Influence of water coupling coefficient on the blasting effect of red sandstone specimens

This study investigates the impact of different water coupling coefficients on the blasting effect of red sandstone.The analysis is based on the theories of detonation wave and elastic wave,focusing on the variation in wall pressure of the blasting holes.Using DDNP explosive as the explosive load,blasting tests were conducted on red sandstone specimens with four different water coupling coefficients:1.20,1.33,1.50,and 2.00.The study examines the morphologies of the rock specimens after blasting under these different water coupling coefficients.Additionally,the fractal dimensions of the surface cracks resulting from the blasting were calculated to provide a quantitative evaluation of the extent of rock damage.CT scanning and 3D reconstruction were performed on the post-blasting specimens to visually depict the extent of damage and fractures within the rock.Additionally,the volume fractal dimension and damage degree of the post-blasting specimens are calculated.The findings are then combined with numerical simulation to facilitate auxiliary analysis.The results demonstrate that an increase in the water coupling coefficient leads to a reduction in the peak pressure on the hole wall and the crushing zone,enabling more of the explosion energy to be utilized for crack propagation following the explosion.The specimens exhibited distinct failure patterns,resulting in corresponding changes in fractal dimensions.The simulated pore wall pressure–time curve validated the derived theoretical results,whereas the stress cloud map and explosion energy-time curve demonstrated the buffering effect of the water medium.As the water coupling coefficient increases,the buffering effect of the water medium becomes increasingly prominent.

Distribution and dynamics of niche and interspecific association of dominant phytoplankton species in the Feiyun River basin,Zhejiang,China

To investigate the dominant species and interspecific association in the phytoplankton community of the Feiyun River basin in Zhejiang Province,East China,the main stream and the Shanxi Zhaoshandu Reservoir in the downstream were chosen as the study area,for which 22 sampling sites were designated.Sampling was conducted in September 2021,January,May,and July 2022.Phytoplankton species were identified from both quantitative samples and in-vivo observations.Phytoplankton was quantified by direct counting.Results show that there were 98 species belonging to 6 phyla and 78 genera.In addition,to clarify the niches of the dominant phytoplankton species and their interspecific association,the dominance index was calculated,and a comprehensive analysis was conducted including niche width,niche overlap value,ecological response rate,overall association,chi-square test,and the stability.The phytoplankton community exhibited characteristics of a Cyanobacteria-Chlorophyta-Diatom type community,showing higher diversity in spring and lower diversity in summer.Among 11 dominants phytoplankton species from 3 phyla,both frequency and dominance degree varied seasonally,of which Microcystis sp.was the dominant species in Spring,Autumn,and Winter.The niche widths of the dominant species ranged from 0.234 to 0.933,and were categorized into three groups.The niche overlap values of the 11 dominant species ranged from 0.359 to 0.959,exhibiting significant seasonal differences-highest in winter followed by autumn,spring,and summer in turn.The overall correlation among dominant species in all four seasons revealed a non-significant negative association,resulting in an unstable community structure.A significant portion(84.2%)of species pairs displayed positive associations,suggesting a successional pattern where Diatoms dominated while other dominant species shared resources and space.Despite this pattern,stability measurements indicated that the dominant species community remained unstable.Therefore,careful monitoring is recommended for potential water environment issues arising from abnormal proliferation of dominant species in the watershed during winter.This research built a theoretical foundation with a data support to the early warning of eutrophication and provided a reference for water resources management in similar watersheds along the eastern coast of China.

Prediction of Coefficient of Restitution for Impact Elastoplastic Spheres Considering Finite Plate Thickness

Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of restitution is a critical parameter in the analysis of collision processes.Many experiments have shown that the coefficient of restitution is closely related to the plate thickness,and the smaller the plate thickness,the more inaccurate the coefficient of restitution predicted by the existing model,which seriously affects the process of collision analysis.To remedy this shortcoming,this paper proposes a plate thickness influence factor with the ratio of sphere diameter to plate thickness as the variable.The plate thickness influence factor can optimize the coefficient of restitution model to effectively predict the coefficient of restitution of impacting elastoplastic spheres with finite plate thickness.Finally,the validity of the new model is verified using a large amount of experimental data.

Species’ geographical range, environmental range and traits lead to specimen collection preference of dominant plant species of grasslands in Northern China

Many different factors,such as species traits,socio-economic factors,geographical and environmental factors,can lead to specimen collection preference.This study aims to determine whether grassland specimen collection in China is preferred by species traits(i.e.,plant height,flowering and fruiting period),environmental range(i.e.,the temperature and precipitation range)and geographical range(i.e.,distribution range and altitudinal range).Ordinary least squares models and phylogenetic generalized linear mixed models were used to analyze the relationships between specimen number and the explanatory variables.Random Forest models were then used to find the most parsimonious multivariate model.The results showed that interannual variation in specimen number between 1900 and 2020 was considerable.Specimen number of these species in southeast China was notably lower than that in northwest China.Environmental range and geographical range of species had significant positive correlations with specimen number.In addition,there were relatively weak but significant associations between specimen number and species trait(i.e.,plant height and flowering and fruiting period).Random Forest models indicated that distribution range was the most important variable,followed by flowering and fruiting period,and altitudinal range.These findings suggest that future floristic surveys should pay more attention to species with small geographical range,narrow environmental range,short plant height,and short flowering and fruiting period.The correction of specimen collection preference will also make the results of species distribution model,species evolution and other works based on specimen data more accurate.

Complex adaptive system theory,agent-based modeling,and simulation in dominant technology formation

Dominant technology formation is the key for the hightech industry to“cross the chasm”and gain an established foothold in the market(and hence disrupt the regime).Therefore,a stimulus-response model is proposed to investigate the dominant technology by exploring its formation process and mechanism.Specifically,based on complex adaptive system theory and the basic stimulus-response model,we use a combination of agent-based modeling and system dynamics modeling to capture the interactions between dominant technology and the socio-technical landscape.The results indicate the following:(i)The dynamic interaction is“stimulus-reaction-selection”,which promotes the dominant technology’s formation.(ii)The dominant technology’s formation can be described as a dynamic process in which the adaptation intensity of technology standards increases continuously until it becomes the leading technology under the dual action of internal and external mechanisms.(iii)The dominant technology’s formation in the high-tech industry is influenced by learning ability,the number of adopting users and adaptability.Therein,a“critical scale”of learning ability exists to promote the formation of leading technology:a large number of adopting users can promote the dominant technology’s formation by influencing the adaptive response of technology standards to the socio-technical landscape and the choice of technology standards by the socio-technical landscape.There is a minimum threshold and a maximum threshold for the role of adaptability in the dominant technology’s formation.(iv)The socio-technical landscape can promote the leading technology’s shaping in the high-tech industry,and different elements have different effects.This study promotes research on the formation mechanism of dominant technology in the high-tech industry,presents new perspectives and methods for researchers,and provides essential enlightenment for managers to formulate technology strategies.

ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS

We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.

Global stability coefficient of large underground caverns under static loading and earthquake wave condition

Underground energy and resource development,deep underground energy storage and other projects involve the global stability of multiple interconnected cavern groups under internal and external dynamic disturbances.An evaluation method of the global stability coefficient of underground caverns based on static overload and dynamic overload was proposed.Firstly,the global failure criterion for caverns was defined based on its band connection of plastic-strain between multi-caverns.Then,overloading calculation of the boundary geostress and seismic intensity on the caverns model was carried out,and the critical unstable state of multi-caverns can be identified,if the plastic-strain band appeared between caverns during these overloading processes.Thus,the global stability coefficient for the multi-caverns under static loading and earthquake was obtained based on the corresponding overloading coefficient.Practical analysis for the Yingliangbao(YLB)hydraulic caverns indicated that this method can not only effectively obtain the global stability coefficient of caverns under static and dynamic earthquake conditions,but also identify the caverns’high-risk zone of local instability through localized plastic strain of surrounding rock.This study can provide some reference for the layout design and seismic optimization of underground cavern group.

Dominant woody plant species recognition with a hierarchical model based on multimodal geospatial data for subtropical forests

Since the launch of the Google Earth Engine(GEE)cloud platform in 2010,it has been widely used,leading to a wealth of valuable information.However,the potential of GEE for forest resource management has not been fully exploited.To extract dominant woody plant species,GEE combined Sen-tinel-1(S1)and Sentinel-2(S2)data with the addition of the National Forest Resources Inventory(NFRI)and topographic data,resulting in a 10 m resolution multimodal geospatial dataset for subtropical forests in southeast China.Spectral and texture features,red-edge bands,and vegetation indices of S1 and S2 data were computed.A hierarchical model obtained information on forest distribution and area and the dominant woody plant species.The results suggest that combining data sources from the S1 winter and S2 yearly ranges enhances accuracy in forest distribution and area extraction compared to using either data source independently.Similarly,for dominant woody species recognition,using S1 winter and S2 data across all four seasons was accurate.Including terrain factors and removing spatial correlation from NFRI sample points further improved the recognition accuracy.The optimal forest extraction achieved an overall accuracy(OA)of 97.4%and a maplevel image classification efficacy(MICE)of 96.7%.OA and MICE were 83.6%and 80.7%for dominant species extraction,respectively.The high accuracy and efficacy values indicate that the hierarchical recognition model based on multimodal remote sensing data performed extremely well for extracting information about dominant woody plant species.Visualizing the results using the GEE application allows for an intuitive display of forest and species distribution,offering significant convenience for forest resource monitoring.

Comparison of transport coefficients before and after density pump-out induced by resonant magnetic perturbation using a BOUT++ six-field model on the EAST tokamak

Many experiments have demonstrated that resonant magnetic perturbation(RMP) can affect the turbulent transport at the edge of the tokamak. Through the Experimental Advanced Superconducting Tokamak(EAST) density modulation experiment, the particle transport coefficients were calculated using the experimental data, and the result shows that the particle transport coefficients increase with RMP. In this study, the six-field two-fluid model in BOUT++ is used to simulate the transport before and after density pump-out induced by RMP,respectively referred as the case without RMP and the case with RMP. In the linear simulations,the instabilities generally decreases for cases with RMP. In the nonlinear simulation, ELM only appears in the case without RMP. Additionally, the particle transport coefficient was analyzed,and the result shows that the particle transport coefficient becomes larger for the case with RMP,which is consistent with the experimental conclusion. Moreover, its magnitude is comparable to the results calculated from experimental data.

Molecular Dynamics, Diffusion Coefficients and Activation Energy of the Electrolyte (Anode) in Lithium (Li and Li+), Sodium (Na and Na+) and Potassium (K and K+)

This work is a simulation modelling with the LAMMPS calculation code of an electrode based on alkali metals (lithium, sodium and potassium) using the MEAM potential. For different multiplicities, two models were studied;with and without gap. In this work, we present the structural, physical and chemical properties of the lithium, sodium and potassium electrodes. For the structural properties, the cohesive energy and the mesh parameters were calculated, revealing that, whatever the chemical element selected, the compact hexagonal hcp structure is the most stable, followed by the face-centred cubic CFC structure, and finally the BCC structure. The most stable structure is lithium, with a cohesion energy of -6570 eV, and the lowest bcc-hcp transition energy of -0.553 eV/atom, followed by sodium. For physical properties, kinetic and potential energies were calculated for each of the sectioned chemical elements, with lithium achieving the highest value. Finally, for the chemical properties, we studied the diffusion coefficient and the activation energy. Only potassium followed an opposite order to the other two, with the quantities with lacunae being greater than those without lacunae, whatever the multiplicity. The order of magnitude of the diffusion coefficients is given by the relationship DLi > DNa > Dk for the multiplicity 6*6*6, while for the activation energy the order is reversed.

Particle residence time distribution and axial dispersion coefficient in a pressurized circulating fluidized bed by using multiphase particle-in-cell simulation

The particle residence time distribution(RTD)and axial dispersion coefficient are key parameters for the design and operation of a pressurized circulating fluidized bed(PCFB).In this study,the effects of pressure(0.1-0.6 MPa),fluidizing gas velocity(2-7 m·s^(-1)),and solid circulation rate(10-90 kg·m^(-2)·s^(-1))on particle RTD and axial dispersion coefficient in a PCFB are numerically investigated based on the multiphase particle-in-cell(MP-PIC)method.The details of the gas-solid flow behaviors of PCFB are revealed.Based on the gas-solid flow pattern,the particles tend to move more orderly under elevated pressures.With an increase in either fluidizing gas velocity or solid circulation rate,the mean residence time of particles decreases while the axial dispersion coefficient increases.With an increase in pressure,the core-annulus flow is strengthened,which leads to a wider shape of the particle RTD curve and a larger mean particle residence time.The back-mixing of particles increases with increasing pressure,resulting in an increase in the axial dispersion coefficient.

GCAGA: A Gini Coefficient-Based Optimization Strategy for Computation Offloading in Multi-User-Multi-Edge MEC System

To support the explosive growth of Information and Communications Technology(ICT),Mobile Edge Comput-ing(MEC)provides users with low latency and high bandwidth service by offloading computational tasks to the network’s edge.However,resource-constrained mobile devices still suffer from a capacity mismatch when faced with latency-sensitive and compute-intensive emerging applications.To address the difficulty of running computationally intensive applications on resource-constrained clients,a model of the computation offloading problem in a network consisting of multiple mobile users and edge cloud servers is studied in this paper.Then a user benefit function EoU(Experience of Users)is proposed jointly considering energy consumption and time delay.The EoU maximization problem is decomposed into two steps,i.e.,resource allocation and offloading decision.The offloading decision is usually given by heuristic algorithms which are often faced with the challenge of slow convergence and poor stability.Thus,a combined offloading algorithm,i.e.,a Gini coefficient-based adaptive genetic algorithm(GCAGA),is proposed to alleviate the dilemma.The proposed algorithm optimizes the offloading decision by maximizing EoU and accelerates the convergence with the Gini coefficient.The simulation compares the proposed algorithm with the genetic algorithm(GA)and adaptive genetic algorithm(AGA).Experiment results show that the Gini coefficient and the adaptive heuristic operators can accelerate the convergence speed,and the proposed algorithm performs better in terms of convergence while obtaining higher EoU.The simulation code of the proposed algorithm is available:https://github.com/Grox888/Mobile_Edge_Computing/tree/GCAGA.

Safety and efficacy of transcatheter arterial embolization in autosomal dominant polycystic kidney patients with gross hematuria: Six case reports

BACKGROUND To retrospectively report the safety and efficacy of renal transcatheter arterial embolization for treating autosomal dominant polycystic kidney disease(ADPKD)patients with gross hematuria.CASE SUMMARY The purpose of this study is to retrospectively report the safety and efficacy of renal transcatheter arterial embolization for treating ADPKD patients with gross hematuria.Materials and methods:During the period from January 2018 to December 2019,renal transcatheter arterial embolization was carried out on 6 patients with polycystic kidneys and gross hematuria.Renal arteriography was performed first,and then we determined the location of the hemorrhage and performed embolization under digital subtraction angiography monitoring.Improvements in routine blood test results,routine urine test results,urine color and postoperative reactions were observed and analyzed.Results:Renal transcatheter arterial embolization was successfully conducted in 6 patients.The indices of 5 patients and the color of gross hematuria improved after surgery compared with before surgery.No severe complication reactions occurred.CONCLUSION For autosomal dominant polycystic kidney syndrome patients with gross hematuria,transcatheter arterial embolization was safe and effective.

Incidental renal cell carcinoma post bilateral nephrectomy in autosomal dominant polycystic kidney disease

BACKGROUND Renal cell carcinoma(RCC)is more common in patients with autosomal dominant polycystic kidney disease(ADPKD)than in the general population.Diagnosing RCC in ADPKD is challenging due to the presence of multiple renal cysts,often leading to delays and difficulties in distinguishing RCC from cyst infection or hemorrhage.A total of 38 kidneys were excised from 19 patients,with a mean age of 56.8 years and an average hemodialysis duration of 84.2 months.Eight patients underwent open nephrectomies,and 11 underwent hand-assisted laparoscopic nephrec-tomies.RCC was detected in 15.8%of kidneys,affecting 21.1%of patients.Two patients had multifocal RCC in both kidneys.All RCC cases were pT1 stage,with the largest lesion averaging 16.5 mm in diameter.The average operative duration was 120 minutes,with intraoperative blood loss averaging 184.2 mL.Five patients required blood transfusions.Postoperative complications occurred in five patients,with a mean hospital stay of 17.1 days.The mean follow-up period was 28.1 months.CONCLUSION The prevalence of RCC is higher in patients with ADPKD with ESRD than in those with ESRD alone.Thus,clinicians should be cautious and implement surveillance programs to monitor the development of RCC in patients with ADPKD,particularly those on dialysis.

The medium-temperature dependence of jet transport coefficient in high-energy nucleus-nucleus collisions

The medium-temperature T dependence of the jet transport coefficient̂q was studied via the nuclear modification factor RAA(p_(T))and elliptical flow parameter v_(2)(p_(T))for large transverse momentum p_(T) hadrons in high-energy nucleus-nucleus collisions.Within a next-to-leading-order perturbative QCD parton model for hard scatterings with modified fragmentation functions due to jet quenching controlled by q,we check the suppression and azimuthal anisotropy for large p_(T) hadrons,and extract q by global fits to RAA(pT)and v_(2)(pT)data in A+A collisions at RHIC and LHC,respectively.The numerical results from the best fits show that q∕T^(3) goes down with local medium-temperature T in the parton jet trajectory.Compared with the case of a constant q∕T^(3),the going-down T dependence of q∕T^(3) makes a hard parton jet to lose more energy near T_(c) and therefore strengthens the azimuthal anisotropy for large pT hadrons.As a result,v_(2)(p_(T))for large pT hadrons was enhanced by approximately 10%to better fit the data at RHIC/LHC.Considering the first-order phase transition from QGP to the hadron phase and the additional energy loss in the hadron phase,v_(2)(p_(T))is again enhanced by 5-10%at RHIC/LHC.

Normalized glandular dose coefficients for digital breast tomosynthesis using detailed Chinese breast models

The rise in breast cancer diagnoses among Chinese women has necessitated the use of X-ray breast screening,which carries a radiation risk.This study aimed to provide a dosimetry protocol for the Chinese female population to replace the traditional standard that utilizes simplified breast models,for the accurate estimation of the mean glandular dose of a patient undergoing digital breast tomosynthesis(DBT).The first set of detailed Chinese female breast models and representative breast parameters was constructed.Considering backscatter radiation and computational efficiency,we improved the combination of these models and the Chinese reference adult female whole-body voxel phantom.Image acquisition for four commercial DBT systems that are widely employed in China was simulated using the Monte Carlo method to obtain the normalized glandular dose coefficients of DBT(D_(gN)^(DBT))and the glandular depth dose(D_(g)^(dep)(z))for different breast characteristics and X-ray spectra.We calculated a series of D_(gN)^(DBT) values for breasts with different percentage mass glandularities(5%,25%,50%,75%,and 100%)and compressed breast thicknesses(2,3,4,5,6,and 7 cm)at various tube potentials(25,28,30,32,35,and 49 kV)and target/filter combinations(W/Rh,W/Al,Mo/Mo,Rh/Rh,and Rh/Ag).The parameter dependence of the breast characteristics and beam conditions on D_(gN)^(DBT) in detailed breast models was investigated.The D_(gN)^(DBT) results were 14.6-51.0%lower than those of the traditional dosimetry standard in China.The difference in D_(gN)^(DBT) was mainly due to a decrease in the depth of the main energy deposition area caused by the glandular distribution along the depth direction.The results obtained in this study may be used to improve breast dosimetry in China and provide more detailed information on risk assessment during DBT.

Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

Quantifying the Role of the Eddy Transfer Coefficient in Simulating the Response of the Southern Ocean Meridional Overturning Circulation to Enhanced Westerlies in a Coarse-resolution Model

This study assesses the capability of a coarse-resolution ocean model to replicate the response of the Southern Ocean Meridional Overturning Circulation(MOC) to intensified westerlies,focusing on the role of the eddy transfer coefficient(κ).κ is a parameter commonly used to represent the velocities induced by unresolved eddies.Our findings reveal that a stratification-dependent κ,incorporating spatiotemporal variability,leads to the most robust eddy-induced MOC response,capturing 82% of the reference eddy-resolving simulation.Decomposing the eddy-induced velocity into its vertical variation(VV) and spatial structure(SS) components unveils that the enhanced eddy compensation response primarily stems from an augmented SS term,while the introduced VV term weakens the response.Furthermore,the temporal variability of the stratification-dependent κ emerges as a key factor in enhancing the eddy compensation response to intensified westerlies.The experiment with stratification-dependent κ exhibits a more potent eddy compensation response compared to the constant κ,attributed to the structure of κ and the vertical variation of the density slope.These results underscore the critical role of accurately representing κ in capturing the response of the Southern Ocean MOC and emphasize the significance of the isopycnal slope in modulating the eddy compensation mechanism.

Adaptive Random Effects/Coefficients Modeling

Adaptive fractional polynomial modeling of general correlated outcomes is formulated to address nonlinearity in means, variances/dispersions, and correlations. Means and variances/dispersions are modeled using generalized linear models in fixed effects/coefficients. Correlations are modeled using random effects/coefficients. Nonlinearity is addressed using power transforms of primary (untransformed) predictors. Parameter estimation is based on extended linear mixed modeling generalizing both generalized estimating equations and linear mixed modeling. Models are evaluated using likelihood cross-validation (LCV) scores and are generated adaptively using a heuristic search controlled by LCV scores. Cases covered include linear, Poisson, logistic, exponential, and discrete regression of correlated continuous, count/rate, dichotomous, positive continuous, and discrete numeric outcomes treated as normally, Poisson, Bernoulli, exponentially, and discrete numerically distributed, respectively. Example analyses are also generated for these five cases to compare adaptive random effects/coefficients modeling of correlated outcomes to previously developed adaptive modeling based on directly specified covariance structures. Adaptive random effects/coefficients modeling substantially outperforms direct covariance modeling in the linear, exponential, and discrete regression example analyses. It generates equivalent results in the logistic regression example analyses and it is substantially outperformed in the Poisson regression case. Random effects/coefficients modeling of correlated outcomes can provide substantial improvements in model selection compared to directly specified covariance modeling. However, directly specified covariance modeling can generate competitive or substantially better results in some cases while usually requiring less computation time.

Evaluation of the coefficient of lateral stress at rest of granular materials under repetitive loading conditions

Although the internal stress state of soils can be affected by repetitive loading,there are few studies evaluating the lateral stress(or K_(0))of soils under repetitive loading.This study investigates the changes in K_(0) and directional shear wave velocity(V_(s))in samples of two granular materials with different particle shapes during repetitive loading.A modified oedometer cell equipped with bender elements and a diaphragm transducer was developed to measure the variations in the lateral stress and the shear wave velocity,under repetitive loading on the loading and unloading paths.The study produced the following results:(1)Repetitive loading on the loading path resulted in an increase in the K_(0) of test samples as a function of cyclic loading number(i),and(2)Repetitive loading on the unloading path resulted in a decrease in K_(0) according to i.The shear wave velocity ratio(i.e.V_(s)(HH)/V_(s)(VH),where the first and second letters in parentheses corresponds to the directions of wave propagation and particle motion,respectively,and V and H corresponds to the vertical and horizontal directions,respectively)according to i supports the experimental observations of this study.However,when the tested material was in lightly over-consolidated state,there was an increase in K_(0) during repetitive loading,indicating that it was the initial K_(0),rather than the loading path,which is responsible for the change in K_(0).The power model can capture the variation in the K_(0) of samples according to i.Notably,the K_(0)=1 line acts as the boundary between the increase and decrease in K_(0) under repetitive loading.