Three-dimensional Mode Research Articles

Magnetic mixed convection within wavy trapezoidal thermal energy storage systems using nano enhanced phase change material

The three-dimensional (3D) MHD mixed convection mode confined 3D wavy trapezoidal enclosure is examined. The bottom plane of the trapezoidal system is irregular, particularly a wavy plane with various undulation numbers \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:N$$\\end{document}. The forced convection phenomenon arises due to the displacement of the top region plane, whereas the porosity-enthalpy methodology characterizes the progression of charging. The heat transfer is enhanced using the nanoencapsulation phase change material (NePCM), consisting of Polyurethane as a shell and Nonadecane as a core, with water as the primary liquid base. The (GFEM) is used to treat the governing system, and a comparison between the HT (heat transmission) irreversibility and FF (fluid friction) irreversibility is performed using the function of the BeAvg. The significant findings revealed that parabolic behaviors for the melting ribbon curve are given at lower values of Re and higher values of Ha. Also, reducing the undulation number is better for obtaining a higher heat transmission rate. The average Nusselt number was lowered by 60% and 19%, respectively, at the highest Reynolds number when the Hartmann number increased from 0 to 100 and N from 2 to 8. Also, the values of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:Re$$\\end{document} between 1 and 100 improve the heat transfer rates up to 51%.

Haar wavelet analysis of axisymmetric vibration of 2-D functionally graded porous thin annular plate resting on the Winkler foundation

Purpose In this paper, free axisymmetric vibration analysis of a two-directional functionally graded porous thin annular plate resting on the Winkler foundation is presented utilizing the classical plate theory (CPT). The mechanical properties are considered to be varying in the radial-thickness plane.Design/methodology/approach Based on the CPT, the governing differential equation of motion is derived. The highest-order derivative of displacement is approximated by Haar wavelets and successive lower-order derivatives are obtained by integration. The integration coefficients are calculated using boundary conditions. The fundamental frequency for clamped-clamped, clamped-simply supported, simply supported-clamped and simply supported-simply supported boundary conditions is obtained.Findings The effects of the porosity coefficient, the coefficient of radial variation, the exponent of power law, the foundation parameter, the aspect ratio and boundary conditions are investigated on fundamental frequency. A convergence study is conducted to validate the present analysis. The accuracy and reliability of the Haar wavelets are shown by comparing frequencies with those available in the literature. Three-dimensional mode shapes in the fundamental mode for all four boundary conditions are presented.Originality/value Based on the Haar wavelet method, a free axisymmetric vibration model of a porous thin annular plate is solved in which 2-D variation of mechanical properties is considered.

On the short-wavelength three-dimensional instability in the cylinder wake

We examine the mechanisms responsible for the onset of the three-dimensional mode B instability in the wake behind a circular cylinder. We show that it is possible to explicitly account for the stabilising effect of spanwise viscous diffusion and then demonstrate that the remaining mechanisms involved in this short-wavelength instability are preserved in the limit of zero wavelength. Using the resulting simplified equations, we show that perturbations in different fluid particles interact only through the in-plane viscous diffusion which turns out to have a destabilising effect. We also show that in the presence of viscous diffusion, the closed trajectories which had been conjectured to play a crucial role in the onset of the mode B instability are not actually a prerequisite for the growth of mode B type perturbations. We combine these observations to identify the three essential ingredients for the development of the mode B instability: (i) the amplification of perturbations in the braid regions due to the stretching mechanism; and the spreading of perturbations through (ii) viscous diffusion, and (iii) cross-flow advection which transports fluid between the two braid regions on either side of the cylinder. Finally, we develop a simple criterion that allows the prediction of the regions where three-dimensional short-wavelength perturbations are amplified by the stretching mechanism. The approach used in our study is general and has the potential to give insights into the onset of three-dimensionality via short-wavelength instabilities in other flows.

Image quality in three-dimensional (3D) contrast-enhanced dynamic magnetic resonance imaging of the abdomen using deep learning denoising technique: intraindividual comparison between T1-weighted sequences with compressed sensing and with a modified Fast 3D mode wheel.

To assess the image quality of a modified Fast three-dimensional (Fast 3D) mode wheel with sequential data filling (mFast 3D wheel) combined with a deep learning denoising technique (Advanced Intelligent Clear-IQ Engine [AiCE]) in contrast-enhanced (CE) 3D dynamic magnetic resonance (MR) imaging of the abdomen during a single breath hold (BH) by intra-individual comparison with compressed sensing (CS) with AiCE. Forty-two patients who underwent multiphasic CE dynamic MRI obtained with both mFast 3D wheel using AiCE and CS using AiCE in the same patient were retrospectively included. The conspicuity, artifacts, image quality, signal intensity ratio (SIR), signal-to-noise ratio (SNR), contrast ratio (CR), and contrast enhancement ratio (CER) of the organs were compared between these 2 sequences. Conspicuity, artifacts, and overall image quality were significantly better in the mFast 3D wheel using AiCE than in the CS with AiCE (all p < 0.001). The SNR of the liver in CS with AiCE was significantly better than that in the mFast 3D wheel using AiCE (p < 0.01). There were no significant differences in the SIR, CR, and CER between the two sequences. A mFast 3D wheel using AiCE as a deep learning denoising technique improved the conspicuity of abdominal organs and intrahepatic structures and the overall image quality with sufficient contrast enhancement effects, making it feasible for BH 3D CE dynamic MR imaging of the abdomen.

Train-track-bridge interaction effects on highly skewed girder bridges of short-to-medium spans for increasing operating speeds

This paper contributes to comprehend the vertical vibrational response of oblique, simply-supported girder bridges on high-speed railway lines. Simplified methods adopted for dynamic analysis of such structures admit 2D beam-type models for the assessment of the Serviceability Limit State associated to traffic safety. However, in skewed bridges with multi-track decks and open sections, the dynamic response under railway loads is rather complex due to the coupled participation of three-dimensional modes. Based on experimental data from two existing bridges of different span lengths, detailed digital twins which include an explicit representation of the ballast track are implemented. Taking these models as reference, the influence of skewness on the modal parameters and maximum acceleration under passing trains is evaluated considering bridge variants. Correlation with the presence of transverse diaphragms at the supports and the restraining effect of the ballast track between spans is investigated as well. Finally, the adequacy of considering vehicle-bridge-interaction effects is assessed through numerical-experimental comparisons. The results reveal a reduction in maximum acceleration levels with increasing skewness and a notably weak coupling between consecutive spans, suggesting that classical single-span models may not always safely estimate the deck's maximum vertical response.

Formation mechanism and oil-bearing properties of gravity flow sand body of Chang 63 sub-member of Yanchang Formation in Huaqing area, Ordos Basin

Abstract Gravity flow sand body is an important reservoir for deep water deposition. The in-depth study of its formation mechanism and oil enrichment law can provide important guidance for oil and gas exploration in deep water areas. In this article, taking the deep-water gravity flow sand body of the Triassic Chang 63 sub-member in the Huaqing area as an example, the identification characteristics, formation mechanism, and oil-bearing characteristics of the gravity flow sand body are systematically discussed. The results show that sandy debris flow, turbidite flow, and mixed event flow present different superposition combination modes on vertical gravity flow deposition. The lithofacies of the gravity flow sandstone complex are mainly affected by lake level fluctuation, provenance supply, and hydrodynamic conditions. According to the formation conditions, sedimentary types. and distribution characteristics of deep water gravity flow sand bodies, a three-dimensional sedimentary mode of deep water gravity flow sand bodies is established. It is found that the physical and oil-bearing properties of the sandy debris flow sand body are better than those of the turbidity flow sand body. The reason is that the proportion of debris in the sand body of sandy debris flow is high, and the content of debris particles is generally greater than 70% according to the statistics of thin sections, which is conducive to the formation of pores. Second, sandy debris flow belongs to block transport, and the mixing of lithology is not sufficient in the process of block flow transport, so some pores will be preserved. Finally, gravity flows, which are dense at the beginning, become less dense later as detrital sediments unload, allowing them to be transported to distant regions. Therefore, the monolayer thickness of the sandy debris flow sand body is large (generally greater than 0.5 m), and the particle size of the debris ranges from 0.03 to 0.3 mm. Finally, the physical and oil-bearing properties of the sandy clastic flow sand body are better than those of the turbidity flow sand body.

Three-dimensional fracture modes decoupling by means of invariant integrals in wood under mixed mode loading

This paper addresses the determination of the energy release rate in an orthotropic elastic material such as wood with a three-dimensional view of the problem. The mixed mode loading associated with the anisotropy of the material required mode decoupling by isolating the energy release rates in mode I, mode II and in mode III. These energy release rates are calculated using the invariant integral M of Linear Elastic Fracture Mechanics (LEFM). This decoupling has necessitated the introduction of kinetically and statically admissible three-dimensional virtual displacement and stress fields in the vicinity of the crack front. The fracture mode decoupling strategy is presented and implemented through finite element modelling of a Mixed Mode Crack Growth (MMCG) specimen. Different thicknesses are investigated to highlight the 3D effects. The modelling highlighted the effect of Mode II at the edges of free surfaces for mixed loadings including mode III (mode III, mode (II+III) and mode (I+II+III)), while mode III was the predominant at the middle of the specimen. In cases of mixed mode (I+II), the energy release rate GI was highest at the middle of the specimen and lowest at the edges of the free surfaces, regardless of the degree of mixing for a given thickness. The correlation between the results obtained using the proposed approach and the non-dependence of the integration domain, as well as with the usual approaches employed in the literature, is demonstrated.

Proper orthogonal decomposition reduced-order model of the global oceans

AbstractA reduced-order model (ROM) of the global oceans is developed by projecting the hydrostatic Boussinesq equations of motion onto a proper orthogonal decomposition (POD) basis. Three-dimensional POD modes are calculated from the ocean fields of an ensemble climate reanalysis dataset. The coefficients in the POD ROM are calculated using a regression approach. The performance of various POD ROM configurations are assessed. Each configuration is derived from an alternate sea-water equation of state, linking the density and temperature fields. POD ROM variants incorporating an equation of state in which density is a quadratic function of temperature, are able to reproduce the statistics of the large-scale structures at a fraction of the computational cost required to numerically simulate this flow. Due to the speed and efficiency of calculation, such reduced-order models of the global geophysical system will enable researchers and policy makers to assess the physical risk for a broader range of potential future climate scenarios.

Contribution of Unsteadiness to Solid Fuel Burning Characteristics in a Scramjet Combustor

The contributions of unsteadiness to solid fuel combustion are investigated numerically and validated against new experiments in a deep cavity scramjet. Large-eddy simulations discretized with discontinuous Galerkin (DG) elements are solved with a flamelet manifold approach in three dimensions. A multiphase model that incorporated thermal decomposition inside the foam layer is coupled with stagnation flow flames to determine the combustion manifold and regression rate. The approach accurately models small-scale experiments of convective burning over solid fuel. The inclusion of the manifold into the DG code features two innovations: a polynomial fitting of the pressure to reduce the interpolation dimensions and the coefficient of determination to include non-monotonic manifolds in DG schemes. Model validation was performed using pressure and averaged regression rate data, both of which showed strong agreement with experiments. Three-dimensional pressure modes in the cavity support a substantial increase in regression rates and a broadening of the peak due to oscillations of the impingement point. The majority of fuel is pyrolyzed at the shear-layer reattachment point in a stagnation flow boundary layer. The fuel in the cavity is pyrolyzed by conductive heat transfer from the main shear layer. Poor combustion is observed in the expanding fuel section.

High-precision ultrasonic atomization using oscillating microchannels: Interplay of three-dimensional vibrational modes and droplet ejection mechanisms

Ultrasonic atomization is a critical process for producing micrometer-diameter droplets, widely utilized in aerosol drug delivery, spectrometry, and printing. The geometry of the vessel containing the fluid being atomized and the oscillations of its sidewalls play a crucial role in controlling the wave patterns and hence the droplet ejection process, especially at actuation frequencies exceeding 1 MHz. However, the mechanisms behind droplet ejection under high-frequency ultrasonic actuation remain poorly understood. We employ oscillating high-aspect-ratio Silicon microchannels to create ideal conditions where capillary forces, microchannel geometry, and oscillatory motion work together to precisely confine a liquid film and generate droplets with controlled diameters. We show that the three-dimensional vibrations of the microchannels, particularly the interplay between actuation frequency, amplitude, and channel geometry, can be used to effectively tune the ligament development and droplet breakup. This understanding allows us to establish conditions to reduce actuation power and hence minimize heating, control shear stresses and tune the droplet size on-demand without compromising uniformity and throughput.

Free vibration analysis of closed and open horizontal cylindrical shells utilizing coupled transfer function method and differential transform method

This article aims to analyze the free vibration of closed and open horizontal circular cylindrical shells based on the concept of state-space transformation in conjunction with the differential transform method (DTM). The governing equations of the cylinders were developed based upon Sanders’ thin shell theory. Then, the set of coupled governing differential equations transformed into nine first-order differential equations. Afterwards, the well-established semi-analytical scheme so-called DTM was employed to solve the differential equations. The numerical investigation of the present method was also comprehensively carried out by analyzing some closed and open cylindrical shells with different boundary and compatibility conditions. To ensure the correctness of the results, the outcomes were compared with experimental and other numerical results, especially with the well-known finite element method. Furthermore, some plots of two-dimensional and three-dimensional mode shapes for the first and second axial modes are depicted.

Nonmodal stability analysis of Poiseuille flow through a porous medium

We unravel the nonmodal stability of a three-dimensional nonstratified Poiseuille flow in a saturated hyperporous medium constrained by impermeable rigid parallel plates. The primary objective is to broaden the scope of previous studies that conducted modal stability analysis for two-dimensional disturbances. Here, we explore both temporal and spatial transient disturbance energy growths for three-dimensional disturbances when the Reynolds number and porosity of the material are high, based on evolution equations with respect to time and space, respectively. Modal stability analysis reveals that the critical Reynolds number for the onset of shear mode instability increases as porosity increases. Moreover, the Darcy viscous drag term stabilizes shear mode instability, resulting in a delay in the transition from laminar flow to turbulence. In addition, it demonstrates the suppression of three-dimensional shear mode instability as the spanwise wavenumber increases, thereby confirming the statement of Squire’s theorem. By contrast, nonmodal stability analysis discloses that both temporal and spatial transient disturbance energy growths curtail as the effect of the Darcy viscous drag force intensifies. But their maximum values behave like O(Re2) for a fixed porous material, where Re is the Reynolds number. However, for different porous materials, the scalings for both temporal and spatial transient disturbance energy growths are different. Furthermore, increasing porosity also suppresses both temporal and spatial disturbance energy growths. Finally, we observe that temporal transient disturbance energy growth becomes larger for a spanwise perturbation, while spatial transient disturbance energy growth becomes larger for a steady perturbation when angular frequency vanishes. The initial disturbance that excites the largest temporal energy amplification generates two sets of alternating high-speed and low-speed elongated streaks in the streamwise direction.

The Impact of The Three-Dimensional Cultivation Model on the Development of the Suzhou Tea Industry: Estimating Value of Output Per Acre and Diversified Sales Models

This article explores the impact of the three-dimensional cultivation mode on the development of the Suzhou tea industry, focusing on the diversified estimation of the value of output per acre and sales mode. It introduces the history and traditional cultivation practices of tea in Suzhou, as well as the current challenges and problems faced by the industry. An in-depth analysis was conducted on the overview and improvement plans of the three-dimensional cultivation mode, covering relevant technical methods. Based on this analysis, the impact of the three-dimensional cultivation on the value of output per acre was studied and predicted. Its potential and advantages were explored and compared with the effectiveness of traditional cultivation models. Additionally, the impact of the three-dimensional cultivation mode on sales was analyzed, examining its market adaptability and competitiveness, as well as its advantages in expanding sales channels and market coverage. The study also focused on the promoting effect of diversified sales models on the Suzhou tea industry, including direct consumption market development, tea processing product development and promotion, and the integration of tea culture and the tourism industry. To ensure sustainable development, the article evaluates the environmental impact, economic feasibility, social benefits, and farmer benefits of the three-dimensional cultivation model. Finally, the prospects for the development of the Suzhou tea industry were discussed, and the positioning and response strategies of the three-dimensional cultivation model were proposed.

Probabilistic analysis of geological and structural Prospects for Oil and gas Potential in Western Yakutia Using three-Dimensional Empirical Mode Decomposition of Potential Fields

Further development of modern formal approaches to extracting geo-structural information from gravimetric and magnetometric data is herein discussed. A practical example of using 3D GEMD (three-dimensional controlled empirical mode decomposition) algorithm to calculate potential fields transforms associated with the impact of deep and medium (of different ranks) geological structures on the adjacent territories of Western Yakutia was considered. Two types of reference groups were determined based on analysis of the known hydrocarbon fields in the Lena-Vilyuy and Lena-Tunguska oil and gas provinces. Statistical efficiency of the observed fields, fields’ area transforms (modified functions of empirical decomposition), and also spatially-linked combinations of the said attributes, aiming to solve the forecasting tasks, was determined. As a result of integration within the testing area, layout diagrams of deep geological and structural prerequisites for oil and gas potential, similar to group standards, were drawn up. A geological interpretation of forecasting and geophysical constructions is presented. It is shown that a number of identified areas predicted with high probabilities correlate with depressions of rift zones. Combined with thick volcanogenic-sedimentary formations, the latter forms most prospective oil and gas content pre-requisites.

The possibilities of echocardiography for detecting cardiotoxic effects of antineoplastic medications

Background. In recent decades, advancements in cancer treatment have resulted in enhanced patient survival rates, yet concurrently, escalated morbidity and mortality due to therapy-induced side effects, with cardiovascular complications (CVC) at the forefront. The risk of cardiovascular disease (CVD) during chemotherapy lies in the potentiality of interrupting or discontinuing the treatment of the underlying ailment, thereby diminishing the patient’s prospects of survival. Regrettably, delayed manifestations of cardiotoxic effects subsequent to the completion of anticancer therapy further diminish the patients’ quality of life and escalate mortality rates. Consequently, early diagnosis and timely identification of cardiotoxic effects induced by anticancer drugs have emerged as paramount objectives, shaping a novel domain in medicine termed cardio-oncology. Purpose. Assess the condition and modern ideas of the development of echocardiography in the assessment of cardiac dysfunction in the context of chemotherapy. Materials and Methods. References were analyzed using English-language biomedical databases (MEDLINE (Pubmed), Web of Science (Web of Knowledge) using the following keywords: «cardiotoxicity», «echocardiography», «chemotherapy», «ventricular dysfunction», «anticancer therapy», «risk stratification» for 2019–2024. Results. Cardiotoxicity arising as a consequence of anticancer therapy can manifest in various forms, including left ventricular (LV) myocardial dysfunction, heart failure (HF), pulmonary hypertension, thromboembolic complications, arterial hypertension, coronary heart disease, pericardial disease, valvular heart disease, and others. Detecting the subclinical variant of cardiotoxicity, which precedes the onset of HF, is of paramount importance. Presently, echocardiography remains the preferred method for evaluating the structural and functional status of the LV myocardium. However, studies have demonstrated that measuring LV ejection fraction (EF) via transthoracic echocardiography may not effectively detect LV dysfunction in its early stages. In recent years, novel myocardial imaging techniques have emerged for this purpose, with speckle-tracking echocardiography (STE) in both two-dimensional and three-dimensional modes showing promise. Соnclusion. The early detection of cardiotoxic effects induced by anticancer drugs emerges as a critical concern in cardiology practice. Evaluation of global myocardial strain derived from two-dimensional LV images provides valuable insights into diagnosing early LV dysfunction, especially in patients undergoing chemotherapy.

A Study on the Sustainable Development Strategy for Cultural Brands from the Perspective of All Media

The era of all media, as a new cognitive background connecting together everything, provides a new perspective for the operation and communication of cultural brands. Taking the connection between all media and cultural brands as the entry point, this paper discusses how to operate cultural brands in a reasonable and efficient manner. On the one hand, the task is on the construction and communication of cultural brands themselves, focusing on the cultural connotations of their brands and the integration of their marketing with multimedia resources; on the other hand, the operation strategy needs to be further improved, such as the innovation of operation concept, balance of brand layout and creation of brand differentiation advantages. In the context of the era of all-media integration, cultural brands create a more comprehensive and three-dimensional communication mode in a more diversified form. Choosing cross-media and multimedia for brand planning and operation is an inevitable choice.

Design of a Continuous-Zoom 2D/3D Microscope with High Zoom Ratio and Full Field of View

A four-group mechanically compensated continuous-zoom microscope is proposed and designed based on the theory of continuous zoom. The system addresses the limitations of traditional continuous-zoom microscopes, including a small zoom ratio, a short working distance, and the loss of details during 2D–3D switching. The system has a magnification of 0.6×~6.0× under two-dimensional observation, adapts to two-third-inch sensors, has a working distance of 130 mm, and adds a 360-degree rotatable beamsplitter for three-dimensional full-field-of-view observation. The magnification, numerical aperture, and sensor dimensions remain unchanged under both two-dimensional and three-dimensional observation. The design results demonstrate that the system is capable of achieving a high zoom ratio of 10× while maintaining a high level of imaging quality in both two-dimensional and three-dimensional modes. The MTF curves for each magnification are in close proximity to the diffraction limit, the spot diagrams are smaller than the airy disk range, and the zoom cam curves are smooth with no inflection points. Furthermore, the system negates the visual discrepancies and loss of detail that arise when switching observation modes due to alterations in system magnification and numerical aperture, thereby broadening the scope of applications for continuous-zoom microscopes.

Dynamo action driven by precessional turbulence.

We reveal and analyze an efficient magnetic dynamo action due to precession-driven hydrodynamic turbulence in the local model of a precessional flow, focusing on the kinematic stage of this dynamo. The growth rate of the magnetic field monotonically increases with the Poincaré number Po, characterizing precession strength, and the magnetic Prandtl number Pm, equal to the ratio of viscosity to resistivity, for the considered ranges of these parameters. The critical Po_{c} for the dynamo onset decreases with increasing Pm. To understand the scale-by-scale evolution (growth) of the precession dynamo and its driving processes, we perform spectral analysis by calculating the spectra of magnetic energy and of different terms in the induction equationin Fourier space. To this end, we decompose the velocity field of precession-driven turbulence into two-dimensional (2D) vortical and three-dimensional (3D) inertial wave modes. It is shown that the dynamo operates across a broad range of scales and exhibits a remarkable transition from a primarily vortex-driven regime at lower Po to a more complex regime at higher Po where it is driven jointly by vortices, inertial waves, and the shear of the background precessional flow. Vortices and shear drive the dynamo mostly at large scales comparable to the flow system size, and at intermediate scales, while at smaller scales it is mainly driven by inertial waves. This study can be important not only for understanding the magnetic dynamo action in precession-driven flows, but also in a general context of flows where vortices emerge and govern the flow dynamics and evolution.

Step-edge-guided nucleation and growth mode transition of α-Ga2O3 heteroepitaxy on vicinal sapphire

Abstract Controlling the epitaxial growth mode of semiconductor layers is crucial for optimizing material properties and device performance. In this work, the growth mode of α-Ga2O3 heteroepitaxial layers was modulated by tuning miscut angles (θ) from 0° to 7° off the (10-10) direction of sapphire (0002) substrate. On flat sapphire surfaces, the growth undergoes a typical three-dimensional (3D) growth mode due to the random nucleation on wide substrate terraces, as evidenced by the hillock morphology and high dislocation densities. As the miscut angle increases to θ=5°, the terrace width of sapphire substrate is comparable to the distance between neighboring nuclei, and consequently, the nucleation is guided by terrace edges, which energetically facilitates the growth mode transition into the desirable two-dimensional coherent growth. Consequently, the mean surface roughness decreases to only 0.62 nm, accompanied by a significant reduction in screw and edge dislocations to 0.16×107 cm-2 and 3.58×109 cm-2, respectively. However, the further increment of miscut angles to θ=7° shrink the terrace width less than nucleation distance, and the step-bunching growth mode is dominant. In this circumstance, the misfit strain is released in the initial growth stage, resulting in surface morphology degradation and increased dislocation densities.

Ultimate Lateral Resistance of Single Piles in Sand

The p-y curve method is currently the most widely utilized analytical approach for horizontally loaded piles. Precisely determining the ultimate soil resistance is essential to enhance the accuracy of the p-y curve. Despite various scholars proposing methods to establish the law governing ultimate soil resistance with soil depth in the sand, significant discrepancies exist among these approaches. This paper posits that the three-dimensional failure mode of the shallow soil in front of the pile manifests as a cone when it reaches the limit state. The expression for the ultimate soil resistance of a single pile in shallow soil is derived through limit equilibrium theory, and subsequently, the modified p-y curve is obtained. The accuracy was validated through a comparison between the corrected p-y curve and results obtained from centrifugation experiments and field studies. In contrast to the API specification method, the refined hyperbolic function p-y curve demonstrates enhanced precision, facilitating precise predictions of pile head displacement and pile bending moments under horizontal loads.