*2.3. Meshing and Boundary Conditions*

A graded mesh was used in the simulation. Denser meshes and sparser meshes were adopted in the regions close to the anchor and further away from the anchor, respectively. The finite element mesh used for the analysis of the anchor is illustrated in Figure 4. The suction anchor was modeled as rigid bodies, since the anchor is much stiffer than soft clay. The cyclic load amplitude *Fcz* was 20 kN, with a typical cyclic period (*T*) of 10 s. The total calculation time was one hour (360*T*). A drainage boundary at the seabed surface was assumed, that is to say, the upper surface of the seabed layer was allowed to drain freely (i.e., *p* = 0 at z = 0). The displacements were fixed horizontally on the periphery and in both directions at the bottom of the model domain. The conventional Coulomb friction law was adopted to simulate the friction at the interface between the anchor wall and the surrounding soil. The coefficient of wall friction (*tan*δ) was set to 0.42 [30].

seabed layer was allowed to drain freely (i.e., *p* = 0 at z = 0). The displacements were fixed horizontally on the periphery and in both directions at the bottom of the model domain. The conventional Coulomb friction law was adopted to simulate the friction at the interface between the

**Figure 4.** Three-dimensional finite element model **Figure 4.** Three-dimensional finite element model.

### **3. Verification of the Model 3. Verification of the Model**

In this section, we describe the calibration of the proposed bounding surface model with the combined isotropic-kinematic hardening rule against available existing published experimental data, including those of Stipho [31], Tao et al. [29], and Zhong et al. [32]. The triaxial tests included monotonic loading tests on anisotropically consolidated clay, pore pressure response tests under cyclic loads, and tests on the plastic strain accumulation of soft clay under cyclic loads, respectively. The validity of the proposed model was evaluated based on comparisons between numerical results In this section, we describe the calibration of the proposed bounding surface model with the combined isotropic-kinematic hardening rule against available existing published experimental data, including those of Stipho [31], Tao et al. [29], and Zhong et al. [32]. The triaxial tests included monotonic loading tests on anisotropically consolidated clay, pore pressure response tests under cyclic loads, and tests on the plastic strain accumulation of soft clay under cyclic loads, respectively. The validity of the proposed model was evaluated based on comparisons between numerical results and experiments. The properties of the soil adopted in this study were the same as those used in the experiments, as tabulated in Table 2.


and experiments. The properties of the soil adopted in this study were the same as those used in the **Table 2.** Model parameters in verification cases.

*γ* 2 1.72 1.5 *<sup>r</sup> ς* - 3.5 6 η - 120 40 *β* - 0.5 1.5 The first validation case involved monotonic loading tests on anisotropically consolidated clay, which was performed by Stipho [31]. The tests were performed under strain-controlled conditions. The axial strain was applied to the top surface of the specimen with a magnitude of 12% for compression and extension, respectively. The specimen was consolidated under 204 *<sup>0</sup> p =* kPa, with The first validation case involved monotonic loading tests on anisotropically consolidated clay, which was performed by Stipho [31]. The tests were performed under strain-controlled conditions. The axial strain was applied to the top surface of the specimen with a magnitude of 12% for compression and extension, respectively. The specimen was consolidated under *p*<sup>0</sup> = 204 kPa, with the initial void ratio of *e*<sup>0</sup> = 1.1, with the value of *K*<sup>0</sup> being about 0.8. Figure 5a,b show the normalized *q*/*p*<sup>0</sup> versus the axial strain ε<sup>1</sup> and the normalized excess pore water pressure *u*/*p*<sup>0</sup> versus the axial strain ε1, respectively. Figure 5c illustrates a comparison between model simulation and experimental data in terms of stress paths in the normalized *q*/*p*<sup>0</sup> versus *p*/*p*0. As shown in Figure 5c, when it reaches the critical state line(CSL), *p* from the compression test is different from that obtained by extension test. That is to say, the proposed model can capture a non-unique critical state line (CSL) in the *e* − *lnp* space. As one can see, there is an excellent agreement between the model simulation and the experiment.

agreement between the model simulation and the experiment.

the initial void ratio of 1.1 *<sup>0</sup> e =* , with the value of *K0* being about 0.8. Figures 5(a–b) show the normalized *<sup>0</sup> q p* versus the axial strain *<sup>1</sup> ε* and the normalized excess pore water pressure *u p0* versus the axial strain *<sup>1</sup> ε* , respectively. Figure 5(c) illustrates a comparison between model simulation and experimental data in terms of stress paths in the normalized *<sup>0</sup> q p* versus *<sup>0</sup> p p* . As shown in figure5(c), when it reaches the critical state line(CSL), *p* from the compression test is different from that obtained by extension test. That is to say, the proposed model can capture a

(**b**) Pore water pressure–strain curve

**Figure 5.** *Cont.*

(**c**) Effective stress path **Figure 5.** A comparison between the model simulation and experimental data with *K = <sup>0</sup>* 0.8 .

**Figure 5.** A comparison between the model simulation and experimental data with *K = <sup>0</sup>* 0.8 . **Figure 5.** A comparison between the model simulation and experimental data with *K*<sup>0</sup> = 0.8.

The second validation case involved cyclic stress-controlled loading tests on isotropically consolidated clay. Tao et al. [29] carried out a series of cyclic three-axis undrained shearing tests on normally consolidated clays, with an initial void ratio of *<sup>0</sup> e =* 0.62 . The triaxial test loading frequency was 0.1 Hz. Figure 6(a) presents the experimental results and model predictions for a confining pressure of *<sup>0</sup> p =* 450 kPa, and a cyclic stress amplitude of *<sup>d</sup> q =* 116 kPa, and Figure 6(b) presents the experimental results and model predictions for a confining pressure of *<sup>0</sup> p =* 350 kPa, and a cyclic stress amplitude of *<sup>d</sup> q =* 130 kPa. It is found that the pore water pressure versus the The second validation case involved cyclic stress-controlled loading tests on isotropically consolidated clay. Tao et al. [29] carried out a series of cyclic three-axis undrained shearing tests on normally consolidated clays, with an initial void ratio of *e*<sup>0</sup> = 0.62. The triaxial test loading frequency was 0.1 Hz. Figure 6a presents the experimental results and model predictions for a confining pressure of *p*<sup>0</sup> = 450 kPa, and a cyclic stress amplitude of *q<sup>d</sup>* = 116 kPa, and Figure 6b presents the experimental results and model predictions for a confining pressure of *p*<sup>0</sup> = 350 kPa, and a cyclic stress amplitude of *q<sup>d</sup>* = 130 kPa. It is found that the pore water pressure versus the number of cycles can be predicted well by the proposed model. The second validation case involved cyclic stress-controlled loading tests on isotropically consolidated clay. Tao et al. [29] carried out a series of cyclic three-axis undrained shearing tests on normally consolidated clays, with an initial void ratio of *<sup>0</sup> e =* 0.62 . The triaxial test loading frequency was 0.1 Hz. Figure 6(a) presents the experimental results and model predictions for a confining pressure of *<sup>0</sup> p =* 450 kPa, and a cyclic stress amplitude of *<sup>d</sup> q =* 116 kPa, and Figure 6(b) presents the experimental results and model predictions for a confining pressure of *<sup>0</sup> p =* 350 kPa, and a cyclic stress amplitude of *<sup>d</sup> q =* 130 kPa. It is found that the pore water pressure versus the number of cycles can be predicted well by the proposed model.

number of cycles can be predicted well by the proposed model.

(**a**) *<sup>0</sup> p =* 450 kPa, *<sup>d</sup> q =* 116 kPa

(**a**) *<sup>0</sup> p =* 450 kPa, *<sup>d</sup> q =* 116 kPa **Figure 6.** *Cont.*

**Figure 6.** Comparison of pore water pressures between the model simulation and measured data. **Figure 6.** Comparison of pore water pressures between the model simulation and measured data. **Figure 6.** Comparison of pore water pressures between the model simulation and measured data.

The third validation case involved plastic strain accumulation tests on isotropically consolidated clay, which were performed by Zhong et al. [32]. The tests were conducted under stress-controlled conditions. The axial stress was applied to the top surface of the specimen with different amplitudes *<sup>d</sup> q* . The specimen was consolidated under an initial pressure of *<sup>0</sup> p =* 50 kPa, with an initial void ratio of *<sup>0</sup> e =* 1.099 . The triaxial test loading frequency was 0.1 Hz. Figure 7 shows a comparison between the model predictions and the experimental data. Though the permanent strain predicted by the proposed model was smaller than that shown in the experiment at a higher stress level, the general trend was consistent. Figure 8 shows the effective stress path under typical conditions. With the increase in the cyclic number, the soft clay specimen finally The third validation case involved plastic strain accumulation tests on isotropically consolidated clay, which were performed by Zhong et al. [32]. The tests were conducted under stress-controlled conditions. The axial stress was applied to the top surface of the specimen with different amplitudes *q<sup>d</sup>* . The specimen was consolidated under an initial pressure of *p*<sup>0</sup> = 50 kPa, with an initial void ratio of *e*<sup>0</sup> = 1.099. The triaxial test loading frequency was 0.1 Hz. Figure 7 shows a comparison between the model predictions and the experimental data. Though the permanent strain predicted by the proposed model was smaller than that shown in the experiment at a higher stress level, the general trend was consistent. Figure 8 shows the effective stress path under typical conditions. With the increase in the cyclic number, the soft clay specimen finally reached a cyclic steady state, which means that the cyclic shakedown phenomena occur. third validation case plastic strain accumulation on consolidated clay, which were performed by Zhong et al. [32]. The tests were conducted under stress-controlled applied surface with different amplitudes *<sup>d</sup> <sup>q</sup>*. The specimen was consolidated under an initial pressure of *<sup>0</sup> p =*50 kPa, with an initial ratio *0e*  triaxial was shows a comparison between the model predictions and the experimental data. Though the permanent the was than shown experiment at a higher stress level, the general trend was consistent. Figure 8 shows the effective stress path typical the increase the clay finally

reached a cyclic steady state, which means that the cyclic shakedown phenomena occur. Overall, these validation cases demonstrate that cyclic behaviors of soft clay can be well predicted by the present model under cyclic loading conditions. The model is able to capture the build-up of pore water pressure caused by cyclic loads. Overall, these validation cases demonstrate that cyclic behaviors of soft clay can be well predicted by the present model under cyclic loading conditions. The model is able to capture the build-up of pore water pressure caused by cyclic loads. reached a cyclic steady state, which means that the cyclic shakedown phenomena occur. demonstrate behaviors soft clay be well predicted by the present model under cyclic loading conditions. The model is able to capture the pressure caused by

Figure 7. Permanent strain for various amplitudes *<sup>d</sup> q* . Figure 7. Permanent strain for various amplitudes *<sup>d</sup> <sup>q</sup>* . **Figure 7.** Permanent strain for various amplitudes *<sup>q</sup><sup>d</sup>* .

*J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 13 of 21

Figure 8. Effective stress path under typical conditions. **Figure 8.** Effective stress path under typical conditions.
