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Study on dynamic behaviors of a breakwater triggered by earthquakes

To ensure the safety requirement of an artificial island in the construction period, the modified Hardin-Drnevich dynamic constitutive model and strength reduction method was used to analyze the dynamic response of a breakwater under the action of earthquakes. Research indicates the following: (1) the modified Hardin-Drnevich can effectively simulate the soil stress-strain relationship under dynamic action, and obtain strain hysteresis, and get permanent deformation of material; (2) the deeper the buried depth of breakwater, the greater soil pressure; (3) dynamic pressure response is more obvious on both sides of the breakwater at peak time in earthquakes.


Introduction
Artificial islands are located at sea, and as such represent complex environments, subject to the potentially adverse effects such as waves, ocean currents, wind, ice, and earthquakes. Breakwaters are important enclosure structures designed to protect artificial islands, and an instability of a breakwater will have catastrophic consequences for the artificial island it is built upon. China's rapid economic development has brought strain upon land transportation networks. This, when coupled with its long coastline and numerous islands, means the development of coastal traffic has important political and economic significance. Coastal breakwaters in China are near the Circum-Pacific belt; hence, earthquakes happen frequently. These conditions can create numerous problems in engineering, so research in this area is of great significance for the construction of stable, effective breakwaters. As large-scale breakwater projects are in the initial development stages, the related research into breakwaters mainly focuses on construction technologies such as sandy soil liquefaction and static stability analysis [1][2][3][4][5]. WANG [6] applied the nonlinear constitutive model of a multiple shear mechanism type and calculated the effect of rotation of principal stress axis direction. IOP Conf. Series: Materials Science and Engineering 758 (2020) 012033 IOP Publishing doi:10.1088/1757-899X/758/1/012033 2 Matsuda, et al. [7] proposed the damage mechanism of breakwaters during earthquake-tsunami events, in which a simulated breakwater was destabilized by not only wave pressure, but also long-acting tsunami seepage flow and overflow. However, the dynamic stability of breakwaters has not been fully investigated, which may mean the stability requirements are not being met in engineering practices. Based on this concern, a breakwater project in the East China Sea is analyzed in this paper by a strength reduction approach, taking into account the effects of seepage, earthquakes, pore water pressure, and other factors. These research results would provide an important reference for engineering construction. Further, the dynamic characteristics and stability of this breakwater are studied by considering the coupled actions of seepage, earthquakes, and waves. This research provides an important reference for engineering construction.

Soil-fluid interaction
Based on Biot's consolidation theory [8], we can consider the soil-fluid interaction using Darcy's law. The response equation for the pore fluid can be formulated as Here, i q is the seepage vector; v q is the volumetric fluid source intensity; M is the Biot modulus; p is the pore water pressure; a is the Biot ratio;  is the volumetric strain; T is the temperature; t is time and  is the coefficient of thermal expansion for the solid-fluid interaction.
As the artificial island is at sea, its temperature change is relatively small, and has little effect on the stability, deformation, and structural forces. This article considers only the coupled actions of seepage, waves, and earthquakes, without considering the influence of the temperature; hence, Here， ij H is from the given constitutive model； is a history parameter and T ij  is the strain rate determined by temperature variation, for this scenario

Strength Reduction Method
Zheng [10,11] used a new method, referred to as the strength reduction method, to calculate the slope's dynamic stability and consider the slope's dynamic characteristics under earthquake conditions. This method can fully describe soil tensile-shear failure during earthquakes. Traditional static slope stability analysis is based on the limit equilibrium method, and the safety coefficient w relating the anti-sliding force s and sliding force t is expressed as follows: Here, c is the cohesion,  is the angle of internal friction and  is the dynamic shear stress. In the strength reduction method, the slope is made to approach the limit equilibrium state by reducing the shear strength of the soil as where  is the reduction parameter, which is the safety factor. c and  are the values of c and  after reduction, respectively.
However, slope failures under earthquake excitations are the result of both tensile and shear damage; hence, the tensile strength of the rock and soil mass should be considered. When using the strength reduction method, the tensile strength should also be reduced: Here, t  is the tensile strength and t   is the numerical value of t  after reduction.

Basic breakwater set-up
The environment of this breakwater features smooth ocean floors and a simple underwater landscape, which is composed of clay soil, backfill sand, and compaction sand, proportionately. The breakwater structure is composed of a plug-in steel cylinder structure. The steel cylinder is 40 m long, its thickness is 16 mm and its diameter is 22 m. The elevation of the cylinder head is 3.5 m, and the elevation of the cylinder base is -36.5 m. The top level of the soil layer is -8.5 m, and the water level is 2.57 m, as shown in Figure 1. The numerical model is 190 m long, with a height of 80.5 m. The water level for the breakwater is 2.57 m, and the artificial pumping water level is -12.5 m on the inland side. To improve the calculation efficiency and reduce the grid size, a typical cross section was selected in calculation. The cross-sectional element was chosen to simulate the interactions between the cylinder and the surrounding soils. The backfill sand as well as compaction sand are considered as liquefiable soils, and the parameters are shown in Table 1.

Input earthquake wave
The typical earthquake intensity is category VII in the project area, but considering the importance of its strategic location and economic status, category VIII is decided upon for the anti-seismic design. The peak amplitudes of the Kobe earthquake (Japan, 1995) were between 0.2 g and 0.3 g in numerical calculations. The input acceleration amplitude of 0.2 g was used to calculate the stress, acceleration response and stability of the breakwater. The input amplitudes from 0.2 g to 0.3 g were applied to analyze the liquefaction of the artificial island. The input acceleration waveform is shown in Figure 2. Based on the dynamic earth pressure distribution on both sides of the breakwater under earthquake excitations (see Figure 3), it can be concluded that the deeper the buried depth of the breakwater, the greater the dynamic earth pressure. The pressure response on both sides of the breakwater is more notable between 4s and 6s under earthquake conditions.

Stability of the breakwater
The strength reduction method was used to find the dynamic stability of the artificial island. In this method, the artificial island was made to approach the limit equilibrium state by reducing the shear strength of the soil. When the reduction factor 1.39   , the displacements of monitoring points C1 and C2 converged after the earthquake, so the breakwater was stable. When the reduction factor 1.40

 
, the displacements of monitoring points C1 and C2 did not converge and would continue to increase after the earthquake, so the breakwater was not stable and entered the limit equilibrium state (as shown in Figure 4). , the plastic shear zones of the artificial island become connected, and the final failure surface of the artificial island can be seen as the red line shown in Figure 6. Based on the above analysis, the dynamic safety factor of the breakwater is found to 1.39.

Conclusions
(1) When the water level was increased to the design height, the dynamic safety factor of the breakwater calculated with the strength reduction method was 1.39, which meets the safety requirements. The final failure surface appeared at the breakwater-soil interface.
(2) The deeper the buried depth of the breakwater, the greater the dynamic earth pressure will be. The dynamic earth pressure response is more notable on both sides of the breakwater from 4 to 6 s under earthquake conditions. (3) The dynamic safety factor of the breakwater, calculated using the strength reduction method, concerns the water levels. When the water level is pumped to the design height, it can meet the safety requirements. The ultimate failure surface appeared at the breakwater-soil interface.