ssi-example.pdf

7/28/2019 SSI-example.pdf

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ADERS MSc in Analysis and Design of Earthquake Resistant

Structures

SPECIAL TOPICS ON EARTHQUAKE ENGINEERING

SOIL STRUCTURE INTERACTION

PROFESSOR C. SPYRAKOS

NATIONAL TECHNICAL UNIVERSITY OF ATHENS

LABORATORY FOR EARTHQUAKE ENGINEERING

HOMEWORK

At the surface of a soil layer and for =5% damping, a design response spectrum is evaluated, which has a constant spectral

acceleration of1.0g between periods 1 = 0.15 sec and 2 = 0.60 sec. On this layer and at a depth of e = 3.0 m a stiff

structure will be founded, with an active height of h = 4.0 m and circular foundation with a radius of r = 6.0 m. The

stiffness of the structure, if it is considered fixed at its base, is k = 106kN/m, its fundamental period isT = 0.15 sec and

the damping factor is estimated at =5%. The soil layer has a Poisson ratio v=0.4 and unit weight = 18 kN/m3

. The

velocity of shear waves is estimated at VS0 = 150 m/sec. Calculate the design acceleration of the structure,

considering a behavior factor q = 3.5 taking into consideration soil-structure interaction. Consider a spectral

amplification factor aA= 1.84.

EQUATION TABLE

Table 1: Reduction of the velocity of shear waves and the shear modulus as a function of pga

Shear wave velocity

Effective period

Horizontal foundation stiffness

Torsional foundation stiffness


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Evaluation of foundation damping

Soil-structure system damping

Equivalent foundation dimension

Reduction factor due to foundation dimensions

Reduction factor due to foundation depth and pga

Elastic spectral acceleration at the base for 5% damping

Elastic spectral acceleration


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SOIL-STRUCTURE INTERACTION - SOLUTION

From the velocity Vs0, the given table and the relation between the velocity and the shear modulus

we calculate the value of the shear modulus G0=1502*18/10=40500KN/m2.

From the table we find that G/G0=0.42 , which results in a value of G=0.42*40500=17010KN/m2.From the given equations for the stiffnesses and the structure dimensions we find that :

=8*17010*6/(2-0.4)=510300KN/m

=8*17010*63/(3*(1-0.4))=16329600KNm

because for a circular tank rm=ra=R=6m

The effective period is calculated from the given equation for =0.15sec as

=0.15*(1+(106/510300)*(1+510300*42/16329600))0.5=0.3sec

We then calculate the damping factors

=1.5*(3/6)+1=1.75

=1.75*e(4.7-1.6*4/6)=66.22

=1.75*[25*ln(4/6)-16]=-45.74

and the resulting damping is

=66.22*(0.3/0.15-1)+(-45.74)*(0.3/0.15-1)

2

=20.81%

=20.81+5/(0.3/0.15)3=21.45%

The effective foundation dimension is

be=(*62)0.5=10.635m

which leads to

=

=max[1-(1/3390)*(10.635/0.3)1.2,1-(1/3390)*(10.635/0.2)1.2]=0.978


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=

=max[cos(2**3/(0.3*97.5)),0.453,cos(2**3/(0.2*97.5))]=0.797

,

=

=1*0.797*0.978*(7/(2+21.45))0.5=0.426g

and the design acceleration is SA=0.426/3.5=0.122g

Note : for EC8 the damping factor n is n=(10/5+)0.5

ssi-example.pdf

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