Failure Law Research Articles

Mathematical approaches for reliability evaluation of a parallel-series system of order (3,3,1,1) with exponential failure laws

The reliability analysis of a parallel-series system with an order of (3,3,1,1) involving five units (A, B, C, D, and E) organised into three parallel subsystems is investigated. The first subsystem comprises three units (A, B, and C) arranged in series, while the second and third subsystems consist of single units ‘D’ and ‘E’. The failure rates of the units are assumed to follow a negative exponential distribution. The study employs three mathematical methods: decomposition, cut-set, and event space to derive expressions for reliability and mean time to system failure (MTSF). Specific values for these reliability measures are obtained by assuming identical units and assigning particular values to unit failure rate parameters. The sensitivity analysis has been carried out to investigate the overall system reliability by changing the parameter values of the different components and identify the critical components. The practical application of this work is envisioned in power distribution systems.

The formation mechanism of geological disasters on loess fill slopes revealed by the deformation characteristics of remolded loess under different stress paths

In recent years, geological disasters on loess fill slopes have occurred from time to time, which has attracted widespread attention. In order to deeply understand its deformation and failure laws and promote the disaster prevention and mitigation work, this paper takes remolded loess as the research object, systematically explores the effects of three different stress paths (conventional triaxial compression test (CTC), triaxial compression test with constant average principal stress (TC), and triaxial compression test with reduced confining pressure (RTC)) on its mechanical properties, and observes and analyzes its microstructural characteristics by scanning electron microscopy (SEM). The results show that the soil is strain hardening under the CTC path, while it is strain weak hardening under the TC and RTC paths. In the order of CTC, TC, and RTC paths, the shear strength and volume shrinkage of the soil are reduced in turn, and its deformation has both shear reduction and shear expansion plastic deformation. In the order of CTC, TC, and RTC paths, the degree of particle crushing decreases in turn and the pore content increases in turn. It is inferred that in the initial deformation of loess under loading, the soil is compressed and compacted, and its strength is improved to a certain extent. As the loading continues to increase, the deformation rate increases steadily, and the soil deformation develops gradually, which is mainly axial compression deformation, while the lateral bulging deformation is small until it is destroyed. For the deformation behavior in the form of lateral unloading, the soil is maintained in a relatively stable state at the beginning, and the deformation is very small. When the lateral constraint is reduced to a critical state, the structure is completely unstable, and the deformation develops rapidly in a short time until it is destroyed. This study is of great significance for reducing the occurrence of geological disasters on fill slopes in loess areas.

Effect of Indenter Angle on Bearing Performance of Coal and Accompanying Rocks Under Point Load and Characterization of Mechanical Parameters

ABSTRACTCoal, mudstone, sandstone, and limestone, which are common in coal mines, were selected as research objects, and 60°, 90°, and 120° indenters were used to conduct point load tests to study the deformation and failure laws of rocks under point loads. This study identified a process for generating and crushing compacted bodies. As the indenter angle increased, the number of compacted bodies formed decreased significantly, and the stress drop decreased. The ultimate invasion depth upon reaching the failure load decreased as a quadratic function as the indenter angle increased. Under the load of indenter points at different angles, all samples underwent splitting failure along the loading axis. As the indenter angle increased, the indentation diameter increased quadratically. The angle of the indenter had a greater influence on the indentation diameter of low‐strength rocks, and the failure of coal and accompanying rocks was more stable under the action of large‐angle indenters. The point load test data were statistically analyzed. The load intensity of the indenter point at different angles exhibited a linear relationship with the uniaxial compressive strength, tensile strength, and elastic modulus, and the fitting degree was the best when the indenter angle was 120°

Macroscopic and Mesoscopic Damage Characteristics and Energy Evolution Laws of Rock Mass With Double Arcuate Fractures Under Uniaxial Compression

ABSTRACTIn order to reveal the influence of double arc‐shaped fissure dip angles on the macro‐micro failure and energy evolution laws of rock masses, a numerical model of red sandstone was firstly established using the PFC2D. Moreover, mesoscopic parameters of the numerical model were calibrated based on the uniaxial compression tests on intact and single straight fissure red sandstone specimens. Then, particle flow simulation tests of red sandstone with different arc‐shaped fissure dip angles were carried out. The results show that the peak strength and elastic modulus both increase with the increase of arc‐shaped fissure dip angle α, exhibiting an oblique shear‐tensile failure pattern. Six types of cracks evolved during the instability and rupture of the rock mass with double arc‐shaped fissures. The macroscopic fissures in the rock mass ultimately penetrate along the extension direction of the arc‐shaped fissures. As the arc‐shaped fissure dip angle α increases, the crack evolution is positively correlated with the acoustic emission (AE) of the specimen. When approaching instability failure, the AE ringing count rapidly increases. There is a critical angle limit inflection point for the total energy absorbed by the rock between 60° and 75°, with a total energy increase of about 54%. During instability failure, it is dominated by dissipative energy, with elastic energy as a supplement. This article derived a damage constitutive model of red sandstone with different arc‐shaped fissure dip angles, revealing the damage laws of red sandstone under different arc‐shaped fissure dip angles.

Failure Laws of Cyclically Loaded Steel Joints Revealed from a Thermodynamic Perspective

ABSTRACT Using cyclically loaded beam-column joints with cast steel connectors (BCJCC) as a case study (Bao 2012), this work attempts to reveal the failure law from a thermodynamic perspective. By applying a network-free renormalization, modes and characteristic parameters are constructed to characterize stressing state evolution. Due to the attractor effect of phase transition, a clustering algorithm can be applied to reveal the approximate phase transition loads of steel joints. After that, the phase transition loads can be verified using the renormalization perspective, which can also serve as a reference for seismic design.

Reliability Variation Assessment Due to Alteration in Subsystems of a Series-Parallel System under Weibull Failure Laws

Here, we consider a (m, ni) order system having 'm' number of subsystems connected in series and each subsystem has 'n' number of components in parallel. The reliability of the system has been obtained by deleting 'y' number of subsystems (or adding 'x' number of subsystems) from (or to) it. The variation in reliability due to alteration in subsystems has been assessed for a particular system of (4,3) order. A regression approach is used to quantify the strength of variation in reliability due to alteration in subsystems. The coefficient of determination (R2) and adjusted R2 are also obtained to examine the goodness of fit. The variation in reliability has been shown numerically and graphically for particular value of the parameters. The application of the present study can be visualized in an Internally Fused Shunt Capacitor Bank System (electrical system).. KEYWORDS :Reliability variations, Series-Parallel system, Internally fused shunt capacitor bank, Regression Analysis.

Adaptive Mesh Generation and Numerical Verification for Complex Rock Structures Based on Optimization and Iteration Algorithms

ABSTRACTThe modelling of rock structure is of great significance in characterizing rock characteristics and studying the failure laws of rock samples. In order to construct a high‐fidelity model of the rock structure efficiently, this paper proposes an adaptive mesh dissection algorithm based on the Voronoi structure. Image processing techniques, including greyscale, threshold segmentation and edge detection, are applied to simplify the original rock image into a feature edge image. Then, a probability density diagram of the feature image is generated, which provides a probabilistic basis for the subsequent spreading of mesh seed points. Moreover, the concept of polygonal representation rate and the mesh quality evaluation system of four‐dimensional metrics are established to suggest values for the seed point parameters of the initial mesh. The initial mesh is continuously optimized and iterated by barycentric iteration and gradient descent optimization methods to form mesh structural models with high representational performance efficiently. The model tests on particle, fracture and multi‐phase rock images show that the optimized mesh model is highly similar to the original image in terms of similarity and edge fit, and the algorithm significantly reduces the short‐edge rate and improves the shape regularity of the mesh structure. Finally, numerical tests of uniaxial compression are carried out based on the optimized mesh model. The results show that the model has computational potential in numerical calculations. This method builds a procedural structure from digital images to numerical models, which can provide a reliable model basis for simulating the physico‐mechanical behaviour of heterogeneous rocks.

Reliability analysis of the vehicle door system EDCU based on Weibull distribution

The paper established a two-parameter Weibull distribution model to analyze the failure law of key components of metro vehicles and employed the least squares method to fit the parameters of the Weibull function. The paper provided a detailed introduction of the model's parameter fitting method based on actual historical failure data. Taking the EDCU (Electrical Door Control Unit) as an example, the failure rate, cumulative failure rate, and reliability of EDCU for 3 different vehicle models were calculated, and the calculation results were verified to conform to the Weibull distribution through Q-Q diagrams. The results show that although the designed service life of EDCU of vehicle door system is 15 years, the reliability of the EDCU decreases significantly around 10 years. The EDCU reliability of the three vehicle models declines by 22%, 4.2%, 10.6% and the failure rates are 2.7%, 0.57%, 1.13%. Based on the reliability of EDCU mentioned above, while ensuring the reliability of components, the maintenance methods of components can be optimized to reduce maintenance costs.

Behavior of hybrid bonded/bolted GFRP single-lap joint under static tensile loading: An experimental and numerical study

The mechanical performance of the GFRP hybrid bonded/bolted single-lap joints under static tensile loading is experimentally and numerically investigated. Static loading tests considering the hybrid joints with single bolt, four bolts, and nine bolts were first conducted to study the failure process and modes of hybrid joints. Finite element (FE) analysis involving the material degradation and failure laws was also performed to reveal the joints’ internal failure mechanism. Based on the verified FE analysis approach, the effects of plate thickness and bolt end distance on the failure capacity and strength of the hybrid joints were further studied, by conducting a numerical parametric analysis. Results indicate that, the loading process of the hybrid joints can be identified into two stages divided by the bonding failure. The failure patterns mainly include the plate slippage, the inclination of bolts, and the tensile fracture of GFRP plate, and their occurrences vary for the joints with different bolt numbers. Additionally, the rigidity and failure load of joint are also significantly affected by the bolt number. As the plate thickness increases, the ultimate capacity of joints would be improved, while the failure strength decreases. With the bolt end distance getting greater, the ultimate capacity/strength would increase. In general, the achievement of this research work can provide references for the design and further study of the GFRP hybrid joints in civil engineering applications.

Study on the deformation and failure laws of surrounding rock under reduced roof thickness in Salt Cavern Gas Storage

Under the premise of guaranteeing the stability of the gas storage reservoir, reducing the thickness of the salt layer on the top plate of the gas storage reservoir can improve the utilization rate of the salt layer in the construction section and increase the vertical height of the gas storage reservoir cavity, creating a larger gas storage space. The mechanical planar model of the casing-cement sheath-surrounding rock in the top plate of the salt cavern gas storage reservoir yields the elastic–plastic theoretical solution for the stress and deformation of the well wall surrounding rock. Based on this, a three-dimensional mechanical numerical model of the top plate is constructed to compare the effects of various top plate thicknesses on the surrounding rocks of the gas storage reservoir and to analyze the stress and deformation behavior of the wall surrounding the rock of the top plate of the reservoir in the cementing section and bare wells under the long-term injection and extraction cycle. The results indicate that reducing the thickness of the roof salt layer primarily affects vertical displacement, radial displacement, equivalent strain, and principal stress changes in the cement sheath and surrounding rock. All other roof parameters, except for equivalent strain, show an increasing trend. Reducing the salt layer thickness in the cementing section has the least impact on the gas storage roof’s stability. In contrast, reducing the salt layer thickness in the cementing section and bare wells has a moderate impact, while reducing the thickness solely in the bare wells is the most detrimental. These findings provide valuable insights for optimizing the roof thickness of gas storage facilities and enhancing the utilization of the limited salt layer in the reservoir section.

Failure law of hydraulic pipe joints sealing performance under vibration loads

Aviation hydraulic pipe joints are inevitably affected by vibration loads during service. Fatigue relaxation occurs in the pipe joint structure by vibration, and fretting fatigue wear occurs in its sealing interface, leading to a decline in sealing performance. In order to investigate the sealing performance of hydraulic pipe joints affected by vibration load, this paper first analyzes the modal distribution of the sealing system pipeline under different hydraulic pressures and hydraulic fluid flow rates through vibration frequency sweeping experiments. Secondly, the vibration load is applied to the pipe joints for different numbers of cycles, which reveals the microscopic wear behavior of the sealing interfaces under different tightening torques. Finally, by carrying out the leakage measurement experiment under vibration load, the evolution law of the sealing performance of pipe joints under different hydraulic fluid pressures and tightening torques was obtained.

Summary of Rock Damage Mechanics Classification

As an important means to study the mechanical properties and failure mechanism of rock materials and engineering mechanics, damage mechanics is often used to assist in the analysis of the failure process and mechanism of rock, metal, and other materials in the current research. In the use of damage mechanics to study the properties of rock materials and explore the deformation and failure law of rock, important research results have been achieved. The research methods of damage mechanics can be roughly divided into three types: statistical damage model, mesoscopic damage model, and continuous damage model. Based on the existing literature in hand, according to the division of damage mechanics research methods in the academic community, this paper collates and considers that the existing damage model construction can be summarized from the mechanical point of view. The pure theory is derived or fitted from the mathematical point of view. One of them is derived from the mechanism point of view, and the other is derived from the phenomenon point of view. The stress, strain, acoustic emission, and other data are analyzed and reconstructed, and both have advantages and disadvantages.

Study on the Destruction Law and Main Controlling Factors of Corrosion Product Film in H2S-CO2 Coexistence System

Abstract The failure law and main controlling factors of corrosion product film in this corrosion environment were studied according to the characteristics of H2S-CO2 coexistence in a gas field pipeline, so as to provide guidance for corrosion prevention and control of gas field pipeline. Sediment effects of sand particles in the pipeline on corrosion, the influence of flow rate, dissolved oxygen and sediment on corrosion products were analyzed by conducting corrosion experiments at 0.5m/s, 1m/s and 2m/s, corrosion experiments without oxygen and aerobic conditions. The destruction law of corrosion product film in pipeline and the main controlling factors of corrosion product film in single well pipeline and gathering and transportation line were determined. The results show that high flow rate will cause local damage of corrosion product film and promote pitting corrosion, dissolved oxygen will destroy the integrity of corrosion product film, and sediment is one of the factors causing local corrosion and perforation of pipeline inner wall. The corrosion product film structure of the gas field pipeline will be destroyed and pitting corrosion under the condition of high flow rate, oxygen and sand deposition. Meanwhile, the main control factor affecting the corrosion product film destruction of the gas field single well pipeline is dissolved oxygen, and the main control factor affecting the corrosion product film destruction of the gas field gathering and transportation main line is sediment.

Applying a thermodynamic-based method to reveal the failure laws of CFRP stiffened plates

The high specific strength and stiffness of carbon fiber-reinforced polymer (CFRP) stiffened plates make them popular in aerospace and other fields. Nevertheless, CFRP stiffened plates have unique characteristics and complicated and diversified failure patterns, so it is impossible to determine its failure law with a uniform failure criterion accurately. Its load-carrying capacity has always been calculated on the conservative side of empirical estimation. This work uses the stressing state theory to investigate the stressing state evolution of composite stiffened plates under axial loading. It conducts three CFRP stiffened plates of the same configuration from a thermodynamic perspective. By equating stiffened plates to thermodynamic systems, the measured strain data are modeled as state variables, and renormalization and clustering algorithms are applied to determine the phase transition loads of the structure, while the characteristic points before and after normalization are verified for their reasonableness and stability. Accordingly, this work reveals the failure laws of CFRP stiffened plates by applying a thermodynamic-based method. It characterizes the structural failure features by defining catastrophe points throughout the failure process, which provides a new reference for the failure analysis and strength design of CFRP stiffened plates.

Study on signal characteristics of burst tendency coal under different loading rates

In order to study the mechanics, acoustic emission (AE) and electromagnetic emission (EME) response law of bursting liability coal at different loading rates, uniaxial compression tests were carried out on coal mass from Konggu Coal Mine. The corresponding relations among mechanical properties, AE and EME signals in the process of coal failure under loading were analyzed, and the energy evolution law of coal failure with bursting liability under loading rate was discussed. The results show that within a certain range of loading rate, the higher the loading rate, the higher the compressive strength and peak load of bursting liability coal, and the shorter the time for coal to reach the peak load. Under different loading rates, the mechanics, AE and EME signals of coal samples can be well corresponded. When the loading rate is low, the number of blocks destroyed of coal sample is large and the block size is relatively small, and the blocks are mainly scattered around the test platform. When the loading rate is high, the number of damaged blocks is relatively small and the block size is relatively large, and the blocks are far away from the test bench. When loading at a low rate, the internal cracks in coal can be fully developed and connected, and the energy release rate is relatively uniform in the process of loading and failure of coal sample. In the case of high loading rate, the energy release rate of coal sample in the loading process is much smaller than that in the moment of failure. Combining the above test results with the actual situation of the working face, it can be concluded that the total energy stored in the coal of fast mining increases and the threshold of impact decreases compared with that of slow mining. Therefore, under the disturbance of external dynamic load, rapid mining is more likely to induce rock burst.

Revealing failure law of single-track traffic-loaded concrete airport pavement from a thermodynamic perspective

ABSTRACT With the growth of global air traffic and the popularity of large aircraft, the design and life prediction of airport pavements have received increasing attention from scholars. However, concrete airport pavement evaluations based on cracking patterns are often uncertain. A thermodynamic-based failure analysis of the FAA Phase 4 Construction Cycle 8 (CC8) strength and fatigue traffic test is conducted in this work to investigate the failure laws of airport concrete pavements. First, this work equates concrete pavement failure to a phase transition. It converts strain data from full-scale traffic tests into state variables. Based on the Wilson theory definition of phase transition, network-free renormalisation is applied to reveal the concrete slab stressing state evolution and phase transition features. The clustering algorithm that utilises the attractor effect of phase transition points determines characteristic points. In summary, this work applies network-free renormalisation and clustering algorithms to reveal robust concrete pavement failure points, which can provide a reference for airport pavement design, assessment, and failure warning. Furthermore, this work further validates the stressing state theory and network-free renormalisation under high-speed time-varying conditions.

Effects of disc overhang diameter on the uplift bearing capacity of new-type concrete expanded-plate pile groups

The disc overhang diameter can significantly affect the uplift bearing capacity of new concrete expanded-plate pile groups, affecting their design and practical applications. Accordingly, this effect was investigated considering the failure laws of the soil surrounding various pile types and groups. Based on the uplift bearing capacities of single and double piles, a finite element simulation was adopted to establish models for the four-, six-, and nine-pile groups. The relationship between the disc overhang diameter and uplift-bearing capacity of each pile group was explored: as the disk overhang diameter increased, the uplift-bearing capacities of the pile groups increased; however, this relationship is nonlinear. The optimal disc overhang diameter was determined as 1.5–1.75 times the pile diameter. For a constant disc overhang diameter, corner piles have a greater uplift bearing capacity than side piles in the six-pile group, and a greater uplift bearing capacity than the side and center piles in the nine-pile group. Thus, the pile-group effect depends on the pile position. The uplift bearing capacity did not increase linearly with the number of piles, and the average uplift bearing capacity of a pile in a pile group was less than that of a single pile. Therefore, the uplift bearing capacity of the pile groups decreased as the number of piles increased. The reliability of the simulation was verified via visual testing of a small-scale half-cut pile model.

Mathematical Techniques for Computing the Reliability of a Parallel-series System of Order (2,3,1) under Rayleigh Failure Laws

Some well-known mathematical techniques have been used to compute the reliability of a parallel-series system of order (2,3,1). The system is composed of four units labelled as A, B, C and D. The configuration involves two parallel subsystems: the first containing units A, B and C arranged in series and the second comprising a single unit D. The failure rate of units is assumed to follow the Rayleigh distribution. With the use of the decomposition method, cut set method and event space method, expressions for both reliability and Mean Time to System Failure (MTSF) have been derived. By considering all units to be identical, the reliability measures have been obtained numerically for specific parameter values. The trends of these measures have been represented graphically to understand the effect of parameters. The study has its practical significance in assessing the reliability of solar panel system. . KEYWORDS :Parallel-series System, Rayleigh failure laws, Decomposition method, Cut set method, Event space method.

Correction: Study on Roof Deformation and Failure Law of Close Distance Coal Seams Mining Based on Digital Image Correlation

Correction: Study on Roof Deformation and Failure Law of Close Distance Coal Seams Mining Based on Digital Image Correlation

Influence of Pile Spacing on the Compressive Bearing Performance of CEP Groups

Pile spacing is an important factor affecting the bearing capacity of concrete expansion pile (CEP) groups. In this study, a pile group was simulated and analyzed using ANSYS software R19.0. The influence of pile spacing on the bearing capacity of the pile group under a vertical load was determined using three sets of four-, six-, and nine-pile models with different pile spacings. The grid division of the pile soil model adopts a mapping method, using the contact types of rigid and flexible bodies and applying surface loads to the model piles step-by-step. After vertical pressure was applied to the model pile, in-depth analysis was conducted on the displacement cloud map, pile top displacement, and other data. The different stress conditions of corner, edge, and center piles in each model group were compared and analyzed, revealing the relationship between the stress mechanism and failure law of the soil around the pile and the pile spacing. It was found that the soil displacement range of edge piles is slightly larger than that of corner piles. This phenomenon gradually decreases with increasing pile spacing. When the pile spacing increases to four times the cantilever diameter, the difference in soil displacement at different pile positions is small, and the pile spacing has little effect on the compressive bearing capacity of the pile group. Thus, it is reasonable to control the pile spacing at three to four times the cantilever diameter. In the nine-pile model, when the load is loaded to the 20-step level, the displacement value of the central pile is −72.278 mm, while the displacement values of the edge pile and corner pile are −69.012 mm and −66.806 mm. It is shown that increasing the pile spacing can effectively reduce the pile group effect and improve the bearing capacity of the pile foundation. At present, CEP pile groups are gradually being applied in practical engineering, but research on the influence of pile spacing on the compressive bearing performance of CEP pile groups is still at a very early stage. This article reinforces the influence of pile spacing on the compressive bearing performance of CEP pile groups. It provides theoretical support for its application in practical engineering.