Weibull Distribution Theory Research Articles

Numerical research on disastrous mechanism of seepage instability of karst collapse column considering variable mass effect

In order to reveal the disastrous mechanism of seepage instability of karst collapse column considering variable mass effect, a variable mass fluid–solid coupling mechanical model of water inrush is established, by considering the random distribution characteristics of a collapse column. Taking Qianjin coal mine as the research background, based on the Weibull distribution theory, the heterogeneous distribution characteristics of rock mass is described, and COMSOL Multiphysics numerical simulation software is employed to simulate the seepage characteristics and inrush water changes in collapse columns under different conditions of homogeneity, water pressure, and initial porosity. The research results show that the greater the homogeneity is, the more water conduction channels are formed, and the porosity increases accordingly, when considering the influence of different homogeneity on the seepage characteristics of broken rock mass, which eventually leads to water inrush accidents and a sharp increase in water inflow. Besides, when studying the seepage evolution law of different water pressures on a broken rock mass, an elevation of water pressure dramatically increases the porosity and seepage rate of the water. Over time, the broken rock particles gradually migrate and the fine particles are transported and eroded by the water flow, resulting in changes in the seepage characteristics and the formation of potential water diversion channels. Finally, when taking into account the effect of different initial porosity on the fractured rock mass seepage characteristics, the greater the original porosity is, the higher the seepage velocity is, and the particle migration increases the permeability. This leads to a more pronounced conductive water passage formation, which reveals the disastrous mechanism of seepage instability of karst collapse column considering variable mass effect.

Research on joint scheduling method of order grading and machine maintenance

AbstractIn the multi‐variety and large‐scale order production mode, enterprises must balance delivery deadlines and maintain customer satisfaction while also considering the health status of machines. Therefore, the authors propose a method for jointly optimising production scheduling and machine maintenance. Before machine processing, an order value grading and sorting model and a machine health‐status group partitioning model are constructed to classify orders into different production value levels and machines into different health‐status groups, respectively. During machine processing, based on the Weibull distribution theory, a ‘health evaluation function value’ constraint machine preventive maintenance (PM) model and PM strategy are proposed to account for the changing health status of machines; these are integrated with the order allocation machine strategy as decision‐making elements in the production schedule. Finally, two case studies are used to verify the effectiveness of this proposed model and method. The results show that compared to general scheduling schemes, the proposed method can reduce total delay and improve customer satisfaction. Additionally, the PM plan proposed in this method can improve production efficiency and line stability compared to periodic maintenance.

Microstructure analysis and life prediction of DD6 superalloy under 760 °C combined high and low cycle fatigue conditions

The impact of high and low cycle combined loads on the fatigue performance of DD6 alloy was investigated in this work. Specifically, the combined high- and low-cycle fatigue response of DD6 alloy was examined at a temperature of 760 °C under different low cycle stress amplitudes (960, 1000, and 1040 MPa). The findings revealed that higher low cycle stress amplitudes result in shorter combined high and low cycle fatigue life and less dispersion in life. Correlations between the microstructural features (crystal plane distribution, fracture elevation difference, and the area proportion of crack propagation zone) and fatigue performance were accurately established, demonstrating a linear relationship between these microstructural features and the logarithm of fatigue life. The study also uncovered the evolution rule of microstructural features in high- and low-cycle combined fatigue. Furthermore, the fracture mechanism was analyzed and the distribution of high and low cycle combined fatigue life of DD6 alloy at 760 °C was statistically validated using the dual-parameter Weibull distribution theory. Building upon the crystal plasticity theory, a fatigue life prediction model was developed, and the combined cycle fatigue lifespan under various low cycle stress amplitudes was compared. The comparison between the predicted life and actual fatigue life indicated that the predicted lifespan falls in three times the scatter band.

Mechanical properties and damage characteristics of concrete under different atmospheric pressures

The aim of this study was to investigate the mechanical properties and damage characteristics of concrete under different atmospheric pressures (50 kPa, 80 kPa, and 101 kPa). The failure modes, compressive strength, dynamic elastic modulus, stress–strain curve, air pore structure, and acoustic emission (AE) parameters of concrete specimens were evaluated under the different atmospheric pressures. The results showed that as the atmospheric pressure decreased, the concrete damage gradually transitioned from tensile damage to shear damage, the compressive strength and dynamic elastic modulus decreased, and the peak strain increased. The pore structure of the hardened concrete changed, the number of air pores and air content decreased, and the average pore size and pore spacing coefficient increased considerably. Additionally, an analysis of the AE parameters showed that the development pattern of the concrete ringing counts and energy were mostly the same under different atmospheric pressures. The decrease in atmospheric pressure was accompanied by a corresponding gradual decrease in the AE rate of change parameters and cumulative AE parameters, indicating that the concrete crack expansion rate slowed down while the total cracking activity decreased. Moreover, the inverted V-shape of the b-value curve was not obvious, and the peak b-value decreased with decreasing atmospheric pressure. Finally, a combination of the Weibull distribution theory, Lognormal distribution theory, and strain equivalent hypothesis was used to establish a concrete uniaxial compression constitutive model considering atmospheric pressure. The model can reflect the evolution law of the mechanical properties of concrete under uniaxial compression under different atmospheric pressures.

Experimental Study on the Impact Resistance of Polymer-Modified Steel Fiber-Reinforced Recycled Aggregate Concrete

Recycled aggregate concrete (RAC), composed of aggregates sourced from construction solid waste, has garnered significant attention owing to its notable environmental friendliness. In this study, waterborne epoxy resin (WER) and steel fibers (SFs) were introduced into the RAC to enhance its performance. Orthogonal tests were meticulously designed, with the substitution rate of recycled aggregate (RA), SF dosage and WER dosage as variable factors, to comprehensively analyze the splitting tensile strength and impact resistance of concrete. The impact resistance of concrete was investigated via the drop weight test method. Furthermore, scanning electron microscopy (SEM) was employed to scrutinize the microstructure of concrete, investigating the modification mechanism of WER. The results indicated that the addition of SFs exerted the most pronounced influence on the properties of RAC. As the addition of SFs increased from 0 to 1.0%, there were significant enhancements in the splitting tensile strength and impact energy of the specimens. WER exhibited notable improvements, primarily on the splitting tensile strength, while demonstrating an adverse effect on the impact resistance. Utilizing the Weibull distribution theory, the results of the impact tests were fitted and analyzed to predict the impact life of different mixtures. The predicted results showed high correlations with the measured values.

Effect of bolt size on the bearing strength of bolt-connected orthotropic CFRP laminate

Carbon fiber reinforced polymer (CFRP) has the advantages of lightweight, high strength and corrosion resistance. CFRP laminate is widely used in the reinforcement and rehabilitation of concrete and steel structures such as buildings, bridges, and tunnels. In this work, the structural arrangement of six kinds of orthotropic CFRP laminates that would suffer from bearing failure was determined with the help of a failure map. The bearing strength and failure mechanism of the specimens at the joint were studied through tensile bearing tests. Finally, a strength prediction model about the effect of bolt-hole size was established based on the Weibull distribution theory. The research results show that the bearing strength of the CFRP laminates is insignificantly affected by the thickness of the CFRP laminates, however, is greatly affected by the diameter of the bolt under the same thickness and lay-up form. The bearing strength of the CFRP laminates decreases with the increase in the diameter of the bolt hole. It is found that the specimen with a symmetrical layup shows a more obvious size effect compared to the specimen with an asymmetric layup. The model established based on the Weibull distribution theory can well predict the bearing strength of bolted-connected CFRP laminates with different diameters.

Study on mechanical properties and statistical damage constitutive model of red sandstone after heating and water-cooling cycles

The repeated action of high temperature and water cooling will have a strong deteriorating effect on the mechanical properties of the rock, which will eventually lead to the damage and cracking of the rock. In order to study the influence of heating and water-cooling cycles on rocks, the P-wave velocity and mechanical properties of red sandstone after heating and water-cooling cycles were tested. Meanwhile, based on the Weibull distribution theory, a statistical damage constitutive model based on Mohr-Coulomb strength criterion considering the effects of heating and water-cooling cycles was established, and verified based on the results of triaxial tests. The results show that the P-wave velocity and peak intensity decrease with the temperature under the same number of cycles. The elastic modulus will decrease with the temperature and the number of cycles, indicating that the red sandstone will gradually soften and the ductility will increase under repeated high temperature and water-cooling cycles. And the model can well reflect the stress-strain curves of different high temperature and water-cooling cycles. The research results can provide analytical theories and methods for geothermal development projects.

A Degradation Condition Assessment Technique Based on online_ISSE Degradation Feature and Logistic Regression Model

A degradation assessment technique based on an online improved symbol sequence entropy online_ISSE and a logistic regression model is proposed in this paper. Firstly, the threshold factor is introduced to retain the `coarse graining' information of direction changing and amplitude information, the `sensitivity' of improved symbol sequence entropy (SSE) to impact components is reduced and improved symbol sequence entropy (ISSE) is proposed. Then, a sliding window and Weibull distribution theory are used to effectively filter out the influence of fluctuations in the ISSE feature sequence, forming the degradation feature named online_ISSE. Finally, a logistic regression model is trained and constructed, and the health factor CV is calculated online to assess the degradation condition of the unknown signal samples. The lifetime vibration signal of the hoisting gearbox monitored from #8114 quay crane of the Shanghai Port Container Terminal is introduced for instance analysis. The results show that the proposed ISSE has a better effect in describing the complexity pattern than the SSE algorithm and that the degradation condition can be tracked and assessed accurately based on the technique proposed.

Experimental study on the secondary breakup properties of crushed coal through a dynamic porosity model based on Weibull distribution theory

Secondary breakup of the residual coal in goaf caused by periodic weighting changes its gradation, coal-oxygen contact area, stacking structure, etc. It cannot be ignored in studies of spontaneous combustion and compaction character of bulk coal. This paper developed a new dynamic porosity model employing the Weibull function based on the quantitative results of the secondary breakup phenomenon. A precise three-stages compaction process (particles self-organization and re-accumulation stage, secondary breakup stage, and simultaneous compression deformation stage) was observed and designated by this model. The competition mechanism among the deformation modes of coal particles during axial compaction was discussed. The main findings are as follows: (1) The formation mechanism of the stage characteristics in the compaction process for broken coal was actually a competition among the three deformation modes (secondary breakup, inter-particle self-organization, and inter-particle extrusion). (2) The proposed model allowed a finer division of the three stages of compaction from the perspective of the various deformation modes of coal particles. (3) The intensity of secondary breakup was weaker in the early and late stages of compaction and made no dominant contribution to deformation. A secondary breakup–dominated deformation stage was derived through comparing the proposed model with experimental data. (4) In the aforementioned deformation stage, the average relative error between the model’s predictions and the experimental data was 4.63%.

Thermal cracking characteristics and mechanism of sandstone after high‐temperature treatment

AbstractTo study the thermal cracking characteristics and mechanism of sandstone after high‐temperature treatment, the pore size distribution and micromorphology of sandstone were observed by nuclear magnetic resonance and scanning electron microscopy. Then, based on the Weibull distribution theory, a thermal elastic mechanical model of random heterogeneous rock was established for the rock unit, the thermal stress distribution characteristics of sandstone were analyzed, and the thermal fracture mechanism of rock was discussed. The results show that the porosities of the samples increased with increasing temperature and the proportion of large pores increased significantly when exceeded 400°C. Particularly when reached 1000°C, thermal cracking was distributed in a complex network. Additionally, different rock units are in different thermal stress states, which leads to the regional differences in the distribution of rock thermal fracture. When exceeded 400°C, there were obvious thermal cracks near the outer edge that weakened the mechanical properties of rock.

Research on Weibull Distribution Theory for Cubic Compressive Strength Test Method of Raw Earth Materials with Different Curing Methods and Time

Cube compressive strength of raw-soil based mater is an important index of mechanical property. Because the test results vary by different curing modes and trial curing time, compressive strength test on 160 cubic raw-soil test-pieces which were made by 4 curing modes (natural curing, indoor curing, indoor+ preservative film curing, curing in standard curing chamber) and 4 Curing period (4d, 14d, 21d, 28d) was designed.In this study,the failure mechanism, failure mode, force mechanism of test were analyzed.Using Weibull distribution theory, the influence of different environmental factors on material strength is discussed.The research revealed that the different curing methods and curing time had remarkable effect on failure mode of material, but the load displacement curves had not affected. The compressive strength with 21d and 28d ‘s indoor curing and standard curing method were same in the test.The strength of raw soil increases with time, and the curing temperature had a significant effect on the early strength of raw soil materials, but had little effect on the later strength. The humidity had a great influence on the later growth of material strength. Constant temperature and humidity could effectively ensure the full response of internal water loss hardening of raw soil-based materials, and the strength of specimens increases obviously.The recommended curing mode and standard curing time for standard test of raw-soil test-pieces were temperature of 25-30oC, humidity of 50%-55%, and 28day, respectively.

Study on the unloading damage constitutive model of sandstone based on hydro-pressure cycle

The periodic rise and fall of reservoir water level under hydro-pressure cycle leads to the deterioration of physical and mechanical properties of rock and seriously triggers the instability of the reservoir slope. From the laboratory data and characteristics of the stress–strain curve under different hydraulic cycles, combined with the generalized Hooke’s law, the Weibull distribution theory, and the Hoek–Brown strength criterion, the energy dissipation in the unloading process is assumed as the damage variable, and the unloading damage constitutive model of saturated sandstone under hydro-pressure cycle is established. Under hydro-pressure cycle, the parameters m and F of the constitutive model are gradually decreasing, and the sandstone brittleness and macroscopic strength are gradually weakened. In addition, the scattered energy increases, while plastic deformation slowly plays a dominant role. The comparative analysis shows that the constitutive model fits well with the experimental curves. The damage constitutive equation can be expressed under hydro-pressure cycle. This research can help in the stability analysis of rock slope under the reservoir water in the field.

Research on Microscopic Fracture Morphology and Damage Constitutive Model of Red Sandstone Under Seepage Pressure

To explore the influence of seepage pressure on rock failure, the high-pressure triaxial automatic system was used to carry out a triaxial compression test under the condition of seepage pressure on rock samples, and then, the fracture surface of the rock was tested by scanning electron microscope (SEM). The fractal dimension features of rock fractures under different seepage pressures were analyzed by the image segmentation principle and optimal threshold method, and a segmental statistical damage constitutive model considering seepage pressure was established based on the Weibull distribution theory. The results show that (1) the SEM image after binarization has better fractal characteristics, which can represent the roughness of the fracture surface; (2) the fractal dimension ranges from 1.818 to 1.950, which shows a variation law of decreasing with the increase in the seepage pressure; and (3) a piecewise damage constitutive model considering the seepage pressure is proposed, and it provides a more precise prediction for the stress–strain curve characteristics before the peak stress. The research results are beneficial and useful for the analysis of the damage evolution characteristics of engineering rock masses, as well as for the monitoring and prediction of engineering geological hazards.

Study of a Prediction Method of the Failure Time and Failure Voltage of Generator Stator Bars Under the Electrical Stress Test

A method for predicting the failure time and failure voltage of generator stator bars under the electrical stress test was proposed. The method established a general life prediction theory model for the electrical stress test based on the negative power-exponential model, and this model could predict the insulation life of stator bars under the electrical aging test and breakdown test. Then, we utilized Weibull distribution theory to estimate the life factor in the model and predict the failure time and failure voltage of the stator bars under the step-by-step test. The test results were consistent with the estimated results, and the correctness of the proposed method was verified.

A Study of the Impacts of the Spatial Differences in Climate Engineering Programs on the Extreme Intensities of High-Temperature Events in China Under A 1.5癈 Temperature Control Target

Based on the daily maximum temperature data and average temperature data prediction for the period ranging from 2020 to 2099 under the scenario of BNU-ESM climate engineering (G4 test) and non-climate engineering (RCP4.5), the regional differences in the extreme high-temperature intensities in China during the implementation of climate engineering programs (2020 to 2069) and after the implementation of those programs (2070 to 2099) were analyzed using the Weibull Distribution Theory. The results are as follows. (1) The comparison of the two scenarios shows that climate engineering has not fundamentally changed the spatial variation of the intensity of extreme hightemperature events in different recurring periods in China. It was found that in both scenarios, the extreme hightemperature intensities were characterized by the spatial differentiations of low-temperature intensities on the QinghaiTibet Plateau, and high-temperature intensities in the eastern and northwestern region. (2) The comparison of the two scenarios shows that climate engineering in the two study periods could help mitigate the extreme high-temperature intensities with different recurrence periods in China, and the mitigation effects during the implementation period would be significantly higher than those after the implementation. (3) The comparison between the periods ranging from 2020 to 2069 and 2070 to 2099 under the proposed climate engineering scenarios suggests that there would be no strong rebounding of extreme high-temperatures following the implementation of climate engineering programs. Moreover, the mitigation effect of extreme high-temperature intensity during the implementation of climate engineering is significantly higher than that after the completion of climate engineering. (4) According to the comparison between the average temperature changes in China before and after the implementation of the climate project, the average temperature in China has been reduced by at least 1.25 ℃, which effectively alleviates global warming and is conducive to the realization of the 1.5 ℃ temperature control target of the Paris Agreement.

Shear Load-Displacement Curves of PVA Fiber-Reinforced Engineered Cementitious Composite Expansion Joints in Steel Bridges

The concrete in the transition strips of expansion joints can become damaged prematurely during the service period. Polyvinyl alcohol (PVA) fiber-reinforced engineered cementitious composite (ECC) is a kind of high ductility concrete material, and its ultimate uniaxial tensile strain is more than 3%. It can be used to improve the damage status of expansion joints. Based on previous research results, ECCs were used in the pilot project of bridge expansion joints. Under this engineering background, the shear load-displacement curves of ECC expansion joints were studied through 27 groups of compression-shear tests of ECC/steel composite structures. The shear failure characteristics of ECC expansion joints were analyzed by the digital image correlation method. A shear load-displacement curve model of the composite structures was proposed based on the equivalent strain assumption and Weibull distribution theory. The results show that the failure mode of the composite structure specimens was ECC shear cracking. Stress and strain field nephograms were used to explain the failure characteristics of the composite structure specimens. The calculated curves of the shear load-displacement model of the composite structures were in good agreement with the experimental curves. The work is of great importance to the shear design of ECC expansion joints and their further engineering applications.

Experimental Investigation on the Impact Resistance of Carbon Fibers Reinforced Coral Concrete.

In this study, the impact resistance of coral concrete with different carbon fiber (CF) dosages subjected to drop-weight impact test was investigated. For this purpose, three concrete strength grades (C20, C30, C40) and six CF dosages (0.0%, 0.3%, 0.6%, 1.0%, 1.5%, and 2.0% by weight of the binder) were considered, and a total of 18 groups of carbon fibers reinforced coral concrete (CFRCC) were cast. For each group, eight specimens were tested following the drop-weight impact test suggested by CECS 13. Then, the two-parameter Weibull distribution theory was adopted to statistically analyze the variations in experimental results. The results indicated that the addition of CFs could transform the failure pattern from obvious brittleness to relatively good ductility and improve the impact resistance of coral concrete. Moreover, the impact resistance of CFRCC increases with the CF dosage increasing. The statistical analysis showed that the probability distribution of the blow numbers at the initial crack and final failure of CFRCC approximately follows the two-parameter Weibull distribution.

Research on uniaxial compression constitutive model of polypropylene fiber recycled brick concrete

Using single factor experiment, different fiber content of the polypropylene fiber recycled brick concrete uniaxial stress-strain curve are studied, then the polypropylene fiber recycled brick concrete damage constitutive model is given and the damage evolution curve is analyzedbased on the Weibull distribution theory and the principle of equivalent strain assumption. Experimental results and analysis show that the addition of fiber not only changes the brittle failure of recycled concrete, but also increases the plastic deformation capacity of recycled concrete: the theoretical curve and test comparing the measured curve fit well; The fiber can effectively inhibit the development of the cracks, improve the deformation capacity and toughness of concrete in a certain range, which is obtained through the damage evolution process of different fiber content.

Investigation on slag fiber characteristics: Mechanical property and anti-corrosion performance

Inorganic fiber shows good insulation performance in civil construction and industry insulation. In the present paper, tensile strength of slag fiber produced with molten blast furnace slag was investigated systematically with the Weibull distribution theory in comparison with glass and basalt fibers. It was found that the mean tensile strength reached 2578.60MPa and the shape parameter m in Weibull distribution is 2.4494, which indicates a lower uniformity. Anti-corrosion performances were also studied by means of the mass and strength loss after acid and alkaline solution treatment. Furthermore, SEM and FTIR were used to analyze the structural characteristics of original and treated fibers. This work has proved that the H+ and OH− can both break the Si–O bond and then lead to the movement to high wavenumber for the bands of the symmetric stretching vibrations of [SiO4]-tetrahedra. The anti-corrosion results indicated that slag fibers could not be used in acid environment, while its anti-alkali performance is relatively excellent compared with glass and basalt fibers.

Concrete Fatigue Life Characteristics of the Different Survival Rates in the Lateral Pressure Conditions

Under cyclic loading of concrete structures, fatigue failure is the main failure modes of fatigue, which has become the fatigue design of concrete structure must be considered, then the concrete fatigue studies must clarify the fatigue life of concrete under different survival curve S-N curve. Based on the statistics of the two parameter Weibull distribution theory, obtain the concrete under different survival rates of fatigue life distribution, namely to improve survival, reduce the fatigue life; stress level is reduced, the fatigue life is increased; and has set up more than 50% under different survival rates of concrete fatigue equation.