RESEARCH ARTICLE


ARMA Models to Measure the Scale of Fluctuation from CPT Data



Brigid Cami1, Sina Javankhoshdel2, *
iD

1 Geotechnical Software Developer, Rocscience Inc. 54 St.Patrick St., Toronto, Ontario M5T 1V1, Canada
2 Geomechanics Specialist, Rocscience Inc. 54 St.Patrick St., Toronto, Ontario M5T 1V1, Canada


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Creative Commons License
© 2020 Cami and Javankhoshdel.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: (https://creativecommons.org/licenses/by/4.0/legalcode). This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Geomechanics Specialist, Rocscience Inc. 54 St.Patrick St., Toronto, Ontario M5T 1V1, Canada; Tel: (416) 698-8217; E-mail: sina.javankhoshdel@rocscience.com


Abstract

Objective:

Spatial variability is one of the largest sources of uncertainty in geotechnical applications. This variability is primarily characterized by the scale of fluctuation, a parameter that describes the distance over which the parameters of a material are similar. Spatial variability is generally described with traditional methods of time series analysis. In statistics, the Auto-Regressive Moving Average (ARMA) model is commonly used to describe the relationship between two points in time. Instead of assuming an autocorrelation model, the ARMA model calculates the necessary auto-regressive components (AR), as well as a decaying Mean Structure (MA). The advantage of this method is that it is calculated for each specific field study, so that the data is not forced to fit into a fixed autocorrelation model (e.g. Markovian, Gaussian, etc).

Methods:

In this study, the ARMA model is introduced as a means of measuring scale of fluctuation, and two case studies and a simulation are used to compare the scale of fluctuation values from the ARMA model to the other estimates.

Results:

In the first case study, the ARMA model estimated a value of 0.26 m while the other methods ranged from 0.22-0.29 m. In the second case study, the ARMA model estimated a value of 0.40 m while the other methods ranged from 0.40-0.54 m. In the simulated example, where the true value was 5.0 m, the ARMA model estimated a value of 4.73 m while the other methods ranged from 3.24-3.51 m.

Conclusion:

This paper concludes that ARMA is a promising new method for estimating the scale of fluctuation but requires a considerable amount of research before it can become established in the geotechnical sphere.

Keywords: Auto-regressive moving average, Mean structure, Cone penetration test, Autocorrelation model, Auto-regressive components, Geotechnical sphere.