Rotation Of Principal Stress Axes Research Articles

Experimental study on the influence of principal stress axes rotation on sand mechanical behavior and non-coaxiality effects

The soil around the foundations of offshore engineering experienced the principal stress axes rotation caused by the wave loadings. To investigate the influence of the principal stress axes rotation on the soil stress-strain relationship, a series of pure principal stress axes rotation tests under drained/undrained conditions were carried out with a hollow cylinder apparatus. The undrained test results show that the deviatoric stress, relative density, and starting point of rotation affect the mechanical properties of sand. Through the analysis of pore water pressure accumulation in the 1st cycle, it was observed that more pore pressure accumulates in Quadrants II and III, while relatively less accumulates in Quadrants I and IV. Under drained and undrained conditions, the non-coaxial behavior of the soil differs. The non-coaxiality can be significantly observed in the drained test, and the direction of strain increment tends to the stress increment direction when the cycle number increases.

Discrete Element Simple Shear Test Considering Particle Shape

The particle shape has significant effects on the slip and rotation of particles in the shear of geomaterials, which is an important factor in the deformation and strength of geomaterials. This paper employed particle flow code (PFC3D) to simulate the simple shear test, and ellipsoidal particles with different aspect ratios were prepared to study the effects of particle shape on the mechanical behavior and fabric evolution of granular materials under complex stress paths. The numerical results show that the particle shape has a significant effect on the peak strength, dilatancy, non-coaxiality, and other mechanical properties of granular materials. The contact fabric evolves from orthotropy to transverse isotropy under the principal stress axes rotation. This paper will provide a reference for natural granular materials with different shapes in the study of mechanical behavior and the micro-constitutive model.

Experimental study on strain accumulation characteristics of saturated remolded loess under pure rotation of the principal stress axis

The study conducted a pure rotation test of 720° for saturated remolded Q2 loess under principal stress axis (PSA) rotation when deviatoric stress and the intermediate principal stress ratio are different, also paying attention to examining the changes of strain accumulation and pore pressure of such loess. According to the test, as the PSA rotates continuously, the pore water pressure exhibited by saturated remolded loess presents a normal cyclic accumulation elevation, and under the same deviatoric stress conditions, the pore water pressure accumulation trend of different principal stress ratios is the same; however, the magnitude is different. The increment of pore water pressure becomes smaller as the number of cycles increases. When the deviatoric stress level is low, the material hardening is in a cyclic stable state, the strain component remains stable with the continuous rotation of the PSA, and the strain path area is reduced, together with a stable final size. In case of higher deviatoric stress, the material strength cycle becomes weaker and the strain component accumulates slowly as the PSA (the spiral line of the strain path) continuously rotates in the γzθ−(ϵz−ϵθ) plane, and gradually expands until failure. The increased intermediate principal stress is accompanied by accelerated strain development speed and advanced failure.

Tensor tomography of the residual stress field in graded-index YAG’s single crystals

Abstract This work presents an application of tensor field tomography for non-destructive reconstructions of axially symmetric residual stresses in a graded-index YAG single crystal for the case of beam deflection. The axis of the cylinder coincides with the crystallographic axis [001] of the single crystal and it has an axially symmetric refractive index distribution. The transformation of the polarization of light is measured in a plane orthogonal to the axis of the cylinder. Stresses are determined within the framework of the Maxwell piezo-optic law (linear dependence of the permittivity tensor on stresses) and small rotation of quasi principal stress axes. This paper generalizes the method of integrated photoelasticity for the case of ray deflection.

The Hypoplastic Constitutive Model for Sandy Soil Considering the Rotation of the Principal Stress Axis

Considering the influence of fabric on the critical state of sandy soil, an anisotropic hypoplastic constitutive model is developed by introducing the anisotropic critical state line that takes into account the rotation of the principal stress axes. With the introduction of new anisotropic state variables defined by the joint invariants of the stress tensor and fabric tensor, the critical state equation of sandy soil is established to describe the effects of three factors, namely, anisotropic parameters, stress states, and the relationship between principal stresses and fabric directions, on the critical state. The mechanical response of sandy soil under different deposition angles can be described by considering the rotation of principal stresses relative to the fabric. The application range of Wu et al.’s isotropic hypoplastic model (2017) is extended by incorporating the effect of principal stress rotation on the stress–strain relationship of sandy soil. Based on a series of Toyoura sand plane strain tests, the effects of void ratio, confining pressure, and principal stress axis rotation angle on anisotropic strength and deformation characteristics are simulated under low confining pressure. Furthermore, a comparison with Wu’s transversely isotropic hypoplastic model (1998) is made regarding their simulation performances. The proposed model exhibits a balanced performance when simulating the variation of anisotropy in both strength and deformation with respect to the rotation angle, without being overestimated within a certain range of rotation angles. The prediction results demonstrate, to a certain degree, the validity and effectiveness of the proposed model.

Experimental Study of Hollow-cylinder Sandstone Under Constant Mean Stress Considering the Rotation of Principal Stress Axes

Experimental Study of Hollow-cylinder Sandstone Under Constant Mean Stress Considering the Rotation of Principal Stress Axes

Rotation and deflection of 3D principal stress axes induced by a prefabricated single flaw in sandstone: A numerical investigation based on DEM

Fracture structure in the rock mass is an enduring research interest because of its negative impacts on the strength and safety of rocks. Therefore, a series of DEM simulations of two types of fractured sandstones are conducted based on the former published experimental test. It is proved that different fracture structures have various influences on the mechanical properties and failure patterns of sandstone samples, which lead to the redistribution of principal stress in surrounding rock. The main results and conclusions are as follows: 1) fractured sample without filler shows a relatively lower uniaxial compressive strength and a larger elastic modulus, and the flaw free surfaces make the secondary crack band illustrate a typical arc-shape distribution. 2) maximum principal stress concentrations in the open-type flawed sample occur at the left and right flaw tips, the corresponding axes show progressive deflection in the vertical direction, and the intermediate and minimum principal stress axes demonstrate various rotations as the positions move away from the flaw tip. 3) maximum principal stress axes in the cement-filled fractured sample are basically parallel to the external loading direction, the largest deflection occurs in the cement filler material, and the intermediate principal stress axes near the flaw tip are consistently vertical to the flaw strike direction. 4) initiation positions of tensile and shear cracks in the open-type flaw sample are different because of the non-negligible flaw thickness, while all secondary cracks start from the top and bottom tips of the cement-filled flaw.

Anisotropic and Noncoaxial Behavior of Soft Marine Clay under Stress Path Considering the Variation of Principal Stress Direction

The influence of the variation in the principal stress direction on the anisotropic and noncoaxial behavior was investigated through several hollow cylinder apparatus (HCA) tests that were performed on reconstituted soft clay specimens under a stress path with a fixed or continuous rotation of the major principal stress axis. In particular, the varying amplitude of the deviator stress (q) and intermediate principal stress coefficients (b) were focused upon. The results indicated that the shear stiffness and strength were strongly dependent on the fixed major principal stress angle. Furthermore, apparent noncoaxiality was observed between the orientations of the major principal strain increment and the major principal stress. Consequently, the noncoaxial behavior of the reconstituted soft clay was sufficiently and effectively described using rose and polar diagrams. Furthermore, the data fluctuation indicated that the noncoaxiality of soft clay was strongly dependent on both q and b during the pure principal stress rotation (PSR). The results obtained for undisturbed clay and sand are not expected to be applicable to reconstituted clay, because its behavior is in contrast to the former two. Regarding reconstituted soft clay, the degree of noncoaxiality was observed to increase during the second rotation (N = 2) compared with that during the first rotation (N = 1). However, this trend gradually weakened with an increase in q or b values. Moreover, regardless of whether N = 1 or 2, the degrees of noncoaxiality decreased with the increase in q for b = 0.5 whereas it increased with the increase in b values for N = 1. However, those for b = 1 were the smallest for N = 2. The results are expected to provide an experimental basis for the constitutive modeling of soft clay with fixed and continuous rotations of the major principal stress axes in ocean engineering.

Experimental Investigation on the Deformation and Noncoaxial Characteristics of Fiber-Reinforced Aeolian Soil under Traffic Load

The cumulative plastic deformation of a foundation associated with traffic loading causes subgrade instability, and eventually, failure of retaining structures. In the present study, hollow torsional shear tests were conducted on fiber-reinforced aeolian soil involving varying fiber contents, cyclic deviator stresses, cyclic shear stresses, and consolidation confining pressures using the Small-Strain Hollow Cylinder Apparatus, developed by GDS Instruments Ltd. (GDS SS-HCA). This enabled an investigation of the deformation characteristics and noncoaxial angle changes of fiber-reinforced aeolian soil under a heart-shaped stress path. The results indicate that fiber-reinforced soil deformation under cyclic loading involves axial (ɛz), radial (ɛr), circumferential (ɛθ), and shear (γzθ) strains, and deformation increases with increasing the cyclic number. The strain increases rapidly during the first 200 cycles and then gradually. The axial deformation decreases with increasing fiber content when the fiber content is less than 2‰ and increases when the content is more than 2‰. The plastic strain and total deformation decrease with increasing confining pressure but increase as the cyclic dynamic stress and cyclic shear stress amplitudes increase. Functional equations of the cumulative axial plastic strain and vibration numbers are proposed. The relationships between the model parameters, including the fiber content and cyclic torsional shear stress, are analyzed. The principal stress axis rotation causes variations between the major principal strain increment and the principal stress directions, representing the noncoaxial angle (β). The noncoaxial angle fluctuates during each loading cycle, exhibiting a V shape, for principal stress axis angles (ασ) from −90° to −45° and −45° to 30°, and decreasing at angles varying from 30° to 90°, with a maximum noncoaxial angle of approximately 30° per cycle.

Aftershock Moment Tensor Scattering

AbstractCoseismic rotations of principal stress axes can provide insights into the strength of the crust, but it is unclear how common this phenomenon is. We use a nearest‐neighbor clustering algorithm to identify earthquake sequences in the global ISC‐GEM catalog and the regional Southern California catalog. Using an inner‐product‐based pairwise measure of moment tensor similarity, we demonstrate that, in both catalogs, aftershocks are less similar to their respective mainshocks than foreshocks are. We interpret this effect, which we call moment tensor scattering, as evidence for widespread coseismic stress rotations. Moment tensor scattering is observable for a broad range of mainshock magnitudes in both catalogs. We further demonstrate that mainshock‐aftershock similarity recovers logarithmically to pre‐mainshock levels on decadal timescales. We conclude that moment tensor scattering is a generally observable feature of seismic sequences which may be useful in future work to discriminate between models of crustal strength.

Experimental study on the mechanical properties of water-rich mudstone under principal stress axis rotation

Experimental study on the mechanical properties of water-rich mudstone under principal stress axis rotation

Non‐coaxial hypoplastic model for sand with evolving fabric anisotropy including non‐proportional loading

AbstractNon‐coaxial response refers to the deviation between the directions of the principal stress and plastic strain increment. In this paper, an extended hypoplastic model is proposed based on the anisotropic critical state theory, to describe the non‐coaxial and anisotropic response of sand subjected to both monotonic loading and rotation of principal stress axis. A fabric tensor that characterizes the internal structure of sand is introduced into a hypoplastic model, to reflect the effect of fabric anisotropy on the dilatancy and strength of sand. A Lode‐angle‐dependent hypoplastic potential surface is employed, rendering the flow direction no longer co‐directional with the stress tensor in the deviatoric plane. The fabric tensor is further incorporated into the flow direction, enabling the model to generate a non‐coaxial response. Upon shearing, the fabric evolves toward the loading direction following a properly defined evolution law, and the model response becomes purely coaxial at the critical state when the fabric becomes co‐directional with the loading direction. The tangential loading effect is further introduced to simulate the stiffness degradation of sand during undrained rotational shearing. The model is demonstrated to be capable of simulating the prismatic yet complex anisotropic behavior of sand under both proportional and non‐proportional loading conditions.

Hard classification of polyphase fault-slip data: Improvement and application

The quickest approach to the separation of polyphase fault-slip data into single-phase subsets is perhaps the recognition in stress space of the hyperplanes, consisting of their corresponding datum vectors, whose normals are parallel to the solutions of the stress vector. However the uncertainty of the solution sign makes it impossible to distinguish the subsets with respect to the opposite real stress vectors. In order to overcome this drawback the existing hard-classification method was improved by incorporating the slip senses during the separation. A series of artificial two-phase fault-slip datasets with the measurement errors generated under the imposed stresses were taken to test the improved method. There is a high accuracy of the stress solution even when the measurement errors have a range of [-12°, 12°]. The new method is further applied to data of shear bands measured on the limbs of the NNE-trending syncline at the Shihtipin resort, east of Taiwan. Two stress estimates representing the strike-slip or compressional tectonic regimes were obtained on each limb. They indicate an anticlockwise rotation of the maximum principal stress axis from ESE–WNW or SE–NW to E–W during the folding, probably in response to the oblique collision between the Luzon volcanic arc and the South China continent.

Constitutive response predictions of both dense and loose soils with a discrete element model

The capability of a discrete element model to predict the constitutive response of a soil is investigated in this paper. The discrete model is constituted of spherical particles with a contact law embedding inter-particle rolling resistance. The study has been carried out in a constrained framework: the complexity of the model is limited in favour of its simplicity of use, the model calibration is independent of the initial state of the soil, the validation of the model has to be robust in the sense that validation loading paths should differ strongly from the calibration loading paths. To reach these objectives, the contact law of the model was slightly enriched with the implementation of a non-constant friction angle, and both porosity and connectivity are controlled for the numerical simulation of the initial soil state. Numerical predictions of the model on the validation loading paths show that such a modelling framework, associating the model itself and the preparation methodology of the numerical sample, leads to good qualitative and quantitative predictions. This is the case in particular for non-rectilinear loading paths or loading paths involving rotation of principal stress axes, while the model is calibrated from monotonous drained triaxial compressions only.

Three-Dimensional Numerical Modeling of Ground Deformation during Shield Tunneling Considering Principal Stress Rotation

In the process of tunnel excavation, the change of soil stress field will inevitably lead to principal stress axis rotation, which is a common but easily ignored phenomenon in shield tunneling. Therefore, it is necessary to consider the effect of principal stress rotation in the process of shield tunneling. In this paper, the stress field variation and ground surface deformation of cohesive soil are investigated by a numerical method via the strength parameter variation. A UMAT (user material) subroutine is programmed and embedding into the finite-element software to realize the strength parameter variation that is caused by the principal stress direction rotation during the whole tunneling process. The ground deformation considering the variation of the principal stress direction is compared with that when the variation of the principal stress direction is not considered. The simulation results show that the principal stress direction of the soil changes significantly during the tunnel excavation, and the principal stress direction of the soil within 1.5D (D = tunnel diameter) away from the tunnel axis and all the soil above the tunnel changes obviously. In addition, during the excavation, the rotation angle of the principal stress for each point in the soil gradually increases; in the direction perpendicular to the tunnel axis, the rotation angle of the principal stress increases first and then decreases from the tunnel axis to the edge of the model; when the direction of the principal stress changes, the strength parameters of the soil are modified, the ground deformation of which is larger than that before correction.

Pavement design method in Japan with consideration of climate effect and principal stress axis rotation

Current Japanese design guide uses mechanical-empirical criteria to predict the failure loading number against fatigue cracking and rutting. However, these criteria have some limitations that the variation in moduli of base and subgrade layer due to the fluctuation in water contents, freeze–thaw history, and stress states are not considered. As well known, these factors greatly affect the soil mechanical properties like resilient modulus. Besides, present rutting failure criterion provides no indication of the behavior of rutting over time, and the effect of principal stress axis rotation on rutting development is also not captured. To overcome such limitations, this study modified the present Japanese pavement design method through the following two main aspects: (1) Replacing constant elastic modulus of base and subgrade layer to resilient modulus related to stress states and complex climate conditions, which are defined as the combination of fluctuating water content and freeze–thaw action; (2) Modifying rutting failure criterion by considering generally used MEPDG model and also the effect of principal stress axis rotation. All modifications are performed based on laboratory element test like suction-controlled freeze–thaw triaxial test, which could simulate complex climate conditions, and multi-ring shear test, which could simulate principal stress axis rotation. Besides, modified criteria are examined by comparing to long-term measured performance of test pavements built in Hokkaido, the north island of Japan. Modified Japanese pavement design method shows high applicability and accuracy on the pavement life prediction, especially for the flexible pavement in cold regions like Hokkaido.

3D FE-Informed Laboratory Soil Testing for the Design of Offshore Wind Turbine Monopiles

Based on advanced 3D finite element modelling, this paper analyses the stress paths experienced by soil elements in the vicinity of a monopile foundation for offshore wind turbines subjected to cyclic loading with the aim of informing soil laboratory testing in support of monopile foundation design. It is shown that the soil elements in front of the laterally loaded monopile are subjected to complex stress variations, which gradually evolve towards steady stress cycles as the cyclic lateral pile loading proceeds. The amplitude, direction and average value of such steady stress cycles are dependent on the depth and radial distance from the pile of the soil element, but it also invariably involves the cyclic rotation of principal stress axes. Complementary laboratory testing using the hollow-cylinder torsional apparatus was carried out on granular soil samples imposing cyclic stress paths (with up to about 3 × 104 cycles) which resemble those determined after 3D finite element analysis. The importance of considering the cyclic rotation of principal stress axes when investigating the response of soil elements under stress conditions mimicking those around a monopile foundation subjected to cyclic lateral loading is emphasised.

Drained deformation characteristics of granular soil under pure principal stress axis rotation: impact of sample preparation

The distinct initial fabrics of sand may give rise to dramatically different responses to the applied loading, as evidenced by numerous laboratory tests reported in the literature. In this study, both dry deposition (DD) and moist tamping (MT) methods were employed to prepare sand specimens to generate different initial fabrics. Drained tests were conducted on these specimens under pure principal stress axis rotation while keeping the principal stress components constant. The factors that may influence the deformation characteristics of sand, such as deviatoric stress q, coefficient of intermediate principal stress b, and mean principal stress p, were also taken into consideration in the tests. Test results show that the developments of three normal strain components with number of cycles are very different between DD and MT specimens, which is also closely related to the factors of q, b, and p. It is seen that DD specimen tends to generate larger contractive volumetric strains than MT specimen, which is more significant when q and b increase or p decreases. The shear stiffness of DD specimen is greater than that of MT specimen. The shear modulus ratio, Gj/G1, increases with the increase of q and b or the decrease of p, which is more prominent in DD specimen than in MT specimen. It is also shown that DD specimen appears to exhibit stronger non-coaxiality than MT specimen, in which such difference of non-coaxiality tends to decrease with the increase in number of cycles.

Stiffness of granular soils under long-term multiaxial cyclic loading

Geotechnical infrastructures may be subjected over their lifetime to long-term loading cycles of varying amplitude, frequencies and direction as a result of the combination of environmental and operational processes. Soil elements surrounding the foundations of these geotechnical systems are in turn subjected to complex six-dimensional stress paths, invariably involving rotation of principal stress axes. Changes of the soil's mechanical properties can lead to changes of the overall structure dynamics, as well as to an accumulation of irreversible deformations. However, the evolution of the soil's response and stiffness under complex long-term cyclic loading scenarios is neither well known nor adequately understood. In contrast to the conditions imposed by standard laboratory tests, this research used a hollow-cylinder torsional apparatus (HCTA) to explore the evolution of the small-strain stiffness of a granular soil under long-term multiaxial drained stress cycles (up to about 6 × 105). Granular soil samples were subjected to stages of regular low-amplitude stress cycles at different anisotropic stress levels interspersed by periodic large-amplitude cyclic loops. A high-resolution local strain measurement system was employed to determine the vertical Young's modulus and shear modulus, both attained in a HCTA at different stages of the testing. It was found that low-amplitude multiaxial stress cycles, involving continuous rotation of principal stress axes, caused a degradation up to about 20% of these elastic soil properties. Within 104 to 2 × 104 cycles, the degraded stiffnesses reached a stable value, which was maintained up to at least 8 × 104 cycles. The stiffness degradation was more pronounced for the shear modulus than the vertical Young's modulus of the soil.

Three‐dimensional anisotropic plasticity model for sand subjected to principal stress value change and axes rotation

AbstractA three‐dimensional (3D) anisotropic plasticity model for sand is formulated in this study to provide a constitutive description for both radial and principal stress axes rotation (PSAR) loading‐induced behavior under various conditions with a single set of model parameters. The model has zero elastic range, with plastic loading and flow direction dependent on both current stress and stress rate direction. Fabric tensor is introduced along with its evolution to achieve anisotropic plastic modulus, dilatancy, and flow rule formulations. Increase in plastic modulus under continuous PSAR achieves eventual convergence of strain accumulation. A unique decomposition of dilatancy controls the overall contraction and periodic dilatancy oscillation under PSAR. The performance of the model is first thoroughly evaluated based on drained/undrained, monotonic shear/PSAR tests on Toyoura sand, showing its effectiveness in reproducing the behavior of real sand. Discrete element method numerical test results are then adopted for comprehensive calibration of the model parameters, and then for validation of the model under 3D PSAR in any arbitrary direction. These comparisons highlight the model's capability in simulating the behavior of granular soil under 3D stress paths.