<p> Orientations of deformation lamellae in quartz and C-axes of quartz grains containing lamellae were measured at seven locations across a gently folded bed of the Oriskany Sandstone, central Pennsylvania. Lamellae so measured have an average inclination of 20°-30° to the basal plane, and are therefore categorized as "subbasal".</p> <p> Fabrics of poles to deformation lamellae and corresponding C-axis orientations suggest a paleostress field for the fold which had the arrangement; σ1 bedding parallel, σ3 bedding perpendicular, and σ2 fold axis subparallel. Relative magnitudes of the stresses were given by the condition σ1 > σ3. σ2 is believed to have varied in magnitude between σ1 and σ3 during fold development.</p> <p> Exact timing of formation of lamellae is uncertain. Textural evidence shows that they predate a later generation of compressional and tensional microfractures associated with the deformation. The best explanation is that they formed in early stages of layer parallel compaction when compressive stresses in all zones of the fold were greatest. Stress refraction may or may not have been operative.</p> / Thesis / Bachelor of Science (BSc)

The thermodynamic behaviors of multicomponent, elastic, crystalline solids under stress and electro-magnetic fields are developed, including the extension of Euler’s equation, Gibbs equation, Gibbs-Duhem equation, the conditions to be expected at equilibrium, and an extension of the Gibbs phase rule. The predictions of this new phase rule are compared with experimental observations. The stress deformation behaviors of the single martensitic crystal with and without magnetic fields were studied with the stress deformation equation derived by Slattery and Si (2005). One coherent interfacial condition between two martensitic variants was developed and used as one boundary condition of the problem. The dynamic magnetic actuation process of the single crystal actuator was analyzed. The extension velocity and the actuation time of the single crystal actuator are predicted. The relationship between the external stress and the extension velocity and the actuation time with the presence of a large external magnetic field was studied. The extended Gibbs-Duhem equation and Slattery-Lagoudas stress-deformation expression for crystalline solids was used. Interfacial constraints on the elastic portion of stress for crystalline-crystalline interfaces and crystalline-fluids or crystallineamorphous solids interfaces were derived and tested by the oxidation on the exterior of a circular cylinder, one-sided and two-sided oxidation of a plate. An experiment for measuring solid-solid interface surface energies was designed and the silicon-silicon dioxide surface energy was estimated. A new generalized Clausius-Clapeyron equation has been derived for elastic crystalline solids as well as fluids and amorphous solids. Special cases are pertinent to coherent interfaces as well as the latent heat of transformation.

The thermodynamics of three-dimensional, single-component elastic crystalline solids was developed by Slattery and Lagoudas (2005). Considering the in¯nitesimal deformations, the stress can be expressed as a function of the lattice vectors and density in the reference configuration and ¹(I;mn), which is defined as the derivative of specific Helmoholtz free energy with respect to the I(mn). Using the Cauchy - Born rule to connect the interatomic potential energy and the specific Helmholtz free energy, it is possible to calculate the elastic properties of both nano-scale materials such as carbon nanotubes and macro-scale materials such as diamond and silicon. In this study, we used Terso® (1988a) - Brenner (1990b) Potential, Terso® (1988b) potential and Finnis and Sinclair (1984) potential for carbon, silicon, and vanadium systems respectively. Using the interatomic potentials to describe the specific Helmholtz free energy, the elastic properties of graphite, diamond, silicon and vanadium were calculated. This method was also extended to the calculation of Young's modulus of single-walled carbon nanotubes (SWCNTs), which are composed of a two dimensional array of carbon atoms. For SWCNT, we get good agreement with the available experimental data. For diamond and silicon, C11 and C12 were consistent with both the superelastic model and the experimental data. The difference of C44 between the calculation and experimental data was due to accuracy of the potential functions.

In this research, two comprehensive numerical models were developed using ABAQUS/CAE Finite Element (FE) software: 1) geothermal model, and 2) coupled thermo-hydro-mechanical model. In the first model, a purely heat transfer analysis was performed to reproduce the conditions at the site and investigate the subsurface thermal regime beneath the road embankment. The existence of a frozen section (frost bulb) underneath the embankment and its size and location were investigated by the model. The second model concentrated on the mechanical behaviour of the road embankment. Temperature-dependent thermal and mechanical properties were used for all the materials. Model parameters were calibrated using the results of the triaxial and oedometer tests which have been conducted by previous researchers. A fully-coupled and a sequentially-coupled analysis were conducted. The results of the two analyses were compared to each other and to the field measurements. / February 2016

This thesis investigates the effect of scale on themorphology, mechanics and transmissivity of single rockfractures using both laboratory and in-situ experiments, aswell as numerical simulations. Using a laboratory 3D laserscanner, the surface topography of a large silicon-rubberfracture replica of size 1m x 1m, as well as the topography ofboth surfaces of several high-strength concrete fracturereplicas varying in size from 50mmx50mm to 200mm x 200mm, werescanned. A geodetic Total Station and an in-situ 3D laser radarwere also utilized to scan the surface topography of a largenatural road-cut rock face of size 20m x 15m in the field. Thisdigital characterization of the fracture samples was then usedto investigate the scale dependency of the three dimensionalmorphology of the fractures using a fractal approach. Thefractal parameters of the surface roughness of all fracturesamples, including the geometrical aperture of the concretefracture samples, were obtained using the Roughness-Lengthmethod. The results obtained from the fractal characterization ofthe surface roughness of the fracture samples show that bothfractal dimension, D, and amplitude parameter, A, for aself-affine surface are scale-dependent, heterogeneous andanisotropic, and their values generally decrease withincreasing size of the sample. However, this scale-dependencyis limited to a certain size—defined as the stationaritythreshold, where the surface roughness parameters of thefracture samples remain essentially constant beyond thisstationarity threshold. The surface roughness and thegeometrical aperture of the tested concrete fracture replicasin this study did not reach stationarity due to the structuralnon-stationarity of their surface at small scales. Although theaperture histogram of the fractures was almost independent ofthe sample size, below their stationarity threshold both theHurst exponent, Hb, and aperture proportionality constant, Gb,decrease on increasing the sample sizes. To investigate the scale effect on the mechanical propertiesof single rock fractures, several normal loading and directshear tests were performed on the concrete fracture replicassubjected to different normal stresses under Constant NormalLoad (CNL) conditions. The results showed that both normal andshear stiffnesses, as well as the shear strength parameters ofthe fracture samples, decrease on increasing the sample size.It was observed that the structural non-stationarity of surfaceroughness largely controls the contact areas and damage zoneson the fracture surfaces as related to the direction of theshearing. The aperture maps of the concrete fracture replicas ofvarying size and at different shear displacements, obtainedfrom numerical simulation of the aperture evolution duringshearing using their digitized surfaces, were used toinvestigate the effect of scale on the transmissivity of thesingle rock fractures. A FEM code was utilized to numericallysimulate the fluid flow though the single rock fractures ofvarying size. The results showed that flow rate not onlyincreases on increasing the sample size, but also significantlyincreases in the direction perpendicular to the shearing, dueto the anisotropic roughness of the fractures. <b>Key words:</b>Anisotropy, Aperture, Asperity degradation,Contact area, Finite Element Method (FEM), Flow analysis,Fractals, Fracture morphology, Heterogeneity,Stress-deformation, Surface roughness, Roughness-Length method,Scale dependency, Stationarity, Transmissivity, 3D laserscanner.

<p>This thesis investigates the effect of scale on themorphology, mechanics and transmissivity of single rockfractures using both laboratory and in-situ experiments, aswell as numerical simulations. Using a laboratory 3D laserscanner, the surface topography of a large silicon-rubberfracture replica of size 1m x 1m, as well as the topography ofboth surfaces of several high-strength concrete fracturereplicas varying in size from 50mmx50mm to 200mm x 200mm, werescanned. A geodetic Total Station and an in-situ 3D laser radarwere also utilized to scan the surface topography of a largenatural road-cut rock face of size 20m x 15m in the field. Thisdigital characterization of the fracture samples was then usedto investigate the scale dependency of the three dimensionalmorphology of the fractures using a fractal approach. Thefractal parameters of the surface roughness of all fracturesamples, including the geometrical aperture of the concretefracture samples, were obtained using the Roughness-Lengthmethod.</p><p>The results obtained from the fractal characterization ofthe surface roughness of the fracture samples show that bothfractal dimension, D, and amplitude parameter, A, for aself-affine surface are scale-dependent, heterogeneous andanisotropic, and their values generally decrease withincreasing size of the sample. However, this scale-dependencyis limited to a certain size—defined as the stationaritythreshold, where the surface roughness parameters of thefracture samples remain essentially constant beyond thisstationarity threshold. The surface roughness and thegeometrical aperture of the tested concrete fracture replicasin this study did not reach stationarity due to the structuralnon-stationarity of their surface at small scales. Although theaperture histogram of the fractures was almost independent ofthe sample size, below their stationarity threshold both theHurst exponent, Hb, and aperture proportionality constant, Gb,decrease on increasing the sample sizes.</p><p>To investigate the scale effect on the mechanical propertiesof single rock fractures, several normal loading and directshear tests were performed on the concrete fracture replicassubjected to different normal stresses under Constant NormalLoad (CNL) conditions. The results showed that both normal andshear stiffnesses, as well as the shear strength parameters ofthe fracture samples, decrease on increasing the sample size.It was observed that the structural non-stationarity of surfaceroughness largely controls the contact areas and damage zoneson the fracture surfaces as related to the direction of theshearing.</p><p>The aperture maps of the concrete fracture replicas ofvarying size and at different shear displacements, obtainedfrom numerical simulation of the aperture evolution duringshearing using their digitized surfaces, were used toinvestigate the effect of scale on the transmissivity of thesingle rock fractures. A FEM code was utilized to numericallysimulate the fluid flow though the single rock fractures ofvarying size. The results showed that flow rate not onlyincreases on increasing the sample size, but also significantlyincreases in the direction perpendicular to the shearing, dueto the anisotropic roughness of the fractures.</p><p><b>Key words:</b>Anisotropy, Aperture, Asperity degradation,Contact area, Finite Element Method (FEM), Flow analysis,Fractals, Fracture morphology, Heterogeneity,Stress-deformation, Surface roughness, Roughness-Length method,Scale dependency, Stationarity, Transmissivity, 3D laserscanner.</p>

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.