Research on the energy evolution characteristics and the failure intensity of rocks

It is pretty challenging and difficult to quantitatively evaluate the intensity of dynamic disasters in deep mining engineering.Based on the uniaxial loading-unloading experiments for five types of rocks,this paper investigated the energy evolution characteristics,and identified the damage and crack propagation thresholds.Also,the fragment size distributions of the rocks after failure were analyzed.The energy release rate(Ge)and energy dissipation rate(Gd)were then proposed to describe the change of energies per unit volume and per unit strain.Results demonstrated that the more brittle rocks had the shorter stage of unstable crack growth and the lower induced damage at crack damage thresholds.The evolution characteristics of the strain energy rates can be easily identified by the crack propagation thresholds.The failure intensity index(FId),which equals to the values of Ge/Gd at the failure point,was further put forth.It can account for the brittleness of the rocks,the intensity of rock failure as well as the degree of rock fragmentation.It was revealed that a higher FId corresponded to a lower fractal dimension and stronger dynamic failure.

Arithmetic Reduction of Intensity or Age Models with Bathtub Failure Intensity

In this paper, the authors will study the estimation of maintenance efficiency in Arithmetic Reduction of Intensity （ARI） and Arithmetic Reduction of Age （ARA） models with a memory m. These models have been proposed by Doyen （2005）, the failure process is simply Non Homogeneous Poisson Process （NHPP）. Our models are defined by reformulation of ARI and ARA ones using bathtub failure intensity. This form is presented like a superposition of two NHPP and Homogeneous Poisson Process （HPP）. Moreover, the particularity of this model allows taking account of system state improvement in time course. The maintenance effect is characterized by the change induced on the failure intensity before and after failure during degradation period. To simplify study, the asymptotic properties of failure process are derived. Then, the asymptotic normality of several maintenance efficiency estimators can be proved in the case where the failure process without maintenance is known. Practically, the coverage rate of the asymptotic confidence intervals issued from those estimators is studied.

One-Sample Bayesian Predictive Analyses for a Nonhomogeneous Poisson Process with Delayed S-Shaped Intensity Function Using Non-Informative Priors

The delayed S-shaped software reliability growth model (SRGM) is one of the non-homogeneous Poisson process (NHPP) models which have been proposed for software reliability assessment. The model is distinctive because it has a mean value function that reflects the delay in failure reporting: there is a delay between failure detection and reporting time. The model captures error detection, isolation, and removal processes, thus is appropriate for software reliability analysis. Predictive analysis in software testing is useful in modifying, debugging, and determining when to terminate software development testing processes. However, Bayesian predictive analyses on the delayed S-shaped model have not been extensively explored. This paper uses the delayed S-shaped SRGM to address four issues in one-sample prediction associated with the software development testing process. Bayesian approach based on non-informative priors was used to derive explicit solutions for the four issues, and the developed methodologies were illustrated using real data.

Failure behavior of highly stressed rocks under quasi-static and intensive unloading conditions

Unloading failure of rocks,especially highly stressed rocks,is one of the key issues in construction of underground structures.Based on this,analytical models for rocks under quasi-static and intensive unloading conditions are established to study the failure behavior of highly stressed rocks.In case of rock failure under quasi-static unloading,the rock mass ahead of working face is regarded as an elasto-brittle material,and the stress-displacement curves are used to characterize the tensile fracture of peak-stress area.It is observed that,when intensive unloading happens,there is an elastic unloading wave（perturbation wave） propagating in the rock mass.If the initial stress exceeds the critical stress,there will be a fracture wave,following the elastic unloading wave.To study the propagation feature of fracture wave,the conservation laws of mass,momentum and energy are employed.Results show that the post-peak deformation,strength and energy dissipation are essential to the failure process of highly stressed rocks.

Effects of external dynamic disturbances and structural plane on rock fracturing around deep underground cavern

The occurrence of disasters in deep mining engineering has been confirmed to be closely related to the external dynamic disturbances and geological discontinuities.Thus,a combined finite-element method was employed to simulate the failure process of an underground cavern,which provided insights into the failure mechanism of deep hard rock affected by factors such as the dynamic stress-wave amplitudes,disturbance direction,and dip angles of the structural plane.The crack-propagation process,stress-field distribution,displacement,velocity of failed rock,and failure zone around the circular cavern were analyzed to identify the dynamic response and failure properties of the underground structures.The simulation results indicate that the dynamic disturbance direction had less influence on the dynamic response for the constant in situ stress state,while the failure intensity and damage range around the cavern always exhibited a monotonically increasing trend with an increase in the dynamic load.The crack distribution around the circular cavern exhibited an asymmetric pattern,possibly owing to the stress-wave reflection behavior and attenuation effect along the propagation route.Geological discontinuities significantly affected the stability of nearby caverns subjected to dynamic disturbances,during which the failure intensity exhibited the pattern of an initial increase followed by a decrease with an increase in the dip angle of the structural plane.Additionally,the dynamic disturbance direction led to variations in the crack distribution for specific structural planes and stress states.These results indicate that the failure behavior should be the integrated response of the excavation unloading effect,geological conditions,and external dynamic disturbances.

Imperfect preventive maintenance for numerical control machine tools with log-linear virtual age process

Based on the log-linear virtual age process, an imperfect preventive maintenance policy for numerical control(NC)machine tools with random maintenance quality is proposed. The proposed model is a combination of the Kijima type virtual age model and the failure intensity adjustment model. Maintenance intervals of the proposed hybrid model are derived when the failure intensity increase factor and the restoration factor are both random variables with uniform distribution. The optimal maintenance policy in infinite time horizon is presented. A numerical example is given when the failures of NC machine tools are described by the log-linear process. Finally, a discussion is presented to show how the optimal results depend on the different cost parameters.

Two new multi-phase reliability growth models from the perspective of time between failures and their applications

Aviation products would go through a multi-phase improvement in reliability performance during the research and development process.In the literature,most of the existing reliability growth models assume a constant failure intensity in each test phase,which inevitably limits the scope of the application.To address this problem,we propose two new models considering timevarying failure intensity in each stage.The proposed models borrow the idea from the accelerated failure-time models.It is assumed that time between failures follow the log-location-scale distribution and the scale parameters in each phase do not change,which forms the basis for integrating the data from all test stages.For the test-find-test scenario,an improvement factor is introduced to construct the relationship between two successive location parameters.Whereas for the test-fix-test scenario,the instantaneous cumulative time between failures is assumed to be consistent with Duane model and derive the formulation of location parameter.Likelihood ratio test is further utilized to test whether the assumption of constant failure intensity in each phase is suitable.Several applications with real reliability growth data show that the assumptions are reasonable and the proposed models outperform the existing models.