# The Effect of Subgrade Coefficient on Static Work of a Pontoon Made as a Monolithic Closed Tank
## 1 Introduction  
Monolithic rectangular tanks can be used as single, ready-made elements serving as floats for buildings or as components for constructing floating platforms intended, among other purposes, for mooring vessels. Recently, stationary floating structures have seen an increased global interest [1]. It can be estimated that there are 40,000 to 50,000 of these objects in the world [2]. Such interest should not come as a surprise, as design solutions supporting amphibious construction can be applied in a wide manner. This is due to numerous reasons, ranging from the interest in the land--water interface as a very attractive site for the tourism industry to the increased expansion of living space in densely populated countries. Another developmental contributor to amphibious construction might be progressive climate change, which causes heavy rainfall, inundation and flooding. It is anticipated that, by the end of this century, water levels will have risen by a meter [3]. Amphibious construction is one of several methods oriented towards urbanisation of floodplains [4, 5]. Floats can be made of various materials depending on their design purpose. The market offers floats made of plastic, metal or reinforced concrete. Reinforced concrete pontoons consist of a box filled with polystyrene and a cover plate installed later. The solution always poses a risk of inaccuracies in assembly, subsequent leaks and shorteruse [6]. A more advantageous solution, although more computationally and executively challenging, is to design and produce a tank as a single, ready-made element, possible to be built without any additional construction work [7,8]. Typisation and prefabrication are two of the most important directions in construction today. By optimizing prefabricated structures, the aim is to achieve the best material consumption while ensuring the load-bearing capacity of the structure and--consequently--economic benefits. The pontoon mentioned in this article was a single-piece tank made in one stage, i.e., a closed box without any contacts or joints. This excluded the possibility of leakage or flooding of the structure. To minimize the risk of the pontoon filling with water, it was tightly filled with Styrfoam. The literature on the subject provides few publications on closed tasks made in one stage [7,8] and taking into account the effect of the substrate, which--for the pontoon in question--was Styrfoam [9]. Since the technical literature has not yet provided solutions for this type of tank taking into account the effect of its substrate, it was decided that a dedicated numerical analysis would be performed for the purposes of this study. In building structures, plates often rest on a substrate made of materials other than the buildings. The most commonly applied substrate scheme is a Winkler elastic substrate [10]. This static scheme is a system of infinitely closely arranged springs of equal stiffness. The Winkler model specifies a substrate with the use of one parameter, assuming that the working load is equal to the product of plate deflection and substrate stiffness. Thus, the deflection of the substrate occurs only on the surface on which the load acts. Figure 1 schematically presents the Winkler elastic substrate, while Equation (1) provides the aforementioned correlation [11]. \[\mathrm{p}=\mathrm{K_{z}}\cdot\mathrm{w} \tag{1}\]  
where  
p--load (\(\mathrm{kN/m^{2}}\)),  
w--deflection (m), and  
K\({}_{\mathrm{z}}\)--substrate stiffness (\(\mathrm{kN/m^{3}}\)). Another model of the two-parameter Winkler-type substrate is proposed in [12], where instead of springs, a system of densely spaced bars with a specific bending stiffness value was introduced. In the Filonenka--Borodic model, it is assumed that a Winkler-type substrate is covered on its upper surface by an unlimited membrane, tensioned with evenly distributed tensile forces [11]. The model of [PERSON] is one of the more accurate models of substrate mapping.