Study on creep deformation and energy development of underground surrounding rock under four‐dimensional support

There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(hereinafter 4D support),as a new support technology,can set the roadway surrounding rock under three‐dimensional pressure in the new balanced structure,and prevent instability of surrounding rock in underground engineering.However,the influence of roadway depth and creep deformation on the surrounding rock supported by 4D support is still unknown.This study investigated the influence of roadway depth and creep deformation time on the instability of surrounding rock by analyzing the energy development.The elastic strain energy was analyzed using the program redeveloped in FLAC3D.The numerical simulation results indicate that the combined support mode of 4D roof supports and conventional side supports is highly applicable to the stability control of surrounding rock with a roadway depth exceeding 520 m.With the increase of roadway depth,4D support can effectively restrain the area and depth of plastic deformation in the surrounding rock.Further,4D support limits the accumulation range and rate of elastic strain energy as the creep deformation time increases.4D support can effectively reduce the plastic deformation of roadway surrounding rock and maintain the stability for a long deformation period of 6 months.As confirmed by in situ monitoring results,4D support is more effective for the long‐term stability control of surrounding rock than conventional support.

Origin of High Elastic Recovery of Hard-elastic Polypropylene Film at Room Temperature: the Mixed Contribution of Energy Elasticity and Entropy Elasticity

The crystalline and amorphous regions were alternately arranged in the hard elastic polypropylene(PP)films with row-nucleated lamellae.In this work,their structure evolution during stretching and recovery at room temperature was followed and the elastic recovery mechanism was discussed by twice cyclic tensile experiment.During the first stretching to 100%,the lamellae crystals are parallel separated and the intercrystallite crazing is formed at the first yield point.Many nano-cavities within the intercrystallite crazing appear when the strain reaches 20%.The strain-hardening process accompanies with the lamellae long period increasing and the intercrystallite crazing enlargement.After the secondary yield point,the lamellae cluster is further separated and more nano-cavities appear.The first and second recovery processes are complete overlap.During recovery,firstly,the energy elasticity provided by nano-cavities surface tension drives the shrinkage of material,and then the entropy elasticity related to amorphous chain relaxation plays a leading role when the strain is smaller than the secondary yield point.The elastic recovery process of hard elastic material is the co-contribution of energy elasticity and entropy elasticity.This work gives a clearer recognition about the source of hard elastic property and the role of amorphous region in material's deformation.

Effect of dynamic loading conditions on the dynamic performance of MP1 energy-absorbing rockbolts:Insight from laboratory drop test

Energy-absorbing rockbolts have been widely adopted in burst-prone excavation support, and their serviceability is closely related to the frequency and magnitude of seismic events. In this research, the splittube drop test with varying impact energy was conducted to reproduce the dynamic performance of MP1rockbolts under a wide range of seismic event magnitudes. The test results showed that the impact process could be subdivided into four distinct stages, i.e. mobilization, strain hardening, plastic flow(ductile), and rebound stage, of which strain hardening and plastic flow are the primary energy absorbing stages. As the impact energy per drop increases from 8.1 to 46.7 k J, the strain rate of the shank varies between 1.20 and 2.70 s^(-1), and the average impact load is between 240 and 270kN, which may be considered as constant. The MP1 rockbolt has a cumulative maximum energy absorption(CMEA) of 31.9–40.0 k J/m, with an average of 35.0 k J/m, and the elongation rate is 11.4%–14.7%, with an average of 12.7%, both of which are negatively correlated with the impact energy per drop. Regression analysis shows that energy absorption and shank elongation, as well as momentum input and impact duration,conform to the linear relationship. The complete dynamic capacity envelope of MP1 rockbolts is proposed, which reflects the dynamic bearing capacity, elongation, and distinct stages. This study is helpful to better understand the dynamic characteristics of energy-absorbing rockbolts and assist design engineers in robust reinforcement systems design to mitigate rockburst damage in seismically active underground excavations.

A new criterion of coal burst proneness based on the residual elastic energy index

To evaluate the coal burst proneness more precisely,a new energy criterion namely the residual elastic energy index was proposed.This study begins by performing the single-cyclic loading-unloading uniaxial compression tests with five pre-peak unloading stress levels to explore the energy storage characteristics of coal.Five types of coals from different mines were tested,and the instantaneous destruction process of the coal specimens under compression loading was recorded using a high speed camera.The results showed a linear relationship between the elastic strain energy density and input energy density,which confirms the linear energy storage law of coal.Based on this linear energy storage law,the peak elastic strain energy density of each coal specimen was obtained precisely.Subsequently,a new energy criterion of coal burst proneness was established,which was called the residual elastic energy index(defined as the difference between the peak elastic strain energy density and post peak failure energy density).Considering the destruction process and actual failure characteristics of coal specimens,the accuracy of evaluating coal burst proneness based on the residual elastic energy index was examined.The results indicated that the residual elastic energy index enables reliable and precise evaluations of the coal burst proneness.

Experiments on rockburst proneness of pre-heated granite at different temperatures: Insights from energy storage, dissipation and surplus

Many underground engineering projects show that rockburst can occur in rocks at great depth and high temperature, and temperature is a critical factor affecting the intensity of rockburst. In general, temperature can affect the energy storage, dissipation, and surplus in rock. To explore the influence of temperature on the energy storage and dissipation characteristics and rockburst proneness, the present study has carried out a range of the uniaxial compression(UC) and single-cyclic loading-unloading uniaxial compression(SCLUC) tests on pre-heated granite specimens at 20℃-700℃. The results demonstrate that the rockburst proneness of pre-heated granite initially increases and subsequently decreases with the increase of temperature. The temperature of 300℃ has been found to be the threshold for rockburst proneness. Meanwhile, it is found that the elastic strain energy density increases linearly with the total input strain energy density for the pre-heated granites, confirming that the linear energy property of granite has not been altered by temperature. According to this inherent property, the peak elastic strain energy of pre-heated granites can be calculated accurately. On this basis, utilising the residual elastic energy index, the rockburst proneness of pre-heated granite can be determined quantitatively. The obtained results from high to low are: 317.9 k J/m^(3)(300℃), 264.1 k J/m^(3)(100℃), 260.6 k J/m^(3)(20℃), 235.5 k J/m^(3)(500℃), 158.9 k J/m^(3)(700℃), which are consistent with the intensity of actual rockburst for specimens. In addition, the relationship between temperature and energy storage capacity(ESC) of granite was discussed, revealing that high temperature impairs ESC of rocks, which is essential for reducing the rockburst proneness. This study provides some new insights into the rockburst proneness evaluation in high-temperature rock engineering.

CFD Simulation and Experimental Study of a New Elastic Blade Wave Energy Converter

Small moving vehicles represent an important category of marine engineering tools and devices(equipment)typically used for ocean resource detection and maintenance of marine rights and interests.The lack of efficient power supply modes is one of the technical bottlenecks restricting the effective utilisation of this type of equipment.In this work,the performance characteristics of a new type of elastic-blade/wave-energy converter(EBWEC)and its core energy conversion component(named wave energy absorber)are comprehensively studied.In particular,computational fluid dynamics(CFD)simulations and experiments have been used to analyze the hydrodynamics and performance characteristics of the EBWEC.The pressure cloud diagrams relating to the surface of the elastic blade were obtained through two-way fluid-solid coupling simulations.The influence of blade thickness and relative speed on the performance characteristics of EBWEC was analyzed accordingly.A prototype of the EBWEC and its bucket test platform were also developed.The power characteristics of the EBWEC were analyzed and studied by using the blade thickness and motion cycle as control variables.The present research shows that the EBWEC can effectively overcome the performance disadvantages related to the transmission shaft torque load and power curve fluctuations of rigid blade wave energy converters(RBWEC).

Rockburst mechanism and the law of energy accumulation and release in mining roadway: a case study

The rockburst dynamic disasters in the process of deep coal mining become more and more serious.Taking the rockburst occurred in the 23130 working face of Yuejin Coal Mine as the engineering background,we study the characteristics of mining stress feld around roadway,the plastic failure morphological characteristics of surrounding rock and the accumulation/release law of elastic energy before and after burst.An analysis model quantitatively describing the physical process of rockburst in the mining roadway is established,and the calculation method of dynamic release of elastic energy in the physical process of rockburst is educed.The mechanism of rockburst in mining roadway is revealed.The results show that an“L-shaped”stress concentration zone is formed within 100 m of the 23130 working face,and the principal stress ratio of the surrounding rock of the transportation roadway is 2.59–4.26.The change of the direction of the maximum principal stress has a signifcant efect on the burst appearance characteristics.The failure strength of diferent sections of the mining roadway is characterized by the elastic energy release value.With the increase of the working face distance,the elastic energy released by burst failure and the expansion variation of failure boundary radius show a nonlinear variation law that tends to decrease steadily after sharp fuctuation.The closer to the working face,the higher the burst risk.At a distance of 10 m from the working surface,the maximum principal stress reaches its maximum value.The butterfy-shaped failure system generated by the surrounding rock of the roadway has energy self-sustainability,and the elastic energy released by the sudden expansion of the butterfy leaf is enough to cause a burst damage of 1.9 magnitude.This work could provide theoretical support for the prediction and prevention of rockburst.

Effect of elastic strain energy on grain growth and texture in AZ31 magnesium alloy by phase-field simulation

A phase-field model is modified to investigate the grain growth and texture evolution in AZ31 magnesium alloy during stressing at elevated temperatures. The order parameters are defined to represent a physical variable of grain orientation in terms of three angles in spatial coordinates so that the grain volume of different order parameters can be used to indicate the texture of the alloy. The stiffness tensors for different grains are different because of elastic anisotropy of the magnesium lattice. The tensor is defined by transforming the standard stiffness tensor according to the angle between the （0001） plane of a grain and the direction of applied stress. Therefore, different grains contribute to different amounts of work under applied stress. The simulation results are well-explained by using the limited experimental data available, and the texture results are in good agreement with the experimental observations. The simulation results reveal that the applied stress strongly influences AZ31 alloy grain growth and that the grain-growth rate increases with the applied stress increasing, particularly when the stress is less than 400 MPa. A parameter （△d） is introduced to characterize the degree of grain-size variation due to abnormal grain growth; the △d increases with applied stress increasing and becomes considerably large only when the stress is greater than 800 MPa. Moreover, the applied stress also results in an intensive texture of the 〈0001〉 axis parallel to the direction of compressive stress in AZ31 alloy after growing at elevated temperatures, only when the applied stress is greater than 500 MPa.

Interaction energy of interface dislocation loops in piezoelectric bi-crystals

Interface dislocations may dramatically change the electric properties, such as polarization, of the piezoelectric crystals. In this paper, we study the linear interactions of two interface dislocation loops with arbitrary shape in generally anisotropic piezoelectric bi-crystals. A simple formula for calculating the interaction energy of the interface dislocation loops is derived and given by a double line integral along two closed dislocation curves. Particularly, interactions between two straight segments of the interface dislocations are solved analytically, which can be applied to approximate any curved loop so that an analytical solution can be also achieved. Numerical results show the influence of the bi-crystal interface as well as the material orientation on the interaction of interface dislocation loops.

Evaluation of rockburst proneness considering specimen shape by storable elastic strain energy

To systematically assess the rockburst proneness considering specimen shape,multiple groups of laboratory tests were performed on 5 rock materials in cylindrical and cuboid shapes.The linear energy storage(LES)law of both cylindrical and cuboid rock specimens under uniaxial compressive load was confirmed,and the energy storage coefficient was found to be unrelated to specimen shape.On the basis of LES law,two rockburst proneness indexes,namely the strain energy storage index(W_(et))and the potential energy of elastic strain(PES),were modified.Subsequently,the W_(et),PES,peak-strength strain energy storage index(W_(et))p,and peak-strength potential energy of elastic strain(PESp)were used to assess the rockburst proneness of the cylindrical and cuboid specimens.In addition,the fragment ejection course of specimens under test was recorded by a high-speed camera.Then,the rockburst proneness judgments obtained from the 4 indexes were compared with the qualitative data during rock destruction.The results show that,under similar stress conditions,specimen shape has an ignorable effect on the rockburst proneness as a whole.The judgment accuracy of the two modified indexes,especially that of the PESp,is favorably improved to evaluate the rockburst proneness of both cylindrical and cuboid specimens.However,misjudgment ofW_(et)^(p)and PESp may still occur in the assessment of rockburst proneness as these two indexes only consider the energy state before rock peak strength and the W_(et)^(p)is formulated in a ratio form.

A new mixed-mode phase-field model for crack propagation of brittle rock

Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.

Experimental Study on the Mechanical Parameters Relating to the Impact Tendency of Coal Sample

Coal burst remains one of the gravest safety risks that will be encountered in mining in the future, because the stress conditions will become more complex as mining depths increase. Various influencing elements exist, and varied geological and mining circumstances might result in diverse coal burst phenomena. The impact propensity of coal has variations as a result of the distinct physical and mechanical qualities of each. To identify the impact propensity of coal and then understand the rules of coal burst occurrence, laboratory tests can be conducted to identify the physical and mechanical parameters affecting coal samples. The mechanical properties, energy absorption, and energy dissipation characteristics of coal samples were examined experimentally in this paper using coal samples that were taken from the mine. On the basis of the evaluation of the impact inclination parameters for four fundamental coal samples, novel impact inclination indicators and the relationship between the fractures in the coal sample and the impact inclination parameters were discussed. The following are the key conclusions: 1) On-site samples of No. 15 coal from the Qi yuan Coal Mine were taken (15 s) and processed in accordance with the guidelines for the coal specimen impact inclination test. The accuracy of the specimen was sufficient for the test. 2) Analysis is done on the mechanical relevance and calculation techniques of the four fundamental coal sample impact tendency characteristics, dynamic failure time (DT), elastic strain energy index (WET), impact energy index (KE), as well as uniaxial compressive strength (RC). 3) Regarding the rock burst danger of rock samples, the potential use of the ratio of pre-peak and post- peak deformation modulus to Kλ and the residual elastic strain energy index CEF as the impact propensity indices of coal samples are discussed. It is possible to utilize two new impact propensity indices to evaluate the impact propensity of coal samples, according to test results that reveal a linear correlation between two new impact inclination indexes and four fundamental impact tendency indexes. 4) The statistical analysis of the crack ratio with the four impact propensity indicators after coal specimen failure, and the correlation among the crack ratio with the indicators, are both done. The findings indicate that the four impact propensity indicators have a linear relationship with the crack ratio of the coal sample surface cracks.

A Review on Methods for Determining the Vibratory Damping Ratio

This article aims to popularize the methods for determining the vibratory damping ratio, to explain the various mathematical and physical theorems related to the establishment of literal expressions. Vibration damping is an essential parameter to reduce the dynamic responses of structures. The study aimed at its determination is necessary and essential for the safeguard of buildings and human lives during the earthquake. Among the main methods studied in this article, the free vibration attenuation method seems to be easy to implement but requires a state-of-the-art device to capture the responses. In addition to this device, the other methods require other equipment for the vibration of the system and the transformation of the responses in the frequency domain.

Rockburst mechanism in soft coal seam within deep coal mines

A number of rockburst accidents occurring in soft coal seams have shown that the rockburst mechanism involved in soft coal seams is significantly different from that involved in hard coal seams. Therefore, the method used to evaluate rockburst in hard coal seams is not applicable to soft coal seams. This paper established an energy integral model for the rockburst-inducing area and a friction work calculation model for the plastic area. If the remaining energy after the coal seam is broken in the rockburstinducing area is greater than the friction work required for the coal to burst out, then a rockburst accident will occur. Mechanisms of ‘‘quaking without bursting" and ‘‘quaking and bursting" are clarified for soft coal seams and corresponding control measures are proposed as the optimization of roadway layouts and use of ‘‘three strong systems"(strong de-stressing, strong supporting, and strong monitoring).

Anchoring properties of substrate with a grating surface

The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal （NLC） in a grating surface originates from two mechanisms, thus the anchoring energy consists of two parts. One originates from the interaction potential between NLC molecules and the molecules on the substrate surface, and the other stems from the increased elastic strain energy. Based on the two mechanisms, the expression of anchoring energy per unit area of a projected plane of this grating surface is deduced and called the equivalent anchoring energy formula. Both the strength and the easy direction of equivalent anchoring energy are a function of the geometrical parameters （amplitude and pitch） of a grating surface. By using this formula, the grating surface can be replaced by its projected plane and its anchoring properties can be described by the equivalent anchoring energy formula.

Computer simulation of strain-induced morphological transformation of coherent precipitates

The coherent elastic strain-induced morphological transformation of a binarycubic model alloy was simulated with different strain energy parameters. The microscopic diffusionequation was combined with the theory of microscopic elasticity. The results show that when thestrain energy is neglected, the randomly distributed equiaxed particles are obtained with isotropiccharacteristic. It is coarsening that follows the Ostwald ripening mechanism: smaller particlesdwindle and larger particles grow; when the elastic strain is considered, plate precipitates tend toalign along the elastically soft directions <01> with anisotropic characteristic. The particlesgrow in the soft directions and coarsen further; particles dwindle in out of the soft directions.While the coarsening of the particles localized in the same row or column follows the rule: smallerparticles shrink and larger ones grow.

Discrete element modeling of acoustic emission in rock fracture

The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a result of the heterogeneity in rock specimen, the failure criterion of bonded particle is coupled by the shear and tensile strengths, which follow a normal probability distribution. The Kaiser effect is simulated in the fracture process, for a cubic rock specimen under uniaxial compression with a constant rate. The AE number is estimated with breakages of bonded particles using a pair of parameters, in the temporal and spatial scale, respectively. It is found that the AE numbers and the elastic energy release curves coincide. The range for the Kaiser effect from the AE number and the elastic energy release are the same. Furthermore, the frequency-magnitude relation of the AE number shows that the value of B determined with DEM is consistent with the experimental data.

An analytical solution for the elastic fields near spheroidal nano-inclusions

When the size of an inclusion shrinks to nanometers, interface energy plays an important role in the deformation around it. In the present paper, we consider the effect of interface energy on the elastic fields near a spheroidal nanoinclusion embedded in an elastic medium on the basis of surface elasticity theory. Using Boussinesq-Sadowsky potential function method, we obtain the deformation field near the inclusion subjected to a uniformly uniaxial loading at infinity. The results show that the elastic fields near the nano-inclusion depend strongly on the interface properties, the size and shape of inclusion. These new characteristics may be helpful to understand various relevant mechanical performances of nanosized inhomogeneities.

Phase-field study of the second phase particle effect on texture evolution of polycrystalline material

The second phase particle effect on texture evolution of polycrystalline material is studied through phase-field method. A unique field variable is introduced into the phase-field model to represent the second phase particles. Elastic interaction between particles and grains is also considered. Results indicate that in the presence of second phase particles the average particle diameter turns smaller than in the absence of these particles and retards texture formation by pinning effect. The second phase particles change the strain energy profile, which tremendously influences the pinning effect.

Bi-stable states of initially stressed elastic cylindrical shell structures with two piezoelectric surface layers

A theoretical model is proposed in this paper to predict the bi-stable states of initially stressed cylindrical shell structures attached by surface anisotropic piezoelectric layers.The condition for existence of bi-stability of the shell structural system is presented and analytical expressions for corresponding rolled-up radii of the stable shell are given based on the principle of minimum strain energy.The resulting solution indicates that the shell system may have two stable configurations besides its initial state under a combined action of the actuating electric field and initial stresses characterized by the bending moment.If the piezoelectric layer materials act as only sensor materials without the actuating electric field,initial stresses may produce the bi-stable states,but one corresponding to its initial state.For the shell without initial stresses,the magnitude in the actuating electric field determines the number of the stable states,one or two stable configurations besides the initial state.The theoretical prediction for the bi-stable states is verified by finite element method（FEM） simulation by using the ABAQUS code.