Multi-level Loading Research Articles

Dynamic Fracture and Energy Evolution Characterization of Naturally Fractured Granite Subjected to Multilevel Cyclic Loads

Naturally fractured rock mass is susceptible to stress disturbance and could result in the stimulation of natural fractures and even serious geological hazards. In this work, multilevel uniaxial fatigue loading experiments were carried out to reveal the fracture and energy evolution of naturally fractured granite using stress-strain descriptions and energy evolution analysis. Results reveal the influence of natural fracture on mechanical properties of granite, regarding the fatigue lifetime, fatigue deformation characteristics, fatigue damage, energy evolution, and fatigue failure pattern. Volumetric and shear processes caused by the sliding and shearing along the natural fracture control the whole failure process. The energy dissipation and release characteristics are strongly impacted by natural fractures. The elastic energy and dissipated energy both decrease with increasing natural fracture volume, growth of the dissipated energy becomes faster for rock near to failure. It is proved that the dissipated energy is mainly used to activate the preexisting natural fractures.

Experimental study of the creep properties of coal considering initial damage

In underground tunnels, caverns or pillar goaf, the time-dependent deformation or failure of the rock or coal mass is a major safety concern, which affects the mechanical properties and stability of the coal and rock in the underground excavations. However, the damage surrounding rock or coal usually occurs from the time mining starts. This initial damage is rarely considered during the current creep tests used for coal. In the present study, an experimental specimen processing method to identify the initial damage to a coal deposit is suggested. The effect of the strain history on the deformation of coal samples with initial damage during multi-level loading triaxial compression creep tests was studied. The laboratory tests showed that the strain versus creep curve of the coal samples experiences three typical creep stages of deceleration creep in the early stage, constant velocity creep in the medium term and catastrophic accelerated creep in the later stage. With the increase in initial damage, it was observed the gradual decrease in total creep time, deviating stress of creep failure, stress threshold of accelerated creep and starting time of the volume expansion. When the initial damage value increased from 0.0 to 0.50, the deviating stress of creep failure, stress threshold of accelerated creep and starting time of the volume expansion of the coal decreased by 42.3%, 48.5% and 51.4%, respectively. The study is of great significance to conduct researches on the deformation, mechanical characteristics and long-term strength of coal pillar with initial damages under long-term pressure, and also provides insight into the underground excavations and the design of supports to the opneings under such disturbance.

Design tool for dynamic loading conditions: a coupled multi-level approach

Conceptualizing a sound mechanical system exposed to dynamic loading conditions throughout its lifetime is a challenging task ill-supported by current design tooling. Current approaches typically use a Shock Response Spectrum (SRS) as design specification that describes the maximum dynamic response of a single subsystem component due to a given loading condition. However, for complex systems during the early stages of the design, there is a need to gain quick insights into the impact of dynamic loading conditions applied to system level as well as to subsystem and component levels simultaneously. Hereto, in this study, a coupled multi-level model has been developed that describes all essential elements of a system. The advantage of this approach is that rather than one single SRS, now upon each element an SRS can be prescribed. Multi-level shock response spectra can be computed in a time-efficient manner and, for the first time, peak acceleration and displacement for various combinations of natural frequencies may be displayed. Hence, effectively translating how subsystems and components within a multi-level dynamic system may be mounted or suspended constructively. Subsystem components and the system as a whole can be analysed simultaneously, and the sensitivity of subsystem conceptual design choices can be examined. This allows design engineers to get detailed overviews of (sub)system-level responses due to (critical) dynamic loading conditions and multi-level loading scenarios. Design insights can be evaluated within minutes aiding to find potential configurations that match the design requirements. Moreover, the developed design tool aids in both dealing with uncertainty of requirements during the project definition phase and designing a robust system against late-stage requirement updates.

Triaxial Creep Behavior of Red Sandstone in Freeze-Thaw Environments

To investigate the time-dependent mechanical properties of rock masses in cold regions under the effects of freeze-thaw cycling and long-term loading, triaxial multilevel loading and unloading creep tests were performed on saturated red sandstone samples subjected to different numbers of freeze-thaw cycles. The effects of freeze-thaw cycles and confining pressure on the creep properties, long-term strength, and creep failure mode of the rock were analyzed. The effect of freeze-thaw cycles on the microstructure of the rock was analyzed using scanning electron microscopy. The results showed that as the number of freeze-thaw cycles increased, the rock particle boundaries became more distinct, and more pores formed. The effect of freeze-thaw cycles on the creep deformation of red sandstone was related to the loading stress level. At low stress levels, the rock viscoelastic strain increased gradually and almost linearly with an increasing number of freeze-thaw cycles; in contrast, at high stress levels, the rock viscoelastic strain increased nonlinearly. The viscoplastic strain increased almost linearly with increasing freeze-thaw cycles. The fourth loading stress level (70% σ c ) corresponded to the transition of the creep deformation of the red sandstone. When the confining pressure was low, a higher stress level caused the confining pressure to have a more significant effect on the creep strain. However, as the confining pressure continued to increase, the effect of the confining pressure on the creep strain eventually disappeared. The long-term strength of the red sandstone decreased approximately linearly with an increase in the number of freeze-thaw cycles. When the number of freeze-thaw cycles and the confining pressure were high, the rock samples formed a transverse shear plane and were more fragmented than those without a transverse shear plane. These results provide a reference for construction in rock mass engineering and long-term stability analysis in cold regions.

Nonlinear fatigue life prediction model based on material memory

New nonlinear fatigue damage accumulation model is established on the basis of material memory theory and fatigue driving energy damage parameters to evaluate high-cycle fatigue life under multilevel variable amplitude loading. The loading interaction factor is constructed on the basis of damage degree and then the model is modified to consider the effect of loading interaction on fatigue damage accumulation. The two proposed models are convenient for calculation and have only two parameters that can be easily identified through experiments. In accordance with the test data of aluminum alloy Al-2024-T42, titanium alloy Ti-6Al-4V, nodular cast iron GS61, Q235B welded joint, and hot-rolled 16Mn steel, the two models developed in this study have been verified to predict fatigue life effectively. For multilevel loading, the modified model achieves higher prediction accuracy and its results are closer to the actual test data compared with those of the other models.

Uniaxial compression creep and acoustic emission characteristics of sandstone under loading-unloading paths

Specimens of red sandstone are subjected to creep and acoustic emission (AE) tests under only multi-level loading and multi-level loading-unloading. Creep deformation characteristics and AE parameters of the red sandstone specimens under these two loading paths are compared and analyzed, and a creep AE damage-variable model is used for the damage evolution of the micro-cracked structures inside the rock during the creep process. The research results reveal the following: (1) During the creep process involving multi-level loading-unloading, the temporal variation of the AE amplitude is similar to that observed during the creep process involving only multi-level loading. (2) The variations of the cumulative AE event and cumulative AE ring-down count in the creep process involving multi-level loading-unloading are similar to those in the creep process involving only multi-level loading, while the actual values are higher in the former process. (3) The creep AE damage-variable model performs well on characterizing the damage evolution of the internal micro-crack structure of the rock in both creep processes.

Experimental and numerical study on the cracking characteristics of repetitive electrohydraulic discharge shock waves

The application of repetitive electrohydraulic shock waves (EHSs) is a developing underwater discharge technology; however, its cracking characteristics on rock under different loading modes are rarely studied. In this paper, an experimental platform of electrohydraulic discharge is built, and test results show that repetitive EHSs can cause obvious macroscopic cracks on samples. A fitting method is proposed for the time-domain waveform of the EHS. The mechanism of the EHS cracking process (liquid–solid interface transmission process, cracking process in rock) is analyzed, and the cracking criterion and fracture zone range of a single EHS on rock are given. In addition, PFC3D simulation is used to establish a three-dimensional numerical model of the test sample under the experimental conditions, and the development characteristics of the damage shape and crack density inside the rock under the action of repetitive EHSs are deeply analyzed. Under different repetitive loading modes with the same loading total energy, the simulation results show the following cracking characteristics: in single-level mode, the crack density is mainly related to the energy of the single loading. The higher the single-loading energy, the more conducive it is to the growth of the number of main cracks, but it will form a crushing zone to cause energy loss; lower single-loading energy is more favorable to the length of main cracks. In the multi-level loading mode, the degraded loading mode has a higher crack density than the upgraded loading mode. Compared to the single-level loading mode, the multi-level loading mode can effectively promote the development of the number and length of main cracks, and effectively reduce the range of the crushing zone. This paper provides theoretical and simulation guidance for the research and application of repetitive EHSs.

Investigation of nonlinear energy dissipation and storage characteristics for evaluating rockburst proneness of granite and sandstone

Nonlinear energy storage and dissipation of rocks are common in earthquake, tunnel, and mining engineering. To investigate the nonlinear energy characteristics of rocks, multi-level cyclic loading–unloading triaxial compression (CLTC) tests were performed on early Cretaceous granite and Permian red sandstone. The failure modes of the granite and sandstone specimens under CLTC tests were studied. The energy parameters, such as the input, elastic, and dissipated energy densities (IE, EE, and DE, respectively), of the two types of rocks under different confining pressures were calculated, and the nonlinear interrelations among the three energy parameters were investigated. The results indicated that in the CLTC tests, the failure modes of sandstone were all shear failure. The granite specimens in the CLTC tests failed via splitting. The confining pressure had no effect on the peak strength strain energy storage index at the failure of the rock specimens, which tended to be constant. The nonlinear evolution of the DE of the granite and sandstone with respect to the EE and IE in the CLTC process was divided into three stages: an initial stage, a linear stage, and an accelerated stage. Furthermore, according to the nonlinear energy-conversion mechanism, a self-inhibition energy-conversion model was established in consideration of the confining-pressure effects. Using this nonlinear energy-conversion model, the EE and DE at any strain level can be determined. The peak strength strain energy storage index was calculated to evaluate the rockburst proneness of granite and sandstone. The results agreed well with those of the uniaxial compression test.

Fatigue life prediction based on a novel improved version of the Corten-Dolan model considering load interaction effect

Corten-Dolan nonlinear damage accumulation model can well describe the fatigue behavior of engineering materials and structures under variable amplitude loads, while the determination of parameter d is difficult and still open. In this paper, a new improved version of Corten-Dolan model is proposed in which the parameter d is modified by introducing the power form of the stress ratio between two consecutive load levels to reflect the nonlinear effect of load interaction. Furthermore, a generalized expression of the new model is developed, which gives a unified theoretical formulation for the presented and some typical existing versions. The proposed model is validated by comparison with existing versions based on the experimental data of typical engineering materials under two-level and multilevel loads. An effective validation scheme is introduced to comprehensively investigate the validity and applicability of the developed model. In this scheme, parts of data those are not used in modeling are regarded as the check data to examine the prediction accuracy. The results show that the developed model can well reflect load interaction effect and give more satisfactory prediction of fatigue life.

Deformation characteristics and failure modes of sandstones under discontinuous multi-level cyclic loads

Rock often suffers from discontinuous fatigue damages in geotechnical engineering, so it is of great significance to study deformation characteristics and failure modes of sandstone under discontinuous multi-level cyclic loading and unloading. By conducting continuous (only dynamic loading) and discontinuous (combined static and dynamic loading) multi-level cyclic loading and unloading tests, this study explored deformation characteristics and failure modes of sandstone. The test results demonstrated that the sandstone mainly suffered from large deformation dominated by dilation in circumferential direction when it was damaged after compression. After multi-level loading and unloading, evolution characteristics of deformation parameters showed characteristics of stepwise growth. However, the introduction of static loading changed such characteristics. In the process of combined static and dynamic loading, due to short action time, dynamic loading mainly promoted nucleation and sudden changes of cracks, while static loading affected crack development process mainly in the early compaction stage and late crack propagation and coalescence stage. Moreover, static loading showed small effects in elastic stage. In the compaction stage, the compacted micro-cracks reopened and cracks were affected by inertial damages in crack propagation stage and interconnected more thoroughly, so that the sandstone was finally more fragmented.

Study and Application on Statistic Power Flow Index

Power grid control center safeguards the bulk power system by monitoring active power flow and managing network congestions. By far, EMS only provided two-dimensional visualized power flow chart, which focused on the power flow limits and real-time monitoring. This paper suggested a multidimensional statistic Power Flow Index (PFI) which was able to analyze, forecast and evaluate grid reliability based on the date mining of operating parameters. PFI helped to discover the potential congestion and enhanced the efficiency of power transmission by plotting power flow distribution curve. By using adjustable time windows and multi-level facility load factors, it is suitable for long-term statistical analysis of different facilities. PFI was one of the essential tools of self-optimal East China Smart Power Grid.

Effect of loading frequency on the deformation behaviours of sandstones subjected to cyclic loads and its underlying mechanism

To explore the mechanism of frequency on the evolution of deformation parameters, triaxial compression tests under multi-level loading were carried out at different frequencies. The results show that increasing the frequency by reducing the duration of loading cycles can inhibit the development of primary and new fractures in a rock in the compaction and plastic stages, thus hardening the rock and improving the strength. The increase in frequency induced by an excessive increase in loading cycles causes the rock more compact. The cumulant of irreversible deformation greatly increased to degrade the strength. Additionally, loading cycles plays a more important role.

The Attenuation of Physical-Physiological Stresses through Musical-High Intensity Exercise Co-Treatment in Non-Athlete Individual

Exercise is a very effective strategy to improve people’s health. However, the unwell managed exercise potentially causes distress and decreases the health. Therefore, this research aimed to know the correlation of exercise combined with music to control stress/tissue injury by using physical-physiological neurohormonal paradigm approach. This study used randomized control group pre-test and post-test design with the sample of 30 non-athlete individuals randomly selected with the age range of 19-23 years old, the body mass index (BMI) of 19-23, VO2 Max of 46-56 ml/kg/BB, and they do not smoke. The experiment group was divided into high-intensity exercise by listening to hard beat music, high intensity-exercise by listening to slow beat music, high-intensity exercise without listening to the music. The high intensity, in this research, means the intensity with 85% load of maximum working capacity with the multilevel load test using ergometer. The measurement of distress level was performed by taking the sample of 10 ccs of the blood of cube vein and the measurement of heart rate before and after doing an exercise. The distress level was determined using a biomaterial secretion indicator in the form of cortisol hormone, endorphin, cytokine interleukin-6 (IL-6), and the heart work. The method that was used to check the blood sample to know the cortisol, endorphin, and IL-6 content was ELISA (Enzyme-Linked Immunosorbent Assay), while the measurement of heart work was carried out using polar heart rate monitor. The research results showed that there was a significant difference in circulating level of endorphin and IL-6 (P < 0.05) after treatment by listening to slow beat music compared to the other experimental groups. Nevertheless, there was no significant difference in the circulating levels of cortisol (P > 0.05). In summary, giving co-treatment of high-intensity exercise with slow beat music could decrease the physical-physiological stress of non-athlete individual. It is suggested that the treatment could decrease the inflammatory within the skeletal muscle and improve the decrease in physiological stress by modulating the anti-physiological stress neurohormonal secretion.

Strain energy-based fatigue life prediction under variable amplitude loadings

With the aim to evaluate the fatigue damage accumulation and predict the residual life of engineering components under variable amplitude loadings, this paper proposed a new strain energy-based damage accumulation model by considering both effects of mean stress and load interaction on fatigue life in a low cycle fatigue (LCF) regime. Moreover, an integrated procedure is elaborated for facilitating its application based on S-N curve and loading conditions. Eight experimental datasets of aluminum alloys and steels are utilized for model validation and comparison. Through comparing experimental results with model predictions by the proposed, Miner\'s rule, damaged stress model (DSM) and damaged energy model (DEM), results show that the proposed one provides more accurate predictions than others, which can be extended for further application under multi-level stress loadings.

Study on the Estimation of Rock Rheological Parameters under Multi-level Loading and Unloading Conditions

Determining reasonable rheological constitutive models based on laboratory rock creep test data and estimating rheological parameters are important means of studying rheological mechanical property of rocks. Previous rock uniaxial or triaxial compression creep tests mostly adopted the method of multi-level loading. In order to study the influence of unloading stress on the estimation of rock rheological parameters, rock triaxial creep tester RLW-2000 was used in this paper to carry out triaxial compression creep tests for granites in a given area with two different stress paths of multi-level loading and stepwise unloading. Study results indicate that rock rheological parameters obtained vary with different stress paths. The instantaneous elastic modulus and viscosity coefficient obtained through loading show a stepwise increase, while the viscoelastic modulus shows a progressive decrease.

Optimal reliability improvement strategy in radial distribution networks with island operation of distributed generation

This study presents a mixed integer linear programming-based approach for determining the optimal strategy for reliability improvement in radial distribution networks where island operation of distributed generators (DGs) is allowed. The proposed approach simultaneously defines the optimal number, type, and location of new automation devices (ADs) to be installed in a network, the optimal relocation of the existing ADs and the optimal creation of DG islands. The load curtailment possibility in creating islands is considered along with the multi-level load model. The presented numerical results indicate the effectiveness of the proposed approach and the importance of simultaneous consideration of the aforementioned individual strategies in determining the best reliability improvement strategy in radial distribution networks with DGs.

Creep Behavior of Intact and Cracked Limestone Under Multi-Level Loading and Unloading Cycles

A series of triaxial creep tests were carried out on intact and cracked Maokou limestone specimens under multi-level loading and unloading cycles. A new data processing algorithm is proposed to analyze the experimental data and divide the total strain into instantaneous and creep strains, with the instantaneous strain consisting of instantaneous elastic and plastic strains and the creep strain consisting of viscoelastic and visco-plastic strains. The results show that the viscoelastic strain converges to a certain value with time, but the visco-plastic strain keeps increasing with time, although both tend to increase with higher deviatoric stress. The ratio of the visco-plastic strain to the total creep strain also tends to increase when the deviatoric stress is higher. The steady-state creep strain rate increases with higher deviatoric stress or lower confining pressure, and the relation between the steady-state creep strain rate and the deviatoric stress can be well described by an exponential expression. The results also show that the preexisting cracks in the limestone have a great effect on its creep properties. At the same confining pressure and deviatoric stress, the cracked limestone shows larger instantaneous and creep strains (especially visco-plastic strains), longer duration of primary creep, and a higher steady-state creep strain rate than the intact limestone.

Optimal Allocation of DGs and Reconfiguration of Radial Distribution Systems Using an Intelligent Search-based TLBO

This paper addresses an application of Teaching-Learning-Based Optimization method for the optimal allocation of Distributed Generations (DGs) in radial distribution systems. The problem is formulated to maximize annual energy loss reduction while maintaining better node voltage profiles using penalty function approach. A piecewise linear multi-level load pattern is considered, and the distribution network is reconfigured after optimal placement of DGs in the distribution network. A probability-based heuristic intelligent search (IS) is suggested to enhance the accuracy and convergence of the optimization techniques. IS directs optimization techniques to efficiently scan the problem search space in such a way that a fair candidature is available to all decision variables of the problem. It virtually squeezes the search space while maintaining adequate diversity in population. The proposed method is investigated on the benchmark IEEE 33-bus, 69-bus test distribution systems, and 83-bus real distribution system. The application results show that the proposed optimization methodology provides substantial improvement in convergence characteristics and quality of solutions.

국내 전력계통 안정화를 위한 다단계 부하차단 제어전략 수립에 관한 연구

국내 전력계통 안정화를 위한 다단계 부하차단 제어전략 수립에 관한 연구

Optimal DG Allocation in Distribution Networks using Cat Swarm Optimization

Dispersed or Distributed Generations (DGs) are becoming more popular on account of socio-economic reasons and also to enhance performance of distribution systems. Cat Swarm Optimization (CSO) is one of the recent swarm-intelligence-based optimization techniques which provides local and global search simultaneously. The aim of this study is to introduce the application of CSO method for optimal allocation of DGs in distribution networks. The problem is formulated to maximize annual energy loss reduction and to maintain a better node voltage profile under piece-wise multi-level load profile using penalty factor approach. Modification is suggested in CSO to enhance its exploration and exploitation potentials. In addition, clever search is proposed to enhance overall performance of the optimizing tool. The proposed method is applied on the benchmark IEEE 33-bus and 69-bus system and the obtained results are promising.