Worked Example T-shaped Gravity Wall - Eurocodes - Europa

Eurocodes:Background & ApplicationsGEOTECHNICAL DESIGN with worked examples 13-14 June 2013, Dublin

Worked example –Worked example T-shaped gravity wall

Dr Andrew BondDirector, Geocentrix LtdChairman TC250/SC7


Worked example –T-shaped gravity wall

DESIGN SITUATIONT shaped gravity wall

Eurocodes:Background & Applications

GEOTECHNICAL DESIGN ith k d l 13 14 J D bliGEOTECHNICAL DESIGN with worked examples 13-14 June, Dublin

Design situation for gravity wall example

©2005-13 Geocentrix Ltd. All rights reserved3



Earth pressure theory

Use Rankine’s equation for Ka:

⎛ ⎞β

β β ϕβ

β β ϕ

⎛ ⎞− −⎜ ⎟=⎜ ⎟+ −⎝ ⎠

2 2

, 2 2a

cos cos cosK cos

cos cos cos

Horizontal and vertical component of Ka are:

β β ϕ+⎝ ⎠cos cos cos

( )β β= ×, ,a h aK K cos

( )β β β= × = ×, , ,sin tana v a a hK K K




Some numbers to save you time...

Self-weight of wall stem γ= × ×, ,stem k c k sW t H

k

Self-weight of wall base

= × × =25 0.7 6 105kN m

γ= × ×, ,base k c k bW t B

= × × =25 0.8 3.9 78kN m

⎛ ⎞H hSelf-weight of backfill γ +⎛ ⎞= × × ⎜ ⎟⎝ ⎠⎛ ⎞

, 2f

fill k k heel

H hW b

+⎛ ⎞= × × =⎜ ⎟⎝ ⎠

6 6.8219 2.25 274

2kN m




Bearing capacity coefficients

ϕ Nq ϕ Nq

20 6 4 30 18 420 6.4 30 18.4

21 7.1 31 20.6

22 7.8 32 23.2

23 8.7 33 26.1

24 9.6 34 29.4

25 10.7 35 33.3

26 11.9 36 37.8

27 13 2 37 42 927 13.2 37 42.9

28 14.7 38 48.9

29 16.4 39 56.0




Worksheet – T-shaped gravity wall

Calculate:1. Earth pressure coefficient Ka1. Earth pressure coefficient Ka

2. Moments about wall toe, the determine eccentricity of loadingloading

3. Bearing resistance under eccentric, inclined loads

4 Sliding resistance4. Sliding resistance5. Toppling resistance



Worked example –T-shaped gravity wall

SOLUTIONT shaped gravity wall



Solutions DA1/DA2* – T-shaped gravity wall

Verification DA1 DA2* Traditional

DA1-1 DA1-2DA1 1 DA1 2

Sliding 66% 85% 99% Fs = 1.52

Bearing 125% 230% 93% Fb = 2.03

Eccentricity 0.92 m 0.64 m 0.42 m Same as DA2*Effective width 2.05 m 2.63 m 3.06 m

Toppling 31% 31% 31% FO = 4.35




Summary of key points

DA2* requires a wall base of width B ≥ 3.9 mEquivalent to traditional Fs = 1.5 and Fb = 2.0Equivalent to traditional Fs 1.5 and Fb 2.0

DA1 requires a wall base of width B ≥ 5.1 mE i l t t t diti l F 1 86 d F 3 93Equivalent to traditional Fs = 1.86 and Fb = 3.93

Main difference between DAs 1 and 2* is bearing resistanceCalculated load eccentricity is very differentEffective width is much smaller in DA1



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Worked Example T-shaped Gravity Wall - Eurocodes - Europa