Is Complexity the Answer to the Continuum vs. Discontinuum Question in Rock Engineering?

Abstract The question for which rock masses discontinuum modeling must be used and which can be abstracted as a continuum concerned rock engineering for decades. This paper proposes that the answer to the continuum versus discontinuum question lies in the relative structural complexity of the rock mass and its discontinuities. Complexity in this case refers to discretely computed parameters that put a number on the perceived complexity of a rock mass and quantify its emergent properties. Parameters like the multiscale structural complexity, the Shannon entropy, the compression complexity or the Euler characteristic are implemented in a computational framework. It is shown that there are two scale-dependent low complexity end members: on the one hand, massive rock masses with very few discontinuities or very small rock samples, and on the other, rock masses with a very high discontinuity density approaching soil-like material or mountain-range scale samples. In between, however, lies a spectrum where rock mass complexity increases rapidly with increasing discontinuity density and then decreases again. Based on this observation, we assert that the discontinuum approach should be used for the majority of rock masses, but the continuum approach can be justified in cases of low complexity. Two case studies show how these theoretical insights support conceptual approaches in real rock engineering cases. The full code and data for the executed simulations are provided to facilitate further studies on this topic.