Initial Strength Distribution Research Articles

Stress-based forecasting of induced seismicity with instantaneous earthquake failure functions: Applications to the Groningen gas reservoir

In this study we use the Groningen gas field to test a new method to assess stress changes due to gas extraction and forecast induced seismicity. We take advantage of the detailed knowledge of the reservoir geometry and production history, and of the availability of surface subsidence measurements and high quality seismicity data. The subsurface is represented as a homogeneous isotropic linear poroelastic half-space subject to stress changes in three-dimensional space due to reservoir compaction and pore pressure variations. The reservoir is represented with cuboidal strain volumes. Stress changes within and outside the reservoir are calculated using a convolution with semi-analytical Green functions. The uniaxial compressibility of the reservoir is spatially variable and constrained with surface subsidence data. We calculate stress changes since the onset of gas production. Coulomb stress changes are maximum near the top and bottom of the reservoir where the reservoir is offset by faults. To assess earthquake probability, we use the standard Mohr-Coulomb failure criterion assuming instantaneous nucleation and a non-critical initial stress. The distribution of initial strength excess, the difference between the initial Coulomb stress and the critical Coulomb stress at failure, is treated as a stochastic variable and estimated from the observations and the modelled stress changes. The exponential rise of seismicity nearly 30 years after the onset of production, provides constraints on the distribution of initial strength. The lag and exponential onset of seismicity are well reproduced assuming either a generalized Pareto distribution, which can represent the tail of any distribution, or a Gaussian distribution, to describe both the tail and body of the distribution. The Gaussian distribution allows to test if the induced seismicity at Groningen has transitioned to the steady-state where seismicity rate is proportional to the stressing rate. We find no evidence that the system has reached such a steady-state regime. The modeling framework is computationally efficient making it possible to test the sensitivity to modeling assumptions regarding the estimation of stress changes. The forecast is found robust to uncertainties about the ability of the model to represent accurately the physical processes. It does not require in particular a priori knowledge of the location and orientation of the faults that can be activated. The method presented here is in principle applicable to induced seismicity in any setting provided deformation and seismicity data are available to calibrate the model.

Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution

The time-dependent stress-strength reliability models deal with systems whose strength or the stress imposed on it or both are time-dependent. In this paper, we consider time-dependent stress-strength reliability model which is subjected to constant stress and it causes a change in the strength of the system over each run of the system. Assuming a continuous phase- type distribution for the initial strength and exponential distribution for the duration of each run of the system called cycle time we derived the expression for the stress-strength reliability of the system at time t. The model is further extended to the cases where cycle time distribution is Gamma and Weibull. Simulation studies are conducted to assess the variations in stress-strength reliability, R(t) at different time points, corresponding to the changes in the initial strength distribution and cycle time distribution.

The Structure and Stability of the Mg-HZSM-5/Al2O3 Catalyst for Synthesis of Olefins from DME: The Influence of Thermal and Hydrothermal Treatment

The studies were focused on changes in the structure, texture and acid properties of the Mg-HZSM-5/Al2O3catalyst upon its treatment at different temperatures (400 and 500 °С) and times (6 and 12 h). Physicochemical techniques such as X-ray fluorescence analysis, XPS, solid-state27Al NMR, nitrogen adsorption, DRIFT spectroscopy, ammonia TPD were used for sample characterization. The catalytic activitites of the initial and treated samples were studied regarding conversion of dimethyl ether (DME) to lower olefins. It was shown that the initial activity of the Mg-containing zeolite catalyst was dependent of the total acidity of the surface and independent of the initial strength distribution of the acid sites, and the catalyst stability depended on the morphology.

Dynamic rupture of the 2011 Mw 9.0 Tohoku‐Oki earthquake: Roles of a possible subducting seamount

Using a hybrid MPI/OpenMP parallel finite element method for spontaneous rupture and seismic wave propagation simulations, we investigate features in rupture propagation, slip distribution, seismic radiation, and seafloor deformation of the 2011 Mw 9.0 Tohoku‐Oki earthquake to gain physical insights into the event. With simplified shallow dipping (10°) planar fault geometry, 1D velocity structure, and a slip‐weakening friction law, we primarily investigate initial stress and strength conditions that can produce rupture and seismic radiation characteristics of the event revealed by kinematic inversions, and seafloor displacements observed near the epicenter. By a large suite of numerical experiments aided by parallel computing on modern supercomputers, we find that a seamount of a dimension of ∼70 km by 23 km just updip of the hypocenter on the subducting plane, parameterized by higher static friction, lower pore fluid pressure, and higher initial stress than surrounding regions, may play a dominant role in the 2011 event. Its high strength stalls updip rupture for tens of seconds, and its high stress drop generates large slip. Its failure drives the rupture to propagate into the shallow portion that is likely velocity‐strengthening, resulting in significant slip near the trench within a limited area. However, the preferred model suggests that the largest slip in the event occurs near the hypocenter. High‐strength patches along the downdip portion of the subducting plane are most effective among several possible factors in generating high‐frequency seismic radiations, suggesting the initial strength distribution there is very heterogeneous.

Statistical characterization of fatigue lifetime of polysilicon thin films

This paper discusses, from a statistical point of view, whether the fatigue behavior of polysilicon thin films can be formulated uniquely on the basis of initial defects which determine their strength distribution. The fatigue process determining the lifetime is modeled with a power law similar to the well-known Paris law as the fatigue crack extension process from the initial defects whose equivalent crack lengths were evaluated from the initial strength distribution. The parameters in the power law were here fit to the results of tensile fatigue tests performed on three groups of specimens patterned using three different conditions leading to different etching damage. The results showed that the obtained power law parameters of polysilicon are spread over a range where the calculated behavior changes insignificantly in spite of the different etching conditions leading to different initial strength distributions. They support a possibility that the fatigue fracture is caused by the accumulation of defects and that therefore the fatigue lifetimes can be practically predicted from their strength distributions by using the same values of the parameters in the power law.

DEM simulation of particle attrition in dilute-phase pneumatic conveying

Three dimensional numerical simulations of particles motion in a given geometry pneumatic conveying system are conducted in order to obtain a better understanding of the attrition process. A new and innovative procedure of implementing empirical comminution functions (Kalman et al. in Gran Mat 11:253–266, 2009) into DEM-CFD simulations was used and modified. The comminution functions include: initial strength distribution, selection function, breakage function, equivalence function and fatigue function. The implementation involves converting the probability comminution functions into individual particle properties by a random method and then converting the velocity dependent comminution functions into strength-dependent ones. The predictions of the numerical simulations are used to analyze the flow field characteristics and the size reduction process.

Characteristics of Reliability-Dependent Hazard Rate for Composites Under Fatigue Loading

AbstractThis paper studies the characteristics of a proposed reliability-dependent hazard rate function for composites under fatigue loading. The hazard rate function, in terms of reliability R, is in the form of e+c (1-R)p called (ecp) model, where e denotes the imbedded defects of material strength, c the coefficient of strength degradation, and p the memory characteristics of distributions of both applied stress and fatigue strength during the cumulative damage process. By taking a typical residual strength model in Monte Carlo simulation, this paper presents the time changing of the residual strength distribution and hazard rate of composite under various constant-amplitude cyclic stresses. The values of (e, c, p) are decided by fitting hazard rate function to the data generated in simulation. The results show that, under a suitable suggested value of e, p is a constant depending on the characteristics of stress distribution as well as the residual strength model used in Monte Carlo stimulation, and c is correlated to the maximum cyclic stress in a power-law relationship. Only by knowing the initial strength distribution and the maximum cyclic stress, the fatigue life can be easily estimated by integrating the reliability with time or its equivalent, i.e., the reciprocal of hazard rate function with reliability. Finally, by a proposed approximated equation of fatigue life, the (ecp) model is checked to be highly consistent with S-N curve in both the physical means and the equation form. The analysis presented here may be helpful in designing and maintenance planning of composite under fatigue loading.

A new method to implement comminution functions into DEM simulation of a size reduction system due to particle-wall collisions

The ability to design a size reduction system prior to full scale experiments and to optimize existing systems has long been a goal of designers. Such a design and optimization could be achieved by correctly simulating any system under any operating condition. In this paper we present a new and innovative procedure to implement empirical comminution functions into DEM–CFD simulations. The paper is focused on the implementation procedures and not the DEM/CFD simulations, which deserve full attention. Therefore, this paper is not aimed to study any specific mill. The comminution functions include: initial strength distribution, selection function, breakage function and fatigue function. First, the traditional comminution functions (strength distribution, selection and breakage functions) and the recently investigated fatigue function are briefly described and modified. Then a procedure for implementing the functions into a DEM–CFD model or any other source to provide impact velocities and number of impacts, is described in detail. The implementation involves converting the probability comminution functions into individual particle properties by a random method and then converting the velocity dependent comminution functions into strength dependent ones. In this way, and mainly owing to the use of the fatigue function (which defines the weakening of those particles that are not breaking), a real size reduction system, in which each particle is subjected to multiple impacts at various velocities can be simulated. Three case studies for multiple impact conditions at the same average velocity (several impacts at the same velocity, various velocities at each impact and randomly selected velocities) are presented and analyzed in order to confirm qualitatively the procedure, although the comminution functions need to be further quantitatively modified. It should be emphasized that although the new procedure presents a step towards the final goal, some limitations do exist and some questions remain open.

Mechanical effect of fluid migration on the complexity of seismicity

Spatio‐temporal variation of earthquake activity is modeled assuming fluid migration in a narrow porous fault zone whose boundaries are impermeable. The duration of earthquake sequence is assumed to be much shorter than the recurrence period of characteristic events on the fault. Principle of the effective stress coupled to the Coulomb failure criterion introduces mechanical coupling between fault slip and pore fluid pressure. A linear relation is assumed in our simulations between the accumulated slip and fault zone width on the basis of laboratory and field observations. High complexity is observed in the rupture activity so long as an inhomogeneity is introduced in the spatial distribution of initial strength, which is defined as the fracture threshold stress before the intrusion of the fluid. Frequency‐magnitude statistics of intermediate‐size events obeys the Gutenberg‐Richter relation for all the models in which spatial heterogeneity is introduced for the initial strength. The behavior of larger‐size events seems to be rather model dependent. It is also observed that the rupture occurrence tends to be inactivated immediately before the occurrence of the largest event in a sequence. This never happens if a brittle rupture is assumed in an elastic medium with no mechanical effect of fluid. This inactivation will occur because it takes much time to build up fluid pressure to break a fault segment having high initial strength, whose rupture triggers the largest event in a sequence. Our calculations also show that a single predominant principal event cannot be observed in a sequence when both the variance and average value of the distributed initial strengths are large. This may explain a feature observed for earthquake swarm.

Cyclic fatigue behaviour of eutectoid aged Mg-PSZ ceramics with processing flaws

Abstract The cyclic fatigue behaviour of Mg-PSZ in the asfired state and after eutectoid aging (1400°C for 2 and 16 h) were investigated in four-point bending tests. A large number of specimens with processing flaws were used to measure the initial strength distribution and the cyclic fatigue lifetime at a stress ratio R = 0·3. From these experimental data a modified ‘stresstime-probability’ (S-T-P) diagram can be constructed using a statistical approach. The residual strength of the survivor specimens, which is lower than their corresponding initial strength, has also been measured, confirming that pronounced cyclic fatigue damage does occur in these Mg-PSZ ceramics. The experimental results are discussed in terms of transformation toughening, microcracking and precipitate hardening mechanisms.

Static and cyclic fatigue of 2Y-TZP ceramics with natural flaws

Abstract Static and cyclic fatigue properties of two 2Y-TZP ceramics with average grain sizes of 0·2 and 1·6 μm were studied in bending tests. A large number of specimens with natural flaws were used for the measurement of the initial strength distribution and for the static and cyclic fatigue (stress ratios R = 0·2 and −1) tests at a single maximum stress level. From these experimental data the modified stress-life time (σ−tf) curve and the crack propagation relation ( d a d t −K I curve) can be calculated using both the fracture mechanics and the statistical approaches. It was found that the measured time to failure under cyclic loadings, especially with the stress ratio of −1, is much shorter than under static loadings. The crack growth relation for the natural flaws can be described by the power law function d a d t = AK I n . Fatigue crack velocities under cyclic loadings are much higher than those under static loading at the same stress intensity. A significant cyclic fatigue effect can be concluded for the 2Y-TZP materials. Besides this cyclic fatigue effect a strengthening effect was also found for the survivor specimens after static and cyclic loading which is believed to be due to a modification of the initial flaws during the long term fatigue loadings.