885
Technical Committee 104 /
Comité technique 104
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
2 1
1
2 1
2 1
(
)
( )
(
)
u u
u z u
z z
z z
(5)
Shear stress is evaluated using Zeghal
and Elgamal’s
expression with the in
obtained from Eq. (5) with z=0:
To calculate the damping ratio in each cycle of
motion (Eq. 9), first, dissipated energy
terpolated surface acceleration
1 ( )
( (0) ( ))
2
z
z u u z
(6)
If only two instruments are present in a given soil layer,
a simple firs
calculate shear strain:
t order approximation must be applied to
2 1
2 1
(
)
(
)
u u
z z
(7)
This applies for any point between instruments 1 and 2,
and as such is more appropriate for the midpoint. Figure
3 shows Stress–strain loops at P1 and P2 in reinforced
and unreinforced sides of test with TC =40%.
r
Figure 3. Shear stress-strain loops for unreinforced and
reinforced models with TC
r
=40%
It is clear that the hysteresis loops in unreinforced model
tends to become progressively flatter and narrower as
the sample begins to liquefy and display a clear
reduction in stiffness. One reason for the good
performance of sand-tire chips mixture in reducing
generation of excess pore water pressure and increasing
liquefaction resistance is high permeability of reinforced
mixture, as compared with the pure sand. Another
reason is probably that the stiffness of tire chip particles
is less than that of sand grains, consequently allowing
some volume compression under developed excess pore
water pressure. Thus the volume compression of tire
hip produces a situation similar to dr
c
ainage or
xcess pore
ed from the ratio of the
difference in maximum and minimum stress and strain
developed in desired lo
dewatering which decreases the extent of e
water pressure
(Towhata, 2008).
3.3.
Shear modulus and damping ratio
Shear modulus is obtain
op.
(8)
(
) and
absorbed energy (
) must be calculated (Fig. 4).
(9)
Figure 4. Definition of Damping ratio and Shear Modulus
Shear modules and damping ratios at 0.3m depth for all
reinforced and unreinforced models are shown in Fig. 5.
(a)
(b)
(c)
(d)
Figure 5. Shear modulus of Reinforced and Unreinforced
models: a) TCr=10% b) TCr=20% c) TCr=30% d) TCr=40%
As it is depicted in Fig. 11, the shear modulus curve of
reinforced model is placed over the unreinforced one.
