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Fault normal stress (σn) changes dynamically during earthquakes. However, the impact of these changes on fault strength is poorly understood. We explore the effects of rapidly varying σn by conducting rotary‐shear experiments on simulated fault gouges at 1 μm/s, under well‐drained, hydrothermal conditions. Our results show both elastic and anelastic (time‐dependent but recoverable) changes in gouge layer thickness in response to step changes and sinusoidal oscillations in σn. In particular, we observe dilation associated with marked weakening during ongoing σn‐oscillations at frequencies >0.1 Hz. Moreover, recovery of shear stress after such oscillations is accompanied by transient (anelastic) compaction. We propose a microphysically based friction model that explains most of the observations made, including the effects of temperature and step versus sinusoidal perturbation modes. Our results highlight that σn‐oscillations above a specific frequency threshold, controlled by the loading regime and frictional properties of the fault, may enhance seismic hazards. Plain Language Summary Faults in the crust sometimes experience rapid stress changes, caused by nearby or remote earthquakes, by seasonal impoundment and discharge of reservoirs, by hydrocarbon or geothermal energy production, or by reservoir stimulation. The impact of these stress changes on the earthquake potential of faults is poorly understood. This study explores such effects through laboratory experiments on simulated faults under upper crustal PT conditions, perturbing the normal stress on the fault in various ways. Our results show that the shear stress supported by the fault, and the fault thickness, respond instantly to normal stress changes, followed by a transient evolution. In particular, we observed dilation (fault‐normal expansion) associated with marked weakening during fast oscillation. We propose a micromechanical model that can qualitatively explain the general experimental observations. Our results indicate that varying the normal stress on a fault at frequencies above a specific threshold may enhance seismic hazard. Key Points We observed dynamic weakening and dilation of shearing gouges subjected to rapid oscillations in normal stress Fault compaction/dilation explains the shear stress evolution in response to different modes of normal stress perturbation We propose a micromechanical model for gouge friction under time‐variable normal stress conditions

The study of commercial low-density polyethylenes (LDPEs) has always focused on the effects of the molecular architecture of the polymer on its shear and extensional rheological properties due to their direct influence on manufacturability. However, the complex morphology of industrial-grade LDPEs also affects the crystallization kinetics and dynamic mechanical properties of the polymers, which are key to the processibility and applications. Therefore, a comprehensive investigation was conducted into the areas of crystallization kinetics, crystallinity, dynamic mechanical, and linear and non-linear shear rheological properties of two industrial-grade LDPEs to build a cohesive insight into the influence of morphology on these material properties. We further analyzed the steady-state and transient shear viscosity data obtained from the two LDPEs in comparison with constitutive model predictions using the hierarchical multi-mode molecular stress function (HMMSF) and found excellent agreement within experimental accuracy between predictions by the HMMSF model and shear stress as well as normal stress data of the LDPEs investigated.

Various seismological methods are used to determine crustal stress fields, but most only provide stress changes, not absolute amounts of stress. In this study, we used Global Navigation Satellite System data to determine the spatiotemporal slip distribution of four slow slip events (SSEs) in the Bungo Channel between Shikoku and Kyushu Islands, Japan. Based on the obtained relationship between shear stress change and slip velocity, we plotted slip trajectories that were similar to theoretically stable trajectories for a spring-slider system subject to velocity weakening following a rate- and state-dependent friction law. Accordingly, we estimated the absolute values of the effective normal stress during SSE slip acceleration to have been 18–45 MPa at depths of 16.5–21.5 km. These values are very small compared to the lithostatic pressure at the depths investigated, suggesting the existence of very high pore fluid pressures at the plate boundary in the SSE source area. Our results and previous results obtained for SSEs off the Boso Peninsula, Japan, outline a positive correlation between the effective normal stress and total slip. Therefore, pore fluid pressure values at plate boundary interfaces may be an indicator of the amount of slip during SSEs. Graphical Abstract

Induced earthquakes are occasionally associated with stress oscillations resulting from periodic industrial activities. Yet, the effects of stress oscillations on fault friction under realistic subsurface conditions are not fully clear. We conducted normal stress oscillations experiments using simulated fault gouges derived from the major reservoirs and caprocks of the Changning shale gas field under in situ conditions. Our experimental results reveal that most gouges are velocity‐strengthening under quasi‐static loading. Interestingly, after applying normal stress oscillation, they show similar shear stress evolution with different oscillation amplitudes, frequencies and load‐point velocity, suggesting a negligible effect of the rock composition and the applied P‐T conditions. We successfully reproduce our experimental results using an extended CNS (Chen‐Niemeijer‐Spiers) model and the model proposed by Linker and Dieterich (1992, https://doi.org/10.1029/92jb00017). Therefore, these experimental observations and friction models can be reliably extrapolated to more heterogeneous field cases and other regions with similar lithology distribution. Plain Language Summary Some induced seismicity events show periodic characteristics due to stress oscillations on faults caused by industrial activities. To our knowledge, effects of stress oscillation on the frictional properties of natural fault gouges under subsurface conditions have not been investigated yet. In this study, we conducted normal stress oscillation experiments on the gouge samples collected from Changning shale gas field under realistic pressure and temperature for each layer. For the samples that exhibit stable sliding under quasi‐static loading, their mechanical responses are similar regardless of gouge composition, applied pressure and temperature conditions. We successfully reproduced the experimental data using a microphysical friction model and a classical friction model. This work suggests that our experimental observations and existing friction models can be reliably used to predict the impacts of stress oscillation on the fault mechanical behaviors in more heterogeneous field case and other places with comparable lithology distribution. Key Points Normal stress oscillation experiments were conducted on natural fault gouges under in situ subsurface conditions All velocity‐strengthening materials exhibit similar evolution of shear stress under normal stress oscillation The experimental results can be reliably reproduced using both the Linker and Dieterich (1992, https://doi.org/10.1029/92jb00017) model and the extended CNS model

In Enhanced Geothermal Systems (EGS), rock fractures in the reservoir are often subjected to cyclic changes in effective stress at elevated temperatures, causing permeability variations. In this study, the effect of cyclic normal stress on permeability evolution of rough fractures in Gonghe granite at elevated temperature was investigated through flow-through experiments. The results show that the fracture permeability decreases with increasing normal load and partially recovers as the normal load releases. Under a constant normal stress, the fractures gradually close, exhibiting viscoelastic-plastic behavior that can be characterized using the Nishihara model. Based on these characteristics, a fracture-creep deformation model has been developed considering the stress history using a combination of the Hopkins fracture closure model and the Nishihara model. This study investigated the effects of cyclic stress on the internal geometric features of fractures at elevated temperature, calculated the fracture deformation and the corresponding permeability during the loading and unloading process, and validated the accuracy of the proposed model. The study reveals the primary mechanisms responsible for fracture permeability evolution under cyclic effective stress at elevated temperatures, providing valuable insights for the sustainable development of EGS.HighlightsThe viscoelastic–plastic behavior of rough fractures in Gonghe granite subjected to cyclic normal stress has been demonstrated in the flow-through experiments.A fracture-creep deformation model for a single rough fracture is developed considering the stress history using a combination of the Hopkins fracture closure model and the Nishihara model.The fracture permeability is calculated according to the geometric characteristics of the fracture, which has been validated by laboratory permeability measurements.

In-extruder measurements of shear viscosity and normal stresses are important as these measurement techniques allow determining the rheological state of the polymer melt at processing conditions up to high shear rates. However, validation of viscosity and normal stress data obtained by in-line slit rheometers at high shear rates is difficult due to a lack of overlap of the in-line data and the off-line measurements by rotational rheometers limited to lower shear rates. Here, shear viscosity and normal stress data measured in-line at large shear rates during extrusion and off-line at low shear rates are compared to predictions of the Doi-Edwards model and the Hierarchical Multi-Mode Molecular Stress Function (HMMSF) model using linear-viscoelastic off-line small amplitude oscillating shear data of two polystyrenes and a low-density polyethylene as input parameters. For polystyrene, the results of this investigation do not only validate the experimental data obtained by rotational as well as slit-die rheometry, but also demonstrate the agreement between experiments and models up to very high shear rates, which were not experimentally accessible earlier. The low-density polyethylene shows a more complex behaviour, which follows the HMMSF model at low shear rates, but approaches the Doi-Edwards model at high shear rates.

Excavation, river incision and anchor cable relaxation would result in unloading of stress in at least one direction of rock masses in caverns or slopes, and the unloading failure is prominent and it even shows remarkable tensile failure. The previous direct shear tests with constant normal stress can no longer meet these circumstances. However, the experimental study of rock shear behavior under unloading normal stress condition is rare. This paper presents an innovative experimental method to study the mechanical behaviors of sandstone containing a pre-existing flaw under unloading normal stress with constant shear stress. Five failure patterns were identified based on the analysis of crack propagation and their mechanical properties. The failure pattern transforms from mixed tensile–shear failure to tensile failure then to shear failure with the increase of flaw angle. Initial normal stress is greater, the propagating cracks behave as stronger tensile fractures. The peak dilatancy angle increases and decreases with the increase of the initial normal and shear stresses, respectively. Internal friction angle and cohesion both decrease first and then increase with the increase of flaw angle. The branch crack, extent of exfoliation, shear scratch and failure pattern are different from that in the traditional direct shear tests. Unloading normal stress significantly weakens the shear strength compared to traditional direct shear tests, suggesting that the shear strength parameters used in stability evaluation of rock excavation engineering should be determined by unloading tests. The results enrich the basic theory of rock mechanics.

In the field of crack mechanics, predicting the direction of a crack is important because this will evaluate whether, when the crack propagates, it penetrates into important areas and whether the structure is dangerous or not. This paper will refer to three theories that predict the propagation direction of cracks: a theory of maximum tangential normal stress, a theory of maximum energy release, and a theory of minimum strain energy density. At the same time, the finite element method (FEM)–ANSYS program will be used to calculate stress intensity factors (SIFs), strain energy release rate (J-integral), stress field, displacement near a crack tip, and crack propagation phenomenon based on the above theories. The calculated results were compared with the results in other scientific papers and experimental results. This research used ANSYS program, an experimental method combined with FEM based on the above energy theories to simulate the J-integral, the SIFs, and the crack propagation. The errors of the SIFs of the FGM rectangular plate has a through-thickness center crack of 1.77%, J-integral of 4.49%, and crack propagation angle θc of 0.15%. The FEM gave good errors compared to experimental and exact methods.

This is Part II of a multipart article on a hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress. We introduce an isogeometric discretization method for incompressible materials and present test computations. Accounting for the out-of-plane normal stress distribution in the out-of-plane direction affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the shell. The return is more than what we get from accounting for the out-of-plane deformation mapping. The traction acting on the shell can be specified on the upper and lower surfaces separately. With that, the model is now free from the “midsurface’ location in terms of specifying the traction. In dealing with incompressible materials, we start with an augmented formulation that includes the pressure as a Lagrange multiplier and then eliminate it by using the geometrical representation of the incompressibility constraint. The resulting model is an extended one, in the Kirchhoff–Love category in the degree-of-freedom count, and encompassing all other extensions in the isogeometric subcategory. We include ordered details as a recipe for making the implementation practical. The implementation has two components that will not be obvious but might be critical in boundary integration. The first one is related to the edge-surface moment created by the Kirchhoff–Love assumption. The second one is related to the pressure/traction integrations over all the surfaces of the finite-thickness geometry. The test computations are for dome-shaped inflation of a flat circular shell, rolling of a rectangular plate, pinching of a cylindrical shell, and uniform hydrostatic pressurization of the pinched cylindrical shell. We compute with neo-Hookean and Mooney–Rivlin material models. To understand the effect of the terms added in the extended model, we compare with models that exclude some of those terms.

To gain deeper insight into the effects of unloading normal stress on shear mechanical behaviour, laboratory tests are carried out on the red-sandstone specimens containing a parallel fissure pair under the constant shear stress and the unloading normal stress. The results reveal that the trace of the entire rupture surface is mainly controlled by the rock bridge, and the impacts of the rupture surfaces of the unloading tests are narrower than those of the direct shear tests. Tensile failure, tension–shear failure, shear failure, and two-stage failure are observed, the failure rules of rock bridges are further summarized according to the ranges of the length and inclination of the rock bridge. The shear strength of the normal unloading test has a slight increase compared with that of the direct shear test. With an increase in the initial normal/shear stress, the shear strength of rock specimens increase; under the low to medium initial stress conditions, the shear strength increment has a linear growth tendency, but under the medium to high initial stress conditions, the growth trend slows down. The ratio of shear deformation on rupture surface increases with the increase of the initial shear stress but decreases with the increase of the initial normal stress. The ratio of shear deformation on rupture plane increases with the increase of the initial shear stress, and decreases with the increase of the initial normal stress, There is a little difference in the deformation ratio (shear damage deformation divided by tensile damage deformation, ΔDrs/ΔDrn) between the observed tensile failure and tension–shear failure. The dominate damage deformation under different geometric conditions is closely related to the failure patterns.