Horizontal Bedding Planes Research Articles

Physical model test and application of 3D printing rock-like specimens to laminated rock tunnels

Weak structural plane deformation is responsible for the non-uniform large deformation disasters in layered rock tunnels, resulting in steel arch distortion and secondary lining cracking. In this study, a servo biaxial testing system was employed to conduct physical modeling tests on layered rock tunnels with bedding planes of varying dip angles. The influence of structural anisotropy in layered rocks on the micro displacement and strain field of surrounding rocks was analyzed using digital image correlation (DIC) technology. The spatiotemporal evolution of non-uniform deformation of surrounding rocks was investigated, and numerical simulation was performed to verify the experimental results. The findings indicate that the displacement and strain field of the surrounding layered rocks are all maximized at the horizontal bedding planes and decrease linearly with the increasing dip angle. The failure of the layered surrounding rock with different dip angles occurs and extends along the bedding planes. Compressive strain failure occurs after excavation under high horizontal stress. This study provides significant theoretical support for the analysis, prediction, and control of non-uniform deformation of tunnel surrounding rocks.

Third‐order elasticity of transversely isotropic field shales

AbstractThe formations above a producing reservoir can exhibit large mechanical changes, creating a risk of significant subsidence and loss of rock integrity. These changes can be monitored by time‐lapse seismic acquisition, which measures the corresponding velocity changes via time‐shifts. Third‐order elastic theory can be used to connect subsurface strains and stress changes to these seismic attribute changes. Existing models assume isotropic strain dependence of the dynamic stiffness in shales. It is important to re‐evaluate this isotropic assumption considering the inherent anisotropy of shales and their abundance in the overburden. Thus, we instead propose a third‐order elastic model with a transversely isotropic strain dependence of the dynamic stiffness. When calibrated, this new model satisfactorily predicted P‐wave velocity changes determined in undrained laboratory experiments conducted on overburden field shales, covering a wide range of propagation directions and stress variations. The shales exhibit anisotropic dynamic strain sensitivity, resulting in a significantly higher strain sensitivity predicted for Thomsen's anisotropy parameters epsilon and delta subjected to a uniaxial strain parallel to the horizontal bedding plane compared to the vertical direction. Geomechanical modelling, considering a depleting disk‐shaped reservoir surrounded by shales, was employed to predict the dynamic stiffness changes of the overburden using the laboratory‐calibrated third‐order elastic model. The overburden time‐shifts increased with offset angle, peaking at about 45°, suggesting a strong influence of shear strains on the time‐shifts. In contrast, a corresponding model with an isotropic third‐order elastic tensor, calibrated to the same data, exhibited a significantly lower sensitivity to the shear strains. These results underscore the importance of considering the anisotropic strain dependence of the dynamic stiffness when studying shales. Interpreting offset‐dependent trends in pre‐stack time‐lapse seismic data, along with geomechanical modelling and an appropriate strain‐dependent rock physics model, can assist in quantifying subsurface strains and stress changes.

Influence of distinct testing methods on the mode-I fracture toughness of Longmaxi shale

Abundant shale gas in shale reservoirs can be successfully extracted by the fracking technique. The formation of hydraulic fractures is related to the mode-I fracture toughness that represents the resistance to cracking propagation. Two typical Longmaxi shale samples with horizontal and vertical bedding planes are selected in this work. To adequately measure the mode-I fracture resistance of shale, this research adopts four mode-I test specimens with different geometries (cuboid, cylinder, disk, and semi-disk). The experimental results demonstrate that there is an acceptable linear correlation between mode-I fracture resistance and critical T-stress. Further, the discrepancies in mode-I fracture resistance are due to distinct T-stresses that exist in the mode-I test specimens. Consequently, the mode-I fracture toughness KIc for the shale with horizontal bedding is 1.57 MPa·m0.5, while that for the shale with vertical bedding is 1.36 MPa·m0.5. Considering the influences of singular and non-singular stress terms, the GMTSN (generalized maximum tangential strain) and GMTSEDF (generalized maximum tangential strain energy density factor) fracture criteria can provide theoretical explanations for the variation of mode-I fracture resistance measurements. Based on the AE (acoustic emission) technique, the classical RA-AF method can identify the fracture mechanisms of distinct mode-I test specimens. However, the differences in the high-density zones of the RA-AF distribution are conspicuous for distinct mode-I testing methods.

Constitutive modelling of fabric effect on sand liquefaction

Sand liquefaction under static and dynamic loading can cause failure of embankments, slopes, bridges and other important infrastructure. Sand liquefaction in the seabed can also cause submarine landslides and tsunamis. Fabric anisotropy related to the internal soil structure such as particle orientation, force network and void space is found to have profound influence on sand liquefaction. A constitutive model accounting for the effect of anisotropy on sand liquefaction is proposed. Evolution of fabric anisotropy during loading is considered according to the anisotropic critical state theory for sand. The model has been validated by extensive test results on Toyoura sand with different initial densities and stress states. The effect of sample preparation method on sand liquefaction is qualitatively analysed. The model has been used to investigate the response of a sand ground under earthquake loading. It is shown that sand with horizontal bedding plane has the highest resistance to liquefaction when the sand deposit is anisotropic, which is consistent with the centrifuge test results. The initial degree of fabric anisotropy has a more significant influence on the liquefaction resistance. Sand with more anisotropic fabric that can be caused by previous loading history or compaction methods has lower liquefaction resistance.

Research on the influence of stress on the penetration behavior of hydraulic fracture: Perspective from failure type of beddings

The failure types of bedding determine the penetration behavior of hydraulic fracture. A stratum model containing bedding was established based on the 3D block distinct element method to explore the penetration behavior of hydraulic fractures with different types of bedding. The mechanics of hydraulic fractures penetrating the shear- failure bedding plane and tensile-failure bedding plane were analyzed. The results showed that the shear-failure bedding plane was more difficult to expand than the tensile-failure bedding plane after the hydraulic fracture turns to bedding plane. The initial stress magnitude controls the expansion difficulty of hydraulic fractures, and the high stress magnitude attenuated penetration behavior. The vertical stress affected the shear failure by increasing the shear strength of the bedding plane. It affected the tensile failure by increasing the initiation stress of the bedding plane. The effect of horizontal stress on the penetration behavior included the influence on the initiation stress of vertical joints and the enhancement of the interference stress on the horizontal bedding plane. The conclusions can provide the guidance for hydraulic fracturing in reservoir with bedding planes.

The Origin of the Fracture Networks in the Mudstones of Gale Crater Mars; Their Implications Regarding the State of Stress and Fluid Pressure During Their Formation and the Depth to Which They Were Buried

AbstractThe aim of this article is to establish what can be determined about conditions on Mars during the formation of the fractures and veins that characterize the mudstones which crops out in Gale crater, and to determine whether these rocks represent superficial, alluvial deposits which have remained close to the surface or whether they have been subjected to significant burial and compaction. Spectacular, close‐up images of the fracture and vein networks on horizontal bedding planes reveal their geometries in great detail and this facilitates fracture analysis, a technique that can be used to determine the order in which the various fractures were formed and the stress field operating during their formation. The veins and their textures give an indication of the mechanism of formation of the fractures and of the possible role of high fluid pressures. In addition, the geometry of the veins when viewed in a vertical section can be used to indicate the amount of compaction that the mudstones have experienced which can be used to estimate the minimum depth of burial that has occurred.

Fractures in the Niagara Escarpment in Ontario, Canada: distribution, connectivity, and geohazard implications

AbstractThe Niagara Escarpment is a geological feature located in southern Ontario, Canada, and the northeastern United States, comprising highly fractured sandstone, shale and carbonates deposited during the Ordovician and Silurian periods. Differential erosion of the strata has generated a steep cliff face which bisects the city of Hamilton, Ontario. Geological fractures are widespread in the escarpment and result in the formation of unstable blocks of rock subject to erosion through rockfall. This presents structural stability issues of concern due to the proximity of the escarpment to urban infrastructure. We quantify and analyse fracture networks in the escarpment using a combined field- and numerical-modelling-based approach. The location, orientation and aperture of fractures were documented from local outcrops using scanline and area survey methods. Clusters of poles describing the orientation of geological discontinuities were identified in spherical projections, defining three sets: (1) a sub-vertical stratabound set striking N–S, (2) a sub-vertical stratabound set striking E–W, and (3) a set parallel to horizontal sedimentary bedding planes which we infer controlled sub-vertical fracture geometry. Discrete fracture network modelling of fracture sets highlights their high degree of connectivity, and contribution to local geohazards, and quantifies their role in controlling fluid flow through escarpment strata, which is dependent on fracture aperture. Additionally, bedding planes have the potential to act as free surfaces, facilitating stress conditions in which approximately cuboid blocks are produced, and increasing the risk of rockfalls. We conclude that fractures present a first-order control on the fluid-flow properties and stability of the Niagara Escarpment.

A new approach for investigating spatial relationships of ichnofossils: a case study of Ediacaran–Cambrian animal traces

AbstractTrace fossils record foraging behaviors, the search for resources in patchy environments, of animals in the rock record. Quantification of the strength, density, and nature of foraging behaviors enables the investigation of how these may have changed through time. Here, we present a novel approach to explore such patterns using spatial point process analyses to quantify the scale and strength of ichnofossil spatial distributions on horizontal bedding planes. To demonstrate the utility of this approach, we use two samples from the terminal Ediacaran Shibantan Member in South China (between 551 and 543 Ma) and the early Cambrian Nagaur Sandstone in northwestern India (between 539 and 509 Ma). We find that ichnotaxa on both surfaces exhibited significant nonhomogeneous lateral patterns, with distinct levels of heterogeneity exhibited by different types of trace fossils. In the Shibantan, two ichnotaxa show evidence for mutual positive aggregation over a shared resource, suggesting the ability to focus on optimal resource areas. Trace fossils from the Nagaur Sandstone exhibit more sophisticated foraging behavior, with greater niche differentiation. Critically, mark correlation functions highlight significant spatial autocorrelation of trace fossil orientations, demonstrating the greater ability of these Cambrian tracemakers to focus on optimal patches. Despite potential limitations, these analyses hint at changes in the development and optimization of foraging at the Ediacaran/Cambrian transition and highlight the potential of spatial point process analysis to tease apart subtle differences in behavior in the trace fossil record.

Incipient karst generation in jointed layered carbonates: Insights from three-dimensional hydro-chemical simulations

We develop a hydro-chemical model to simulate incipient karst generation in three-dimensional (3D) jointed layered carbonates. The discrete fracture networks consist of fractures that are represented by two-dimensional (2D) planes. The numerical model couples the important physical processes of fluid flow, reactive transport, and dissolutional growth of fracture aperture. We represent the typical layered joint systems by the synthetic fracture networks composed of two jointed layers separated by a horizontal bedding plane. By considering a wide range of initial flow rates and aperture distributions of the joints and bedding plane, the combined effects of the penetration length and the flow localization on karst evolution are systematically investigated. The simulation results confirm that different flow regimes (i.e. joint-dominated, transitional, and bedding plane-dominated) may induce distinct features of incipient karst morphologies observed in nature (i.e. pipe-like, stripe-like and sheet-like), which is attributed to the flow reorganization and the scale alteration of effective flow region. We further found the diversity of morphologies also depends on the initial penetration length, which plays a primary role in controlling dissolution patterns in joint-dominated systems. In addition, introducing the second joint set results in distinct 3D flow structure and dissolutional behavior comparing to single joint system. Our findings highlight the importance of 3D hydro-chemical modeling for realistic engineering applications as the structural complexity of 3D fractured rocks may be underrepresented by the previous studies using simplified conduit networks.

The Effect of Hydraulic Fracture Geometry on Well Productivity in Shale Oil Plays with High Pore Pressure

We propose three idealized hydraulic fracture geometries (“fracture scenarios”) likely to occur in shale oil reservoirs characterized by high pore pressure and low differential in situ stresses. We integrate these geometries into a commercial reservoir simulator (CMG-IMEX) and examine their effect on reservoir fluids production. Our first, reference fracture scenario includes only vertical, planar hydraulic fractures. The second scenario has stimulated vertical natural fractures oriented perpendicularly to the vertical hydraulic fractures. The third fracture scenario has stimulated horizontal bedding planes intersecting the vertical hydraulic fractures. This last scenario may occur in mudrock plays characterized by high pore pressure and transitional strike-slip to reverse faulting stress regimes. We demonstrate that the vertical and planar fractures are an oversimplification of the hydraulic fracture geometry in anisotropic shale plays. They fail to represent the stimulated volume geometric complexity in the reservoir simulations and may confuse hydrocarbon production forecast. We also show that stimulating mechanically weak bedding planes harms hydrocarbon production, while stimulated natural fractures may enhance initial production. Our findings reveal that stimulated horizontal bedding planes might decrease the cumulative hydrocarbon production by as much as 20%, and the initial hydrocarbon production by about 50% compared with the reference scenario. We present unique reservoir simulations that enable practical assessment of the impact of varied hydraulic fracture configurations on hydrocarbon production and highlight the importance of constraining present-day in situ stress state and pore pressure conditions to obtain a realistic hydrocarbon production forecast.

Failure behavior and acoustic emission characteristics of shale after subjection to high temperature

Uniaxial compression tests and acoustic emission (AE) monitoring on shale specimens with horizontal bedding planes and perpendicular bedding planes after subjection to high temperatures (25°C, 100°C, 150°C and 200°C) were performed to investigate the effect of high-temperature environment on shale in rock engineering. Results show that specimens in the two bedding directions experienced severe rockburst failure, and the increasing temperature made rockburst failure more intense. The rockburst phenomena for all the specimens were similar and consistent, including spalling, particle ejection and block collapse. Temperature had no significant effect on the failure mode of specimens with perpendicular bedding planes, while specimens with horizontal bedding planes turned to splitting with the increasing temperature. Fractal dimension of fragmentation increased with the increasing temperature, and that for specimens with perpendicular bedding planes increased much more than that for specimens with horizontal bedding planes. Before the peak, the cumulative AE counts can be divided into three stages by stress level of 40% and 80%.

The deformation and failure of strip footings on anisotropic cohesionless sloping grounds

AbstractFooting foundations are sometimes built on sloping grounds of natural sand which is highly anisotropic. The anisotropic mechanical behaviour of sand can significantly influence the bearing capacity of a foundation and the failure mechanism of its supporting slope. Neglecting sand anisotropy may lead to overestimated bearing capacity and under‐design of foundations. A numerical investigation on the response of a supporting slope under a strip footing is presented, placing a special focus on the effect of sand anisotropy. A critical state sand model accounting for fabric evolution is used. The nonlocal method has been used to regularize the mesh‐dependency of the numerical solutions. Predictions of the anisotropic model on the bearing capacity of strip footings on slopes are validated by centrifuge test data on Toyoura sand. Compared to the centrifuge test data, an isotropic model may overpredict the bearing capacity of the footing by up to 100% when the model parameters are determined based on test data on a horizontal bedding plane case. When the isotropic model parameters are determined based on test data where the bedding plane is vertical, the predictions of bearing capacity can be improved for some cases but the settlement at failure may be significantly overestimated. The soil body tends to move along the bedding plane upon the footing loading due to the non‐coaxial strain increment caused by fabric anisotropy. The slip surface appears to be deeper with lower bearing capacity when the preferred soil movement direction caused by bedding plane is towards the slope.

CO2-Driven Hydraulic Fracturing Trajectories across a Preexisting Fracture

Defining the trajectory of hydraulic fractures crossing bedding planes and other fractures is a significant issue in determining the effectiveness of the stimulation. In this work, a damage evolution law is used to describe the initiation and propagation of the fracture. The model couples rock deformation and gas seepage using the finite element method and is validated against classical theoretical analysis. The simulation results define four basic intersection scenarios between the fluid-driven and preexisting fractures: (a) inserting—the hydraulic fracture inserts into a bedding plane and continues to propagate along it; (b) L-shaped crossing—the hydraulic fracture approaches the fracture/bedding plane then branches into the plane without crossing it; (c) T-shaped crossing—the hydraulic fracture approaches the fracture/bedding plane, branches into it, and crosses through it; (d) direct crossing—the hydraulic fracture crosses one or more bedding planes without branching into them. The intersection scenario changes from (a) → (b) → (c) → (d) in specimens with horizontal bedding planes when the stress ratio β ( β = σ y / σ x ) increases from 0.2 to 5. Similarly, the intersection type changes from (d) → (c) → (a) with an increase in the bedding plane angle α (0° → 90°). Stiffness of the bedding planes also exerts a significant influence on the propagation of hydraulic fractures. As the stiffness ratio E 1 ¯ / E 2 ¯ increases from 0.1 to 0.4 and 0.8, the seepage area decreases from 22.2% to 41.8%, and the intersection type changes from a T-shaped crossing to a direct crossing.

Constitutive model for monotonic and cyclic loading on anisotropic clays

In the present work, a constitutive model for anisotropic clays is proposed and evaluated under monotonic and cyclic loading. To that end, the hypoplastic model for anisotropic clays by Mašín is extended to consider the effects observed on cyclic loading. The extension follows from the intergranular strain anisotropy (ISA) approach by Fuentes and Triantafyllidis. Similar to the intergranular strain (IS) theory by Niemunis and Herle, the ISA extension enhances the model in many aspects, such as the increase of the stiffness and reduction of the plastic strain rate on cyclic loading. Different monotonic and cyclic tests are simulated to evaluate the model's capabilities with the use of samples having vertical and horizontal bedding planes. Simulations obtained with the proposed model and the three-surface kinematic hardening model with transverse isotropic stiffness according to the work of Graham and Houlsby in 1983 (hereafter denoted A3-SKH) are directly compared and analysed. Some additional simulations with the same hypoplastic model extended through the conventional IS theory are also included. The results indicate that a better agreement of the pore pressure accumulation, and some effects emerging from the sample anisotropy, such as ‘inclined’ q–p cycles under undrained conditions, and the dependency of the pore pressure accumulation on the bedding plane direction, are provided by the proposed model. On the other hand, the A3-SKH model estimates with more accuracy the vertical strain accumulation on samples with vertical and horizontal bedding planes.

The hydraulic conductivity of peat with respect to scaling, botanical composition, and greenhouse gas transport: Mini-aquifer tests from the Red Lake Peatland, Minnesota

Hydraulic conductivity (K) is a key but problematic parameter in groundwater models particularly those that simulate flow in weak, readily deformable media, such as peat deposits. As a result, K represents a critical source of error in models that couple hydrological processes with the carbon balance of peatlands, a globally important source for greenhouse gases. We therefore conducted mini-aquifer tests on two mesoscale bog landforms within the large 1300 km2 Red Lake Peatland of northern Minnesota. These tests offer the dual advantage of determining the fine-scale distribution of K within a large (>900 m3) model domain. In addition, the stress created by a 24 h pumping operation should be capable of mobilizing pools of biogenic gases thoughout a deep peat deposit. The pumping results were monitored by 24 to 38 wells in order to calibrate a 3D finite-volume groundwater model with the aid of PEST (Parameter Estimation Analysis). High K values were determined at a Bog Forest (10−5 to 10−6 m s−1) and Bog Lawn (10−3 to 10−4 m s−1) sites, throughout their deep (>4 m) peat profiles. These tests also detected vertically continuous zones of unexpectedly high or low K values in contrast to the horizontal bedding planes and increasing degree of decomposition with depth. The vertical K zones are suggestive of three different modes of bubble transport that either locally dilate or partially block the peat pores. In addition, the tests provided new insights on a conceptual model linking K to the development of all large (>20 km2) forested bog complexes in mid-continental boreal North America.

A new interpretation for formation of orthogonal joints in quartz sandstone

Abstract Two vertical and orthogonal systematic joint sets are generally arrayed in a grid pattern on the bedding surface, which are the significant features of flat-lying sandstone terrains. Although extensive researches are reported on this topic, many fundamental problems have still not been solved. Such mutually perpendicular opening-mode fractures are an obvious manifestation of effective tensile stresses in two orthogonal directions in the horizontal bedding plane. A good understanding of these orthogonal joint systems is a key to structural analysis, landscape interpretation, and guidance of resolving a number of very practical problems in engineering, mining and hydrologic projects. Based on an anatomic investigation on the orthogonal joints in the Potsdam sandstone of Cambrian age at Ausable Chasm (New York State, USA) and Beauharnois (Quebec, Canada), we proposed that the orthogonal joints may result from the auxetic effects of quartz-rich sandstone rather than local or regional rotation of the maximum tensile stress (σ3) direction by about 90°. The sandstone beds with negative Poisson's ratios are so fascinating that, when placed under vertical burial compression and layer-parallel extension in one direction (σ3), it becomes stretched in the transverse direction (σ2), producing two orthogonal sets of mutual abutting and intersecting joints (J1 and J2 normal to σ3 and σ2, respectively), and both are normal to the bedding surface. Joint set J1 is more closely-spaced than J2 by a factor of ∼3.3, which is correlated with an average Poisson's ratio of −0.3 for the Potsdam sandstone at the time of joint formation.

Behavior of transversely isotropic shale observed in triaxial tests and Brazilian disc tests

Shale rock is widely distributed in nature and must be taken into account in some rock engineering applications. In this research, three kinds of experiments, namely the conventional triaxial compression test, reducing confining pressure test, and Brazilian test were conducted on a type of shale rock specimen with a horizontal bedding plane and a vertical bedding plane collected from Lushan city, Jiangxi Province, China to further investigate the bedding effect on the mechanical properties of shale rock. An acoustic emission (AE) monitoring system was used to study the fracture process under the conventional triaxial compression test, whereas a digital image correlation (DIC) system was employed to monitor the deformation of disk faces during the failure process under the Brazilian test. Another key issue addressed in this research is the failure process and mechanism of shale specimens with horizontal and vertical bedding planes under the reducing confining pressure test. The conventional triaxial compression test shows that the bedding plane could easily affect the elasticity modulus and failure pattern, and the failure of the bedding plane can lead to stronger energy release and a higher AE count level. The reducing confining pressure test shows that the dissipated energy magnitude of unloading Path II (reducing confining pressure and increasing axial stress) is much larger than that of unloading Path I (reducing confining pressure and keeping axial strain constant), and that continuous energy input and larger energy dissipation led the specimens under unloading Path II to fail faster than those under unloading Path I. The Brazilian test further revealed that the bedding plane has a significant effect on the tensile strength and failure pattern of shale rock.

Fracture Development at Laminated Floor Layers Under Longwall Face in Deep Coal Mining

The increment of stress level and fracture depth in deep longwall mining can cause groundwater inrush accidents frequently, and it is essential to study the characteristics of fracture development around laminated rock layers at the floor. This can help to understand the mechanism of groundwater inrush events and to reduce the potential risk. According to the rock mass stress–strain curve and the stress redistribution around the floor area in a deep longwall face, this study focused on the failure mechanisms in this area. A physical longwall model was established to study fracture development at the unloading zone around the floor area. The results showed that the plastic fracture at the floor was generated by high compressive stress around the floor and coal rib area after the breakage of main roof. The unloading starting point of stress changed nonlinearly, and the unloading stress increased nonlinearly. Therefore, the unloading fracture depth and the floor heave deformation can be much larger than those in shallow mining. In addition, the horizontal bedding plane can accelerate fracture development. When the unloading stresses increase, the branch fractures develop downward and connect the original joints and bedding planes at deeper floors. The dominant angle of main cracks varies in the range of 50°–85°, and the number of branch fractures can reduce when the dip angle of the main cracks increases (close to 85°). In addition, the direction of main fractures was nearly vertical, and it was hard to connect them to the horizontal joints and bedding planes.

Numerical simulation analysis of vertical propagation of hydraulic fracture in bedding plane

Hydraulic fracturing is one of the principle technologies employed for achieving the efficient development of shale oil and gas reservoirs, and the bedding plane of the reservoir is a key factor affecting the geometrical distribution of hydraulic fractures in three dimensions. The present study adopts cohesive force unit theory to construct a multi-layer hydraulic fracture propagation model with coupling stress damage filtration, and the effects of changes in the reservoir stress field, angle of the bedding planes relative to vertically propagating hydraulic fractures, and tensile strength of the bedding planes on the vertical propagation of hydraulic fractures are analyzed. The simulation results show that the hydraulic fracturing process of penetrating the bedding planes can be divided into three stages. Here, the hydraulic fracture propagates in the rock matrix and intersects with the bedding planes with continuous injection of fracturing fluid in stages I and II, while the vertical stress, bedding plane angle, and tensile strength of the bedding planes determine the direction of hydraulic fracture propagation in the third stage. Reservoirs with low vertical stress differences and nearly horizontal bedding planes with low dip angles are found to be favorable for opening the bedding planes, and reservoirs with high vertical stress differences and bedding plane dip angles are favorable for the longitudinal expansion of hydraulic fractures. Simultaneously, the degree of opening of the bedding planes also increases as the tensile strength of the bedding planes decreases. This is mainly because the energy consumption of the bedding layer opening process decreases as the tensile strength of the bedding planes decreases.

AVISA: anisotropic visco-ISA model and its performance at cyclic loading

In this work, a constitutive model able to capture the strain rate dependency, small strain effects and the inherent anisotropy is proposed considering the influence of the overconsolidation ratio (OCR). Small strain effects are captured by using an extended ISA plasticity formulation (Fuentes and Triantafyllidis in Int J Numer Anal Methods Geomech 39(11):1235–1254, 2015). The strain rate dependency is reproduced by incorporating a third strain rate mechanism (in addition to the elastic and hypoplastic strain rate). A loading surface has been incorporated to define a three-dimensional (3D) overconsolidation ratio and to account for its effects on the simulations. Experimental investigations using Kaolin Clay and Lower Rhine Clay with horizontal bedding plane have shown that under undrained cycles of small strain amplitudes (<10^{-4}), the effective stress path in the p–q space is significantly inclined towards the left upper corner of the p - q plane. Consequently, a transversely (hypo)elastic stiffness has been successfully formulated to capture this behaviour. The performance of the model has been inspected by simulating the database of approximately 50 cyclic undrained triaxial (CUT) tests on low-plasticity Kaolin Clay (Wichtmann and Triantafyllidis) considering different deviatoric stress amplitudes, initial stress ratios, displacement rate, overconsolidation ratio and cutting direction. Furthermore, 4 CUT tests conducted on high-plasticity Lower Rhine Clay were simulated, whereby the influence of the displacement rate, as well as the deviatoric stress amplitude, has been analysed. The simulations showed a good congruence with the experimental observations.