(A16)

.

(A8)

where *a *is the acceleration. The model law and

scale factor *K*Fi for the inertia force is

From the definition of *weight force*, the weight

force model law and scale factor *K*Fw is

=

.

(A17)

=

= *K*l2

(A9)

From the definition of acceleration it follows that

= m.

(A18)

sidering eq A6, A9 and the relation KF w = *K*F = *K * l2

from eq A8,

From eq A6 and A18, eq A17 becomes

1

=

.

(A10)

= 2.

(A19)

Equation A10 implies that geotechnical model-

Because *K*Fi must equal *K*F = *K*l2 , then

ing requires a technique that elevates the gravi-

tational acceleration of the model.

(A20)

The scale factor for an *external force K*Fe must

satisfy eq A8, and only technical constraints should

That is, the time scale factor is equal to the length

limit this.

scale factor if the inertia force is to be scaled like

A *viscous force *acting on a small area *A *can be

the weight force.

defined as

A *seepage force *can be written as

d*v*

(A21)

(A11)

d*n*

where *W*F is the weight of the fluid phase and *i *is

where s is the viscosity of the soil skeleton and

the hydraulic gradient defined by

d*v*/d*n *is the velocity gradient. The model law

and scale factor for the viscous force *K*Fv can then

(A22)

be written

sm d*v*m d*n*p Am

in which *v *is the superficial velocity of the fluid

=

.

(A12)

and *k *is Darcy's coefficient of permeability. From

sp d*v*p d*n*m Ap

eq A21 and A22 the scale factor *K*Fs for the seep-

age force can be written as

From the definition of velocity it follows that

=

.

(A23)

=

.

(A13)

Equation A8 implies that

From eq A1, A4 and A13 and the fact that viscos-

ity is independent of gravity, *K*Fv can be written

= *K*F = *K*l2 .

(A24)

.

(A14)

Then, from eq A13 and A24, eq A23 becomes

Because *K*Fv must equal *K*F = *K*l2 , then

=

.

(A25)

(A15)

That is, the time scale factor is 1 if the viscous

A general expression for the coefficient of per-

force is to be scaled like the weight force.

meability is (Mitchell 1976)

An *inertia force *can be written as

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