## 1 Introduction  
According to the European Commission, inland waterway transportation (IWT) is classified as one of the five transport modes. It can release traffic congestion and reduce greenhouse gas emissions. For countries with strong winters, the development of IWT must take into account the impact of ice problems on ice-going ships. The most common problems are the ship resistance in icy waters and impact ice loading on the hull. There are many available empirical methods [1; 2; 3] for ice-induced resistance calculation. Hence the problem could as an initial step be solved by increasing the propulsion power. For ice impact load, several methods can be used. In principle, ice-hull collision occurs in the bow area. Therefore, it is critical to put focus on the bow structure in the design process and to study the hull design parameters and their influences on the ice impact load. One way is to utilize the probabilistic method which simplifies the ice pressure in relation to the contact area,  
\[\alpha\ =\ C\alpha^{\rm D}, \tag{1}\]  
where C and D are constants for a given ice condition, \(\alpha\) is pressure on structure in [MPa] and \(a\) is contact area between ice floe and ship structure in [m\({}^{2}\)]. The probabilistic method aims to estimate extreme ice load and is easy to apply compared to other methods. However, this method is proposed for sea-ice going ships with severe ice conditions and the existing values of the two constants come from sea trial tests [4; 5]. The inland waterway (IWW) ice condition is however drastically different compared to the sea ice condition and the discrepancies in ice properties are significant, resulting in a different scale of ice loading. It can result in extreme high pressure for light ice condition. The ship design with regards to the corresponding ice prediction is too conservative and not efficient. Moreover, concerning IWW ice conditions, there are uncertainties due to the lack of research and test data and that make it difficult to estimate the ice properties and ice loads accurately [6]. Nevertheless, it is still a good approach to estimate an extreme load even when several design parameters are unknown. Practically, when it comes to the ship design, more parameters and their effects on ice load are usually required. However, the direct ice load prediction needs more refined models as there are lots of influencing parameters both from hull geometry and ice properties. Another approach is to consider the physical phenomena and reduce the complex scenario to single events by studying the ice-hull interaction mechanism and ice failure modes (e.g., crushing, bending, splitting, sliding). The studies based on ice-hull interaction process are more reliable and efficient for practical ice collision scenarios and ship design aspects. Studies, presented in the literature available either study ice crushing or ice bending, but the combination of the two failure modes are limited. Investigating the two modes together has a significant meaning. By considering the two failure modes simultaneously, a more reliable ice load prediction model should be obtained. In this work, ice-hull impact is studied, and the focus is on both of the ice crushing and ice bending case, with the contact area connecting the two modes. Normally, ice bending failure is widely accepted as the dominant ice breaking pattern with the largest force. The same assumption is applied to the current model to ensure the accuracy of the model. The purpose of the paper is to propose a feasible and reliable model for ice load prediction, especially the ice impact force, \(F_{i}\) on ship hull. The energy method [7] is chosen as to calculate the crushing force and the contact area. The stem collision and the shoulder collision are evaluated with two different contact area cases respectively. The bending scenario is equivalent to a wedge-shaped beam failure model and is represented by a semi-plate resting on a Winkler foundation with the ice flexural strength, \(\sigma_{f}\) as the failure criterion.