The Anisotropic Behavior of a Clay Shale: Strength, Hydro‐Mechanical Couplings and Failure Processes

Many rocks exhibit a structural composition, which leads to an anisotropic behavior of different properties. A proper understanding of the directional dependency of these properties is required to analyze and predict the failure behavior of the rock mass upon stress changes during many geo‐engineering applications. This study investigates the selected host rock for nuclear waste disposal in Switzerland, Opalinus Clay, for its anisotropic unconfined compressive and tensile strength, poromechanical response, and effective shear strength in an extensive laboratory testing campaign. The results show the lowest unconfined compressive strength at angles of 30°–45° between the bedding plane and the compressive load direction, whereby the lowest tensile strength is found to be normal to the bedding orientation. Triaxial consolidated‐undrained compression tests reveal an anisotropic poromechanical behavior as well as peak and residual effective strength values, which are largely controlled by the orientation of the bedding plane with respect to the maximum principal stress. The magnitude of excess pore water pressures and dilation are both functions of loading configuration. The comparison of peak strength values for different loading angles indicates that the lowest effective shear strength can be expected at a loading configuration of approximately 45° between bedding orientation and the loading axis. The variation in the hydro‐mechanical response is associated with the microstructure controlling the poroelasticity and the failure processes. The results provide a deeper understanding of failure in anisotropic rocks contributing to the development of constitutive models for predicting the rock mass response.


Introduction
Anisotropic rocks and geomaterials are ubiquitous in the Earth's subsurface and play an important role in geo-engineering applications such as mining, underground excavations, deep well drilling, and the construction of repositories for nuclear waste (Amadei, 1996).For the latter application, it is especially important to describe the anisotropic hydro-mechanical behavior of the rock mass during and after the tunnel excavation to make predictions of the geological barrier integrity.Clay shales and similar clay-rich rocks are considered suitable host rocks for the storage of nuclear waste in deep underground repositories (e.g., Andra, 2005;Bossart et al., 2018;Nagra, 2002;ONDRAF/NIRAS, 2001).Favorable characteristics are the low permeability, the self-sealing potential of fractures, and the radionuclide retention ability.However, these rock types show a complex hydro-mechanical behavior, which often requires the integration of both soil and rock mechanical concepts to properly describe their constitutive behavior.
Abstract Many rocks exhibit a structural composition, which leads to an anisotropic behavior of different properties.A proper understanding of the directional dependency of these properties is required to analyze and predict the failure behavior of the rock mass upon stress changes during many geo-engineering applications.This study investigates the selected host rock for nuclear waste disposal in Switzerland, Opalinus Clay, for its anisotropic unconfined compressive and tensile strength, poromechanical response, and effective shear strength in an extensive laboratory testing campaign.The results show the lowest unconfined compressive strength at angles of 30°-45° between the bedding plane and the compressive load direction, whereby the lowest tensile strength is found to be normal to the bedding orientation.Triaxial consolidated-undrained compression tests reveal an anisotropic poromechanical behavior as well as peak and residual effective strength values, which are largely controlled by the orientation of the bedding plane with respect to the maximum principal stress.The magnitude of excess pore water pressures and dilation are both functions of loading configuration.The comparison of peak strength values for different loading angles indicates that the lowest effective shear strength can be expected at a loading configuration of approximately 45° between bedding orientation and the loading axis.The variation in the hydro-mechanical response is associated with the microstructure controlling the poroelasticity and the failure processes.The results provide a deeper understanding of failure in anisotropic rocks contributing to the development of constitutive models for predicting the rock mass response.

Plain Language Summary
The structural composition of many rocks, governed by the arrangement of grains and pores, often creates an anisotropy influencing the mechanical, hydraulic, and hydro-mechanical properties.For different geo-engineering applications, a proper knowledge of these properties with respect to the structural anisotropy is very important to understand and predict the response of rock masses due to changing stress conditions.The Opalinus Clay formation is the selected host rock for nuclear waste disposal in Switzerland and the subject of this study is to determine the directional dependency of elasticity, strength, poromechanical and failure behavior through a variety of experimental laboratory tests.The results show that the lowest unconfined and confined compressive shear strength is found for angles of 30°-45° between the plane of isotropy and the compressive load direction.The least stress is required for failure in tension applied normal to the anisotropy plane.In triaxial tests under undrained conditions and for different loading angles, the effective stress change during load application shows significant differences indicating different amounts of dilation which is supported by the analysis of deformation zones in the failed specimens on the microscale.WINHAUSEN ET AL.The high clay mineral content and associated phenomena like swelling or shrinkage processes at different saturation stages, potential chemical changes with aqueous solutions, and the pronounced microstructural fabric pose challenges in describing the physical behavior of such rocks.The (micro-)structural composition is expressed by different causes such as layered sequences of slightly different mineralogical composition and/or the preferred orientation of mineral grains and aggregates.This superposition leads to a distinct structural anisotropy, that is, in the case of shales and other sedimentary rocks, the bedding plane.The high amount of clay minerals of up to 60% and their morphological appearance with elongated platelets as well as the sometimes considerable amount of physical compaction during burial create anisotropy.More specifically, sedimentary rocks exhibit transversal isotropy which means that hydraulic and mechanical properties, for example, permeability coefficients and elastic constants, respectively, are considered equal parallel to the bedding plane but unequal to those normal to the bedding plane.
Most of the above-mentioned studies either performed unconsolidated-undrained tests (UU-tests), where effective stresses remain unknown, or they focused on the end-member loading configurations, where the maximum load is applied either parallel or normal to the plane of isotropy.This is, however, insufficient for describing the complete hydro-mechanical behavior in terms of all loading configurations expressed by the angle between maximum principal stress and the bedding plane orientation.In particular, for the purpose of describing the in-situ rock mass response around a repository tunnel and predicting the development of an excavation-induced damage zone, the hydro-mechanical behavior of all loading configurations is important as most angles lie between the end-member types of 0° and 90°.Furthermore, the poromechanical response, that is, compaction or dilation, and associated pore pressure developments are of great interest as they influence the rock mass stability around the excavation.Conceptually, tangential stresses (σ Θ ) and radial stresses (σ r ) are assumed to be maximum and minimum, respectively, very close to the tunnel circumference and, hence, the maximum (tangential) compressive load is applied either parallel (P-configuration), normal (S-configuration) or at any angle in between (Z-configuration) to the plane of isotropy.This study provides an in-depth analysis of the influence of structural anisotropy on the strength, hydro-mechanical couplings, and failure behavior of Opalinus Clay (OPA).This clay shale has been selected as the host rock formation for nuclear waste disposal in Switzerland.Numerous experimental studies described the mechanical and hydro-mechanical behavior of OPA, which can be attributed to characteristics typical for brittle rocks and stiff soils (Amann et al., 2018, and references therein).In most of these studies, the maximum and minimum load were applied either parallel or normal to the bedding plane orientation for both uniaxial (Amann et al., 2011;Bock, 2001;Wild et al., 2015) and triaxial compression (Favero et al., 2018;Minardi et al., 2021;Wild & Amann, 2018a, 2018b) as well as tensile strength testing (Wild et al., 2015).It was found that the pronounced bedding governs the anisotropy in elasticity, dilatancy, and strength.Furthermore, experimental and numerical investigations on fracture mechanics demonstrated the strong influence of the structural anisotropy on fracture propagation for OPA (Morgan & Einstein, 2017;Nejati et al., 2020).However, only limited research was conducted on intermediate loading configurations, which usually included only a single intermediate loading angle (Lozovyi & Bauer, 2019;Naumann et al., 2007;Schuster et al., 2021).Additionally, in most of these studies, the effective hydromechanical properties of OPA have not been determined either.Hence, a thorough and complete investigation in terms of multiple loading configurations of the hydro-mechanical, transversely-isotropic behavior of OPA is missing to date.
In this contribution, we attempt to investigate the influence of anisotropy in a systematic way through an extensive laboratory testing campaign.This is preceded by both unconfined compressive and indirect tensile strength tests and extended by undrained triaxial compression tests of fully-saturated specimens, revealing the anisotropic hydro-mechanical behavior of OPA.The analyses of failure processes and mechanisms are supported 10.1029/2023JB027382 3 of 23 by microstructural post-experimental inspections of deformed specimens using broad ion-beam polishing and scanning electron microscopy (BIB-SEM).

Material Description
The shale under investigation in this study is the Jurassic formation Opalinus Clay sampled from the Mont Terri underground research laboratory (MT-URL) in Switzerland.Three different lithofacies are encountered in the URL (Lauper et al., 2018, and references therein) differentiated by their mineralogy, whereas here only the shaly facies was used as sample material.Shaly OPA is a dark-gray colored and, on a macro-and mesoscale ranging from cm to mm, relatively homogeneous clay shale.Its structural fabric consisting of a fine-grained layered matrix with occasional encounters of mm-sized embedded calcite and iron-rich clasts (Figures 1a and 1b).On the microscale, the matrix appears as an accumulation of different minerals of very small grain sizes dominated by clay minerals, with considerable amounts of quartz and calcite grains as well as some accessory contributions of iron-rich minerals such as pyrite and siderite, and organic matter components (Figure 1c).The calcite mineral phase is also present in form of fossil fragments.Our petrographic description based on SEM-images is in agreement with quantitative mineralogical X-ray diffraction analysis presenting a composition with 58-76 wt% clay minerals, 5-28 wt% calcite, 6-24 wt% quartz followed by minor amounts of accessory minerals named above plus some dolomite/ankerite, K-feldspar and albite (Pearson et al., 2003).
The transversely isotropic nature is due to the preferred alignment of elongated calcite and clay-minerals (Wenk et al., 2008) in response to sedimentation, compaction, and diagenesis along the burial history of the shallow marine fine sediments (e.g., Potter et al., 2012).Furthermore, BIB-SEM analyses showed that the pore geometry shows a directional dependence displayed by the preferred orientation (sub-)parallel to the bedding orientation in particular in the clay matrix (Houben et al., 2013;Keller et al., 2013).The reconstructed 3D pore space based on focused ion beam nanotomography confirms the preferred alignment and also leads to an anisotropic pore space connectivity due to a "higher pore path density, lower geometric pore path tortuosity and longer pore paths within the bedding plane" (Keller et al., 2013).The shaly facies is characterized by a porosity ranging between 15% and 20% (e.g., Minardi et al., 2021;Wild & Amann, 2018a;Winhausen et al., 2021a) depending on sample preservation and measurement technique (Busch et al., 2017).Governed by the preferred orientation of pores along the bedding plane, the hydraulic conductivity is directional-dependent with differences by two orders of magnitude between 1E−12 m/s and 1E−14 m/s parallel and normal to the plane of isotropy, respectively (Marschall et al., 2004).Laboratory studies using various different techniques to determine the permeability coefficients confirm the given range (Al Reda et al., 2020;Winhausen et al., 2021a;Yu et al., 2018).

Sampling and Specimen Preparation
Opalinus Clay specimens were prepared from 101-mm-diameter cores extracted from the MT-URL from the shaly facies by triple-tube core barrel drilling and compressed air flushing.Subsequently, the cores were hermetically sealed in vacuum-conditioned foils.Specimen preparation was conducted under dry conditions by coring the 101-mm drill cores using a diamond-equipped core bit drilling machine (Cardi T2 220-EL) operating at 520 rotations/min at a manually-controlled feed rate and compressed air flushing at 150 kPa.Cutting of end faces and ensuring surface parallelism was achieved by using an electronically controlled cutting machine (Dramet BS230 XY) using a diamond-equipped band saw blade operating with a band speed of 1,200 m/min and automatically-controlled feed-rate of 4 mm/min.End caps of the specimens were used for determining the water content of the specimens during preparation.The drilling and cutting process was performed within 20-30 min to minimize the environmental exposure time.

Specimen Storage Under Controlled Environmental Conditions
Prior to the experiments, the samples were stored in boxes of controlled relative humidity (RH) and temperature to achieve well-defined saturation degrees and associated suction pressures.In case of the specimens used for the rock mechanical strength tests, that is, uniaxial compressive and indirect tensile strength tests, the temperature was controlled by a climate chamber maintaining constant temperatures of 30°C.The specimens used for the triaxial tests were mainly tested right after specimen preparation or stored at room temperature conditions of approximately 20°C for a couple of days only.The RH in the storage boxes was maintained by placing containers with super-saturated salt solutions.KNO 3 -and KCl-salts were used to achieve RH values of approximately 92% and 84%, respectively (Rockland, 1960).The choice of using these salts and the respective relative humidities was based on a consideration between a high saturation degree, resembling in-situ conditions, on one hand, and a reduced swelling (damage) potential, on the other hand.Monitoring of temperature and humidity was performed by DHT22 sensors (accuracy of ±0.5°C and ±2%, resolution of 0.1°C and 1%, respectively), which were installed in each box.The specimen saturation Sr was calculated according to Equation 1: where w is the water content in wt%, ρ d is dry density in g/cm 3 , ϕ is the porosity in %, and ρ w the density of water in g/cm 3 at 30°C.The water content after specimen preparation (w prep ) and prior to testing (w test ) and related saturation values were derived from the weight of the specimens after oven-drying at 105°C from at least 4-5 days to constant weight (Franklin, 1979).Porosity values were calculated from dry and grain density values, whereas the latter has been taken as an average of 2.7 kg/m 3 (Busch et al., 2017;Keller & Giger, 2019;Pearson et al., 2003).Suction pressures were calculated based on Kelvin's relationship using Equation 2: where ψ is the suction in Pa, R the ideal gas constant in J/mol/K, T the temperature in K, V w the specific volume of water in m 3 /kg, M w the molecular mass of water in kg/mol.The ratio of p, the vapor pressure of water in the system in MPa, and p 0 , the vapor pressure of pure water in MPa, is equivalent to the RH of the system and can also be taken as the saturation after water content equilibration of the specimens.
Table 1 presents the petrophysical results including the average values of water content, porosity, and saturation of the specimens after preparation and prior to testing.Porosity values were in agreement with literature values in the range between 15% and 17% (e.g., Minardi et al., 2021;Wild et al., 2017).The high degree of initial saturation demonstrates excellent conditions of the core sample material.Saturation values exceeding 100% were associated with differences in the grain density for which an average literature value was taken.On average, the storage time for the specimens exposed to controlled RH environments ranged from 30 to 72 days.For the majority of specimens, the saturation and associated suction values are in good agreement with the theoretical ones (Table 1), which confirms the storage time required for the specimens to equilibrate under controlled environmental conditions.
Specimens used for tensile testing, however, showed a difference of 12% between the (theoretical) RH and the average saturation degree calculated from the specimens' water content.This discrepancy is either associated with the dissipation of water vapor out of the box as a result of leakage or the salt solution not being supersaturated.

Rock Mechanical Strength Tests
For the uniaxial compressive strength (UCS) tests, 56 specimens were prepared with an average length and diameter of approximately 60 and 30 mm, respectively, to yield a height-to-diameter ratio of 2:1.For the Brazilian tensile strength (BTS) tests, in total 40 specimens were prepared with diameters and thicknesses of approximately 30 and 15 mm, respectively.To capture the strength anisotropy, specimens were prepared with different orientations with respect to the bedding plane orientation in steps of 15° between the bedding plane to the sample's axis and loading direction, respectively (Figure 2).Specimens prepared with long axis parallel (90°) and normal (0°) to the bedding plane orientation were denoted as P-and S-specimens, respectively, whereas all remaining angles were defined as Z-specimens.
The uniaxial compressive and BTS tests were performed using a ZwickRoell 100 kN testing machine.For the UCS tests, different test settings were performed under different displacement rates.Past studies on Opalinus Clay revealed different failure strains between P-and S-loading directions, and for equal loading rates, different  times to failure can be associated.To investigate this aspect and to reveal the influence of specimens' exposure to ambient laboratory conditions, and possible desiccation during the time of testing, different experiment procedures were applied.Three main testing series (Table 1) were performed: (a) at a constant displacement rate of 0.03 mm/min, (b) at various displacement rates aiming for specimen failure within 20 min, and (c) at a constant displacement rate of 0.1 mm/min.The linear portion of the axial stress-axial strain curve was taken for the determination of the Young's modulus by linear fitting.Tests were performed until a major stress drop was detected.For the BTS tests, a constant loading rate of 0.6 kN/min was chosen.The maximum load during each test was used to determine the indirect tensile strength (σ t ) according to the suggested method (Bieniawski & Hawkes, 1978) using Equation 3: where F max is the maximum load in N, d and l are the specimen's diameter and thickness in m, respectively.After each test, the deformation structures, that is, fractures and/or failure surface, were inspected and photographed.

Consolidated, Undrained Triaxial Compression Tests
For the triaxial compressive strength tests (TRX), specimens with similar dimensions as those of the UCS test were used.For two specimens prepared, the bedding plane orientation deviated slightly from the angle intended (see Table 3).The tests were conducted under fully-saturated, consolidated-undrained conditions (CU tests) at different effective consolidation stresses of 4, 5, and 10 MPa (Table 1).We define the effective stress (σ′) after Terzaghi as the total stress (σ) minus the pore water pressure (u) and assume the Biot effective stress coefficient to be 1.
The tests were performed using a triaxial cell (GL TestSystems) connected to a confining pressure pump with a maximum capacity of 30 MPa.The cell is placed under a 100 kN axial load frame operated by a 14 kHz digital feedback controller (Walter&Bai).Pore water pressure was monitored by two relative pressure transducers at the top and bottom of the specimen.For equal drainage along the surfaces, a porous sintered steel plate was placed on each specimen's end face.Back-pressure saturation was conducted using a pump with a maximum capacity of 10 MPa containing artificial pore water prepared after Mäder (2011) which resembles the natural pore water chemistry at the MT-URL.An internal load cell and the strain measurement system were placed close to or on the specimen to prevent a correction for machine compliance or friction.For measuring axial displacements, three linear variable differential transformers were installed next to the sample inside the pressure cell.The radial displacement was measured using a diametral extensometer, which was in contact with the sample via steel plugs embedded in the specimen jacket.The entire experimental setup is located in a climate chamber maintaining a constant temperature of 30°C to avoid any influence on the, in particular, pore water pressure measurements.A graphical representation of the setup can be found in Winhausen et al. (2022).
The experimental procedure consists of a saturation phase, a phase for verifying the saturation (B-check), a consolidation phase, and a shearing phase very similar to those described in Wild et al. (2017).The initial saturation phase was performed by applying a total, isostatic (confining) stress (σ) of 1.0 MPa and a pore water pressure (u) of 0.3 MPa.While the poroelastic effect and also the hydration of clay minerals would lead to swelling, the confining stress was increased from 1.0 MPa in such a way that it counteracts the volume increase of the specimen.Therefore, the confining pressure was increased to suppress any expansion of the specimen normal to the bedding plane orientation, for which the swelling strains are considered highest.For a P-specimen as an example, the radial displacement normal to the bedding plane was actively kept constant by the control system while increasing confining pressure.The initial saturation was completed when the total confining stress was equilibrated and subsequently, the specimen was subjected to several saturation checks.Therefore, the total stress was increased by steps of 0.5 MPa under undrained conditions and the Skempton B-value (Skempton, 1954) was calculated according to Equation 4 once the pore water pressure was equilibrated to a constant level.
Afterward, the pore water pressure was increased to fulfill the case for B equals unity to maintain a constant effective stress during saturation.If two successive B-values changed not more than 0.05, the specimen was considered saturated.During the consolidation stage, the total confining stress and pore water pressure were increased by ramp loading to the desired consolidation stress.The loading rate was dependent on the specimen configuration and ranged from 5 hr for P-specimens to 15 hr for S-specimens.Once strains and the back flow of the pore water pressure from the specimen were equilibrated, the specimen was considered consolidated.The time for consolidation ranged between 1 and 2 days for P-and similar configurations, and more than 20 days for S-and similar configurations.Since the effective stress exceeded the desired effective consolidation stress of 4 MPa in one test (OPA-Z60-5), this specimen was consolidated to 5 MPa effective stress.Finally, the shearing phase was performed by increasing the axial load based on a constant strain rate ranging from 5E−07 to 5E−08 s −1 depending on the specimen configuration (Table 3).Theoretical considerations on the application of sufficiently small strain rates for uniform pore pressure distribution within the specimen are based on the time for pore water pressure to equalize depending on the drainage conditions, the specimen's dimensions, and the coefficient of consolidation (Blight, 1963).Accordingly, strain rates should be applied considering the estimated time to failure in combination with the strain at failure.Due to the ramp loading in the initial consolidation stage and the resulting time-delayed consolidation-settlement curves, the consolidation coefficients were taken from literature ranging from 0.03 to 0.1 mm 2 /s and from 0.003 to 0.006 mm 2 /s for P-and S-specimens, respectively (Crisci et al., 2019;Ferrari et al., 2016;Giger et al., 2018;Minardi et al., 2021).Considering axial failure strains between 1.0% and 2.0%, axial strain rates for the end-member loading configurations were estimated to lie in the range of 6.9E−07 s −1 and 5.6E−08 s −1 , respectively for P-and S-specimens.The strain rates applied in our study were chosen to be slightly lower than the calculated values and are in agreement with those applied in similar experimental studies on OPA (Favero et al., 2018;Giger et al., 2018;Minardi et al., 2021;Wild & Amann, 2018a;Wild et al., 2017).So far, no CU-triaxial compression tests have been reported for intermediate loading angles.Therefore, we assumed intermediate strain rates analogous to expected intermediate coefficients of consolidation, that is, coefficients greater than those for S-specimens and smaller than those for P-specimens.Differential shearing was conducted until the specimens reached constant effective stress levels in the post-peak phase.The experimental time for one test including all the above-described steps lasted between 8 and 45 days for P-and S-specimens, respectively.
We determined the elastic parameters from the axial stress-axial strain response by calculating both the tangent Young's modulus E t and the secant Young's modulus E s incrementally over the loading path and at 50% of the peak differential stress.

Microstructural Analysis
The structural analysis included both macroscopic observations on the cm-to mm-scale using high-resolution photography and microstructure inspections using a scanning electron microscope (SEM) on the mm-to μm-scale.After the specimens were dried, they were covered and stabilized by epoxy resin.Thereafter, the specimens were dry-cut into two halves normal to the shear zone plane and manually polished using SiC grinding papers down to P2000 grade.These surfaces were photographed and regions of interest were selected for high-resolution SEM-imaging.The subsamples were subjected to broad-ion-beam milling using a Leica TiC3X machine.Three ion-guns operated at 3 and 6 kV polished the surface of the sample, which was installed on a rotary stage and positioned at different incident angles of 4.5° and 10.5° (for more details see Winhausen et al., 2022).Imaging was performed on a Zeiss Supra-55 electron microscope equipped using a secondary electron detector and back-scattered electron detector.

Uniaxial Compressive and Indirect Tensile Strength
The results of UCS tests showed a clear dependency on the loading direction toward bedding angle orientation (Figure 3).The comparison of axial stress-axial strain curve for different loading orientations presents an anisotropy in elasticity, strength, and accumulated strain at failure (Figure 3a, Table 2).All loading configurations were characterized by an initial phase of non-linear compaction followed by a linear axial compaction until a final stress drop.Loading orientations of 60° and 45° accumulated the least axial shortening before failure.The highest strength values were observed where the bedding was orientated normal to the loading direction, S-specimen configuration (see Figure 3b).The second end-member orientation, P-specimen configuration, showed strength values about 10%-15% below those of S-specimens.The lowest strength was observed for samples oriented at 45° toward the loading direction except for one testing series for suction values of 23 MPa (Figure 3b), where the minimum strength was observed for the orientation of 60°.According to Ramamurthy (1993), the anisotropy ratio R 0 , expressed as maximum strength over minimum strength, yields values of approximately 3.2-3.4for suction values around 23-24 MPa and 6.0 for suction values of approximately 10 MPa, which classifies OPA as a medium to highly anisotropic rock.No significant differences in terms of strength and stiffness were observed for the different loading rates applied.
Specimens at higher suction values of approximately 23 MPa showed for different loading orientations in the range of 3.2-4.7 MPa higher UCS values in comparison to specimens with suction pressures of approximately 10 MPa (Figure 3b) with the exception for the 30°-specimen configuration.The influence of bedding inclination on the elastic modulus is presented in Figure 3c where the tangential Young's modulus is shown.Stiffness is highest for the P-specimens (E ‖ ) and lowest for the S-specimens (E ⊥ ), resulting in an elasticity ratio of approximately 4.8 for suctions of approximately 10 MPa and 3.2 to 3.8 for suctions in the range of approximately 23-24 MPa.Elastic constants between the end-member configurations show an S-shaped curve.Similar to strength, elasticity is reduced with lower suction values.
For suction pressures of approximately 47 MPa, indirect tensile strength values determined from the Brazilian tests were observed to be highest for the normal-to-bedding orientation (90°-specimen configuration) and lowest for the parallel-to-bedding orientation (0°-specimen configuration, Figure 4).Strength values in-between followed an S-shaped curve constrained by 1.1 MPa for tensile strength normal to the bedding orientation and 2.55 MPa for indirect tensile strength parallel to the bedding orientation.We denote the strength values obtained in this study as apparent indirect tensile strength since failure deviated from failure requirements for the calculation of tensile strength in Brazilian tests (see discussion section).

Effective Geomechanical Properties
For the complete analysis of anisotropy, we included two experiments (OPA-P-4 and OPA-P-10) first presented by Winhausen et al. (2022) but performed new data analyses on these tests.All tests have been performed using the same triaxial machine and the same experimental protocol and are thus comparable.
From macroscopic observations on prepared specimens, which were resin-stabilized, cut, and polished (Figure 9), it became apparent that the bedding orientation deviated slightly from those aimed for according to Figure 3.These discrepancies can either be related to the difficulties of determining the bedding orientation during specimen preparation or these angles can be artifacts due to the apparent dip angle if cutting is not entirely normal to the bedding plane and shear plane orientation, respectively.Therefore, two specimen orientations (Z37-4 MPa and Z25-10 MPa) had been corrected according to the structural mapping (Figure 9), which showed deviations of 7° and 5° from the intended angles.
In the following, we present our results in terms of differential stress (q) and mean effective stress  ( ′  ) according to Equation 5.
Figure 5 shows the differential stress and excess pore water pressure during undrained shearing for specimens with different bedding orientations.All loading orientations showed a pronounced non-linear response of stress and excess pore water pressure with increasing axial strain.Due to the highly non-linear character of OPA, both tangent (E t ) and secant elastic modulus (E s ) showed a major decrease with increasing axial strain (Figure 6a).
In test OPA-Z30-10 as an example, a reduction to half of the initial value was reached at an axial strain of 0.1%-0.2%.Since some stress-strain curves indicated minor initial compaction in the very early stress-strain response, we compared the tangent and secant modulus at 50% of differential stress (Figure 6b).While tangent moduli were smaller, both types showed a similar relationship between elasticity and loading angle as observed in unconfined compression (Figure 3c) and specimens appeared stiffer at higher effective stresses.
Failure stress taken as the peak of the differential stress curve was also strongly dependent on the bedding orientation as well as the axial strain reached at failure (Figures 5a and 5c; Table 1).All specimens showed a strain-softening behavior indicated by a major stress drop after peak stress.Residual differential strength values were reached after different axial strains (Figures 5a and 5c), and ratios between residual and peak differential stress showed an increase from 0.52 for the P-specimen to 0.76 for the S-specimen.
A similar response in terms of pressure increase and drop to a residual value was observed for excess pore water pressure curves (Figures 5b and 5d).All specimens developed an increase in pore water pressure, whereas the development is also strongly controlled by the bedding orientation.Here, the highest increase with axial strain was observed for the S-specimens, and lower excess pore water pressure developments with increasing bedding angle orientations.Similar to the stress response, the pore water pressure curves are non-linear and reach a peak followed by a pressure drop and eventually reach nearly steady-state conditions in the post-peak region.The pore  water pressures at the residual state were higher than the initial starting pressure except for two tests performed at lower effective consolidation stresses (OPA-P-4, OPA-Z75-4).Similar to the UCS tests, the axial strain at the pore pressure peak was dependent on loading orientation and showed similar dependencies as for the stress-strain behavior.
The direct comparison of peak differential stress values (q peak ) of all configurations showed that the highest strength of the specimens with consolidation stresses of 10 MPa was reached for the P-specimens (90°) and lowest for the Z30-specimen closely followed by the slightly higher Z45-specimen (Figure 7a).The peak strength values presented a smooth and continuous dependency on the loading direction and led to a ratio between minimum and maximum peak stress of 0.81 (q 45 /q 90 ).For the case of the three specimens consolidated to 4 MPa effective stress, the results suggest that a similar trend can be expected.The residual strength values (q res ) also showed a dependency on loading configurations, however, the anisotropy is less pronounced compared to the peak strength values.Except for the Z30-specimen, a smooth variation along the different loading configurations was observed with a minimum strength expected around the 45°-orientation.
The values of maximum excess pore water pressure showed an inverse S-shaped curve for the orientations from 0° to 90°, where the highest maximum pore water pressure was observed for the S-specimen (Figure 7b).
The anisotropic, undrained loading behavior revealing the hydro-mechanical bulk deformation for different loading configurations is presented by comparing the effective stress paths.In the following, the analysis of effective stress paths will focus on the tests performed at 10 MPa effective consolidation stress for the purpose of comparing all loading configurations at equal initial stress states.
The development of mean effective stress for all loading configurations was characterized by a short phase of non-linearity up to approximately 1.0 MPa differential stress and a subsequent nearly linear change in the mean effective stress (Figure 8).This change was strongly controlled by the loading configuration.In general, there are three cases to be distinguished: (a) an increase in effective mean stress was observed for the P-and Z75-orientations, (b) a    , residual differential stress; Δu max , maximum excess pore water pressure; ɛ Δu max , axial strain at maximum excess pore water pressure; q D , differential stress at onset of plasticity; AB, Skempton pore pressure coefficient.relatively constant or only slightly changing effective mean stress shown by the Z60-and Z45-orientations, and (c) for orientations of the Z30-, Z15-, and S-specimen, a significant decrease in mean effective stress was detected.

Table 3 Overview of Testing Conditions and Results of the Consolidated-Undrained Triaxial Tests
The point at which this nearly linear behavior changes to non-linearity coincides with the point where the curve of excess pore water pressure versus differential stress deviated from linearity and is called here D. Figure 9a shows these response curves for the P-, Z60-, Z45-, and the S-specimen loading configurations.The ratio between the change in excess pore water pressure (Δu) and the change in differential stress (Δq) gives the change in pore pressure due to shear stress and is here, for loading with constant total radial stress, expressed by the Skempton AB parameter (Skempton, 1954).This pore pressure coefficient is highly anisotropic whereby the highest values were observed for the S-specimen and lowest for the P-specimen (Figure 9b).From point D on, effective stress paths were characterized by a curvature toward increasing mean effective stresses up to peak stress (Figure 8).Another peculiarity in the hydro-mechanical behavior of the different loading configurations was the simultaneous peak in differential stress and excess pore water pressure for loading orientations between Z30 and Z75.In contrast, the peak in excess pore water pressure for the S-, Z15-, and P-specimen was reached considerably earlier along the effective stress path.The behavior in the post-peak phase was again dependent on the loading configuration since the mean effective stress increased for the S-, Z15, and Z30-specimens and decreased for all other bedding orientations.In the case of the Z45-, Z60-, and the Z75-specimens, the post-peak effective stress path followed that of the pre-peak phase.

Structural Appearance of Failure on the Macro-and Microscale
The specimens presented distinct fractures, along which they failed, so that the tested specimens were split and disintegrated into two or more parts (Figure 10).In the case of UCS-tests, the specimens showed axial splitting with multiple sub-parallel axial fractures, which was mainly observed for the P-specimens.For specimens tested at 75°, 60°, 45°, and 30°-loading configurations, failure occurred by shear fracturing along the bedding plane,  , d) excess pore water pressure-axial strain curves for higher effective consolidation stress (10 MPa, upper part) and lower effective consolidation stress (4 and 5 MPa, lower part) for all loading orientations.While all tests show a non-linear response in stress and pore water pressure and a strain softening behavior after peak, the value and the axial strain at peak stress and pore water pressure were found to be highly dependent on loading orientation.
whereas the Z15-and the S-specimens showed fracturing across the bedding plane.In the latter case, the shear fracture is characterized by changing inclinations presenting a step-wise pattern (Figure 11).On the microscale, the UCS specimens loaded normal to the bedding plane orientation presented inclined fractures crossing and fragmenting elongated calcite minerals indicating shear straining (Figure 11a).The opposite case, that is, tensile fracturing, occurred for specimens loaded normal to the bedding orientation with fractures formed along grain boundaries, that is, (sub-)parallel to the bedding plane (Figure 11b).
The specimens subjected to Brazilian testing showed varying fracture inclinations depending on the loading configuration (Figure 10a).Specimens with loading configurations of 0° presented axial fractures along the bedding plane.Similar observations were made for the 15°-and 30°-configurations, but here the fracture presented a step-wise propagation with alternating sequences of splitting parallel and across the bedding plane (Figure 11c).Deviations from axially-orientated fracturing were observed for specimens loaded at 30°, 60°, and 75°-configurations.The specimens were characterized by failure at the bottom where the fracture partly followed The specimens tested under triaxial compression were characterized by structural failure in the form of a macroscopic shear fracture crossing the specimen with a relatively constant inclination throughout the specimen (Figure 10b).The dip direction of the shear fracture was always oriented normal to the strike of the bedding plane direction.In plane view parallel to the bedding, the shear fracture was oriented obliquely to the bedding plane orientation except for the two Z60-specimens tested at effective consolidation stresses of 5 and 10 MPa, in which the shear fracture propagated parallel to the bedding plane.The shear plane inclination increased with increasing bedding plane orientation from 45° for the S-specimen to approximately 67° for the P-specimen.Macrostructural observations suggested that these shear fractures consist of a network of thin anastomosing shear fractures particularly observed in the Z30-specimen.
Recent high-resolution BIB-SEM studies on OPA deformed under triaxial stress conditions (Schuster et al., 2021;Winhausen et al., 2021bWinhausen et al., , 2022) ) showed that the macroscopic shear fractures constitute shear zones with up to hundreds of micrometer thickness containing a deformed microstructural fabric, in respect of changes in grain structure and pore space.Our microscopic SEM-image analyses confirmed the prior observations on the macroscale indicating that the shear fractures consisted of shear zones of variable width.The analyses also showed that shear strain localized along the macroscopic shear fracture observed on the microscale presented microfabric changes in terms of (a) pore size and pore morphology, and (b) changes in the orientation of mineral grains.For instance, the shear zones showed a constant inclination in the case of the P-specimens (Figure 11d) and a wavy, anastomosing structural alignment for the Z30-specimen (Figure 11e).The structural pattern was also observed at the grain scale where the shear zone in the P-specimen was characterized by a well-defined orientation of grains parallel to the macroscopic shear fracture and rotation of the surrounding fabric.In the Z30-specimen, on the other hand, the orientation of grains in the shear zone appeared less structured closely resembling the wavy structural alignment at lower magnifications.Besides the open space in the shear fracture displayed as black phase in the SEM-images, which is inferred to be artificial due to unloading and sample preparation (see also Schuck et al., 2020;Winhausen et al., 2021b), the microstructure in the surrounding was characterized by an apparently increased porosity.In the Z30-specimen, pore space was enlarged by intergranular fractures and porous rims around clasts.In the shear zones of specimens where maximum loading was applied parallel to the bedding plane orientation, the shear zones presented a denser packing with less abundant intergranular fractures.

Influence of Anisotropy in UCS and BTS Tests
The influence of the structural anisotropy on the results of the rock mechanical tests is demonstrated by the strength and elastic anisotropy as well as the structural appearance of the failure surface.As reported in previous studies, specimens subjected to uniaxial loading show a suction-dependent strength (Wild et al., 2015).Our study showed that for two different suction values the anisotropic character of UCS remained similar.In the UCS tests, macroscopic failure occurred either by (a) predominant mode-I (tensile) fracturing normal to the bedding plane orientation as observed for the P-specimens (Figure 10) or by (b) a combination of mode-I and model-II (shear mode) for all other loading configurations with an increasing amount of shear mode induced failure with increasing angles between applied load and the bedding orientation.These findings are in agreement with earlier interpretations of different failure modes for varying loading configurations due to the transversely-isotropic mechanical character (Amadei, 1996;Barla, 1972) and are well-supported by studies on other shales (e.g., Jin et al., 2018).For OPA, similar dependencies of failure mode have been used in finite and discrete element models implementing discrete crack elements, which showed a change from tensile splitting toward shear fracturing plus some tensile fracturing for loading parallel to perpendicular with respect to the bedding plane under uniaxial compression (Lisjak et al., 2014).These observations suggest that the structural anisotropy, governed by the microstructural composition, leads to different local stress states, that is, tensile or shear stresses, depending on the orientation of maximum stress and the (elongated) grain and pore orientation, thus resulting in different failure modes on the microscale.Bulk compressive strength is highest for S-specimens because local shearing across the bedding plane requires more stress for fractures to form and propagate, thus to overcome cohesive bonds.This is due to the preferred alignment of grains, clay platelets, and pores being oblique to the shear direction.On the other hand, mode-I fracturing as observed on the P-specimens requires slightly lower compressive stresses due to the preferential alignment of pores parallel to the tensile fracture formation and propagation.For angles between 30° and 75°, the alignment of pores and elongated minerals are in favor of reducing the stresses required to exceed the cohesive bonds on the microscale.The lowest strength values observed for Z45-and Z60-specimens are in agreement with macro-structural observations where shear fractures were predominantly oriented parallel to the bedding direction.
This concept can partly be transferred to explain the failure appearance observed in the BTS-tests of our as well as past studies on different transversely isotropic rock specimens (Dan et al., 2013;Debecker & Vervoort, 2009;Tavallali & Vervoort, 2010).Tensile "axial" splitting occurred for loading applied at 0° to the bedding plane, favoring tensile stresses normal to the preferred structural alignment of pores and minerals leading to minimum tensile strength values.The other end-member case (90°-loading) showed higher tensile strength values due to the least-preferred orientation of the microstructure.For all other cases, a mixed-mode failure is inferred by a combination of mode-I failure across the bedding and mode-II along the bedding (Figure 10a).For the correct determination of indirect tensile strength from Brazilian tests, an axial fracture must initiate at the center of the disc and must propagate vertically (Bieniawski & Hawkes, 1978).However, the results demonstrate that in those tests where the bedding orientation was not oriented either 0° or 90° to the loading direction, vertical fracture propagation was not the case, and the application of this analysis method is limited.Therefore, the analysis should be handled with caution.Since the fracture mode and, hence, the stress state during fracture formation and propagation might deviate from the expected pure tensile mode, the precise determination for indirect tensile strength values for angles between 0° and 90° remains inconclusive.Nevertheless, the strength variation along the different loading configurations is in agreement with analytical solutions for the indirect tensile strength of transversely isotropic rocks (Claesson & Bohloli, 2002).

Anisotropic Poromechanical Coupling and Failure Behavior
Besides the anisotropic behavior observed for the uniaxial and tensile strength also the effective strength and the poromechanical response including elastic and plastic strain during shearing appear to be strongly controlled by the microstructural fabric, defined by the arrangements of grains and pores.
For the analysis of hydro-mechanically-coupled deformation under undrained loading, volumetric changes of the specimens for various loading directions are compared.Since radial strain was measured only in one direction, the volumetric strain cannot be calculated due to the anisotropic deformation character related to the different radial strains either normal or parallel to the bedding plane (see e.g., Minardi et al., 2021).However, we infer changes in volumetric strain from the pore water pressure response assuming that the compressibilities of the solid phase and pore space, that is, of grains and pore water, are negligibly small and equal among all tests, and hence the pore space changes are equivalent to bulk volume changes.In the early stage up to 1.0 MPa differential stress, the specimens, in particular, those with bedding inclinations from 0° to 60°, were subjected to non-elastic compaction associated with the closure of isolated micro-cracks and pores oriented (sub-)parallel to the bedding inclination (Figure 8).In the subsequent phase, the bulk volume continues to decrease due to quasi-elastic compression (Figures 8 and 9), whereas the anisotropic elasticity controls the development of pore water pressure due to shear stresses.A high AB-value for an S-specimen indi cates a high pore water pressure built-up during shearing (Figure 9b) due to the low bulk stiffness and a more compressible pore space, which is also in agreement with a lower Young's modulus observed in unconfined and triaxial conditions (Figures 3c and 6b).This is due to the higher compressibility of elongated pores and minerals, in particular, clay aggregates, normal to their long axes.The opposite scenario, in which the preferred alignment of pores and minerals is parallel to the direction of compression (P-specimens), shows higher stiffness and less compressible pore space, resulting in lower AB-values.Consequently, the development of a higher pore water pressure built-up for the S-specimen configuration indicates a higher volumetric compaction in comparison to the P-specimen configuration.For the Z45-and Z60-specimens, AB-values were between 0.3 and 0.4, and are therefore close to the 1/3 value assumed for isotropic materials under triaxial loading with Δσ 1 > Δσ 2 = Δσ 3 = 0 (Skempton, 1954).Under these total stress conditions and according to the theory of Biot (1941), a value of 1/3 implies that no volumetric deformation occurs, since the deviatoric stress change corresponds to the change in pore water pressure.Poromechnical changes in rocks in response to shear stresses, such as pore collapse or dilation, lead to deviations from this value, which has also been shown for OPA before (Aristorenas, 1992;Minardi et al., 2021;Wild & Amann, 2018a).Overall, our analysis shows that, while all specimens are subjected to volumetric compression, the changes in volumetric deformation can be considered either lower where AB > 1/3 (0°-30°), zero to very minor where AB ≈ 1/3, or higher where AB < 1/3 (60°-90°) at initial effective consolidation stresses of 10 MPa.Hence, the Skempton AB-value can be taken as a poroelastic modulus equivalent to the inverse of the bulk elastic modulus (E), which is also confirmed by the similar S-shaped variation along the different orientations resembling the Young's moduli measured in the UCS and TRX tests.The overall variation of AB-values governing the anisotropic poroelastic behavior is in agreement with AB-values for other shales presented by Holt et al. (2018) and Soldal et al. (2022) who fitted their data using an analytical solution for AB-values based on anisotropic B-values (B ‖ , B ⊥ ).A similar but more detailed analytical approach for evaluating the anisotropic poroelastic behavior was developed by Wong (2017) presenting a model not only for shales but generalized for rocks with penny-shaped cracks.
During the change from elasticity to plasticity, which is considered as irreversible changes in the pore structure and here determined to start from point D, increasing shear stress leads to a deviation of the pore water pressure curve from linearity and it is inferred to be the onset of dilatancy (Figures 7 and 8).For tests performed at 10 MPa effective consolidation stress, the onset of dilation was reached between 52% and 72% of the maximum differential stress.Common mechanisms leading to dilatancy are micro-crack development in favor of delamination of clay aggregates, which has been shown for OPA and other similar shales to occur at significantly lower differential stress regimes (e.g., Amann et al., 2011;Bonnelye et al., 2017a;Popp & Salzer, 2007;Winhausen et al., 2021b).The continuously increasing volume of the pore space leads to an increasing amount of dilation until the pore water pressure peak (u max ) is reached, which marks the state from which dilation is dominating over compaction resulting in a net dilation of the specimen during shearing (Figure 8).For the Z30-, Z45-, Z60, and Z75-specimens, the onset of net dilation (peak of pore water pressure) coincides with the onset of failure (peak stress), whereby for the other configurations, dilation precedes failure.This shows that for loading orientations of 0°, 15°, and 90° more plastic strain is accumulating before failure, which can be explained by the formation of the shear zone: while these end-member orientations show the highest discrepancies between the bedding orientation and the shear plane orientation (Figure 10), more plastic strain, that is, the rearrangement of grains and pores by rotation and translational sliding or shear fracturing, is required for the formation of the microscopic shear zones eventually leading to failure (see also Winhausen et al., 2022).Furthermore, this process leads to higher magnitudes of dilation compared to those orientations where the initial bedding orientation is closer to the shear zone orientation, which facilitates the formation of the microscopic shear zone since no rearrangement of fabric is required.The similarity of the pre-peak and post-peak stress paths for the Z45-, Z60-and Z75-specimen as well as the only marginal changes in mean effective stress during shearing indicate minor dilation and rather constant volume strain throughout the complete effective stress path.The Z30-specimen presented a transitional behavior where (a) dilation coincides with peak stress and (b) the post-peak stress path indicates dilation.This is associated with the complex fabric of the shear zone, comprised of alternating shear orientations either crossing or following the bedding orientation (Figure 10).

Anisotropic Elasticity and Effective Strength Analysis
The directional dependence of elastic constants both under uniaxial and triaxial compression can be described using the theoretical constitutive equations for transversely isotropic rocks based on the five independent elastic parameters E 1 (E ‖ ), E 2 (E ⊥ ), ν 1 (ν ‖ ), ν 2 (ν ⊥ ), and G 2 (Barla, 1972), see also Cho et al. (2012).Figure 12 presents our experimentally derived undrained Young's moduli for uniaxial and triaxial stress conditions and fitting curves applying the least-squared difference method using the elasticity constants as fitting parameters presented (see Figure 12).While the overall trend for both experimental boundary conditions is in agreement with the predicted variation along loading configuration and coefficients of determination (R 2 ) present a reasonable fit, minor deviations from the theoretical model are associated with the difficulties of determining the elastic constants in these tests.The comparison of results from UCS and TRX tests shows a large similarity of the orientation-dependent elasticity.Hence, the anisotropy of elasticity remains fairly similar independent of the confinement stresses used in our study.
To overcome the above mentioned difficulties in determining the elastic constants, some studies on OPA performed unloading cycles and compared the tangent, secant, and/or small to zero strain modulus within that phase (Crisci et al., 2021;Giger et al., 2018;Minardi et al., 2021).It was found by these authors that, depending on the method used, undrained Young's moduli can differ by up to a factor of two in the effective stress range considered in this study.Even though shaly OPA can be considered as a soft rock given the Young's moduli determined under uniaxial and triaxial stress conditions and an explicit determination of elastic constants for OPA remains challenging, the anisotropic character of elasticity could be quantified.
The influence of loading configuration on the undrained shear strength (Figure 7a) should be analyzed with caution since the anisotropic poromechanical response leads to different pore water pressures and, thus, to different effective stresses at failure.Most analytical models describing the strength of anisotropic rocks, for example, the single plane of weakness model by Jaeger (1960), compare axial failure stresses of different loading orientations for tests at equal radial stresses, that is, equal total stress paths for drained or dry conditions.Therefore, when performing undrained tests, the different effective stress paths and failure stresses do not permit model fittings unless a considerable amount of tests have been performed under various effective consolidation stresses resulting in shear stresses at equal mean effective stresses for different loading constellations.Similar conclusions have been drawn by Duda et al. (2022) who accounted for the anisotropic pore pressure parameters resulting in substantial differences in modeled shear strength.
Instead, we analyzed the dependency of failure strength on the loading configuration by comparing all mean effective and differential stresses at failure as presented in Figure 13.Our triaxial compressive strength results for loading configurations where the maximum load is applied either normal or parallel to the bedding are in agreement with recent studies on Opalinus Clay (Minardi et al., 2021;Wild & Amann, 2018a).For comparison, we inserted the failure boundary by linear regression for P-and S-specimens based on our and the reported literature data.Our results indicate that the peak stresses of nearly all intermediate loading configurations fall below these boundaries and, therefore, we demonstrate that failure for inclined bedding orientations occurs at lower differential stress when compared to similar effective mean stresses.Based on this comparison, the loading configuration of 45° between the maximum principal effective stress and the bedding  3) and (b) TRX test at 50% of peak differential stress (E t ) for effective consolidation stresses of 10 MPa.Curve fitting was applied using the four elastic constants as fitting parameters and the constitutive equations for elasticity of transversely isotropic rocks (Barla, 1972).R 2 denotes the coefficient of determination.
inclination is able to carry the least shear stress.This is in agreement with the lowest UCS observed for this loading configuration.The highest compressive shear strength is expected for P-specimen configurations followed by S-specimen configurations.

Summary and Conclusions
In this study, the anisotropic behavior of shaly Opalinus Clay was analyzed using multiple mechanical and hydro-mechanical laboratory tests including uniaxial compressive and Brazilian indirect tensile strength as well as CU triaxial compression experiments.The results in terms of unconfined strength, both compressive and tensile strength, as well as triaxial strength, showed a strong dependency on the angle between the applied maximum principal stress and bedding plane orientation.Furthermore, the poromechanical response by means of compaction-induced pore pressure response, dilation, and failure behavior is strongly controlled by the structural anisotropy.This structural anisotropy, represented by the microstructure as preferred shape and orientation of grains and pores, results in the bedding plane orientation on the macroscale and leads to different deformation processes on the microscale for different loading configurations.
In this study, orientations of 45° and 60° between the bedding plane orientation and the maximum principal stress direction, here defined as Z45-and Z30-specimens, showed the lowest compressive strength in CU triaxial tests.Compared to the triaxial tests, unconfined tests showed slightly different variations for different loading configurations which are associated with complex interactions of mode-I and mode-II fracturing during the failure process.Brazilian tests showed that tensile strength normal to the bedding orientation is higher by a factor of approximately 2.5 compared to the tensile strength parallel to the bedding orientation.For orientations between these end-member orientations, failure was very likely expressed by a mixed-mode failure based on structural observations, and tensile strength for these orientations is handled with caution.
The anisotropic poromechanical response leads to different effective stress paths and to failure at different effective mean stresses.Furthermore, the anisotropy controls the magnitude of dilation, which is highest for S-specimens and minor for Z45-and Z60-specimens.The comparison of all peak stresses at different consolidation stresses show that the lowest compressive strength is expected for orientations in the range of 45° between maximum compressive stress and the bedding orientation.
This experimental study provides a comprehensive data set that allows for proper calibration of constitutive models to capture the hydro-mechanical anisotropic, elasto-plastic behavior of Opalinus Clay.Usually, experimental data exploring the full anisotropy are sparse because testing of low-permeable clay-rich rocks is time-consuming and requires specialized equipment.Therefore, many models consider simplifications such as the adaptation of the strength anisotropy inferred from UU-tests under uniaxial and/or triaxial loading conditions.While these tests show anisotropies of peak strength values similar to those performed within this study, the effective mean stresses at failure are unknown.Our results have shown that the knowledge of effective stresses, however, is crucial.While a P-specimen shows the highest compressive strength compared to all loading configurations at an effective consolidation stresses at 10 MPa, a S-specimen fails at a lower differential stress value but also at a considerably lower effective mean stress.Hence, for a proper description of strength anisotropy and for the construction of failure criteria, the knowledge of effective mean stresses at failure is of uttermost importance.
These findings can be transferred to the application of tunnel excavation for the construction of a repository of nuclear waste.During the excavation processes in anisotropic rocks, here Opalinus Clay, the elastic and plastic deformation developed due to induced stress redistribution are highly dependent on the bedding orientation of the rock mass.Consequently, different types of deformations and anisotropic excavation-damage zones are expected around the tunnel circumference.The results obtained in this study contribute to the development of an anisotropic-elasto-plastic damage model (Khaledi et al., 2023) and support recent efforts for simulating excavation processes including the formation of an excavation damage zone (e.g., Mánica et al., 2021).

Figure 1 .
Figure 1.Photograph and broad ion-beam polishing-scanning electron microscopy (BIB-SEM) images presenting the microstructure of Opalinus Clay on different scales.(a) On the macroscale, the fine-grained, laminated structure is visible on a broken drill core.(b) On the mesoscale, at 200× magnification, the structures is presented by a fine-grained matrix and larger clasts of calcite (cal) and pyrite mineral aggregates (Fe).(b) On the microscale, at 5,000× magnification, individual mineral components can be distinguished (qtz, quartz; fos, cal-rich fossil shells; OM, organic matter).The bedding plane orientation is indicated by the arrows.

Figure 2 .
Figure 2. Loading configurations for the uniaxial compressive strength and consolidated-undrained triaxial tests as well as indirect tensile strength tests.

Figure 4 .
Figure 4. Apparent indirect tensile strength for different loading directions from Brazilian tests at suction values of 46 MPa.The S-shaped variation of strength is constrained by the highest values for parallel-to-bedding orientations and the lowest for normal-to-bedding orientations.Error bars indicate the standard deviation of test results within each class of loading configuration.

Figure 5 .
Figure 5. (a, c) Differential stress-strain curves and (b, d) excess pore water pressure-axial strain curves for higher effective consolidation stress (10 MPa, upper part) and lower effective consolidation stress (4 and 5 MPa, lower part) for all loading orientations.While all tests show a non-linear response in stress and pore water pressure and a strain softening behavior after peak, the value and the axial strain at peak stress and pore water pressure were found to be highly dependent on loading orientation.

Figure 6 .
Figure 6.(a) Evolution of tangent and secant undrained Young's moduli (E t , E s ) along axial strain shown for test OPA-Z30-10.(b) Comparison of E t and E s for all triaxial tests at various loading configurations.

Figure 7 .
Figure 7. (a) Peak differential stress (q peak ) and residual differential stress (q res ) and (b) maximum excess pore water pressure (Δu max ) for all specimens tested at different consolidation stresses of 4, 5, and 10 MPa.

Figure 8 .
Figure 8. Effective stress path for various specimen orientations at 10 MPa effective consolidation stresses.Effective stress paths of specimens with different loading configurations show a different hydro-mechanical response mainly associated with different amounts of developed excess pore water pressures.Dashed line indicates the drained stress path.

Figure 9 .
Figure 9. (a) Development of excess pore water pressure with increasing differential stress.Slope of this linearly fitted line presents the pore pressure coefficient AB.(b) Skempton AB for all test performed at 10 MPa effective consolidation stress.

Figure 10 .
Figure 10.Macroscopic appearance of specimens of different bedding orientations after failure for the Brazilian tensile strength tests (BTS), and consolidated-undrained triaxial test (CU-TRX) at 10 MPa effective consolidation stress.The boxes above photographs show a schematic sketch of the bedding orientation (dashed lines) and failure plane orientation (red).

Figure 11 .
Figure 11.Microstructure of specimens subjected to uniaxial compressive strength (UCS) tests (a, b), Brazilian tensile strength (BTS) test (c), and triaxial (TRX) tests (d, e).The location of images (d) and (e) are indicated in Figure 10.White arrows show the bedding plane orientation.Local straining (shear or tensile fracture formation) is indicated by yellow arrows and structural fabric changes on the grain scale, such as grain rotation and intergranular fracturing in the vicinity of the shear zone, are indicated by dashed red lines.

Figure 12 .
Figure 12.Elastic constants determined from (a) UCS tests (E t ) for different test configurations (see Figure3) and (b) TRX test at 50% of peak differential stress (E t ) for effective consolidation stresses of 10 MPa.Curve fitting was applied using the four elastic constants as fitting parameters and the constitutive equations for elasticity of transversely isotropic rocks(Barla, 1972).R 2 denotes the coefficient of determination.

Figure 13 .
Figure 13.Comparison of peak strength values for different loading configurations where angles are given for bedding plane orientation and direction of maximum principal stress.Data from Minardi et al. (2021) as well as Wild and Amann (2018a) are also included.The dashed lines indicate the failure boundary for P-and S-specimens with linear regression based on data from this study and the literature given.

Table 1
Note.All values are averaged over the total amount of tests performed (n) for each testing series and standard deviations are indicated.̇ , displacement rate used for UCS tests;  Ḟ , loading rate used for BTS tests denoted with ⋆ ; RH, relative humidity used for specimen storage; w prep , water content after specimen preparation; ϕ, porosity; Sr prep , saturation after specimen preparation; Sr test , saturation after storage and prior to testing; ψ calc , suction value calculated from specimen saturation; ψ theor , theoretical suction value calculated from relative humidity.Overview of Specimen Condition and Testing Configurations for Rock-Mechanical Tests

Table 2
Overview of Testing Conditions and Results of Uniaxial Compressive and Brazilian Tensile Strength Tests