## 1 Introduction  
The offshore structures installed in shallow water usually suffer highly nonlinear wave breaking impacts. Many coastal and offshore structures consist of cylinders with different inclined angles, such as supporting structures of wind turbines, platforms, and large floating bridges. The breaking waves normally hit the structures within a very short duration and cause a large wave impact force, which can lead to a significant damage to the structures. Therefore, accurately predicting the wave impact forces on standing cylindrical structures with different inclined angles is of great concern for the design of coastal and offshore structures. Because the characteristics of wave breaking are strongly nonlinear, most early research was mainly based on experimental investigations. [PERSON] and [PERSON] [1] performed breaking wave force experiments on two and three vertical cylinders situated in the breaking wave zone parallel and normal to the direction of wave propagation. The experimental results showed that the incident wave steepness and the distance between the cylinders were two important factors, especially when the cylinders are arranged in orientations normal to the wave propagation than parallel to the wave propagation. [PERSON] et al. [2] conducted large-scale experimental studies on breaking wave impacts on a vertical cylindrical pile. It was presented that the total breaking wave force is the sum of the quasi-static force calculated by the Morison equations and the slamming force considering the duration of the impact. [PERSON] et al. [3] employed the Fast Fourier Transform (FFT) low-pass filter and the Empirical Mode Decomposition (EMD) to separate the experimental data of breaking wave forces on a vertical cylinder into two components, i.e., the quasi-static loading and the dynamic force. They found that the calculation methods overestimated the quasi-static force in the region of the maximum impact. However, measuring velocity, acceleration, and turbulent properties during wave breaking are challenging tasks in the experiment [4]. Moreover, the appropriate experimental facilities, as well as minimizing human and instrument errors have important influences on experimental results. With the increase in computational capabilities, a good alternative approach is Computational Fluid Dynamics (CFD), which can be applied to simulate the impact of the breaking waves on marine structures for both research and engineering design purposes. [PERSON] et al. [5] used a Navier-Stokes solver with the VOF technique to study the wave run-up and breaking wave forces on a vertical cylinder. They found that the peak value of the horizontal breaking wave force under a plunging breaker was much larger than that under a spilling breaker. [PERSON] [6] employed the incompressible smoothed particle hydrodynamic (ISPH) method coupled with \(k-\varepsilon\) turbulence model to simulate the spilling and plunging waves by solving RANS equations. It was found that the SPH method can accurately capture the free surfaces without the numerical diffusion compared with the Euler grid method. [PERSON] et al. [7] simulated non-breaking and breaking waves past a vertical cylinder with the improved ISPH method. They found that the maximum loading on the structure was related to the free surface elevation and steepness of the wave across the cylinder. Local pressures on the cylinder near the free surface under breaking waves are higher than those of non-breaking waves. [PERSON] and [PERSON] [8] computed breaking wave forces on wind turbines using the VOF method without considering turbulence effects. Their results suggest that the peak force become smaller when the breaking wave is more developed for the spilling breakers. [PERSON] and [PERSON] [9] investigated the wave run-up and breaking wave impacts on a vertical cylinder located at different positions using the \(k-\varepsilon\) turbulence model with the VOF method.