Principal Stress Rotation Research Articles

Shear stress-strain relationships and anisotropy in silty soil: The role of principal stress rotation

Shear stress-strain relationships and anisotropy in silty soil: The role of principal stress rotation

Study on micromechanical behavior and energy evolution of granular material generated by latent diffusion model under rotation of principal stresses

In this study, advanced image processing technology is used to analyze the three-dimensional sand composite image, and the topography features of sand particles are successfully extracted and saved as high-quality image files. These image files were then trained using the latent diffusion model (LDM) to generate a large number of sand particles with real morphology, which were then applied to numerical studies. The effects of particle morphology on the macroscopic mechanical behavior and microscopic energy evolution of sand under complex stress paths were studied in detail, combined with the circular and elliptical particles widely used in current tests. The results show that with the increase of the irregularity of the sample shape, the cycle period and radius of the closed circle formed by the partial strain curve gradually decrease, and the center of the circle gradually shifts. In addition, the volume strain and liquefaction strength of sand samples increase with the increase of particle shape irregularity. It is particularly noteworthy that obvious vortex structures exist in the positions near the center where deformation is severe in the samples of circular and elliptical particles. However, such structures are difficult to be directly observed in sample with irregular particles. This phenomenon reveals the influence of particle morphology on the complexity of the mechanical behavior of sand, providing us with new insights into the understanding of the response mechanism of sand soil under complex stress conditions.

Permanent deformation and particle crushability of calcareous sands under cyclic traffic-induced loadings through simple shear apparatus

This study focuses on investigating permanent deformations, encompassing normal and shear strains, of calcareous sandy soils subjected to drained cyclic traffic-induced loadings. The investigation utilizes a Simple Shear (SS) apparatus allowing for variations in both normal and shear stress components over each cycle and incorporates Principal Stress Rotation (PSR), a feature not replicable in conventional cyclic uniaxial triaxial tests which is the key aspect of this research. The study also accounts for the harmonically changing the effective horizontal stress resulting from cyclic variations of effective vertical stress, conducted under a horizontally constrained boundary condition with zero lateral strain. A series of drained cyclic simple shear experiments is carried out, implementing a heart-shaped stress path, encompassing up to 1000 cycles. The objective of the study is to analyze permanent normal and shear deformations, along with associated total particle crushing, using both sieving analyses and 2D image processing of particles. The study also evaluates the impact of an initial static shear stress originating from the longitudinal slope of roads. The findings highlight the influences of induced cyclic amplitudes of stress components, principal stress and strain rate rotation, and initial static shear stress on the development of permanent strains. Furthermore, the research characterizes particle crushability in terms of total crushability over such loading, examining its dependency on relative density and variations in both shear and normal stress components.

Experimental investigation of cyclic responses of frozen soil under principal stress rotation induced by wave loads

Experimental investigation of cyclic responses of frozen soil under principal stress rotation induced by wave loads

In-plane biaxial fatigue life prediction model for high-cycle fatigue under synchronous sinusoidal loading

The unique advantage of in-plane biaxial loading is no rotation of the maximum principal stress during cyclic loading, which has a distinct effect on fatigue life. This study aims to propose a life prediction model for in-plane biaxial fatigue encompassing both in-phase and out-of-phase conditions. For synchronous sinusoidal loadings, an equivalent stress expression is derived using the integral method, accounting for the influences of shear and normal stresses across all planes. The equivalent stress is then compared to a reversed uniaxial constant amplitude loading to predict fatigue life. To validate and compare the model, in-phase and out-of-phase in-plane biaxial fatigue experiments were conducted using 24 nickel-based superalloy cruciform specimens at temperatures of 420℃, 550℃, and 600℃. The results show that the proposed model is superior to conventional stress-invariant based models, with most results staying within the ± 2 error bands. Using the proposed model, the effects of mean tensile stress, biaxiality and phase shift are discussed. Additionally, a novel non-proportional factor is introduced to enhance multiaxial fatigue life prediction by distinctly separating the effects of principal stress and its directional variations.

An analytical modelling of the rotation of in-situ principal stresses orientation in the vicinity of an underground opening

ABSTRACT An underground excavation would lead to the redistribution of not only stress magnitude but also stress direction in the host rock mass. In this paper, an equation was derived to quantify the principal stress orientation rotation angle along the roadway radial direction. Besides, the principal stress orientation rotation gradient was analytically modelled followed by a sensitivity analysis of various influential factors on the principal stress orientation rotation. It was found that the principal stress orientation rotation angle tends to decrease as moving further radially into the rock mass from the excavation surface, where the principal stress rotation angle reaches its maximum value of 90°. Four zones have been classified according to the principal stress orientation rotation gradient including high-frequency , medium-frequency, low-frequency and no rotation zone. Finally, the numerical analysis confirmed the redistribution of the principal stress difference and the rotation angle and provided guidance for optimising the bolts setting angle.

Soft rock deformation and failure modes under principal stress rotation from roadway excavation

Soft rock deformation and failure modes under principal stress rotation from roadway excavation

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.

Influence and Mechanism of the Excavation Width on Excavation Deformations in Shanghai Soft Clay

This study investigated the influence and mechanism of the excavation width on excavation deformations in Shanghai soft clay. Based on three excavations that had different final excavation depths, dissimilar retaining structures and diverse geological conditions, 40 sets of two-dimensional numerical models with different excavation widths were employed to analyze the deformation rules affected by the excavation width. Moreover, a series of simplified models with different excavation widths were employed to analyze the effect of the excavation width on excavation deformations. The results show that under the same excavation depth, both the horizontal displacements of the retaining walls and ground surface settlements increase as the excavation width increases, but the increasing rate gradually decreases. Factors such as the unloading influence depth, the overlap degree of the passive zones, the stress state of the basal soils and the development of the relative shear stress have a significant influence on excavation deformations. With increasing excavation width, the unloading influence depth gradually deepens, the overlap area of the passive zones gradually decreases, the direction of the rotation of the major principal stress gradually reduces and the relative shear stress of the distant and deep soils gradually expands. Therefore, the constraint ability of the passive zones on excavation deformation gradually reduces and excavation deformations gradually increase.

Impact of particle arrangement and model dimensions on DEM modeling of high-speed railway ballasted tracks in 2D and 3D

Modelling railway projects has a main challenge in the discrete element method (DEM). The granular material of the embankment consists of millions of fine angular particles which are difficult to model due to the long computational time. The long computational time also prevents the modeling of the higher number of loading cycles. As a result, researchers prefer to simulate the project in 2D to accelerate the simulation. While 2D simulations present a seemingly simple option for modeling railways, they tend to oversimplify the intricacies of particle interactions and the distribution of stress. Nonetheless, the extent to which these simplifications affect the authenticity of the simulations has remained ambiguous. In this study, the periodic cell replication method is used to build extensive long railway tracks significantly faster than conventional methods. Then, this DEM model is calibrated against the measurement results of a physical full-scale ballasted track. The model is then used to simulate several railway projects with different initial particle arrangements and model dimensions in both 2D and 3D. The results show that the 2D models are more dependant on the initial particle arrangement which shows different behavior for the same model. In addition, 2D simulations are incapable of reproducing the principal stress rotation in granular layers due to the moving load of the train wheel. As a result, 3D DEM simulations using the periodic cell replication method is suggested for studying the railway tracks.

Rock strength weakening subject to principal stress rotation: Experimental and numerical investigations

During the construction and operation of gas storage reservoirs, changes in the principal stress direction can induce fracture propagation under conditions of lower differential stress, potentially leading to failure in the surrounding rock. However, the weakening of strength due to pure stress rotation has not yet been investigated. Based on fracture mechanics, an enhanced Mohr-Coulomb strength criterion considering stress rotation is proposed and verified with experimental and numerical simulations. The micro-damage state and the evolution of the rock under the pure stress-rotation condition are analyzed. The findings indicate that differential stress exceeding the crack initiation stress is a prerequisite for stress rotation to promote the development of rock damage. As the differential stress increases, stress rotation is more likely to induce rock damage, leading to a transition from brittle to plastic failure, characterized by wider fractures and a more complex fracture network. Overall, a negative exponential relationship exists between the stress rotation angle required for rock failure and the differential stress. The feasibility of applying the enhanced criterion to practical engineering is discussed using monitoring data obtained from a mine-by tunnel. This study introduces new concepts for understanding the damage evolution of the surrounding rock under complex stress paths and offers a new theoretical basis for predicting the damage of gas storage reservoirs.

Modified SANISAND‐F model for simple shear path

AbstractSimple shear behavior of sand is representative in geotechnical engineering with potential failure occurred along a thin shear zone. The strength and deformation of sand under simple shear are accompanied with principal stress rotation (PSR). This study proposes a modified SANISAND‐F model to capture the simple shear behavior of sand with PSR. A new plastic flow rule along with a kinematic hardening modulus is proposed to consider the evolution of the PSR and intermediate stress ratio. The developed model, with thirteen parameters, can reasonably the capture the stress‐strain and PSR of sand under simple shear.

Granular behaviour under bi-directional shear with constant vertical stress and constant volume

This paper aims to investigate the role of bi-directional shear in the mechanical behaviour of granular materials and macro-micro relations by conducting experiments and discrete element method (DEM) modelling. The bi-directional shear consists of a static shear consolidation and subsequent shear under constant vertical stress and constant volume conditions. A side wall node loading method is used to exert bi-directional shear of various angles. The results show that bi-directional shear can significantly influence the mechanical behaviour of granular materials. However, the relationship between bi-directional shear and mechanical responses relies on loading conditions, i.e. constant vertical stress or constant volume conditions. The stress states induced by static shear consolidation are affected by loading angles, which are enlarged by subsequent shear, consistent with the relationship between bi-directional shear and principal stresses. It provides evidence for the dissipation of stresses accompanying static liquefaction of granular materials. The presence of bi-directional principal stress rotation (PSR) is demonstrated, which evidences why the bi-directional shear of loading angles with components in two directions results in faster dissipations of stresses with static liquefaction. Contant volume shearing leads to cross-anisotropic stress and fabric at micro-contacts, but constant vertical stress shearing leads to complete anisotropic stress and fabric at micro-contacts. It explains the differentiating relationship between stress-strain responses and fabric anisotropy under these two conditions. Micromechanical signatures such as the slip state of micro-contacts and coordination number are also examined, providing further insights into understanding granular behaviour under bi-directional shear.

Unified modeling for clay and sand with a hybrid-driven fabric evolution law

This paper presents a novel critical state model for both clay and sand considering the inherent and induced anisotropy, named as CASM-h. The CASM-h model is developed based on the well-calibrated CASM model and incorporates the concepts of subloading surface and fabric anisotropy. To describe the induced anisotropy, a hybrid-driven fabric evolution law is proposed, defining fabric evolution as driven jointly by stress and strain rates. Subsequently, the fabric tensor together with its evolution law is appropriately incorporated into constitutive relation by employing the anisotropic transformed stress approach, without introducing additional mechanical mechanisms. The CASM-h model is validated under a series of stress paths, including triaxial tests, simple shear tests, shear tests with fixed principal stress direction as well as principal stress rotation (PSR) tests. The simulation results show that CASM-h model can satisfactorily capture the anisotropic behaviours of both clay and sand, such as the loading direction dependency of strength, non-coaxial behaviour, PSR effects and so on.

Macro-micro numerical analysis of granular materials considering principal stress rotation based on DEM simulation of dynamic hollow cylinder test

The granular materials were subjected to the principal stress rotation effect induced by traffic loads, wave loads, and earthquake loads in geotechnical engineering practice. In order to reveal the influence of principal stress rotation on the macro-micro dynamic characteristics, this study proposed a numerical simulation method modeling physical dynamic hollow cylinder tests. Taking the dynamic stress state induced by traffic loading as an example, the numerical test model of the dynamic hollow cylinder was conducted on the subgrade soil, and the influence of principal stress rotation on the macro-micro evolution of dynamic characteristics was analyzed.The results showed that the principal stress rotation accelerated the development of vertical accumulative plastic strain and particle displacement, which aggravated micro-structure destruction of granular material. Moreover, the increase of confining stress declined the variations of normal contact numbers in each direction, which resisted the shear stress induced by principal stress rotation. This study provided a novel method to investigate the macro-micro dynamic characteristics of granular materials subjected to principal stress rotation, which made up for the inability of physical hollow cylinder tests to study microscopic evolution.

Experimental study of stress direction dependence of sand under biaxial rotation of principal stress

Experimental study of stress direction dependence of sand under biaxial rotation of principal stress

Cumulative deformation and non-coaxial characteristics of fiber and cement-modified iron tailings under the rotation of principal stress

In order to study the deformation characteristics of fiber and cement-modified iron tailings (FCIT) under traffic loads, the cumulative deformation, stress–strain paths, cyclic stiffness, and non-coaxial characteristics of FCIT under the coupling of different cyclic stress ratios (CSR) and torsional shear stress ratios (η) were analyzed by using a heart-shaped stress path. The results indicate that: 1) The cumulative strain and torsional shear strain of FCIT under the rotation of the principal stress vary with CSR and η. The established empirical formula for the cumulative strain can be used to calculate the cumulative deformation of FCIT under different principal stress rotations based on the results of cyclic triaxial tests. 2) The difference between shear stiffness and positive deviation stiffness is the inherent mechanism that induces the non-coaxial characteristics of FCIT, that is, shear stiffness is subjected to torsional shear stress more than positive deviation stiffness is subjected to axial stress. 3) The non-coaxial characteristics of FCIT gradually weaken with the increase of axial force and torsional shear force, while the non-coaxial angle between the direction of strain increment and the direction of stress decreases.

DEM study on the non-coaxial deformation characteristics of granular soils under various traffic loading conditions

Although the macro-scale stress–strain relations of sands under traffic loading can be investigated using hollow cylinder apparatus, the microscopic mechanism of the deformation accumulation and the non-coaxial behavior of sands under principal stress rotation induced by the traffic loading has not been fully understood. In this paper, both isotropic and transversely isotropic specimens comprised of elongated particles were generated using the discrete element method. The non-coaxial deformation characteristics of granular soils under various types of cardioid-shaped loading paths are illustrated in detail. The simulation results show that a greater cyclic vertical stress ratio and cyclic torsional stress ratio can lead to a smaller non-coaxial angle between the principal directions of stress and strain increment. The evolution of the internal structure is quantified by the contact-normal-based fabric tensor, which describes the load-bearing structure of granular specimens. The transversely isotropic specimen exhibits more significant non-coaxiality between the loading direction and the principal direction of the fabric and therefore greater volumetric contraction than that of the isotropic specimens. Moreover, the transversely isotropic specimen shows smaller normal strain accumulation than that of the isotropic specimen, which can be well explained by the interplay between the modulus of the specimen and the fabric evolutions.

Experimental Study on the Axial Deformation Characteristics of Compacted Lanzhou Loess under Traffic Loads

It is beneficial to the sustainable development of expressway engineering to reuse excavated soil as roadbed filling material. There are a large number of filling projects using loess as a filling material in Northwest China. In this paper, the loess subgrade of an expressway in Lanzhou is taken as the research object, and a series of experimental studies are conducted using a hollow cylindrical torsion shear system to simulate the formation of a “heart-shaped” stress path and the principal stress rotation (PSR) under long-term traffic loads. The effects of the vertical cyclic dynamic stress ratio, torsion shear stress ratio, initial static shear stress, and intermediate principal stress coefficient on the axial plastic deformation and rebound deformation of compacted loess in Lanzhou were studied. The results show that the vertical cyclic stress ratio (VCSR) has a significant effect on the axial deformation of compacted loess in Lanzhou. When the VCSR is less than 0.6, all the axial strain curves develop stably with the number of cycles. With an increasing VCSR, the axial plastic deformation increases obviously, and the axial rebound deformation also increases. The vertical cyclic dynamic stress of the specimen is constant. Moreover, increasing the torsional shear stress ratio (that is, increasing the amplitude of cyclic shear stress) can greatly increase the development of axial deformation, but it has no effect on the rebound deformation curve. When the initial static shear stress exists in the specimen, the larger the initial static stress ratio (SSR) is, the larger the axial plastic deformation. The axial plastic deformation increases by approximately 33% for every 0.1 increase in the SSR. The rebound deformation of different SSRs fluctuates at the initial stage of cyclic loading, but the final stable rebound deformation is basically the same as that at the initial stage of cyclic loading. The intermediate principal stress coefficient has no effect on the development of axial strain, and the effect on axial rebound deformation is negligible. Finally, the calculation model of the axial plastic strain of Lanzhou compacted loess under traffic loads is obtained. The research results can provide a reference for the durability and settlement prediction in loess engineering.

Dynamic properties of dredger fill involved coupling action of initial stress and principal stress rotation

GCTS hollow cylinder apparatus was used to perform a series of tests on dredger fill from Tianjin under different initial stress states. This cyclic loading mode can simulate the rotation of the principal stress direction induced by wave loading. The effects of the initial intermediate principal stress parameter, initial shear stress and initial orientation angle of principal stress on softening index of dredger fill were investigated. A stiffness softening model which can consider different initial stress states was established. The test results show that when two of the three initial stress parameters remain unchanged, the softening index decreased with the increase of any other parameter. Among them, the initial orientation angle of principal stress has a great influence on stiffness softening. Based on the regression analysis of the test data, the relationship between the generalized shear strain ratio and the number of cycles under different cyclic shear stress amplitudes is proposed. Subsequently, the dynamic strength characteristics of the dredger fill were studied. It is found that the dynamic strength decreased significantly with the increasing initial angle of the principal stress, which can be accurately described by the model proposed in this article.