WSM – Cantilevered Retaining Wall

WSM – Cantilevered Retaining Wall

FRILO Software GmbH

www.frilo.com

[email protected]

As of 18/01/2017

WSM

FRILO Software GmbH Page 3

WSM – Cantilevered Retaining Wall

Note: This document describes the Eurocode-specific application. Documents containing old standards are available in our documentation archive at www.frilo.de Dokumentation ManualsArchive.

Contents

Application options 4 Basis of calculation 6 Definition of the structural system 9 Slope 11 Loads 12 Design settings - soil and wall parameters 13 Soil layers 14 Soil in front of the cantilevered retaining wall 14 Program settings 15 Output 16 Results 16 Annex: Block load 18

Vertical stress due to block load at the depth z 18 Horizontal stress due to the block load 20 Consideration of the horizontal and vertical forces due to the block load and the heavy-duty truck 21

Reference literature 22

Further information and descriptions are available in the relevant documentations:

FDC – Basic Operating Instructions General instructions for the manipulation of the user interface

FDC – Menu items General description of the typical menu items of Frilo software applications

FDC – Output and printing Output and printing

FDC - Import and export Interfaces to other applications (ASCII, RTF, DXF …)

FCC Frilo.Control.Center - the easy-to-use administration module for projects and items

FDD Frilo.Document.Designer - document management based on PDF

Frilo.System.Next Installation, configuration, network, database

http://www.frilo.eu/

http://www.frilo.eu/de/service/dokumentationen/archiv-handbuecher.html

Cantilevered Retaining Wall

Page 4 Software for structural calculation and design

Application options

The WSM2 application allows the verification of the structural safety and the design of cantilevered retaining walls of reinforced concrete. The retaining wall can have a heel at the front and the rear. The rear heel and the wall front and rear surfaces can be slanted. The base (sole) can be inclined.

The ground surface behind the wall can be horizontally level, or sloped with a polygonal or continuous profile. (An inclination towards the bottom is not available).

The soil can consist of up to 21 horizontally limited soil layers. The option to define a polygonal ground surface in combination with layered soil allows the calculation of ground retaining walls in WSM2.

Available standards

You can base the calculation of the reinforcement either on

- DIN EN 1992-1-1:2011/2012/2013/2015

- ÖNORM EN 1992-1-1:2011

- BS EN 1992:2004/2009/2015

- EN 1992:2010/2014

Additionally available are:

- DIN 1045 / DIN 1045-1

Foundation engineering standards

The verifications of the stability against lateral buckling and sliding as well as the calculation of the soil and/or bearing pressures can optionally be based on the following standards:

- DIN EN 1997-1

- ÖNORM EN 1997-1

Additionally available:

- DIN 1054

Loading

- Uniformly distributed load as permanent load applying to the front heel

- Uniformly distributed load as permanent and/or live load applying to the rear heel

- Vertical force as permanent and/or live load applying to the wall crown

- Horizontal force as permanent and/or live load applying to the wall crown

- Moment as permanent and/or live load applying to the wall crown

- Heavy-duty trucks (HDT) as live load above and behind the rear heel

- Block load as permanent or live load applying above and behind the rear heel

Cantilevered retaining wall with masonry facing

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Results

The software puts out the following results for all load cases:

- Lateral buckling stability

- Stability against sliding

- Load application point of the total resultant

- Length of the gaping joint

- Soil pressure at the front

- Soil pressure at the rear

- Mean value of the soil pressure as per DIN

- Internal forces in all of the five sections

- Reinforcement in five sections (5.1)

- Shear reinforcement in three sections

- Output of the earth pressure behaviour on the wall and the sliding surface as a graphic and in the form of tables.

Optionally, the user can include the vertical component of the earth pressure force Eav into the calculation.

Base failure analysis

Base failure analysis is implemented. Tick the Options in the output-section. Normen:

- DIN EN 1997

- ÖNORM B 1997-1 [2007-11] combined with ÖNORM B 4435-2 [1999-10]

- DIN 1054:2005 combined with DIN 4017:2006

Earth pressure component on the vertical sliding joint at the end of the heel



Basis of calculation

The calculation is based on earth pressure coefficients that are calculated from given soil parameters such as the specific weight, the angle of internal friction, the angle of wall friction and the ground slope (/2/).

The software allows you to select either a vertical sliding surface at the end of the heel or an inclined sliding surface that reaches from the end of the heel either up to the ground surface or up to the wall surface, depending on the length of the heel.

A vertical sliding surface at the heel end is not allowed in combination with a discontinuous ground surface in accordance with DIN 4085. In this case, the sloped sliding surface is assumed automatically by the software. In case of several soil layers, the theta angle, which refers to the inclination angle of the sliding surface, is determined by averaging the theta angles of the different layers.

The earth pressure portion due to a polygonal ground surface is taken into account in the software as follows:

1. Consideration of a ground polygon in the calculation of the earth pressure on the wall (for the wall design): The weight of the ground polygon above the ground level of the wall head is calculated in an area that extends from the wall head to the intersection point of the leg of the 45 ° load propagation angle with the ground top edge. An equivalent load is determined by dividing the ground weight by the width of the examined ground area. The calculation of the earth pressure on the wall is then performed for the horizontal ground pressing against the wall that is loaded in addition by this uniformly distributed equivalent load.

2. Consideration of a soil polygon in the calculation of the earth pressure on the sloped sliding surface (for the wall design): The weight of the ground polygon above the ground pressing at the level of the intersection point is calculated in an area that extends from the intersection point of the sliding surface with the ground top edge to the intersection point of the leg of the 45 ° load propagation angle with the ground top edge. An equivalent load is determined by dividing the ground weight by the width of the examined ground area. The calculation of the earth pressure on the wall is then performed for the horizontal ground pressing against the sliding surface that is loaded in addition by this uniformly distributed equivalent load.

In addition, a continuous slope can be taken into account in the approach of the sloped sliding surface. Whereas, if you have selected the vertical sliding surface, a continuous slope is taken into account via an increased earth pressure coefficient (kah).

The wall design can optionally be based either on the earth pressure distribution in accordance with Coulomb or on a trapezoidal earth pressure distribution from which the soil self-weight over the wall height is calculated in accordance with DIN 4085 5.9.2. If the trapezoidal earth pressure distribution is used, the lower earth pressure coordinate is twice as high as the upper (Ill. 2).

The sliding safety of an inclined base (inclination angle ) is determined in accordance with the VSS approach (Vereinigung Schweizerischer Straßenfachmänner = Association of Swiss Road Engineering Experts) as well as with Spang. See /6/ p. 24.

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According to the VSS approach, the safety against sliding results obtained with the help of the following equation:

= tans / tan(R - s).

s = base friction angle

R = inclination angle of the resultant (tan R = H / V)

s = inclination of the foundation joint

Spang prescribes an additional verification for a horizontal equivalent shear joint.

= V tan+ ph / Eah.

ph is only effective in front of the inclined base, because digging off is not allowed there.

The earth pressure coefficient for the stability verification is calculated for a vertical plane at the end of the rear heel.

The following five load cases are examined in the calculation:

LC0 permanent loads

LC1 as LC0 and live load portion of the uniformly distributed load at the end of the rear heel

LC2 as LC0 and live portion of the uniformly distributed load, the block load and the HDT load behind and above the rear heel.

LC3 as LC1 with live portions of the wall line loads

LC4 as LC2 with live portions of the wall line loads

Lateral earth pressure pattern as per DIN 4085

eE

h

eE

h

a oah

a uah

22

22

2343

= ⋅

= ⋅



The calculation is based on the assumption that the cantilevered retaining wall and the soil above the rear heel are rigid bodies.

For the calculation of the compression, the lateral earth pressure pattern at the heel end should be used.

Note: This calculation model can only be used up to a particular heel length. Heels with higher

lengths shall be designed as beams with an elastic foundation.

In addition to the calculation approaches used until recently, an additional approach to the calculation of the internal moments at the rear heel is alternatively available.

The method is based on a concept of equilibrium that considers the base friction force and the vertical component of the earth pressure force acting on the wall in view of their effect on the internal moments in the heel (/5/).

Application of the forces on the cantilevered wall in accordance with Mesterom

Note: The amount of the vertical earth pressure component plays a decisive role in this

equilibrium concept. Therefore, you should determine the wall friction angle at this point with utmost care.

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Definition of the structural system

Select first the desired reinforced concrete and foundation engineering standards

see Application options

In the "Settings" section, accessible via the main menu, you can define whether a minimum reinforcement should be considered.

Select the material subsequently.

Geometry

The illustration shows the dimensions to be defined.

You can define a base inclination either by specifying the base (sole) inclination angle or the height increment H (Delta H) due to the inclination.

Wall

Specify a value > 0.01 kN/m3 for Gamma. The default setting in the software is 25 kN/m3.

Reinforcement layer

Define the reinforcement layers d1 = top and d2 = bottom as well as the Durability ( button) Reinforcement layer: see also the illustration in the output example.

Ill.: Reinforcement layer



Optimization - heel dimensions

In the definition section "Increase heel (tails) length...", you can define whether the software shall increase the heel lengths automatically in order to comply with particular given conditions.

According to selected options, the front or rear heel or the total of both heels is increased automatically in increments of 5 cm.

You define here also the criteria that should trigger the incremental increase.

Optimization target Abortion criterion

Stability against sliding 1.5 (load case 1) or 1.35 (load cases 2 and 3)

Stability against lateral buckling Resultant of the first core width, load cases 0 or 2. Core width (other load cases)

Length of the gaping joint Length of the gaping joint = 0 in load case 0

After having selected the desired options, click on the Optimize button.

New optimization

All user-defined optimization criteria are deleted and you can define new ones.

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Slope In addition to a horizontal ground surface, you can define a sloped ground surface behind the wall, either as continuously sloped or polygonal ground surface.

When defining a polygonal ground surface, you should note that the ground polygon can only develop in a rising or horizontal level manner, i.e. negative ground inclination is not available.

The software considers a horizontal ground area from the wall head to a distance twice as long as the retaining wall height behind the rear heel, i.e. the highest ground elevation that the software considers lies in this area.

You can define up to 21 horizontally limited soil layers. The top layer with the layer height HS(1) reaches up to the highest ground elevation in the horizontal area behind the wall head with an extension of twice the wall height behind the rear end of the rear heel.



Loads Click on the "loads" button to access the load definition dialog.

When you click into a field, its function is displayed in the status line (on bottom left).

Block load

A block load acts with both its vertical and horizontal components on the retaining wall.

g amount of the block load, optionally as g- or p-load.

Depth vertical distance from the wall head (downwards is positive)

Distance horizontal distance from the wall head

Width width of the block load (measured in a right angle to the wall)

Length length of the block load (measured in parallel to the wall). Specify "-1" to define an unlimited block load length.

Superimposed load by heavy-duty truck (HDT)

Acc. to DIN 1072, a HDT has a size of 6.00 x 3.00 m.

It is treated like an unlimited block load applying in parallel to the wall with a width of 3 m.

In accordance with DIN 1072, HDT are categorised as follows:

- HDT 60 with an equivalent area load of p = 33.3 kN/m²

- HDT 30 with an equivalent area load of p = 16.7 kN/m²

Factor you can enter a load factor (0.5 < factor < 5).

Distance horizontal distance of the HDT to the wall.

In accordance with /1/, you can assume in the calculation a load propagation angle of 30 ° under the equivalent area load.

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Facing masonry

You can define facing masonry on the free wall face. It is defined by specifying the specific weight Gamma and the thickness of the masonry.

See also "Block load" in the annex:

Block load

- Vertical stress due to block load at a depth z

- Horizontal stress due to block load

- Consideration of horizontal and vertical forces due to block load and HDT

Design settings - soil and wall parameters Click on the "soil parameter" button to access the corresponding definition dialog.

Earth pressure

You can assume the earth pressure distribution as per DIN 4085, para. 5.9.2 (/2/) or in accordance with Coulomb.

Eav - vertical earth pressure component

You can optionally consider the vertical earth pressure component.

Sliding surface

This section allows you to define whether a vertical or sloped sliding surface should be assumed at the rear end of the heel and included in the calculation.

Design of the wall and the heel(s)

You can specify here whether the coefficient of earth pressure at rest should be included in the design of the wall and the heel(s).

Design (friction force in the foundation joint)

Optionally with or without consideration of the friction force in the foundation joint.



Soil layers

Set soil pressure coefficients

When checking this option, the software calculates the earth pressure coefficients based on the defined soil parameters. If you leave the option unchecked, you need to specify the soil pressure coefficients (kah, kph) manually.

For each layer, you need to define the layer thickness as well as the soil characteristics such as Gamma (), the angle of the inner friction Phi () and the cohesion c.

The individual layers must have a minimum thickness of 0.5 m. The number of layers is limited to 25. The top layer with the layer height HS(1) reaches up to the highest ground elevation in the horizontal area behind the wall head with an extension of twice the wall height behind the rear end of the rear heel. (See also Slope definition.)

Soil in front of the cantilevered retaining wall h for the calculation of the passive earth pressure

h,GBr for the soil failure analysis

See also the corresponding options in the Program settings dialog.

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Program settings

The corresponding item in the main menu allows you to access the program settings dialog. The available options are self-evident, see also the illustration on the right.



Output

Output of the system data, results and graphics on the screen or printer.

The durability requirements and the earth pressure diagram can optionally be included in the output scope.

Screen displays the values in a text window on the screen

Printer starts the output on the printer

Word if installed on your computer, the text editor MS Word is launched and the output data are transferred. You can edit the data in Word as required.

Print Preview displays a print preview of the PDF file.

Results The results are put out for the decisive load cases: These are the load cases 0 to 2 and also 3 and 4 if line loads apply to the wall.

The following Calculation results are put out:

- Lateral buckling stability for LC1 and LC2 as well as LC3 and LC4, if applicable

- Stability against sliding for LC1 and LC2 as well as LC3 and LC4, if applicable

- Load application point of the total resultant

- Gaping joint

- Soil pressure at the front

- Soil pressure at the rear

- Mean value of the soil pressure as per DIN 1054

- Earth pressure on the wall and the sliding surface in the form of graphics and tables

For the sections

Section I at half of the wall height

Section II at the wall base

Section III at half of the rear heel length

Section IV at the front part of the rear heel

Section V at the front heel

the following values are put out in addition:

- moment

- shear force

- axial force and kh-value (for the wall)

- required reinforcement for section III and IV

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Example on the reinforcement of the retaining wall

The location and run of the dashed line is generally agreed as follows:

- on the left side of the wall

- underneath the heel (front and rear)

The following applies to the req. reinforcement in regard to the moment:

- if the moment is positive, the tension side is that of the dashed line,

- if the moment is negative, the tension side is opposite to the dashed line.

Example:

Note: As1 is the tensile reinforcement, AS2 is the required compressive reinforcement, if necessary.

Design by DIN EN 1992-1-1/NA Berichtigung 1:2012-06 section I , II : wall center , below III , IV : behind tailskid centre , in the front V : front tailskid Md Vd Nd kx as1 as2 section lc (kNm) (kN) (kN) (cm2/m) I 2 -38.79 47.55 -33.95 0.03 6.0 0.0→ earth side 4 -38.79 47.55 -33.95 0.03 6.0 0.0 II 2 -167.36 112.23 -73.88 0.04 8.8 0.0→ earth side 4 -167.36 112.23 -73.88 0.04 8.8 0.0 III 0 -71.41 82.82 0.00 0.09 5.1 0.0→ top 1 -75.53 90.17 0.00 0.09 5.4 0.0 2 -76.42 89.40 0.00 0.09 5.4 0.0 3 -75.53 90.17 0.00 0.09 5.4 0.0 4 -76.42 89.40 0.00 0.09 5.4 0.0 IV 0 -164.80 92.11 0.00 0.19 12.5 0.0→ top 1 -177.72 101.47 0.00 0.21 13.6 0.0 2 -178.36 102.13 0.00 0.21 13.7 0.0 3 -177.72 101.47 0.00 0.21 13.6 0.0 4 -178.36 102.13 0.00 0.21 13.7 0.0 V 0 25.05 -70.60 0.05 3.1 0.0→ bottom 1 27.20 -76.30 0.05 3.1 0.0 2 26.69 -75.17 0.05 3.1 0.0 3 27.20 -76.30 0.05 3.1 0.0 4 26.69 -75.17 0.05 3.1 0.0



Annex: Block load

The block load is defined by its distance to the wall, its length L1 perpendicular to the wall, its length L2 in parallel to the wall and its height level. The height level dimension is positive when the block load applies below the wall head (and negative if it applies above).

The heavy-duty truck (HDT) is defined by its type (HTD 30, HTD 60) and its distance to the wall.

Vertical stress due to block load at the depth z

Illustration: Vertical stress due to the block load

( ) ( )z o o

Pa 2 z tan30 b 2 z tan30

s =+ ◊ ◊ ◊ + ◊ ◊

zP

z z1 2 tan30 1 2 tan30a b

∞ ∞s =

Ê ˆ Ê ˆ+ ◊ ◊ ◊ + ◊ ◊Á ˜ Á ˜Ë ¯ Ë ¯

PMit a 3m,b 6mundp gilt :

a b= = =

◊

zo o

p2 21 z tan30 1 z tan303 6

s =Ê ˆ Ê ˆ+ ◊ ◊ ◊ + ◊ ◊Á ˜ Á ˜Ë ¯ Ë ¯

( ) ( )zp

1 0,3849 z 1 0,19245 zs =

+ ◊ ◊ + ◊

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This equation corresponds to equation 4 as per /3/ by Funke:

a + a= 1 2tan tana

3 (equation 2 in /3/)

analog: a + a= 1 2tan tan

b6

with 1 = 2 = 30°: o o

o o

tan30 tan30a 0,3849

3

tan30 tan30b 0,1924

6

+= =

+= =

The following vertical forces are distributed over the rear heel with the width b5.

= s ◊= s ◊

1 z1 51

2 z2 52

V bV b

In the illustration, z1 refers to the depth at which the leg of the load propagation angle intersects the wall, and z2 to the distance from the ground surface to the top edge of the rear heel.

Illustration: Vertical stress acting on the heel



Horizontal stress due to the block load Due to the block load, the following earth pressure pattern is generated in accordance with /4/:

Illustration: Horizontal stress due to the block load

For the earth pressure coordinate ebl the following expression is true:

( ) ( )dQ = J - f

J - f-dQ= ◊ ◊-bl

3 1

cossin

cos

e 2 p bT T

Illustration: Distribution of the foundation loads

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Consideration of the horizontal and vertical forces due to the block load and the heavy-duty truck You can optionally treat the block load as a g-load or p-load. The HDT is handled as a p-load by the software. A block load defined as a live load and the HDT are assigned to load case 2.

The vertical force is included in the calculation of the compression, of the stability against sliding and lateral buckling as well as in the heel design, as shown in the illustration "Vertical stress on the heel".

The horizontal force, i.e. the additional earth pressure force, is considered automatically in the wall design, in the calculation of the compression and in the safety verifications.

In the wall design, the earth pressure force is included as shown in the illustration "Horizontal stress caused by the block load".

The earth pressure force from the ground top edge down to the bottom edge of the rear heel is taken into account for the verification of the stability against lateral buckling and sliding, the calculation of the compression and in the heel design.

There are three possible load positions in relation to the vertical section at the end of the rear heel:

If earth pressure at rest is considered, the block load generates pressure from the left and from the right on the sliding surface if it applies on both sides of the section (case 1 to case 3). Whereas in connection with active earth pressure, only the portion of the load acting on the sliding body is considered (case 1).

Case 1: The block load applies entirely on the right of the section.

Illustration: Block load on the right of the section

Case 2: The block load applies entirely on the left of the section.

Illustration: Block load on the left of the section



Case 3: The block load applies on both sides of the section.

Illustration: Block load on both sides of the section

Reference literature

/1/ Jenne, G.: "Erddruck". In: Beton-Kalender II, 1973, S.89.

/2/ Simmer, K. und Schulze, W.E.: Grundbau Teil 1. Bodenmechanik und erdstatische Berechnungen. (B.G.Teubner) Stuttgart 1974.

/3/ Funke, L.: "Erddruck auf Stützbauwerke infolge Straßenverkehrslasten nach DIN 1072", in: Bauingenieur 58, 1983, S.349.

/4/ Hoesch Stahl AG (Hg.): Spundwand-Handbuch Berechnung. Dortmund 1986.

/5/ Mesterom, K.-L.: "Beitrag zur Bemessung des erdseitigen Spornes von Winkelstützmauern", in: Bautechnik 7, 1985, S. 235-237.

/6/ Henner Türke.: "Statik im Erdbau“ Ernst & Sohn 3.Auflage.