Gobi spans a large area of China,surpassing the combined expanse of mobile dunes and semi-fixed dunes.Its presence significantly influences the movement of sand and dust.However,the complex origins and diverse materia...Gobi spans a large area of China,surpassing the combined expanse of mobile dunes and semi-fixed dunes.Its presence significantly influences the movement of sand and dust.However,the complex origins and diverse materials constituting the Gobi result in notable differences in saltation processes across various Gobi surfaces.It is challenging to describe these processes according to a uniform morphology.Therefore,it becomes imperative to articulate surface characteristics through parameters such as the three-dimensional(3D)size and shape of gravel.Collecting morphology information for Gobi gravels is essential for studying its genesis and sand saltation.To enhance the efficiency and information yield of gravel parameter measurements,this study conducted field experiments in the Gobi region across Dunhuang City,Guazhou County,and Yumen City(administrated by Jiuquan City),Gansu Province,China in March 2023.A research framework and methodology for measuring 3D parameters of gravel using point cloud were developed,alongside improved calculation formulas for 3D parameters including gravel grain size,volume,flatness,roundness,sphericity,and equivalent grain size.Leveraging multi-view geometry technology for 3D reconstruction allowed for establishing an optimal data acquisition scheme characterized by high point cloud reconstruction efficiency and clear quality.Additionally,the proposed methodology incorporated point cloud clustering,segmentation,and filtering techniques to isolate individual gravel point clouds.Advanced point cloud algorithms,including the Oriented Bounding Box(OBB),point cloud slicing method,and point cloud triangulation,were then deployed to calculate the 3D parameters of individual gravels.These systematic processes allow precise and detailed characterization of individual gravels.For gravel grain size and volume,the correlation coefficients between point cloud and manual measurements all exceeded 0.9000,confirming the feasibility of the proposed methodology for measuring 3D parameters of individual gravels.The proposed workflow yields accurate calculations of relevant parameters for Gobi gravels,providing essential data support for subsequent studies on Gobi environments.展开更多
The 2D limit equilibrium method is widely used for slope stability analysis.However,with the advancement of dump engineering,composite slopes often exhibit significant 3D mechanical effects.Consequently,it is of signi...The 2D limit equilibrium method is widely used for slope stability analysis.However,with the advancement of dump engineering,composite slopes often exhibit significant 3D mechanical effects.Consequently,it is of significant importance to develop an effective 3D stability calculation method for composite slopes to enhance the design and stability control of open-pit slope engineering.Using the composite slope formed by the mining stope and inner dump in Baiyinhua No.1 and No.2 open-pit coal mine as a case study,this research investigates the failure mode of composite slopes and establishes spatial shape equations for the sliding mass.By integrating the shear resistance and sliding force of each row of microstrip columns onto the bottom surface of the strip corresponding to the main sliding surface,a novel 2D equivalent physical and mechanical parameters analysis method for the strips on the main sliding surface of 3D sliding masses is proposed.Subsequently,a comprehensive 3D stability calculation method for composite slopes is developed,and the quantitative relationship between the coordinated development distance and its 3D stability coefficients is examined.The analysis reveals that the failure mode of the composite slope is characterized by cutting-bedding sliding,with the arc serving as the side interface and the weak layer as the bottom interface,while the destabilization mechanism primarily involves shear failure.The spatial form equation of the sliding mass comprises an ellipsoid and weak plane equation.The analysis revealed that when the coordinated development distance is 1500 m,the error rate between the 3D stability calculation result and the 2D stability calculation result of the composite slope is less than 8%,thereby verifying the proposed analytical method of equivalent physical and mechanical parameters and the 3D stability calculation method for composite slopes.Furthermore,the3D stability coefficient of the composite slope exhibits an exponential correlation with the coordinated development distance,with the coefficient gradually decreasing as the coordinated development distance increases.These findings provide a theoretical guideline for designing similar slope shape parameters and conducting stability analysis.展开更多
Background: As the population age structure gradually ages, more and more elderly people were found to have pulmonary nodules during physical examinations. Most elderly people had underlying diseases such as heart, lu...Background: As the population age structure gradually ages, more and more elderly people were found to have pulmonary nodules during physical examinations. Most elderly people had underlying diseases such as heart, lung, brain and blood vessels and cannot tolerate surgery. Computed tomography (CT)-guided percutaneous core needle biopsy (CNB) was the first choice for pathological diagnosis and subsequent targeted drugs, immune drugs or ablation treatment. CT-guided percutaneous CNB requires clinicians with rich CNB experience to ensure high CNB accuracy, but it was easy to cause complications such as pneumothorax and hemorrhage. Three-dimensional (3D) printing coplanar template (PCT) combined with CT-guided percutaneous pulmonary CNB biopsy has been used in clinical practice, but there was no prospective, randomized controlled study. Methods: Elderly patients with lung nodules admitted to the Department of Oncology of our hospital from January 2019 to January 2023 were selected. A total of 225 elderly patients were screened, and 30 patients were included after screening. They were randomly divided into experimental group (Group A: 30 cases) and control group (Group B: 30 cases). Group A was given 3D-PCT combined with CT-guided percutaneous pulmonary CNB biopsy, Group B underwent CT-guided percutaneous pulmonary CNB. The primary outcome measure of this study was the accuracy of diagnostic CNB, and the secondary outcome measures were CNB time, number of CNB needles, number of pathological tissues and complications. Results: The diagnostic accuracy of group A and group B was 96.67% and 76.67%, respectively (P = 0.026). There were statistical differences between group A and group B in average CNB time (P = 0.001), number of CNB (1 vs more than 1, P = 0.029), and pathological tissue obtained by CNB (3 vs 1, P = 0.040). There was no statistical difference in the incidence of pneumothorax and hemorrhage between the two groups (P > 0.05). Conclusions: 3D-PCT combined with CT-guided percutaneous CNB can improve the puncture accuracy of elderly patients, shorten the puncture time, reduce the number of punctures, and increase the amount of puncture pathological tissue, without increasing pneumothorax and hemorrhage complications. We look forward to verifying this in a phase III randomized controlled clinical study. .展开更多
Three-dimensional(3D) synthetic aperture radar(SAR)extends the conventional 2D images into 3D features by several acquisitions in different aspects. Compared with 3D techniques via multiple observations in elevation, ...Three-dimensional(3D) synthetic aperture radar(SAR)extends the conventional 2D images into 3D features by several acquisitions in different aspects. Compared with 3D techniques via multiple observations in elevation, e.g. SAR interferometry(InSAR) and SAR tomography(TomoSAR), holographic SAR can retrieve 3D structure by observations in azimuth. This paper focuses on designing a novel type of orbit to achieve SAR regional all-azimuth observation(AAO) for embedded targets detection and holographic 3D reconstruction. The ground tracks of the AAO orbit separate the earth surface into grids. Target in these grids can be accessed with an azimuth angle span of360°, which is similar to the flight path of airborne circular SAR(CSAR). Inspired from the successive coverage orbits of optical sensors, several optimizations are made in the proposed method to ensure favorable grazing angles, the performance of 3D reconstruction, and long-term supervision for SAR sensors. Simulation experiments show the regional AAO can be completed within five hours. In addition, a second AAO of the same area can be duplicated in two days. Finally, an airborne SAR data process result is presented to illustrate the significance of AAO in 3D reconstruction.展开更多
Light field 3D display technology is considered a revolutionary technology to address the critical visual fatigue issues in the existing 3D displays.Tabletop light field 3D display provides a brand-new display form th...Light field 3D display technology is considered a revolutionary technology to address the critical visual fatigue issues in the existing 3D displays.Tabletop light field 3D display provides a brand-new display form that satisfies multi-user shared viewing and collaborative works,and it is poised to become a potential alternative to the traditional wall and portable display forms.However,a large radial viewing angle and correct radial perspective and parallax are still out of reach for most current tabletop light field 3D displays due to the limited amount of spatial information.To address the viewing angle and perspective issues,a novel integral imaging-based tabletop light field 3D display with a simple flat-panel structure is proposed and developed by applying a compound lens array,two spliced 8K liquid crystal display panels,and a light shaping diffuser screen.The compound lens array is designed to be composed of multiple three-piece compound lens units by employing a reverse design scheme,which greatly extends the radial viewing angle in the case of a limited amount of spatial information and balances other important 3D display parameters.The proposed display has a radial viewing angle of 68.7°in a large display size of 43.5 inches,which is larger than the conventional tabletop light field 3D displays.The radial perspective and parallax are correct,and high-resolution 3D images can be reproduced in large radial viewing positions.We envision that this proposed display opens up possibility for redefining the display forms of consumer electronics.展开更多
The shear failure of intact rock under thermo-mechanical(TM)coupling conditions is common,such as in enhanced geothermal mining and deep mine construction.Under the effect of a continuous engineering disturbance,shear...The shear failure of intact rock under thermo-mechanical(TM)coupling conditions is common,such as in enhanced geothermal mining and deep mine construction.Under the effect of a continuous engineering disturbance,shear-formed fractures are prone to secondary instability,posing a severe threat to deep engineering.Although numerous studies regarding three-dimensional(3D)morphologies of fracture surfaces have been conducted,the understanding of shear-formed fractures under TM coupling conditions is limited.In this study,direct shear tests of intact granite under various TM coupling conditions were conducted,followed by 3D laser scanning tests of shear-formed fractures.Test results demonstrated that the peak shear strength of intact granite is positively correlated with the normal stress,whereas it is negatively correlated with the temperature.The internal friction angle and cohesion of intact granite significantly decrease with an increase in the temperature.The anisotropy,roughness value,and height of the asperities on the fracture surfaces are reduced as the normal stress increases,whereas their variation trends are the opposite as the temperature increases.The macroscopic failure mode of intact granite under TM coupling conditions is dominated by mixed tensileeshear and shear failures.As the normal stress increases,intragranular fractures are developed ranging from a local to a global distribution,and the macroscopic failure mode of intact granite changes from mixed tensileeshear to shear failure.Finally,3D morphological characteristics of the asperities on the shear-formed fracture surfaces were analyzed,and a quadrangular pyramid conceptual model representing these asperities was proposed and sufficiently verified.展开更多
This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is...This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.展开更多
To reduce the computing time of composite computer-generated holograms (CGHs) gen- eration based upon the angular projection algorithm for holographic three-dimensional (3D) display, a grid-based holographic displ...To reduce the computing time of composite computer-generated holograms (CGHs) gen- eration based upon the angular projection algorithm for holographic three-dimensional (3D) display, a grid-based holographic display ( GHD ) scheme was designed. The grid computing technology was applied to numerically process the different angular projections of an object in distributed-parallel manner to create the corresponding CGHs. The whole treatment of a projection was regarded as a job executed on the grid node machine. The number of jobs which were submitted to grid nodes, therefore, was equal to that of the projections of the object. A Condor-based grid testbed was constructed to verify the feasibility of the GHD scheme, and a graphical user interface (GUI) program and several service modules were developed for it. A 3D terrain model as an example was processed on the testbed. The result showed that the scheme was feasible and able to improve the execution elficiency greatly.展开更多
Adhesions between different cells and extracellular matrix have been studied extensively in vitro, but little is known about their functions in testicular tissue counterparts. Spermatogonia and their companion somatic...Adhesions between different cells and extracellular matrix have been studied extensively in vitro, but little is known about their functions in testicular tissue counterparts. Spermatogonia and their companion somatic cells maintain a close association throughout spermatogenesis and this association is necessary for normal spermatogenesis. In order to keep the relative integrity of the testicular tissues, and to detect the development in vitro, culture testicular tissues in a three- dimensional (3D) agarose matrix was examined. Testicular tissues isolated from 6.5 d postpartum (dpp) mouse were cultured on the top of the matrix for 26 d with a medium height up to 4/5 of the 3D agarose matrix. The results showed that in this 3D culture environment, each type of testicular cells kept the same structure, localization and function as in vivo and might be more biologically relevant to living organisms. After culture, germ cell marker VASA and meiosis markers DAZL and SCP3 showed typical positive analysed by immunofluorescence staining and RT-PCR. It demonstrated that this 3D culture system was able to maintain the number of germ cells and promote the meiosis initiation of male germ cells.展开更多
To model a true three-dimensional(3D)display system,we introduced the method of voxel molding to obtain the stereoscopic imaging space of the system.For the distribution of each voxel,we proposed a four-dimensional(4D...To model a true three-dimensional(3D)display system,we introduced the method of voxel molding to obtain the stereoscopic imaging space of the system.For the distribution of each voxel,we proposed a four-dimensional(4D)Givone–Roessor(GR)model for state-space representation—that is,we established a local state-space model with the 3D position and one-dimensional time coordi-nates to describe the system.First,we extended the original elementary operation approach to a 4D condition and proposed the implementation steps of the realiza-tion matrix of the 4D GR model.Then,we described the working process of a true 3D display system,analyzed its real-time performance,introduced the fixed-point quantization model to simplify the system matrix,and derived the conditions for the global asymptotic stability of the system after quantization.Finally,we provided an example to prove the true 3D display system’s feasibility by simulation.The GR-model-representation method and its implementation steps proposed in this paper simplified the system’s mathematical expression and facilitated the microcon-troller software implementation.Real-time and stability analyses can be used widely to analyze and design true 3D display systems.展开更多
The mechanical characteristics of crystalline rocks are affected by the heterogeneity of the spatial distribution of minerals.In this paper,a novel three-dimensional(3D)grain-based model(GBM)based on particle flow cod...The mechanical characteristics of crystalline rocks are affected by the heterogeneity of the spatial distribution of minerals.In this paper,a novel three-dimensional(3D)grain-based model(GBM)based on particle flow code(PFC),i.e.PFC3D-GBM,is proposed.This model can accomplish the grouping of mineral grains at the 3D scale and then filling them.Then,the effect of the position distribution,geometric size,and volume composite of mineral grains on the cracking behaviour and macroscopic properties of granite are examined by conducting Brazilian splitting tests.The numerical results show that when an external load is applied to a sample,force chains will form around each contact,and the orientation distribution of the force chains is uniform,which is independent of the external load level.Furthermore,the number of high-strength force chains is proportional to the external load level,and the main orientation distribution is consistent with the external loading direction.The main orientation of the cracks is vertical to that of the high-strength force chains.The geometric size of the mineral grains controls the mechanical behaviours.As the average grain size increases,the number of transgranular contacts with higher bonding strength in the region connecting both loading points increases.The number of high-strength force chains increases,leading to an increase in the stress concentration value required for the macroscopic failure of the sample.Due to the highest bonding strength,the generation of transgranular cracks in quartz requires a higher concentrated stress value.With increasing volume composition of quartz,the number of transgranular cracks in quartz distributed in the region connecting both loading points increases,which requires many high-strength force chains.The load level rises,leading to an increase in the tensile strength of the numerical sample.展开更多
Virtual reality(VR)and augmented reality(AR)are revolutionizing our lives.Near-eye displays are crucial technologies for VR and AR.Despite the rapid advances in near-eye display technologies,there are still challenges...Virtual reality(VR)and augmented reality(AR)are revolutionizing our lives.Near-eye displays are crucial technologies for VR and AR.Despite the rapid advances in near-eye display technologies,there are still challenges such as large field of view,high resolution,high image quality,natural free 3D effect,and compact form factor.Great efforts have been devoted to striking a balance between visual performance and device compactness.While traditional optics are nearing their limitations in addressing these challenges,ultra-thin metasurface optics,with their high light-modulating capabilities,may present a promising solution.In this review,we first introduce VR and AR near-eye displays,and then briefly explain the working principles of light-modulating metasurfaces,review recent developments in metasurface devices geared toward near-eye display applications,delved into several advanced natural 3D near-eye display technologies based on metasurfaces,and finally discuss about the remaining challenges and future perspectives associated with metasurfaces for near-eye display applications.展开更多
In airborne array synthetic aperture radar(SAR), the three-dimensional(3D) imaging performance and cross-track resolution depends on the length of the equivalent array. In this paper, Barker sequence criterion is used...In airborne array synthetic aperture radar(SAR), the three-dimensional(3D) imaging performance and cross-track resolution depends on the length of the equivalent array. In this paper, Barker sequence criterion is used for sparse flight sampling of airborne array SAR, in order to obtain high cross-track resolution in as few times of flights as possible. Under each flight, the imaging algorithm of back projection(BP) and the data extraction method based on modified uniformly redundant arrays(MURAs) are utilized to obtain complex 3D image pairs. To solve the side-lobe noise in images, the interferometry between each image pair is implemented, and compressed sensing(CS) reconstruction is adopted in the frequency domain. Furthermore, to restore the geometrical relationship between each flight, the phase information corresponding to negative MURA is compensated on each single-pass image reconstructed by CS. Finally,by coherent accumulation of each complex image, the high resolution in cross-track direction is obtained. Simulations and experiments in X-band verify the availability.展开更多
A switchable autostereoscopic 3-dimensional(3D) display device with wide color gamut is introduced in this paper. In conjunction with a novel directional quantum-dot(QD) backlight, the precise scanning control strateg...A switchable autostereoscopic 3-dimensional(3D) display device with wide color gamut is introduced in this paper. In conjunction with a novel directional quantum-dot(QD) backlight, the precise scanning control strategy, and the eye-tracking system, this spatial-sequential solution enables our autostereoscopic display to combine all the advantages of full resolution,wide color gamut, low crosstalk, and switchable 2D/3D. And also, we fabricated an autostereoscopic display prototype and demonstrated its performances effectively. The results indicate that our system can both break the limitation of viewing position and provide high-quality 3D images. We present two working modes in this system. In the spatial-sequential mode,the crosstalk is about 6%. In the time-multiplexed mode, the viewer should wear auxiliary and the crosstalk is about 1%,just next to that of a commercial 3D display(BENQ XL2707-B and View Sonic VX2268 WM). Additionally, our system is also completely compatible with active shutter glasses and its 3D resolution is same as its 2D resolution. Because of the excellent properties of the QD material, the color gamut can be widely extended to 77.98% according to the ITU-R recommendation BT.2020(Rec.2020).展开更多
Due to seasonal climate alterations,the microstructure and permeability of granite residual soil are easily affected by multiple dry-wet cycles.The X-ray micro computed tomography(micro-CT)acted as a nondestructive to...Due to seasonal climate alterations,the microstructure and permeability of granite residual soil are easily affected by multiple dry-wet cycles.The X-ray micro computed tomography(micro-CT)acted as a nondestructive tool for characterizing the microstructure of soil samples exposed to a range of damage levels induced by dry-wet cycles.Subsequently,the variations of pore distribution and permeability due to drywet cycling effects were revealed based on three-dimensional(3D)pore distribution analysis and seepage simulations.According to the results,granite residual soils could be separated into four different components,namely,pores,clay,quartz,and hematite,from micro-CT images.The reconstructed 3D pore models dynamically demonstrated the expanding and connecting patterns of pore structures during drywet cycles.The values of porosity and connectivity are positively correlated with the number of dry-wet cycles,which were expressed by exponential and linear functions,respectively.The pore volume probability distribution curves of granite residual soil coincide with the χ^(2)distribution curve,which verifies the effectiveness of the assumption of χ^(2)distribution probability.The pore volume distribution curves suggest that the pores in soils were divided into four types based on their volumes,i.e.micropores,mesopores,macropores,and cracks.From a quantitative and visual perspective,considerable small pores are gradually transformed into cracks with a large volume and a high connectivity.Under the action of dry-wet cycles,the number of seepage flow streamlines which contribute to water permeation in seepage simulation increases distinctly,as well as the permeability and hydraulic conductivity.The calculated hydraulic conductivity is comparable with measured ones with an acceptable error margin in general,verifying the accuracy of seepage simulations based on micro-CT results.展开更多
Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional (3D) icosahedral quasicrystals are dis- cussed by a complex variable function method. For th...Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional (3D) icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.展开更多
In the last two decades,significant research has been conducted in the field of automated extraction of rock mass discontinuity characteristics from three-dimensional(3D)models.This provides several methodologies for ...In the last two decades,significant research has been conducted in the field of automated extraction of rock mass discontinuity characteristics from three-dimensional(3D)models.This provides several methodologies for acquiring discontinuity measurements from 3D models,such as point clouds generated using laser scanning or photogrammetry.However,even with numerous automated and semiautomated methods presented in the literature,there is not one single method that can automatically characterize discontinuities accurately in a minimum of time.In this paper,we critically review all the existing methods proposed in the literature for the extraction of discontinuity characteristics such as joint sets and orientations,persistence,joint spacing,roughness and block size using point clouds,digital elevation maps,or meshes.As a result of this review,we identify the strengths and drawbacks of each method used for extracting those characteristics.We found that the approaches based on voxels and region growing are superior in extracting joint planes from 3D point clouds.Normal tensor voting with trace growth algorithm is a robust method for measuring joint trace length from 3D meshes.Spacing is estimated by calculating the perpendicular distance between joint planes.Several independent roughness indices are presented to quantify roughness from 3D surface models,but there is a need to incorporate these indices into automated methodologies.There is a lack of efficient algorithms for direct computation of block size from 3D rock mass surface models.展开更多
Dithering optimization techniques can be divided into the phase-optimized technique and the intensity-optimized technique. The problem with the former is the poor sensitivity to various defocusing amounts, and the pro...Dithering optimization techniques can be divided into the phase-optimized technique and the intensity-optimized technique. The problem with the former is the poor sensitivity to various defocusing amounts, and the problem with the latter is that it cannot enhance phase quality directly nor efficiently. In this paper, we present a multi-objective optimization framework for three-dimensional(3D) measurement by utilizing binary defocusing technique. Moreover, a binary patch optimization technique is used to solve the time-consuming issue of genetic algorithm. It is demonstrated that the presented technique consistently obtains significant phase performance improvement under various defocusing amounts.展开更多
The smooth convex generalized failure function, which represents 1/6 part of envelope in tile deviatoric plane, is proposed. The proposed function relies on four shape parameters (L, a, b and c), in which two parame...The smooth convex generalized failure function, which represents 1/6 part of envelope in tile deviatoric plane, is proposed. The proposed function relies on four shape parameters (L, a, b and c), in which two parameters (a and b) are dependent on the others. The parameter Ls is called extension ratio. The proposed failure function could be incorporated with any two-dimensional (2D) failure criteria to make it a three-dimensional (3D) version. In this paper, a mathematical formulation for incorporation of Hoek-Brown failure criterion with the proposed function is presented. The Hoek-Brown failure criterion is the most suited 2D failure criterion tbr geomaterials. Two types of analyses for best-fitting solution of published true tri-axial test data were made by considering (1) constant extension ratio and (2) variable extension ratio. The shape and strength parameters for different types of rocks have been determined by best-fitting the published true tri-axial test data for both the analyses. It is observed from the best-fitting solution by considering uniform extension ratio (L~) that shape constants have a correlation with Hoek-Brown strength parameters. Thus, only two parameters (c~. and m) are needed for representing the 3D failure criterion for intact rock. The statistical expression between shape and Hoek-Brown strength parameters is given. In the second analysis, when considering varying extension ratio, another parameterfis introduced. The modified extension ratio is related tofand extension ratio. The results at minimum mean misfit for all the nine rocks indicate that the range off varies from 0.7 to 1.0. It is found that mean misfit by considering varying extension ratio is lower than that in the first analysis. But it requires three parameters. A statistical expression betweenfand Hoek-Brown strength parameters has been established. Though coefficient of correlation is not reasonable, we may eliminate it as an extra parameter. At the end of the paper, a methodology has also been given for its application to isotropic jointed rock mass, so that it can be implemented in a numerical code for stability analysis of jointed rock mass structures.展开更多
基金funded by the National Natural Science Foundation of China(42071014).
文摘Gobi spans a large area of China,surpassing the combined expanse of mobile dunes and semi-fixed dunes.Its presence significantly influences the movement of sand and dust.However,the complex origins and diverse materials constituting the Gobi result in notable differences in saltation processes across various Gobi surfaces.It is challenging to describe these processes according to a uniform morphology.Therefore,it becomes imperative to articulate surface characteristics through parameters such as the three-dimensional(3D)size and shape of gravel.Collecting morphology information for Gobi gravels is essential for studying its genesis and sand saltation.To enhance the efficiency and information yield of gravel parameter measurements,this study conducted field experiments in the Gobi region across Dunhuang City,Guazhou County,and Yumen City(administrated by Jiuquan City),Gansu Province,China in March 2023.A research framework and methodology for measuring 3D parameters of gravel using point cloud were developed,alongside improved calculation formulas for 3D parameters including gravel grain size,volume,flatness,roundness,sphericity,and equivalent grain size.Leveraging multi-view geometry technology for 3D reconstruction allowed for establishing an optimal data acquisition scheme characterized by high point cloud reconstruction efficiency and clear quality.Additionally,the proposed methodology incorporated point cloud clustering,segmentation,and filtering techniques to isolate individual gravel point clouds.Advanced point cloud algorithms,including the Oriented Bounding Box(OBB),point cloud slicing method,and point cloud triangulation,were then deployed to calculate the 3D parameters of individual gravels.These systematic processes allow precise and detailed characterization of individual gravels.For gravel grain size and volume,the correlation coefficients between point cloud and manual measurements all exceeded 0.9000,confirming the feasibility of the proposed methodology for measuring 3D parameters of individual gravels.The proposed workflow yields accurate calculations of relevant parameters for Gobi gravels,providing essential data support for subsequent studies on Gobi environments.
基金supported by the National Natural Science Foundation of China (No.52374124)National Youth Science Foundation of China (No.52204135)+3 种基金Xing Liao Talent Plan (No.XLYC2202004)Young Elite Scientists Sponsorship Program by CAST (No.2023QNRC001)Liaoning Province International Science and Technology Cooperation Plan (No.2022JH2/1070004)Liaoning Natural Science Foundation Program (No.2022-BS-327)。
文摘The 2D limit equilibrium method is widely used for slope stability analysis.However,with the advancement of dump engineering,composite slopes often exhibit significant 3D mechanical effects.Consequently,it is of significant importance to develop an effective 3D stability calculation method for composite slopes to enhance the design and stability control of open-pit slope engineering.Using the composite slope formed by the mining stope and inner dump in Baiyinhua No.1 and No.2 open-pit coal mine as a case study,this research investigates the failure mode of composite slopes and establishes spatial shape equations for the sliding mass.By integrating the shear resistance and sliding force of each row of microstrip columns onto the bottom surface of the strip corresponding to the main sliding surface,a novel 2D equivalent physical and mechanical parameters analysis method for the strips on the main sliding surface of 3D sliding masses is proposed.Subsequently,a comprehensive 3D stability calculation method for composite slopes is developed,and the quantitative relationship between the coordinated development distance and its 3D stability coefficients is examined.The analysis reveals that the failure mode of the composite slope is characterized by cutting-bedding sliding,with the arc serving as the side interface and the weak layer as the bottom interface,while the destabilization mechanism primarily involves shear failure.The spatial form equation of the sliding mass comprises an ellipsoid and weak plane equation.The analysis revealed that when the coordinated development distance is 1500 m,the error rate between the 3D stability calculation result and the 2D stability calculation result of the composite slope is less than 8%,thereby verifying the proposed analytical method of equivalent physical and mechanical parameters and the 3D stability calculation method for composite slopes.Furthermore,the3D stability coefficient of the composite slope exhibits an exponential correlation with the coordinated development distance,with the coefficient gradually decreasing as the coordinated development distance increases.These findings provide a theoretical guideline for designing similar slope shape parameters and conducting stability analysis.
文摘Background: As the population age structure gradually ages, more and more elderly people were found to have pulmonary nodules during physical examinations. Most elderly people had underlying diseases such as heart, lung, brain and blood vessels and cannot tolerate surgery. Computed tomography (CT)-guided percutaneous core needle biopsy (CNB) was the first choice for pathological diagnosis and subsequent targeted drugs, immune drugs or ablation treatment. CT-guided percutaneous CNB requires clinicians with rich CNB experience to ensure high CNB accuracy, but it was easy to cause complications such as pneumothorax and hemorrhage. Three-dimensional (3D) printing coplanar template (PCT) combined with CT-guided percutaneous pulmonary CNB biopsy has been used in clinical practice, but there was no prospective, randomized controlled study. Methods: Elderly patients with lung nodules admitted to the Department of Oncology of our hospital from January 2019 to January 2023 were selected. A total of 225 elderly patients were screened, and 30 patients were included after screening. They were randomly divided into experimental group (Group A: 30 cases) and control group (Group B: 30 cases). Group A was given 3D-PCT combined with CT-guided percutaneous pulmonary CNB biopsy, Group B underwent CT-guided percutaneous pulmonary CNB. The primary outcome measure of this study was the accuracy of diagnostic CNB, and the secondary outcome measures were CNB time, number of CNB needles, number of pathological tissues and complications. Results: The diagnostic accuracy of group A and group B was 96.67% and 76.67%, respectively (P = 0.026). There were statistical differences between group A and group B in average CNB time (P = 0.001), number of CNB (1 vs more than 1, P = 0.029), and pathological tissue obtained by CNB (3 vs 1, P = 0.040). There was no statistical difference in the incidence of pneumothorax and hemorrhage between the two groups (P > 0.05). Conclusions: 3D-PCT combined with CT-guided percutaneous CNB can improve the puncture accuracy of elderly patients, shorten the puncture time, reduce the number of punctures, and increase the amount of puncture pathological tissue, without increasing pneumothorax and hemorrhage complications. We look forward to verifying this in a phase III randomized controlled clinical study. .
基金supported by the National Natural Science Foundation of China (62001436)the Natural Science Foundation of Jiangsu Province under (BK 20190143,JSGG20190823094603691)。
文摘Three-dimensional(3D) synthetic aperture radar(SAR)extends the conventional 2D images into 3D features by several acquisitions in different aspects. Compared with 3D techniques via multiple observations in elevation, e.g. SAR interferometry(InSAR) and SAR tomography(TomoSAR), holographic SAR can retrieve 3D structure by observations in azimuth. This paper focuses on designing a novel type of orbit to achieve SAR regional all-azimuth observation(AAO) for embedded targets detection and holographic 3D reconstruction. The ground tracks of the AAO orbit separate the earth surface into grids. Target in these grids can be accessed with an azimuth angle span of360°, which is similar to the flight path of airborne circular SAR(CSAR). Inspired from the successive coverage orbits of optical sensors, several optimizations are made in the proposed method to ensure favorable grazing angles, the performance of 3D reconstruction, and long-term supervision for SAR sensors. Simulation experiments show the regional AAO can be completed within five hours. In addition, a second AAO of the same area can be duplicated in two days. Finally, an airborne SAR data process result is presented to illustrate the significance of AAO in 3D reconstruction.
基金We are grateful for financial supports from National Key R&D Program of China(Grant No.2021YFB2802300)the National Natural Science Foundation of China(Grant Nos.62105014,62105016,and 62020106010)。
文摘Light field 3D display technology is considered a revolutionary technology to address the critical visual fatigue issues in the existing 3D displays.Tabletop light field 3D display provides a brand-new display form that satisfies multi-user shared viewing and collaborative works,and it is poised to become a potential alternative to the traditional wall and portable display forms.However,a large radial viewing angle and correct radial perspective and parallax are still out of reach for most current tabletop light field 3D displays due to the limited amount of spatial information.To address the viewing angle and perspective issues,a novel integral imaging-based tabletop light field 3D display with a simple flat-panel structure is proposed and developed by applying a compound lens array,two spliced 8K liquid crystal display panels,and a light shaping diffuser screen.The compound lens array is designed to be composed of multiple three-piece compound lens units by employing a reverse design scheme,which greatly extends the radial viewing angle in the case of a limited amount of spatial information and balances other important 3D display parameters.The proposed display has a radial viewing angle of 68.7°in a large display size of 43.5 inches,which is larger than the conventional tabletop light field 3D displays.The radial perspective and parallax are correct,and high-resolution 3D images can be reproduced in large radial viewing positions.We envision that this proposed display opens up possibility for redefining the display forms of consumer electronics.
基金supported by the National Natural Science Foundation of China(Grant No.51974173)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2020QD122).
文摘The shear failure of intact rock under thermo-mechanical(TM)coupling conditions is common,such as in enhanced geothermal mining and deep mine construction.Under the effect of a continuous engineering disturbance,shear-formed fractures are prone to secondary instability,posing a severe threat to deep engineering.Although numerous studies regarding three-dimensional(3D)morphologies of fracture surfaces have been conducted,the understanding of shear-formed fractures under TM coupling conditions is limited.In this study,direct shear tests of intact granite under various TM coupling conditions were conducted,followed by 3D laser scanning tests of shear-formed fractures.Test results demonstrated that the peak shear strength of intact granite is positively correlated with the normal stress,whereas it is negatively correlated with the temperature.The internal friction angle and cohesion of intact granite significantly decrease with an increase in the temperature.The anisotropy,roughness value,and height of the asperities on the fracture surfaces are reduced as the normal stress increases,whereas their variation trends are the opposite as the temperature increases.The macroscopic failure mode of intact granite under TM coupling conditions is dominated by mixed tensileeshear and shear failures.As the normal stress increases,intragranular fractures are developed ranging from a local to a global distribution,and the macroscopic failure mode of intact granite changes from mixed tensileeshear to shear failure.Finally,3D morphological characteristics of the asperities on the shear-formed fracture surfaces were analyzed,and a quadrangular pyramid conceptual model representing these asperities was proposed and sufficiently verified.
基金Project supported by the Executive Agency for Higher Education Research Development and Innovation Funding of Romania(No.PN-III-P4-PCE-2021-0993)。
文摘This study is concerned with the three-dimensional(3D)stagnation-point for the mixed convection flow past a vertical surface considering the first-order and secondorder velocity slips.To the authors’knowledge,this is the first study presenting this very interesting analysis.Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations(ODEs)by using appropriate similarity transformation.These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language.The effects of the governing parameters on the non-dimensional velocity profiles,temperature profiles,skin friction coefficients,and the local Nusselt number are presented in detail through a series of graphs and tables.Interestingly,it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation.The numerical computations of the present work are compared with those from other research available in specific situations,and an excellent consensus is observed.Another exciting feature for this work is the existence of dual solutions.An important remark is that the dual solutions exist for both assisting and opposing flows.A linear stability analysis is performed showing that one solution is stable and the other solution is not stable.We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics.These effects are depicted in graphs and discussed in this paper.The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow,as well as on the heat transfer characteristics.
文摘To reduce the computing time of composite computer-generated holograms (CGHs) gen- eration based upon the angular projection algorithm for holographic three-dimensional (3D) display, a grid-based holographic display ( GHD ) scheme was designed. The grid computing technology was applied to numerically process the different angular projections of an object in distributed-parallel manner to create the corresponding CGHs. The whole treatment of a projection was regarded as a job executed on the grid node machine. The number of jobs which were submitted to grid nodes, therefore, was equal to that of the projections of the object. A Condor-based grid testbed was constructed to verify the feasibility of the GHD scheme, and a graphical user interface (GUI) program and several service modules were developed for it. A 3D terrain model as an example was processed on the testbed. The result showed that the scheme was feasible and able to improve the execution elficiency greatly.
基金supported by the National Natural Science Foundation of China(31272518)the program for the New Century Excellent Talents of Ministry of Education of China(NCET-09-0654)+1 种基金the Doctoral Fund of Ministry of Education of P.R.China(RFDP,20120204110030)the Fundamental Research Funds for the Central Universities,China(QN2011012)
文摘Adhesions between different cells and extracellular matrix have been studied extensively in vitro, but little is known about their functions in testicular tissue counterparts. Spermatogonia and their companion somatic cells maintain a close association throughout spermatogenesis and this association is necessary for normal spermatogenesis. In order to keep the relative integrity of the testicular tissues, and to detect the development in vitro, culture testicular tissues in a three- dimensional (3D) agarose matrix was examined. Testicular tissues isolated from 6.5 d postpartum (dpp) mouse were cultured on the top of the matrix for 26 d with a medium height up to 4/5 of the 3D agarose matrix. The results showed that in this 3D culture environment, each type of testicular cells kept the same structure, localization and function as in vivo and might be more biologically relevant to living organisms. After culture, germ cell marker VASA and meiosis markers DAZL and SCP3 showed typical positive analysed by immunofluorescence staining and RT-PCR. It demonstrated that this 3D culture system was able to maintain the number of germ cells and promote the meiosis initiation of male germ cells.
基金This work was supported by the Key Research and Development Projects of Science and Technology Development Plan of Jilin Provincial Department of Science and Technology(20180201090gx).
文摘To model a true three-dimensional(3D)display system,we introduced the method of voxel molding to obtain the stereoscopic imaging space of the system.For the distribution of each voxel,we proposed a four-dimensional(4D)Givone–Roessor(GR)model for state-space representation—that is,we established a local state-space model with the 3D position and one-dimensional time coordi-nates to describe the system.First,we extended the original elementary operation approach to a 4D condition and proposed the implementation steps of the realiza-tion matrix of the 4D GR model.Then,we described the working process of a true 3D display system,analyzed its real-time performance,introduced the fixed-point quantization model to simplify the system matrix,and derived the conditions for the global asymptotic stability of the system after quantization.Finally,we provided an example to prove the true 3D display system’s feasibility by simulation.The GR-model-representation method and its implementation steps proposed in this paper simplified the system’s mathematical expression and facilitated the microcon-troller software implementation.Real-time and stability analyses can be used widely to analyze and design true 3D display systems.
基金the financial support of the National Natural Science Foundation of China(Grant No.52179118)the Graduate Innovation Program of China University of Mining and Technology(Grant No.2022WLKXJ032)the Postgraduate Research and Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX22_2581).
文摘The mechanical characteristics of crystalline rocks are affected by the heterogeneity of the spatial distribution of minerals.In this paper,a novel three-dimensional(3D)grain-based model(GBM)based on particle flow code(PFC),i.e.PFC3D-GBM,is proposed.This model can accomplish the grouping of mineral grains at the 3D scale and then filling them.Then,the effect of the position distribution,geometric size,and volume composite of mineral grains on the cracking behaviour and macroscopic properties of granite are examined by conducting Brazilian splitting tests.The numerical results show that when an external load is applied to a sample,force chains will form around each contact,and the orientation distribution of the force chains is uniform,which is independent of the external load level.Furthermore,the number of high-strength force chains is proportional to the external load level,and the main orientation distribution is consistent with the external loading direction.The main orientation of the cracks is vertical to that of the high-strength force chains.The geometric size of the mineral grains controls the mechanical behaviours.As the average grain size increases,the number of transgranular contacts with higher bonding strength in the region connecting both loading points increases.The number of high-strength force chains increases,leading to an increase in the stress concentration value required for the macroscopic failure of the sample.Due to the highest bonding strength,the generation of transgranular cracks in quartz requires a higher concentrated stress value.With increasing volume composition of quartz,the number of transgranular cracks in quartz distributed in the region connecting both loading points increases,which requires many high-strength force chains.The load level rises,leading to an increase in the tensile strength of the numerical sample.
基金supports from the National Key Research and Development Program of China (2021YFB2802100)the National Natural Science Foundation of China (62075127 and 62105203).
文摘Virtual reality(VR)and augmented reality(AR)are revolutionizing our lives.Near-eye displays are crucial technologies for VR and AR.Despite the rapid advances in near-eye display technologies,there are still challenges such as large field of view,high resolution,high image quality,natural free 3D effect,and compact form factor.Great efforts have been devoted to striking a balance between visual performance and device compactness.While traditional optics are nearing their limitations in addressing these challenges,ultra-thin metasurface optics,with their high light-modulating capabilities,may present a promising solution.In this review,we first introduce VR and AR near-eye displays,and then briefly explain the working principles of light-modulating metasurfaces,review recent developments in metasurface devices geared toward near-eye display applications,delved into several advanced natural 3D near-eye display technologies based on metasurfaces,and finally discuss about the remaining challenges and future perspectives associated with metasurfaces for near-eye display applications.
文摘In airborne array synthetic aperture radar(SAR), the three-dimensional(3D) imaging performance and cross-track resolution depends on the length of the equivalent array. In this paper, Barker sequence criterion is used for sparse flight sampling of airborne array SAR, in order to obtain high cross-track resolution in as few times of flights as possible. Under each flight, the imaging algorithm of back projection(BP) and the data extraction method based on modified uniformly redundant arrays(MURAs) are utilized to obtain complex 3D image pairs. To solve the side-lobe noise in images, the interferometry between each image pair is implemented, and compressed sensing(CS) reconstruction is adopted in the frequency domain. Furthermore, to restore the geometrical relationship between each flight, the phase information corresponding to negative MURA is compensated on each single-pass image reconstructed by CS. Finally,by coherent accumulation of each complex image, the high resolution in cross-track direction is obtained. Simulations and experiments in X-band verify the availability.
基金Project supported by the National Key R&D Program of China(Grant No.2016YFB0401503)the R&D Plan of Jiangsu Science and Technology Department,China(Grant No.BE2016173)
文摘A switchable autostereoscopic 3-dimensional(3D) display device with wide color gamut is introduced in this paper. In conjunction with a novel directional quantum-dot(QD) backlight, the precise scanning control strategy, and the eye-tracking system, this spatial-sequential solution enables our autostereoscopic display to combine all the advantages of full resolution,wide color gamut, low crosstalk, and switchable 2D/3D. And also, we fabricated an autostereoscopic display prototype and demonstrated its performances effectively. The results indicate that our system can both break the limitation of viewing position and provide high-quality 3D images. We present two working modes in this system. In the spatial-sequential mode,the crosstalk is about 6%. In the time-multiplexed mode, the viewer should wear auxiliary and the crosstalk is about 1%,just next to that of a commercial 3D display(BENQ XL2707-B and View Sonic VX2268 WM). Additionally, our system is also completely compatible with active shutter glasses and its 3D resolution is same as its 2D resolution. Because of the excellent properties of the QD material, the color gamut can be widely extended to 77.98% according to the ITU-R recommendation BT.2020(Rec.2020).
基金supported by the National Natural Science Foundation of China (Grant Nos. 12102312 and 41372314)State Key Laboratory of Geohazard Prevention and Geoenvironment Protection Open Foundation, Chengdu University of Technology, China (Grant No. SKLGP2021K011)
文摘Due to seasonal climate alterations,the microstructure and permeability of granite residual soil are easily affected by multiple dry-wet cycles.The X-ray micro computed tomography(micro-CT)acted as a nondestructive tool for characterizing the microstructure of soil samples exposed to a range of damage levels induced by dry-wet cycles.Subsequently,the variations of pore distribution and permeability due to drywet cycling effects were revealed based on three-dimensional(3D)pore distribution analysis and seepage simulations.According to the results,granite residual soils could be separated into four different components,namely,pores,clay,quartz,and hematite,from micro-CT images.The reconstructed 3D pore models dynamically demonstrated the expanding and connecting patterns of pore structures during drywet cycles.The values of porosity and connectivity are positively correlated with the number of dry-wet cycles,which were expressed by exponential and linear functions,respectively.The pore volume probability distribution curves of granite residual soil coincide with the χ^(2)distribution curve,which verifies the effectiveness of the assumption of χ^(2)distribution probability.The pore volume distribution curves suggest that the pores in soils were divided into four types based on their volumes,i.e.micropores,mesopores,macropores,and cracks.From a quantitative and visual perspective,considerable small pores are gradually transformed into cracks with a large volume and a high connectivity.Under the action of dry-wet cycles,the number of seepage flow streamlines which contribute to water permeation in seepage simulation increases distinctly,as well as the permeability and hydraulic conductivity.The calculated hydraulic conductivity is comparable with measured ones with an acceptable error margin in general,verifying the accuracy of seepage simulations based on micro-CT results.
基金supported by the National Natural Science Foundation of China(Nos.11362018,11261045,and 11261401)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20116401110002)
文摘Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional (3D) icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.
基金funded by the U.S.National Institute for Occupational Safety and Health(NIOSH)under the Contract No.75D30119C06044。
文摘In the last two decades,significant research has been conducted in the field of automated extraction of rock mass discontinuity characteristics from three-dimensional(3D)models.This provides several methodologies for acquiring discontinuity measurements from 3D models,such as point clouds generated using laser scanning or photogrammetry.However,even with numerous automated and semiautomated methods presented in the literature,there is not one single method that can automatically characterize discontinuities accurately in a minimum of time.In this paper,we critically review all the existing methods proposed in the literature for the extraction of discontinuity characteristics such as joint sets and orientations,persistence,joint spacing,roughness and block size using point clouds,digital elevation maps,or meshes.As a result of this review,we identify the strengths and drawbacks of each method used for extracting those characteristics.We found that the approaches based on voxels and region growing are superior in extracting joint planes from 3D point clouds.Normal tensor voting with trace growth algorithm is a robust method for measuring joint trace length from 3D meshes.Spacing is estimated by calculating the perpendicular distance between joint planes.Several independent roughness indices are presented to quantify roughness from 3D surface models,but there is a need to incorporate these indices into automated methodologies.There is a lack of efficient algorithms for direct computation of block size from 3D rock mass surface models.
基金Project supported by the Zhejiang Provincial Welfare Technology Applied Research Project,China(Grant No.2017C31080)
文摘Dithering optimization techniques can be divided into the phase-optimized technique and the intensity-optimized technique. The problem with the former is the poor sensitivity to various defocusing amounts, and the problem with the latter is that it cannot enhance phase quality directly nor efficiently. In this paper, we present a multi-objective optimization framework for three-dimensional(3D) measurement by utilizing binary defocusing technique. Moreover, a binary patch optimization technique is used to solve the time-consuming issue of genetic algorithm. It is demonstrated that the presented technique consistently obtains significant phase performance improvement under various defocusing amounts.
基金the Department of Science and Technology, India, fast track project scheme(SR/FTP/ETA-17-2007)
文摘The smooth convex generalized failure function, which represents 1/6 part of envelope in tile deviatoric plane, is proposed. The proposed function relies on four shape parameters (L, a, b and c), in which two parameters (a and b) are dependent on the others. The parameter Ls is called extension ratio. The proposed failure function could be incorporated with any two-dimensional (2D) failure criteria to make it a three-dimensional (3D) version. In this paper, a mathematical formulation for incorporation of Hoek-Brown failure criterion with the proposed function is presented. The Hoek-Brown failure criterion is the most suited 2D failure criterion tbr geomaterials. Two types of analyses for best-fitting solution of published true tri-axial test data were made by considering (1) constant extension ratio and (2) variable extension ratio. The shape and strength parameters for different types of rocks have been determined by best-fitting the published true tri-axial test data for both the analyses. It is observed from the best-fitting solution by considering uniform extension ratio (L~) that shape constants have a correlation with Hoek-Brown strength parameters. Thus, only two parameters (c~. and m) are needed for representing the 3D failure criterion for intact rock. The statistical expression between shape and Hoek-Brown strength parameters is given. In the second analysis, when considering varying extension ratio, another parameterfis introduced. The modified extension ratio is related tofand extension ratio. The results at minimum mean misfit for all the nine rocks indicate that the range off varies from 0.7 to 1.0. It is found that mean misfit by considering varying extension ratio is lower than that in the first analysis. But it requires three parameters. A statistical expression betweenfand Hoek-Brown strength parameters has been established. Though coefficient of correlation is not reasonable, we may eliminate it as an extra parameter. At the end of the paper, a methodology has also been given for its application to isotropic jointed rock mass, so that it can be implemented in a numerical code for stability analysis of jointed rock mass structures.