### 1. Introduction

### 2. Methodology

### 2.1 BS EN ISO 19905-1(2016) Method

*B*that penetrates single-layer and multi-layered soils composed of marine sand and clay. The theoretical equations for the bearing capacity of single-layer sand and clay soils are given in Eqs. (1) and (2). They include dimensionless bearing capacity factors,

*N*,

_{c}*N*and

_{γ}*N*, presented by Houlsby and Martin (2003) and Martin (2004). In the equations below,

_{q}*N*= 6.0 is applied if the spudcan foundation has a circular shape. where

_{c}s_{c}*s*is the bearing capacity shape factor;

_{c}*s*is the undrained shear strength of clay;

_{u}*γ*′ is the submerged unit weight of the soil;

*d*is the bearing capacity depth factor:

_{c}*d*= 1+0.2(

_{c}*D*/

*B*) ≤ 1.5;

*d*is the depth factor on surcharge for drained soils, and equals to 1.0;

_{γ}*d*is the depth factor for drained soils:

_{q}*d*= 1+2tan

_{q}*ϕ*′(1 − sin

*ϕ*′)

^{2}arctan(

*D*/

*B*);

*D*is the embedment depth; and

*p*′

_{0}denotes the effective overburden pressure at depth,

*D*, of the maximum bearing area.

*B*′) of the cross-section in contact with the surface of the clay soil, as expressed by Eq. (3). The weight of the sand plug generated by spudcan penetration is calculated by substituting

*B*′ into Eq. (4). Finally, the total capacity (

*Q*) is calculated by subtracting the weight (

_{v}*W*) of the sand plug from the ultimate vertical foundation bearing capacity for the fictitious footing at the interface between the sand and clay layers with no backfill (

*Q*), as expressed by Eq. (5) and shown schematically in Fig. 1. where,

_{u,b}*H*is the distance from the spudcan maximum bearing area to the weaker layer below (m);

*n*represents the load spread factor for sand overlying clay, which ranges from 3 to 5, but

_{s}*n*= 3 is usually applied.

_{s}*a*,

_{s}*b*, and

_{s}*T*are the bearing capacity squeezing factor constant, bearing capacity squeezing factor constant dependent on the spudcan diameter, and thickness of the weak clay layer underneath the spudcan, respectively:

*a*= 5.00 and

_{s}*b*= 0.33 in this study. The left-hand term of the equation represents an empirical formula for calculating the bearing capacity of the spudcan considering squeezing, and the right-hand side term equation refers to the vertical bearing capacity for a single clay layer and represents the lower limit of the left-hand term. When applying Eq. (6), the soil should be regarded as a single clay layer under the conditions of

_{s}*B*≥ 3.45

*T*(1+1.1

*D*/

*B*) for

*D*/

*B*≤ 2.5 when the spudcan penetrates a two-layer soil consisting of a weak layer over a hard layer. On the other hand, at

*T*≪

*B*, a squeezing effect occurs because of the influence of the bearing capacity of the lower strong layer.

### 2.2 InSafeJIP Report (2011) Method

*V*, from the ground surface, as expressed by Eq. (7). Eq. (7) is the theoretical equation for vertical bearing capacity according to the embedment depth of the spudcan. where

_{c}*D*is the effective diameter of the spudcan in contact with soil, and

_{eff}*β*is the average spudcan cone angle and refers to the angle of the cone whose tip is the embedded spigot and whose diameter is the effective diameter of the spudcan, as shown in Fig. 3.

*h*. Hence, the vertical bearing capacity of a spudcan is determined using Eq. (8) (Hossain et al., 2004; Hossain et al., 2005). where

_{c}*s*is the undrained shear strength of clay at depth

_{uh}*h*; the value of is determined from

_{c}*s*=

_{uh}*s*+

_{um}*ρh*.

_{c}*D*is the widest diameter of spudcan.

*s*

_{u}_{0}is undrained shear strength at the ground surface, and

*A*represents the effective spudcan bearing area in contact with soil; the value of

_{eff}*A*is determined from

_{eff}*N*is a bearing capacity factor.

_{c}*V*, is determined using Eq. (7) dependent on

_{c}*β*at that depth, which is the same equation for a clay layer. For the backflow that occurs due to the difference in the outer diameters between the leg and the spudcan when a spudcan penetrates a sand layer, it is necessary to consider the volume of backfill soil,

*V*, as shown in Fig. 4. On the other hand, the leg and the spudcan of the jack-up spudcan analyzed in this study have the same outer diameter, so the backflow is not considered. Therefore, the bearing capacity of the spudcan according to the embedment depth is expressed using Eqs. (12) and (13). where

_{soil}*N*is Martin (2004)’s the bearing capacity factor, and

_{γ}*N*(bearing capacity factor),

_{q}*ξ*(depth factor),

_{hr}*ξ*(shape factor), and

_{sq}*ξ*(depth factor) are

_{hq}*ξ*= 1.0,

_{hr}*ξ*= 1 + tan

_{sq}*ϕ′*and

### 2.3 Centrifuge Model Test

*N*times the gravitational acceleration to reproduce the same stress state as the site soil at each depth for the 1/

*N*scale model fabricated for the centrifuge model test. Table 1 lists the scaling factors of the major physical quantities.

### 3. Centrifuge Model Test for Foundation Installation

### 3.1 Centrifuge Test Condition

#### 3.1.1 Model spudcan

#### 3.1.2 Model soil

*w*) of 120%, which is twice the liquid limit (

*LL*), using a mixer. The slurry mixture was placed in a soil container. The clay layers were then prepared by consolidating the mixture at pressures up to 800 kPa using a preconsolidation actuator system.

### 3.2 Testing System

#### 3.2.1 Geotechnical centrifuge

#### 3.2.2 Vertical load control equipment

#### 3.2.3 Miniature cone penetration test (CPT)

*s*, of soils, as shown in Fig. 10. The miniature cone penetrometer was made from aluminum. A small load cell with a maximum load capacity of 200 kgf (20 kN) was installed at the connection between the vertical actuator and the CPT apparatus to measure the load during penetration. The load cell attached to the mini-CPT apparatus was a DSCS-200 kg tension/compression universal load cell, which has a capacity of 200 kg and a sensitivity of 3.0 mV/V (Sespene and Choo, 2018). The CPTs were performed with the penetration rate of 1 mm/s before the penetration of the spudcan after the arrival at the target g-level of 50 g. A Keyence IL-600 non-contact laser sensor was installed to measure the displacement during penetration. The cone penetration resistance,

_{u}*q*, according to the embedment depth, was calculated using the load and displacement values measured by the load cell and the laser sensor, as shown in Fig. 11. Even though a sand plug was not trapped during the penetration of the cone into loose sand in the case of sand over clay, the cone tip resistance decreased as the tip of the cone penetrometer approached the sand-clay interface but it increased again as the tip of the cone penetrometer penetrated the clay layer, resembling a punch-through effect.

_{c}### 4. Test Results

### 4.1 Cone Penetration

*q*) measured through the cone penetration test, the undrained shear strength,

_{c}*s*, of the clay layer was calculated, as shown in Fig. 12 (Falcon et al., 2021a; Falcon et al., 2021b). This calculated undrained shear strength was used to calculate the penetration resistance of a spudcan by using the theoretical equations of ISO (2016) and the InSafeJIP report (Osbone et al., 2011). The undrained shear strength,

_{u}*s*, calculated ranges 118–195 kPa in the clay layer situated at a depth of 4.9 to 8.7 m in SC1 (loose sand-clay) and 105–234 kPa in the clay layer of SC2 (loose sand-clay-dense sand). The undrained shear strength of SC2 was greater than that of SC1 at 8.7 m (clay-sand interface) because of the influence of dense sand of the deeper layer of SC2, but the undrained shear strengths of SC2 and SC1 were in a similar range.

_{u}### 4.2 Spudcan Penetration

### 5. Discussion

*Q*

_{u}_{,}

*(ultimate vertical foundation bearing resistance for the fictitious footing at the interface between the sand and clay layers with no backfill) because of the high undrained shear strength (>100 kPa) of the clay layer surface. On the other hand, the punch-through phenomenon did not occur because the high undrained shear strength did not significantly affect the load reduction effect due to the sand plug formed underneath the spudcan.*

_{b}### 6. Conclusions

In centrifuge model tests on the vertical penetration of a jack-up spudcan, while the spudcan was penetrating the upper loose sand layer, the vertical bearing resistance tended to decrease before penetrating the lower clay layer as the spudcan approached the sand-clay interface. This decrease in vertical bearing resistance is likely caused by the penetration of the sand plug trapped beneath the spudcan into the lower clay layer earlier than the actual spudcan. On the other hand, vertical bearing resistance increased again as the spudcan penetrated the clay layer. in the case of such soil conditions for installing of the offshore wind jack-up substructure, the punch-through effect is not expected to occur predominantly, but fast running is expected to occur at depths where vertical bearing resistance decreases. Fast running refers to the phenomenon in which the spudcan penetrates the soil rapidly and uncontrollably without penetration resistance increase and sinks deep into the soil at depths where vertical bearing resistance decreases during the installation of the jack-up spudcan. In addition, a squeezing effect is possibly expected when there is a stronger soil layer (dense sand) beneath a clay layer; that is a hard soil stratum underlying a weak soil layer causes an increase in the vertical bearing resistance as the spudcan approaches the interface between weaker and stronger soil strata.

The analysis results obtained using the ISO method (2016) showed a similar trend to the centrifuge model test regarding the vertical bearing resistance. In particular, the vertical bearing resistance in the upper loose sand layer was similar to the test data, but the punch-through phenomenon showing a decrease in vertical bearing resistance was not observed. In addition, in the soil condition of sand over clay, the estimates obtained using the ISO formula did not show a decrease in load arising from the impact of a high undrained shear strength of more than 100 kPa. In the soil condition of clay-over-dense sand, which is the condition of weak soil over a stronger stratum soil, the increase in vertical bearing resistance due to the squeezing effect was not prominent compared to the test results. In addition, the ISO method does not provide a method for calculating the vertical bearing resistance of a spudcan in multi-layered soils with three or more layers. Thus, when the ISO method is used to calculate the vertical bearing resistance in such soil conditions, a multi-layered soil with three or more strata is assumed to be a single sand–soil layer, so this method tends to predict very large vertical bearing resistances in such cases.

The InSafeJIP method (Osbone et al., 2011) showed a vertical bearing resistance pattern similar to that of the ISO (2016) method, but the estimated vertical bearing resistance obtained using the InSafeJIP method was more than two times larger than the value obtained using the ISO method in the upper sand layer in the soil condition of under loose sand over clay. In particular, because the InSafeJIP method predicted an excessively high vertical bearing resistance from the initial stage of penetration, it is considered more appropriate also to analyze the vertical bearing capacity under the condition of a single-layer sand soil when estimating vertical bearing resistance at the initial stage of penetration and predict vertical bearing resistance at a shallow depth by using the lower limit value. In addition, an analysis using the InSafeJIP method resulted in a more prominent punch-through effect than the centrifuge model test and ISO method. In the InSafeJIP method, the dense sand layer, which is the lowest layer among the loose sand-clay-dense layers, was assumed to be a single-layer sand soil, which is similar with the ISO method. On the other hand, the estimate by the InSafeJIP method was considerably lower than the value obtained by the ISO method because of the difference in the bearing capacity factors utilized in both methods, and it was even somewhat lower than the test result.

The measured vertical bearing resistances of a spudcan of the centrifuge model test differed in absolute value from the estimates calculated by theoretical formulas. Regarding the overall pattern of estimates, however, the ISO (ISO, 2016) and InSafeJIP methods (Osbone et al., 2011) predicted a penetration behavior that essentially matched the test data. On the other hand, in the case of a strong sand layer, compared to the test results, the InSafeJIP method predicted a smaller vertical bearing resistance, and the ISO predicted a very high vertical bearing resistance. When calculating the vertical bearing resistance of a spudcan using such theoretical equations, the geotechnical properties of friction angle and undrained shear strength of soils significantly impact the calculation of the bearing capacity factors for both clay and sand layers. Therefore, the cone penetration tests (CPT) and laboratory testing using site specimen should also be carried out to estimate the shear strength parameters of soils and comprehensively evaluate the vertical bearing resistance of a spudcan at the stage of a site investigation when designing offshore wind turbines.