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.

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

An approximate analytical model for unconventional reservoir considering variable matrix blocks and simultaneous matrix depletion

In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate production evaluations because of the absence of matrix-macrofracture communication.In addition,most of the existing models are solved analytically based on Laplace transform and numerical inversion.Hence,an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation,the simultaneous matrix depletion is divided into two parts:one part feeding the macrofractures and the other part feeding the microfractures.Then,a series of partial differential equations(PDEs)describing the transient flow and boundary conditions are constructed and solved analytically by integration.Finally,a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models.When the microfracture system and matrix-macrofracture communication is neglected,the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model,respectively.Certainly,the new model also has an excellent agreement with the numerical model.The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin.After identifying the flow regime,the solution suitably matches the field production data,and the model parameters are determined.Through these output parameters,we can accurately forecast the production and even estimate the petrophysical properties.

Analytical and Experimental Research on Wave Scattering by an Open-Type Rectangular Breakwater with Horizontal Perforated Plates

This study proposes a novel open-type rectangular breakwater combined with horizontal perforated plates on both sides to enhance the sheltering effect of the rectangular box-type breakwaters against longer waves.The hydrodynamic characteristics of this breakwater are analyzed through analytical potential solutions and experimental tests.The quadratic pressure drop conditions are exerted on the horizontal perforated plates to facilitate assessing the effect of wave height on the dissipated wave energy of breakwater through the analytical solution.The hydrodynamic quantities of the breakwater,including the reflection,transmission,and energyloss coefficients,together with vertical and horizontal wave forces,are calculated using the velocity potential decomposition method as well as an iterative algorithm.Furthermore,the reflection and transmission coefficients of the breakwater are measured by conducting experimental tests at various wave periods,wave heights,and both porosities and widths of the horizontal perforated plates.The analytical predicted results demonstrate good agreement with the iterative boundary element method solution and measured data.The influences of variable incident waves and structure parameters on the hydrodynamic characteristics of the breakwater are investigated through further calculations based on analytical solutions.Results indicate that horizontal perforated plates placed on the water surface for both sides of the rectangular breakwater can enhance the wave dissipation ability of the breakwater while effectively decreasing the transmission and reflection coefficients.

Analytical modeling of piezoelectric meta-beams with unidirectional circuit for broadband vibration attenuation

Broadband vibration attenuation is a challenging task in engineering since it is difficult to achieve low-frequency and broadband vibration control simultaneously.To solve this problem,this paper designs a piezoelectric meta-beam with unidirectional electric circuits,exhibiting promising broadband attenuation capabilities.An analytical model in a closed form for achieving the solution of unidirectional vibration transmission of the designed meta-beam is developed based on the state-space transfer function method.The method can analyze the forward and backward vibration transmission of the piezoelectric meta-beam in a unified manner,providing reliable dynamics solutions of the beam.The analytical results indicate that the meta-beam effectively reduces the unidirectional vibration across a broad low-frequency range,which is also verified by the solutions obtained from finite element analyses.The designed meta-beam and the proposed analytical method facilitate a comprehensive investigation into the distinctive unidirectional transmission behavior and superb broadband vibration attenuation performance.

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 solutions to the precession relaxation of magnetization with uniaxial anisotropy

Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.

A coupled Legendre-Laguerre polynomial method with analytical integration for the Rayleigh waves in a quasicrystal layered half-space with an imperfect interface

The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.

Utility and Application of a Versatile Analytical Method for MMF Calculation in AC Machines

A versatile analytical method(VAM) for calculating the harmonic components of the magnetomotive force(MMF) generated by diverse armature windings in AC machines has been proposed, and the versatility of this method has been established in early literature. However, its practical applications and significance in advancing the analysis of AC machines need further elaboration. This paper aims to complement VAM by augmenting its theory, offering additional insights into its conclusions, as well as demonstrating its utility in assessing armature windings and its application of calculating torque for permanent magnet synchronous machines(PMSM). This work contributes to advancing the analysis of AC machines and underscores the potential for improved design and performance optimization.

Analytical solutions fractional order partial differential equations arising in fluid dynamics

This article describes the solution procedure of the fractional Pade-Ⅱ equation and generalized Zakharov equation(GSEs)using the sine-cosine method.Pade-Ⅱ is an important nonlinear wave equation modeling unidirectional propagation of long-wave in dispersive media and GSEs are used to model the interaction between one-dimensional high,and low-frequency waves.Classes of trigonometric and hyperbolic function solutions in fractional calculus are discussed.Graphical simulations of the numerical solutions are flaunted by MATLAB.

Review on analytical technologies and applications in metabolomics

Over the past decade,the swift advancement of metabolomics can be credited to significant progress in technologies such as mass spectrometry,nuclear magnetic resonance,and multivariate statistics.Currently,metabolomics garners widespread application across diverse fields including drug research and development,early disease detection,toxicology,food and nutrition science,biology,prescription,and chinmedomics,among others.Metabolomics serves as an effective characterization technique,offering insights into physiological process alterations in vivo.These changes may result from various exogenous factors like environmental conditions,stress,medications,as well as endogenous elements including genetic and protein-based influences.The potential scientific outcomes gleaned from these insights have catalyzed the formulation of innovative methods,poised to further broaden the scope of this domain.Today,metabolomics has evolved into a valuable and widely accepted instrument in the life sciences.However,comprehensive reviews focusing on the sample preparation and analytical methodologies employed in metabolomics within the life sciences are surprisingly scant.This review aims to fill that gap,providing an overview of current trends and recent advancements in metabolomics.Particular emphasis is placed on sample preparation,sophisticated analytical techniques,and their applications in life science research.

Exploration of Ideological and Political Materials for the Course of Inorganic and Analytical Chemistry for Environmental and Ecological Engineering Major

Integrating ideological and political theories teaching into the whole process of classroom teaching construction is a new requirement for implementing the fundamental task of cultivating people by virtue and playing the role of collaborative education.In order to realize the seamless integration of inorganic and analytical chemistry courses and ideological and political education,this paper summarizes the current situation of ideological and political research on inorganic and analytical chemistry courses in three major databases in China(VIP,CNKI and Wanfang),and sorts out the knowledge points,ideological and political elements and educational goals according to the content of the course chapters,to provide a basic guarantee for the ideological and political education construction of the course.

Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

Analytical Solutions for Testing of Baroclinic and Wind-Driven Three-Dimensional Hydrodynamic Models

It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.

GIS-Based Multi-Criteria Decision Analysis (MCDA) and Analytical Hierarchy Process (AHP) Techniques to Derive Flood Risks Management on Rice Productivity in Gishari Marshland

Floods are phenomenon with significant socio-economic implications mainly for human loss, agriculture, livestock, soil loss and land degradation, for which many researchers try to identify the most appropriate methodologies by analyzing their temporal and spatial development. This study therefore attempts to employ the GIS-based multi-criteria decision analysis and analytical hierarchy process techniques to derive the flood risks management on rice productivity in the Gishari Agricultural Marshland in Rwamagana district, Rwanda. Here, six influencing potential factors to flooding, including river slope, soil texture, Land Use Land Cover through Land Sat 8, rainfall, river distance and Digital Elevation Model are considered for the delineation of flood risk zones. Data acquisition like Landsat 8 images, DEM, land use land cover, slope, and soil class in the study area were considered. Results showed that if the DEM is outdated or inaccurate due to changes in the terrain, such as construction, excavation, or erosion, the predicted flood patterns might not reflect the actual water flow. This could result unexpected flood extents and depths, potentially inundating rice fields that were not previously at risk and this, expectedly explained that the increase 1 m in elevation would reduce the rice productivity by 0.17% due to unplanned flood risks in marshland. It was found that the change in rainfall distribution in Gishari agricultural marshland would also decrease the rice productivity by 0.0018%, which is a sign that rainfall is a major factor of flooding in rice scheme. Rainfall distribution plays a crucial role in flooding analysis and can directly impact rice productivity. Oppositely, another causal factor was Land Use Land Cover (LULC), where the Multivariate Logistic Regression Model Analysis findings showed that the increase of one unit in Land Use Land Cover would increase rice productivity by 0.17% of the total rice productivity from the Gishari Agricultural Marshland. Based on findings from these techniques, the Gishari Agricultural Marshlands having steeped land with grassland is classified into five classes of flooding namely very low, low, moderate, high, and very high which include 430%, 361%, 292%, 223%, and 154%. Government of Rwanda and other implementing agencies and major key actors have to contribute on soil and water conservation strategies to reduce the runoff and soil erosion as major contributors of flooding.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Understanding Pseudocapacitance Mechanisms by Synchrotron X-ray Analytical Techniques

Pseudocapacitive materials that store charges via reversible surface or near-surface faradaic reactions are capable of overcoming the capacity limitations of electrical double-layer capacitors.Revealing the structure–activity relationship between the microstructural features of pseudocapacitive materials and their electrochemical performance on the atomic scale is the key to build high-performance capacitor-type devices containing ideal pseudocapacitance effect.Currently,the high brightness(flux),and spectral and coherent nature of synchrotron X-ray analytical techniques make it a powerful tool for probing the structure–property relationship of pseudocapacitive materials.Herein,we report a comprehensive and systematic review of four typical characterization techniques(synchrotron X-ray diffraction,pair distribution function[PDF]analysis,soft X-ray absorption spectroscopy,and hard X-ray absorption spectroscopy)for the study of pseudocapacitance mechanisms.In addition,we offered significant insights for understanding and identifying pseudocapacitance mechanisms(surface redox pseudocapacitance,intercalation pseudocapacitance,and the extrinsic pseudocapacitance phenomenon in battery materials)by combining in situ hard XAS and electrochemical analyses.Finally,a perspective for further depth of understanding into the pseudocapacitance mechanism using synchrotron X-ray analytical techniques is proposed.

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.

UV/Vis-based process analytical technology to improve monoclonal antibody and host cell protein separation

Process analytical technology(PAT) is gaining more interest in the biomanufacturing industry because of its potential to improve operational control and compliance through real-time quality assurance.Currently, biopharmaceutical producers mainly monitor chromatographic processes with ultraviolet/visible(UV/Vis) absorbance. However, this measurement has a very limited correlation with purity and quantity. The current study aims to determine the concentration of monoclonal antibody(mAb) and host cell proteins(HCPs) using a build-in UV/Vis monitoring during Protein A affinity chromatography and to optimize the separation conditions for high purity of mAb and minimizing the HCPs content. The eluate was analyzed through in-line UV/Vis at 280 and 410 nm, representing mAb and HCPs concentration,respectively. Each 0.1 column volume(CV) fraction of UV/Vis chromatogram peak area were calculated,and different separation conditions were then compared. The optimum conditions of mAb separation were found as 12 CV loading, elution at pH 3.5, and starting the collection at 0.5 CV point, resulting in high m Ab recovery of 95.92% and additional removal of 49.98% of HCP comparing with whole elution pool. This study concluded that UV/Vis-based in-line monitoring at 280 and 410 nm showed a high potential to optimize and real-time control Protein A affinity chromatography for mAb purification from HCPs.