The spatial variability of seabed soils has been reported for the North Sea (Høeg and Tang, 1976; Tang, 1979; Wu et al., 1987; Nadim, 1988; Keaveny et al., 1989; Lacasse and de Lamballerie, 1995; Uzielli et al., 2006), the Gulf of Mexico (Cheon and Gilbert, 2014), and offshore Australia (Randolph et al., 1998; Bienen et al., 2011; Li et al., 2015b). Lacasse and Nadim (1996) reviewed offshore soils and found that the undrained shear strength (su) of clay followed a normal or lognormal distribution with its coefficient of variation (COV) ranging between 5% and 35%. Uzielli et al. (2006) analysed the cone resistance of Troll clay off the shore of Norway and reported that the undrained shear strength increased with depth. The mean value of the Troll clay increased  from

12.7 kPa to 36.3 kPa with its standard deviation increasing from

2.0 kPa to 5.3 kPa. For offshore clays in Timor Sea, north-west of Australia, Randolph et al. (1998) found that the undrained shear

Fig. 2. Finite element model and boundary conditions.

Scales of fluctuation used in this study.

3. Random finite element method

A circular spudcan foundation of diameter B that was embedded into used in this study represents a generic spudcan in the field, which was spudcan was considered “wished-in-place” and embedded at a   depth strength of the clays increased bi-linearly with depth based on T-bar penetrometer tests. The undrained shear strength of the soil at the seabed level is site-specific, typically 2–10 kPa, although as high as 40–200 kPa in the North Sea has been observed (Poulos, 1988; Cassidy et al., 2002; Hossain and Randolph, 2009). Bienen et al. (2011) found that the COV of offshore soils varied between 2% and 41% with a mean value of 23% based on data from 14 offshore clay sites. The spatial variation of the seabed soils was investigated using ran- dom field theory by many researchers (e.g., Tang, 1979; Wu et al., 1987; Keaveny et al., 1989; Lacasse and de Lamballerie, 1995; Cheon and Gilbert, 2014; Li et al., 2015a, 2015b). The scale of fluctu- ation of the undrained shear strength and cone penetration resis- tance are reviewed and summarised in Table 1. The vertical scale of fluctuation ranges from 0.05 m to 14 m. The scale of fluctuation in the horizontal direction varies over a large  range  from  7  m  to 9000 m, which is much larger than that in the vertical direction. This strong anisotropy in soil strength has also been observed in on- shore  soils (e.g., Firouzianbandpey et  al.,   2014).

is considered here without modelling the leg that attached to the spudcan. The circular spudcan is ideally modelled as a three dimen- sional problem with a 3D random field to describe the soil variability. However, to model this in 3D is both a technical and computational challenge for the 3D finite element model and also the spatial variability generation and mapping. Thus, a plane strain condition with 2D spatial variability generation is used here to understand the problem.

To simulate the spatial variability of the seabed soils, the undrained shear strength of clay was modelled as a random field. The mean value of the undrained shear strength was set as 10 kPa, and the COV was 30%. A square exponential model (Baecher and Christian, 2003) was used to describe the autocorrelation of the undrained shear strength. As the scale of fluctuation of the seabed soils varied over a wide range both horizontally and vertically, 9 cases with different scales of fluctuation were investigated, as shown in Table 2. The horizontal scale of fluctua- tion in Cases I to V was set to 54 m, with their vertical scales of fluctua- tion increasing from 1.08 m to 54 m. Cases VI to IX and Case II have the same vertical scale of fluctuation of 3 m and various horizontal scales of fluctuation from 3 m to 150 m. The 9 cases encompass almost all situations of practical interest. The aspect ratio between the horizontal scale of fluctuation and the vertical scale of fluctuation is also listed in