MODIFIED BARTLETT TEST FOR GEOSTATISTICAL ANALYSIS

Abstract

The identification of stationary in-situ test records is important for accurate description of the inherent variability of the soil. In this study, the modified Bartlett statistical test is proposed to test the second-order stationarity of in-situ test records. The new criteria for the modified Bartlett statistical test are developed using Monte Carlo simulation. The criteria are dependent on the scale of fluctuation, the sample size, the window size, and the form of the autocorrelation model. The criteria are compiled into short formula and can be conveniently used in practice.

As a prelude to the main study, the characteristics of the spectral representation method used in the Monte Carlo simulation is investigated. The ergodic characteristics of the mean, the autocovariance function, and the exceedence probability of the cosine series representation and the sine-cosine series representation models are studied to verify the simulation procedure. The cosine series model is more efficient in simulating stationary and ergodic stochastic processes, and is selected to perform the subsequent analyses.

From physical point of view, stationarity may arise if the data come from a kind of homogeneous material. The process of obtaining stationary records inevitably contributes to the demarcation of soil boundaries. A new soil boundary identification procedure is suggested using the modified Bartlett statistical test. The procedure of the modified Bartlett statistical test and its application on soil boundary identification are illustrated using a CPTU cone tip resistance profile. The boundaries of the underlying soil is successfully delineated through the stationary test of the cone tip resistance profile. Based on the test results of second-order stationarity, important statistics, such as standard deviation, coefficient of variation, and scale of fluctuation, are evaluated in a statistically consistent manner. The data points from the identified stationary cone tip resistance profiles were plotted on Robertson's CPTU soil classification chart. It is observed that statistical stationarity of the cone tip resistance profile corresponds to physical homogeneity of the material, which validates the soil boundary identification procedure based on the modified Bartlett stationary test.