**1. Introduction**

Various types of offshore platforms are applied for energy production in deep-water environments. As the water depth increases, the offshore platform that rests upon the seabed and relies on gravity base foundations or traditional pile foundations is uneconomical and impractical. The suction anchor is widely used as a cost-effective mooring foundation for floating production systems [1,2], as shown schematically in Figure 1. In natural marine environments, suction anchors are subjected to cyclic loads produced by the floating platform. With the increase in the cyclic numbers, excess pore water pressure is developed and accumulated in a soft clay seabed; therefore, the soft clay structure is degraded, followed by degradation in strength and a reduction in stiffness [3]. Such a phenomenon may reduce the uplift capacity of the suction anchor, and it is, thus, essential to assess the accumulation of the pore water pressure within the seabed around the suction anchor subjected to vertical cyclic loads.

**Figure 1.** Schematic view of a platform anchored to suction caissons at the seabed. **Figure 1.** Schematic view of a platform anchored to suction caissons at the seabed.

In previous research, experimental studies attempted to research the response of suction caissons subjected to cyclic loads. Cheng and Wang [4] conducted a series of small-scale laboratory model tests to predict the stability of the suction anchor under cyclic loading conditions. Wallace et al. [5] studied the response of suction caisson foundations with cyclic loads in soft clay by means of centrifuge testing. Dyvik et al. [6] investigated the cyclic response of the suction anchor under vertical loads by carrying out field tests on a model foundation. In general, the experimental study of the seabed response around a suction caisson primarily contains single-gravity mode tests, centrifuge model tests, and reduced scale field tests. Only a small number of field tests on suction anchors have been reported in the previously published literature [7]. The pore pressure response in soft clay is difficult to measure accurately under cyclic loading conditions. This is because scaling rules for different aspects of behavior are conflicting in small models [8]. This is the reason for the general lack of available data on pore pressure in the existing model experiments [9–12]. Currently, a direct comparative analysis seems impossible. A reasonable numerical analysis model needs to be In previous research, experimental studies attempted to research the response of suction caissons subjected to cyclic loads. Cheng and Wang [4] conducted a series of small-scale laboratory model tests to predict the stability of the suction anchor under cyclic loading conditions. Wallace et al. [5] studied the response of suction caisson foundations with cyclic loads in soft clay by means of centrifuge testing. Dyvik et al. [6] investigated the cyclic response of the suction anchor under vertical loads by carrying out field tests on a model foundation. In general, the experimental study of the seabed response around a suction caisson primarily contains single-gravity mode tests, centrifuge model tests, and reduced scale field tests. Only a small number of field tests on suction anchors have been reported in the previously published literature [7]. The pore pressure response in soft clay is difficult to measure accurately under cyclic loading conditions. This is because scaling rules for different aspects of behavior are conflicting in small models [8]. This is the reason for the general lack of available data on pore pressure in the existing model experiments [9–12]. Currently, a direct comparative analysis seems impossible. A reasonable numerical analysis model needs to be developed to capture the accumulation of pore water pressure.

developed to capture the accumulation of pore water pressure. To date, considerable effort has been devoted to investigating the pore pressure response within the seabed around the offshore foundation by numerical methods [13,14]. The first method is the semi-empirical method, which is based on the simplified elastic-plastic model and predicts the pore pressure response around the offshore foundation subjected to cyclic loads [15,16]. The method is simple, which is suitable for the analysis of the oscillatory pore pressure response induced by waves acting on the sandy seabed. The second method is to apply Biot's poro-elastic theory for soil models to describe the pore pressure response [17–21]. Based on Biot's poro-elastic theory, Shen et al. [22] first explored the pore-pressure response in the soil around the suction To date, considerable effort has been devoted to investigating the pore pressure response within the seabed around the offshore foundation by numerical methods [13,14]. The first method is the semi-empirical method, which is based on the simplified elastic-plastic model and predicts the pore pressure response around the offshore foundation subjected to cyclic loads [15,16]. The method is simple, which is suitable for the analysis of the oscillatory pore pressure response induced by waves acting on the sandy seabed. The second method is to apply Biot's poro-elastic theory for soil models to describe the pore pressure response [17–21]. Based on Biot's poro-elastic theory, Shen et al. [22] first explored the pore-pressure response in the soil around the suction anchor under cyclic loading conditions, but this was limited to the sandy seabed.

anchor under cyclic loading conditions, but this was limited to the sandy seabed. For soft clay seabeds, the classical elasto-plastic theory is based on the assumption that the soil is completely elastic within the yielding surface. It fails to describe the accumulation of pore water pressure, nonlinearity of modulus, and other cyclic behaviors of soft clay [23]. The bounding surface theory based on plastic hardening modulus presents a general framework to describe the cyclic behaviors of soft clay. However, the conventional bounding surface models [24,25] are generally based on the assumption that the mapping origin is fixed at the coordinate origin and the unloading stage is completely elastic, thereby failing to capture the real soil behaviors, such as For soft clay seabeds, the classical elasto-plastic theory is based on the assumption that the soil is completely elastic within the yielding surface. It fails to describe the accumulation of pore water pressure, nonlinearity of modulus, and other cyclic behaviors of soft clay [23]. The bounding surface theory based on plastic hardening modulus presents a general framework to describe the cyclic behaviors of soft clay. However, the conventional bounding surface models [24,25] are generally based on the assumption that the mapping origin is fixed at the coordinate origin and the unloading stage is completely elastic, thereby failing to capture the real soil behaviors, such as cyclic stiffness degradation and initial anisotropy, under cyclic loads.

cyclic stiffness degradation and initial anisotropy, under cyclic loads. This study proposes a bounding surface plasticity model with the mixed hardening rule to This study proposes a bounding surface plasticity model with the mixed hardening rule to predict the development of pore water pressure within the seabed around the suction anchor under vertical

cyclic loading conditions. A damage parameter and initial anisotropic tensors are introduced into the bounding surface model, to represent the remolding of the soil structure and initial anisotropy, respectively. The present model is efficient at capturing the development of pore water pressure in the soft clay seabed subjected to cyclic loads. It is validated against available experimental laboratory data. Subsequently, the influences of the load amplitude and soil material on the distribution of the residual pore pressure around the suction anchor are examined. Finally, according to distribution characteristics of the residual pore pressure, an improved rational structure named the perforated suction anchor is proposed. *J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 3 of 21 vertical cyclic loading conditions. A damage parameter and initial anisotropic tensors are introduced into the bounding surface model, to represent the remolding of the soil structure and initial anisotropy, respectively. The present model is efficient at capturing the development of pore water pressure in the soft clay seabed subjected to cyclic loads. It is validated against available experimental laboratory data. Subsequently, the influences of the load amplitude and soil material on the distribution of the residual pore pressure around the suction anchor are examined. Finally,

#### **2. Theoretical Formulations and Numerical Approach** according to distribution characteristics of the residual pore pressure, an improved rational structure named the perforated suction anchor is proposed.

**2. Theoretical Formulations and Numerical Approach** 
