Engineering Analysis Research Articles

Engineering and Modeling of Water Flow via Computational Fluid Dynamics (CFD) and Modern Hydraulic Analysis Methods

The manuscripts presented in this Special Issue will both present engineering analyses of problems of contemporary importance in fluid mechanics and hydrodynamics and describe historical water systems and the technologies used to design and operate them by ancient Old and New World water engineers [...]

Defining a maximum heat release rate probability distribution function for design fires in sprinkler‐protected residential buildings

AbstractIn fire safety engineering analysis of sprinkler‐protected residential buildings, the maximum heat release rate is a key parameter requiring consideration. Several documents provide advice for estimating the heat release rate of a sprinkler‐controlled fire, with a prevailing suggestion that it is fixed upon activation of the first sprinkler. When carrying out deterministic analysis, this requires the engineer to assume fixed fire parameters and consider that sprinklers limit fire growth. To explore these assumptions, the study uses three deterministic models to estimate a sprinkler‐controlled maximum heat release rate for a representative apartment layout. The models include Alpert's correlation, a B‐RISK zone model and a computational fluid dynamics model in the Fire Dynamics Simulator. These deterministic models are compared to a probabilistic model in B‐RISK, where Monte Carlo simulations are used to generate a range of maximum heat release rates from distribution functions for fire and sprinkler properties. An output distribution function is generated with a mean of 296.6 kW and a standard deviation of 503.8 kW, with a lognormal distribution (μ = 5.014, σ = 1.165) estimated as a best‐fit. The deterministic models are estimated to sit in the 92–98 percentile range of this function, indicating that common deterministic assumptions are reasonably conservative. The article concludes with suggesting that, for deterministic analysis, a percentile between the 80th and 99th (340–2640 kW) could be qualitatively selected based on the design objectives, building situation and relative consequence of a fire. Further research is needed to establish guidelines for selecting appropriate percentiles across various building scenarios.

Modifying the Refuse Chute Design to Prevent Infection Spread: Engineering Analysis and Optimization

Considering the presence of airborne viruses, there is a need for renovation in refuse chutes, regarded as the first step in recycling household waste in buildings. This study aimed to revise the design of existing refuse chutes in light of the challenging experiences in waste management and public health during the coronavirus pandemic. This research primarily focused on the risks posed by various types of coronaviruses, such as the novel coronavirus (COVID-19) and acute respiratory syndrome (SARS and SARS-CoV), on stainless steel surfaces, with evidence of their survival under certain conditions. Refuse chutes are manufactured from stainless steel to resist the corrosive effects of waste. In examining the existing studies, it was observed that Casanova et al. and Chowdhury et al. found that the survival time of coronaviruses on stainless steel surfaces decreases as the temperature increases. Based on these studies, mechanical revisions have been made to the sanitation system of the refuse chute, thus increasing the washing water temperature. Additionally, through mechanical improvements, an automatic solution spray entry is provided before the intake doors are opened. Furthermore, to understand airflow and clarify flow parameters related to airborne infection transmission on residential floors in buildings equipped with refuse chutes, a computational fluid dynamics (CFD) analysis was conducted using a sample three-story refuse chute system. Based on the simulation results, a fan motor was integrated into the system to prevent pathogens from affecting users on other floors through airflow. Thus, airborne pathogens were periodically expelled into the atmosphere via a fan shortly before the intake doors were opened, supported by a PLC unit. Additionally, the intake doors were electronically interlocked, ensuring that all other intake doors remained locked while any single door was in use, thereby ensuring user safety. In a sample refuse chute, numerical calculations were performed to evaluate parameters such as the static suitability of the chute body thickness, static compliance of the chute support dimensions, chute diameter, chute thickness, fan airflow rate, ventilation duct diameter, minimum rock wool thickness for human contact safety, and the required number of spare containers. Additionally, a MATLAB code was developed to facilitate these numerical calculations, with values optimized using the Fmincon function. This allowed for the easy calculation of outputs for the new refuse chute systems and enabled the conversion of existing systems, evaluating compatibility with the new design for cost-effective upgrades. This refuse chute design aims to serve as a resource for readers in case of infection risks and contribute to the literature. The new refuse chute design supports the global circular economy (CE) model by enabling waste disinfection under pandemic conditions and ensuring cleaner source separation and collection for recycling. Due to its adaptability to different pandemic conditions including pathogens beyond coronavirus and potential new virus strains, the designed system is intended to contribute to the global health framework. In addition to the health measures described, this study calls for future research on how evolving global health conditions might impact refuse chute design.

A Digital Engineering Analysis of an Additively Manufactured Turbine Vane

Abstract Additive manufacturing (AM) has transformed the ability to accelerate gas turbine component research and development at a fraction of the cost and time associated with conventional manufacturing. However, whereas prior works have assessed manufacturing variability in cast turbine airfoils, limited data are available to understand the impact of as-built deviations in AM turbine parts. As metal additive airfoils are becoming more prevalent in research turbine architectures, it is increasingly important to understand the effects of potential hardware deviations specific to additively manufactured parts. With this goal in mind, the current study utilizes a digital engineering approach to evaluate the aerodynamic impact of surface deviations on a high-pressure turbine vane design created for research purposes. RANS-based CFD studies derived from structured light scans of as-built turbine vanes are used to quantify performance relative to design intent geometries. Further computational analyses compare results from individual serialized parts with an average vane doublet geometry serving as a surrogate for the entire wheel. Particular emphasis in the study focuses on external surface defects caused by internal cooling features that are inherent through additive manufacturing and how these features can impact the vane performance. Ultimately, this study identifies specific regions of the vane that are subject to increased sensitivity, which benefits future designers intending to use AM as a tool for turbine research and development.

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. This paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

Amputated life-testing based on extended Dagum percentiles for type of group inspection plans: optimal sample sizes, termination time ratios analysis

This paper introduces a novel approach to life-testing using Extended Dagum (EXD) percentiles within the framework of group inspection plans. The methodology focuses on optimizing sample sizes and analyzing termination time ratios to enhance the reliability of quality control procedures. By leveraging the flexibility of the EXD distribution, the proposed approach accurately models complex survival data, accommodating heavy-tailed characteristics often encountered in practice. The study presents a detailed analysis of optimal sample sizes and the critical termination time ratios that balance producer and consumer risks. Through comprehensive simulations and real applications, the paper demonstrates the effectiveness of the proposed methodology in ensuring robust and efficient life-testing strategies, offering valuable insights for practitioners in industries such as manufacturing, engineering, and reliability analysis.

Preface: 3rd International Conference on Management Engineering and Economic Analysis (MEEA 2024)

The 2024 3rd International Conference on Management Engineering and Economic Analysis (MEEA 2024) was held in London, United Kingdom during August 17-18, 2024. This conference is to bring together innovative academics and experts in the fields of management engineering, business statistics, marketing strategies, financial economics and economic analysis to a common forum. The primary goal of the conference is to promote research and developmental activities and another goal is to promote information interchange between researchers, developers, engineers, students, and practitioners working all around the world. The conference model of MEEA 2024 was divided into two sessions, including oral presentations and keynote speeches. In the first part, some scholars, whose submissions were selected as the excellent papers, were given 10-15 minutes to perform their oral presentations one by one. Then in the second part, keynote speakers were each allocated 35-45 minutes to hold their speeches. We are glad to share with you that we received lots of submissions from the conference and we selected a bunch of high-quality papers and compiled them into the proceedings after rigorous reviewing. We are really grateful to the keynote speakers, session chairs, organizing committee members, student volunteers, and publication house. Also, we are thankful to all the authors for contributing a large number of papers in the conference. It was the quality of their presentations and their passion to communicate with the other participants that really make this conference series a great success. MEEA 2024 Organizing Committees London, United Kingdom

Preface to the special issue on model-driven engineering and system analysis and modelling

Preface to the special issue on model-driven engineering and system analysis and modelling

The Concept of Technological Support of Operational Properties Based on Stabilization of Mechanical Properties of Gear Materials in a Gas Turbine Engine Drive System

Modern production of gears for gas turbine engines for aviation, marine and land use is inherently related to the calculation of the stress state of the working surfaces of the mating teeth. To create conditions for the operability of the gear train and the drive system as a whole, an engineering analysis of the contact endurance of the mating surfaces is a necessary criterion. The contact strength determines the life of the gear mechanism. The value of the contact strength, taking into account its distribution in the contact zone of the working mating surfaces of the gears, is determined by the processing technology and operation, but the mechanical properties and texture of the material have the greatest influence. This determines the requirements for the stability of the mechanical properties of the materials used for the manufacture of gears, making a topical question on their study. The technology of manufacturing the gears in the gas turbine engine drives forms the layer structure of the toothed crown because of the use of chemical-thermal treatment. The surface hardened layer of the gear tooth after chemical-thermal treatment is saturated with carbon and nitrogen, and as a result of thermal action acquires mechanical properties and structure different from the material in the supply. The paper presents the results of practical research of evolution of mechanical properties of structural steels 20H3MVF-Sh, 18H2N4MA, 16H3NVFM-Sh and 12H2N4A-Sh based on various types of chemical-thermal treatment, as well as microstructure of toughened layer and core of the part. The steel mechanical properties stabilization evaluation in the process of gear technology was performed. The presented results of experimental studies of mechanical properties of the material prove stabilization of mechanical and structural indicators, which are responsible for the contact strength of the mating surfaces of toothed gears.

Production-Enhancement-Candidate Screening Powered by ML Unlocks Brownfield Potential

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 215244, “Automated Production-Enhancement-Candidates Screening Powered by Machine Learning Unlocks Untapped Potential in Matured Oil Fields: A Case Study,” by Nusheena M. Khair, SPE, M. Farid Zaizakrani, SPE, and Nur A.I.Z. Azhar, Petronas, et al. The paper has not been peer reviewed. _ Field A offshore East Malaysia has been a productive conventional oil field for more than 3 decades. It has encountered several surface and subsurface issues, including sand production, increasing water cut, and reservoir-pressure depletion. The complete paper presents the process of identifying production-enhancement opportunities, develops a methodology to identify underperforming candidates and analyze well-integrity issues, and describes how data science and engineering analyses are integrated. Introduction Field A is undergoing redevelopment, including activities such as enhanced oil recovery, production-enhancement (PE) initiatives, idle-well reactivation (IWR), and infill drilling. However, Field A’s operations and PE initiatives face multiple challenges. These include a shortage of comprehensive data affecting reservoir management and forecasting, difficulties in managing wells on unmanned platforms during adverse weather, and high logistical costs in offshore interventions that affect the economic feasibility of certain PE and IWR jobs. Recognizing these issues, the operator team is taking a proactive approach by embarking on enhancing PE and IWR candidate generation by machine learning (ML), a strategy that aims to expedite well-by-well review (WBWR) to streamline candidate-generation processes and enhance decision-making. Production Enhancement Candidate Generation and Screening (PECGS) Methodology PECGS is a petroleum engineering advisory system that helps operators improve the efficiency of PE and IWR candidate screening and intervention planning. PECGS automatically generates a list of underperforming wells along with recommendations for remedial actions. PECGS works by first evaluating each well’s production potential and risk assessment through use of a data-driven advisory system that combines analytical and ML models with industry-standard petroleum and reservoir management logic. Once the wells have been evaluated, PECGS generates a live automated opportunity register with a ranking of candidate wells. Technical Solution The technical solution in PECGS includes four main stages: knowledge base, technical analysis, chance of success, and economic analysis. The knowledge base of PECGS is formed through data integration from various sources. Static data have been standardized and validated by subject-matter experts before being uploaded into the advisory-system database. Dynamic data, such as production and well test, are integrated daily into the advisory system database according to a predefined schedule. The technical analysis is leveraged with proven analysis methods to identify well constraints and recommend PE opportunities and present estimated production gain, success probability, and profitability. The workflow uses multicriteria ranking, or the analytical hierarchy process (AHP), to rank screened wells based on production and petrophysical key performance indicators. Once a potential PE candidate has been identified through an automated screening, the next step is to review the chance of success. Next, the engineers perform an economic analysis to evaluate the potential profitability of the PE job. The economic analysis uses a variety of factors, including the cost of the intervention, the expected increase in production, and the value of the produced oil or gas in order to calculate the net present value (NPV) of the job. If the NPV is positive, then the intervention is profitable.

Influence of manufacturing parameters on bioactive glass 45S5: Structural analysis and applications in bone tissue engineering

Bioactive glass (BG-45S5) production through the melting process is affected by a wide variety of parameters. This study investigated the synthesis of BG-45S5 granules and the process variables to produce a bioactive and osteoinductive BG for bone grafting applications. The melting process was initially analyzed by varying parameters such as crucible type and pouring environment using P2O5 as phosphorus precursor. The obtained products were characterized by crystalline phases, characteristic chemical groups, particle size distribution, and chemical composition. Materials poured into graphite or steel molds resulted in particle sizes more suitable for applications in granular form. Using a platinum crucible yielded a chemical composition closer to the target when compared with another ceramic crucible. Subsequently, the melting process was evaluated to different phosphorus precursor (P2O5 or Na2HPO4) and melting duration (1 or 2 h) in a platinum crucible verifying their effects on the thermal behavior, chemical composition and structure of BG-45S5. Employing Na2HPO4 as a precursor led to higher glass transition and crystallization temperatures as compared to P2O5, enhancing glass homogeneity and structural stability. The product with better characteristics in terms of composition and structure was further characterized for bioactivity and cell culture behavior, showing a greater amount of mineralization nodules when compared to commercial hydroxyapatite. This is particularly due to its behavior as the solubility and interaction in biological environments.

Experimental investigation of failure mechanism of fissure-filled sandstone under hydro-mechanical conditions

Fissure fillings are critical to the hydro-mechanical properties of jointed rock masses in rock engineering. In this study, triaxial seepage tests were performed on standard cylindrical fissure-filled sandstone. The characteristics of stress–strain relationships, absorption and consumption of energy, variations in deformation resistance, and permeability evolution during the experimental process, along with the crack development observed in post-failure computed tomography scan images of the sandstone specimens were analyzed. The results demonstrate that the fillings improve the energy capacity and reduce the damage accumulation of sandstone specimens, with sand-filled specimens performing better than mud-filled specimens, especially at lower bridge angles. The fillings can reduce the depth of crack extension and lessen the influence of prefabricated fissures on sandstone failure, with this effect diminishing as the rock bridge angle increases. Permeability decreases in the pre-peak failure stage as the fillings improve the deformation resistance of the sandstone specimens. In the post-peak failure stage, the fillings and rock debris generated by the sandstone failure move within the developed fractures, causing significant fluctuations in permeability. These findings deepen the understanding of the hydro-mechanical properties of jointed rocks and provide a scientific basis for stability analysis in rock engineering.

Shakedown analysis of incompressible materials under cyclic loads: A locking-free CS-FEM-Q5 numerical approach

Volumetric locking may occur in plastic analysis of incompressible materials using low-order finite elements due to incompressibility constraints. This study presents a locking-free smoothed five-node quadrilateral element-based approach for plastic analysis in structural engineering. The proposed Q5-element employing four cell-based smoothing domains effectively alleviates the volumetric locking issues, here in the problems under plane strain conditions. The resulting large-scale optimization problem is formulated in a conic programming form, enabling efficient use of the interior-point optimizer. Numerical investigations demonstrate the method’s effectiveness in alleviating volumetric locking, accurately predicting collapse and shakedown limits, and generating interaction diagrams for load-carrying capacity and structural collapse mechanisms.

From Sensors to Standardized Financial Reports: A Proposed Automated Accounting System Integrating IoT, Blockchain, and XBRL

Modern advances in technology have increased the demand for traditional accounting systems to be upgraded for real-time data processing, security, and standardized reports. Thus, this paper proposes a new accounting information system that integrates IoT, blockchain, and XBRL. The proposed system aims to automate the accounting process by using IoT to collect data and send it automatically to a blockchain, which acts as a database that will generate journal entries automatically through smart contracts. XBRL will then be used as an output method for standardized financial reports based on the data transferred from the blockchain. This paper uses a qualitative research design based on semi-structured interviews with 13 industry experts from IT engineering, academia, and financial systems analysis. NVivo software was used to conduct a thematic analysis of interview transcripts. The findings demonstrated that integrating IoT, blockchain, and XBRL is technically feasible, with significant potential to enhance accounting systems. Additionally, the findings identified key challenges of the proposed system, including the complexity of integration, data validation across technologies, costs, user adoption, and scalability concerns. However, the results showed that this system offers substantial benefits, such as real-time data capture from IoT devices, secure data storage and immutability through blockchain, standardized financial reporting via XBRL, accounting process automation, improved data accuracy, and enhanced security and transparency in financial reporting. The study also identified an optimal mechanism for ensuring seamless data transmission between these technologies. The study makes a valuable contribution to the accounting field by providing a new framework for automating data collection, enhancing data security, and streamlining financial reporting, with significant potential to advance accounting systems and improve transparency, accuracy, and efficiency in financial reporting. The study’s potential to impact accounting systems and financial reporting research and practice emphasizes its importance.

Back analysis of geomechanical parameters based on a data augmentation algorithm and machine learning technique

Accurate geomechanical parameters are key factors for stability evaluation, disaster forecasting, structural design, and supporting optimization. The intelligent back analysis method based on the monitored information is widely recognized as the most efficient and cost-effective technique for inverting parameters. To address the low accuracy of measured data, and the scarcity of comprehensive datasets, this study proposes an innovative back analysis framework tailored for small sample sizes. We introduce a multi-faceted back analysis approach that combines data augmentation with advanced optimization and machine learning techniques. The auxiliary classifier generative adversarial network (ACGAN)-based data augmentation algorithm is first employed to generate synthetic yet realistic samples that adhere to the underlying probability distribution of the original data, thereby expanding the dataset and mitigating the impact of small sample sizes. Subsequently, we harness the power of optimized particle swarm optimization (OPSO) integrated with support vector machine (SVM) to mine the intricate nonlinear relationships between input and output variables. Then, relying on a case study, the validity of the augmented data and the performance of the developed OPSO-SVM algorithms based on two different sample sizes are studied. Results show that the new datasets generated by ACGAN almost coincide with the actual monitored convergences, exhibiting a correlation coefficient exceeding 0.86. Furthermore, the superiority of the OPSO-SVM algorithm is also demonstrated by comparing the displacement prediction capability of various algorithms through four indices. It is also indicated that the relative error of the predicted displacement values reduces from almost 20% to 5% for the OPSO-SVM model trained with 25 samples and that trained with 625 samples. Finally, the inversed parameters and corresponding convergences predicted by the two OPSO-SVM models trained with different samples are discussed, indicating the feasibility of the combination application of ACGAN and OPSO-SVM in back analysis of geomechanical parameters. This endeavor not only facilitates the progression of underground engineering analysis in scenarios with limited data, but also serves as a pivotal reference for both researchers and practitioners alike.

Reliability engineering principles and maintenance scheduling for plant recovery

Plant operation and management require data from which information can be extracted to determine the state of the plant, and predict its health and anticipated failure interval in the future. The data is lacking in most companies in Nigeria and sometimes when available are not organized in the proper form to extract useful information. This research described the use of reliability engineering principles to perform maintenance practice in a brewery industry. The operational data were obtained from the log book of the plant and subjected to reliability engineering analysis. The average reliabilities of the plant was: 0.431, 0.376, 0.434, 0.603 and 0.722 with average availability of 0.985, 0.986, 0.987, 0.988 and 0.996 respectively. The results show that reliability engineering principles can be used to determine the health and performance of the plant is highly suggested for adoption and implementation.

Physical analysis of high refractive index metamaterial-based radiation aggregation engineering of planar dipole antenna for gain enhancement of mm-wave applications

A metamaterial-incorporated high-gain and broadband dipole antenna is proposed for 5G mm-wave applications. The designed high refractive index metamaterial (HRIM) properties are presented in detail with supporting results. The proposed dipole antenna achieved broadband features, and the antenna gain increased significantly by incorporating HRIM in the electromagnetic (EM) wave propagation path. Besides, the EM wave aggregation engineering of utilizing the HRIM on the dipole antenna is analyzed using the electric field, magnetic field, and power flow distributions. Both conventional and HRIM-based dipole antenna (HRIMDA) were fabricated on thin (0.254 mm) Rogers RT5880 substrate material with a low dielectric constant of 2.2, where the noticeable gain enhancement by HRIM is observed. The measured results show the operational bandwidth (BW) from 23 to 38 GHz frequency, and the highest gain of 9.5 dBi is accomplished at 35 GHz frequency. Finally, a four-element MIMO configuration is numerically and experimentally analyzed where the isolation of the two conjugated MIMO elements is < − 20 dB. The MIMO parameters like envelop correlation coefficient (ECC) < 1 × 10–3 and diversity gain (DG) value of > 9.9 were also achieved. Hence, the proposed HRIM base dipole antenna is a potential candidate for 5G mm-wave applications.

Importance of higher-order epistasis in large protein sequence-function relationships.

Epistasis complicates our understanding of protein sequence-function relationships and impedes our ability to build accurate predictive models for novel genotypes. Although pairwise epistasis has been extensively studied in proteins, the significance of higher-order epistasis for protein sequence-function relationships remains contentious, largely due to challenges in fitting higher-order epistatatic interactions for full-length proteins. Here, we introduce a novel transformer-based approach. The key feature of our method is that we can adjust the order of interactions fit by the model by changing the number of attention layers while also accounting for any global nonlinearity induced by the experimental conditions. This allows us to test if inclusion of higher-order interactions leads to enhanced model performance. Applying our method to 10 large protein sequence-function datasets, we found that the importance of higher-order epistasis differs substantially between proteins, accounting for up to 60% of the total variance attributed to epistasis. We also found that including higher-order epistasis is particularly important for generalizing locally sampled fitness data to distant regions of sequence space and for modeling an additional multipeak fitness landscape derived from combining mutagenesis data from 4 orthologous green fluorescencent proteins. Our findings suggest that higher-order epistasis often does play an important role in protein sequence-function relationships, and thus should be properly incorporated during protein engineering and evolutionary data analysis.

Fatigue Failure Of Steam Turbine Discs - A Centenary Tribute To Wilfred Campbell

Abstract The year 2024 marks one hundred years since Wilfred Campbell published his landmark work on vibrational analysis of rotating disc following a series of disc failures in steam turbines. Despite the absence of advanced engineering analytical tools, Campbell came up with an elegant method to visually demonstrate and capture the mode shapes in rotating discs. The first part of this paper reviews Campbell?s life and analytical and experimental work in this area. Regardless of the current advanced engineering capabilities to predict nodal shapes in turbine discs, turbine discs still experience failures related to vibration. The second part of the paper discusses a recent case study where a turbine disc failure occurred as a result of vibration. The discussion includes metallurgical root cause failure analysis and engineering analysis to predict the vibrational characteristics. Metallurgical failure analysis confirmed that the primary mode of failure was fatigue and did not have any issues with the disc material or its mechanical properties. Finite element modeling and analysis were used for the engineering analysis to predict the natural frequencies of the bladed-disc. The engineering analysis showed the evidence of potential resonance, and the failure was related to nodal vibration issues.

Research on Rock Energy Constitutive Model Based on Functional Principle

The essence of rock fracture can be broadly categorized into four processes: energy input, energy accumulation, energy dissipation, and energy release. From the perspective of energy consumption, the failure of rock materials must be accompanied by energy dissipation. Dissipated energy serves as the internal driving force behind rock damage and progressive failure. Given that the process of rock loading and deformation involves energy accumulation and dissipation, the rock constitutive model theory is expanded by incorporating energy principles. By introducing the dynamic energy correction coefficient, according to the law of the conservation of energy, the total energy exerted by external loads on rocks is equal to the energy dissipated through the dynamic energy inside the rocks. A new type of energy constitutive model is established through the functional principle and momentum principle. To validate the model’s accuracy, a triaxial compression test was conducted on sandstone to examine the stress–strain behavior of the rock during the failure process. A sensitivity analysis of the parameters introduced into the model was conducted by comparing the model results, which helped to clarify the innate laws of significance of these parameters. The results indicated that the energy model more accurately captures the non-linear mechanical behavior of sandstone under high-stress loading conditions. The model curve fits the test data to a high degree. The fitting curve was basically consistent with the changing trend of the test curve, and the correlation coefficients were all above 0.90. Compared with other models, the model based on the energy principle not only accurately reflects the rock’s stress–strain curve, but also reflects the energy change law of rock. This has reference value for the safety analysis of rock mass engineering under loading conditions and aids in the development of anchoring and support schemes. The research results can fill in the blanks that exist in the energy method in terms of rock deformation and failure and provide a theoretical basis for deep rock engineering. Moreover, this research can further improve and extend the rock mechanics research system based on energy.