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S H A R I F O F U N I V E R S I T Y O F

T H E C N O L O G Y

D Y N A M I C O F S O I L - S T R U C T U R

I N T E R A C T I O N

P R O J E C T T E R M

K E S H A V A R Z . M O H A M M A D R E Z A - M O H A M M A D P O U R

P O U Y A

R O O M N U M B E R

Lecture's name:

Professor M.Ali.Ghannad

2014- winter- February

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Problem define:

Two stories shear building with embedment square (10*10) m^2 foundation

Using CONAN software to plot the soil dynamic stiffness coefficients variations and

foundation input motion to dimensionless frequency (0

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0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

kh,c

h

a0

Sway dynamic stiffness coefficients kh ch

0.00

5.00

10.00

15.00

20.00

0 1 2 3 4 5

kh,c

h

a0

Sway DOF for surface foundationkh Embedment foundation:

For a0 more than 1.23 leads to ch

approximate equal to 1.22 and kh

values for a0 more than 0.95 are

less than 1 and converge to zero.

Surface foundation:

For a0 more than 0.45 leads to ch

approximate equal to less than1

and kh values are going converge

to zero but with lower speed than

the embedment foundation.

Static stiffness (horizontal) = 2.0831e+09

Static stiffness = 1.2130e+09 (surface foundation)

Using excel to plot the data as this way:

This graph express the variation of dynamic coefficients for sway DOF (horizontal) for different

values of dimensionless frequency (a0=.r

).as it's shown for lower values of a0, the dynamic

damping coefficient is very frequency dependent. And for excitation frequency till 25 rad/sec stiffness

coefficient kh=1. If compare this model of building with the surface foundation case we see that

there is some different and it's about that in this case we see, the ch is effected by soil-structure

interaction less than the embedment case.

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0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

kr,c

r

a0

Rocking dynamic stiffness coefficient kr cr

Static stiffness (rocking) = 9.4319e+10

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

ugh

/uc

a0

Sway FIM Re(ugh/uc) Im(ugh/uc)

This graph express the variation of dynamic coefficients for rocking DOF for different values of

dimensionless frequency (a0=.r

).

Conclusion:

The embedment foundations are more effected by increasing in damping ratio of soil-structure

system, in other hands by increasing embedment ratio (

), soil-structure systems affected in

damping ratio more than stiffness.

We run Conan again by input txt file and for foundation input motion plot graph like this:

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-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

ugr

/uc

a0

Rocking FIM Re(ugr/uc) Im(ugr/uc)

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

-10 0 10 20 30 40 50

acce

lera

tio

n (

g)

Time (sec)

Free Field Motion (FFM)

These graphs express how is the

For excitation data as *.txt file plot the dynamic stiffness coefficients variations and foundation

input motion to dimensionless frequency.

For determine the dynamic stiffness coefficients variations and FIM along the specific

earthquake, it should be in frequency domain, so we have to choose the suitable software to

change earthquake data from time domain to frequency domain.

We could us of Microsoft office excel or SIESMO SIGNAL or Matlab.

Now we have frequency domain data:

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-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 10 20 30 40 50 60

FFT

mag

f (Hz)

Fourier amplitude of FFM

Free field motion in frequency domain:

Foundation input motion for excitation in control point motion as a specific time-history data:

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Matlab code that is used for plot these graphs:

clc;

clear all;

load FFM.txt;

load h.txt;

load r.txt;

dt=input('please enter time step of inserted record> ');

a_surf=FFM';

H=h';

R=r';

n=length(a_surf);

F=zeros(2,n+1);

for index=1:n+1

F(1,index)=H(1,index)+1i*H(2,index);

F(2,index)=R(1,index)+1i*R(2,index);

end

b=a_surf(2,:);

acc=[0,b];

df=1/(n*dt);

t=0:dt:n*dt;

f=0:df:n*df;

a_fft=fft(acc)/n;

A_time=zeros(2,n+1);

for j=1:2

a_freq=a_fft.*F(j,:);

a_time=n*real(ifft(a_freq));

figure(j);

hold on;

if j==1

title('Horizontal FIM');

xlabel('Time (sec.)');

ylabel('ugh (m)');

else

title('Rocking FIM');

xlabel('Time (sec.)');

ylabel('ugr (Rad)');

end;

plot(t,a_time);

hold off;

figure(2+j);

hold on;

if j==1

title('Horizontal FIM');

xlabel('Frequency (Hz)');

ylabel('ugh (m)');

else

title('Rocking FIM');

xlabel('Frequency (Hz)');

ylabel('ugr (Rad)');

end;

plot(f,n*a_freq);

hold off;

end;

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~

~ ~

~

~

Using Cone model concept for specific frequency to determine dynamic stiffness

coefficients, to simplify use the approximate formula in ATC3-06 for compute the period of

soil-structure system.

Page56 on ATC3-06:

Ta=CT.hn3/4 where for concrete frames: CT= 0.025

Ta=0.025*(22.965879)3/4=0.26sec

Page387 on ATC3-06:

For embedment foundation:

ky=8

2 1 +

2

3

=842.75(106)5.64

20.41 +

2

3

4

5.64= 1775.55E06 (N/m)

k=8^3

3(1) 1 + 2

=842.75(106)5.71^3

3(10.4)1 + 2

4

5.71= 84930.42E06 (N/m)

Page65 on ATC3-06:

W= 0.7*(280ton) = 196 ton, K=42

^2=42

196

0.26^2=114.46405E06 (N/m), h=0.7*7=4.9m

T=T1 +

ky(1 +

ky.2

k)=0.26*1 + 114.46405E06

1775.55E06(N/m)(1 +

1775.55E06(N/m).(4.9m)2

84930.42E06(N/m))=0.

27 sec

T

T=0.27

0.26=1.038,

H

=5.8

5.675=1.02

graph on page 71

0=0.025

= 0+0.05

(1.04)^3=0.07

So =2

T=23.27rad/sec ao=

.r

= (23.27*5.675)/150=0.88 dimensionless

frequency

a0 kh ch kr Cr

0.88 9.05E-01 1.28E+00 8.43E-01 3.77E-01

Static stiffness (horizontal) = 2.0831e+09, Static stiffness (rocking) = 9.4319e+10

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S (a0=0.88) = (2.0831e+09)*( 9.05E-01+i*0.88*1.28E+00)= 1.8852e+09 +2.3464e+09i for sway DOF

S (a0=0.88) = (9.4319e+10)*( 8.43E-01+i*0.88*3.77E-01)= 7.9511e+10 +3.1291e+10i for rocking DOF

Modeling for standard software to analysis soil-structure interaction we should use above

coefficients for setting dashpot and spring for sway and rocking like this figure:

ky=1.8852e+09 (N/m)

cy=2.3464e+09(N.s/m)

kt= 7.9511e+10 (N/m)

ct= 10 +3.1291e+10(N.s/m)

Using reference [2] and compute the damping ratio and stiffness of soil-structure system for

first mod.

At the first we must write the mass and stiffness matrices:

m=[90 00 90

] , K=[2

],

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~

~

A=k-2.m=103[430 215215 215

]=0, 1=x110^3

90=30.21rad/sec

fix=30.21rad/sec Tfix=0.207sec, ao=1.14

a0 kh ch kr cr

1.14 8.71E-01 1.24E+00 7.97E-01 3.74E-01

With assumption that the lateral force act to each story related by weight of itself, we have:

1=(12.5648.374

) mStr=173.1 ton, H=5.8 m,

=0.578,

=

=

(.)(+.)

(.+)(. +..+)(+.)=

0.0215 - 0.0399i=

=

.^2=(.+)(. +..)(+.)

(.)(.)(+.)=

13.7795 + 8.4522i=

=1+ + * + * * =15.7787 + 7.8703i

=fix2

+24(1+)= 29.1051 + 0.9915i

d=Real

() =29.1051 T= 0.22 sec and =

()

()=0.0340

T

T=0.22

0.207=1.063, 0=0.034

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~

~

~

Using ATC3-06 to compute reduction of base shear for this building.

For no interaction effect:

A=0.3 for high relative hazard, B=2.75 from standard spectrum, I=1 for

building with intermediate importance factor, R=7 for intermediate concert moment frame

Cs(T, )=

=0.32.751

7=0.1179

V= Cs.W=0.1179*180ton=21.21ton For interaction effect:

= [Cs(T, ) Cs(T, ) (

) ^0.4]

Cs(T, )=0.1179

= [0.1179 0.1179 (0.05

0.07) ^0.4]

=2.6 Conclusion

For this specific building if use ATC guideline for SSI we reduce base shear

about 10% and if compare it with damping ratio that come from modal

simplified method, can see the increasing in damping ratio computed by

ATC approach it's not real and for this case SSI it's not so important and if

we want done with SSI, the more exact approaches is required.