Is no-tension design of concrete or rock structures always safe? - Fracture analysis

Plain concrete structures such as dams or retaining walls, as well as rock structures such as tunnels, caverns, excavations, and rock slopes, have commonly been designed by elastic-perfectly plastic analysis in which the tensile yield strength of the material is taken as zero. The paper analyzes the safety of this "no-tension" design in the light of the finiteness of the tensile strength of concrete or the tensile strength of rock between the joints. Through examples, it is demonstrated that: (1) the calculated length of cracks or cracking zones can correspond to an unstable state; (2) the uncracked ligament of the cross section, available for resisting horizontal shear loads, can be predicted much too large, compared to the fracture mechanics prediction; (3) the calculated load-deflection diagram can lie lower than that obtained by fracture mechanics; (4) the no-tension load capacity for a combination of crack face pressure and loads remote from the crack front, calculated by elastic analysis on the basis of allowable compressive stress, can be higher than that obtained by fracture mechanics; and (5) an increase in the tensile strength of the material can cause the load capacity of the structure to decrease. Due to the size effect, these facts are true not only for zero fracture toughness (no-toughness design) but also for finite fracture toughness provided that the structure size is large enough. Several previous studies on the safety of no-tension design, including the finite-element analysis of a gravity dam, are also reviewed. It is concluded that if the no-tension limit design is used, the safety factors of concrete or rock structures cannot be guaranteed to have the specified values. Fracture mechanics is required for that.