*2.2. Model of Soil*

**Figure 4.** The dimensions of footings: flat base footing, fusiform spudcan footing and skirted footing. The diameter of all the footings is *D* = 15 m and the height of the max area is *H*t = 1.75 m. The geometry of the spudcan follows Liu et al. [26] and Yu et al. [27]. The geometry of the skirted footing is *Hs* = 0.25*D* = 3.75 m and *T*s = 1.75 m; where *Hs* is the height of the skirt and *T*s is the thickness of the The diameter of all the footings is *D* = 15 m and the height of the max area is *H*t = 1.75 m. The geometry of the spudcan follows Liu et al. [26] and Yu et al. [27]. The geometry of the skirted footing is *Hs* = 0.25*D* = 3.75 m and *T*s = 1.75 m; where *Hs* is the height of the skirt and *T*s is the thickness of the skirt. The geometry of the fusiform spudcan footing is *D* = 15 m, *H*1 = 2.5 m and *H*2 = 3.3 m. The distance from the center of Section 1.1 to the reference point (RP) for flat base footing is *Ha* =1.75 m, for fusiform spudcan footing is *Ha* =7.55 m, for skirted footing is *Ha* =5.5 m. To simplify the problem, the leg and footing are constrained as rigid. To simplify the problem, the footprint in this study is idealized as a reverse conical cave on the soil surface. The ideal elasto-plastic model is used to describe the stress–strain relationship of the soil, obeying the Mohr–Coulomb strength criterion. The undrained shear strength profile is *s*<sup>u</sup> = 7.5 + 0.92*z* kPa, where *z* is the soil depth from the mudline. The Poisson's ratio is ν = 0.49. The elastic modulus is *E* = 500*su*. The effective unit weight is γ' = 6.82 kN/m<sup>3</sup> . The internal friction angle and the dilation angle are ϕ = Ψ = 0 ◦ . The load is achieved by displacement control at a rate of *v* = 0.5 m/s, which is a compromise between the accuracy and the efficiency.

skirt. The geometry of the fusiform spudcan footing is *D* = 15 m, *H*1 = 2.5 m and *H*2 = 3.3 m. The distance from the center of Section 1.1 to the reference point (RP) for flat base footing is *Ha* =1.75 m, for fusiform spudcan footing is *Ha* =7.55 m, for skirted footing is *Ha* =5.5 m. To simplify the problem, the leg and footing are constrained as rigid. *2.2. Model of Soil*  To simplify the problem, the footprint in this study is idealized as a reverse conical cave on the The principle of universal contact is used to simulate the contact property between footing and soil. In tangential direction, the penalty function is selected to model the friction condition, thus different frictions can be tested. In normal direction, "hard" contact is set to simulate the interface, which can transfer positive pressure without limitation but separate under tension.

*2.2. Model of Soil*  To simplify the problem, the footprint in this study is idealized as a reverse conical cave on the soil surface. The ideal elasto-plastic model is used to describe the stress–strain relationship of the soil, obeying the Mohr–Coulomb strength criterion. The undrained shear strength profile is *s*u = 7.5 + 0.92*z* kPa, where *z* is the soil depth from the mudline. The Poisson's ratio is *ν* = 0.49. The elastic modulus is *E* = 500*su*. The effective unit weight is *γ*' = 6.82 kN/m3. The internal friction angle and the dilation angle are *φ* = *Ψ* = 0°. The load is achieved by displacement control at a rate of *v* = 0.5 m/s, which is a compromise between the accuracy and the efficiency. soil surface. The ideal elasto-plastic model is used to describe the stress–strain relationship of the soil, obeying the Mohr–Coulomb strength criterion. The undrained shear strength profile is *s*u = 7.5 + 0.92*z* kPa, where *z* is the soil depth from the mudline. The Poisson's ratio is *ν* = 0.49. The elastic modulus is *E* = 500*su*. The effective unit weight is *γ*' = 6.82 kN/m3. The internal friction angle and the dilation angle are *φ* = *Ψ* = 0°. The load is achieved by displacement control at a rate of *v* = 0.5 m/s, which is a compromise between the accuracy and the efficiency. The principle of universal contact is used to simulate the contact property between footing and soil. In tangential direction, the penalty function is selected to model the friction condition, thus different frictions can be tested. In normal direction, "hard" contact is set to simulate the interface, which can transfer positive pressure without limitation but separate under tension. A half model is modeled because of the symmetry. Both a cuboid soil domain and a cylindrical one have been tested. The results show that the former is more efficient and easier to mesh without the loss of accuracy. Thus, the cuboid soil domain, as shown in Figure 5, is used in this study. The soil is modeled by EC3D8R element (three-dimensional, eight-node linear brick, multimaterial, reduced integration with hourglass control) and the footings are modeled by C3D8R (three-dimensional, eight-node linear brick, reduced integration with hourglass control) element in ABAQUS/Explicit. In order to eliminate the influence of boundary effect, the width, depth, and thickness of the soil are 8*D*, 4*D*, and 4*D,* respectively. In addition, there is an empty element layer, 4 m thick, at the top of the soil to heave up during reinstallation. The mesh close to the footing penetrating path is refined.

which can transfer positive pressure without limitation but separate under tension.

The principle of universal contact is used to simulate the contact property between footing and

The minimum element size is *d*min/*D* = 1/30 = 0.5 m. The mesh density and soil domain have been proved to be with acceptable accuracy. penetrating path is refined. The minimum element size is *d*min/*D* = 1/30 = 0.5 m. The mesh density and soil domain have been proved to be with acceptable accuracy. penetrating path is refined. The minimum element size is *d*min/*D* = 1/30 = 0.5 m. The mesh density and soil domain have been proved to be with acceptable accuracy.

m thick, at the top of the soil to heave up during reinstallation. The mesh close to the footing

m thick, at the top of the soil to heave up during reinstallation. The mesh close to the footing

*J. Mar. Sci. Eng.* **2019**, *7*, 175 5 of 19

*J. Mar. Sci. Eng.* **2019**, *7*, 175 5 of 19

A half model is modeled because of the symmetry. Both a cuboid soil domain and a cylindrical one have been tested. The results show that the former is more efficient and easier to mesh without the loss of accuracy. Thus, the cuboid soil domain, as shown in Figure 5, is used in this study. The soil is modeled by EC3D8R element (three-dimensional, eight-node linear brick, multimaterial, reduced integration with hourglass control) and the footings are modeled by C3D8R (threedimensional, eight-node linear brick, reduced integration with hourglass control) element in ABAQUS/Explicit. In order to eliminate the influence of boundary effect, the width, depth, and

A half model is modeled because of the symmetry. Both a cuboid soil domain and a cylindrical one have been tested. The results show that the former is more efficient and easier to mesh without the loss of accuracy. Thus, the cuboid soil domain, as shown in Figure 5, is used in this study. The soil is modeled by EC3D8R element (three-dimensional, eight-node linear brick, multimaterial, reduced integration with hourglass control) and the footings are modeled by C3D8R (threedimensional, eight-node linear brick, reduced integration with hourglass control) element in ABAQUS/Explicit. In order to eliminate the influence of boundary effect, the width, depth, and

**Figure 5.** The mesh of soil. **Figure 5.** The mesh of soil. **Figure 5.** The mesh of soil.

#### *2.3. Numerical Cases 2.3. Numerical Cases 2.3. Numerical Cases*

In this study, the reinstallation process of three 15 m diameter footings with offset distances of *β*/*D* = 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, and 2.0 are simulated respectively. Four types of footprints (one of them is a flat surface field) are simulated, as listed in Figure 6. TA, TB, and TC are three footprints with various depths, and FS means flat surface (no footprint). The naming rule of each case is similar to that of Kong et al. [13]. For example, TB*-*2*D-*0.25*D* means the footprint is TB type with a diameter of *D*F = 2*D*, and the eccentricity of reinstallation is *β* = 0.25*D*. All the cases investigated in the paper are listed in Table 1. In this study, the reinstallation process of three 15 m diameter footings with offset distances of β/*D* = 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, and 2.0 are simulated respectively. Four types of footprints (one of them is a flat surface field) are simulated, as listed in Figure 6. TA, TB, and TC are three footprints with various depths, and FS means flat surface (no footprint). The naming rule of each case is similar to that of Kong et al. [13]. For example, TB*-*2*D-*0.25*D* means the footprint is TB type with a diameter of *D*<sup>F</sup> = 2*D*, and the eccentricity of reinstallation is β = 0.25*D*. All the cases investigated in the paper are listed in Table 1. In this study, the reinstallation process of three 15 m diameter footings with offset distances of *β*/*D* = 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, and 2.0 are simulated respectively. Four types of footprints (one of them is a flat surface field) are simulated, as listed in Figure 6. TA, TB, and TC are three footprints with various depths, and FS means flat surface (no footprint). The naming rule of each case is similar to that of Kong et al. [13]. For example, TB*-*2*D-*0.25*D* means the footprint is TB type with a diameter of *D*F = 2*D*, and the eccentricity of reinstallation is *β* = 0.25*D*. All the cases investigated in the paper are listed in Table 1.

**Figure 6.** Dimensions of three types of footprint. **Figure 6.** Dimensions of three types of footprint. **Figure 6.** Dimensions of three types of footprint.

**Table 1.** Numerical cases. **Table 1.** Numerical cases. **Table 1.** Numerical cases.

