# Assessment of Spatial Variability in Ground Models Using Mini-Cone Penetration Testing
## 1 Introduction  
The ground on which construction typically occurs encompasses many uncertainties. One factor contributing to these uncertainties is spatial variability (1; 2), which implies that drill core samples or the physical and chemical properties of rocks collected from the same location can vary. This difference is one of the primary factors determining the homogeneity or heterogeneity of the ground. Many researchers have elucidated spatial variability in the ground through field tests such as the DHT (Downhole Test), the CPT (Cone Penetration Test), and the SPT (Standard Penetration Test). However, due to practical limitations, construction often proceeds without considering the certainty of these ground properties in most sites (3; 4; 5; 6; 7; 8; 9)). Additionally, such spatial variability is also used in analyses through numerical modeling. In these numerical analyses, the use of spatial variability is primarily employed when generating random field models. When creating models as random fields for analysis, the spatial variability in the ground cannot be considered by modeling the variables representing ground properties as a single random variable; it is more appropriate to model it as a random field to represent spatial variability (10). Spatial variability has been studied through numerical analysis for various geotechnical structures. This variability has been theoretically and numerically investigated in relation to strip foundations and pile foundations (11; 12; 13). Additionally, various studies have been conducted on slope stability (14; 15; 16; 17), retaining walls (18), and more. Additionally, in evaluating such spatial variability, [PERSON] et al. (19) proposed a novel method for determining efficient locations for characterizing spatial variability, while [PERSON] and [PERSON] (20) suggested a new non-parametricmethod using a discrete cosine transform (DCT)-based auto-correlation function (ACF) approach to evaluate the statistical homogeneity of a single CPT data profile, effectively distinguishing heterogeneity without requiring a parametric correlation function. However, evaluating spatial variability in the ground through field experiments involves many constraints such as uncertain ground conditions. Laboratory tests such as the CPT in a ground model are very useful to better understand spatial variability in the ground. Unlike field experiments, laboratory experiments conducted in a more controlled environment can more precisely determine spatial variability in the ground. As few studies have been conducted on the evaluation of spatial variability in ground models in the laboratory, in this study, a ground model was constructed in a soil tank, and the cone penetration resistance was measured using the Mini-CPT. In order to investigate the spatial range in which the characteristics of the ground show a strong correlation, the vertical and horizontal spatial variabilities in the ground were assessed through the coefficient of variation (\(CV\)) [21] and the correlation length (\(CL\)) [22]. The \(CV\) is a numerical expression of the uncertainty degree of cone penetration resistance within a soil layer, and the \(CL\) is a numerical value that represents the correlation of cone penetration resistance according to the separation distance. In assessing spatial variability, the average values of \(CV\) and \(CL\) through cone penetration resistance measured in the field could be confirmed through a literature review. The average \(CV\) on sand ground was 38% [23], the average vertical \(CL\) was 1.6 to 3 m, and the horizontal \(CL\) was 14 to 38 m [1,22]. In the case of \(CL\), it is very difficult to compare the \(CL\) due to the difference in scale between the field and laboratory. Therefore, it is necessary to compare the results in the field through the \(CV\).