soil mechanics in_pavement_engineering

44
Soil mechanics in pavement engineering S. F. BROWN Application of soil mechanics principles to the design of pavement foundations, the design of complete pavements and to their structural evaluation ‘in-service’ has lagged some way behind knowledge accumulated through re- search. Present design methods are generally empirical and often based on use of the California Bearing Ratio test, which was aban- doned in California some fifty years ago. The soil mechanics problem is one of under- standing how soils and granular materials respond to repeated loading and applying this knowledge to pavement design with the aid of appropriate theoretical analysis and an under- standing of failure mechanisms. Non-linear stress-strain characteristics are a particular feature of the problem and have to be catered for in design and evaluation. Various ‘tools’ are available to assist the pavement engineer. These include theoretical analysis, laboratory testing apparatus, field testing and full-scale trials with appropriate instrumentation. The resilient and permanent strain response of clays and granular materials is reviewed in the context of the requirements for design. The essentially empirical UK Highways Agency method of design and its evolution are discussed in the light of current soil mechanics knowledge. By contrast, the development of mechanistically based approaches is outlined, together with suggestions for the implementation of present knowledge in a practical method of design for pavement foundations. Parallels are drawn between road and rail track design and devel- opments relating to the latter are also reviewed. A forward look suggests that further research to improve understanding of the effective stress state below pavements and the application of recent theoretical work on partially saturated soils could form the basis for improved pave- ment engineering in the future. KEYWORDS: pavements and roads; design; repeated loading; clays; field instrumentation; deformation; laboratory tests. L’application des principes de la me ´canique des sols a ` la conception des couches de fondation et de chausse ´es entie `res, ainsi qu’a ` l’e ´valuation structurale des chausse ´es en service a un certain retard sur l’e ´tat actuel des connaissances. Les me ´thodes de conception actuelles tendent a `e ˆtre empiriques et reposent souvent sur l’essai de portance californien, que la Californie elle- me ˆme n’utilise plus depuis une cinquantaine d’anne ´es. Le de ´fi qui se pose a ` la me ´canique des sols est de comprendre la re ´action des sols et des mate ´riaux granulaires a ` des charges re ´pe ´- te ´es et d’appliquer les lec ¸ons qu’on en tire a ` la conception des chausse ´es en s’appuyant sur une analyse the ´orique judicieuse et sur la compre ´- hension des me ´canismes de rupture. Un aspect particulier de cette question est les caracte ´ris- tiques de tension-de ´formation non line ´aires, dont il faut tenir compte dans la conception et l’e ´valuation. L’inge ´nieur des chausse ´es dispose a ` cette fin d’une panoplie d’outils: analyse the ´ori- que, essais en laboratoire, essais sur le terrain et essais en vraie grandeur sur chausse ´es in- strumente ´es. On examine ici les de ´formations e ´lastiques et permanentes d’argiles et de mate ´- riaux granulaires dans le contexte des crite `res de conception. On analyse aussi la me ´thode de conception, essentiellement empirique, utilise ´e par l’administration routie `re du Royaume-Uni (UK Highways Agency), ainsi que son e ´volution, a ` la lumie `re de ce que l’on sait actuellement sur la me ´canique des sols. Par opposition, l’expose ´ de ´crit brie `vement les me ´thodes me ´canistes qui ont e ´te ´ formule ´es et pre ´conise l’application des connaissances actuelles dans une me ´thode pra- tique de conception des couches de fondation. Il compare la conception des routes et celle des voies ferre ´es et examine les progre `s re ´alise ´s dans ce dernier domaine. Pour ce qui est de l’avenir, le ge ´nie routier aurait fort a ` gagner de recherches plus pousse ´es sur les tensions effi- caces dans le sous-sol, ainsi que de l’application de re ´cents travaux the ´oriques sur des sols partiellement sature ´s. INTRODUCTION Pavements are civil engineering structures used for the purpose of operating wheeled vehicles safely and economically. There is a very wide range of Brown, S. F. (1996). Ge ´otechnique 46, No. 3, 383–426 383 Professor of Civil Engineering, University of Notting- ham, UK.

Upload: alexander-gomez

Post on 19-Jan-2015

1.172 views

Category:

Technology


7 download

DESCRIPTION

 

TRANSCRIPT

Page 1: Soil mechanics in_pavement_engineering

Soil mechanics in pavement engineering

S. F. BROWN�

Application of soil mechanics principles to thedesign of pavement foundations, the design ofcomplete pavements and to their structuralevaluation `in-service' has lagged some waybehind knowledge accumulated through re-search. Present design methods are generallyempirical and often based on use of theCalifornia Bearing Ratio test, which was aban-doned in California some ®fty years ago.

The soil mechanics problem is one of under-standing how soils and granular materialsrespond to repeated loading and applying thisknowledge to pavement design with the aid ofappropriate theoretical analysis and an under-standing of failure mechanisms. Non-linearstress-strain characteristics are a particularfeature of the problem and have to be cateredfor in design and evaluation. Various `tools' areavailable to assist the pavement engineer. Theseinclude theoretical analysis, laboratory testingapparatus, ®eld testing and full-scale trials withappropriate instrumentation.

The resilient and permanent strain responseof clays and granular materials is reviewed inthe context of the requirements for design. Theessentially empirical UK Highways Agencymethod of design and its evolution are discussedin the light of current soil mechanics knowledge.By contrast, the development of mechanisticallybased approaches is outlined, together withsuggestions for the implementation of presentknowledge in a practical method of design forpavement foundations. Parallels are drawnbetween road and rail track design and devel-opments relating to the latter are also reviewed.A forward look suggests that further research toimprove understanding of the effective stressstate below pavements and the application ofrecent theoretical work on partially saturatedsoils could form the basis for improved pave-ment engineering in the future.

KEYWORDS: pavements and roads; design; repeatedloading; clays; ®eld instrumentation; deformation;laboratory tests.

L'application des principes de la meÂcanique dessols aÁ la conception des couches de fondation etde chausseÂes entieÁres, ainsi qu'aÁ l'eÂvaluationstructurale des chausseÂes en service a un certainretard sur l'eÂtat actuel des connaissances. LesmeÂthodes de conception actuelles tendent aÁ eÃtreempiriques et reposent souvent sur l'essai deportance californien, que la Californie elle-meÃme n'utilise plus depuis une cinquantained'anneÂes. Le de® qui se pose aÁ la meÂcanique dessols est de comprendre la reÂaction des sols etdes mateÂriaux granulaires aÁ des charges reÂpeÂ-teÂes et d'appliquer les lecËons qu'on en tire aÁ laconception des chausseÂes en s'appuyant sur uneanalyse theÂorique judicieuse et sur la compreÂ-hension des meÂcanismes de rupture. Un aspectparticulier de cette question est les caracteÂris-tiques de tension-deÂformation non lineÂaires,dont il faut tenir compte dans la conception etl'eÂvaluation. L'ingeÂnieur des chausseÂes dispose aÁcette ®n d'une panoplie d'outils: analyse theÂori-que, essais en laboratoire, essais sur le terrainet essais en vraie grandeur sur chausseÂes in-strumenteÂes. On examine ici les deÂformationseÂlastiques et permanentes d'argiles et de mateÂ-riaux granulaires dans le contexte des criteÁresde conception. On analyse aussi la meÂthode deconception, essentiellement empirique, utiliseÂepar l'administration routieÁre du Royaume-Uni(UK Highways Agency), ainsi que son eÂvolution,aÁ la lumieÁre de ce que l'on sait actuellement surla meÂcanique des sols. Par opposition, l'exposeÂdeÂcrit brieÁvement les meÂthodes meÂcanistes quiont eÂte formuleÂes et preÂconise l'application desconnaissances actuelles dans une meÂthode pra-tique de conception des couches de fondation. Ilcompare la conception des routes et celle desvoies ferreÂes et examine les progreÁs reÂaliseÂsdans ce dernier domaine. Pour ce qui est del'avenir, le geÂnie routier aurait fort aÁ gagner derecherches plus pousseÂes sur les tensions ef®-caces dans le sous-sol, ainsi que de l'applicationde reÂcents travaux theÂoriques sur des solspartiellement satureÂs.

INTRODUCTION

Pavements are civil engineering structures used forthe purpose of operating wheeled vehicles safelyand economically. There is a very wide range of

Brown, S. F. (1996). GeÂotechnique 46, No. 3, 383±426

383

� Professor of Civil Engineering, University of Notting-ham, UK.

Page 2: Soil mechanics in_pavement_engineering

pavement structures depending on the nature of thevehicles to be accommodated, the wheel loadsinvolved and the numbers of such loads to becarried over a given time period. Fig. 1 showscross-sections for a number of different pavementtypes ranging from unsurfaced `gravel' roadscommonly found in developing countries, to heavyduty ¯exible bituminous or rigid concrete pave-ments used for the motorway systems of indus-trialized countries. Railway track is included asanother specialist type of pavement in whichthe method of transmitting load to the soil differsfrom a highway or airport pavement but for whichthe essential principles of soil mechanics equallyapply.

It is clear from the structures in Fig. 1 that thescope of pavement engineering is rather wide. Anessential ingredient is soil mechanics since all thestructures are in intimate contact with the groundand most combine one or more layers of unboundgranular material. In addition, the complete pave-ment engineer needs to understand the principlesof asphalt mechanics, of concrete technology andof stabilization as well as the more complexstructural con®gurations used in railway track.The engineer needs to be concerned with vehicleloading, whether from trucks, aircraft, containerterminal traf®c or railway rolling stock and withthe in¯uence of the environment (notably tempera-ture and water) on the pavement structure. The

proper use of geosynthetics for drainage, ®ltration,separation and reinforcement is also important, asare the uses of other ground improvement tech-niques such as stabilization and the effects of frost.

Increasingly, the profession is becoming con-cerned with the evaluation and maintenance ofpavements rather than the design and constructionof new works. Structural evaluation and the designof remedial treatment are rapidly expandingactivities in which the role of soil mechanics,while not as signi®cant as for new construction, isnonetheless of considerable importance. This paperdoes not attempt to cover all aspects of pavementengineering or to consider all pavement types.Rather, it concentrates on the role of soil mech-anics and, hence, on the pavement foundation,which can broadly be de®ned as one or morelayers of compacted unbound granular materialplaced over the subgrade soil (Fig. 2). The soilmay be either undisturbed, in cuttings, or re-moulded, on embankments. Since the interactionbetween the foundation and the bituminous orconcrete construction placed over it is central topavement design and to structural evaluationprocedures, some discussion of bound materialsand of failure mechanisms is required. This allowsthe proper application of soil mechanics principlesfor the foundation to be put in its correct context.In order to do this, only bituminous constructionwill be considered. Reference is made to rail-trackconstruction but this topic is adequately covered bySelig & Waters (1994).

The paper presents the design problem, explain-ing the background to current, essentially empiri-cal, practice and presenting the most signi®cantresults of research carried out since the mid-1950swith emphasis on recent developments. Discus-sion covers design philosophy, theoretical analysis,material properties, laboratory tests, ®eld testing,pilot-scale experiments and extensions of presentknowledge to engineering practice.

Although pavement engineering procedures varysomewhat around the world, the essential featuresof present practice are generally common andrather empirical. In looking at the details and how

Granular Granular

Granular

Granular

Granular

Soil

Soil

Soil

Soil

(a) Gravel road

(c) Asphalt pavement

(e) Composite pavement

(g) Block pavement

Asphaltic

AsphalticCement treated or concrete

Concrete or brickblocks on sand

Asphaltic or cement treated

Granular

Granular

Bitumen seal

Soil

Soil

Soil

Soil

Concrete

Concrete

Cement treated

Rail on sleepers

Ballast (granular)

Sub-Ballast (granular)

(b) Sealed gravel road

(d) Concrete pavement

(f) Heavy duty concrete

(h) Railway

Fig. 1. Cross-sections of various pavement types

Moving wheelLoad Load

Surfacing

Base

Sub-base

Subgrade

Rails on sleepers

Ballast

Sub-ballast

Subgrade

(a) (b)

Foundation

Fig. 2. De®nition of pavement foundation: (a) road;(b) rail track

384 BROWN

Page 3: Soil mechanics in_pavement_engineering

these could be improved by implementation ofresearch, the situation in the UK is considered.

A study of the major sources of soil mechanicspapers, both journals and conferences, over thepast thirty years clearly demonstrates that soilmechanics for pavements has become a very minorpart of geotechnical engineering. Although therehave been major research studies on soils andgranular materials for pavements, these havegenerally not been published or discussed inserious soil mechanics journals or conferences.Moreover, as research has concentrated increas-ingly on heavy duty pavements, problems asso-ciated with the bituminous and concrete layershave dominated. The early stages of the UK'smotorway reconstruction programme in the late1970s clearly identi®ed the need for sound foun-dation design (Cox, 1980). Excavations revealedwet and inadequate sub-bases with drainage thathad often ceased to function or not been present.These revelations, together with the realizationthat some structural or surface maintenance ofmajor highways was always going to be required atintervals in future, pointed to the need for improvedfoundation design and construction practice to avoidperiodically having completely to reconstruct thepavement. Unfortunately, this was not accompaniedby serious Department of Transport research intothe real soil mechanics problems involved. How-ever, the need for foundations which would nothave to be replaced but could serve below re-habilitated pavements in future was apparent. Anessential feature of this was the need for improveddrainage design and maintenance.

The role of the Transport Research Laboratory(TRL) has always been central to developments inpavement engineering practice in the UK. After thesecond World War, they adopted US procedures forsoil testing and pavement design (Davis, 1949).This was followed by an extensive programme ofresearch on moisture conditions in subgrades leadby Dr David Croney. This work drew its inspira-tion from agricultural soil physics rather than fromthe emerging discipline of soil mechanics. Croney& Coleman (1948) argued that since subgradefoundations were above the water table, the waterconditions were similar to those of interest toagronomists. This signi®cant investment in studiesof ground water conditions below sealed surfacescontinued for about 15 years, apparently in isola-tion from parallel developments in soil mechanics.The two met at the conference on Pore Pressureand Suction in Soils in 1960 at which it wasapparent that differences of de®nition, of para-meters and of philosophy had advanced to thepoint where bridging the gap was a non-trivialmatter (Cooling et al., 1961). Application of theprinciple of effective stress was central to theproblem. This and related matters are reviewed in

the section on Pavement Design Developments. Itis important to recognize that the background topresent UK practice for the characterization ofsubgrades for pavement design developed fromessentially different origins to those of Terzhagi,Skempton, Roscoe and the other pioneers ofmodern soil mechanics.

A programme of full-scale experiments onpublic roads was introduced by TRL in the1960s. The performance of these has largelyformed the basis for present UK design andmaintenance practice. Although only 4% of theUK's road network is the responsibility of theDepartment of Transport, through the HighwaysAgency, the standards, speci®cations and designrecommendations set by this body (HighwaysAgency, 1994b) dominate practice for most pave-ments in the highway sector.

The much smaller aircraft pavement sector hasevolved its own procedures with little reference toUK highway practice but with a common root inUS World War II developments, augmented bytheory and practice since (British Airports Author-ity, 1993).

For railways, traditional empirical procedureshave always dominated, although the British RailTechnical Centre in Derby did develop a methodof design based on appropriate soil testing inthe 1970s (Heath et al., 1972) but this was neverformally implemented. Their subsequent work con-centrated on maintenance techniques and under-standing track/vehicle dynamic interactions. Overthe past 20 years, the work of Professor Selig andhis colleagues in the USA has brought a properapplication of soil mechanics to railway geotech-nology, but implementation of research remainssparse.

Quite apart from the independent developmentof subgrade research in the UK at TRL, the soilmechanics requirements for pavement engineeringdo differ signi®cantly from those of importance inother geotechnical applications. The essential dif-ferences may be summarized as follows.

(a) Soil below pavements and granular materialsin pavements exist above the water table butbeneath a sealed surface, although this doesnot completely inhibit ingress of water. Hence,both saturated and partially saturated condi-tions can occur.

(b) Soils and granular materials in completedpavements are subjected to large numbers ofload applications at stress levels well belowtheir shear strength (as illustrated by the ®elddata in Fig. 3(a) obtained from a full-scale trialat Wake®eld (Brunton & Akroyde, 1990).

(c) Under partially completed pavements, whenconstruction traf®c is applied directly to thegranular layer, the number of load applications

SOIL MECHANICS IN PAVEMENT ENGINEERING 385

Page 4: Soil mechanics in_pavement_engineering

is fewer but the stress levels are much higheras shown in Fig. 3(b). These data were ob-tained from a haul road experiment at theBothkennar soft clay site in Scotland (seep. 392).

(d) Under a single application of a moving wheelload, a pavement responds in an essentiallyresilient manner. However, irrecoverable plasticand viscous strains can accumulate underrepeated loading. This presents the opportunityto separate the theoretical analysis of pave-

ments into two parts rather than to apply asingle elasto±plastic (or elasto±visco±plastic)analysis as is common for monotonic loadingproblems in geotechnics.

Other branches of soil mechanics which havesomething in common with pavements includeearthquake engineering, off-shore foundation engi-neering and machine foundation design. In allcases, there is the common theme of repeated orcyclic loading. It is signi®cant to note that the lateProfessor Harry Seed, who contributed so much tounderstanding soil mechanics in the context ofearthquake loading, began his interests in repeatedloading with the pavement problem (Seed et al.,1955). Furthermore, when, the ®rst major struc-tures were being designed for North Sea oilexploitation in the 1970s, the experience of re-peated loading of subgrades was used to evolveresearch programmes for clays of relevance towave loading (Andersen et al., 1976).

These interactions between pavement soil mech-anics and other areas involving cyclic loading haveformed an important element of the author's workat the University of Nottingham since 1963. Anattempt has been made to apply the principles ofsoil mechanics to the pavement problem within theoverall context of developing improved methodsof design and structural evaluation. Blending workon asphalt mechanics to that of soil mechanicshas been a central theme, as has the evaluationof appropriate, simpli®ed test methods to aidimplementation in practice. This paper drawsprincipally on the work carried out at Nottinghamby the author and his colleagues, all of which hasbeen made possible by the award of researchcontracts and grants from a wide range of organ-izations both from the UK and overseas. The workhas parallelled that at TRL and, to an increasingextent in recent years, had some in¯uence on theevolution of Highways Agency standards and thework of the British and European Standards organ-izations.

Space has prohibited any discussion in thispaper of several important subjects including drain-age, application of geosynthetics, stabilization,frost effects and the special problems associatedwith aircraft pavements.

PAVEMENT ENGINEERING TOOLS

TheoryThere has been extensive application of the

theory of elasticity to the analysis of layeredpavement systems. Burmister (1943) developedthe essential equations, and, following early setsof tabulated solutions, (e.g. Acum & Fox, 1951)various computer programs were developed toassist in obtaining results in a convenient form.

Fig. 3. In situ vertical stress measurements in sub-grades: (a) below 165 mm asphalt construction atWake®eld; (b) below 350 mm granular layer atBothkennar

1.00.80.60.40.20

120

100

80

60

40

20

0

Time: s

(b)

Ver

tical

str

ess:

kP

a

0.80.60.40.2

20

15

10

5

0

Time: s

(a)

Ver

tical

str

ess:

kP

a386 BROWN

Page 5: Soil mechanics in_pavement_engineering

Today the most widely used are the BISAR (de Jonget al., 1973) and ELSYM 5 (Warren & Diekmann,1963) programs originally developed by researchersin the Shell and Chevron oil companies respec-tively. In both cases, the pavement layers areassumed to be linear elastic and values of stress,strain and de¯ection components at any de®nedpoints in the structure can be computed from givengeometry and surface loading. Typical details areshown in Fig. 4. Wheel loading is represented byuniformly distributed pressure over a circular areaand dual or multi-wheel con®gurations can beaccommodated.

In real pavements, loading is transient, the soiland granular layers (the pavement foundation) havemarkedly non-linear stress±strain relationships,which are in¯uenced by a range of variables, andthe bituminous layer has properties which aresensitive to loading rate and to temperature. Fig.5(a) shows the shear stress±strain relationship for acompacted silty clay determined from combiningin situ measurements of total stress and of strain(Brown & Bush, 1972). These were obtained frompilot-scale test pit experiments subjected to dy-namic plate loading and superposition of in situmeasurements at various depths and orientations.The non-linear stress±strain relationship is clearlyillustrated. Similar data from measurements in alayer of compacted crushed rock are shown inFig. 5(b) in the form of Young's modulus plottedagainst the ®rst stress invariant (Brown & Pell,1967). Notwithstanding these non-linearities, theability to carry out linear elastic structural analysisof pavements has proved extremely useful indeveloping design methods, particularly as the realcharacteristics of the constituent materials havebecome better appreciated.

The main justi®cation for using elastic theory is

that under a single load application, most pave-ments will respond in a resilient manner. Anyirrecoverable deformations will be small relative tothe resilient component. Fig. 6 shows a verticalstrain pulse measured within a bituminous layer asa result of a moving wheel load. There is adelayed elastic response but no residual strain. Thevalidity of using linear elastic theory was the mainobjective of many fullÐand pilotÐscale experi-ments carried out in the 1960s and 1970s. (e.g.Brown & Pell, 1967, Bleyenberg et al., 1977).

Conventionally, each layer is characterized by avalue of Young's modulus and Poisson's ratio. Inview of the differences between real and idealizedbehaviour of pavement materials, the parameter`resilient modulus' was introduced in Californiaduring the 1950s following the pioneering work of

E1 ν1 h1

E2 ν2 h2

E3 ν3 h3

E4 ν4

(x, z)

(x, z)

(x, z)

z

p 5 contact pressureE, ν, h 5 Young's Modulus, Poison's ratio andE, ν, h 5 thickness for each layer

px

x

a

Fig. 4. Linear elastic system for pavement analysis

Fig. 5. Non-linearity from in situ measurements: (a)shear stress±strain relationship for silty clay (afterBrown & Bush, 1972); (b) resilient modulus against1st stress invariant for crushed rock (after Brown &Pell, 1967).

500040003000200010000

5.0

4.0

3.0

2.0

1.0

0

Octahedral shear strain (microstrain)(a)

Oct

ahed

ral s

hear

str

ess:

psi

504030201051

30000

20000

10000

5000

1000

1st stress invariant: psi

(b)

Res

ilien

t mod

ulus

: psi

SOIL MECHANICS IN PAVEMENT ENGINEERING 387

Page 6: Soil mechanics in_pavement_engineering

Francis Hveem, the State's Materials Engineer andProfessor Harry Seed and his colleagues at theUniversity of California, Berkeley. Hveem was ®rstto recognize the importance of resilient propertiesfor pavement foundations and to associate themwith the incidence of fatigue cracking in bitumi-nous surfacing (Hveem, 1955). Seed and hiscolleagues carried out repeated load triaxial testson compacted soils and de®ned the resilientmodulus as the magnitude of repeated deviatorstress divided by the resilient axial strain, whichmakes it equivalent to a resilient Young's modulus.A similar de®nition was applied in later work byHicks & Monismith (1971) when testing com-pacted granular materials. This work is furtherdiscussed in the section on Pavement DesignDevelopments.

In asphalt technology, the term `stiffness' wasintroduced by Van der Poel (1954) and de®ned asuniaxial stress divided by uniaxial strain. When thestrain component is essentially recoverable, this isagain equivalent to Young's modulus but can beapplied over a wide range of loading time and

temperature conditions. Bituminous materials ex-hibit elastic, brittle behaviour at low temperaturesand short loading times, viscous behaviour at theother end of the spectrum and visco±elastic re-sponse at intermediate conditions. For pavementdesign calculations, when moving traf®c is con-sidered under normal temperatures, the response ofa bituminous mixture to a load pulse will beessentially resilient as illustrated in Fig. 6. Finegrained soils too, can behave in a visco±elasticmanner, as shown in Fig. 7 taken from repeatedload triaxial tests on saturated reconstituted siltyclay (Hyde, 1974).

Linear elastic analysis can be used with reason-able con®dence for pavements with thick bitumi-nous or concrete layers but is inappropriate forunsurfaced or thinly surfaced pavements unlessapproximate account can be taken of non-linearbehaviour as discussed below. For bituminouspavements under normal moving traf®c conditions,once a vehicle speed and, hence, loading time isspeci®ed and a temperature condition known, thebituminous layer may be assumed to behave in anessentially linear elastic manner. Conversely, whenthe pavement response to load is dominated by theresilient properties of the granular materials andsoil, their non-linear characteristics must be pro-perly taken into account in theoretical analysis.

The non-linear stress±resilient strain character-istics of soils and granular materials under re-peated loading are discussed in the section onBehaviour of Soils and Granular Materials underRepeated Loading. In pavement engineering, ithas been usual to express the resilient modulusas a function of the applied stress level. To accom-modate this in theoretical analysis, two generalapproaches have been adopted. The simplest in-volves an iterative procedure using linear elasticlayered system solutions. The layers of granularmaterial and soil are subdivided into sublayers to

87654321020.1020.0520.00

0.05

0.100.15

0.200.250.300.35

0.400.450.50

Time: s

Vol

tage

: V

Fig. 6. Vertical strain pulse in bituminous pavementfrom in situ measurement

8 7 6 5 4 3 2 1 0Time: s

Deviatorstress

Axialdeformation Elastic

deformation

Delayed elastic deformation

Fig. 7. Response of overconsolidated silty clay to bursts of undrained repeated loading (after Hyde, 1974)

388 BROWN

Page 7: Soil mechanics in_pavement_engineering

accommodate variations in resilient moduluscaused by the changes in stress which occur withdepth. The stresses involved are those due both totraf®c loading and to overburden.

The general analytical procedure is as follows.

(a) Subdivide the real layers into sublayersÐthegreater the number the greater the accuracy.

(b) Estimate a value of Young's modulus for eachlayer. This may involve a single value for allthe granular material layers and another singlevalue for the subgrade.

(c) Compute the traf®c plus self weight stressesat the centre of each layer. The actual stresscomponents will depend on the non-linearmodel being used.

(d) Adjust the sublayer values of resilient modulusby way of the model and recompute stresses.

(e) Repeat the process until the values of resilientmodulus used for all layers are compatiblewith the computed stresses.

This procedure takes no account of variations instress which take place in the horizontal direction.Hence, the logical extension of the above simpleanalysis process is to adopt the ®nite elementmethod. Most of the serious pavement analysisin recent times which accommodates non-linearstress±strain models has used one of a number of®nite element packages which have been developedspecially for the pavement problem. These in-clude SENOL (SEcant modulus NOn-Linear analysis(Brown & Pappin, 1981) and FENLAP (Finite ElementNon-Linear Analysis for Pavements) (Brunton &d'Almeida, 1992) developed at Nottingham, GT-PAVE

(Tutumluer & Barksdale, 1995) from GeorgiaInstitute of Technology and, for rail track, ILLI-

TRACK (Robnett et al., 1975) developed at theUniversity of Illinois.

FENLAP uses an axisymmetric idealization of thepavement structure under a vertical circular load(Fig. 8). Various boundary conditions are availableto the user but that illustrated in Fig. 8 d'Almeida(1993) appears to be most realistic. Duncan et al.(1968) suggested that analysis should extend to 50times the radius of the loaded area in the verticaldirection but could be limited to 20 times theradius horizontally. In order to minimize comput-ing time, the lower boundary in FENLAP is re-presented as an elastic half space which can becharacterized in various ways. It can include arigid base which may be of use when analysingpavements over ground in which shallow rock orother rigid inclusion is present.

Simple, eight node rectangular elements areused with automatic mesh generation. Input datainclude unit weights of materials, water tableposition, estimated suction values and K0 values.These last allow the user to recognize thatsigni®cant lateral stresses can accumulate in gran-

ular layers as a result of the compaction process.This is analogous to the results of overconsolida-tion in clays leading to K0 . 1. It has proveddif®cult in practice to measure lateral residualstresses. Some results from box tests on railwayballast reported by Stewart et al. (1985) indicateK0 values up to as high as 11 and the authorsconsidered values up to 6 to be quite possible inpractice.

The computation procedure in FENLAP takesplace in two stages, dealing successively with selfweight stresses followed by application of thewheel load. The stress±strain relationship for eachmaterial may be selected from a menu of possi-bilities. The bituminous layer is treated as linearelastic.

The self weight stresses dictate the startingvalues of Young's modulus and Poisson's ratio foreach element. Stresses caused by wheel loading arethen computed and added to the self weight values.An iterative procedure follows until the values ofelastic parameters have stabilized. These are secantvalues but, since the effects of wheel loading areof primary interest, the chord values mobilizedonly by the wheel loading may be calculated. Thecorresponding stresses and displacements are thoseof interest in design. Fig. 9 illustrates these points.

One of the problems encountered by allresearchers developing ®nite element analysispackages for systems involving compacted granu-lar material over soil concerns the tendency forhorizontal tensile stresses to be computed at thebottom of the granular layer. Since unboundmaterials have negligible tensile strength, asidefrom that induced by suction and particle interlock,adjustments to the computational procedures arenormally applied to avoid false failure conditionsdeveloping in certain elements. Strictly speaking,if the constitutive models for the materials areprecise, such corrections would not be needed.However, in reality they are.

In the SENOL program, a value of resilientYoung's modulus equal to 100 MPa is assigned toany element where the mean normal effectivestress becomes tensile, this stress being the netvalue caused by overburden and by the wheel load.In FENLAP, a `no-tension' procedure is adoptedusing the principle of stress transfer (d'Almeida,1993). This involves speci®cation of a nominaltensile strength. If a computed principal tensilestress exceeds this, it is set at zero and aredistribution of stresses computed. This appliesfor the tangential direction, which is also aprincipal stress direction. On the radial plane, themaximum compressive stress is assumed to remainconstant, and the Mohr's circle is shifted toeliminate tensile stress as shown in Fig. 10.

Rowe et al. (1995) have recently developed a®nite element program called PACE. This allows the

SOIL MECHANICS IN PAVEMENT ENGINEERING 389

Page 8: Soil mechanics in_pavement_engineering

bituminous layers to be characterized by visco±elasto±plastic rheological models with a view tobetter representing the actual behaviour of bitu-minous mixtures under a range of loading andenvironmental conditions. At this stage in theprogram's development, the pavement foundationlayers are modelled as linear elastic. This programdoes, however, provide improved computation ofrutting in asphalt layers and allows values of

dissipated energy under repeated loading to bedetermined as an indicator of fatigue crackingfailure in bituminous layers (van Dijk & Visser,1977). In future, by combining the merits ofFENLAP and PACE a comprehensive analysis pack-age will be available to model ¯exible pavementbehaviour more accurately.

An interesting theoretical model of rail trackdeveloped by Chang et al. (1979) at the University

Half-space with E 5 200 MPa and ν 5 0.45

Pressure600kPa

γ 5 23 kN/m3

E 5 2000 MPaν 5 0.35

AsphaltLinear elastic

Sub-baseγ 5 21kN/m3

s 5 3 kPaKo 5 1.0K-θ model, equation (22)K1 5 8000K2 5 0.70(σ in kPa)ν 5 0.30

Subgradeγ 5 20 kN/m3

Brown's model, equation (6)K 5 50 MPan 5 0.40ν 5 0.45

2.00

1.60

1.30

1.00

0.70

0.50

0.30

0.20

0.10

0.05

0

1.000.800.600.400.300.200.100.050 r : m

z: m

Fig. 8. FENLAP representation of pavement structure (after d'Almeida, 1993)

390 BROWN

Page 9: Soil mechanics in_pavement_engineering

of Massachusetts is known as GEOTRACK. Fig. 11illustrates the elements. The rails are elastic beamssupported by a set of 11 sleepers. The ballast, sub-ballast and soil are modelled as a series of linearelastic layers. The non-linear characteristics ofsoils and granular layers are accounted for by aniterative procedure similar to that described forhighway pavements.

Pavement experimentsIntroduction. A large number of full-scale and

pilot-scale experiments have been conducted toobtain an insight into the response of pavements totransient wheel loading. Appropriate instrumenta-tion has been developed to monitor the keyparameters. Other, more numerous experiments,have been concerned with monitoring pavementdeterioration under traf®c and environmentalcycles. Such experiments have, generally, not

included much instrumentation, but have reliedon super®cial observations and measurements. TheTRL's experiments on the A1 at Alconbury Hill(Lee & Croney, 1962) and the AASHO Road Test(Liddle, 1962) in Illinois are classic examples ofthis type of experiment, the data from which haveformed the basis for the empirical pavement designmethods widely used today.

Accelerated loading devices. Another importantseries of experiments, principally concerned withpavement deterioration, are those involving accel-erated loading devices at full scale. The mostextensive programme was that carried out in SouthAfrica using the Heavy Vehicle Simulator (HVS)(Walker, 1985). This device is mobile and severalunits were used on sites in different locations to testsections of pavement in their `as built' condition.By using high wheel loads repeatedly and con-tinuously over several weeks, the equivalent ofmany years' traf®c loading could be applied.Several basic techniques were used to investigatehow pavements deteriorated as a result of thisloading regime. Careful trenching and examinationof each layer after a period of traf®cking allowedthe development of failure mechanisms to bemonitored. The vast data bank generated by theHVS test programme formed the basis for the SouthAfrican pavement design system (NITRR, 1985a).Theoretical modelling was used to interpret theresearch results and extend them to design.

A similar accelerated loading device and testphilosophy is used in Australia (Metcalf et al.,1985). Stationary test facilities either linear orcircular have been used in other countries to studypavement behaviour under accelerated loading.These devices are stationary in the sense thatthey are positioned in one location and different

Resilient

Strain

Chord Modulus

Secant moduli

Strain

Str

ess

Whe

el

load

Ove

rbur

den

Fig. 9. De®nition of resilient strain in ®nite elementcomputations

Original stresses (σ*, τ*)

Corrected stresses (σ, τ)

σ*1 = σ1 σ

αα

(σz, τ)

(σ*r 2 τ*)(σr 2 τ)

σ*3

(σz*, τ*)

τ

Fig. 10. Tensile stress correction in FENLAP (afterd'Almeida, 1993)

Wheel load

Rail

Sleeper

Ballast

Subballast

Subgrade layer 1

Subgrade layer 2

Bedrock

Fig. 11. Geotrack model for railtrack (after Selig &Waters, 1994)

SOIL MECHANICS IN PAVEMENT ENGINEERING 391

Page 10: Soil mechanics in_pavement_engineering

pavement constructions are built for testing at thatlocation.

Most of the data obtained from these acceler-ated loading devices have related to failuremechanisms, principally in the bound pavementlayers. Consequently, little soil mechanics know-ledge has been accumulated. One exception con-cerns the South African experiments involvinginjection of water into the granular layer andobservations of the associated build-up of perma-nent deformation described by Freeme & Servas(1985). Fig. 12 illustrates typical data for pavementswith different qualities of granular layer. Theadvantages of using good quality dense crushedrock, type G1 (NITRR, 1985b) are apparent. Thein¯uence of effective drainage can also be noted.

At Nottingham, a pilot scale facility (Brown &Brodrick, 1981a) has been used for over 20 yearsto study a range of pavement problems undercontrolled conditions. Loads up to 1´7 t can beapplied and speeds up to 16 km/h on pavementsconstructed in a 1´5 m deep test pit, 4´8 m longand 2´4 m wide.

Pavement instrumentation. For experiments in-volving in situ instrumentation, several transducershave proved effective in monitoring both responseto individual wheel loads and the changes in stress,strain and de¯ection with repeated loading. Inaddition to these three parameters, temperaturesand pore pressures have also been measured, theformer with great success, using simple thermo-couples, the latter with more limited success. Thisis unfortunate, since stress determination in andbelow pavements involves total stress, so withoutsuction or pore pressure measurements, the effec-tive stress state is not reliably known.

Appropriate instrumentation is reviewed inBrown (1978) and that applied in pilot and full-scale experiments at Nottingham is described by

Brown & Brodrick (1981b). The most usefulinstruments have proved to be a pressure cellincorporating a simple strain gauged diaphragmand inductance strain coils. For full-scale experi-ments carried out in South Africa and Australia,the multi-depth de¯ectometer has also provedextremely useful for measuring de¯ections atvarious points within the depth of a pavement(Basson et al., 1981).

A promising low cost technique for measuringwater content is currently being used in the USAin pavement test sections forming part of theFederal Highway Administration's Long TermPavement Performance experiments. The TimeDomain Re¯ectometry (TDR) principle is utilizedby inserting a three-pronged probe into the soil.The transmission and re¯ection of an electro-magnetic pulse allow an apparent length of theprobe to be determined. This is a function of thesoil dielectric constant which is directly related tothe volumetric water content using equationsdevised by Topp et al., (1984). The usual watercontent by mass can then be calculated knowingthe dry density of the soil.

The Bothkennar pavement experiments. In 1987,the Science and Engineering Research Councilpurchased a soft clay site at Bothkennar near theForth Estuary and established it for full-scaleexperimental geotechnical research. Full details ofthe site and results of extensive tests on the clay aredescribed in Greenwood et al., (1992).

An unsurfaced pavement loop was constructedin 1989 incorporating 16 test sections with theprincipal objective of studying the reinforcingeffects of various geosynthetics placed at theinterface between a granular layer and the clay(Little, 1993). The data which were gathered onthe performance of these sections under repeatedtruck loading were used to assess design methodsfor both reinforced and unreinforced haul roads.

Over 400 instruments were installed, nearly allsections being involved. The instrumentation layoutwas designed to measure speci®c effects related toassumptions in the design methods. Inductancestrain coils were used to measure both transientstrain under a passing wheel load and permanentstrain accumulation under repeated loading. Highair entry piezometers were installed 200 mm belowformation level but proved unsuccessful in prac-tice, since they were measuring suction and aireasily entered the system. Standpipes were pro-vided at four locations along the road to determinewater table position.

Loading of the pavements was provided by alorry with known axle weights driving down thecentre line of the sections. Fig. 13(a) shows typicalrecorded outputs from a strain coil pair measuringvertical strain at formation level, while output from

Number of load applications

Per

man

ent d

efor

mat

ion:

mm

20

10

0

Waterremoved

Ingressof water

Material type

Ingressof water

G4G3

G2

G1

Fig. 12. In¯uence of water, drainage and granularmaterial type on accumulation of permanent deforma-tion (after Freeme & Servas, 1985)

392 BROWN

Page 11: Soil mechanics in_pavement_engineering

a pressure cell at the same depth is presented inFig. 13(b).

Laboratory testingFigure 14 illustrates the general stress regime

experienced by an element of material in or belowa pavement structure as a result of a moving wheelload within the plane of the wheel track, that is,the longitudinal plane. There are pulses of verticaland horizontal stress accompanied by a doublepulse of shear stress with a sign reversal on thevertical and horizontal planes. Fig. 15 shows theassociated pattern of principal stresses illustratingthe rotation of principal planes which takes place.For elements of material in the lower part of abituminous or concrete layer, the horizontal stres-ses are tensile, elsewhere they are compressive.

One approach to laboratory testing is to selectthe equipment which reproduces the ®eld situation.

Clearly, for pavements this would demand complexfacilities. A close match to ®eld conditions can beobtained by use of a Hollow Cylinder Apparatus(HCA). This allows control of both normal andshear stress in a manner which can match the insitu case as shown in Fig. 16. Repeated loadHCAs have been developed at the University ofCalifornia, Berkeley (Alavi, 1992) principally totest bituminous materials, and at Nottingham forgranular materials (Chan & Brown, 1994).

Interest in the HCA was partly stimulated bythe problems associated with the Simple ShearApparatus (SSA), which also has the potentialto reproduce the in situ stress regime. The mostserious dif®culties with the SSA were applicationsof uniform stress conditions and accurate measure-ment of stresses and deformations on the specimenunder repeated loading conditions. Shaw & Brown(1986) describe an SSA in which both the verticaland shear stresses can be applied cyclically, but forwhich the problems of stress measurement wereidenti®ed.

Fig. 13. In situ measurements from Bothkennar haulroad experiments (after Little, 1993): (a) verticalstrain at formation level; (b) vertical stress atformation level

1.0

0.5

0

3.02.52.01.51.00.50

Time: s(a)

Str

ain:

%

2.01.61.20.80.40

60

50

40

30

20

10

0

Time: s

(b)

Ver

tical

str

ess:

kP

a

Fig. 14. Stress conditions under a moving wheel load:(a) stresses on pavement element; (b) variation ofstresses with time

Moving wheel load

Pavement structureVerticalstress

Shearstress

Horizontalstress

Typical pavement element

(a)

Vertical stress

Horizontal stress

Shear stress whenwheel moves inopposite direction

Time

Stress

(b)

Shear stress

SOIL MECHANICS IN PAVEMENT ENGINEERING 393

Page 12: Soil mechanics in_pavement_engineering

Since the HCA and SSA are essentially researchtools and have limited productivity, most testingof soils, granular materials and bound materialsfor pavements has involved simpler con®gurations.The approach has been either to concentrate on thatpart of the applied stress regime which is of mostsigni®cance, or to carry out a test programme of amore fundamental nature using stress invariants.This latter approach allows the ®eld stress regimeto be expressed in terms of octahedral shear andnormal stresses and to study material response inthe laboratory under a range of values for thesetwo parameters. This latter approach involves an

inherent assumption that the materials are isotropicand presents problems in dealing with the rotationof principal planes. However, Brown (1975) demon-strated this approach for bituminous layers andBrown & Bell (1977) adopted it in predictivecalculations for rutting in bituminous pavements.Data reported by Chan & Brown (1994) forgranular materials indicated that shear reversal isonly of signi®cance when considering the develop-ment of plastic strains.

The invariant approach has formed the basis forthe application of repeated load triaxial testing tostudies of soils and granular materials in recentyears (Boyce et al., 1976). Fig. 17 shows the

Fig. 15. Stresses on a pavement element: (a) principalstresses ± element rotates; (b) no rotation ± shearstress reversal

(a)

(b)

W

MT

PiPO

z

rθσz

τzθ

σθ

σr

Fig. 16. Stress conditions in a Hollow Cylinder Test

Fig. 17. Equipment for repeated load triaxial testingof soils (after Raybould, 1992): (a) axial stress anddeformation system; (b) con®ning stress and radialdeformation system

Tocomputer

Strain gaugeddiaphragm

LVDTs

(a)

Loadcell

Testspecimen

Piston

Servohydraulicsupply

LVDT

Actuator

Transducer

Tocomputer

Cylinder

LVDT

Actuator

Servohydraulicsupply

Proximitytransducers

(b)

Testspecimen

394 BROWN

Page 13: Soil mechanics in_pavement_engineering

apparatus developed at Nottingham for testing75 mm dia. soil specimens under cyclic loading.The essential features are

(a) use of closed loop servo-hydraulic loadingsystems for cycling both deviator and con®n-ing stresses

(b) accurate measurement of axial and radialdeformations directly on the test specimenusing LVDTs and proximity transducers re-spectively

(c) measurement of axial load on the top platen(d) measurement of pore pressure both at the

bottom platen and near the centre of thespecimen; the central transducer is locatedprior to consolidating reconstituted specimensbut is not used for ®eld samples

(e) computer control and data acquisition.

This equipment is fully described by Brown etal., (1980) and Raybould (1992). It has been usedfor studies relating to off-shore structure founda-tions (Brown et al., 1977) and earthquake loading(Raybould & Brown, 1993) in addition to thepavement problem of interest here.

For testing granular materials with particle sizesup to 40 mm, a larger repeated load triaxialapparatus was developed at Nottingham cateringfor 150 mm dia. specimens (Brown et al., 1989).Fig. 18 shows this apparatus which embraces mostof the relevant features of the smaller soil testingfacility. In this case, radial deformations aremeasured by cast epoxy strain hoops ®tted withfoil strain gauges. Similar apparatus has been usedin France (Paute et al., 1993), while 400 mm dia.specimens were adopted in the Dutch equipmentdeveloped by Sweere (1990). He demonstrated thatthe large diameter was needed to accommodateparticle sizes up to 40 mm since inaccurate resultswere obtained when using smaller specimens.Equally, if the grading is scaled down or thelarger fractions omitted when using smaller speci-mens, unrepresentative data are obtained.

In recent times, simpli®ed pieces of apparatushave been developed for use in engineeringpractice, derived from the more complex facilitiesused in research studies. For bituminous mixtures,the Nottingham Asphalt Tester (Cooper & Brown,1989), has emerged as a practical and reliable toolfor measuring the key mechanical properties ofbituminous materials. The development of compar-able, simpli®ed testing facilities for soils andgranular materials has not progressed as far asfor bituminous mixtures. This is somewhat surpris-ing since repeated load triaxial testing has beenused in the USA since the 1950s (Seed et al.,1955). The US Transportation Research Boardissued a detailed guide for such testing in 1975(Transportation Research Board, 1975) and thereis an AASHTO speci®cation for such tests

(AASHTO, 1986). Because soils testing is inher-ently more dif®cult to perform than asphalt testing,simpli®ed techniques present more of a challenge.One of the principal problems is that of preparingreliable and representative specimens. However,recent work at Nottingham, in conjunction withTRL, has endeavoured to develop practical tests forsoils and granular materials which could be adoptedfor design purposes.

A pneumatically operated repeated load triaxial

Fig. 18. Equipment for repeated load triaxial testingof granular materials (after Brown et al., 1989): (a)diagram of loading equipment; (b) position of straintransducers

Hand jack

Pressuresensor

Triaxialcell

Load cell onloading rod

Hydraulic supply

Actuator withservo-value

Pressurecylinder

Hydraulicsupply

Actuator withservo-value

Electroniccontrolsystem

Computer

(a)

(b)

150 mm

180 mmdrainage

membrane

'o' rings toseal membrane

Strain ringshown insection only

LVDT

Rod attachedto location stud

300

mm

75 m

m

SOIL MECHANICS IN PAVEMENT ENGINEERING 395

Page 14: Soil mechanics in_pavement_engineering

system for soil testing is shown in Fig. 19. Itaccommodates 100 mm dia. specimens in a stan-dard cell and is ®tted with `on-specimen' deform-ation measuring transducers that are easy toassemble. Fig. 20 shows the technique used foraxial deformation, the active element being a straingauged phosphor bronze strip on an assemblyweighing just 26 g. Measurements are made atdiametrically opposite locations. These transducersare for reading small resilient strains underrepeated loading and can resolve to 28 microstrain.An external LVDT is used to measure the largerplastic strains and total strains in monotonic teststo failure.

For radial strain, the same proximity transducersare used as for the cyclic loading facility (Fig.17(b)). The `target' for each transducer is a 30 mmsquare of aluminium foil placed inside the latexmembrane. Radial strains can be resolved to 10microstrain. No provision is made for pore pres-sure measurement, since specimens will, in gen-eral, be partially saturated and independent soilsuction determination is recommended.

The axial load is measured by a load cellformed from strain gauging a narrowed section ofthe loading rod inside the triaxial cell, a techniqueused earlier by Austin (1979). The applied load iscontrolled by an electro-pneumatic regulator ®ttednear the actuator. Deviator stresses up to 200 kPacan be applied. The con®ning pressure medium

is air with a maximum value of 200 kPa but withno facilities for cyclic application. A computerizedsystem is used to control experiments and tomonitor the data. A Windows environment with

Fig. 19. Simpli®ed repeated load triaxial system for soils (after Cheung, 1994)

Aluminiumblock withcup fitting

Straingauges

Phospherbronze strip0.56 mm thick

Hollow brasstube 5 mm dia.

'O' ring

Spe

cim

en

82 m

m

CruciformvaneAdjustable

fixing

40 mm

Fig. 20. Axial deformation measuring system for soils(after Cheung, 1994)

396 BROWN

Page 15: Soil mechanics in_pavement_engineering

DCS software (Sousa & Chan, 1991) provides avery user-friendly control and data acquisitionsystem.

The equipment developed for granular materialsis shown in Fig. 21. The test specimens are280 mm in diameter which, following a study ofwork elsewhere, was considered adequate forparticle sizes up to 40 mm recognizing that fewparticles of this size are actually included aggre-gate graded to this nominal maximum size.

The constant con®ning stress is applied by usinga partial internal vacuum via porous ®ttings inboth platens, thus allowing the triaxial cell to bedispensed with. This arrangement allows con®n-ing stresses up to 90 kPa. The axial load canbe applied in three different ways depending onavailability of facilities. If closed loop servo-hydraulics are available, then this system canprovide the usual sophisticated load control formonotonic or repeated load tests. A suitableactuator is shown on the right of the test framein Fig. 21.

A manually operated hydraulic actuator, asshown in Fig. 21 above the test specimen, can beused for simple repeated loading to determine

resilient characteristics which, for these materials,are not sensitive to loading rates. However, only alimited number of load applications can realisti-cally be applied. A simple, manually operatedfalling hammer device is somewhat more suitablefor repeated loading to study the accumulation ofplastic strains. A 10 kg mass falling throughheights up to 500 mm provides peak stresses upto 700 kPa. The hydraulic actuators shown inFig. 21 are each capable of applying loads up to100 kN (deviator stresses of 1624 kPa). A load cellis located immediately above the top platen.

The test specimen is sealed with a pvc mem-brane while in the compaction mould, which isremoved following application of the internalpartial vacuum. The deformation measuring de-vices are shown in Fig. 22. Axial measurementsare effected by LVDTs between blocks glued to themembrane. This technique was carefully checkedto ensure that slippage between the membrane andthe test specimen did not occur. The precision ofmeasurement is 17 microstrain. The large deforma-tions associated with monotonic tests to failure aremeasured with a 100 mm stroke LVDT insertedin the loading actuator, which can read to an

Fig. 21. Simpli®ed repeated load triaxial system forgranular materials (after Cheung, 1994)

Fig. 22. Deformation measuring system for granularmaterials (after Cheung, 1994)

SOIL MECHANICS IN PAVEMENT ENGINEERING 397

Page 16: Soil mechanics in_pavement_engineering

accuracy of 86 microstrain. Radial deformation isobtained from three LVDT outputs, ®tted to aperspex ring as shown in Fig. 22 with the coresbeing spring loaded against thin metal plates gluedto the membrane. The perspex carrier ring issupported on three blocks which are also glued tothe membrane. The precision of these measure-ments is 27 microstrain.

Although further development work is neededfor the two triaxial facilities described above, theyhave the potential for use in engineering designpractice to measure resilient modulus, permanentdeformation characteristics and shear strength ofsoils and granular materials. Some typical resultsfrom several of the laboratory test methodsreviewed here are given in the section on Beha-viour of Soils and Granular Materials underRepeated Loading.

Field testingLaboratory testing of small elements always

raises questions about whether the results arerepresentative of ®eld conditions for the soil inbulk. Field testing, though more expensive, hastherefore become an increasingly important part ofgeotechnical engineering. For pavement soil mech-anics, static plate loading tests have been used formany years, initially to determine a `modulus ofsubgrade reaction' in connection with concretepavement design and as an indirect technique forassessing the California Bearing Ratio (Croney,1977), a test discussed on pp. 412±416.

The static plate loading test is however, cum-bersome and time consuming. More importantly, itdoes not reproduce real wheel loading conditionsfor which the time factor is important. In par-ticular, a static test on material with a high degreeof saturation can allow pore pressure dissipationand result in more favourable results than atransient load test which is essentially an undrainedevent.

Sweere (1990) conducted a useful review of insitu testing devices and concluded that a dynamicplate loading test was appropriate for assessing theresilient modulus of granular layers. This test is aspecial version of the more sophisticated FallingWeight De¯ectometer (FWD) apparatus (Sorenson& Hayven, 1982), the principles of each beingshown in Fig. 23. In both cases, a load pulse isgenerated by a mass falling onto a spring above aload platen. The peak load is measured and, usingthe FWD, the de¯ected shape of the loaded surfaceis recorded from a set of geophones measuring atpoints up to a radius of some 2 m from the platen.A single electronic integration of the geophonevelocity measurements yields de¯ections. In thedynamic plate loading test, only the de¯ection ofthe load platen is recorded. Using this parameter

and the peak load, an `effective foundation stiff-ness modulus' (Ef ) can be computed using theequation:

Ef � 2pa(1ÿ í2)

d1

(1)

where p is the contact pressure below the plate, a isthe plate radius, í is Poisson's ratio and d1 is themeasured plate de¯ection.

The FWD is generally used for testing `in-service' pavements to assess structural integrity(Brown et al., 1987). Analytical procedures havebeen developed which involve a back-analysis ofthe de¯ected surface under the given load todetermine the effective resilient modulus of eachprincipal pavement layer. The layer thicknessesneed to be known and are obtained from coringor can be estimated from ground radar surveys(Highways Agency, 1994a).

Fig. 23. Falling weight plate loading tests (afterSweere, 1990): (a) principle of dynamic plate bearingtest; (b) principle of the falling weight de¯ectometertest

Geophone

Drop weight

(a)

Drop weight

Loading plate/bufferRubber Geophone

Deflection

300mm 200mm 500mm 500mm 500mm(Typical dimensions)

(b)

398 BROWN

Page 17: Soil mechanics in_pavement_engineering

Several analytical procedures have been devel-oped in the form of computer programs for back-analysis of de¯ection `bowls'. The most reliableones (e.g. Brown et al., 1986) take account ofthe non-linear resilient properties of soils and,where necessary, granular layers (e.g. Brunton &d'Almeida, 1992) while bituminous or concretelayers are treated as linear elastic. The centralanalytical tools are those outlined previously but®nite element analysis is not used routinely becauseof the computing time involved. This subject isfurther discussed in the ®nal section. These proce-dures allow the parameters in simple non-linearresilient soil models to be calculated and, bymatching theory to measurement by way of thesurface de¯ection pro®le, provide a sound basis forfurther theoretical analyses of the pavement.

The basic back-analysis procedure can also beused when tests are conducted on pavement foun-dations, although the data tend to be less precisebecause of the rough surface, compared with acompleted pavement, which can interfere with thegeophones.

The procedure was used on the Bothkennar haulroad experiments (d'Almeida, 1993) and on theA564, Derby Southern By-Pass, some typicalresults from which are presented on pp. 417±418.

PAVEMENT FAILURE MECHANISMS

CrackingCracking of bituminous pavements under the

in¯uence of repeated wheel loading is a fatiguephenomenon. Fig. 24 shows a typical failurecondition with a pattern of cracks in the wheelpaths. Hveem (1955) was the ®rst engineer toidentify the relationship between fatigue crackingand the resilience of the supporting pavementstructure, which was principally in¯uenced by thesoil characteristics. For the thin surfacing com-monly used in the 1950s, Hveem's theory, illus-trated in Fig. 25, relates to surface cracking outsidethe loaded area induced by horizontal tensile

stresses or strains resulting from ¯exure of thepavement. As thicker bituminous layers wereintroduced and in situ measurements were madeof tensile strains, it became apparent that themaximum value occurred at the bottom of thelayer rather than at the surface, as illustrated inFig. 26 taken from Klomp & Niesman (1967).

Laboratory studies in the 1950s and 1960s (e.g.Pell & Taylor, 1969) revealed that crack initiationof bituminous mixtures under repeated ¯exure iscontrolled by the level of principal tensile strain.Fatigue relationships, such as that shown in Fig.27, were developed for various bituminous mix-tures. Consequently, the theoretical basis for designcalculations to deal with fatigue cracking involvesuse of the horizontal tensile strain at the bottomof the bituminous layer as the principal designcriterion. Numerous design methods have been

Fig. 24. Asphalt fatigue cracking failure

Resistance in theseupper regions dependsupon flexural strength(tensile, cohesion)

Resistance inthis lower region isprimarily dependentupon interparticlefriction (R-value)

Probable pathsof particle flow

Weight of materialoutside of loadalso providesrestraint

Load

SurfaceBase

Fig. 25. Illustration of failure modes (after Hveem &Sherman, 1962)

Depth: mm Temp.: °C

0

30

22

23

Wheel position

20 cm right-hand side

80 20

140 19

Wheel loadVehicle speed

16.5 kN30 km/h

1 s

Fig. 26. In situ horizontal strain measurements in anasphalt layer under wheel loading (after Klomp &Niesman, 1967)

SOIL MECHANICS IN PAVEMENT ENGINEERING 399

Page 18: Soil mechanics in_pavement_engineering

developed using linear elastic theory and incorpor-ating this concept (e.g. Brown et al., 1985).

Research into crack propagation has revealedthat, once a crack has been initiated, its rate ofpropagation depends on the tensile stress at thecrack tip (Ramsamooj et al., 1972). There are,therefore, con¯icting requirements between theneed to avoid crack initiation, which requires ahigh asphalt stiffness, and to minimize crackpropagation, which requires a low stiffness. Thelayer thickness is also in¯uential. The generalapproach is to use low stiffnesses for bituminoussurfacing which is less than 100 mm thick andhigh stiffnesses for the greater thicknesses whichembrace all modern major pavement construction.

Theoretical analysis allows an indication to beobtained of the in¯uence which soil resilientmodulus has on the tensile stress and strain inthe bituminous layer. A sensitivity analysis re-ported by Dawson & Plaistow (1993) based oncomputations with the FENLAP program revealedthat a change in the resilient modulus of thesubgrade from 40 to 90 MPa caused a change inthe asphalt tensile strain criterion of less than 2%.Changes in the resilient characteristics of thegranular layer over a realistic range, using non-linear models, were more signi®cant, causing theasphalt tensile strain to vary by up to 70%. Thesecalculations involved bituminous layer thicknessesbetween 100 and 250 mm with stiffness modulusvalues of between 2 and 8 GPa. It would appear,therefore, that the cracking phenomenon is notgreatly in¯uenced by soil resilience when areasonably thick bituminous layer is used. Con-versely, the resilience of the supporting granularlayer is very signi®cant.

RuttingThe second traf®c related failure mechanism in

¯exible pavements is rutting. This arises throughthe accumulation of vertical permanent strains inthe wheel track (Fig. 28) which can, in principle,include contributions from all layers in the pave-ment. Some typical data from ®eld experimentscarried out on the A1 by Lister (1972) are shownin Fig. 29 to illustrate this point.

For thick asphalt pavements, rutting usuallyarises from permanent deformations in the bitumi-nous layers, often the surface course. Interpretationof Lister's data for pavements with hot rolledasphalt surfaces and base layers over traditionalfoundations, by Brown & Brunton (1984) indicatedthat a 20 mm rut might involve a 48% contribu-tion from the bituminous layers. It is dif®cult togeneralize about this matter, since permanentdeformations will develop wherever there is aweakness in the structure. For heavily traf®ckedUK roads, this is likely to be in the surfacing, butfor pavements with thin bituminous layers, the

Test Series

Temp. °C

Symbol

F G

+10 0 +10 +20 +30

Test Series

Frequency

Symbol

varies

P

Cycles to failure2 x 103 104 105 106 107Te

nsile

str

ain:

mic

rost

rain 700

500

100

50

Fig. 27. Typical asphalt fatigue relationship (after Pell& Taylor, 1969)

Heavy clay

Sub-base

Base +surfacing

Subgrade

TotalRolled asphaltRolled asphaltBallast

(100 mm)(150 mm)(150 mm)

Def

orm

atio

n: m

m

10

8

6

4

2

01968 1969 1970 1971

Year

Fig. 29. Development of permanent deformation inTRL experiments at Alconbury Hill (after Lister,1972)

Rut depth

Load

Bituminous

Granular

Subgrade

Fig. 28. De®nition of rut depth

400 BROWN

Page 19: Soil mechanics in_pavement_engineering

granular layer and subgrade are likely to dominate,particularly if drainage conditions are unsatisfac-tory.

For construction traf®c operating on the pave-ment foundation, rutting is a major concern andmust be limited to avoid undue damage to thislayer or to the subgrade below. In the Bothkennarpavement experiments (Little, 1993), the granularlayer contributed up to a third of the surface rut,but there were cases where all the deformationdeveloped in the subgrade.

The sensitivity analysis carried out by Dawson& Plaistow (1993) used the ratio of shear tonormal stress as the parameter most likely toin¯uence plastic strain developed in soils andgranular materials. For unsurfaced pavements, theresilient characteristics of the granular layer weremost in¯uential for stress ratios at the top of bothlayers. A realistic range of parameters for the non-linear resilient granular layer model indicatedchanges of up to 15 and 40% in the stress ratiosfor the top of the granular layer and of thesubgrade respectively. The resilient modulus of thesubgrade had some in¯uence on the stress ratio atformation level.

In addition to quantifying the non-linear resilientcharacteristics of granular materials and soils, it isclearly necessary to understand the relationshipbetween the accumulation of plastic strain andapplied stress together with relevant variables thatmay in¯uence this relationship.

Rail trackFailure mechanisms in rail track are well

described by Selig & Waters (1994). Under re-peated loading, differential permanent strainsdevelop in the ballast which cause the rail lineand level to change and the ride quality todeteriorate. Fig. 30 (taken from Brown & Selig,1991) shows this pattern for a well establishedtrack with a stable subgrade subjected to periodicmaintenance by tamping to restore the railgeometry. If the voids in the ballast are allowedto ®ll with ®ne material, a failure condition can

develop with high plastic strains, partly becauseof a decrease in permeability impeding drainage.One source of contamination is pumping of ®nesfrom the sub-ballast or subgrade if these materialsbecome saturated.

Permanent deformation of the track is onlyin¯uenced by the subgrade in the long term exceptwhen the track is newly constructed. Unless highwater contents have developed, normal transientstress levels, on clay subgrades, tend to result in astable situation after initial plastic strain develop-ment.

Fig. 31 presents ®eld data from a full-scale railtrack experiment in Colorado reported by Selig &Waters (1994), showing the relative contributionsto surface deformation of each layer in thestructure. In this case, which involved a new track,about half the surface deformation arose from theballast.

BEHAVIOUR OF SOILS AND GRANULAR

MATERIALS UNDER REPEATED LOADING

IntroductionThe foregoing discussion on failure mechanisms

in pavements suggests that an ability to design forprevention of failure requires a knowledge of howsoils and granular materials respond to repeatedloading of the type imposed by moving traf®c.Under repeated loading, there are recoverable andirrecoverable components of deformation. Theformer dictate the value of resilient modulus,which is required to carry out structural analysisof pavements, while the latter needs to be quanti-®ed to deal with design to minimize rutting.

Properties of the subgradeThe mechanical properties of the subgrade are

in¯uenced by the imposed stress regime. This mustbe considered in two parts; that resulting from theequilibrium conditions established after construc-

Cumulative Traffic

Tamping

SubgradeSub-ballast

Ballast

Set

tlem

ent

Fig. 30. Effects of traf®c and tamping on rail trackdeformation (after Brown & Selig, 1991)

Traffic: MGT

Sub-ballast

Subgrade

Ballast

Total

Traffic: GN

0 25 50 75 100 125 150 175 200 225

Set

tlem

ent:

in

0.8

0.6

0.4

0.2

0.0 5 10 15 20 250

5

10

15

20

Set

tlem

ent:

mm

Fig. 31. Development of permanent deformation inrail track experiments at Colorado (after Selig &Waters, 1994)

SOIL MECHANICS IN PAVEMENT ENGINEERING 401

Page 20: Soil mechanics in_pavement_engineering

tion, when moisture conditions have stabilized andthat imposed transiently by a moving wheel load.These will be considered in turn.

Equilibrium stress conditions. The response ofan element of soil to applied load depends cruciallyon its consolidation stress history and the currenteffective stress state. Since formation levels insubgrades exist above the water table, the determi-nation of pore pressure and, hence, effective stressis generally not straightforward. Immediately abovethe water table, where the soil is saturated, thenegative pore pressure is proportional to heightabove the water table. The proportionality breaksdown as the soil becomes partially saturated atgreater heights as illustrated in Fig. 32. The soiltype will greatly in¯uence this pore pressuredistribution.

For ®ne-grained soils and shallow water tables,conditions which apply to most of the UK, thesituation is simpli®ed since saturated conditionsmay be assumed up to formation level, certainlyfor design purposes, and pore pressure can bedetermined. Unfortunately, there are very few ®eldmeasurements of pore pressures above the watertable. However, the experiments conducted in the1950s by Black et al. (1958) are worth noting,not least because the results formed part of thebackground used to establish the current UKmethod for assessing pavement subgrade strengths.Fig. 33 shows the measurements made usingtensiometers at various depths below concreteslabs. The original data have been replotted andthe linear relationship between negative porepressure and height above the water table superim-posed. The soil pro®le consisted of a brickearthwhich was a mixture of sandy and silty clay abovea sandy gravel where the water table was located.

The results in Fig. 33 are typical of the

measurements made at four locations. In Area Ethe negative pore pressures were below the hydro-static values, while in Area G slightly highervalues were recorded. There were only smallseasonal variations, supporting the concept ofequilibrium water content under sealed surfaces.Use of the hydrostatic value for design whendealing with more highly plastic clays couldprobably be justi®ed but good quality ®eld dataare clearly needed.

The soil beneath a pavement may be in itsnatural undisturbed state or be remoulded depend-ing on whether the section of pavement is in a`cut' or `®ll' area. These two situations requireseparate consideration.

For undisturbed clays, the stress history is re-presented by Fig. 34. The parameters used are

mean normal effective stress p9 � (ó9v � 2ó9h)=3

(2)

deviator stress q � ó9vó9h (3)

where ó9v and ó9h are the vertical and horizontaleffective stresses, respectively.

specific volume v � 1� wGs � 1� e (4)

where w � water content, Gs � speci®c gravity of

Pavement surface

Formation levelPore pressure

Water table

?

−ve +ve

Fig. 32. Pore pressure in subgrade

Hydrostaticline

Formation level

Sandyclay

Siltyclay

Sandy clay

SandyGravel

Area E

Sandyclay

Siltyclay

Sandy clay

SandyGravel

Area G

Formation level

Hydrostaticline

Hei

ght a

bove

wat

er ta

ble:

mH

eigh

t abo

ve w

ater

tabl

e: m

Pore pressure: kPa

−25 −20 −15 −10 −5 0

1

2

0

1

2

3

Fig. 33. Pore pressure measurements in RRL experi-ments below sealed surfaces (after Black et al., 1958)

402 BROWN

Page 21: Soil mechanics in_pavement_engineering

soil soilds and e � void ratio. Saturated conditionsare assumed.

Fig. 34 shows preconsolidation involving com-pression to point C and subsequent swelling topoint A, all under anisotropic conditions (zerolateral strains). This historical sequence generatesan overconsolidated soil, being typical of a stiffclay deposit.

The construction operation involves three pro-cesses which will in¯uence the effective stress inthe soil. These are

(a) removal of overburden during earthworksconstruction

(b) lowering of the water table by provision ofdrainage

(c) addition of overburden due to the pavementconstruction.

The nett effect of these operations will be forthe effective stress state to move from point A inFig. 34 to point P by way of P9.

Fig. 35 shows an enlarged view of the plot of p9against q to illustrate these three changes. Removalof overburden will cause no immediate change ineffective stress but will reduce the deviator stressby AB. As pore pressures reach equilibrium andfurther swelling occurs, the effective stress will

move from B towards P9. The extent to which itwill approach P9 depends on the time scale and onthe soil permeability and consolidation character-istics. It would be usual to install side drains toprovide a lowering of the water table in a cutting.This process also takes time to become effectivebut would cause a reduction in pore pressure andan increase in effective stress along P9E towards D.Construction of the pavement will almost certainlytake place before point D is reached. Thisincreases the overburden, say from E to F interms of the deviator stress and, as the associatedpositive change in pore pressure dissipates, theeffective stress will move towards equilibrium at P.In reality, because of the time needed for thesewater content changes to take place, the actualstress path during the entire construction operationis likely to be represented by the curved dottedline BGEP.

For soil which is cut, transported and compactedas ®ll in an embankment, the effective stressregime is rather different and less well understood.A suggested scenario is presented in Fig. 36. Thescraper operation causes the soil to be taken tofailure in an undrained state represented by AB.The subsequent change in stress state will dependon the environment in which it is placed andcompacted and on weather conditions. If conditionsare dry and the soil is placed well above the watertable, suctions will be high and the effectivestresses will tend to increase to a point such as Q.If wet weather conditions pertain, the soil which isunder suction will absorb water, reducing itseffective stress and will move to a point such asQ9. Subsequently, equilibrium conditions which arelikely to move it from Q9 towards Q will beestablished. This will be assisted by the addition ofoverburden through construction of the pavement.The nett effect of these operations is that the soilis likely still to be in an overconsolidated statebut with a reduced overconsolidation ratio p9X/p9Qcompared with p9C/p9A before excavation.

Compression

Swelling

Mean normal effective stress, p′

Effects of construction

C

O P AP′

Dev

iato

r st

ress

, q

Compression

Swelling

A

C

P

P′

p′A p′c

Spe

cific

vol

ume,

v

Mean normal effective stress, p′

Fig. 34. Stress history for soil in `cut'

Pavementconstruction

Loweringwatertable

F P

D

E

G B

Removal of overburden

P′

A

Swelling line

Mean normal effective stress, p′

Dev

iato

r st

ress

, q

Fig. 35. Effects of construction operations on stressconditions in `cut'

SOIL MECHANICS IN PAVEMENT ENGINEERING 403

Page 22: Soil mechanics in_pavement_engineering

This discussion assumes that the soil remains ina saturated state throughout the sequence of events.While this may well be true for the cutting, on anembankment, the situation is less certain. Farrer(1979) reported pore pressures below the pavementin a 12 m high embankment of London clay. Hismeasurements were consistent with the water tablebeing at formation level four years after construc-tion. This suggests that saturated conditions maybe appropriate. Conceptually, it could be arguedthat the excavation and recompaction involveproducing pieces of saturated soil which are thenrecombined into a saturated mass as a result ofcompaction. Even if some air is included, whichseems likely, much of the soil mass will be in asaturated state and this assumption is appropriatelyconservative for design purposes.

Traf®c stresses. A moving wheel load will resultin a transient stress pulse being transmitted to thesoil element. This might involve a change in totalstress along a path such as PT in Fig. 37 formaterial at P in the cutting. Since the loading eventis rapid, there will be no change in effective stress,so a transient pore press, äu, develops at peakstress. The effective stress follows the path PEPcorresponding to the transient deviator stress ofmagnitude qr.

Soils are essentially elasto±plastic materials.Hence, the stress history for soil at P will haveestablished a yield surface through C, the precon-solidation stress, so that in the zone beneath this

Mean normal effective stress p′O A

B XC

Q

Q′

CSL (failure)

Dev

iato

r st

ress

, q

Compression

Swelling

CSL (failure)

C

XQBQ′

A

Mean normal effective stress p′

Spe

cific

vol

ume,

v

Fig. 36. Possible stress regime for construction in `®ll'

Notional yield surfaces

Dev

iato

r st

ress

, q

C

XF

Q (Fill)

TSPESP

EWheel loading

Time

δq

qr

δu

Wheel loading

Time

δq

qr

P (Cut)Mean normal effective stress, p′

T

Fig. 37. Stress paths for wheel loading

404 BROWN

Page 23: Soil mechanics in_pavement_engineering

yield surface it should not develop plastic strains.Hence, the stress path PEP should result in soilbehaving as a resilient material.

The soil on the embankment at point Q inFig. 37 is much nearer to its associated yieldsurface. Hence, the same traf®c induced stress, qr

will cause the effective stress to probe beyond theyield surface at F, resulting in some plastic strainsdeveloping.

An assumption of elasto±plastic behaviour is,however, too simple for dealing with transient loadproblems. O'Reilly et al., (1989) have demon-strated that silty clay responds in a viscous mannerand that it is possible to apply transient stressesabove the static yield surface without signi®cantplastic strains developing immediately. However,under repeated loading, such strains may accumu-late, their magnitude depending on the cyclicdeviator stress amplitude.

A conceptual model was proposed which in-volves expansion of a viscous yield surface underrepeated loading, the extent of the expansiondepending on strain rate. These ideas representan extension of the rate effects well known frommonotonic tests on clays.

Further evidence of this type of behaviour underloading conditions relevant to pavements wasreported by Brown et al., (1987) for overconsoli-dated silty clay. Reconstituted specimens weresubjected to anisotropic compression in a triaxialcell leading to overconsolidation ratios of 6, 12and 18. These stress histories led to low effectivestresses of 33±100 kPa representative of soil in cutbelow pavements. Traf®c loading was simulated byapplying 0´1 s deviator stress pulses with 0´25 srest periods between. The specimens were testedundrained and careful pore pressure and deforma-tion measurements were made using the equipmentillustrated in Fig. 17.

The results indicated a possible threshold stresslevel, above which serious plastic strains accumu-lated and below which the strains and porepressures were negligible. Fig. 38 illustrates thispoint for two specimens subjected to successivebursts of repeated loading at gradually increaseddeviator stress levels. These and related datashowed that the threshold stress was at a deviatorstress of 1´3 times the value of static yield over therange of initial effective stresses studied, support-ing the concept of an expanding viscous yieldenvelope under repeated loading. This correspondsto a ratio of transient deviator stress to meannormal effective stress of about 1´5, recognizingthat the initial deviator stress following consolida-tion was slightly negative (Figs 34 and 37).

A similar pattern emerged from the dataobtained by Loach (1987) from repeated loadtriaxial tests on compacted specimens of threeclays with degrees of saturation in excess of 85%,

using apparatus similar to that shown in Fig. 19.While this study was principally concerned withresilient behaviour of the soils, the deviator stressat which permanent strains started to accumulatewas recorded. These data are summarized inFig. 39 showing the level of deviator stress as afunction of the soil suction in each specimen.

These results suggest a simple design criterion

Fig. 38. Accumulation of plastic strain in reconstitutedsilty clay at 100 kPa effective stress (after Brown et al.,1987): (a) overconsolidation ratio � 6; (b) overcon-solidation ratio � 18

Locus ofvalues forqr = 30 to75 kPa

qr = 125 kPa

Number of load cycles(a)

Per

man

ent s

hear

str

ain:

%

1 101 102 103 104 105 106 107

2.5

2.0

1.5

1.0

0.5

0

Locus ofvalues forq = 40 to130 kPa

qr = 175 kPa

Number of load cycles(b)

Per

man

ent s

hear

str

ain:

%

1 101 102 103 104 105 106 107

2.0

1.0

0

3.0

4.0

5.0

6.0

Suction: kPa20 30 40 50 60 70 80 90 1000 10

50

40

30

20

10

0

Dev

iato

r st

ress

pul

se a

t ons

et o

fpe

rman

ent s

trai

n: k

Pa

Soil type

Keuper Marl

London Clay

Gault Clay

Confining stress: kPa0 15 30

Fig. 39. Threshold deviator stress as a function ofsuction for three clays (after Loach, 1987)

SOIL MECHANICS IN PAVEMENT ENGINEERING 405

Page 24: Soil mechanics in_pavement_engineering

for subgrades to prevent any signi®cant contribu-tion to permanent deformation in the pavement.This would involve ensuring that the ratio ofdeviator stress to mean normal effective stress orsoil suction was kept below a critical value. Brown& Dawson (1992) used this approach for designand suggested a ratio of 2 for pavement founda-tions, recognizing that some plastic strain in thesubgrade at this stage in the construction ispermissible. They also noted that the reconstitutedsoil specimens (Brown et al., 1987) had beentested at a higher frequency than the compactedspecimens (Loach, 1987), which will have in¯u-enced the result in view of the noted viscousbehaviour.

Later, more extensive testing by Cheung (1994)on compacted clays using the apparatus shown inFig. 19, produced data such as those shown inFig. 40. These resulted from tests involving 1000cycle bursts of repeated deviator stress at 2 Hz oncompacted, uncon®ned specimens of Keuper Marland London Clay, two of the soils tested by Loach(1987). The suction for the specimen featured inFig. 40 was 44 kPa leading to a threshold deviatorstress, according to Loach, of 22 kPa. This point isseen to coincide with the sharp change in slope ofthe line in Fig. 40. However, not all of Cheung'sdata demonstrated this clear change in slope.

Cheung used an alternative approach to designsuggesting that the plastic strain after 1000 cyclesshould be limited to 1%. The deviator stresscausing this (qt) was related to soil suction,yielding ratios of qt/s of 0´8 for Keuper Marl,(wL � 33´7%, wp � 17´6%), 0´4 for Bothkennarclay (wL � 54´3%, wp � 25´1%) and 0´5 for Lon-don Clay (wL � 76%, wp � 25´2%). The range ofsoil suction for Cheung's specimens was 20±80 kPa.

These various triaxial test results suggest thatthe allowable transient deviator stress is a functionof the effective stress state of the soil. Since theinitial stress state, particularly for compacted soil,is uncertain, precise application of these data is

dif®cult. However, a pragmatic approach is sug-gested in the ®nal section of this paper. If theactual value of accumulated plastic shear strainafter N cycles is required, Cheung proposed thefollowing relationship based on testing up to 1000cycles

åp(N) � Aqr

s

� �b

(log N � B) (5)

where A, b and B can be de®ned for the particularsoil. Although equation (5) is only valid forrelatively few load applications, this could stillbe of use in pavement foundation design wherethe number of construction traf®c movements islimited.

Much more research has been devoted to themeasurement of resilient soil properties underrepeated loading. The parameter, resilient modulus,was introduced by Seed et al. (1962) and de®nedas repeated deviator stress divided by recoverable(resilient) axial strain in the triaxial test. Theydemonstrated that it varied with the magnitude ofthe repeated deviator stress, as shown in Fig. 41.Later work by Dehlen & Monismith (1970) showedthat suction also had an important in¯uence. The®rst attempt to relate resilient modulus to theeffective stress was reported by Brown et al.(1975) who, working with reconstituted silty clay,obtained the data in Fig. 42 for a range of initialspeci®c volumes, overconsolidation ratios andinitial effective stresses. These data were used todeduce the empirical relationship:

Er � Kp90qr

� �n

(6)

where K and n depend on the soil type, p90 is theinitial mean normal effective stress and qr is the

Repeated deviator stress: kPa

0 10 20 30 40 50

Per

man

ent a

xial

str

ain:

%

1.0

0.8

0.6

0.4

0.2

0

Fig. 40. Plastic strain after 1000 cycles against re-peated deviator stress for compacted silty clay (afterCheung, 1994)

Deviator stress: psi

Res

ilien

t mod

ulus

: psi

0 5 10 15 20 25 30 35 40

16000

14000

12000

10000

8000

6000

4000

2000

0

Fig. 41. Relationship between resilient modulus (after105 repetitions) and repeated deviator stress for a siltyclay (after Seed et al., 1962)

406 BROWN

Page 25: Soil mechanics in_pavement_engineering

repeated deviator stress. For saturated, undrainedconditions, Er � 3Gr where Gr is the resilient shearmodulus.

The more accurate experiments reported byBrown et al. (1987) using the apparatus shown inFig. 17 yielded a slightly different empirical modelof the form

Gr � qr

C

p90qr

� �m

(7)

where C and m depend on the soil type.This was developed for (qr/p90) values between

0´2±0´6 and resilient shear strains from 100±500microstrain (0´01±0´05%). An important feature ofthese relationships is that they emphasize theimportance of the stress ratio (qr/p90) and areindependent of overconsolidation ratio and speci®cvolume.

Experiments conducted on compacted specimensof the same silty clay, together with Gault Clayand London Clay using the simpler apparatus inFig. 19 demonstrated that equation (7) for resilientshear modulus was applicable with p90 replaced bysuction (Brown et al. 1987).

This model re¯ects the non-linear resilientbehaviour of clays and, when applied to pavementanalysis, demonstrates a sharp increase in stiffnesswith depth as shown in Fig. 43 taken from Brownet al., (1987). It is also able to model the in¯uenceof water table position. Its main shortcoming isthat unrealistically high values of resilient modulusare predicted at low deviator stresses. Dawson andGomes Correia (1993) suggested an improvedexpression for resilient modulus as follows

Er � D� Ep90 ÿ Fqr (8)

in which D, E and F can be determined from thetest data. Fig. 44 indicates the quality of ®t for a setof tests on compacted London Clay. By examiningBrown et al.'s data for Keuper Marl, London Clayand Gault Clay, together with data on Kaolin from

Gomes Correia (1985), they were able to suggest anapproximate general equation to estimate resilientmodulus from the stress conditions and the plasticlimit wp as follows:

Er � 49 200� 950p90 ÿ 370qr ÿ 2400wp (9)

in which Er, p90 and qr are in kPa and wp is apercentage. The equation is compared with experi-mental data in Fig. 45 and applies only for resilientmodulus values up to 80 MPa, which covers thepractical range for clay subgrades in the UK. In thecase of compacted clays, p90 is taken as the soilsuction.

Symbol OCRσ3′kPa

24102041020

3801907638

40)))

qr/σ3′0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Res

ilien

t mod

ulus

: MP

a

300

250

200

150

100

50

0

Fig. 42. Resilient modulus of reconstituted silty clay asa function of stress condition (after Brown et al., 1975)

Elastic stiffness: MPa

Dep

th: m

Asphalt (Stiffness 7000 MPa)

Granular

Subgrade

6004002000

1

2

3

4

Case B: Water table 1 mCase B: below formation

Case A: Water tableCase B: at formation

Case B

Case A

Fig. 43. Computed variations of resilient modulus withdepth (after Brown et al., 1975)

Repeated deviator stress: kPa

504030201000

10

20

30

40

50

60

70

80

19

32.5

43

76

76

Key

Loach (1987) data

New model fitted

Soil suction: kPa

Res

ilien

t mod

ulus

: MP

a

Fig. 44. Comparison of `model' and data for resilientmodulus of London Clay (after Dawson & Correia,1993)

SOIL MECHANICS IN PAVEMENT ENGINEERING 407

Page 26: Soil mechanics in_pavement_engineering

In other branches of geotechnical engineering,stress±strain non-linearity is expressed in terms ofa relationship between a normalized shear modulusand shear strain. The normalizing parameter is thevalue of shear modulus G0 at very low strains, thatis, the maximum practical value.

Roblee et al., (1994) published the relationshipsshown in Fig. 46 drawn from cyclic loading testslargely associated with earthquake-related researchVucetic and Dobry (1991); Sun et al. (1988). Therelationship between G/G0 and cyclic shear strainis shown to depend on the plasticity index of thesoil. Various proposals have been made for esti-mating G0 for clays including

(a) Hardin & Drnevich (1972) who gave it as afunction of void ratio, overconsolidation ratioand mean normal effective stress

(b) Weiler (1988), who presented G0 as propor-tional to undrained shear strength, the con-stant of proportionality depending on plasticityindex

(c) Viggiani & Atkinson (1995) who used theequation

G0

pa

� Hp90pa

� �n

Rs0 (10)

in which pa is a reference stress, such as atmos-

pheric pressure, R0 is overconsolidation ratio, andH, n and s are constants which may be estimatedfrom the plasticity index.

Experimental techniques have also been used tomeasure shear modulus at very low strains, mostcommonly using the resonant column apparatus.Viggiani & Atkinson (1995) present results fromexperiments involving piezoelectric bender ele-ments. These allow shear waves to be transmittedthrough a triaxial test specimen and the velocity ofpropagation Vs to be measured. The maximumshear modulus is thus calculated from:

G0 � rV 2s (11)

where r is soil density.In using these general relationships at strains

other than very low values, it is necessary todistinguish between the shear modulus for mono-tonic loading and that for cyclic or rapidlyrepeated loading. At very low strains, the soilbehaves in an essentially elastic manner, so themode of loading is unimportant.

The stress dependent expression for resilientmodulus, equation (7) should be consistent withthe strain dependence shown in Fig. 46 if the dataare reanalysed. The experiments reported by Brownet al., (1987) involved overconsolidation ratios of6, 12 and 18 and initial mean normal effectivestresses of 33, 65 and 100 kPa. Repeated loadingwas then conducted, undrained, with various levelsof deviator stress. Using the data presented byViggiani & Atkinson (1995) the values of G0

for the extreme cases of R0 � 6, p90 � 100 kPa andfor R0 � 18, p90 � 33 kPa were calculated using theplasticity index of 19% reported by Brown et al. fortheir silty clay.

Equation (7) was based on curve ®tting the datain Fig. 47 using a set of strain contours. For thissoil, the relationship is

Line of equality

Measured resilient modulus: MPa0 20 40 60 80 100

100

80

60

40

20

0Com

pute

d re

silie

nt m

odul

us: M

Pa

Fig. 45. Predicted against measured values of resilientmodulus for clays (after Dawson & Correia, 1993)

Cyclic shear strain: %310.10.010.0010.0001

Nor

mal

ized

mod

ulus

: G/G

max

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.20.1

0

Vucetic & Dobry 1991(solid lines)

PI=0PI=15

PI=30PI=50

PI=100PI=200

Mexico CityPI>80

PI=40–80PI=20–40

PI=10–20PI=5–10

Sun et al. 1988(dashed lines)

Fig. 46. Relationships between shear modulus andshear strain (after Roblee et al., 1994)

Res

ilien

t she

ar s

trai

n: µ

ε

q r/p

′ e

po′/pe′0 0.1 0.2 0.3

500

400

300

200

100

0.2

0.1

0

Fig. 47. Contours of resilient strain for reconstituted,overconsolidated silty clay (after Brown et al., 1987).[pe9 � equivalent pressure (Scho®eld and Wroth,1968)]

408 BROWN

Page 27: Soil mechanics in_pavement_engineering

åsr � 1�11� 10ÿ3 qr

p90

� �1�52

(12)

Since

Gr � qr

3åsr

(13)

Gr � 29�3p90å0�34

sr

(14)

and

Gr

G0

� p9058

1

R0�20

1

å0�34sr

(15)

For the two stress history cases considered, andchanging resilient shear strain åsr to resilient engi-neer's strain (ãr), the parameter normally used,yields

Gr

G0

� 0�26

ã0�34r

for R0 � 6, p90 � 100 kPa (16)

and

Gr

G0

� 0�15

ã0�34r

for R0 � 18, p90 � 33 kPa (17)

in which ãr is in % strain.In Fig. 48 these relationships are plotted to

indicate the range of Brown et al.'s results. Apredicted relationship based on the data in Fig. 46accumulated by Roblee et al., (1994) for aplasticity index of 19% is shown for comparison.It is seen to pass through the centre of the rangede®ned by Loach's model for his experiments. Anattempt was also made to use the Hardin &Drnevich method to estimate G0 for Loach's soilbut this led to unrealistically high values.

The philosophy of expressing shear modulus interms of deviator stress or shear strain is worthexamining. In pavement engineering, the soil issubjected to a stress-controlled environment exceptfor situations below very stiff pavements. Thismeans that the strain which develops in the soildepends on the applied stress and the soil stiffness.

In earthquake engineering, from which the use ofshear strain as the independent variable originates,the problem is one of strain control. This arisesbecause the soil deposit is being deformed by theearthquake movements of the rock below and, inthis case, the stress level is a function of theapplied strain and the soil stiffness.

Properties of the granular layersThe resilient behaviour of granular material has

been shown to be of prime importance forpavement analysis, both in connection with foun-dation design and for completed constructions. Forthese materials, both volumetric and shear strainsneed to be quanti®ed since volume change willgenerally occur under repeated loading unless thedegree of saturation is very high. Most of theresearch used to de®ne the non-linear stress±resilient strain behaviour of granular materialshas used the dry state. Repeated load triaxial testswith the apparatus in Fig. 18 (Pappin & Brown,1980) generated the contours of shear and volu-metric strain shown in Fig. 49 which formed thebasis for de®ning stress-dependent bulk and shearmoduli.

Noting that increments of deviator stress cancause volumetric strain and of mean normal stresscan cause shear strain, Boyce (1980) used thetheorem of reciprocity, implying:

@åí@q� @ås

@p9(18)

This led to the de®nition of expressions for resilientbulk Kr and shear Gr moduli as follows

K r � K1p9(1ÿc)

1ÿ â(q=p9)2(19)

Gr � G1p9(1ÿc) (20)

where â � (1 ÿ c)K1/G1 and the parameters K1, G1

and c need to be determined experimentally.This model and the contours in Fig. 49 predict

dilatant behaviour at high values of deviator stress.Lytton (1995) comments that this tendency forincrease in resilient volumetric strain generates anincrease in mean normal effective stress in agranular layer under load. This effectively `pre-stresses' the material, inhibiting the developmentof tensile stresses and mobilizing higher stiff-nesses.

Although Boyce's model satis®es the laws ofthermodynamics, it does not ®t experimental dataas convincingly as design engineers might require.Jouve & Elhannani (1993) proposed a moregeneral model derived from Boyce's work, inwhich the elastic potential implied by the expres-sion for â was replaced, since its use did notconform with experimental evidence. However, the

Resilient shear strain: %

Gr/

Go

1.2

1

0.8

0.6

0.4

0.2

00.001 0.01 0.1 1

Predictionpo′ = 33 kPa, Ro = 18

po′ = 100 kPa, Ro = 6

Fig. 48. Comparison of Loach model for resilientmodulus with data from elsewhere

SOIL MECHANICS IN PAVEMENT ENGINEERING 409

Page 28: Soil mechanics in_pavement_engineering

modi®ed model, which also allowed for anisotropicbehaviour, required four or ®ve parameters to bequanti®ed. Sweere (1990) also suggested a prac-tical modi®cation to the Boyce model by allowingthe exponent c in equations (19) and (20) to bedifferent for Kr and Gr and by removing therelationship between â and the other parameters.This increases the number of parameters to bedetermined from three to ®ve but gives a better ®tto experimental data.

Because the modelling of resilient behaviourfor granular materials is complex, simpli®ed ap-proaches have been adopted for design. The mosttrivial involves constant Poisson's ratio, usually 0´3,and a resilient modulus given by

Er � Hp9d (21)

where H and d are constants for the material, or, inits more popular version, known as the K±è model

Er � K1èK2 (22)

where K1 and K2 are the constants and è � 3p9.This simple approach cannot be realistically

used to compute stress conditions in a granularlayer or a sand subgrade. However, it is of use formodelling a granular layer when effects in thebituminous material or the soil below are ofinterest. Equations (21) and (22) could be regardedas a lower bound to data of the type shown inFig. 50 where the effects of both deviator stressand mean normal effective stress are illustrated.If resilient properties are de®ned in terms ofthe parameter Er, then a corresponding value ofPoisson's ratio is required which should itself bestress-dependent as noted by Sweere (1990), al-though, in practice, a constant value, usually 0´3, isused.

An important aspect of the contours in Fig. 49is the dependence on stress ratio (ç � q/p9) whichit emphasizes. This is in keeping with the fric-tional characteristics of the material and re¯ectssimilar behaviour to that observed for clays asillustrated in Fig. 47.

The models for resilient strain noted above arebased on a pragmatic approach to pavement designin which the peak to peak values of stress andstrain are considered. They ignore the detailedrelationships within individual cycles. This isjusti®ed on the basis that the pavement problemis one in which very large numbers of cycles areinvolved and analysis at the micro level is of lessimportance than for problems involving smallnumbers of cycles. Reference should be made toO'Reilly (1985) and Pappin et al., (1992) forconsideration of hysteresis effects and changes ofstiffness within cycles based on experiments withdry granular materials.

Shaw & Brown (1988) demonstrated that the`contour model' behaviour of Fig. 49 developedfrom data in the axisymmetric triaxial test con-

Fig. 49. Strain contours for crushed carboniferouslimestone (after Pappin & Brown, 1980): (a) normal-ized shear strain; (b) volumetric strain

Normal stress p: kPa

Dev

iato

r st

ress

q: k

Pa

Shear strain(microstrain)

200

160

130

100

70

40

FAIL

UR

E

300200100

(a)

100

200

300

400

(−15,−6)

Normal stress p: kPa

Volumetric strain(microstrain)

Dev

iato

r st

ress

q: k

Pa

100 200

300

400

100

200

400

0

500

200

400

600

800 10

00 1200

1400

FAIL

UR

E

(b)

300

Peak mean normal effective stress: kPa

Res

ilien

t mod

ulus

: MP

a

‘Pessimumline of fit’

Increasing deviator stress1000

800

600

400

200

00 50 100 150

Fig. 50. Resilient modulus for crushed dolomitic lime-stone as a function of applied stresses

410 BROWN

Page 29: Soil mechanics in_pavement_engineering

®guration could be used successfully to predictresilient response in a biaxial apparatus. Thisinvolved the application of two independent prin-cipal stresses and was built to study the responseof scaled-down railway ballast under conditionsappropriate to the repeated loading and subsequenttamping operations to which such material isexposed.

Pappin et al. (1992) showed that the resilientresponse modelled for dry granular material isequally applicable to saturated and partially satur-ated conditions, provided the principle of effectivestress is observed. In practice, estimation of theeffective stress state in a pavement granular layermay not be straightforward.

Another factor to be considered in extrapolatingtriaxial test conditions to those in a pavement isthe rotation of principal planes associated withshear stress reversal under a rolling wheel load(Figs 14 and 15). Using the Hollow CylinderApparatus (Fig. 16), Chan (1990) demonstratedthat resilient strains were unaffected by thisphenomenon. He also showed that the principalplanes of strain remained coincident with thoseof stress. These ®ndings are helpful in that theysupport the use of an invariant approach forpavement analysis and the use of relatively simpleresilient strain models derived from triaxial testsrather than more complex apparatus.

It should be noted that, in general, the pre-diction of volumetric strain through the modelsdiscussed above is less satisfactory than that ofshear strain.

The accumulation of plastic strain under re-peated loading of granular materials has receivedrelatively less experimental attention than theresilient strain±stress relationships. This is partlybecause the experiments are inherently destructiveand many more specimens need to be tested toacquire adequate data compared with the lowerstress level, essentially non-destructive, resilientstrain tests for which multiple stress paths can beapplied to a single specimen generating extensivedata.

The threshold stress concept discussed for claysalso appears appropriate for granular materials.The data of Boyce (1976) and of Pappin (1979)demonstrated that insigni®cant plastic strainsdevelop if the peak stress ratio in repeated loadingremains below 70% of static failure. Fig. 51contrasts results for three stress paths with varyingpeak values and lengths taken from Pappin (1979).He demonstrated that the accumulation of plasticshear strain åsp, after the ®rst 100 cycles followeda relationship of the form

åsp � f (N )lr(ç̂ )t (23)

in which f(N) depends on the number of loadapplications, lr is the stress path length and ç̂ is

the peak ratio of deviator stress to mean normaleffective stress. The parameter t is dependent on thematerial under test. The ®rst 100 cycles producedvariable results and were regarded as a settling-inphase of the tests. It was considered more important

Fig. 51. Accumulation of plastic strain in crushedcarboniferous limestone (after Pappin, 1979): (a) re-peated stress paths applied; (b) plastic strain develop-ment

Limit ofresilientstraintests

Normal stress, p: kPa

Dev

iato

r st

ress

, q: k

Pa

500

400

300

200

100

0 100 200 300

C

A

B

Failure

(a)

Number of cycles

Per

man

ent s

hear

str

ain:

%

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

1 10 102 103 104 105 106

(b)

C

A

B

SOIL MECHANICS IN PAVEMENT ENGINEERING 411

Page 30: Soil mechanics in_pavement_engineering

to try to model the strain accumulation under thelarge numbers of cycles relevant to pavementloading. Pappin's results did not produce a corre-sponding expression for volumetric plastic strain.

Paute et al., (1993) describe the proceduresderived from Pappin's work which are used inFrance to characterize permanent strains for granu-lar materials. Only axial permanent strain isconsidered. Their data showed an experimentalrelationship between strain rate _å1p (strain percycle) and number of cycles which they expressedas

ln _å1p � a� b ln N (24)

For plastic strain developed after 100 cycles (�åp1),

this becomes�åp1 � A[1ÿ (N=100)ÿB] (25)

where B is positive.The parameter A was shown to relate to the

peak applied stress ratio ç as follows

A � ç

cÿ dç(26)

in which c and d are constant for the material andc/d � çf , the stress ratio at failure. This hyperbolicrelationship is similar to that proposed by Lentz &Badady (1980) for sands. Equation (26) impliesthat as ç approaches failure, A, and therefore theaccumulated strain, become very large.

Although empirical models have been developedto match the measured data for repeated loadtriaxial tests on granular materials, in particularcases, testing is still needed to determine thevarious parameters. The models therefore onlyprovide a framework within which experiencesuggests that the data may be interpreted. Thom& Brown (1988) proposed a series of stress pathsthat could be applied to evaluate routinely bothresilient and plastic strain characteristics. These areillustrated in Fig. 52 and show 19 stress paths todeal with resilient response, all of which involvepeak values below the threshold, and a single,20th, path to characterize plastic strain. Finally,unless failure has developed under repeated load-ing, a monotonic test can follow to measure shearstrength. About 20 cycles on each of the pathsfor resilient strain are adequate, while the moredamaging paths for plastic strain could be appliedfor 104±105 cycles. A frequency of 1 Hz is ap-propriate.

Chan's (1990) experiments with the HollowCylinder Apparatus demonstrated that shear rever-sal (rotating principal planes) does in¯uence plasticstrain accumulation under repeated loading. This isillustrated by the data in Fig. 53 from Chan &Brown (1994) showing the increased rate of strainwhen shear reversal is introduced to a specimeninitially subjected to triaxial stress conditions.

Brown & Chan (1996) have shown that there is adifference between unidirectional and bidirectionalshear reversal (representing one-way and two-waywheel loading respectively), the former leading tolower strains than the latter and hence smaller rutdepths. Their work was based on both HCA andwheel tracking tests.

PAVEMENT DESIGN DEVELOPMENTS

The CBR methodBackground. The most in¯uential early work on

pavement design and associated soil testing wascarried out by the California Division of High-ways. Porter (1938) presented early recommenda-tions for pavement layer thicknesses, based on

Mean normal effective stress: kPaD

evia

tor

stre

ss: k

Pa

Stress paths for resilient strain testing

Stress paths for plastic strain testing

200

100

00 100 200

Fig. 52. Suggested repeated stress paths for testinggranular material (after Thom & Brown, 1988)

Number of load cycles

Axi

al s

trai

n: %

With shearreversal

Triaxial

Recoverablestrain

Permanentstrain

5 10 25 50

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Fig. 53. In¯uence of shear stress reversal on accumu-lation of plastic strain in a dry crushed rock (afterChan & Brown, 1994)

412 BROWN

Page 31: Soil mechanics in_pavement_engineering

experience and the use of bearing value andexpansion tests. The former, developed in 1929and illustrated in Fig. 54, concerned resistance todisplacement of the soil under wheel loading andthe latter to volume increase on wetting. Thebearing value test later became known as theCalifornia Bearing Ratio (CBR) test and is stilluniversally used to test soils and granular materialsby highway laboratories. It is worth examining howthis empirical index test became so widely used andso strongly established in practice. Porter (1938)noted:

`. . . that the bearing values are not a directmeasure of the supporting value of materials' andlater, (Porter, 1950): . . . `the results are in¯u-enced only to a minor degree by elasticdeformation'.

Shortly after Francis Hveem became the materi-als engineer for the state of California, the CBRtest was phased out there and a much morerational approach adopted. This occurred between1944 and 1947 (Vallerga, 1996) and was describedin two major papers (Hveem & Carmany, 1948;Hveem, 1955) which have remained classics.

Meanwhile, the US Army Corps of Engineersdecided to adopt the CBR method of design duringWorld War II in order to meet the challengesposed by new requirements for air®eld pavements.They needed something practical, so extended thehighway design curves to cope with the higherwheel loads applied by aircraft. Elastic theory was

used by Middlebrooks & Bertram (1950) sincethey appreciated that elastic deformations wereimportant. The stress tables published by JuÈrgensen(1934) helped them to back-calculate shear stressesin the subgrade to deduce allowable values. Theirlayer thickness adjustments were con®rmed by®eld loading trials and independent computationsusing different approaches.

Turnbull (1950) commented on the CBR test:

`. . . [it] is essentially a simple shear test and theCBR is an index of shearing strength'.

He noted that the CBR design curves gave a totalthickness of pavement to prevent shear deformationin the soil.

The closing discussion of the ASCE Symposiumthat described these developments (ASCE, 1950)emphasized that the design curves were for opera-tional runways to last `days and weeks not years'.It is clear from this symposium that the CBR testwas regarded as an index test for shear strengthand that the design principles were based onprevention of subgrade shear failure in pavementswith thin surfacings. The use of elastic theoryignored the stiffness of the bituminous surface andno repeated loading or resilient effects wereconsidered. A serious constraint to the develop-ment of a proper theoretical treatment was theabsence of solutions to the analytical problemposed by the layered pavement construction.Although Burmister (1943) developed the theoryin 1943, it was not until Fox (1948) published histables of solutions in 1948 that the ®rst usefulnumbers became available.

In the UK, the American developments weretaken seriously. Davis (1949) describes how theRoad Research Laboratory (RRL) adopted theCBR method of design. He and Professor Skemp-ton reanalysed the US Army Corps of Engineers'®eld trials data to assess the viability of the USdesign curves. The performance of UK roads atseven sites also helped with this process.

The CBR method was gradually adopted in theUK and elsewhere. It formed the basic method ofpavement design in practice and, though re®nedover the years, is still very widely used. In the UK,the original thickness curves have been replacedbut the CBR test remains as the recommendedmethod for characterizing subgrades. Current prac-tice is described in Volume 7 of the DesignManual for Roads and Bridges (Highways Agency,1994b). Foundation layer thicknesses are empiri-cally determined from simple charts based onsubgrade CBR which may be estimated fromplasticity data, approximate water table position,`construction conditions' and choice of `thick' or`thin' pavement. An analytical approach may beused as an alternative and a `stiffness modulus' forthe subgrade can be estimated from the CBR using

Testing machine

Taperedlugs

3 in2 area

Penetrationpiston

6 Cylindricalmould

010

20

30

4060

70

80

90

Head

Fig. 54. Apparatus for Soil Bearing Test (after Porter,1938)

SOIL MECHANICS IN PAVEMENT ENGINEERING 413

Page 32: Soil mechanics in_pavement_engineering

an empirical equation reported by Powell et al.,(1984)

E � 17�6CBR0�64MPa (27)

In view of the earlier observations, quotedabove, to the effect that CBR relates to shearstrength, con®rmed in some detail by Black(1962), it is surprising that is should be used toestimate what is effectively the resilient modulusEr of the soil. Brown et al., (1990) demonstratedthat Er was not a simple function of CBR butdepended on soil type and the applied deviatorstress level. Their results are summarized in Fig.55. In Fig. 55(a), the dependence of the relation-ship on deviator stress for Keuper Marl is clear. InFig. 55(b) results for three soils at a deviator stressof 40 kPa are compared with equation (27) and thesimpler, Mr � 10 CBR (MPa), frequently used indesign. Sweere (1990) could ®nd no correlationbetween the CBR and resilient modulus for a rangeof granular materials.

The research on subgrades which forms thebackground to current UK practice is reviewed

below in an attempt to put matters into perspectivein relation to the soil mechanics of pavementsoutlined in the previous section.

UK subgrade research. Between 1943 and 1961,Dr Croney and his colleagues at RRL conductedextensive research on pavement subgrades. Theirwork was aimed at the determination of watercontent pro®les beneath pavements and they usedsoil suction as a major parameter taking, as theirstarting point, research done by agronomists,notably Scho®eld (1935). He proposed the pF scalefor measuring soil suction, where the pF value islog10 (suction in cm of water). The `p' comes froman analogy with the logarithmic scale of acidity(pH) and the `F' stands for `Free energy'. Croney'sde®nition of suction (s) differs from that generallyaccepted in studies of partially saturated soils andknown as matrix suction

s � ua ÿ uw (28)

where ua is pore air pressure and uw is pore waterpressure.

Croney assumed ua � 0 and de®ned suction asÿuw under zero external stress. The effect ofapplied total stress p was taken into account byuse of a `compressibility coef®cient' á as follows

u � s� áp (29)

in which s is a negative quantity.It is important to note that p was de®ned by the

experiments of Black et al., (1958) as a hydrostaticpressure whereas, in the practical application of theideas to predictions of water content pro®les in the®eld, Croney & Coleman (1952) had regarded itsimply as the vertical component of stress.

There has been dif®culty over the years inunderstanding the correct de®nitions and applica-tion of the á parameter. A useful discussion can befound in Jones (1979) and Black (1979), though astudy of Croney (1952) and Croney & Coleman(1952) provide fuller explanations.

It is worth noting that, for saturated clays, á � 1and hence

s � uÿ p � ÿ(pÿ u) (30)

where p is the mean normal total stress.As s is a negative quantity, it follows that it is

equal to the mean normal effective stress p9 since

p9 � pÿ u (31)

This has allowed some bridges to be builtbetween conventional Terzhagi soil mechanics andthe soil physics approach of Croney and hiscolleagues. (Croney, 1977). This link is alsoapparent in the expression for resilient modulusequation (7). Croney & Coleman (1948) regardedthe pavement as a two-layer elastic system andstated:

Fig. 55. Relationships between CBR and resilientmodulus for clays (after Brown et al., 1987): (a)Keuper marl; (b) Three soils compared with empiricalpredictions at deviator stress of 40 kPa

Dev

iato

r st

erss

: kP

a

20

40

6080100

CBR: %

(a)

0 2 4 6 8 10

Res

ilien

t mod

ulus

: MP

a

300

200

100

0

CBR: %

(b)

0 2 4 6 8 10

120

80

40

0

Keuper Marl

M = 10 CBR

Mr = 17.6 CBR0.64

London Clay

Gault Clay

Res

ilien

t mod

ulus

: at d

evia

tor

stre

ss o

f 40

kPA

: MP

a414 BROWN

Page 33: Soil mechanics in_pavement_engineering

`The maximum stress which the soil will carrywithout permanent deformation is the factorwhich decides the minimum thickness of con-struction'.

However, the main thrust of their work was todetermine the equilibrium water content below apavement since this related to soil strength. Theydid this with some success for both saturated andpartially saturated conditions comparing predictionswith ®eld measurements (Black et al., 1958).

A fascinating aspect of the extensive investiga-tions into water content ± soil suction relationships,conducted by Dr Croney and his team, is theparallel which can be drawn with Critical StateSoil Mechanics. Brady (1988) drew attention to thesimilarity between the soil suction ± water contentrelationship for continuously disturbed LondonClay (Croney & Coleman, 1954) and the CriticalState Line projection onto an effective stress p9 ±speci®c volume v plane (Scho®eld & Wroth,1968). Once again, the equivalence of suctionand effective stress is apparent. This matter hasbeen investigated more recently by Ridley (1995)using Kaolin. He concluded that the suction±watercontent relationship is parallel to the critical stateline but below it in v ÿ p9 space.

Black (1962) developed a Suction Index methodto predict CBR from plasticity data. He regardedthe CBR as a measure of undrained shear strengthsince, experimentally, the procedure is like a small-scale bearing capacity test.

Black & Lister (1979) used the large back-ground knowledge on soil suction ± water contentrelationships to develop a predictive method basedon plasticity data. They selected a representativeequilibrium suction value of 18 kPa correspondingto a water table position 0´6 m below formationunder a typical pavement construction. This wasre®ned by Powell et al., (1984) in providing thebackground to current UK practice (HighwaysAgency, 1994b).

Notwithstanding the recognition that soil stiff-ness is an important parameter (Black & Lister,1979; Croney, 1977), current UK practice ignoresit. Croney (1977) notes:

`The shear strength of soil is not of direct interestto the road engineer in connection with thebehaviour of pavements under traf®c. To providea satisfactory subgrade, the soil should operate atstress levels within the `elastic range' . . .. Thepavement engineer is, therefore, more concernedwith the elastic modulus of the soil and thebehaviour under repeated loading'.

Grainger & Lister (1962) developed repeatedload triaxial test facilities at RRL to measure`elastic moduli' but their early work was curtailed.

In an attempt to improve understanding of theCBR test and the interpretation of results fromit, Hight & Stevens (1982) carried out a criticalreview. They noted that the effective stress state inthe mould is unknown and that there is no controlof drainage. Using the ®nite element method, theyexplored relationships between CBR, stiffness andstrength for four saturated clays. They concludedthat CBR is a measure of undrained shear strengthfor stiff clays but cannot distinguish between lowstrain stiffnesses. Specimens with very differentshaped stress±strain relationships can have the sameCBR.

By allowing either a 2´5 or 5 mm penetrationto be used in the determination of CBR incon-sistences arise because different blends of stiffnessand mobilized strength arise for different soils.The smaller value is more likely to correlate withstiffness. They recommended that soil suctionshould be measured in the test specimen and thatit should be at the appropriate water content andeffective stress to represent in situ conditions.Furthermore, it should either be intact (for cut) orcompacted (for ®ll).

Nutt (1982) showed that lateral stresses devel-oped during compaction have a signi®cant effecton measured CBR for partially saturated soils. Heconcluded that there was no simple relationshipbetween CBR and either strength or stiffness.

Noting that Hight and Stevens considered thefull load±penetration curve could be used toimprove the estimate of stiffness, Loach (1987)obtained data from reconstituted and compactedsoils. He also carried out some repeated load CBRtests, typical results of which are shown in Fig. 56for an overconsolidated silty clay. In general,the initial slopes of the load±penetration curves,whether in cycle 1 or subsequently, correlated withCBR, although there was experimental dif®culty inobtaining accurate values of penetration. Since CBRdid not correlate with resilient modulus, it wasconcluded that the CBR test con®guration is nothelpful in determining soil stiffness for pavementdesign.

This critical review of UK developments in

Penetration: mm

Plu

nger

load

: kN

0 1 2 3 4 5 6 7 8

1.0

0.75

0.5

0.25

0

Fig. 56. Repeated load CBR tests on reconstituted siltyclay (after Loach, 1987)

SOIL MECHANICS IN PAVEMENT ENGINEERING 415

Page 34: Soil mechanics in_pavement_engineering

subgrade soil mechanics reveals the need forimproved test methods to quantify the resilientmodulus. Such equipment has been available formany years and has emerged from being a researchtool to a practical test for design application. Thismatter is further discussed in the ®nal section.

The rational approachWhile the US Army Corps of Engineers were

enthusiastically embracing the CBR approach topavement design, Hveem and his colleagues inCalifornia were devising new tests and developingtheories as to how pavements developed failureconditions. Fig. 25 is the classical cross-sectionthey drew to demonstrate cracking and deforma-tion. They invented the Stabilometer test tomeasure the frictional characteristics of unboundmaterials and the Cohesiometer to determinetensile strength of surfacing. The Stabilometer,shown in Fig. 57, is still used today and is a formof triaxial test from which a resistance value R isdetermined using the equation

R � 1ÿ (óh=óv)

100(32)

where óh is measured for a typical value of óv �1100 kPa.

Hveem & Carmany (1948) state that R is ameasure of the ratio of maximum shear stress tomajor principal stress (ô/ó1) as follows

100R � 1ÿ (óh=óv) � (ô=ó1) (33)

However, simple analysis of the Mohr's circlereveals that

1ÿ (óh=óv) � q=ó1 � 2ô=ó1 (34)

where ó1 � óv and q � óv ÿ óh � 2ôNotwithstanding the disputed factor of two, R is

seen to be a reasonably fundamental measure of

shear to normal stress at failure and, hence, relatesstrongly to the angle of shearing resistance.

Hveem & Carmany (1948), recognized that the`dynamic modulus of elasticity' for the subgradewas a parameter of relevance to understanding thefatigue cracking of asphalt surfaces and thatmonotonic loading would not be adequate for itsdetermination. Hveem (1955) in his classical paperto the Highway Research Board developed thetheme of resilient behaviour of pavements. Hedevised a repeated load version of the Stabilometertest known as the Resiliometer to characterizesubgrades. There was an appreciation of the factthat a low stabilometer value (strength) does notalways correlate with high resilience. By collating®eld measurements of surface de¯ection with theincidence of cracking, he was able to suggestallowable de¯ection values for different pavementconstructions. This led to the worldwide adoptionof surface de¯ection measurement as a routinemethod for assessing the structural condition ofpavements.

The K-mould devised by Handy & Fox (1987)and evolved by Semmelink & de Beer (1993,1995) has similarities to the Resiliometer. Lateralstress is mobilized by an elastic support systemwith a stiffness which can be varied between15±60 MPa, designed to simulate in situ conditions.This provides a state somewhere between K0 (zerolateral strain) and uncon®ned. Preliminary resultshave been obtained for resilient properties and forpermanent deformation characteristics of granularmaterials.

The pioneering work of Hveem and his col-leagues combined theoretical concepts, ®eld ob-servations and the development of innovativelaboratory tests in a co-ordinated manner whichis still a model for good research and development.

Professor Seed and his colleagues at theUniversity of California at Berkeley followed thelead established by Hveem. They developed therepeated load triaxial test and introduced the term`modulus of resilience' (Seed et al., 1955). Thiswas later changed to `resilient modulus' (Seed etal., 1962) which is de®ned on p. 406 where thestress dependence of resilient modulus is illustratedby Fig. 41. Seed et al., (1962, 1965) demonstratedthat de¯ection in repeated plate loading tests couldbe predicted using their laboratory data andappropriate elastic theory.

The early work on fatigue testing of bituminousmixtures was also pursued at Berkeley underProfessor Carl Monismith (Monismith et al.,1961) and, quite independently, at Nottingham byProfessor Peter Pell (Pell, 1962).

An understanding of the non-linear properties ofsoils and granular materials evolved simultaneouslyat Berkeley and Nottingham in the 1960s. Hicks &Monismith (1971) reported comprehensive data for

Pressuregauge

Adjustablestage

Displacementpump

Dialgauge

Piston forapplyingload to specimen

Liquid

Flexiblediagram

Platen oftesting machine

Load

Head of testing machine

Testspecimen

Fig. 57. The Hveem stabilometer (after Hveem &Carmany, 1948)

416 BROWN

Page 35: Soil mechanics in_pavement_engineering

granular materials from repeated load triaxial testswhile Brown & Pell (1967) and Brown & Bush(1972) deduced results from in situ measurements(e.g. Fig. 5).

The increasing availability of linear±elastictheoretical solutions for pavement analysis fromthe mid 1960s combined with the ability to carryout relevant laboratory tests on soils, granularmaterials and bituminous materials led to thedevelopment of several analytically based pave-ment design methods in the 1970s and 1980s (e.g.Claessen et al., 1977, Brown et al., 1984). Thesemethods have generally used two design criteria,the tensile elastic strain of the bottom of thebituminous layer, to deal with fatigue cracking,and the vertical elastic strain at the top of thesubgrade. This latter was derived from back-analy-sis of pavements of known performance withrespect to rut development and is a semi-empiricalattempt to deal with this failure mechanism using alinear elastic based theory for design. (Brown &Brunton, 1984).

Little serious soil mechanics is incorporated inmost of the available design methods based on amechanistic approach although the effects of non-linear behaviour in soil and granular materials aretaken into account either directly or indirectly bymost of them.

The validity of theoretical models for pavementsystems has been quite widely studied with com-parisons between computed and measured values ofthe key design parameters generally giving reason-able con®dence for use of the theory in design.

The use of back-analysis to determine resilientproperties has been widely implemented in practice(Brunton et al., 1992). It is a good example of thesensible use of analytical techniques and only givesplausible results when the non-linear properties ofthe subgrade and, in certain cases, the sub-base aretaken into account. The programs LEAD and FEAD

developed by d'Almeida et al., (1993) allow thetwo parameters in each of equations (6) and (22)to be determined through an iterative procedure.The bituminous or cement treated layers areassumed to be linear elastic and effective stiff-nesses are computed for these. The effectivestiffness accounts for the reduction in stiffnesscaused by cracking and general deteriorationrelative to the `as built' value for the undamagedlayer.

Fig. 58 shows a typical pro®le of vertical elasticstrain through a pavement structure. Summation ofthis strain with depth yields the surface de¯ec-tion. The large contribution from the subgrade isapparent, demonstrating the importance of propercharacterization of resilient properties for the soil.

An attraction of using theory in back analysis isthat the model is calibrated to the structure throughthe matching of surface de¯ection pro®les. The

resulting resilient moduli of its layers can then beused with some con®dence in design calculationsto assess residual life and determine structuralrequirements for future life. This may take theform of a strengthening overlay or of partial re-construction.

The technique has recently been used inconjunction with a case study to compare newideas on pavement foundation design with currentempirical practice. Two sections of the A564Derby Southern By-Pass were tested at variousstages of construction. One section was in cut andthe other on an embankment. The soil was a siltyclay in both cases, the capping was locally wonsand and gravel, the sub-base was crushed lime-stone in the cutting and granite on the embank-ment and the road base was a dense bituminousmaterial. The FWD was used to obtain de¯ectiondata and the results were back-analysed to deter-mine effective resilient moduli for pavement layersas construction proceeded. The data in Table 1 forthe section in cut show how the capping andsubgrade mobilized higher resilient moduli whencovered by sub-base and road base owing toincreased con®ning stress and decreased deviatorstress in keeping with the non-linear stress±strainrelationships.

Asphaltlayer

Granularlayer

Subgrade

Vertical strain: microstrain

10005000

0.5

1.0

1.5

2.0

Dep

th: m

Surface deflectionunder centre of load = shaded area

Fig. 58. Typical variation of resilient vertical strainwith depth through an asphalt pavement (after Brownet al., 1987)

SOIL MECHANICS IN PAVEMENT ENGINEERING 417

Page 36: Soil mechanics in_pavement_engineering

Table 2 shows values of equivalent foundationstiffness computed using equation (1) and thecentral de¯ection measurement only. The valuesincreased as tests were conducted successively onthe subgrade, capping and sub-base of the em-bankment. This shows the effect of building up thefoundation on the stiffness of support provided tolayers placed above.

A PRACTICAL APPROACH TO PAVEMENT

FOUNDATION DESIGN

IntroductionThis section outlines an approach to pavement

foundation design based on the use of theoreticalconcepts and measured properties of the soil andgranular layer. It is based on research carriedout for the TRL reported by Thom et al. (1993) andDawson et al. (1993). The objective was to producea relatively simple, implementable system usingreasonably priced facilities which could be adoptedby design laboratories.

PhilosophyFig. 59 shows the sequence of design and

testing proposed by Dawson et al. (1993). It in-cludes laboratory testing of representative samplesof the subgrade and the aggregates(s), designcalculations using analytical techniques and ®eldmeasurements as construction proceeds to provide acheck on the design.

Materials testingThe simpli®ed repeated load triaxial apparatus

in Fig. 19 can be used to determine resilientproperties and permanent deformation character-istics of soils. These are modelled by equation (8)for the resilient modulus and a simpli®ed version

of equation (5) for the plastic strain accumulatedafter N load applications

åp(N) � A log N (qr=s)B (35)

The shear strength is also determined.A similar procedure is recommended for charac-

terizing the granular materials to be used incapping and in sub-base. The equipment is shownin Fig. 21. The resilient modulus is modelled usingthe simple equation (22) in which è is taken astotal stress because the suction will not usuallybe known. Simple repeated load tests allow theconstants to be determined for the equations. Sincepermanent deformation resistance correlates withthe angle of shearing resistance ö9 only strengthtesting is needed for this property.

Design criteriaThe design criteria fall into two categories,

those concerned with rutting and those concernedwith the resilient behaviour of the foundation. Therut at sub-base level may result from plastic strainaccumulation in the aggregate layer(s) alone, in thesubgrade alone or within all layers.

The resilient behaviour of the foundation can beexpressed as an equivalent value for the structurebased on its resilient surface de¯ection underload. Two loading situations arise: that due to theconstruction of the bound layers above and thatresulting from traf®c once the pavement is com-

Table 1. Back-analysed effective values of resilientmodulus for road in cutting

Pavement layer Effective Er: MPa

Test on capping Test on road base

Road base ± 3200Sub-base ± 240Capping 90 200Subgrade 70 200

Table 2. Equivalent foundation stiffness values forroad on embankment

Test on Equivalent foundationstiffness: MPa

Subgrade 30Capping 50Sub-base 90

Measure subgrade characteristics in laboratory

Select aggregate(s)

Measure aggregate characteristics in laboratory

Design foundation

Prepare subgrade

Check in situ performance

Performance satisfactory?

Place aggregate?

Check in situ performance

Performance satisfactory?

Foundation Complete

YES

YES

NO

NO

if aggregateis unsatisfactory

Fig. 59. Proposed procedure for pavement foundationdesign (after Dawson et al., 1993)

418 BROWN

Page 37: Soil mechanics in_pavement_engineering

plete. The former affects constructability of thebituminous layer and the latter in¯uences its long-term performance.

Analytical techniquesA quasi-failure analysis using the wedge model

in Fig. 60 is proposed to deal with rutting in thegranular material. The force P required to pushthe central wedge down by the allowable rut depth(say 40 mm) is computed using static equilibriumtechniques. Resistance to P is mobilized by thevalues of apparent cohesion c and angle ofshearing resistance, ö for the aggregate layersand the allowable deviator stress on the subgradeqa. This is determined from equation (35) using anallowable plastic strain of 0´6% for the requirednumber of load applications N. This strain level isregarded as a tentative suggestion at present. Fulldetails of the wedge model are described by Thomet al. (1993). An iterative computation is used toobtain a solution.

For the situation where the rutting is entirelycontributed by the subgrade and for the determina-tion of equivalent foundation resilient modulus,linear elastic layered system analysis is used. Thenon-linear resilient properties of the materials areaccounted for by using the iterative approachdescribed on p. 389. This allows compatibility ofstresses and resilient moduli to be established. Forthe subgrade rutting criterion, the deviator stress atformation is calculated and equation (35) used tocheck whether the allowable strain of 0´6% isexceeded.

The equivalent foundation stiffness is deter-mined using the computed surface de¯ection forthe layered system and calculating the resilientmodulus for an equivalent semi-in®nite elastic halfspace using equation (1). The analysis described

above can be performed using the PAFODE compu-ter program developed by Dawson & Thom (1994).

Validation of the methodPreliminary validation of the design method

has been carried out using performance data fromfull-scale trials at Bothkennar and Loughborough(Dawson et al., 1993). The predictions of rut depthdevelopment using the wedge model are comparedwith measurements in Fig. 61. Results for theLoughborough trials are satisfactory but for Both-

C

φFcb

Rcbθc

B

Fb Ra

Rb

Rba

Fba

θa A

P

2r

h

Fig. 60. Proposed `wedge model' for calculating rutting in pavement foundations (after Thom et al., 1993)

Fig. 61. Predicted rut depths compared with measure-ments at full-scale (after Dawson et al., 1993) (a)Loughborough trials; (b) Bothkennar trials

Limestone

Number of passes1 10 100 1000

predictedmeasured

Rut

dep

th: m

m

0102030

4050607080

Granodiorite

Ash

Sand &Gravel

(a)

10 100 1000 10 000

predictedmeasured

Rut

dep

th: m

m

0102030

4050607080

(b)

Granite(550 mm)

Gravel(400 mm)

SOIL MECHANICS IN PAVEMENT ENGINEERING 419

Page 38: Soil mechanics in_pavement_engineering

kennar the model overpredicted rutting. The labora-tory test data to support the Bothkennar calculationswere less complete than for the Loughborough tests.

The method clearly needs to be used more ex-tensively for a wider range of materials and condi-tions and to be re®ned. It is, however, consideredto provide the basis for improved design ofpavement foundations in the future.

Railtrack designLi (1994) presents a good summary of proce-

dures for the determination of granular layerthicknesses in railtrack. He describes a methoddeveloped at the University of Massachusettswhich uses the GEOTRACK program for modellingresponse to wheel loading. The design criteria arevertical plastic strain and vertical permanentdeformation at formation level. The former is toprevent plastic ¯ow, which leads to progressivefailure of the top of the subgrade, while the latterrelates to the overall deformation of the subgrade.Varying the thickness of the granular layersin¯uences the transient deviator stress level inthe subgrade and, hence, the plastic strain åp. Theplastic strain after N cycles is computed by thefollowing equation, derived from repeated loadtriaxial tests on clays

å1p � A(qr=cu)mNb (36)

in which A, m and b are experimentally deter-mined, N is the number of load applications, cu isthe undrained shear strength and qr is the repeateddeviator stress.

CONCLUSIONS

This wide ranging review of soil mechanics inpavement engineering has outlined the techniqueswhich are available to study the problem usingtheory, laboratory testing and ®eld experiments. Ithas primarily been concerned with bituminouspavements for highways but other pavement typesobey similar principles. The particular character-istics of railtrack have also been described.

It was considered helpful to place presentknowledge and practice in a historical perspective,since pavement soil mechanics has developed, tosome extent, in isolation from mainstream geo-technics. It is ironic that much of the research onrepeated loading of soil and granular materials hasbeen quite sophisticated and comparable in qualitywith that developed in other ®elds of soil mech-anics, but procedures used in current practiceremain empirical and backward. Much the samecan be said of theoretical modelling.

The background knowledge accumulated fromresearch presents an opportunity for improvingcurrent practice. A simpli®ed approach to founda-

tion design has been outlined which, with a littlefurther development, could provide the basis toupgrade present practice. One feature of this isthe simpli®ed test procedures for materials whichcould be made more user-friendly in the mannerachieved for bituminous materials using the Not-tingham Asphalt Tester (Cooper & Brown, 1989). Awide range of soils and granular materials, under avariety of conditions, needs to be tested.

Further research is needed, notably to obtain abetter understanding of the effective stress statein pavement foundations. This will require goodquality, long-term ®eld monitoring using moistureand suction measuring techniques for which therehave been recent advances. The signi®cant im-provement in understanding of partially saturatedsoils through the work of Wheeler & Karube(1995), Alonso et al. (1990) and Fredlund &Rahardjo (1993) provides a sound basis to improvethe models used for pavement design. These couldbe combined with elasto±visco±plastic models forbituminous materials to provide a comprehensivetheoretical framework for ¯exible pavements in thefuture.

Little or nothing has been reported herein on thevital matter of pavement drainage. Suf®ce it to saythat improvements in the effectiveness and relia-bility of drainage so that water conditions belowpavements remain stable and water contents atreasonable levels continue to be a desirable aim.

ACKNOWLEDGEMENTS

In preparing this Rankine Lecture, the Authorhas drawn liberally on the research carried out byhis colleagues at Nottingham University over manyyears. The successive research staff who havecontributed new ideas and brought a variety ofskills to bear on both experimental and theoreticalwork have provided a stimulating environment anda large source of information. Particular thanks areexpressed to: Ahmed Lashine, Adrian Hyde, JohnBoyce, Jack Pappin, Simon Loach, Peter Ansell,Phil Shaw, Joao d'Almeida, Bob Overy, MikeO'Reilly, Matthew Raybould, Alex Tam and PeterLittle, all of whom have moved on to other places,and to present colleagues at Nottingham and SWKPavement Engineering Ltd; Andrew Dawson, NickThom, Ron Jones, Ian Richardson, Barry Brodrick,Francis Chan, Lam Wah Cheung and John Nutt.Grateful thanks are also extended to CarolynParkinson and Hayley Drabble, who dealt withthe text and ®gures respectively.

Without the work of all these people, thislecture would not have been possible.

Permission was granted by the HighwaysAgency to conduct tests on the A564 DerbySouthern By-Pass and particular thanks are ex-pressed to Tarmac Construction Ltd. and to Scott

420 BROWN

Page 39: Soil mechanics in_pavement_engineering

Wilson Kirkpatrick, the consulting engineers, andin particular to Phil Staten, their GeotechnicalResident Engineer who facilitated the work.

The Author is also indebted to Professor CarlMonismith from the University of California atBerkeley and to Barney Vallerga from Oakland,California for the provision of information on earlydevelopments in their State.

The invitation to deliver a Rankine Lecture isvery special and a great honour. The Author willbe eternally grateful to the British GeotechnicalSociety's Committee under Andrew Lord for givinghim the privilege of being able to respond on this,the 36th occasion.

The research at Nottingham University has beenfunded by a large number of organizations overthe years including the Science and EngineeringResearch Council, the Transport Research Labora-tory, the Building Research Station, British Rail,Shell, the US Air Force and the US Army. Thissupport is gratefully acknowledged.

On a personal note, the Author would like tothank his wife, Maryse, for constant encourage-ment in this endeavour through the sleepless nightsand the long days in the study.

REFERENCESAcum, W. E. A. & Fox, L. (1951). Computation of load

stresses in a three layer elastic system, GeÂotechnique2, 293±300.

Alavi, S. H. (1992). Viscoelastic and permanent deforma-tion characteristics of asphalt-aggregate mixes testedas hollow cylinders and subjected to dynamic axialand shear loads, PhD thesis, University of California.

Alonso, E. E., Gens, A. and Josa, A. (1990). Aconstitutive model for partially saturated soils, GeÂo-technique 40, No. 3, 405±430.

American Association of State Highway and Transporta-tion Of®cials (1986). Standard method of test forresilient modulus of subgrade soils. AASHTO Desig-nation: T272±82.

American Society of Civil Engineers (1950). Discussion,Development of CBR ¯exible pavement design methodfor air®elds ± a symposium, Trans. Am. Soc. Civ.Engrs, 115, 555±589.

Andersen, K. H., Brown, S. F., Foss, I., Pool, J. H. &Rosenbrand, W. F. (1976). Effect of cyclic loading onclay behaviour, Proc. Conf. Design and Constructionof Offshore Structures, Institution of Civil Engineers,75±79.

Austin, G. (1979). The behaviour of Keuper Marl underundrained creep and repeated loading, PhD thesis,University of Nottingham.

Basson, J. E. B., Wijnberger, O. J. & Skultety, J. (1981).The Multidepth De¯ectometer: a multi-stage sensorfor the measurement of resilient de¯ections andpermanent deformations at various depths in roadpavements, Report No. RP/3.81, NITRR, CSIR,Pretoria.

Black, W. P. M. (1979). Reply to discussion on roadsubgrades, Clay ®lls, 243±244. London: Institution of

Civil Engineers.Black, W. P. M. (1962). A method of estimating the

California Bearing Ratio of cohesive soils fromplasticity data, GeÂotechnique 11, No. 1, 14±21.

Black, W. P. M., Croney, D. & Jacobs, J. C. (1958). Fieldstudies of the movement of soil moisture, Road Res.Tech. Paper No. 41, DSIR, HMSO.

Black, W. P. M. & Lister, N. W. (1979). The strength ofclay ®ll subgrades: its prediction and relation to roadperformance, Clay ®lls, 37±48, London: Institution ofCivil Engineers.

Bleyenberg, W. G., Claessen, A. I. M., van Gorkum, F.,Heukelom, W. & Pronk, A. C. (1977). Fully moni-tored motorway trials in the Netherlands corroboratelinear elastic design theory, Proc. 4th Int. Conf.Structural Design of Asphalt Pavements, Ann Arbor,Michigan, 1, 75±98.

Boyce, J. R. (1976). The behaviour of a granularmaterial under repeated loading, PhD thesis, Uni-versity of Nottingham.

Boyce, J. R. (1980). A non-linear model for the elasticbehaviour of granular materials under repeatedloading, Proc. Int. Symp. soils under cyclic andtransient loading, Swansea, 285±294.

Boyce, J. R., Brown, S. F. & Pell, P. S. (1976). Theresilient behaviour of a granular material underrepeated loading, Proc. Aust. Road Research Board28, 8±19.

Brady, K. C. (1988). Soil suction and the Critical State,GeÂotechnique 38, No. 1, 117±120.

British Airports Authority (1993). Aircraft pavements:pavement design guide for heavy aircraft loading,Internal Report No. P2833-RP-CE-001-01.

Brown, S. F. (1975). Improved framework for predictingpermanent deformation in asphalt layers, Transp. Res.Record No. 537, Transportation Research Board,Washington, DC, 18±30.

Brown, S. F. (1978). State-of-the-art report on ®eldinstrumentation for pavement experiments, Transp.Res. Record No. 640, Transportation Research Board,Washington, DC, 13±28.

Brown, S. F., Andersen, K. H. & McElvaney, J. (1977).The effect of drainage on cyclic loading of clay, Proc.9th Int. Conf. Soil Mech. Foundation Engng, Tokyo, 2,195±200.

Brown, S. F., Austin, G. & Overy, R. F. (1980). Aninstrumented triaxial cell for cyclic loading of clays,Geotech. Testing J., ASTM, 3, No. 4, 145±152.

Brown, S. F. & Bell, C. A. (1977). The validity of designprocedures for the permanent deformation of asphaltpavements, Proc. 4th Int. Conf. Structural Design ofAsphalt Pavements, Ann Arbor, Michigan, 1, 467±482.

Brown, S. F. & Brodrick, B. V. (1981a). Nottinghampavement test facility, Transp. Res. Record No. 810,Transportation Research Board, Washington, DC, 67±72.

Brown, S. F. & Brodrick, B. V. (1981b). Instrumentationfor the Nottingham Pavement Test Facility, Transp.Res. Record No. 810, Transportation Research Board,Washington, DC, 73±79.

Brown, S. F. & Brunton, J. M. (1984). Improvements topavement subgrade strain criterion, J. Transp. EngngAm. Soc. Civ. Engrs, 110, No. 6, 551±567.

Brown, S. F., Brunton, J. M. & Stock, A. F. (1985). Theanalytical design of bituminous pavements, Proc.

SOIL MECHANICS IN PAVEMENT ENGINEERING 421

Page 40: Soil mechanics in_pavement_engineering

Instn Civ. Engrs, 79, Pt. 2, 1±31.Brown, S. F. & Bush, D. I. (1972). Dynamic response of

model pavement structure, J. Transp. Engng, Am. Soc.Civ. Engrs, 98, TE4, 1005±1022.

Brown, S. F., O'Reilly, M. P. & Pappin, J. W. (1989). Arepeated load triaxial apparatus for granular materials,in Unbound Aggregates in Roads, London, Butter-worth, 143±158.

Brown, S. F. & Chan, F. W. K. (1996) Reduced rutting inunbound granular pavement layers through improvedgrading design, Proc. Instn Civ. Engrs Transport, 117,40±49.

Brown, S. F. & Dawson, A. R. (1992). Two-stageapproach to asphalt pavement design, Proc. 7th Int.Conf. Asphalt Pavements, Nottingham, 1, 16±34.

Brown, S. F., Lashine, A. K. F. & Hyde, A. F. L. (1975).Repeated load triaxial testing of a silty clay, GeÂo-technique 25, No. 1, 95±114.

Brown, S. F., Loach, S. C. & O'Reilly, M. P. (1987).Repeated loading of ®ne grained soils, ContractorReport 72, Transportation Research Laboratory.

Brown, S. F., O'Reilly, M. P. & Loach, S. C. (1990). Therelationship between California Bearing Ratio andelastic stiffness for compacted clays, Ground Engng,23, No. 8, 27±31.

Brown, S. F. & Pappin, J. W. (1981). Analysis ofpavements with granular bases, Transp. Res. RecordNo. 810, Transportation Research Board, Washington,DC, 17±22.

Brown, S. F. & Pell, P. S. (1967). An experimentalinvestigation of the stresses, strains and de¯ectionsin a layered pavement structure subjected to dynamicloads, Proc. 2nd Int. Conf. Structural Design ofAsphalt Pavements, Ann Arbor, Michigan, 487±504.

Brown, S. F. & Selig, E. T. (1991). The design ofpavement and rail track foundations, Chapter 6 inCyclic loading of soils: from theory to design,Blackie, Glasgow and London, 249±305.

Brown, S. F., Tam, W. S. & Brunton, J. M. (1986).Development of an analytical method for the struc-tural evaluation of pavements, Proc. 2nd Int. Conf.Bearing Capacity of Roads and Air®elds, Plymouth,1, 267±276.

Brown, S. F., Tam, W. S. & Brunton, J. M. (1987).Structural evaluation and overlay design: analysis andimplementation, Proc. 6th Int. Conf. Structural De-sign of Asphalt Pavements, Ann Arbor, Michigan, 1,1013±1028.

Brunton, J. M. & Akroyde, P. M. (1990). Monitoring theperformance of a full-scale experimental pavement,Proc. 3rd Int. Conf. Bearing Capacity of Roads andAir®elds, Trondheim, 585±594.

Brunton, J. M. & d'Almeida, J. R. (1992). Modelingmaterial non-linearity in a pavement backcalculationprocedure, Transp. Res. Record No. 1377, Transporta-tion Research Board, Washington, DC, 99±106.

Brunton, J. M., Armitage, R. J. & Brown, S. F. (1992).Seven years' experience of pavement evaluation,Proc. 7th Int. Conf. on Asphalt Pavements, Notting-ham, 3, 17±30.

Burmister, D. M. (1943). Theory of stresses anddisplacements in layered systems and application tothe design of airport runways, Proc. Highway Res.Board, 23, Washington, DC, 126±148.

Chan, F. W. K. (1990). Permanent deformation resistance

of granular layers in pavements, PhD thesis, Uni-versity of Nottingham.

Chan, F. W. K. & Brown, S. F. (1994). Signi®cance ofprincipal stress rotation in pavements, Proc. 13th Int.Conf. Soil Mech. Foundn Engng, Delhi, 4, 1823±1826.

Chang, C. S., Adegoke, C. W. & Selig, E. T. (1979). Astudy of analytical models for track support systems,Transp. Res. Record No. 733, Transportation ResearchBoard, Washington, DC, 12±19.

Cheung, L. W. (1994). Laboratory assessment of pave-ment foundation materials, PhD thesis, University ofNottingham.

Claessen, A. I. M., Edwards, J. M., Sommer, P. & UgeÂ, P.(1977). Asphalt pavement design ± the Shell Method,Proc. 4th Int. Conf. Structural Design of AsphaltPavements, Ann Arbor, Michigan, 1, 39±74.

Cooling, L. F. et al. (1961), Discussion on Session 3:Roads and Runways and Agriculture in Pore pressureand suction in soils, London, Butterworth, 143±151.

Cooper, K. E. & Brown, S. F. (1989). Development of asimple apparatus for the measurement of the mech-anical properties of asphalt mixes, Proc. EurobitumeSymposium, Madrid, 494±498.

Cox, B. (1980). Reconstruction, including design plan-ning and execution from the engineer's point of view,Highway Engr., 27, No. 12, 13±15.

Croney, D. (1952). The movement and distribution ofwater in soils, GeÂotechnique 5, No. 1, 1±16.

Croney, D. (1977). The design and performance of roadpavements, London, HMSO.

Croney, D. & Coleman, J. D. (1948). Soil thermo-dynamics applied to the movement of moisture inroad foundations, Proc. 7th Int. Conf. Appl. Mech.,London, 3, 163±177.

Croney, D. & Coleman, J. D. (1952). The estimation ofthe vertical moisture distribution with depth inunsaturated cohesive soils, Road Note No. 1709,DSIR, HMSO.

Croney, D. & Coleman, J. D. (1954). Soil structure inrelation to soil suction (pF), J. Soil Sci. 5, No. 1,75±84.

d'Almeida, J. C. G. R. (1993). Analytical techniques forthe structural evaluation of pavements, PhD thesis,University of Nottingham.

d'Almeida, J. R., Brown, S. F. & Thom, N. H. (1994). Apavement evaluation procedure incorporating materialnon-linearity. Non-destructive testing and back-calcu-lation of moduli. (2nd Vol.), American Society forTesting and Materials, STP 1198, 218±232.

Davis, E. H. (1949). The California Bearing Ratiomethod for the design of ¯exible roads and runways,GeÂotechnique 1, No. 4, 249±263.

Dawson, A. R., Brown, S. F., Thom, N. H. & Cheung, L.W. (1993). Improvements to road foundation design:laboratory tests and design method, Report PRG93023, University of Nottingham.

Dawson, A. R. & Plaistow, L. (1993). Parametric study ±¯exible pavements, Flexible Pavements, Balkema,229±237.

Dawson, A. R. & Gomes Correia, A. (1993). The effectsof subgrade clay condition on the structural behaviourof road pavements, Flexible Pavements, Balkema,113±119.

Dawson, A. R. & Thom, N. H. (1994). Software manual

422 BROWN

Page 41: Soil mechanics in_pavement_engineering

for the program PAFODE, Report PRG 94004, Uni-versity of Nottingham.

Dehlen, G. C. & Monismith, C. L. (1970). Effect of non-linear material response on the behaviour of pave-ments under traf®c, Highway Res. Record No. 310,Highway Research Board, Washington, DC, 1±16.

de Jong, D. L., Peutz, M. G. F. & Korswagen, A. R.(1973). Computer program BISAR: layered systemsunder normal and tangential loads, Koninklike ShellLaboratorium, Amsterdam, Rep. No. AMSR 0006.73.

Duncan, J. M., Monismith, C. L. & Wilson, E. L. (1968).Finite element analysis of pavements, Highway Res.Record No. 228, Highway Research Board, Washing-ton, DC, 18±33.

Farrer, D. M. (1979). Settlement and pore-water pressuredissipation within an embankment built of Londonclay, Clay ®lls, 101±106. London, Institution of CivilEngineers.

Fox, L. (1948). Computation of traf®c stresses in a simpleroad structure, Road Res. Tech. Paper No. 9, DSIR,HMSO.

Fredlund, D. G. & Rahardjo, H. (1993). Soil mechanicsfor unsaturated soils, John Wiley, Chichester.

Freeme, C. R. & Servas, V. P. (1985). Advances inpavement design and rehabilitation, in AcceleratedTesting of Pavements, CSIR, Pretoria.

Gomes Correia, A. (1985). Contribution aÁ l'eÂtudemechanique des sols soumis aÁ des changementscycliques, Dr Eng. thesis, Ecole Nat. des Ponts etChausseÂes, Paris.

Grainger, G. D. & Lister, N. W. (1962). A laboratoryapparatus for studying the behaviour of soils underrepeated loading, GeÂotechnique 12, No. 1, 3±14.

Greenwood, D. A. et al. (1992). Bothkennar Soft Claytest site: Characterization and lessons learned, 8thGeÂotechnique Symp., GeÂotechnique 52, No. 2, 161±378.

Handy, R. L. & Fox, D. E. (1987). K-tests for subgradeand base evaluation, Proc. Annual Transp. Conven-tion, CSIR, Pretoria, 6.

Hardin, B. O. & Drnevich, V. P. (1972). Shear modulusand damping in soils I. Measurements and parametereffects, J. Geotech. Engng Div., Am. Soc. Civ. Engrs,102, No. GT9, 975±987.

Heath, D. L., Shenton, M. J., Sparrow, R. W. & Waters, J.M. (1972). Design of conventional rail track founda-tions, Proc. Instn Civ. Engrs, 51, No. 2, 251±267.

Hicks, R. G. & Monismith, C. L. (1971). Factorsin¯uencing the resilient response of granular mater-ials, Highway Res. Record No. 345, Highway Re-search Board, Washington, DC, 15±31.

Hight, D. W. & Stevens, M. G. H. (1982). An analysis ofthe California Bearing Ratio test in saturated clays,GeÂotechnique 32, No. 4, 315±322.

Highways Agency (1994a). Use and limitations of groundpenetrating radar for pavement assessment, HA72/94,HMSO.

Highways Agency (1994b). Design manual for roads andbridges: Vol 7, Pavement design and maintenance,HMSO.

Hveem, F. N. (1955). Pavement de¯ections and fatiguefailures, Highway Res. Board Bulletin No. 114,Washington, DC, 43±87.

Hveem, F. N. & Carmany, R. M. (1948). The factorsunderlying the rational design of pavements, Proc.

Highway Res. Board, 28, Washington, DC, 101±136.Hveem, F. N. & Sherman, G. B. (1962). California

method for the structural design of ¯exible pave-ments, Proc. Int. Conf. Structural Design of AsphaltPavement, Ann Arbor, Michigan, 851±866.

Hyde, A. F. L. (1974). Repeated load triaxial testing ofsoils, PhD thesis, University of Nottingham.

Jones, R. H. (1979). Discussion on road subgrades, Clay®lls, 243, London, Institution of Civil Engineers.

Jouve, P. & Elhannani, M. (1993). Application desmodeÁles non-lineÂaires au calcul des chausseÂes soup-les, Bulletin de liaison des Laboratoires des Ponts etChausseÂes, No. 190, 30±35.

JuÈrgenson, L. (1934). Application of elastic theory andplasticity to foundation problems, J. Boston Soc. Civ.Engrs, 242.

Klomp, A. J. G. & Niesman, Th. W. (1967). Observedand calculated strains at various depths in asphaltpavements, Proc. 2nd Int. Conf. Structural Design ofAsphalt Pavements, Ann Arbor, Michigan, 671±688.

Lee, A. R. & Croney, D. (1962). British full-scalepavement design experiments, Proc. Int. Conf. Struc-tural Design of Asphalt Pavements, Ann Arbor,Michigan, 114±136.

Lentz, R. W. & Balady, G. Y. (1980). Simpli®edprocedure to characterise permanent strains in sandsubjected to cyclic loading, Proc. Int. Symp. Soilsunder Cyclic and Transient Loading, Swansea, 280±294.

Li, D. (1994). Railway track granular layer thicknessdesign based on subgrade performance under re-peated loading, PhD thesis, University of Massachu-setts.

Liddle, W. J. (1962). Application of AASHO road testresults to the design of ¯exible pavement structures,Proc. Int. Conf. Structural Design of Asphalt Pave-ments, Ann Arbor, Michigan, 42±51.

Lister, N. W. (1972). The transient and long termperformance of pavements in relation to temperature,Proc. 3rd Int. Conf. Structural Design of AsphaltPavements, London, 1, 94±100.

Little, P. H. (1993). The design of unsurfaced roads usinggeosynthetics, PhD thesis, University of Nottingham.

Loach, S. C. (1987). Repeated loading of ®ne grainedsoils for pavement design, PhD thesis, University ofNottingham.

Lytton, R. (1995). Foundations and pavements onunsaturated soils, Keynote Address, 1st Int. Conf. onUnsaturated Soils, Paris.

Metcalf, J. B., McLean, J. R. & Kadar, P. (1985). Thedevelopment and implementation of the AustralianAccelerated Loading Facility (ALF) program, inAccelerated Testing of pavements, CSIR, Pretoria.

Middlebrooks, T. A. & Bertram, G. E. (1950). Adaptationto the design of air®eld pavements, Development ofCBR ¯exible pavement design method for air®elds ± asymposium, Trans Am. Soc. Civ. Engrs, 468±471.

Monismith, C. L., Secor, K. E. & Blackmer, W. (1961).Asphalt mixture behaviour in repeated ¯exure, Proc.Assoc. of Asphalt Paving Techn., 30, 188±222.

National Institution for Transport and Road Research(1985a). Structural design of interurban and ruralroad pavements, TRH4, CSIR, Pretoria.

National Institute for Transport and Road Research(1985b). Guidelines for Road Construction Materials,

SOIL MECHANICS IN PAVEMENT ENGINEERING 423

Page 42: Soil mechanics in_pavement_engineering

TRH 14, CSIR, Pretoria.Nutt, J. L. (1982). Finite element modelling of partially

saturated soils for a study of the California BearingRatio test, MSc thesis, Imperial College, University ofLondon.

O'Reilly, M. P. (1985). Mechanical properties of granularmaterials for use in thermal energy stores, PhDthesis, University of Nottingham.

O'Reilly, M. P., Brown, S. F. & Overy, R. F. (1989).Viscous effects observed in tests on an anisotropicallynormally consolidated silty clay, GeÂotechnique 39,No. 1, 153±158.

Pappin, J. W. (1979). Characteristics of a granularmaterial for pavement design, PhD thesis, Universityof Nottingham.

Pappin, J. W. & Brown, S. F. (1980). Resilient stress-strain behaviour of a crushed rock, Proc. Int. Symp.Soils under cyclic and transient loading, Swansea, 1,169±177.

Pappin, J. W., Brown, S. F. & O'Reilly, M. P. (1992).Effective stress behaviour of saturated and partiallysaturated granular material subjected to repeatedloading, GeÂotechnique 42, No. 3, 485±497.

Paute, J-L., Hornych, P. & Beraben, J.-P. (1993).Repeated load triaxial testing of granular materialson the French network of Laboratoires des Ponts etChausseÂes, Flexible Roads, Balkema, 53±64.

Pell, P. S. (1962). Fatigue characteristics of bitumen andbituminous mixes, Proc. Int. Conf. Structural Designof Asphalt Pavements, Ann Arbor, Michigan, 310±323.

Pell, P. S. & Taylor, I. F. (1969). Asphaltic road materialsin fatigue, Proc. Assoc. Asphalt Paving Tech., 38,371±422.

Porter, O. J. (1938). The preparation of subgrades, Proc.Highway Res. Board, 18, No. 2, Washington, DC,324±331.

Porter, J. (1950). Development of the original method forhighway design, Development of CBR ¯exible pave-ment design method for air®elds ± a symposium,Trans. Am. Soc. Civ. Engrs, 115, 461±467.

Powell, W. D., Potter, J. F., Mayhew, H. C. & Nunn, M.E. (1984). The structural design of bituminous roads,Lab. Report 1132, TRRL.

Ramsamooj, D. V., Majidzadeh, K. & Kauffmann, E. M.(1972). The analysis and design of the ¯exibility ofpavements, Proc. 3rd Int. Conf. Structural Design ofAsphalt Pavements, London, 692±704.

Raybould, M. R. (1992). The response of silt-claymixtures to cyclic loading, PhD thesis, University ofNottingham.

Raybould, M. J. & Brown, S. F. (1993). Experimentalmethods in determining cyclic response of soils withparticular reference to triaxial tests on Hostun sand,Proc. Conf. Experimental Methods in EarthquakeEng. and Struct. Dynamics, St.-Remy-leÁs-Chevreuse,France, 156±168.

Ridley, A. M. (1995). Strength±suction±moisture contentrelationships for kaolin under normal atmosphericconditions, Proc. 1st Int. Conf. on Unsaturated Soils,Paris, 645±651.

Roblee, C. J., Xiang-Song, L., Chan, C. K., Idriss, I. M.,Wang, G., Herrmann, L. R. & Jackura, K. A. (1994).Feasibility of a tool for in situ measurement ofmaterial properties of clays over a wide strain range,Dynamic Geot. Testing II, American Society for

Testing and Materials, STP 1213, 134±161.Robnett, Q. L., Thompson, M. R., Knutson, R. M. &

Tayabji, S. D. (1975). Development of a structuralmodel and materials evaluation procedures, Universityof Illinois, Report No. DoT-Fl-30038.

Rowe, G. M., Brown, S. F., Sharrock, M. J. & Bouldin,M. G. (1995). Visco-elastic analysis of hot mixasphalt pavement structures, Transp. Res. Record No.1482, Transportation Research Board, Washington,DC, 44±51.

Scho®eld, R. K. (1935). The pF of the water in soil,Trans. 3rd Int. Congress on Soil Science, 2, Oxford,37±48.

Scho®eld, A. N. & Wroth, C. P. (1968). Critical state soilmechanics, McGraw-Hill, London.

Seed, H. B., Chan, C. K. & Lee, C. E. (1962). Resiliencecharacteristics of subgrade soils and their relation tofatigue failures, Proc. Int. Conf. Structural Design ofAsphalt Pavements, Ann Arbor, Michigan, 611±636.

Seed, H. B., Chan, C. K. & Monismith, C. L. (1955).Effects of repeated loading on the strength anddeformation of compacted clay, Proc. High. Res.Board, 34, Washington, DC, 541±558.

Selig, E. T. & Waters, J. M. (1994). Track geotechnologyand substructure management, Thomas Telford, Lon-don.

Semmelink, C. J. & de Beer, M. (1993). Development ofa dynamic DRTT K-mould system, Res. Report DPVT216, Roads and Transp. Tech., CSIR, Pretoria.

Semmelink, C. J. & de Beer, M. (1995). Rapid determi-nation of elastic and shear properties of road buildingmaterials with the K-mould, in Unbound aggregatesin roads, University of Nottingham, 151±162.

Shaw, P. & Brown, S. F. (1986). Cyclic simple sheartesting of granular materials, Geotech. Testing J.American Society for Testing and Materials 9, No. 4,213±220.

Shaw, P. & Brown, S. F. (1988). The behaviour of drygranular materials under repeated load biaxial andtriaxial stress conditions, GeÂotechnique 38, No. 4,627±634.

Sorenson, A. & Hayven, M. (1982). The Dynatest 8000Falling Weight De¯ectometer test system, Proc. Int.Symp. Bearing Capacity of Roads and Air®elds,Trondheim, 1, 464±470.

Sousa, J. B. & Chan, C. K. (1991). Computer applica-tions in the geotechnical laboratories of the Universityof California at Berkeley, Proc. Geotech. Eng. Conf.,Boulder, Colorado, American Society of Civil Engi-neers.

Stewart, H. E., Selig, E. T. & Norman-Gregory, G. M.(1985). Failure criteria and lateral stresses in trackfoundations, Transp. Res. Record No. 1027, Trans-portation Research Board, Washington, DC, 59±64.

Sun, J. I., Golesorkhi, R. & Seed, H. B. (1988). DynamicModuli and Damping Ratios for Cohesive Soils.Report No. UBC/EERC-88/15, Earthquake Engineer-ing Research Center, 42.

Sweere, G. T. H. (1990). Unbound granular bases forroads, Doctoral thesis, Delft University of Technology.

Thom, N. H. & Brown, S. F. (1988). The effect ofgrading and density on the mechanical properties of acrushed dolomitic limestone, Proc. Aust. Road Res.Board, 14, Pt. 7, 94±100.

Thom, N. H., Dawson, A. R. & Brown, S. F. (1993).

424 BROWN

Page 43: Soil mechanics in_pavement_engineering

Improvements to road foundation design: developmentof pavement foundation design, Report PRG 93012,University of Nottingham.

Topp, G. C., Davis, J. L., Bailey, W. G. & Zebchuk,W. D. (1984). The measurement of soil water contentusing a portable TDR hand probe, Canad. J. Soil Sci.64, 313±321.

Transportation Research Board (1975). Test proceduresfor characterizing dynamic stress±strain properties ofpavement materials, Special Report 162, Washington,D.C.

Turnbull, W. J. (1950). Appraisal of the CBR method,Development of CBR ¯exible pavement design methodfor air®elds ± a symposium, Trans. Am. Soc. Civ.Engrs, 547±554.

Tutumluer, E. & Barksdale, R. D. (1995). Behaviour ofpavements with granular bases ± prediction andperformance, in Unbound aggregates in roads, Uni-versity of Nottingham, 173±183.

Vallerga, B. (1996). Private communication.Van der Poel, C. (1954). A general system describing the

visco-elastic properties of bitumens and its relation totest data, J. Appl. Chem. 4, 221±236.

van Dijk, W. & Visser, W. (1977). The energy approachto fatigue for pavement design, Proc. Assoc. AsphaltPaving Technologists, 46, 1±40.

Viggiani, G. & Atkinson, J. H. (1995). Stiffness of ®ne-grained soil at very small strains, GeÂotechnique 45,No. 2, 249±265.

Vucetic, M., & Dobry, R. (1991). Effect of Soil Plasticityon Cyclic Response, J. Geotech. Engrg, ASCE, 117,No. 1, 89±107.

Walker, R. N. (1985). The South African Heavy VehicleSimulator, Accelerated Testing of Pavements, CSIR,Pretoria.

Warren, H. & Dieckmann, W. L. (1963). Numericalcomputation of stresses and strains in a multiple-layerasphalt pavement system, Internal Report, ChevronRes. Corp, California.

Weiler, W. A. (1988). Small strain shear modulus of clay,Earthquake Eng. and Soil Dynamics II ± RecentAdvances in Ground Motion Evaluation, Geot. SpecialReport No. 20, Am. Soc. Civ. Engrs, 331±345.

Wheeler, S. J. & Karube, D. (1995). State of the artreport ± constitutive modelling, Proc. 1st Int. Conf.Unsaturated Soils, Paris.

VOTE OF THANKS

DR R. H. JONES, Senior lecturer in Civil Engineering,

University of Nottingham.

It is an honour and a great pleasure to proposethe vote of thanks to the thirty-sixth RankineLecturer. All Rankine Lectures and lecturers canlay claim to being unique; this one was the ®rstfrom the East Midlands and the ®rst by apavement engineer. The linking is highly appro-priate. The region provides raw materials neededby pavement engineers, including beer and crushedrock granular sub-base. More signi®cantly, it isthe place where ¯exible pavements originated. In1901, E. Purnell Hooley, the County Surveyor ofNottinghamshire, observed the binding effect of tar

which had been accidentally spilt on an unboundroad. Thus Tarmacadam (Tarmac) was born ± a newmaterial, a new company and a new word added tothe English language. It was a happy coincidencethat, some time later, the University of Nottinghamshould become involved in research on ¯exiblepavements. Stephen Brown joined the team veryearly and has made a major contribution to thedevelopment of what has become an internationallyrecognised research group.

To date, pavement engineering has been asomewhat neglected part of geotechnics. Tonight,however, we have been treated to a worldwidereview of pavement engineering in a lucid, wellillustrated, and nicely paced lecture.

Essentially, we have heard of a soil±structureinteraction problem, although the elements may bea little unfamiliar to the foundation engineer. Thestructure is the rails and sleepers of a railway orthe bound layers of a road or air®eld pavement,together with the underlying unbound layer(s) ofgranular materials. The soil considered was a claysubgrade, since granular materials behave as engi-neering soils whether within, or below the structure.

Professor Brown reviewed the relevant theoryand practical tools (pavement experiments andlaboratory and ®eld testing, often with ingeniousapparatus) and has examined the system require-ments which are essentially dominated by service-ability.

In particular, features of the soil mechanics ofpavements are transient, repeated loads applied tosoils above the water table. The emphasis is onstrength and stiffness characterized by permanentdeformation and resilient modulus. We have heardabout models of behaviour involving viscousresponse and demonstrating the importance ofthreshold stress ratio values. The history of thesubject and particularly of the contributions ofCalifornia and T/RRL were also covered.

Whilst pavement engineering may have been aneglected part of geotechnics the reverse is nottrue. Developments such as the ®nite elementmethod, the critical state framework and in theunderstanding of earthquake engineering and ofpartially saturated soils have all been applied tothe subject. Like Hooley, our Lecturer is a keenobserver and sees the technical, engineering andcommercial applications of his observations. Overthe years, he has instilled these qualities into histeam so that they have amassed a wealth of highquality data. The Rankine Lecture has givenStephen Brown the opportunity to present athoughtful revisit of earlier work and to re-analysethe data in the light of the current theoreticalconcepts.

The Lecture has given a fascinating insight intothe behaviour of materials and the application ofdesign methods. It concluded with proposals for

SOIL MECHANICS IN PAVEMENT ENGINEERING 425

Page 44: Soil mechanics in_pavement_engineering

practical designs which could lead to a moretheoretical approach than is currently used in theUK. Some empiricism would remain, but at alower level in the hierarchy.

We have been privileged to hear an acknow-ledged master of his subject demonstrate clearlythe role of soil mechanics in pavement engineer-

ing. It was an ambitious lecture presented with alight, deft, touch. When he started, pavement engi-neering may have been a Cinderella but oureighteenth home Lecturer has ensured that it hascome of age.

I ask you to join with me in showing yourappreciation and thanks by acclamation.

426 BROWN