A Micromechanical Method to Predict Macroscopic Behavior of Brittle Creep Failure in Rock

2016 ◽  
Vol 08 (08) ◽  
pp. 1650089 ◽  
Author(s):  
Xiaozhao Li ◽  
Zhushan Shao
Keyword(s):  
Model Comparison ◽  
Time Dependent ◽  
Similar Process ◽  
Model Parameters ◽  
Suggested Model ◽  
Wing Crack ◽  
Creep Failure ◽  
Brittle Creep ◽  
Deep Underground ◽  
Definition Of

Brittle creep in rock has great significance for the prediction of important geohazards and stability of deep underground excavations. A major challenge in this area is to link the time-dependent cracking with macroscopic mechanical behavior. In this paper, Ashby and Sammis’ microcrack model and Charles’ crack growth law are employed to investigate the time-dependent cracking during brittle creep in rock. Based on the macroscopic and micromechanical definition of damage in rock, a new theoretical model is suggested to establish the linkage between microcrack length and macroscopic strain. In order to verify the rationality of the suggested model, comparison between theoretical and experimental results is presented. Using this new model, brittle creep of Sanxia granite is investigated and discussed in detail. It is found that evolutions of wing crack length, strain, and damage perform a similar process during brittle creep and could be divided into three phases. Effects of model parameters on creep failure behaviors also are studied.

scholarly journals A Time-Dependent Double Hardening Model for Soft Rock

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Mohammed Saiful Alam Siddiquee ◽  
Amin Hamdi
Keyword(s):  
Yield Surface ◽  
Triaxial Compression ◽  
Soft Rock ◽  
Time Dependent ◽  
Model Parameters ◽  
Compression Tests ◽  
Creep Failure ◽  
Hardening Model ◽  
Compression Direction ◽  
New Formulation

The time-dependent behavior of soft rock is very important in tunnel construction through soft rock. There is always a chance of creep failure due to sustained loading along the crest of the tunnel. In this research, a three-component elasto-visco-plastic framework is used to develop a time-dependent double hardening model to predict the behavior of soft rock both in compression and shear. Due to the limitation of time-dependent single yield hardening model in predicting the behavior of soft rock in compression direction (volumetric deformation) of loading, another time-dependent yield surface is added to the compression direction. The intersection of two-yield surface usually gives rise to singularity phenomenon, which is avoided by using Koiter’s generalization principle. A new formulation of the stress-integration of incremental stress-strain equations is proposed. A series of triaxial compression tests were carried out at different strain rates to calculate the model parameters. Then, the model is used to simulate the various behavioral features of soft rock.

scholarly journals Unraveling the time-dependent relevance of input model uncertainties for a lumped hydrologic model of a pre-alpine karst system

2021 ◽  
Author(s):  
Daniel Bittner ◽  
Beatrice Richieri ◽  
Gabriele Chiogna
Keyword(s):  
Groundwater Recharge ◽  
Temporal Variations ◽  
Hydrologic Model ◽  
Time Dependent ◽  
Model Parameters ◽  
Lumped Parameter ◽  
Hydrodynamic Processes ◽  
Input Model ◽  
Karst Model ◽  
Input Uncertainties

AbstractUncertainties in hydrologic model outputs can arise for many reasons such as structural, parametric and input uncertainty. Identification of the sources of uncertainties and the quantification of their impacts on model results are important to appropriately reproduce hydrodynamic processes in karst aquifers and to support decision-making. The present study investigates the time-dependent relevance of model input uncertainties, defined as the conceptual uncertainties affecting the representation and parameterization of processes relevant for groundwater recharge, i.e. interception, evapotranspiration and snow dynamic, on the lumped karst model LuKARS. A total of nine different models are applied, three to compute interception (DVWK, Gash and Liu), three to compute evapotranspiration (Thornthwaite, Hamon and Oudin) and three to compute snow processes (Martinec, Girons Lopez and Magnusson). All the input model combinations are tested for the case study of the Kerschbaum spring in Austria. The model parameters are kept constant for all combinations. While parametric uncertainties computed for the same model in previous studies do not show pronounced temporal variations, the results of the present work show that input uncertainties are seasonally varying. Moreover, the input uncertainties of evapotranspiration and snowmelt are higher than the interception uncertainties. The results show that the importance of a specific process for groundwater recharge can be estimated from the respective input uncertainties. These findings have practical implications as they can guide researchers to obtain relevant field data to improve the representation of different processes in lumped parameter models and to support model calibration.

scholarly journals The seven sisters DANCe

2018 ◽  
Vol 612 ◽  
pp. A70 ◽  
Author(s):  
J. Olivares ◽  
E. Moraux ◽  
L. M. Sarro ◽  
H. Bouy ◽  
A. Berihuete ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Model Comparison ◽  
Precise Determination ◽  
Model Parameters ◽  
Data Sets ◽  
Adequate Model ◽  
Comparison Results ◽  
Bayesian Evidence ◽  
Mass Segregation

Context. Membership analyses of the DANCe and Tycho + DANCe data sets provide the largest and least contaminated sample of Pleiades candidate members to date. Aims. We aim at reassessing the different proposals for the number surface density of the Pleiades in the light of the new and most complete list of candidate members, and inferring the parameters of the most adequate model. Methods. We compute the Bayesian evidence and Bayes Factors for variations of the classical radial models. These include elliptical symmetry, and luminosity segregation. As a by-product of the model comparison, we obtain posterior distributions for each set of model parameters. Results. We find that the model comparison results depend on the spatial extent of the region used for the analysis. For a circle of 11.5 parsecs around the cluster centre (the most homogeneous and complete region), we find no compelling reason to abandon King’s model, although the Generalised King model introduced here has slightly better fitting properties. Furthermore, we find strong evidence against radially symmetric models when compared to the elliptic extensions. Finally, we find that including mass segregation in the form of luminosity segregation in the J band is strongly supported in all our models. Conclusions. We have put the question of the projected spatial distribution of the Pleiades cluster on a solid probabilistic framework, and inferred its properties using the most exhaustive and least contaminated list of Pleiades candidate members available to date. Our results suggest however that this sample may still lack about 20% of the expected number of cluster members. Therefore, this study should be revised when the completeness and homogeneity of the data can be extended beyond the 11.5 parsecs limit. Such a study will allow for more precise determination of the Pleiades spatial distribution, its tidal radius, ellipticity, number of objects and total mass.

Hysteretic Poisson INGARCH model for integer-valued time series

2017 ◽  
Vol 17 (6) ◽  
pp. 401-422 ◽  
Author(s):  
Buu-Chau Truong ◽  
Cathy WS Chen ◽  
Songsak Sriboonchitta
Keyword(s):  
Time Series ◽  
Model Comparison ◽  
Monte Carlo Sampling ◽  
Information Criteria ◽  
Model Parameters ◽  
Modelling Framework ◽  
South Wales ◽  
Proposed Model ◽  
Over Dispersion ◽  
Ingarch Model

This study proposes a new model for integer-valued time series—the hysteretic Poisson integer-valued generalized autoregressive conditionally heteroskedastic (INGARCH) model—which has an integrated hysteresis zone in the switching mechanism of the conditional expectation. Our modelling framework provides a parsimonious representation of the salient features of integer-valued time series, such as discreteness, over-dispersion, asymmetry and structural change. We adopt Bayesian methods with a Markov chain Monte Carlo sampling scheme to estimate model parameters and utilize the Bayesian information criteria for model comparison. We then apply the proposed model to five real time series of criminal incidents recorded by the New South Wales Police Force in Australia. Simulation results and empirical analysis highlight the better performance of hysteresis in modelling the integer-valued time series.

scholarly journals Inter-trial effects in priming of pop-out: Comparison of computational updating models

2021 ◽  
Vol 17 (9) ◽  
pp. e1009332
Author(s):  
Fredrik Allenmark ◽  
Ahu Gokce ◽  
Thomas Geyer ◽  
Artyom Zinchenko ◽  
Hermann J. Müller ◽  
...  
Keyword(s):  
Model Comparison ◽  
Response Times ◽  
Target Position ◽  
Preceding Trial ◽  
Target Color ◽  
Model Parameters ◽  
Target Feature ◽  
Modeling Framework ◽  
Trial Effect ◽  
Starting Point

In visual search tasks, repeating features or the position of the target results in faster response times. Such inter-trial ‘priming’ effects occur not just for repetitions from the immediately preceding trial but also from trials further back. A paradigm known to produce particularly long-lasting inter-trial effects–of the target-defining feature, target position, and response (feature)–is the ‘priming of pop-out’ (PoP) paradigm, which typically uses sparse search displays and random swapping across trials of target- and distractor-defining features. However, the mechanisms underlying these inter-trial effects are still not well understood. To address this, we applied a modeling framework combining an evidence accumulation (EA) model with different computational updating rules of the model parameters (i.e., the drift rate and starting point of EA) for different aspects of stimulus history, to data from a (previously published) PoP study that had revealed significant inter-trial effects from several trials back for repetitions of the target color, the target position, and (response-critical) target feature. By performing a systematic model comparison, we aimed to determine which EA model parameter and which updating rule for that parameter best accounts for each inter-trial effect and the associated n-back temporal profile. We found that, in general, our modeling framework could accurately predict the n-back temporal profiles. Further, target color- and position-based inter-trial effects were best understood as arising from redistribution of a limited-capacity weight resource which determines the EA rate. In contrast, response-based inter-trial effects were best explained by a bias of the starting point towards the response associated with a previous target; this bias appeared largely tied to the position of the target. These findings elucidate how our cognitive system continually tracks, and updates an internal predictive model of, a number of separable stimulus and response parameters in order to optimize task performance.

CONSTANT ELASTICITY OF VARIANCE OPTION PRICING MODEL WITH TIME-DEPENDENT PARAMETERS

2000 ◽  
Vol 03 (04) ◽  
pp. 661-674 ◽  
Author(s):  
C. F. LO ◽  
P. H. YUEN ◽  
C. H. HUI
Keyword(s):  
Option Pricing ◽  
Algebraic Approach ◽  
Time Dependent ◽  
Model Parameters ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Pricing Options ◽  
Term Structures ◽  
Option Values

This paper provides a method for pricing options in the constant elasticity of variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for the option values incorporating time-dependent model parameters are obtained in various CEV processes with different elasticity factors. The numerical results indicate that option values are sensitive to volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. Furthermore, the Lie-algebraic approach is very simple and can be easily extended to other option pricing models with well-defined algebraic structures.

Turing and Benjamin–Feir instability mechanisms in non-autonomous systems

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200003 ◽  
Author(s):  
Robert A. Van Gorder
Keyword(s):  
Autonomous Systems ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Time Dependent ◽  
Model Parameters ◽  
Time Varying ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Dependent Model ◽  
Spatio Temporal

The Turing and Benjamin–Feir instabilities are two of the primary instability mechanisms useful for studying the transition from homogeneous states to heterogeneous spatial or spatio-temporal states in reaction–diffusion systems. We consider the case when the underlying reaction–diffusion system is non-autonomous or has a base state which varies in time, as in this case standard approaches, which rely on temporal eigenvalues, break down. We are able to establish respective criteria for the onset of each instability using comparison principles, obtaining inequalities which involve the in general time-dependent model parameters and their time derivatives. In the autonomous limit where the base state is constant in time, our results exactly recover the respective Turing and Benjamin–Feir conditions known in the literature. Our results make the Turing and Benjamin–Feir analysis amenable for a wide collection of applications, and allow one to better understand instabilities emergent due to a variety of non-autonomous mechanisms, including time-varying diffusion coefficients, time-varying reaction rates, time-dependent transitions between reaction kinetics and base states which change in time (such as heteroclinic connections between unique steady states, or limit cycles), to name a few examples.

scholarly journals Modeling Growth, Containment and Decay of the COVID-19 Epidemic in Italy

2020 ◽  
Vol 8 ◽  
Author(s):  
Francesco Capuano
Keyword(s):  
Exponential Growth ◽  
Compartment Model ◽  
Growth Behavior ◽  
Time Dependent ◽  
Model Parameters ◽  
Susceptible Population ◽  
Dependent Rate ◽  
Slow Decay ◽  
Cumulative Curve ◽  
Modeling Growth

A careful inspection of the cumulative curve of confirmed COVID-19 infections in Italy and in other hard-hit countries reveals three distinct phases: i) an initial exponential growth (unconstrained phase), ii) an algebraic, power-law growth (containment phase), and iii) a relatively slow decay. We propose a parsimonious compartment model based on a time-dependent rate of depletion of the susceptible population that captures all such phases for a plausible range of model parameters. The results suggest an intimate interplay between the growth behavior, the timing and implementation of containment strategies, and the subsequent saturation of the outbreak.

scholarly journals Time-dependent brittle creep in Darley Dale sandstone

2009 ◽  
Vol 114 (B7) ◽  
Author(s):  
M. J. Heap ◽  
P. Baud ◽  
P. G. Meredith ◽  
A. F. Bell ◽  
I. G. Main
Keyword(s):  
Time Dependent ◽  
Brittle Creep

Application of the Tornado-Like Flow Theory to the Study of Blood Flow in the Heart and Main Vessels: Study of the Potential Swirling Jets Structure in an Arbitrary Viscous Medium

2019 ◽  
Author(s):  
E. Talygin ◽  
G. Kiknadze ◽  
A. Agafonov ◽  
A. Gorodkov
Keyword(s):  
Blood Flow ◽  
Velocity Field ◽  
Analytical Solution ◽  
Coordinate System ◽  
Biologically Active ◽  
Time Dependent ◽  
Characteristic Functions ◽  
Swirling Jet ◽  
Cylindrical Coordinate ◽  
Definition Of

Abstract In previous works it has been proved that the dynamic geometry of the streamlined surface of the flow channel of the heart chambers and main arteries corresponds with a good agreement to the shape of the swirling flow streamlines. The vectorial velocity field of such a flow in a cylindrical coordinate system was described by means of specific analytical solution basing on the potentiality of the longitudinal and radial velocity components. The viscosity of the medium was taken into account only in the expression for the azimuthal velocity component and the significant effect of viscosity was manifested only in a narrow axial region of a swirling jet. The flow described by the above relations is quasipotential, axisymmetric, and convergent. The structural organization of this flow implies the elimination of rupture and stagnation zones, and minimizes the viscous losses. The proximity of the real blood flow under the normal conditions to the specified class of swirling flows allows us to determine the basic properties of the blood flow possessing the high pressure-flow characteristics without stability loss. The blood flow has an external border, and the interaction with the channel wall and between moving fluid elements is weak. These properties of the jet explain the possibility of a balanced blood flow in biologically active boundaries. Violation of the jet properties can lead to the excitation of biologically active components and trigger the corresponding cascade protective and compensatory processes. The evolution of the flow is determined by the time-dependent characteristic functions, which are the frequency characteristics of the rotating jet, as well as functions depending on the dimension of the swirling jet. Previous experimental studies revealed close connection between changes in the characteristic functions and dynamics of the cardiac cycle. Therefore, it is natural to express these functions in analytical form. For these purposes it was necessary to establish the link between these functions and the spatial characteristics of the swirling jet. To solve this problem the analytical solution for the velocity field of a swirling jet was substituted into the Navier-Stokes system and continuity differential equations in a cylindrical coordinate system. As a result, a new system of differential equations was obtained where the characteristic functions could be derived. The solution of these equations allows the identification of time-dependent characteristic functions, and the establishment of a link between the characteristic functions and the spatial coordinates of the swirling jet. This link gives the opportunity to substantiate a theoretical possibility for the modeling of quasipotential viscous flows with a given structure. The definition of characteristic functions makes it possible to obtain the exact solution which allows formalization of the boundary conditions for physical modeling and experimental study of this flow type. Such transformations allow the definition of the conditions supporting renewable swirling blood flow in the transport arterial segment of the circulatory system and provide the basis for new principles of modeling, diagnosis and surgical treatment of circulatory disorders associated with the changes in geometry of the heart and great vessels.

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