scholarly journals On The Time Dependence, Probability Distribution, and Size Effect of Rock Strength

2020 ◽  
Vol 136 (1) ◽  
pp. 1-7
Author(s):  
Kimihiro HASHIBA ◽  
Katsunori FUKUI
Keyword(s):  
Probability Distribution ◽  
Size Effect ◽  
Time Dependence ◽  
Rock Strength

scholarly journals Study on the Rock Size Effect of Quasistatic and Dynamic Compression Characteristics

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jun Zhou ◽  
Xiangrui Meng ◽  
Chongyan Liu ◽  
Zhixi Liu ◽  
Wensong Xu ◽  
...  
Keyword(s):  
Compressive Strength ◽  
Size Effect ◽  
Strain Rate ◽  
Failure Modes ◽  
Rock Strength ◽  
Dynamic Compression ◽  
Testing Machine ◽  
Impact Testing ◽  
Dynamic Compressive Strength ◽  
Quasistatic Loading

To study the size effect of rock under quasistatic and dynamic conditions, the changes in compressive strength with the change in specimen size are measured. Cylindrical granite specimens with length-diameter ratios in the range of 0.5∼1 are used for uniaxial compression tests using an RMT testing machine and an SPHB impact testing machine. Under quasistatic loading, the failure modes of the specimens with different length-diameter ratios are different. The larger the size of the specimen structure is, the greater the probability of defects such as joints and micro cracks is and the smaller the influence of the specimen on the distribution of a three-dimensional stress state is. The rock strength decreases with increasing length-diameter ratio. Using the improved Weibull formula, the size of the specimen is expressed by the volume, and the calculated rock strength of different volumes is similar to the compressive strength from the quasistatic tests. Under dynamic loading, the dynamic compressive strengths of the specimens with different length-diameter ratios are similar, and the failure mode of the specimens is different from that under quasistatic loading. Soon after a crack appears in a specimen, the specimen splits. As the size of the specimens decreases, the fragments size to approach the millimeter scale. By improving the Weibull distribution formula and considering variation in strain rate caused by the size of the specimen, the dynamic compressive strength of rocks of different volumes is calculated by introducing the critical strain rate and related parameters, and the results are similar to the experimental dynamic compressive strength obtained. The improved Weibull formula based on the strength size effect can accurately describe the quasistatic and dynamic compressive strength laws.

On the Time Dependence of Size Effect in Polydimethylsiloxane

2013 ◽  
Author(s):  
F. Alisafaei ◽  
Seyed Hamid Reza Sanei ◽  
E. J. Smith ◽  
Chung-Souk Han
Keyword(s):  
Size Effect ◽  
Time Dependence ◽  
Size Effects ◽  
Indentation Depth ◽  
Applied Force ◽  
Experimental Results ◽  
Time Dependent ◽  
Deformation Mechanisms ◽  
Indentation Size ◽  
Hardness Model

Nanoindentation tests at the nano-micrometer scales are conducted to investigate the depth and time dependent deformation mechanisms of polydimethylsiloxane (PDMS). Astonishing indentation size effects observed in these experiments are analyzed with an existing theoretical hardness model, and the effects of loading time on the hardness and indentation stiffness of PDMS are studied. The change in the indentation recovery with respect to indentation depth and loading time are analyzed. Furthermore, it is shown that the stiffness of PDMS obtained at the maximum applied force can be efficiently applied to validate the applied theoretical hardness model with the experimental results.

Preferential frequency and size effect of the Brownian force acting on a nanoparticle

2017 ◽  
Vol 828 ◽  
pp. 648-660
Author(s):  
Hanhui Jin ◽  
Ningning Liu ◽  
Xiaoke Ku ◽  
Jianren Fan
Keyword(s):  
Probability Distribution ◽  
Size Effect ◽  
Noise Spectrum ◽  
Self Similarity ◽  
Langevin Model ◽  
Gas Molecule ◽  
Spectrum Distribution ◽  
Brownian Force ◽  
Molecular Forces ◽  
New Phenomena

The Brownian motion of a nanoparticle in fluid depends on the molecular forces acting on it. Because of the small size and the high frequency, it is difficult to make experimental measurements of these forces. In the present work, Brownian forces acting on a nanoparticle are numerically investigated with the molecular dynamics method. Some new phenomena are disclosed. (i) The probability distribution shows that the Brownian forces conform to the Gaussian distribution and self-similarity of the probability distribution is also found for different $1/Kn$ numbers which are characterized with the particle radius and the mean path $\unicode[STIX]{x1D706}$ of the gas molecule $(1/Kn=R/\unicode[STIX]{x1D706})$. (ii) The frequency spectrum distribution of the Brownian force is not a white noise spectrum, which is different from the assumption commonly used in Langevin model. The preferential frequency of the Brownian force is found. (iii) The size effect relating to the Brownian forces is not monotonically varying with $1/Kn=R/\unicode[STIX]{x1D706}$ and is also found. It first increases and then decreases after it reaches the maximum value at $1/Kn\approx 250$. The variation process for $1/Kn<250$ observed in the present work has not been reported in previous research to date.

scholarly journals On the time behaviour of Okazaki fragments

2006 ◽  
Vol 43 (02) ◽  
pp. 500-509
Author(s):  
Krzysztof Bartoszek ◽  
Wojciech Bartoszek
Keyword(s):  
Dna Replication ◽  
Probability Distribution ◽  
Time Dependence ◽  
Time Behaviour ◽  
Okazaki Fragments ◽  
Analytical Formulae ◽  
Asymptotic Probability

We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.

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