**4. Numerical Results and Interpretations 4. Numerical Results and Interpretations 4. Numerical Results and Interpretations**

### *4.1. Accumulation of Pore Water Pressure Around the Suction Anchor 4.1. Accumulation of Pore Water Pressure Around the Suction Anchor*

*4.1. Accumulation of Pore Water Pressure Around the Suction Anchor*  Figure 9 indicates the residual pore pressure ( *<sup>s</sup> p* ) distribution within the seabed around a suction anchor at different times. The maximum excess pore water pressure appeared at the base of the suction anchor. The excess pore water pressure accumulated primarily on the outside of the suction anchor, while the negative pore water pressure built up mainly on the inside. With the Figure 9 indicates the residual pore pressure (*ps*) distribution within the seabed around a suction anchor at different times. The maximum excess pore water pressure appeared at the base of the suction anchor. The excess pore water pressure accumulated primarily on the outside of the suction anchor, while the negative pore water pressure built up mainly on the inside. With the increase in loading time, the negative pore water pressure inside the suction anchor gradually developed upwards. Figure 9 indicates the residual pore pressure ( *<sup>s</sup> p* ) distribution within the seabed around a suction anchor at different times. The maximum excess pore water pressure appeared at the base of the suction anchor. The excess pore water pressure accumulated primarily on the outside of the suction anchor, while the negative pore water pressure built up mainly on the inside. With the increase in loading time, the negative pore water pressure inside the suction anchor gradually developed upwards.

(**a**) 600 s, 60 T. (**b**) 1200 s,120 T. **Figure 9.** *Cont.*

times.

**Figure 9.** Distribution of the residual pore pressure in the soil around a suction anchor at different **Figure 9.** Distribution of the residual pore pressure in the soil around a suction anchor at different times.

Figure 10 indicates the vertical distribution of the residual pore pressure within the seabed along the anchor wall. As can be seen from the figures, with an increase in the loading time, the residual pore pressures on both sides of the anchor wall increased remarkably. The maximum residual pore pressure was distributed in the region of 0.9 < *z/h* <1. The maximum value of excess pore water pressure was about 3 kPa, and the maximum value of negative pore water pressure was about 4 kPa. The maximum value of residual pore pressure for both sides appeared in the deep layer of the seabed, due to the larger effective stress acting on the anchor wall. It is worth noting that, in this region, the length of the suction anchor accounted for 10% of the total length, but the excess pore water pressure accounted for 27~31% of the total excess pore water pressure, and the negative pore water pressure accounted for 15.6~22% of the total negative pore water pressure. The external wall friction force was reduced, according to the principle of effective stress. Therefore, the uplift capacity of the suction anchor was diminished. The residual pore pressure at the seabed surface was zero. Figure 10 indicates the vertical distribution of the residual pore pressure within the seabed along the anchor wall. As can be seen from the figures, with an increase in the loading time, the residual porepressures on both sides of the anchor wall increased remarkably. The maximum residual pore pressurewas distributed in the region of 0.9 <sup>&</sup>lt; *<sup>z</sup>*/*<sup>h</sup>* <sup>&</sup>lt;1. The maximum value of excess pore water pressure wasabout 3 kPa, and the maximum value of negative pore water pressure was about 4 kPa. The maximumvalue of residual pore pressure for both sides appeared in the deep layer of the seabed, due to thelarger effective stress acting on the anchor wall. It is worth noting that, in this region, the length of thesuction anchor accounted for 10% of the total length, but the excess pore water pressure accountedfor 27~31% of the total excess pore water pressure, and the negative pore water pressure accountedfor 15.6~22% of the total negative pore water pressure. The external wall friction force was reduced, according to the principle of effective stress. Therefore, the uplift capacity of the suction anchor wasdiminished. The residual pore pressure at the seabed surface was zero. This is because, during cyclicloading, drainage occurs at the seabed surface.

This is because, during cyclic loading, drainage occurs at the seabed surface.

*J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 15 of 21

**Figure 10.** Vertical distribution of the residual pore pressures in the soil along the anchor wall. **Figure 10.** Vertical distribution of the residual pore pressures in the soil along the anchor wall. **Figure 10.** Vertical distribution of the residual pore pressures in the soil along the anchor wall.

Figure 11 illustrates the time series of residual pore pressure at position *z/h* = 0.95 within the seabed, where the maximum residual pore pressure occurred. Figures 11(a–b) show the accumulation of pore water pressure on the inside and outside of the suction anchor, respectively. The values of residual pore pressures increased continuously over time. On the outside of the anchor, the rate of increase in excess pore water pressure was rapid in the initial loading stage. Thereafter, the rate became slower with time. It is noted that the excess pore water pressure did not reach a steady state. On the inside of the anchor, the negative pore water pressure experienced a rapid increase in the initial loading stage, and then gradually reached a relatively steady state. A potential reason that might account for this phenomenon is that the soil inside the suction anchor showed shear dilatation characteristics under cyclic loads. When the plastic deformation reached a certain level, plastic deformation no longer increased due to the limitation of the anchor wall. Figure 11 illustrates the time series of residual pore pressure at position *z*/*h* = 0.95 within the seabed, where the maximum residual pore pressure occurred. Figure 11a,b show the accumulation of pore water pressure on the inside and outside of the suction anchor, respectively. The values of residual pore pressures increased continuously over time. On the outside of the anchor, the rate of increase in excess pore water pressure was rapid in the initial loading stage. Thereafter, the rate became slower with time. It is noted that the excess pore water pressure did not reach a steady state. On the inside of the anchor, the negative pore water pressure experienced a rapid increase in the initial loading stage, and then gradually reached a relatively steady state. A potential reason that might account for this phenomenon is that the soil inside the suction anchor showed shear dilatation characteristics under cyclic loads. When the plastic deformation reached a certain level, plastic deformation no longer increased due to the limitation of the anchor wall. Figure 11 illustrates the time series of residual pore pressure at position *z/h* = 0.95 within the seabed, where the maximum residual pore pressure occurred. Figures 11(a–b) show the accumulation of pore water pressure on the inside and outside of the suction anchor, respectively. The values of residual pore pressures increased continuously over time. On the outside of the anchor, the rate of increase in excess pore water pressure was rapid in the initial loading stage. Thereafter, the rate became slower with time. It is noted that the excess pore water pressure did not reach a steady state. On the inside of the anchor, the negative pore water pressure experienced a rapid increase in the initial loading stage, and then gradually reached a relatively steady state. A potential reason that might account for this phenomenon is that the soil inside the suction anchor showed shear dilatation characteristics under cyclic loads. When the plastic deformation reached a certain level, plastic deformation no longer increased due to the limitation of the anchor wall.

(**a**) On the inside of the anchor. (**b**) On the outside of the anchor. (**a**) On the inside of the anchor. (**b**) On the outside of the anchor.

**Figure 11.** Time series of pore water pressure at the location z/h = 0.95 within the seabed. **Figure 11.** Time series of pore water pressure at the location z/h = 0.95 within the seabed. **Figure 11.** Time series of pore water pressure at the location z/h = 0.95 within the seabed.

The method used to determine the uplift capacity was adopted from the limit equilibrium method for a suction anchor in clay recommended by API. For a fully sealed anchor, the failure mechanism of the suction anchor is usually assumed that the soil plug is broken and the soil plug is The method used to determine the uplift capacity was adopted from the limit equilibrium method for a suction anchor in clay recommended by API. For a fully sealed anchor, the failure mechanism of the suction anchor is usually assumed that the soil plug is broken and the soil plug is The method used to determine the uplift capacity was adopted from the limit equilibrium method for a suction anchor in clay recommended by API. For a fully sealed anchor, the failure mechanism of the suction anchor is usually assumed that the soil plug is broken and the soil plug is pulled out

pulled out together with the anchor. This failure mechanism has been verified by tests for anchors

pulled out together with the anchor. This failure mechanism has been verified by tests for anchors

with aspect ratios between 1.7 and 10 [33,34]. The uplift capacity can be expressed as:

with aspect ratios between 1.7 and 10 [33,34]. The uplift capacity can be expressed as:

*R=Q +Q +W f P* , (27)

*R=Q +Q +W f P* , (27)

together with the anchor. This failure mechanism has been verified by tests for anchors with aspect ratios between 1.7 and 10 [33,34]. The uplift capacity can be expressed as:

$$R = Q\_f + Q\_P + \mathcal{W}\_\prime \tag{27}$$

where *W* and *Q<sup>P</sup>* are the soil plug weight and reverse end bearing, respectively. *Q<sup>f</sup>* is the external wall friction force, which can be calculated as: where *W* and *QP* are the soil plug weight and reverse end bearing, respectively. *Qf* is the external

$$Q\_f = \int\_0^\hbar \sigma'\_v dz (\text{K} t \text{m} \delta) (\pi D), \tag{28}$$

in which *h* represents the embedded depth, *K* is the lateral pressure coefficient, σ 0 *<sup>v</sup>* denotes the effective vertical stress in soil, and *D* represents the external diameter of the anchor. in which *h* represents the embedded depth, *K* is the lateral pressure coefficient, σ*v* ′ denotes the effective vertical stress in soil, and *D* represents the external diameter of the anchor.

It is acknowledged that the excess pore water pressure in the seabed soil could diminish the effective stress in soil, consequently, reducing the friction along the external wall–soil interface. By assuming that *K* and δ remain as constants, the interface friction can be calculated according to Equation (28), and normalized by the initial values. It is acknowledged that the excess pore water pressure in the seabed soil could diminish the effective stress in soil, consequently, reducing the friction along the external wall–soil interface. By assuming that *K* and *δ* remain as constants, the interface friction can be calculated according to Equation (28), and normalized by the initial values.

Figure 12 illustrates the relationship between the normalized friction force versus the loading time at the soil–anchor interface. It is shown that the increase in excess pore water pressure led to a slight decrease in the friction force. Under current conditions, the external wall–soil friction is reduced by about 4%. Figure 12 illustrates the relationship between the normalized friction force versus the loading time at the soil–anchor interface. It is shown that the increase in excess pore water pressure led to a slight decrease in the friction force. Under current conditions, the external wall–soil friction is reduced by about 4%.

**Figure 12.** Normalized friction force on the external wall. **Figure 12.** Normalized friction force on the external wall.

### *4.2. Effect of Load Amplitude 4.2. E*ff*ect of Load Amplitude*

increased gradually.

To investigate the effect of the load amplitude, four grades of load amplitudes (*FCZ* = 10, 20, 30, and 40 kN) were adopted in the simulation. The period of cyclic loads was 10 s. The total calculation time was one hour (360*T*). The seabed parameters remained constant. The residual pore pressure distributions on both sides of the anchor wall for various load amplitudes are plotted in Figure 13. It is shown that the load amplitude has a remarkable influence on the distribution characteristics of the pore water pressure. The increase in the load amplitude resulted in a remarkable increase in the residual pore pressure. In the region of 0.9 < *z/h* <1, the excess pore water pressure accounted for 17~31% of the total excess pore water pressure. As the load amplitude increased, the proportion To investigate the effect of the load amplitude, four grades of load amplitudes (*FCZ* = 10, 20, 30, and 40 kN) were adopted in the simulation. The period of cyclic loads was 10 s. The total calculation time was one hour (360*T*). The seabed parameters remained constant. The residual pore pressure distributions on both sides of the anchor wall for various load amplitudes are plotted in Figure 13. It is shown that the load amplitude has a remarkable influence on the distribution characteristics of the pore water pressure. The increase in the load amplitude resulted in a remarkable increase in the residual pore pressure. In the region of 0.9 < *z*/*h* <1, the excess pore water pressure accounted for 17~31% of the total excess pore water pressure. As the load amplitude increased, the proportion increased gradually.

**Figure 13.** Vertical distribution of the residual pore pressures within the seabed along the anchor wall for various load amplitudes. **Figure 13.** Vertical distribution of the residual pore pressures within the seabed along the anchor wallfor various load amplitudes. **Figure 13.** Vertical distribution of the residual pore pressures within the seabed along the anchor wall for various load amplitudes.

#### *4.3. Effect of λ and κ 4.3. E*ff*ect of* λ *and* κ *4.3. Effect of λ and κ*

**5. Perforated Suction Anchor** 

**5. Perforated Suction Anchor** 

*5.1. New Anchor Structure Style* 

*5.1. New Anchor Structure Style* 

The soil properties are key influential factors that determine the development of residual pore pressure within the seabed. Among those soil properties, the compression index (λ) and swelling index (κ) have important effects on the distribution of the residual pore pressure [35]. To evaluate the effect of λ and κ on the distributions of residual pore pressure, κ was kept constant, and λ was changed. Analyses were performed with κ = 0.034 and κ/λ ranging from 0.2 to 0.4 [36]. Figure 14 shows the residual pore pressure distributions along the anchor wall when κ was 0.034 and λ was varied from 0.17 to 0.85. It is shown that κ/λ and the load amplitude had opposite effects on the residual pore pressure distribution. As κ/λ increases, the residual pore pressures on both sides of the anchor wall showed obvious decreases. In the region of 0.9 < z/h <1, the proportion of excess pore water pressure to the total excess pore water pressure increased from 20.1% at κ/λ = 0.4 to 31.3% at κ/λ = 0.2. The negative pore pressures inside of the anchor accounting for the total negative pore water pressures increases from 6.9% to15.6%. The soil properties are key influential factors that determine the development of residual pore pressure within the seabed. Among those soil properties, the compression index (λ) and swelling index (κ) have important effects on the distribution of the residual pore pressure [35]. To evaluate the effect of λ and κ on the distributions of residual pore pressure, κ was kept constant, and λ was changed. Analyses were performed with κ = 0.034 and κ/λ ranging from 0.2 to 0.4 [36]. Figure 14 shows the residual pore pressure distributions along the anchor wall when κ was 0.034 and λ was varied from 0.17 to 0.85. It is shown that κ/λ and the load amplitude had opposite effects on the residual pore pressure distribution. As κ/λ increases, the residual pore pressures on both sides of the anchor wall showed obvious decreases. In the region of 0.9 < z/h <1, the proportion of excess pore water pressure to the total excess pore water pressure increased from 20.1% at κ/λ = 0.4 to 31.3% at κ/λ = 0.2. The negative pore pressures inside of the anchor accounting for the total negative pore water pressures increases from 6.9% to15.6%. The soil properties are key influential factors that determine the development of residual pore pressure within the seabed. Among those soil properties, the compression index (λ) and swelling index (κ) have important effects on the distribution of the residual pore pressure [35]. To evaluate the effect of λ and κ on the distributions of residual pore pressure, κ was kept constant, and λ was changed. Analyses were performed with κ = 0.034 and κ/λ ranging from 0.2 to 0.4 [36]. Figure 14 shows the residual pore pressure distributions along the anchor wall when κ was 0.034 and λ was varied from 0.17 to 0.85. It is shown that κ/λ and the load amplitude had opposite effects on the residual pore pressure distribution. As κ/λ increases, the residual pore pressures on both sides of the anchor wall showed obvious decreases. In the region of 0.9 < z/h <1, the proportion of excess pore water pressure to the total excess pore water pressure increased from 20.1% at κ/λ = 0.4 to 31.3% at κ/λ = 0.2. The negative pore pressures inside of the anchor accounting for the total negative pore water pressures increases from 6.9% to15.6%.

**Figure 14.** Vertical distribution of the residual pore pressures within the seabed along the anchor wall for various κ/λ. **Figure 14.** Vertical distribution of the residual pore pressures within the seabed along the anchor wall for various κ/λ. **Figure 14.** Vertical distribution of the residual pore pressures within the seabed along the anchor wall for various κ/λ.

(**a**) On the inside of the anchor. (**b**) On the outside of the anchor.

### **5. Perforated Suction Anchor** *J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 18 of 21
