ABSTRACT
If we consider the equilibrium of an element of unit cross-sectional area and of thickness Sz taken from a column of soil at the surface of the earth (Fig 6.2a) then we know that the increase of stress through the element must balance the weight of the element (which itself comes from the gravitational pull of the earth) in order to prevent any acceleration of the element:
5av = pgdz (6.1) and, with constant density, at a depth z below the free surface
crv = I pgdz = pgz (6.2)
On the centrifuge, if we consider the equilibrium of an element of unit crosssectional area and of thickness 6z (Fig 6.2b), then we see that the stress increase must provide the force necessary to generate the centripetal acceleration. The equation of motion becomes:
8<jv = pngSz and at depth z/n below the free surface (assiiminp-mnsta.nt Hfinsitv^
(6.3)
(6.4)
re '= 1 Hp itv n
v2/W <
r
I
l>z/n GV = I npgdz = pg
Figure 6.3: Finite dimensions of two-dimensional centrifuge model of embankment
Thus stresses are identical at geometrically equivalent points in the prototype and in the centrifuge model, provided the linear scale in the model is the inverse of the acceleration scale ng = n = 1/n^ (Table 5.4). Consequently we can expect that if mechanical behaviour of the soil is strongly dependent on stress level then such behaviour should be correctly reproduced in our centrifuge model.
