Simple Method to simulate the
Motion of the Caisson Type Bulk Head
at the Earth Quake time


To evaluate the stableness of the gravity type
caisson retain wall, we have adopted the so called
quake-coefficient method.
But the Bulkhead slided about two to three 
meters at the Kobe Earth Quake.
(Biggest Slide was four to five meters)
In order not to slide so much, people are thinking 
the increasing of the coefficient.
But it is not rational according to my opinion.
It is appearent that the result will not be
reliable nor economical.
The quake coefficient method coes not describe anything about
the motion of the caisson.
The quake coefficient method is even harmful, because 
the idea for the structure, which enables 
freedom from the earth quake can not come appear.

I woul like now to show you the better way to calculate
the motion of the caisson.
This, I believe, is simple and understandable to most of 
the people whose education background is over highscool.

My tracing method is stand on the basic Newton's Lows.

The point to look is the difference of the velocities 
between the Ground and the Caisson.
If the verocities of the Ground and the Caisson 
become same in a dt time,
the acceleration given to the Caisson from Ground is:
a={(velocity of ground)-(velocity of Caisson)}/dt
On the other hand, the Maximum acceleration obtainable 
from the ground is somrthing 
based on the fliction force from the ground.
b={(Fliction Force)+(Earth Pressure)}/(Mass of the Caisson)

So we can trace the motion as follows:
(velocity)
Vi=Vi-1 + ai-1 dt
(displacement)
Xi=Xi-1 + Vi-1 dt+(1/2)ai-1 dtdt

where, ai is the smaller value either, 
a(acceleration in the two velocites) 
or 
b(fliction based acceleration).


The figure shows the result of tracing the motion of caisson.



1)Fig-1(case1)Constsnt Earth Pressure 
2)Fig-1(case2)Earth Pressure Decreases because Back Fill Height  
			decreases when the Caisson Slides. 
3)Fig-1(Case3)Caisson size is Double of the Case-2
4)Fig-1(Case4)Caisson size is Triple of the Case-2
5)Cycle time, T=1.0 sec, Amplitude, 50cm
   Action of Ground X=0.25 sin(wt),  	where, w=2pai/T^2=6.24
	a w2= 9 m/sec2	

6)Fig-2 shows the effect of the cycle time which affects 
	to the acceleration of the ground.



(4) Summary
	Now it bacame clear enogh about the motion of the
	Caisson. 
	The action of the caisson depends on the velocity of the 
	ground and obtainable force and its acting time.
	Mere acceleration of the ground is not enogh to
	describe the caisson movement.

(5) The Rocking Motion
	
	I also tried to show the rocking motion of the Caisson, 
	in a simplified model.
	Fig-3	Rocking Motion