Young's modulus interpreted from plane compressions of geomaterials between rough end blocks

This note derives an approximate expression of the true Young's modulus of a rectangular solid under plane compression between two rough end blocks, provided that the Poisson's ratio ν of the solid is known. The friction between the loading platens and the ends of the specimen is assumed to be large enough to restrain slippage at the contact. By using the function space concept of Prager and Synge (1947), a correction factor λ with calculable error is obtained which can be multiplied to the apparent Young's modulus (i.e., the one obtained by assuming uniform stress field) to yield the true Young's modulus; it is evaluated numerically for 0 ≤ ν ≤ 0.49 and 0 ≤ η ≤ 3 (where η = b/h with b and h being the half width and half length of the specimen). In general, λ increases with ν and η for both plane strain and plane stress compressions. Within this range of ν and η, λ may vary from 0.37-1.0 for the plane strain case and from 0.84-1.0 for the plane stress case. Thus, the assumption of uniform stress field may lead to erroneous interpretation of the Young's modulus. When the special case of ν = 1/3 and η = 1 is considered, we obtain λ = 0.9356, which compares well with 0.9359 obtained by Greenberg and Truell (1948).