The strength of geological materials is a fundamental property used in the design of civil engineering works; including projects constructed in complex geological mixtures or fragmented rocks such as melanges, fault rocks, coarse pyroclastic rocks, breccias and sheared serpentines. These and other, often chaotic, mechanically and/or spatially heterogeneous rock masses are composed of relatively strong rock blocks surrounded by weaker matrix rocks. These common rock mixtures, known as bimrocks (block-in-matrix-rocks) or bimsoils (when the matrix material is soil-like) are very difficult to evaluate. It is almost impossible to recover high quality, undisturbed drill core samples or to prepare laboratory specimens perform laboratory studies and evaluate geomechanical parameters such as cohesion, internal friction angle and uniaxial compressive strength from these complex mixtures. There is sparse literature describing empirical and laboratory studies on strength of bimrocks. Hence, this study was devised to develop a preliminary Bim strength criterion, a generalized conceptual empirical approach for predicting the overall strength of unwelded bimrocks and bimsoils. The approach considered fundamental rules of rock and soil mechanics and the reported mechanical behavior of bimrocks as a function of volumetric block proportion (VBP), as reported in literature. In addition, cores of artificial bimrock were prepared in the laboratory for uniaxial and triaxial compression testing. Empirical equations useful for predicting the strength of bimrocks were devised, which depend on practical charts and input parameters, such as parameter "A", defined to relate the contact strength between matrix and blocks. The predictive equations were calibrated by using the literature database. The predictive performance of the preliminary Bim strength criterion for bimrocks and bimsoils was checked by using the established database, and was found to have high predictability, although erring slightly on the conservative side. (C) 2014 Elsevier B.V. All rights reserved.