Principal Stress Angle Research Articles

Strength Model for Prestressed Concrete Beams Subjected to Pure Torsion

A torsional strength model for prestressed concrete beams was proposed considering the initial crack angle, principal stress angle, and longitudinal strain, which are affected by the axial stress induced by the effective prestress. The use of the torsional effective thickness was also proposed to calculate the torsional strength of prestressed concrete beams by considering the effect of prestress. The shear element in the torsional member was simplified under the assumption that the principal tensile stress and principal compressive strain were negligible in the ultimate state. The torsional strength was determined when the principal compressive stress or shear stress at the crack surface in the shear element reached the failure criterion according to the multipotential capacity model, which considers concrete crushing and aggregate interlocking as the main resistances to the applied load. The proposed strength model was verified using test specimens collected from existing experimental studies. The proposed model accurately evaluated the torsional strength of prestressed concrete beam specimens, regardless of the key variables of the prestressed concrete specimens, where the mean value of the tested results to the calculated torsional strengths was 1.123, and the corresponding coefficient of variation was 17.7% for 104 prestressed concrete beam specimens, while the ACI 318-19 torsional design method gave the mean and coefficient of variation of 0.880 and 24.3%, respectively.

Full-field stress-strain analysis of octagonal shape PMMA using reflection photoelasticity

This research involves stress-strain analysis in poly(methyl methacrylate) (PMMA) octagonal shape compressed by hydraulic system. The observation of uniaxially stressed samples was carried out using reflection photoelasticity technique. The results of fringe order number and principal stress angle were used to determine stress and strain distribution in the samples by shear difference method. It was found that high stress-strain region was close to the contact point where compressive force was applied but it was zero at the edge of the samples. The area of high strain region increased as the magnitude of force was increased but it decreased as the dimension of octagonal shape was increased.

Analysis of strength characteristics of loess before and after freezing using a hollow cylinder torsional shear apparatus

This paper aims to comprehensively analyze the influence of the principal stress angle rotation and intermediate principal stress on loess's strength and deformation characteristics. A hollow cylinder torsional shear apparatus was utilized to conduct tests on remolded samples under both normal and frozen conditions to investigate the mechanical properties and deformation behavior of loess under complex stress conditions. The results indicate significant differences in the internal changes of soil particles, unfrozen water, and relative positions in soil samples under normal and frozen conditions, leading to noticeable variations in strength and strain development. In frozen state, loess experiences primarily compressive failure with a slow growth of cracks, while at normal temperature, it predominantly exhibits shear failure. With the increase in the principal stress angle, the deformation patterns of the soil samples under different conditions become essentially consistent, gradually transitioning from compression to extension, accompanied by a reduction in axial strength. The gradual increase in the principal stress axis angle (α) reduces the strength of the generalized shear stress and shear strain curves. Under an increasing α, frozen soil exhibits strain-hardening characteristics, with the maximum shear strength occurring at α = 45°. The intermediate principal stress coefficient (b) also significantly impacts the strength of frozen soil, with an increasing b resulting in a gradual decrease in generalized shear stress strength. This study provides a reference for comprehensively exploring the mechanical properties of soil under traffic load and a reliable theoretical basis for the design and maintenance of roadbeds.

Failure mechanism and stability control of surrounding rock in mining roadway with gentle slope and close distance

In this study, theoretical analysis, numerical simulation and field measurement were adopted to analyze the difficult problem of controlling the stability of surrounding rock in gently inclined and close-distance coal seam mining roadways. The results showed that: (1) According to the properties and stress environment of the roadway roof, to determine the specific spatial range of the original roof stage, transition stage and regeneration roof stage of the roadway, and corresponding to the distribution of plastic zones in the spatial stages, was an important basis for analyzing the deformation mechanism of the roadway and proposing a phased collaborative control plan. (2) Under the influence of mining, the plastic zone of the transportation roadway expanded violently by about 10 m ahead of the working face. Within the range of roadway passing the overlying goaf, the plastic zone of the surrounding rock between the layers runed through, especially extending to the roof and two shoulder corners of the roadway. The roof and two shoulder corners of the roadway became the key parts for the stability control of the surrounding rock. (3) The mechanical mechanism of asymmetric expansion of the plastic zone was obtained as follows: the range was determined by the magnitude of the deviatoric stress and the orientation was dominated by the direction of the principal stress. The combined effect of the magnitude of deviatoric stress and the angle of principal stress caused asymmetric expansion of the plastic zone. (4) A phased collaborative control scheme was proposed, and numerical simulation and industrial verification were carried out on the proposed scheme. The deformation of the surrounding rock of the roadway at the engineering site was less than 150 mm, and the control effect of the surrounding rock was good, ensuring the safe and efficient recovery of the fully mechanized mining face. The present study revealed the mechanical mechanism of failure and instability of the surrounding rock of the gently inclined close distance coal seam mining roadway and proposed a phased collaborative control scheme, which could provide valuable information for mining research.

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.

Field evaluation of the three-dimensional dynamic stress state of the subgrade induced by the heavy-haul train load

The three-dimensional stress state of subgrade soil elements plays a crucial role in railway subgrade design and service life evaluation, especially in heavy-haul railways. To solve the complex problem of the field test of three-dimensional stress state in subgrade induced by train vehicles, a novel regular dodecahedron soil pressure sensor (RDSPS) was developed and applied to field tests, which can measure dynamic stress components, including normal stress and shear stress in ×,y and z directions. Then the field test of total stress components of subgrade was carried out on the Datong-Qinhuangdao heavy-haul railway. The dynamic stress, including three normal stresses and three shear stresses, was determined at seven points in the subgrade for trains with 25 t axle load at different speeds (45, 55, and 60 km/h). The result indicates that the distributions of dynamic stresses of railway subgrade show periodic fluctuation subjected to moving train load, and each bogie can be regarded as a loading point for the field test section. Meanwhile, the stress path of soil elements in the subgrade changes continuously during the passage of a heavy-haul train, and the maximum principal stress angle changes between -π/2 and π/2. The normal stress in the × and y directions decreases first slowly and then rapidly with the depth of subgrade, while the attenuation law of normal stress in the z-direction with the depth of subgrade is just the opposite. Due to the stress superposition effect, the normal stress in the y-direction of the measuring points below the track centerline is greater than that at other measuring points. A calculation model of vertical normal stress was proposed based on the measured data. The empirical model for the attenuation coefficient of normal stress in the ×, y, and z directions was established to predict the stress attenuation coefficient more accurately. In this paper, the total stress components of the railway subgrade were measured for the first time during the passage of the train, which can provide helpful guidance for a better understanding of the dynamic response of the subgrade.

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

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

Assessing the undrained strength cross-anisotropy of three tailings types

The cross-anisotropic nature of soil strength has been studied and documented for decades, including the increased propensity for cross-anisotropy in layered materials. However, current engineering practice for tailings storage facilities (TSFs) does not appear to generally include cross-anisotropy considerations in the development of shear strengths. This is despite the very commonly seen layering profile in subaerially deposited tailings. To provide additional data to highlight the strength cross-anisotropy of tailings, high-quality block samples from three TSFs were obtained and trimmed to enable hollow cylinder torsional shear tests to be sheared at principal stress angles of 0 and 45° during undrained shearing. The consolidation procedures were carried out such that the drained rotation of principal stress angle that would precede potential undrained shear events for below-slope tailings was reasonably simulated. The results indicated the significant effects of cross-anisotropy on the undrained strength, instability stress ratio, contractive tendency and brittleness of each of the three tailings types. The magnitude of cross-anisotropy effects seen was generally consistent with previous published data on sands.

Damage of Rock Mass by Double-Hole Blasting with Slit Charge and Development of Stress Wave under High In Situ Stress

To study the influence of high ground stress on crack propagation and stress propagation during deep rock blasting, a theoretical model of blasting stress wave propagation and rock damage under in situ stress conditions is developed. The implicit-display coupling method of ANSYS/LS-DYNA is used to numerically simulate the double-hole blasting of the slit charge under two-way equal pressure and two-way different pressures. A theoretical analysis shows that, in blasting under ground stress conditions, at the near end of the blasting source, the loading stress does not increase sufficiently upon unloading, and the stress wave peak value decreases with the increase in ground stress, while the opposite behavior is obtained at the far end of the blasting source. Under the two-way isostatic condition, the crack that develops at 45° deviates from the principal stress direction. Under the condition of two-way different pressures, the crack develops in the direction of θ (θ = arctan (σx/σy)) with the principal stress angle. The numerical results under the two-way equal pressure conditions show that a higher ground stress leads to a larger suppression of the blasting effect. When the ground stress is smaller, the slit charge cannot be effectively suppressed, and the cracks are biased toward the cutting direction. The numerical results under two-way different pressures show that the in situ stress has a significant inhibitory effect on the vertical cracks and that the cracks are more likely to develop in the direction of high stress after blasting. These results provide a reference for directional blasting of deep rock masses.

On some uncertainties related to static liquefaction triggering assessments

Static liquefaction has been identified as the cause of several recent tailings storage facility (TSF) failures. Partially based on the investigations carried out, significant advances on the analysis of static liquefaction triggering (SLT) have been made. These include applications of critical-state-based models in a stress–deformation framework to identify if in situ conditions are approaching a level where SLT could occur. However, several important uncertainties remain. In this work, three of these uncertainties (geostatic stress ratio K0, intermediate principal stress ratio and principal stress angle from vertical) were investigated, along with their effects (both independently and in conjunction) on the identification of SLT and slope failure. These uncertainties were examined through a series of numerical analyses of an idealised TSF. Various values of K0 were used to examine their effect on SLT, while different approaches were taken to assess the potential effects of the intermediate principal stress ratio and the principal stress angle from vertical on instability. This work revealed that the current state of knowledge in these areas is such that significant uncertainty seems unavoidable in attempting to identify exactly when a particular slope may undergo SLT. Experimental and in situ test programmes that may be useful in reducing this uncertainty are outlined.

Failure Mechanism and Stability Control of Surrounding Rock of Docking Roadway under Multiple Dynamic Pressures in Extrathick Coal Seam

In view of multiseam mining under goaf, the surrounding rock control problem of lower coal roadway will be affected by concentrated coal pillar left in upper coal seam goaf and dynamic pressure superposition of working face in this coal seam. Under the geological environment of No. 16 extrathick coal seam in the Laoshidan coal mine and taking the working face 031604 as the research background, the reasonable docking position selection of the withdrawal roadway and the docking roadway in the middle mining period and the surrounding rock stability control problems of the withdrawal roadway and the docking roadway during the final mining period were studied by using the methods of field theoretical analysis, numerical simulation, and field measurement. The mechanical mechanism of the nonuniform failure of the retreating roadway and the docking roadway during the final mining period is shown, and the control method of the surrounding rock stability of the roadway is put forward and applied. The results show that (1) through the analysis of the superimposed stress under the concentrated coal pillar and the coal seam in advance, the specific butt joint position is arranged at 860 m away from the open-off cut, which is 10 m away from the goaf of No. 12 coal seam. (2) With the working face 031604 advancing through the process, the deviatoric stress value of the withdrawal roadway gradually increases, the maximum principal stress of the two sides of the roadway deflects clockwise from the vertical direction to the horizontal direction, its angle also gradually increases, and the shape of the plastic zone gradually expands from symmetry to asymmetry. (3) It is revealed that the peak value of deviatoric stress on both sides of the docking position of docking roadway increases gradually under the influence of mining and deflects anticlockwise to the vertical direction with the principal stress angle. The joint action of both is the mechanical mechanism that causes the plastic zone to expand in an asymmetric shape. (4) The coordinated control scheme of support (anchor bolt and anchor cable)—modified (grouting)—is adopted for the withdrawal roadway, and the coordinated control scheme of support (anchor bolt and anchor cable)—changing the cross-section shape of the roadway—is adopted for the docking roadway. The purpose of the smooth connection of working face and rapid and safe withdrawal of equipment is achieved on site.

Direct Measurement on the Residual Stress in $$\hbox {YBa}_2\hbox {Cu}_3\hbox {O}_{7\text {-}\updelta }$$ Bulk Superconductors Fabricated by Top-Seed Melt-Textured Method

The residual stress is formed in $$\hbox {YBa}_{\mathrm {2}}\hbox {Cu}_{\mathrm {3}}\hbox {O}_{{7\text {-}\updelta }}$$ (YBCO) bulk superconductors, which undergoes a complex fabrication process and experienced a huge temperature change about $$1000^{\circ }\,\hbox {C}$$ . The residual stress may result in micro-cracks in YBCO bulks and cause degradation of its superconducting and mechanical properties. It will be greatly helpful to reform the structural designs if the distribution of residual stress in YBCO bulk can be investigated. The traditional method of measuring residual stress does not apply to oxide ceramics as they are brittle materials. In this paper, a YBCO bulk was sliced into pieces of several millimeters in height, which could thus be treated as a plane-stress problem. The residual stress and principal stress angle for YBCO bulk have been obtained by an artificial hole-drilling method with very low speed.

On the effect of anisotropy on drained static liquefaction triggering

A number of recent tailings storage facility (TSF) failures has been indicated through post-failure investigations to have been triggered in tailings that were under drained conditions up to the initiation of instability. Such field-scale behaviour is consistent with many laboratory element studies on drained triggering of instability. However, essentially all available data on the drained initiation of instability has been carried out under conditions where the principal stress angle (α) is zero. This is despite the principal stress angle in zones of TSFs where instability is likely to be triggered being below-slope, where α is higher than zero. To assess the implications of anisotropy on the drained initiation of instability, the limited data available that enables assessment of the effects of α on instability in undrained testing is referenced. These data suggest that the likely range of principal stress angles below-slope areas of TSFs are such that anisotropy should be considered in estimating relevant triggering stress ratios. The need for more experimental data of drained triggering of instability at principal stress angles relevant to below-slope conditions is outlined.

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.

Improved Boundary Conditions for a 3D DEM Simple Shear Model

In this study, a 3D simple shear model using DEM is built based on the boundary condition of an NGI‐type bidirectional simple shear apparatus. Stack of rings used as lateral constraints in a bidirectional simple shear test is modelled by layers of clumps which is possible to be moved by particles; different contact types and parameters are used to model the sand‐loading caps, sand‐latex membrane, and sand‐sand contacts. A simple shear test using the bidirectional simple shear apparatus is performed for the calibration of the 3D DEM simple shear model. By analyzing the simulation results, the following can be concluded. (1) Rings generated by clumps can provide an accurate boundary condition, effective in computation since no contact force is needed for a clump. (2) In the simulation, the orientation of average contact force changed dramatically during shear. It is in the vertical direction (90°) before shear and changes to 45° at 40% shear strain. No shear band is observed which is consistent with the test, and particles move uniformly. (3) In the simulation, the degree of noncoaxiality is the greatest at the beginning of shear, and it is decreased during shear. However, the degree of noncoaxiality is still large at 20% shear strain where there is a 10° difference between the rotation angle of principal stress and principal strain increment.

Quantitative Investigation into the Relation between Force Chains and Stress Transmission During High-Velocity Compaction of Powder

High-velocity compaction (HVC), an innovative approach to obtain green compacts with high and uniform density, is widely used in the powder metallurgy industry. In this study, meso force chains, macro stress transmission, and their relation were investigated using the discrete element method. The simulation details of HVC and the quantitative characterization of force chains and stress transmission were shown. Then, the relation between force chains and stress was investigated. The evolution of force chains showed the same change tendency as the stress distribution. They evolved from top to bottom and then reflected backwards in HVC while they did not show this trend in conventional compaction. The strength of the force chains maintained good consistency with the stress magnitude. Meanwhile, the length of the force chains presented a negative correlation with the stress magnitude, and high stress may cause new force chains to shorten. The average collimation coefficient was affected by the transmission of stress, and the short force chains had better straightness. Furthermore, force chains parallel to the direction of gravity were observed in the region with no stress concentration. The directional coefficient of force chains also had the same fluctuation trend as the variation in the principal stress angle.

A study of principle stress rotation on granular soils using DEM simulation of hollow cylinder test

This study presents the numerical modeling of a hollow cylinder test (HCT) on granular soils by modifying the TRUBAL code. The discrete element method (DEM) was employed for this purpose. Owing to the significant expenditure of the HCT, a verified numerical modeling for this test was developed. The introduced numerical model (HCTBALL) defines plane and cylindrical walls for the boundary conditions to be applied. In addition, the article presents an efficient method to apply the torque. The displacements of the inner and outer walls are interdependent while torsion was applied to control the intermediate principal stress parameter (b). To verify the model, the paper employs results from experimental HCTs on Firoozkooh sand under both monotonic loading and drained conditions. A comparison of the presented model and the experimental results shows that both are closely concordant.It was shown that the deviatoric stress decreases as the principal stress angle (α) increases. In addition, it was observed that by increasing the confining pressure, the internal friction angle (φ′) decreases; however, at higher confining pressures, this reduction is insignificant. Furthermore, this study investigates the coordination number and its relationship to volumetric strain variations.

交番磁束下における無方向性電磁鋼板のベクトル磁気特性に及ぼす主応力角度の影響

This paper presents influence of angle of principal stress on vector magnetic properties of a non-oriented electrical steel sheet under alternating magnetic flux conditions. The magnetic flux density and magnetic field strength vector under alternating magnetic flux conditions are measured by changing the angle of the principal stress. From these results, it was clarified that amplitude and the angle of the loci of the magnetic field strength vector, and magnetic power loss differ by changing the angle of the principal stress. It is possible to improve the magnetic properties of the non-oriented electrical steel sheet by controlling the angle of the principal stress.

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.

Explicit Model for Cumulative Pore Pressure of Saturated Soft Clay

The principal stress axial would cyclic rotate when the moving pressure passed. In order to analyze long-term settlement of the ground subjected to traffic loading, the simplified method based on explicit model for predicting the accumulative deformations is usually preferred. The traditional model could not reflect the phenomenon of principal stress rotation. After the axial stress controlled equation and circumferential shear stress controlled equation were derived, A series of consolidated undrained cyclic shear tests were performed under the condition that the general shear stress value was constant and the principal stress angle was rotating. The explicit pore pressure model reference was verified to calculate the accumulative pore pressure caused by the principal stress axial cyclic loading.