RESEARCH ON MORPHOLOGIES OF ROCK FRACTURE SURFACES BASED ON MATHEMATICAL METHODS

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550039
Author(s):  
XUEZAI PAN
Keyword(s):  
Interpolation Method ◽  
Rock Fracture ◽  
Small Island ◽  
Fractal Interpolation ◽  
Mathematical Methods ◽  
Fractal Method ◽  
Fracture Surfaces ◽  
Power Spectral ◽  
Rock Fracture Mechanics ◽  
Spectral Density Method

In order to research mechanics of rock fracture instant, it is one of methods that rock fracture mechanics are researched by rock fracture surfaces’ morphology. Some researched results which come from international and domestic researches in decades are described and summarized from mathematics in this paper. For example, fractal dimension method, “Small Island Method”, fractal interpolation method, Multi-fractal method, the accumulation power spectral density method. In addition, advantages and insufficiencies of every method are reviewed and commented. In the end, the future researched expectations are put forward from three aspects of rock fracture surfaces’ morphology.

The Offshore Wave Simulation Based on the Improved P-M Spectrum and Multiple Fractal Interpolation

2014 ◽  
Vol 1030-1032 ◽  
pp. 1832-1836
Author(s):  
Ying Li ◽  
Rui Zhou ◽  
Hao Kuan Li ◽  
Ming Wang
Keyword(s):  
Shallow Water ◽  
Interpolation Method ◽  
Fractal Interpolation ◽  
Fractal Method ◽  
Growth State ◽  
Water Factor ◽  
Proposed Model ◽  
Simulation Based ◽  
Offshore Wave ◽  
The Waves

The Pierson - Moskowitz model is only applicable to full growth state of the waves, and it has low authenticity and hopping phenomenon under the condition of offshore shallow water. This paper proposes a simulation model of offshore wave based on the improved P-M spectrum and multiple fractal interpolation methods. In order to calculate the sea wave with shallow water, a spectrum peak regulation factor and a depth of the water factor are introduced to the P - M spectrum model. Based on this model, the wavelength and wave speed are used as the initial values of wave height. Then, the amplitude and the number of iterations in diamond square fractal method are controlled to obtain the fractal static sea. In order to reduce the influence of the hopping phenomenon to the simulation authenticity, meanwhile, a multiple dynamic non-uniform interpolation method is proposed. The experimental results show that the proposed model can simulate offshore wave with better effect and in real time.

Study on generation of rock fracture surfaces by using fractal interpolation

2001 ◽  
Vol 38 (32-33) ◽  
pp. 5765-5787 ◽  
Author(s):  
Heping Xie ◽  
Hongquan Sun ◽  
Yang Ju ◽  
Zhigang Feng
Keyword(s):  
Rock Fracture ◽  
Fractal Interpolation ◽  
Fracture Surfaces

A controlled fractal interpolation method based on random midpoint displacement for coastline

GEOMATICA ◽  
2017 ◽  
Vol 71 (2) ◽  
pp. 89-99
Author(s):  
Baode Jiang ◽  
Dongqi Wei ◽  
Zhong Xie ◽  
Zhanlong Chen
Keyword(s):  
Spatial Data ◽  
Interpolation Method ◽  
Fractal Interpolation ◽  
Quality Requirements ◽  
One Dimensional ◽  
Fractal Characteristic ◽  
Fractal Interpolation Function ◽  
Proper Order ◽  
Fractal Characteristics ◽  
Original Scale

Coastline has different geographical bending characteristics in different coastal geomorphic regions. The existing fractal interpolation methods for coastline mostly focus on how to simulate its fractal characteristic but neglect the geographical bending characteristic. This study presents an improved controlled fractal inter polation method based on one-dimensional Random Midpoint Displacement (RMD) that aims to preserve both the bending characteristics and fractal characteristics of coastline. First, the coastline is divided into sev eral parts based on its bending characteristics, in order to conserve the geographical bending struc ture of the coastline and change the uncontrollable general fractal interpolation into a combination of sev er al piece-wise interpolation units. Second, the fractal interpolation function of one-dimensional RMD is used for each divided bending unit of the coastline, and the parameters of RMD function are restricted by the con straints of each unit bending characteristics. Third, the results of fractal interpolation of each unit are linked together in proper order to obtain the approximate coastline. The experiments show that this method can maintain the geographical bending characteristics and fractal characteristics of coastline, and when the ratio of target scale to the original scale is not more than 3 times, the accuracy of interpolation spatial coor di nates can meet the quality requirements of spatial data.

Distribution of Sub and Super Harmonic Solution of Mathieu Equation Within Stable Zones

2005 ◽  
Author(s):  
G. Nakhaie Jazar ◽  
M. Mahinfalah ◽  
M. Rastgaar Aagaah ◽  
N. Mahmoudian
Keyword(s):  
Spectral Density ◽  
Periodic Solutions ◽  
Mathieu Equation ◽  
Stable Region ◽  
Transition Curve ◽  
Harmonic Solution ◽  
The Third ◽  
Power Spectral ◽  
Stability Chart ◽  
Spectral Density Method

The third stable region of the Mathieu stability chart, surrounded by one π-transition and one 2π-transition curve is investigated. It is known that the solution of Mathieu equation is either periodic or quasi-periodic when its parameters are within stable regions. Periodic responses occur when they are on a “splitting curve”. Splitting curves are within stable regions and are corresponding to coexisting of periodic curves where an instability tongue closes. Distributions of sub and super-harmonics, as well as quasi-periodic solutions are analyzed using power spectral density method.

Introduction to Rock Fracture Mechanics

2013 ◽  
pp. 5-18
Author(s):  
Baotang Shen ◽  
Ove Stephansson ◽  
Mikael Rinne
Keyword(s):  
Fracture Mechanics ◽  
Rock Fracture ◽  
Rock Fracture Mechanics

scholarly journals Application of a Fractal Method to Quantitatively Describe Some Typical Fracture Surfaces

2001 ◽  
Vol 42 (1) ◽  
pp. 128-131 ◽  
Author(s):  
X. W. Li ◽  
J. F. Tian ◽  
S. X. Li ◽  
Z. G. Wang
Keyword(s):  
Fractal Method ◽  
Fracture Surfaces

Basics of Rock Fracture Mechanics

1983 ◽  
pp. 1-29 ◽  
Author(s):  
R. A. Schmidt ◽  
H. P. Rossmanith
Keyword(s):  
Fracture Mechanics ◽  
Rock Fracture ◽  
Rock Fracture Mechanics
Sign in / Sign up

Export Citation Format

Share Document