Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: This research study investigates the influence of specimen geometry and grading curve, on the performance of a typical South African unbound granular material. The experimental design incorporates three grading curves to evaluate the influence of grading. In addition, to evaluate the influence of specimen geometry, two specimen sizes were included into the experimental design. Laboratory testing consisted of monotonic tri-axial tests to evaluate the shear performance (Cohesion and Friction Angle) and more complex short duration dynamic tri-axial tests to evaluate the load spreading ability/stiffness (Resilient Modulus) of the selected materials. In order to achieve the objectives of this study, a large tri-axial apparatus was needed that could accommodate specimens as large as 300mm ϕ * 600mm high. This would allow a full grading of large aggregate (up to 50mm particle size) to be accurately evaluated. Further development and commissioning of such a large triaxial apparatus therefore formed part of this study. The representative parent material selected for testing consisted of a G2 graded crushed Hornfels stone. The material was dried and sieved into fractions where after it was carefully reconstituted to allow for accurate control of specimen grading during specimen preparation. The three grading curves consisted of two adjusted grading curves (referred to as S19 and G19C), adjusted from the full G2 grading, and the full G2 grading itself (referred to as the Full grading curve). Material property tests, Sieve Analysis, Bulk Relative Density (BRD) and Optimum Moisture Content (OMC) tests were performed to gain an understanding of the material characteristics. Moisture-Density relationship curves were developed to identify a common Moisture Content that, for all three grading curves, would yield a common Dry Density. A Moisture Content of 4.7% was identified that would yield a Dry Density of 2340 kg/m3 for all three grading curves. This density could be achieved for both sizes of specimen preparation apparatuses without damaging material particles. Specimens were compacted using the representative vibratory hammer compaction method, sealed and left for 24 hours to allow redistribution of moisture and initial development of Cohesion. The shear parameters (Cohesion and Friction Angle) were investigated through monotonic tri-axial testing. It was found that Cohesion and Friction Angle are influenced by both grading curve and specimen geometry. Cohesion was found to reduce as the coarseness of the material grading increased (i.e. finer S19 grading yielded higher Cohesion than its coarser G19C counterpart) and the Friction Angle was found to increase with increase coarseness (i.e. finer S19 grading yielded lower Friction Angles when compared to the G19C grading). The influence of specimen geometry was also investigated. It was observed than Cohesion decreased with an increase in specimen size. Friction Angle on the other hand was found to increase with increased specimen size. From dynamic tri-axial test results, it was observed that the Resilient Modulus is influenced by both specimen geometry and grading curve. The influence of specimen geometry however is complex and no constant trend throughout the grading curves tested could be identified. Grading curve however was found to increase the Resilient Modulus for coarser gradings (i.e. coarser G19C vs finer S19). Increased large particle-to-particle contact area yields higher friction within the material specimen, resulting in lower strains induced by higher stresses, i.e. higher Resilient Modulus. It was shown, for both monotonic and dynamic tri-axial tests, that the coarser G19C grading curve yields more representative results to that of the Full grading curve when compared to the finer S19 grading. This was observed for shear and resilient performance properties. Additionally, a simple design case study yields similar trends. In conclusion, material characterisation plays an important role in the design of unbound granular materials (UGM’s). Current laboratory characterisation techniques however used adjusted gradings to limit the effects stemming from the ratio between specimen diameter and maximum particle size. This research has shown that some of the current practices do not best represent the true in-situ grading. It has been shown that both grading curve and specimen geometry influence the performance of UGM’s which, in turn, influences the design of a pavement structure. Therefore, accurate modelling of the true in-situ grading, through testing apparatuses capable of accommodating in-situ gradings, is required. / AFRIKAANSE OPSOMMING: Hierdie navorsingsstudie evalueer die invloed van proefstukgeometrie en gradering, op die gedragseienskappe van ‘n tipiese Suid Afrikaanse ongebinde granulêre aggregaat. Om die invloed van gradering te evalueer, is ‘n eksperimentele ontwerp ontwikkel wat drie materiaal graderings insluit. Verder, om die invloed van proefstukgeometrie te evalueer, is twee proefstukgroottes toegevoeg tot die eksperimentele ontwerp. Monotoniese drie-assige toetse is uitgevoer om die skuifsterkte (Kohesie en Wrywingshoek) van die materiaal te ondersoek. Addisioneel is die styfheid (Veerkragmodulus) van die materiaal ondersoek deur dinamiese drieassige toetse. Om die doelwitte van hierdie studie te bereik was ‘n groot skaalse die-assige toets apparaat benodig wat groot, 300mm ϕ * 600mm hoogte, proefstukke kan akkommodeer. So ‘n apparaat laat toe dat die volle gradering van aggregaat (tot en met 50mm korrels) akkuraat geëvalueer kan word. Daarom vorm die ontwikkeling en opstelling van so ‘n apparaat deel van hierdie studie. Die tipiese Hornfels gebreekte klip, met ‘n G2 gradering, wat ondersoek is, was gedroog en in verskeie fraksies gesif om die akkuraatheid van proefstuk voorbereiding te beheer. Die drie graderings bestaan uit twee aangepaste graderings (S19 en G19C gradering skale), aangepas vanaf die volle G2 gradering, en die vol G2 gradering homself (verwys na as die “Full” gradering skaal). Materiaal gedragstoetse, Sif Analises, Nat Gekompakteerde Relatiewe Digtheid (BRD) en Optimum Vog Inhoud (OVI) toetse, was uitgevoer om die materiaal eienskappe te ondersoek. Om ‘n gemeenskaplike Vog Inhoud en Droë Digtheid, wat vir al drie graderings geld, te vind, is Vog-Digtheid verhoudingskurwes ontwikkel. Vanaf die kurwes is identifiseer dat ‘n Vog Inhoud van 4.7% ‘n Droë Digtheid van 2340 kg/m3 vir al drie graderings sal lewer. Vibrasie kompaksie is toegepas om albei skale van proefstukke te kompakteer waarna die proefstukke vir 24 uur geseel is om vogverspreiding en ontwikkeling van Kohesie toe te laat. Monotoniese drie-assige toetse is uitgevoer om die skuifsterkte parameters (Kohesie en Wrywingshoek) te ondersoek. Die resultate het gewys dat beide gradering en proefstukgeometrie die Kohesie en Wrywinshoek beinvloed. gradering lewer hoër Kohesie waardes i.v.m. die growwer G19C gradering). Die Wrywingshoek is gevind om te verhoog soos die grofheid van die gradering verhoog (m.a.w. die fyner S19 gradering het laer Wrywingshoeke gelewer i.v.m. die growwer G19C gradering). Resultate het verder gewys dat groter proefstukke laer Kohesie en hoër Wrywingshoeke lewer. Daar kan wel gedebateer word dat variasie in materiaal die verandering van die skuifsterkte parameters gee, maar die proefstukvariasie is beperk om sodoende die invloed daarvan onopmerkbaar te maak.. Verder is die verlaging in Kohesie en verhoging in Wrywingshoek, a.g.v. ‘n vergroting in proefstuk grootte, vir albei aangepaste graderings geobserveer. Dit is ‘n moontlike aanduiding dat die verandering nie materiaal afhanklik is nie maar eerder beinvloed word deur die grens toestande tydens kompaksie. Dinamiese drie-assige toets resultate het gewys dat die Veerkragmodulus beinvloed word deur beide proefstuk geometrie en gradering. Daar is gevind dat die invloed van proefstukgeometrie kompleks is, en geen konstante verhouding, wat vir alle toets graderings geld, kon identifiseer word nie. Vir die invloed van gradering is daar gewys dat die Veerkragmodulus hoër is vir die growwer gradering (m.a.w. G19C gradering lewer hoër styfheid as S19 gradering). ‘n Verhoging in korrel-tot-korrel kontak area lewer hoër interne wrywing in die proefstuk wat bydrae tot laer vervorming by hoër spannings, m.a.w. hoër Veerkragmodulus. Baie interessant, vir beide monotoniese en dinamiese drie-assige toetse is gevind dat die growwer G19C gradering, i.v.m. die fyner S19 gradering, die ware G2 (Full) gradering beter verteenwoordig. Hierdie observasie is geldig vir beide die skuifsterkte parameters en weerstands eienskappe. Aggregaat karakterisering is ‘n belangrike deel in die ontwerp van ‘n ongebinde granulêre materiaal laag. Huidige karakterisering metodes gebruik aangepaste graderings sodat resultate nie beinvloed word deur die verhouding tussen proefstuk diameter en maksimum klipgrootte nie. Hierdie ondersoek het gevind dat van die huidige aanpassings nie die ware gradering verteenwoordig nie. Die resultate wys dat beide gradering en proefstuk geometrie die gedrag van die ongebinde granulêre materiaal beinvloed, so ook die ontwerp van ‘n padstruktuur. Daar is dus ‘n behoefte om die ware gradering te ondersoek wat slegs moontlik is met groot skaalse toets apparaat, wat groot klip korrels kan toets. Verder, indien daar ‘n verstandhouding tussen huidige (klein skaalse) toets apparaat en groot skaalse apparaat ontwikkel kan word, kan resultate aangepas word, vanaf die klein skaalse resultate, om die ware materiaal gedrag meer te verteenwoordig.

Unbound granular material is used in the pavement structure and usually comprises the bulk of the structural and foundation layers of a typical South African pavement. The term ‘unbound granular material’ refers to the classification of natural material, which has not been modified in any way. Various mechanistic-empirical models for the resilient response of unbound granular material have been developed over the years. However, few have incorporated important influencing parameters such as moisture or density on the basic stress-strain relationship or linked variables of the models to basic engineering properties of unbound granular material. This study builds on previous work by Theyse (2008a) and the cord modulus model developed by Theyse (2012). The Theyse (2012) model was selected to be further investigated, since it modelled the trends observed in the data realistically. The model depicts the stress dependent behaviour of unbound granular material, where an increase initial modulus is observed for increasing confinement pressure, as well as initial stress-softening with increasing stress ratio followed by stress stiffening. The model was calibrated for all bulk material samples under consideration in this thesis. The calibration process included linking variables of the model to mathematical functions that approximate the trends observed when variables were considered against level of saturation. A parametric analysis indicated that the saturation and stress-dependent cord modulus model realistically predict material behaviour. The saturation and stress-dependent cord modulus model was refined further and calibrated for crushed and natural unbound granular material. This refinement did not negatively influence the accuracy or ability to realistically predict the material behaviour. Basic material properties could be linked to predictive statistical distributions that could estimate the range of modulus values that can be expected for the material under consideration. However, the variables of the saturation and stress-dependent cord modulus model could not be linked to basic material properties due to the limit set of results available. / Thesis (PhD)--University of Pretoria, 2013. / gm2013 / Civil Engineering / unrestricted

Laboratory characterization of subgrade soils and unbound granular materials is an essential component of the Mechanistic-Empirical Pavement Design Guide (Pavement ME). The design thickness and performance of a pavement structure are highly dependent on the deformation behaviour of subgrade and granular material. Specifications for granular materials vary among transportation agencies based on the availability of materials, climatic conditions, and function. Specifications aim to provide durable materials that meet design requirements and achieve the target design life with cost effective materials. The objectives of the research are to: • evaluate resilient modulus of typical fine-grained soils under traffic loading. • evaluate resilient modulus, permanent deformation, and permeability of typical unbound granular materials. • evaluate the effect of moisture and fines fraction on the performance of unbound granular materials and subgrade soil. • develop prediction models for resilient modulus to improve reliability of Level 2 inputs in the Pavement ME. • provide test data in support of updating Manitoba Infrastructure and Transportation specifications for unbound granular materials to improve the performance of pavement structures. Resilient modulus tests were conducted on three types of subgrade soil (high plastic clay, sandy clay, and silty sand/sandy silt) at four levels of moisture content. Resilient modulus, permanent deformation and permeability tests were conducted on six gradations representing two types of granular material (100% crushed limestone and gravel) at two levels of moisture content. Prediction models were developed for resilient modulus and compared to the models developed under the Long Term Pavement Performance program. The proposed models provided more reliable predictions with lower root mean square error. The deformation behaviour of the granular materials was classified according to the shakedown and dissipated energy approaches. Among the tested fines contents, limestone and gravel materials with optimum fines contents of 4.5% and 9%, respectively, had better resistance to plastic deformation and higher resilient modulus. The dissipated energy approach can be used to determine the stress ratio for the boundary between post compaction and stable zones from multistage triaxial testing. Result of permeability tests showed that the hydraulic conductivity of unbound granular material increased as the fines content decreased. / February 2016

Ziel der vorliegenden Dissertation war die Erweiterung der Kenntnisse über das nichtlinear-elastische Spannungs-Verformungsverhalten von Tragschichten ohne Bindemittel (ToB). Ein analytisches Bemessungsverfahren ist aufgrund der schwierigen Modellierbarkeit des Verformungsverhalten der einzelnen Straßenbaustoffe bisher nicht existent. Die Dissertation soll einen Beitrag zur Entwicklung eines solchen Bemessungsverfahrens leisten. Eine Literaturrecherche zum Verformungsverhalten von ToB bildet die Grundlage für die Festlegung der Vorgehensweise. Basis der weiteren Untersuchungen sind Triaxialversuche, die an der Universität Nottingham an verschiedenen Gesteinskörnungen durchgeführt wurden. Mit Hilfe der Shakedown-Theorie konnte belegt werden, dass sich ToB in unterschiedlichen Beanspruchungsbereichen nach verschiedenen Gesetzmäßigkeiten verhalten und dass Modelle zur Beschreibung des Verformungsverhaltens von ToB bereichsweise verschieden formuliert werden müssen. Somit ist es möglich, Gültigkeitsgrenzen für elastische Stoffmodelle zu ermitteln sowie Beanspruchungsgrenzen für ToB festzulegen. Mit ausgewählten Stoffmodellen erfolgten Beanspruchungsberechnungen nach der Finite-Elemente Methode (FEM). Die beste Annäherung zwischen Messwerten und Rechenergebnissen ergibt sich bei Anwendung des DRESDNER Modells. Berechnungen für Befestigungen nach den RStO 01 haben gezeigt, dass die Beanspruchungen auf den ToB bei Anwendung des DRESDNER Modells stark von denen bei Anwendung linearer Elastizität abweichen können. Durch unterschiedliche Überbauungsdicken der ToB besitzen diese einen verschieden hohen Anteil am Tragverhalten der Befestigung. Abschließend wird eine Methode zur Ermittlung von Sicherheitsniveaus vorgestellt. Bei Kenntnis der entsprechenden Schichtparameter lassen sich die Beanspruchungen jeder beliebigen Bauweise mit denen von Bauweisen nach RStO vergleichen. Als Ergebnis kann festgehalten werden, dass das Sicherheitsniveau einer bestimmten Bauweise nach RStO genauso groß ist, wie eine Befestigung mit einer dünneren Asphalttragschicht, dafür jedoch einer steiferen ToB. / The aim of this thesis was the extension of the knowledge about the resilient stress-deformation behaviour of unbound granular materials (UGM). Due to difficulties in modelling the behaviour of the single materials an analytical design method does not exist at present. Therefore this thesis makes a contribution for developing such a design method. A study of international publications about the current knowledge of the stress-deformation behaviour of UGM and repeated load triaxial tests, which have been performed at Nottingham University, were the base for all further investigations. With the shakedown concept it could be shown that materials behave in a different manner depending on the applied stress level and that material laws for describing the resilient deformation behaviour of UGM have to be formulated separately for different stress ranges. Within this thesis a method is introduced which helps to find boarders for the applicability of different material laws and limiting stress lines where below the lines stable behaviour and admissible deformations for the material are expected. Applying selected material laws finite element calculations have been performed. Comparing calculation results with measurement results it can be shown that the Dresden model offers the best approach. Calculations for pavement constructions applying the Dresden model have resulted that the vertical stresses differ very much in comparison with elastic behaviour for the UGM. It can be concluded that the thickness of the covering bounded layers have an effect to the contribution of the unbound granular layers at the complete deformation behaviour of the pavement construction. Finishing a method is introduced to determine the safety levels of pavement constructions. It seems to be possible to compare the stress-strain levels of any pavement construction with those from the german standard RStO 01. Existing functions could be modified to determine safety coefficients, i. e. ratios between admissible and existing numbers of load cycles. It can be concluded that there are the same safety levels for different pavement constructions ? a thinner asphalt layer can be compensated with a stiffer UGM.

Ziel der vorliegenden Dissertation war die Erweiterung der Kenntnisse über das nichtlinear-elastische Spannungs-Verformungsverhalten von Tragschichten ohne Bindemittel (ToB). Ein analytisches Bemessungsverfahren ist aufgrund der schwierigen Modellierbarkeit des Verformungsverhalten der einzelnen Straßenbaustoffe bisher nicht existent. Die Dissertation soll einen Beitrag zur Entwicklung eines solchen Bemessungsverfahrens leisten. Eine Literaturrecherche zum Verformungsverhalten von ToB bildet die Grundlage für die Festlegung der Vorgehensweise. Basis der weiteren Untersuchungen sind Triaxialversuche, die an der Universität Nottingham an verschiedenen Gesteinskörnungen durchgeführt wurden. Mit Hilfe der Shakedown-Theorie konnte belegt werden, dass sich ToB in unterschiedlichen Beanspruchungsbereichen nach verschiedenen Gesetzmäßigkeiten verhalten und dass Modelle zur Beschreibung des Verformungsverhaltens von ToB bereichsweise verschieden formuliert werden müssen. Somit ist es möglich, Gültigkeitsgrenzen für elastische Stoffmodelle zu ermitteln sowie Beanspruchungsgrenzen für ToB festzulegen. Mit ausgewählten Stoffmodellen erfolgten Beanspruchungsberechnungen nach der Finite-Elemente Methode (FEM). Die beste Annäherung zwischen Messwerten und Rechenergebnissen ergibt sich bei Anwendung des DRESDNER Modells. Berechnungen für Befestigungen nach den RStO 01 haben gezeigt, dass die Beanspruchungen auf den ToB bei Anwendung des DRESDNER Modells stark von denen bei Anwendung linearer Elastizität abweichen können. Durch unterschiedliche Überbauungsdicken der ToB besitzen diese einen verschieden hohen Anteil am Tragverhalten der Befestigung. Abschließend wird eine Methode zur Ermittlung von Sicherheitsniveaus vorgestellt. Bei Kenntnis der entsprechenden Schichtparameter lassen sich die Beanspruchungen jeder beliebigen Bauweise mit denen von Bauweisen nach RStO vergleichen. Als Ergebnis kann festgehalten werden, dass das Sicherheitsniveau einer bestimmten Bauweise nach RStO genauso groß ist, wie eine Befestigung mit einer dünneren Asphalttragschicht, dafür jedoch einer steiferen ToB. / The aim of this thesis was the extension of the knowledge about the resilient stress-deformation behaviour of unbound granular materials (UGM). Due to difficulties in modelling the behaviour of the single materials an analytical design method does not exist at present. Therefore this thesis makes a contribution for developing such a design method. A study of international publications about the current knowledge of the stress-deformation behaviour of UGM and repeated load triaxial tests, which have been performed at Nottingham University, were the base for all further investigations. With the shakedown concept it could be shown that materials behave in a different manner depending on the applied stress level and that material laws for describing the resilient deformation behaviour of UGM have to be formulated separately for different stress ranges. Within this thesis a method is introduced which helps to find boarders for the applicability of different material laws and limiting stress lines where below the lines stable behaviour and admissible deformations for the material are expected. Applying selected material laws finite element calculations have been performed. Comparing calculation results with measurement results it can be shown that the Dresden model offers the best approach. Calculations for pavement constructions applying the Dresden model have resulted that the vertical stresses differ very much in comparison with elastic behaviour for the UGM. It can be concluded that the thickness of the covering bounded layers have an effect to the contribution of the unbound granular layers at the complete deformation behaviour of the pavement construction. Finishing a method is introduced to determine the safety levels of pavement constructions. It seems to be possible to compare the stress-strain levels of any pavement construction with those from the german standard RStO 01. Existing functions could be modified to determine safety coefficients, i. e. ratios between admissible and existing numbers of load cycles. It can be concluded that there are the same safety levels for different pavement constructions ? a thinner asphalt layer can be compensated with a stiffer UGM.