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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.

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