S1: Correct. According to the Kozeny-Carman equation, At a given porosity (which fixes the
void ratio e), permeability is inversely proportional to the square of the specific surface area 
where (Sv) is the specific surface area per unit volume.
S2: Incorrect. Consolidation is a function of effective stress, not total stress. Water drains out
of the soil pores as excess pore water pressure dissipates, transferring the load to the soil
skeleton (increasing effective stress).
S3: Incorrect. For a fully saturated soil, Skempton's pore pressure parameter (B) is equal to
1 (not zero). A value of zero corresponds to a completely dry soil.
S4: Correct. One of the fundamental assumptions of Terzaghi's one-dimensional
consolidation theory is that it only considers primary consolidation (due to the expulsion of
pore water) and completely neglects secondary compression (due to plastic readjustment of
soil solids).