Development of upper and lower bounds to describe engineering properties as a function of macroporosity

The engineering and mechanical properties of macroporous rock are highly variable and exhibit considerable scatter when unconfined compressive strength or deformation modulus are plotted as functions of macroporosity. One approach to such describe such highly scattered data is to constrain them with derived upper and lower bounds. The data set for this investigation consisted of experimental data from plaster of Paris specimens containing Styrofoam macropores of various shapes and sizes. Two methods, traditional regression analysis and local regression analysis, were applied in an attempt to develop upper and lower bounds to unconfined compressive strength and deformation modulus data as a function of macroporosity. Both methods produced bounds that exponentially decreased as macroporosity increased. However, traditional regression analysis was not able to provide bounds to the majority of the experimental data and expected modulus behavior was not satisfactorily described. Local regression was able to provide bounds to the majority of the experimental data and could describe the expected behavior of the macroporous specimens.