Debris flows in essence are the process of mass transportation controlled by the constitution featured by a wide-ranged distribution of grain size. Debris-flow samples of different densities collected from different r...Debris flows in essence are the process of mass transportation controlled by the constitution featured by a wide-ranged distribution of grain size. Debris-flow samples of different densities collected from different regions and gullies reveal that cumulative curve of grain composition, in particular for debris flows of high density, ρ5〉2 g/cm^3, can be fitted well by exponential function with exponents varying with regions and gullies. Debris flows fall into a narrow-valued domain of the exponent, as evidenced by Jiangjiagou Gully （JJG） with high occurrence frequency of debris flows. Furthermore, fractality of grain composition and porosity have been derived from cumulative curves in a certain size range, a range that determines the upper limit of grains constituting the matrix of debris flows. One can conclude that fractal structure of porosity plays crucial roles in soil fluidization that initiates debris flows, and debris flows occur at some range of fractal dimension, in coincidence with field observations.展开更多
On the basis of the basic model of the kinetic theory of aging of living systems,mathematical modeling of various characteristics of aging of mankind,state,generation,human body,organs and cells has been carried out.T...On the basis of the basic model of the kinetic theory of aging of living systems,mathematical modeling of various characteristics of aging of mankind,state,generation,human body,organs and cells has been carried out.These results are compared with experimental and calculated data of other authors.The analysis of the works presented here and those carried out earlier gave reason to believe that the basic mathematical model of the evolution of aging of living dynamic systems of various hierarchical levels and nature is the invariant differential equation of the kinetic theory of aging,as a manifestation of the fractality property of living systems.展开更多
<strong>Background:</strong> The basal metabolic rate has a scaling by tumor mass on the exponent of 3/4, while a simple surface-supplied volume of the mass would have a lower exponent, 2/3. The higher exp...<strong>Background:</strong> The basal metabolic rate has a scaling by tumor mass on the exponent of 3/4, while a simple surface-supplied volume of the mass would have a lower exponent, 2/3. The higher exponent can be explained by optimizing the overall energy distribution in the tumor, assuming that the target is four-dimensional. There are two possible ways of approximating the metabolic rate of the malignant tumor: 1) the volume blood-supply remains, but the surface and the length of the vessel network are modified;or 2) assuming that the malignant cell clusters try to maximize their metabolic rate to energize their proliferation by the longer length of the vessels. Our objective is to study how vascular fractality changes due to the greater demand for nutrients due to the proliferation of cancerous tissue. <strong>Results: </strong>It is shown that when a malignant tumor remains in expected four-dimensional volumetric conditions, it has a lower metabolic rate than the maximal metabolic potential in the actual demand of the proliferating cancer tissue. By maximizing the metabolic rate in malignant conditions, the allometric exponent will be smaller than 3/4, so the observed “dimensionality” of the metabolic rate versus mass becomes greater than four. The first growing period is exponential and keeps the “four-dimensional volume”, but the growth process turns to the sigmoidal phase in higher metabolic demand, and the tumor uses other optimizing strategies, further lowering the scaling exponent of metabolic rate. <strong>Conclusion:</strong> It is shown that a malignant cellular cluster changes its metabolic scaling exponent when maximizing its energy intake in various alimentary conditions.展开更多
We applied the Koch snowflake fractal antenna in planning calibration of the Five-hundred-meter Aperture Spherical radio Telescope(FAST), hypothesizing second-order fractal primary reflectors can optimize the orientat...We applied the Koch snowflake fractal antenna in planning calibration of the Five-hundred-meter Aperture Spherical radio Telescope(FAST), hypothesizing second-order fractal primary reflectors can optimize the orientated sensitivity of the telescope. Meanwhile, on the grounds of NASA Science Working Group Report in 1984, we reexamine the strategy of Search for Extraterrestrial Intelligence(SETI).A mathematical analysis of the radar equation will be performed in the first section, aiming to make it convenient to design a receiver system that can detect activities of an extraterrestrial civilization, according to the observable region of the narrowband. Taking advantage of the inherent potential of FAST, we simulate the theoretical detection of a Kardashev Type I civilization by a snowflake-selected reflecting area(Drake et al.).展开更多
Fracability is a critical indicator for evaluating the exploration and development potential of coalbed methane reservoirs and assessing the effectiveness of hydraulic fracturing stimulation operations.Its core functi...Fracability is a critical indicator for evaluating the exploration and development potential of coalbed methane reservoirs and assessing the effectiveness of hydraulic fracturing stimulation operations.Its core function is to characterize the complexity of the induced fracture network and the resulting effective stimulated volume.In this study,we quantified fracture area and geometric complexity using true triaxial fracturing experiments and computed tomography three-dimensional(3D)reconstruction technology,combined with the box-counting method to calculate the 3D fractal dimension of the fracture surfaces.The results revealed that the total fracture surface area per unit volume of the stimulated reservoir effectively characterized reservoir fracability;specifically,both a larger total fracture surface area and a higher fractal dimension corresponded to better reservoir fracability.Fracture complexity was enhanced by a decrease in the horizontal principal stress difference or an increase in the injection rate.Under optimal conditions of a 3 MPa stress difference and an injection rate of 60 mL/min,fracability improved by 27.6%.Furthermore,liquid carbon dioxide(CO_(2))improved fracability by 50.7%compared to using water as the fracturing fluid,a result attributed to its low viscosity and strong diffusion capacity,which activated a greater number of natural fractures.A fracability evaluation model integrating brittleness,fracture toughness,and dimensionless net pressure was developed using regression analysis,which demonstrated high reliability with a strong determination coefficient(R^(2))of 0.9019.This study clarifies the logical relationships among fracture area,complexity,and fractal dimension,providing a novel method for evaluating the fracability of coal reservoirs.展开更多
In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical m...In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical model,and its validity was verified using a simple impact test.A crushable discrete element method(DEM)framework is built based on the previously established theoretical model.The tensile strength,which considers the fractal theory,size effect,and Weibull variation,was assigned to each generated particle.The assigned strength is then used for crush detection by comparing it with its maximum tensile stress.Mass conservation is ensured by inserting a series of sub-particles whose total mass was equal to the quality loss.Based on the crushable DEM framework,a numerical simulation of the crushing behavior of a pebble bed with hollow cylindrical geometry under a uniaxial compression test was performed.The results of this investigation showed that the particle withstands the external load by contact and sliding at the beginning of the compression process,and the results confirmed that crushing can be considered an important method of resisting the increasing external load.A relatively regular particle arrangement aids in resisting the load and reduces the occurrence of particle crushing.However,a limit exists to the promotion of resistance.When the strain increases beyond this limit,the distribution of the crushing position tends to be isotropic over the entire pebble bed.The theoretical model and crushable DEM framework provide a new method for exploring the pebble bed in a fusion reactor,considering particle crushing.展开更多
To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with g...To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with graphene oxide(GO).The micro-pore structure of GOPM is characterized using LF-NMR and SEM.Fractal theory is applied to calculate the fractal dimension of pore volume,and the deterioration patterns are analyzed based on the evolution characteristics of capillary pores.The experimental results indicate that,after 25 salt-freeze-thaw cycles(SFTc),SO2-4 ions penetrate the matrix,generating corrosion products that fill existing pores and enhance the compactness of the specimen.As the number of cycles increases,the ongoing formation and expansion of corrosion products within the matrix,combined with persistent freezing forces,and result in the degradation of the pore structure.Therefore,the mass loss rate(MLR)of the specimens shows a trend of first decreasing and then increasing,while the relative dynamic elastic modulus(RDEM)initially increases and then decreases.Compared to the PC group specimens,the G3PM group specimens show a 28.71% reduction in MLR and a 31.42% increase in RDEM after 150 SFTc.The fractal dimensions of the transition pores,capillary pores,and macropores in the G3PM specimens first increase and then decrease as the number of SFTc increases.Among them,the capillary pores show the highest correlation with MLR and RDEM,with correlation coefficients of 0.97438 and 0.98555,respectively.展开更多
Driven by advancements in mobile internet technology,images have become a crucial data medium.Ensuring the security of image information during transmission has thus emerged as an urgent challenge.This study proposes ...Driven by advancements in mobile internet technology,images have become a crucial data medium.Ensuring the security of image information during transmission has thus emerged as an urgent challenge.This study proposes a novel image encryption algorithm specifically designed for grayscale image security.This research introduces a new Cantor diagonal matrix permutation method.The proposed permutation method uses row and column index sequences to control the Cantor diagonal matrix,where the row and column index sequences are generated by a spatiotemporal chaotic system named coupled map lattice(CML).The high initial value sensitivity of the CML system makes the permutation method highly sensitive and secure.Additionally,leveraging fractal theory,this study introduces a chaotic fractal matrix and applies this matrix in the diffusion process.This chaotic fractal matrix exhibits selfsimilarity and irregularity.Using the Cantor diagonal matrix and chaotic fractal matrix,this paper introduces a fast image encryption algorithm involving two diffusion steps and one permutation step.Moreover,the algorithm achieves robust security with only a single encryption round,ensuring high operational efficiency.Experimental results show that the proposed algorithm features an expansive key space,robust security,high sensitivity,high efficiency,and superior statistical properties for the ciphered images.Thus,the proposed algorithm not only provides a practical solution for secure image transmission but also bridges fractal theory with image encryption techniques,thereby opening new research avenues in chaotic cryptography and advancing the development of information security technology.展开更多
Internal structural defects in engineering rock masses vary in size,exhibit complex shapes,and are unevenly distributed.Dominant fractures within a rock mass often play a critical to its mechanical behavior,directly a...Internal structural defects in engineering rock masses vary in size,exhibit complex shapes,and are unevenly distributed.Dominant fractures within a rock mass often play a critical to its mechanical behavior,directly affecting the macromechanical properties and failure modes.These fractures affect the instability and failure of the surrounding rock,significantlyimpacting the overall stability of engineering structures.Herein,sand-powder three-dimensional(3D)printing technology was used to prepare rock-like specimens with internal fracture networks.Triaxial compression testing,post-failure fracture mapping,and fractal dimension analysis of the fracture surfaces were conducted to investigate the effects of dominant fracture angles on the strength and deformation of rocks with internal fracture networks under triaxial stress.The results indicate that the dominant fracture angle has a pronounced effect on the mechanical behavior of rock.With increasing angle,both compressive strength and elastic modulus exhibit an initial decline followed by an increase.Moreover,higher confiningpressure significantlyimproves the compressive strength of fractured rock.This enhancement weakens as the confiningpressure further increases.Moreover,with increasing confiningpressure,the differences between the maximum and minimum values of elastic moduli and lateral strain ratios in fractured rock gradually decrease.Thus,the impact of the dominant fracture angle on rock mass deformation decreases with increasing confiningpressure.This research elucidates the effects of dominant fracture angles on the mechanical and failure properties of complex fractured rock masses and the influenceof the confiningpressure on these relationships.It provides valuable theoretical insights and practical guidance for stability analyses in engineering rock masses.展开更多
Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and intro...Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and introducing CO_(2)nanobubble technology to improve the performance of cement-fly ash-based backfill materials(CFB).The properties including fluidity,setting time,uniaxial compressive strength,elastic modulus,porosity,microstructure and CO_(2)storage performance were systematically studied through methods such as fluidity evaluation,time test,uniaxial compression test,mercury intrusion porosimetry(MIP),scanning electron microscopy-energy dispersive spectroscopy analysis(SEM-EDS),and thermogravimetric-differential thermogravimetric analysis(TG-DTG).The experimental results show that the density and strength of the material are significantly improved under the synergistic effect of fractal dimension and CO_(2)nanobubbles.When the fractal dimension reaches 2.65,the mass ratio of coarse and fine aggregates reaches the optimal balance,and the structural density is greatly improved at the same time.At this time,the uniaxial compressive strength and elastic modulus reach their peak values,with increases of up to 13.46%and 27.47%,respectively.CO_(2)nanobubbles enhance the material properties by promoting hydration reaction and carbonization.At the microscopic level,CO_(2)nanobubble water promotes the formation of C-S-H(hydrated calcium silicate),C-A-S-H(hydrated calcium aluminium silicate)gel and CaCO_(3),which is the main way to enhance the performance.Thermogravimetric studies have shown that when the fractal dimension is 2.65,the dehydration of hydration products and the decarbonization process of CaCO_(3)are most obvious,and CO_(2)nanobubble water promotes the carbonization reaction,making it surpass the natural state.The CO_(2)sequestration quality of cement-fly ash-based materials treated with CO_(2)nanobubble water at different fractal dimensions increased by 12.4wt%to 99.8wt%.The results not only provide scientific insights for the design and implementation of low-carbon filling materials,but also provide a solid theoretical basis for strengthening green mining practices and promoting sustainable resource utilization.展开更多
Extensive engineering experience and research findings suggest that rock mass instability is typically attributed to human engineering activities and natural disturbances,resulting in general dynamic mechanical proper...Extensive engineering experience and research findings suggest that rock mass instability is typically attributed to human engineering activities and natural disturbances,resulting in general dynamic mechanical properties.This is attributed to external interference resulting from the extensive use of the mechanical and blasting techniques necessary for mineral extraction.Quantifying the impact of dynamic disturbances on rock deformation behavior is essential for comprehending the long-term response of surrounding rock during excavation.This study placed the rock to sustained pressure and investigated the impact of varying hammer heights and dry and wet(W-D)damage on its shear failure behavior.This study investigated the fatigue disturbance studies on W-D damaged sandstone samples via W-D equipment,a disturbance creep device,digital image correlation(DIC),and acoustic emission(AE)technology.The experimental findings suggest that acoustic emission sensors can be utilized to quantify the internal damage of rock samples during cyclic impact,whereas DIC technology(optical measurement)is capable of capturing the surface crack propagation of samples.Under repeated impact and the combined action of W-D conditions,the bearing capacity of sandstone decreases,whereas the deformation capacity increases.Furthermore,the W-D cycles and impact strength are inversely related to the fatigue life.The intensity of W-D damage and disturbances further accelerates the development and propagation of cracks under cyclic disturbances.The research results are of preventive significance to ensure the safety and sustainable development of engineering construction.展开更多
In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth su...In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack.In fact,the surface of a crack formed during the fracture is usually very irregular.So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one.Considering the irregularity of a real fracture surface or a real crack profile,the crack is taken as a fractal one,and then the real asymptotic form at the crack tip is developed by applying Griffith's energy balance principle and fractal geometry.Through the developed asymptotic form,it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.展开更多
The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution ki...The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution kinetics of primary carbides during either heating or soaking.Dissolution of carbides proceeded in three stages(fast→slow→faster)as either temperature or holding time was increased.During the heating process and during the first and third stages of the soaking process,the original size of the carbides determined the steepness of the slope,but during the middle(“slow”)stage of the soaking process,the slope remained zero.The initial size of the carbides varied greatly,but their final dissolution temperature fell within the narrow range of 1210-1235℃,and the holding time remained within 50 min.Fractal analysis was used to study the morphological characteristics of small and medium-sized carbides during the dissolution process.According to changes in the fractal dimension before and after soaking,the carbides tended to evolve towards a more regular morphology.展开更多
Low porosity is very significant for cementitious composite materials(CCM)under freeze-thaw conditions.To reduce the porosity of CCM,we used wollastonite mineral fibers as a partial replacement for cement and aggregat...Low porosity is very significant for cementitious composite materials(CCM)under freeze-thaw conditions.To reduce the porosity of CCM,we used wollastonite mineral fibers as a partial replacement for cement and aggregate.The five combinations,in which 10%,32%,and 48%Wollastonite were added,were made for scanning using both scanning electron microscopy(SEM)and computed tomography scan technology(CT).Then,the 2D SEM pictures and the 3D pore distribution curves are obtained before and after the freezing and thawing processes,where the micro-pores in the CCM materials are shown.The fractal dimension is used to quantify the topography image in two dimensions,as well as the pore distribution in three dimensions.This method allows for the determination of both surface porosity and volume porosity,both of which show an increase in response to an escalation of freeze-thaw cycles.It is also found that the micro-damage in the concrete is of self-similarity,and in the context of the fractal dimension,the pore evolution can be quantitatively characterized across different sizes,ranging from local to global levels,before and after freezing and thawing.展开更多
The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and...The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.展开更多
As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal...As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.展开更多
The accurate identification of microporosity is crucial for the characterization of hydrocarbon reservoir permeability and production.Scanning electron microscopy(SEM)is among the limited number of methods available t...The accurate identification of microporosity is crucial for the characterization of hydrocarbon reservoir permeability and production.Scanning electron microscopy(SEM)is among the limited number of methods available to directly observe the microscopic structure of the hydrocarbon reservoir rocks.Nevertheless,precise segmentation of microscopic pores at different depths in SEM images remains an unsolved challenge,known as the‘depth-related resolution loss'problem.Therefore,in this study,a 3D reconstruction technique for regions of interest(ROI)was developed for in-depth pixel analysis and differentiation among various depths of SEM images.The processed SEM images,together with the processing outcomes of this technique,were used as the input database to train a stochastic depth with multi-channel residual pathways(SdstMcrp)deep learning model programmed in Python to develop a tool for segmenting the microscopic pore spaces in SEM images obtained from the Beibuwan Basin.The more accurate segmentation helped to detect an average of 1.2 times more microporosity in SEM images,accounting for about 1.6 times more pixels and 1.2 times more pore surface area.Finally,the impact of the accurate segmentation on the calculation of permeability,a significant reservoir production property,was investigated using fractal geometry models and sensitivity analysis.The results showed that the obtained permeability values would vary by a factor of 6,which represents a considerable difference.These findings demonstrate that the proposed models can effectively identify features across a wide range of grayscale values in SEM images.展开更多
To investigate the effects of the maximum principal stress direction(θ)and cross-section shape on the failure characteristics of sandstone,true-triaxial compression experiments were conducted using cubic samples with...To investigate the effects of the maximum principal stress direction(θ)and cross-section shape on the failure characteristics of sandstone,true-triaxial compression experiments were conducted using cubic samples with rectangular,circular,and D-shaped holes.Asθincreases from 0°to 60°in the rectangular hole,the left failure location shifts from the left corner to the left sidewall,the left corner,and then the floor,while the right failure location shifts from the right corner to the right sidewall,right roof corner,and then the roof.Furthermore,the initial failure vertical stress first decreases and then increases.In comparison,the failure severity in the rectangular hole decreases for variousθvalues as 30°>45°>60°>0°.With increasingθ,the fractal dimension(D)of rock slices first increases and then decreases.For the rectangular and D-shaped holes,whenθ=0°,30°,and 90°,D for the rectangular hole is less than that of the D-shaped hole.Whenθ=45°and 60°,D for the rectangular hole is greater than that of the D-shaped hole.Theoretical analysis indicates that the stress concentration at the rectangular and D-shaped corners is greater than the other areas.The failure location rotates with the rotation ofθ,and the failure occurs on the side with a high concentration of compressive stress,while the side with the tensile and compressive stresses remains relatively stable.Therefore,the fundamental reason for the rotation of failure location is the rotation of stress concentration,and the external influencing factor is the rotation ofθ.展开更多
Insight into the growth of internal microstructure and surface morphology is critical for understanding the robustness of red sandstone artifacts in frigid environments.Since freeze–thaw(F-T)cycles can exacerbate the...Insight into the growth of internal microstructure and surface morphology is critical for understanding the robustness of red sandstone artifacts in frigid environments.Since freeze–thaw(F-T)cycles can exacerbate the surface deterioration of water-bearing sandstone,a series of investigation on fresh and weathered water-bearing sandstone samples with different F-T cycle numbers(i.e.0–100)is performed in this study,including three-dimensional(3D)laser scanning,scanning electron microscope(SEM)and computed tomography(CT)scanning tests,thermal property tests,Brazilian tests,and multi-field numerical simulations.Our results demonstrate that with increasing F-T cycles,the surface fractal dimension and specific surface area of red sandstone samples increase,and the pore size distribution inside rocks shifts from ultrananopores(10–100 nm)to micro-pores(0.1–100μm)and ultramicropores(100μm+).Spatially,the pores generated by the F-T cycles are more prominent near the surfaces of rock samples.Numerical simulation indicates that the uneven pore distribution leads to surface degradation.After 100 F-T cycles,the intergranular(IG)cement of the samples cracks,and the IG fractures are widened;eventually,due to the structural integrity weakening,the tensile strength is drastically reduced by over half.The thermal properties of the water-saturated sandstone can be improved during the F-T cycles,and a strong coefficient of determination of 0.98 exists between the fractal dimensions of sandstone surface and the tensile strength.When assessing the mechanical properties of stone artifacts under F-T cycles,the morphological damage of red sandstone should first be investigated when in situ sampling is inappropriate.展开更多
基金N ationalN aturalScience Foundation ofChina,N o.40101001N o.40025103
文摘Debris flows in essence are the process of mass transportation controlled by the constitution featured by a wide-ranged distribution of grain size. Debris-flow samples of different densities collected from different regions and gullies reveal that cumulative curve of grain composition, in particular for debris flows of high density, ρ5〉2 g/cm^3, can be fitted well by exponential function with exponents varying with regions and gullies. Debris flows fall into a narrow-valued domain of the exponent, as evidenced by Jiangjiagou Gully （JJG） with high occurrence frequency of debris flows. Furthermore, fractality of grain composition and porosity have been derived from cumulative curves in a certain size range, a range that determines the upper limit of grains constituting the matrix of debris flows. One can conclude that fractal structure of porosity plays crucial roles in soil fluidization that initiates debris flows, and debris flows occur at some range of fractal dimension, in coincidence with field observations.
文摘On the basis of the basic model of the kinetic theory of aging of living systems,mathematical modeling of various characteristics of aging of mankind,state,generation,human body,organs and cells has been carried out.These results are compared with experimental and calculated data of other authors.The analysis of the works presented here and those carried out earlier gave reason to believe that the basic mathematical model of the evolution of aging of living dynamic systems of various hierarchical levels and nature is the invariant differential equation of the kinetic theory of aging,as a manifestation of the fractality property of living systems.
文摘<strong>Background:</strong> The basal metabolic rate has a scaling by tumor mass on the exponent of 3/4, while a simple surface-supplied volume of the mass would have a lower exponent, 2/3. The higher exponent can be explained by optimizing the overall energy distribution in the tumor, assuming that the target is four-dimensional. There are two possible ways of approximating the metabolic rate of the malignant tumor: 1) the volume blood-supply remains, but the surface and the length of the vessel network are modified;or 2) assuming that the malignant cell clusters try to maximize their metabolic rate to energize their proliferation by the longer length of the vessels. Our objective is to study how vascular fractality changes due to the greater demand for nutrients due to the proliferation of cancerous tissue. <strong>Results: </strong>It is shown that when a malignant tumor remains in expected four-dimensional volumetric conditions, it has a lower metabolic rate than the maximal metabolic potential in the actual demand of the proliferating cancer tissue. By maximizing the metabolic rate in malignant conditions, the allometric exponent will be smaller than 3/4, so the observed “dimensionality” of the metabolic rate versus mass becomes greater than four. The first growing period is exponential and keeps the “four-dimensional volume”, but the growth process turns to the sigmoidal phase in higher metabolic demand, and the tumor uses other optimizing strategies, further lowering the scaling exponent of metabolic rate. <strong>Conclusion:</strong> It is shown that a malignant cellular cluster changes its metabolic scaling exponent when maximizing its energy intake in various alimentary conditions.
基金supported by the National Natural Science Foundation of China(Grant No.11929301)National Key R&D Program of China(2017YFA0402600)。
文摘We applied the Koch snowflake fractal antenna in planning calibration of the Five-hundred-meter Aperture Spherical radio Telescope(FAST), hypothesizing second-order fractal primary reflectors can optimize the orientated sensitivity of the telescope. Meanwhile, on the grounds of NASA Science Working Group Report in 1984, we reexamine the strategy of Search for Extraterrestrial Intelligence(SETI).A mathematical analysis of the radar equation will be performed in the first section, aiming to make it convenient to design a receiver system that can detect activities of an extraterrestrial civilization, according to the observable region of the narrowband. Taking advantage of the inherent potential of FAST, we simulate the theoretical detection of a Kardashev Type I civilization by a snowflake-selected reflecting area(Drake et al.).
基金supported by the Natural Science Foundation of China(Grant No.52574047 and Grant No.52374045)Key Project of Sichuan Provincial Joint Fund for Science Technology and Education,China(Grant No.2025NSFSC2008).
文摘Fracability is a critical indicator for evaluating the exploration and development potential of coalbed methane reservoirs and assessing the effectiveness of hydraulic fracturing stimulation operations.Its core function is to characterize the complexity of the induced fracture network and the resulting effective stimulated volume.In this study,we quantified fracture area and geometric complexity using true triaxial fracturing experiments and computed tomography three-dimensional(3D)reconstruction technology,combined with the box-counting method to calculate the 3D fractal dimension of the fracture surfaces.The results revealed that the total fracture surface area per unit volume of the stimulated reservoir effectively characterized reservoir fracability;specifically,both a larger total fracture surface area and a higher fractal dimension corresponded to better reservoir fracability.Fracture complexity was enhanced by a decrease in the horizontal principal stress difference or an increase in the injection rate.Under optimal conditions of a 3 MPa stress difference and an injection rate of 60 mL/min,fracability improved by 27.6%.Furthermore,liquid carbon dioxide(CO_(2))improved fracability by 50.7%compared to using water as the fracturing fluid,a result attributed to its low viscosity and strong diffusion capacity,which activated a greater number of natural fractures.A fracability evaluation model integrating brittleness,fracture toughness,and dimensionless net pressure was developed using regression analysis,which demonstrated high reliability with a strong determination coefficient(R^(2))of 0.9019.This study clarifies the logical relationships among fracture area,complexity,and fractal dimension,providing a novel method for evaluating the fracability of coal reservoirs.
基金supported by Anhui Provincial Natural Science Foundation(2408085QA030)Natural Science Research Project of Anhui Educational Committee,China(2022AH050825)+3 种基金Medical Special Cultivation Project of Anhui University of Science and Technology(YZ2023H2C008)the Excellent Research and Innovation Team of Anhui Province,China(2022AH010052)the Scientific Research Foundation for High-level Talents of Anhui University of Science and Technology,China(2021yjrc51)Collaborative Innovation Program of Hefei Science Center,CAS,China(2019HSC-CIP006).
文摘In this paper,a novel method for investigating the particle-crushing behavior of breeding particles in a fusion blanket is proposed.The fractal theory and Weibull distribution are combined to establish a theoretical model,and its validity was verified using a simple impact test.A crushable discrete element method(DEM)framework is built based on the previously established theoretical model.The tensile strength,which considers the fractal theory,size effect,and Weibull variation,was assigned to each generated particle.The assigned strength is then used for crush detection by comparing it with its maximum tensile stress.Mass conservation is ensured by inserting a series of sub-particles whose total mass was equal to the quality loss.Based on the crushable DEM framework,a numerical simulation of the crushing behavior of a pebble bed with hollow cylindrical geometry under a uniaxial compression test was performed.The results of this investigation showed that the particle withstands the external load by contact and sliding at the beginning of the compression process,and the results confirmed that crushing can be considered an important method of resisting the increasing external load.A relatively regular particle arrangement aids in resisting the load and reduces the occurrence of particle crushing.However,a limit exists to the promotion of resistance.When the strain increases beyond this limit,the distribution of the crushing position tends to be isotropic over the entire pebble bed.The theoretical model and crushable DEM framework provide a new method for exploring the pebble bed in a fusion reactor,considering particle crushing.
基金Funded by the National Natural Science Foundation of China(Nos.5226804252468035)。
文摘To investigate the pore structure of graphene oxide modified polymer cement mortar(GOPM)under salt-freeze-thaw(SFT)coupling effects and its impact on deterioration,this study modifies polymer cement mortar(EMCM)with graphene oxide(GO).The micro-pore structure of GOPM is characterized using LF-NMR and SEM.Fractal theory is applied to calculate the fractal dimension of pore volume,and the deterioration patterns are analyzed based on the evolution characteristics of capillary pores.The experimental results indicate that,after 25 salt-freeze-thaw cycles(SFTc),SO2-4 ions penetrate the matrix,generating corrosion products that fill existing pores and enhance the compactness of the specimen.As the number of cycles increases,the ongoing formation and expansion of corrosion products within the matrix,combined with persistent freezing forces,and result in the degradation of the pore structure.Therefore,the mass loss rate(MLR)of the specimens shows a trend of first decreasing and then increasing,while the relative dynamic elastic modulus(RDEM)initially increases and then decreases.Compared to the PC group specimens,the G3PM group specimens show a 28.71% reduction in MLR and a 31.42% increase in RDEM after 150 SFTc.The fractal dimensions of the transition pores,capillary pores,and macropores in the G3PM specimens first increase and then decrease as the number of SFTc increases.Among them,the capillary pores show the highest correlation with MLR and RDEM,with correlation coefficients of 0.97438 and 0.98555,respectively.
基金supported by the National Natural Science Foundation of China(62376106)The Science and Technology Development Plan of Jilin Province(20250102212JC).
文摘Driven by advancements in mobile internet technology,images have become a crucial data medium.Ensuring the security of image information during transmission has thus emerged as an urgent challenge.This study proposes a novel image encryption algorithm specifically designed for grayscale image security.This research introduces a new Cantor diagonal matrix permutation method.The proposed permutation method uses row and column index sequences to control the Cantor diagonal matrix,where the row and column index sequences are generated by a spatiotemporal chaotic system named coupled map lattice(CML).The high initial value sensitivity of the CML system makes the permutation method highly sensitive and secure.Additionally,leveraging fractal theory,this study introduces a chaotic fractal matrix and applies this matrix in the diffusion process.This chaotic fractal matrix exhibits selfsimilarity and irregularity.Using the Cantor diagonal matrix and chaotic fractal matrix,this paper introduces a fast image encryption algorithm involving two diffusion steps and one permutation step.Moreover,the algorithm achieves robust security with only a single encryption round,ensuring high operational efficiency.Experimental results show that the proposed algorithm features an expansive key space,robust security,high sensitivity,high efficiency,and superior statistical properties for the ciphered images.Thus,the proposed algorithm not only provides a practical solution for secure image transmission but also bridges fractal theory with image encryption techniques,thereby opening new research avenues in chaotic cryptography and advancing the development of information security technology.
基金supported by the National Key Research and Development Program Young Scientist Project(Grant No.2024YFC2911000)the National Natural Science Foundation of China(Grant No.52474103)the Major Basic Research Project of the Natural Science Foundation of Shandong Province(Grant No.ZR2024ZD22).
文摘Internal structural defects in engineering rock masses vary in size,exhibit complex shapes,and are unevenly distributed.Dominant fractures within a rock mass often play a critical to its mechanical behavior,directly affecting the macromechanical properties and failure modes.These fractures affect the instability and failure of the surrounding rock,significantlyimpacting the overall stability of engineering structures.Herein,sand-powder three-dimensional(3D)printing technology was used to prepare rock-like specimens with internal fracture networks.Triaxial compression testing,post-failure fracture mapping,and fractal dimension analysis of the fracture surfaces were conducted to investigate the effects of dominant fracture angles on the strength and deformation of rocks with internal fracture networks under triaxial stress.The results indicate that the dominant fracture angle has a pronounced effect on the mechanical behavior of rock.With increasing angle,both compressive strength and elastic modulus exhibit an initial decline followed by an increase.Moreover,higher confiningpressure significantlyimproves the compressive strength of fractured rock.This enhancement weakens as the confiningpressure further increases.Moreover,with increasing confiningpressure,the differences between the maximum and minimum values of elastic moduli and lateral strain ratios in fractured rock gradually decrease.Thus,the impact of the dominant fracture angle on rock mass deformation decreases with increasing confiningpressure.This research elucidates the effects of dominant fracture angles on the mechanical and failure properties of complex fractured rock masses and the influenceof the confiningpressure on these relationships.It provides valuable theoretical insights and practical guidance for stability analyses in engineering rock masses.
基金financially supported by the China Scholarship Council(CSC)。
文摘Mine filling materials urgently need to improve mechanical properties and achieve low-carbon transformation.This study explores the mechanism of the synergistic effect of optimizing aggregate fractal grading and introducing CO_(2)nanobubble technology to improve the performance of cement-fly ash-based backfill materials(CFB).The properties including fluidity,setting time,uniaxial compressive strength,elastic modulus,porosity,microstructure and CO_(2)storage performance were systematically studied through methods such as fluidity evaluation,time test,uniaxial compression test,mercury intrusion porosimetry(MIP),scanning electron microscopy-energy dispersive spectroscopy analysis(SEM-EDS),and thermogravimetric-differential thermogravimetric analysis(TG-DTG).The experimental results show that the density and strength of the material are significantly improved under the synergistic effect of fractal dimension and CO_(2)nanobubbles.When the fractal dimension reaches 2.65,the mass ratio of coarse and fine aggregates reaches the optimal balance,and the structural density is greatly improved at the same time.At this time,the uniaxial compressive strength and elastic modulus reach their peak values,with increases of up to 13.46%and 27.47%,respectively.CO_(2)nanobubbles enhance the material properties by promoting hydration reaction and carbonization.At the microscopic level,CO_(2)nanobubble water promotes the formation of C-S-H(hydrated calcium silicate),C-A-S-H(hydrated calcium aluminium silicate)gel and CaCO_(3),which is the main way to enhance the performance.Thermogravimetric studies have shown that when the fractal dimension is 2.65,the dehydration of hydration products and the decarbonization process of CaCO_(3)are most obvious,and CO_(2)nanobubble water promotes the carbonization reaction,making it surpass the natural state.The CO_(2)sequestration quality of cement-fly ash-based materials treated with CO_(2)nanobubble water at different fractal dimensions increased by 12.4wt%to 99.8wt%.The results not only provide scientific insights for the design and implementation of low-carbon filling materials,but also provide a solid theoretical basis for strengthening green mining practices and promoting sustainable resource utilization.
基金supported by National Natural Science Foundation of China(Grant Nos.52364004 and 52264006)The Youth Talent Growth Project of Guizhou Provincial Department of Education(Grant No.QianJiaoJi[2024]18).
文摘Extensive engineering experience and research findings suggest that rock mass instability is typically attributed to human engineering activities and natural disturbances,resulting in general dynamic mechanical properties.This is attributed to external interference resulting from the extensive use of the mechanical and blasting techniques necessary for mineral extraction.Quantifying the impact of dynamic disturbances on rock deformation behavior is essential for comprehending the long-term response of surrounding rock during excavation.This study placed the rock to sustained pressure and investigated the impact of varying hammer heights and dry and wet(W-D)damage on its shear failure behavior.This study investigated the fatigue disturbance studies on W-D damaged sandstone samples via W-D equipment,a disturbance creep device,digital image correlation(DIC),and acoustic emission(AE)technology.The experimental findings suggest that acoustic emission sensors can be utilized to quantify the internal damage of rock samples during cyclic impact,whereas DIC technology(optical measurement)is capable of capturing the surface crack propagation of samples.Under repeated impact and the combined action of W-D conditions,the bearing capacity of sandstone decreases,whereas the deformation capacity increases.Furthermore,the W-D cycles and impact strength are inversely related to the fatigue life.The intensity of W-D damage and disturbances further accelerates the development and propagation of cracks under cyclic disturbances.The research results are of preventive significance to ensure the safety and sustainable development of engineering construction.
基金Supported by the National Natural Science Foundation of China(Grant Nos.50539030,50539010,50539110 and 50579010)the National Science and Technology Supporting Program(Grant No.2006BAC14B03)the National Science Foundation of Hohai University(Grant No.2008426811)
文摘In the classic theory of fracture mechanics,expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack.In fact,the surface of a crack formed during the fracture is usually very irregular.So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one.Considering the irregularity of a real fracture surface or a real crack profile,the crack is taken as a fractal one,and then the real asymptotic form at the crack tip is developed by applying Griffith's energy balance principle and fractal geometry.Through the developed asymptotic form,it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.
基金supported by Independent Research Project of State Key Laboratory of Advanced Special Steel,Shanghai Key Laboratory of Advanced Ferrometallurgy,Shanghai University(SKLASS-2023-Z13)the Science and Technology Commission of Shanghai Municipality(No.19DZ2270200)+1 种基金A portion of the work was performed at US National High Magnetic Field Laboratory,which is supported by the National Science Foundation(Cooperative Agreement No.DMR-1157490 and DMR-1644779)the State of Florida.Thanks also to Mary Tyler for editing.
文摘The high-temperature dissolution behavior of primary carbides in samples taken from GCr15 continuous-casting bloom was observed in-situ by confocal laser scanning microscopy.Equations were fitted to the dissolution kinetics of primary carbides during either heating or soaking.Dissolution of carbides proceeded in three stages(fast→slow→faster)as either temperature or holding time was increased.During the heating process and during the first and third stages of the soaking process,the original size of the carbides determined the steepness of the slope,but during the middle(“slow”)stage of the soaking process,the slope remained zero.The initial size of the carbides varied greatly,but their final dissolution temperature fell within the narrow range of 1210-1235℃,and the holding time remained within 50 min.Fractal analysis was used to study the morphological characteristics of small and medium-sized carbides during the dissolution process.According to changes in the fractal dimension before and after soaking,the carbides tended to evolve towards a more regular morphology.
文摘Low porosity is very significant for cementitious composite materials(CCM)under freeze-thaw conditions.To reduce the porosity of CCM,we used wollastonite mineral fibers as a partial replacement for cement and aggregate.The five combinations,in which 10%,32%,and 48%Wollastonite were added,were made for scanning using both scanning electron microscopy(SEM)and computed tomography scan technology(CT).Then,the 2D SEM pictures and the 3D pore distribution curves are obtained before and after the freezing and thawing processes,where the micro-pores in the CCM materials are shown.The fractal dimension is used to quantify the topography image in two dimensions,as well as the pore distribution in three dimensions.This method allows for the determination of both surface porosity and volume porosity,both of which show an increase in response to an escalation of freeze-thaw cycles.It is also found that the micro-damage in the concrete is of self-similarity,and in the context of the fractal dimension,the pore evolution can be quantitatively characterized across different sizes,ranging from local to global levels,before and after freezing and thawing.
基金supported by the Guangdong Province Introduced Innovative R&D Team of Big Data-Mathematical Earth Sciences and Extreme Geological Events Team(grant number 2021ZT09H399)the National Natural Science Foundation of China(grant number 42430111,42050103).
文摘The investigations of physical attributes of oceans,including parameters such as heat flow and bathymetry,have garnered substantial attention and are particularly valuable for examining Earth’s thermal structures and dynamic processes.Nevertheless,classical plate cooling models exhibit disparities when predicting observed heat flow and seafloor depth for extremely young and old lithospheres.Furthermore,a comprehensive analysis of global heat flow predictions and regional ocean heat flow or bathymetry data with physical models has been lacking.In this study,we employed power-law models derived from the singularity theory of fractal density to meticulously fit the latest ocean heat flow and bathymetry.Notably,power-law models offer distinct advantages over traditional plate cooling models,showcasing robust self-similarity,scale invariance,or scaling properties,and providing a better fit to observed data.The outcomes of our singularity analysis concerning heat flow and bathymetry across diverse oceanic regions exhibit a degree of consistency with the global ocean spreading rate model.In addition,we applied the similarity method to predict a higher resolution(0.1°×0.1°)global heat flow map based on the most recent heat flow data and geological/geophysical observables refined through linear correlation analysis.Regions displaying significant disparities between predicted and observed heat flow are closely linked to hydrothermal vent fields and active structures.Finally,combining the actual bathymetry and predicted heat flow with the power-law models allows for the quantitative and comprehensive detection of anomalous regions of ocean subsidence and heat flow,which deviate from traditional plate cooling models.The anomalous regions of subsidence and heat flow show different degrees of anisotropy,providing new ideas and clues for further analysis of ocean topography or hydrothermal circulation of mid-ocean ridges.
基金financially supported by the National Key R&D Program of China(No.2022YFE0121300)the National Natural Science Foundation of China(No.52374376)the Introduction Plan for High-end Foreign Experts(No.G2023105001L)。
文摘As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future.
基金the Natural Science Foundation of Shandong Province of China(Nos.ZR2022QD080 , ZR2025MS575)the National Natural Science Foundation of China(Nos.W25322063,42250410333,52250410357)+1 种基金the Fundamental Research Funds for the Central Universities,CHD(No.300102263103)the Young Talent Fund of Association for Science and Technology in Shaanxi,China(No.20230703)。
文摘The accurate identification of microporosity is crucial for the characterization of hydrocarbon reservoir permeability and production.Scanning electron microscopy(SEM)is among the limited number of methods available to directly observe the microscopic structure of the hydrocarbon reservoir rocks.Nevertheless,precise segmentation of microscopic pores at different depths in SEM images remains an unsolved challenge,known as the‘depth-related resolution loss'problem.Therefore,in this study,a 3D reconstruction technique for regions of interest(ROI)was developed for in-depth pixel analysis and differentiation among various depths of SEM images.The processed SEM images,together with the processing outcomes of this technique,were used as the input database to train a stochastic depth with multi-channel residual pathways(SdstMcrp)deep learning model programmed in Python to develop a tool for segmenting the microscopic pore spaces in SEM images obtained from the Beibuwan Basin.The more accurate segmentation helped to detect an average of 1.2 times more microporosity in SEM images,accounting for about 1.6 times more pixels and 1.2 times more pore surface area.Finally,the impact of the accurate segmentation on the calculation of permeability,a significant reservoir production property,was investigated using fractal geometry models and sensitivity analysis.The results showed that the obtained permeability values would vary by a factor of 6,which represents a considerable difference.These findings demonstrate that the proposed models can effectively identify features across a wide range of grayscale values in SEM images.
基金supported by the National Natural Science Foundation of China (Grant Nos.52304227 and 52104133)Scientific and Technological Research Platform for Disaster Prevention and Control of Deep Coal Mining (Anhui University of Science and Technology) (Grant No.DPDCM2208).
文摘To investigate the effects of the maximum principal stress direction(θ)and cross-section shape on the failure characteristics of sandstone,true-triaxial compression experiments were conducted using cubic samples with rectangular,circular,and D-shaped holes.Asθincreases from 0°to 60°in the rectangular hole,the left failure location shifts from the left corner to the left sidewall,the left corner,and then the floor,while the right failure location shifts from the right corner to the right sidewall,right roof corner,and then the roof.Furthermore,the initial failure vertical stress first decreases and then increases.In comparison,the failure severity in the rectangular hole decreases for variousθvalues as 30°>45°>60°>0°.With increasingθ,the fractal dimension(D)of rock slices first increases and then decreases.For the rectangular and D-shaped holes,whenθ=0°,30°,and 90°,D for the rectangular hole is less than that of the D-shaped hole.Whenθ=45°and 60°,D for the rectangular hole is greater than that of the D-shaped hole.Theoretical analysis indicates that the stress concentration at the rectangular and D-shaped corners is greater than the other areas.The failure location rotates with the rotation ofθ,and the failure occurs on the side with a high concentration of compressive stress,while the side with the tensile and compressive stresses remains relatively stable.Therefore,the fundamental reason for the rotation of failure location is the rotation of stress concentration,and the external influencing factor is the rotation ofθ.
基金supported by the National Natural Science Foundation of China(Grant Nos.41772304 and 42277171).
文摘Insight into the growth of internal microstructure and surface morphology is critical for understanding the robustness of red sandstone artifacts in frigid environments.Since freeze–thaw(F-T)cycles can exacerbate the surface deterioration of water-bearing sandstone,a series of investigation on fresh and weathered water-bearing sandstone samples with different F-T cycle numbers(i.e.0–100)is performed in this study,including three-dimensional(3D)laser scanning,scanning electron microscope(SEM)and computed tomography(CT)scanning tests,thermal property tests,Brazilian tests,and multi-field numerical simulations.Our results demonstrate that with increasing F-T cycles,the surface fractal dimension and specific surface area of red sandstone samples increase,and the pore size distribution inside rocks shifts from ultrananopores(10–100 nm)to micro-pores(0.1–100μm)and ultramicropores(100μm+).Spatially,the pores generated by the F-T cycles are more prominent near the surfaces of rock samples.Numerical simulation indicates that the uneven pore distribution leads to surface degradation.After 100 F-T cycles,the intergranular(IG)cement of the samples cracks,and the IG fractures are widened;eventually,due to the structural integrity weakening,the tensile strength is drastically reduced by over half.The thermal properties of the water-saturated sandstone can be improved during the F-T cycles,and a strong coefficient of determination of 0.98 exists between the fractal dimensions of sandstone surface and the tensile strength.When assessing the mechanical properties of stone artifacts under F-T cycles,the morphological damage of red sandstone should first be investigated when in situ sampling is inappropriate.
