Mechanical behavior of rock under uniaxial tension:Insights from energy storage and dissipation

Many rock engineering projects show that the growth of tensile cracks is often an important cause of engineering disasters,and the mechanical behavior of rocks is essentially the transmission,storage,dissipation and release of energy.To investigate the tensile behavior of rock from the perspective of energy,uniaxial tension tests(UTTs)and uniaxial compression tests(UCTs)were carried out on three typical rocks(granite,sandstone and marble).Different unloading points were set before the peak stress to separate elastic energy and dissipated energy.The input energy density ut,elastic energy density ue,and dissipated energy density ud at each unloading point were calculated by integrating stress-strain curves.The results show that there is a strong linear relationship between the three energy parameters and the square of the unloading stress in UCT,but this linear relationship is weaker in UTT.The ue and ud increase linearly with the increase in ut in UCT and UTT.Based on the phenomenon that ue and ud increase linearly with ut,the applicability of W_(et)^(p) index in UTT was proved and the relative energy storage capacity and absolute energy distribution characteristics of three rocks in UCT and UTT were evaluated.The tensile behavior of marble and sandstone in UTT can be divided into two stages vaguely according to the energy distribution,but granite is not the case.In addition,based on dissipated energy,the damage evolution of three types of rocks in UCT and UTT was discussed.This study provides some new insights for understanding the tensile behavior of rock.

Mechanical response and dilatancy characteristics of deep marble under different stress paths:A sight from energy dissipation

Dilatancy is a fundamental volumetric growth behavior observed during loading and serves as a key index to comprehending the intricate nonlinear behavior and constitutive equation structure of rock.This study focuses on Jinping marble obtained from the Jinping Underground Laboratory in China at a depth of 2400 m.Various uniaxial and triaxial tests at different strain rates,along with constant confining pressure tests and reduced confining pressure tests under different confining pressures were conducted to analyze the mechanical response and dilatancy characteristics of the marble under four stress paths.Subsequently,a new empirical dilatancy coefficient is proposed based on the energy dissipation method.The results show that brittle failure characteristics of marble under uniaxial compression are more obvious with the strain rate increasing,and plastic failure characteristics of marble under triaxial compression are gradually strengthened.Furthermore,compared to the constant confining pressure,the volume expansion is relatively lower under unloading condition.The energy dissipation is closely linked to the process of dilatancy,with a rapid increase of dissipated energy coinciding with the beginning of dilatancy.A new empirical dilatancy coefficient is defined according to the change trend of energy dissipation rate curve,of which change trend is consistent with the actual dilatancy response in marble under different stress paths.The existing empirical and theoretical dilatancy models are analyzed,which shows that the empirical dilatancy coefficient based on the energy background is more universal.

Relationship between energy dissipation rate and channel morphology in the development of the model braided channel

A certain pattern of channel is the product of its self-adjustment under given boundary, discharge and sediment conditions. Based upon the principle of process-response model, an experimental study with 18 runs is carried out in LESRC. This paper is focused on the variation of the energy dissipation versus the channel morphology during and after the bedmaking process of braided channel. The results show that there exists a good empirical relationship between the energy dissipation rate and channel morphology. According to this relationship and the theory of minimum rate of energy dissipation, the authors explain the metamorphosis of the model channel with the development of the braided river.

Energy dissipation rate: An indicator of coal deformation and failure under static and dynamic compressive loads

Dynamic disasters in Chinese coal mines pose a significant threat to coal productivity. Thus, a thorough understanding of the deformation and failure processes of coal is necessary. In this study, the energy dissipation rate is proposed as a novel indicator of coal deformation and failure under static and dynamic compressive loads. The relationship between stress-strain, uniaxial compressive strength, displacement rate, loading rate, fractal dimension, and energy dissipation rate was investigated through experiments conducted using the MTS C60 tests(static loads) and split Hopkinson pressure bar system(dynamic loads). The results show that the energy dissipation rate peaks are associated with stress drop during coal deformation, and also positively related to the uniaxial compressive strength. A higher displacement rate of quasi-static loads leads to an initial increase and then a decrease in energy dissipation rate, whereas a higher loading rate of dynamic loads results in larger energy dissipation rate. Theoretical analysis indicates that a sudden increase in energy dissipation rate suggests partial fracture occurring within coal under both quasi-static and dynamic loads. Hence, the energy dissipation rate is an essential indicator of partial fracture and final failure within coal, as well as a prospective precursor for catastrophic failure in coal mine.

C haracteristics of turbulent kinetic energy dissipation rate and turbidity near the coast of East China Sea

The East China Sea(ECS) has a high suspended-sediment concentration because of the influence of the Changjiang River,indicated by high turbidity in the water.Considering the islands off the coast and the complex topography,and the strong influence of tides and wind,the coast off the ECS is a typical region with strong oceanic mixing processes.The changes in the dynamic processes near the bottom play an important role in the control of water turbidity.The turbulent kinetic energy dissipation rate(ε) is a parameter that shows the strength of ocean mixing.This is estimated based on a structure method using current velocity that is measured by a high-frequency Acoustic Doppler Current Profiler(ADCP) from a seafloor observatory in the ECS.The results indicate strong ocean mixing processes with a mean e value of 5.7×10^(-5) W/kg and distinct tidal variations in the dissipation rate.Conversely,the variation of the water turbidity leads to changes in the water dynamical structure near the bottom.Comparing the dissipation rate with the turbidity near the bottom boundary layer,we find that the high turbidity mimics strong ocean mixing.

Effect of specimen size on energy dissipation characteristics of red sandstone under high strain rate

In this experiment, red sandstone specimens, having slenderness ratios of 0.5, 0.7, 0.9 and 1.1 respectively, were subjected to blow tests using a Split Hopkinson Pressure Bar(SHPB) system at a pressure of 0.4 atmospheres. In this paper, we have analyzed the effect of slenderness ratio on the mechanical properties and energy dissipation characteristics of red sandstone under high strain rates. The processes of compaction, elastic deformation and stress softening deformation of specimens contract with an increase in slenderness ratio, whilst the nonlinear deformation process extends correspondingly. In addition, degrees of damage of specimens reduced gradually and the type of destruction showed a transformation trend from stretching failure towards shear failure when the slenderness ratio increased. A model of dynamic damage evolution in red sandstone was established and the parameters of the constitutive model at different ratios of length to diameter were determined. By comparison with the experimental curve, the accuracy of the model, which could reflect the stress–strain dynamic characteristics of red sandstone, was verified. From the view of energy dissipation, an increase in slenderness ratio of a specimen decreased the proportion of energy dissipation and caused a gradual fall in the capability of energy dissipation during the specimen failure process. To some extent, the study indicated the effects of slenderness ratios on the mechanical properties and energy dissipation characteristics of red sandstone under the high strain rate, which provides valuable references to related engineering designs and academic researches.

Anisotropic characteristics of layered backfill:Mechanical properties and energy dissipation

Layered backfill is commonly used in mining operations,and its mechanical behavior is strongly influenced by delamination parameters.In this study,13 specimens with different numbers of delamination and delamination angle were prepared to investigate the anisotropic mechanical behavior,energy dissipation characteristics and crack development of backfill.P-wave velocity,uniaxial compression,scanning electron microscope(SEM),and acoustic emission(AE)experiments were conducted.The results indicate that:(1)The P-wave velocity has linear and elliptical relationships with the number of delamination surface and delamination angle,respectively;the strength,delamination parameters and P-wave velocity show a high degree of coincidence in terms of their function relationship,which can realize the rapid prediction of strength.(2)The microstructure of the delaminated surface is looser than that of the matrix,leading to a decrease in strength and an increase at the pore-fissure compaction stage.The number and angle of delamination increase linearly with the anisotropy coefficient.(3)The energy evolution in angle-cut backfill can be divided into four stages,with a decrease in the proportion of elastic energy at the initiation stress and peak stress with increasing number of delamination planes and delamination angle.(4)Crack development increases with the number of delamination surface and delamination angle,resulting in a decrease in energy dissipation coefficient and peak AE energy.These findings provide valuable insights for the design of filling materials and processes in mining operations.

Response Spectrum Analysis of 7-story Assembled Frame Structure with Energy Dissipation System

Viscoelastic damper is an effective passive damping device,which can reduce the seismic response of the structure by increasing the damping and dissipating the vibration energy of structures.It has a wide application prospect in actual structural vibration control because of simple device and economical material.In view of the poor seismic behaviors of assembled frame structure connections,various energy dissipation devices are proposed to improve the seismic performance.The finite element numerical analysis method is adopted to analyze relevant energy dissipation structural parameters.The response spectrum of a 7-story assembled frame structure combined the ordinary steel support,ordinary viscoelastic damper,and viscoelastic damper with displacement amplification device is analyzed.The analysis results show that the mechanical behavior of assembled frame structure with ordinary steel supports are not significantly different from those without energy dissipation devices.The assembled frame structure with viscoelastic damper has better seismic performance and energy dissipation,especially for the viscoelastic damper with displacement amplification devices.The maximum value of inter-story displacement angle decreases by 32.24%;the maximum floor displacement decreases by 31.91%,and the base shear decreases by 13.62%compared with the assembled frame structures without energy dissipation devices.The results show that the seismic fortification ability of the structure is significantly improved,and the overall structure is more uniformly stressed.The damping structure with viscoelastic damper mainly reduces the dynamic response of the structure by increasing the damping coefficient,rather than by changing the natural vibration period of the structure.This paper provides an effective theoretical basis and reference for improving the energy dissipation system and the seismic performance of assembled frame structures.

System Energy and Efficiency Analysis of 12.5 W VRFB with Different Flow Rates

Vanadium redox flow battery(VRFB)is considered one of the most potential large-scale energy storage technolo-gies in the future,and its electrolyte flow rate is an important factor affecting the performance of VRFB.To study the effect of electrolyte flow rate on the performance of VRFB,the hydrodynamic model is established and a VRFB system is developed.The results show that under constant current density,with the increase of electrolyte flow rate,not only the coulombic efficiency,energy efficiency,and voltage efficiency will increase,but also the capacity and energy discharged by VRFB will also increase.But on the other hand,as the flow rate increases,the power of the pump also increases,resulting in a decrease in system efficiency.The energy discharged by the system does not increase with the increase in flow rate.Considering the balance between efficiency and pump power loss,it is experimentally proved that 120 mL·min-1 is the optimal working flow rate of the VRFB system,which can maximize the battery performance and discharge more energy.

Sb-Cu alloy cathode with a novel lithiation mechanism of ternary intermetallic formation: Enabling high energy density and superior rate capability of liquid metal battery

Antimony(Sb) is an attractive cathode for liquid metal batteries(LMBs) because of its high theoretical voltage and low cost.The main obstacles associated with the Sb-based cathodes are unsatisfactory energy density and poor rate-capability.Herein,we propose a novel Sb_(64)Cu_(36)cathode that effectively tackles these issues.The Sb_(64)Cu_(36)(melting point:525℃) cathode presents a novel lithiation mechanism involving sequentially the generation of Li_(2)CuSb,the formation of Li_(3)Sb,and the conversion reaction of Li_(2)CuSb to Li_(3)Sb and Cu.The generated intermetallic compounds show a unique microstructure of the upper floated Li_(2)CuSb layer and the below cross-linked structure with interpenetrated Li_(2)CuSb and Li_(3)Sb phases.Compared with Li_(3)Sb,the lower Li migration energy barrier(0.188 eV) of Li_(2)CuSb significantly facilitates the lithium diffusion across the intermediate compounds and accelerates the reaction kinetics.Consequently,the Li‖Sb_(64)Cu_(36)cell delivers a more excellent electrochemical performance(energy density:353 W h kg^(-1)at 0.4 A cm^(-2);rate capability:0.59 V at 2.0 A cm^(-2)),and a much lower energy storage cost of only 38.45 $ kW h^(-1)than other previously reported Sb-based LMBs.This work provides a novel cathode design concept for the development of high-performance LMBs in applications for large-scale energy storage.

Energy dissipation through wind-generated breaking waves

Wave breaking is an important process that controls turbulence properties and fluxes of heat and mass in the upper oceanic layer.A model is described for energy dissipation per unit area at the ocean surface attributed to wind-generated breaking waves,in terms of ratio of energy dissipation to energy input,windgenerated wave spectrum,and wave growth rate.Also advanced is a vertical distribution model of turbulent kinetic energy,based on an exponential distribution method.The result shows that energy dissipation rate depends heavily on wind speed and sea state.Our results agree well with predictions of previous works.

Load-bearing characteristics and energy evolution of fractured rock masses after granite and sandstone grouting

Experiments on grouting-reinforced rock mass specimens with different particle sizes and features were carried out in this study to examine the effects of grouting reinforcement on the load-bearing characteristics of fractured rock mass.The strength and deformation features of grouting-reinforced rock mass were analyzed under different loading manners;the energy evolution mechanism of grouting-reinforced rock mass specimens with different particle sizes and features was investigated;the energy dissipation ratio and post-peak stress decreasing rate were employed to evaluate the bearing stability of grouting-reinforced rock mass.The results show that the strength and ductility of granite-reinforced rock mass(GRM)under biaxial loading are higher than that of sandstone-reinforced rock mass(SRM)under uniaxial loading.Besides,the energy evolution characteristics of grouting-reinforced rock mass under uniaxial and biaxial loading mainly could be divided into early,middle,and late stages.In the early stage,total,elastic,and dissipation energies were quite small with flatter curves;in the middle stage,elastic energy increased rapidly,whereas dissipation energy increased slowly;in the late stage,dissipation energy increased sharply.The energy dissipation ratio was used to represent the pre-peak plastic deformation.Under uniaxial loading,this ratio increased as the particle size increased and the pre-peak plastic deformation of grouting-reinforced rock mass became larger;under biaxial loading,it dropped as the particle size increased,and the pre-peak plastic deformation of grouting-reinforced rock mass became smaller.The post-peak stress decline rate A_(v) was used to assess the post-peak bearing performance of grouting-reinforced rock mass.Under uniaxial loading,parameter A_(v) exhibited reduction as the particle size kept increasing,and the ability of post-peak of grouting-reinforced rock mass to allow deformation development was greater,and the bearing capacity was greater;under biaxial loading,A_(v) increased with the particle size,and the ability of post-peak of grouting-reinforced rock mass to allow deformation development was low and the bearing capacity was reduced.The findings are considered instrumental in improving the stability of the roadway-surrounding rock by granite and sandstone grouting.

Estimation of Turbulent Kinetic Energy Dissipation Rate in the Bottom Boundary Layer of the Pearl River Estuary

A structure function approach is applied to estimate the turbulent kinetic energy （TKE） dissipation rate in the bottom boundary layer of the Pearl River Estuary （PRE）. Simultaneous measurements with an acoustic Doppler velocimeter （ADV） supplied independent data for the verification of the structure function method. The results show that, 1） the structure function approach is reliable and successfully applied method to estimate the TKE dissipation rate. The observed dissipation rates range between 8.3 ×10^-4 W/kg and 4.9× 10^-6 W/kg in YM01 and between 3.4×10^-4 W/kg and 4.8×10^-7 W/kg in YM03, respectively, while exhibiting a strong quarter-diurnal variation. 2） The balance between the shear production and viscous dissipation is better achieved in the straight river. This first-order balance is significantly broken in the estuary by non-shear production/dissipation due to wave-induced fluctuations.

Unit stream power,minimum energy dissipation rate,and river engineering

Unit stream power is the most important and dominant parameter for the determination of transport rate of sand,gravel,and hyper-concentrated sediment with wash load.Minimum energy dissipation rate theory,or its simplified minimum unit stream power and minimum stream power theories,can provide engineers the needed theoretical basis for river morphology and river engineering studies.The Generalized Sediment Transport model for Alluvial River Simulation computer mode series have been developed based on the above theories.The computer model series have been successfully applied in many countries.Examples will be used to illustrate the applications of the computer models to solving a wide range of river morphology and river engineering problems.

Energy evolution and structural health monitoring of coal under different failure modes:An experimental study

Structural instability in underground engineering,especially in coal-rock structures,poses significant safety risks.Thus,the development of an accurate monitoring method for the health of coal-rock bodies is crucial.The focus of this work is on understanding energy evolution patterns in coal-rock bodies under complex conditions by using shear,splitting,and uniaxial compression tests.We examine the changes in energy parameters during various loading stages and the effects of various failure modes,resulting in an innovative energy dissipation-based health evaluation technique for coal.Key results show that coal bodies go through transitions between strain hardening and softening mechanisms during loading,indicated by fluctuations in elastic energy and dissipation energy density.For tensile failure,the energy profile of coal shows a pattern of “high dissipation and low accumulation” before peak stress.On the other hand,shear failure is described by “high accumulation and low dissipation” in energy trends.Different failure modes correlate with an accelerated increase in the dissipation energy before destabilization,and a significant positive correlation is present between the energy dissipation rate and the stress state of the coal samples.A novel mathematical and statistical approach is developed,establishing a dissipation energy anomaly index,W,which categorizes the structural health of coal into different danger levels.This method provides a quantitative standard for early warning systems and is adaptable for monitoring structural health in complex underground engineering environments,contributing to the development of structural health monitoring technology.

Characteristics of Rock Mechanics Response and Energy Evolution Regime of Deep Reservoirs in the Bozhong Sag,Bohai Bay Basin

Hydraulic fracturing is a mature and effectivemethod for deep oil and gas production,which provides a foundation for deep oil and gas production.One of the key aspects of implementing hydraulic fracturing technology lies in understanding mechanics response characteristics of rocks in deep reservoirs under complex stress conditions.In this work,based on outcrop core samples,high-stress triaxial compression tests were designed to simulate the rock mechanics behavior of deep reservoirs in Bozhong Sag.Additionally,this study analyzes the deformation and damage law for rock under different stress conditions.Wherein,with a particular focus on combining energy dissipation theory to further understand damage law for deep reservoirs.The experimental results show that regardless of stress conditions,the process of deformation/failure of deep-seated reservoirs goes through five stages:Fracture compaction,newfracture formation,stable fracture expansion,unstable fracture expansion,and post-peak residual deformation.Under different stress conditions,the energy change laws of specimens are similar.The energy dissipation process of rocks corresponds closely to the trend of deformation-failure curve,then displays distinctive stage characteristics.Wherein,in stage of rock fracture compaction,the input energy curve is approximately coincident with the elastic strain energy curve,while the dissipation energy curve remains near zero.With the increase of strain,the growth rate of elastic strain energy increases gradually,but with the deformation entering the crack propagation stage,the growth rate of elastic strain energy slows down and the dissipation energy increases gradually.Finally,in the post-peak stage,rock fracture releases a lot of energy,which leads to the sharp decline of elastic strain energy curve.In addition,the introduction of damage variable D quantifies the analysis of the extent of failure for rocks.During the process of increasing strain,rock damage exhibits nonlinear growth with increasing stress.

Energy-Efficient Traffic Offloading for RSMA-Based Hybrid Satellite Terrestrial Networks with Deep Reinforcement Learning

As the demands of massive connections and vast coverage rapidly grow in the next wireless communication networks, rate splitting multiple access(RSMA) is considered to be the new promising access scheme since it can provide higher efficiency with limited spectrum resources. In this paper, combining spectrum splitting with rate splitting, we propose to allocate resources with traffic offloading in hybrid satellite terrestrial networks. A novel deep reinforcement learning method is adopted to solve this challenging non-convex problem. However, the neverending learning process could prohibit its practical implementation. Therefore, we introduce the switch mechanism to avoid unnecessary learning. Additionally, the QoS constraint in the scheme can rule out unsuccessful transmission. The simulation results validates the energy efficiency performance and the convergence speed of the proposed algorithm.

Mechanical and energy dissipation characteristics of granite under cyclic impact loading

This study investigated the effect of repeated blasting on the stability of surrounding rock during the construction of a tunnel or city underground engineering.The split Hopkinson pressure bar(SHPB)was used to carry out cyclic impact tests on granite samples,each having a circular hole,under different axial pressures,and the cumulative specific energy was proposed to characterize the damage characteristics of the rock during the cyclic impact.The mechanical properties and the energy absorbed by the granite samples under cyclic impact loads were analyzed.The results showed that under different axial pressures,the reflected waveform from the samples was characterized by“double-peak”phenomenon,which gradually changed to“single-peak”wi th the increase in damage value.The dynamic peak stress of the sample first increased and then decreased with an increase in impact times.The damage value criterion established based on the energy dissipation could well characterize the relationship between the damage and the number of impacts,which showed a slow increase,steady increase,and high-speed increase,and the damage value depended mainly on the last impact.Under the action of different axial pressures,all the failure modes of the samples were axial splitting failures.As the strain rate increased,with an increase in the dimension of the block,the sizes of the rock fragments decreased,and the fragmentation became more severe.

Effect of thermal treatment on energy dissipation of granite under cyclic impact loading

High temperature treatment causes thermal damage to rocks in deep mining.To study the thermal effect on the energy dissipation of rocks during the dynamic cyclic loading,cyclic impact loading experiments of heat-treated rocks were carried out using the splitting Hopkinson pressure bar(SHPB)experimental system.The correlations among the energy dissipation,energy dissipation rate,impact times,accumulated absorbed energy per volume,failure mode and temperature were analyzed.The results show that the reflected energy under the first impact increases and finally exceeds the absorbed energy when the temperature increases;however,the total reflected energy decreases above 200℃.The absorbed energy under the first impact and the total absorbed energy all decrease as the temperature increases,the rates of which decrease accordingly.And the same phenomenon appears for the transmitted energy and the rate of the transmitted energy.On the contrary,the rate of the reflected energy increases with the rising temperature.When the temperature increases,the fewer impact times are needed to destroy the sample.In addition,the failure modes are different when the rock is treated at different temperatures;that is,when the temperature is high,even though the absorbed energy is low,the sample breaks into powder after several impacts.

Energy dissipation of coal and rock during damage and failure process based on EMR

The physical and mechanical change processes of coal and rock are closely related to energy transformation,and the destruction and failure of coal and rock is an instability phenomena driven by energy change.However,the energy change of large-scale coal rock in the mine site is hardly calculated accurately,making it difficult to monitor coal-rock systematic failure and collapse from the perspective of energy.By the energy dissipation EMR monitoring system,we studied the damage and failure of coal and rock with bursting liability from the energy dissipation point using the geophysical method-EMR,and explored the energy dissipation characteristics during uniaxial compression and their main influencing factors.The results show that under displacement-control loading mode,there are 2 types of energy dissipation trends for both coal and rock with bursting liability.The type Ⅰ trend is a steady increase one during the whole process,therein,the energy dissipation of rock samples is accelerated at the peak load.The type Ⅱ trend energy is a W-shaped fluctuating one containing 6 stages.Under load-control loading mode,there is one energy dissipation trend of shock downward-steady rise.Besides that,rock samples also present a trend of 4 stages.The energy dissipation characteristics of coal and rockduring loading failure process can be used as effective criteria to assess whether they are in a stable or destructive stage.The factors influencing energy dissipation in the loading failure process of coal and rock mainly include strength,homogeneity,and energy input efficiency.