Modeling statistics and kinetics of the natural aggregation structures and processes with the solution of generalized logistic equation

Maslov, L. A.; Chebotarev, V. I.

doi:10.1016/j.physa.2016.10.057

Cited by 7 publications

(5 citation statements)

References 21 publications

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“…In this direction, one of the approach currently exercised is the generalization of GR law. Recent works based on generalized logistic equation [11,12], Bayesian statistics [13] and non-extensive statistical mechanics [14] are promising and needs to be explored further.…”

Section: Discussionmentioning

confidence: 99%

The universality of b-value and size effect in acoustic emission: Experimental investigations in quasi-brittle fracture

Burud¹

2019

Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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Convergence of the b-value, the exponent of Gutenberg-Richter law, to unity near failure is considered as a universal phenomenon observed in many natural and artificial complex systems. The existence of universality implies that the underlying mechanism in various systems at the critical stage is universal too, irrespective of size, shape, and ingredient (heterogeneity) of the medium. The present work intends to discuss the size effect phenomenon on the b-value and apparent universality through experimental evidences. To study the size effect on the acoustic emission in concrete, geometrically similar, single edge notch beams of three different sizes are tested under three-point bending. The trend exhibited by critical b-value with respect to specimen size confirms its size-dependence which indeed originates from the size dependence of the fracture process zone.

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Section: Discussionmentioning

confidence: 99%

The universality of b-value and size effect in acoustic emission: Experimental investigations in quasi-brittle fracture

Burud¹

2019

Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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“…This two-parameter model considers the nonlinearity of the CFD across the entire magnitude range, incorporating a gentle cut-off for larger magnitudes. This model by Maslov et al [6] is characterised by a unique fractional power-law exponent, indicating that growth of microcracks follow a logistic or sigmoid pattern rather than a power-law. It has been concluded by Burud et al [8] that the b-value derived from the logistic equation demonstrates compliance with damage behavior.…”

Section: B-value Analysis Utilizing Generalised Logistic Equationmentioning

confidence: 98%

“…To address this, the CFD must incorporate small magnitude events and consider the presence of a large magnitude cut-off and logconcavity. An approach based on logistic equation proposed by Maslov et al [6] has been proven to be effective in considering the log-concavity and cut-off magnitude of the cumulative frequency distribution as nonlinearities [8]. This two-parameter model considers the nonlinearity of the CFD across the entire magnitude range, incorporating a gentle cut-off for larger magnitudes.…”

Section: B-value Analysis Utilizing Generalised Logistic Equationmentioning

confidence: 99%

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Investigation On The Influence Of Interfacial Transition Zone (ITZ) On Concrete Cracking Using Acoustic Emission Technique

Samal,

Ray,

Thiyagarajan

2023

Proceedings of the 11th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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The interfacial transition zone (ITZ) is the region between the aggregate and the cement paste in concrete, where the two materials come into contact and interact. It is a critical region in concrete as it represents the gradual transition in composition, microstructure, and properties from those of the aggregate to those of the cement paste. The properties of the ITZ are influenced by various factors, including the properties of the aggregate, curing conditions, and water-cement ratio. The interfacial transition zone plays a crucial role in the behavior of concrete structures due to its unique composition and properties. This study focuses on investigating the cracking mechanisms in concrete with different water-cement ratios using the acoustic emission technique and to evaluate the influence of ITZ volume fraction on cracking in concrete. Notched plain concrete beam specimens of dimensions 700 mm x 150 mm x 80 mm were cast with water-cement ratios varying between 0.3-0.5. Aggregates with a nominal maximum size of 12.5 mm have been used for this study. Experiments have been performed in a closed-loop servo-controlled Controls testing machine with a load cell of 10 kN capacity under centre point monotonic loading. The beams are tested under crack mouth opening displacement (CMOD) control at a rate of 0.5 µm/s. Acoustic emission technique was used to identify and monitor the development of cracks in the specimens, and the ITZ volume fraction was determined using the mathematical model proposed by authors. Correlations between acoustic emission parameters and ITZ volume fraction were analyzed to describe the effect of ITZ volume fraction on concrete damage. Based on the present study, it has been observed that the volume fraction of ITZ has a significant influence on concrete fracture. This study provides insights into the behavior of the interfacial transition zone and its effect on concrete damage and cracking process. Damage in concrete, due to the cracking has been studied with the help of statistical analysis of critical AE parameters such as rise time, average frequency, reverberation frequency etc. The acoustic emission parameters, including counts, absolute energy, and amplitude, were found to be positively correlated. The effect of ITZ volume fraction on the damage and fracture has been studied through b-value analysis using the generalised logistic equation. Inter-event time distribution analysis has been performed to evaluate the 1

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“…Recently, Maslov et al [12] proposed a new equation to study the statistics of earthquake distribution by calling it as "the generalized logistic equation". A special case of Maslov's generalized logistic equation can be written in the following form,…”

Section: Generalized Logistic Equationmentioning

confidence: 99%

Application of generalized logistic equation for b-value analysis in fracture of plain concrete beams under flexure

Burud

Kishen

2019

Engineering Fracture Mechanics

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A B S T R A C TThis work investigates the effect of finite size and evolution of fracture process zone on b-value of acoustic emission in concrete beams. It is shown that the AE b-value determined using the Gutenberg-Richter (GR) law varies with beam size and invalidates universality. Since GR law fits the frequency-magnitude curve partially, a recently proposed Maslov's generalized logistic equation (GLE) is used for b-value analysis. The existence of cut-off magnitude and nonlinearity of frequency-magnitude distribution is explained through crack interaction mechanisms occurring within the FPZ. The growth of micro and macro cracking in concrete is observed to follow logistic or sigmoid growth law rather than the power law. The b-values obtained from GR and GLE are compared and it is found that the b-value of GLE correlates well with the effective crack length during damage process of plain concrete thereby exhibiting damage compliant behavior which could be used in health monitoring of structures. As GR law was first introduced for statistical analysis of earthquakes and applied without any modification to acoustic emission https://doi.T due to its reasonable interpretation of this phenomenon [2], it is necessary to review its development in seismological studies. Therefore, the present work mostly reviews seismological and geophysical literature. Mainly, three different types of approaches are followed in literature to improve b-value estimation: (1) employing statistics based formulation by accounting nonlinearity while preserving pure GR law, (2) modifying GR law at large magnitudes by associating it with a polynomial or exponential or logarithmic cut-off and (3) suggesting an alternative model or generalizing GR law to consider the shape of distribution. By idealizing the occurrence of earthquakes as a Poisson process, the first approach with validity of GR law has yielded various statistical b-value estimates such as maximum likelihood estimate or Aki's formula [3], improved b-value [4], Weichert's formula [5], generalized Aki-Utsu β-estimator [6] and few others. An alternate approach based on robust fitting [7] has been proposed which is shown to be more efficient than maximum likelihood estimate. Cut-off on maximum magnitude approach has resulted in many of upper bound models such as tapered GR, truncated Gamma law, truncated GR, etc. The third approach has not received significant contribution except for a few which are noted further. The recent development in Tsallis nonextensive statistical mechanics has offered a generalized form of GR law [8-10] based on Tsallis entropy. A Bayesian approach [11] is also notable in the category of generalized GR law. Apart from the above mentioned contributions, an approach based on logistic equation proposed by Maslov et al. [12] is distinct due to its fractional power-law exponent. This two parameter model regards nonlinear CFD over whole magnitude range with soft cut-off for larger magnitudes. The overall shape of CFD suggest that the growth of microcracks is log...

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Modeling statistics and kinetics of the natural aggregation structures and processes with the solution of generalized logistic equation

Abstract: The generalized logistic equation is derived to model kinetics and statistics of natural processes such as earthquakes, forest fires, floods, landslides, and many others. This equation has the form

Cited by 7 publications

References 21 publications

The universality of b-value and size effect in acoustic emission: Experimental investigations in quasi-brittle fracture

The universality of b-value and size effect in acoustic emission: Experimental investigations in quasi-brittle fracture

Investigation On The Influence Of Interfacial Transition Zone (ITZ) On Concrete Cracking Using Acoustic Emission Technique

Application of generalized logistic equation for b-value analysis in fracture of plain concrete beams under flexure

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