Acoustic Emission Asymmetry in Mixed-Mode Rock Fracture

Fracture in rock rarely develops as a purely geometric extension of a pre-existing notch or crack. Even when the external loading condition is well defined, the material surrounding the crack tip responds through a localized process of microcracking, damage accumulation, and fracture process zone development. This distinction becomes especially important in quasi-brittle materials, where the crack tip can be considered as a finite region in which local tensile and shear influences may coexist. For mixed-mode fracture, the difficulty is therefore to both predict the direction of crack growth as well as understand how the local condition near the fracture tip differs from the nominal boundary condition imposed on the specimen. Classical linear elastic fracture mechanics provides a useful starting point. Under mixed tensile and in-plane shear loading, the local crack-tip stress intensity factors after an infinitesimal kink do not simply reproduce the global mode I and mode II components. The criterion of local symmetry was developed from this observation: fracture tends to evolve in a direction that removes the local mode II contribution, so that a mode I condition is eventually reached. However, this reasoning is most straightforward under small scale yielding, where the crack tip can be treated as an idealized point. In rock under large scale yielding, the fracture process zone has a finite size, and the local shear influence may not be visible as a simple kink angle or as sliding displacement along the fracture path. In a recent research paper published in Engineering Fracture Mechanics, Professor Peng-Zhi Pan from the State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences led his team to develop an acoustic-emission-based method for visualizing and quantifying fracture asymmetry caused by local shear influence in rock under large scale yielding. They introduced the parameter ξ as an area-ratio measure of the symmetry degree of acoustic emission clusters on the two sides of a fracture trajectory. They also separated acoustic emission events by energy level, showing that local shear influence is concentrated mainly in Level 2 and Level 3 events rather than in the high-energy Level 1 events that dominate fracture creation. This combination of spatial cluster analysis and energy-level classification is the technically distinct contribution of the study.

The authors’ experimental strategy focused on a carefully chosen comparison between mode I and mixed-mode fracture. They tested Berea sandstone specimens using single edge notched bend geometry for mode I loading and eccentric single edge notched bend geometry for mixed-mode loading. The use of relatively small specimens was important because it placed the fracture process under large scale yielding conditions, where the fracture process zone becomes central to the interpretation. Acoustic emission sensors were arranged around the notch region, and the recorded events were located and classified by relative energy. In the mode I specimens, the acoustic emission clusters remained approximately symmetric around the fracture trajectory. This behavior provided the reference state needed to interpret the mixed-mode results. In the eccentric specimens, by contrast, acoustic emission events were distributed asymmetrically on the two sides of the fracture trajectory. High-energy Level 1 events, which accounted for most of the total acoustic emission energy, remained essentially symmetric. Medium- and low-energy events, designated Level 2 and Level 3, showed clear asymmetry in the mixed-mode specimens. This energy-dependent pattern is central to the interpretation, because the local shear influence was not distributed uniformly across the fracture process, but appeared mainly in the lower-energy and more numerous acoustic emission populations. To quantify this observation, the authors introduced the parameter ξ, defined as the ratio between the larger and smaller areas covered by acoustic emission events on opposite sides of the fracture trajectory. Because ξ is an area ratio rather than a direct stress measurement, it is best understood as an indicator of local shear influence rather than as a calibrated measure of local shear stress. The researchers determined acoustic emission cluster boundaries through a combination of event filtering and an alpha-shape procedure, then calculated separate ξ values for different acoustic emission energy levels.  The mode I tests gave reference values of about 1.3 for ξ₂ and 1.8 for ξ₃, reflecting the practical fact that perfect symmetry is not expected in real sandstone specimens and acoustic emission location data. In mixed-mode fracture, the initial ξ values were much larger than these reference levels. For Level 2 events, initial ξ values generally fell in the range of about 2 to 4.5, while Level 3 values could be much higher in some specimens. These elevated initial values supported the interpretation that local shear influence was present when the fracture initiated.

The evolution of ξ during fracture growth was equally important. In most mixed-mode specimens, ξ₂ gradually decreased toward the mode I reference value as the fracture process developed. This trend indicates that the local shear influence associated with Level 2 acoustic emission events was progressively removed. Level 3 events behaved less uniformly: ξ₃ also tended to decrease, but in some specimens it remained above the reference value even after substantial fracture development. Because Level 3 events accounted for less than five percent of the total acoustic emission energy, the authors interpreted this residual asymmetry as limited in its contribution to the dominant fracture process. The main fracture, in energetic terms, moved toward a mode I condition.

The engineering applications of the findings of Professor Peng-Zhi Pan and colleagues are in the modelling of mixed-mode fracture in rock and other quasi-brittle materials. In underground excavations, rock slopes, foundations, boreholes, and hydraulic-fracturing-related problems, cracks often develop under combined tensile and shear conditions rather than under pure opening mode. The study shows that local shear influence may be expressed through asymmetric acoustic emission damage around the fracture trajectory, even when the dominant fracture process progressively approaches a mode I condition. This is important because the visible crack path alone may not capture the full local fracture state. By introducing the symmetry parameter ξ and separating acoustic emission events by energy level, the work provides a practical way to quantify damage asymmetry and to follow the gradual reduction of local shear influence during fracture growth.

The findings are also relevant to acoustic-emission-based structural health monitoring and constitutive modelling of geomaterials. AE monitoring is widely used to detect microcracking in rock-like materials, but this study shows that the spatial pattern of AE events carries additional mechanical information. In particular, the asymmetry of medium- and low-energy AE clusters can indicate the presence of local shear influence, while the symmetry of high-energy events suggests that the main fracture core remains governed largely by opening damage. This distinction provides a more refined picture of the fracture process zone which suggest that local shear does not affect the whole damage field uniformly but acts more strongly on selected damage populations.