In laboratory experiments, there is a kind of experiences where we can take a reduced model from a real project, and we apply experiences to this reduced model, for example, we went to show the behavior of a foundation resting over soft soil, we take a reduced model in laboratory, we apply loading at surface of the reduced model of the foundation, and we measure vertical displacements, but, how we can select dimensions of this reduced model? Are there any correlation’s to choose those dimensions?
It depends on what kind of experiment you perform. In case of the centrifuge testing, the scaling factor is N (for lengths) which is same as the factor used to increase the gravitational acceleration (Ng) in centrifuge.
For rockfills, see the paper "The effect of size on the strength of coarse rock aggregates and large rockfill samples through experimental data", Ovalle et al. 2014, Acta Mechanica
for piled raft or piles group or raft foundation: you can choose any dimensions depending on the size of soil tank but you should take into account the stiffness of raft and piles. moreover, for vertical loading the ratio between the diameter of the tank and the raft side should be greater than 3. for horizontal loading the soil tank should be extended to 12x pile dia. The vertical distance between the piles tip and the base of soil tank should be kept at least L, which is the pile length. Depending on these dimensions of the tank, you can choose raft and piles with any material and size, just check their stiffness to get the desired stiffness ( flexible or rigid )
ASTM D3080/D3080M-11 (2012) suggests: the minimum specimen diameter for circular specimens, or width for square specimens, shall be 50 mm, or not less than ten times the maximum particle size; the minimum initial specimen thickness shall be 13 mm, but not less than six times the maximum particle size; the minimum specimen diameter to thickness or width to thickness ratio shall be 2:1.