scholarly journals The Hurst Effect: The scale of fluctuation approach

1993 ◽  
Vol 29 (12) ◽  
pp. 3995-4002 ◽  
Author(s):  
Oscar J. Mesa ◽  
German Poveda
Keyword(s):  
Scale Of Fluctuation ◽  
Hurst Effect

scholarly journals Probabilistic Bearing Capacity of a Pavement Resting on Fibre Reinforced Embankment Considering Soil Spatial Variability

2021 ◽  
Vol 7 ◽  
Author(s):  
Kouseya Choudhuri ◽  
Debarghya Chakraborty
Keyword(s):  
Spatial Variability ◽  
Soil Properties ◽  
Bearing Capacity ◽  
Coefficient Of Variation ◽  
Friction Angle ◽  
Horizontal Scale ◽  
Vertical Scale ◽  
Scale Of Fluctuation ◽  
The Mean ◽  
The Finite Difference Method

This paper intends to examine the influence of spatial variability of soil properties on the probabilistic bearing capacity of a pavement located on the crest of a fibre reinforced embankment. An anisotropic random field, in combination with the finite difference method, is used to carry out the probabilistic analyses. The cohesion and internal friction angle of the soil are assumed to be lognormally distributed. The Monte Carlo simulations are carried out to obtain the mean and coefficient of variation of the pavement bearing capacity. The mean bearing capacity of the pavement is found to decrease with the increase in horizontal scale of fluctuation for a constant vertical scale of fluctuation; whereas, the coefficient of variation of the bearing capacity increases with the increase in horizontal scale of fluctuation. However, both the mean and coefficient of variation of bearing capacity of the pavement are observed to be increasing with the increase in vertical scale of fluctuation for a constant horizontal scale of fluctuation. Apart from the different scales of fluctuation, the effects of out of the plane length of the embankment and randomness in soil properties on the probabilistic bearing capacity are also investigated in the present study.

Characterizing geotechnical anisotropic spatial variations using random field theory

2013 ◽  
Vol 50 (7) ◽  
pp. 723-734 ◽  
Author(s):  
H. Zhu ◽  
L.M. Zhang
Keyword(s):  
Field Theory ◽  
Random Field ◽  
Random Fields ◽  
Correlated Data ◽  
Random Field Theory ◽  
Sample Mean ◽  
Transverse Anisotropy ◽  
Analysis And Design ◽  
Scale Of Fluctuation ◽  
Correlation Structures

In this study, anisotropic heterogeneous geotechnical fields are characterized using random field theory, in which five basic patterns of material anisotropy are simulated including isotropy, transverse anisotropy, rotated anisotropy, general anisotropy, and general rotated anisotropy. Theoretical formulations of scale of fluctuation as a function of directional angle are developed for the five basic patterns of anisotropy through modifications of the coordinate system. These formulations of scale of fluctuation are identical for different correlation structures. Correlation functions for the exponential and Gaussian correlation structures are also derived. The matrix decomposition method is then applied to generate anisotropic random fields. The generated random field correlated data are verified with two realizations of transverse anisotropy and general rotated anisotropy random fields. Test values of the sample mean, sample deviation, and scales of fluctuation in six directions match well with the prescribed values. This study provides a technique to characterize inherent geotechnical variability and anisotropy, which is required to realistically simulate complex geological properties in engineering reliability analysis and design.

New Discretization Methodology for Three-Dimensional Mechanical Parameters Considering Spatial Variations

2019 ◽  
Vol 11 (10) ◽  
pp. 1950095
Author(s):  
Tao Wang ◽  
Di Wang ◽  
Daqing Xu ◽  
Guoqing Zhou
Keyword(s):  
Three Dimensional ◽  
Analytical Formula ◽  
Spatial Variations ◽  
Mechanical Parameters ◽  
Fe Method ◽  
Stochastic Effects ◽  
Analysis Process ◽  
Scale Of Fluctuation ◽  
Computer Codes ◽  
Local Average

In this paper, the uncertain mechanical parameters are modeled as spatial random fields (RFs). A new tetrahedral discretization methodology of three-dimensional (3D) RF is proposed based on the local average (LA) theory. An analytical formula and a numerical formula of the covariance for any two tetrahedral RF elements are developed. Its main advantage, compared to similar studies employing hexahedral discretization method, is that tetrahedral LA method can perfectly combine with tetrahedral finite element (FE) method. Also, the corresponding relation between RF mesh and FE mesh is clearer and the computer codes are simpler. The accuracy of proposed LA method in this study was verified by comparing with other discretization techniques of RF. Finally, an illustrative example is presented to demonstrate the analysis process. The validity and the advantage of the proposed LA method are proven. Taking the spatial variations of uncertain mechanical parameters into account, the stochastic effects of scale of fluctuation on the RF are estimated. The proposed method can be widely applied to 3D stochastic FE analysis, and the sample results will improve our understanding of the stochastic influence of scale of fluctuation on the RF.

The Hurst effect under trends

1983 ◽  
Vol 20 (3) ◽  
pp. 649-662 ◽  
Author(s):  
R. N. Bhattacharya ◽  
Vijay K. Gupta ◽  
Ed Waymire
Keyword(s):  
Hurst Exponent ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stationary Sequence ◽  
Monotonic Trend ◽  
Weakly Dependent Random Variables ◽  
Necessary And Sufficient ◽  
Hurst Effect ◽  
Weakly Dependent ◽  
Negative Parameter

Necessary and sufficient conditions for the so-called Hurst effect are given in the case of a weakly dependent stationary sequence of random variables perturbed by a trend. As a consequence of this general result it is shown that the Hurst effect is present in the case of weakly dependent random variables with a small monotonic trend of the form f(n) = c(m + n)ß, where m is an arbitrary non-negative parameter and c is not 0. For – ½ < ß < 0 the Hurst exponent is shown to be precisely given by 1 + ß. For ß ≦ – ½ and for ß = 0 the Hurst exponent is 0.5, while for ß > 0 it is 1. This simple mathematical model, motivated by empirical evidence in various geophysical records, demonstrates the presence of the Hurst effect in a direction not explored before.

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