Scale Factors in Geomechanics

This study addresses the limitations of conventional methods employed in Rock Mass Classifications for establishing scale factors. An innovative approach is introduced to determine scale factors pertaining to rock mass strength, deformation modulus, creep behavior, and angle of internal friction (AIF). Rooted in fractal analysis principles, the approach relies on the constancy of the ratio of block dimension to joint spacing within hierarchical blocky structures. The scale factor for rock mass strength is determined based on insights gleaned from Kim’s models of blocky structures with varying intact strengths of equivalent materials, tested under uniaxial compressive stress. Equations for quantifying the reduction in elastic constants over time are presented. Additionally, the author introduces the creep constant to tackle viscoelastic issues. Furthermore, correlation equations for four types of rock have been formulated to determine the creep constant as a function of modulus elasticity. It was found, based on an elastic-plastic solution, that the ratio of displacements at the opening contour to displacements within the non-elastic zone can be approximated by a function that relies solely on the AIF. This concept was then utilized to determine the AIF of the rock mass through back analysis of field measurements. Examples of this approach under diverse geomechanical conditions are discussed, including observations on the decreasing AIF over time. Furthermore, two hypotheses are posited: Hypothesis A suggests that the scale factor for the same block structure is contingent on intact compressive strength with lower values for hard, brittle rock compared to soft, plastic rock; Hypothesis B proposes that the duration of stress relaxation and creep deformation may escalate with the scale of the rock mass. While the author presents preliminary evidence in support of these hypotheses, further investigation is warranted to pinpoint specific contributing factors.