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.

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 bidirectional 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 bidirectional 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.

Cyclic strength of sand under a nonstandard elliptical rotation stress path induced by wave loading

The principal stress rotation is one of the most important features of the stress state in a seabed subjected to wave loading. Most prior investigations focused their attention on the cyclic behaviour of soil deposits under the circular rotation stress path based on the analytical solutions for a seabed of infinite thickness. In this paper, the nonstandard elliptical, i.e., non-circular, rotation stress path is shown to be a more common state in the soil sediments of a finite seabed with an alternating changeover in stress due to a travelling regular wave. Then an experimental investigation in a hollow cylinder triaxial-torsional apparatus is conducted into the effect of the nonstandard elliptical stress path on the cyclic strength. A special attention is placed on the difference between the circular rotation stress path and the elliptical rotation stress path. The results and observations show that the shear characteristics for the circular rotation stress path in the literature are not applicable for analyzing the cyclic strength of sand in a finite seabed, and also indicate that due to the influence of three parameters about the size and the shape of a nonstandard ellipse, the cyclic strength under a nonstandard elliptical rotation stress path is evidently more complex and diversified as compared with that under a circular rotation stress path. Especially the influence of the initial phase difference on the cyclic strength is significant.

Influence of principal stress rotation of unequal tensile and compressive stress amplitudes on characteristics of soft clay

Soil behavior can reflect the characteristics of principal stress rotation under dynamic wave and traffic loads. Unequal amplitudes of tensile and compressive stresses applied to soils have complex effects on foundation soils in comparison with the pure principal stress rotation path. A series of undrained cyclic hollow torsional shear tests were performed on typical remolded soft clay from the Hexi area of Nanjing, China. The main control parameters were the tensile and compressive stress amplitude ratio(α) and the cyclic dynamic stress ratio(η). It was found that the critical η tended to remain constant at 0.13, when the value of the compressive stress amplitude was higher than the tensile stress amplitude. However, the influence of the tensile stress was limited by the dynamic stress level when α= 1.For obvious structural change in the soil, the corresponding numbers of cyclic vibration cycles were found to be independent of α at low stress levels and were only related to η. Finally, a new method for evaluating the failure of remolded soft clay was presented. It considers the influence of the tensile and compressive stresses which caused by complex stress paths of the principal stress rotation. This criterion can distinguish stable, critical, and destructive states based on the pore-water-pressure-strain coupling curve while also providing a range of failure strain and vibration cycles. These results provide the theoretical support for systematic studies of principal stress rotation using constitutive models.

Dynamic strength characteristics and failure criteria of anisotropically consolidated silt under principal stress rotation

In order to identify the critical properties and failure criteria of in-situ silt under vehicle or wave loading, anisotropically consolidated silt under undrained cyclic principal stress rotation was studied with hollow cylinder dynamic tests. The results show that for the slightly anisotropically consolidated samples with consolidation ratios no larger than 1.5, the structure collapses and the deviator strain and pore pressure increase sharply to fail after collapse. For the highly anisotropically consolidated samples with consolidation ratios larger than 1.5, the strain increases steadily to high values, which shows characteristics of ductile failure. 4% is suggested to be the threshold value of deviator stain to determine the occurrence of collapse. The normalized relationship between pore pressure and deviator strain can be correlated by a power fimction for all the anisotropically consolidated samples. Based on it, for the highly anisotropically consolidated samples, the appearance of inflection point on the power function curve is suggested to sign the failure. It can be predicted through the convex pore pressure at this point, whose ratio to the ultimate pore pressure is around linear with the consolidation ratio in spite of the dynamic shear stress level. And the corresponding deviator strain is between 3% and 6%. The strain failure criterion can also be adopted, but the limited value of stain should be determined according to engineering practice. As for the slightly anisotropically consolidated samples, the turning points appear after collapse. So, the failure is suggested to be defined with the occurrence of collapse and the collapse pore pressure can be predicted with the ultimate pore pressure and consolidation ratio.

Undrained response of reconstituted clay to cyclic pure principal stress rotation

A series of monotonic and rotational shearing tests are carried out on reconstituted clay using a hollow cylinder apparatus under undrained condition. In the rotational shearing tests, the principal stress axes rotate cyclically with the magnitudes of the principal stresses keeping constant. The anisotropy of the reconstituted clay is analyzed from the monotonic shearing tests. Obvious pore pressure is induced by the principal stress rotation alone even with shear stress q0=5 k Pa. Strain components also accumulate with increasing the number of cycles and increases suddenly at the onset of failure. The deviatoric shear strain of 7.5% can be taken as the failure criterion for clay subjected to the pure cyclic principal stress rotation. The intermediate principal stress parameter b plays a significant role in the development of pore pressure and strain. Specimens are weakened by cyclic rotational shearing as the shear modulus decreases with increasing the number of cycles, and the shear modulus reduces more quickly with larger b. Clear deviation between the directions of the principal plastic strain increment and the principal stress is observed during pure principal stress rotation. Both the coaxial and non-coaxial plastic mechanisms should be taken into consideration to simulate the deformation behavior of clay under pure principal stress rotation. The mechanism of the soil response to the pure principal stress rotation is discussed based on the experimental observations.

Pore Water Pressure Buildup Under Cyclic Rotation of Principal Stress and Stability Evaluation of Seabed Deposit

The cyclic rotation of principal stress direction with a constant amplitude is the characteristics of cyclic stress in seabed deposit induced by travelling waves. Presented in the paper are the results obtained from tests simulating the cyclic stress characteristics, with emphasis laid on the buildup of pore water pressure in soil samples. Regression analysis of test data shows that the pore water pressure can be expressed as the function of the number of cycles of cyclic loading, or as the function of generalized shear strain. Using the results thus obtained, the possibility of failure of seabed deposit under cyclic loading induced by travelling waves can be evaluated. The comparison with the results of conventional cyclic torsional shear tests shows that neglect of the effect of the cyclic rotation of the principal stress direction will result in considerable over-estimation of the stability of seabed deposit.

Calibration and validation of a sand model considering the effects of wave-induced principal stress axes rotation

Principal stress axes rotation influences the stress-strain behavior of sand under wave loading. A constitutive model for sand, which considers principal stress orientation and is based on generalized plasticity theory, is proposed. The new model, which employs stress invariants and a discrete memory factor during reloading, is original because it quantifies model parameters using experimental data. Four sets of hollow torsion experiments were conducted to calibrate the parameters and predict the capability of the proposed model, which describes the effects of principal stress orientation on the behavior of sand. The results prove the effectiveness of the proposed calibration method.

THE GENERAL STRESS STRAIN RELATION OF SOILS INVOLVING THE ROTATION OF PRINCIPAL STRESS AXES

In the light of matrix theory, the character of stress increment which causes the rotation of principal stress axes is analysed and the general stress increment is decomposed into two parts: coaxial part and rotational part. Based on these, the complex three dimensional (3-D) problem involving the rotation of principal stress axes is simplified to the combination of the 3-D coaxial model and the theory about pure rotation of principal stress axes that is only around one principal stress axes. The difficulty of analysis is reduced significantly. The concrete calculating method of general 3-D problem is provided and other applications are also presented.

Stiffness Degradation of Undisturbed Saturated Soft Clay in the Yangtze Estuary Under Complex Stress Conditions

Stiffness degradation will occur due to the generation of accumulated pore pressure in saturated soft clays under cyclic loading. The soil static-dynamic multi-purpose triaxial and torsional shear apparatus in Dalian University of Technology was employed to perform different types of test on the saturated soft marine clay in the Yangtze Estuary. Undisturbed samples of the clay were subjected to undrained cyclic vertical and torsional coupling shear and cyclic torsional shear after three-directional anisotropic consolidation with different initial consolidation parameters. Investigated were the effects of the initial orientation angle of the major principal stress, initial ratio of deviatoric stress, initial coefficient of intermediate principal stress and continuous rotation of principal stress axes on the stiffness degradation. It is found that the degradation index decreases （or degradation degree increases） significantly with increasing initial orientation angle of the major principal stress and initial ratio of deviatoric stress. Compared with the effects of the initial orientation angle of the major principal stress and initial ratio of deviatoric stress, the effect of initial coefficient of intermediate principal stress is less evident and this trend is more clearly reflected by the results of the cyclic torsional shear tests than those of the cyclic coupling shear tests. At the same cycle number, the degradation index obtained from the cyclic torsional shear test is higher than that from the cyclic coupling shear test. The main reason is that the continuous rotation in principal stress directions during cyclic coupling shear damages the original structure of the soil more than the cyclic torsional shear does.Based on a series of experiments, a mathematical model for stiffness degradation is proposed and the relevant parameters are determined.

Pore Pressure Accumulation of Anisotropically Consolidated Soft Clay Subjected to Complex Loads Under Different Stress Paths

Owing to different influence factors of foundation soil,the initial stress state of the soil under various working conditions is complex.To simulate this situation,in this paper,a series of tests on undisturbed soft clay under pure principal stress axis rotation were carried out by using the hollow cylinder apparatus(HCA).The influence of initial consolidation angle ζ(the angle between the vertical direction and direction of the applied load in consolidation)and intermediate principal stress coefficient b on pore water pressure accumulation of undisturbed soft clay were mainly studied.The test results show that,during pure principal stress axis rotation,the pore water pressure accumulation of the undisturbed soft clay fluctuates and increases with the rotation of the major principal stress;the values of major principal stress anglesα,corresponding to the peak value of the pore water pressure in a certain cycle,are different with different initial consolidation angles;the pore water pressure accumulation of soft clay is greatly affected by the intermediate principal stress coefficient b.With the fixed initial consolidation angle ζ,the variation trend of the maximum pore water pressure for each cycle is appropriately the same with different b values.With the increase of cycles,the difference value of pore water pressure between b=0 and b=1 in each cycle increases gradually with different initial consolidation angles ζ.While with different initial consolidation anglesζ,the increase of the pore water pressure when b increases from 0 to 0.5 is different with that when b increases from 0.5 to 1;the variation of maximum pore water pressure withζis significantly affected by the value of b;the value of maximum pore water pressure increases with the cycle number increases under all test conditions,but the growth rate decreases gradually.And the variation of maximum pore water pressure with the cycle number N is obviously influenced by both ζ and b.

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 stressesσ1,σ2 andσ3 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.

Effect of Poisson’s ratio on stress state in the Wenchuan M_S8.0 earthquake fault

The Wenchuan Ms8.0 earthquake occurred on the Longmenshan fault which inclines at a dip angle exceeding 60 degrees. Since most thrust earthquakes occur on faults with dip angles of about 30 degrees, it is enigmatic why the Wenchuan earthquake occurred on such a steep fault. In this study we use a simple finite element model to investigate how the stress state in the fault changes with the variation of Poisson＇s ratio. The results show that, with the Poisson＇s ratio in the fault increasing, the magnitudes of the principal stresses increase and the maximum Shear stress decrease, and, especially, the angle between the maximum principal stress and the fault plane decreases, which will enhance the driving force to overcome the frictional resistance on the fault. The increase of Poisson＇s ratio in the fault may be an important factor to affect the occurrence of the fault earthquakes with large angles between maximum principal stress and fault plane.

A STRESS VECTOR-BASED CONSTITUTIVE MODEL FOR COHESIONLESS SOIL (Ⅰ)-THEORY

On the basis of the sufficient consideration of vectorial characteristics of stress, a new nonlinear constitutive model for cohesionless soil under plane strain and 3-D conditions was presented in a way that the action effects of stress vector are decomposed into the action effect of mean effective stress and that of the stress ratio vector (ratio of deviatoric stress vector to mean effective stress). The constitutive model can take account of the influence of both numerical and directional changes of stress vector on deformation of soil simultaneously, and is applicable of both static and dynamic loading.

Steady rotation of a composite sphere in a concentric spherical cavity

The problem of steady rotation of a composite sphere located at the centre of a spherical container has been investigated. A composite particle referred to in this paper is a spherical solid core covered with a permeable spherical shell. The Brinkman＇s model for the flow inside the compos- ite sphere and the Stokes equation for the flow in the spheri- cal container were used to study the motion. The torque ex- perienced by the porous spherical particle in the presence of cavity is obtained. The wall correction factor is calculated. In the limiting cases, the analytical solution describing the torque for a porous sphere and for a solid sphere in an un- bounded medium are obtained from the present analysis.

A STRESS VECTOR-BASED CONSTITUTIVE MODEL FOR COHESIONLESS SOIL (Ⅱ)-APPLICATION

The stress vector-based constitutive model for cohesionless soil, proposed by SHI Hong-yan et al., was applied to analyze the deformation behaviors of materials subjected to various stress paths. The result of analysis shows that the constitutive model can capture well the main deformation behavior of cohesionless soil, such as stress-strain nonlinearity, hardening property, dilatancy, stress path dependency, non-coaxiality between the principal stress and the principal strain increment directions, and the coupling of mean effective and deviatoric stress with deformation. In addition, the model can also take into account the rotation of principal stress axes and the influence of intermediate principal stress on deformation and strength of soil simultaneously. The excellent agreement between the predicted and measured behavior indicates the comprehensive applicability of the model.

Three Dimension Finite Element Analysis of the Influence Factors of Stress Responses in the Roadbed and Ground under a Moving Load

Focusing on the vibration of the roadbed and ground induced by high-speed train load, a three dimensional finite element model which includes the roadbed and horizontal layered site is established to study how the site conditions, the load moving speed and the depth of the soil element influence the soil element stress response. Based on a track-subsoil analytical model in which the rail is simulated as an Euler-Bernoulli beam resting on Winkler foundation in the vertical plane, the reaction force between the sleeper and roadbed excited by a single axle is presented, and then that is exerted on relevant elements to simulate the moving load. The dynamic response in the roadbed and subsoil excited by a single axle moving load is computed based on the parallel computing platform of the ABAQUS finite element software, and the stress time-history, stress path and curves of the principal stress axes rotation of the soil element under the track are presented. The results show that： the soil element stress path is an apple-shaped curve in the horizontal shear stress τd versus the stress difference （σsh - σch ）/2 coordinate system; the principal stress axes rotate 180° for the soil element under the load moving line during the load running, and the stress state changes from the pure shear to triaxial shear and then back to the pure shear again. The element dynamic stress increases as the moving load speed increases, which increases sharply when the load speed approaches the Rayleigh wave velocity of soil layer; the site conditions and the soil element depth affect the soil element stress path significantly.

Macro-micro investigation of granular materials in torsional shear test

A three-dimensional numerical torsion shear test is presented on hollow cylinder specimen which is performed on a spherical assemblage with fixed principal stress axes using the discrete element code PFC3D.Stack wall technique boundary conditions are employed and optimized to reasonably capture the microstructure evolution.Parametric studies are conducted in terms of the ratio κ,normal and shear stiffness of particles,wall stiffness and friction coefficients.Afterwards,in comparison with physical test,numerical results for a fixed principal stress angle(α=45°) are presented.The results show that the numerical test could capture the macro-micro mechanical behavior of the spherical particle assembly.The evolution of the coordination number demonstrates that particles in shear banding undergo remarkable decrease.The effects of localization on specimens illustrate that global stress and strain recorded from a hollow cylinder apparatus could not represent the localized response.The shearing band initiation and evolution from porosity and shear rate are visualized by contour lines in different shear strains.

Undrained anisotropy and non-coaxial behavior of clayey soil under principal stress rotation

In this study, a series of undrained tests were conducted on both intact and reconstituted clay using an automatic hollow cylinder apparatus. Monotonic shearing tests with fixed principal stress directions were carried out, pure and cyclic prin- cipal stress rotation tests were also performed. The non-coaxiality, defined as the non-coincidence of the principal plastic strain increment direction and the corresponding principal stress direction, of clayey soil was studied experimentally. The effects of the intermediate principal stress, shear stress level, and inherent anisotropy were highlighted. Clear non-coaxiality was observed during pure principal stress rotation, in both intact and reconstituted clay. The influence of the intermediate principal stress pa- rameter, shear stress level, and inherent anisotropy on the non-coaxial behavior of the clayey soil was found to be insignificant when compared with the sand. The non-coaxial behavior of the clayey soil depended more on the stress paths. Under undrained conditions, the contribution of elastic strain to the direction of the total principal strain increment cannot be ignored.

Application of artificial neural network for calculating anisotropic friction angle of sands and effect on slope stability

The anisotropy effect is one of the most prominent phenomena in soil mechanics. Although many experimental programs have investigated anisotropy in sand, a computational procedure for determining anisotropy is lacking. Thus, this work aims to develop a procedure for connecting the sand friction angle and the loading orientation. All principal stress rotation tests in the literatures were processed via an artificial neural network. Then, with sensitivity analysis, the effect of intrinsic soil properties,consolidation history, and test sample characteristics on enhancing anisotropy was examined. The results imply that decreasing the grain size of the soil increases the effect of anisotropy on soil shear strength. In addition, increasing the angularity of grains increases the anisotropy effect in the sample. The stability of a sandy slope was also examined by considering the anisotropy in shear strength parameters. If the anisotropy effect is neglected, slope safety is overestimated by 5%-25%. This deviation is more apparent in flatter slopes than in steeper ones. However, the critical slip surface in the most slopes is the same in isotropic and anisotropic conditions.