Study on Statistical Damage Softening Constitutive Model and Determination of Parameters for Rock Based on Lognormal Distribution

2011 ◽  
Vol 69 ◽  
pp. 33-38
Author(s):  
Jian Hua Wen ◽  
Cui Ying Zhou ◽  
Li Huang ◽  
Ye Cheng ◽  
Lin Chong Huang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Lognormal Distribution ◽  
Strain Softening ◽  
Model Parameters ◽  
Kolmogorov Smirnov ◽  
Random Distributions ◽  
Determination Of Parameters ◽  
Smirnov Test ◽  
Statistical Damage

Based on the property that micro-cells strength is consistent with lognormal distribution function, this paper presented a new statistical damage softening constitutive model simulating the full process of strain softening for rock. Through discussing the characteristics of random distributions for rock micro-cells strength, lognormal distribution assumption is tested by Kolmogorov-Smirnov test in statistics, and the reasonable method of geometry boundary condition is selected to determine model parameters that can be easily applied to the situations under different complex conditions. Gabbro experiment comparative analyses show that the new damage softening constitutive model is rational and convenient in engineering.

Statistical damage model with strain softening and hardening for rocks under the influence of voids and volume changes

2010 ◽  
Vol 47 (8) ◽  
pp. 857-871 ◽  
Author(s):  
Wen-Gui Cao ◽  
Heng Zhao ◽  
Xiang Li ◽  
Yong-Jie Zhang
Keyword(s):  
Constitutive Model ◽  
Strain Softening ◽  
Triaxial Compression ◽  
Damage Model ◽  
Damage Threshold ◽  
Model Parameters ◽  
Volume Changes ◽  
Conventional Triaxial Compression ◽  
Damage Constitutive Model ◽  
Statistical Damage

With regards to the composition of natural rocks including voids or pores, deformation behavior is strongly affected by variation in porosity. By using a statistical damage-based approach, the characteristics of strain softening and hardening under the influence of voids and volume changes are investigated in the present paper. Suppose that a rock consists of three parts: voids, a damaged part, and an undamaged part. The effects of voids and volume changes on rock behavior are first analyzed through determination of the porosity and an associated damage model is then developed. Later, a statistical evolution equation describing the influence of the damage threshold on the propagation condition of rock damage is formulated based on measurement of the mesoscopic element strength. A statistical damage constitutive model reflecting strain softening and hardening behavior for rocks loaded in conventional triaxial compression is further developed and a corresponding method for determining the model parameters is also provided. Theoretical results of this proposed model are then compared with those observed experimentally. Finally, several aspects of the present constitutive model, which affect the relevant behavior of rocks, are particularly discussed.

scholarly journals Dynamical Age Determination of Open Clusters

1980 ◽  
Vol 85 ◽  
pp. 221-222
Author(s):  
M. Buchholz ◽  
Th. Schmidt-Kaler
Keyword(s):  
Age Determination ◽  
Dynamical Theory ◽  
Distribution Functions ◽  
Open Clusters ◽  
Kolmogorov Smirnov ◽  
The Difference ◽  
Absolute Age ◽  
Image Position ◽  
Smirnov Test

The radial mass distribution (obtained by counting stars in strips) of the real cluster is compared successively to the distribution functions of a simulated cluster of 100 stars, each of which corresponds to a certain dynamical age, Tdyn, The value of Tdyn, belonging to the function most similar to the observed one is taken to be the dynamical age of the cluster. The radius is given in units of R1/2 (sphere containing half of the total mass); this unit is nearly time-independent. The difference between the distribution functions is measured by the maximum Δmax of the Kolmogorov-Smirnov test which is free from assumptions on the form of the distributions. The minimum in the plot Δmax vs Tdyn, indicates the age of the cluster. It is then converted into an absolute age, Tabs (in years), by The error due to the dynamical theory (limited number of distribution functions, etc.) is estimated at 12%, the error due to the uncertainty of diameter and mass of the cluster is about 30%. Unreliable results were obtained in case of strongly inhomogeneous reddening of the cluster. As an example, the plot of the test values for NGC 457 is given in Figure 1.

DETERMINATION OF THE JOHNSON-COOK CONSTITUTIVE MODEL PARAMETERS OF AISI 5160 STEEL

2019 ◽  
Author(s):  
OURONON MARIE ROSALIE BEUGRE ◽  
Edison Gonçalves ◽  
Miguel Calle
Keyword(s):  
Constitutive Model ◽  
Model Parameters

Investigation of students’ level of imagination and sport confidence studying at School of Physical Education and Sports

2018 ◽  
Vol 10 (2) ◽  
pp. 148-157
Author(s):  
Aysegul Funda Alp ◽  
Rasit Oz ◽  
Mehmet Ali Horozoğlu
Keyword(s):  
Social Sciences ◽  
Physical Education ◽  
Research Group ◽  
Significant Difference ◽  
Kolmogorov Smirnov ◽  
Class Variable ◽  
Smirnov Test

AbstractThe aim of the study is to investigate students’ level of imagination and their athletic confidence The research group was made up of 62 female and 135 male, 197 in total, studying at the School of Physical Education and Sports, Karamanoglu Mehmetbey University. To achieve the purpose of the research, ‘A Scale of Achievement Imagery Questionnaire in Sports’ and ‘Confidence Questionnaire in Sports’ (Trait Sport Confidence-SSGO) were applied to the students who participated in the research. In the analysis and assessment of the data, Kolmogorov–Smirnov test, Kruskal Wallis H test and Mann–Whitney U test were used and significance was taken as P < 0.05 and in the evaluation of the data and for the determination of the calculated values, Statistical Package for Social Sciences was used. According to the results of the study, there is a significant difference in sub-dimension of athletic confidence according to the department and class variable.

A Statistical Damage Constitutive Model for Brittle Rocks Based on the Lade-Duncan Failure Criterion

2014 ◽  
Vol 919-921 ◽  
pp. 632-636 ◽  
Author(s):  
Zhen Yuan Tian ◽  
Wei Wang ◽  
Xue Hao Li ◽  
Wei Ya Xu
Keyword(s):  
Constitutive Model ◽  
Failure Criterion ◽  
Elastic Characteristic ◽  
Damage Threshold ◽  
Model Parameters ◽  
Brittle Rocks ◽  
Good Accord ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Statistical Damage

Micro-unit strength of rock is randomly distributed based on Lemaitres strain equivalence assumptions. The paper presents a method for measuring micro-unit strength taking into account the damage threshold. Assuming that the micro-unit strength obeys the Weibull distribution, combined with the Lade-Duncan failure criterion, a new statistical damage constitutive model for brittle rocks is established and the model parameters m and F0 are determined. The model can simulate the stress-strain relation of full process of rock failure well, especially reflects the influence of different stress on damage threshold and the linear elastic characteristic under low stress for rock. The good accord verifies the validity and feasibility of the new model.

scholarly journals Determination of parameters of a viscous-cohesive fracture model by inverse analysis

2015 ◽  
Vol 8 (5) ◽  
pp. 669-706 ◽  
Author(s):  
F. L. Gea dos Santos ◽  
J. L. A. O. Sousa
Keyword(s):  
Inverse Analysis ◽  
Fracture Process ◽  
Loading Rate ◽  
Process Zone ◽  
High Strength ◽  
Model Parameters ◽  
Cohesive Fracture ◽  
Cohesive Model ◽  
Determination Of Parameters

ABSTRACTThe quasi-brittle, loading rate dependent behaviour of the concrete, characterized by a fracture process zone (FPZ) ahead of the crack front, can be described through a viscous-cohesive model. In this paper, a viscous cohesive model proposed in a former paper is evaluated for a group of high strength concrete beams loaded at rates from 10-5 mm/s to 10+1 mm/s. A software has been developed to enable the automatic determination of the viscous-cohesive model parameters through inverse analysis on load-versus loading-point displacement (P-d) from threepoint bend tests on notched prismatic specimens. The strategy allowed the sensitivity analysis of the parameters related to viscous behaviour. The analysis of results shows that the formerly proposed model can be improved for a better simulation of the loading rate dependence on the cohesive fracture process.

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