Statistics and size effect in cementitious materials

The statistical size effect in cementitious beams is examined using the assumption that the critical threshold stress to cause a strain-softened fracture process zone to be initiated follows the Weibull distribution. The fictitious crack line model and the K-superposition theory, in combination with the statistical strain-softening relationship, are used to determine the strength of plain and notched beams. For notched beams the statistical effect on the strength is only important for small beams, but causes a large variation in all sizes of plain beams.