INPUT:

n 6 Location: Sfantu Gheorghe

H 2.5m 0.25m n 4 m Hfrost 1.0m

qk 15kN

m2

0.5kN

m2n 12

kN

m2

Df Hfrost 15cm 1.15m

β 11deg 0.2 deg n 9.8 deg

First layer: Second layer:

h1 2m 0.3m n 3.8m h2 10m

γk1 18kN

m3

γk2 18.2kN

m3

ϕk1.prim 13 deg 0.5 deg n 16 deg ϕk2.prim 24.5 deg 0.1 deg n 25.1 deg

ck1.prim 10kPa 0.2kPa n 11.2 kPa ck2.prim 15kPa 0.45kPa n 17.7 kPa

Design againts sliding:

Determination of safety partial factors for DA1 combination 1:

γG.fav 1 permanent actions (favourable)

γG.unf 1.35 permanent actions (unfavourable)

γQ.fav 0 variable action (favourable)

γQ.unf 1.5 variable actions (unfavourable)

γφ.prim 1 angle of eff shearing resist

γc.prim 1 effective cohesion

γγ 1 weight density

γR.h 1 sliding resistance

γR.v 1 bearing capacity

Calculation of active pressure and earth thrust:

ϕ1 ϕk1.prim 16 deg α1 0 deg δ1 ϕ1 16 deg

ϕ2 ϕk2.prim 25.1 deg α2 23.12 deg δ21 ϕ2 25.1 deg δ222

3ϕ2 16.733 deg

δ23 ϕ2 25.1 deg

ka1

cos ϕ1 α1 2

cos α1 2 cos α1 δ1 1sin ϕ1 δ1 sin ϕ1 β

cos α1 δ1 cos β α1

2

0.619

ka2

cos ϕ2 α1 2

cos α1 2 cos α1 δ21 1sin ϕ2 δ21 sin ϕ2 β

cos α1 δ21 cos β α1

2

0.415

ka3

cos ϕ2 α1 2

cos α1 2 cos α1 δ22 1sin ϕ2 δ22 sin ϕ2 β

cos α1 δ22 cos β α1

2

0.418

ka4

cos ϕ2 α2 2

cos α2 2 cos α2 δ23 1sin ϕ2 δ23 sin ϕ2 β

cos α1 δ23 cos β α2

2

0.228

cd1.prim ck1.prim cd2.prim ck2.prim hI 3.8m hII 0.1m hIII 0.5m hIV 1.30m

pa10 γQ.unf qk ka1 γG.unf 2 cd1.prim ka1 12.65 kPa

pa11 γQ.unf qk ka1 γG.unf γk1 hI ka1 2 cd1.prim ka1 44.541 kPa

pa20 γQ.unf qk ka2 γG.unf γk1 hI ka2 2 cd2.prim ka2 15.027 kPa

pa21 γQ.unf qk ka2 γG.unf γk1 hI ka2 γk2 hII ka2 2 cd2.prim ka2 16.048 kPa

pa30 γQ.unf qk ka3 γG.unf γk1 hI ka3 γk2 hII ka3 2 cd2.prim ka3 16.227 kPa

pa31 γQ.unf qk ka3 γG.unf γk1 hI ka3 γk2 hII ka3 γk2 hIII ka3 2 cd2.prim ka3 21.358 kPa

pa40 γQ.unf qk ka4 γG.unf γk1 hI ka4 γk2 hII ka4 γk2 hIII ka4 2 cd2.prim ka4 5.727 kPa

pa41 γQ.unf qk ka4 γG.unf γk1 hI ka4 γk2 hII ka4 γk2 hIII ka4 γk2 hIV ka4 2 cd2.prim ka4

pa41 13.022 kPa

x 2.9595

Pa1 pa11x

2 65.91 kPa

Pa21 pa20

hII

m 1.503 kPa Pa22 pa21 pa20

hII

2m 0.051 kPa

Pa31 pa30

hIII

m 8.113 kPa Pa32 pa31 pa30

hIII

2m 1.283 kPa

Pa41 pa40

hIV

m 7.445 kPa Pa42 pa41 pa40

hIV

2m 4.741 kPa

Pa1.H Pa1 cos α1 δ1 63.357 kPa Pa1.V Pa1 sin α1 δ1 18.167 kPa

Pa21.H Pa21 cos α1 δ21 1.361 kPa Pa21.V Pa21 sin α1 δ21 0.637 kPa

Pa22.H Pa22 cos α1 δ21 0.046 kPa Pa22.V Pa22 sin α1 δ21 0.022 kPa

Pa31.H Pa31 cos α1 δ22 7.77 kPa Pa31.V Pa31 sin α1 δ22 2.336 kPa

Pa32.H Pa32 cos α1 δ22 1.228 kPa Pa32.V Pa32 sin α1 δ22 0.369 kPa

Pa41.H Pa41 cos α2 δ23 7.441 kPa Pa41.V Pa41 sin α2 δ23 0.257 kPa

Pa42.H Pa42 cos α2 δ23 4.739 kPa Pa42.V Pa42 sin α2 δ23 0.164 kPa

γdr 20kN

m3

γc 24kN

m3

γfill 15kN

m3

Gdr γdr 2.916 m21 m 58.32 kN

Gwall γc 9.615 m21 m 230.76 kN

Gfill γfill 0.2853 m21 m 1.35 5.777 kN

PG

Gdr Gwall Gfill 2.85m 1 m

103.459 kPa

Hd Pa1.H Pa21.H Pa31.H Pa41.H Pa22.H Pa32.H Pa42.H 85.942 kPa

Vd Pa1.V Pa21.V Pa31.V Pa41.V Pa22.V Pa32.V Pa42.V PG 125.412 kPa

ε 10.12deg

Vd.prim Vd cos ε( ) Hd sin ε( ) 138.561 kPa

Hd.prim Hd cos ε( ) Vd sin ε( ) 62.569 kPa

ϕcwd.prim ϕk2.prim 25.1 deg γR 18.2kN

m3

Rd.prim Vd.prim tan ϕcwd.prim 64.907 kPa

Hd.prim Rd.prim The equation verifies -> NO SLIDING!

Design against bearing capacity failure to SR EN 1997-1:

Bending moment:

ya1.H 1.65m xa1.V 1.68m

ya21.H 1.65m xa21.V 1.68m

ya22.H 1.56m xa22.V 1.68m

ya31.H 1.56m xa31.V 1.68m

ya32.H 1.09m xa32.V 1.68m

ya41.H 1.09m xa41.V 1.68m

ya42.H 0.2 m xa42.V 1.13m

a Pa1.H ya1.H Pa21.H ya21.H Pa22.H ya22.H Pa31.H ya31.H

b Pa32.H ya32.H Pa41.H ya41.H Pa42.H ya42.H

MEd.H a b 1.275 105

kg

s2

c Pa1.V xa1.V Pa21.V xa21.V Pa22.V xa22.V Pa31.V xa31.V

d Pa32.V xa32.V Pa41.V xa41.V Pa42.V xa42.V

MEd.V c d 3.679 104

kg

s2

xdr 1.30m xwall 0.18m xfill 1.28 m

MEd.G Gdr xdr Gwall xwall Gfill xfill 109.958 kN m

MEd MEd.H MEd.V m2 MEd.G 19.269 kN m MB MEd B 2.8m

L 1meB

MB

Vd 2.8m2

0.055 mB

60.467 m

Bprim B 2eB 2.69m Lprim L

Aprim Bprim Lprim 2.69m2

e 2.718 ϕprim ϕk2.prim 25.1 deg

cd.prim ck2.prim 17.7 kPa

Nq eπ tan ϕprim

tan 45degϕprim

2

6.85

Nc Nq 1 1

tan ϕprim 12.489

Nγ 2 Nq 1 tan ϕprim 5.481

bq 1 α2 tan ϕprim 2 1.414

bγ bq 1.414

bc bq

1 bq Nc tan ϕprim

1.485

sq 1Bprim

Lprim

sin ϕprim 2.141 rectangular shape

sγ 1 0.3Bprim

Lprim

0.193

sc

sq Nq 1 Nq 1

2.336

m

2Bprim

Lprim

1Bprim

Lprim

1.271 mb m 1.271

iq 1Hd

Vd Aprim cd.prim cot ϕprim .N

m

1

iγ 1Hd

Vd Aprim cd.prim cot ϕprim .N

m 1

1

ic iq

1 iq Nc tan ϕprim

1

qprim Df γk2 20.93 kPa Aprim 2.698

peff

Vd

Aprim46.483 kPa

pacc cd.prim Nc bc sc ic qprim Nq bq sq iq 0.5γk2 Bprim Nγ bγ sγ iγ 1.237 103

kPa

peff pacc The equation verifies! The soil bears the wall!

Design against overturning (toppling) according SR EN 1997-1:

Determination of safety partial factors for EQU

γG.stb 0.9 stab. fav. perm. act.

γG.dst 1.1 destab. unf. perm. act.

γQ.stb 0 stab. fav. var. act

γQ.dst 1.5 destab. unf. var. act

γϕ.prim 1.25 angle of eff. shearing resistance

γc.pr 1.25 effective cohesion

γγ.pr 1.0 weight density

cd1.pr

ck1.prim

γc.pr8.96 kPa cd2.pr

ck2.prim

γc.pr14.16 kPa

ka1 0.619 ka2 0.415 ka3 0.418 ka4 0.228

pa10.equ γQ.dst qk ka1 γG.dst 2 cd1.pr ka1 4.365 kPa

pa11.equ γQ.dst qk ka1 γG.dst γk1 hI ka1 2 cd1.pr ka1 42.236 kPa

pa20.equ γQ.dst qk ka2 γG.dst γk1 hI ka2 2 cd2.pr ka2 18.648 kPa

pa21.equ γQ.dst qk ka2 γG.dst γk1 hI ka2 γk2 hII ka2 2 cd2.pr ka2 19.479 kPa

pa30.equ γQ.dst qk ka3 γG.dst γk1 hI ka3 γk2 hII ka3 2 cd2.pr ka3 19.647 kPa

pa31.equ γQ.dst qk ka3 γG.dst γk1 hI ka3 γk2 hII ka3 γk2 hIII ka3 2 cd2.pr ka3 23.828 kPa

pa40.equ γQ.dst qk ka4 γG.dst γk1 hI ka4 γk2 hII ka4 γk2 hIII ka4 2 cd2.pr ka4 9.15 kPa

pa41.equ γQ.stb qk ka4 γG.stb γk1 hI ka4 γk2 hII ka4 γk2 hIII ka4 γk2 hIV ka4 2 cd2.pr ka4

hI.equ 3.8m hII.equ 0.1m

hIII.equ 0.5m hIV.equ 1.3m

pa41.equ 8.986 kPa

Pa1.equ pa11.equx

2 62.499 kPa

Pa21.equ pa20.equ

hII.equ

m 1.865 kPa Pa22.equ pa21.equ pa20.equ

hII.equ

2m 0.042 kPa

Pa31.equ pa30.equ

hIII.equ

m 9.824 kPa Pa32.equ pa31.equ pa30.equ

hIII.equ

2m 1.045 kPa

Pa41.equ pa40.equ

hIV.equ

m 11.895 kPa Pa42.equ pa41.equ pa40.equ

hIV.equ

2m 0.107 kPa

Pa1.H.equ Pa1.equ cos α1 δ1 60.077 kPa

Pa21.H.equ Pa21.equ cos α1 δ21 1.689 kPa

Pa22.H.equ Pa22.equ cos α1 δ21 0.038 kPa

Pa31.H.equ Pa31.equ cos α1 δ22 9.408 kPa

Pa32.H.equ Pa32.equ cos α1 δ22 1.001 kPa

Pa41.H.equ Pa41.equ cos α2 δ23 11.887 kPa

Pa42.H.equ Pa42.equ cos α2 δ23 0.106 kPa

Pa1.V.equ Pa1.equ sin α1 δ1 17.227 kPa

Pa21.V.equ Pa21.equ sin α1 δ21 0.791 kPa

Pa22.V.equ Pa22.equ sin α1 δ21 0.018 kPa

Pa31.V.equ Pa31.equ sin α1 δ22 2.828 kPa

Pa32.V.equ Pa32.equ sin α1 δ22 0.301 kPa

Pa41.V.equ Pa41.equ sin α2 δ23 0.411 kPa

Pa42.V.equ Pa42.equ sin α2 δ23 3.681 103

kPa

a Pa1.H.equ 1.35 m Pa21.H.equ 1.35 m Pa22.H.equ 1.25 m Pa31.H.equ 1.25 m a 338.7608kN m

b Pa32.H.equ 0.75 m Pa41.H.equ 0.75 m Pa42.H.equ 0.5 m b 23.8056kN m

Mdst a b 362.566 kN m

c Pa1.V.equ 3.35 m Pa21.V.equ 3.35 m Pa22.V.equ 3.35 m Pa31.V.equ 3.35 m c 248.738kN m

d Pa32.V.equ 3.35 m Pa41.V.equ 3.35 m Pa42.H.equ 2.8 m d 9.548kN m

e Gwall 1.85 m Gdr 2.975 m Gfill 0.395 m e 602.69 kN m

Mstb c d e 860.976 kN m

Mdst Mstb The equation verifies! The wall will NOT overturn!

Design against dangerous sectionsFor C16/20

pef.min

Vd

B 1 m1

6 eB

B

0.0311

mMPa

pef.min ftd 1.9MPa

pef.max

Vd

B 1 m1

6 eB

B

0.0391

mMPa pef.max fcd 16MPa