Designers analyzed the structures assuming they behave as a rigid body in the fast. Today, technology has developed and there are may software than can be used to model the soil.
Analysis of raft foundations, combined footings, analysis of piles for lateral loads and model the buckling of piles in weak ground. There are many methods to find the subgrade reaction using the bearing capacity or standard penetration value(SPT) in addition to testing methods.
Methods of obtaining the subgrader reaction is given in the book, foundation analysis and design by Bowles. Simplified empirical equation is given to calculate the subgrade reaction. Following is extracted from the bowles foundation analysis and design book.
"It has been found that bending moments and the computed soil pressure are not very sensitive to what is used for ks because the structural member stiffness is usually 10 or more times as great as the soil stiffness as defined by ks. Recognizing this, the author has suggested the following for approximating ks from the allowable bearing capacity qa furnished by the geotechnical consultant:
SI : ks = 40(SF)qa kN/m3
Fps: ks = l2(SF)qa k/ft3 (9-9)
where qa is furnished in ksf or kPa. This equation is based on qa = qult/SF and the ultimate
soil pressure is at a settlement ∆H = 0.0254 m or 1 in. (1/12 ft) and ks is qult/AH. For
AH = 6, 12, 20 mm, etc., the factor 40 (or 12) can be adjusted to 160 (or 48), 83 (or 24), 50
(or 16), etc.; 40 is reasonably conservative but smaller assumed displacements can always
be used."
If we know the allowable baring capacity and the safety factor used to find the allowable bearing capacity, subgrade reaction can be calculated. Generally for cohesive soils a factor of 3 and cohesionless soils a factor of 2 are assumed by the engineers. However, it is advisable to get the correct factor of safety from geotechnical engineer.
Subgrade reaction found from above equation can be used to model raft foundations, footings and combined footings. However, when we model piles, it is better to refer some other method of obtaining sub-grade reaction even though this above method may be used for the analysis.
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