Analytical model for predicting time-dependent lateral deformation of geosynthetics-reinforced soil walls with modular block facing

To date,few models are available in the literature to consider the creep behavior of geosynthetics when predicting the lateral deformation(d)of geosynthetics-reinforced soil(GRS)retaining walls.In this study,a general hyperbolic creep model was first introduced to describe the long-term deformation of geosynthetics,which is a function of elapsed time and two empirical parameters a and b.The conventional creep tests with three different tensile loads(Pr)were conducted on two uniaxial geogrids to determine their creep behavior,as well as the a-Pr and b-Pr relationships.The test results show that increasing Pr accelerates the development of creep deformation for both geogrids.Meanwhile,a and b respectively show exponential and negatively linear relationships with Pr,which were confirmed by abundant experimental data available in other studies.Based on the above creep model and relationships,an accurate and reliable analytical model was then proposed for predicting the time-dependent d of GRS walls with modular block facing,which was further validated using a relevant numerical investigation from the previous literature.Performance evaluation and comparison of the proposed model with six available prediction models were performed.Then a parametric study was carried out to evaluate the effects of wall height,vertical spacing of geogrids,unit weight and internal friction angle of backfills,and factor of safety against pullout on d at the end of construction and 5 years afterwards.The findings show that the creep effect not only promotes d but also raises the elevation of the maximum d along the wall height.Finally,the limitations and application prospects of the proposed model were discussed and analyzed.

Analytical Modeling and Mechanism Analysis of Time-Varying Excitation for Surface Defects in Rolling Element Bearings

Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechanism analysis and fault feature extraction.However,in conventional investigations,this issue is not well and fully addressed from the perspective of theoretical analysis and physical derivation.In this study,an improved analytical model for time-varying displacement excitations(TVDEs)caused by surface defects is theoretically formulated.First and foremost,the physical mechanism for the effect of defect sizes on the physical process of rolling element-defect interaction is revealed.According to the physical interaction mechanism between the rolling element and different types of defects,the relationship between time-varying displacement pulse and defect sizes is further analytically derived.With the obtained time-varying displacement pulse,the dynamic model for the deep groove bearings considering the internal excitation caused by the surface defect is established.The nonlinear vibration responses and fault features induced by surface defects are analyzed using the proposed TVDE model.The results suggest that the presence of surface defects may result in the occurrence of the dual-impulse phenomenon,which can serve as indexes for surface-defect fault diagnosis.

Analytical model of 2D leakoff in waterflood-induced fractures

Waterflood-induced fractures,also known as self-induced fractures,spontaneously form at injection wells during waterflooding.These fractures propagate long distances through rock,allowing injected fluids to travel far away from a well,both within and outside the flooding layer.Essentially,the me-chanics of waterflood-induced fracture propagation is similar to that of hydraulic fractures,which are intentionally created for reservoir stimulation.Fracturing models developed for hydraulic fractures can also be applied to waterflood-induced fractures.However,waterflood-induced fractures are typically pumped with much larger volumes of water or brine and grow much longer in time.As a result,fluid leakoff from waterflood fractures into the formation is more extensive and two-dimensional(2D),a characteristic that is often ignored in a majority of modern fracturing simulators,making their appli-cation to waterflood fractures unreliable.In this work,we revisit the problem of leakoff for long-growing waterflood-induced fractures and develop a new analytical model for fluid leakoff that provides improved predictions of fracture geometry and can be easily implemented in fracturing simulators.We incorporate the developed solution into the classical Perkins-Kern-Nordgren(PKN)model of fracture growth,which shows that the choice of the Carter or a 2D leakoff model greatly impacts fracture ge-ometry at large time.The conducted parametric study shows while a toughness-dominated regime af-fects fracture evolution,most of fracture lifetime occurs in a viscosity-and-leakoff-dominated regime.We also develop an asymptotic solution for a leakoff profile in the limiting case of 2D leakoff domination(~~M and~~K).Finally,we study 3D fracture growth and out-of-zone injection with three layers and a complex structure of zones.The study shows that ignoring the 2D leakoff during simulation results in a significant overestimation of fracture geometry predictions.The present work,thus,plays an important role in improving waterflood fracture modelling,as it highlights the significance of 2D leakoff in waterflood-induced fractures and provides a reliable analytical model for fluid leakoff that can be incorporated into modern fracture simulators.

Experimental investigation and analytically modeling of hysteretic behavior of rigid bus-flexible connectors of 220 kV electrical substations

This paper describes the quasi-static testing and analytical modelling of the hysteretic behavior of aluminum alloy rigid bus-flexible connectors of 220 kV electrical substations.The main objective of the study is to experimentally investigate the hysteretic behavior of six different types of rigid bus-flexible connectors 220 kV electrical substations when subjected to cyclic loading.Another objective is to theoretically study the flexibility and effectiveness of a previously proposed analytical model in fitting the experimental hysteresis loops of the tested rigid bus-flexible connectors.The experimental investigation indicates that the tested rigid bus-flexible connectors exhibit highly asymmetric hysteresis behavior along with tension stiffening effect.The theoretical study demonstrates that the generalized Bouc-Wen model has high flexibility and is effective in fitting the experimental hysteresis resisting force-displacement curves of the six tested rigid bus-flexible connectors.

Three-Dimensional Analytical Modeling of Axial-Flux Permanent Magnet Drivers

In this paper, the axial-flux permanent magnet driver is modeledand analyzed in a simple and novel way under three-dimensional cylindricalcoordinates. The inherent three-dimensional characteristics of the deviceare comprehensively considered, and the governing equations are solved bysimplifying the boundary conditions. The axial magnetization of the sectorshapedpermanent magnets is accurately described in an algebraic form bythe parameters, which makes the physical meaning more explicit than thepurely mathematical expression in general series forms. The parameters of theBessel function are determined simply and the magnetic field distribution ofpermanent magnets and the air-gap is solved. Furthermore, the field solutionsare completely analytical, which provides convenience and satisfactoryaccuracy for modeling a series of electromagnetic performance parameters,such as the axial electromagnetic force density, axial electromagnetic force,and electromagnetic torque. The correctness and accuracy of the analyticalmodels are fully verified by three-dimensional finite element simulations and a15 kW prototype and the results of calculations, simulations, and experimentsunder three methods are highly consistent. The influence of several designparameters on magnetic field distribution and performance is studied and discussed.The results indicate that the modeling method proposed in this papercan calculate the magnetic field distribution and performance accurately andrapidly, which affords an important reference for the design and optimizationof axial-flux permanent magnet drivers.

Consolidation of high replacement ratio stone column-reinforced ground:Analytical solutions incorporating clogging effect

The utilization of stone columns has emerged as a popular ground improvement strategy,whereas the drainage performance can be adversely hampered by clogging effect.Despite the ample progress of calculation methods for the consolidation of stone column-improved ground,theoretical investigations into the clogging effect have not been thoroughly explored.Furthermore,it is imperative to involve the column consolidation deformation to mitigate computational error on the consolidation of composite ground with high replacement ratios.In this context,an analytical model accounting for the initial clogging and coupled time and depth-dependent clogging of stone columns is established.Then,the resulting governing equations and analytical solutions are obtained under a new flow continuity relationship to incorporate column consolidation deformation.The accuracy and reliability of the proposed model are illustrated by degradation analysis and case studies with good agreements.Subsequently,the computed results of the current study are juxtaposed against the existing models,and an in-depth assessment of the impacts of several crucial parameters on the consolidation behavior is conducted.The results reveal that ignoring column consolidation deformation leads to an overestimate of the consolidation rate,with maximum error reaching up to 16%as the replacement ratio increases.Furthermore,the initial clogging also has a significant influence on the consolidation performance.Additionally,the increment of depth and time-clogging factors a and b will induce a noticeable retardation of the consolidation process,particularly in the later stage.

A new analytical model for thermal stresses in multi-phase materials and lifetime prediction methods

Based on the fundamental equations of the mechanics of solid continuum, the paper employs an analytical model for determination of elastic thermal stresses in isotropic continuum represented by periodically distributed spherical particles with different distributions in an infinite matrix, imaginarily divided into identical cells with dimensions equal to inter-particle distances, containing a central spherical particle with or without a spherical envelope on the particle surface. Consequently, the multi-particle-（envelope）- matrix system, as a model system regarding the analytical modelling, is applicable to four types of multi-phase materials. As functions of the particle volume fraction v, the inter-particle distances dl, d2, d3 along three mutually per- pendicular axes, and the particle and envelope radii, R1 and R2, respectively, the thermal stresses within the cell, are originated during a cooling process as a consequence of the difference in thermal expansion coefficients of phases rep- resented by the matrix, envelope and particle. Analytical-（experimental）-computational lifetime prediction methods for multi-phase materials are proposed, which can be used in engineering with appropriate values of parameters of real multi-phase materials.

Simple analytical model for depth-averaged velocity in meandering compound channels

A simple but applicable analytical model is presented to predict the lat- eral distribution of the depth-averaged velocity in meandering compound channels. The governing equation with curvilinear coordinates is derived from the momentum equation and the flow continuity equation under the condition of quasi-uniform flow. A series of experiments are conducted in a large-scale meandering compound channel. Based on the experimental data, a magnitude analysis is carried out for the governing equation, and two lower-order shear stress terms are ignored. Four groups of experimental data from different sources are used to verify the predictive capability of this model, and good predictions are obtained. Finally, the determination of the velocity parameter and the limitation of this model are discussed.

ANALYTICAL MODEL ALGORITHM FOR DYNAMICS OF ROBOTIC MANIPULATORS

A simple analytical model method for dynamics of robotic manipulators is proposed.Problem of deriving model matrix elements is transformed into problem of solving for driving forceand driving torque under specified condition by recursive dynamic equations. Expressions of reaction force in arbitrary joint in numeric-symbolic form are also derived. The properties of modelmatrices are given. Corresponding software which can recognize and manipulate symbols is developed and can be used to generate model and real-time code of robotic dynamics.

AN ANALYTICAL SOLUTION FOR THE MODEL OF DRUG DISTRIBUTION AND ABSORPTION IN SMALL INTESTINE

According to the physiological and anatomical characteristics of small intestine,neglecting the effect of its motility on the distribution and absorption of drug and nutrient,Y.Miyamoto et al.proposed a model of two-dimensional laminar flow in a circular porous tube with permeable wall and calculated the concentration profile of drugby numerical analysis.In this paper,we give a steady-state analytical solution of the above model including deactivationterm.The obtained results are in agreement with the results of their numerical analysis. Moreover the analytical solution presented in this paper reveals the relation among the physiological parameters of the model and describes the basic absorption rule of drug and nutrient through the intestinal wall and hence pro- vides a theoretical basis for determining the permeability and reflection coefficient through in situ experiments.

A two-dimensional analytical subthreshold behavior model for junctionless dual-material cylindrical surrounding-gate MOSFETs

A two-dimensional analytical subthreshold behavior model for junctionless dual-material cylindrical surrounding- gate （JLDMCSG） metal-oxide-semiconductor field-effect transistors （MOSFETs） is proposed. It is derived by solving the two-dimensional Poisson＇s equation in two continuous cylindrical regions with any simplifying assumption. Using this analytical model, the subthreshold characteristics of JLDMCSG MOSFETs are investigated in terms of channel electro- static potential, horizontal electric field, and subthreshold current. Compared to junctionless single-material cylindrical surrounding-gate MOSFETs, JLDMCSG MOSFETs can effectively suppress short-channel effects and simultaneously im- prove carrier transport efficiency. It is found that the subthreshold current of JLDMCSG MOSFETs can be significantly reduced by adopting both a thin oxide and thin silicon channel. The accuracy of the analytical model is verified by its good agreement with the three-dimensional numerical simulator ISE TCAD.

Analytical model of tilted driver–pickup coils for eddy current nondestructive evaluation

A driver-pickup probe possesses better sensitivity and flexibility due to individual optimization of a coil. It is fre- quently observed in an eddy current （EC） array probe. In this work, a tilted non-coaxial driver-pickup probe above a multilayered conducting plate is analytically modeled with spatial transformation for eddy current nondestructive evalua- tion. Basically, the core of the formulation is to obtain the projection of magnetic vector potential （MVP） from the driver coil onto the vector along the tilted pickup coil, which is divided into two key steps. The first step is to make a projection of MVP along the pickup coil onto a horizontal plane, and the second one is to build the relationship between the pr, ojected MVP and the MVP along the driver coil. Afterwards, an analytical model for the case of a layered plate is established with the reflection and transmission theory of electromagnetic fields. The calculated values from the resulting model indicate good agreement with those from the finite element model （FEM） and experiments, which validates the developed analytical model.

Analytical Model of Elastic Modulus and Coefficient of Thermal Expansion for 2.5D C/SiC Composite

To make better use of 2.5D C/SiC composites in industry, it is necessary to understand the mechanical properties. A finite element model＇of 2.5D composites is established, by considering the fiber undulation and the porosity in 2.5D C/SiC composites. The fiber direction of warp is defined by cosine function to simulate the undulation of warp, and based on uniform strain assumption, analytical model of the elastic modulus and coefficient of thermal expansion （CTE） for 2.5D C/SiC composites were established by using dual- scale model. The result is found to correlate reasonably well with the predicted results and experimental results. The parametric study also demonstrates the effects of the fiber volume fraction, distance of warp yarn, and porosity in micro-scale on the mechanical properties and the coefficients of thermal expansion.

Analytical modeling of sandwich beam for piezoelectric bender elements

Piezoelectric bender elements are widely used as electromechanical sensors and actuators, An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory （FSDT）, which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simplysupported bender elements was carried out and the numerical results showed that, solutions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.

Analytical Model for Underwater Wireless Sensor Network Energy Consumption Reduction

In an Underwater Wireless Sensor Network(UWSN),extreme energy loss is carried out by the early expiration of sensor nodes and causes a reduction in efficiency in the submerged acoustic sensor system.Systems based on clustering strategies,instead of each node sending information by itself,utilize cluster heads to collect information inside the clusters for forwarding collective information to sink.This can effectively minimize the total energy loss during transmission.The environment of UWSN is 3D architecture-based and follows a complex hierarchical clustering strategy involving its most effecting unique parameters such as propagation delay and limited transmission bandwidth.Round base clustering strategy works in rounds,where each round comprises three fundamental stages:cluster head selection,grouping or node association,and data aggregation followed by forwarding data to the sink.In UWSN,the energy consumed during the formation of clusters has been considered casually or completely evaded in the previous works.In this paper,the cluster head setup period has been considered the main contributor to extra energy utilizer.A numerical channel model is proposed to compute extra energy.It is performed by using a UWSN broad model.The results have shown that extra maximum energy consumption is approximately 12.9 percent of the system total energy consumed in information transmissions.

Analytical modeling of complex contact behavior between rock mass and lining structure

Based on the nondestructive test data of operating railway tunnels in China, this paper summarizes the basic characteristics of the complex contact behavior between the rock mass and lining structure. The contact modes are classified into dense contact, local non-contact, and loose contact. Subsequently, the corresponding mechanical model for each contact mode is developed according to its mechanical characteristics using the complex variable method. In the proposed mechanical model, a special algorithm is introduced to detect whether the local non-contact zone is re-contacted. Besides, a novel conformal mapping method is also proposed to accurately calculate the mechanical response of the concrete lining. Finally, the accuracy of the proposed method is verified by comparing it with the finite element method(FEM). Several parameter investigations are conducted to analyze the effects of different contact modes on the rock-lining interaction. The results show that:(i) the height of the local noncontact area does not have a significant effect on the contact stress distribution if no re-contact occurs;(ii) backfill grouting can reduce the local stress concentration caused by poor contact modes;and(iii) reducing the friction coefficient of the interface can lead to a more uniform distribution of internal forces in the concrete lining.

Analytical Model for the Palaeoenvironmental Evolution of the Nihewan Beds

In this paper, the evolutional characteristics of palaeoclimate and oxidation-reduction conditions as well asacidity-alkalinity environment are discussed by means of the step-regression, cluster, optimal partitioning andcorrelation analyses of CaCO_3, C / P_2O_5, Fe^(2+) / Fe^(3+), pH and Eh values, taking the Xiaodukou section in theNihewan basin as an example. The CaCO_3, C / P_2O_5 and pH were calculated respectively using the optimalpartitioning method. Thus five cold zones and six warm zones as well as five reduction and six oxidation zoneswere distinguished. Then the inductive method was used to produce four numerical groups: 8.10, 8.3-8.4,8.6-8.7 and 8.9-8,97. The above-mentioned results are respectively based on CaCO_3 content, C/P_2O_5 andpH values. From Fig. 3, Tables 1 and 2 it can be seen that the Nihewan Beds were formed mainly under a re-duction and slightly alkaline environment of cold climate, with pH values of 8.3-8.4. Fig. 3 shows that bed 35is approximately near the boundary between the Brunhes and Matuyama polarity epochs, 0.73 Ma in age; bed26 is roughly near the Jaramillo event (base), 0.97 Ma in age; bed 18 coincides roughly with themagnetostratigraphic boundary of 2.00 Ma (?). Bed 13 may be the Pleistocene-Pliocene boundary, 2.48 Ma inage. Thus geochemical zones Ⅰ, Ⅱ, Ⅲ and Ⅳ include respectively cold zones 1; 2 and 3; 4; and 5.

Sulfate diffusion in coal pillar:experimental data and prediction model

The stability of coal pillar dams is crucial for the long-term service of underground reservoirs storing water or heat.Chemi-cal damage of coal dams induced by ions-atttacking in coal is one of the main reasons for the premature failure of coal dams.However,the diffusion process of harmful ions in coal is far from clear,limiting the reliability and durability of coal dam designs.This paper investigates sulfate diffusion in coal pillar through experimental and analytical methods.Coal specimens are prepared and exposed to sulfate solutions with different concentrations.The sulfate concentrations at different locations and time are measured.Based on experimental data and Fick's law,the time-dependent surface concentration of sulfate and diffusion coefficient are determined and formulated.Further,an analytical model for predicting sulfate diffusion in coal pillar is developed by considering dual time-dependent characteristics and Laplace transformations.Through comparisons with experimental data,the accuracy of the analytical model for predicting sulfate diffusion is verified.Further,sulfate diffusions in coal dams for different concentrations of sulfate in mine water are investigated.It has been found that the sulfate concen-tration of exposure surface and diffusion coefficient in coal are both time-dependent and increase with time.Conventional Fick's law is not able to predict the sulfate diffusion in coal pillar due to the dual time-dependent characteristics.The sulfate attacking makes the coal dam a typical heterogeneous gradient structure.For sulfate concentrations 0.01-0.20 mol/L in mine water,it takes almost 1.5 and 4 years for sulfate ions to diffuse 9.46 and 18.92 m,respectively.The experimental data and developed model provide a practical method for predicting sulfate diffusion in coal pillar,which helps the service life design of coal dams.

Analytical modelling of the mechanical damage of soil induced by lightning strikes capturing electro-thermal,thermo-osmotic,and electro-osmotic effects

This article presents a mathematical model for simulating the mechanical behaviour of lightning strikes and analysing the resulting damage to the soil.This article focuses on the electro-thermal effect and seepage caused by lightning strikes in particular.Then,a numerical model based on the conservation laws of momentum,mass and energy is developed for soil subjected to lightning strikes.Comparisons to field observations and theoretical calculations are used to demonstrate the efficacy and accuracy of numerical simulations.The findings demonstrate that lightning strikes can cause soils to experience both seepage force and heat stress.Under the calculative condition of this article:by increasing the intrinsic permeability of the soil,k_(p)(≥10^(-10)m^(2)),the seepage force can be effectively reduced,hence reducing the risk of lightning strikes;improving the electrical conductivity of the soil β(≥10^(-1) S/m^(2))and lowering its thermal expansion coefficient(≤10^(-6)K^(-1))can greatly reduce the damage caused by lightning strikes to the soil.The preceding investigations demonstrate that the suggested model is capable of evaluating mechanical damage caused by lightning in the soil,and the findings contribute to a better understanding of soil mechanical response to lightning strikes.

A quantum efficiency analytical model for complementary metal–oxide–semiconductor image pixels with a pinned photodiode structure

A quantum efficiency analytical model for complementary metal–oxide–semiconductor（CMOS） image pixels with a pinned photodiode structure is developed. The proposed model takes account of the non-uniform doping distribution in the N-type region due to the impurity compensation formed by the actual fabricating process. The characteristics of two boundary PN junctions located in the N-type region for the particular spectral response of a pinned photodiode, are quantitatively analyzed. By solving the minority carrier steady-state diffusion equations and the barrier region photocurrent density equations successively, the analytical relationship between the quantum efficiency and the corresponding parameters such as incident wavelength, N-type width, peak doping concentration, and impurity density gradient of the N-type region is established. The validity of the model is verified by the measurement results with a test chip of 160×160 pixels array,which provides the accurate process with a theoretical guidance for quantum efficiency design in pinned photodiode pixels.