USING 3D ELEMENTS IN MODELING OF A RECTANGULAR TANK. Key words: Rectangular Tank, SSI, FEM, Settlement

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1 USING 3D ELEMENTS IN MODELING OF A RECTANGULAR TANK Lenka Uhlířová 1 Slovak University of Technology in Bratislava, Faculty of Civil Engineering Abstract: Tanks have currently been used for storage of different substances and products. Most often they serve as reservoirs for drinking water, for wastewater treatment and storage of various technical liquids. Rectangular tanks are less common, still there are many benefits of their using, e.g. lower sensitivity to unilateral load and better use of space. The rectangular tank solved in this article is filled with water. Our investigation is focused on static analysis of the tank (displacements, settlement) and its interaction with subsoil (SSI - Structure-Solid- Interaction). There are several options of modeling. In our case, the ANSYS software based on the Finite Element Method, including the 3D elements, has been used. Key words: Rectangular Tank, SSI, FEM, Settlement 1. Introduction Reinforced concrete rectangular tanks have been used to store liquid, loose, and gaseous substances. To avoid the failures, proper structural design is requisite. This article is focused on a rectangular reinforced concrete tank filled with water. Within the modeling of a structure, there exist several possibilities how to create a structural model. To solve the mechanics of continuum, which is very complicated, three numerical methods have been developed (the Finite Element Method, the Finite Strip Method and the Boundary Element Method). Thanks to the computer hardware advances and to the development of computational programs, the Finite Element Method (FEM) became the most widely used method. It is based on variational principles. ANSYS Academic software has been used in this article. To consider in the modal analysis, the loading due to the tank content, one can use: Hydrodynamic load that representing the content or tank Mass of water inserted into nodes in the tank walls Modeling of tank content using 3D fluid elements To consider the interaction between the structure and the subsoil, one can use: Fixed support on the ground level Elastic support with the spring stiffness corresponding with the stiffness of subsoil 1 Lenka Uhlirova, Ing., Slovak University of Technology in Bratislava, Faculty of Civil Engineering. Radlinskeho 11, Bratislava. Slovak Republic. lenka.uhlirova@stuba.sk

2 Modeling of subsoil via 3D elements with characteristics specified for each subsoil layer individually In particular, the static analysis of the rectangular above ground tank will be performed. The displacements of the tank and its settlement are therefore the objects of interest of our investigations. 2. Interaction between the Structure and Subsoil To consider the interaction between the structure and the subsoil, three methods can be used [1]: One-parametric model of subsoil - Winkler's model Two-parametric model of subsoil - Pasternak model Elastic half-space - Boussinesque model For the tank analysed in the article, the Boussinesque subsoil model was used. In addition to [1], the interaction between structure and subsoil has been analyzed also in [2] [3], [4], [5] Elastic Half-Space In problems of elastic half-space, the elastic subsoil has been modeled using spatial (3D) finite elements. A block-shaped finite element (eight-node hexahedron) was used for modeling the spatial body. The most commonly used are finite elements, in which only three displacements in the direction of coordinate axes are considered in nodes. With the finite element which is block-shaped and having eight nodes and three displacements in each node, the stiffness matrix has a dimension 24x24. The dimension of the modeled space must be large enough to capture the entire deformation below the structure. Fixed support was used to depth ending. 3. Structural Model This article deals with a rectangular above ground tank filled with water. Its ground plan dimensions are 7.5 x 11 m and its height is 4.5 m. 3D modeling elements were used for modeling of water and subsoil (Figure 1). A SOLID186 element was used for modeling of the tank structure. Water was modeled using the element FLUID80 while elements SOLID186 were used for modeling the subsoil. Fig. 1. Model of a tank filled with water resting on a specific subsoil

3 The subsoil under the tank was modeled on a floor plan 30 x 30 m and 19.5 m deep. The reason is that prior to construction, the 1st layer (dump) will be removed and the tank will therefore be rested on the 2nd layer (see chapter 3.1) Geological Characteristics The values of geological characteristics used in the article have been obtained from the report of an engineering geological survey on the land in Bratislava Dump Clay sandy light brown solid Gravel with fine grain soil, moderately lean Sand poorly grained, brownish, moderately lean Gravel with fine grain soil, moderately lean Gravel, clay, bluish Granite conglomerate, sandy to sandy clay Granite conglomerate, clay to gravel clay Granite conglomerate of solid to hard consistency Granite conglomerate with spots of the character R3 to R2 The characteristics and classification of the individual soil layers were prepared according to STN [6]. 4. Results Obtained values of the displacements of tank walls, as well as the tank settlement and subsoil displacement were objects of our interest. The value of displacement of the tank walls reached 1,433 mm along the shorter wall and 5,49 mm along the longer wall (Figure 2). The red point in Figure 2 represents the center of gravity of the tank mass. Fig. 2. The tank displacement [mm]

4 Settlement The settlement below the tank reached the value 21,855 mm (Figure 3) and occurred up to a depth of 12,5 m (Figure 4). Fig. 3. Settlement of the tank In Fig. 4 a graphical representation of displacement of the subsoil below the tank is shown. On the horizontal axis, the depth of the subsoil below the tank is plotted, and on the vertical axis there is the size of the displacement of subsoil (settlement). It can be seen that the displacement is nearly zero at a depth of 12.5 m. Depth of the subsoil Fig. 4. Depth of the subsoil displacement due to the tank settlement The settlement of the tank causes not only the displacement of the subsoil directly below the tank but also the displacement of the surrounding terrain. In the lateral crosssection (in the x-axis direction) it can be seen that the subsoil is displaced even in an area 11 m distant from the edge of the tank (Figures 5 and 6).

5 Fig. 5. Overall subsoil displacement in the x-axis direction Fig. 6. Subsoil surface displacement in the x-axis direction On the longitudinal cross-section (in the y-axis direction) it can be seen that the subsoil is displaced even in an area 13 m distant from the edge of the tank (Figures 7-8). Fig. 7. Overall subsoil displacement in the y-axis direction

6 Fig. 8. Subsoil surface displacement in the y-axis direction Acknowledgement This paper was supported by Grant Agency VEGA, project No. 1/0412/18 This paper was supported by Student Grant REFERENCES [1] JENDŽELOVSKÝ, N.: Modelovanie základových konštrukcií v MKP. 1.vyd. Bratislava : STU v Bratislave, s. ISBN [2] KOTRASOVÁ, K. - HARABINOVÁ, S. - PANULINOVÁ, E. - KORMANÍKOVÁ, E.: Seismic analysis of cylindrical liquid storage tanks considering of fluid-structuresoil interaction. In Advances and Trends in Engineering Sciences and Technologies Proceedings of the International Conference on Engineering Sciences and Technologies, ESaT 2015, 2016, pp , SCOPUS. [3] JENDŽELOVSKÝ, N.: Modelovanie základových dosiek na pružnom polpriestore. In Statika stavieb 2006 : Zborník príspevkov z 11.konferencie./Piešťany, Piešťany : Spolok statikov Slovenska, 2006, s ISBN [4] CAJKA, R. MYNARCIK, P. - LABUDKOVA, J.: Numerical solution of soilfoundation interaction and comparison of results with experimental measurements. International Journal of GEOMATE, Vol. 11, 2016, pp [5] VASKOVA J. CAJKA R.: Subsoil-structure interaction solved in different FEM programs. In SGEM 2017: 17 th International Multidisciplinary Scientific GeoConference. Conference Proceedings, Vol June-5 July, 2017, Bulgaria, pp [6] STN : Geotechnické konštrukcie. Zakladanie stavieb. Bratislava: SÚTN 2010, s. 40