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To study the cumulative damage evolution law of multi-anchor circular piles (MACP) under earthquake action, data such as acceleration and axial force of anchor cables of MACP were obtained by shaking table tests. An index of plastic effect coefficient (PEC) was proposed to quantitatively analyze the damage degree of MACP. The influence of multi-factor coupling on the cumulative damage evolution law of MACP was clarified. A landslide deformation prediction method with the axial force of anchor cable as a monitoring index was established. The results confirmed that PEC fully considered the plastic deformation characteristics of concrete materials and was more effective than the pile peak displacement (PPD) in evaluating the seismic cumulative damage effect of MACP. The cumulative damage of MACP was a result of multi-factor coupling, and multiple earthquakes led to a nonlinear increase in the damage degree of MACP. The axial force-ground motion intensity curve of the anchor cable was similar to the landslide deformation curve. The use of the axial force of the anchor cable to predict the deformation of MACP-reinforced landslides was recommended based on the idea of monitoring landslide deformation by Newton force.HighlightsThe shaking table test of multi-anchor circular piles (MACP) reinforced landslide was carried out.A plastic effect coefficient (PEC) was proposed to quantitatively analyze the damage degree of MACP.The influence of multi-factor coupling on the cumulative damage evolution law of MACP was elucidated.A landslide deformation prediction method using the axial force of the anchor cable as a monitoring index was proposed.

The cumulative damage effects of surrounding rock under single full-face blasting and multiple full-face blasting of a large cross-section tunnel are comparatively studied in this paper. The damage processes of the single and multiple full-face blasting of the tunnel are simulated by the established rock damage model embedded into the LS-DYNA computer code through its user subroutines and a cumulative damage simulation technology in the LS-DYNA. The simulation results are verified against field test data. The results demonstrate that the numerically predicted peak particle velocity (PPV) of the surrounding rock under multiple full-face blasting is more consistent with field test data than that under single full-face blasting, which indicates the advantages of multiple full-face blasting in comparison to single full-face blasting in simulating the blasting process of a tunnel. The maximum damage depth in the middle of the tunnel invert is mostly affected by multiple full-face blasting. Both the maximum damage depth and the maximum PPV occur in the middle of the tunnel invert under single and multiple full-face blasting. Based on the defined damage threshold Dcr and the modeled maximum damage depth of the surrounding rock, the influence of initiation sequence on the critical PPV for rock damage is analyzed, and a critical PPV of rock damage is proposed to provide a safety criterion for tunnel blasting excavation.

The tunnel drilling and blasting method inevitably causes damage to the rock mass during the blasting process. This article takes a certain tunnel as the research object, proposes to simulate the process of continuous blasting and repeated blasting in each section of the tunnel, and quantifies the cumulative damage range of surrounding rock under each working condition. The results indicate that: (1) it is advantageous to use equivalent loads to simulate blasting loads when calculating large-scale blasting damage simulations; (2) The damage to surrounding rock caused by single cycle excavation of tunnels is caused by the superposition of multiple stages of delayed blasting, mainly influenced by adjacent auxiliary equipment.

Fatigue design of engineering structures is typically based on lifetime calculation using a cumulative damage law. The linear damage rule by Miner is the universal standard for fatigue design even though numerous experimental studies have shown its deficiencies and possible non-conservative outcomes. In an effort to overcome these deficiencies, many nonlinear cumulative damage models and life prediction models have been developed since; however, none of them have found wide acceptance. This review article aims to provide a comprehensive overview of the state-of-the art in cumulative damage and lifetime prediction models for endurance based high-cycle fatigue design of metal structures.

This article establishes a numerical model for cumulative damage of surrounding rock that can simulate the characteristics of progressive cyclic blasting in tunnels based on explicit dynamics and “restart” technology, and conducts research on the cumulative damage law of surrounding rock induced by tunnel blasting. The results show that: (1) considering the characteristics of progressive cyclic blasting in tunnels, the degree and range of surrounding rock damage are significantly increased compared to single blasting, with an increase of about 50%; (2) the amount of damage caused by blasting in the surrounding rock follows a Boltamann function (S-shaped curve) evolution feature as the distance between the blasting centers increases. In practical applications, when evaluating the degree and range of damage to the surrounding rock at the current location, additional cumulative damage caused by adjacent footage cycles should be considered, and the damage value can be 1.5 times the damage value of the current single blasting condition

We investigate a bivariate replacement policy for a system under shocks effect. A system including two units experiences to one of two types of shocks. Whenever a type I shock arrives, unit 1 has a minor failure which can be removed through a minimal repair; while a type II shock leads to a catastrophic failure of the system. The occurrence probabilities of shock types depend on the number of shocks since the last replacement. Whenever unit 1 suffers a minor failure, it causes some additive damage to unit 2. Once cumulative damage of unit 2 reaches a threshold level L, unit 2 will fail, which will also cause unit 1 to fail at the same time, causing a catastrophic failure of the system. Furthermore, unit 2 whose cumulative damage is x may fail minorly with probability π(x) at the instant of minor failure of unit 1, and requires minimal repair when it fails. It is assumed that the system implements preventive replacement as the system’s age reaches T, or the mth type I shock occurs, or corrective replacement as a type II shock occurs or the cumulative damage to unit 2 reaches a threshold level L, whichever comes first. For this model, we derive the formula for the mean cost rate and determine analytically and numerically the corresponding optimal policy. Finally, it is also shown that the policy can be regarded as a generalization of existing policies. This generalization makes our policy more flexible and applicable in real situations than existing policies.

Drilling and blasting method used for excavation causes damage to surrounding rock mass, and frequent blasting often leads to cumulative damage effects. Thus, understanding the distribution of Blast-Induced Damage (BID) zone is critical to assess the slope stability of open-pit mines. Herein, this study aims to investigate the cumulative damage effects and safety control criteria on the final wall of the open-pit slope under blasting. The cumulative damage zone was defined using a continuous damage model coupled with tensile damage and Drucker–Prager yield criteria embedded in the finite difference method. The simulation results were validated against field data collected from the Wushan open-pit mine in Inner Mongolia, China. The results demonstrate that the cumulative damage of the final wall exhibited a non-linear decreasing trend from the bench face to the interior of the slope, successfully reproducing the spatial distribution of the BID obtained from the in situ test, and revealing that the maximum cumulative damage depth occurred at the slope crest. Additionally, a safety control criterion for the critical damage zone of open-pit final slope was proposed based on the investigation of the effects of dynamic loading rate and stemming length on excessive overbreak. The results highlight how important it is to account for cumulative damage effects when assessing the final slope stability of an open pit and optimizing the mining design.HighlightsThe cumulative damage effects on the final wall of the open-pit under blasting are investigated.A model coupled with tensile damage and Drucker-Prager yield criteria is established and incorporated into finite difference method to simulate the blast-induced damage zone.The subsurface damage depth is obtained using the digital drilling images technology.The dynamic loading rate and stemming length could significantly affect the excessive overbreak along the crest.

Solid propellant is a composite material exhibiting classic nonlinear viscoelastic mechanical characteristic, which is due in a large part to a cumulative damage process caused by the formation and growth of microflaws inside. The standard relaxation tests and uniaxial tension tests under different velocities of hydroxyl-terminated polybutadiene (HTPB) propellant are carried out in this paper, where Digital Image Correlation (DIC) technique is applied to record deformation. The experimental results show that the material mechanical behavior is rate-dependent. It is also observed that the yield stress and failure stress are significantly rate-dependent on the tensile velocity. Based on these experimental results, it can be inferred that the stiffness degradation and damage evolution of HTPB propellant are a rate-dependent processes. Therefore, the damage accumulation of HTPB propellant is considered rate-dependent in this research. In order to describe the mechanical characteristic precisely, a nonlinear viscoelastic constitutive model with rate-dependent cumulative damage is developed. The damage model is developed based on the concept of pseudo strain, in which a Prony series representation of viscoelastic material functions is applied. Besides, a rate-dependent damage variable is introduced into the model through considering the rate-dependent characteristics of cumulative damage process. In addition, a new normalized failure criterion is derived on the basis of the proposed damage model, which is independent of strain-rate after normalization. Finally, it is implemented in commercial finite element software for stress analysis to verify the predictive capacities of the damage model. The accuracy of the constitutive model and failure criterion is validated under uniaxial tensile tests of various strain rates.

To understand rubber concrete’s mechanical and fatigue performance under uniaxial compression, a 0 %, 8 %, 15 %, 20 %, and 25 % rubber particle incorporated mineral admixture, combined with 0 %, 4 %, 8 % and 15 % fly ash (FA) and 0 %, 5 %, 10 % and 15 % silica fume (SF), was used to prepare rubber concrete. Mechanical performance and uniaxial compression fatigue tests under constant amplitude cyclic loading were conducted. A damage model for rubber concrete fatigue strain was developed based on Miner’s cumulative damage theory. A reliability analysis of the fatigue life of rubber concrete was conducted using probabilistic statistical methods and experimental data. The distribution characteristics under uniaxial compression with constant amplitude cyclic loading were determined. The results indicate that rubber concrete incorporated with mineral admixture exhibits a significantly longer fatigue life compared to ordinary cement concrete under the same stress levels. Including 8 % fly ash (FA), 10 % silica fume (SF), and 15 % crumb rubber (CR) enhanced the mechanical properties of the concrete, leading to a 7.5 % increase in fatigue life. The incorporation of rubber particles also reduces the range of changes in stress strength factors. The evolution of fatigue strain in rubber concrete follows a three-stage pattern similar to that of conventional concrete, and its fatigue life is consistent with a logarithmic normal distribution. The equation for fatigue strain and damage amount of rubber concrete suggests that adding rubber may increase the fatigue deformation capacity of concrete to some extent, with the degree of improvement being independent of stress level.

The performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.