Principal Stress Ratio Research Articles

On the patterns of wing cracks along an outcrop scale flaw: A numerical modeling approach using complementarity

The 2D Displacement Discontinuity Method (DDM) is combined with a complementarity algorithm to model the quasi‐static formation and patterns of wing cracks that emanate from regions of stress concentration along a sliding frictional flaw in an otherwise homogeneous and isotropic elastic material. Because stress states and geometry change with sliding on the flaw and wing crack propagation, one cannot specify the boundary conditions a priori. Under these circumstances complementarity is superior to other well‐known contact algorithms. We focus on meter scale phenomena where mineralogical heterogeneity (common to centimeter‐scale laboratory samples) and 3D geometry (common to kilometer‐scale crustal structures) reasonably can be ignored. Analytical solutions to the elastic boundary value problem of the closed sliding flaw include those that assume no friction, uniform friction, and a cohesive end zone (CEZ), and those that assume infinitesimal or straight wing cracks. Here we generalize the problem to consider linearly varying friction in the CEZ and curved wing cracks, and we allow the sliding flaw to open when mechanical interaction with the wing crack dictates that it should. Trace lengths of 135 strike‐slip faults in sandstone are linearly related to wing crack lengths ranging from 0.16 to 72 m and correspond to a range of remote principal stress ratios: 0.06 ≤σ2/σ1≤ 0.2. Opening displacement profiles of wing cracks from the numerical model can be significantly different from analytical solutions. These solutions may produce significant errors in stable crack length for curved propagation paths. The smeared out stress concentration in the CEZ and the heterogeneity in strength of rock suggest that multiple wing cracks may form in one slip event. The mechanical interactions of these cracks leads to kink angles that increase with distance from the flaw tip, a relationship commonly observed in nature.

Experimental observations on the response of loose sand under simultaneous increase in stress ratio and rotation of principal stresses

The drained response of loose sand (relative density of 30%) under simultaneous increase in principal stress ratio (R = σ'1/σ'3) and the inclination of major principal stress to the vertical (ασ) is examined using data from hollow cylinder torsional shear testing. The study specifically pertains to the behaviour of loose sand subject to monotonic linear stress path loadings in the R–ασspace, within the domain of R ≤ 2, ασ < 45°, while intermediate principal stress parameter (b) and effective mean normal stress (σ'm) are held constant. The relationship between horizontal shear stress (τzt) and horizontal shear strain (γzt) of loose sand under such loadings is shown to be unique and stress-path independent. At any stress state, the horizontal shear stiffness (dτzt/dγzt) for a given σ'mdepends only on the current value of τzt, and not on the value of individual components of normal effective stress, or their increments. When R and ασare increased simultaneously in a linear manner, loose sand initially exhibits linear strain paths, suggesting no significant changes to the inherent anisotropy during the early stages of such loading. The directions of principal stress increment (αΔσ) and principal strain increment (αΔε) are found coincident, when αΔσ < 45°. An approach to predict the response of loose sand under simultaneous increase in R and ασwith constant b and σ'mhas been developed based on these findings.

Shear behavior of coarse aggregates for dam construction under varied stress paths

Coarse aggregates are the major infrastructure materials of concrete-faced rock-fill dams and are consolidated to bear upper and lateral loads. With the increase of dam height, high confining pressure and complex stress states complicate the shear behavior of coarse aggregates, and thus impede the high dam's proper construction, operation and maintenance. An experimental program was conducted to study the shear behavior of dam coarse aggregates using a large-scale triaxial shear apparatus. Through triaxial shear tests, the strain-stress behaviors of aggregates were observed under constant confining pressures: 300 kPa, 600 kPa, 900 kPa and 1200 kPa. Shear strengths and aggregate breakage characteristics associated with high pressure shear processes are discussed. Stress path tests were conducted to observe and analyze coarse aggregate response under complex stress states. In triaxial shear tests, it was found that peak deviator stresses increase along with confining pressures, whereas the peak principal stress ratios decrease as confining pressures increase. With increasing confining pressures, the dilation decreases and the contraction eventually prevails. Initial strength parameters (Poisson's ratio and tangent modulus) show a nonlinear relationship with confining pressures when the pressures are relatively low. Shear strength parameters decrease with increasing confining pressures. The failure envelope lines are convex curves, with clear curvature under low confining pressures. Under moderate confining pressures, dilation is offset by particle breakage. Under high confining pressures, dilation disappears.

Permanent Deformation Behavior of Naturally Occurring Bituminous Sands

Oil sand, or tar sand, is a generic name given to bituminous sand deposits that are rich in bitumen or asphalt content to the extent that oil can be extracted from these deposits. The typical 8% to 15% presence of bitumen in the soil composition makes these naturally occurring sands low load-bearing materials. In this study, repeated load triaxial tests were conducted on three types of oil sand materials with natural bitumen contents of 8.5%, 13.3%, and 14.5% by weight. The oil sand specimens were compacted close to field densities and then tested for permanent deformation at two temperatures using a newly proposed test procedure. The procedure applied stress states and ratios determined from field-loading characteristics of haul trucks and mining equipment at two different load pulse durations or loading frequencies (related to field-trafficking speeds). Both the test data and axial permanent strain models developed in the form of power functions of the number of repeated load applications indicated a strong dependency of oil sand permanent strain development on the applied vertical to horizontal (or major to minor principal) stress ratio. Using the test data, permanent strain and deformation models were developed with high correlation coefficients to account for the applied stress states and ratios, test temperature, and bitumen content. These models generalized for oil sand deformation behavior may be used as practical predictive equations to estimate the amount of rutting in oil sand materials and to alleviate potential sinkage problems faced by off-road haul trucks, shovels, and other mining equipment in the field.

Viscous Property of Loose Sand in Triaxial Compression, Extension and Cyclic Loading

ABSTRACT The viscous property of sand under triaxial compression (TC), triaxial extension (TE) and cyclic triaxial loading conditions was evaluated by using reconstituted loose samples of three types of relatively fine uniform and relatively angular sand (Silica No. 8, Toyoura and Hostun). The viscous property was quantified mainly by changing stepwise the axial strain rate many times and partially by performing drained sustained loading, both during otherwise monotonic loading (ML) at a constant strain rate. Such a peculiar feature of viscous property as that the viscous stress increment decays with an increase in the irreversible strain during ML at a constant strain rate (i.e., the so-called TESRA viscosity), which has been observed with Toyoura and Hostun sands in previous studies, was observed also with Silica No. 8 sand. The magnitude of viscous property is represented by the rate-sensitivity coefficient, β, defined as the slope of the Δ R / R − log { ( γ . ir ) after / ( γ . ir ) before } relation, where Δ R is a sudden change in the principal stress ratio, R=σ1′/σ3′, caused by a step change in the irreversible shear strain rate from ( γ . ir ) before to ( γ . ir ) after at a given R value during otherwise ML. The following was found. The same definition for β is relevant to drained TC and TE tests. In drained cyclic triaxial loading, the β value is obtained from the above-shown equation after re-defining the sign of Δ R and proportionally scaling the value of R. With the respective type of sand, the β values under these different loading conditions are very similar. The effect of overconsolidation on the β value is insignificant. The β values of these three types of sand are similar to each other and also to those of other ordinary types of sand and gravel having largely different particle sizes. The decay rate of viscous stress increment with an increase in the irreversible shear strain, which is another factor of the viscous property, is rather similar among the three types of sand, while the decay rate is slightly lower in ML TC than in ML TE. The effect of overconsolidation on the decay rate is insignificant.

Experimental study of strength and deformation of plain concrete under biaxial compression after freezing and thawing cycles

This study attempts to generate information about the strength and deformation behavior of plain concrete under biaxial compression after 0, 25, 50 and 75 cycles of freezing and thawing. Concrete cubes were tested under biaxial compressive stresses. Five principal compression stress ratios and four different cycles of freeze–thaw were the main variables. Static compressive strengths, stress–strain relationships and failure modes were examined. Failure modes of specimens are also described. The experimental results showed that the biaxial compressive strength of plain concrete decreased as the freeze–thaw cycles were repeated. The influence of freeze–thaw cycles and the stress ratio on the biaxial strength, the strain corresponding to peak stress and the elastic modulus after freeze–thaw cycles was also analyzed. The formula of the biaxial compressive strength in principal stress space is proposed.

Prediction and avoidance of high temperature damage in long product hot rolling

There is currently a drive towards higher contribution steels with improved machinability (in the case of free cutting steels (FCS)) and higher surface quality and consistency. This, together with the potential future implementation of the European legislation (ELVD) to promote lead substitutes in machinable steels (Bi, Te, high S) is leading to the requirement to develop a more thorough understanding of the cause of cracking during hot rolling of bloom and billets of low ductility steels. Physical understanding of the causes and mechanisms of damage initiation and growth (from micro- to macro-scale) at high temperature and relatively high strain rate has not been up to now a major focus of interest, compared to developments in room temperature brittle and ductile fracture, and creep/superplasticity failure. This paper reviews various experimental and modelling approaches (meso- to micro-scale) to develop a better understanding of the influence of thermo-mechanical conditions on damage initiation and growth for as-cast FCS steels. Particular attention is given to the development and use of new/modified mechanical tests. These include double collar and flying saucer axisymmetric tests, U-bending and revised plane strain compression tests using a Gleeble thermo-mechanical simulator to represent the triaxiality, principal stress and strain ratios experienced by the bloom and billet surface during rolling.

Fracture spacing in layered materials and pattern transition from parallel to polygonal fractures

We perform three-dimensional simulations of fracture growth in a three-layered plate model with an embedded heterogeneous layer under horizontal biaxial stretch (representing stretch from directional to isotropic) by the finite element approach. The fractures develop under a quasistatical, slowly increasing biaxial strain. The material inhomogeneities are accounted for by assigning each element a failure threshold that is defined by a given statistical distribution. A universal scale law of fracture spacing to biaxial strain in terms of principal stress ratio is well demonstrated in a three-dimensional fashion. The numerically obtained fracture patterns show a continuous pattern transition from parallel fractures, laddering fracture to polygonal fractures, which depends strongly on the far-field loading conditions in terms of principal stress ratio lambda = sigma(2)/sigma(1), from uniaxial (lambda = 0), anisotropic (0 < lambda < 1) to isotropic stretch (lambda = 1). We find that, except for further opening of existing fractures after they are well-developed (saturation), new fractures may also initiate and propagate along the interface between layers, which may serve as another mechanism to accommodate additional strain for fracture saturated layers.

Failure Criteria for Grouted Concrete Block Masonry under Biaxial Compression

Grouted concrete block masonry (GCBM) exhibits distinct directional properties. By the phenomenological approach, totally 86 tests on 3 kinds of macro-element were conducted for different principal stress ratios under plane stress, and 4 standard specimens were tested in shear. The anisotropic failure criteria are obtained in terms of normalized principal stress space. Comparisons of failure curves for 3 kinds of macro-element are made and it is found that the biaxial compressive strength when the applied stress direction and the material axis coincide is much greater than when the applied stress is inclined to the material axis. By the failure criteria and coordinate transformation, the law relating strength to orientation is obtained. It shows that the degree of anisotropy is affected by the difference of applied stresses. It behaves strongly only when one principal stress predominates and gradually becomes weak as the difference between the two principal compressive stresses decreases. The masonry seems to be isotropic in equal biaxial compression. The work conducted in this paper provides a basis for further theoretical study of the behavior of GCBM under biaxial stress.

2축 압축을 받는 고강도 콘크리트 및 강섬유보강 고강도 콘크리트의 역학적 거동 특성

The purpose of this study is to investigate the mechanical characteristics of plain and steel fiber high strength concrete under uniaxial and biaxial loading condition. A number of plain and steel fiber high strength concrete cubes having 28 days compression strength of 82.7MPa(12,000 psi) were made and tested. Four principal compression stress ratios (=0.00, 050, 0.75 and 1.00), and four fiber concentrations( =0.0, 0.5, 1.0 and ) were selected as major test variables. From test results, it is shown that confinement stress in minor stress direction has pronounced effect on the strength and deformational behavior. Both of the stiffness and ultimate strength of the plain and fiber high strength concrete Increased. The maximum increase of ultimate strength occurred at biaxial stress ratio of 0.5() in the plain high strength concrete and the value were recorded over than the strength under uniaxial condition. The failure modes of plain high strength concrete under uniaxial compression were shown as splitting type of failure but steel fiber concrete specimens under biaxial condition showed shear type failure. The values of elastic modulus were also examined higher than that from ACI and CEB expression under biaxial compression condition.

The Effect of Gypsum Cementation on the Mechanical Behavior of Gravely Sands

Abstract The behavior of a cemented gravely sand is studied using triaxial tests. Drained and undrained tests were performed on dry and saturated specimens, and stress-strain characteristics of the soil, along with volumetric and pore pressure changes, were identified. The gypsum plaster was used as the cement agent and was mixed with the soil in different percentages. The tests were done in the usual range of confining pressures, from 25 to 500 kPa. Test results show that dilation occurs even at the highest confining stress and the least cement content. The behavior of the cemented soil is found to be more brittle in drained condition than the undrained one. However, the brittleness of soil decreases with increase in confining stress. The ratio of cemented soil shear strength to the uncemented one decreases as the confining stress increases. The failure envelopes are curved and the drained failure envelopes are above the undrained ones. The friction angle of soil increases slightly with cement content, but the cohesion intercept increase is more noticeable. The principal stress ratio at failure decreases with increase in confining stress.

Stability and finite strain of homogenized structures soft in shear: Sandwich or fiber composites, and layered bodies

The stability theories energetically associated with different finite strain measures are equivalent if the tangential moduli are transformed as a function of the stress. However, for homogenized soft-in-shear composites, they can differ greatly if the material is in small-strain and constant elastic moduli measured in small-strain tests are used. Only one theory can then be correct. The preceding variational energy analysis showed that, for sandwich columns and elastomeric bearings, respectively, the correct theories are Engesser’s and Haringx’s, associated with Green’s and Almansi’s Lagrangian strain tensors, respectively. This analysis is reviewed, along with supporting experimental and numerical results, and is then extended to arbitrary multiaxially loaded homogenized soft-in-shear orthotropic composites. It is found that, to allow the use of constant shear modulus when the material is in small strain, the correct stability theory is associated with a general Doyle–Ericksen finite strain tensor of exponent m depending on the principal stress ratio. Further it is shown that the standard updated Lagrangian algorithm for finite element analysis, which is associated with Green’s Lagrangian finite strain, can give grossly incorrect results for homogenized soft-in-shear structures and needs to be generalized for arbitrary finite strain measure to allow using constant shear modulus for critical loads at small strain.

Effects of stress ratio on small-strain stiffness during triaxial shearing

A comprehensive series of triaxial tests were performed on granular materials to study the stress-dependence characteristics of small-strain stiffness (i.e. the quasi-elastic Young's modulus). The tests were performed on large prismatic specimens measuring both axial and lateral strains locally. The small-strain stiffness at a given stress state was measured from the stress–strain response obtained by applying very small-amplitude cyclic normal stresses, in which the single-amplitude major principal strain was less than 0·002%. The stress state of a given specimen was varied along various stress paths comprising both ‘small shear’ and ‘large shear’ stresses in both triaxial compression (TC) and triaxial extension (TE) stress space while applying very small stress cycles. At small shear levels (defined as the principal stress ratio within the range between 0·5 and 2·0), small-strain stiffness defined for a given direction was a function of the principal stress in that direction. The unique relationship did not hold at larger shear stress levels when the major-to-minor principal stress ratio was approaching around 3 to 4. In the latter case, both quasi-elastic Young's moduli, defined for both major and minor principal strains, during TC and TE experienced a decrease due to damage to the initial fabric that was triggered by a high rate of plastic straining as well as creep deformation.

Macro- and micro-behaviors of granular materials under different sample preparation methods and stress paths

A series of numerical drained tests have been performed to study the macroscopic and microscopic behaviors of granular materials prepared by three different techniques (isotropic compression, tamping, and dry pluviation). The samples consist of two kinds of ellipsoids with 1170 particles. The two kinds are equal by weight. The aspect ratios (major axis length/minor axis length) of these two kinds are 1.2 and 1.5, respectively. All samples were subjected to an isotropic confining pressure of 100 kPa before loaded along 11 different stress paths. The shear strengths of these drained tests were compared with two published yield models. Good agreement was found in general. One model showed an error of less than 5% for 90% of the time. Two microscopic parameters, the unit contact normal and the contact normal force, were examined for all specimens during axial compression loading. The principal stress ratio was found to correlate better with the contact normal force than the unit contact normal. The evolution of this microscopic descriptor was further investigated for all drained tests. The result showed a unique relationship between the strength descriptor of the contact normal force and the principal stress ratio. Excellent correlations were found for the drained tests with various intermediate stresses.

Anatomy of an Error

Marston’s theory for loads on buried pipe dates from the early 1900s and is commonly used for design. The derivation nevertheless contains a rudimentary error whose effect was neutralized by empirical adjustments based on full-scale experiments. The discrepancy went undiscovered until the 1940s when Terzaghi noted an inconsistency relative to failures of cellular cofferdams. The error then was addressed by Krynine, but no attempt was made to make design adjustments until development of a soil arching theory for retaining walls in the 1980s. The error is simply stated: \IThe Rankine active pressure coefficient\N K\da\N \Irepresents a ratio of principal stresses, and by definition a principal stress cannot contribute to friction\N. The history, significance, and lessons to be learned are discussed, and suggestions are made for modifications of the Marston presentation.

Thermal and Thermal-Stressed States of Railway Wheels in the Process of Local Surface Hardening

We study the thermal and thermal-stressed states of the tires of railway wheels in the process of local surface hardening. For different points of the cross section of a tire, we determine the time dependences of temperature, thermal stresses, strains, strain rates, and the ratios of principal stresses. It is shown that, in the process of hardening, the material is subjected to alternating elastoplastic straining. The influence of location of the plasmotron on the levels of temperatures and thermal stresses is analyzed.

Response of Unsaturated Sandy Soils Under Constant Shear Stress Drained Condition

In order to understand the mechanism and conditions leading to failure of sandy slopes due to the infiltration of rainwater, constant shear stress drained triaxial tests were conducted on three sets of soil samples-normal sand, gravelly sand and silty sand-taken from natural slopes where large-scale landslides have occurred in the past. Water was infiltrated from the bottom of an initially unsaturated soil specimen under constant shear stress drained condition until failure occurred. Such a loading pattern simulated the stress path followed by a soil element on a potential failure plane on a slope subjected to rainwater infiltration. The effects of various parameters reflecting the initial condition, such as relative density, principal stress ratio, degree of saturation and infiltration rate, on the development of deformation during the infiltration process were investigated. The test results confirmed that the development of pore water pressure within the soil is the main reason for the failure of slopes during heavy rainfall. The results obtained can serve as guidelines in developing warning systems against impending rainfall-induced slope failures.

Deformation Behavior of Sandy Slopes During Rainwater Infiltration

Rainfall-induced slope failures often occur within a short period of time during or immediately after heavy rainfall. To analyze the mechanism and conditions leading to such failures, constant shear stress drained triaxial tests, which mimic the field stress path, were conducted on three sets of sandy samples obtained from sites of previous disastrous landslides. The effects of various parameters, such as initial relative density and principal stress ratio, on the temporal development of deformation were examined. Behavior after initiation of failure was significantly affected by the mode of deformation, i.e., whether compressive or dilative. Compressive soil failed rapidly due to increased pore-water pressure associated with the shearing process, while dilative soil exhibited slow failure due to loss in pore-water pressure during dilation that increased the shearing resistance of soil. Moreover, conventional triaxial drained and undrained tests were also performed to illustrate the difference in soil response under different stress paths. The results demonstrated that in analyzing the stability of slopes under rainwater infiltration, the use of strength parameters associated with failure initiation in constant shear stress drained tests may be more appropriate than those obtained from conventional triaxial tests.

The importance of multiaxial stress in creep deformation and rupture

ABSTRACTThis paper investigates the importance of multiaxial stress states by considering several distinct testing techniques used in assessing both creep deformation and creep damage accumulation. The requirements of testing programmes to determine the necessary data are discussed in respect of sensitivity and interdependence of the principal and hydrostatic stress ratios.

3차원 유한요소법을 이용한 나노압입에 의한 균열발생 하한계 해석

In this paper, cracking threshold for nanoindentation is analyzed by using 3D finited-element method. The analysis by maximum principal stress criterion can obtain the reliable results for determining to crack initiation location and load. Because the ratio of maximum principal stress to indentation depth for Victors indentation is smaller than flat-plane-column indentation and cracking for Victors indentation occurs from the inner part of specimen difficult to measure crack length, the nanoindentation facture test for flat-plane-column indentation is more effective.