There first approach is Winkler model which

There is a popular approach in the structural field this approach assumes the base of the structure as a fixed base but in reality, the soil under the structure deforms because the soil has the ability to deform. In the conventional seismic design of buildings frame, the same approach is also assumed. Because of the soil response, the seismic response of the structure gets changed. The soil response may decrease the stiffness of the structure and increase natural periods of the structure. In this paper, the effect of soil flexibility on the performance of medium-high RC framed structure (5bay by 5bay 6 story) with various plan irregularities resting on different types of soil (Hard soil, Medium soil, soft soil) is taken into consideration. Two types of model approaches are used in order to represent the soil- structure interaction(flexibility). The first approach is Winkler model which is developed by using spring stiffness equations. Every spring has six degrees of freedom. Along these six degrees of freedom, the stiffness is determined by using spring stiffness equations. The second approach is elastic continuum which is developed by finite element method using Sap2000. The idealization of elastic continuum depends on a common experience which says deflections in soil media do not happen directly under the loading area but also in certain limited zones outside the loading area. According to on the idealization of the elastic continuum, a soil block of 75m x 75m (1.5 times the width of the structure) is assumed. Soil block is modeled by FEM. Beams and columns are modeled as frame element with 2 nodes having 6 degrees of freedom at each node, the foundation is modeled as 8 nodes concrete element and soil mass beneath the foundation is modeled as 8 nodes solid element with 2 degrees of freedom at each node. In conclusion, when the soil flexibility increases, the response of the structure, beam moment, column moment, and base shear also increase. Irregularity does not have clear effects on the response of the framed structure. Soil-structure interaction has effects on moments of columns and beams. For instance, has been found that the models with soil-structure interaction have high values of moments in columns and beams when compared with models without soil-structure interaction. The results from FEM method are more accurate than Winkler method. FEM method is suggested for analysis of structure resting on soft soil. Finally, when the structure is resting on soft soil, it’s important to consider soil-structure interaction effects.Generally, when a structure is in numerical analysis stage, the effects of soil- structure interaction is ignored because of the complexity in the modeling of the soil and some engineers believe that the soil has beneficial effects on structures. In case of very stiff soils or when the stiffness of the foundation soil is high compared to the stiffness of the structure, the assumption of the fixed base can be adopted because of the soil effects, in this case, are not effective. However, the fixed base assumption neglects the response under seismic demand in some special cases. For medium or loose soils which have high flexibility compared to firm soil, the fundamental period of the soil-structure system and damping are increased because of the high flexibility of these soils. When an earthquake hits foundation of the structure, foundation deforms resulted from the soil-structure interaction. There are two types of soil-structure interaction: Intertial interaction and Kinematic interaction. Internal interaction takes place when foundation moves during an earthquake which can cause the compliant soil to deform. There are six degrees of freedom of the foundation motion that allows for deformation to propagates away from the structure. Kinematic interaction happens when there is an earthquake ground motion in free-field with stiff foundation. This paper focuses on Intertial interaction because Kinematic interaction can be significant in cases have very stiff foundations. According to CEN(2004c) the effects of dynamic soil-structure interaction should be taken in to account only in: a) structures where 2nd order effects play a significant role; b) structures with massive or deep-seated foundations; c) slender tall structures and d) structures supported on very soft soils, with average shear wave velocity less than 100 m/s. Moreover, according to FEMA (2000), the effects of soil-structure interaction must be evaluated for near-field and soft soil sites and also for buildings in which an increase in the fundamental period due to the effects will result in an increase in spectral acceleration. Obviously, in this paper three approaches on numerical modeling of fixity of structure are adopted: conventionally fixed structure, structure on Winkler springs, and structure on half-space. Further, the 2D linear elastic analysis is carried out on 3,7, and 10 stories, 3 bay reinforced concrete frames using time history analysis. The frames assumed to be residential buildings where are found on shallow strip foundations that rest on soft soils consist of two different soil profiles. Reinforced concrete beams and columns are modeled using elastic frame elements assuming gross section properties. All beams have T. cross-section, Lb = 5.0m span length. Also, all columns have square cross-section 40x40cm and Lc = 3.0m which is equal story height. Other geometrical properties of elements are illustrated in table 1. Dumping ratio of the buildings is assumed to be equal to 5%. Rayleigh damping is included in the analysis. Tabatabaiefara and Massumi(2010) have noticed that the distance of the structure center to the soil finite element model boundaries should be three to four times the foundation radius in the horizontal direction and two to three times the foundation radius in the vertical direction. So, the distance between the structure center and the soil finite element model boundaries is taken equal to 50m in the horizontal direction, while the distance between soil boundary and foundation of the building is taken equal to 1000m in the vertical direction to make the effects of the reflexive waves negligible. Two soil profiles are taken in Osijek, Croatia used in the analysis (Book 13, 2008). The soil finite element model was modeled using quadrilateral shell elements having a thickness equal to 1 m. The width of the shell elements is equal to 2,5 m, while the height (i.e. depth) of the shell elements vary from 0.5 to 5 m depending on the thickness of the specific layer of the soil profile provided in Book 13 (2008). Strip footing 1m wide and 16m long is assumed in order to calculate the stiffness and damping of the translational and rotational Winkler springs by depending on Stewart, Fenves, and Seed (1999) suggestions. For all soil layers, Poisson’s coefficient and damping are assumed 0.2 and 8% respectively. But for rock (half-space), damping is assumed 2%. Damping and Poisson’s coefficient are assumed by depending on Book13(2008). Normal weight concrete of class C25/30(CEN,2004a) with compressive cylinder strength at 28 days FC = 25Mpa, Modulus of elasticity Ecm =31000Mpa, and specific weight yc = 25KN/m3 which includes the weight of the reinforcement are assumed for the frame elements, floor slabs, and roof slabs. Floors and roof are assumed to be rigid diaphragms in order to satisfy all the criteria in CEN(2004b). Sap2000 (CSI 2009 version 14.1.0) was used to perform the numerical analysis and calculate the self-weight of the structure. The Dead load is added to floor and roof slabs are equal to 2.0KN/m2 and 3.5KN/m2 respectively. Additional imposed loads for floors and roof is assumed to be equal to 2.0KN/m2 according to code for residential buildings (CEN 2002b). The equation which is used for calculating the value of the mass that should produce intertial effects during earthquake excitation is:  åGk, j “+”åy E,i ×Qk, j ( åy E,i is the ratio of the participating live load during a seismic motion and is taken as 0.15 according to CEN(2004b)). European Strong-motion Database is taken as a resource for selecting ground motions. Response spectrum of ground type A and C is selected according to CEN(2004b). SHAKE2000 is a program for equivalent-Linear site response analysis. The selected ground motions are modified by SHAKE2000. Original motions were applied to the base of the numerical models with soil modelled using shell elements while modified motions, i.e. motions taken from the top of the soil profiles modelled using SHAKE2000 (Ordóñez, 2011) were applied to the base of the numerical models with fixed base conditions and with soil modelled using Winkler spring elements. Selection of ground motions was conducted using the anchoring value of the spectrum ag set to 0,25. Also the limits for magnitude M and source to site distance R was set equal to 6,5 – 7,0 and 0 km – 35 km respectively. Spectrum matching was done by setting maximum deviations, i.e. lower tolerance and upper tolerance to 10 % and 30 % respectively between periods T1 and T2 equal to 0,15 s and 2 s respectively. In conclusion, analysis shows that structure models with soil included have much higher values of story drifts, especially when the soil is modelled using Winkler springs. Moreover, there is common assumption which assumes that including soil to a model of structure would extend fundamental period of structure thus reduces interail force. In this paper, has been found that this assumption is wrong. The fixed base assumption does not seem save for low-rise buildings that founded on soft soil because of high base shear and high story drifts. The models with soil included, compared to conventional fixed-base models, have 70 % higher fundamental periods of vibration but also up to 400% higher base shear.In general, superstructure and sub-structure are analyzed in full isolation which means that the structural engineer and geo-technical engineer seldom interact. Structural engineer cares about the structural arrangement of the building and the allowable bearing capacity of the soil. In contrast, the geo-technical engineer is interested in the soil characteristics like sand, silt, and clay and recommending the best size and design of the foundation. Most of the engineers do not take into account the fact that the supporting soil medium displaced to some extent because of its deformation behavior. This displacement decreases the stiffness of the system, Therefore, the time period of the system increases. The displacement value at the base of the structure depends on load, soil type, size, and type of foundation. The main objective of this paper is studying the effect of soil-structure interaction problem under transient loading for multi-story RC frame structures with raft foundations. In this study, an investigation has been made to understand the seismic performance of superstructure considering the complex dynamic interaction between superstructures. Four models of 10, 15, 20, and 25 story building with 6-bay and 6-bay in two perpendicular directions are assumed to study the soil-structure interaction problem. These models have raft foundations where are resting on different soil conditions like soft, medium, and hard. All parameters considered in this study are illustrated in the following tables:

 The building frames are designed as 3D space frame consisting of four node elements with appropriate dimensions by using SAP2000 software. Slabs and mat foundations are modeled as rigid diaphragm with the help of four node plate elements. The raft foundation is used support structure and it is designed by conventional method assuming that the foundation to be rigid. In modeling the 3D elastic continuum model (FEM model), the finite element method is used. The steps of the finite element methods are a. Pre-processing that includes mesh generation, b. Obtaining the assembled system of equation, for which the elemental matrices and vectors need to be evaluated, c. Applying the boundary conditions, d. Solving the linear system of equations, e. Post-processing. For analysis, the finite element is adopted in this study because of its diversity and flexibility as an analysis tool. The soil- structure interaction (SSI) is represented by using equivalent springs with six degrees of freedom. In two horizontal and vertical axes with rotational springs about those mutually perpendicular axes are considered. These are attached to estimate the effect of soil flexibility. George Gazetas formula is used for determining the stiffness along the six degrees of freedom. The time history analysis is adopted for RC frame structure. Therefore, the earth quack ground motion (Bhuj EQ data) is subjected to the whole system of RC frame structure. According to the results of the analysis, it can be seen that lateral displacement increases as the number of story increases. The increase in the stiffness of soil makes a reduction in displacement. Raft thickness does not have any effects on the displacement of the building. Further, it has been observed that the time period of the building on a different type of soils increases more than the time period in the fixed condition. For instance, the maximum time periods ae observed in FEM models, while the minimum time periods are found in fixed models. When the time period increases, the natural frequency of the building decreases. Finally, as the soil flexibility increases, the bending moment also increases with the increase of the raft thickness and height of the building.         

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