[foundations][1st project] retaining wall (2)

7/28/2019 [Foundations][1st Project] Retaining Wall (2)

1/14

Design of a Retaining Wall

Florian Larisa

Group 3041


2/14

Table of Contents

A. Written part:

1. Presentation Page2. Project Theme3. Table of Contents4. Technical Report5. Calculation Notes

B. Drawings:

1. Cross section scale 1:20

2. Longitudinal profile scale 1:50


3/14

Technical Report

In this project a retaining wall is designed, whose dimensions werechosen according to the verification at sliding, bearing capacity, overturningand structural failure. The verifications were done using Coulombs Theory forthe calculus of active earth pressure.

The dimensions of the gabions were chosen from the retaining wallcatalogue IPTANA.

The walls verification against sliding was done according to theapproach from SR RN 1997-1, for the ultimate limit state GEO, using thedesign approach 1, combination 1.

The verification against bearing capacity failure to SR RN 1997-1 wasdone for the ultimate limit state GEO, using the design approach 1,combination 1.

The design against overturning according to SR RN 1997-1 was done

for ultimate limit state EQU with its corresponding safety factors.The design against dangerous sections was done in the ultimate limit

state STR according to SR RN 1997-1.

Technical conditions of execution

At the execution of the retaining wall all the norms and standards

regarding this activity have to be respected. It should be taken into accountthe followings:1. The execution of the retaining wall will be performed on

alternating sections of 5 m.2. The excavations will be carried out with support sections.3. The poured concrete will be properly vibrated and will be

adherent to the walls of the foundations hole.


4/14

15kN

m2

0.5kN

m2

9 10.5kN

m2

==

2.75m 0.25m 9+ 5 m=:=

8 0.2 9 6.2=:=

1st layer: yallow clay

h1 2m 0.2m 9+ 3.8m=:=

k1 18kN

m3

:=

k1 10 0.5 9+ 14.5deg=:=

ck1 13kPa 0.2kPa 9+ 14.8kP=:=

2nd layer: yellowish brown silty sand

h2

10:=

k2 18.5kN

m3

:=

k2 16.5 0.3 9+ 19.2deg=:=

ck2 15kPa 0.15kPa 9+ 16.35kP=:=

From the retaining wall catalogue:

B 4.6:=

Df 1.5:=

b 1.7:=a 1:=c 1.5:=d 0.:=

3 18 deg:=

11deg:= h3 1.5:=

h2 Hw Df+B

5+ h1 h3 2.12m=:=

Calculation notes


5/14

5.2. Design of the retaining wall

5.2.1. Design against sliding to SR EN 1667-1

Actions

G 1:= permanent favourable action

Pa 1.3:= permanent unfavourable action

Q 0:= variable favourable action

Q.u 1.5:= variable unfavourable action

Geotechnical parameters:

1.:= angle of effective shear resistance

c 1.:= effective cohesion

1.:= weight density

Total resistance of the soil:

R.h 1.:= sliding resitance

R.v 1.:= bearing capacity

Design values for geotechnical parameters:

d1k1

18kN

m3

=:= d2k2

18.5kN

m3

=:=

tg d1tan k1( )

0.259=:= tg d2

tan k2( )

0.348=:=

cd1

c

k1c

14.8kP=:= cd2c

k2c

16.35kP=:=


6/14

Calculation of active pressure and earth thrust:

1 0 :=

1 k1:=

1 :=

ka1

cos k1 1( )2

cos 1( )2

cos 1 1+( ) 1sin k1 1+( ) sin k1 1( )cos 1 1( ) cos 1 1( )

+ 2

0.601=:=

2 0 :=

22

3 k1:=

2 :=

ka2

cos k1 2( )2

cos 2( )2

cos 2 2+( ) 1sin k1 2+( ) sin k1 2( )

cos 2 2( ) cos 2 2( )+

2

0.613=:=

3 3:=

3 k1:=

3 :=

ka3

cos k1 3( )2

cos 3( )2

cos 3 3+( ) 1sin k1 3+( ) sin k1 3( )

cos 3 3( ) cos 3 3( )+

2

0.813=:=

1 d1:= 2 d2:=


7/14

c1 cd1:= c2 cd2:=

pa1 k1 h1 ka1 2cd1 ka1( ) 1.35 qk ka1 1.5+ 33.949kP=:=pa21 k1 h1 ka2 2cd2 ka2( ) 1.35 qk ka2 1.5+ 31.685kP=:=

pa22 k1 h1 k2 h2+( ) ka2 2cd2 ka2 1.35 qk ka2 1.5+ 64.134kP=:=

pa31 k1 h1 k2 h2+( ) ka3 2cd2 ka3 1.35 qk ka3 1.5+ 91.082kP=:=

pa32 k1 h1 k2 h2 h3+( )+ ka3 2cd2 ka3 1.35 qk ka3 1.5+ 121.529kP=:=

Thrust of each layer:

Pa11 pa1

h1

2 1 m 64.503k=:=

Pa21 pa21 h2 1 m 67.172kN=:=

Pa22 pa22 pa21( )h2

2 1 m 34.396k=:=

Pa31 pa31 h3 1 m 136.623k=:=

Pa32 pa32 pa31( ) h32

1 m 22.835k=:=

Deconstruction of thrust in horizontal and vertical components:

Layer 1

Pa11.H Pa11 cos 1 1+( ) 62.448k=:=

Pa11.V Pa11 sin 1 1+( ) 16.15k=:=

Layer 2

Pa21.H Pa21 cos 2 2+( ) 66.218k=:=

Pa21.V Pa21 sin 2 2+( ) 11.279k=:=

Pa22.H Pa22 cos 2 2+( ) 33.908k=:=


8/14

Pa22.V Pa22 sin 2 2+( ) 5.776k=:=

Layer 2 at foundation

Pa31.H Pa31 cos 3 2+ 121.002k=:=

Pa31.V Pa31 sin 3 2+( ) 63.438k=:=

Pa32.H Pa32 cos 3 2+( ) 20.224k=:=

Pa32.V Pa32 sin 3 2+( ) 10.603k=:=

Weights

Gdren 0.8m 4.5 m 1 m 19kN

m3

68.4k=:=

Gwall 14.69m2

1 m 20kN

m3

293.8k=:=

Gbase 6.93m2 1 m 24

kN

m3

166.32k=:=

Calculation of actions

Hd Pa11.H Pa21.H+ Pa22.H+ Pa31.H+ Pa32.H+ 303.801k=:=

Vd 1 Gdren Gwall+ Gbase+( ) Pa11.V+ Pa21.V+ Pa22.V+ Pa31.V+ 625.163k=:=

Evaluation of sliding resistance

11 deg=Vprim e.d Vd cos ( ) Hd sin ( )+ 671.645k=:=

Hprim e.d Hd cos ( ) Vd sin ( ) 178.932k=:=

tan k2( ) 0.348=:=

R

prim e.d

V

prim e.d

233.892k=:=

VERIFICATION AT SLIDING

Hprime.d Rprime.d< 1=


9/14

Design for Bearing Capacity Failure to SR EN 1997-1

yG 1.19:=

y11 3.09m3.08

2m+ 4.63m=:=

y21 3.09:=

y22 1. 075m2.02

2m+ 2.085m=:=

y31 1.075:=

y32 0.75:=

xG 2.17:=

xdren 4.61m xG 2.44m=:=

xwall 3.16m xG 0.99m=:=

xbase 0:=

pr k22

3:=

M

P.H

P

a11.H

y

11

Pa21.H

y

21

+ Pa22.H

y

22

+ Pa31.H

y

31

+ Pa32.H

y

32

+:=

MP.V Pa11.V Pa21.V+ Pa22.V+ Pa31.V+ Pa32.V+( ) x:=

Med MP.H( ) MP.V Gdren xdren Gwall xwall+ Gbase xbase+( ) 19.211kN=:=

cd.pr cd2 16.35kP=:=

eB

Med

Vd

0.031m=:=

Bpr B 2eB 4.539m=:= Lpr 5:=

Apr Bpr 1 m 4.539m2

=:=

pr k2 18.5kN

m3

=:=

qpr Df pr 27.75kP=:=


10/14

Dimensionless factors of the pressure calculation for the foundation terrain

Bearing capacity:

Nq e tan pr( )

tan 45degpr

2+

2 3.204=:=

Nc Nq 1( )1

tan pr( ) 9.7=:=

N 2 Nq 1( ) tan pr( ) 1.001=:=

Inclination of foundation base:

bq 1 3 tan pr( )( ) 2 0.862=:=

b bq:=

bc bq

1 bq( )Nc tan pr( )

0.8=:=

Foundation geometry

sq 1Bpr

Lpr

sin pr( )+ 1.201=:=

s 1 0.3Bpr

Lpr

0.728=:=

sc

sq Nq 1

Nq 22.366=:=

m factor

mL

2Lpr

Bpr

+

1 LprBpr

+

:=

Loading inclination

iq 1Hd

Vd Apr cd.pr cot pr( )+

mL

0.567=:=

i 1Hd

Vd Apr cd.pr cot pr( )+

mL 1+

0.386=:=


11/14

ic iq

1 iq( )Nc tan pr( )

:=

Rd cd.pr Nc bc sc ic qpr Nq bq sq iq+ 0.5 pr Bpr N b s i+( ) Apr 787.859kN=:=

Vd 625.163k=

Vd

Apr

Rd

Apr

< 1=

Design against overturning according to SR EN 1997-1

Partial safety factors for EQU

G.stb 0.:=

G.dst 1.1:=

Q.std 0:=

Q.dst 1.:=

Geotechnical parameters

.pr 1.2:=

c.pr 1.2:= 1.:=

Design values for geotechnical parameters

d1k1

18kN

m3

=:= d2k2

18.5kN

m3

=:=

tgd1

tan k2( ).pr

0.279=:= tgd2

tan k2( ).pr

0.279=:=

d1 atan tgd1( ) 0.272=:= d2 atan tgd2( ) 0.272=:=

cd1.pr

ck1

c.pr11.84kP=:= cd2.pr

ck2

c.pr13.08kP=:=

Thrust


12/14

pa1.ovr k1 h1 ka1 2cd1.pr ka1( ) G.dst qk ka1 Q.dst+ 34.46kP=:=

pa21.ovr k1 h1 ka2 2cd2.pr ka2( ) G.dst qk ka2 Q.dst+ 33.237kP=:=

pa22.ovr k1 h1 k2 h2+( ) ka2 2cd2.pr ka2 G.dst qk ka2 Q.dst+ 59.677kP=:=

pa31.ovr k1 h1 k2 h2+( ) ka3 2cd2.pr ka3 G.dst qk ka3 Q.dst+ 83.071kP=:=

pa32.ovr k1 h1 k2 h2 h3+( )+ ka3 2cd2.pr ka3 G.dst qk ka3 Q.dst+ 107.88kP=:=

Thrust of each layer:

Pa11 pa1.ovr

h1

2 1 m 65.475kN=:=

Pa21 pa21.ovr h2 1 m 70.462k=:=

Pa22 pa22.ovr pa21.ovr( )h2

2 1 m 28.026k=:=

Pa31 pa31.ovr h3 1 m 124.607k=:=

Pa32 pa32.ovr pa31.ovr( )h3

2 1 m 18.606k=:=

Deconstruction of thrust in horizontal and vertical components:

Layer 1

Pa11.H Pa11 cos 1 1+( ) 63.389k=:=

Pa11.V Pa11 sin 1 1+( ) 16.394k=:=

Layer 2

Pa21.H Pa21 cos 2 2+( ) 69.461k=:=

Pa21.V Pa21 sin 2 2+( ) 11.832k=:=

Pa22.H Pa22 cos 2 2+( ) 27.628k=:=

Pa22.V Pa22 sin 2 2+( ) 4.706k=:=

Layer 2 at foundation

Pa31.H Pa31 cos 3 2+( ) 110.36k=:=

Pa31.V Pa31 sin 3 2+ 57.858k=:=

Pa32.H Pa32 cos 3 2+ 16.479k=:=

Pa32.V Pa32 sin 3 2+( ) 8.639k=:=


13/14

Destabilising moment

xd.o 400c:=ya1.ovr 329c:=xw.o 268c:=y

a21.ovr163cm

:= xb.o 223c:=ya22.ovr 139cm:=

ya31.ovr 0.1c:=

ya32.ovr 26 cm:=

xa 460cm:=

Mdst.d Pa11.H ya1.ovr Pa21.H ya21.ovr+ Pa22.H ya22.ovr+ Pa31.H ya31.ovr+ Pa32.H ya32.ovr+ 356kN=:=

Mstb.d Pa11.V Pa21.V+ Pa22.V+ Pa31.V+ Pa32.V+( ) xa Gdren xd.o+ Gwall xw.o+ Gbase xb.o+ 1889.25kN=:=

Verification at overturning

Mdst.d Mstb.d< 1= OK

Design against dangerous sections

Axial stress in a-a section

Gk.wall 20kN

m3

82125 cm2 1 m 164.25k=:=

Gk Gk.wall Gdren+ 232.65k=:=

Vd.prime 1.35Gk:=

ha_a 98c:=

pa2.a_a k1 h1 k2 ha_a+( ) ka2 2cd2 ka2 1.35 qk ka2 1.5+ 46.685kP=:=

Pa21.a_a pa21 ha_a 1 m 31.051k=:=

Pa22.a_a pa22 pa21( )ha_a

2 1 m 15.9 k =:=

Pa21.a_a.H Pa21.a_a cos 2 2+( ) 30.61k=:=

Pa22.a_a.H Pa22.a_a cos 2 2+( ) 15.674k=:=

ya_a.1 188. 33cm:=

ya_a.21 47.5c:=

ya_a.22 31.5c:=


14/14

[foundations][1st project] retaining wall (2)

Documents