structure

4. Design of geogrids

5. Design of facing elements





Eurocode 7-1 and national annex

DIN EN 1997-1:2009-09 (Eurocode EC 7-1)

DIN EN 1997-1/NA:2010-12 National annex

DIN 1054:2010-12 Supplementary rules




Introduction to the Recommendations and their Application Principles Demands on Materials Analysis Principles Embankments on Soft Soils Reinforced Foundation Pads Highways Engineering Retaining Structures Landfill Engineering - Reinforcement of Surface-parallel, Stratified Systems Reinforced Earth Structures over Point or Linear Bearing Elements Foundation Systems Using Geotextile-encased Columns Bridging Subsidence Dynamic Actions of Geosynthetic-reinforced Systems

Table of contents

EBGEO,Wiley, 2011




Design approach DA 2*: corresponds to ultimate limit states STR u. GEO-2:

verification:

design- effects

Ah,d= AGh,k·gG+ AQh,k·gQ

resistances

Eph,d= Eph,k/ gEp

MR,d= MR,k/ gmaterial

Zd= Min {ZAk/gA; ZMk/gM}

characteristic actions effects

Ah,k

Bh,k

MS,k

Eagh,k t

Eph,k

yield-moment MR,k= MF

Detail

Zk

characteristic resistances

MR,k

earth-support (GEO-2)

Eph,d - Bh,d 0

anchor (STR and GEO-2)

Zd - Ah,d 0

sheet-pile profile (STR)

MR,d - MS,d 0

Mh,d= MGh,k·gG+ MQh,k·gQ

Bh,d= BGh,k·gG+ BQh,k·gQ

1. Complete static calculation with characteristic values to determine the characteristic effects 2. Determination of characteristic resistances 3. Determination of design effects (increasing) and design resistances (decreasing) 4. Verification of safety




Design approach DA 3: corresponds to ultimate limit state GEO-3 for slope stability

Qk

Gk jk , ck

Initial situation

Qd = Qk. gQ (1,3)

Gd = Gk . gG (1,0) jk , ck

tan jd= tan jk/ gj (1,25)

Cd = Ck/ gc (1,25)

Rd = Nd.tan jd

Design situation (here: DS-1)

Nd

Utilization-factor

0M)c,tan(M d,Tddd,H j

Verification:

1rsinQGrCtanN

MM

ididi

dididi

d,T

dH,

j

1. Before starting the calculation change characteristic values to design values 2. Calculation of the overall stability with design values 3. Determination of the utilization-factor by equalizing resistant design moments with acting design moments




characteristic values of soil parameters

partial factors on soil parameters, DS-P

design values of soil parameters

j'k = 35,5° gj' = 1,25 j'd = 29,71°

c'k = 0 kN/m2 gc' = 1,25 c'd = 0 kN/m2

characteristic values of actions

partial factors on actions, DS-P

design values of actions

gk = 18 kN/m3 gG = 1,0 gd = 18 kN/m3

pk = 10,0 kN/m2 gQ = 1,3 pd = 13,0 kN/m2

characteristic values of actions

partial factors on actions, DS-P

partial factors on resistances, DS-P

sliding gG = 1,35 and gQ = 1,5 gRh = 1,1

bearing capacity gG = 1,35 and gQ = 1,5 gRv = 1,4

earth resistance gG = 1,35 and gQ = 1,5 gRe = 1,4

Design approach DA2* (STR, GEO-2)

Design approach DA3 (GEO-3)

Partial safety factors

DS-P = permanent design situation




Situation




s = 2,65 g/cm³

Density of solid particles capillary pyknometer

g = 18 kN/m³

Unit weight and water content Drying chamber

gd = 18 kN/m³

w = 4%




d [g/cm³] 1,777 1,725 1,639 1,604

tf [kN/m²] 82,4 73,4 70,0 67,5

pr = 1,725 g/cm³

Proctor-density

97% = 1,673 g/cm³




d [g/cm³] 1,777 1,725 1,639 1,604

tf [kN/m²] 82,4 73,4 70,0 67,5

Shear strength Shear box

673,1725,197,0 100D

prpr

d

59,011,6732,651- e

d

s




0

25

50

75

100

0 100 200

shea

r stre

ng t

f[k

N/m

²]

vertical pressure s [kN/m²]

j' ≈ 35,5

tf ≈ 71,5 kN/m²

t

sv

jk´= 35,5°




B=0,7H

H

l v

Earth pressure eh(z)

Eh

G

Formation as a rigid block

Behaviour of the reinforced structure like a gravity wall




B=0,7H

H

l v

Eh

G

Verification of the rigid block

- Sliding (GEO-2) - Bearing capacity (GEO-2)

- Overturning (excentricity SLS)

- Overall stability (GEO-3)

Ultimate limit states (ULS) Serviceability limit states (SLS)

- settlements - inclination - …

To be defined site-specific

Behaviour of the reinforced structure like a gravity wall





2

a

aagh

coscosßsinsin1cos

cosK

jj

j

Kagh,k = cos 30 − −10

cos −10 ⋅ 1+ sin 30 ⋅ 5 3 ⋅ sin 30 cos −10 ⋅ cos −10 + 2 3 ⋅ 30

2= 0,228 = Kaph,k

Calculation of earth pressure coefficient

Natural soil: jk=30°

GEO-2

Kagh,d = cos 29,71° − −10°

cos −10° ⋅ 1+ sin 29,71° ⋅ 5 3 ⋅ sin 29,71°cos −10° ⋅ cos −10° + 2 3 ⋅ 29,71°

2= 0,232

backfill: jk=35,5°

backfill: jd=29,7°

GEO-3




B=0,7H

H=8

,0m

l v

Ehg

G


Eagh,k = 0,5 ∙ 0,228 ∙ 19 kN/m³ ∙ (8,0 m)² = 138,62 kN/m

Eagv,k = 138,62 kN/m ∙ tan ( 2 3 ∙ 30 ) = 50,46 kN/m

Eaph,k = 0,228 ∙ 10 kN/m² ∙ 5,6 m = 12,77 kN/m

Eapv,k = 12,77 kN/m ∙ tan ( 2 3 ∙ 30 ) = 4,65 kN/m

Kagh,k = 0,228 = Kaph,k

Ehp

p=10kN/m

j=30 g=19kN/m3

Calculation of characteristic earth pressure

permanent

transient




Gk = 18 kN/m³ ∙ 8 m ∙ 5,6 m = 806,4 kN/m

Qk = 10 kN/m² ∙ 5,6 m = 56 kN/m

Eagh,k = 138,62 kN/m

Eagv,k = 138,62 kN/m ∙ tan ( 2 3 ∙ 30 ) = 50,46 kN/m

Eaph,k = 12,77 kN/m

Eapv,k = 12,77 kN/m ∙ tan ( 2 3 ∙ 30 ) = 4,65 kN/m

e = Mk Nk

eg+q = Mg,k + Mq,k Ng,k + Nq,k

= 228,37 kN + 12,77 kN/m ∙ 8,0 m/2 – 4,65 kN/m ∙ 5,6 m/2

856,86 kNm + 56 kN

m + 4,65 kNm

= 0,29 m < b3

= 1,87 m

eg eq b/2

Q

G

eg = Mg,k Ng,k

= 138,62 kN

m ∙ 8,0 m3 − 50,46 kN

m ∙5,6 m/2

806,4 kNm + 50,46 kN

m

= 228,37 kN

856,86 kN/m= 0,27 m <

b6

= 0,93 m

Proof of resultant load excenticity (SLS)




Rn,k = a`b` (g2 b` Nb + g1 d Nd + c Nc )

with: Nb = Nb0 • nb • ib • lb • xb

Nd = Nd0 • nd • id • ld • xd

Nc = Nc0 • nc • ic • lc • xc

with:

Ni0: Bearing capacity coefficients

ni: Coeff. for shape of fondation

ii: Coeff. for load inclination

li: Coeff. for slope inclination

xi: Coeff. for contact area

w

Proof of bearing capacity following DIN 4017:2006-03 (GEO-2)




Nd = gG∙ NG,k+ gQ∙ NQ,k

= 1,35 ∙(Gk + Eagv,k) + 1,5 ∙ (Pk + Eapv,k)

= 1,35 ∙(806,4 kN/m + 50,46 kN/m) + 1,5 ∙ (56 kN/m + 4,65 kN/m)= 1247,74 kN/m

Proof of bearing capacity following DIN 4017:2006-03 (GEO-2)

Resultant vertical design load

Rn,d = 1

gR,v∙ a′ ∙ b′ ∙ (g ∙ b′ ∙ Nb) =

1gR,v

∙ (b – 2 ∙ eg+p,k)² ∙ g ∙ Nb0 ∙ ib

= 1

gR,v∙ (b – 2 ∙ eg+p,k)² ∙ g ∙ Nb0 ∙ (1 − tan k )m+1

= 1

1,4 ∙ (5,6 m – 2 ∙ 0,29 m)² ∙ 19 kN/m³ ∙ 10 ∙ (1 – 138,62 kN

m + 12,77 kN/m

917,51 kNm

)

2+1

= 2786,66 kN/m

Resultant vertical design resistance

Verification

Nd = 1274,74 ≤ Rn,d = 2786,66 kN/m




Hd = gG∙ HG,k+ gQ∙ HQ,k

= 1,35 ∙ Eagh,k + 1,5 ∙ Eaph,k=1,35 ∙ 138,62 + 1,5 ∙ 12,77 = 206,29kNm

b/2

Q

G H

Proof of sliding (GEO-2)

Resultant horizontal design load

Rt,d = 1

gR,h∙ Nk∙ tan s,k =

1gR,h

∙ Nk∙l∙ tan jk

= 1

1,1∙ (806,4 kN/m + 50,46 kN/m + 4,65 kN/m) ∙ 0,8 ∙ tan (30 ) = 361,74

kNm

Resultant horizontal design resistance

N

Rt

Verification

Hd = 206,29 ≤ Rt,d = 361,74 kN/m




Proof of overall stability (slope failure) (GEO-3)

Calculation with reduced shear parameter: tanjd=tanjk/gj

Most unfavorable coefficient of utilization:

= 0,89 ≤ 1,0




pk=10,0 kN/m² pk=10,0 kN/m²

≥ boundary

< boundary layer 1

layer 16

layer 12

SEi,d

Qd

Nd

Rd jd

SEi,d

Gd

G1d

G2d

Determination of the decisive geogrid effect by variation of the geometry of the failure mechanism

Design of geogrids




8,00 m

0,50 m

5,60 m

41,6

SEi,d

Qd

Nd

Rd jd

Gd

Pd

Ea(g+p)h,d

Ea(g+p)v,d 2,10 m

5,90 m

layer 16 layer 15 layer 14 layer 13 layer 12 layer 11 layer 10 layer 9 layer 8 layer 7 layer 6 layer 5 layer 4 layer 3 layer 2 layer 1

A = 5,6 m ⋅ 8,0 m − 0,5 ⋅ 5,6 m ⋅ 5,90 m = 28,3 m2

Pd = pd ⋅ b = 13,0 kN m2 ⋅ 5,6 m = 72,8 kN m Gd = A ⋅ γd = 28,3 m2 ⋅ 18 kN m3 = 509,4 kN m

Eagh,d = 0,5 ⋅ 2,10 m ⋅ 8,80 kN m2 = 9,24 kN m

eagh,d 2,1 m =g⋅ h ⋅ Kagh,d = 18 kN m3 ⋅ 2,10 m ⋅ 0,232 = 8,80 kN m2

Eagv,d =Eagh,d ⋅ tan(a+)= 1,60 kN m




8,00 m

0,50 m

5,60 m

41,6

SEi,d

Qd

Nd

Rd jd

Gd

Pd

Ea(g+p)h,d

Ea(g+p)v,d 2,11 m

5,90 m

layer 16 layer 15 layer 14 layer 13 layer 12 layer 11 layer 10 layer 9 layer 8 layer 7 layer 6 layer 5 layer 4 layer 3 layer 2 layer 1

Rd

Nd

Gd

Pd

Qd

jd

Ea(g+p),d

SEi,d

Ei,d= Ei,d LAi

∙LAi




Effect of geogrids depending on the geometry of failure mechanism

=41,6°




Characteristic long term strength of geosynthetics

RB,k = 1

A1⋅A2⋅A3⋅A4⋅A5 ⋅ RB,k0

RB,k0 = characteristic short term strength A1 = creeping A2 = damages during installation or transportation A3 = overlaps A4 = environmental influences A5 = dynamic stress γM= partial safety factor for the structural resistance

Design value of long term strength

RB,d = RB,k ⋅ 1γM




LA2 RAi,k = 2 ⋅ σvi,k ⋅ LAi ⋅fsg,k

Characteristic pull-out resistance

RAi,k = characteristic pull-out resistance of the reinforcement relative to 1 m width svi,k = characteristic value of the normal stress in the reinforcement plane LAi = anchorage length of reinforcement behind the failure plane under consideration fsg,k = characteristic value of the mean friction coefficient between the fill soil and the plane formed by the geosynthetics and the intermediate ground n = number of adoptable friction surfaces.

RAi,d =RAi,k / γB

Design value of pull-out resistance

sv2LA2fsg,k

h2 sv2=gh2




layer LAi svi,d Ei,d RAi,d RBi,d Min (RAi,d;RBi,d) [m] [kN/m] [kN/m] [kN/m] [kN/m] [kN/m]

1 5,600 144 21,68 657,37 25,5 25,5 2 5,125 135 19,84 564,01 25,5 25,5 3 4,650 126 18,00 477,62 25,5 25,5 4 4,175 117 16,16 398,20 25,5 25,5 5 3,700 108 14,33 325,75 25,5 25,5 6 3,225 99 12,49 260,27 25,5 25,5 7 2,750 90 10,65 201,76 25,5 25,5 8 2,275 81 8,81 150,22 25,5 25,5 9 1,800 72 6,97 105,65 25,5 25,5

10 1,325 63 5,13 68,05 25,5 25,5 11 0,850 54 3,29 37,42 25,5 25,5 12 0,375 45 1,45 13,76 25,5 13,8 ∑ 35,85

Proof of effects and resistances for each geogrid layer Ei,d≤Min(Rai,d;Rbi,d)




Geogrid reinforced retaining structure Earth pressure eh(z)

DEah,i

Determination of the characteristic connection force of the facing

effect of geogrid layer proportionately to corresponding earth pressure

Z(x)

La

vs

t

Lai

vs

Fi,k t Zi,k

inactive area

1,0 withZL2ZF k,iak,ik,i t

Connecting force at facing:

depending of the stiffness of facing: 0,5< <1,0




Deformability of facing elements (EBGEO, 2011)




H

h=0,

4H

0,5 0,7 1,0

efacing,i,d = ηg ⋅ Kagh,k ⋅ γk ⋅ hi ⋅ γG + ηq ⋅Kaph,k ⋅ pk ⋅ γQ .




layer i+1

lv

layer i

layer i-1

ea,i+1,d

ea,i,d

hi

Ea,d

Efacing,i,d=efacing,i,d + efacing,i+1,d

2

efacing,i,d = ηg ⋅ Kagh,k ⋅ γk ⋅ hi ⋅ γG + ηq ⋅Kaph,k ⋅ pk ⋅ γQ .




layer hi eagh,d g eaph,d q efacing,i.d Efacing,i,d

[m] [kN/m²] [-] [kN/m²] [-] [kN/m²] [kN/m] 1 8,0 45,1 0,7 3,5 1,0 35,1 17,1 2 7,5 42,3 0,7 3,5 1,0 33,1 16,1 3 7,0 39,5 0,7 3,5 1,0 31,2 15,1 4 6,5 36,6 0,7 3,5 1,0 29,1 14,1 5 6,0 33,8 0,7 3,5 1,0 27,2 13,1 6 5,5 31,0 0,7 3,5 1,0 25,2 12,1 7 5,0 28,2 0,7 3,5 1,0 23,2 11,1 8 4,5 25,4 0,7 3,5 1,0 21,3 10,2 9 4,0 22,6 0,7 3,5 1,0 19,3 9,2

10 3,5 19,7 0,7 3,5 1,0 17,3 9,4 11 3,0 16,9 1,0 3,5 1,0 20,4 9,5 12 2,5 14,1 1,0 3,5 1,0 17,6 8,1 13 2,0 11,3 1,0 3,5 1,0 14,8 6,7 14 1,5 8,5 1,0 3,5 1,0 12,0 5,3 15 1,0 5,6 1,0 3,5 1,0 9,1 3,9 16 0,5 2,8 1,0 3,5 1,0 6,3 1,6

gk = 18 kN/m², Kagh = Kaqh = 0,232 (= Kaph) , pk = 10 kN/m² , partial safety factors (BS-P, GEO-2): gG = 1,35, gQ = 1,5

Earth pressure on facing (welded steel wire mesh = partially deformable)




layer hi Ei,d eagh,d eaph,d g = q efacing,i.d Efacing,i,d

[m] [kN/m] [kN/m²] [kN/m²] [-] [kN/m²] [kN/m] 1 8,0 21,7 45,1 3,5 1,0 48,6 23,6 2 7,5 19,8 42,3 3,5 1,0 45,8 22,2 3 7,0 18,0 39,5 3,5 1,0 42,9 20,8 4 6,5 16,2 36,6 3,5 1,0 40,1 19,4 5 6,0 14,3 33,8 3,5 1,0 37,3 18,0 6 5,5 12,5 31,0 3,5 1,0 34,5 16,6 7 5,0 10,7 28,2 3,5 1,0 31,7 15,1 8 4,5 8,8 25,4 3,5 1,0 28,8 13,7 9 4,0 7,0 22,6 3,5 1,0 26,0 12,3

10 3,5 5,1 19,7 3,5 1,0 23,2 10,9 11 3,0 3,3 16,9 3,5 1,0 20,4 9,5 12 2,5 1,5 14,1 3,5 1,0 17,6 8,1 13 2,0 - 11,3 3,5 1,0 14,8 6,7 14 1,5 - 8,5 3,5 1,0 12,0 5,3 15 1,0 - 5,6 3,5 1,0 9,1 3,9 16 0,5 - 2,8 3,5 1,0 6,3 1,6

gk = 18 kN/m², Kagh = Kaqh = 0,232 (= Kaph) , pk = 10 kN/m² , partial safety factors (BS-P, GEO-2): gG = 1,35, gQ = 1,5

Ei,d from failure mechanism Earth pressure without reduction

Determination of the decisive effect of the facing




layer

Decisive design

effect on facing

resistance

Efacing,i,d RMFi,d [kN/m] [kN/m]

1 17,1 24,2 2 16,1 24,2 3 15,1 24,2 4 14,1 24,2 5 13,1 24,2 6 12,1 24,2 7 11,1 24,2 8 10,2 24,2 9 9,2 24,2

10 9,4 24,2 11 9,5 24,2 12 8,1 24,2 13 6,7 24,2 14 5,3 24,2 15 3,9 24,2 16 1,6 24,2

Manufacturers´ instructions:

Characteristic junction strength:

RMFi,k= 34 kN/m

Design value of junction strength:

RMFi,d= RMFi,k/gB = 34/1,4 = 24,2 kN/m

Verification:

Efacing,i,d ≤ RMFi,d

example: geogrid reinforced wall - congreso · pdf filedin 1054:2010-12 . supplementary rules...

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