This study shows it is sufficient to use only the tensile strength ft to describe the size effect on quasi-brittle fracture behaviors of brittle heterogeneous solids such as rock and concrete. Another essential material property, the average grain size G for rock or the maximum aggregate size dmax for concrete, should be determined separately before fracture analysis. Quasi-brittle fracture behaviors of heterogeneous specimens or structures, small or large and notched or un-notched, can all be described by the "one-parameter ft criterion" evolved from the boundary effect model (BEM). Using the mean and standard deviation from normal distribution analysis of test data, the simplified BEM can predict the mean quasi-brittle fracture curve and statistical scatters with 95% reliability, covering the entire fracture range from the strength ft criterion to the fracture toughness KIC criterion (LEFM), and the quasi-brittle fracture region in-between. KIC is fully determined by ft and G, making the oneparameter ft approach possible. This one-parameter approach thus requires only "one measurement" from a group of specimens of any size with any notch length. The 95% reliability band established statistically can be conveniently used in design applications.