Centrifuge Modeling of Seismic Performance of Reinforced Earth Structures - Reinforced Soil Engineering: Advances in Research and Practice - page 409

factor of the model slope (F sm ) can be given by Eq. (4).

s p
n tanf p
t p
n

c p þ

t fm
t m ¼

c m þ s m tanf m
t m

nc p þ s p tanf p
t p

F sm ¼ ¼ ¼

c p þ s P tanf p

t p

$ ¼ ð Þ

F sp 4

Here m and p denote model and prototype, respectively.
For the model with saturated clay, in which f u ¼ 0 can be assumed in the

undrained condition. Eq. (4) becomes

F sm ¼ nF sp ð 5 Þ

For the model with cohesionless dry sand, the following relation is derived;

F sm ¼ F sp ð 6 Þ

Equations (4) and (5) clearly show that it is very difficult to simulate a large
deformation or failure in a small-scale model under a normal gravity field. The
discrepancy in F s in the 1/N-scale model and the prototype can be solved by
subjecting the model to an inertial acceleration of intensity N times the earth's
gravity, because the stresses at a homologous point in the model become identical
with those in the prototype, i.e., s m ¼

s p , t m ¼

t p . This stress similitude is the

basic scaling law of centrifuge modeling.
From Eq.(6), the small-scale gravity model seems to give similar behavior
of the prototype for cohesionless soils. However, Eq. (6) is derived under the
conditions that strength parameters are identical between the model and
prototype, which can hardly be assumed for soils, because soil behavior is a
function of stress level and stress history. For example, the peak angle of the
internal friction of soil of a given density decreases as the applied effective stress
increases due to the suspension of dilation. This again proves the necessity of the
stress similitude in the small-scale model.

2.2 Advantages and Limitations of Centrifuge Modeling

2.2.1 Advantages of Centrifuge Modeling

As detailed scaling laws and applications of centrifuge technology in
geotechnical engineering field have already been given in various sources,
such as Schofield (1980) and Taylor (1995), specific advantages and limitations
of centrifuge modeling for reinforced earth structures are outlined in this section.