SIMULATING A CURVE AVERAGE IN A STATIONARY NORMAL RANDOM FIELD USING FOURIER SERIES METHOD

Jian-Ye Ching ； Shang-Ping Sung

《Journal of GeoEngineering》 11卷1期 (2016/04) Pp. 33-43

https://doi.org/10.6310/jog.2016.11(1).4

並列摘要

Spatial averaging along a curve in two dimensions (2D) is of practical interest to geotechnical engineers, because it is the averaged soil shear strength along the critical slip curve that governs the ultimate failure of a 2D spatially variable soil mass. However, techniques that are able to simulate such a ＂curve average＂ are not available in the literature, because the random process along a curve is in general non-stationary, even if the 2D random field is stationary. This paper proposes a method of simulating such a curve average in a 2D stationary normal random field for a curve approximated by connecting line segments. This method is also able to calculate the variance reduction factor due to the approximate curve averaging. The proposed method is validated by several 1D problems with analytical solutions. It is shown that the proposed method produces results identical to the 1D analytical solutions. Two geotechnical analysis examples are used to demonstrate the applications of the proposed method.

並列關鍵字

Spatial variability ； curve averaging ； random field ； geotechnical engineering ； slope stability