3-D Numerical and Analog Models of Macroporous Rock:Investigating the Influence of Void Characteristics on Elastic Modulus

Macroporosity in rock has detrimental effects on both strength and deformability of a rockmass; however, limited research has attempted to quantify such relationships. Macropores can be extremely variable with regard to void shapes, sizes, locations, and distribution, making it difficult to core specimens from rock samples and impractical to perform tests on the myriad of feasible combinations. Numerical models are used as an alternative to physical testing to further investigate such material [1]. This study attempts to quantify how variation in overall porosity and in void characteristics - namely size and porosity - affects the elastic modulus of a rock like material. Right circular cylinders 5.1 cm (2 in) by 10.2 cm (4 in) were constructed out of plaster of Paris with Styrofoam® spheres and tested in unconfined compression. Identical cylinders with linear elastic matrix properties were simulated, with spherical voids having null material properties. The numerical models of macroporous materials were produced using both a finite difference approach (FLAC3D) and a finite element approach (TNO Diana). Results of the numerical models are contrasted with a database of tests conducted on plaster of Paris specimens containing Styrofoam® spheres with various void sizes and porosities. The great scatter in the laboratory testing data - with larger scatter among the low porosities - limited the ability to quantify the relationship. Conversely, the numerical models had greater scatter among higher porosities and produced elastic moduli at the high end of the laboratory data cloud. A discussion of the advantages and limitations of the different numerical approaches also ensues regarding why the numerical models came up with larger moduli than the laboratory testing.