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Analytical solution for longitudinal responses of tunnels under combined effects of seismic waves and strike-slip faulting 认领 引用 被引量：1
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作者 Jie Tang Manchao He +2 位作者 Yafei Qiao Hanbing Bian Chun Zhu 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2026年第2期1266-1289,共24页
Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analyt... Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analytical solution to determine the longitudinal mechanical responses of tunnels subjected to the combined effects of seismic waves and strike-slip faulting.Adopting the elastic springbeam model,the seismic waves are modelled as shear horizontal(SH)waves and the fault dislocation follows an S-shaped pattern;the superposition principle for free-fielddisplacements caused by both effects is assumed.In addition,the transmission and reflectionof seismic waves at the fault-rock geological interface and the tangential contact conditions at the tunnel-rock interface are considered.The analytical model is validated against numerical simulations,confirmingits accuracy in calculating tunnel responses.Moreover,a parametric study is conducted to evaluate the impact of key factors,including fault displacement,fault zone width,fault dip angle,earthquake frequency,rock conditions,tunnel lining stiffness,and tangential contact conditions,on tunnel responses.Compared with each effect alone,the combined effects of seismic waves and strike-slip faulting significantlychange the tunnel deformation and internal forces,leading to increased tunnel responses,especially within the fault zone and near the fault-rock interfaces.Depending on specificparameters,tunnel responses can be classifiedinto seismic-dominated,faulting-dominated,and seismic-faulting coupled responses on the basis of the relative contributions of each effect.The proposed analytical solution can be applied to quickly predict the longitudinal mechanical behaviour of tunnels under such combined effects in engineering applications. 展开更多
关键词 Strike-slip faulting Longitudinal tunnel response Analytical solution Seismic waves Wave transmissions and reflections
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Analytical solution for longitudinal seismic response of variable stiffness tunnel with isolation layers under shear waves 认领 引用
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作者 LIU Xiang YANG Jiao-jiao +3 位作者 LI Kui-chen LU Tong JIANG An-nan FANG Qian 《Journal of Central South University》 SCIE EI CAS CSCD 2026年第6期2844-2867,共24页
Seismic isolation design typically emphasizes transverse responses of tunnels,with comparatively limited research on longitudinal isolation responses.Previous analytical solutions for isolation response are inapplicab... Seismic isolation design typically emphasizes transverse responses of tunnels,with comparatively limited research on longitudinal isolation responses.Previous analytical solutions for isolation response are inapplicable to variable stiffness tunnels.To address research gaps,analytical solutions for longitudinal seismic responses of variable stiffness tunnels with isolation layers are proposed.The solution can be applied to engineering practice.The mechanical model of isolation layers is developed using the Kelvin model.The variable stiffness tunnel is simplified as two semi-infinite beams embedded in homogeneous and isotropic soil layers.Governing equations are solved using integral transformations and continuity conditions.Analytical expressions are obtained by introducing displacement phase angles to simulate traveling wave effects.The proposed analytical solutions are validated through comparisons with results from existing literature and verified using numerical simulations.Parametric sensitivity analyses are conducted to investigate effects of tunnels with and without an isolation layer,isolation layer thickness and elastic modulus,tunnel stiffness ratio,and wavelength and amplitude of shear waves on seismic responses of variable stiffness tunnels.Changes in stiffness have a more significant effect on internal forces than displacements.Additionally,isolation layer's thickness and elastic modulus can be optimized through our method to balance structural performance and economic efficiency. 展开更多
关键词 isolation layer variable stiffness tunnel analytical solution seismic response shear waves
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Hydromechanical modeling of CO2 injection into a saline aquifer:Analytical solution and fault-related seismicity assessment 认领 引用
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作者 Yan Zou Bing Bai +3 位作者 Hongwu Lei Mingyao Wei Haiqing Wu Derek Elsworth 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2026年第7期5125-5145,共21页
The injection of substantial quantities of carbon dioxide into subsurface reservoirs may alter the stress state of geological formations,potentially reactivating pre-existing faults and triggering induced seismicity.C... The injection of substantial quantities of carbon dioxide into subsurface reservoirs may alter the stress state of geological formations,potentially reactivating pre-existing faults and triggering induced seismicity.Comprehensive hydromechanical coupling analytical approaches for predicting CO2 injectioninduced earthquakes remain underdeveloped.This study proposed an analytical solution for fullycoupled hydromechanical modeling of a saline aquifer due to CO2 injection and applied it to the assessment of fault-related seismicity induced by CO2 geological storage.Firstly,we derived the analytical solutions for pore pressure buildup and stress change,considering not only pore pressure diffusion but also poroelastic stressing and caprock stiffness.Then,we quantifiedthe relative seismicity rates from Coulomb failure stress change using Dieterich's rate-and-state seismicity model.Subsequently,we investigated the occurrence rates and exceedance probabilities of CO2 injection-induced earthquakes with different magnitudes according to a hybrid physical-statistical approach.Finally,we conducted a series of parametric studies to reveal the influenceof several factors on induced seismicity.The results demonstrate several key findings.First,the proposed analytical solutions showed good agreement with multiphysics multiphase numerical simulation.Second,the traditional pure-hydraulic diffusion model overestimated the relative seismicity rate compared to the fully-coupled hydromechanical poroelastic model under a normal faulting stress regime.Third,the newly presented formula for the radius of the perturbed region was appropriate in reflectingthe spatial-temporal evolution of seismicity rate.Finally,among the factors,the CO2 injection rate had the largest impact on the occurrence rate and exceedance probability of induced earthquakes.In summary,this study established a comprehensive framework for evaluating CO2 injection-induced seismicity according to fully-coupled hydromechanical analytical solutions. 展开更多
关键词 Carbon dioxide(CO2)geological storage Injection-induced earthquake Poroelastic effect Analytical solution Probabilistic seismic risk assessment
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Analytical solution for heat conduction in multi-layered geomaterials with thermal resistance:A case study of nuclear waste repository 认领 引用
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作者 Xiangyun Zhou Xun Xu +2 位作者 De'an Sun You Gao Minjie Wen 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2026年第7期5711-5730,共20页
Heat conduction in multi-layered geomaterials was a pervasive phenomenon in various engineering applications,such as nuclear waste repositories,energy piles,and abandoned oil wells.The incomplete contact between adjac... Heat conduction in multi-layered geomaterials was a pervasive phenomenon in various engineering applications,such as nuclear waste repositories,energy piles,and abandoned oil wells.The incomplete contact between adjacent geomaterials will impede the heat transfer at interfaces,known as the interfacial thermal resistance effect.In this regard,a two-dimensional axisymmetric mathematical model for transient heat conduction in multi-layered geomaterials with interfacial thermal resistance was established.Employing Green's function formalism,the thermal transport system was mathematically resolved through a closed-form analytical solution that provides continuum-level characterization of thermal evolution across all spatial-temporal coordinates.A numerical model for threelayered geomaterials and a benchmark test for double-layered geomaterials were constructed to verify the analytical solution.Finally,the solution was applied to simulate the temperature evolutions in a nuclear waste repository with three-and four-layered barrier systems with interfacial thermal resistance.The results indicated that the existence of interfacial thermal resistance caused heat accumulation at interfaces,thereby resulting in an increase in overall temperature within the repository.Moreover,the temperature rises in the bentonite block layer and bentonite granule layer were obviously greater than that in the surrounding rock.Due to the interfacial thermal resistance effect,a notable temperature difference was observed at the interfaces.Specifically,for every increment of 0.03(K m2)/W in interfacial thermal resistance,the temperature difference increased by 1.5℃.A comparative analysis of temperature fieldsin repositories with three-and four-layered barrier systems revealed that the gap between the canister and bentonite block significantlyaffects the peak temperature in the buffer layer. 展开更多
关键词 Analytical solution Multi-layered geomaterial Heat conduction Interfacial thermal resistance Nuclear waste repository
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Analytical solutions on dynamic response of a thin-walled curved beam subjected to two-axle moving load with variable speed 认领 引用
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作者 Xiaoyong Lv Liupeng Li +1 位作者 Zhiwu Yu Peng Liu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第2期237-251,共15页
This paper proposes the analytical solutions involving damping effects for the dynamic response of a simply supported thin-walled curved beam under uniformly variable two-axle moving loads in four directions:vertical,... This paper proposes the analytical solutions involving damping effects for the dynamic response of a simply supported thin-walled curved beam under uniformly variable two-axle moving loads in four directions:vertical,torsional,radial,and axial.The warping stiffness and damping of the thin-walled beam were comprehensively considered in the vibration control equations.Unlike traditional one-axle load cases,this study employs a more realistic two-axle vehicle load model.Based on the modal superposition method,the control vibration equations for thin-walled curved beams in-plane and out-ofplane under variable speed moving loads were solved using a combination of the Fourier sine transform method,the Galerkin method,and the Laplace transform method.Analytical solutions for the dynamic responses were derived in integral form,facilitating direct numerical computation.The proposed computational method’s effectiveness and accuracy were validated against published research.Subsequently,the dynamic responses of the thin-walled curved beam under one-axle and two-axle moving load models were compared,and the effects of initial load velocity,load acceleration,and center angle of the curved beam on the dynamic responses were investigated through extensive parameter research.The research results provide valuable insights into the structural behavior of thin-walled curved beams under the moving loading with variable speed. 展开更多
关键词 Thin-walled curved beam Dynamic response Variable speed Two-axle moving load Analytical solution
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Online reentry guidance algorithm based on trajectory analytical solutions 认领 引用
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作者 SUN Weibo MA Ping +2 位作者 LI Xiaonan WANG Songyan CHAO Tao 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2026年第3期1002-1018,共17页
To enhance the real-time performance and accuracy of guidance command generation,we propose an online reentry guidance algorithm based on analytical solutions of the hypersonic glide trajectory(HGT).Initially,an altit... To enhance the real-time performance and accuracy of guidance command generation,we propose an online reentry guidance algorithm based on analytical solutions of the hypersonic glide trajectory(HGT).Initially,an altitude-velocity profile is designed in the longitudinal plane to satisfy both path and terminal constraints.Based on this profile,we derive analytical solutions for the flight path angle(FPA)and bank angle.Subsequently,by employing the Newton-Raphson method to linearize the reentry motion equations,analytical solutions for the latitude and heading angle are obtained.Furthermore,we introduce an improved particle swarm optimization(IPSO)algorithm to optimize the profile parameters.This approach significantly enhances the algorithm's global convergence by narrowing the parameter optimization range and adaptively adjusting the inertia weight and cognitive factors.Finally,we present an online guidance algorithm that combines the HGT analytical solutions with the IPSO algorithm.This algorithm effectively achieves longitudinal and lateral guidance by continuously updating the altitude-velocity profile and bank angle symbol in real time.Simulation results demonstrate that the proposed algorithm is fast,efficient,accurate,and holds significant potential for broader application. 展开更多
关键词 altitude-velocity profile analytical solution improved particle swarm optimization(IPSO) online reentry guidance
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General Analytical Solutions to Fractional Differential Equations 认领 引用
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作者 Hanan S.Gafel 《Journal of Applied Mathematics and Physics》 2026年第1期373-383,共11页
This research introduces a new global technique for addressing fractional differential equations(FDEs),referred to as the N-Transform(NT).This method serves as a comprehensive integral transform,encompassing both Lapl... This research introduces a new global technique for addressing fractional differential equations(FDEs),referred to as the N-Transform(NT).This method serves as a comprehensive integral transform,encompassing both Laplace and Sumudu transforms.A fixed point theorem is used to prove the existence and uniqueness of solutions.Finding general solutions to specific fractional differential equations and proving their uniqueness through the application of a fixed point theorem are the main goals of this study.The fractional derivatives are expressed in the Caputo framework.The findings indicate that this method is highly effective,straightforward,and applicable to differential equations across various fields of science. 展开更多
关键词 Caputo Sense N-Transform Fractional Differential Equations A Fixed Point Theorem General Analytical Solutions
Analytical solution for estimating the minimum required strength of sill mat by considering failure due to rock wall closure 认领 引用 被引量：2
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作者 Chuan Fan Li Li +3 位作者 Guangsheng Liu Xiaocong Yang Lijie Guo Jing Tang 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2025年第2期996-1007,共12页
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
关键词 Underhand cut-and-fill mining Cemented backfill Wall closure Crushing Required strength Analytical solution
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Analytical solution for determining wall closure associated with stope excavation underneath sill mat constructed by cemented backfill 认领 引用 被引量：2
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作者 Chuan Fan Li Li +3 位作者 Xiaocong Yang Guangsheng Liu Lijie Guo Jing Tang 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2025年第2期983-995,共13页
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
关键词 Underhand cut-and-fill mining Backfill Wall closure Analytical solution FLAC3D Flamant model
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New analytical solutions for free vibration of embedded magneto-electro-elastic cylindrical shells with step-wise thickness variations 认领 引用 被引量：2
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作者 Jufang JIA Huilin YIN +3 位作者 Qinyu YU Jiabin SUN Xinsheng XU Zhenhuan ZHOU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2025年第3期447-466,共20页
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
关键词 analytical solution free vibration magneto-electro-elastic(MEE)material cylindrical shell with variable thickness symplectic method
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General analytical solutions for one-dimensional diffusion of degradable organic contaminant in the multi-layered media containing geomembranes 认领 引用 被引量：1
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作者 JIANG Wen-hao GE Shang-qi LI Jiang-shan 《Journal of Central South University》 SCIE EI CAS CSCD 2025年第10期3895-3910,共16页
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
关键词 general analytical solutions degradable organic contaminant diffusion behavior multi-layered media containing geomembranes composite barrier system
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Computational method for analytical solution with finite elements(CMAS-FE):Deriving approximate analytical solution for an isotropic homogeneous elastic medium with linear finite element method 认领 引用
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作者 Jiajia Yue Zifeng Yuan 《Theoretical & Applied Mechanics Letters》 EI CAS CSCD 2025年第6期540-550,共11页
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
关键词 CMAS-FE Finite element method Linear elastic problem Analytical solution
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Analytical Solution of Optimal Geometric Configuration Based on PDOP for DOA FDOA and TDOA 认领 引用
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作者 Junhua Yang Hao Huan Ran Tao 《Journal of Beijing Institute of Technology》 EI CAS 2025年第6期535-544,共10页
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
关键词 optimal geometric configuration analytical solution position dilution of precision direction of arrival(DOA) frequency difference of arrival(FDOA) time difference of arrival(TDOA)
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3D Analytical Solution to Tidal Equations in a Narrow Bay with Combined Lateral and Longitudinal Varying Topography 认领 引用
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作者 CUI Yanxing JIANG Wensheng 《Journal of Ocean University of China》 SCIE CAS CSCD 2025年第4期851-864,共14页
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
关键词 analytical solution land reclamation varying topography tidal level tidal current
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Three-dimensional analytical solution of acoustic emission source location for cuboid monitoring network without pre-measured wave velocity 认领 引用 被引量：26
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作者 董陇军 李夕兵 +2 位作者 周子龙 陈光辉 马举 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2015年第1期293-302,共10页
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
关键词 acoustic emission seismic source sensor location analytical solution
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Unified analytical solutions for a circular opening based on non-linear unified failure criterion 认领 引用 被引量：9
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作者 Chang-guang ZHANG Qing-he ZHANG +2 位作者 Jun-hai ZHAO Fei XU Chuang-zhou WU 《Journal of Zhejiang University-SCIENCE A》 SCIE EI CAS 2010年第2期71-79,共9页
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
关键词 Analytical solution Elastic-brittle-plastic rock Non-linear unified failure criterion Intermediate principal stress Dilatancy
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Analytical solutions of transient heat conduction in multilayered slabs and application to thermal analysis of landfills 认领 引用 被引量：7
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作者 WU Xun SHI Jian-yong +2 位作者 LEI Hao LI Yu-ping Leslie OKINE 《Journal of Central South University》 SCIE EI CAS CSCD 2019年第11期3175-3187,共13页
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
关键词 heat conduction multilayered slab heat generation analytical solutions landfill
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Two dimensional analytical solution for a partially vegetated compound channel flow 认领 引用 被引量：7
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作者 槐文信 徐治钢 +1 位作者 杨中华 曾玉红 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第8期1077-1084,共8页
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
关键词 compound channel depth-averaged velocity drag force eddy viscosity model analytical solution vegetation
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Analytical solution to one-dimensional consolidation in unsaturated soils 认领 引用 被引量：7
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作者 秦爱芳 陈光敬 +1 位作者 谈永卫 孙德安 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第10期1329-1340,共12页
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
关键词 unsaturated soil one-dimensional consolidation settlement analytical solution excess pore-air pressure excess pore-water pressure
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Scattering of plane P waves by a semi-cylindrical hill: analytical solution 认领 引用 被引量：16
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作者 梁建文 张彦帅 Vincent W Lee 《Earthquake Engineering and Engineering Vibration》 EI 2005年第1期27-36,共10页
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
关键词 hill plane P waves scattering analytical solution amplification
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