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Material behavior can be idealized as consisting of an 'elastic' domain and a 'plastic' domain. For almost 200 years, structural design has been based on an elastic theory which assumes that structures display a linear response throughout their loading history, ignoring the post-yielding stage of behavior. Current design practice for reinforced concrete structures is a curious blend of elastic analysis to compute forces and moments, plasticity theory to proportion cross-sections for the moment and axial, load, and empirical mumbo-jumbo to proportion members for shear. From the book "Design of Concrete Structures with Stress Fields" by A. Muttoni, J. Schwartz and B.Thurliman.

If you are having a geotechnical report with you, there must be clearly stated value of spring constant with the name Modulus of Subgrade Reaction. Incase soil investigation have not been done on site for any reasons, you can use a tentative value for k by following relation. k = 3 x qa x 12 (in FPS in k/ft3) k = 3 x qa x 40 (in SI in KN/m3) where qa = allowable bearing capacity. and 3 is Factor of safety applied on soil while determining bearing capacity of soil. For the reference of this formula, please read the attached document. Correlation_BC_and_K.pdf