Underhand cut-and-fill mining has been widely used in underground mining operations,especially when the rock mass or orebody is of poor quality or prone to rockburst due to high stress.In such cases,mining workers sho...Underhand cut-and-fill mining has been widely used in underground mining operations,especially when the rock mass or orebody is of poor quality or prone to rockburst due to high stress.In such cases,mining workers should carry out all production activities under the cemented backfill roof or sill mat instead of a highly fractured and unstable rock roof or a strong rock roof with a high potential of rockburst.Therefore,the stability and required strength of the sill mat are critical issues for mining engineers.In 1991,Mitchell considered that sill mat could fail by caving,sliding,rotation,and flexure.Mitchell also proposed an analytical solution to determine the minimum required strength of the sill mat for each type of failure based on two stiff or immobile rock walls.However,recent publications using numerical modeling and field measurements indicate that the compressive stresses in the sill mat induced by rock wall closure due to a stope excavation beneath the sill mat can be significant.It is thus highly necessary to investigate the required strength of the sill mat by considering rock wall closure.In this study,the crushing failure of sill mat due to rock wall closure generated by underground excavation and a new failure mode called"crushing and caving”is revealed by numerical modeling.An analytical solution corresponding to each failure mode is then developed to estimate the minimum required cohesion(cmin)of the sill mat.A criterion is also proposed to determine if the sill mat fails by crushing or crushing-and-caving failure.The proposed analytical solution does not involve any correction coefficients.The validity of the proposed analytical solution is demonstrated by numerical modeling.The proposed analytical solution can thus be employed to predict the cmin of sill mat subjected to wall closure generated by underlying stope excavation.展开更多
In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs...In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs.A critical issue is to determine the minimum required strength of the sill mat to ensure a safe and cost-effective design.Until now,Mitchell’s analytical solution is the only available option,considering two stiff and immobile rock walls.Unavoidable rock wall closure associated with stope excavation below the sill mat was neglected.This,along with other undefined parameters,explains why Mitchell’s solution is rarely used in sill mat design.A new analytical solution for determining the minimum required strength of the sill mat accounting for wall closure is necessary.In this study,a closed-form analytical solution for estimating rock wall closure generated by stope excavation below a sill mat is developed by using Salamon’s and Flamant’s models.The proposed analytical solution does not contain any coefficients of correction or calibration.Despite several assumptions(or somewhat of oversimplifications)necessary to render a simple analytical solution possible,good agreements are obtained between the rock wall closures predicted by applying the proposed analytical solution and those obtained numerically with FLAC3D for many cases with arbitrarily chosen geometrical and material parameters.The proposed analytical solution is therefore validated and can be used to evaluate the rock wall closure generated by stope excavation below a sill mat.展开更多
Progressive modifications in submarine topography and shorelines drastically affect tidal dynamics in bays.This study examines the influence of topographic slope,bay length,and driving forces on tidal currents followi...Progressive modifications in submarine topography and shorelines drastically affect tidal dynamics in bays.This study examines the influence of topographic slope,bay length,and driving forces on tidal currents following land reclamation.Tidal equa-tions are analytically solved using infinite series,deriving expressions for tidal levels and currents in narrow bays with varying topog-raphy.Tidal levels,influenced by topographic variations,are characterized by amplitude and phase lag of their complex amplitude.These levels demonstrate high sensitivity to longitudinal slope variations but remain relatively stable under lateral slope changes.Un-der constant topographic slopes,even minor changes in bay length can drastically modify amplitude and phase lag,highlighting the sensitivity of tidal dynamics to geometric alterations.Tidal velocity notably increases with steeper longitudinal slopes and modestly rises with elevated lateral slopes.However,changes in longitudinal and lateral slopes do not considerably alter flow patterns.While external forces predominantly regulate tidal velocity with negligible effects on flow patterns,endogenous resistance influences veloci-ty but minimally impacts flow structure.These findings enhance the understanding of tidal responses to geometric and topographic changes,providing valuable guidance for land reclamation projects and coastal management strategies.展开更多
In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still...In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still needs to be further improved.In this work,general analytical solutions are derived for one-dimensional diffusion of degradable organic contaminant(DOC)in the multi-layered media containing geomembranes under a time-varying concentration boundary condition,where the variable substitution and separated variable approaches are employed.These analytical solutions with clear expressions can be used not only to study the diffusion behaviors of DOC in bottom and vertical composite barrier systems,but also to verify other complex numerical models.The proposed general analytical solutions are then fully validated via three comparative analyses,including comparisons with the experimental measurements,an existing analytical solution,and a finite-difference solution.Ultimately,the influences of different factors on the composite cutoff wall’s(CCW,which consists of two soil-bentonite layers and a geomembrane)service performance are investigated through a composite vertical barrier system as the application example.The findings obtained from this investigation can provide scientific guidance for the barrier performance evaluation and the engineering design of CCWs.This application example also exhibits the necessity and effectiveness of the developed analytical solutions.展开更多
In recent years,magneto-electro-elastic(MEE)cylindrical shells with step-wise thicknesses have shown significant potential in the field of vibration energy harvesting.To aid the design of such energy harvesting device...In recent years,magneto-electro-elastic(MEE)cylindrical shells with step-wise thicknesses have shown significant potential in the field of vibration energy harvesting.To aid the design of such energy harvesting devices,an accurate free vibration analysis of embedded MEE cylindrical shells with step-wise thicknesses is performed within the framework of symplectic mechanics.By using the Legendre transformation,a new known vector is defined to transform the higher-order partial differential governing equations into a set of lower-order ordinary differential equations.Therefore,the original vibration analysis is regarded as an eigen problem in the symplectic space,and analytical solutions can be represented by the symplectic series.In numerical examples,the new analytical solutions are compared with the existing results,and good agreement is observed.Furthermore,the effects of critical design parameters on free vibration characteristics are thoroughly investigated.All numerical results can serve as benchmarks for the development of other approximate or numerical methods.展开更多
This study presents a novel methodology to obtain an approximate analytical solution for an isotropic homo-geneous elastic medium with displacement and traction boundary conditions.The solution is derived through solv...This study presents a novel methodology to obtain an approximate analytical solution for an isotropic homo-geneous elastic medium with displacement and traction boundary conditions.The solution is derived through solving a specific numerical problem under the scope of the linear finite element method(LFEM),so the method is termed computational method for analytical solutions with finite elements(CMAS-FE).The primary objective of the CMAS-FE is to construct analytical expressions for displacements and reaction forces at nodes,as well as for strains and stresses at elemental quadrature points,all of which are formulated as infinite series solutions of various orders of Poisson’s ratios.Like the conventional LFEM,the CMAS-FE forms global sparse linear equations,but the Young’s modulus and Poisson’s ratio remain variables(or symbols).By employing a direct inverse method to solve these symbolic linear systems,an analytical expression of the displacement field can be constructed.The CMAS-FE is validated via patch and bending tests,which demonstrate convergence with mesh and term refine-ment.Furthermore,the CMAS-FE is applied to obtain the bending stiffness of a beam structure and to estimate an approximate stress intensity factor for a straight crack within a square-shaped plate.展开更多
The radar radiation source signals hold extremely high reconnaissance value.Accurately positioning these signals constitutes one of the key technologies in safeguarding the security of the electromagnetic space.The po...The radar radiation source signals hold extremely high reconnaissance value.Accurately positioning these signals constitutes one of the key technologies in safeguarding the security of the electromagnetic space.The positioning error in multi-station scenarios is influenced not only by the accuracy of positioning parameter estimation but also by the geometric configuration of the positioning platform.This paper focuses on the direction of arrival(DOA),frequency difference of arrival(FDOA),and time difference of arrival(TDOA)methods,analyzing the optimal configuration,optimal detection area,and optimal position dilution of precision in both elevation-known and elevation-unknown scenarios.Specifically,the paper constructs a signal receiving model,establishes the corresponding positioning equations,and performs dimensional normalization on these equations to derive measurement values in meters.Through differential processing,the position dilution of precision is obtained,which is then used as the optimization function to determine the optimal configuration,optimal detection area,and optimal position dilution of precision.Simulation results validate the accuracy of the proposed formulas.展开更多
To find analytical solutions of nonlinear systems for locating the acoustic emission/microseismic（AE/MS） source without knowing the wave velocity of structures, the sensor location coordinates were simplified as a c...To find analytical solutions of nonlinear systems for locating the acoustic emission/microseismic（AE/MS） source without knowing the wave velocity of structures, the sensor location coordinates were simplified as a cuboid monitoring network. Different locations of sensors on upper and lower surfaces were considered and used to establish nonlinear equations. Based on the proposed functions of time difference of arrivals, the analytical solutions were obtained using five sensors under three networks. The proposed analytical solutions were validated using authentic data of numerical tests and experiments. The results show that located results are consistent with authentic data, and the outstanding characteristics of the new solution are that the solved process is not influenced by the wave velocity knowledge and iterated algorithms.展开更多
To find the analytical solution of the acoustic emission/microseismic(AE/MS) source location coordinates, the sensor location coordinates were optimized and simplified. A cube monitoring network of sensor location was...To find the analytical solution of the acoustic emission/microseismic(AE/MS) source location coordinates, the sensor location coordinates were optimized and simplified. A cube monitoring network of sensor location was selected, and the AE/MS source localization equations were established. A location method with P-wave velocity by analytical solutions (P-VAS) was obtained with these equations. The virtual location tests show that the relocation results of analytical method are fully consistent with the actual coordinates for events both inside and outside the monitoring network; whereas the location error of traditional time difference method is between 0.01 and 0.03 m for events inside the sensor array, and the location errors are larger, which is up to 1080986 m for events outside the sensor array. The broken pencil location tests were carried out in the cross section of 100 mm×98 mm, 350 mm-length granite rock specimen using five AE sensors. Five AE sources were relocated with the conventional method and the P-VAS method. For the four events outside monitoring network, the positioning accuracy by P-VAS method is higher than that by the traditional method, and the location accuracy of the larger one can be increased by 17.61 mm. The results of both virtual and broken pencil location tests show that the proposed analytical solution is effective to improve the positioning accuracy. It can locate the coordinates of AE/MS source only using simple four arithmetic operations, without determining the fitting initial value and iterative calculation, which can be solved by a conventional calculator or Microsoft Excel.展开更多
Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distributi...Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.展开更多
Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. ...Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. Unified analytical solutions not only involve generally traditional solutions which are based on the Hock-Brown （H-B） failure criterion or the non-linear twin-shear failure criterion, but also involve other new results. The results of the radius of plastic zone, radial displacements and stresses are obviously different using three rock masses when different values of the unified failure criterion parameter or different material behavior models are used. For a given condition, the radius of plastic zone and radial displacements are reduced by increasing the unified failure criterion parameter. The latent potentialities of rock mass result from considering the effect of intermediate principal stress. It is shown that proper choices of the failure criterion and the material behavior model for rock mass are significant in the tunnel design.展开更多
The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitr...The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.展开更多
The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordin...The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.展开更多
Chemo-mechanical coupling exists in a lot of intelligent materials including hy- drogels, biological tissues and other soft materials. These materials are able to respond to ex- ternal stimulus, such as temperature, c...Chemo-mechanical coupling exists in a lot of intelligent materials including hy- drogels, biological tissues and other soft materials. These materials are able to respond to ex- ternal stimulus, such as temperature, chemical concentration, and pH value. In this paper, a one-dimensional theoretical model for chemo-mechanical coupling is proposed for analyzing the uniaxial stress/strain state of coupling materials. Based on the chemo-mechanical coupled gov- erning equation, the displacement function and concentration function are derived and the stress and chemical potential are obtained. It is shown that the present chemo-mechanical theory can characterize the chemo-mechanical coupling behavior of intelligent materials.展开更多
An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The ...An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.展开更多
Following exploitation of a coal seam, the final stress field is the sum of in situ stress field and an excavation stress field. Based on this feature, we firstly established a mechanics analytical model of the mining...Following exploitation of a coal seam, the final stress field is the sum of in situ stress field and an excavation stress field. Based on this feature, we firstly established a mechanics analytical model of the mining floor strata. Then the study applied Fourier integral transform to solve a biharmonic equation,obtaining the analytical solution of the stress and displacement of the mining floor. Additionally, this investigation used the Mohr–Coulomb yield criterion to determine the plastic failure depth of the floor strata. The calculation process showed that the plastic failure depth of the floor and floor heave are related to the mining width, burial depth and physical–mechanical properties. The results from an example show that the curve of the plastic failure depth of the mining floor is characterized by a funnel shape and the maximum failure depth generates in the middle of mining floor; and that the maximum and minimum principal stresses change distinctly in the shallow layer and tend to a fixed value with an increase in depth. Based on the displacement results, the maximum floor heave appears in the middle of the stope and its value is 0.107 m. This will provide a basis for floor control. Lastly, we have verified the analytical results using FLAC3 Dto simulate floor excavation and find that there is some deviation between the two results, but their overall tendency is consistent which illustrates that the analysis method can well solve the stress and displacement of the floor.展开更多
Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeabili...Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.展开更多
The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the un...The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item, The compound channel is divided into 3 sub-regions in the transverse direction, and the coefficients in every region＇s differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vegetated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical solution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.展开更多
This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the ...This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund＇s one-dimensional consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy＇s law and Fick＇s law. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soil from an- alytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct.展开更多
Based on the assumption that solute transport in a semi-infinite soil columnor in a field soil profile can be described by the boundary-layer method, an analytical solution ispresented for the advance of a solute fron...Based on the assumption that solute transport in a semi-infinite soil columnor in a field soil profile can be described by the boundary-layer method, an analytical solution ispresented for the advance of a solute front with time. The traditional convection-dispersionequation (CDE) subjected to two boundary conditions: 1) at the soil surface (or inlet boundary) and2) at the solute front, was solved using a Laplace transformation. A comparison of residentconcentrations using a boundary-layer method and an exact solution (in a semi-infinite-domain)showed that both were in good agreement within the range between the two boundaries. This led to anew method for estimating solute transport parameters in soils, requiring only observation ofadvance of the solute front with time. This may be corroborated visually using a tracer solutionwith marking-dye or measured utilizing time domain reflectometry (TDR). This method is applicable toboth laboratory soil columns and field soils. Thus, it could be a step forward for modeling solutetransport in field soils and for better understanding of the transport processes in soils.展开更多
基金financial support from the Young Scientist Project of the National Key Research and Development Program of China(Grant No.2021YFC2900600)Beijing Nova Program(Grant No.20220484057)+1 种基金The authors acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2018-06902)industrial partners of the Research Institute on Mines and the Environment(RIME UQAT-Polytechnique:https://irme.ca/en/).
文摘Underhand cut-and-fill mining has been widely used in underground mining operations,especially when the rock mass or orebody is of poor quality or prone to rockburst due to high stress.In such cases,mining workers should carry out all production activities under the cemented backfill roof or sill mat instead of a highly fractured and unstable rock roof or a strong rock roof with a high potential of rockburst.Therefore,the stability and required strength of the sill mat are critical issues for mining engineers.In 1991,Mitchell considered that sill mat could fail by caving,sliding,rotation,and flexure.Mitchell also proposed an analytical solution to determine the minimum required strength of the sill mat for each type of failure based on two stiff or immobile rock walls.However,recent publications using numerical modeling and field measurements indicate that the compressive stresses in the sill mat induced by rock wall closure due to a stope excavation beneath the sill mat can be significant.It is thus highly necessary to investigate the required strength of the sill mat by considering rock wall closure.In this study,the crushing failure of sill mat due to rock wall closure generated by underground excavation and a new failure mode called"crushing and caving”is revealed by numerical modeling.An analytical solution corresponding to each failure mode is then developed to estimate the minimum required cohesion(cmin)of the sill mat.A criterion is also proposed to determine if the sill mat fails by crushing or crushing-and-caving failure.The proposed analytical solution does not involve any correction coefficients.The validity of the proposed analytical solution is demonstrated by numerical modeling.The proposed analytical solution can thus be employed to predict the cmin of sill mat subjected to wall closure generated by underlying stope excavation.
基金financial support from the Young Scientist Project of the National Key Research and Development Program of China(Grant No.2021YFC2900600)the Beijing Nova Program(Grant No.20220484057)+1 种基金The authors acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2018-06902)industrial partners of the Research Institute on Mines and the Environment(RIME UQAT-Polytechnique:https://irme.ca/en/).
文摘In the underhand cut-and-fill mining method,a sill mat(i.e.an artificial horizontal pillar)constructed by cemented backfill is essential to prevent mine workers from being directly exposed under problematic rock roofs.A critical issue is to determine the minimum required strength of the sill mat to ensure a safe and cost-effective design.Until now,Mitchell’s analytical solution is the only available option,considering two stiff and immobile rock walls.Unavoidable rock wall closure associated with stope excavation below the sill mat was neglected.This,along with other undefined parameters,explains why Mitchell’s solution is rarely used in sill mat design.A new analytical solution for determining the minimum required strength of the sill mat accounting for wall closure is necessary.In this study,a closed-form analytical solution for estimating rock wall closure generated by stope excavation below a sill mat is developed by using Salamon’s and Flamant’s models.The proposed analytical solution does not contain any coefficients of correction or calibration.Despite several assumptions(or somewhat of oversimplifications)necessary to render a simple analytical solution possible,good agreements are obtained between the rock wall closures predicted by applying the proposed analytical solution and those obtained numerically with FLAC3D for many cases with arbitrarily chosen geometrical and material parameters.The proposed analytical solution is therefore validated and can be used to evaluate the rock wall closure generated by stope excavation below a sill mat.
基金supported by the National Natural Sci-ence Foundation of China(No.U2106204)the Shanxi Water Conservancy Science and Technology Re-search and Extension Project(No.2023ZF19).
文摘Progressive modifications in submarine topography and shorelines drastically affect tidal dynamics in bays.This study examines the influence of topographic slope,bay length,and driving forces on tidal currents following land reclamation.Tidal equa-tions are analytically solved using infinite series,deriving expressions for tidal levels and currents in narrow bays with varying topog-raphy.Tidal levels,influenced by topographic variations,are characterized by amplitude and phase lag of their complex amplitude.These levels demonstrate high sensitivity to longitudinal slope variations but remain relatively stable under lateral slope changes.Un-der constant topographic slopes,even minor changes in bay length can drastically modify amplitude and phase lag,highlighting the sensitivity of tidal dynamics to geometric alterations.Tidal velocity notably increases with steeper longitudinal slopes and modestly rises with elevated lateral slopes.However,changes in longitudinal and lateral slopes do not considerably alter flow patterns.While external forces predominantly regulate tidal velocity with negligible effects on flow patterns,endogenous resistance influences veloci-ty but minimally impacts flow structure.These findings enhance the understanding of tidal responses to geometric and topographic changes,providing valuable guidance for land reclamation projects and coastal management strategies.
基金Project(2023YFC3707800)supported by the National Key Research and Development Program of China。
文摘In practical engineering construction,multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants.However,the associated analytical theory on pollutants diffusion still needs to be further improved.In this work,general analytical solutions are derived for one-dimensional diffusion of degradable organic contaminant(DOC)in the multi-layered media containing geomembranes under a time-varying concentration boundary condition,where the variable substitution and separated variable approaches are employed.These analytical solutions with clear expressions can be used not only to study the diffusion behaviors of DOC in bottom and vertical composite barrier systems,but also to verify other complex numerical models.The proposed general analytical solutions are then fully validated via three comparative analyses,including comparisons with the experimental measurements,an existing analytical solution,and a finite-difference solution.Ultimately,the influences of different factors on the composite cutoff wall’s(CCW,which consists of two soil-bentonite layers and a geomembrane)service performance are investigated through a composite vertical barrier system as the application example.The findings obtained from this investigation can provide scientific guidance for the barrier performance evaluation and the engineering design of CCWs.This application example also exhibits the necessity and effectiveness of the developed analytical solutions.
基金Project supported by the Science and Technology Plan Joint Program of Liaoning Province of China(Natural Science Foundation-Doctoral Research Launch Project)(No.2024-BSLH-027)the Fundamental Research Funds for Undergraduate Universities of Liaoning Province of China(No.LJBKY2024033)+1 种基金the National Natural Science Foundation of China(No.12472064)the Natural Science Foundation of Liaoning Province of China(No.2023-MS-118)。
文摘In recent years,magneto-electro-elastic(MEE)cylindrical shells with step-wise thicknesses have shown significant potential in the field of vibration energy harvesting.To aid the design of such energy harvesting devices,an accurate free vibration analysis of embedded MEE cylindrical shells with step-wise thicknesses is performed within the framework of symplectic mechanics.By using the Legendre transformation,a new known vector is defined to transform the higher-order partial differential governing equations into a set of lower-order ordinary differential equations.Therefore,the original vibration analysis is regarded as an eigen problem in the symplectic space,and analytical solutions can be represented by the symplectic series.In numerical examples,the new analytical solutions are compared with the existing results,and good agreement is observed.Furthermore,the effects of critical design parameters on free vibration characteristics are thoroughly investigated.All numerical results can serve as benchmarks for the development of other approximate or numerical methods.
基金supported by the National Natural Science Foundation of China Excellence Research Group Program for“Multiscale Problems in Nonlinear Mechanics”(Grant No.12588201)the National Key R&D Program of China(Grant No.2023YFA1008901)+1 种基金the National Nat-ural Science Foundation of China(Grant No.12172009)supported by“The Fundamental Research Funds for the Central Universities,Peking University”.
文摘This study presents a novel methodology to obtain an approximate analytical solution for an isotropic homo-geneous elastic medium with displacement and traction boundary conditions.The solution is derived through solving a specific numerical problem under the scope of the linear finite element method(LFEM),so the method is termed computational method for analytical solutions with finite elements(CMAS-FE).The primary objective of the CMAS-FE is to construct analytical expressions for displacements and reaction forces at nodes,as well as for strains and stresses at elemental quadrature points,all of which are formulated as infinite series solutions of various orders of Poisson’s ratios.Like the conventional LFEM,the CMAS-FE forms global sparse linear equations,but the Young’s modulus and Poisson’s ratio remain variables(or symbols).By employing a direct inverse method to solve these symbolic linear systems,an analytical expression of the displacement field can be constructed.The CMAS-FE is validated via patch and bending tests,which demonstrate convergence with mesh and term refine-ment.Furthermore,the CMAS-FE is applied to obtain the bending stiffness of a beam structure and to estimate an approximate stress intensity factor for a straight crack within a square-shaped plate.
基金supported by the National Natural Science Foundation of China(Nos.62027801,62301035).
文摘The radar radiation source signals hold extremely high reconnaissance value.Accurately positioning these signals constitutes one of the key technologies in safeguarding the security of the electromagnetic space.The positioning error in multi-station scenarios is influenced not only by the accuracy of positioning parameter estimation but also by the geometric configuration of the positioning platform.This paper focuses on the direction of arrival(DOA),frequency difference of arrival(FDOA),and time difference of arrival(TDOA)methods,analyzing the optimal configuration,optimal detection area,and optimal position dilution of precision in both elevation-known and elevation-unknown scenarios.Specifically,the paper constructs a signal receiving model,establishes the corresponding positioning equations,and performs dimensional normalization on these equations to derive measurement values in meters.Through differential processing,the position dilution of precision is obtained,which is then used as the optimization function to determine the optimal configuration,optimal detection area,and optimal position dilution of precision.Simulation results validate the accuracy of the proposed formulas.
基金Projects(11447242,41272304,51209236,51274254)supported by the National Natural Science Foundation of ChinaProject(2015CB060200)supported by the National Basic Research Program of China
文摘To find analytical solutions of nonlinear systems for locating the acoustic emission/microseismic（AE/MS） source without knowing the wave velocity of structures, the sensor location coordinates were simplified as a cuboid monitoring network. Different locations of sensors on upper and lower surfaces were considered and used to establish nonlinear equations. Based on the proposed functions of time difference of arrivals, the analytical solutions were obtained using five sensors under three networks. The proposed analytical solutions were validated using authentic data of numerical tests and experiments. The results show that located results are consistent with authentic data, and the outstanding characteristics of the new solution are that the solved process is not influenced by the wave velocity knowledge and iterated algorithms.
基金Project (10872218) supported by the National Natural Science Foundation of ChinaProject (2010CB732004) supported by the National Basic Research Program of China+1 种基金Project (kjdb2010-6) supported by Doctoral Candidate Innovation Research Support Program of Science & Technology ReviewProject (201105) supported by Scholarship Award for Excellent Doctoral Student of Ministry of Education of China
文摘To find the analytical solution of the acoustic emission/microseismic(AE/MS) source location coordinates, the sensor location coordinates were optimized and simplified. A cube monitoring network of sensor location was selected, and the AE/MS source localization equations were established. A location method with P-wave velocity by analytical solutions (P-VAS) was obtained with these equations. The virtual location tests show that the relocation results of analytical method are fully consistent with the actual coordinates for events both inside and outside the monitoring network; whereas the location error of traditional time difference method is between 0.01 and 0.03 m for events inside the sensor array, and the location errors are larger, which is up to 1080986 m for events outside the sensor array. The broken pencil location tests were carried out in the cross section of 100 mm×98 mm, 350 mm-length granite rock specimen using five AE sensors. Five AE sources were relocated with the conventional method and the P-VAS method. For the four events outside monitoring network, the positioning accuracy by P-VAS method is higher than that by the traditional method, and the location accuracy of the larger one can be increased by 17.61 mm. The results of both virtual and broken pencil location tests show that the proposed analytical solution is effective to improve the positioning accuracy. It can locate the coordinates of AE/MS source only using simple four arithmetic operations, without determining the fitting initial value and iterative calculation, which can be solved by a conventional calculator or Microsoft Excel.
文摘Using the variable transformation method,the formulae of the axial symmetrical wall temperature distribution during steady heat conduction of a hollow cylinder are derived in this paper.The wall temperature distribution and the wall heat flux distribution in both axial and radial direction can be calculated by the temperature distribution of the liquid medium both inside and outside the cylinder with temperature changing in axial direction.The calculation results are almost consistent with the experience results.The applicative condition of the formulae in this paper consists with most of practice.They can be applied to the engineering calculation of the steady heat conduction.The calculation is simple and accurate.
基金Project (No.SJ08E204) supported by the Natural Science Foundation of Shanxi Province,China
文摘Unified analytical solutions are presented for the predictions of the stresses and displacements around a circular opening based on nonqinear unified failure criterion and the elastic-brittle-plastic softening model. Unified analytical solutions not only involve generally traditional solutions which are based on the Hock-Brown （H-B） failure criterion or the non-linear twin-shear failure criterion, but also involve other new results. The results of the radius of plastic zone, radial displacements and stresses are obviously different using three rock masses when different values of the unified failure criterion parameter or different material behavior models are used. For a given condition, the radius of plastic zone and radial displacements are reduced by increasing the unified failure criterion parameter. The latent potentialities of rock mass result from considering the effect of intermediate principal stress. It is shown that proper choices of the failure criterion and the material behavior model for rock mass are significant in the tunnel design.
基金Projects(41530637,41877222,41702290)supported by the National Natural Science Foundation of China
文摘The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.
基金Project supported by the National Natural Science Foundation of China (Nos. 10472102 and 1043203)the Foundation of Ningbo University (No. 2005014), China
文摘The bending problem of a functionally graded anisotropic cantilever beam subjected to thermal and uniformly dis-tributed load is investigated,with material parameters being arbitrary functions of the thickness coordinate. The heat conduction problem is treated as a 1D problem through the thickness. Based on the elementary formulations for plane stress problem,the stress function is assumed to be in the form of polynomial of the longitudinal coordinate variable,from which the stresses can be derived. The stress function is then determined completely with the compatibility equation and boundary conditions. A practical example is presented to show the application of the method.
基金The project supported by the National Natural Science Foundation of China(Nos.10872011 and 11172012)the Municipal Natural Science Foundation of Beijing(No.3092006)
文摘Chemo-mechanical coupling exists in a lot of intelligent materials including hy- drogels, biological tissues and other soft materials. These materials are able to respond to ex- ternal stimulus, such as temperature, chemical concentration, and pH value. In this paper, a one-dimensional theoretical model for chemo-mechanical coupling is proposed for analyzing the uniaxial stress/strain state of coupling materials. Based on the chemo-mechanical coupled gov- erning equation, the displacement function and concentration function are derived and the stress and chemical potential are obtained. It is shown that the present chemo-mechanical theory can characterize the chemo-mechanical coupling behavior of intelligent materials.
基金National Natural Science Foundation of China Under Grant No.50378063Excellent Young Teacher Program of Ministry of Education
文摘An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.
基金the National Basic Research Program of China(No.2014CB046300)the National Natural Science Foundation of China(No.51174196)
文摘Following exploitation of a coal seam, the final stress field is the sum of in situ stress field and an excavation stress field. Based on this feature, we firstly established a mechanics analytical model of the mining floor strata. Then the study applied Fourier integral transform to solve a biharmonic equation,obtaining the analytical solution of the stress and displacement of the mining floor. Additionally, this investigation used the Mohr–Coulomb yield criterion to determine the plastic failure depth of the floor strata. The calculation process showed that the plastic failure depth of the floor and floor heave are related to the mining width, burial depth and physical–mechanical properties. The results from an example show that the curve of the plastic failure depth of the mining floor is characterized by a funnel shape and the maximum failure depth generates in the middle of mining floor; and that the maximum and minimum principal stresses change distinctly in the shallow layer and tend to a fixed value with an increase in depth. Based on the displacement results, the maximum floor heave appears in the middle of the stope and its value is 0.107 m. This will provide a basis for floor control. Lastly, we have verified the analytical results using FLAC3 Dto simulate floor excavation and find that there is some deviation between the two results, but their overall tendency is consistent which illustrates that the analysis method can well solve the stress and displacement of the floor.
基金supported by the National Natural Science Foundation of China(11102237)Program for Changjiang Scholars and Innovative Research Team in University(IRT1294)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(20110133120012)China Scholarship Council(CSC)
文摘Based on Huang＇s accurate tri-sectional nonlin- ear kinematic equation （1997）, a dimensionless simplified mathematical model for nonlinear flow in one-dimensional semi-infinite long porous media with low permeability is presented for the case of a constant flow rate on the inner boundary. This model contains double moving boundaries, including an internal moving boundary and an external mov- ing boundary, which are different from the classical Stefan problem in heat conduction： The velocity of the external moving boundary is proportional to the second derivative of the unknown pressure function with respect to the distance parameter on this boundary. Through a similarity transfor- mation, the nonlinear partial differential equation （PDE） sys- tem is transformed into a linear PDE system. Then an ana- lytical solution is obtained for the dimensionless simplified mathematical model. This solution can be used for strictly checking the validity of numerical methods in solving such nonlinear mathematical models for flows in low-permeable porous media for petroleum engineering applications. Finally, through plotted comparison curves from the exact an- alytical solution, the sensitive effects of three characteristic parameters are discussed. It is concluded that with a decrease in the dimensionless critical pressure gradient, the sensi- tive effects of the dimensionless variable on the dimension- less pressure distribution and dimensionless pressure gradi- ent distribution become more serious; with an increase in the dimensionless pseudo threshold pressure gradient, the sensi- tive effects of the dimensionless variable become more serious; the dimensionless threshold pressure gradient （TPG） has a great effect on the external moving boundary but has little effect on the internal moving boundary.
基金the National Natural Science Foundation of China(Nos.50679061,50709025and50749031)
文摘The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item, The compound channel is divided into 3 sub-regions in the transverse direction, and the coefficients in every region＇s differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vegetated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical solution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.
文摘This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund＇s one-dimensional consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy＇s law and Fick＇s law. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soil from an- alytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct.
基金Project supported by the National Key Basic Research Support Foundation of China (No. 2000018605) the National Natural Science Foundation of China (Nos. 40025106 and 40371060).
文摘Based on the assumption that solute transport in a semi-infinite soil columnor in a field soil profile can be described by the boundary-layer method, an analytical solution ispresented for the advance of a solute front with time. The traditional convection-dispersionequation (CDE) subjected to two boundary conditions: 1) at the soil surface (or inlet boundary) and2) at the solute front, was solved using a Laplace transformation. A comparison of residentconcentrations using a boundary-layer method and an exact solution (in a semi-infinite-domain)showed that both were in good agreement within the range between the two boundaries. This led to anew method for estimating solute transport parameters in soils, requiring only observation ofadvance of the solute front with time. This may be corroborated visually using a tracer solutionwith marking-dye or measured utilizing time domain reflectometry (TDR). This method is applicable toboth laboratory soil columns and field soils. Thus, it could be a step forward for modeling solutetransport in field soils and for better understanding of the transport processes in soils.
