Rotation Of Stress Axes Research Articles

A Constitutive Model for Anisotropic Sand Considering Fabric Evolution Under Proportional and Non‐Proportional Loadings

ABSTRACTA critical state plasticity model is proposed to describe the anisotropic sand behaviour under both proportional and non‐proportional loading conditions. An evolving fabric tensor is introduced into the model to reflect the influence of fabric anisotropy on the stress‐strain relation of sand. By employing a fabric‐dependent plastic flow direction, the non‐coaxial response can be simulated in a simple way. A non‐proportional loading mechanism is incorporated to consider the plastic deformation induced by the stress increment tangential to the yield surface. The influence of accumulative plastic strain on the dilatancy function and plastic modulus is properly considered, enabling the model to reasonably capture the evolutions of volumetric and deviatoric strains under both drained and undrained principal stress axes rotation. The model was validated based on the simulations of experimental results for monotonic loading and pure principal stress axes rotation tests covering a wide range of conditions.

Influence mechanism of the principal stress axis rotation effect on the propagation of blast-induced cracks under in-situ stress

In-situ stress plays a pivotal role in controlling both the propagation speed and trajectory of blast-induced cracks. Previous studies have primarily placed emphasis on the qualitative analysis of the propagation morphology of such cracks, but the principal stress axis rotation effect under static-dynamic coupling loading was ignored. Consequently, the mechanical mechanism of the propagation of blast-induced cracks has not been figured out yet. In this study, a combination of laboratory tests, theoretical analysis, and numerical simulations was employed to explore the influence mechanism of the principal stress axis rotation effect on the propagation of blast-induced cracks under in-situ stress. The results suggest that the hydrostatic pressure does not change the propagation trajectory of blast-induced cracks, but a higher hydrostatic pressure will inhibit both their propagation speed and length. In contrast, the deviatoric stress can change the propagation trajectory of blast-induced cracks, and a higher deviatoric stress makes it easier for blast-induced cracks to deflect to the maximum loading stress direction. Besides, the propagation of blast-induced cracks exhibits different features in different stages under in-situ stress. In the zone near the blast source, the dynamic stress is dominant; the maximum principal stress of the mass points is distributed in the radial direction; and blast-induced cracks expand mainly along the radial direction. On the contrary, in the zone far from the blast source, the static load is dominant; the maximum stress direction of the mass point alters to the maximum loading stress direction; and blast-induced cracks deflect from the radial direction to the maximum loading stress direction. Therefore, the propagation of blast-induced cracks under in-situ stress is a dynamic process in which dynamic and static stresses compete for crack initiation, and the changes in both stress value and principal stress direction are identified as the main reasons for the deflection of blast-induced cracks.

Analytical model and stress behavior of consolidated load bearing geotextile tubes

Accurately predicting stress-strain characteristics is crucial to ensuring the regulated capacity and controlled deformation of the tubes during and after construction. However, research on the shear strength of geotextile tubes under surcharge loading, especially after dewatering, is insufficient. This study proposes an analytical model with a Stress-State Boundary (SSB) and Yield Function to comprehensively describe the stress-strain behavior of Load-Bearing Geotextile Tubes (LGTs). The SSB is designed to predict the initial state of stress in the infill soil prior to load application, while the Yield Function is formulated to express the shear stress path experienced by the LGT before fabric failure. The model considers various factors that affect LGT behavior, including diverse soil mechanical parameters, nonlinear fabric stiffness, initial tension due to self-weight and principal stress axes rotation. Results show that a decrease in Poisson's ratio corresponds to an increase in failure stress. Moreover, it was demonstrated that the axial failure strain can be influenced by the geotextile linear or nonlinear behavior. Notably, the study highlights that tube height and inclination angle significantly affect the geotextile's confining effect. Beyond theoretical contributions, the analytical model serves as a valuable tool for optimizing geotextile tube design and execution, contributing to project success and longevity through enhanced structural stability.

Deformation Characteristics and Noncoaxial Behavior of Fiber-Reinforced Soil under Pure Principal Stress Axis Rotation

Deformation Characteristics and Noncoaxial Behavior of Fiber-Reinforced Soil under Pure Principal Stress Axis Rotation

Mechanism of principal stress rotation and deformation failure behavior induced by excavation in roadways

The failure modes of rock after roadway excavation are diverse and complex. A comprehensive investigation of the internal stress field and the rotation behavior of the stress axis in roadways is essential for elucidating the mechanism of roadway failure. This study aimed to examine the spatial relationship between roadways and stress fields. The law of stress axis rotation under three-dimensional (3D) stress has been extensively studied. A stress model of roadways in the spatial stress field was established, and the far-field stress state at different spatial positions of the roadways was analyzed. A mechanical model of roadways under a 3D stress state was established using far-field stress solutions as boundary conditions. The distribution of principal stresses σ1, σ2 and σ3 around the roadways and the variation of the stress principal axis were solved. It was found that the stability boundary of the stress principal axis exhibits hysteresis when compared with that of the principal stress magnitudes. A numerical analysis model for spatial roadways was established to validate the distribution of principal stress and the mechanism of principal axis rotation. Research has demonstrated that the stress axis undergoes varying degrees of spatial rotation in different orientations and radial depths. Based on the distribution of principal stress and the rotation law of the stress principal axis, the entire evolution mechanism of the two stress adjustments to form the final failure form after roadway excavation has been revealed. The on-site detection results also corroborate the findings presented in this paper. The results provide a basis for the analysis of the failure mechanism under a 3D stress state.

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.

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 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.

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

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.

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.

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.

Coupled Directional Dilation–Damage Approach to Model the Cyclic-Undrained Response of Soft Clay under Pure Principal Stress Axes Rotation

AbstractThis study presents a directional constitutive model to predict the nonproportional cyclic behavior of undrained soft clay. A novel strategy consisting of a combination of directional dilat...

Experimental Study on Noncoaxial Characteristics of Saturated Remolded Loess

In practical engineering, if the influence of noncoaxial stress and strain is not considered, part of soil deformation will be ignored, resulting in the structural design which is not safe enough. A series of undrained tests was performed on remolded loess specimens using a hollow cylinder apparatus to examine the coupling between principal stress magnitude and direction in these specimens. First, the elastic parameters of remolded loess were obtained, and these parameters were used as the basis for investigating the noncoaxiality of the soil body under principal stress axis rotation (PSAR). The effects of elastic strain, intermediate principal stress coefficient, and magnitude of the deviatoric stress on the noncoaxiality of remolded loess were also investigated. The results of these experiments show that remolded loess exhibits significant noncoaxial behavior during PSAR. The noncoaxiality angle of remolded loess cyclically fluctuates with increases in the principal stress angle. It was also observed that the noncoaxiality angle will be overestimated if the effects of elastic strain are overlooked. Reversals in the direction of PSAR cause dramatic changes in the noncoaxiality angle. Increases in the intermediate principal stress coefficient are accompanied by increases in the noncoaxiality angle, up to a certain degree; however, these changes do not affect the development of the noncoaxiality angle. In coupled rotational tests with a range of deviatoric stress amplitudes, it was observed that changes in the deviatoric stress amplitude will affect the development of the noncoaxiality angle; increases in the deviatoric stress amplitude cause the noncoaxiality angle versus principle stress angle plot to shift to the left gradually, thus accelerating the trends of the noncoaxiality angle. Increases in the cycle number also increase the noncoaxiality of remolded loess.

Applicability of Modified University of Illinois at Urbana–Champaign Model for Unbound Aggregate Material with Different Water Content

This paper proposes a modified University of Illinois at Urbana–Champaign (UIUC) model to predict permanent deformation behavior of unbound aggregate materials. Most existing models relate permanent deformation to resilient properties, whereas the UIUC model treats shear strength as a critical factor in permanent deformation behavior. Three types of test, monotonic shearing test, cyclic axial loading test, and cyclic axial and shear loading test, were conducted by multi-ring shear apparatus on two kinds of parallel grading aggregate materials, natural crusher-run and recycled crusher-run obtained from demolished concrete structure. Test results demonstrate that shear strength is the core factor in permanent deformation behavior, compared with resilient properties, and principal stress axis rotation (PSAR) greatly increases the permanent deformation. By considering the effect of PSAR on permanent deformation, a new parameter, ( Rs)ave, is added to the conventional UIUC model to modify it. Regression analysis results verify that the modified UIUC model has good applicability for predicting permanent deformation of aggregates with different water contents and stress states, and with and without PSAR. The modified UIUC model builds a relation between test results with and without PSAR. A simple framework is also proposed for predicting permanent deformation in flexible pavement structures based on the modified UIUC model.

Application of the UIUC model for predicting ballast settlement to unsaturated ballasts under moving wheel loads

Abstract The main objective of this study is to evaluate the practicality of the UIUC model to the Japanese design standard for ballasted tracks of aged lines as well as of new lines by considering some uncertain effects which are not verified and incorporated in the UIUC model, like the effects of ballast fouling, fluctuation in moisture content, and principal stress axis rotation. For this reason, in this study, first the trends in the permanent deformation accumulation of ballasts with various moisture contents and fine fraction contents under moving wheel loads were examined based on the results of advanced laboratory element tests such as triaxial compression tests on unsaturated ballasts and multi-ring shear tests on ballasts under moving wheel loads. Next, the applicability of the UIUC models to the estimation of the permanent deformation accumulation of ballasts were verified by considering the influences of fine fraction content, moisture content, and principal stress axis rotation, and a modification method of the UIUC model necessary for improving the prediction precision and extending the applicability was proposed.

Analysis of dynamic stress path in inhomogenous subgrade under moving aircraft load

Considering the cut and fill alternating characteristic of airport subgrade in mountainous area, especially in the runway direction, a semi-analytic finite element method was proposed to analyze the dynamic response of inhomogenous subgrade under moving aircraft load. This method can decrease the computational cost effectively by using the Fourier Transform in the transverse direction of the runway to reduce the dimension of the 3D problem and account for the traveling wave effect of moving load. The dynamic responses of a soil element in homogenous and inhomogeneous subgrade subjected to single-wheel aircraft load were analyzed comparatively. The results show that the dynamic stresses generated in soil element are mainly vertical normal stress and in-plane shear stress, forming stress paths with the characteristic of complex principal cyclic stress axis rotation. Due to the traveling wave effect, the dynamic responses of soil are not antisymmetric when the moving load approaches and leaves the observation point. In the homogeneous subgrade, the dynamic stress path in the plane of the two shear stress components is egg-shaped with a tilting angle. As the moving load velocity grows, the long axis of the egg-shaped stress path rotates counterclockwise. In the inhomogeneous subgrade, the dynamic stress is concentrated near the junction of cut and fill areas, and the peak value of the vertical dynamic stress is 1.35 times that in the homogeneous subgrade. Moreover, the stress path near the junction tends to be more prolate and spindle-shaped.