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.

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.

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.

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.

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.

Quantitative calculation for the dissipated energy of fault rock burst based on gradient-dependent plasticity

The capacity of energy absorption by fault bands after rock burst wascalculated quantitatively according to shear stress-shear deformation curves considering theinteractions and interplaying among microstructures due to the heterogeneity of strain softeningrock materials. The post-peak stiffness of rock specimens subjected to direct shear was derivedstrictly based on gradient-dependent plasticity, which can not be obtained from the classicalelastoplastic theory. Analytical solutions for the dissipated energy of rock burst were proposedwhether the slope of the post-peak shear stress-shear deformation curve is positive or not. Theanalytical solutions show that shear stress level, confining pressure, shear strength, brittleness,strain rate and heterogeneity of rock materials have important influence on the dissipated energy.The larger value of the dissipated energy means that the capacity of energy dissipation in the formof shear bands is superior and a lower magnitude of rock burst is expected under the condition ofthe same work done by external shear force. The possibility of rock burst is reduced for a lowersoftening modulus or a larger thickness of shear bands.

Fractal and chaotic laws on seismic dissipated energy in an energy system of enginering structures

Fractal and chaotic laws of engineering structures are discussed in this paper, it means that the intrinsic essences and laws on dynamic systems which are made from seismic dissipated energy intensity E d and intensity of seismic dissipated energy moment I e are analyzed. Based on the intrinsic characters of chaotic and fractal dynamic system of E d and I e, three kinds of approximate dynamic models are rebuilt one by one: index autoregressive model, threshold autoregressive model and local-approximate autoregressive model. The innate laws, essences and systematic error of evolutional behavior I e are explained over all, the short-term behavior predictability and long-term behavior probability of which are analyzed in the end. That may be valuable for earthquake-resistant theory and analysis method in practical engineering structures.

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.

A Four-Level Theory on Energy Transfer of the Light-Harvesting Complex Ⅱ in PS Ⅱ in Higher Plants

With reference to the recent achivements about the structure, spectra and kinetics of light_harvesting complex (LHCⅡ) in PSⅡ of higher plants, a four_level model was provided to simulate the energy transfer process from LHC Ⅱ to the reaction center. On the basis of this model, a set of rate equation was established. Analysis of its algebra solution led to a general picture of energy transfer process in LHC Ⅱ of higher plants and the strong interaction among pigment molecules in this process. Based on the spectra, kinetics and biological structural data providing some information of energy transfer path and energy dissipation mechanism, it has been found that energy transfer mainly happened between the pigments whose energy level was most closely adjacent, the loss of energy had a close relation to the process of energy transfer and tended to increase with the decrease of energy level. The protective mechanism of antenna system was also discussed.

Effect of diagenetic variation on the static and dynamic mechanical behavior of coral reef limestone

Coral reef limestone at different depositional depths and facies differ remarkably on the textural and mineralogical characteristics,owing to the complex sedimentary diagenesis.To explore the effects of pore structure and mineral composition associated with diagenetic variation on the mechanical behavior of reef limestone,a series of quasi-static and dynamic compression tests along with microscopic examinations were performed on the reef limestone at shallow and deep burial depths.It is revealed that the shallow reef limestone(SRL)is classified as a porous aragonite-type carbonate rock with high porosity(55.3±3.2)%and pore connectivity.In comparison,the deep reef limestone(DRL)is mainly composed of dense calcite-type calcium carbonate with low porosity(4.9±1.6)%and pore connectivity.The DRL strengthened and stiffened by the tight grain framework consistently displays much higher values of the dynamic compressive strength,elastic modulus,brittleness index,and specific energy absorption than those of the SRL.The gap between two types of limestone further increases with an increase in strain rate.It appears that the failure pattern of SRL is dominated by the inherent defects like weak bonding interfaces and growth lines,revealed by the intricate fracturing network and mixed failure.Likewise,although the preexisting megapores in DRL may affect the crack propagation on pore tips to a certain distance,it hardly alters the axial splitting failure of DRL under impacts.The stress wave propagation and attenuation in SRL is primarily controlled by the reflection and diffusion caused by plenty mesopores,as well as an energy dissipation in layer-wise pore collapse and adjacent grain crushing,while the stress wave in DRL is highly hinged on the insulation and diffraction induced by the isolated megapores.This process is accompanied by the energy dissipation behavior of inelastic deformation resulted from the pore-emanated microcracking.

Sliding and damming properties of granular debris with different geometric configurations and grain size distributions

Granular debris plays a significant role in determining damming deposit characteristics. An indepth understanding of how variations in grain size distribution(GSD) and geometric configurations impact the behavior of granular debris during the occurrence of granular debris is essential for precise assessment and effective mitigation of landslide hazards in mountainous terrains. This research aims to investigate the impact of GSD and geometric configurations on sliding and damming properties through laboratory experiments. The geometric configurations were categorized into three categories based on the spatial distribution of maximum volume: located at the front(Type Ⅰ), middle(Type Ⅱ), and rear(Type Ⅲ) of the granular debris. Our experimental findings highlight that the sliding and damming processes primarily depend on the interaction among the geometric configuration, grain size, and GSD in granular debris. Different sliding and damming mechanisms across various geometric configurations induce variability in motion parameters and deposition patterns. For Type Ⅰ configurations, the front debris functions as the critical and primary driving component, with energy dissipation primarily occurring through inter-grain interactions. In contrast, Type Ⅱ configurations feature the middle debris as the dominant driving component, experiencing hindrance from the front debris and propulsion from the rear, leading to complex alterations in sliding motion. Here, energy dissipation arises from a combination of inter-grain and grain-substrate interactions. Lastly, in Type Ⅲ configurations, both the middle and rear debris serve as the main driving components, with the rear sliding debris impeded by the front. In this case, energy dissipation predominantly results from grainsubstrate interaction. Moreover, we have quantitatively demonstrated that the inverse grading in damming deposits, where coarse grain moves upward and fine grain moves downward, is primarily caused by grain sorting due to collisions among the grains and between the grain and the base. The impact of grain on the horizontal channel further aids grain sorting and contributes to inverse grading. The proposed classification of three geometric configurations in our study enhances the understanding of damming properties from the view of mechanism, which provides valuable insights for related study about damming granular debris.

孔隙率对矩形沟槽上垂直多孔屏障的波浪散射效应影响

The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.

Energy analysis and criteria for structural failure of rocks

The intrinsic relationships between energy dissipation,energy release,strength and abrupt structural failure are key to understanding the evolution of deformational processes in rocks.Theoretical and experimental studies confirm that energy plays an important role in rock deformation and failure.Dissipated energy from external forces produces damage and irreversible deformation within rock and decreases rock strength over time.Structural failure of rocks is caused by an abrupt release of strain energy that manifests as a catastrophic breakdown of the rock under certain conditions.The strain energy released in the rock volume plays a pivotal role in generating this abrupt structural failure in the rocks.In this paper,we propose criteria governing（1） the deterioration of rock strength based on energy dissipation and（2） the abrupt structural failure of rocks based on energy release.The critical stresses at the time of abrupt structural failure under various stress states can be determined by these criteria.As an example,the criteria have been used to analyze the failure conditions of surrounding rock of a circular tunnel.

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.

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.

Bearing capacity of foundation on slope determined by energy dissipation method and model experiments

To determine the ultimate bearing capacity of foundations on sloping ground surface in practice, energy dissipation method was used to formulate the beating capacity as programming problem, and full-scale model experiments were investigated to analyze the performance of the soil slopes loaded by a strip footing in laboratory. The soil failure is governed by a linear Mohr-Coulomb yield criterion, and soil deformation follows an associated flow rule. Based on the energy dissipation method of plastic mechanics, a multi-wedge translational failure mechanism was employed to obtain the three bearing capacity factors related to cohesion, equivalent surcharge load and the unit gravity for various slope inclination angles. Numerical results were compared with those of the published solutions using finite element method and those of model experiments. The bearing capacity factors were presented in the form of design charts for practical use in engineering. The results show that limit analysis solutions approximate to those of model tests, and that the energy dissipation method is effective to estimate bearing capacity of soil slope.

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.

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.