Energy release induced rockbursts based on butterfly-shaped plastic zones in roadways of coal reservoirs

According to the theories of rockburst based on butterfly-shaped plastic zones, a plane strain mechanical model was established for stress distribution around the holes in homogeneous elastoplastic media. Based on the Mohr-Coulomb yield criterion and the generalized form of Hooke’s law, the equation for the elastic strain-energy density of units at a 3D stress state was deduced. On this basis, the energy absorption and release in rocks surrounding a roadway during the evolution thereof in a coal reservoir tend to rock bursting were quantified. Through Flac3D 5.0 numerical simulation software, the energy released from a homogeneous circular roadway at different development states of plastic zones was investigated. By investigating conditions at the 21141 working face in Qianqiu Coal Mine, Henan Province, China, subjected to rockburst, a numerical model was established to calculate the energy released by a rockburst working face. The calculated results approximated the data monitored at the outburst site, with the same energy level recorded. The theoretical calculation for energy release from the rock surrounding a roadway is expected to reference engineering practice.

Statistical Damage Constitutive Model for High-Strength Concrete Based on Dissipation Energy Density

To study the energy evolution law and damage constitutive behavior of high-strength concrete based on the conventional triaxial compression tests of C60 and C70 high-strength concrete subjected to five different confining pressures, the failure characteristics of high-strength concrete are analyzed at different confining pressures, and the evolution of the input energy density, elastic strain energy density, and dissipation energy density with axial strain and confining pressure are quantified. Combined with a continuous damage theory and non-equilibrium statistical method, the ratio of dissipation energy density of concrete to dissipation energy density corresponding to peak stress is used as the mechanical parameter. Assuming that the mechanical parameter obeys the Weibull distribution laws, the statistical damage variable describing the damage characteristics of concrete were derived. According to the Lemaitre strain equivalent principle, the damage variable is introduced to the generalized Hooke law to establish the statistical damage constitutive model for high-strength concrete. The results show that: (1) the input energy density and dissipation energy density increases with the increase of axial strain, while the elastic strain energy density increases first and then decreases as a function of the axial strain and reaches the maximum value at the peak stress; (2) the input, elastic strain, and dissipated energy densities corresponding to the peak stress of the two high-strength concretes all increase as a function of confining pressure, and the elastic strain energy density corresponding to the peak stress increases linearly as a function of the confining pressure; (3) the statistical damage constitutive model results of C60 and C70 high-strength concrete are in good agreement with the test results, and the average relative standard deviations are only 3.64% and 3.99%. These outcomes verify the rationality and accuracy of the model.

A Modified Bursting Energy Index for Evaluating Coal Burst Proneness and Its Application in Ordos Coalfield, China

Coal burst is a type of dynamic geological hazard in coal mine. In this study, a modified bursting energy index, which is defined as the ratio of elastic strain energy at the peak strength to the released strain energy density at the post-peak stage, was proposed to evaluate the coal burst proneness. The calculation method for this index was also introduced. Two coal mines (PJ and TJH coal mines) located in Ordos coalfield were used to verify the validity of the proposed method. The tests results indicate that modified bursting energy index increases linearly with increasing uniaxial compressive strength. The parameter A, which is used to fit relation between total input and elastic strain energy density, has a significant effect on the modified bursting energy index. A large value of parameter A means more elastic strain energy before the peak strength while a small value indicates most of input energy was dissipated. Finally, the coal burst proneness of these two coal mines was evaluated with the modified index. The results of modified index are consistent with that of laboratory tests, and more reasonable than that from original bursting energy index because it removed the dissipated strain energy from the total input strain energy density.

Effect of Nonparallel End Face on Energy Dissipation Analyses of Rocklike Materials Based on SHPB Tests

To evaluate the effect of nonparallel end face of rocklike specimens in SHPB tests, the characteristics of energy dissipation are analyzed based on numerical simulations for end-face nonparallelism from 0% to 0.40% and Young’s modulus from 14 GPa to 42 GPa. With the increment of end-face nonparallelism, both energy consumption density and dissipated energy density show a slight increase trend, while releasable elastic strain energy density presents a slight decrease trend. Existence of elastic unloading in the damaged rocklike specimen leads to a reduction of energy consumption density and a constant dissipated energy density during total strain shrinkage. At peak dynamic stress, dissipated energy density presents a linear upward trend with the increment of end-face nonparallelism and Young’s modulus, while releasable elastic strain energy density shows an inverse trend. A binary linear regression equation is deduced to estimate the energy dissipation ratio. Mechanical damage evolution of the rocklike specimen is divided into two regions in line with the two regions in dynamic stress-strain curves, and the transition between the slow-growth region and rapid-growth region is shifted to the right with the increment of end-face nonparallelism. Due to the presence of nonparallel end face, fluctuation presents in energy density evolution and mechanical damage evolution. The fluctuation is enhanced with the increment of end-face nonparallelism and weakened with the increase of Young’s modulus. Based on energy density evolution and mechanical damage evolution analyses, the maximum end-face nonparallelism should be controlled within 0.20%, twice the value in ISRM suggested methods, which reduces the cost and time for processing rocklike specimens.

Strain energy-and stress-based approaches revisited in notch fatigue of ductile steels

The constant amplitude, zero-mean stress, axial-fatigue behaviour of plain and bluntly notched AISI 304 L stainless steel specimens is investigated in terms of strain energy density. Concerning plain material, it was found that at the fatigue knee the plastic strain energy density is 1.49 times higher than the elastic strain energy density. In the authors’ opinion, the presence of plasticity at the fatigue knee is responsible for the unsuitableness of classical stress - based approaches to synthesise the fatigue behaviour of this material. On the contrary, the elastic-plastic strain energy density was found an efficient parameter to rationalise in a single scatter band fatigue data of plain and bluntly notched specimens. Based on this result, the classic stress-and the point stress-based approaches were revisited taking into account the presence of plasticity at the fatigue knee, by introducing an equivalent fully elastic material having a linear elastic strain energy density at the fatigue knee equal to that of the actual material. Accordingly, a coefficient of plasticity Kp was successfully introduced to modify the classical definition of fatigue strength reduction factor, Kf.

Scanning X-ray nanodiffraction from ferroelectric domains in strained K0.75Na0.25NbO3 epitaxial films grown on (110) TbScO3

Scanning X-ray nanodiffraction on a highly periodic ferroelectric domain pattern of a strained K0.75Na0.25NbO3 epitaxial layer has been performed by using a focused X-ray beam of about 100 nm probe size. A 90°-rotated domain variant which is aligned along [1{\overline 1}2]TSO has been found in addition to the predominant domain variant where the domains are aligned along the [{\overline 1}12]TSO direction of the underlying (110) TbScO3 (TSO) orthorhombic substrate. Owing to the larger elastic strain energy density, the 90°-rotated domains appear with significantly reduced probability. Furthermore, the 90°-rotated variant shows a larger vertical lattice spacing than the 0°-rotated domain variant. Calculations based on linear elasticity theory substantiate that this difference is caused by the elastic anisotropy of the K0.75Na0.25NbO3 epitaxial layer.