aes/re/10-28 stability analysis of embankments located ... · road embankment slope stability limit...

AES/RE/10-28 Stability analysis of Embankments located within A-8 interstate motorway Wrocław by-pass

1st July 2010 Samuel Woldeyohannes

Title : Stability analysis of Embankments located within A-8

interstate motorway Wrocław by-pass Author(s) : Samuel Woldeyohannes Date : 1st July, 2010 Professor(s) : Ir. Hans de Ruiter Supervisor(s) : Dr. Witold Pytel TA Report number : AES/RE/10-28

Postal Address : Section for Geo–Engineering Department of Applied Earth Sciences Delft University of Technology P.O. Box 5028 The Netherlands Telephone : (31) 15 2781328 (secretary) Telefax : (31) 15 2781189

Copyright ©2010 Section for Geo-Engineering All rights reserved. No parts of this publication may be reproduced, Stored in a retrieval system, or transmitted, In any form or by any means, electronic, Mechanical, photocopying, recording, or otherwise, Without the prior written permission of the Section for Geo-Engineering.

Faculty of Geoengineering, Mining and Geology

MASTER THESIS

STABILITY ANALYSIS OF EMBANKMENTS LOCATED WITHIN A-8 INTERSTATE

MOTORWAY WROCŁAW BY-PASS

author

Samuel Yilma Woldeyohannes

supervisor

Professor Witold Pytel, Ph.D., D.Sc, Civ.Eng., MBA

Road embankment

Slope stability Limit equilibrium methods

Critical surfaces Factor of safety

Short summary

The stability analysis of the embankments of A-8 motorway Wroclaw bypass was carried out on selected road sections by using the secondary data obtained. Slide 2D computer analysis program that adopts limit equilibrium methods was used to model the actual embankment in order to compute the factor of safety. The assessment of the factor of safety was executed by referring to the slope stability requirements by polish regulations.

First of all I would like to thank and praise the Almighty God who made it possible for the successful completion of this work.

Proff. Witold Pytel, KGHM CUPRUM his critical comments, advice and guidance have been invaluable to me during this research. Above all, am highly grateful for his timely comments and corrections.

I would like to extend my heartfelt acknowledgment to Joanna Switon, KGHM CUPRUM. This study would have never been possible if it was not her support in various ways. She not only helps me in the modelling work but also in translating the data obtained from project office. I am greatly indebted for her patience, understanding and encouragement.

I would like to thank GEOTECH sp.zo.o project office for providing me the necessary secondary data for this research, which has got a major role in the present work. Special thanks to Pitor Mertuszka, KGHM CUPRUM for helping me in delivering the necessary documents required for this work. My acknowledgment to KGHM CUPRUM for the logistic supports providing me for this work.

The professional advice I got from Daniel Teklu, a graduate student at the University of Alberta, Department of Geotechnical Engineering has been invaluable and useful to the extent I could have imagined.

My special acknowledgment goes out to my friends Biniam Mamush, Henok Woldegiorgis and Mesay Mamo for their help in sending the necessary reading materials which have direct relevance to the present work.

I would like to express my deepest gratitude to Dr.Gabriela Paszkowska who helped me throughout the period of my study and all EMMEP coordinators, teachers, classmates in the program.

Last but not least I would like to express my heartfelt gratitude to my family for their assistance and continuous encouragement throughout my study.

i

1. Chapter I Introduction ......................................................................... 1

1.1 Rationale and background...................................................................................... 1

1.2 Problem definition ................................................................................................. 1

1.3 General project description .................................................................................... 2

1.4 Objectives of the study........................................................................................... 4

1.5 Approach and methodology ................................................................................... 4

1.6 Analytical tools and materials used ....................................................................... 5

1.7 Scope and limitation of the study........................................................................... 5

2. Chapter 2 Structural characteristics of road embankments ............ 7

2.1 Preamble ................................................................................................................ 7

2.2 Road embankment definition ................................................................................. 7

2.2.1 Height of embankment ................................................................................................... 7

2.2.2 Embankment slopes ........................................................................................................ 8

2.2.3 Embankment foundations .............................................................................................. 8

2.3 Legal documents and regulations concerned with embankment ........................... 8

2.4 Embankment construction ................................................................................... 10

2.4.1 Construction of earth embankments ............................................................................ 10

2.4.2 Reinforced earth embankments ................................................................................... 10

2.5 Materials used for embankments ......................................................................... 11

2.5.1 Basic soil properties ...................................................................................................... 11

2.5.2 Aggregates .................................................................................................................... 11

2.5.2.1 Properties of aggregates ........................................................................................... 11

2.5.3 Bituminous materials .................................................................................................... 12

2.6 Soil compaction ................................................................................................... 14

2.7 Bridge-embankment joints ................................................................................... 14

2.8 Special cases of embankment structures .............................................................. 16

2.8.1 Inclined embankments .................................................................................................. 16

2.9 Embankments on mud or peats ............................................................................ 17

2.9.1 Decomposition of sub Soil and road embankments ..................................................... 19

ii

2.9.2 Fluctuation of surface and groundwater ...................................................................... 19

2.10 Widening and re-construction of the existing embankments ............................... 19

3. Chapter 3 Basic hazards of road embankments ....... 21

3.1 Settlement ............................................................................................................ 21

3.1.1 Case example of settlement ......................................................................................... 22

3.2 Mass movements .................................................................................................. 23

3.2.1 Case examples of mass movements ............................................................................. 24

3.3 Abutments damages due to large earth pressure .................................................. 25

3.3.1 The At-rest condition .................................................................................................... 26

3.3.2 The Active condition ..................................................................................................... 27

3.3.3 The Passive condition .................................................................................................... 28

3.3.4 Earth pressure due to compaction ............................................................................... 30

3.4 Parameters of road hazard .................................................................................... 30

3.4.1 Water ............................................................................................................................ 30

3.4.2 Dynamic action.............................................................................................................. 31

3.4.2.1 Case example of failure of a road embankment during the 2004 Niigata earthquake

31

3.4.2.2 Case example of slumping of embankments due to earthquakes ............................ 31

3.4.3 Mining related deformations ........................................................................................ 32

3.4.4 Erosion .......................................................................................................................... 32

4. Chapter 4 Strengthening and reinforcement of road embankments

34

4.1 Preamble .............................................................................................................. 34

4.2 Seeding and slope hardening of pavement........................................................... 36

4.2.1 General design considerations ...................................................................................... 36

4.3 Surface slope protection ....................................................................................... 37

4.3.1 General design considerations ...................................................................................... 37

4.3.2 Shotcrete ....................................................................................................................... 38

4.3.3 Rip-rap ........................................................................................................................... 38

4.4 Buttressing ........................................................................................................... 39

4.4.1 Soil and rock Fill ............................................................................................................ 39

iii

4.4.2 Counter berms .............................................................................................................. 40

4.4.3 Mechanically stabilized embankments ......................................................................... 40

4.5 Retaining walls..................................................................................................... 40

4.6 Drainage ............................................................................................................... 41

4.6.1 Vertical drainage ........................................................................................................... 41

4.6.2 Vacuum drainage .......................................................................................................... 42

4.7 Soil modification methods ................................................................................... 42

4.7.1 Compacted soil-cement fill ........................................................................................... 43

4.7.2 Preconsolidation ........................................................................................................... 43

4.7.3 Injection methods ......................................................................................................... 44

4.7.3.1 Cement grouting ....................................................................................................... 44

4.7.3.2 Lime piles and slurry walls ........................................................................................ 45

4.7.4 Literature reviews on soil modification methods ......................................................... 45

5. Chapter 5 Embankments stability analysis

techniques ........................................................................................................ 47

5.1 Slope stability concepts........................................................................................ 47

5.1.1 Typical input data for slope stability analysis ............................................................... 47

5.1.2 Definition of factor of safety ......................................................................................... 47

5.2 Methods for embankment stability analysis ........................................................ 48

5.2.1 Limit equilibrium methods ............................................................................................ 48

5.2.2 Numerical modelling ..................................................................................................... 53

5.2.3 Probabilistic analysis ..................................................................................................... 53

5.2.4 Seismic analysis ............................................................................................................. 54

5.2.5 Available computer programs for stability analysis ...................................................... 55

6. Chapter 6 Developing the A-8 motorway embankment models for

stability analysis .............................................................................................. 56

6.1 Profile of the selected road sections..................................................................... 56

6.2 Geologic and subsurface conditions .................................................................... 57

6.3 Selection of boreholes for modelling A-8 motorway embankment foundation .. 58

6.4 Supporting and loading conditions ...................................................................... 59

6.5 Data inputs used for A-8 motorway embankment model .................................... 61

iv

6.6 The A-8 motorway embankment models ............................................................. 62

1. Concrete (Black colour). ............................................................................................... 62

6.7 A-8 Motorway model Section A .......................................................................... 62

6.8 A-8 Motorway model section B ........................................................................... 63

7. Chapter 7 Result and Discussion ...................................................... 65

7.1 Result ................................................................................................................... 65

7.1.1 Stability factor of the A-8 motorway embankment models ......................................... 65

7.2 Discussion ............................................................................................................ 66

7.2.1 Stability factor assessment of the A-8 motorway embankment .................................. 66

7.2.1.1 Model section-A FoS assessment .............................................................................. 66

7.2.1.1.1 Ordinary method ................................................................................................ 67

7.2.1.1.2 Bishop simplified method ................................................................................... 68

7.2.1.1.3 Janbu simplified method ..................................................................................... 70

7.2.1.1.4 Spencer method .................................................................................................. 72

7.2.1.1.5 GLE/Morgenstern method .................................................................................. 73

7.2.1.2 Model section-B FoS assessment .............................................................................. 73

7.2.1.2.1 Ordinary method ................................................................................................ 74

7.2.1.2.2 Bishop simplified method ................................................................................... 76

7.2.1.2.3 Janbu simplified method ..................................................................................... 78

7.2.1.2.4 Spencer method .................................................................................................. 79

7.2.1.2.5 GLE/Morgenstern method .................................................................................. 80

8. Chapter 8 Conclusion and

Recommendation ............................................................................................ 81

8.1 Conclusion ........................................................................................................... 81

8.2 Recommendation ................................................................................................. 81

v

Abbreviations

A-1= AASHTO class 1 soil type

A-3= AASHTO class 3 soil type

AASHTO=American Association of State Highway and Transportation Officials system

BEM= Boundary element method

DEM= Discrete element method

FDM= Finite difference method

FEM= Finite element method

GLE= Generalized limit equilibrium

IFCO= Iranian Fuel Conservation Organization

MSE= mechanically stabilized embankments

OCR= over consolidation ratio of soil

PS= Pseudo-static

PVD= prefabricated vertical drains

FoS= factor of safety FoSf= factor of safety using force equilibrium

FoSReq= required factor of safety

FoSm= factor of safety using moment equilibrium

List of symbols

Pc= permeability coefficient, [m/s]

Cc= compression index, [1]

Cv= consolidation coefficient, [m2/s]

= unit weight, [kN/m3]

H= height,[m]

σ = total stress, [N/m2]

σ’= total effective stress, [kPa]

σz’= vertical effective stress, [kPa]

vi

σx’= horizontal effective pressure, [kPa]

Єz= vertical strain,[1]

δc= consolidation settlement, [m]

Vv= volume of void, [m3]

δs= secondary compression settlement, [m]

δd= distortion settlement, [m]

K= coefficient of lateral earth pressure, [1]

Ko= coefficient of lateral earth pressure at rest, [1]

Ka= coefficient of active earth pressure, [1]

Kp= coefficient of passive earth pressure, [1]

= friction angle, *:+

’= effective friction angle, *:+

u= pore pressure, [kPa]

b= unit width of wall, [m]

τ = shear stress, [kPa]

Kh= horizontal seismic coefficient, [1]

Kv = vertical seismic coefficient, [1]

Tlim= long term capacity of reinforcing material, [N/m]

T= down slope weight, [N]

ws= bulk unit weight, [N]

β= slope angle, *:+

S= total shear strength, [kPa]

ΔSR= increase in shear strength per unit area, [kPa]

ΔS= change in shear strength, [kPa]

c’= effective cohesion, [kPa]

L= length, [m]

c’= effective cohesion, [kPa]

1= unit weight of soil above groundwater table, [kN/m3]

vii

2= unit weight of soil below groundwater table, [kN/m3]

F= forces, [N]

Rr= tensile strength, [kN/m]

q= distributed load, [kPa]

Mr= sum of the resisting moment, [N.m]

Md= sum of driving moment, [N.m]

Fr= sum of resisting forces, [N]

Fd= sum of driving forces, [N]

Ha= height of section A, [m]

Hb= height of section B, [m]

viii

List of figures

Figure 1. 1 Location of the A-8 motorway Wroclaw bypass (Google Earth and GEOTECHsp.zo.o

Project Office, 2010). .............................................................................................................................. 2

Figure 1. 2 Panoramic view of the A-8 motorway Wroclaw bypass under construction near node

“Widawa” (GEOTECHsp.zo.o Project Office, 2010) ................................................................................. 3

Figure 1. 3 Visualization of node"Widawa"A8 highway with the national road No.5 (GEOTECHsp.zo.o

Project Office, 2010). .............................................................................................................................. 3

Figure 1. 4 Visulaization of a bridge over Odra river the Rędziny water degree in Wroclaw

(GEOTECHsp.zo.o Project Office, 2010). ................................................................................................. 4

Figure 2. 1 Typical cross section of road embankment (DoLIDAR: Elements of Road Formation,2009). 7 Figure 2. 2 The bauxite-Residue embankment (Kehagia, F.,2009). ...................................................... 12

Figure 2. 3 Cross-section of fly ash based road formation with flexible pavement showing flyash and

soil layers on side slope and below pavement (Kumar, S., & Patil, C.,2006). ....................................... 13

Figure 2. 4 Embankment constructed with expanded polystrene blocks (Thompsett, D. J., et.al, 1995).

.............................................................................................................................................................. 14

Figure 2. 5 Traditional design concept (Seo, J. B.,2003). ...................................................................... 15

Figure 2. 6 Integral abutment bridge design (Seo, J. B.,2003). ............................................................. 16

Figure 2. 7 Schematic representation of failure of National road from Grevena to Loannina

(Pantelidis, L.,2008) ............................................................................................................................... 17

Figure 2. 8The model in one of cases considered (F.Maltinti, 2007). ................................................... 17

Figure 2. 9 Stability conditions for an embankment slope over a clay foundation (Abramson, L. W.,

et.al., 1995). .......................................................................................................................................... 18

Figure 2. 10 Widening of embankment (Witteveen, G., & Bos.,2001). ................................................ 20

Figure 3. 1 Disortion settlement beneath a small loaded area (Coduto, D. P.,1998)……………………… 21 Figure 3. 2 The approach fills adjacent to this bridge in California have settled. However, the bridge,

being supported on pile foundations, has not. Note the abrupt change in grade in sidewalk, and the

asphalt patch between the two signs (Coduto, D. P.,1998). ................................................................ 23

Figure 3. 3 Road construction subsidence North Yorkshire, England (Cooper, A. H., & Jones, J.

C.,2005). ................................................................................................................................................ 23

Figure 3. 4 Indications of the instability in 2003(Hadjigeorgiou J., et.al, 2003). .................................. 24

Figure 3. 5 Cracks along Pentalia in 2005 (Hadjigeorgiou J., et.al, 2003). ............................................ 24

Figure 3. 6 Rockfall and embankment against rockfall, Noto Peninsula (Masuya H.,et.al, 2009). ....... 25

Figure 3. 7 View of cracks on embankment debris flow (Wooten, R., & Latham, R.,2006).................. 25

Figure 3. 8 Lateral earth pressures imparted from a soil on to a vertical or near vertical structure

(Coduto, D. P.,1998). ............................................................................................................................. 26

Figure 3. 9 At-rest pressure acting on a retaining wall (Coduto, D. P., 1998)....................................... 27

Figure 3. 10 Development of shear failure planes in soil behind a wall as it transitions from at-rest

condition to the active condition (Coduto, D. P., 1998). ...................................................................... 28

Figure 3. 11 Changes in stress conditions in a soil as it transitions from the at-rest condition to the

active condition (Coduto, D. P., 1998). ................................................................................................. 28

Figure 3. 12 Development of shear failure planes in the soil behind a wall as it transitions from the

at-rest conditions to the passive condition (Coduto, D. P., 1998). ....................................................... 29

Figure 3. 13 Changes in the stress condition in a soil as it transitions from the at-rest condition to the

passive condition (Coduto, D. P., 1998). ............................................................................................... 29

ix

Figure 3. 14 Active and Passive pressure acting on the wall (Coduto, D. P., 1998). ............................. 30

Figure 3. 15 Failure of road embankment during the 2004 Niigata-Chuetsu earthquake (Sugita, H.,

et.al, 2007). ........................................................................................................................................... 31

Figure 3. 16 Failure of road embankment at Chiebunnai in 1994 (Sugita, H., et.al, 2007). ................. 32

Figure 3. 17 Surface displacement due to mining subsidence (Colin Jones, J. J.,1996). ....................... 32

Figure 4. 1 Potential modes of failure of reinforced embankments :( a) foundation failure with rotational of the crest; (b) foundation failure with rotational sliding through embankment; (c) excessive elongation of reinforcement (Modified from Haliburton, T. A., et.al,1978)…………………… 35 Figure 4. 2 Forces on a soil mass about to slide (Bache & MacAskill, 1984). ....................................... 36

Figure 4. 3 Use of shotcrete for slope stabilization (REED.,2003). ....................................................... 38

Figure 4. 4 Weep hole detail (Laska, W.,1992). .................................................................................... 38

Figure 4. 5 Rip rap to protect erosion at the toe of a slope (FHWA.,2005). ......................................... 39

Figure 4. 6 Rock-fill Buttresses (Léger, P.,2006).................................................................................... 39

Figure 4. 7 Wire-faced MSE Wall (Masse et. al, 2003). ......................................................................... 40

Figure 4. 8 Different wall stability criteria (Abramson, L. W.,et.al.,1995). ........................................... 41

Figure 4. 9 Vertical drainage applied for widening a highroad on soft soil (Barends, F. B.,2009). ....... 42

Figure 4. 10 Vacuum consolidation (Barends, F. B.,2009). ................................................................... 42

Figure 4. 11 Soil-cement fill slope used to stabilize a landslide (BMPS.,1998). .................................... 43

Figure 4. 12 Preloading design-compensation for primary settlement by temporary surcharge fills

(Abramson, L. W.,et.al.,1995). .............................................................................................................. 43

Figure 4. 13 Stabilization of landslide at Fenny Compton, England by injection of neat cement grout

(Pubrick, M., & Ayres, D.,1956). ............................................................................................................ 44

Figure 4. 14 Unconfined compressive strength of montimorillonite with various additions of lime

(Bell, F. G.,1996). ................................................................................................................................... 46

Figure 4. 15 Unconfined compressive strength of kaolinite with various additions of lime (Bell, F.

G.,1996). ................................................................................................................................................ 46

Figure 5. 1 The method of slices for analyzing rotational shear failures (Sjoberg, J., 1999). …………….50

Figure 5. 2 Search for critical slip surface using a grid search pattern (Mostyn and Small, 1987). ...... 52

Figure 5. 3 Three-dimensional failure geometry of a circular shear failure (Hoek and Bray, 1981;

Franklin and Dusseault, 1991). ............................................................................................................. 53

Figure 5. 4 Pseudo static slope stability analysis (Chen W.F. & Liew R., J.Y., 2002). ............................ 55

Figure 6. 1 Section used for modelling crossection A representing from Km 22+668.50 to Km 23+240.00) of the motorway (GEOTECHsp.zo.o project office, 2010). 56

Figure 6. 2 Section used for modelling crossection B representing from Km22+132 to Km 22 +668.50

of the motorway (GEOTECHsp.zo.o project office, 2010). ................................................................... 57

Figure 6. 3 A 1:1000 project plan illustrating the location of borehole series 1-9 used for exploratory

work from Km 23+400 to Km 23+500 (GEOTECHsp.zo.o project office,2006). .................................... 58

Figure 6. 4 Geological and geotechnical log of bore hole 8 (see: Appendix V)..................................... 59

Figure 6. 5 Geological and geotechnical log of borehole 9(see: Appendix V) ...................................... 60

Figure 6. 6 Model section A developed for stability analysis................................................................ 63

Figure 6. 7 Model section B developed for stability analysis. ............................................................... 63

Figure 7. 1 Ordinary method of analysis of model section-A ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface inslice division (d) FoS along the slope surface…….. 67

x

Figure 7. 2 Bishop’s method of analysis of model section-A ;(a)Global minimum surfaces (b) All

minimum surfaces(c)Global minimum surface in slice division (d) FoS along slope surface. .............. 68

Figure 7. 3 Bishop’s method of interslice forces resolution of slices for model section-A. .................. 69

Figure 7. 4 Janbu’s method of analysis of model section-A ;(a)Global minimum surfaces (b) All

minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface. ........ 70

Figure 7. 5 Spencer method of analysis of model section-A ;(a)Global minimum surfaces (b) All


Figure 7. 6 GLE/Morgenstern method of analysis of model section-A ;(a)Global minimum surfaces (b)

All minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface. ... 72

Figure 7. 7 Ordinary method of analysis of model section-B ;(a)Global minimum surfaces (b) All


Figure 7. 8 Bishop’s method of analysis of model section-B ;(a)Global minimum surfaces (b) All


Figure 7. 9Bishop’s method of interslice forces resolution of slices for model section-B. ................... 76

Figure 7. 10 Janbu method of analysis of model section-B ;(a)Global minimum surfaces (b) All


Figure 7. 11 Spencer method of analysis of model section-B ;(a)Global minimum surfaces (b) All


Figure 7. 12 GLE/Morgenstern method of analysis of model section-B ;(a)Global minimum surfaces

(b) All minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface.

.............................................................................................................................................................. 79

xi

List of Tables

Table 5. 1 Limit equilibrium slope stability methods and equilibrium equations that satisfy

(Abramson et al, 2001). ........................................................................................................................ 50

Table 5. 2 Summary of Procedures for Limit equilibrium slope stability analysis, and their usefulness

(Adapted from, Abramson et al 1995 and Duncan, J. M., & Wright, S. G.,2005). ................................ 51

Table 6. 1 Borehole selection based on the thickness of clayey and sand layers of the profiles 1-9 ... 58

Table 6. 2 Geological and engineering geological classification used for exploring the foundation (see:

Appendix II). .......................................................................................................................................... 60

Table 6. 3 Geological classification symbols used for the A-8 motorway project (see: Appendix II). .. 61

Table 6. 4 Strength parameters used for modelling sections A and B (on basis of PN-59/B-03020)

(GEOTECHsp.zo.o Project Office, 2010). ............................................................................................... 62

Table 7. 1 Factor of safety results of model sections A and B in different analysis methods. 65

Table 7. 2 Range of factor of safety and their intercept on the slope surface for both Model sections.

.............................................................................................................................................................. 66

List of Appendices

Appendix I. 1 A 1:100 structural section of the main sequence of the A-8 motorway from Km 22+132.00 to Km 24+000.00 for (GEOTECHsp.zo.o project office, 2009). ........................................... 88 Appendix II. 1 Explanation of symbols and characters used in research documents, substratum according to the standard PN-86/B-02480. .......................................................................................... 89 Appendix III. 1 Key to section of A-8 motorway Wroclaw bypass ........................................................ 90 Appendix IV. 1 1:500/1:1000 Engineering geological cross sections. ................................................... 91 Appendix V. 1 Documentation of the test wells of A-8 motorway Wroclaw bypass. ........................... 94 Appendix VI. 1Material and reinforcement strength property entry of data used for the analysis .. 103 Appendix VII. 1Full section model of an A-8 motorway embankment with material and reinforcement strength property ................................................................................................................................ 105 Appendix VIII. 1 Slide analysis information ......................................................................................... 106

1

1. Chapter I Introduction

1.1 Rationale and background Roads support our daily life, and play crucial role in supporting the infrastructure for

economic activities. However, road disaster can be caused by different natural conditions of slope failures such as rainfall, steep topography, brittle geology, etc (Wantanabe et.al,2002).A road disaster occurrences do not only cause the primary disaster from the infrastructure point of view; but also the secondary disaster, hindrance to the society and the economic activity by traffic stops.

In order to prevent or mitigate such road disasters caused by diverse reasons; measures should be taken in every phases of road engineering practices, usually mainly thorough investigation about the surface geology, the subsurface conditions of the foundation and the careful testing of the construction materials principally. Hence detailed investigation about the site is compulsory before commencing the design and construction phases. In addition, post construction phases mainly regular monitoring and maintenance must be undertaken to give the intended service of the highway.

The term 'slope' refers to any natural and engineered slopes. Examples of manmade slopes include fills such as embankments, earth dams or cuts etc. Assessment of stability of the slopes is one of the earliest problems faced by geotechnical engineers. An understanding of geology, hydrology, and soil properties are central to applying slope stability principles properly. Analysis must be based up on a model that accurately represents site subsurface conditions, ground behaviour, and applied loads. Judgments regarding acceptable risk or safety factors must be made to assess the results of analyses. These analyses are generally carried out at the beginning, and sometimes throughout the life, of projects during planning, design, construction, improvement, rehabilitation, and maintenance (Abramson et.al, 1995).

Limit equilibrium method is one of the most widely used stability analysis in practice due to its reliability for most practical cases. Its simplified approach can be used in the preliminary assessment only while more complex analysis that gives more accurate results can be carried out with computer programs (Duncan, J.M, 1996).

The paper presents the assessment of the A-8 highway motorway Wroclaw bypass, on selected sections to give a preliminary stability assessment of the road, taking in to account the strength parameters of the construction materials, reinforcing materials and the foundation condition of the road path aligned.

1.2 Problem definition Roads are one of the infrastructures that could easily be affected by natural or technical

problems causing instability. One should be able to assess cautiously in such a way that could really define the mechanisms of the instability, the hazardous areas, and possibly the remedial measures for the affected sections.

In road engineering works, failures could be instigated by natural hazards or insufficient site investigation, termed as technical problems. Road instabilities that could occur with insufficient site investigation are due to the construction of the roads in foundations with sensitive and weak subsurface conditions with lower bearing capacity.

Therefore to reduce the above mentioned problems that might occur during the construction of A-8 highway motorway Wroclaw bypass, it is essential to point out the sections which are prone to slope instabilities and to give remedial measures to those

2

sections having negative effect on the road to ensure the intended serviceability of the road.

In other words stability analysis of the embankments of the road using Limit equilibrium method will help to perform a preliminary investigation on identifying the unstable zones of the road, and hence in the minimization of the socio-economic impact due to road hazards..

1.3 General project description The investment includes the construction of the A-8 motorway Wroclaw bypass drawn

in a new path with a total length of 26.765 km, section S8 expressway with a length of 0.5 km, and two connectors: Kobierzyce in Southwest and Długołęka in Northeast with a total length of 8.15 km. The project is located on the outskirts of the city in the north-western part(Figure 1. 1).The primary investment objective is to relieve the central thoroughfares, streets and other existing road in Wrocław and directing traffic away from the transit district. This will positively improve safety on national Road No. 8-sections: Długołęka-Wrocław and Wrocław-Kobierzyce and No. 5 – section: Trzebnica-Wrocław and streamline the movement of transit traffic (GEOTECHsp.zo.o Project Office, 2010).

Figure 1. 1 Location of the A-8 motorway Wroclaw bypass (Google Earth and GEOTECHsp.zo.o Project Office, 2010).

Implementation of the project was divided into three separate tasks:

Job I (Part 1) – a section from Km1+603 to Km 13+500 + Kobierzyce connector from km 0+000 to km 2+489.

Job IIA (Part 2a) – building a bridge over the Odra river, together with access flyover on the section from Km 18+174 to Km 19+960 over the highway ring road of Wrocław A-8.

Job IIB (part 2) – section from Km 13+500.00 to Km 18+174.00 and from Km 19+960.00 to Km 28+368.75 section of S8 expressway from Km 0+000.00 to Km 0+

3

500.00 in „Pawłowice” node and „Długołęka” connector from Km 0+575.00 to Km 6+235.85 (GEOTECHsp.zo.o Project Office, 2010).

Here are some visualizations of the project at various sites and stages of construction:

Figure 1. 2 Panoramic view of the A-8 motorway Wroclaw bypass under construction near node “Widawa” (GEOTECHsp.zo.o Project Office, 2010)

Figure 1. 3 Visualization of node"Widawa"A8 highway with the national road No.5 (GEOTECHsp.zo.o Project Office, 2010).

4

Figure 1. 4 Visulaization of a bridge over Odra river the Rędziny water degree in Wroclaw (GEOTECHsp.zo.o Project Office, 2010).

1.4 Objectives of the study This study has significance in minimization /prevention of the risk of the potential hazard

that might happen in the construction of A-8 motorway Wroclaw bypass and give variable mitigation measures for those sections in susceptible condition to failures based on the degree of the instability of the road sections analyzed by using Limit equilibrium methods. The overall objective of the study includes:

To conduct slope stability analysis on the two road sections that are selected based on their height difference, applied reinforcement variability and failure susceptible foundation condition by utilizing the available secondary data.

To recommend the suitable analysis method of Limit equilibrium technique that mimics the slope condition of the road embankment.

To determine the critical failure surfaces and their intercepts along the face of the slope that could enable to recommend the requirements for stabilization purpose.

To find the lowest factor of safety and recommend the improvement mechanism to meet the required factor of safety by Polish regulations public road safety (The Decree of the Minister of Transportation and Water Management: Dz. U. Nr 43/1999).

Furthermore to propose a safe slope design for the critical sections to ensure their stability and hence keep the road in standard for the national welfare.

1.5 Approach and methodology So as to accomplish the above mentioned objectives, the following methodology was

used in a systematic manner:

Literature reviews about the structural characteristics of road embankments, basic road hazards, reinforcements of the embankments and different stability analysis methods that are commonly used.

5

Collection of existing secondary data which includes the dimensions of the road, the strength parameters of the road construction materials, foundation layers and the reinforcing materials applied.

Selection of two road sections of the road for analysis purpose; section A(representing from Km 22+668.50 to Km 23+240.00) and section B(representing from Km22+132 to Km 22 +668.50) based on dissimilarity in height, supporting conditions that both having geogrid while geomattress/rock mattress is missing in section B.

Modeling of the section A and section B based on the secondary data obtained from project office and carryout computation using computer program Slide 2D that utilize Limit equilibrium approach.

Using the results obtained from the analysis; factor of safety from both models; Model section-A and section-B for was reviewed for each analysing methods.

Selecting the appropriate analysing methods based on the assumptions of mimicking the real road embankment situation and hence recommending the factor of safety for future use.

After recommending the appropriate analysing methods’ results, respective improvements and possible slope design options were suggested inorder to meet the public road safety as per polish regulation and to ascertain the serviceability of the road.

1.6 Analytical tools and materials used For the fulfilment of the general and specific objectives of the research the following

tools and materials were used:

1:100 road profile sections of the main sequences of the A-8 motorway Wroclaw bypass representing from Km 22+132.00 to Km 24+000.00 was used to select two sections A and B used in order to develop the models for analysis work.

A project report outline of the A-8 motorway Wroclaw bypass, was used for selection of the borehole profiles for the modeling of foundation of both sections to perform analysis work.

An AutoCAD program was used to draw both sections to use as an input in the analysing program.

To compute the stability analysis of the selected sections, a computer program, Slide 2D adopting the Limit equilibrium approach was used.

1.7 Scope and limitation of the study The stability analysis of the A-8 motorway Wroclaw bypass was carried out on the two

selected sections based on the variation in height, applied reinforcements and clayey abundance of the foundation under observation. In this study, the observed limitations were the following:

Limitations on time have constrained to analyse multiple road sections to perform a wider scale of stability assessment.

Lack of reliable data from the primary source mainly related to the strength parameters of materials lead the analysis to have the uncertainty of result.

6

Lack of detailed data concerning the bearing capacity of the foundation as the selection criteria of the sensitive section for analysis works. However despite the above mentioned limitations, all efforts were made to execute the analysis by selecting some sections by using secondary data obtained from project office.

7

2. Chapter 2 Structural characteristics of road embankments

2.1 Preamble Construction of new roads, especially major highways, nearly always involves the

movement of soil and rock prior to building the road pavement. Construction of embankments is one of special features of the earthworks. Earthwork operations are classified as:

Clearing and grubbing

Excavation

Construction of embankments

Compaction

Finishing operations (Robinson, R., & Thagesen, B.,2006).

Design requirements for a highway embankment will depend on a number of factors, including the height and width of the embankment, the type of soil supporting the embankment and the location of the ground water table.

2.2 Road embankment definition Embankments are used in road construction when the vertical alignment of the road has

to be raised above the level of the existing ground to satisfy design standards, or prevent damage from surface or ground water. Many embankments are only 0.5-1.5m high, but heights of 5m or more may be used on major highways (Robinson, R., & Thagesen, B.,2006).

Figure 2. 1 Typical cross section of road embankment (DoLIDAR: Elements of Road Formation,2009).

2.2.1 Height of embankment The height an embankment is generally fixed by considerations related to the general

location of the highway in the area. In low-lying areas where the water table is at or close to the surface of the ground, the minimum height of the embankment is frequently established by the desirability of preventing the intrusion of ground water in to the sub grade and base. In such cases the elevation of the top of the sub grade is generally required to be at least 0.61m above the water table, and it may be considerably more when soils subject to capillary are used in the construction of the embankment or in the areas subject to frost. If free water is expected in the area crossed by the embankment, the minimum distance

8

above the expected water level may be further increased in interests of protecting the embankment and pavement structure (Wright, P. H., & Parquette, R. J.,1987).

2.2.2 Embankment slopes The cross section of a highway embankment consists of a flat, horizontal top section

with generally symmetrical slopes on either side that horizontal cap section with generally symmetrical slopes on either side that begin at the top and continue until they intersect the natural ground surface (Figure 2. 1). The width of the top section depends on the required pavement and shoulder dimensions and is typically a minimum of 12.19m for a two lane roadway.

Generally, flat side slopes are preferred to satisfy standards and to facilitate maintenance. Embankments constructed of high-quality materials (e.g., A-1 and A-3, AASHTO classifications) can be constructed with slopes as steep as 1.5:1 without concern for soils stability. For other soil classifications, a maximum slope of 2:1 has been recommended, and where the embankment will be subjected to flooding, a 3:1 slope is preferred.

2.2.3 Embankment foundations The design should also include an examination of the soil beneath the embankment

proper, or the embankment “foundation”. An embankment may fail because the stresses imposed on the underlying soil layer due to the weight of the fill are greater than the shearing resistance of the foundation soils. In such a case, the underlying soil layer generally would flow laterally with resulting subsidence of the fill. The embankment on which a pavement surface has been placed may also fail in its supporting function by continued settlement due to consolidation of the underlying soil layers. Either of these situations is likely to occur when a high fill is founded on cohesive or where the foundation material is a soft, compressible, fine-grained soil, such as an organic silt or clay, peat. Where any doubt exists as to the stability of the embankment foundation, the shearing stresses that will be created in the foundation should be compared with the available shearing resistance of the soils involved, the consolidation characteristics of the layer determined, and a settlement analysis made. The measurement of the shearing resistance and the consolidation characteristics must both be based on the laboratory testing of undisturbed samples taken from the foundation soil (Wright, P. H., & Parquette, R. J.,1987).

2.3 Legal documents and regulations concerned with embankment There are several requirements that must be satisfied when evaluating the stability of

roadway embankments (Millard, R.s., 1993 and TRL, 1993).

I. Loading cases a. End-of-construction loading

This loading case occurs as the embankment is constructed. The primary design issue is whether the existing foundation soil can support instability or excessive settlement. These conditions are the most critical when soft cohesive soils make up the subgrade.The end-of -construction evaluations may determine that the rate of construction needs to be controlled to prevent construction failures or that ground improvement methods must be used. This is especially important because the rate of construction is not known at the time of design.

b. Long term operational loading This loading case occurs after the embankment has been constructed after the final

grade and excess pore water pressures have dissipated. The long-term stability of

9

embankment slopes should be analyzed especially in fine grained soils. In the event the foundation soils are cohesive and not heavily over consolidated, settlement will be a design concern. Consolidation settlement and secondary compression can continue for many years and, depending on the thickness of the fine grained soils and the amount of loading can be several meters or more. Significant settlement can result in distress to the pavement at the top of the embankment, as well as bumps and dips in the pavement at the bridge approach, and at the transition to bridges.

II. Site characterization: This should be done to characterize embankment foundation materials at a site. The

depth of the borings during the exploration program will typically extend to twice the bottom width of the embankment. However, depending up on the foundation soil conditions, (Cohesive or Non-Cohesive), the required boring depths could be significantly deeper or shallower than this rough approximation. It is also important to determine the groundwater table elevation.

III. Settlement design criteria: The amount of total and differential settlement that can be tolerated during and

following embankment construction should be evaluated. Design criteria for side slope and for bearing stability also must be met. The project geotechnical specialist will determine the applicable design criteria on a project-by-project basis considering several factors when determining the allowable settlement. These factors involve both road ways maintenance and safety issues resulting from the amount and rate at which the settlement occurs.

IV. Side Slope stability and bearing capacity Evaluate side slope stability and bearing capacity of foundation of soils for both

short-term and long term loading conditions. The short-term loading condition occurs during construction, and can limit the rate of construction for fine-grained soils. For these soils, the rate of construction is such that pore pressures in fine-grained soils do not always dissipate quickly enough to support the increased loads, potentially resulting in bearing and side slope failure during placement of the embankment fill.

V. Embankment settlement The magnitude and rate of embankment settlement are important long-term

(operational) Considerations, particularly where thick deposits of cohesive soil occur. Conducting settlement analysis helps to determine the amount of settlement after construction is within the project criteria. If the settlement appears to be excessive, then measures may be required to improve the soil or to force settlement to occur during construction.

VI. Seismic performance of road embankment A design seismic event can cause significant damage to an embankment, depending

on the level of ground shaking and the type of foundation soil. The most serious damage is normally associated with liquefaction of the foundation material. Consequences of liquefaction potentially include post-earthquake settlement, side slope instabilities and bearing failures (Millard, R.s., 1993 and TRL, 1993).

10

The following information shall be considered when summarizing the results of embankment stability and settlement analyses which include the following information regarding the analyses:

Plan drawings showing the existing topography and the locations of explorations, roadways and other external loads;

Cross-section drawings that were used to set up the stability and settlement models, including primary soil or rock layering, location of ground water and test hole logs summarizing soil or rock conditions;

Strengths, consolidation parameters (Pc, Cc, and Cv), Void ratios and unit weights assigned to each soil or rock layer.

Parameters used for seismic analyses, including residual strengths and details for the liquefaction analyses.

The method of analysis used in the determination of slope stability and settlement. If computer methods are used for slope stability evaluations, identify the computer program and the method of analysis. (e.g., Spencer’ s procedure, Ordinary Method of Slices) and include copies of the input/output files (Geotechnical Report Appendices); and

Conclusions from the stability and settlement analyses, including a discussion of uncertainties in the analyses and recommendations on the method of mitigation, if appropriate (Geotechnical Report), (Millard R.S., 1993 and TRL, 1993).

2.4 Embankment construction Embankments can be considered in three separate phases: Investigation, design and

construction. All three aspects should be combined since is believed that this combination will serve to emphasize the close interrelationship for successful civil engineering work. A number of issues related to embankment construction may need to be addressed in the Geotechnical design. These issues range from giving guidance for compaction and moisture control to assessing problematic soil conditions (TRH 9, 1982).The following aspects need to be considered in construction phase of embankment:

2.4.1 Construction of earth embankments Rolled Earth embankments are constructed in relatively thin layers of loose soil. Each

layer is rolled to a satisfactory degree of density before the next layer is placed, and the fill is thus built up to the desired height by the formation of successive layers. The layers are required to be formed by spreading the soil to approximately uniform thickness over the entire width and length of the embankment section at the level concerned.

2.4.2 Reinforced earth embankments It is the construction of embankments composed of soil fill strengthened by the

inclusion of rods, fibres or nets which interact with the soil by means of frictional resistance. Reinforced earth system facilitates the support of sections of highway along steep slopes. Such systems are especially advantageous in urban areas where rights of way are limited and land is expensive. Reinforced earth fills can be constructed on relatively weak foundations since the loads are spread over a large area and can be built to great heights (Wright, P. H., & Parquette, R. J.,1987).

11

2.5 Materials used for embankments Earth materials are used for embankment fills and backfills behind retaining structures

because of the widespread availability and relative economy. Embankment fills are generally consist of

Cohesion less soils (sands and gravels): generally consist of relatively clean sands and gravels that remain pervious when compacted. Compacted cohesion less soils are not affected significantly by water content because they are relatively previous.

Cohesive soils (silts and clays): consist of those that contain sufficient quantities of silt and clay to render the soil mass relatively impermeable when properly compacted. Unlike compacted cohesion less soils, whose physical properties are generally improved by compaction to the maximum dry unit density, the physical properties of cohesive soils are not necessarily improved by compaction to a maximum dry density.

Earth-Rock mixtures: heterogeneous mixtures of cohesion less and cohesive soils, ranging from large boulders to clay .The mixing of the larger size particles enhances the workability of the soil in the field and increases the overall strength of the soil.

Organic soils, soft clays, and silts are usually avoided. The ranges of particle embankment fills is governed, for economic purposes, by the availability of materials from nearby borrow areas (Abramson, L. W., & others.,1995).

2.5.1 Basic soil properties To understand soil action, certain basic soil properties should be known. The properties

of any given soil depend not only on its general type but also on its condition at the time when it is being examined; Moisture content is defined as the weight of the water contained in a given soil mass compared with the oven-dry weight of the soil and is usually expressed as percentage. Unit weight is the weight of the soil mass per unit volume and is expressed in Kilo Newton per cubic meter. Shear resistance are failures that occur in soil masses as a result of the action of highway loads principally. Therefore, the factors that go to make up the shearing resistance of a soil are of importance. Shearing resistance with in the soil masses is commonly attributed to the existence of internal friction and cohesion (Wright, P.

H., & Parquette, R. J.,1987).

2.5.2 Aggregates The term aggregates refers to granular mineral particles that are widely used for

highway bases, sub bases, and backfill. Aggregates are also used in combination with a cementing material to form concretes for bases, sub bases, wearing surfaces, and drainage structures. Sources of aggregates include natural deposits of sand and gravel, pulverized concrete and asphalt pavements, crushed stone, and basalt-furnace slag.

2.5.2.1 Properties of aggregates The most important properties of aggregates used for highway construction are;

Particle size and gradation

Hardness or resistance to wear

Durability or resistance to weathering

Specific gravity and absorption

Chemical stability

12

Particle shape and surface texture

Freedom from deleterious particles or substances (Wright, P. H., & Parquette, R.

J.,1987).

2.5.3 Bituminous materials Bitumen are sticky, adhesive substances that are dark brown to black in color, frequently

associated with sharp, characteristic odour, and that are usually liquid at the time of their application to mineral aggregates or similar in road construction. Bituminous materials are of used in highway works because of their binding or cementing power and their waterproofing properties. They are divided in to the following types for the simplification (1) Tars, (2) Asphalt: (a) Petroleum; (b) Native (Wright, P. H., & Parquette, R. J.

(1987). In addition to the above listed materials, various materials were used as embankment fill

based on their availability and environmentally sustainability of materials:

I. Bauxite residue or so called Red mud is soil remainder of the bauxite industrial treatment that is used successfully for road embankment construction in Greece. Due to increasing amounts of bauxite residue material and decreasing landfill space, combined with concerns about environmental impact of dumping red mud to the sea, the perspective reuse and recycling of this material has gained utmost importance. It seems that the material exhibits excellent performance in earthwork construction and constitutes an effective solution in projects where borrow-pits are rare and other local materials prove inapplicable. It is absolutely certain that the by-product presents a time-hardening behaviour as a result of binding internal stresses developing after laying (Kehagia, F.,2009).

Figure 2. 2 The bauxite-Residue embankment (Kehagia, F.,2009).

II. Used-tire chips mixed with clayey soils as fill material is possible to use with mixtures of 20% coarse grained tire-chips and 30% fine grained tire-chips can be used above ground water tables where weight, low permeability and high strength are needed in fills such as highway embankments. They should not be used where drainage is needed to prevent the development of pore pressures during loading of fills under saturated conditions. Every year, millions of scrap

13

tires are either discarded in huge piles across the landscape or dumped in landfills in large volumes (Cetin, H., et.al, 2006).

III. Fly ash that generated by coal based thermal power plants, can be used as resource savings of resources namely soil, stone aggregate, stone chips, sand and cement in embankment due to fly ash utilization in road construction in India (Kumar, S., & Patil, C.,2006).

Figure 2. 3 Cross-section of fly ash based road formation with flexible pavement showing flyash and soil layers on side slope and below pavement (Kumar, S., & Patil, C.,2006).

IV. Sedimentary late rite soil constitute as a good engineering construction based on geotechnical properties as well as its consolidation and permeability behaviours of compacted state , this material as it has already been successfully used as base and sub base material in road construction. It is also found that this late rite soil is also suitable for the use as fill materials in embankment and dam construction (Ogunsanwo, O.,1989).

V. Mine stone utilization is reclamation of soil heaps by adapting them to landscaping. Earth structures offer the best possibilities of this utilization to minimize disposal cost and harmful environmental effects. This has been conducted in various countries in Europe like Poland, have led to the use of many tonnes of wastes in the construction of road and, river embankments and land reclamations (Skarkynska, K. M.,1995).

VI. The use of expanded polystyrene blocks for lightweight fill has become standard practice in road construction in Norway and Sweden. Embankments over ground with low bearing capabilities expanded polystyrene blocks offer an extremely lightweight solution which greatly reduces the likelihood of the settlement usually associated with heavier fills.

14

Figure 2. 4 Embankment constructed with expanded polystrene blocks (Thompsett, D. J., et.al, 1995).

2.6 Soil compaction Compaction increases the density of material by expelling air from the voids in the

material and, thereby, bringing the particles in to more intimate contact each other. It is the cheapest and simplest method for improving the shearing resistance of soil and minimizing future settlements, but not necessarily settlement due to consolidation or shearing failure of the embankment foundation (Wright, P. H., & Parquette, R. J.,1987) .Therefore, soils in embankments and sub grades in cuttings are usually compacted using special compacting equipment, such as rollers, vibrators or tampers. The result of compaction work depends primarily on the moisture content of the soil, the type of the soil, the compaction equipment used and the energy applied.

For most soil types, the maximum dry density is achieved at particular moisture content, the so called optimum moisture content. Because of the moisture-density relation, water must be added to dry soils, and overlay wet soils must be aerated before compaction. However in dry areas, where difficult to provide the large amount of water needed to bring the moisture content of a dry soil to the optimum level, it may be better to compact the soil in the dry state rather than adding an insufficient amount of water to the soil. In rainy season, it may be necessary to replace an overlay wet soil with more suitable material, to stabilize the wet soil with lime.

The greater the permeability, the easier it is to expel air from the soil. This partly explains why gravel and sand can usually be compacted to greater density than clay. In well-graded soils, the smaller particles may fill some voids between the larger particles. Thus, well graded soils can achieve a greater density than uniformly graded soils (Robinson, R., &

Thagesen, B.,2006).

2.7 Bridge-embankment joints The major design concepts, conventional bridges and integral abutment bridges, are

currently used for road bridges. The conventional design type has a superstructure resting on an abutment at each end as shown in( Figure 2. 5 ).The basic concept of this design is to make the superstructure unconstrained. Expansion joints and bearings at each end of the superstructure are used to accommodate the seasonal relative movement between superstructure and abutment and to prevent temperature-induced stress from developing

15

within the superstructure. Conventional bridges have shown good performance for a long time, but they lead to a high maintenance cost because of corrosion and other physical deterioration of the bridge bearings and joints (Seo, J. B.,2003).

Figure 2. 5 Traditional design concept (Seo, J. B.,2003).

Because of these flaws, a new design concept consists of physically and structurally connecting the superstructure and abutments as shown in ( Figure 2. 6).This type of bridge usually has an approach slab to provide a smooth transition between the integral abutment bridge and adjacent approach embankments. In doing so, some problems associated with the conventional bridge concept can be minimized but other problems such as the bump at the end of the bridge can be worsened.

Bridge abutments support the structural loads and the abutment wall, together with the wing walls, retains the approach embankment. Several types of abutments commonly are used and the sequence of construction. Conventional bridge abutments provide supports for the superstructure through bearings with an expansion joint and allow relative movement between the abutment and the deck. The expansion joint accommodates thermal strain in the deck and potential lateral movements of the abutment. An integral abutment (Figure 2. 6 ) is connected to the bridge as a single structure with no expansion joint between them. For integral abutments which do not have an expansion joint, thermal movement of an integral abutment can cause compression of the adjacent fill, creating a void. Integral bridges with approach slabs tied to the bridge are deteriorated at both ends of the approach slab (Seo, J. B.,2003).

16

Figure 2. 6 Integral abutment bridge design (Seo, J. B.,2003).

2.8 Special cases of embankment structures Embankments must have suitable scarp slope to assure road solid stability and to

infrastructure durability and the inclination established for scarps must be verified through geotechnics methods. Optimum inclination of embankment scraps along with soil mechanical properties, ground conditions and embankment height is crucial:

to guarantee road solid stability and so infrastructure durability;

to limit the volumes of filling material;

to limit the ground surface taken up by the infrastructure

to limit construction and expropriation costs (F.Maltinti, 2007).

2.8.1 Inclined embankments The stability of inclined base highway embankments is often questionable, particularly in

cases where they are founded on steep natural slopes and/or on low-friction materials. A translational failure can occur either in the form of overall instability or in the form of local instability.

The infiltration of water inside the bodies of the embankments is the most important precursor for instability. The construction of embankments on inclined bases obstructs the natural water flow. If no drainage measures have been undertaken to prevent water infiltration, the water will flow either through the fill body or it will flow surficially; where part of it may ingress through the unpaved shoulders and/or fill slopes. The stability of an embankment, founded on an inclined base, may also be affected the presence of underground water. However, embankments constructed by non-cohesive materials are more prone to fail locally in the region of slope toe than as whole body (Pantelidis, L.,2008).

17

Figure 2. 7 Schematic representation of failure of National road from Grevena to Loannina (Pantelidis, L.,2008)

Landslides are hastened by road construction because the infrastructure weight modifies mechanical equilibrium of the ground mass. Often, the cause of the accident is the inadequate evaluation of embankment scarps slope related to soil mechanical characteristics, and ground inclination.

As a matter of fact, it is well known that embankment must have suitable scarps slope to assure road solid stability and so infrastructure durability. The inclination established for scarps must be verified through geotechnics methods like finite element method (FEM),to find out the correlation between scarps slope and ground inclination. Hence inclination of scarps with mechanical properties of soil with which the embankment is made of can be correlated as well (F.Maltinti, 2007).

Figure 2. 8The model in one of cases considered (F.Maltinti, 2007).

2.9 Embankments on mud or peats Embankments are sometimes built on weak foundations. Sinking, spreading, and piping

failures may occur irrespective of the stability of the new overlying embankment material. Consideration of the internal stability of an embankment-foundation system, rather than just the embankment, may be necessary. A simple rule of thumb based on bearing capacity theory can be used to make a preliminary estimate of the factor of safety against circular arc failure for an embankment built over a clay foundation.

18

Figure 2. 9 Stability conditions for an embankment slope over a clay foundation (Abramson, L. W., et.al., 1995).

fillfill H

cFoS

6 (2.1)

Where FoS=factor of safety, c=cohesion of foundation clay, fill =unit weight of the

embankment fill, fillH =height of embankment fill.

The factor of safety computed using this rule serves only as rough preliminary estimate of the stability of an embankment over a clay foundation and should not be used for final design.

Figure 2. 9 shows the variations in safety factor, strength, pore pressures, load, and shear stresses with time for an embankment constructed over clay deposit. Over time, the excess pore pressure in the clay foundation diminishes the shear strength of the clay increases, and the factor of safety for slope failure increases (Abramson, L. W., et.al., 1995).

The cost to construction related to swelling clay soils is greater than the damage caused by floods, landslides and earthquakes together. They have been called “a hidden disaster”. The challenges faced by engineers on road construction over peats and organics soils include limited accessibility, expectations of very large settlements over an extended time period, and possibility of stability problems. The high compressibility, low shear strength and high ground water level causes specific problems for designing and constructing structures on such types of soil. The construction of embankments on peat and organic soil

19

deposits tends to result in sliding failure or sudden settlement of substrata. There are also some problems with up thrusting, side flows, and subsidence due to the falls of ground water levels, vibration damage from construction machinery and traffic, and damage due to earth quakes (Barends, F. B.,2009).

2.9.1 Decomposition of sub Soil and road embankments Sub-soil and road embankments road that are composed of peaty fill material are

vulnerable to decomposition. The infiltration of aerated and nutrient-rich water into the soil body may lead to a gradual decomposition of the peat. The decomposition rate of peat materials can be high. In the Netherlands, more than half of the surface subsidence of low more peat land of western Netherlands was accounted by decomposition (Schothorst, C.,1982).The use of peaty materials is therefore not recommended, not only because of the decomposition factors but also due to the possible fire hazard and vulnerability of the materials to erosion.

2.9.2 Fluctuation of surface and groundwater The ground and water level fluctuate both in natural and developed condition of peat

land. Various hydrological processes such as precipitation, evapo transpiration and discharge are causes of fluctuations. Rain and inflow from surrounding areas raises the groundwater level while evapo transpiration and discharge lower it. Hydro geological management is one of the most important keys when dealing with fluctuation of water level in peat land. Lowering the water table will generate settlement due to inelastic compression of the peat layer and will increase the decomposition of the exposed peat (Schothorst, C.,1982).

2.10 Widening and re-construction of the existing embankments Widening of existing highways helps to facilitate construction of longer, safer

acceleration and deceleration lanes, and to increase the traffic capacity and efficiency of existing thoroughfares. Highways on embankments require special consideration since the embankments are typically widened to increase the roadway width. A number of technically sound solutions can be implemented to widen existing highways on embankments including:

Widening of the embankment while maintaining side slope geometry

Construction of retaining structures at the embankment toe and widening the crest

Steepening of existing side slopes while maintaining the toe; and

Reinforcement and steepening of existing while maintaining the toe (Deschamps, R., et.al., 1999).

Embankment widening on peat and organic soil causes distress to the existing road. In case where the distress was more severe, scarps may be visible .Problems may arise due to the disturbance of the new structures and the differential settlement between the two structures with resulting cracks and faults around the boundary between the old and the new embankment, (Figure 2. 10).

During road widening, the likely non-uniform settlements and associated shear force could cause longitudinal pavement cracking along the joint between the original and new pavements. The possible causes of non-uniform settlements and pavement cracking include:

20

Different soil compressibility of the pavement and consolidation rates between the original and new embankments

Uneven stress distribution in the original road caused by widening; and

Different structural capacities between the original and new pavements.

Several investigators studied the deformation behaviour of the embankment during road widening through numerical analysis, experimental and field investigations. The proposed three possible failure mechanisms in road widening include:

Shear cracking caused by embankment slippage

Bottom-up cracking caused by vehicle load; and

Top-down cracking caused by non uniform deformation (Xiao-ming, H., & Hao, W.,2009).

Figure 2. 10 Widening of embankment (Witteveen, G., & Bos.,2001).

21

3. Chapter 3 Basic hazards of road embankments Failures of embankments are often caused by processes that increase shear stresses or

decrease shears strengths of the soil mass. Some of the processes that mostly commonly cause an increase in the shear stresses acting on slopes are listed below (Abramson, L. W., et.al.,1995).

3.1 Settlement Placing engineering structures impose loads on to the ground, which produce

corresponding increases in the vertical effective stress, σz’.These increases are important

because they induce vertical strains, Єz, in the soil, and thus cause the ground surface to

move downward, termed as settlement. Settlement occurring in large area, termed as Subsidence (Coduto, D. P.,1998).The three physical processes that produce settlement in soils;

Consolidation settlement also termed as primary consolidation settlement, δc, occurs

when a soil is subjected to an increase in σz’.This process causes a decrease in the

volume of voids Vv. If the soil is saturated (S=100%), this reduction in Vv can occur if

some of the pore water is squeezed out of the soil. All soils experience some

consolidation when they are subjected to an increase in σz’, and this is the most

important source of settlement.

Secondary compression settlement δs, is due to particle reorientation, creep, and decomposition of organic materials, and does not require the expulsion of porewater.Secondary compression can be significant in highly plastic clays and organic soils, but is negligible in sands and gravels. Unlike consolidation settlement,

secondary compression settlement is not due to changes in σz’. Distortion settlement, δd, results from lateral movements of the soil in response to

changes in σz’.These movements occur when the load is confined to small area, such

as a structural foundation, or near the edges of large loaded areas, such as embankments.

The settlement at the ground surface, δ, is the sum of these three components (Coduto, D. P.,1998):

δ=δc+ δs +δd (3.1)

Figure 3. 1 Disortion settlement beneath a small loaded area (Coduto, D. P.,1998).

22

High embankments impose a heavy load on the underlying foundation soil. On some soils, this may result in settlements. If the foundation soil is extremely weak, a slip failure may occur. Settlement becomes more serious when differential, commonly due to uneven loading, lateral change of silt content in soil, rock head slope or uncontrolled drainage. Tilting of structures creates differential loading, and then creates differential settlement. Transported soils like windblown sands and alluvial clays including marsh soils, are prone to settlement (Su et.al, 1971).

It is accepted that settlements of structures resting on compressible saturated clays can be separated in to the following three components:

An immediate settlement due to elastic deformations taking place at constant volume.

A settlement due to primary consolidation where in volume change in effective stresses as a result of the dissipation of excess pore water pressure.

A settlement due to the so-called secondary compression where volume change continues after excess pore water pressures are essentially dissipated.

Basically, these settlements occur in the order listed although some secondary compression does take place during primary consolidation. For majority of the soil deposits, the amount of settlement due to secondary compression may be negligible compared to that resulting from primary compression, but for some highly compressible soils and organic deposits it may be a large portion of the total settlement. The effects of these two compression components must be considered separately if they are to be included in the overall settlement analysis. For road embankments, foundation soils are analyzed only for primary compression. After an attempt of resolving unclear aspects of embankment settlement analysis, secondary compression was selected as a central topic for study based largely on the following considerations:

I. Secondary compression is neglected in most road embankments foundation investigations although it is one of the components contributing to total compression.

II. Secondary compression occurs both during and after completion of primary compression. Therefore, the effects of secondary compression on time-settlement relationship obtained from a theory that was originally developed only for primary compression may be appreciable.

III. Discrepancies between predicted and measured settlements cover the entire range of the time-settlement diagram (that is, both short and long term).It is in this same range that secondary compression occurs (Su et.al,1971).

3.1.1 Case example of settlement Highway bridge underlain by a soft clay deposit; this soil is not able to support

the weight of the bridge, so pile foundations were installed through the clay in to harder soils below and the bridge was built on the piles. These foundations protect it from large settlements. It was also necessary to place fill adjacent to the bridge abutments so the roadway could reach the bridge deck. These fills are very heavy, so their weight increased σz’ in the clay, causing to settle. When the photograph was taken,

23

about twelve years after the bridge was built, the fill had settled about 1m, as shown in side walk in the fore ground.

Figure 3. 2 The approach fills adjacent to this bridge in California have settled. However, the bridge, being supported on pile foundations, has not.

Note the abrupt change in grade in sidewalk, and the asphalt patch between the two signs (Coduto, D. P.,1998).

Road construction over voids was caused by active gypsum dissolution, North Yorkshire, England. A sudden subsidence problem, caused by gypsum karst developed in the Permian sequence of Northern England, has caused difficult conditions for road construction. Road construction over such gypsiferous deposits with karst problems including progressive dissolution, sink hole formation and poor ground conditions caused by collapsed strata or the residue of weak and brecciated strata. Building roads over former gypsum mine workings also presents similar conditions. Where gypsum is present in the bedrock, either as massive beds or as veins, it can be associated with sulphur-rich groundwater that may damage concrete, and precautions should be considered.

Figure 3. 3 Road construction subsidence North Yorkshire, England (Cooper, A. H., & Jones, J. C.,2005).

3.2 Mass movements Roads passing through steep slopes are exposed to risks imposed by natural hazards,

such as landslides, rock falls and avalanches. Regarding rock falls, occurrence position on the slope and movement, its kinetic energy and possible impact forces are required to plan measures. In most cases, rock falls occurs accidentally. At present, to predict the occurrence of rock fall event is generally quite difficult, because useful and sufficient data is mostly not

24

available. However, information related to the location and frequency of already occurred rock falls in the field can be obtained (Masuya H., et.al, 2009).

3.2.1 Case examples of mass movements I. The south West area of Cyprus slope stability problems which was mechanism

for road embankment failures; the location and extent of these landslides has been influenced by ground morphology, geological structure and the presence of weak rocks and cohesive soils. The main triggering mechanisms have been precipitation and/or seismic events (Hadjigeorgiou J., et.al, 2003).

Figure 3. 4 Indications of the instability in 2003(Hadjigeorgiou J., et.al, 2003).

Figure 3. 5 Cracks along Pentalia in 2005 (Hadjigeorgiou J., et.al, 2003).

II. The Suzu-Maura area on Noto Peninsula in Japan is not only known as a scenic spot, but also as dangerous zone, in which Rockall occurs frequently (Masuya H., et.al 2009).

25

Figure 3. 6 Rockfall and embankment against rockfall, Noto Peninsula (Masuya H.,et.al, 2009).

III. Embankment failure-debris flow tentatively names “Cascades” development in Haywood country, North Carolina, on September 8, 2006.Heavy rain associated with the remnants of tropical storm triggered the debris flow. Likely contributing factors in the embankment failure include: woody debris flow and graphitic-sulfidic bedrock fragments in the embankment (is a well documented rock type prone to acid runoff and instability); a steep embankment slope placed on a steep natural slope overlying a steeply inclined, weathered bedrock surface; and, a possible seepage zone beneath the embankment (Wooten, R., & Latham, R.,2006).

Figure 3. 7 View of cracks on embankment debris flow (Wooten, R., & Latham, R.,2006).

3.3 Abutments damages due to large earth pressure Lateral earth pressures are those imparted by soils on to vertical or non-vertical

structures. They may induce both normal and shear pressures, as shown in (Figure 3. 8). The lateral earth pressure is a function of the materials and surcharges, the groundwater and foundation conditions, and the mode and magnitude of the movement that results from the soil-structure-foundation interaction.

26

Figure 3. 8 Lateral earth pressures imparted from a soil on to a vertical or near vertical structure (Coduto, D. P.,1998).

Lateral earth pressures are the direct result of horizontal stresses in the soil. Stress at any point in a soil as the coefficient of lateral earth pressure, K:

'

'

z

xK

(3.2)

Where; K=Coefficient of lateral earth pressure; 'x =horizontal effective pressure;

σz’=vertical effective pressure

K is important because it is an indicator of the lateral earth pressures acting on an abutment. For purpose of describing lateral earth pressures; geotechnical engineers have defined three important soil conditions: the at-rest condition, the active condition, and the passive condition (Coduto, D. P.,1998). The terms ‘active’ and ‘passive’ are commonly used to describe the limiting conditions of earth pressure. Active earth pressure is the lateral pressure exerted by the soil on the back of abutment when it moves sufficiently outwards for the pressure to reach a minimum value. Passive earth pressure is the lateral pressure exerted on abutment when it moves sufficiently towards the soil for the pressure to reach a maximum value. The movements required to reach the active state are very small. Large movements are required to reach the passive state (GCO; Review of Design Methods for Excavations, 1990).

3.3.1 The At-rest condition Is the condition where walls are built so that no lateral stresses in the ground are same

as they were in its natural undisturbed state, as rigid wall that does not experience any flexural movements are assumed.

The value of K in this situation is Ko, is the coefficient of lateral earth pressure at rest.

The most reliable method of assessing Ko is to use in-situ tests such as the dilatometer test

or pressure meter. Several correlations have been developed; including the following one from (Mayne, P. W.,et.al.,1982):

'sin)'sin1( OCRKo (3.3)

27

Where:’=effective friction angle of soil; OCR=over consolidation ratio of soil Ko usually falls in the range between 0.3 and 1.4.If no groundwater (u=0), the lateral earth pressure, σ, acting on this wall is equal to the horizontal effective stress in the soil:

ozx k'' (3.4)

In the at-rest case, τ, acting between the soil and the wall is zero. In a homogeneous

soil above the groundwater table, ko is a constant and σz’ varies linearly with depth.

Therefore, in theory, σ also varies linearly with depth, forming a triangular pressure distribution, shown (Figure 3. 9).Thus if at-rest conditions are present, the horizontal force acting on a unit length of a vertical wall is the area of this triangle: (Coduto, D. P., 1998).

2

2

oo KH

b

P (3.5)

Where: b

po = normal force acting between soil and wall per unit length of wall; b=unit

length of wall (usually 1m); =unit weight of soil; H=height of wall

Figure 3. 9 At-rest pressure acting on a retaining wall (Coduto, D. P., 1998).

3.3.2 The Active condition Permitting the wall to move outward a short distance, either in translational or

rotational about the bottom of the wall, relieves some of the horizontal stress, causing the Mohr circle to expand to the left. Continuing this process until the circle reaches the failure envelope and the soil fails in shear (circle B).This shear failure will occur along the planes

shown in (Figure 3. 10) which are inclined at an angle of 45+2

degrees from the

horizontal. A soil that has completed this process is said to be in active condition. The value

of k in a cohesion less soil in the active condition is known as Ka, the coefficient of active

earth pressure. Once the soil attains the active condition, the horizontal stress in the soil (and the pressure acting on the wall) will have reached its lower bound.

28

Figure 3. 10 Development of shear failure planes in soil behind a wall as it transitions from at-rest condition

to the active condition (Coduto, D. P., 1998).

The Mohr’s circles A in (Figure 3. 11) represents the state of stress at a point in the soil the soil behind the wall in (Figure 3. 10), and suppose this soil is in the at-rest condition. The inclined lines represent the Mohr-Coulomb failure envelope. Because the Mohr’s circle does not touch the failure envelope, the shear stress, τ, is less than the shear strength,S (Donald P., 1998).

Figure 3. 11 Changes in stress conditions in a soil as it transitions from the at-rest condition to the active

condition (Coduto, D. P., 1998).

3.3.3 The Passive condition The passive condition is the opposite of the active condition. In this case the, the wall

moves in to the backfill, as shown in (Figure 3. 12), and the Mohr’s circle changes, as shown in (Figure 3. 13).Notice that the vertical stress remains constant where as the horizontal stress changes in response to the induced horizontal strains.

29

Figure 3. 12 Development of shear failure planes in the soil behind a wall as it transitions from the at-rest

conditions to the passive condition (Coduto, D. P., 1998).

Figure 3. 13 Changes in the stress condition in a soil as it transitions from the at-rest condition to the passive

condition (Coduto, D. P., 1998).

In a homogenous soil, the shear failure planes in the passive case are inclined at an

angle of 45-2

degrees from the horizontal. The value of k in a cohesion less soil in the

passive condition is known as kp, the coefficient of passive earth pressure. This is the upper

bound of k and produces the upper bound of pressure that act on the wall. Engineers often use the passive pressure that develops along the toe of the wall

footing to resist sliding, as shown in (Figure 3. 14). In this case the wall is the side of the footing. More movement must occur to attain the passive condition than for the active condition (Donald P., 1998).

30

Figure 3. 14 Active and Passive pressure acting on the wall (Coduto, D. P., 1998).

The mode of movement has a considerable influence on both the magnitude and distribution of the lateral earth pressure. Compaction of backfill can cause relatively large earth pressure near the top of an abutment. Depending on the size of the compaction plant used, the locked -in earth pressures can be very high (GCO: Review of Design Methods for Excavations, 1990).

3.3.4 Earth pressure due to compaction Compaction of fills in to minimum dry density is routinely specified to ensure that it has

adequate shear strength and stiffness. While compaction is important, the use of heavy compaction plant near a retaining wall can sometimes cause distress. This is because compaction induces large horizontal earth pressures which are subsequently locked in to the soil mass.

Compaction induced earth pressure can sometimes be significant part of the total pressure against structures. For reasons of economy, it is often worth limiting the loading due to compaction plant within a certain distance behind the wall (GCO: Review of Design Methods for Excavations, 1990).

3.4 Parameters of road hazard A hazard on road embankments occurs due to various factors among which some are

mentioned below:

3.4.1 Water In earth work engineering, the influence of water and dry density of compacted soils

deformation is a fundamental issue, which is important for the use of clays in embankments. It has been shown that such materials can be a source of short-term and long-term disorders in road structures, thus generating non negligible maintenance costs. The swelling behaviour of these materials in embankments slopes is one of the phenomena related to these disorders.

One of the characteristics of road embankments is the significant heterogeneity in terms of dry density, water content and soils nature. Thus it is important to assess the influence of these parameters of the deformation of embankments (Ferber, V., et.al, 2008).

31

3.4.2 Dynamic action In seismically active regions, earthquakes are a major trigger for instability of natural and

man-made slopes. Hence seismic effects are essential design considerations for slope stability and other engineering structures. Currently, the conventional pseudo-static (PS) approach is still widely accepted as a means for evaluating slope stability. In the PS method,

the earthquake effects are simplified as horizontal and/or vertical seismic coefficients (kh

and kv). The magnitude of the coefficients is expressed in terms of a percentage of gravity

acceleration. Due to the simplicity of the PS approach, it has drawn the attention of a number of investigators .It should be noted that by using complicated dynamic response analysis coupled with appropriate constitutive laws, a more precise seismic evaluation for slopes could be obtained. However, the PS method is still recommended as a screening procedure to identify the requirement for more sophisticated dynamic analyses. The pseudo-static approach has certain limitations, but this methodology is considered to be generally conservative, and is the one most often used in current practice (Li, A., et.al, 2008).

3.4.2.1 Case example of failure of a road embankment during the 2004 Niigata earthquake

Chuetsu earthquake, Japan which was situated up on a small valley, the failed earth is overtopped by stream water. This failure was probably caused by a combination of two reasons, which are elevated water table in the fill as well as the weak stream deposit that was not fully removed during construction. Thus, an embankment constructed up on a stream needs special care such as drainage and reinforcement at the toe of a slope (Sugita, H., et.al, 2007).

Figure 3. 15 Failure of road embankment during the 2004 Niigata-Chuetsu earthquake (Sugita, H., et.al, 2007).

3.4.2.2 Case example of slumping of embankments due to earthquakes Slumping is another important kind of failure of an embankment. The (Figure 3. 16) demonstrates an example failure of a road embankment at Chiebunnai bridge during 1994 Hokkaido-Toho-Oki earthquake. This fill was constructed a deposit of a small stream. Thus, an embankment resting up on soft soil deposit is vulnerable to earthquake induced failure.

32

Figure 3. 16 Failure of road embankment at Chiebunnai in 1994 (Sugita, H., et.al, 2007).

3.4.3 Mining related deformations In mining areas, geotechnical parameters of constructions are of a crucial importance.

Underground mining adversely affects the ground surface and the structures built on it. Formation displacements; continuous and discontinuous, changes in the water regime, leading to further deformations, and underground shocks causing subsoil tremors occur in mining areas (Elżbieta,S.S., & Waldemar, T.,2004).

The movements, known collectively as subsidence, are three-dimensional in nature, any affected point having components of displacement along all three axes of a general Cartesian coordinate system. The displacements are imposed on any structure in the affected zone and may result in damage or even collapse unless adequate safeguards have been in the design of the structure. The design of the ground subjected to mining subsidence is illustrated in (Figure 3. 17) (Colin Jones, J. J.,1996).

Figure 3. 17 Surface displacement due to mining subsidence (Colin Jones, J. J.,1996).

Therefore the foundations of engineering structures erected there must be specially designed to withstand such adverse effects. Mining damages embankments in such a way that large horizontal and vertical deformations and loosening occur (Elżbieta,S.S., & Waldemar, T.,2004).

3.4.4 Erosion Road construction can lead to changes in three types of water resources: surface water

flows, ground water flows and water quality degradation. The effect of water flows is

33

evidenced through flooding, soil erosion and channel modification. By modifying the natural flow of surface water, stream channels are disrupted by artificial changes in channel depth, width or shape. Such channels are associated with stream relocation, channelization, confinement in culvert, or disruption by bridges or abutments. Straightened channelized streams usually permit faster passage of water than in undisturbed streams. This may lead to erosion or downstream flooding. Alternatively, water backed up at the constriction may cause bank over flow and upstream flooding (Robinson, R., & Thagesen, B.,2006).

34

4. Chapter 4 Strengthening and reinforcement of road embankments

4.1 Preamble Reinforcement can be used to improve the stability of slopes and embankments, making

it possible to construct slopes and embankments steeper and higher than would otherwise be possible. Reinforcement at the bottom of an embankment on a weak foundation can increase the factor of safety for slip surfaces passing through the embankment, making it possible to construct the embankment higher than would be possible without reinforcement.

Reinforcement near the base of an embankment can be used to improve stability with regard to shear failure through the embankment and foundation. With reinforcement at the bottom of the embankment, the slopes can be made steep as for an embankment constructed on firm foundation. The volume of the embankment and the total load it imposes on the foundation can be reduced and its height can be increased (Duncan, J. M., & Wright, S. G.,2005).

Modes of failure: Three modes of Potential modes of failure of reinforced embankments on weak foundations have been discussed by (Bonaparte, R., & Christopher, B. R.,1987).Three possible modes of failure are shown in Figure 4. 1below:

(a)

(b)

(c)

35

Figure 4. 1 Potential modes of failure of reinforced embankments :( a) foundation failure with rotational of the crest; (b) foundation failure with rotational sliding through embankment; (c) excessive elongation of reinforcement (Modified

from Haliburton, T. A., et.al,1978).

(Figure 4. 1a) shows the embankment sliding across the top of the reinforcing. This mode of failure is most likely if the interface friction angle between the embankment and the reinforcement is low, as it may be with geotextile reinforcement. A wedge analysis can be used to assess the safety of the embankment with regard to this mode of failure.

(Figure 4. 1b) shows a shear surface cutting across the reinforcement and into the weak foundation. This mode of failure can occur only if the reinforcement ruptures or pulls out. Safety with regard to this mode of failure can be evaluated using circular, wedge, or non circular slip surfaces, including reinforcement forces.

(Figure 4. 1c) shows large settlement of the embankment resulting from excessive elongation of the reinforcement. This mode of failure can occur if the strain in the reinforcement required to mobilize the reinforcement load is too large.

I. Types of reinforcement The principal types of reinforcing materials that have been used for slopes and

embankments are geotextile fabrics, geogrids, steel strips, steel grids, and high strength steel tendons.Geogrids are manufactured by stretching sheets of polymer plastic in one or both directions to form a high-strength grid. Stretching the polymeric materials makes them stiffer and stronger.

II. Reinforcement forces The long-term capacity of reinforcement, denoted here as Tlim, depends on some of

following factors:

Tensile strength: For steel, the tensile strength is the yield strength. For geosynthesis, the tensile strength is measured using short-term wide-width tensile test. Durability: The mechanical properties of geosynthetics are subject to deterioration during service as a result of attack by chemical and biological agents. Steel is subject to corrosion. Pullout resistance: Near the ends of the reinforcement, capacity is limited by the resistance to pullout, or slip between the reinforcement and the soil which is embedded.

Reinforcement stiffness and tolerable strain within slope: To be useful for slope reinforcement, the reinforcing material must have stiffness as well as strength. A very strong but easily extensible rubber band would not provide effective reinforcement, because it would have to stretch so much to mobilize its tensile capacity that it would not be able to limit the deformation of the slope (Duncan, J. M., & Wright, S. G.,2005).

Slope stabilization methods generally reduce driving forces, increase, or both. Driving forces can be reduced by excavation of material from the appropriate part of the unstable ground and drainage of water to reduce the hydrostatic pressures acting on the unstable zone. Resisting forces can be increased by

I. Drainage that increases the shear strength of the ground II. Elimination of weak strata or other potential failure zones III. Building of retaining structures or other supports IV. Provision of in situ reinforcement of the ground

36

V. Chemical treatment (hardening of soils) to increase shear strength of the ground.

As an alternative to slope stabilization, the unstable slope can be avoided by adjusting the location of construction or selecting a different site all together. Before the best method can be selected, the actual and potential causes of slope instability must be determined. There are multiple contributing factors that cause or could slope instability. Failure to identify contributing causes of failure could render the stabilization work ineffective and slope instability recurrent. There are various methods of slope stabilization (Abramson, L. W., et.al.,1995).

4.2 Seeding and slope hardening of pavement Vegetation (grass, shrubs, and trees) is highly effective and advantageous for soil

stabilization purposes. Removal of earth to construct embankments inevitably removes the vegetation covering and the surface soils are left exposed and susceptible to runoff and wind attack. Vegetation stabilizes the soil surface by the intertwining of its roots, minimizes seepage of runoff in to the soil by intercepting rainfall, and retards runoff velocity. In addition, vegetation may have an indirect influence on deep-seated stability by depleting soil moisture, attenuating depth of frost penetration, and providing a favourable habitat for the establishment of deeper-rooted vegetation (shrubs and trees).

Vegetation is multifunctional, relatively inexpensive, self-repairing, visually attractive and does not require heavy or elaborate equipment for its installation. However, there are certain limitations. Vegetation is susceptible to blight and drought. It is unable to resist severe scour or wave action, and is slow to become established.

4.2.1 General design considerations Vegetation can affect the balance of stresses in a slope due to mechanical reinforcement

from the root system of trees, slope surcharge from the weight of trees, modification of soil moisture, reduction of pore pressures by interception and transpiration from the foliage, attenuation of frost depth penetration, and lateral restraint by buttressing and soil-arching action from trunks or stems.

Figure 4. 2 Forces on a soil mass about to slide (Bache & MacAskill, 1984).

37

Figure 4. 2 shows how root strength can be incorporated in to stability analyses. The down slope component of soil weight can be expressed as

T=Wssinβ (4.1)

Where: ws=bulk unit weight of the soil; β=slope angle

The total shear strength, S, of the soil/root system, reinforced by roots contributing an increase in shear strength of ΔSR ,is given by the modified form of coloumb’s equation for shear strength:

S= (Ss+ΔSR) +σ’tan ' (4.2)

Where Ss=Shear strength of the root-free soil;σ ‘=effective normal stress; ' =effective angle

of friction of the soil.Therefore,

sin

'tancos''

W

WLscFoS s

(4.3)

Where: W’s=buoyant weight of the soil= 1 h1+ ( 2 - w ) h2; Ws= 1 h1+ 2 h2; c’=effective

cohesion of root-free soil; ΔS=shear strength increment per unit area of soil where

ΔSR=ΔSL; 1 =unit weight of soil above groundwater table; 2 =unit weight of soil below

groundwater table Hydrologic Effect: Vegetation can affect the stability of slopes by modifying the

hydrologic regime of the soil. Interception and transpiration of moisture by trees tend to maintain drier soils and mitigate or delay the onset of waterlogged or saturated soil conditions. Such conditions have been known to cause slope failure. Conversely, felling trees tends to produce wetter soils and faster recharge times following intense rainstorms.

Vegetation species: Since plants and grass absorb different amounts of water depending on the type of soil they grow in, there are several different criteria for the section of the most appropriate species. A general rule of thumb is to use local plants and grass that are adaptable to local climate. Deciding exactly what types or species are needed requires the aid of horticulture and landscaping experts. In general, vegetation that absorbs large amounts of water from the soil are best in clayey soils to ensure a drier and stronger soil crust. On the contrary, species that absorb less water would be ideal for sandy soils because intense drying of sandy surface soils makes them more susceptible to erosion (Abramson, L. W., et.al.,1995).

4.3 Surface slope protection The objective of surface slope protection is to prevent infiltration by rainfall so that the

slope can be maintained dry or partially dry. Surface slope protection measures include application of shotcrete or riprap etc.

4.3.1 General design considerations The slope protection measures above are intended to provide near-impermeable

surface protection of slopes. In design, they are not considered to provide resisting forces to the slope like retaining structures, anchoring systems, and buttresses. Because of the near-impermeable nature of slope protection, consideration should be given to providing

38

drainage of water from the slope. The selection of slope surface protection measures depends on the overall cost of the work involved (Abramson, L. W., & others.,1995).

4.3.2 Shotcrete The main purpose of shotcrete is to protect the slope from rainfall infiltration. The

specifications for materials use are similar to those adopted for conventional concreting, although the aggregates are specially selected not only to meet the requirements of the finished surface but also to prevent segregation while the shotcrete is being pumped and applied. Careful consideration must be given to drying and consequent shrinkage cracking that occurs when shotcrete is used for slope surfacing (Figure 4. 3).The performance of the field test panel, with respect to durability, permeability, and shrinkage should be assessed and, if necessary, the mix should be modified to meet all requirements. To facilitate drainage, weep holes should be installed in the shotcrete surface, especially where areas of seepage are noted prior to applying the shotcrete (Figure 4. 4), (Abramson, L. W., & others.,1995).

Figure 4. 3 Use of shotcrete for slope stabilization (REED.,2003).

Figure 4. 4 Weep hole detail (Laska, W.,1992).

4.3.3 Rip-rap Erosion of toes of slopes by moving water in rivers, streams, and oceans is common and

often causes instability if left unattended. The general solution for this problem is to protect the toe of the slope with layers of rip-rap placed for the base of the slope to an elevation of about (0.91-1.52 meter) above the mean high-water level (Figure 4. 5).

39

Figure 4. 5 Rip rap to protect erosion at the toe of a slope (FHWA.,2005).

Where eroding forces are substantial, a lining of reinforced concrete with hydraulic detailing is constructed to dissipate the eroding forces from the water flow. Rip-rap should be hard and tolerable against weathering and heavy enough to resist displacement by running water or wave action (Abramson, L. W.,et.al.,1995).

4.4 Buttressing Buttressing is a technique used to offset or counter the driving forces of a slope by an

externally applied force system that increases the resisting force.Butresses may consist of

I. Soil and rock fill II. Counter berms III. Mechanically stabilized embankments (MSE), (Abramson, L. W.,et.al.,1995).

4.4.1 Soil and rock Fill Soil and rock fill is used to provide sufficient dead weight near the toe of an unstable

slope to prevent movement (Figure 4. 6). Where resources are available and where soil and rock fill can be found locally, this method is the most practical way to arrest further movement of an unstable slope.

Figure 4. 6 Rock-fill Buttresses (Léger, P.,2006).

40

4.4.2 Counter berms A counter berm is used to provide weight at the toe of a slope and to increase the shear

strength below the toe. This is particularly useful for embankments over soft soils where the ground at the toe can remove upward and form a bulge. By locating a counterpart where the upheaval is expected to occur, the resistance against sliding is also increased. The counterpart must be carefully designed in order to utilize the weight most effectively and to assure that it is stable itself. Unless careful investigation and thorough analysis are made, there is a danger that the additional load imposed by the counter may increase the driving force rather than provide added resistance against sliding.

4.4.3 Mechanically stabilized embankments Mechanically stabilized embankments (MSE) involve the designed use of backfill soil and

thin metallic strips, mesh, or geosynthetic reinforcement mesh to form a gravity mass capable of supporting or restraining large imposed loads (Figure 4. 7).The MSE slope face is either vertical or inclined, and the backfill material is typically confined behind metal, reinforced concrete, or shotcrete facing. The mesh or geosynthetic is sometimes wrapped around the soil at the face between reinforcement layers (Abramson, L. W.,et.al.,1995).

Figure 4. 7 Wire-faced MSE Wall (Masse et. al, 2003).

4.5 Retaining walls The most common use of retaining walls for slope stabilization is when a cut or fill is

required and there is not sufficient space or right-of-way available for just the slope itself. The wall should be deep enough so that the critical slip surface passes around it with an adequate FoS, as shown in (Figure 4. 8).In addition, the ability of the retaining wall to perform as a stabilizing mass is a function of how well it will resist overturning moments, sliding forces at or below its base, and internal shear forces and bending stresses.

41

Figure 4. 8 Different wall stability criteria (Abramson, L. W.,et.al.,1995).

Retaining wall types include: I. Conventional gravity or cantilever retaining walls II. Driven piles III. Drilled shaft walls IV. Tieback walls (Abramson, L. W.,et.al.,1995).

4.6 Drainage Soft soil is often improved prior to building on/in it. This can be motivated by the

otherwise excessive settlement of foundations, which would compromise serviceability and would require excessive maintenance, and saving on otherwise heavy foundations. Draining is one of the several ground improvements;

4.6.1 Vertical drainage Embankments built over soft soil, call for such enhanced drainage, and a method of

vertical drainage by means of wick drains is much used for this purpose. The method is sometimes designated as prefabricated vertical drains (PVD).The drains consist of a core of polypropylene with grooves and a filter fabric as wrapping. They are pressed in to the soil by a mandrel, and are repeated at distances of between 1 to 3m.Stressed pore water in the soft layers passes through the filter fabric in to the grooves and travels upwards to the surface where excess pressure is absent. From there it is drained off to ditches, etc. Hence, the soil consolidates and settles more rapidly.

Drainage can also occur downwards to a draining layer of sand. This is quite possible in the areas where the formation underlying the soft deposits have potential heads equal to or even lower than the surface ditch levels.

42

Figure 4. 9 Vertical drainage applied for widening a highroad on soft soil (Barends, F. B.,2009).

The flow of water escaping from the soft soil is predominantly horizontal when vertical drains are present. The length of the flow in the soft soil is drastically reduced by the vertical drains, to at most one half of the centre-to-centre distance of the drains (Barends, F. B.,2009).

4.6.2 Vacuum drainage It is newer method that has been developed making use of vacuum drainage. The

vacuum can be applied to a sand fill, which is covered by impervious membranes, there by drawing the pore water up to the surface. Vertical drains enhance the action. Sometimes the lateral boundaries of the area are sealed off by e.g. slurry walls to prevent drawing in water from the vicinity.One of such methods (Beaudrain) applied the vacuum directly to vertical drains, and another method (IFCO walls) uses a plough-like device to bury horizontal drains at the bottom of a trench, which is back-filled with sand.

These methods have in common that the amount of applied vacuum increases the hydraulic gradient, which determines the rate of flow of pore water from the soil. When sufficient consolidation has been achieved, the vacuum pumps are turned off, and slight swelling of the soil may occur as water is drawn back in to the soil. The reduction of potential head with in the soil mass by vacuum has added advantage of increasing the stability of the sides of the embankment (Barends, F. B.,2009).

Figure 4. 10 Vacuum consolidation (Barends, F. B.,2009).

4.7 Soil modification methods Stabilization of slopes by drainage may not always be effective in cohesive soils that

have low to very low permeability. In these situations, methods of foundation engineering can be adapted (Duncan, J. M., & Wright, S. G.,2005).

43

4.7.1 Compacted soil-cement fill Compacted soil-cement fill (cement mixed with local soil material) has been used to

construct embankments where in the embankment side slopes could be steepened to 1.5H: 1V or 1H: 1V because of higher shear strength of soil cement. For slope remedial, soil-cement fill can be used to rebuild a failed slope by forming an earth berm to provide stabilizing resisting forces (Abramson, L. W.,et.al.,1995).

Figure 4. 11 Soil-cement fill slope used to stabilize a landslide (BMPS.,1998).

By mixing an increasing amounts of cement with soil, the shear strength of the compacted soil cement increases substantially. The mix design is determined in the laboratory for a given soil and desired strength.Cement mixing not only increases the shear strength of the soil, but also reduces its permeability. This effect poses two concerns about using compacted soil-cement fill (Abramson, L. W.,et.al.,1995).

4.7.2 Preconsolidation Another slope stabilization technique is to increase the strength of clayey soils by

acceleration of consolidation through the use of a surcharge fill, sometimes in combination of wick drains or sand drains. The technique is suitable for embankment slopes overlying soft foundation soils. The design concept of this technique is to cause a portion of total settlement to occur before paving or other construction takes place. This can be achieved by placing surcharge fill over the embankment to an elevation that would give the same primary consolidation settlement as would have been induced by the embankment fill alone at a certain time period (Figure 4. 12).

Figure 4. 12 Preloading design-compensation for primary settlement by temporary surcharge fills (Abramson, L. W.,et.al.,1995).

44

If the time to reach the required settlement under the surcharge and embankment fills is long and impractical, wick drains or sand drains commonly are used to expedite the rate of consolidation of the foundation soils by increasing the rate of pore pressure dissipation.

Staged embankment construction is commonly carried out over soft compressible foundation soils in an attempt to minimize global failures and, at the same time, to increase the shear strength of the soft soils. Two to three stages of embankment construction are used with each stage, causing a predetermined amount of consolidation of the underlying materials and dissipation of excess pore pressures to acceptable levels. The rate of pore pressure dissipation usually is monitored by piezometers. However; field piezometer measurements in soft soils are sometimes inconsistent and unreliable. To solve this difficulty, it may be necessary to rely on settlement trends to interpret the degree of consolidation. Design of staged construction must estimate the initial strength of cohesive soil and its rate of increase with time due to consolidation under applied loading (Abramson, L. W.,et.al.,1995).

4.7.3 Injection methods Injection methods are attractive because they can be implemented at relatively low

cost. Their drawback is that it is difficult to quantify the beneficial effects. In addition, when the fluids are injected, the short term effect may be to make the slope less stable. The beneficial effects may be achieved only later, when the injected material has hardened or has reacted with the soil to alter its properties (Duncan, J. M., & Wright, S. G.,2005).

4.7.3.1 Cement grouting One of the most useful aspects of the method is that it is used to stabilize landslides in

clay. Cement cannot penetrate the voids of clays because the particles are too large, and the grout pressures cannot cause compaction if the clay is saturated, as it often is. Nevertheless, the method is effective. Trenches excavated in to the treated area show the method works. (Figure 4. 13) shows a cross section revealed in one such trench. The grout did not penetrate the voids of the clay or the fissures in the clay but did penetrate the voids of the coarser fill called ash, which has gravel sized particles. Within the clay, the grout penetrated along the rupture surface, lifting the mass above, and a solid mass of neat cement concrete was formed the slip surface when it hardened (Duncan, J. M., & Wright, S. G.,2005).

Figure 4. 13 Stabilization of landslide at Fenny Compton, England by injection of neat cement grout (Pubrick,

M., & Ayres, D.,1956).

45

4.7.3.2 Lime piles and slurry walls Lime piles are drilled holes filled with lime. Lime slurry piles filled with slurry of lime and

water. Lime piles and lime slurry piles are used to stabilize slopes, and the mechanisms through which they improve soil strength and stability (Duncan, J. M., & Wright, S. G.,2005).

4.7.4 Literature reviews on soil modification methods 1. When soils at the site are loose or highly compressible, or when they have unsuitable

consistency indices, too high permeability, or any other undesirable property making them unsuitable for use in a construction project, they may have to be stabilized. There are various stabilization methods one of which is chemical stabilization. The stabilization, especially with lime, is common applied method among the others due to its effective and economic usage. The finding from the previous studies shows that when lime is added to clay soils in the presence of water, a reaction including cat ion exchange and flocculation takes place. It is stated that flocculation is primarily responsible for the modification of the engineering properties of clay soils when treated with even small amount of lime. The studies reported in the literature showed that the addition of lime increased the optimum water content, shrinkage limit and strength, and reduced the swelling potential, liquid limit, plasticity index and maximum dry density of the soil (Eren, S., & Filiz, M.,2009).

2. The three major constituents in clay soils are kaolinite, montimorillonite and fine grained quartz. A series of tests were carried out on these minerals to assess the influence up on them of the addition of various amounts of lime. All the same, the properties of such soil-lime mixtures vary depend upon the character of the clay soil, the type and length of curing, and the method and quality of construction. When lime is added to clay soils, calcium ions initially are combined with or adsorbed by clay minerals. The addition of the lime contributes towards the improvement of soil workability but not to an increase in strength. The effectiveness of lime stabilization process is dependent up on the development of reaction products formed from the attack of lime on the minerals in a deposit of clay. Lime treatment increases the strength of clay materials.Montomorillonite clays respond much more rapidly to lime stabilization, and so exhibit earlier gains in strength than do kaolinitic clays. Clays generally show a significant increase in strength when lime is used for stabilization. Expansive clays respond more quickly to strength increase. For instance, montomorillonite showed a rapid initial increase in unconfined compressive strength with small additions of lime. Its lime strength optimum was around 4% compared with that of kaolinite which varied between 4 and 6%.Indeed strength does not increase linearly with lime content, and excessive addition of lime reduces strength. This is due to the fact that lime itself has neither appreciable friction nor cohesion (Bell, F. G.,1996).

46

Figure 4. 14 Unconfined compressive strength of montimorillonite with various additions of lime (Bell, F.

G.,1996).

Figure 4. 15 Unconfined compressive strength of kaolinite with various additions of lime (Bell, F. G.,1996).

47

5. Chapter 5 Embankments stability analysis techniques

5.1 Slope stability concepts Once the slope geometry and subsoil conditions have been determined, the stability of a

slope may be assessed using either published chart solutions or a computer analysis. Most of the computer programs used for slope stability are based on the limiting equilibrium approach for a two dimensional model, with some also allowing three dimensional analysis.

More complex programs that use the finite element or boundary element methods are also available, and allow performing two or three dimensional slope evaluations. However such analyses require a relatively complete model of the sub soils and their constitutive parameters determined by an extensive program of laboratory tests. Concerns about the laboratory testing, lack of familiarity with the methodology, and the requirements for extensive computing for each analysis have generally restricted the use of the finite element approach to only a few special cases for highway slopes (Abramson, L. W., & others.,1995).

5.1.1 Typical input data for slope stability analysis To perform slope stability analyses, it is essential to understand mainly the Geologic

conditions, material properties, site topography, groundwater conditions and seismicity of the site which have pronounce effect on the stability analysis.

5.1.2 Definition of factor of safety The factor of safety for slope stability is usually defined as the ratio of the ultimate shear

strength divided by the mobilized shear stress at the incipient failure. The most common formulation for FoS assumes the factor of safety to be constant along the slip surface, and it is defined with respect to the force or moment equilibrium:

Moment equilibrium: Generally used for the analysis of rotational landslides. Considering a slip surface, the factor of safety FoSm defined with respect to moment is given by:

d

r

mM

MFoS

(5.1)

Where Mr is the sum of the resisting moments and Md is the sum of the driving moment. For a circular failure surface, the centre of the circle is usually taken as the moment point for convenience.

Force equilibrium: Generally applied to translational or rotational failures composed of planar or polygonal slip surfaces. The factor of safety FoSf defined with respect to force is given by:

d

r

fF

FFoS

(5.2)

Where Fr is the sum of the resisting forces and Fd is the sum of the driving forces. A slope may actually possess several factors of safety according to the methods of analysis.

A slope is considered as unstable if FoS≤1.0.It is however common that many natural stable slopes have factors of safety less than 1.0 according to the commonly adopted design practice and this phenomenon can be attributed to:

The use of a heavy rainfall with a long recurrent period in the analysis.

Three-dimensional effects are not considered in the analysis

48

Additional stabilization due to the presence of vegetation or soil suction is not considered (Cheng, Y., & Lau, C.,2008).

5.2 Methods for embankment stability analysis There are many methods available for this type of analysis, including both limit

equilibrium and numerical analysis. Among the available analysis methods for assessing the stability (stress vs. strength) of a slope, two distinctly different approaches to slope analysis can be distinguished: deterministic and probabilistic analysis methods. In a deterministic approach analysis, a point estimate of each variable is assumed to represent the variable with certainty (Coates, 1977).A hypothesis and a corresponding mathematical model for failure must be postulated. Possible uncertainties are accounted for afterward by adjusting the results through the inclusion of a factor of safety .This is the classical engineering approach to a construction problem, and it has the advantage that it is relatively easy to comprehend and apply.

In a probabilistic approach, it is realized that all factors governing slope exhibit variations and representative point estimates are very difficult, if not impossible, to obtain. The variability of these properties is accounted for in the analysis process. Parameters are described as distributions of values, each value having a different likelihood of occurrence. By combining the probabilities of each parameter value, the probability of slope failure can be calculated (sage, 1976; Coates, 1977).It is important to note that the conventional approach in probabilistic analysis requires that a deterministic model of failure exists. Unlike deterministic methods, this approach recognizes that there may be cases when the slope is unstable, although the average values of the parameters suggest that it would be stable. Probabilistic methods emphasize the fact that it may not be possible to completely avoid slope instabilities. Consequently, a probabilistic approach can predict the risk of failure and be extended to a financial analysis of stability.

In the following, deterministic analysis methods are first described. These include (1) Limit equilibrium methods, and (2) numerical modelling.

5.2.1 Limit equilibrium methods Limit equilibrium analysis is a simplification of the more rigorous limit theory, and has

become the preferred method for routine slope stability analysis in soil mechanics. In limit equilibrium analysis, the failure surface must be assumed. Normally, the shear strength of the material is described by the Mohr-Coulomb criterion. None of the basic equations of continuum mechanics regarding equilibrium, deformation and constitutive behaviour are satisfied completely. The deformation of the material is not taken into account at all, and the condition of equilibrium is normally satisfied only for forces (chen, 1975).Using limit equilibrium analysis, it is not possible to judge whether the solution represents the upper or lower bound of the collapse load. The exception is a circular failure surface in a cohesive

material with friction angle equal to zero ( =0), in a Mohr-Coulomb material, which give an

upper bound solution. However, the upper bound solution is not conservative, and comparisons with lower bound solutions are few. In the study by Yu et al. (1998), both lower and upper bound solutions were compared with results from limit equilibrium analysis. It was found that limit equilibrium analysis gave accurate results for homogeneous slopes, but underestimated the stability of heterogeneous slopes with low slope angles.

In the simplest form of limit equilibrium analysis, only the equilibrium of forces is satisfied. The sum of forces acting to induce sliding of parts of slope is compared with the

49

sum of the forces available to resist failure. The ration between these two sums is defined as the factor of safety, FoS:

)(

)(Re

forcesDriving

forcessisitingFoS

(5.3)

The factor of safety can also be formulated as a ratio the actual cohesion or friction angle of slope and the cohesion or friction required for slope to be stable (Stacey,1968), or in terms of resisting and driving moments, which is useful for the analysis of circular(rotational) shear failure.

A safety factor of less than 1.0 indicates that failure is possible. If there are several potential failure modes or different failure surfaces that have a calculated safety factor less than 1.0, all these can fail. It is important to note that the condition of limit equilibrium strictly means that the only admissible factor of safety is 1.0.At this point, the resisting and driving forces (or moment) on the slope balance each other.

Two-dimensional methods

Only a two-dimensional section of the slope is considered in this approach. Consequently, release surfaces must be present to allow failure to occur. For the two-dimensional section shown in Figure 5. 1, the forces acting on each slice are (1) the shear and normal forces on the failure surface, (2) the normal and shear forces acting at the boundaries of each slice (often referred as interslice forces), (3) the weight of the slice, and (4) the external loads acting at the top of each slice.

A large number of methods for analyzing rotational shear using the above approach have been developed, for example, Bishop(1955),Spencer(1967),etc.These methods differ in how well the conditions of equilibrium are satisfied and how the interslice forces are included in the solution. They can be divided in to simple, complex and rigorous methods. For simple methods, the effects of interslice forces are neglected, whereas the interslice forces are included in the formulation of complex methods. Methods where all conditions of static equilibrium are satisfied are called rigorous methods. The various slice methods also differ with respect to the failure surface shape that can be analyzed. For many of the methods, only a failure surface in the form of a circular arc is allowed. There are, however, an increasing number of methods where the failure surface can be non-circular, or even partly composed of straight lines (e.g., sliding along an existing discontinuity combined with rotational shear).

50

Figure 5. 1 The method of slices for analyzing rotational shear failures (Sjoberg, J., 1999).

There are different methods based on their analysis and the conditions of static equilibrium to satisfy in determining the factor of safety (Table 5. 1); Bishop simplified GLE/Morgenstern-Price, Janbu simplified, Ordinary/Fellenius and Spencer are among the most widely used.

Table 5. 1 Limit equilibrium slope stability methods and equilibrium equations that satisfy (Abramson et al, 2001).

Method Satisfaction of Force Equilibrium Satisfaction of Moment Equilibrium Horizontal Vertical

Ordinary Method No No Yes

Bishop Simplified No Yes Yes

Janbu Simplified Yes Yes No

Corps of Engineers 1&2

Yes Yes No

GLE Yes Yes Yes

Spencer Yes Yes Yes

51

Because the formulation of the stability of a slope in limit equilibrium terms is a statically indeterminate problem (the number of equations is less than the number of unknowns), all approaches based on the method of slices use simplifying assumptions.

The method selected for analyzing a specified slope problem must be suitable for the slope conditions being analyzed (Abramson et al, 2001). Table 5. 2 below is a summary of the conditions under which the various methods are most suitable.

Table 5. 2 Summary of Procedures for Limit equilibrium slope stability analysis, and their usefulness (Adapted from, Abramson et al 1995 and Duncan, J. M., & Wright, S. G.,2005).

Procedure Uses and assumptions

Ordinary method of Slices

Applicable to non homogenous slopes and c- soils where slip surface can be

approximated by a circle. Neglects all interslice forces, fails to satisfy

force equilibrium, and assumes that the resultant interslice forces are

inclined at angle that is parallel to the base of the slice, which is the

shortcoming of the method.

Simplified Bishop's

Applicable to non homogeneous slopes c- soils where slip surface can

be approximated by a circle. More accurate than Ordinary Method of slices for

high pore pressures. Assumes interslice shear forces are zero, and satisfy

the vertical force and moment equilibrium.

Janbu's

Uses the method of slices to determine the stability of slices and assumes the

interslice shear force is zero. It satisfies the both force equilibrium though

the moment equilibrium is not satisfied.

Spencer's

An accurate procedure applicable to virtually all slope geometries and soil profiles.

It satisfies both static equilibrium assuming the resultant interslice force

has a constant but unknown inclination.

The simplest complete equilibrium procedure for computing the FoS.

Morgenstern and Price's

An accurate procedure applicable to virtually all slope geometries and soil profiles.

Proposes similar to Spencer's method, except that the inclination of the interslice

resultant force is assumed to vary accordingly.

Rigorous, well established complete equilibrium procedure.

Search for the critical slip surface

The assumption of a certain shape and location for the failure surface in a slope and the application of any of the slice methods only yield one value of the safety factor, or the collapse load. This might not be the lowest value; thus, the failure surface might not be the most critical one. Consequently, it is necessary to try several potential failure surfaces and go through the calculations for each slope. In many cases, the failure surface is assumed to pass through the toe of the slope, but this is not a necessary condition for a failure.

52

It can be tricky mathematical problem to find the local minimum of the safety factor or collapse load. A commonly used search technique for circular failure surfaces is to define a grid in which each point represents the centre of a circular arc. Different radii of the failure surface are then tested for each node, and the corresponding factor of safety is calculated for each of these potential slip circles. When a number of potential slip surfaces have been analysed, the values of the minimum safety factor in each node are contoured on the defined grid (see Figure 5. 2).If closed contours are obtained, a local minimum of the safety has been found. Otherwise, a larger search grid must be defined. The obtained local minimum does not necessarily have to be the only minimum value of the safety factor. There may be several local minima, but only one corresponds to the critical slip surface. The gird-search technique is simple but it can be time consuming for large problems (Nash, 1987; Bromhead, 1992).

Figure 5. 2 Search for critical slip surface using a grid search pattern (Mostyn and Small, 1987).

Three-dimensional methods In reality, the failure surface of a circular shear failure will probably be bowl-shaped

(see Figure 5. 3).In a two-dimensional analysis, the shear resistance of the end surfaces is not included in the formulation; hence, this will yield conservative results when applied to a three-dimensional geometry. Three-dimensional slice methods have been developed to overcome these limitations-see e.g., Hungr et al. (1989), and Lam and Fredlund (1993).Unfortunately, three-dimensional methods are much more complex than two-dimensional analyses. The biggest drawback is not increased calculation time, but the difficulty in defining the three-dimensional failure surface. Currently, there is limited knowledge of how the failure mechanism acts to form a failure surface and what factors affect the shape even in a two-dimensional cross-section of the slip surface. Before three-dimensional limit equilibrium methods can be used routinely, better knowledge regarding the fundamental mechanisms of slope must be gained.

53

Figure 5. 3 Three-dimensional failure geometry of a circular shear failure (Hoek and Bray, 1981; Franklin and Dusseault, 1991).

5.2.2 Numerical modelling Using numerical analysis, it is possible to solve the equations of equilibrium, the strain

compatibility equations, and the constitutive equations for a material for prescribed boundary conditions. The major benefits of numerical modelling are that (1) both the stress and the displacements can be calculated, and (2) different constitutive relations can be employed. A number of different numerical methods exisits-e.g., Boundary Element Methods (BEM), Finite Element Methods and Finite Difference Methods (FDM).In boundary element methods, only the boundaries of a problem need to be discretized in to elements. For finite element and finite difference methods, the entire problem domain must be discretized in to elements. Another class of methods is Discrete Element Method (DEM).While BEM, FEM and FDM all are continuum methods, DEM is a discontinuum method in which discontinuities present are modelled explicitly.

5.2.3 Probabilistic analysis In a probabilistic analysis, the stochastic nature of the input parameters is included and

the resulting chance (probability) of failure is calculated. Considering probabilities of failure rather than safety factors is an acknowledgment that there is always a finite chance of failure, although it can be very small.

Slope stability applications For large scale slopes, there have been some attempts at analysing circular failure

using a probabilistic approach. These are also based on a limit equilibrium failure model. In none of these attempts was a full search routine used for determining the factor for a specific set of random samples of the input parameters. Instead, assumptions were made regarding the location of the most critical failure surface. This reduces the calculation time (fewer iterations in the Monte Carlo simulation), but it is not very rigorous. However, both circular and non-circular failure surfaces can be analyzed in this way.

It was shown by Oka and Wu (1990) that the failure surface with the minimum factor of safety does not necessarily have to be the failure surface with the maximum probability of failure. It is therefore necessary to evaluate the probability of the entire system, perhaps including several possible failure surfaces at the same instant (Chowdhury, 1987; Mostyn

54

and Li, 1993). The combined probability of failure can be significantly higher than the probability of failure along a single failure surface. Juang et.al (1998) also found that the critical sliding surface was a “bind” rather than one well-defined surface.

5.2.4 Seismic analysis Earthquake ground motions are capable of inducing large destabilizing inertial forces, of

a cyclic nature, in slopes and embankments. Also, the shear strength of the soil may be reduced due to transient loads (i.e., cyclic strains) or due to the generation of excess pore water pressures. The combined effect of the seismic loads and the changes in shear strength will result in an overall decrease in the stability of the affected slope.

Typically, cyclic loads will generate excess pore water pressures in loose, saturated cohesion less materials (gravels, sands, and non plastic silts), which may liquefy with a considerable loss of pre-earthquake strength. However, cohesive soils and dry cohesion less materials are not generally affected by cyclic loads to the same extent (Abramson et.al, 1995).

Surveys of earth works performance during earthquakes suggest that embankments constructed of materials that are not vulnerable to severe strength loss as a result of earthquake shaking (most well compacted clayey materials, unsaturated cohesion less materials, and some dense saturated sands, gravels, and silts) generally perform well during earthquakes. The embankment, however, may undergo some level of permanent deformation as a result of the earthquake shaking. With well built earth embankments experiencing moderate earthquakes, the magnitude of permanent seismic deformations should be small, but marginally stable earth embankments experiencing major earthquakes may undergo large deformations that may jeopardize the structure’s intergrity.Simplified procedures have been developed to evaluate the potential for seismic instability and seismically induced permanent deformations, which can be used to evaluate the seismic performance of earthen structures and natural slopes (Chen W.F. & Liew R.,J.Y.,2002).

In pseudo static slope stability analyses, a factor of safety against failure is computed using a static limit equilibrium stability procedure in which a pseudo static, horizontal inertial force, which represents the destabilizing effects of the earthquake, is applied to the potential sliding mass(Figure 5. 4). The horizontal inertial force is expressed as the product of a seismic coefficient, k, and the weight, w, of the potential sliding mass. If the factor of safety approaches unity, the embankment is considered unsafe. Since the seismic coefficient designates the horizontal force to be used in stability analysis, its selection is crucial. The selection of seismic coefficient must be coordinated with the selection of the dynamic material strength and minimum factor of safety, however as these parameters work together to achieve a satisfactory design. For example, seed (1979) recommends using appropriate dynamic material strengths, a seismic coefficient of 0.15, and a minimum factor of safety of 1.15 to ensure that an embankment composed of materials that do not undergo severe strength loss performs satisfactorily during a major earthquake (Chen W.F. & Liew R.,J.Y.,2002).

55

Figure 5. 4 Pseudo static slope stability analysis (Chen W.F. & Liew R., J.Y., 2002).

5.2.5 Available computer programs for stability analysis Computer programs are available that can handle a wide variety of slope geometries,

soil stratigraphies, soil shear strength, pore water pressure conditions, external loads, and internal soil reinforcement. Most programs have also capabilities for automatically searching for the most critical slip surface with the lowest factor of safety and can handle slip surfaces of both circular and non circular shapes. Most programs also have graphics capabilities for displaying the input data and the results of the slope stability computations.

Types of computer programs

Two types of computer programs are available for slope stability analyses: The first type of computer program allows the user to specify as input data the slope geometry, soil properties, pore pressure conditions, external loads, and soil reinforcement, and computes a factor of safety for the prescribed set of conditions. These programs are referred to as analysis programs. They represent the more general type of slope stability computer programs and are almost based on one or more of the procedures of slices. There are many computer programs available for analyzing the stability of slopes ,among the most commonly used are ; GEO-SlOPE, GEOSOFT, SLIDE, CLARA etc.

The second type of computer program is the design program. These programs are intended to determine what slope conditions are required to provide one or more factors of safety that the user specifies. These programs allow the user to specify as input data general information about the slope geometry, such as slope height and external loads, along with the soil properties. The programs may also receive input on candidate reinforcement materials. The computer programs then determine what type and extent of reinforcement are required to produce suitable factors of safety. The design programs may be based on either procedures of slices or single-free body procedures (Duncan, J. M., & Wright, S. G.,2005).

56

6. Chapter 6 Developing the A-8 motorway embankment models for stability analysis

In order to select the road sections for performing the stability analysis of the A-8 Motorway Wroclaw bypass (Figure 6. 1), a 1:1000 Project plan (Appendix I. 1), depicting the profile of these two sections specifically shown in (Figure 6. 1 and Figure 6. 2) were used. In addition borehole series (Figure 6. 3) data and their profiles (Appendix V. 1) obtained from the GEOTECHsp.zo.o project office were used carefully to select the specific boreholes that are used to model the actual road embankment foundation conditions by observing the geologic profiles.

(a) Cross section A without Geo-mattress support, representing from Km 22+668.50 to Km 23+240.00 was used as a geometric entry to create Model section-A.

Figure 6. 1 Section used for modelling crossection A representing from Km 22+668.50 to Km 23+240.00) of the motorway (GEOTECHsp.zo.o project office, 2010).

6.1 Profile of the selected road sections The following layers represent the selected sections A and B from top to bottom (with

the external boundaries of each layers in the (Appendix VIII. 1), however in case of model

section A Rock mattress is missing.

Concrete layer having a thickness of 0.72 meter composed of a blend of mineral

and asphalt, asphalt concrete, crushed-stone aggregate and layer of stabilized

soil represents the topmost layer of the road section.

Embankment construction materials of homogenous gravel composition, having

6 meter thickness in case of section A and 7meter for section B which includes

the thickness of Concrete for both sections and Rock mattress exclusive of

section A.

Rock Mattress /crushed rock are the bottom most layers with thickness of

0.35meter used in section B.

Geogrid

http://www.proz.com/kudoz/polish_to_english/construction_civil_engineering/2274457-kruszywo_%C5%82amane.html

57

6.2 Geologic and subsurface conditions The Project area is covered by quaternary (recent) soil deposit, underlain by the Pliocene

sediments which are the youngest sequence of Tertiary Period; and Glacial deposits (Table 6. 2) respectively. These geological sequence and geotechnical classification of the area is illustrated in the Borehole profiles (Appendix III. 1).

In this study nine Boreholes data were obtained (Figure 6. 3), which were used for exploratory works of the subsurface conditions (Appendix V. 1) and to prepare the geological logs that used in the classification of geotechnical layers for design considerations (Appendix III. 1).The water table is in shallow conditions in all profiles ranging from 0.6-1m depth with reference to the topmost quaternary soil layer (Appendix IV. 1).

(b) Cross section B with Geo-mattress Support, representing from Km22+132 to Km 22 +668.50 was used as geometric entry of the Model section-B.

Figure 6. 2 Section used for modelling crossection B representing from Km22+132 to Km 22 +668.50 of the motorway (GEOTECHsp.zo.o project office, 2010).

Geo-mattress

58

Figure 6. 3 A 1:1000 project plan illustrating the location of borehole series 1-9 used for exploratory work from Km 23+400 to Km 23+500 (GEOTECHsp.zo.o project office,2006).

6.3 Selection of boreholes for modelling A-8 motorway embankment foundation

The foundation condition of the embankment was incorporated in actual models for the stability analysis, by selecting the worst conditions out of the nine boreholes (Appendix V. 1) that were used for exploratory works in WA-23 project plan as shown (Figure 6. 3) and their profiles.

Table 6. 1 Borehole selection based on the thickness of clayey and sand layers of the profiles 1-9

Boreholes description(m) Bh1 Bh2 Bh3 Bh4 Bh5 Bh6 Bh7 Bh8 Bh9

Water table 0.7 0.6 0.7 0.7 0.8 0.7 0.7 1 0.8

Top sand layer (Ia & Ib) 2 1.8 1.4 1.6 2 1.5 1.4 1.3 1.4

Underlying clayey layers (IIa & IIb) 4.4 6 4.2 3.4 5.7 5.9 2.8 5.9 6

The larger the content of clay minerals, and the more active the clay mineral, the greater is its potential for swelling, creep, strain softening and changes in behaviour which have direct relevance with the reduction of the shear strength of the soils. The mechanical

59

behaviour of clays is affected by the physicochemical interaction between clay particles, the water that fills the voids between the particles, and the ions in the water (Duncan, J. M., & Wright, S. G.,2005).

Hence, based on the combined effect of shallow sand layers (Ia and Ib) and dominance of clayey layers in shallow water table (IIa and IIb) as depicted in (Table 6. 1, Appendix III. 1and Appendix V. 1) on top of their profile, borehole series 8 and 9 (Figure 6. 4and Figure 6. 5) were chosen to incorporate in modelling of the foundation condition of both models. This was carried out by using (Table 6. 2), explaining the composition of the geotechnical layers and (Table 6. 3), explaining the individual soil types comprising the layers.

The two selected bore holes are regarded as the worst scenarios which might have a pronounce effect on the stability of the embankment. This leads to the lowest factor of safety which is the interest of the stability analysis to take remedial actions.

Figure 6. 4 Geological and geotechnical log of bore hole 8 (see: Appendix V).

6.4 Supporting and loading conditions In addition to the above mentioned data the supporting parameters and loading

conditions were included. Support conditions:

I. Type: Geogrid Securgrid Q1 60/60 (x7), Length H ≈9.0 m,

Distance between Geogrids=0.5 m Tensile strength Rr = 50 kN/m.

60

II. Rock Mattress (applied in section B only)

Id > 0.98 so = 42o (on basis of PN-59/B-03020),

Mattress is wrapped up in a Geogrid anchoraged to a slope face. Loading conditions: The slope stability analysis was supposed to include an average load from vehicles as a constant distributed load q = 25 kPa with vertical orientation. (GEOTECHsp.zo.o project office, 2010).

Figure 6. 5 Geological and geotechnical log of borehole 9(see: Appendix V)

Table 6. 2 Geological and engineering geological classification used for exploring the foundation (see: Appendix II).

Lithostratigraphic sequence

Number of Geotechnical layers

Symbols

PI (Fluvio- glacial)

Ia Pd

Ib Ps,Pr//Ps,Pr+Z

Ic Pd,Pd/Pπ,Pd//пp

Id Pπ,Pπ//пp,Pπ//Pd,Pπ/Pd,Pd,Pd/Pp

Glacial Clays

IIa Pg,Gp+Z,GpZ(H)+Z,Gp/GpZ,Gp/Pg+Z,GπZ

IIb Gp+Z(+k),Gp/Pg+z,Pg/Gp+Z(//Pπ),Gp+Pg,Gp//пp+Z+K

IIc Gp+Z,Gp/Pg+Z,Gpz(/Jp,Gp)+Z,п/Gπ(//пp,Pπ),пp,Gπ(//п,Pπ)

61

Table 6. 3 Geological classification symbols used for the A-8 motorway project (see: Appendix II).

Geological classification symbols of the project site

No. Symbol Soil and rock Type No. Symbol Soil and rock Type 1 Z Gravel 11 п Silt

2 Zg Clayey Gravel 12 Gp Sandy clay

3 Po Sandy Gravel 13 G Clay

4 Pog Clay,sandy Gravel 14 Gπ Silty Sand

5 Pr Coarse Sand 15 GpZ Compact sandy clay

6 Ps Medium Sand 16 GZ Compact clay

7 Pd Fine Sand 17 GπZ Compact silty clay

8 Pπ Silty Sand 18 Ip Sandy Loam

9 Pg Clayey Sand 19 I Loam

10 пp Sandy Silt 20 Iπ Silty Loam

6.5 Data inputs used for A-8 motorway embankment model In order to model the actual embankment of the A-8 motorway Wroclaw bypass, the

parameters listed in (Table 6. 4) that represent the actual embankment construction materials, reinforcing materials (geogrid and geo mattress) and the foundations conditions i.e. borehole 8(Figure 6. 4) and 9(Figure 6. 5) were fed as inputs in computer analysis program, Slide in the readymade geometry of the layers.

In this research, one of the most commonly used computer analysis method, Slide was used for stability analysis of the embankment of A-8 motorway Wroclaw by-pass. Slide is a 2D limit equilibrium slope stability program for evaluating the safety factor or probability of failure of circular or non-circular failure surfaces in soil or rock slopes. It is used to determine the factor of safety of a 2 horizontal to 1 vertical (2H: 1) slope placed on underlying constructed and natural layers, including a geomattress with low friction angle (RocScience, 2006).

The stability of a slope is influenced by factors such as geological conditions (soil and rock layers, discontinuities, groundwater conditions, etc), material properties, and geometry. As a rule many of these factors cannot be defined with much certainty. The above listed strength parameters; were all obeying the Mohr-Coulomb’s strength criteria in case of both Model sections A and B.

62

Table 6. 4 Strength parameters used for modelling sections A and B (on basis of PN-59/B-03020) (GEOTECHsp.zo.o Project Office, 2010).

Layers of Model

Unit weight (kN/m3)

c (kPa) (o)

Concrete

23.0 20 45

Embankment

20.0 0 41

Rock Mattress

20.0 0 42

Ia and water table

17.5 2.0 22

Ib

19.5 0 31

Id

19.5 0 31

IIa

21.0 13 13

IIb

22.0 16 14

IIc

22.0 37 21

6.6 The A-8 motorway embankment models The models of the A-8 motorway Wroclaw bypass was developed by defining the

material strength properties shown in (Table 6. 4) as well as geogrids support parameters, to carry out the stability analysis as shown below:

The following list of layers and colours represents the model layers of both sections A and B from top to bottom (with the external boundaries of each layers in the Appendix VIII. 1); however in case of model section A Rock mattress is missing.

1. Concrete (Black colour). 2. Embankment – gravel (Grey ,, ). 3. Rock Mattress – crushed rock (Green ,, ). 4. Layer 1 – I a: fine sand (Yellow ,, ). 5. Layer 2 – Ib: medium sand (Orange ,, ). 6. Layer 3 – IIa: clayey sand, compact sandy clay with gravel (Pink colour). 7. Layer 4 – IIb: sandy clay with gravel, sandy clay with silty sand and gravel (Red ,, ). 8. Layer 5 – IIc: compact sandy clay with silty sand and gravel, silt with silty clay, the

border between sandy clay and loam (Blue colour). 9. Layer 6: Id: the border between fine sand and silty sand (Brown ,, ).

6.7 A-8 Motorway model Section A Section A has an Embankment height Ha=6.0, half embankment width≈26.65m, Slope

ratio=1:1.5, water table ranging in 1.0-0.8m (left to the right) passing through the same layer as shown in the following (Figure 6. 6) above.

63

Based on the strength parameter entry of the layers’, reinforcing materials i.e. geogrids, loading conditions and the water table as illustrated in (Appendix VIII. 1), with the exception of the geo-mattress support, Model section A was developed as follows:

Figure 6. 6 Model section A developed for stability analysis.

6.8 A-8 Motorway model section B Section B has an Embankment height Hb=7.0,half embankment width≈31m, Slope ratio

1:1.5, water table ranging in 1.0-0.8m (left to the right) and different layers and supporting materials as shown in the following (Figure 6. 7).

Figure 6. 7 Model section B developed for stability analysis.

64

Based on the strength parameters entry of the layers’, reinforcing materials i.e geogrids, loading conditions, the water table, loading conditions together with geo-mattress support as illustrated in (Appendix VIII. 1), were used to develop model section B as follows:

65

7. Chapter 7 Result and Discussion

7.1 Result Using the computation by the analysis program Side 2D, model sections A (Figure 6. 6)

and B (Figure 6. 7), yield variable factor of safety for each analysing methods adopted in the program. In addition the critical surfaces intercepts along the slope surfaces gave different range of values:

7.1.1 Stability factor of the A-8 motorway embankment models As stated in the above Slide 2D, computer program was used for stability analysis which

applies limit equilibrium approach .The stability of the sections is generally assessed using factor of safety that is estimated as the ratio of the soil strength and driving stress acting along the potential failure surface. Five methods of limit equilibrium analysis adopted in Slide 2D were selected for this study i.e., Ordinary/Fellenius, Bishop Modified, Janbu Simplified, Spencer, GLE/Morgenstern for analysing both Models section A and B. Each method has its own assumptions (Table 5. 2) and hence yielding different factors of safety.

Once the models are developed for the analysis, i.e Model section A and B, defining the type failure surface shape was next step for the analysis. In this project homogeneous gravel

material was used as the construction material for the embankment with c=0kPa, =41:

(Table 6. 4) which is cohesionless. Circular failure surfaces are the most critical in slopes consisting of homogenous materials (Abramson, L. W.,et.al.,1995).

Hence for both model sections; A and B, circular failure surface type was chosen each having 6m and 7m height respectively. Slip surfaces are most likely to pass through weak layers usually in cohesionless material.

Hence based on the above assumptions the analysis was carried on and gave results of various factor of safety for models section A and B (Table 7. 1):

Table 7. 1 Factor of safety results of model sections A and B in different analysis methods.

Analysis Methods Factor of Safety/FoS

Model section-A Model section-B

Ordinary/Fellenius 1.20626 1.30194

Bishop simplified 1.48144 1.49874

Janbu simplified 1.29305 1.31944

Spencer 1.4546 1.46888

GLE/Morgenstern-Price 1.45136 1.47269

The detailed results of the analysis are indicated in (Appendix VIII. 1) along with other assumptions used as inputs in the analysis. In addition to the factor of safety increment (from model section A to B) and variability of the factor of safety values among methods, the minimum surfaces’ intercepts on the slope surfaces were observed as a few meters extended in Model section-B than A as shown in (Table 7. 2).The range of the minimum failure surfaces can be also observed from the contours of factor of safety in the analysis though the global critical surface found to be the smallest value in the range.

66

Table 7. 2 Range of factor of safety and their intercept on the slope surface for both Model sections.

Analysis methods

Model section-A Model section-B

Range of FoS

Critical surface intercept x(m)

Range of FoS

Critical surface intercept x(m)

Ordinary/Fellenius 1.206-1.25 0&17.5 1.302-1.25 0 & 20-22

Bishop simplified 1.481-1.5 2&17.5 1.499-1.5 0&20

Janbu simplified 1.293-1.5 0&17 1.319-1.5 0&20

Spencer 1.455-1.5 2&17.2 1.469-1.5 0&22

GLE/Morgenstern-Price

1.451-1.5 2 &17.5 1.473-1.5 0&20

7.2 Discussion The factor of safety in each analysis methods were discussed in light of the static equilibrium

conditions fulfilling and the requirements as per polish regulations for slope stability.

7.2.1 Stability factor assessment of the A-8 motorway embankment The assessment was performed in case of both model sections A and B for each analysing

methods here mentioned below:

7.2.1.1 Model section-A FoS assessment In case of model section A, where geogrids were used only as supporting material most

of the minimum surfaces were passing through the weak layers beyond the geogrid reinforcement (for all analysing methods), however the range of factor of safety was

Ordinary/Fellenius: Global Minimum FoS=1.206

(a)

(b)

67

(c)

(d)

Figure 7. 1 Ordinary method of analysis of model section-A ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface inslice division (d) FoS along the slope surface.

variable due to the difference in the assumptions among each method (Table 5. 2) and the static equilibrium conditions to meet (Table 5. 1).

7.2.1.1.1 Ordinary method

In Ordinary method the minimum surfaces falls in range of factor of safety 1.206-1.25 and global minimum having FoS=1.206 , where the dominant minimum surfaces and a global minimum surface passes through geotechnical layer of IIb (sandy clay with gravel and silty sand),having lower cohesion c=16 .

Bishop Simplified: Global Minimum FoS=1.481

(a)

(b)

68

(c)

(d)

Figure 7. 2 Bishop’s method of analysis of model section-A ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface in slice division (d) FoS along slope surface.

In addition the factor of safety gave variable values along slope surface from left to right boundaries where the failure surfaces were assumed to intercept to get the minimum surfaces, and was found out the minimum values occurred at x=0m and x≈17.5m(Figure 7.

1d); and the surfaces connecting these points made minimum surfaces while the critical minimal surfaces were found in an automatic search that gave the global minimum value of 1.206.Considering those locations where the minimum surfaces intercept helps to demarcate the zones that require reinforcement.

The global minimum safety factor was divided by 25 slices (Figure 7. 1c); and the force and moment equilibrium was calculated based on the assumptions of this method which satisfied the horizontal force and moment part of the static equilibrium but not the vertical force equilibrium (Figure 7.3).

7.2.1.1.2 Bishop simplified method

In Bishop Simplified method the minimum surfaces falls in range of factor of safety 1.481-1.5 and global minimum having FoS=1.481, where the dominant minimum surfaces passes through geotechnical layer of IIb (sandy clay with gravel and silty sand), having cohesion c=16, however the global minimum surface transects layer IIa (clayey sand, compact sandy clay with gravel), having lower cohesion c=13 following lower cohesive layer than observed in Ordinary method.

69

Slice Number: 7 (bishop

simplified)

Factor of Safety: 1.48144

Slice Weight: 52.4133 kN

Shear Strength: 28.7279 kPa

Base Shear Force: 12.9763

kN

Pore Pressure: 12.3933 kPa

Base Normal Force: 53.8795

kN


Mobilized Shear Resistance:

19.3919 kPa

Left Side Normal Force:

84.1003 kN

Right Side Normal Force:

102.133 kN

Resultant Seismic Force: 0

kN

It can be observed that the dominant force that prevails on

the slice is Left and Right Normal Forces that accounts 85kN

and 102KN respectively. Furthermore the weight of the slice

and the uplift pore pressure has also determining effect. The

detailed results are shown in (Appendix VIII. 1).These forces

are resolved in such a way that the resultant forces can be

calculated for the driving and resisting forces to ease the

determination of the factor of safety, FoS= 481.13919.19

7279.28

Note that, Since the project site was aseismic, resultant

seismic loading was found to be zero.

The minimum values occurred at x≈2m and x≈17.5m(Figure 7. 2d); and the surfaces

connecting these points made minimum surfaces while the critical minimal surfaces were found to give the global minimum value of, FoS=1.481.

Usually for circular failure surfaces, the simplified Bishop’s method is strongly recommended for use (Abramson, L. W., et.al.,1995).However the methods that mimic the

Figure 7. 3 Bishop’s method of interslice forces resolution of slices for model section-A.

70

condition of the embankment and site should be verified as the best analysis method rather than giving the generalization to all circular failures elsewhere.

Janbu Simplified: Global Minimum FoS=1.293

(a)

(b)

(c)

(d)

Figure 7. 4 Janbu’s method of analysis of model section-A ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface.

7.2.1.1.3 Janbu simplified method

In Janbu Simplified method the minimum surfaces falls in range of factor of safety 1.293-1.5 and global minimum having FoS=1.293, where the dominant minimum surfaces and a global minimum surface pass through geotechnical layer of IIb (sandy clay with gravel and

71

silty sand), having cohesion c=16, which follow the same layer of the foundation as observed in Ordinary method.

The global minimum surfaces were also divided into slices to resolve the forces acting on individual slices in order to calculate the driving and resisting forces to ease the computation of the factor of safety in such a way that the above methods performed.

The minimum values occurred at x≈0m and x≈17m(Figure 7. 4d); and the surfaces

connecting these points made minimum surfaces while the critical minimal surface was found and give the global minimum value of 1.293. Janbu simplified method satisfies the vertical and horizontal force equilibrium however it did not satisfy moment equilibrium (Table 5. 1).

Spencer: Global Minimum FoS=1.455

(a)

(b)

(c)

(d)

Figure 7. 5 Spencer method of analysis of model section-A ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface.

72

7.2.1.1.4 Spencer method

In Spencer method the minimum surfaces falls in range of factor of safety 1.455-1.5 and global minimum was found, FoS=1.455, where the dominant minimum surfaces pass through geotechnical layer of IIb (sandy clay with gravel and silty sand), having cohesion c=16, however the global minimum surface transects layer IIa (clayey sand, compact sandy clay with gravel), having cohesion c=13 which followed the same trend of layer like observed in Bishop method.

The minimum values occurred at x≈2m and x≈17.2m (Figure 7. 5d); and the surfaces

connecting these points made minimum surfaces while the critical minimal surfaces were found to be a value of 1.455. Spencer method satisfies all vertical, horizontal force and moment equilibrium (Table 5. 1).

GLE/Morgenstern-Price: Global Minimum FoS=1.451

(a)

(b)

(c)

(d)

Figure 7. 6 GLE/Morgenstern method of analysis of model section-A ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface.

73

7.2.1.1.5 GLE/Morgenstern method

In GLE/Morgenstern method the minimum surfaces falls in range of factor of safety 1.451-1.5 and global minimum of 1.451, where the dominant minimum surfaces passes through geotechnical layer of IIb (sandy clay with gravel and silty sand), having cohesion C=16, however the global minimum surface transects layer IIa (clayey sand, compact sandy clay with gravel), having cohesion C=13 which followed the same trend of weaker layer like observed in Bishop and Spencer methods. The minimum values occurred at x≈2m and x≈17.5m(Figure 7. 6d); and the surfaces

connecting these points made minimum surfaces while the critical minimal ones was found to give the global minimum value of 1.451.Considering those locations where the minimum surfaces intercept helps to delineate the zones that require reinforcement. GLE/Morgenstern method satisfies all vertical, horizontal force and moment equilibrium (Table 5. 1).

It can be seen in (Table 7. 1) that the calculated factors of safety obtained from Bishop, Spencer and GLE/Morgenstern methods are generally similar however Ordinary and Janbu methods -15% than other values. In this case, Spencer’s method yields higher FoS than Fellenius and Janbu methods. Interestingly enough, the factor of safety calculated using Bishop’s modified method, which only satisfies the moment equilibrium, consistently similar to those computed using Spencer and GLE/Morgenstern’s method that satisfies both moment and force equilibriums. The Fellenius and Janbu methods generally resulted lower factor of Safety than Bishop and Spencer.

Though the admissible factor of safety value is unity, the required value of the stability index was assumed in accordance with the Polish regulations referring to the designing of road embankments of public roads, that is FoSreq = 1.50 (The Decree of the Minister of Transportation and Water Management:Dz. U. Nr 43/1999).

For slopes with significant forces due to reinforcement, the direction of the inclination of the interslice force could be different from usual direction (Duncan, J. M., & Wright, S. G.,2005).In these research reinforcements are used which are likely to have significant forces on the slices of the embankment to produce interslice/shear forces. Hence more flexible equilibrium procedures are considered with Spencer and GLE/Morgenstern procedures, which need to be considered for this study.

Moreover, Spencer and GLE/Morgenstern have satisfied all static equilibrium conditions which gave marginal value of FoS, 1.45≈1.5 which is mostly recommended for Public roads;

however it still needs some requirement to ensure the stability of the highway.

7.2.1.2 Model section-B FoS assessment In case of model section B, where geogrids and geomattress were used as supporting

material most of the minimum surfaces were passing through the weak layers beyond the geogrid reinforcement (for all analysing methods), however factor of safety of this model was higher and the critical slip surfaces were deepened than model section-A. The range of factor of safety found variable (Table 7. 1) as the same assumptions (Table 5. 2) that held in the previous model were kept entirely the same among each analysing methods;

74

Ordinary/Fellenius: Global Minimum FoS=1.302

(a)

(b)

(c)

(d)

Figure 7. 7 Ordinary method of analysis of model section-B ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface.

7.2.1.2.1 Ordinary method

In Ordinary method analysis of the second model the minimum surfaces falls in the range of factor of safety 1.302-1.25 and global minimum value of having FoS=1.302, where the dominant minimum surfaces and global minimum surface pass through geotechnical layer of IIb (sandy clay with gravel and silty sand), having cohesion c=16 which followed the same trend as the previous model though the slip surface was deepened.

In addition, the factor of safety gave variable values along slope surface from left to right boundaries where the failure surfaces were assumed to intercept in order to search the

75

minimum surfaces, and the minimum values occurred at x=0m and x≈20-22m(Figure 7. 7d);

which have extended a few meters distance than the previous model; and the surfaces connecting those points made minimum surfaces while the critical minimal surfaces were found to give the global minimum value of 1.302.Considering those locations where the minimum surfaces intercept helps to demarcate the zones that require reinforcement.

The global minimum safety factor was divided by 25 slices (Figure 7. 7c); and the force and moment equilibrium was calculated based on the assumptions of this method which satisfied the horizontal force and moment equilibrium of the static equilibrium condition (Table 5. 1).

Bishop Simplified: Global Minimum FoS=1.499

(a)

(b)

(c)

(d)

Figure 7. 8 Bishop’s method of analysis of model section-B ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface.

76

7.2.1.2.2 Bishop simplified method

In Bishop Simplified method the minimum surfaces falls in range of factor of safety 1.499-1.5 and global minimum of having FoS=1.499, where the dominant minimum surfaces and global minimum surface pass through geotechnical layer of IIb (sandy clay with gravel and silty sand), having cohesion c=16, which followed the less cohesiveness layer like observed in Ordinary method though the critical slip surface deepened due to the addition of geomatress as reinforcement unlike the Bishop method in Model section-A and lower height of section B.

The minimum values occurred at x≈0m and x≈20m (Figure 7. 8d); which have extended a

few meters distance than the previous model and the surfaces connecting those points made minimum surfaces while the critical minimal surfaces were found to give the global minimum value of FoS=1.499.

Slice Number: 7 (bishop simplified)



Base Shear Force: 22.3245 kN


Base Normal Force: 92.7375 kN

Left Side Normal Force: 137.129

kN

Right Side Normal Force: 181.287

kN

Resultant Seismic Force: 0 kN


Mobilized Shear Resistance:

22.3508 kPa

Figure 7. 9Bishop’s method of interslice forces resolution of slices for model section-B.

It can be observed that the dominant force that prevails on the slice is on the left and right side of the slice that accounts 137.129kN and 181.287KN respectively which had considerable increment than observed in the Bishop analysis of the previous Model section-A ,which is due to additional reinforcement. Furthermore the weights of the slice and the uplift pore pressure have also determining effect on the FoS. The detailed results are shown in Appendix VIII. 1.These forces are resolved in such a way that the resultant forces can be

77

calculated for the driving and resisting scenarios to ease the calculation of the factor of

safety, FoS= 499.13508.22

498.33 .Note that, since the project site was aseismic, resultant seismic

loading was found to be zero.

Usually for circular failure surfaces, the simplified Bishop’s method is strongly recommended for use (Abramson, L. W.,et.al.,1995).However the methods that mimic the embankment and foundation condition of the site should be verified as the best analysis method rather than giving the generalization to all circular failures elsewhere.

Janbu Simplified: Global Minimum FoS=1.319

(a)

(b)

(b)

(d)

Figure 7. 10 Janbu method of analysis of model section-B ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface.

78

7.2.1.2.3 Janbu simplified method

In Janbu Simplified method the minimum surfaces falls in range of factor of safety 1.319-1.5 and global minimum of FoS=1.319, where the dominant minimum surfaces and a global minimum surface pass through geotechnical layer of IIb (sandy clay with gravel and silty sand), having cohesion c=16, which passes through the less cohesive layer like observed in Ordinary and Bishop methods.

The minimum values occurred at x≈0m and x≈20m (Figure 7. 10d); which have extended

a few meter distances than the previous model and the surfaces connecting these points made minimum surfaces while the critical minimal surfaces were found in an automatic search that gave the global minimum value of FoS= 1.293. Janbu simplified method satisfies the vertical and horizontal force equilibrium however it did not satisfy moment equilibrium (Table 5. 1).

Spencer: Global Minimum FoS=1.469

(a)

(b)

(c)

(d)

Figure 7. 11 Spencer method of analysis of model section-B ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface.

79

7.2.1.2.4 Spencer method

In Spencer method the minimum surfaces falls in range of factor of safety 1.469-1.5 and global minimum having FoS=1.469, where the dominant minimum surfaces and global minimum surface pass through geotechnical layer of IIb (sandy clay with gravel and silty sand), having cohesion c=16, which follows the same trend in the lower cohesiveness layer like observed in Ordinary, Bishop and Janbu methods.

The minimum values occurred at x≈0m and x≈20m (Figure 7. 11d); which have extended

few meters distance than the previous model and the surfaces connecting these points made minimum surfaces while the critical minimal surfaces were found to gave the global minimum value of FoS=1.469. Spencer method satisfies all vertical, horizontal force and moment equilibrium (Table 5. 1).

GLE/Morgenstern-Price: Global Minimum FoS=1.473

(a)

(b)

(c)

(d)

Figure 7. 12 GLE/Morgenstern method of analysis of model section-B ;(a)Global minimum surfaces (b) All minimum surfaces(c)Global minimum surface in slice division (d) FoS along the slope surface.

80

7.2.1.2.5 GLE/Morgenstern method

In GLE/Morgenstern method the minimum surfaces falls in range of factor of safety 1.473-1.5 and global minimum having FoS=1.473, where the dominant minimum surfaces and the global minimum surface pass through geotechnical layer of IIb (sandy clay with gravel and silty sand), having cohesion c=16, following the lower cohesive layer like observed in Spencer, Ordinary, Bishop and Janbu methods. The minimum values occurred at x≈0m and x≈20m (Figure 7. 12); which have extended a

few meters distances than the previous model and the surfaces connecting these points made minimum surfaces while the critical minimal surfaces were found to give the global minimum value of FoS= 1.473. GLE/Morgenstern method satisfies all vertical, horizontal force and moment equilibrium (Table 5. 1).

It can be seen in Table 7. 1, that the calculated factors of safety obtained from Bishop, Spencer and GLE/Morgenstern methods are generally similar however Ordinary and Janbu methods have≈-12% than other values. In this case, Spencer’s method yields higher

FoS than Fellenius and Janbu methods. Interestingly enough, the Factor of Safety calculated using Bishop’s modified method, which only satisfies the moment equilibrium, consistently similar to those computed using Spencer and GLE/Morgenstern’s method that satisfies both moment and force equilibriums. The Fellenius and Janbu methods generally result in lower factor of safety than Bishop and Spencer. In the second model section-B was noticed that for all analysis methods the range of FoS values increases and the critical slip surfaces followed longer perimeter of circular failure surface (deepened) than are than model section-A though in both cases the critical surface occurs beyond the geogrid .Those imbalances of result between the two models happened due to the additional reinforcement and height difference.

Though the admissible factor of safety value is unity, the required value of the stability index was assumed in accordance with Polish regulations referring to the designing of road embankments of the public roads, that is FoSReq = 1.50 (The Decree of the Minister of Transportation and Water Management:Dz. U. Nr 43/1999).

For slopes with significant forces due to reinforcement, the direction of the inclination of the interslice force could be different from usual direction (Duncan, J. M., & Wright, S. G.,2005). In this study reinforcement are used and are likely to have significant forces on the slices of the embankment to produce interslice/shear forces. Hence more flexible equilibrium procedures are considered with Spencer and GLE/Morgenstern procedures, which needs to be considered for this study.

Moreover, Spencer and GLE/Morgenstern has satisfied all static equilibrium conditions which gave marginal value of FoS, 1.46≈1.5 which is mostly recommended for Public roads;

however it still needs some requirement to ensure the stability of the highway.

81

8. Chapter 8 Conclusion and Recommendation

8.1 Conclusion The assessment of slope stability in road engineering is indispensible for the evaluation

of their safe maintenance. The values of the stability analysis i.e. the factor of safety was found diverse for the same problem, in case of both sections treated in this research on the basis of the type of methods used in the analysis of each model.

Understanding the process that can lead to the instability of slope is quite a complex task asking for a very long and exhaustive investigation of the area. It could even get worse if lack of primary data is there. But efforts were put to check the susceptibility of failures by limit equilibrium analysis as a preliminary study which narrows down this problem and helps to give an invaluable aid in understanding the stability of the road. Based on the analysis the following conclusions were drawn;

In both models analysis, five methods were used each having different assumptions (Table 5. 1), however it is recommended to use the methods that satisfy both force and moment equilibrium to minimise the error in calculating the factor of safety of the slope.

From the analysis it is shown that section B has more FoS than model section A and the critical surfaces are deepened and passed beyond the geogrid support; so to meet the required FoSReq=1.5 for public roads (Regulations for public Roads: Dz. U. Nr 43/1999), slight modification in reinforcement is needed in both cases.

Results from two model sections cannot be reliable enough for the stability assessment of the total length of the road. In addition to that generalization of the stability analysis value obtained from two analysed sections cannot be applied for the whole road section.

8.2 Recommendation The present study has a significant implication for the stability of the A-8 Motorway in a

preliminary scale. However, further stability analysis of limit equilibrium methods should be undertaken in other sections having lower bearing capacity if necessary data is available. This helps to demarcate the critical segments that raise negative influence on the proper functioning of the road though tedious work. Furthermore based on the analysis and conclusion, the following points are recommended:

Analysis of selected sections shows an increment in the FoS from Model section-A to

Model section-B, which is due to an additional supports rock mattress used and

lower height of section B, hence only slight modification (since marginally stable) in

reinforcement could be needed to meet the required FoSReq=1.5 (The Decree of the

Minister of Transportation and Water Management regarding technical conditions

required of public roads and their location. Dz. U. Nr 43/1999 r.):

Extending the length of the Geogrids or using additional Geogrid for both Model section-A and Model section-B.

Lowering the side slope ratio for instance 1:2 if feasible. The gentler slopes are the more resistant to settlement and lateral movement in both the embankment and foundation (Dupont B., & Allen D.L., 2002).

Lowering the height of the embankment might stabilize the slope section if feasible to do so.

82

Rock Mattresses and geotextiles can be used in sections where intermediate bearing capacity of foundation is encountered. In addition to that other remedial measure should be taken depending on the compressibility of the foundation conditions, as the geological conditions basically vary in spatial manner.

Reinforcing using micro piles in sections where there are compressible soils may prove costly but would be reliable to ensure the long-term stability of the road.

Although the analysis of Model sections- A and B both manifest marginally stable condition under different conditions, there might be chances of instability in the long term due to the integral effect of the shallow groundwater level and clayey content of foundation condition. As a result seasonal monitoring of groundwater should be carried out to ensure the stability of the section.

The factor of safety approach utilizes the average values of parameters and thus can use erroneous values of parameters either by underestimating or overestimating; which might affect the result of the stability analysis. Hence probabilistic analysis approach is recommended provided the required data is available.

Despite the powerful ability to analyze the stability condition, limit equilibrium analysis has limitation, so other techniques like FEM which incorporates deformation/stress analysis of soil should be performed to get sound result.

The present study was made to conduct the preliminary assessment on analyzing the stability of selected portions of the road sections. For example, (Zonberg et al, 1998) have shown through centrifuge tests that limit equilibrium analyses provide valid indications of factor of safety and failure mechanisms for reinforced slope. Hence it is recommended that necessary laboratory and field observations must be undertaken in a systematic manner before implementing the recommendations made through the present study.

83

References

Abramson, L. W., & others. (1995). Slope Stability and Stabilization Methods. New York: John Wiley

&sons, INC.

Abramson, L. W., Thomas, L. S., Sharma, S., & G.M. (2001). Slope Stability and Stabilization Methods.

New York: Boyce John Wiley & Sons.

Allen, D. L., & Dupont, B. (2002). Movements and settlement of Highway Bridge Approaches.

Kentucky: Kentucky Transportation Centre.

Bache, D., & I.A, M. (1984). Vegetation in Civil and Landscape Engineering. London: Granda.

Barends, F. B. (2009). An Introduction to GeoEngineering: Soil mechanics application.4th ed. Delft:

Deltares & TUDelft.

Batog, A. e. (2009). New Approach to Assessment of Road Embankment stability. Studia Geotechnica

et Mechanica,Vol.XXXI , No.3.

Bell, F. G. (1996). Lime stabilization of clay minerals and soils. Elsevier:Journal of Engineering Geology

, 223-237.

Bishop, A. (1955). The use of Slip Circle in the Stability Analysis of Earth Slopes. Geotechnique , 5-17.

BMPS. (n.d.). Slope stabilization and stability of cuts and Fills. Retrieved March 20, 2010, from

http://ntl.bts.gov/lib/24000/24600/24650/Chapters/M_Ch11_Slope_Stabilization.pdf

Bonaparte, R., & Christopher, B. R. (1987). Design and Construction of reinforced embankments over

weak foundations. Transportation Research Board, National Research Council. , 26-39.

Bromhead, E. N. (1992). The Stability of Slopes. New York: Blackie.

Cetin, H., Fener, M., & Gunaydin, O. (2006). Geotechnical properties of tire-cohesive clayey soil

mixtures as a fill material. Science Direct , 110-120.

Chen, W. F. (1975). Limit Analysis and Soil Plasticity. Developments in Geotechnical Engineering,7.

Amsterdam: Elsevier Scientific Publishing Company.

Chen, W., & Liew, J. R. (2002). The Civil Engineering Hand Book:2nd ed.

London,NewYork,Washington: CRC Press.

Cheng, Y., & Lau, C. (2008). Slope Stability Analysis and Stabilization: New Methods and Inslight.

London: Book Now Ltd.

Chowdhury, R. (1987). Practical Aspects of Probabilistic Studies for Slopes. In Soil Slope Instability

and Stabilization(Sydney Nov 3-Dec-2,eds.B.F.Walker and R.Fell) , 299-304.

Coates, D. F. (1977). Pit Slope Manual Chapter 5-Design CANMET REPORT. Toronto: CANMET

(Canada Centre for Mineral and Energy Technology).

Coduto, D. P. (1998). Geotechnical Engineering: Principles and Practices. New Jersey: Prentice Hall.

84

Colin Jones, J. J. (1996). Earth reinforcement and soil structures. Newcastle: Thomas Telford

publishing and ASCE press.

Cooper, A. H., & Jones, J. C. (2005). Road construction over voids caused by active gypsum

dissolution, with an example from Ripon,North Yorkshire England. Environ Geol , 384-394.

Deschamps, R., Hynes, C., & Bourdeau, P. h. (1999). Embankment Widening Design Guidelines and

Construction Procedures. Indiana: Indiana Department of Transportation and the U.S. Department of

Transportation, Federal Highway Administratio.

DoLIDAR. (2009). Elements of Road Formation. Retrieved March 1, 2010, from Technical

Specifications: http://www.ruralinfras.gov.np/downloads/Technical%20manual%20voll%202.pdf

Duncan, J. M. (1996). State of the art:Limit equilibrium and finite-element analysis of slopes. ASCE

Journal of Geotechnical Engineering , 577-596.

Duncan, J. M., & Wright, S. G. (2005). Soi Strength and Slope Stability. New Jersey: John Wiley &Sons,

INC.

Dupont, B., & Allen, D. L. (2002). Movements and settlements of Highway Bridge Approaches.

Kentucky: Kentucky Transporation Center.

Elżbieta, S. S., & Waldemar, T. (2004). Effect of Mining Deformations on Stability of Transport

Embankments. Studia Geotechnica et Mechanica, Vol. XXVI , 3-4.

Eren, S., & Filiz, M. (2009). Comparing the conventional soil stabilization methods to the consolid

system used as an alternative admixture matter in Isparta Darıdere material. Construction and

Building materials:Elsevier Science Direct , 2473-2480.

F, M. (2007). Numerical Analysis to define the Optimum Inclination of Embankment Slopes. 4th

international SIIV congress (pp. 1-12). Palermo: University of Cagliari.

Ferber, V., Auriol, J., & Cui Jea, Y. J. (2008). On the swelling potential of compacted high plasticity

clays. Elsevier:Engineering Geology , 200-210.

FHWA. (2005, August). Retrieved March 28, 2010, from Standard and specifications for riprap slope

protection:

http://www.co.suffolk.ny.us/stormwater/Construction%20BMPs/Construction%20BMPs/Permanent

%20Structural%20Measures/Riprap%20Slope%20Protection.pdf

Franklin, J. A., & M., B. D. (1991). Rock Engineering Applications. New York: McGraw-Hill, Inc.

GCO. (1990). Review of Design Methods for Excavations. Retrieved April 4, 2010, from Earth pressure

due to Compaction. GCO Publication No.1/90:

http://www.cedd.gov.hk/eng/publications/manuals/doc/eg1_chapter6.pdf

Hadjigeorgiou, J., Kyriakou, E., & Papanastasiou, P. (2003). A Road Embankment Failure near Pentalia

in SouthWest Cyprus. International Symposium on Stability of Rock Slopes in Open Pit Mining and

Civil Engineering (pp. 1-11). Cyprus: The South African Institute of Mining and Metallurgy.

85

Haliburton, T. A., Anglin, C. C., & Lawmaster, J. D. (1978). Testing of geotechnical fabric for use as

reinforcement. Geotechnical Testing Journal , Vol.1, ASTM , 203-212.

Hoek, E., & J.W., B. (1981). Rock Slope Engineering. London: Institution of Mining and Metallurgy.

Hungr, O. F., M, S., & P.M, B. (1989). Evaluation of A Three-Dimensional Method of Slope Stability

Analysis. Canadian Geotechnical Journal,26,No.4 , 679-686.

John, B., & E, H. (2008). MDT Geotechnical Manual. Retrieved February 27, 2010, from Roadway

Slopes and Embankments:

http://www.mdt.mt.gov/other/materials/external/geotech_manual/Chapter13.pdf

Juang, C., Y-Y, J., & D-H, L. (1998). Stability Analysis of Existing Slops Considering Uncertainity.

Engineering Geology, 49 , 111-122.

Kehagia, F. (2009). Resourses, Conservation and Recycling:A successful Pilot Project demonstrating

the re-use potential of bauxite residue in Embankment construction. Elsevier , xxx-xxx.

Kumar, S., & Patil, C. (2006). Estimation of resource savings due to fly ash utilization in road

construction. Elsevier Science Direct , 125-140.

Lam, L., & D.G., F. (1993). A General Limit Model for Three-Dimensional Slope Stability. Canadian

Geotechnical Journal,30,No.4 , 905-919.

Laska, W. (1992). Proper Drainage for weep holes. Retrieved May 5, 2010, from Weep hole details:

ftp://imgs.ebuild.com/woc/M920313.pdf

Léger, P. (2006). Retrieved April 1, 2010, from Rock fill Buttresses:

http://www.for.gov.bc.ca/hfd/pubs/docs/Lmh/Lmh18-09.pdf

Li, A. e. (2008). Seismic rock slope stability charts based on limit analysis methods. ScienceDirect ,

135-148.

Masse, F., pearlman, S., & Bloomfield, R. (2003). Support of MSE walls and reinforced embankments

using ground improvement. Retrieved May 3, 2010, from Wire face MSE wall: http://www.dgi-

menard.com/Support%20of%20MSE%20walls%20-%20final%20062507.pdf

Masuya, H., Amanuma, K., & Nishikawa, Y. (2009). Basic Rock fall Simulation with consideration of

vegetation and application to protection measure. Natural hazards and Earth system Sciences ,

1835-1843.

Mayne, P. W., Kulhawy, & Fred, H. (1982). Ko-OCR Relationships in Soil. Journal of Geotechnical

Engineering Division, Vol.108,No.Sm5 , 63-91,ASCE.

Millard, R. S. (1993). TRL state of the Art review No.9:Road building in tropics. London:

H.M.Stationary Office.

Mostyn, G., & J.C, S. (1987). Methods of Stability Analysis.In Slope stability and Stabilization.

Rotterdam: A.A.Balkema.

86

Mostyn, G., & K, S. L. ( 1993). Probabilistic Slope Analysis-State-of-Play. In Probabilistic Methods in

Geotechnical Engineering. Proc. (Canberra, ) (pp. 89-109). Rotterdam: A A.Balkema.

Nash, D., K.S., R., & M.G.Anderson. (1987). A Comparative Review of Limit Equlibrium Methods of

Stability Analysis.In Slope Stability.Geotechnical Engineering and Geomorphology. Chicheste: John

Wiley &Sons.

Ogunsanwo, O. (1989). Some Properties of a Sedimentary Laterite Soil as Engineering Construction.

BULLETIN of the International Association of ENGINEERING GEOLOGY.No 39, Paris , 1-5.

Oka, Y., & T., H. (1990). System Reliability of Slope Stability. J.Geotechnical Eng., 116, No 8 , 1185-

1189.

Pantelidis, L. (2008). Stability against Translational Failure of Non-cohesive Embankments Founded

on Natural Slopes. The 12th International Conference of International Association for Computer

Methods and Advances in Geomechanics (pp. 1-6). Goa,India: Dept. of Civil Engineering, Aristotle

University of Thessaloniki, Greece.

Pubrick, M., & Ayres, D. (1956). Uses of aerated cement grout and mortar in stabilizing of slips in

embankments, large scale tunnel works and other works. Institution of Civil Engineers, part II, Vol.5,

No.1.

REED. (2003). Shotcrete. Retrieved April 1, 2010, from Retaining walls constructed with wet or dry

Shotcrete: http://www.reedpumps.com/retainingwalls.htm

Robinson, R., & Thagesen, B. (2006). Road Engineering for Development.2nd ed. London and

NewYork: CPI Antony Rowe,Eastbourne.

RocScience. (2006). Geomechanics software solutions used worldwide by geotechnical engineers.

Retrieved from http://www.rocscience.com/

S.A, A., & S.A, A. (2003). Embankments. Retrieved March 15, 2010, from Embankments Egnatia

Highway, Northern Greece: http://www.omikronkappa.gr/22-Stuff/04-Erga/04-01-Ektelesmena/04-

01-02en-EPIXOMATA.pdf

Sage, R. (. (1976). Pit Slope Manual Chapter 1-summary. CAN. MET (Canada Centre for Mineral and

Energy Technology):CANMET REPORT 76-22 , 65.

Schothorst, C. (1982). Drainage and behaviour of peat soils, Proc. Symp. Peatlands below sealevel.

ILRI publication nr. 30,Wageningen .

Seed, H. (1979). Considerations in the earthquake-resistant design of earth and rock fill dams.

Geotechnique .

Seo, J. B. (2003). The Bump at the end of the Bridge: An Investigation. Texas: Phd Dissertation, Texas

A&M University.

Sjoberg, J. (1999). Analysis of large scale rock slopes. Lulea: Phd Dissertation,Lulea University of

Technology.

87

Skarkynska, K. M. (1995). Reuse of Coal Mining Wastes in Civil Engineering: Utilization of Milestone.

Elsevier Science , 83-126.

Spencer, E. (1967). A method of Analysis of the stability of Embankments Assuming Parallel Inter-

Slice Forces. Geotechnique, 17 , 11-26.

Stacey, T. (1968). Stability of Rock Slopes in Open Pit Mines. National Mechanical Engineering

Research Institute. Council for scientific and Industrial Research 66p. Pretoria, South Africa: CSIR

Report MEG 737.

Su, Hsieh, H., Prysock, & R.H. (1971). Secondary compression in Embankment Foundations. California:

Department of Transportation, Federal Highway Administration.

Sugita, H., Sasaki, T., & Nakajima., S. (2007). Damage Investigation of Road Embankment. Soil

Mechanics and Dynamics Research , 1-11.

The Decree of the Minister of Transportation and Water Management regarding technical conditions

required of public roads and their location. Dz. U. Nr 43/1999 r.

Thompsett, D. J., Walker, A., Radley, R. J., & Grieveson, B. M. (1995). Design and construction of

expanded polystyrene embankments: Practical design methods as used in the United Kingdom.

Elsevier Science , 403-411.

TRH, 9. (1982). Construction for Road Embankments. Retrieved March 15, 2010, from

http://www.nra.co.za/content/Blogin/11.pdf

TRL. (1993). A guide to the structural design of bitumen-surfaced roads in tropical and sub-tropical

countries. Crowthrone: Overseas Road Note 31,4th edition: Transport Research Laboratory.

Wantanbe, T., Okimura, T., & Torii, N. (2002). Risk Evaluation Method for Road Slopes. Japan: Kobe

University: Graduate school of Science and Technology.

Witteveen, G., & Bos. (2001). Regional Teaching Program 2001:General properties & road problems

G3 - V1. MoU on soft soil Engineering (pp. 1-25). Republic of Indonesia &: TOT-G3-L2.

Wooten, R., & Latham, R. (2006, August 31). North Carolina Geological survey Report. Retrieved

March 14, 2010, from Embankment Failure: Debris Flow at the Cascades Development.:

http://www.geology.enr.state.nc.us/Landslide_Info/pdfs/Eaglenest_Ridge_Debris_Flow_Final.pdf

Wright, P. H., & Parquette, R. J. (1987). Highway Engineering.5th ed. New York: John Wiley &sons,

INC.

Xiao-ming, H., & Hao, W. (2009). Comparison between responses of reinforced and unreinforced

embankments due to road widening. Springer , 857-864.

Yu, H.S, R, S., S.W, S., & J.M, K. (1998). Limit Analysis versus Limit Equilibrium for slope stability.

Journal of Geotechnical and Geoenvironmental Engineering.124,No.1 , 1-11.

Zonberg, J., Sitar, N., & Mitchell, J. (1998). Limit equilibrium as a basis for design of geosynthetic

reinforced slopes, ASCE. Jounral of Geotechnical and Geoenvironmental Engineering , 670-683.

88

Appendices

Appendix-I

Appendix I. 1 A 1:100 structural section of the main sequence of the A-8 motorway from Km 22+132.00 to Km 24+000.00 for (GEOTECHsp.zo.o project office, 2009).

89

Appendix-II

Appendix II. 1 Explanation of symbols and characters used in research documents, substratum according to the standard PN-86/B-02480.

90

Appendix-III

Appendix III. 1 Key to section of A-8 motorway Wroclaw bypass

91

Appendix-IV

Appendix IV. 1 1:500/1:1000 Engineering geological cross sections.

Part I

92

Part II

93

Part III

94

Appendix-V

Appendix V. 1 Documentation of the test wells of A-8 motorway Wroclaw bypass.

Borehole-1

95

Borehole-2

96

Borehole-3

97

Borehole-4

98

Borehole-5

99

Borehole-6

100

Borehole-7

101

Borehole-8

102

Borehole-9

103

Appendix VI

Appendix VI. 1Material and reinforcement strength property entry of data used for the analysis

I-Material properties

105

II-Reinforcement properties

Appendix-VII

Appendix VII. 1Full section model of an A-8 motorway embankment with material and reinforcement strength property

106

Appendix-VIII Appendix VIII. 1 Slide analysis information

I-Section A

Project Settings

Project Title: SLIDE - An Interactive Slope

Stability Program

Failure Direction: Right to Left

Units of Measurement: SI Units

Pore Fluid Unit Weight: 9.81 kN/m3

Groundwater Method: Water Surfaces

Data Output: Standard

Calculate Excess Pore Pressure: Off

Allow Ru with Water Surfaces or Grids: Off

Random Numbers: Pseudo-random Seed

Random Number Seed: 10116

Random Number Generation Method: Park

and Miller v.3

Analysis Methods

Analysis Methods used:

Bishop simplified

GLE/Morgenstern-Price with interslice force

function: Half Sine

Janbu simplified

Ordinary/Fellenius

Spencer

Number of slices: 25

Tolerance: 0.005

Maximum number of iterations: 50

Material: Ib

Strength Type: Mohr-Coulomb

Unit Weight: 19.5 kN/m3

Cohesion: 0 kPa

Friction Angle: 31 degrees

Water Surface: Water Table

Custom Hu value: 1

Material: Id



Surface Options

Surface Type: Circular

Search Method: Grid Search

Radius increment: 10

Composite Surfaces: Disabled

Reverse Curvature: Create Tension

Crack

Minimum Elevation: Not Defined

Minimum Depth: Not Defined

Loading

1 Distributed Load present:

Distributed Load Constant Distribution,

Orientation: Vertical, Magnitude: 25

kN/m2

Material Properties

Material: Embankment


Unit Weight: 20 kN/m3

Cohesion: 0 kPa


Water Surface: None

Material: Ia



Cohesion: 2 kPa



Custom Hu value: 1

Material: IIa



Cohesion: 13 kPa



107

Cohesion: 0 kPa



Custom Hu value: 1

Material: IIc Strength Type: Mohr-Coulomb Unit Weight: 22 kN/m3 Cohesion: 37 kPa Friction Angle: 21 degrees Water Surface: Water Table Custom Hu value: 1

Custom Hu value: 1

Material: IIb



Cohesion: 16 kPa



Custom Hu value: 1

Material: Concrete Strength Type: Mohr-Coulomb Unit Weight: 23 kN/m3 Cohesion: 20 kPa Friction Angle: 45 degrees Water Surface: None

Support Properties

Support: GeoGrid

GeoGrid

Support Type: GeoTextile

Force Application: Passive

Force Orientation: Parallel to

Reinforcement

Anchorage: Slope Face

Shear Strength Model: Linear

Strip Coverage: 100 percent

Tensile Strength: 50 kN/m

Pullout Strength Adhesion: 5 kN/m2

Pullout Strength Friction Angle: 41

degrees

Global Minimums

Method: ordinary/fellenius

FS: 1.206260

Center: 8.259, 19.726

Radius: 10.125

Left Slip Surface Endpoint: 0.511, 13.208

Right Slip Surface Endpoint: 18.349, 18.886

Resisting Moment=6991.7 kN-m

Method: bishop simplified

FS: 1.481440

Center: 7.190, 21.881

Radius: 10.951

Left Slip Surface Endpoint: 1.977,

12.251

Right Slip Surface Endpoint: 17.718,

18.868


108

Driving Moment=5796.16 kN-m

Method: spencer

FS: 1.454600

Center: 7.190, 21.881

Radius: 10.951





Resisting Horizontal Force=645.669 kN

Driving Horizontal Force=443.882 kN


Method: janbu simplified

FS: 1.293050

Center: 8.259, 19.726

Radius: 10.125


13.208


18.886



Method: gle/morgenstern-price

FS: 1.451360

Center: 7.190, 21.881

Radius: 10.951


12.251


18.868





Components of Bishop slice method Analysis of section-A.



Base Friction Angle: 13 degrees

Base Cohesion: 13 kPa

Slice Width: 0.666181 m

Base Length: 0.66916 m

Angle of Slice Base: -5.40802 degrees


Frictional Strength: 15.7279 kPa

Cohesive Strength: 13 kPa


Mobilized Shear Resistance: 19.3919 kPa



Matric Suction: 0 kPa

Excess Pore Pressure: 0 kPa

Initial Pore Pressure: 12.3933 kPa

Left Side Normal Force: 84.1003 kN

Left Side Shear Force: 0 kN

Left Side Resultant Force: 84.1003 kN

Left Side Force Angle: 0 degrees

Right Side Normal Force: 102.133 kN

Right Side Shear Force: 0 kN

Right Side Resultant Force: 102.133 kN

Right Side Force Angle: 0 degrees

Horizontal Seismic Force: 0 kN

Vertical Seismic Force: 0 kN


109

Base Normal Stress: 80.5181 kPa

Effective Normal Stress: 68.1248 kPa


Positive Pore Pressure: 12.3933 kPa

M-Alpha: 0.980821

Y coordinate - Bottom: 11.0153 m

Y coordinate - Top: 14.8138 m

List of All Coordinates

Water Table

0.000 12.208

31.531 12.408

Search Grid

-0.293 19.726

20.018 19.726

20.018 43.426

-0.293 43.426

Material Boundary

0.000 10.808

31.531 10.908

Material Boundary

0.000 5.808

0.004 5.808

Material Boundary

3.544 13.208

31.531 13.208

Material Boundary

0.0 12.008

31.531 11.608

Material Boundary

7.370 15.901

16.445 15.901

Distributed Load

12.257 18.713

29.528 19.205

Material Boundary

0.000 3.208

3.874 3.208

Material Boundary

0.000 2.008

10.508 2.008

10.515 2.008

Material Boundary

3.585 13.237

12.718 13.237

Material Boundary

4.375 13.793

13.479 13.793

Material Boundary

5.113 14.312

14.212 14.312

Material Boundary

5.874 14.848

14.957 14.848

Material Boundary

6.607 15.363

15.700 15.363

Material Boundary

8.129 16.435

17.208 16.435

External Boundary

3.544 13.208

3.010 12.811

3.010 12.696

2.416 12.251

1.961 12.251

1.370 12.696

31.531 0.000

31.531 5.608

31.531 10.908

31.531 11.608

31.531 11.608

31.531 13.208

110

1.370 12.811

1.002 13.074

0.634 13.074

0.527 13.208

0.000 13.208

0.000 12.008

0.000 11.708

0.000 10.808

0.000 10.808

0.000 5.808

0.000 3.208

0.000 2.008

0.000 0.000

31.531 18.448

31.531 19.086

29.528 19.205

11.259 18.684

10.184 17.911

8.129 16.435

7.370 15.901

6.607 15.363

5.874 14.848

5.113 14.312

4.375 13.793

3.585 13.237

Support

3.585 13.237

12.718 13.237

Support

4.375 13.793

13.479 13.793

Support

5.113 14.312

14.212 14.312

Support

5.874 14.848

14.957 14.848

Support

6.607 15.363

15.700 15.363

Support

7.370 15.901

16.445 15.901

Support

8.129 16.435

17.208 16.435

II-Section B

Project Settings

Project Title: SLIDE - An Interactive Slope

Stability Program

Failure Direction: Right to Left

Units of Measurement: SI Units

Pore Fluid Unit Weight: 9.81 kN/m3

Groundwater Method: Water Surfaces

Data Output: Standard

Surface Options

Surface Type: Circular

Search Method: Grid Search

Radius increment: 10

Composite Surfaces: Disabled

Reverse Curvature: Create

Tension Crack

Minimum Elevation: Not

111

Calculate Excess Pore Pressure: Off

Allow Ru with Water Surfaces or Grids: Off

Random Numbers: Pseudo-random Seed

Random Number Seed: 10116

Random Number Generation Method: Park

and Miller v.3

Analysis Methods

Analysis Methods used:

Bishop simplified

GLE/Morgenstern-Price with interslice force

function: Half Sine

Janbu simplified

Ordinary/Fellenius

Spencer

Number of slices: 25

Tolerance: 0.005

Maximum number of iterations: 50

Material Properties

Material: Embankment



Cohesion: 0 kPa


Water Surface: None

Material: Ia



Cohesion: 2 kPa



Custom Hu value: 1

Defined

Minimum Depth: Not Defined

Loading

1 Distributed Load present:

Distributed Load Constant

Distribution, Orientation: Vertical,

Magnitude: 25 kN/m2

Material: Ib



Cohesion: 0 kPa



Custom Hu value: 1

Material: Id



Cohesion: 0 kPa



Custom Hu value: 1

Material: IIa



Cohesion: 13 kPa



Custom Hu value: 1

Material: IIb



Cohesion: 16 kPa



Custom Hu value: 1

112

Material: Concrete



Cohesion: 20 kPa


Water Surface: None

Support Properties

Support: GeoGrid

GeoGrid

Support Type: GeoTextile

Force Application: Passive

Force Orientation: Parallel to

Reinforcement

Anchorage: Slope Face

Shear Strength Model: Linear

Strip Coverage: 100 percent

Tensile Strength: 50 kN/m

Pullout Strength Adhesion: 5 kN/m2

Pullout Strength Friction Angle: 41 degrees

Material: Mattress



Cohesion: 0 kPa


Water Surface: None

113

Global Minimums

Method: ordinary/fellenius

FS: 1.301940

Center: 10.067, 20.171

Radius: 11.843





Method: bishop simplified

FS: 1.498740

Center: 9.104, 21.302

Radius: 11.875






FS: 1.472690

Center: 9.104, 21.302

Radius: 11.875



Method: janbu simplified

FS: 1.319440

Center: 9.104, 21.302

Radius: 11.875


12.945


19.892



Method: spencer

FS: 1.468880

Center: 9.104, 21.302

Radius: 11.875


12.945


19.892










Components of Bishop Analysis of section-B.



Base Friction Angle: 14 degrees

Base Cohesion: 16 kPa

Slice Width: 0.969095 m

Base Length: 0.998825 m

Angle of Slice Base: -14.0143 degrees


Frictional Strength: 17.498 kPa

Cohesive Strength: 16 kPa


Matric Suction: 0 kPa

Excess Pore Pressure: 0 kPa

Initial Pore Pressure: 22.666 kPa

Left Side Normal Force: 137.129 kN

Left Side Shear Force: 0 kN

Left Side Resultant Force: 137.129 kN

Left Side Force Angle: 0 degrees

Right Side Normal Force: 181.287 kN

Right Side Shear Force: 0 kN

Right Side Resultant Force: 181.287 kN

Right Side Force Angle: 0 degrees

114

Mobilized Shear Resistance: 22.3508 kPa



Base Normal Stress: 92.8466 kPa

Effective Normal Stress: 70.1806 kPa


Positive Pore Pressure: 22.666 kPa

Horizontal Seismic Force: 0 kN

Vertical Seismic Force: 0 kN


M-Alpha: 0.929875

Y coordinate - Bottom: 9.9115 m

Y coordinate - Top: 13.8435 m

List of All Coordinates

Water Table

0.000 12.061

31.052 12.261

Search Grid

0.441 20.171

19.693 20.171

19.693 42.788

0.441 42.788

Material Boundary

5.287 13.520

31.053 13.520

Material Boundary

4.632 13.061

31.053 13.061

Material Boundary

0.000 1.861

7.453 1.861

Material Boundary

12.959 18.909

29.076 19.345

31.053 19.345

Material Boundary

0.000 11.861

2.272 11.861

Material Boundary

3.138 11.861

31.053 11.461

Material Boundary

0.000 11.561

31.053 11.461

Material Boundary

0.000 10.661

31.053 10.761

Material Boundary

0.000 5.661

31.053 5.461

Material Boundary

0.000 3.061

7.453 1.861

Distributed Load

15.065 19.715

29.076 20.139

External Boundary

0.000 0.000

31.053 0.000

31.053 5.461

31.053 10.761

31.053 11.461

6.984 14.713

6.218 14.175

5.450 13.635

5.287 13.520

4.632 13.061

115

31.053 13.061

31.053 13.520

31.053 19.345

31.053 20.000

29.799 20.054

29.731 20.139

29.076 20.139

14.065 19.685

12.959 18.909

10.725 17.340

9.965 16.806

9.183 16.256

8.484 15.766

7.684 15.204

0.000 11.561

0.000 10.661

4.623 13.055

3.518 12.279

3.518 12.143

3.138 11.861

2.940 11.714

2.470 11.714

2.272 11.861

1.892 12.143

1.892 12.279

0.939 12.945

0.558 12.945

0.470 13.061

0.000 13.061

0.000 11.861

0.000 5.661

0.000 3.061

0.000 1.861

Support

5.450 13.635

14.549 13.635

Support

6.218 14.175

15.318 14.175

Support

6.984 14.713

16.084 14.713

Support

7.684 15.204

16.784 15.204

Support

8.484 15.766

17.584 15.766

Support

9.183 16.256

18.282 16.25

Support

9.965 16.806

19.064 16.806

Support

10.725 17.340

19.825 17.340

Support

4.632 13.061

5.287 13.520

Support

5.287 13.520

31.053 13.52

Support

4.632 13.061

31.053 13.061

aes/re/10-28 stability analysis of embankments located ... · road embankment slope stability limit...

Documents