Improvement of slope stability of dikes by application of geotextile or geogrid materials

INTERNATIONAL

INSTITUTE FOR INFRASTRUCTURAL,

HYDRAULIC AND ENVIRONMENTAL

ENGINEERING

Improvement

of Slope Stability of Dikes by

The findings, interpretations and conclusions expressed in this study do neither necessarily reflect the views of the Internationallnstitute tor Hydraulic and Environmental Engineering, nor of the

IMPROVEl\ffiNr

OF SLOPE STABILITY OF DIKES BY

APPLICATION

OF GEOTEXTILE

OR GEOGRID MATERIALS

Master of Science Thesis

by

E. Welle Ndikilo

Examination Committee

Prof. B. Petry

Chairman

Ing. R. Termaat

Member

Ir. W. Voskamp

Member

TABLE OF CONTENfS

Page AKNOWLEDGEMENTS ABSTRACT NOTATION 1 ili v Chapter 1 INTRODUCTION 1.1 Background

1.2 Reinforeed Soil Structures 1.2.1 Geosynthetic products 1.2.2 Steep slope reinforcement 1.3 Objective of Research 1.4 Scope of Research 1 1 1 2 3 6 7 9 Chapter 2

IMPORTANT FACTORS AND PROPERTIES OF GEOTEXTILES AND GEOGRIDS FOR SOn.., REINFORCEMENT DESIGN

2.1 General

10

10 10

Chapter 3

STUDY OF THE AVAILABLE DESIGN METHODS FOR GEOGRID IGEOTEXTILE REINFORCED SLOPES

3.1 General 3.2 Design considerations 16 16 16 18

Table of Contents

Page

3.3 Design Methods 20

3.3.1 Current North American Practice 20

3.3.2 Broms Method 27

3.3.3 Design Charts according to Jewell 31

3.3.4 Design guidelines 38

3.3.5 Forest service Method, Collin Method, Bonaparte et al. Method,

l..eshchinsky& Perry Method, and Schmertmann et al. Method 47

3.3.6 Computer Models 49

Chapter 4 51

CO:MPARISON OF CURRENT DESIGN METHODS 51

4.1 Genera! 51

4.2 Design of a geogrid reinforeed slope 53

4.2.1 Design Results 54

4.3 Conclusions 70

~~ff5 TI

CASE STUDIES 72

Table of Contents

Page

Chapter 6

CONCLUSIONS AND RECOMMENDATIONS

93 93

REFERENCES

96

AKNOWLEDGEMENTS

1 am very grateful to many people who have contributed to the successful accomplishment of this thesis. It would take too much time and spaceto express my thanks to all of them.

First of all 1 would like to thank my supervisor, Prof. B. Petry, Professor of Hydraulic Engineering, International Institute for Hydraulic and Environmental Engineering (lliE) for his assistance and guidance which enabled me to pursue this research.

1 am highly indebted to my mentor, Ir. P. Lubking, Senior Leeturer, International Institute for Hydraulic and Environmental Engineering and Senior Consultant, Delft Geotechnics for proposing the research topic. He provided me with useful advice and constructive criticism of the draft reports.

I am also grateful to my supervisor, Ing. R. Termaat, Head of Geotechnical Research, Ministry of Public Works and Water Management, Delft, for his critical review of the draft reports and for his assistance in the Finite Element analysis (PLAXIS).

I wish to express my gratitude to Ir. W. Voskamp, Manager Geotechnics, Akzo Industrial Systems bv, Arnhem, for his critical review of the draft reports and also for his valuable advice on how to use the Akzo Sliding program in geogrid reinforeed slopes.

Aknowledgements

Rufiji Basin Development Authority (RUBADA) of the United Republic of Tanzania for allowing me to continue with my studiesinThe Netherlands.

And lastbutcertainly not least,I am very grateful to my parents, brothers and sisters for their encouragement, patience, moral and spiritual support throughout the period of my study in The Netherlands.

ABSTRACT

The low-lying countries as The Netherlands are strongly dependent on good (safe) river and seadefences. Driven by the necessity to withstand the water, during centuries the engineers built up their knowledge on hydraulic engineering, and particularly on constructing of dikes and proteetion measures. The design of these dikes has been carried out using traditional methods whereby, construction materials such as rock, gravel, sand and clay have been used extensively. The dikes are always with slopes limited to 1:2 or 1:3 to avoid loss of stability.

Improvement of slope stability of dikes by the use of polymerie geogrids or geotextiles could be an alternative for achieving an effective and economical design of dikes because of the less required quantity of fill material and shorter construction time than traditionally built slopes. Geogrid reinforeed dikes do not require vast area of land because they are constructed with

steep slopes.

In the ground, the geogrid may be exposed to various agents that promote chemical, biological or mechanical degradation, hence resulting in poor durability. But, good information is available in the geotechnical literature regarding the durability of geogrids whereby the characteristic strength of the fabric must be divided by various reduction factors for mechanical damage, chemical, biological and environmentaI attack. Therefore, the durability

Abstract

To achieve aesthetics (good physicaI appearance) of the geogrid reinforeed slope, grasses can easily be grown because the roots can penetrate through geogrid reinforcements without

difficult. Maintenance of the dike is also possible (e.g grass cutting etc.).

It is lastly recommended to study the possibility of using sisal fabric in slope renforcement. Sisal fibre has a significant modulus of elasticity. The study could be beneficia! to developing countries such as Eastern Africa, Centra! America and Asia where sisal is produced in abundant.

NOTATION {3 ó cl>, rP'cs 'Ymax B FS. H

Slope angle from the horizontal

Angle of shearing resistance between soil and plane reinforcement surface Required stress in the soil to be provided by reinforcement

Available stress in the soil from the reinforcement Effective angle of friction

Critical state or large strain angle of shearing resistance Design value of effective angle of shearing resistance Unit weight of soil

Maximum unit weight of soil Design value of unit weight

Partial factor between the allowable and limiting reinforcement forces Uniform vertical surcharge

Pore water pressure coefficient

Vertical spacing between reinforcement layers Horizontal spacing between reinforcement layers Design time under load for reinforcement

Depth below the ground surface

Depth (or thickness) of grid reinforcement bearing surfaces Factor of safety on peak shearing resistance

Nouuion

AASHTO FHWA

Minimum required length for satisfactory direct sliding equilibrium Allowable reinforcement force

Design temperature Maximum tensile force Ultimate Tensile Strength

American Association of State and Highway Transportation Official Federal Highway Administration

Chapter 1

INTRODUCTION

1.1 Background

Reinforeed earth, is the association of earth and strips, which, by their tensile strength, give cohesion to the soil. The concept of earth reinforcement is not new, the basic principles are demonstrated abundantly in nature by animals and birds and the action of tree roots. The techniques involved are simple to grasp and have been used by man for centuries.

The Agar-Quf soil reinforeed "ziggurrai"; in Baghdad was constructed of clay bricks varying in thickness between 130-400mm, reinforeed with woven mats of reed laid horizontallyon a layer of sand and gravel at vertical spacings varying between 0.5 and 2.0m (Bagir, 1944). The Agar-Quf structure is now 45m tall, originally it is believed to have been over 80m high; it is thought to be over 3000 years old.

The Great Wallof China, parts of which were completed circa 200 B.C., contains examples of reinforeed soil, in this case use was made of mixtures of clay and gravel reinforeed with tamarisk branches (Department of Transport, 1977).

The Romans are also known to have used earth reinforcing techniques, and reed reinforeed earth levees were constructed along Tiber. The Roman army, 1900 years ago, constructed a timber wharf for the Port of Londinium which was 2m high and was formed from oak baulks measuring up to 9m in length, having a vertical face held in place by timber reinforcing elements embedded in the backfill (Bassett, 1981). In parallel with the Romans, the Gaul also made use of earth reinforcement technique in the construction of fortifications, the technique

1 Iruroduction

The concept of reinforcing soil has also attracted the attention of the academie world, for

although the concept is easily grasped the theoretical aspects involved are numerous. As a

result, much research and development work has been undertaken in Universities and

laboratories and soil reinforcing is now recorgnised as a separate subject in its own right in the geotechnical field.

The modern uses of soil reinforcement appeared in the 1960s with the development of

Reinforeed Earth retaining walls and geotextile stabilization of haul roads and access roads.

Todate, thousands of retaining structures have been constructed with the Reinforeed Earth

technique and many thousands of roads with geotextiles.

According to Vidal (1969) and Schlosser and Vidal (1969), a reinforeed earth wall consists

of three main components; soil, reinforcing elements and the facing elements, whereas

reinforeed concrete or prestressed concrete are composed of four elements: Aggregate, sand,

cement and reinforcement. With that composition, a reinforeed earth structure has shown

promising strength which can be relied upon.

Since the introduetion of the reinforeed earth concepts, various reinforcing materials have

been developed. A lot of them have been used successfully to a wide range of applications.

Researchs are still going on to establish more reinforcing materials as weIl as their various applications.

1.2 Reinforeed Soil Structures.

The main types of reinforeed soil structures can be subdivided into two broad categories,

earth structures and load supporting structures: The former include slopes, walls,

embankments, low-permeability soillayers used in dams and waste containment facilities, and

some "soillayers on non-uniform foundations" such as roads and embankments over karst

topography. Earth structures do not normally support significant external loads, and the

1Introduetion

include flexible pavements,unpaved roads,railroad track structures,andload supporting pads such as drilling pads, fabrication yards, and construction staging areas. These struetures are usuallystabie under theirown weight, and the primary design consideration is the strueture's ability to support the applied loads (usually traffic loads ) with limited deformations. In these applications, the reinforcement is either located inside the structure or at the interface between the strueture and the foundation soil.

A variety of materials can be used as soil reinforcements. Those that have been used sueeessfully include steel,concrete,glass fibre,wood,rubber, aluminium and thermoplasties.

Polymerie materials are those whieh include geotextiles and geotextile related produets such as geogrids, strips, mats, webs, meshes and nets.

Today, the most eommonly used materials are geotextiles and geogrids made of polyethylene, polyester, and polypropylene. Metallic reinforcements are becoming unfavourable due to their relatively high cost andtheir long-term susceptibility to corrosion.

1.2.1 Geosynthetic produets

The history or/and the origin of geotextiles is traeed by most authors back to the end of the fifties. Geotextiles made from man-made fibres were (for the first time) developed in the Netherlands after the 1953 catastrophic flood which claimed many lives and damaged properties. The catastrophe initiated the world famous Delta Works from which revolutionary civil engineering works had to be made, arnongst them civil engineering fabrics made of man';'

made fibres were used. Several experimental applications of geotextiles were carried out by Dutch scientists in early 1970's, however, the use of geotextile as filter materials in dikes was

1Introduetion

Geosynthetic is a more generic term which includes geotextiles, geomembranes, geogrids, geonets,geocomposites,andallother similar materials used by civil engineers to improve or modify the behaviour of soils. They are characterised as extensible materials. The basic types and functions of geosynthetics are related to their most commonly applied engineering functions, for example, geogrids are for reinforcements only, geotextiles are used in reinforcement, separation,cushioning, filtratien and transmission. Geocompositesand geonets are used in isolation i.e retention of one fluid or the separation of two fluids.

In the reinforcement function, the purpose of the geosynthetic is to add tensile properties to soil, much in the same way that reinforcing steel is used in concrete. Inbothcases, materials with good compressive properties (soiland concrete) are combined with materials with good tensile properties (geogrids, geotextiles and steel) to construct a structure with adequate compressive and tensiIe strengths.

(a) Geotextlles

Geotextiles (Figure'1) are defined as any permeable textile used in conjunction with geotechnical materials as an integral part of a man made project, structure, or system (Robnett et al., 1982).These textile materials are made of elements such as individual fibres, filaments yams, tapes, etc that are long, small in cross section and strong in tension (Leflaive, 1988). They are characterised by their flexibility, tensile resistance and porous nature.

Figure 1 Geotextiles

These characteristics are essential for

a good association with soil partic1eswhile performing their mechanical and hydraulic • . • •• • • t , • ~

• , I •• I

... ! • I •

J Introduetion

functions. Their fibrous character is an important feature as itappears that it is in this form that the highest tensile resistance of a material is obtained. This is due to the fact that the fibres obtain a high degree of molecular orientation either, for polymers, by stretching or drawing or, for natural fibres, by natural growth (Leflaive, 1988). The three main types of geotextiles are wovens, nonwovens, and knitted.

(b) Geogrids

Geogrids (Figure 2) are reinforcing elements formed from transverse and longitudinal members, in which the transverse members run parallel to the face or free edge of the structure and behave as abutments or anchors.

They are formed from polymers and

are normall y in the form of an

expanded proprietary plastic product.

They posses a high Youngs

Modulus.

The basic principle of reinforcement

Figure 2 Geogrids

with geogrids is the mobilization of

a high tensile force at low strain within the soil structure. This is achieved by an interlocking bond between fill and grid. In addition, geogrids, offer an ability to make designs at strains which are compatible with expected soil strains.

1lntroduction

There are two main types of geogrids: those manufactured by drawing a perforated

polymer sheet in one or two perpendicular directions; and those manufactured by

overlapping perpendicular, or nearly perpendicular, polymer strands and then bonding

these strands at their junctions. Todate, geogrids manufactured using the fust method

have been the mostwidely used for soil reinforcement applications.

Geotextiles and geogrids are finding an ever larger application in the improvement of grounds as they are yielding good results. The later material has been prefered most than the former.

For example, a survey of reinforeed soil walls with geosynthetic reinforcement constructed

in North America until1987 has been presented by Yako and Christopher (1987). The survey

shows that in the vast majority of the more recently builty walis, geogrids (as opposed to

geotextiles) have been used as reinforcing elements. This may be attributed to the fact that

the principal geogrid manufacturer has provided strong technical support service and/or that the high strength of geogrids may have appeared attractive to designers because they could reduce the number of reinforcing layers. The economie benefits to he gained however, will only then be fully effective if the application takes the material characteristics (as described in chapter 2) into account.

1.2.2 Sleep slope reinforcement

Reinforcement is used to construct slopes steeper than would be possible without

reinforcement. For instanee,unreinforced sand is stabie on slopes up to about 30° to 400 (i.e

angle of repose is equal to the angle of intemal friction, (3mu.

=

<1>'). Intemal reinforcement

of a sand mass will permit it to stand even at very steep angles. Practically, there are no limits on the steepness of reinforeed slopes. Very steep and even vertical slopes can he built using polymerie geogrids or geotextiles in slope reinforcement.

Reinforeed slopes are compacted fill embankments that incorporate tensile reinforcement to

enhance stability. The tensile reinforcement ties or holds the soil mass together across any

1Introduetion

The basic principle of soil reinforcement as described by Jewell (1982) is that when an orientated reinforcement is included, a higher strength is developed in the soil. This is the result of an increase of the normal stress across the potential rupture plane, and simultaneously,a decrease of the shear stress acting in the soil.

Many present Dutch dikes are constructed with slopes lirnited to 1:2 or 1:3 to avoid 1055of

stability. With the use of geotextile or geogrid materials it is possible to increase the dike slopes theoretically even up to the vertical.

1.3 Objective of research

The low-lying countries as the Netherlands are strongly dependent on good (safe) river and seadefences. Driven by the necessity to withstand the water, during centuries the engineers built up their knowledge on hydraulic engineering, and particularly on constructing of dikes and proteetion measures (revetments).These structures are mainly composed ofmaterials such as rock, gravel, sand and clay.

The increased demand on reliable design methods for protective structures has resulted in increased research in various fields of engineering. The following two cases highlight this demand. The first one concerns an embankment section near the town of Bergambacht, 20

kmeast of Rotterdam which after reconstruction 12 years ago, the road on top showed severe damage due to deformations (Appendix I-a). Maintenance was necessary each year. Also the toe of the embankment moved landwards.This dike exists on a relatively impenneable heavy clay and is constructed on relatively impermeable and weak subsoil of peat and clay. The pore

1Iruroduction

A study was conducted to determine the reasons behind the horizontal deformations and to propose the possible solutions to the problem. Itwas thereafter concluded that,the observed horizontal deformations ofthe weak toplayer behind the embankrnent were caused by uplift. A plan for reconstruction of the river embankrnent was made, taking into account the houses at the toe of the embankrnent. One among the alternatives was to reduce the weight of the embankrnent by constructing the dike slope with either geotextile or geogrid materials. The second alternative was to add weight in the uplift zone by constructing a berm as illustrated in Appendix l-b.

The second case is the heightening of the dike at a section near the town of Ophemert which was hit by severe flood from the Waal river during winter period of december, 1993. The original crest level ofthe dike at section 43.00 is 10.61m+NAP whereas the maximum water level (MHW) during winter is 10.84m+NAP. A plan for the heightening ofthis dike section was made, taking into consideration the houses in the polder side of the dike. A crest level and width of 11.34m+NAP and 8.oom respectively, are the necessary requirements for the dike heightening, if floods are to be prevented in the town of Ophemert (Appendix l-c).

There is already an alternative design which has been presented for the purpose of heightening the crest level of the dike at section 43.00 as illustrated in Appendix l-c. The design is based on traditional methods which have been used for many centuries here in the Netherlands. But, with the big thrust of geosynthetic reinforeed slopes occupying the civil engineering industry, it is possible that the heightening of this dike could be successfully and more economically done using geotextiles or geogrids.

The main objective of this research is therefore the improvement of slope stability of dikes by application of geotextile or geogrid materials.

1 Introduetion

1.4 Scope of research

The scope of this research will be as

follows:-(a) To do aliterature study with respect to geosynthetic reinforeed slopes and a review of geosynthetic properties (i.e geotextiles and geogrids)

(b) To study the available design methods (including computer modeIs) for slope

stability reinforcement with either geotextile or geogrid materials.

(c) To do sensitivity studies with several methods (including computer modeIs) on

the stability of geogrid or geotextile reinforeed slopes.

(d) To make a comparison of traditional cross sections of dikes with either

geotextile or geogrid reinforeed cross sections of typical Dutch dikes.

Chapter 2

IMPORTANT FACTORS AND PROPERTIES OF GEOTEXTILES

AND GEOGRIDS FOR SOIL REINFORCEMENT

DESIGN

2.1 General

The geotextile and geogrid properties required, stem primarily from the function they must fulfill. For reinforcement, the emphasis is on mechanical properties such as tensile strength, tensile stiffness, boundary friction characteristics, pullout behaviour, fatigue resistance, creep resistance, relaxation characteristics and seam strength.Depending on the specific application and life time required, durability will be demanded on ultra-violet light resistance, resistance to biological attack and abrasion resistance. They must also have resistance to wear and tear when construction equipment is to be expected to drive over the fabric (constructibility).

The suitability of a geotextile or geogrid should be checked against these functional requirements during the design of a civil engineering construction.

(a) Mechanical damage

Loads due to heavy traffic, compacting equipment and construction materials can damage the fabric, and then affect the mat's strength. Physical damage can include punctures to the fabric, tearing, piereed holes in which the yams are separated but not tom, as well as abrasion of the yams themselves. There have been many tests in which geotextiles and geogrids have been buried in soil, extracted and in some cases mechanically tested, but little systematic study is done about the nature of the damage. The effect of angular gravel and sand on a geogrid has been described by Bush (1988). Apart from general abrasion, the only damage observed was incidental splits, bruises and edge fibrillation. At no point was a single grid element fully severed. Some of the results of the tests indicate the favourable effect of a coating on top of the yams. Geogrids have a PVC coating for ultraviolet proteetion and proteetion against mechanical damage.

2 Properties of Geotextiles/Geogrids

Mechanical damage locally reduces the cross-section of the material supporting the load,

thereby locally raising the stress. The time required to cause stress-rupture at the damaged

section will be correspondingly reduced. However, because the damage is local, the overall

shape of the load-extension curve, whichis dominated by the bulk of undamaged material,

will remain almost unchanged. Thus mechanical damage is likely to reduce the strength properties of polymer reinforcement materials while having little effect on the stiffness properties. The extension to rupture will be reduced similarly. Constant rate of strain tests on recovered samples of damaged geogrid show almost no change in stiffness, a small

reduction in peak load, but a more significant reduction in strain to rupture.

There is, however, no simple test suitable for estimating the susceptibility of a geotextile to

mechanical damage and actual performance tests are recommended for angular or aggressive

fill material. Based on existing evidence, a range of partial factors is proposed.

(b)Biological attack

Geotextiles and geogrids do not corrode and therefore their strength reductions are likely to

occur from bacteriological environments, such as are commonly found in soil. Several tests

executed at laboratories confirmed that synthetic materials are generally resistant to such attack and although bacteria may occur on fibres there is little evidence of any breakdown of

the polymer chains and any attendant reduction in strength. Animal and insects such as

termites and rats may chew a way through synthetic materials but will not eat them as food.

2 Propenies of Georextiles/Geogrids

(c) Chemica) conditions

Ifthe reinforcement is to be used in an area where there are chemieals that are normally present in the soil, the effect of these chemieals on the reinforcement bas 10 be checked. Polyester yams and fabrics have been tested for the effects of hundreds of different chemieals

in various combinations. In normal soil conditions, no strength reduction has been found (i.e pH 9-5). At high acidic levels a reduction has been found and a reduction factor of 1.05 is advised (i.e pH

<

4). In alkaline conditions (i.e pH> 10), polyester is affected by hydrolysis. This occurs at higher temperatures (above 300-40°Celsius) and in combination with water and in a highly alkaline environment. Under norm al soil conditions no hydrolysis effects are 10 be expected. For pH> 10 a reduction factor of 1.12 is advised. For pH values and temperatures which are not included in the above indicated range, it is advised to contact the manufacturers for more informations.

(d)Resistanee to Ultra violet

All synthetic fibre materials are vulnerable to ultra violet. Sometimes the loss of strength is very fast, sometimes slow, depending on the polymer used and additives to the pure polymer (e.g polyester is better than the others). The effects of sunlight can be overcome by protecting the material with a PVC coating for a case of geogrids or by covering up the face with suitable vegetation as the fabric can be easily penetrated by roots of plants and grass. An effective method to speed up the natura! process is hydroseeding. Until the resulting vegetation takes over, the hydroseeding layer also acts as a proteetion against ultra violet (Enka publication, 1985). As the reinforcement is placed in the soil and the period in which it is exposed is shortly, no problems are to be expected, provided that the design is made in such a way that the fabric is always protected against direct sunlight.

2 Properties of Geotextiles/Geogrids

(e) Time effects

All polymerie materials exhibit time-dependent behaviour. Creep is the time-dependent deformation of a specimen under constant tensile load. Stress-relaxationis the time-dependent reduetionin tensile load carried by the reinforcement under constant tensile strain. Both creep and stress relaxation can occur in polymerie reinforcement during the service life of a typical

earth strueture. These time effects win significantly influence the mobilized tension and elongation of the reinforcement. Reinforcement creep has been investigated toonly a limited extent. Stress-relaxation effects have been studied even less. Reinforcement stress-relaxation is not considered in mostpractical design problems.

Creep test procedures and their interpretation require a long period of study and therefore, material ereep testing is not feasible on a project-by-project basis. It is usually recommended that, creep test results should be provided by the material manufacturers at the time of design.

<0

Temperature effects

The temperature has a considerable effect on the tensile properties of a geotextile and geogrid.

As geotextiles are used both in tropieal areas and in polar regions, the influence of a range of temperatures has been investigated on the tensile behaviour of five different polymers, namely, polyethylene monofil(PE), polypropylene splitfibre (PP), polyamide 66 multifilament (PA66), polyamide 6 multifilament (PA6) and polyester multifllament (pETP). Results have shown that, in relation to the tensiIe strength at 20°C, all materials show a decrease in strength with inereasing temperature. The extent of decrease being different for each material e.g the temperature where the remaining strength is 50% of the 200C-strength is for PE

2 Properties of Geotextiles/Geogrids

(g) Additional considerations

(i)Hydrostatic pressure

,"

-•I ,.

'i

~

_,

.

.

I: .' .. ,

j

:

f t; f " / ,',1 ' " ; : I ;:.- .; I ,!j !. .~ "r; . I: I " r

.f

--_~ --_{._}---_1:---_{.._ ':I:} -_b: ( '''.

Figure 3 Load-elongation curve for polyethylene

monofilament at different temperatures

Most reinforeed soil walls (metallic and polymer reinforced) have been built using

free-draining backfill material and have been equipped with drainage system to prevent the

accumulation of water behind the wall. If finer backfill material is used, it should include a

drain and the pore water pressure on the wall canbecomputed using classical soil mechanics

procedures. Also, when using cohesive backfill material, surface drainage should be provided

in order to avoid ponding of surface runoff. As reported by Burwash and Frost (1991), the

accumulation of surface water can lead to saturation of the backfill material causing in some

2 Properties of Geotextiles/Geogrids

(ü) Lateral wall defonnation

With granular backfill material, firm foundation soil and limited deformation of the reinforcement material, the lateral wall movement occurs mainly during construction. The amount of walI movement is influenced by various factors including reinforcement extensibility, compaction density, slack in the reinforcement and reinforcement-to-facing conneetion and the reinforcement length. The latter appears to be a decisive factor if the length to height ratio of the reinforeed soil wall becomes less than 0.5 (Christopher et al.,

1989).

The current practice is to use a lengthto height ratio of not less than 0.7. This together with the use of simplified design methods based on limit equilibrium conditions appear to limit the lateral wall deformation to within acceptablelimits.

Chapter 3

STUDY OF THE AVAILABLE DESIGN METIlODS FOR

GEOGRID/GEOTEXTILE

REINFORCED

SLOPES

3.1 General.

Since the development of the Reinforeed Earth technique, a number of diverse methods have been proposed for the design of geosynthetic reinforeed soil walis. The various methods yield widely varying results. All of the methods normally considered applicable to routine design use limiting equilibrium analysis to determine the factors of safety against failure; however, they vary in the assumptions that are made regarding stress distributions, failure surfaces, safety factors, and the inclination of the reinforcement at the failure surface. Most of them use conceptually simple analysis of destabilizing horizontaI forces resulting from earth

pressures and stabilizing horizontaI forces provided by the reinforcement (e.g Schlosser and Vidal, 1969, Steward et al., 1977, Bonaparte et al., 1987, etc). Others use methods of evaluating force and/or moment equilibrium along an assumed failure surface similar to conventional slope stability analysis but with the inclusion of the balancing force/moment provided by the reinforcement.

Other limit equilibrium methods involve more complicated assumptions satisfying more realistic kinematic and static considerations (e.g Juran and Schlosser, 1978, Leshchinsky and Perry, 1987 and Juran et al., 1990). Additionally, Finite Element methods have been used by various reseachers to study the behaviour of reinforeed soil walls (e.g Romstad et al., 1976 and Al-Hussaini and Johnson, 1978 and Fishman and Desai, 1991). Computer models based on limiting equilibrium analysis have been developed e.g MSTAB program developed at Delft Geotechnics to solve simple slope stability problems with geotextile or geogrid reinforcements. There is also a slope stability computer program developed for Akzo Industrial Systems by Jewell,R.A (1990) to compute steep slopes reinforeed with either geotextile or geogrid materials. In North America, there are currently two commercial programs recommended for the design and analysis of geosynthetic reinforeed soil retaining

3 Design Methods

walls. These are Geosynthetic Reinforeed Soil Wall (GRSWALL) and Geosynthetic Wall

(GEOWALL).

These limiting equilibrium methods typically do not take into account the displacement and deformation behaviour of the geotextile or geogrid embedded in the soil. For the limit equilibrium methods the strain compatibility between soil and geotextilelgeogrid is not satisfied. Furthermore, the limit equilibrium analysis is not able 10 model the stress distribution of a surface load and the interaction between soil and reinforcements. But, by applying the Finite Element method such as PLAXIS (i.e Plasticity Axisymmetric) 10 reinforeed soil systems, the soil geotextile/geogrid interaction as well as the stress distribution can be taken into account.

However, Jewell et al., (1990) method described under 3.3.3 has been developed to take into account the displacement and deformation behaviour of the geotextile or geogrid material

embedded in the soil. The method is summarized in "simple" Revised Design Charts

(Jewell,R.A 1990).

The majority of design methods available for reinforeed soil walls are for granular backfill

soils. Cohesion is not taken into account, and also, all require good foundation soils.

Therefore, an overall stability analysis must be made.

Despite the wide variety of available techniques, only the simplified limit equilibrium analysis is currently suggested for general use in design (US Forest Service, Task Force # 27, and Christopher et al., 1989). By using limiting equilibrium analysis, full-scale geotextile reinforeed structures have been constructed and tested in order to develop reliable design

3 Design Methods

1990). Furthermore, large sca1emodeltests ofpolymerie grid-reinforced retaining wall have been carried out at the Royal Military College of Canada, whereby, tests have been extensively monitored and a collection of high quality data has been accumulated that can be used to calibrate analytica1 models (Bathurst, J.R and Jarrett, P.M 1990).

3.2 Design considerations

The design of geosynthetie reinforeed slopes has to take into consideration both the internal and the external stability of the strueture. In addition to internal stability, horizontal

deformation is also an important consideration for reinforeed soil walls (especially when using extensible reinforeements).

(a) Internal stability

The reinforeed zone is assumed to eonsist of an aetive zone and a resisting zone. The reinforcing elements must provide the necessary anehorage for the system stability by extending a sufficient distance into the resisting zone. The failure surface separating the active and resisting zones is assumed to coineide with the locus of maximum tension in the reinforcements. The internal stability therefore eontrols the quantity, strength, length, and vertical spacing of the reinforeement elements.

The design is based on preventing two modes of failure:

(i) Rupture within the aetive zone:This mode will occur if the tension force in the geotextiles or in the longitudinal ribs of geogrids exceeds the tensile capacity of the reinforeing material.

(ii) Pullout of the reinforcing elements from the resisting zone: This mode will be due to the reinforcement beyond the failure plane being inadequate to develop the required anchorage capacity.

3 Design Methods

A third, and equally important aspect, only in vertical wall design is the strength of the conneetion between the reinforcement and the facing elements. In case of slopes with inclination{3<90°, facing units are often not used.

(b) External stability

The composite wall interacts with its foundation soil and is subjected to lateral pressures induced by the soil retained behind the reinforeed portion. Itis very important that the effects of these factors are also considered, otherwise, an intemally stabie geosynthetic reinforeed slope may have unacceptable extemal stability. Typically, the reinforeed structure is taken as a monolithic block having to be stable under the following

conditions:-(i) overtuming about the toe of the wall

(ii) sliding along the base of the structure at the foundation/backfill interface.

(iii) overall slope stability

(iv) bearing capacity failure of the base of the wall

Satisfaction of the above stability criteria does not quarantee tolerabie settlements.Therefore calculations should be done to check the allowable settlement of the structure because excessive settlements may affect serviceability although not causing catastrophic failure.

3 Design Methods

3.3 Design Methods

3.3.1 Current North American Practice

3.3.1.1 General

The design of geotextile-reinforced soil walls in North America is based on a limit equilibrium approach for external and internal stability of the reinforeed soil mass. Soil strength is defined in terms of Mohr-Coulomb parameters (c', 4>') taken at peak shearing resistance. External modes of failure are related to a reinforeed soil mass that is assumed to act as a gravity structure. The essential feature of internal stability analysis is the use of a "tie-back wedge" approach to estimate the distribution of lateral earth pressures to reinforcement layers.

3.3.1.2 Design procedure

The recommended approach to analyse and design geosynthetic reinforeed retaining wall structures is based on concepts of classical Rankine or Coulomb earth pressure theory. The relative stability of these structures is quantified on the basis of conventional geotechnical concepts of factor of safety against shear failure of the soil and tensile fallure of the reinforcement at limit equilibrium.

Calculations related to the pullout capacity of a geosynthetic layer, external stability and internal stability of the reinforeed soil mass are carried out once a trial arrangement is established.

3 Design Methods

(a) Extemal stability

External stability calculations

assume that the reinforeed zone

acts as a monolithic block of

material. This homogenization of the reinforeed zone for modular

facing systems is assured by

limiting the spacing between

layers (e.g not more than 1m according to FHW A, 1989). The composite mass must be stabie against sliding along the base of

the structure at the

foundation/backfill interface,

overturning about the toe, and

bearing capacity failure of the

supporting foundation soils

(figure 4). a)sliding (F.S.>1.5) c) bearing capacity (FS >2.5)

(~

b)overtuming (F.S.>2.0) dlglobel stability (F.S.>125 - 1.5)

(nol considered in design programmes)

Figure 4 Potential modes of failure for external stability calculations

Typical ratios of length of reinforcement to height of wall are from 0.5 to 0.7. AASHTO

(1990) recommends that the ratio of reinforcement length to wall height be not less than0.7

or that the reinforcement leng th be not less than 2.4m, whichever makes the reinforcement

length greater. This American practice restriets the design and analysis procedures to walls

3 Design Methods

The forces and geometry considered in externalstability ca1culationsare illustrated in Figure

5. In accordance with conventional geotechnicalpractice, the structure must be located so that

it is not part of a larger global instability.

(b) Internal failure

H

Potential intemal failure mechanisms are illustrated in Figure 6 and include the

following:-(i)

(ii)

(iii)

Figure 5 Forces used in external stability calculations

rupture of the reinforcement due to tensile over-stressing.

pull-out of the reinforcement within the reinforeed soit mass.

3 Design Methods

a)tensile over-stressing bIreintorc:ement

puUout

cl connection

over- stressing Figure 6 Internat modes of failure

The recomrnended method of analysis to determine the spacing, length and number of reinforcement layers is based on a "tie-back wedge" method of limit equilibrium analysis.In

this approach, the factor of safety of each layer of reinforcement against over-stressing and pull-out is referenced to an intemal Rankine active plane propagating from thetoeof the wall at an angle of 450+ct>/2 to the horizontal, where ct> is the peak friction angle of the reinforeed

3 Design Methods

The allowable design load TI,of the reinforcement is calculated from the following

formula:-T

L

Figure 7 CaJculation of tensile laad in reinforcement layers and reinforcement pullout capacity

TI = CRF

*

Tuil''FC

*

FD * FS

>

TIII&X = KI*S (-vz+q)VI

Where,

(1)

Creep Reduction Factor (i.e 0.2 ..0.4)

ti

Partial factor of safety for environment degradation (i.e 1.25.. 3.0)

Partial factor for construction darnage (i.e 1.1..2.0)

CRF

=

FC =

3 Design Methods

FS = Panial factor for overall uncertainty in problem geometry, soil

properties and boundary loading (FS> 1.5)

K.

= Rankine coefficient for active earth pressure

T

uh = Ultimate strength in kN

T

max = Maximum tensile strength in kN

z = Depth in metres

q = Surcharge load in kN/m2

"Y = Unit weight in kN/m3

Sv = Contributary area about each reinforcement layer in m2/m

Most manufacturers can provide recommended allowable design load data based on creep testing and site specific soil data.

(c) Pull-out capacity of a geosyntbetic layer

Pullout tests model conditions associated with reinforcement slip. The pullout test failure mechanism is appropriate for the determination of the required reinforcement embedment length. The calculation of the pull-out capacity of a geosynthetic layer is dependent on the geometry of the material and the efficiency of geosynthetic-soilload transfer.

3 Design Methods

Where,

= Coefficient of interaction (AASHTO 1990,recommended value 0.5..0.7)

Anchorage length beyond the internal failure plane in metres Friction anglein degrees

(ii) Geotextiles

The following pullout capacity (Tp) equation is recommended by

AASHTO(1990):-(3)

Where,

=

Friction angle describing peak shear resistance along the soil-geotextile interface (i.e 2<1>/3) in degrees

Anchorage length in metres (i.e minimum anchorage length is 1m to ensure adequate embedment of reinforcement layers in the resistant soil zone)

3 Design Methods

3.3.2 Broms Method

3.3.2.1 General

Broms method determines the reduction of horizontal or lateral ea.rth pressure on the face of asteep slope by considering the equilibrium of the forces exerted by two reinforeed mats. The method involves three consecutive

steps:-(i) spacing and anchor length of reinforcing layers (ii) internal stability of the reinforeed section (iii) overall stability of the slope

(a) Spacing and anchor length

The maximum spacing between two reinforcing mats is determined by

considering:-• the effective load take-up by the reinforcing mat.

• the distribution of the lateral pressure on the inside of folded-back envelopes.

3 Design Methods

a...=Ko"Z

lal FOAEST SERVICf

0",= l(,iYZ+91_ , [k.ll('T,l+3gl . 21 l3(y,'.Q) Il,L): Ie, :3ON...Plt.RTf ET AL t"-IIJDsC'C)f r'... , fOI" .t..-.o I. ~ IN""'orceo"WIl' ~" :() 651(.(1Sq+TH) (DI8AOUS T

i

(q:O)

r

I

I I H

1

°h(kF'11)a'57l(m) 0'"(pal,.. IOOZllll @l<02H ~,-' ... 6"lkF'11)a3,I4H(m) 11I'I(PSI"'2OH(II) @l>O.2M .l.. '___-' : "lkF'11I=236 "mI a",psfl-'5ti(1I1 Iq COLLNlGEOTEXTLE: LEGEND Cl" - ~ _Ihore.... H-~OI ... Y - BDfllIil ~"

Q= IIC.,SIICNrgII ., lap ot ...

Kot I· .

K.z..,,2(45'.• /2)

• - ..., IncbanangII Ol

bàlllOl

I-dIpII'I beIDIr lap Ol ...

Figure 8 Earth pressure distributions used for ried-back wedge methods

Therefore, UH = O.65K_(1.5q.

+

-yH) Where, K_ -y = =

Rankine coefficient for active earth pressure Bulk unit weight of fill in kN/m3

3 Design Methods

H = Height of earth retaining structure in metres Static overburden pressure in kN/m2

factor of safety to cover the natura! variations inlateral earth pressure and the variations of the unit weight and the angle of intemal friction of the soil.

q.

0.65 = =

The spacing D, between two reinforcing mats [rn] is calculated using the following

formula:-D =

(5)

Where,

Nmax = Allowable permanent load on the mat [kN] after considering all relevant partial safety factors

The required anchor length L, is calculated using the following formula:

-(6)

3 Design Methods

Where,

<I>

FS

= <I>wil! <I>fabric

Factor of safety

Note: A length of 2.5m is normally taken for the anchor length of the fabric folded back at the top side

=

(b) Internal stability of the reinforeed soiUsection

A limit equilibrium analysis is used in which a large number of potential failure surfaces are

considered to determine the internal stability of the reinfoeed slope. For each failure surface a safety factor is ca1culatedwhich represents the ratio between the available shear strength of the soil and the shear stress required for equilibrium. Of all the potential failure surfaces considered the failure surface which gives the lowest safety factor is decisive. Consequently, on the basis of these results the selected reinforcement layout can be changed to obtain a

required safety factor (TRRL, 1977).

(c) Overall slope stability

Although steep sloped reinforeed structures may be built on good quality soil, it is advisable

to ensure overall stability of the design derived from steps (a) and (b) above. This is done

with the current methods for deep failure surfaces, e.g Bishop, adapted for reinforcement layers intersecting the failure surface. But, the safety against tilting, horizontal movement and bearing capacity failure are checked using conventional methods of retaining walls.

3 Design Methods

3.3.3 Design Charts according to Jewell

3.3.3.1 General

Design charts for steep reinforeed slopes published by Jewell et al., (1984) have provided greater economy and flexibility in design. The charts enable to design avertical reinforeed case, and are valid for the range of polymer grids. The slopes as pointed out in 3.1, are assumed to rest on a competent and level foundation. The crest of the slope is level. Uniform vertical surcharge loading is allowed, but point loads and earthquakes are not included in these design charts.

The focus of attention for steep slopes is the distribution of maximum required stress in the slope and the provision of reinforcement with a sufficient strength and spacing so that the minimum available stress exceeds the maximum required stress at every depth.

Jewell et al. ,(1984) Design Chart Method may be considered as a stress method which is based on lateral earth pressure considerations. Limiting equilibrium analysis is used to equate the force tending to cause instability to the stabilizing force provided by the horizontal reinforcement.

3.3.3.2 Internal, Overall and External equilibrium

3 Design Methods

design is shown in Figure

9. The available stress

must equal or exceed the maximum required stress at every depth. A shortfall in the provision of reinforcementat anydepth

could result in local

s t r e s s in g of a reinforcement layer above

the allowable force. The

magnitude and distribution

of maximum required stress in a reinforeed slope is similar to that in the conventional retaining wall design.

I ~I I I I

I

I

q

..

~ .. .r.

li

1

/

I

Y

I r--'

I

Spac,ng' ~

"

"

~

L

.

"

.

c

_

_

_

.1L

_

r

Spaong 2

Figure 9 Maximum required messes exceeded everywhere by available stresses from the reinforcements

The minimum required reinforcementlength satisfies both intemal and overall equilibrium (i.e more deep-seated potential failure surfaces), and prevents direct sliding through the reinforeed block.

(b)Extemal equilibrium

As stated earlier on section 3.3.3.1 the Jewell et al., Design Charts apply only to slopes on competent foundation soils. However, there are typically three concerns for extemal equilibrium in steep reinforeed slope design: (a) direct outward sliding of the reinforeed block, (b) local hearing capacity failure beneath the required zone, and (c) complete failure of the whole reinforeed slope. Mechanisms (b) and (c) have not been included in the design charts. The assumption bas been made that the foundation has adequate capacity. For very steep slopes,

~>

85°,particular attention should be given to checking mechanism (b), using the conventional adaption of the Meyer-hof (1953) bearing capacity rules commonly applied

in conventional reinforeed soilwall design. For flatter slopes, particular attention should be given to checking mechanism (c); using routine slope stability calculations.

3 Design Methods

Therefore, external equilibrium involving potential failure mechanisms passing around the

reinforeed zone and local bearing capacity failure in the foundation beneath the reinforeed zone in very steep slopes haveto be checked separately.

3.3.3.3 Material properties and safety margin

The selection of the design values for the material properties of the soil and the reinforcement and the selection of safety margins is certainly the most important step in design. The selection procedures follow the design philosophy which has been fully described by Iewell and Greenwood (1988).

(i) SoiI properties

• The recommended approach with polymer reinforcement materials istoselect directly a design value for the soil shearing resistance equal to the critical state shearing resistance 4>d'= 4>t.'. Selection of 4>d'

=

4>c.'removes the need to consider the influence of the reinforcement stiffness for stability analysis purpose.

• Placement of fill during construction is normally weU controlled in the field so that the maximum expected soil unit weight may he selected directly for design, ')'d=')'maJl.

3 Design Methods

A design valuefor the pore water pressure coefficientr, introduced by Bishop and Morgenstern (1960) is best selected by considering the magnitude of the pore water pressures that it implies and comparing these with the worst expected pore water pressures in the slope. The coefficient r, is not an ideal description of the pattem of pore water pressures which might develop with water infiltration or flow through a slope, but it is the only non-dimensional description of pore water pressure available.

• The slope dimensions H and{j may be taken equal to their expected values for design. Inclusion of a nomina] verticaI surcharge of the order 10 kN/nr would be prudent in routine design to allow for some margin on over-filling, and other temporary loadings on the slope crest. VerticaI surcharge loading is taken into account by designing an equivalent slope of increased height H' .

(H) Reinforcement properties

There are two aspects: load carrying capacity and bond. The allowable force Pall for the

reinforcement must apply for conditions in the ground, at the end of the design life

(tJ

at the design temperature (TJ and for the material having been subject to installation mechanical damage and the subsequent action of the soil chemical and microbiological environment. A procedure for evaluating such an allowable force is given by Greenwood and Jewell (1989) who give recommended values for the safety margin fmbetween the allowable force and the

3 Design Merhods

(7)

/'"

(The magnitude of fm includes for (among other factors) the amount of extrapolation

of the reinforcement test data required to reach the envisaged conditions at the design time and temperature)

For geotextiles, the bond coefficient, fbmay be determined in a conventional direct sheartest

for "skin friction", or direct sliding, as in this case fb=fcla=tanMtanq,. If the measured

coefficient is less than that assumed in the design charts i.e feb

<

0.80 then greater length to

resist direct sliding will be required than that indicated in the charts.

The bond coefficient for grid reinforcement is in the range 1.0> fb> 0.3. The bond coefficient for a grid depends on the shearing resistance of the soil and can change by a factor of 2 depending on whether the grid is to be used in compacted sand fill or compacted c1ayfill. The direct sliding resistance for grid reinforcement may be measured in a direct shear test, and this should be checked to ensure that it falls within the range for which the design charts apply.

3 Design Methods

(i) determining the required stress

(ii) determining the reinforcement length (iii) determining the reinforcement spacing

Practical design would normallyinvolve two zones of reinforcement. The maximum allowable spacing is set by the lowest layer in any zone. For all slopes the lowest zone extends from the base, where the selected reinforcement must satisfy the inequality:

-(8)

If the spacing is changed at a depthZ2 below the slope crest, the above inequality must again be satisfied but using the depth ~ rather than H. An envelope of available stress is then constructed showing depths at which the spacing may be changed and showing positions of the reinforcement layers as shown in Figure lO(b). The practical limits to the maximum vertical spacing which are suggested for design are as shown below:

(S)max s;; Minimum of (H, lm)

8

(9)

Unifonn vertical surcharge qlV at the slope crest is allowed for by designing the slope with an artificially greater height as shown below

:-3Design Methods

H'

=

H+qsv Yd

(10)

In the design calculations, the height H' is used instead of H for the slope height. The reinforcement layout is simply terminated at the physical height of the slope.

This procedure is exact for the required stress, but is only approximate (but safe) for the

required reinforcement length.

I

Reinfol'cement ~ spKIng2

I

Reinforcement ~ spaClng 1

K~=K....,)(IOad'Sl'Ieddlng allowanee

(al

Ze",JH=LIJiL~

0

_.

=:'.H(Ls ILI<)Kqoo

, _

28

IL.. - Ioad-sl'leddlng a"owanee

Maximum

reqUlled

Slress

z

3 Design Methods

3.3.4 Design guidelines

3.3.4.1 General

As a typical example of guidelines for the design of geogridlgeotextile reinforcing slopes, reference is made to the ones developed by Akzo Industrial Systems bv in The Netherlands. About 25 years ago no design guidelines were available and procedures were based on leaming by trial and error. The requirements reinforcing mats had 10 meet were not yet known and had to be defined by full-scale testing etc. Past experience in ~einforcing fabrics made it possible to developed guidelines for soil reinforcement under embankments on low bearing capacity soils so as to increase the overall stability of the embankment, but also for soil reinforcement in asteep slope embankment to reinforce the soil to such an extent that the slope remains stabie under slope angles steeper than the normal equilibrium angle.

(a) Reinforcing mat

Usually design methods used for steep embankrnents are based on limit equilibrium conditions. The factor of safety against sliding is calculated for all possible intemal sliding planes using two or three wedges. An optimization of the layout of the reinforcement layers is done using the computer programs whereas the overall stability of the reinforeed embankment is checked as described by methods 3.3.1 and 3.3.2 above.

3 Design Methods

The design calculationslead to either a required reinforcement strength or are partly based on allowable strength in certain types of reinforcement materials. In this design attention is given to the strain in the reinforcing mat. From a soil mechanics point of view, the allowable strain in soilis limited.Too much strain could lead to a decreased shear strength in the limit state.The strain to be developed during the service life of the reinforeed structure should also be checked because they can induce deformations which are unacceptable.

(i) Maximum allowable load

The allowable design strength of a reinforcing mat is the ultimate tensile strength minus factors or values for creep, temperature effects, chemical or biological attack, mechanical damage during installation, etc. For a safe design, it is required that all these factors be

determined correctly and long-term effects of the combination of these factors betaken into account. The effects of most of these mechanisms are known to polymer scientists, but often this know-how cannot be directly translated into parameters understandable to civil engineers.

An example of design method is presented by Voskamp, W. (1989). According to this reference the maximum allowable load of a reinforcing mat is found by the formula:

3 Design Methods

The ultimate breaking strength, Pcw, based on creep performance for stabilenka polyester fabric has been executed at various load levels and for a period of approximately ten years. The results are combined in the stress-rupture line of Figure 11 where the characteristic

strengths, (Pcbar), of Figure 11

different design life periods can be found as a

percentage of the ultimate tensile strength. This is the strength above which the material will fail in tension. Data have been extrapolated to allow the characteristic strength for design lives of up to 120 years to be determined. The value of Pcbar of equation 11 for a specific design

life time can be found by means of the graph of Figure 11 as follows:-Where, P

₌

PCba!

=

ILJ

=

1L2 = 1L3 = FJ = =

Maximum allowable load in kN

Ultimate breaking strength based on creep performance in kN Mechanical damage

Chemical environment factor Bacteriological environment factor

Factor of safety that covers possible deviation in regard to the parameter values above.

Traditional factor of safety (i.e 1.35 )

'00

,

so

r

en 60

1--

I

::l Ö I e..!E_ .10 20 0

----, n 1WK ,yr 10yrs 120yrs 4 '0logtmln duratIon olloadlng

Ultimate breaking strength of fabrie based on ereep

performance (i.e stress-rupture line)

3 Design Methods

PCbar = ( % stress ratio) x UTS

Where,

% stress ratio is the factor of the applied load divided by the ultimate tensile strength (UTS) of that material.

When reinforcing mats areinsta11edduring constructions, the matscanbe damaged by the fill being compacted on top of it. Tests on polyester reinforcing fabrics give strength reductions as shown in Table 1.And therefore the mechanica! damage factors for polyester reinforcing fabrics are shown in Table 2. Also, the chemica! environment of the fill around the reinforcing mats influence the strength of the mat. Tests on polyester give decrease of strength as shown in Figure 12 for resistance in sea water and resistance in acid media. So the chemica! environment factors are as shown in Table 3.

Table 1Streogth reductioos Table 2 Mechanical damage factors

25%

Sand Sand 1.17

sharp gravel

15%

3 Design Methods

Table 3 Chemical environment

factors for polyester

fabrics

Table 4 Partial safety factor (f'.,.)

pH 9 1.12

pH 8-5 1.0

pH4 1.05

Design life Safety factors

(years) (fml)

120 1.3

60 1.2

Table 5 Partia! safety factor-mechanica! installation damage (fll>2')

Material fiIl weIl graded Maximum partiele Safety factor (fmll) size (mm)

Coarse aggregate 60-125 1.40

Gravels 2-60 1.30

Sand s2 1.10

Table 6 Partia! safety factor (fmn)

Soil pH level Safety factor

(PH) (fm22)

9.0-9.5 1.15

4.1-8.9 1.00

2.0-4.0 1.10

3 Design Merhods - 100 I '#. ._-,

11

95 ~ 90 Il) :::s ~ 85 ~ c::: ...

_...

-._

_.

_{_.}

-.-._

.._--- .. -- PES -.- PA 10 20 Time (months) Resistance in acid media pH

=

5

.-.

---PES _.- PA

_e_

pp 30 10 20 30 40 Time (months) Resistance in sea-water

Figure 12 Chemica! environment for polyester fabrics

3 Design Merhods

(ii) Anchor length of a reinforeed mat

The reinforcing mat must be anchored in the surrounding soil and transfer the load from the reinforcing mat to the soil by friction or bond. Bond parameters of stabilenka have been established using a shear box tests. The following coefficients of interaction were determined:

Sand Ct 0.83 .... 0.90

Gravel Ct 0.83 .... 0.86

For sand and gravel the required anchor length can be found (bond at two sides of the fabric) by the following relationship:

where, L

₌

P

₌

(fv

=

el>,

₌

FS

₌

Ct

=

ó'

₌

L

=

(12)

Required length in metres

Maximum reinforcement load in kNfm

Effective vertical stress in kNfm2

Angle of internal friction of the soil in degrees Factor of safety (mostly 1.5)

Coefficient of interaction ( tanó'ftanel> ')

Effective angle of soil-fabric bond stress in degrees

The above data used in the design apply for the particular reinforcing fabrics considered and may not be applicable for other geotextile materials because the type of weaving structure and the type of yam have influence on the results.

3 Design Methods

(b) Geogrids

(i) The maximum allowable load

The maximum allowable force that the reinforcement can be relied upon to deliver at the end of the design lifeis calculated using the following relationship:

Where, fm

₌

fm2

=

fml

=

fm21

=

fm22

-PalJ

=

Peur

=

(13)

fmlX fm2 (overall material safety factor)

fm21 x fm22

Partial safety factor for manufacture and extrapolation data

Partial safety factor for mechanica! installation damage Partial safety factor for environmental effects

Maximum allowable force in kN/m

Characteristictensile strength for a certain design life in kN/m

3 Design Methods

To allow for variation in

manufacture and product

dimensions and to account for extrapolation of data,

an appropriate value for fml should be selected from

Table 4. The partial factor for loss of strength due to mechanical damage (fm2l) , ,....~- . :'\',,?- ""':-1: ::-- :e-~7 .r-', .~ ,., ~ -

_?

ç;; o ?- >- _'" ~ >- 0 ~ :; >- ₀ s:2 Q) '-' > -~ ~,~ ...,..: -:::'"'_---- ~.1

-

_

-that may be sustained c'o-:

during installation is selected from Table 5. The partial safety factors given for site damage assume that well-graded material is used. Certain materials,

e.g crushed hard rock with sharp edges, may require a higher mechanical damage factor or

,--,_ --" "-_,---- ---- -..,

r

- ... - - c

:_.-::-.::'":. :~~;ng~'::'91_. J

Figure 13 Time to rupture under varying load for fortrac geogrid

(Reference: Akzo Fortrac geogrid)

a protective layer of fine material.

Reduction factor due to environmental conditions (~2) for Fortrac geogrid is selected from Table 6.

Once the allowable load is obtained, the design procedure for a structure reinforeed with geogrids proceeds in the same way as for Stabilenka reinforcing mats.

3 Design Methods

3.3.5 Forest Service Method, Collin Method, Bonaparte et al. Method,

Leshchinsky

&

Perry Method, and Schmertmann et al. Method

3.3.5.1 Description of methods

(a) Forest Service Method, Collin Method and Bonaparte et al. Method

The Forest Service Method, the Collin Method and the Bonaparte et al. method are based on lateral earth pressure considerations, whereby limiting equilibrium analysis is used to equate the horizontalforces due to lateral earth pressures tending to cause instability to the stabilizing tensile forces in the horizontal reinforcement.

These methods typica11y presurne aplanar failure surface through the reinforeed mass described by the Rankine active failure condition. The reinforcements extend beyond the assumed failure surface and are considered to be tension-resistant tiebacks for the assumed failure wedge. As aresuit, they are frequently collectively reffered to as "tied-back wedge"analysis methods.

Although tied-back wedge methods have many similarities, they use different lateral earth pressure distributions to describe the horizontalforces that need to be resisted.These methods assume that Rankine's active failure surface is applicabie; however, the pressure distributions are all different from Rankine's active earth pressure distributions.Juran (1977) demonstrated that the presence ofreinforcement alters the stresses and strains in the soil mass, consequently causing the failure surface to be different from that for an unreinforced soil mass. The earth

3 Design Methods

(b)

Leshchinsky

&

Perry Method and Schmertmann et al Method

The Leshchinky&Perry and the Schmertrnannet al Methods employ the approach commonly used in conventional slope stability analysis, but modified slightly to account for the inclusion of tension reinforcements and using varying assumptions conceming the inclination of the reinforcements at the failure surface. They are reffered to as "slope stability"methods. Leshchinsky and Perry used limiting equilibrium analysis of rotational (log-spiral) and translational (planar) failure surfaces (Figures 14a and 14b respectively). The Schmertrnann et al. method is based on limiting equilibrium analysis using wedge failure models. Straight line and bi-linear wedges are used for different aspects of the analysis. Extended versions of Bishop's and Speneer's methods of slope stability analysis are used to modify the results of the wedge analysis.

Due to their complicated computations, the Leshchinsky and Perry and Schmertmann et al. methods both use design charts. Both of these methods can be used for steep slopes as weU as for vertical to nearly vertical walls.