2 Design of Cantilever Wall

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Chapter 2. Design of Cantilever wall In this chapter, the design of cantilever wall and its overall analysis is described.

Assignment

Design a cantilever wall with a height of 4,0 m and analyze it by EN 1997-1 (EC 7-1, Design

approach 1). The terrain behind the structure is horizontal. The ground water table is 2,0 meters deep.

Behind the wall acts a strip surcharge with a length of 5,0 meters and with a magnitude of 10 kN/m2.

The foundation soil consists of MS –Sandy silt, stiff consistency, 8,0<rS , allowable bearing capacity

is 175 kPa. The soil behind the wall will consist of S-F – Sand with trace of fines, medium dense soil.

The cantilever wall will be made of reinforced concrete of class C 20/25.

Scheme of the cantilever wall - Assignment

Solution:

For solving this problem, we will use the GEO5 program, Cantilever wall. In this text, we will

explain solving this example step by step.

In the frame “Settings” click on “Select” and then choose analysis setting Nr. 3 – “Standard –

EN 1997 – DA1”.


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Dialog window “Settings list”

In the frame “Geometry” choose the wall shape and enter its dimensions.

Frame “Geometry”


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In the frame “Material” enter the material of the wall.

Frame “Material” – Input of material characteristics of the structure

Then, define the parameters of soil by clicking “Add” in the frame “Soils”. Wall stem

is normally analyzed for pressure at rest. For pressure at rest analysis, select “Cohesionless”.

Dialog window “Add new soils”


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Note: The magnitude of active pressure depends also on the friction between the structure and soil.

The friction angle depends on the material of construction and the angle of internal soil friction –

normally entered in the interval ( ) efϕδ ⋅÷≈ 32

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Table with the soil parameters

Soil

(Soil classification)

Profile

[ ]m

Unit weight

[ ]3mkNγ

Angle of

internal

friction

[ ]°efϕ

Cohesion

of soil

[ ]kPacef

Angle of

friction

structure – soil

[ ]°=δ

S-F – Sand with trace of

fines, medium dense soil 0,0 – 4,0 17,5 28,0 0,0 18,5

MS – Sandy silt, stiff

consistency, 8,0<rS from 4,0 18,0 26,5 30,0 17,5

In the frame “Terrain” choose the horizontal terrain shape.

Frame “Terrain”

The ground water table is at a depth of 2,0 meters. In the frame “Water” select the type of water

close to the structure and its parameters.


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Frame “Water”

In the next frame define “Surcharge”. Here, select permanent and strip surcharge on the terrain

acting as a dead load.

Dialog window “New surcharge”

In the frame “FF resistance” select the terrain shape in front of the wall and then define other

parameters of resistance on the front face.


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Frame “FF resistance”

Note: In this case, we do not consider the resistance on the front face, so the results will be

conservative. The FF resistance depends on the quality of soil and allowable displacement of the

structure. We can consider pressure at rest for the original soil, or well compacted soil. It is possible to

consider the passive pressure if displacement of structure is allowed. (for more information, see HELP

– F1)

Then, in the frame “Stage settings” choose the type of design situation. In this case,

it will be permanent. Also choose the pressure acting on the wall. In our case, we will choose active

pressure, as the wall can move.

Frame “Stage settings”

Note: Wall stem is dimensioned always on earth pressure at rest, i.e., the wall can´t be moved.

The possibility of evaluating the stem and the wall of the active pressure is considered only in

exceptional cases - such as the effects of the earthquake (seismic design situation with partial coefficient

equals 1.0).


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Now, open up the frame “Verification”, where you analyze the results of overturning and slip

of the cantilever wall.

Frame “Verification”

Note: The button “In detail” in the right section of the screen opens a dialog window with detailed

information about the analysis results.

Analysis results:

The verification of slip is not satisfactory, utilization of structure is

− Overturning: 52,8 % 97,10933,208 =>= klvzd MM [kNm/m] SATISFACTORY.

− Slip: 124,6 % 94,8178,65 =<= posvzd HH [kN/m] NOT OK.

Now we have several possibilities how to improve the design. For example, we can:

- Use better soil behind the wall

- Anchor the base

- Increase the friction by bowing the footing bottom

- Anchor the stem

These changes would be economically and technologically complicated, so choose the easiest

alternative. The most efficient way is to change the shape of the wall and introduce a wall jump.


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Change of the design: change of the geometry of the wall

Return to the frame “Geometry” and change the shape of the cantilever wall. For increasing

the resistance against slip we introduce a base jump.

Frame “Geometry” (Changing dimensions of cantilever wall)

Note: A base jump is usually analyzed as an inclined footing bottom. If the influence of the base jump

is considered as front face resistance, then the program analyses it with a straight footing bottom, but

FF resistance of the construction is analyzed to the depth of the down part of the base jump

(More info in HELP – F1)

Then analyze the newly designed construction for overturning and slip.


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Frame “Verification”

Now, the overturning and slip of the wall are both satisfactory.

Then, in the frame “Bearing capacity”, perform an analysis for design bearing capacity

of the foundation soil 175 kPa.

Frame “Bearing capacity”

Note: In this case, we analyze the bearing capacity of the foundation soil on an input value, which we

can get from geological survey, resp. from some standards. These values are normally highly

conservative, so it is generally better to analyze the bearing capacity of the foundation soil in the


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program Spread footing that takes into account other influences like inclination of load, depth of

foundation etc.

Next, in the frame “Dimensioning” chose wall stem check. Design the main reinforcement

into the stem – 10 pcs. Ø 12 mm, which satisfies in point of bearing capacity and all design principles.

Frame “Dimensioning”

Then, open up the frame “Stability” and analyze the overall stability of the wall. In our case,

we will use the method “Bishop”, which result in conservative results. Perform the analysis

with optimization of circular slip surface and then leave the program by clicking “OK”.

Results or pictures will be shown in the report of analysis in the program Cantilever wall.


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“Slope stability” program

Conclusion/ Result of analysis – bearing capacity:

− Overturning: 49,5 % 16,10852,218 =>= klvzd MM [kNm/m] SATISFACTORY

− Slip: 64,9 % 47,6427,99 =>= posvzd HH [kN/m] SATISFACTORY

− Bearing capacity: 86,3 00,17506,151 =>= σdR [kPa] SATISFACTORY

− Wall stem check: 78,7 % 71,13392,169 =>= EdRd MM [kN·m] SATISFACTORY

− Overall stability: 40,8 % Method – Bishop (optimization) SATISFACTORY

This cantilever wall is SATISFACTORY.

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2 Design of Cantilever Wall