Behaviour of Geocell Reinforced Sand Supporting Footings Using Response Surface Method

Abstract

The bearing capacity of shallow foundations on geocell-reinforced sand (GRS) depends not only on the soil characteristics but also on the geometries and properties of geocell. The geometry characteristics of GRS comprise height, length and cell aperture size of geocell as well as the sand layer thickness engaged between footing and GRS layer. Using the design-of-experiments (DOE) method the trends of bearing capacity ratio (BCR) as a function of selected geometry parameters of geocell are systematically visualized. Furthermore, trends of BCR as a function of geocell-selected geometry parameters are analysed. To this end, the study deploys the response surface methodology (RSM) to identify several configurations of geocell by conducting only twenty-seven laboratory tests. The results show that the DOE-RSM method gives an efficient interpretation of the variable’s interaction while it lessens the number of tests. In addition, it has been found that the geocell height is the most influential parameter on BCR of footings on GRS. Moreover, an interaction between geocell aperture size and geocell height is recognised. The results are formulated and compared with the literature, resulting in good agreement.

Appendices

Appendix 1

In this section, components of an Analysis of Variance (ANOVA) table are described:

• Source: Indicates the source of variation, either from the factor, interaction, or error. The total is the sum of all sources.

• DF: Degrees of freedom from each source. If a factor has three levels, the degrees of freedom are 2(n - 1). If there exists a total of 30 observations, the degrees of freedom are 29(n - 1).

• SS: Sum of squares between groups (factor) and the sum of squares within groups (error).

• MS: Mean squares are found by dividing the sum of squares by degrees of freedom.

• F: Calculate by dividing the factor MS by the error MS; we can compare this ratio against a critical F found in a table or we can use the p value to determine whether a factor is significant.

• P: Use to determine whether a factor is significant; typically compare against an alpha value of 0.05. If the p value is lower than 0.05, then the factor is significant.

Appendix 2

In the first step of RSM analysis, an analysis that contains full quadratic items including linear, square and interaction effects is carried out. According to Table AII-1, although R square values are to some extent over 90%, here the significance of the factors is more important. Nevertheless, statistical significance does not necessarily imply practical significance.

The p values for the main effects and two-way interactions are significant at alpha = 0.05 significance level. The analysis of the variance table and the estimated effects and coefficients table show the p values associated with each model term. The p values indicate that just one two-way interaction h/B × d/B (p = 0.035), and three main effects h/B (p =  < 0.001), b/B (p =  < 0.001), and d/B (p = 0.003) are significant. However, because three of these main effects are involved in an interaction, it is necessary to understand the nature of the interaction before these main effects can be considered. The lack of fit should be insignificant, yet its p value is 0.012. Thus, the model is not fitted to the test data properly.

Appendix 3

The normal probability plot is a visual method to distinguish if a data set distribution is normal (Chambers et al., 2018). The normal distribution in a theoretical line scheme is plotted vs. the data set. The graph should obey to some extent a straight line. More deviation from this straight line results in more deviation from normality. Therefore, if outputs are normal, the plotted points will form an approximately straight line.