Youngs 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 n 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 "0836#\ a correction factor l with calculable error is obtained which can be multiplied to the apparent Young|s modulus "i[e[the one obtained by assuming uniform stress _eld# to yield the true Young|s modulus^ it is evaluated numerically for 9 n 9[38 and 9 h 2 "where h b:h with b and h being the half width and half length of the specimen#[ In general\ l increases with n and h for both plane strain and plane stress compressions[ Within this range of n and h\ l may vary from 9[26 0[9 for the plane strain case and from 9[73 0[9 for the plane stress case[ Thus\ the assumption of uniform stress _eld may lead to erroneous interpretation of the Young|s modulus[ When the special case of n 0:2 and h 0 is considered\ we obtain l 9[8245\ which compares well with 9[8248 obtained by Greenberg and Truell "0837#[