A state-based peridynamic model is proposed to simulate the failure mechanisms in porous rocks, using Bentheim sandstone as a specific example. Experimental observations reveal a transition from brittle to ductile failure under increasing triaxial compression. This behavior is attributed to pore compaction. The peridynamic model is enhanced to capture the strain hardening observed in hydrostatic compression experiments and calibrated to reproduce pore-collapse behavior. Rock heterogeneity is incorporated through Weibull-distributed strength parameters, reflecting the stochastic nature of material properties. Simulations of indentation tests for four specimen sizes demonstrate the predictive capability of the model. A qualitative validation is established through acoustic emission data, while a quantitative validation relies on the comparison of numerical force-penetration and indentation pressure-penetration relationships with experimental results. Beyond reproducing macroscopic force responses, the model captures the spatiotemporal evolution of the compaction zone, and an energy-based analysis shows that grain comminution prior to failure contributes significantly to the total energy dissipation.

Hornblende amphibole is difficult to deform plastically in experiments due to its anisotropic nature and breakdown at relatively low temperatures (similar to 850 degrees C). The lack of experimental analysis of hornblende plasticity hampers interpreting the deformation mechanisms of natural samples, which remain unresolved and debated. Here, we used strongly textured amphibolite, oriented for the activation of hornblende's cleavage and/or easy slip system, to investigate the interplay of brittle and plastic deformation mechanisms. Samples with the lineation oriented at 30 degrees to the loading direction were deformed at a confining pressure of 1 GPa, strain rates of 10-5 to 10-4 s-1, and temperatures of 400, 600, and 800 degrees C. Deformed samples exhibit marked tilting of significant subvolumes manifested as kink bands. On the grain scale, deformation is accommodated by fracturing and dislocation mechanisms. A significant decrease in sample strength with temperature is accompanied by an increase in intragrain misorientations due to an increase in dislocation activity. The dominant orientation of the intragrain misorientation axis shifts from [001] at 400 degrees C to [010] at 800 degrees C. Nano-scale analysis revealed that at 800 degrees C, intragrain misorientation occurs through a sequence in which dislocation structures develop first and then act as sites for fracture nucleation. The observed intragrain misorientation is corroborated by an example from the Javanahalli schist belt (India). We conclude that the experimentally observed transition in the dominant intragrain misorientation axis accompanying the transition from fracture to dislocation-mediated deformation can be used to interpret conditions experienced by naturally deformed samples.

Despite hornblende’s widespread occurrence in deformed rocks from exhumed crustal shear zones and metamorphic soles, its dominant deformation mechanism(s) and the respective microstructural fingerprints remain poorly constrained. Several deformation mechanisms have been documented in hornblende, including cataclastic flow, twinning, dissolution–precipitation, and dislocation-mediated deformation. Hornblende’s easy slip system, (100)[001], can be inferred from observations of intragrain misorientation axes (MOA) or crystallographic rotation about the [010] axis (Meher et al., 2026). Notably, even where some contribution from dislocation-mediated deformation is observed, hornblende is rarely deformed solely by dislocation creep. While crystallographic preferred orientation (CPO) and recrystallization suggest dislocation creep for most minerals (e.g., calcite, quartz, and olivine), in hornblende, these features seldom arise from alternative mechanisms.We used electron backscatter diffraction (EBSD) to analyze microstructures in four natural hornblende-rich samples spanning a range of P-T conditions: (1) Mamonia complex, Cyprus (0.5 GPa, ~ 600 °C), comprising mm-scale conjugated kink bands. (2) Koralpe, Austrian Alps (~2.1 GPa, 750 °C), dominated by sigmoidal hornblende porphyroclasts surrounded by smaller, tabular grains. (3) Mayodiya, India (0.78–0.82 GPa, 770–820 °C), containing large grains with high intragrain misorientations and some twinning, and smaller needle-shaped grains with serrated boundaries between large grains. And (4) Koraput, India (0.76–0.84 GPa, 860–883 °C), which exhibits recrystallization of a centimeter-scale porphyroclast with smaller grains with lobate boundaries forming a core–mantle microstructure. By examining both CPO and MOA using detailed EBSD analysis, our goal is to (i) constrain the underlying deformation mechanism in these samples, and (ii) identify temperature-dependent transitions under natural conditions.The Mamonia sample that experienced the lowest deformation temperatures exhibits deformation through fractures and kink bands, with no evidence of recrystallization. However, the MOA cluster is oriented toward [010], consistent with dislocation glide, suggesting semi-brittle deformation (e.g., Meher et al., 2026). The Koralpe sample exhibits a characteristic recrystallization microstructure, strain-free grains around large and highly strained porphyroclasts, and an MOA clustering around [101], which fits the orientation of (-101) twin planes and suggests twinning-driven recrystallization. The Mayodiya sample exhibits elongated recrystallized grains with MOA clustering around [001], while the porphyroclast exhibits MOA toward [010], again indicating twinning-driven recrystallization. The Koraput sample displays recrystallized grains that are slightly rotated compared to the parent porpyroclast with rotation around [010], consistent with hornblende’s easy slip system, (100)[001].We infer that at low P-T conditions, hornblende deforms through semi-brittle deformation. At intermediate temperatures (Koralpe and Mayodiya), twinning-driven recrystallization dominates, activated via the (-101)[101] and (100)[001] twinning systems, respectively. At the highest temperatures (Koraput), hornblende undergoes grain-size reduction via dislocation-driven recrystallization. Together, those samples suggest a temperature-controlled transition from semi-brittle to dislocation creep mediated deformation between < 600 to > 850 °C. Meher, B., Incel, S., Renner, J. and Boneh, Y., 2026. Experimental deformation of textured amphibolites in the semi‐brittle regime: Microstructural signatures of dislocation‐mediated deformation. Journal of Geophysical Research: Solid Earth, 131(1), p.e2025JB031852.

We investigated the usefulness of the fractal diffusion equation, also known as generalized radial flow (GRF) equation, to characterize hydraulic properties and flow dimensions of the subsurface. Unlike other methods for deriving hydraulic properties that require selecting the flow dimension, analyses based on the GRF equation in principle constrain both, flow dimension and hydraulic properties. We utilized the GFR equation to analyze periodic pumping tests carried out in boreholes penetrating gneiss rocks in the research mine Reiche Zeche, Freiberg, Germany. These tests involved one injection borehole, where flow rate and injection pressure were recorded, and four monitoring boreholes, where pressure responses were monitored. Phase-shifts and amplitude ratios were derived through interference analysis, involving a comparison of the periodic signals of injection and monitoring pressure, as well as injectivity analysis, consisting of a comparison of the periodic flow rate and injection pressure. The pumping tests were conducted at three distinct intervals within the injection borehole, isolated by a double-packer probe and selected based on the characteristics of the fractures intersecting the borehole. One interval contained a natural fracture zone characterized by a high fracture density with a high mean aperture. The others were previously hydraulically stimulated. While one of them had a single pre-existing fracture, the other was entirely intact before the stimulation that led to an induced fracture with feather geometry, as typical for a borehole that does not follow a principal stress axis. Several observations suggest that the gneiss volume is hydraulically heterogeneous: a) the hydraulic properties and flow dimensions vary with pumping period; b) estimated diffusivity values and flow dimensions differ for interference and injectivity analyses; c) discernible differences in diffusivity values and flow dimensions along diverse hydraulic paths, as determined by interference analysis. Furthermore, pressure dependence in hydraulic properties and flow dimensions are observed for all intervals. The hydraulic response of the fault-zone interval exhibits a greater sensitivity to variations in mean pumping pressure than the two stimulated intervals.

The viscoelastic complex Poisson’s ratio, which describes the frequency-dependent ratio of transverse and longitudinal strains, can be determined directly from simultaneous strain measurements or indirectly from successively measured complex moduli based on the elastic-viscoelastic correspondence principle (EVCP). There has been considerable debate regarding its definition and measurability, with common but often incorrect analogies to complex moduli and compliances. We investigated cylindrical samples of polymethyl methacrylate (PMMA) and Berea sandstone using different measurement set-ups to compare the two methods. For direct measurement, we used strain gauges in harmonic uniaxial tension and compression tests to measure longitudinal and transversal strains. For the indirect method, we measured the complex Young’s and shear moduli by complementing uniaxial tests with torsion experiments on the same specimen under the same conditions using a torsional-axial rheometer. Our analysis on samples from a single product line showed that both methods yielded consistent values for the absolute value of the complex Poisson’s ratio. However, the direct method provided a more accurate determination of its loss factor. Experimental results confirmed that the loss factor of the complex Poisson’s ratio can be positive or negative, depending on which strain lags more behind the axial force excitation, aligning with theoretical expectations.

Due to contrasting results between laboratory tests, geophysical data, and field observations, the strength of the plagioclase-rich lower continental crust remains a topic of debate. It has been shown that its strength highly depends on the presence of fluids as they trigger metamorphic reactions that can result in permanent weakening. An important metamorphic reaction in the lower continental crust is the breakdown or hydration of plagioclase and the associated growth of epidote-group minerals, kyanite, quartz, and jadeite/albite. To investigate the impact of this particular reaction on the strength of the lower continental crust, we combined experimental work, i.e., Griggs-deformation tests, with extensive microstructural observations of the recovered experimental samples. Experimental conditions were 1 to 1.5 GPa confining pressure, 550 to 950 °C, and for the deformation tests, we used strain rates ranging from 10-6 to 10-5 s-1. Our results reveal two main findings. First, deformed plagioclase aggregates as well as deformed granulite drill cores show that deformation-induced features in plagioclase grains, e.g., cleavage cracks and twin boundaries, act as nucleation sites for metamorphic reactions and melting. Consequently, reaction can progress faster in deformed samples as the effective reactive surface area is increased relative to undeformed counterparts. Second, when deformed under identical experimental conditions, pure epidote aggregates are consistently stronger or show equal strengths than pure plagioclase aggregates. Hence, a partial plagioclase breakdown, i.e., the exclusive growth of epidote-group minerals at low reaction progress, is not expected to result in permanent weakening. This result further strengthens the idea that a process akin to Zener pinning is a viable mechanism to cause long-term weakening in rocks.

Abstract. The DECOVALEX Task SAFENET is dedicated to advancing the understanding of fracture nucleation and evolution processes in crystalline rocks, with applications in nuclear waste management and geothermal reservoir engineering. Further improvements to fracture mechanics models are required in two distinct areas. Firstly, there is a need to enhance numerical methods for fracture mechanics under varying thermo-hydro-mechanical (THM) conditions. Secondly, there is a requirement to develop applied tools for performance and safety assessment in the context of nuclear waste management, as well as for reservoir optimisation in geothermal applications. Building on the achievements of SAFENET, which concentrated on benchmarking fracture models and experimental laboratory analyses, SAFENET-2 is dedicated to extending and validating models from the laboratory to the field scale. This paper gives a detailed description of the SAFENET-2 experimental programme work plan and modelling exercises. The experiments will be carried out at the rock mechanics laboratories of the University of Edinburgh and Chongqing University. For field data, the STIMTEC experiment at the Reiche Zeche teaching and research mine (Technische Universität Bergakademie Freiberg) is used. The individual steps of the Task are described in detail in this paper. As a result of SAFENET, the benchmark suite will be made available as interactive exercises via a web portal, thus promoting the concept of open science. The paper is a tool for teams to organise their work efficiently and is also an overview and insight for the community.

Abstract In natural lower crustal rocks, we observe that plagioclase breakdown is often partial as evidenced by the presence of epidote‐group minerals and the absence of the remaining reaction products for example, kyanite and quartz. Due to the lack of experimental data on epidote deformation, it is unclear if this partial reaction would affect the strength of the plagioclase‐rich lower continental crust. We experimentally investigated the relative strength of pure epidote and pure plagioclase aggregates at a confining pressure of 1 GPa, two different temperatures (550 and 650°C) and two different strain rates (5 × 10−5 and 5 × 10−6 s−1) using a Griggs apparatus. Furthermore, we investigated potential strength differences due to differences in grain size by deforming aggregates with grain‐size ranges of either ≈90–135 μm or <25 μm. Under identical conditions, epidote aggregates are either as strong as their plagioclase counterparts or moderately stronger, suggesting that the partial replacement of plagioclase by epidote‐group minerals would not have a permanent weakening effect on the strength of the lower continental crust.

Previous investigations of rock-cutting tool interaction by normal indentation of rocks were mostly conducted at ambient pressure, a condition not representative of the lateral stresses at the excavation face. Despite recent advances in understanding rock-cutting tool interactions with lateral confinement, working out the details of the relationship between rock fracture due to indentation and confinement still requires experimental investigations and theoretical analyses. We conducted a series of normal indentation tests on samples of Gildehaus Bentheim sandstone at lateral confinement up to 20 MPa using a set-up that allowed us to monitor lateral sample deformation and acoustic-emission activity. Experimental observations show that lateral confinement has a significant effect on the load responses and suppresses sample dilation; furthermore, the propagation path of the macroscopic fracture deviates from the indentation direction as confinement increases. The peak indentation pressure increases with confinement and its occurrence is accompanied by significant dilation and acoustic emission activity indicating that it coincides with initiation of macroscopic tensile fracturing. A cavity-expansion-based theoretical model, that accounts for the increases in compressive strength and fracture toughness with lateral confinement, captures the trend of increasing indentation pressure with lateral confinement. In addition, the good agreement between theoretical predictions and experimental data indicates that lateral confinement promotes the growth of the damage zone under the indenter preceding potential macroscopic tensile failure. The model correlates thrust required to break rocks in-situ with rock strength parameters, tool shape parameters, and lateral confinement, thus providing a starting point for optimizing the design of cutting tools.

Hydraulic Data from pumping tests, i.e., injection and production, and pressure monitoring in various boreholes drilled in Reiche Zeche (Freiberg, Germany) during the projects STIMTEC and STIMTEC-X

Hydro-mechanically induced transient changes in fracture volume elude an analysis of pressure and flow rate transients by conventional diffusion-based models. We used a previously developed fully coupled, inherently non-linear numerical simulation model to demonstrate that harmonic hydraulic excitation of fractures leads to systematic overtones in the response spectrum that can thus be used as a diagnostic criterion for hydro-mechanical interaction. The examination of response spectra, obtained from harmonic testing at four different field sites, for the occurrence of overtones confirmed their potential for the hydro-mechanical characterization of tested reservoirs. A non-dimensional analysis identified relative aperture change as the critical system parameter.

Dilatometer measurements from various of the boreholes in Reiche Zeche (Freiberg, Germany) during the projects STIMTEC and STIMTEC-X

&lt;p&gt;In the plagioclase-rich lower continental crust, hydrous epidote-group minerals will, among other phases, replace plagioclase in the presence of minor amounts of fluids. It has previously been shown that this reaction has a significant impact on the strength of plagioclase aggregates, with reacting aggregates being much weaker than their unreacted counterparts (St&amp;#252;nitz and Tullis, 2001). Hence, reactions taking place in the lower continental crust may have a strong influence on its deformation behaviour and thus on its strength. Yet, it still remains unclear if the observed weakening is due to the nucleation and growth of inherently weaker product phases, e.g., epidote-group minerals, or due to inhibited grain growth in a polyphase aggregate as a result of Zener pinning. We experimentally investigated the relative strength of pure epidote and pure plagioclase aggregates at a confining pressure of 1 GPa, two different temperatures (550 and 650 &amp;#176;C) and two different strain rates (5&amp;#183;10&lt;sup&gt;-5&lt;/sup&gt; and 5&amp;#183;10&lt;sup&gt;-6&lt;/sup&gt; s&lt;sup&gt;-1&lt;/sup&gt;) using a solid-medium Griggs-deformation apparatus. Furthermore, we also investigated potential strength differences due to differences in grain size by deforming aggregates with a grain-size range of either 90-135 &amp;#956;m or &lt;25 &amp;#956;m. After deformation under 650 &amp;#176;C, the epidote aggregates reveal the nucleation and growth of new phases indicating that epidote was no longer stable. The amount of product phases found in the epidote aggregates scales with the duration of deformation. At the explored experimental conditions, the compressive strength of plagioclase and epidote aggregates depends on temperature and strain rate with a decrease in strength with an increase in temperature or a decrease in strain rate. At identical conditions, the epidote aggregates are either significantly stronger or show a similar strength as the plagioclase aggregates. Microstructural analyses of the recovered samples reveal that deformation in both aggregates was almost exclusively accommodated by grain fracturing and occasionally slip along cleavage planes, and remained non-localized except for the epidote aggregate deformed at 650 &amp;#176;C with a strain rate of 5&amp;#183;10&lt;sup&gt;-6&lt;/sup&gt; s&lt;sup&gt;-1&lt;/sup&gt;, exhibiting kinetically-controlled faulting due to reaction.&lt;/p&gt; &lt;p&gt;&amp;#160;&lt;/p&gt; &lt;p&gt;St&amp;#252;nitz, H. and Tullis, J. (2001). Weakening and strain localization produced by syn-deformational reaction of&lt;br /&gt;plagioclase. International Journal of Earth Sciences, 90(1):136{148.&lt;/p&gt;

Clock documentation to synchronize hydraulic measuring systems, and the seismic and hydraulic measuring systems used in projects STIMTEC and STIMTEC-X (Freiberg, Germany)

ABSTRACT Stress tensor determination is of importance in many aspects of geothermal energy provision, from the understanding of the propagation orientation of newly created fractures to the control of the pre-dominant stimulation mechanism, hydro-fracturing vs. hydro-shearing. Hydraulic stimulation experiments were carried out in the research mine Reiche Zeche in Freiberg, Germany, in the framework of the STIMTEC and STIMTEC-X projects. Key objectives were to characterize the stress field of the rock volume and evaluate and enhance hydraulic properties. Injection tests were performed in 28 intervals with 0.7 m length enclosed by a double-packer probe, either with pre-existing fractures or initially intact, in 7 boreholes crisscrossing a rock volume of 60×30×30 m3. The data from the injection experiments typically used to determine components of the stress tensor comprise shut-in and jacking pressures, and the orientation of the pressurized fractures. Impression packer testing and acoustic televiewer logging revealed multiple fracture traces for a number of intervals, and thus we face ambiguity regarding the hydraulically relevant fractures. In total, the data set comprises 28 characteristic pressures assumed to correspond to the normal stress on a fracture, but in total 60 fracture traces were detected with a maximum of four fractures in a single interval. The uncertainty in the association of the characteristic pressure with a fracture trace and the fact that a unique stress tensor cannot explain all the observed data, i.e., the stress field is heterogeneous, motivated a Monte Carlo analysis to characterize the stress field in the rock volume. We randomly select subgroups of 5 out of the tested intervals, with one fracture trace randomly selected out of the observed traces for each interval, and then determine the misfit between observed characteristic pressures and the normal stress on the selected fracture trace associated with randomly selected stress parameters. Selecting 5 intervals in principle sufficed to invert the stress field, since we constrained the vertical stress by the known overburden. The total number of combinations of intervals and fracture traces precludes a systematic stress-parameter determination. The Monte Carlo approach allows us to statistically investigate the role of each particular interval and fracture trace for stress magnitude and stress regime.

Foils and orientation information from impression packer testing performed in the projects STIMTEC and STIMTEC-X in various boreholes located in Reiche Zeche (Freiberg, Germany)

AbstractThe mechanized tunnel construction is carried out by tunnel boring machines, in which the soil in front of the working face is removed, and the tunnel lining is carried out with shotcrete or the setting of segments and their back injection. Advancements in this field aim towards increase of the excavation efficiency and increase of the tool lifetime, especially in rock-dominated grounds. The latter is achieved by understanding the wear mechanisms abrasion and surface-fatigue, and by knowledge of the microstructure-property relation of the utilized materials. Improvements for tool concepts are derived, based on experiments and simulations. A key parameter towards efficient rock excavation is the shape of the cutting edge of the utilized disc cutters. Sharp cutting edges have proven to generate higher rock excavation rates compared to blunt ones. The compressive strength of the utilized steel has to be high, to inhibit plastic deformation and thereby to maintain sharp cutting edges. This requirement competes with the demand for toughness, which is necessary to avoid crack-growth in the case of cyclic loading. Solutions for this contradiction lie in specially designed multiphase microstructures, containing both hard particles and ductile microstructural constituents. Besides adapting the alloying concept, these required microstructures and the associated properties can be adjusted by specific heat-treatments.

Many geoscientific problems require us to exploit synergies of experimental and numerical approaches, which in turn lead to questions regarding the significance of experimental details for validation of numerical codes. We report results of an interlaboratory comparison regarding experimental determination of mechanical and hydraulic properties of samples from five rock types, three sandstone varieties with porosities ranging from 5% to 20%, a marble, and a granite. The objective of this study was to build confidence in the participating laboratories’ testing approaches and to establish tractable standards for several physical properties of rocks. We addressed the issue of sample-to-sample variability by investigating the variability of basic physical properties of samples of a particular rock type and by performing repeat tests. Compressive strength of the different rock types spans an order of magnitude and shows close agreement between the laboratories. However, differences among stress–strain relations indicate that the external measurement of axial displacement and the determination of system stiffness require special attention, apparently more so than the external load measurement. Furthermore, post-failure behavior seems to exhibit some machine-dependence. The different methods used for the determination of hydraulic permeability, covering six orders of magnitude for the sample suite, yield differences in absolute values and pressure dependence for some rocks but not for others. The origin of the differences in permeability, in no case exceeding an order of magnitude, correlate with the compressive strength and potentially reflect a convolution of end plug–sample interaction, sample-to-sample variability, heterogeneity on sample scale, and/or anisotropy, the last two aspects are notably not accounted for by the applied evaluation procedures. Our study provides an extensive data set apt for “benchmarking” considerations, be it regarding new laboratory equipment or numerical modeling approaches.

Fractures can significantly impact fluid flow and pore pressure distribution in the subsurface. Understanding the mechanisms and conditions influencing their ability to transport fluids and to promote pore pressure diffusion is key for many activities relying on fracture-controlled flow such as, for example, enhanced geothermal systems. In situ characterization of these properties is typically done by performing hydraulic tests in selected intervals of a borehole and their interpretation relies on the solution of a linear pressure diffusion equation. However, it has been shown that the hydraulic behavior of fractures as well as the associated near borehole flow regimes can be largely affected by the coupling between the solid deformation and fluid pressure upon injection/production. In this work, we explore these effects by performing a series of harmonic injection tests (HIT) as well as non-harmonic production tests (NHPT) in a packed-off interval of a borehole containing multiple natural fractures. The borehole is located in the Bedretto Underground Laboratory for Geosciences and Geoenergies in Switzerland and penetrates granitic rock mass. The two kinds of tests consist of a periodic repetition of the same injection or production protocol. Flow rates, interval pressures as well as pressures above and below the double-packer probe are recorded at the surface. An important advantage of periodic testing is that it permits a continuous tracking of hydraulic changes during the test. For our study, we conducted a so-called injectivity analysis, in which the phase-shift (time delay) and amplitude ratio between flow rate and interval pressure are used to infer effective hydraulic properties. We performed over 200 periodic tests including both HIT and NHPT with a large range of periods (7.5 s to 1800 s) as well as varying mean interval pressures (~1300 kPa to 2100 kPa) and flow oscillation amplitudes. As a result, we obtained a robust constraint of the radial flow regime prevailing in the fractures. Overall, we found that results from HIT and NHPT are in very good agreement despite the remarkably different injection protocols. For all cases, a prominent and consistent period dependence of phase shifts and amplitude ratios of flow rates and interval pressure was observed, in which both increase as the oscillatory period decreases. Amplitude ratios showed almost no variation with mean interval pressure regardless of the injection protocol. In contrast, a prominent pressure dependence of the phase shifts is captured by the HIT but not the NHPT data. Using the pressure-independent NHPT results, we reconstruct the general hydraulic response of the tested fractured section, which can be well represented by an analytical solution of the pressure-diffusion equation. This general trend explains the HIT data as well, although evidence of significant variations that are correlated with the amplitude of the pressure oscillations points to the predominant role of hydromechanical coupling effects on the fluid pressure diffusion process.