Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,

Weak form equation–based finite-element modeling of viscoelastic asphalt mixtures

The objective of this study is to demonstrate using weak form partial differential equation (PDE) method for a finite-element (FE) modeling of a new constitutive relation without the need of user subroutine programming. The viscoelastic asphalt mixtures were modeled by the weak form PDE-based FE method as the examples in the paper. A solid-like generalized Maxwell model was used to represent the deforming mechanism of a viscoelastic material, the constitutive relations of which were derived and implemented in the weak form PDE module of Comsol Multiphysics, a commercial FE program. The weak form PDE modeling of viscoelasticity was verified by comparing Comsol and Abaqus simulations, which employed the same loading configurations and material property inputs in virtual laboratory test simulations. Both produced identical results in terms of axial and radial strain responses. The weak form PDE modeling of viscoelasticity was further validated by comparing the weak form PDE predictions with real laboratory test results of six types of asphalt mixtures with two air void contents and three aging periods. The viscoelastic material properties such as the coefficients of a Prony series model for the relaxation modulus were obtained by converting from the master curves of dynamic modulus and phase angle. Strain responses of compressive creep tests at three temperatures and cyclic load tests were predicted using the weak form PDE modeling and found to be comparable with the measurements of the real laboratory tests. It was demonstrated that the weak form PDE-based FE modeling can serve as an efficient method to implement new constitutive models and can free engineers from user subroutine programming.

Interpretation of the Superpave IDT strength test using a viscoelastic-damage constitutive model

This paper presents a new interpretation for the Superpave IDT strength test based on a viscoelastic-damage framework. The framework is based on continuum damage mechanics and the thermodynamics of irreversible processes with an anisotropic damage representation. The new approach introduces considerations for the viscoelastic effects and the damage accumulation that accompanies the fracture process in the interpretation of the Superpave IDT strength test for the identification of the Dissipated Creep Strain Energy (DCSE) limit from the test result. The viscoelastic model is implemented in a Finite Element Method (FEM) program for the simulation of the Superpave IDT strength test. The DCSE values obtained using the new approach is compared with the values obtained using the conventional approach to evaluate the validity of the assumptions made in the conventional interpretation of the test results. The result shows that the conventional approach over-estimates the DCSE value with increasing estimation error at higher deformation rates.

Effect of water on olivine single crystals plasticity, deformed under high pressure and high temperature

The Earth's upper mantle, mainly composed of olivine, is seismically anisotropic. Seismic anisotropy attenuation has been observed at 220km depth. Karato et al. (1992) attributed this attenuation to a transition between two deformation mechanisms, from dislocation creep above 220km to diffusion creep below 220km, induced by a change in water content. Couvy (2005) and Mainprice et al. (2005) predicted a change in Lattice Preferred Orientation induced by pressure, which comes from a change of slip system, from [100] slip to [001] slip, and is responsible for the seismic anisotropy attenuation. Raterron et al. (2007) ran single crystal deformation experiments under anhydrous conditions and observed that the slip system transition occurs around 8GPa, which corresponds to a depth of 260Km. Experiments were done to quantify the effects of water on olivine single crystals deformed using D-DIA press and synchrotron beam. Deformations were carried out in uniaxial compression along [110]c, [011]c, and [101]c, crystallographic directions, at pressure ranging from 4 to 8GPa and temperature between 1373 and 1473K. Talc sleeves about the annulus of the single crystals were used as source of water in the assembly. Stress and specimen strain rates were calculated by in-situ X-ray diffraction and time resolved imaging, respectively. By direct comparison of single crystals strain rates, we observed that [110]c deforms faster than [011]c below 5GPa. However above 6GPa [011]c deforms faster than [110]c. This revealed that [100](010) is the dominant slip system below 5GPa, and above 6GPa [001](010) becomes dominant. According to our results, the slip system transition, which is induced by pressure, occurs at 6GPa. Water influences the pressure where the switch over occurs, by lowering the transition pressure. The pressure effect on the slip systems activity has been quantified and the hydrolytic weakening has also been estimated for both orientations. Data also shows that temperature affects the slip system activity. The regional variation of the depth for the seismic anisotropy attenuation, which would depend on local hydroxyl content and temperature variations and explains the seismic anisotropy attenuation occurring at about 220Km depth in the mantle, where the pressure is about 6GPa. Deformation of MgO single crystal oriented [100], [110] and [111] were also performed. The results predict a change in the slip system activity at 23GPa, again induced by pressure. This explains the seismic anisotropy observed in the lower mantle.

Development of Innovative Load Transfer Mechanism to Reduce Hurricane-Induced Failures in New and Existing Residential Construction

Implicit in current design practice of minimum uplift capacity, is the assumption that the connection's capacity is proportional to the number of fasteners per connection joint. This assumption may overestimate the capacity of joints by a factor of two or more and maybe the cause of connection failures in extreme wind events. The current research serves to modify the current practice by proposing a realistic relationship between the number of fasteners and the capacity of the joint. The research is also aimed at further development of non-intrusive continuous load path (CLP) connection system using Glass Fiber Reinforced Polymer (GFRP) and epoxy. Suitable designs were developed for stud to top plate and gable end connections and tests were performed to evaluate the ultimate load, creep and fatigue behavior. The objective was to determine the performance of the connections under simulated sustained hurricane conditions. The performance of the new connections was satisfactory.

(Table 1) Sample characteristics, test consolidations and calculated elastic parameters of ODP Sites 194-1193 and 194-1196

This study is based on rock mechanical tests of samples from platform carbonate strata to document their petrophysical properties and determine their potential for porosity loss by mechanical compaction. Sixteen core-plug samples, including eleven limestones and five dolostones, from Miocene carbonate platforms on the Marion Plateau, offshore northeast Australia, were tested at vertical effective stress, sigma1', of 0-70 MPa, as lateral strain was kept equal to zero. The samples were deposited as bioclastic facies in platform-top settings having paleo-water depths of <10-90 m. They were variably cemented with low-Mg calcite and five of the samples were dolomitized before burial to present depths of 39-635 m below sea floor with porosities of 8-46%. Ten samples tested under dry conditions had up to 0.22% strain at sigma1' = 50 MPa, whereas six samples tested saturated with brine, under drained conditions, had up to 0.33% strain. The yield strength was reached in five of the plugs. The measured strains show an overall positive correlation with porosity. Vp ranges from 3640 to 5660 m/s and Vs from 1840 to 3530 m/s. Poisson coefficient is 0.20-0.33 and Young's modulus at 30 MPa ranged between 5 and 40 GPa. Water saturated samples had lower shear moduli and slightly higher P- to S-wave velocity ratios. Creep at constant stress was observed only in samples affected by pore collapse, indicating propagation of microcracks. Although deposited as loose carbonate sand and mud, the studied carbonates acquired reef-like petrophysical properties by early calcite and dolomite cementation. The small strains observed experimentally at 50 MPa indicate that little mechanical compaction would occur at deeper burial. However, as these rocks are unlikely to preserve their present high porosities to 4-5 km depth, further porosity loss would proceed mainly by chemical compaction and cementation.

Permafrost mapping on glaciers in the Ötztal, Austria

The occurrence of permafrost in the region of the Hochebenkar rock glaciers has been mapped in detail. For this purpose basal temperatures of the winter snow cover were measured at over 250 sites (BTS-method), II refraction-seismic profiles were taken in frozen and unfrozen unconsolidated sediments and 12 springs were investigated in terms of their summer temperature 128 W. Haeberli und G. PatzeIt variations. The combination of seismic refraction and the BTS-method allows rapid and reliable mapping of alpine permafrost, and at the same time enables differences in active-Iayer thickness to be established. The resuIts of the observations confirm the ideas developed in the Swiss Alps in recent years about the relationships between permafrost and rock glaciers: rock glaciers are creep phenomena of discontinuous alpine permafrost.

Ecological classification of Herschel Island based on supervised classification of multispectral satellite imagery

Permafrost landscapes experience different disturbances and store large amounts of organic matter, which may become a source of greenhouse gases upon permafrost degradation. We analysed the influence of terrain and geomorphic disturbances (e.g. soil creep, active-layer detachment, gullying, thaw slumping, accumulation of fluvial deposits) on soil organic carbon (SOC) and total nitrogen (TN) storage using 11 permafrost cores from Herschel Island, western Canadian Arctic. Our results indicate a strong correlation between SOC storage and the topographic wetness index. Undisturbed sites stored the majority of SOC and TN in the upper 70 cm of soil. Sites characterised by mass wasting showed significant SOC depletion and soil compaction, whereas sites characterised by the accumulation of peat and fluvial deposits store SOC and TN along the whole core. We upscaled SOC and TN to estimate total stocks using the ecological units determined from vegetation composition, slope angle and the geomorphic disturbance regime. The ecological units were delineated with a supervised classification based on RapidEye multispectral satellite imagery and slope angle. Mean SOC and TN storage for the uppermost 1?m of soil on Herschel Island are 34.8 kg C/m**2 and 3.4 kg N/m**2, respectively.

Time-dependency of Rocks and Implications Associated with Tunnelling

The formulation of a geotechnical model and the associated prediction of the mechanical behaviour is a challenge engineers need to overcome in order to optimize tunnel design and meet project requirements. Special challenges arise in cases where rocks and rockmasses are susceptible to time-effects and time-dependent processes govern. Progressive rockmass deformation and instability, time-dependent overloading of support and delayed failures are commonly the result of time-dependent phenomena. The research work presented in this thesis serves as an attempt to provide more insight into the time-dependent behaviour of rocks. Emphasis is given on investigating and analyzing creep deformation and time-dependent stress relaxation phenomenon at the laboratory scale and in-depth analyses are presented. This thesis further develops the understanding of these phenomena and practical yet scientific tools for estimating and predicting the long-term strength and the maximum stress relaxation of rock materials are proposed. The identification of the existence of three distinct behavioural stages during stress relaxation is presented and discussed. The main observations associated with time-dependent behaviour are employed in numerical analyses and applied at the tunnel scale. A new approach for simulating and capturing the time-dependent behaviour coupled with the tunnel advancement effect is also developed and analyzed. Guidance is provided to increase the understanding of the support-rockmass interaction and the main implications and significance of time-dependent behaviour associated with rock tunnelling are discussed. The work presented in this thesis advances the scientific understanding of time-dependent rock and rockmass behaviour, increases the awareness of how such phenomena are captured numerically, and lays out a framework for dealing with such deformations when predicting tunnel deformations. Practical aspects of this thesis are also presented, which will increase their usage in the associated industries and close the gap between the scientific and industry communities.

Laboratory performance evaluation of CIR-emulsion and its comparison against CIR-foam test results from Phase III, TR-578

Currently, no standard mix design procedure is available for CIR-emulsion in Iowa. The CIR-foam mix design process developed during the previous phase is applied for CIR-emulsion mixtures with varying emulsified asphalt contents. Dynamic modulus test, dynamic creep test, static creep test and raveling test were conducted to evaluate the short- and long-term performance of CIR-emulsion mixtures at various testing temperatures and loading conditions. A potential benefit of this research is a better understanding of CIR-emulsion material properties in comparison with those of CIR-foam material that would allow for the selection of the most appropriate CIR technology and the type and amount of the optimum stabilization material. Dynamic modulus, flow number and flow time of CIR-emulsion mixtures using CSS-1h were generally higher than those of HFMS-2p. Flow number and flow time of CIR-emulsion using RAP materials from Story County was higher than those from Clayton County. Flow number and flow time of CIR-emulsion with 0.5% emulsified asphalt was higher than CIR-emulsion with 1.0% or 1.5%. Raveling loss of CIR-emulsion with 1.5% emulsified was significantly less than those with 0.5% and 1.0%. Test results in terms of dynamic modulus, flow number, flow time and raveling loss of CIR-foam mixtures are generally better than those of CIR-emulsion mixtures. Given the limited RAP sources used for this study, it is recommended that the CIR-emulsion mix design procedure should be validated against several RAP sources and emulsion types.

Studio reologico di mastici per miscele di conglomerato bituminoso drenante contenente polverino di gomma da pfu

Le prestazioni meccaniche di una miscela di conglomerato bituminoso dipendono principalmente dai materiali che la compongono e dalla loro interazione. La risposta tenso-deformativa delle sovrastrutture stradali è strettamente legata al comportamento reologico del legante bituminoso e dalla sua interazione con lo scheletro litico. In particolare nelle pavimentazioni drenanti, a causa dell’elevato contenuto di vuoti, il legame che si crea tra il legante (mastice bituminoso) e l’aggregato è molto forte, per questo motivo è importante migliorarne le prestazioni. Additivando il mastice con polverino di gomma da PFU (pneumatici fuori uso), non solo si migliorano prestazioni, resistenza alle deformazioni permanenti ed elastoplasticità del materiale, ma si sfruttano anche materiali di recupero, portando vantaggi anche dal punto di vista ambientale. In quest’ottica la ricerca effettuata nella tesi si pone come obiettivo l’analisi reologica e lo studio di mastici additivati con polverino di gomma ricavato da PFU, per la realizzazione di conglomerati bituminosi drenanti. In particolare, partendo da un bitume di base, sono stati preparati due mastici: il primo ottenuto miscelando bitume modificato e filler calcareo, il secondo aggiungendo al precedente anche il polverino di gomma. Tale studio è stato eseguito mediante l’utilizzo del DSR (Dynamic Shear Rheometer – UNI EN 14770), con il quale sono state affrontate tre prove: Amplitude Sweep test, per la valutazione del valore di deformazione di taglio γ entro il quale il materiale si mantiene all’interno del campo di viscoelasticità lineare (Linear visco-elasticity, LVE); Frequency Sweep test, per l’estrapolazione delle master curves; Multiple stress Creep Recovery, per valutare la resistenza del materiale alle deformazioni permanenti. Dall’analisi dei dati è stato possibile definire il comportamento reologico di entrambi i mastici e, in seconda analisi, confrontarne le caratteristiche e le prestazioni.

Studio sperimentale del coefficiente di compressibilità secondaria al variare del contenuto organico

Questa tesi svolta nell’ambito della geotecnica ha L’obiettivo di porre l’attenzione sul comportamento dei cedimenti secondari, quindi sul coefficiente di consolidazione secondaria Cα mediante l’esecuzione di una prova edometrica su di una sezione di campione estratto in sito, dove si evidenzia una percentuale di contenuto organico molto alta (torba).Si introduce il concetto di terreno organico a partire dalla genesi fino ad una classificazione atta a distinguere terreni con percentuali di componente organica differenti. Si spiega la teoria della consolidazione monodimensionale, quindi la prova edometrica, riportando in maniera grafica e analitica tutti i coefficienti che da essa si possono ricavare a partire dai parametri di compressione volumetrica fino alla consolidazione primaria e secondaria (o creep)si descrivono dettagliatamente la strumentazione e la procedura di prova. Descrivendo l’edometro utilizzato in laboratorio e tutti gli accessori ad esso collegati, il campione da analizzare, la procedura di preparazione del campione alla prova edometrica, trovando alcune proprietà fisiche del campione, come il contenuto d’acqua e il contenuto organico, ed in fine riportando i passaggi della prova edometrica in modo tale da poter essere riprodotta.Si analizzano tutti i risultati ottenuti durante la prova in maniera analitica e grafica, osservando e commentando la forma dei grafici ottenuti in relazione al materiale che compone il campione ed i tempi impiegati per eseguire la prova.

Analisi del comportamento sperimentale di lunga-durata di elementi in FRC

Si analizza il comportamento e la risposta di elementi sottoposti a diversi tipi di sollecitazione. Lo scopo ultimo è quello di valutare l’applicabilità di un modello che permetta di ricavare il comportamento di creep a trazione nei calcestruzzi fibrorinforzati, partendo dai risultati delle prove di creep a compressione e creep a flessione.

A three dimensional finite volume approach to the thermo-mechanical modelling of the shape casting of metals

This paper presents a three dimensional, thermos-mechanical modelling approach to the cooling and solidification phases associated with the shape casting of metals ei. Die, sand and investment casting. Novel vortex-based Finite Volume (FV) methods are described and employed with regard to the small strain, non-linear Computational Solid Mechanics (CSM) capabilities required to model shape casting. The CSM capabilities include the non-linear material phenomena of creep and thermo-elasto-visco-plasticity at high temperatures and thermo-elasto-visco-plasticity at low temperatures and also multi body deformable contact with which can occur between the metal casting of the mould. The vortex-based FV methods, which can be readily applied to unstructured meshes, are included within a comprehensive FV modelling framework, PHYSICA. The additional heat transfer, by conduction and convection, filling, porosity and solidification algorithms existing within PHYSICA for the complete modelling of all shape casting process employ cell-centred FV methods. The termo-mechanical coupling is performed in a staggered incremental fashion, which addresses the possible gap formation between the component and the mould, and is ultimately validated against a variety of shape casting benchmarks.