Geo5 Engineering Manuals Em3 1

Eng i ne e r i ngma nua l s Par t1

Engineering manuals for GEO5 programs Part 1 Chapter 1. Analysis settings and settings administrator ................................... 3 Chapter 2.

Design of Cantilever wall ............................................................... 11

Chapter 3. Verification of gravity wall ............................................................. 22 Chapter 4. Design of non-anchored restraint retaining wall .......................... 31 Chapter 5. Design of anchored retaining wall.................................................. 38 Chapter 6. Verification of retaining wall with one anchor row...................... 42 Chapter 7. Verification of multi-anchored wall ............................................... 53 Chapter 8. Analysis of slope stability ................................................................ 53 Chapter 9. Stability of slope with retaining wall.............................................. 76 Chapter 10. Design of geometry of spread footing........................................... 85 Chapter 11. Settlement of spread footing ......................................................... 90 Chapter 12. Analysis of consolidation under embankment ............................ 96

Introduction

Engineering manuals are new teaching material for GEO5 software. They were developed as a reaction to hotline and frequently asked questions of users. The objective of each chapter is to explain how to solve the concrete engineering problems using GEO5 software. Each chapter is divided to a few sections: Introduction – theoretical introduction to the problem Assignment – here the problem is described with all input data needed for solving the problem in selected the program Solution – in this section, the problem is solved step by step Conclusion – has the conclusion of the problem and the final verification of the construction. It tells if the structure is satisfactory or not and if there are any modifications needed. In each chapter there are also notes, which explain the problem in general as well as links to other materials. The basic educational materials of GEO5 software suite (from FINE s r.o.) are: −

Context help – explains the functions of the program in detail

−

Video tutorials – show the basic work with the software and its effective use

−

Engineering manuals – explain how concrete engineering problems are solved

−

Verification manuals – verify the satisfaction of the results, by comparing the results from programs with hand calculation or other programs

The first chapter explains how to set standards and chose an analysis method, which is the same for all GEO5 programs. In further chapters one standard is selected, by which the construction is verified.

2 Engineering manuals for GEO5 programs - Part 1

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Chapter 1. Analysis settings and settings administrator This chapter explains the correct use of Settings administrator that serves to choose standards, partial factors and verification methodology. It is the basic step needed for all GEO5 programs. Introduction GEO5 software is used in 90 countries worldwide. Engineering tasks are the same everywhere – to prove that the construction is safe and well designed. The basic characteristic of structures (eg. geometry of wall, terrain, localization of anchors etc.) are the same all over the world; the way of proving that the construction is safe and the theory of analysis used are different. Large quantities of new theories and mainly partial factors of analysis lead to input of large amounts of data and complicated programs. The Settings administrator was created in GEO5 for version 15 to simplify this process. In the Settings administrator are defined all input parameters, including standards, methods and coefficients for the current country. The idea is that each user will understand the Settings defined in the program (or will define a new Setting of analysis), which the user then uses in their work. To the Settings administrator and Settings editor the user then goes only occasionally. Assignment: Perform an analysis of a gravity wall per the picture below for overturning and slip according to these standards and procedures: 1) CSN 73 0037 2) EN 1997 – DA1 3) EN 1997 – DA2 4) EN 1997 – DA3 5) Safety factor on SF=1.6


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Scheme of the gravity wall for analysis

Solution Firstly, input the data about the construction and geological conditions in the frames: “Geometry”, “Assign” and “Soils”. Skip the other frames because they are not important for this example.

Frame “Geometry” – input of dimensions of the gravity wal 4 Engineering manuals for GEO5 programs - Part 1

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Table with the soil parameters

Soil

Unit weight

(Soil classification)

γ [kN m

MG – Gravelly silt, firm consistency

3

]

19,0

of Cohesion internal friction of soil Angle

Angle of friction structure

ϕ ef [°]

cef [kPa]

δ = [°]

30,0

0

15,0

–

soil

In the frame “Assign”, the first soil will be assigned automatically to the layer or layers. This can be changed when necessary. When the basic input of construction is done, we can choose standards, and then finally run the analysis of the gravity wall. In the frame “Settings” click the button “Select” and choose number 8 – “Czech Republic – old standards CSN (73 1001, 73 1002, 73 0037)”.

Dialog window “Settings list”

Note: The look of this window depends on standards that are currently active in the Settings administrator – more information in the help of the program (press F1). If the setting you want to use isn`t on the list in the dialog window “Settings list”, you can activate it in the Settings administrator. Now, open up the frame “Verification” and after analyzing the example record the utilization of construction (in the frame “Verification”) - 53,1% resp. 66,5%. 5 Engineering manuals for GEO5 programs - Part 1

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Frame “Verification” – results of the analysis using CSN 73 0037 standard Then return to the frame “Settings” and choose number 3 – “Standard – EN 1997 – DA1”.

Dialog window “Settings list”


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Again, open the frame “Verification” and record the result (55,6% and 74,7%) for EN 1997, DA1.

Frame “Verification” – results of analysis for EN 1997, DA1 Repeat this procedure for settings number 4 – “Standard – EN 1997 – DA2” and number 5 – “Standard – EN 1997 – DA3”. The analyzed utilization of constructions is (77,8% and 69,7%) for EN 1997, DA2 or (53,5% and 74,7%) for EN 1997, DA3.


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Variant 5 (analysis using Safety factors) is not as simple. In the frame “Settings” click on “Edit”. This will show you the current analysis settings. Change the verification methodology to “Safety factors (ASD)” and then input safety factor for overturning and sliding resistance as 1.6.

Dialog window “Edit current settings: Gravity wall” Press OK and run the analysis. (69,0% and 77,1%).

Frame “Verification” – analysis results for SF = 1.6 8 Engineering manuals for GEO5 programs - Part 1

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If you would like to use this setting more often, it is good to save this setting by clicking on “Add to administrator”, rename is as shown below, and next time use it as a standard setting.

Dialog window “Add current settings to the Administrator”

Dialog window “Settings list” then looks like this

Dialog window “Settings list” 9 Engineering manuals for GEO5 programs - Part 1

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Verification Utilization in percentage using each standard is: Overturning

Slip

1) CSN 73 0037

53,1

66,5

2) EN 1997 – DA1

55,6

74,7

3) EN 1997 – DA2

77,8

69,7

4) EN 1997 – DA3

53,3

74,7

5) Safety factor on SF=1.6

69,0

77,1

The analysis is satisfactory using the selected analysis standards. Note: This simple method can be used to compare retaining structures or stability analyses. When analyzing foundations, the load (basic input data) must be computed according to relevant standards. That is the reason why it doesn’t make sense, to compare foundation design by various standards with the same values of load (nominal values).


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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, S r < 0,8 , 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” 12 Engineering manuals for GEO5 programs - Part 1

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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 –

(3

normally entered in the interval δ ≈ 1 ÷ 2

3

)⋅ ϕ

ef

Table with the soil parameters

Angle of

Cohesion

Angle of

of soil

friction

Soil

Profile

Unit weight

internal


[m ]

γ [kN m 3 ]

friction

ϕ ef [°]

cef [kPa ]

0,0 – 4,0

17,5

28,0

0,0

18,5

from 4,0

18,0

26,5

30,0

17,5

S-F – Sand with trace of fines, medium dense soil MS – Sandy silt, stiff consistency, S r < 0,8

structure – soil

δ = [°]

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). 16 Engineering manuals for GEO5 programs - Part 1

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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 %

M vzd = 208,33 > M kl = 109,97 [kNm/m]

SATISFACTORY.

−

Slip: 124,6 %

H vzd = 65 ,78 < H pos = 81,94

NOT OK.

[kN/m]

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:

M vzd = 218,52 > M kl = 108,16 [kNm/m]

−

Overturning: 49,5 %

−

Slip: 64,9 %

−

Bearing capacity: 86,3

Rd = 151,06 > σ = 175,00

−

Wall stem check: 78,7 %

M Rd = 169,92 > M Ed = 133,71 [kN·m]

SATISFACTORY

−

Overall stability: 40,8 %

Method – Bishop (optimization)

SATISFACTORY

H vzd = 99,27 > H pos = 64,47

[kN/m] [kPa]

SATISFACTORY SATISFACTORY SATISFACTORY

This cantilever wall is SATISFACTORY.


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Chapter 3. Verification of gravity wall In this chapter an analysis of an existing gravity wall for permanent and accidental design situations is performed. Construction stages are also explained. Assignment Using EN 1997-1 (EC 7-1, DA2) standard, analyze an existing gravity wall for stability, overturning, and slip . Road traffic acts on the wall with magnitude of 10 kPa. Check the possibility to install the barrier on the top of the wall. An accidental load from a car crash is considered as 50 kN/m and it acts horizontally at 1,0 m. Dimensions and shape of the concrete wall can be seen in the picture below. Inclination of the terrain behind the construction is β = 10° , the foundation soil consists of silty sand. The friction angle between the soil and wall is δ = 18° . Determination of bearing capacity and dimensioning of the wall is not part of this task. In this analysis, consider effective parameters of soil.

Scheme of the gravity wall – assignment Solution: For analyzing this task, use the GEO5 program – Gravity wall. In this text, we will describe the steps of analyzing this example in two construction stages. −

1st construction stage – analyzing the existing wall for road traffic.

−

2nd construction stage – analyzing impact of vehicle to the barrier on the top of the wall.

Basic input: Stage 1 22 Engineering manuals for GEO5 programs - Part 1

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In the frame “Settings” click on “Select” and choose Nr. 4 – “Standard – EN 1997 – DA2”.

Dialog window “Settings list” Then, in the frame “Geometry”, select the shape of the gravity wall and define its parameters.

Frame “Geometry”


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In the next step, input the material of the wall and geological profile. Unit weight of wall is

γ = 24 kN m 3 . Wall is made from concrete C 12/15 and steel B500. Then define parameters of soil and assign them to the profile. Table with the soil parameters

Soil

Unit weight


γ [kN m 3 ]

MS – Sandy silt, firm consistency

Angle of internal friction

Cohesion of soil

Angle of friction structure – soil

ϕ ef [°]

cef [kPa]

δ = [°]

26,5

12,0

18,0

18,0

Dialog window “Add new soils” Note: The magnitude of active pressure depends also on friction between the structure and soil in the

(3

angle “ δ ≈ 1 ÷ 2

3

)⋅ ϕ

ef

“. In this case we consider the influence of friction between the structure

and soil with value of 2 ⋅ ϕ ef ( δ =18° ), when analyzing earth pressure. (More info in HELP – F1).

3

In the frame “Terrain” select the shape of terrain behind the wall. Define its parameters, in terms of embankment length and slope angle as shown below.

Frame “Terrain” In the next frame, define “Surcharge”. Input the surcharge from road traffic as Strip, with its location on terrain, and as a type of action select “Variable”.


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Dialog window “Edit surcharge” In the frame “FF resistance” choose the shape of the terrain in front of the wall and define the other parameters of front face resistance.

Frame “Front face resistance” Note: In this case, we do not consider 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 consider pressure at rest for the original soil or well compacted soil. It is possible to consider passive pressure only if displacement of structure is allowed. (More info in HELP – F1). 25 Engineering manuals for GEO5 programs - Part 1

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In the frame “Stage settings” select the type of design situation. In the first construction stage, consider the “permanent” design situation.

Frame “Stage settings” Now open up the frame “Verification”, where we analyse the gravity wall for overturning and slip.

Frame “Verification – stage 1” Note: The button “In detail” in the right section of the screen opens a dialog window with detailed information about the results of the analysis.


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Dialog window “Verification (in detail)” Note: For analyses based on EN-1997, the program determines if the force acts favorably or unfavorably. Next each force is multiplied by the corresponding partial factor which is them on the report. Then, open up the frame “Stability” and analyze the overall stability of the wall. In our case, we will use the method “Bishop”, which results in conservative results. Perform an analysis with optimization of circular slip surface and then validate everything by clicking “OK”. Results or pictures will be shown in the report of analysis in the program Gravity wall.

Program “Slope stability – stage 1” −

Analysis results: Stage 1 27

Engineering manuals for GEO5 programs - Part 1

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When analyzing bearing capacity, we are looking for values of overturning and slip of the wall on the footing bottom. Then we need to know its overall stability. In our case, the utilization of the wall is: Overturning: 70,0 %

M vzd = 376,91 > M kl = 263,73 [kNm/m]

SATISFACTORY. Slip: 90,6 %

H vzd = 152,53 > H pos = 138,17 [kN/m]

SATISFACTORY. Overall stability: 72,3 % Method – Bishop (optimization) SATISFACTORY.


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Basic input: Stage 2 Now, add construction stage 2 using tool bar in the upper left corner of the screen.

Toolbar “Stage of construction” In this stage, define the load from the impact of the vehicle to the barrier, using the frame “Input forces”. The load is accidental and considers the impact of a vehicle with a weight of 5 tons.

Dialog window “Edit force” – construction stage 2 (accidental design situation)

Then open the frame “Stage settings” change the design situation on “accidental”.

Frame “Stage settings” The data in the other frames that we entered in stage 1 has not changed, so we don’t have to open these frames again. Select the frame “Verification” to perform the verification on overturning and slip again.


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Frame “Verification – stage 2” −

Analysis results: Stage 2 From the results, we see, that the existing wall is not satisfactory for impact of a vehicle

to the barrier. In this case, utilization of the wall is: −

Overturning: 116,3 %

M vzd = 488,62 < M kl = 568,13 [kNm/m]

NOT OK.

−

Slip: 102,9 %

H vzd = 138,39 < H pos = 142,35 [kN/m]

NOT OK.

Conclusion The existing gravity wall in case of bearing capacity satisfies only for the first construction stage, where road traffic acts. For the second construction stage, which is represented as impact to the barrier on the top of the wall by a vehicle of 5 tons, the wall is not satisfactory. As a solution to increase bearing capacity for overturning and slip it is possible to introduce soil anchors. alternatively it is possible to place a barrier on the edge of the road, so the wall is not loaded by a force from the crashing car.


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Chapter 4. Design of non-anchored restraint retaining wall In this chapter is the design of non-anchored retaining wall for permanent and accidental loads (flooding). Assignment Design non-anchored retaining wall from pile sheeting using the EN 1997-1 (EC 7-1, DA3) standard in non-homogenous geologic layers. The depth of excavation is 2,5 m. The ground water table is at a depth of 1,0 m. Analyze the construction also for flooding; when the water is 1,0 m above the top of the wall (mobile anti-flood barriers should be installed).

Scheme of non-anchored wall from pile sheeting – assignment Solution: For solving this problem, we will use the GEO5 program, Sheeting design. In this text, we will explain each step to solve this example: −

1st construction stage: permanent design situation

−

2nd construction stage: accidental design situation

−

Design of geometry of the pile sheeting

−

Analysis result (conclusion).


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Basic input: Construction stage 1 In the frame “Settings” click on “Select” and then choose Nr. 5 – “Standard – EN 1997 – DA3”.

Dialog window “Settings list” Then, input the geological profile, parameters of soil and assign them to the profile.

Dialog window “Add new soils”


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Table with the soil parameters Angle of internal friction

Cohesion of soil

ϕ ef [°]

cef [kPa]

δ = [°]

17,5

29,5

0,0

14,0

1,5 – 2,5

18,5

27,0

8,0

14,0

from 2,5

21,0

19,0

12,0

14,0

Soil

Profile

Unit weight


[m]

γ [kN m3 ]

S-F – Sand with trace of fines, medium dense soil

0,0 – 1,5

SC – Clayey sand, medium dense soil CL, CI – Clay with low or medium plasticity, firm consistency

Angle of friction structure – soil

In the frame “Geometry”, select the shape of bottom of the excavation and input its depth.

Frame “Geometry”

Note: coefficient of reduction of earth pressure below the ditch is considered while analyzing braced sheeting (retaining wall with soldier beams) only; for a standard sheeting pile wall it equals 1,0 For more information, see HELP (F1). In this case, we do not use the frames “Anchors”, “Props”, “Supports”, “Pressure determination”, “Surcharge” and “Applied forces”. The frame “Earthquake” also has no influence for this analysis, because the construction is not located in seismic-active area. In the frame “Terrain”, it remains horizontal. 33 Engineering manuals for GEO5 programs - Part 1

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In the frame “Water” input the GWT value – 1,0 m.

Frame “Water” – 1st construction stage Then, in the frame “Stage settings”, select the design situation as permanent.

Frame “Stage settings” Now, open up the frame “Analysis” and click on the button “Analyze”. This will perform the analysis of the retaining wall.

Frame “Analysis” Note: For cohesive soils is recommended by many standards to use minimal dimensioning pressure acting on the retaining wall. The standard value for the coefficient of minimal dimensioning pressure is Ka = 0,2. It means that minimum pressure on the structure is 0,2 of geostatic stress – never less.


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Within the design of pile sheeting retaining wall, we are interested in the depth of construction in the soil and internal forces on the structure. For the 1st construction stage, the results of analysis are: −

Length of structure:

4,83 m

−

Needed depth in the soil:

2,33 m

−

Maximum bending moment:

M 1,max = 28,21 kNm m

−

Maximum shear force:

Q1,max = 56,98 kN m

In the next stage, we are going to show you how to analyse the minimum depth in soil and internal forces in the soil for the accidental design situation – floods. Basic input – Construction stage 2 Now, select stage 2 on the toolbar “Stage of construction” on the upper left corner of your screen. (If needed, add a new one)

Toolbar: Stage of construction In the frame “Water”, change the GWT behind the structure to a value -1,0 m. We will not consider water in front of the structure.

Frame “Water” 35 Engineering manuals for GEO5 programs - Part 1

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Then, in the frame “Stage settings”, select the design situation “Accidental”.

Frame “Stage settings” All other values are the same as in the 1st construction stage, so we don’t have to change data in other frames, so we go on to the frame “Analysis” and click again on the button “Analyze”.

Frame “Analysis” In the 2nd construction stage the analysis results are: −

Length of structure:

6,56 m

−

Needed depth in the soil:

4,06 m

−

Maximum bending moment:

M 2,max = 142,00 kNm m

−


Q2,max = 185,17 kN m

Using the maximum bending moment, we will design pile sheeting. The minimum length of pile sheeting is set as the maximum of necessary length from construction stage 1 and construction stage 2.

Design of pile sheeting: 36 Engineering manuals for GEO5 programs - Part 1

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We design the pile sheeting based on the maximum bending moment using the table of pile sheeting with allowable bearing capacities shown below.

Design of pile sheeting according to CSN EN 10 248-1 standards. Based on the chart, we will select the pile sheeting VL 503 (500 × 340 × 9,7 mm), the steel grade S 270 GP, of which the maximum bending moment is M max = 224 , 0 kN m . Safe design of structure is verified by equation:

M dov = 224 kN m > M max = 142 kNm m

Analysis result: In the design of non-anchored restraint retaining wall, we are verifying values of minimum depth of the structure in the soil, and the internal forces in the structure: −

Minimum depth of the structure in first stage:

2,33 m

−

Minimum depth of the structure in second stage:

4,06 m

So, we will design a pile sheeting with depth in the soil of 4,1 m and overall length of 6,6 meters.

Conclusion: The designed pile sheeting retaining wall VL 503 from S 270 steel with length of 6,6 meters satisfies.


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Chapter 5. Design of anchored retaining wall In this chapter, we will show you how to design a retaining wall with one row of anchors. Assignment: Design a retaining wall with one anchor row made from pile sheeting using EN 1997-1 (EC 7-1, DA3) standard. The depth of ditch is 5,0 m. The anchor row is 1,5 m below the surface. The soils, geological profile, ground water table and shape of terrain are the same as in the last task. Remove construction stage two so as to not consider flooding.

Scheme of the anchored wall from pile sheeting – assignment Solution: For solving this problem, we will use a GEO5 program, Sheeting design. In this text, we will explain each step of this example: − Analysis 1: permanent design situation - wall fixed at heel − Analysis 2: permanent design situation - wall hinged at heel − Analysis result (conclusion)


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Basic input: Analysis 1 Leave the frames “Settings”, “Profile”, “Soils”, “Terrain”, “Water” and “Stage settings” from the previous problem without changes. Also, delete construction stage 2 if you are reusing the file from problem 4. In the frame “Geometry”, input the depth of the ditch as 5,0 m. Open up the frame “Anchors” and click on the button “Add”. For this case, add one anchor row in the depth of 1,5 m below the top of the wall with anchor spacing at 2,5 m. Also define the length of the anchors (which has no effect in the Sheeting design program, it is only for visualization) and slope of the anchors (15 degrees). In frame „Stage Settings“ choose “permanent“.

Frame ”Anchors” In the frame “Analysis” select support at heel. For now, select “Wall fixed at heel”. Now perform the analysis.

Frame ”Analysis” – Stage of construction 1 (Wall fixed at heel)


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In our case, we need to know the sheet pile embedment depth and also the anchor force. For the wall fixed at heel, the values are: −

Length of construction:

−

Depth in soil:

5,72 m

−

Anchor force:

165,77 kN

−

Maximum moment:

89,16 kNm / m

−


128,27 kN / m

10,72 m

Now, perform an analysis for wall hinged at heel (construction stage 2). Then, compare the results and, depending on comparison, design the embedment depth. Basic input: Analysis 2 Now, add a new verification in the upper left corner of the frame.

Toolbar: Verification Select the option “Wall hinged at heel” and perform the analysis.

Frame “Analysis” – Stage of construction 2 (Wall hinged at heel)


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For the wall hinged at heel, the values are: −

Length of construction:

−

Depth in soil:

2,85 m

−

Anchor force:

201,68 kN

−

Maximum moment:

119,35 kNm / m

−


69,84 kN / m

7,85 m

The results of analysis The overall length of the structure should be in the interval of “Hfixed – Hhinged”. For wall fixed at heel is the length of the structure is longer, but the anchor force is smaller. For wall hinged at heel, it is the opposite, so larger anchor force and shorter length of the construction. It is the user‘s task to design the dimensions of the structure.

Conclusion In our design, we will use pile sheeting VL 503 from steel S 270 with an overall length of 9,0 m, anchors with size of force 240 kN with anchor spacing of 2,5 m. In the next chapter, we will check this structure in the program “Sheeting check”.

Note: The design cannot be taken as the final and it needs to be checked in the Sheeting check program, because on the real structure there is redistribution of earth pressure due to anchoring.


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Chapter 6. Verification of retaining wall with one anchor row In this chapter, we will show you how to verify a designed retaining wall with verification of its dimensioning, next inner stability of the anchors and overall stability of the structure. Assignment Verify the retaining wall that you designed in task 5. Solution: For solving this problem, we will use the GEO5 program, Sheeting Check. In this text, we will explain each step to solve this task: −

Construction stage 1: excavation of ditch to a depth of 2,5 m, geometry of the wall,

−

Construction stage 2: anchoring of the wall,

−

Construction stage 3: excavation of ditch to a depth of 5,0 m,

−

Verification of inner stability of the anchors, next overall stability of the structure and dimensioning of steel section (sheet pile).

Basic input: Construction stage 1 To make our work easier, we can copy the data from the last task, when we designed the wall in the “Sheeting design” program by clicking in this program on “Edit” on the upper toolbar and selecting “Copy data”. In “Sheeting check” program click on “Edit” and then “Paste data”. Now we have most of the important data from the last task copied in to this program, so we don’t have to input much of the needed data.

Dialog window “Insert data” 42 Engineering manuals for GEO5 programs - Part 1

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In the frame “Settings”, select again the number 5 “Standard – EN 1997, DA3”. Select the analysis

of

depending

pressures

as

“Reduce

according

to

analysis

settings”.

Leave the coefficient for minimum dimensioning pressure as k = 0,2 .

Frame “Settings” (Analysis of pressures)

Note: The selection “Analysis of depending pressures – do not reduce” allows the analysis of limit pressures (active and passive) without the reduction of input parameters by partial factors. This is better for estimation of real behaviour of construction. On the other hand, it does not follow EN 1997-1 Standard (More info in HELP – F1).

Then, open up the frame “Modulus k h ”, and choose the selection “analyze – Schmitt”. This method for the determination of modulus of subsoil reaction depends on the oedometric modulus and stiffness of the structure (More info in HELP – F1).

Frame “Modulus k h ”

Note: the modulus of subsoil reaction is an important input when analyzing a structure by the method of dependent pressures (elastic-plastic nonlinear model). The modulus k h affects the deformation, which is needed to reach active or passive pressures (More info in HELP – F1).


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In the frame “Geometry” define the parameters of the sheet pile – type of wall and section length l = 9 m . From the sheet pile database, select the GU 6N (600 × 154,5 × 6 mm).

Dialog window “Edit section” In the frame “Material”, from the catalogue, then select the appropriate class of steel for the structure. In this case, select the type of EN 10248-1: S 240 GP.

Dialog window “Catalogue of materials”


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Now, in the frame “Excavation” define the first ditch depth – 2,50 m for the first construction stage.

Frame “Excavation” – Stage of construction 1 Now, go to frame “Analysis”. In the left part of the frame, you can see the modulus of subsoil reaction, in the right section shape of deformed structure, real and limit earth pressures and displacement (For more information, see HELP – F1).

Frame “Analysis” – Stage of construction 1 45 Engineering manuals for GEO5 programs - Part 1

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Basic input: Construction stage 2 Add another construction stage as indicated below. Here we define the anchoring of the wall. We cannot change the frames “Settings”, “Profile”, “Modulus k h ”, “Soils” and “Geometry”, because these data are the same for all construction stages. In the frame “Anchors” push the button “Add”. For sheet pile wall design one row of anchors in depth 1,5 m under ground level. Define the parameters of anchor: −

Total length of anchors: l c = 10 m (length of root l k = 3 m , free length of anchor l = 7 m )

−

Slope of anchors: α = 15° ,

−

Spacing between anchors: b = 2,5 m . Then input the necessary parameters for calculation of anchor stiffness (diameter d = 32 mm

and modulus of elasticity E = 210 GPa ) and prestress force F = 240 kN .

Dialog window “New anchor”

Note: For once anchored walls are advantageous to introduce an anchor in a separate stage of construction, then own excavation modelled in the following stage. This is iteration of modulus of subsoil reaction – in modelling of anchors and excavation at one stage may become unstable calculation and not finding solutions.

Note: The stiffness of the anchors is taken into account in next stages of construction. Due to the deformation of construction the forces in anchors are changing (More info in HELP – F1). 46 Engineering manuals for GEO5 programs - Part 1

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The other input parameters doesn´t change. Now, perform the analysis.

Frame “Analysis” – Stage of construction 2 On the previous figure is shown that the added anchor caused push from the structure towards into the soil. Soil pressure near the anchor is increased up to the size of the passive pressure or redistribution occurred sizes earth pressures acting on the structure.

Basic input: Construction stage 3 In this stage of construction define the overall excavation of the ditch. In the frame “Excavation”, change the depth of the ditch to the final depth – 5,0 m.

Frame “Excavation” – Stage of construction 2 47 Engineering manuals for GEO5 programs - Part 1

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Now, perform the analysis to view the distribution of internal forces and displacement of the anchored structure.

Frame “Analysis” – Stage of construction 3

− Max. shear force:

Qmax = 72,46 kN/m ,

− Max. bending moment:

M max = 97,02 kNm/m ,

− Max. displacement:

umax = 25,4 mm .

Frame “Analysis” – Stage of construction 3 (Internal forces) 48 Engineering manuals for GEO5 programs - Part 1

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Frame “Analysis” – Stage of construction 3 (Displacement and earth pressure on the structure)

Verification of material and cross section of sheet pile: Then, open up the frame “Dimensioning”. Maximum observed moment on the structure is 97.02 kNm / m. Overall utilization of sheet pile of type GU 6N from steel EN 10248-1: S 240 GP is 64.7%. The maximum displacement of the structure 25.4 mm is also satisfactory.

Frame “Analysis” – Stage of construction 3 (Total utilization of sheet pile of type GU 6N) 49 Engineering manuals for GEO5 programs - Part 1

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Verification of anchor stability Now, open the frame “Internal stability”. You can see, that the internal stability of anchors is not satisfactory (total utilization is 209,05%) . This means, that the anchor could tear from the soil.

Frame “Internal stability” – Stage of construction 3 (not satisfactory result) The reason for this is that the anchor is too short, so in the frame “Anchors” (in stage of construction 2), change its free length to 9,5 meters. Total length of anchor is 12,5 m.

Dialog window “Edit anchor” – Stage of construction 2 50 Engineering manuals for GEO5 programs - Part 1

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Then switch back to the 3rd stage of construction, we will calculate and return again to the frame “Internal stability”. The following figure shows that the newly designed anchor satisfies the internal stability requirements (total utilization is 95,37%).

Frame “Internal stability” – Stage of construction 3 (satisfactory result) The last needed check is overall stability of the structure. Click on the button “External stability”. This will open the “Slope stability” program. In the frame “Analysis” click on “Analyze”. We can see, that the overall stability is acceptable.

Frame “External stability” 51 Engineering manuals for GEO5 programs - Part 1

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Conclusion: Analysis results The designed structure of sheet pile wall satisfies in all checked parameters: −

Utilization of steel section: 64,7 %

SATISFACTORY.

−

Internal stability: 95,37 %

Fmax = 336,99 kN > Fzad = 321,4 kN

IS OK.

−

Overall stability: 82,1 %


IS OK.

When adjusting the length of the anchor l c = 12,5 m there is a change in the calculation of internal forces, deformations and earth pressures. For the last stage of construction then based on the resulting values as follows: −

Max. shear force:

Qmax = 72,42 kN/m ,

−

Max. bending moment:

M max = 96,92 kNm/m ,

−

Max. displacement:

u max = 26,1 mm .


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Chapter 7. Verification of multi-anchored wall In this chapter, we are showing how to design and verify a multi-anchored wall. Introduction The basic assumption of the method is that the soil or rock in the vicinity of wall

behaves as ideally elastic-plastic Winkler material. This material is determined by the modulus of subsoil reaction k h , which characterizes the deformation in the elastic region and by additional limiting deformations. When exceeding these deformations the material behaves as ideally plastic.

The following assumptions are used: − The pressure acting on a wall may attain an arbitrary value between active and passive pressure – but it cannot fall outside of these boundaries. − The pressure at rest acts on an undeformed structure ( w = 0 ). Assignment

Verify a multi-anchored wall made from steel soldier piles I 400 with a length of l = 21 m . Depth of the ditch is h = 15 m . The terrain is horizontal. The surcharge acts at the surface and is permanent with size of q = 25 kN m 2 . The GWT behind the construction is 10 m below the surface. Spacing between centres of steel profiles is a = 2 m .

Scheme of the wall anchored in multiple layers – Stage of construction 1


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Table with the soil and rock basic parameters

Table with the soil and rock additional parameters Profile [m]

Poisson’s Ratio ν [−]

Deformation modulus Edef [MPa ]

Type of soil

0,0 – 2,0

0,4

6

cohesive

CS – Sandy clay

2,0 – 4,5

0,35

7

cohesive

R4 (good rock)

4,5 – 12,0

0,3

40

cohesive

R3 (good rock)

12,0 – 16,6

0,25

50

cohesive

R5 (poor rock)

16,6 – 17,4

0,3

40

cohesive

GL R5 (poor rock)

17,4 – 25,0

0,25

55

cohesive

P R5 (poor rock)

from 25,0

0,2

100

cohesive

Soil, rock (classification) CL, CI – Clay with medium plasticity

Unit weight of soil γ is the same as the Unit weight of saturated soil γ sat . All anchors have a diameter d = 32 mm , modulus of elasticity E = 210 GPa . Anchor spacing is b = 4 m . Anchor no.

Depth z [m]

Length l [m]

Root lk [m]

Slope α [°]

1 2 3 4 5

2,5 5,5 8,5 11 13

19 16,5 13 10 8

0,01 0,01 0,01 0,01 0,01

15 17,5 20 22,5 25

Anchor force Stage construction F [kN] for a new anchor 300 350 400 400 400

2 4 6 8 10

Table with position and geometry of the anchors 54 Engineering manuals for GEO5 programs - Part 1

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Solution

For solving this task, use the GEO5 program – Sheeting Check. The analysis will be performed without reduction of input data so the real behaviour of the structure will be grasped. In the frame “Settings” select option no. 2 “Standard – limit states”. We consider the minimum dimensioning pressure as k = 0,2 . We leave the number of FEs to discretize wall as 30 (see figure).

Frame “Settings”

Note: For more complex tasks (e.g. multiple anchored wall), the authors of the program recommends to compute limit pressures without reduction of soil input parameters, respectively without reducing the size of appropriate partial factors for earth pressures. Method of dependent pressures without reduction of soil input parameters corresponds better to the real behaviour of the structure (the user receive the real values of displacement), and this way of calculation is similar to the numerical solution by FEM (see HELP – F1). In the frame “Material”, from the catalogue, then select the appropriate class of steel for the structure. In this case, select the type of EN 10210-1: S 355.

Dialog window “Catalogue of materials” 55 Engineering manuals for GEO5 programs - Part 1

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In the frame “Geometry” define the parameters for braced sheeting – type of wall and section length l = 21 m . From the database of I-sections, select the section I (IPN) 400. Spacing between

centres of steel profiles equals to a = 2 m . Then, we define the coefficient of pressure reduction below the ditch bottom, which is in this case 0,4.

Dialog window “New section”

Note:

The

coefficient

of

reduction

of

earth

pressures

below

the

excavation

reduces the pressures in the soil. For classical retaining walls this is equal 1.0, for braced sheeting it is less than or equal to one. It depends on size and spacing of braces (More info in help – F1). Now, we will describe the building of the wall stage by stage. It is necessary to model the task in stages, to reflect how it will be constructed in reality. In each stage it is necessary to look at values of internal forces and displacement. If the braced sheeting is not stable in some stage of construction or if the analyzed deformation is too large, then we need to change structure – for example to make the wall embedment longer, make the ditch shallower, increase the anchor forces etc. 56 Engineering manuals for GEO5 programs - Part 1

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In the first stage of construction we define surface permanent surcharge q = 25 kN m 2 .

Frame “Surcharge” In construction stage 1, the ditch is made to depth of h = 3 m . In the stage 2, anchor is placed at a depth of z = 2,5 m . The GWT behind and in front of the structure is at a depth of h1 = h2 = 10 m beneath the surface (ground level).

Frame “Anchors” – Stage of construction 2 57 Engineering manuals for GEO5 programs - Part 1

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In the 3rd stage of construction, the ditch is excavated to a depth of h = 6,5 m . In the 4th stage, anchor is placed at a depth of z = 5,5 m . The GWT is not changed so far.

Frame “Anchors” – Stage of construction 4 In the 5th construction stage, the ditch is excavated to a depth of h = 9 m . In the 6th stage, anchor is placed at the depth of z = 8,5 m . The depth of GWT is not changed.

Frame “Anchors” – Stage of construction 6


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In 7th construction stage, the ditch is excavated to a depth of h = 11,5 m . In 8th construction stage, an anchor is placed at the depth of z = 11 m . The GWT in front of the wall is now at a depth of h2 = 12 m below the surface. The GWT behind the structure is not changed.

Frame “Anchors” – Stage of construction 8 In the 9th construction stage, the ditch is excavated to a depth of h = 13,5 m . The GWT in front of the structure is h2 = 15,5 m below the surface. Then in the 10th stage, an anchor is placed at the depth of z = 13 m .

Frame “Anchors” – Stage of construction 10 59 Engineering manuals for GEO5 programs - Part 1

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In the 11th, and last, construction stage, the ditch is excavated to a depth of h = 15 m . We will not add new anchors. The GWT has not change since 9th stage of construction (in front of the wall is at a depth of h2 = 15,5 m , behind the wall it is at a depth of h1 = 10 m ).

Frame “Anchors” – Stage of construction 11

Note: Due to deformation of the structure the forces in anchors are changing. These changes depend on the stiffness of the anchors and the deformation of the anchor’s head. The force can decrease (due to loss of pre-stress force) or increase. The forces can be pre-stressed in any stage of construction again to the required force.


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Results of analysis

On the pictures below are shown the results of analysis (internal forces – bending moment and shear force, displacement of structure and earths pressure) of the last, 11th construction stage.

Frame “Analysis” – Stage of construction 11 (modulus of subsoil reaction)

Frame “Analysis” – Stage of construction 11 (Internal forces)

Frame “Analysis” – Stage of construction 11 (Displacement of structure + earth pressures) 61 Engineering manuals for GEO5 programs - Part 1

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All the stages are analyzed. That means that the structure of braced sheeting is stable and functional in all stages of the construction. The displacement must also be checked that it is not too large, as well as that the anchor force does not exceed the bearing capacity of the anchor (The user must check this as this is not checked by the program Sheeting Check). For the last, 11th stage of construction the results are following:

− Max. shear force:

Qmax = 149,97 kN/m ,

− Max. bending moment:

M max = 167,97 kNm/m ,

− Max. earth pressure:

σ x = 250,01 kPa ,

− Max. displacement:

u max = 32,8 mm , it´s satisfactory.

Note: If the program does not find a solution in some of the construction stages, then the data must be revised – e.g. to make the structure longer, make the forces in anchors larger, change the number or position of anchors, etc.

Verification of cross-section of the structure

Open the frame “Dimensioning” in the last, 11st construction stage, where you can see the maximum and minimum values of variables (envelopes of internal forces).

− Maximum shear force (minimum):

Qmax,min = −149,97 kN/m

− Maximum bending moment (minimum):

M max,min = −167,97 kNm/m

Internal forces are calculated per one meter (foot) of construction in the program Sheeting check. For actual design of soldier beams (steel I-section) we have to multiply these values with the spacing between profiles a = 2 m , to obtain internal forces in the cross-section. − Max. shear force for dimensioning:

QEd ,max = 149,97 ⋅ 2,0 = 299,3 kN ,

− Max. bending moment for dimensioning:

M Ed ,max = 167,97 ⋅ 2,0 = 335,95 kNm .

Program performs the assessment of soldier beams (steel I-section) with the extreme values of internal forces according to EN 1993-1-1 (EC 3). For the time being, we leave a reduction coefficient of bearing capacity as 1,0. In this case the results are following: 62 Engineering manuals for GEO5 programs - Part 1

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− Bearing capacity of cross-section:

M Rd = 516,61 kNm ≥ M Ed ,max = 335,95 kNm .

− Total utilization of steel I-section:

65 %

I-section satisfies analysis criteria.

Frame „Dimensioning“ – Stage of construction 11 (Assessment of steel I- section I 400) In the calculation we have retained the size of limit earth pressures non-reduced, or the load is lower than would be according to the EN 1997-1. However, the internal forces suited to the real behaviour of the structure. Changes of the earth pressures lead to improving safety, but also to distort the results of analysis. That´s why, for the assessment of the steel section we introduce a custom value of reduction coefficient of bearing capacity. Note: EN 1997-1 standard assumes the partial factor for permanent load as γ Q = 1,5 , for variable load equals to γ Q = 1,5 . In this case, all surcharge and load act as a permanent, we consider a partial factor γ G as 1,35.

The combination of permanent and variable loads we have to determine the value of the design partial factor estimates, ranging from 1.35 to 1.5 of the ratios in dependence of the components of the load, which is prevalent. Now, we change a reduction coefficient of bearing capacity to 1,35. Internal forces acting in the cross-section of soldier beam we multiply by this partial factor. In this case the internal forces are following:


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− Max. shear force for dimensioning: QEd ,max = (149,97 ⋅ 2) ⋅ 1,35 = 404,91 kN , − Max. bending moment for dimensioning:

M Ed ,max = (167,97 ⋅ 2) ⋅ 1,35 = 453,53 kNm .

Frame „Dimensioning“ – Stage of construction 11 (New assessment of steel I- section I 400) In this case (assessment with influence of reduction coefficient of bearing capacity as 1,35) the results are following: − Bearing capacity of cross-section:

M Rd = 516,61 kNm ≥ M Ed ,max = 453,53 kNm .

− Total utilization of steel I-section:

87,8 %

I-section satisfies analysis criteria.


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Analysis of internal stability

Go to the frame “Internal stability” in the last construction stage and look at maximum allowable force in each anchor.

Note: The verification is done this way. At first we iterate the force in the anchor, resulting in equilibrium of all forces acting on the earth wedge. This earth wedge is bordered by construction, terrain, the middle of the roots of anchors and the theoretical heel of structure (more info in Help – F1). If an anchor is not satisfactory the best way to resolve the issue is to make it longer or decrease the pre-stressed force. We receive a maximum force in anchor (row no. 4) from the calculation and then total utilization of anchor: − Internal stability: 19,41 %

Fmax = 4093,86 kN > Fzad = 794,63 kN

Satisfactory.

Frame “Internal stability” – Stage of construction 11


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Verification of external (overall) stability

The last required analysis is external stability. The button will automatically open the program “Slope stability”, where we perform overall stability.

Program “Slope Stability” – Bishop method with optimization of circular slip surface

Conclusion, completion of the results:

The structure was successfully designed with a maximum deformation of 32,8 mm. This is satisfactory for this type of construction. Additionally, the limits of forces in anchors were not exceeded. − Bearing capacity: 87,8 %

SATISFACTORY.

− Internal stability: 19,41 %

Fmax = 4093,86 kN > Fzad = 794,63 kN

Satisfactory.

− Overall stability: 46,7 %


Satisfactory.

The designed braced sheeting satisfies evaluation criteria.


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Chapter 8. Analysis of slope stability In this chapter, we are going to show you how to verify the slope stability for critical circular and polygonal slip surfaces (using its optimization), and the differences between methods of analysis of slope stability. Assignment

Perform a slope stability analysis for a designed slope with a gravity wall. This is a permanent design situation. The required safety factor is SF = 1,50. There is no water in the slope.

Scheme of the assignment Solution

For solving this problem, we will use the GEO5 program, Slope stability. In this text, we will explain each step to solve this problem:

• Analysis nr. 1: optimization of circular slip surface (Bishop) • Analysis nr. 2: verification of slope stability for all methods • Analysis nr. 3: optimization of polygonal slip surface (Spencer) • Analysis result (conclusion)


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Basic input – Analysis 1:

In the frame “Settings” click on “Select” and choose option nr. 1 – “Standard – safety factors”.

Dialog window “Settings list” Then model the interface layers, resp. terrain using these coordinates:

Adding interface points Firstly, in the frame “Interface” input the coordinate range of the assignment. „Depth of deepest interface point“ is only for visualization of the example – it has no influence on the analysis.


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Then, input the geological profile, define the parameters of soil, and assign them to the profile.

Dialog window “Add new soils” Note: In this analysis, we are verifying the long-term slope stability. Therefore we are solving this task with effective parameters of slip strength of soils ( ϕ ef , c ef ). Foliation of soils – worse or different parameters of soil in one direction - are not considered in the assigned soils. 69 Engineering manuals for GEO5 programs - Part 1

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Table with the soil parameters Soil (Soil classification) MG – Gravelly silt, firm consistency S-F – Sand with trace of fines, dense soil MS – Sandy silt, stiff consistency, S r > 0,8

Unit weight γ kN m 3

Angle of internal friction ϕ ef [°]

Cohesion of soil cef [kPa]

19,0

29,0

8,0

17,5

31,5

0,0

18,0

26,5

16,0

[

]

Assigned Soil Region 1 3 4

Model the gravity wall as a Rigid Body with a unit weight of γ = 23,0 kN m 3 . The slip surface does not pass through this object because it is an area with large strength. (More info in HELP – F1) In the next step, define a surcharge, which we consider as permanent and strip with its location on the terrain surface.

Dialog window “New surcharges”


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Note: A surcharge is entered on 1 m of width of the slope. The only exception is concentrated surcharge, where the program calculates the effect of the load to the analyzed profile. For more information, see HELP (F1). Skip the frames “Embankment”, “Earth cut”, “Anchors”, “Reinforcements” and “Water”. The frame “Earthquake” has no influence on this analysis, because the slope is not located in seismically active area. Then, in the frame “Stage settings”, select the design situation. In this case, we consider it as “Permanent” design situation.

Frame “Stage settings” Analysis 1 – circular slip surface

Now open up the frame “Analysis”, where the user enters the initial slip surface using coordinates of the center ( x, y ) and its radius or using the mouse directly on the desktop – by clicking on the interface to enter three points through which the slip surface passes. Note: In cohesive soils rotational slip surfaces occur most often. These are modeled using circular slip surfaces. This surface is used to find critical areas of an analyzed slope. For noncohesive soils, an analysis using an polygonal slip surface should be also performed for slope stability verification (see HELP – F1). Now, select “Bishop” as the analysis method, and then set type of analysis as “Optimization”. Then perform the actual verification by clicking on “Analyze”.


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Frame “Analysis” – Bishop – optimization of circular slip surface Note: optimization consists in finding the circular slip surface with the smallest stability– the critical slip surface. The optimization of circular slip surfaces in the program Slope stability evaluates the entire slope, and is very reliable. For different initial slip surfaces, we get the same result for a critical slip surface The level of stability defined for critical slip surface when using the “Bishop” evaluation method is satisfactory :

SF = 1,82 > SFs = 1,50

SATISFACTORY.

Analysis 2:

Now select another analysis on the toolbar in upper right corner of your Analysis frame in GEO5.

Toolbar “Analysis” In the frame Analysis, change the analysis type to “Standard” and as method select “All methods”. Then click on “Analyze”. 72 Engineering manuals for GEO5 programs - Part 1

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Frame “Analysis” – All methods – standard type of analysis

Note: Using this procedure, the slip surface made for all methods corresponds to critical slip surface from the previous analysis scenario using the Bishop method. For better results the user should choose the method and then perform an optimization of slip surfaces. The values of the level of slope stability are: − Bishop:

SF = 1,82 > SFs = 1,50

SATISFACTORY.

− Fellenius / Petterson:

SF = 1,61 > SFs = 1,50

SATISFACTORY.

− Spencer:

SF = 1,79 > SFs = 1,50

SATISFACTORY.

− Janbu:

SF = 1,80 > SFs = 1,50

SATISFACTORY.

− Morgenstern-Price:

SF = 1,80 > SFs = 1,50

SATISFACTORY.

− Šachuňanc:

SF = 1,63 > SFs = 1,50

SATISFACTORY.

Note: the selection of method of analysis depends on experience of the user. The most popular methods are the method of slices, from which the most used, is the Bishop method. The Bishop method does yield conservative results. For reinforced or anchored slopes other rigorous methods (Janbu, Spencer and MorgensternPrice) are preferable. These more rigorous methods meet all conditions of balance, and they better describe real slope behavior. It is not needed (or correct) to analyze a slope with all methods of analysis. For example, the Swedish method Fellenius – Petterson yields very conservative results, so the safety factors could be unrealistically low in the result. Because this method is famous and in some countries required for slope stability analysis, it is a part of GEO5 software.


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Analysis 3 – polygonal slip surface

In the last step of analysis, input the polygonal slip surface. As a method of analysis, select “Spencer”, as analysis type select “optimization”, enter a polygonal slip surface and perform the analysis.

Frame “Analysis” – Spencer – optimization of polygonal slip surface The values of the level of slope stability are:

SF = 1,58 > SFs = 1,50

SATISFACTORY.

Note: Optimization of a polygonal slip surface is gradual and depends on the location of the initial slip surface. This means that it is good to make several analyses with different initial slip surfaces and with different numbers of sections. Optimization of polygonal slip surfaces can be also affected by local minimums of factor of safety. This means the real critical surface does need to be found. Sometimes it is more efficient for the user to enter the starting polygonal slip surface in a similar shape and place as an optimized circular slip surface.


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Local minimums

Note: We often get complaints from users that the slip surface after the optimization “disappeared”. For non-cohesive soils, where c ef = 0 kPa the critical slip surface is the same as the most inclined line of slope surface. In this case, the user should change parameters of the soil or enter restrictions in which the slip surface can’t pass. Conclusion

The slope stability after optimization is:

SF = 1,82 > SFs = 1,50

− Bishop (circular - optimization):

SATISFACTORY.

SF = 1,58 > SFs = 1,50

− Spencer (polygonal - optimization):

SATISFACTORY. This designed slope with a gravity wall satisfies stability requirements.


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Chapter 9. Stability of slope with retaining wall In this chapter, we are going to describe the stability analysis of an existing slope, then how to model a sheeting wall being built, and how to check its internal and external stability. Assignment:

Perform an analysis of an existing slope and then verify the design of an underground wall for construction of parking areas. When performing the analysis, consider the permanent design situation in all construction stages. Verify the stability using safety factors. The safety factor needed is SFs = 1,50 . All stability analyses are performed using the Bishop method with optimization of circular slip surface.

Scheme of assignment The wall is made from concrete class C 30/37, the thickness of the wall is h = 0,5 m . The calculated shear resistance of the wall is VRd = 325 kN m . Solution:

For solving this task, use the GEO5 program – Slope Stability. In this text, we will describe the solution of this task step by step. − Construction stage 1: slope modeling, determination of safety factor of the existing

slope; − Construction stage 2: making the earth cut for the parking (only as a working stage) − Construction stage 3: construction of the wall, analysis of internal and external stability; 76 Engineering manuals for GEO5 programs - Part 1

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− Analysis results (Conclusion).

Construction stage 1: slope modeling

In the frame “Settings”, click on “Select” and then choose analysis settings nr. 1 “Standard – safety factors”. Then, model the interface of layers, resp. terrain using these coordinates.

“ Interface coordinates” Note: If data is entered incorrectly, it can be undone using the button UNDO (shortcut CtrlZ). In the same manner, we can use the opposite function REDO (Shortcut Ctrl-Y).

Buttons “Undo” and “Redo”


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Then define the soil parameters and assign them to the profile. Table with the soil parameters Soil (Soil classification) SM – Silty sand, medium dense soil ML, MI – Silt with low or medium plasticity, stiff consistency, S r < 0,8 MS – Sandy silt, firm consistency

Unit weight γ kN m 3


Cohesion of soil c ef [kPa ]

18,0

29,0

5,0

20,0

21,0

30,0

18,0

26,5

12,0

[

]

In the frame “Stage settings” choose permanent design situation. Analysis 1 – stability of existing slope

Now open up the frame “Analysis” and run the verification of stability of the original slope. As a verification method select “Bishop” and then perform the optimization of circular slip surface. How to input slip surface and optimization principle is described in more detail in the previous chapter and in HELP (F1).


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Analysis 1 – stability of the original slope The factor of safety of the original slope as analyzed by Bishop is:

SF = 2,26 > SFs = 1,50

Satisfactory.

Construction stage 2: earth cut modeling

Now add the second construction stage using the button in the upper left corner of the window.

Toolbar “Construction stages” Add the earth cut to the interface by adding individual points of the considered earth cut (similar to adding points to the current interface) in the frame “Earth cut”. The excavation for the sheeting wall is 0,5 m wide. After you are done with adding the points click on “OK”.


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“Coordinates of the earth cut”

Note: If you define two points with same x coordinate (see picture), the program asks if you want to add the new point to the left or right. The scheme of resulting input of the point is highlighted with red and green color in the dialog window.

Frame “Earth cut”

Construction stage 3: construction of the retaining wall

Now design the sheeting wall. In the frame “Embankment” add the points of the interface of the embankment. With these we actually model the face of the structure of the wall (see picture). 80 Engineering manuals for GEO5 programs - Part 1

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„The points of embankment“

Frame “Embankment” Analysis 2 – internal stability of retaining wall

To verify the internal stability on the circular slip surface it is necessary to model the structure as a stiff soil with fictitious cohesion, and not as rigid body. If it is modeled as a rigid body, the slip surface cannot intersect the structure.

Note: shear resistance of the RC retaining wall is modeled with help of fictitious cohesion, which we can determine as: c fict =

where: h [m]

V Rd 325,0 = = 650 kPa h 0,5

– width of the wall, 81

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VRd [kN m]

– shear resistance of the wall.

Now return to the 1st construction stage and add a new soil with name “Material of the retaining wall”. Define the value of the fictitious cohesion as c ef = 650 kPa , the angle of internal friction as a small value (for example ϕ ef = 1 ° ) since the program doesn’t allow to input 0. Define the unit weight as γ = 25 kN m 3 , which corresponds to structure from reinforced concrete.

Analysis 3 – slope stability behind the earth cut and retaining wall (internal stability) The analysis results of internal stability show that the slope with the earth cut and the retaining wall is stable:

SF = 1,60 > SFs = 1,50

Satisfactory.

Analysis 3 – external stability of retaining wall

Now add another analysis using toolbar in the left downward corner of the program.

Toolbar “More Analyses”


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Before running the analysis of the external slope stability, add restrictions on the optimization procedure using lines that the slip surface can’t intersect when it executes the optimization procedure (More info in HELP – F1). In our example the restriction lines are the same as the borders of the pile sheeting.

Analysis 4 - restrictions on the optimization procedure Note: for analysis of external slope stability it is appropriate to input the retaining wall as a solid body. When the wall is modeled as a solid body, the slip surface doesn’t intersect it during the optimization evaluation.


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Analysis 4 – slope stability with earth cut and retaining wall (external stability) From the results of external stability we can see, that the slope with the earth cut and retaining wall is stable: Conclusion

The objective of this chapter was to verify the slope stability and design of earth cut with retaining wall for the construction of a car park with analysis of internal and external stability. The results of analyses are: This slope with earth cut and retaining wall from concrete (with width of 0,5 m) in terms of long-term stability satisfies evaluation criteria. Note: this designed retaining wall would need to be checked for stress from the bending moment of loading from active earth pressure. This bending moment can be analyzed in the GEO5 programs Sheeting design and Sheeting Check. For the same bending moment it is also necessary to design and check reinforcements – for example in program FIN EC – Concrete 2D.


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Chapter 10. Design of geometry of spread footing In this chapter, we are going to show you how to design spread footing easily and effectively. Assignment: Using EN 1997-1 (EC 7-1, DA1) standards, design the dimensions of a concentric spread footing. Forces from columns act on the top of foundation. Input forces are: N , H x , H y , M x , M y . The terrain behind the structure is horizontal; foundation soil consists of S-F – Sand with trace of fines, medium dense soil. At 6,0 m is Slightly weathered slate. The GWT is also at a depth of 6,0 m. The depth of foundation is 2,5 m below the original terrain.

Scheme of the assignment – analysis of bearing capacity of spread footing Solution For solving this problem, we will use the GEO5 program – Spread footing. Firstly, we input all the data in each frame, except “Geometry”. In the Geometry frame, we will then design the spread footing. Basic input In the frame “Settings”, click on “Select” and then choose nr. 3 – “Standard – EN 1997 – DA1”. 85 Engineering manuals for GEO5 programs - Part 1

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Frame “Settings list” Also select an analysis method – in this case “Analysis for drained conditions”. We will not analyze settlement.

Frame “Settings” Note: Usually, spread footings are analyzed for drained conditions= using the effective parameters of soil ( ϕ ef , c ef ). Analysis for undrained conditions is performed for cohesive soils and short-term performance using total parameters of soil ( ϕ u , cu ). According to EN 1997 total friction considered is always ϕ u = 0 . In the next step enter the geological profile, soil parameters and assign them to the profile.

Table with the soil parameter Cohesion of soil

Soil, rock

Profile

Unit weight

(classification)

[m]

γ [kN m 3 ]

S-F – Sand with trace of fines, medium dense soil

0,0 – 6,0

17,5

29,5

0,0

Slightly weathered slate

from 6,0

22,5

23,0

50,0


cef [kPa]


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In the next step, open up the frame „Foundation“. As a type of foundation, choose „Centric spread footing“ and fill in the dimensions such as depth from the original grade, depth of footing bottom, thickness of foundation and inclination of finished grade. Also, input the weight of overburden, which is the backfill of spread footing after construction.

Frame „Foundation“ Note: The depth of the footing bottom depends on many different factors such as natural and climatic factors, hydrogeology of the construction site and geological conditions. In the Czech Republic the depth of footing bottom is recommended to be at least 0,8 meters beneath the surface due to freezing. For clays it is recommended that the depth be greater, such as 1,6 meters. When analyzing the bearing capacity of a foundation, the depth of the foundation is considered as the minimal vertical distance between the footing bottom and the finished grade. In the frame „Load“ enter the forces and moments acting on the upper part of foundation:

N , H x , H y , M x , M y . These values we obtained from a structural analysis program and we can import them to our analysis by clicking on „Import“.

Frame „Load“ Note: For design of dimensions of spread footing, generally the design load is the deciding load. , However, in this case we are using the analysis settings EN 1997-1 - DA1, and you must enter the value of service load too, because the analysis requires two design combinations.


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Dialog window „Edit load“ In the frame “Material”, input the material characteristics of the foundation. Skip the frame “Surcharge”, as there is no surcharge near the foundation. Note: Surcharge around the foundation influences the analysis for settlement and rotation of the foundation, but not bearing capacity. In the case of vertical bearing capacity it always acts favorably and no theoretical knowledge leads us to analyze this influence. In the frame „Water“ enter the ground water depth as 6,0 meters. We are not going to enter a sand gravel bed because we are considering permeable cohesionless soil at the of footing bottom. Then open up the frame „Stage settings“ and select „permanent“ as the design situation. Design of dimensions of the foundation Now, open the frame „Geometry“ and apply the function „Dimensions design“; with which the program determines the minimum required dimensions of the foundation. These dimensions can be edited later. In the dialog window it is possible to input the bearing capacity of foundation soil Rd or select „Analyze“. We will choose „Analyze“ for now. The program automatically analyzes the foundation weight and weight of soil below foundation and determines the minimum dimensions of the foundation.


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Dialog window „Foundation dimensions design“ Note: Design of centric and eccentric spread footing is always performed such that that the dimensions of foundation are as small as they can be and still maintain an adequate vertical bearing capacity. The option “Input” designs the dimensions of a spread footing based on the entered bearing capacity of the foundation soil. We can verify the design in the frame “Bearing cap.”.

Frame „Bearing capacity“

Vertical bearing capacity: 97,7 %

Rd = 545.22 > σ = 532.59 [kPa]

SATISFACTORY. Conclusion: The bearing capacity of designed foundation (2,0x2,0 m) is satisfactory. 89 Engineering manuals for GEO5 programs - Part 1

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Chapter 11. Settlement of spread footing In this chapter, we describe how analysis of settlement and rotation of a spread footing is performed. Assignment:

Analyze the settlement of centric spread footing designed in last chapter (10. Design of dimensions of spread footing). The geometry of the structure, load, geological profile and soils are the same as in the last chapter. Perform the settlement analysis using the oedometric modulus, and consider the structural strength of soil. Analyze the foundation in terms of limit states of serviceability. For a structurally indeterminate concrete structure, of which the spread footing is a part, the limiting settlement is: sm,lim = 60,0 mm.

Scheme of the assignment – analysis of settlement of spread footing Solution:


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For solving this task, we will use the GEO5 program – Spread footing. We will use the data from the last chapter, where almost all required data is already entered.

Basic Input:

The design of spread footing in the last task was performed using the standard EN 1997, DA1. Eurocodes do not order any theory for the analysis of settlement, so any common settlement theory can be used. Check the setting in the frame “Settings” by clicking on “Edit”. In the tab “Settlement” select the method “Analysis using oedometric modulus” and set Restriction of influence zone to “based on structural strength”.

Dialog window “Edit current settings”

Note: The structural strength represents the resistance of a soil against deformation from a load. It is only used in Czech and Slovak Republic. In other countries, the restriction of the influence zone is described by percentage of Initial in-situ stress. Recommended values of structural strength are from CSN 73 1001 standards (Foundation soil below the foundation)

In the next step, define the parameters of soils for settlement analysis. We need to edit each soil and add values for Poisson´s ratio, coefficient of structural strength and oedometric modulus, resp. deformation modulus.


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Table with the soil parameters Soil, rock (classification) S-F – Sand with trace of fines, medium dense soil Slightly weathered slate

Unit weight γ kN m3

[

]

Angle of Coeff. of Deformation Poisson´s internal structural modulus ratio friction Strength Edef [MPa] ν [−] ϕ ef [°] m

17,5

29,5

0,3

15,5

0,3

22,5

23,0

0,3

500,0

0,25

Analysis:

Now, run the analysis in the frame “Settlement”. Settlement is always analyzed for service load.


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Frame “Settlement”

In the frame “Settlement” it is also needed to input other parameters: -

Initial in-situ stress in the footing bottom is considered from the finished grade

Note: the value of in-situ stress in the footing bottom has influence on the amount of settlement and the depth of influence zone – a larger initial in-situ stress means less settlement. The option of in-situ stress acting on the footing bottom depends on the time the footing bottom is open. If the footing bottom is open for a longer period of time, the soil compaction will be less and it is not possible to consider the original stress conditions of the soil. -

In Reduction coefficient to compute settlement, select the option Consider foundation thickness effect (κ1).


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Note: the coefficient “ κ1 ”reflects the influence of the depth of the foundation and gives more realistic results of the settlement Results of analysis

The final settlement of the structure is 16,9 mm. Within an analysis of limit states of serviceability we compare the values of the analyzed settlement with limit values, which are permissible for the structure. Note: The stiffness of structure (soil-foundation) has a major influence on the settlement. This stiffness is described by the coefficient k – if k is greater then 1, the foundation is considered to be stiff and settlement is calculated under a characteristic point (located in 0,37l or 0,37b from the center of the foundation, where l and b are dimensions of foundation). If coefficient k is lower then 1, the settlement is calculated under the center of foundation. -

Analyzed stiffness of foundation in direction is k = 137,10 . The settlement is computed under the characteristic point of foundation.

Note : Informative values of allowable settlement for different kinds of structures can be found in various standards – for example CSN EN 1997-1 (2006) Design of geotechnical structures. The Spread footing program also provides results for the rotation of the foundation, which is analyzed from the difference of settlement of centers of each edge.

Rotation of the foundation – principle of the analysis 94 Engineering manuals for GEO5 programs - Part 1

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− Rotation in direction x : 0,75 ⋅ (tan∗ 1000) − Rotation in direction y : 1,776 ⋅ (tan∗ 1000) Conclusion

This spread footing in terms of settlement satisfies evaluation criteria. Settlement: sm,lim = 60,0 ≥ s = 16,9 [mm]. It is not necessary to verify rotation of this foundation.


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Chapter 12. Analysis of consolidation under embankment In this chapter, we are going to explain how to analyze consolidation under a constructed embankment. Introduction:

Soil consolidation takes into account the settlement time (calculation of earth deformation) under the effect of external (constant or variable) loads. The surcharge leads to an increase in earth formation stress and the gradual extrusion of water from pores, i.e. soil consolidation. Primary consolidation corresponds to the situation in which there is a complete dissipation of pore pressures in soil, secondary consolidation affects rheological processes in the soil skeleton (the so called "creep effect"). This is a time-dependent process influenced by a number of factors (e.g. soil permeability and compressibility, length of drainage paths, etc.). With regards to the degree of consolidation we distinguish the following cases of ground settlement: − final settlement corresponding to 100% consolidation from the respective surcharge − partial settlement corresponding to a particular degree of consolidation from

the respective surcharge

Assignment:

Determine the settlement value under the centre of an embankment constructed on impermeable clay one year and ten years after its construction. Make the analysis using CSN 73 1001 standards (using oedometric modulus), limit of influence zone consider using coefficient of structure strength.

Scheme of the assignment – consolidation 96 Engineering manuals for GEO5 programs - Part 1

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Solution:

The GEO 5 – Settlement program will be used to solve this task. We are going to model this example step by step: − 1st construction stage – interface modeling, calculation of the initial geostatic stress. − 2nd construction stage – adding a surcharge by means of an embankment. − 3rd up to 5th construction stages – calculation of embankment consolidation

at various time intervals (according to the assignment). − Evaluation of results (conclusion). − Basic assignment (procedure): Stage 1

Check the "Perform consolidation analysis" field in the "Settings" frame. Then select specific settings for calculation of the settlement from "Settings list". This setting describes the analysis method for calculation of the settlement and restriction of influence zone.

Frame "Settings"

Note: This calculation considers the so called primary consolidation (dissipation of pore pressure). Secondary settlement (creep), which may occur mainly with non-consolidated and organic soils, is not solved within this example.

Then we enter the layer interface. The objective is to select two layers between which the consolidation takes place.


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Frame "Interface"

Note: If there is a homogeneous soil, then in order to calculate the consolidation, it is necessary to enter a fictitious layer (use the same parameters for the two soil layers that are separated by the original interface), preferably at the depth of the deformation zone.

Then we define the "Incompressible subsoil" (IS) (at a depth of 10 m) by means of entering coordinates similarly to interface modeling. No settlement takes place under the IS. The soil parameters are entered in the next step. For soils being consolidated, it is required to specify either the coefficient of permeability " k " or the coefficient of consolidation " cv ". Approximate values can be found in HELP (F1).

Dialog window "Modification of soil parameters"


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Table with the soil parameters Unit weight γ kN m 3

Poisson’s Ratio ν [−]

Clayey soil

18,5

0,3

1,0

0,1

1,0 ⋅ 10 −5

Embankment

20,0

0,30

30,0

0,3

1,0 ⋅ 10 −2

Sandy silt

19,5

0,30

30,0

0,3

1,0 ⋅ 10 −2

Soil (Soil classification)

[

]

Oedometric modulus E oed [MPa]

Coeff. of structural strength m [−]

Coeff. of permeability k [m day ]

Then we assign the soils to the profile. The frame surcharge in the 1st construction stage is not taken into consideration, since in this example it will be represented by the actual embankment body (in stages 2 to 5). In the next step, we shall enter the ground water table (hereinafter the "GWT") using the interface points, in our case at ground level. In the frame “Stage settings”, you can only modify layout and refinement of holes, so leave the standard settings. The first "Calculation" stage represents the initial geostatic stress at the initial construction time. However, it is necessary to specify the basic boundary conditions for the consolidation calculation in further stages. The top and bottom interface of the consolidating soil is entered, as well as the direction of water flow from this layer – i.e. the drainage path.


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"Analysis" – Construction stage 1 Note: If you enter "Incompressible subsoil", you shall then consider the direction of flow of water from the consolidating soil only upwards − Basic assignment (procedure): Stages 2 to 5

Let's now move to the 2nd construction stage by tool bar at the top left of the desktop.

Toolbar „Construction stage“

We define the embankment itself by entering coordinates. A specific soil type is assigned to the embankment.

"Stage 2 – Embankment interface points"


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"Stage 2 – Embankment + Assignment"

Note: The embankment acts as a surcharge to the original ground surface. It is assumed that a well-executed (optimally compacted) embankment theoretically does not settle. In a practice, settlement may occur (poor compaction, soil creep effect), but the program Settlement does not address this.

In the "Analysis" frame enter the time duration of the 2nd stage corresponding to the actual embankment construction time. The actual calculation of the settlement cannot be performed yet because, when determining consolidation, it is first necessary to know the whole history of the earthwork structure loading, i.e. all construction stages.


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Frame "Analysis – Construction Stage 2"

Since the embankment is built gradually, we are considering the linear load growth in the 2nd construction stage. In subsequent stages, the duration of the stage is entered (1 year i.e. 365 days – 3rd stage, 10 years i.e. 3,650 days – 4th stage and the overall settlement – 5th stage) and the whole loading is introduced at the beginning of the stage.

The calculations are performed after enter the last construction stage, which is on the "Overall settlement", is turned on (you can check it at any stage apart from the first one).

Frame "Calculation – Construction Stage 5"

Analysis results

Upon the calculation of the overall settlement, we can observe partial consolidation values below the centre of the embankment. We have obtained the following maximum settlement values in individual construction stages:

− Stage 1: only geostatic stress – settlement not calculated. − Stage 2 (surcharge by embankment): for 30 days → 29.2 mm − Stage 3 (unchanged): for 365 days → 113.7 mm − Stage 4 (unchanged): for 3,650 days → 311.7 mm − Stage 5: the overall settlement → 351.2 mm


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"Analysis – Construction stage 5 (Overall settlement)"

As we are interested in the embankment settlement after its construction, we will switch to the results view in the 3rd and 4th stages (the button "Values") to "compared to stage 2" which subtracts the respective settlement value.


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"Analysis – Settlement (differences compared to previous stages)"

Conclusion:

The embankment settlement (under its centre) within one year from its construction is 84.5 mm (= 113.7 – 29.2) and after ten years 282.5 mm (= 311.7 – 29.2).


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Geo5 Engineering Manuals Em3 1

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