A Multi-Scale Equivalent Modelling Framework for Collapse Behavior in Jointed Rock Masses

The stability of underground excavations depends on the subtle interaction between intact rock and the myriad of fractures that cut through it. Engineers and geoscientists have long known that tunnels and caverns do not fail as continuous solids but as mosaics of discrete blocks whose shapes and volumes are defined by networks of joints. The challenge is that these joints exist across a broad range of scales, from tiny cracks that reduce stiffness to large structural planes that define the very geometry of collapses. Capturing this multi-scale reality has proven to be a persistent obstacle for both theoretical modelling and practical design. Traditional laboratory tests on small specimens offer detailed measurements of mechanical response but cannot reflect the behavior of massive structural planes encountered in real projects. In situ tests on large rock volumes provide better scale representation, yet they are logistically demanding and financially prohibitive. Numerical modelling has emerged as an indispensable tool, but even here the problem is not solved. Direct simulation of all fracture scales within a large rock mass quickly becomes computationally overwhelming, while overly simplified homogenization erases the very discontinuities that control failure. Bridging these two extremes requires a careful balance: a framework that recognizes fine-scale features without drowning in detail, and one that preserves large-scale geometry without excessive simplification.

To this account, new research paper published in Tunnelling and Underground Space Technology and led by Professor Shaoshuai Shi  from the Shandong University alongside Dr. Peng He, Zhiqiang Yan, Gang Wang, and Dr. Chengcheng Zheng from the Shandong University of Science and Technology, the authors developed a new multi-scale DFN-DEM equivalent modelling method that merges discrete fracture networks with representative elementary volume concepts to capture joint behavior across scales. Fine joints are absorbed into equivalent continuum parameters but the larger joints remain explicit and preserved both mechanical realism and computational efficiency. They validated framework using simulations of the Erlangshan Tunnel and reproduced collapse morphologies that matched field expectations. This dual-model approach clarifies the distinct roles of small and large fractures in determining fragmentation versus collapse geometry. The researchers began by mapping the joints at the Erlangshan Tunnel site and classifying them according to size. They relied on hierarchical sequence theory, which suggests that fracture systems exhibit self-similar scaling relationships. Using embedding coefficients, the joint network was divided into four categories: micro-joints less than one meter, small joints between one and 2.8 meters, medium joints up to 7.8 meters, and large structural planes extending as far as 22 meters. This classification provided the basis for constructing discrete fracture network models that could be studied at different resolutions.

The next step was to establish representative elementary volumes through virtual compression tests. The researchers generated cubic specimens of varying dimensions with joint distributions appropriate to each scale, and uniaxial loading was applied numerically in three directions. By plotting stress–strain curves and observing when mechanical properties stabilized, the critical size at which fluctuations diminished was identified. For the smallest joint category, a cube of around ten meters produced stable values for strength and stiffness, while larger scales required volumes up to sixteen meters. These stabilized properties were then reassigned to form equivalent continua at the next level of modelling, allowing small-scale fractures to be absorbed into modified rock parameters while keeping only the largest joints explicit. The authors constructed several synthetic rock mass models. Some included all fractures, while others represented only larger-scale joints with the smaller ones already homogenized. Excavation simulations were then carried out to study how blocks detached and accumulated. The full-scale models displayed highly fragmented collapses with many small pieces concentrated near the tunnel spandrels. When the finer joints were equivalently removed, the collapsed blocks became more coherent, though the overall contour of the failure remained similar. At the largest scale, collapses manifested as isolated boulder falls, confirming that block volume is strongly correlated with joint size. A comparison of simulations also revealed that fine joints, although not decisive for the geometry of failure, played a critical role in fragmentation.

The scientific advancement in the paper by Professor Shaoshuai Shi and his team deserves attention for the technical rigor as well as how it reframes a long-standing difficulty in rock mechanics. For decades, the field has wrestled with the problem of scale: whether to treat fractures as detailed geometric features or to smooth them into averaged parameters. Most approaches fall into one of these two extremes, which inevitably distort the mechanics of collapse. What this study offers is an elegant middle ground. The authors successfully show that the different scales of discontinuities can be reconciled without losing their distinct contributions by introducing a stepwise equivalence that progressively absorbs smaller fractures into representative continuum properties while leaving larger structural planes intact.

Moreover, the modelling framework does more than sharpen theoretical understanding. It has direct value for engineers tasked with predicting hazards underground. Tunnel collapses are notoriously difficult to anticipate, not least because existing models either produce overly fine fragments that never appear in reality or else gloss over critical planes of weakness. The multi-scale DFN–DEM approach gives designers the ability to forecast not only the likelihood of collapse but also its character: whether the failure will manifest as a spray of gravel, a cluster of intermediate blocks, or the sudden release of a large boulder. That level of detail is immensely useful when deciding on support strategies. Reinforcement measures can then be tailored—lighter linings and mesh for fragment-prone zones, or heavy anchors and bolts where block falls are expected. It is the difference between reactive mitigation and proactive planning.

Another aspect that should not be underestimated is efficiency. Fully explicit models of fractured rock quickly become computationally intractable, which limits the number of scenarios engineers can test. The authors’ approach trims this complexity by treating the influence of small fractures equivalently, leaving only the dominant structural features to be handled explicitly. The result is a tool that captures the essence of rock mass behavior without overwhelming computational resources. For practitioners, this translates into the ability to run multiple “what if” simulations within realistic time frames, which strengthens the reliability of safety assessments. We believe the broader reach of the study is also worth highlighting. Although developed in the context of tunnelling, the same principles could readily inform stability assessments of slopes, underground storage facilities, or deep mining stopes. The methodology could even cross disciplinary boundaries and can provide petroleum engineers or hydrogeologists a framework for representing fracture systems that control fluid flow or reservoir stability. Ultimately, Shi and his colleagues provide not just a modelling framework, but a perspective that helps us see rock masses as ordered systems rather than chaotic collections of fractures.