Effects Of Principal Stress Rotation Research Articles

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.

A state-dependent multilaminate constitutive model for anisotropic sands

Experimental studies show that initial fabric and its evolution under different stress paths greatly influences soil behaviour. Even though different sample preparation methods create different inherent anisotropies and cause different material responses, the same initial fabric structure under different stress paths also results in different material behaviours. In this paper, a simple state-dependent, bounding surface-based elastoplastic constitutive model, which can simulate the anisotropic nature of sands including the effect of principal stress rotation, is described. The model is developed based on a semi-micromechanical concept within the multilaminate framework and, to include the inherent anisotropy of sand, a deviatoric fabric tensor describing the initial microstructure is introduced. In addition, a fabric evolution rule compatible with anisotropic critical state theory is employed to describe the evolving fabric structure and induced anisotropy towards the critical state. In contrast to the classical strain-driven formulation for fabric evolution, a micro-level evolution rule is proposed. This paper presents concise theoretical aspects of the multilaminate framework and the anisotropic elastoplastic constitutive formulation. The model's capability under drained and undrained monotonic loading conditions at different stress states, relative densities and principal stress orientations is demonstrated by simulating experimental data for Toyoura sand.

Effect of Principal Stress Rotation and Intermediate Principal Stress Changes on the Liquefaction Resistance and Undrained Cyclic Response of Ottawa Sand

Effect of Principal Stress Rotation and Intermediate Principal Stress Changes on the Liquefaction Resistance and Undrained Cyclic Response of Ottawa Sand

Geotechnical rheological modeling of ballasted railway tracks considering the effect of principal stress rotation

The rotation of principal stress direction experienced by the soil elements in a railway track substructure during a train passage influences the magnitude of accumulated settlement. However, the existing methods to evaluate the track response under repeated train loads disregard the influence of principal stress rotation (PSR). This article presents a novel approach for assessing the behavior of ballasted railway tracks incorporating the contribution of PSR on track deformation. The proposed technique employs a geotechnical rheological model to evaluate the track behavior, in which the material plasticity is captured through plastic slider elements. The influence of PSR is accounted for by extending an existing constitutive relationship for the slider elements for the substructure layers, which is successfully validated against experimental data reported in the literature. The results reveal that PSR causes significant cumulative deformation in the substructure layers, and disregarding it in the analysis leads to inaccurate predictions. The proposed approach is then applied to an open track-bridge transition with heterogeneous support conditions, in which the differential settlement is found to be largely influenced by PSR. The findings from this study highlight the importance of including the effect of PSR in predictive models for a reliable evaluation of track performance.

Numerical simulation of cyclic shear tests considering the fabric change and principal stress rotation effects

AbstractCyclic loadings could induce complicated soil responses, including the fabric change and principal stress rotation, both of which would reduce the effective confining pressure and accelerate the build‐up of excess pore water pressures, thus leading to sand liquefaction in undrained conditions. The principal stress rotation, even without the change of principal stress magnitudes, would further generate the accumulative plastic shear strains. However, most of the existing studies focus on their individual effect and the combined effect was seldom considered. In this paper, a numerical approach including an elastoplastic sand constitutive model is proposed to consider the combined effect of the fabric change and principal stress rotation. In this model, the fabric change is considered with the anisotropic critical state theory and the principal stress rotation is considered by splitting the plastic strain increment into the monotonic part and rotational part. By simulating a series of cyclic shear tests, results from the numerical solutions are found showing good agreements with the existing experimental results and the importance of considering the combined effect is demonstrated. The approach can be used to predict the stress‐strain response of sand and guide the design of foundations especially in undrained cyclic loading conditions, for example, earthquake loadings conditions.

Constitutive modeling of principal stress rotation associated with sand under simple shear loading

AbstractAn elasto‐plastic constitutive model is proposed to account for the effect of principal stress rotation that commonly occurs and significantly influences soil behavior. The model is based on a concept of adding plastic strain increments obtained from two mobilized planes: a plane of maximum shear stress which swings as the principal stress rotates, and a horizontal plane which is spatially fixed. Models based on the plane of maximum shear stress alone are particularly sensitive to horizontal effective stress ratioK0(=σ′x/σ′y), whereas the proposed model gives a similar skeleton behavior for soils at the same density and mean effective stress, regardless of the value ofK0, as observed in laboratory tests. The model is firstly calibrated by data from drained and undrained monotonic and cyclic Direct Simple Shear (DSS) tests onK0‐consolidated specimens of Nakdong River sand in loose and dense states. The capability of the proposed model in modeling of the conventional liquefaction effects: initial shear stress conditionα(=τ′xy/σ′y) withKαcorrections, and initial confining stress conditionσ´ywithKσcorrections, is also emphasized in this paper.

Effects of principal stress rotation on deformation behaviour of clay under partially drained and undrained conditions

Subgrade clay in regions with busy roads is more likely to exhibit partially drained than undrained cyclic behaviour considering the long duration of traffic loads. To study the deformation response of soft clay under the two drainage conditions, cyclic tests were conducted on a dynamic hollow cylinder apparatus with and without principal stress rotation. The concept of transitional cyclic stress ratio (CSR) was proposed. When the CSR is lower than the transitional CSR, the partially drained condition causes permanent axial strain enlargement when compared with the undrained conditions; Once the CSR exceeds the transitional CSR, the partially drained condition markedly restricts the development of the permanent axial strain. Moreover, both critical and allowable CSR in the partially drained tests are higher than in the undrained ones, and the allowable CSR under different drainage conditions is smaller than the transitional CSR. Therefore, the influence of the partially drained condition on the cyclic deformation of clay must be considered in practice. Two empirical models were proposed to predict the permanent volumetric strain and permanent axial strain under the partially drained condition.

Deformation Behavior of Saturated Soft Clay under Cyclic Loading with Principal Stress Rotation

Under long-term traffic loading, the soil elements in subgrade are subjected to continuous principal stress rotation. In order to study the deformation properties of soft clays under traffic loading with principal stress rotation, a series of cyclic torsional shear tests were conducted on Wenzhou soft clays under different torsional cyclic stress ratios and degrees of principal stress rotation. The test results showed the stiffness softening of soil under long-term traffic loading. In addition, the principal stress rotation induced by traffic loading aggravated the deformation of clay samples and pore pressure accumulation. A modified dynamic pore pressure model was applied to consider the effect of principal stress rotation on undrained cumulative pore pressure, predicting the growth of cumulative pore pressure at different cycles. Considering loading cycles and the principal stress rotation, a modified Hardin–Drnevich (H-D) backbone curve model under traffic loading with principal stress rotation was proposed, and the predictive values of this model agreed well with the experimental values. Compared with the traditional H–D model, this model better reflects the cyclic deformation of soft clays under long-term traffic loading with principal stress rotation.

The Mechanism of Rock Mass Crack Propagation of Principal Stress Rotation in the Process of Tunnel Excavation

Rock excavation has experienced complex stress paths. The development of the original crack under the path of principal stress magnitude and principal stress direction is a key scientific problem that needs to be solved in rock underground engineering. The principal stress magnitude dominates the initiation and propagation of the crack and increases rock damage under the action of principal stress rotation. In this study, the theoretical calculation and numerical analysis method have been combined with the crack propagation conditions to study the stress-driven mechanism of brittle rock crack propagation under principal stress rotation. The results show that the “relative initial angle” of crack angle is being updated in time during the principal stress rotation process; once the stress is rotated, it will become the next initial crack angle; the crack propagation direction is deviated under the applied shear load, and it is always in the direction of minimum shear load, leading to a certain degree of inhibition of crack propagation depth in the initial direction. According to the results of numerical simulation, the effect of principal stress rotation caused by mining excavation is obvious and has a certain range of influence depth, the stress of surrounding rock of roadway is the highest within the depth range of 1∼2 m, and the maximum principal stress is as high as 26.89 MPa. The rotation of principal stress direction on the roadway surrounding rock surface is the strongest, which makes the surrounding rock more fragmented, and the middle principal stress and the maximum principal stress rotate about 90° counterclockwise along the Ox axis. Studying the action mechanism of principal stress rotation on fractured rock masses can provide scientific basis for geotechnical engineering design and rock mass surrounding support.

Effect of principal stress rotation on deformation behavior of dense sand–clay mixtures

This paper investigated the deformation behaviour of K-consolidated sand–clay mixtures through cyclic triaxial (CT) and hollow cylinder (CHC) tests. The sand–clay mixtures contained 0%, 5%, 10% and 20% clay by weight and were prepared at a relative density of 75%. Clay inclusion caused an increase in the permanent axial strain of mixtures (0.075% to 5% in CT and 0.186% to 5% in CHC), while a relatively insignificant increase in permanent axial strain was observed in the CT specimens containing 5% and 10% clay (0.075% to 1.299%). However, all CHC specimens with clay failed (εz ≥ 5%). It was also observed that shear strain development of sand is significantly influenced by clay inclusion (0.096–2.241%) in CHC tests. Test results clearly show that the effect of a principal stress rotation should be taken into account to better estimate the deformation behaviour of sand–clay mixtures under repetitive traffic loads.

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.

Effect of principal stress rotation on the stability of a roadway constructed in half-coal-rock stratum and its control technology

Engineering disturbance-induced adjustment of the stress field in the surrounding rock is the main reason that leads to dynamic disasters in deep rocks. This study selected the mining roadway in the No. 92125 working face of the Chacheng Coal Mine as the engineering background for in-depth and systematical analysis on the principal stress path and the changes in the principal stress direction of surrounding rocks under excavation-induced disturbance and the resultant damages. Results demonstrate that the fracture planes were along the direction of intermediate principal stress under true triaxial tests and the internal cracks in the rock strongly depend on the direction of the intermediate principal stress. Therefore, variations in the stress path of the roadway surrounding rocks can cause dramatic changes in their fracture characteristics (direction of rupture). The same results were found for the analysis: the variation of the direction of principal stress on the surrounding rocks in the roadway created adverse effects, which thus triggered great damages. The areas of roof and the shoulder angle, etc. were strongly affected by the principal stress rotation, and the damage caused was obvious. According to the damage characteristics of the surrounding rocks caused by the principal stress rotation during excavation in half-coal-rock roadway, the idea of strengthening support in key areas was proposed, and a high-strength pre-tension support scheme using anchor beam, nets, and cables was proposed. Finally, field measurement results of displacement on the surface and in surrounding rocks reveal that using the optimized supporting scheme effectively controlled deformation in the roadway, ensuring stability of the roadway and meeting engineering requirements.

Analysing the effect of principal stress rotation on railway track settlement by discrete element method

Principal stress rotation induced by moving loads from trains significantly influences railway track settlement accumulation. The stationary cyclic loading commonly adopted to study railway ballast behaviour under repeated train loading cannot fully represent the effects of principal stress rotation, which needs to be properly considered in both laboratory tests and numerical simulations for a better understanding of ballast deformation behaviour. This paper focuses on studying railway ballast deformation behaviour with an emphasis on particle scale interactions under two different loading scenarios – namely, stationary cyclic and moving wheel loading. A ballasted track model consisting of five sleepers was established based on the discrete-element method (DEM) with realistic polyhedron-shaped elements. The numerical model was validated first based on the testing results from a full-scale high-speed railway testing facility at Zhejiang University. Numerical results clearly indicated that moving wheel loading induced larger principal stress rotation than stationed cyclic loading did. Larger principal stress rotation mobilised higher particle rotation and displacement, which further increased particle rearrangements through individual particle rolling and sliding, and potentially could cause accelerated ballast degradation. It is recommended to consider principal stress rotation in ballast settlement predictions to prevent possible underestimation by stationary cyclic loading and its limitations.

Assessment of Pohang Earthquake-Induced Liquefaction at Youngil-Man Port Using the UBCSAND2 Model

The practical constitutive model UBCSAND2, which combines two-mobilized planes—a maximum shear stress plane and a horizontal plane within a framework of classical plasticity approach—is used to incorporate shear-induced effects in both loading and unloading as well as principal stress rotation effects. UBCSAND2 was calibrated by capturing cyclic direct simple shear (CDSS) test results of Pohang sand, which was collected from liquefied paddy fields due to the 2017 Pohang earthquake (Mw = 5.4) in South Korea. The model procedure focuses on simple shear condition because it best simulates field conditions under earthquake loading. The calibrated UBCSAND2 model is then used to assess the liquefaction-induced damages that occurred at the quay wall and backfill layer in Youngil-man port near the epicenter of the Pohang earthquake. The numerical results show that liquefaction mostly occurred in silty sand layers, in which the excess pore pressure ratio reached almost one. The estimated displacements of the quay wall and the predicted settlement of reclaimed area obtained from the analysis were in good agreement with those obtained from field measurements.

Influence of Initial Anisotropy, Stress Path and Principal Stress Rotation on Monotonic Behavior of Clean and Mixed Sands

It is widely accepted that soil behavior is complicated taking into account soil anisotropy owing to the fact that this phenomenon arises from oriented soil fabric or structure forged in the deposition stage. In this study, a review of major findings of authors’ previous studies are presented with the main focus on soil anisotropy using extensive experimental results incuding Triaxial (TXT), Simple Shear (SSA), and Hollow Cylinder (HCA) apparatus. Effects of initial anisotropy, fabric evolution, stress path, principal stress rotation and intermediate stress state are evaluated for a crushed silica sand. In addition, the effects of Portland cement content and granulated rubber contents on anisotropic behavior of the sand are investigated. Bender elments are mounted on triaxial specimens both in vertical and horizontal directions to measure the shear wave velocity and hence maximum shear modulus at the end of consolidation as well as during shearing up to large strains at critical state condition, as an index of evaluating the fabric evolution. The effects of principal stress rotation and stress paths reveals the crucial role of soil anisotropy on the behavior of clean sand. However, adding either cement or granulated rubber to the sand has considerably decreased anisotropy.

Effect of principal stress rotation on dynamic characteristics of a sandy seabed under a partially reflected standing wave

Principal stress rotation (PSR) is one of the main stress conditions for a soil element subject to cyclic waves. It is one of the main causes behind generation of excess pore water pressure and cumulative plastic strain in soil deposits when drainage conditions are impeded, and thus compromises the stability of any supported marine structures. This paper aims to investigate the influence of PSR on the cyclic characteristics of soil under standing waves that are partially reflected, in which a generalized plasticity model considering the effect of PSR was adopted to model the soil behavior. Comparisons between the present model, previous hollow cylinder apparatus tests, and geotechnical centrifugal wave tests all show good agreement. Numerical results indicate that ignoring the PSR involved in the standing-wave–seabed interactions will significantly underestimate the build-up of pore water pressure, particularly at the standing wave nodes. Furthermore, the exclusion of the effect of PSR may lead to contradictory results in terms of susceptibility to liquefaction between the antinode and the node, when compared to the wave flume test and geotechnical centrifuge test. Numerical simulation results also demonstrate that while considering the impact of PSR, a sandy seabed exhibits higher liquefaction resistance when subjected to standing waves compared to the case when subjected to progressive waves with an equivalent wave height. Parametric studies show that the coefficient of wave reflection, wave characteristics (wave height, period, and water depth), and soil properties (permeability and saturation) significantly affect the liquefaction characteristics of soil under partially reflected standing waves.

Influences of principal stress rotation (PSR) on the cumulative deformation of remoulded loess with different water contents under traffic loading

In the present paper, a series of cyclic hollow cylinder tests are conducted to study the cyclic principal stress rotation (PSR) in traffic load engineering. The strain accumulation behaviour of remoulded loess with different water contents under traffic load was examined. The test results show that the magnitude of the cyclic deviatoric stress and shear stress and the water content significantly contributes to the differences of the strain accumulation. When the cyclic deviatoric stress and shear stress were held constant, permanent axial strain increased with water content. Permanent axial strain increased with deviatoric stress and shear stress under the same water content. Furthermore, test data could be interpreted within a framework of multiple threshold cyclic stress ratios, and the critical stress ratio in different regions decreases with increase in water content. Finally, a nonlinear empirical formula for permanent axial strain considering the effects of principal stress rotation (PSR) was proposed to be used for the feasibility studies on remoulded loess subjected to traffic loading.

Dynamic characteristics of a sandy seabed under storm wave loading considering the effect of principal stress rotation

This paper aims to investigate the cyclic characteristics of soil under storm waves with the typical irregular character, in which a generalized plasticity model considering the effect of principal stress rotation (PSR) was adopted to model soil behavior. In the present model, the plastic strain generated by principal stress rotation was considered to be an additional item in the constitutive relationship of soil, and the normalized loading and plastic flow directions were determined based on the stress tensor invariants. Comparisons between the present model, previous hollow cylinder apparatus (HCA) tests, and geotechnical centrifugal wave tests all show good agreement. Numerical results indicate that the moveable and random characteristics of the storm wave result in similar and irregular dynamic responses in sandy deposits along the extension direction of the seabed. Moreover, the severest wave loading in a real storm will significantly magnify both the speed and extent of liquefaction of the sandy seabed. Numerical results also demonstrate that ignoring the PSR involved in the storm–wave–seabed interaction will significantly underestimate the build-up of pore water pressure. Additionally, when considering the impact of PSR, the sandy seabed exhibits higher liquefaction resistance when subjected to the random wave compared to the representative regular wave. However, since the sharply weakening liquefaction resistance of soil under the severest wave condition cannot be captured with the regular wave, it is suggested that the random wave be adopted to further investigate the storm–wave–seabed interaction. Parametric studies show that soil properties (e.g., permeability and saturation) significantly affect the liquefaction characteristics of soil under storm waves.

Effects of Principal Stress Rotation on the Fluid-Induced Soil Response in a Porous Seabed

Principal stress rotation (PSR) is an important feature for describing the stress status of marine sediments subject to cyclic loading. In this study, a one-way coupled numerical model that combines the fluid model (for wave–current interactions) and the soil model (including the effect of PSR) was established. Then, the proposed model was incorporated into the finite element analysis procedure DIANA-SWANDYNE II with PSR effects incorporated and further validated by the experimental data available in the literature. Finally, the impact of PSR on the pore-water pressures and the resultant seabed liquefaction were investigated using the numerical model, and it was found that PSR had a significant influence on the seabed response to combined wave and current loading.

Effects of principal stress rotation on wave-induced soil response in a poro-elastoplastic sandy seabed

In this study, a constitutive model is developed in order to investigate wave–seabed interactions. This model takes into account the impact of principal stress rotation (PSR) and is based on the generalized plasticity theory, in which plastic strain generated by PSR is considered an additional item in the constitutive relationship of soil. The normalized loading direction and plastic flow direction were determined based on the stress tensor invariant. Comparisons between the present model and previous Hollow Cylinder Apparatus tests and geotechnical centrifugal wave tests show good agreement. Numerical results show the effects of PSR on predictions of liquefaction potential due to: (a) the cumulative impact of plastic strain in the seafloor and (b) the buildup of pore pressure. Parametric study shows that the model parameters, including the wave and seabed parameters, have significant effects on the wave-induced soil liquefaction.