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

2008 ◽  
Vol 45 (5) ◽  
pp. 597-610 ◽  
Author(s):  
Dharma Wijewickreme ◽  
Yoginder P. Vaid
Keyword(s):  
Principal Stress ◽  
Stress Ratio ◽  
Shear Stiffness ◽  
Stress Path ◽  
Simultaneous Increase ◽  
Loose Sand ◽  
Horizontal Shear ◽  
Principal Stresses ◽  
Inherent Anisotropy ◽  
Strain Paths

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–ασ space, 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'm depends 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 ασ are 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 ασ with constant b and σ'm has been developed based on these findings.

Behaviour of loose sand under simultaneous increase in stress ratio and principal stress rotation

1993 ◽  
Vol 30 (6) ◽  
pp. 953-964 ◽  
Author(s):  
Dharmapriya Wijewickreme ◽  
Yoginder P. Vaid
Keyword(s):  
Stress State ◽  
Principal Stress ◽  
Hollow Cylinder ◽  
Stress Ratio ◽  
Stress Path ◽  
Simultaneous Increase ◽  
Strain Response ◽  
Principal Stress Rotation ◽  
Stress Increment ◽  
Stress Rotation

The drained behaviour of loose sands under simultaneous increase in stress ratio and principal stress rotation is investigated. The hollow cylinder torsional device, which permits independent control of four stress parameters, namely effective mean normal stress [Formula: see text], stress ratio R, intermediate principal stress parameter b, and the inclination ασ of the major principal effective stress [Formula: see text] to the vertical, is adopted as the testing device. Drained tests carried out on saturated sand indicate that deformations under increasing R and ασ are path independent, if the final stress state is within the approximate bounds of R < 2 and ασ < 45°. With increasing stress ratio R and (or) principal stress rotation, deformations gradually become path dependent. Once loaded to a stress state within the domain R < 2 and ασ < 45°, the strain response under subsequent principal stress rotation is shown to be independent of the previous loading history. It is demonstrated that the strain response under any general increasing R − ασ path in the domain of R < 2 and ασ < 45° can be predicted using the results of a limited number of tests characterizing that domain. Strain increment direction αΔε is shown to be approximately coincident with and totally governed by the stress increment direction αΔσ, when the stress increment direction αΔσ is preferentially inclined towards the vertical deposition direction. Key words : sand behaviour, hollow cylinder torsional device, principal stress rotation, stress-path testing.

A critical-state constitutive model for liquefiable sand

2005 ◽  
Vol 42 (3) ◽  
pp. 830-855 ◽  
Author(s):  
SM Reza Imam ◽  
Norbert R Morgenstern ◽  
Peter K Robertson ◽  
David H Chan
Keyword(s):  
Constitutive Model ◽  
Critical State ◽  
Stress Ratio ◽  
Large Strain ◽  
Triaxial Compression ◽  
Loose Sand ◽  
Inherent Anisotropy ◽  
Dense Sand ◽  
Peak Point ◽  
Wide Range

This paper presents a critical-state constitutive model for sands over a wide range of void ratios and consolidation pressures in a triaxial plane. A single set of parameters, including a unique critical-state line reached at large strain, is also used in the model, and differences in behavior in triaxial compression and extension are modeled by accounting for anisotropy at small and medium ranges of strain. The model uses a capped yield surface (YS), which is characterized by its size and shape. Following evidence in past literature, the stress ratio at the peak point of the capped YS of loose sands is approximated by the stress ratio measured at the peak point of their undrained effective stress path. Yielding parameters obtained using this stress ratio are also applied in modeling dense sand behavior and drained loading. These parameters account for the effects of inherent anisotropy, void ratio, and confining pressure on yielding stresses and are readily determined from laboratory tests, but further research is required on their determination from field data. The model accounts for stress-induced and inherent anisotropies, using different parameters, which develop and evolve independently. Emphasis is placed on proper modeling of aspects of loose sand behavior that affect their susceptibility to flow liquefaction.Key words: constitutive modeling, liquefaction, loose sand, critical state, dilatancy, hardening.

Undrained anisotropy of Hostun RF loose sand: new experimental investigations

2006 ◽  
Vol 43 (11) ◽  
pp. 1195-1212 ◽  
Author(s):  
Zeina Finge ◽  
Thiep Doanh ◽  
Phillippe Dubujet
Keyword(s):  
Effective Stress ◽  
Stress Ratio ◽  
Triaxial Compression ◽  
Stress Path ◽  
Experimental Investigations ◽  
Loose Sand ◽  
Induced Anisotropy ◽  
Static Liquefaction ◽  
Stress States ◽  
Effective Stress Ratio

The undrained behaviour of loose and overconsolidated Hostun RF sand in triaxial compression and extension tests is described. The samples are isotropically or anisotropically overconsolidated along several constant effective stress ratio paths with various overconsolidation ratios (OCR), up to 24. To minimize the effect of variation of density on the observed undrained behaviour, all tested samples are required to have a nearly identical void ratio before the final monotonic undrained shearing. Isotropically overconsolidated and normally consolidated samples exhibit the same phenomenon of partial static liquefaction, but anisotropically overconsolidated specimens reveal a completely different undrained behaviour. A common pseudoelastic response is observed for a given overconsolidation history. This response is induced by recent stress history in terms of effective stress paths, independent of the OCR during overconsolidation. The initial gradient of the effective stress paths seems to depend solely on the direction of the previous linear stress path history. This paper offers a comprehensive understanding of the mechanism of the induced anisotropy of loose sand created by simple linear stress paths from three different initial stress states in the classical triaxial plane. The pseudoelastic response can be adequately modelled by a simple hyperelastic component of the elastoplastic framework.Key words: induced anisotropy, overconsolidation, instability, laboratory undrained tests, sand, hyperelasticity.

Orientation and formability of orthotropic sheet metals

1997 ◽  
Vol 32 (1) ◽  
pp. 61-81 ◽  
Author(s):  
D W A Ress ◽  
R K Power
Keyword(s):  
Plane Strain ◽  
Principal Stress ◽  
Stress Ratio ◽  
Rolling Direction ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Sheet Metals ◽  
Principal Stresses ◽  
Thickness Strain ◽  
Automotive Sheet

This paper examines the formability of automotive sheet metals: CR steels and 6000 series aluminium-magnesium alloys. Necking strains are used to determine the forming limits; i.e. a diffuse instability condition is reached under in-plane biaxial stressing. The theory admits material anisotropy, work-hardening and sheet orientation under any ratio of applied principal stresses. It has been programmed to accept orientations between the principal stress axes and the sheets' rolling direction in 15° increments between 0° and 90°. The ratio between the principal stresses may vary between 0 and ± 1. The input data required are the width-thickness strain ratios ( r values) in directions 0°, 45° and 90° to the roll and the Hollomon hardening exponent ( n value). The output is presented in four diagrams: the critical subtangent-stress ratio and plots between three combinations of the limiting principal engineering strains: (a) two in-plane strains, (b) major in-plane strain versus thickness strain and (c) minor in-plane strain versus thickness strain. Each diagram shows the influence of rotating the principal stress axes in increments of 15° to the roll. The forming limit diagram of type (a) gives the traditional presentation of a forming limit diagram (FLD). This FLD may be established experimentally from the strain in a surface grid lying around splits. In practice, a few production panels may be gridded for die-tryout and to examine a change in material. The alternative FLDs, types (b) and (c), are proposed to provide quality control with the increasing use of ultrasonics to monitor thickness of pressed panels. An example of type (b) is determined experimentally for CR1 steel.

scholarly journals Numerical simulation on the simultaneous stress interference of parallel multiple hydraulic fractures

2021 ◽  
pp. 014459872110019
Author(s):  
Weiyong Lu ◽  
Changchun He
Keyword(s):  
Principal Stress ◽  
Hydraulic Fracture ◽  
Stress Ratio ◽  
Fracture Network ◽  
Hydraulic Fractures ◽  
Fracture Spacing ◽  
Induced Stress ◽  
Minimum Principal Stress ◽  
Fracturing Process ◽  
Stress Ratios

During horizontal well staged fracturing, there is stress interference between multiple transverse fractures in the same perforation cluster. Theoretical analysis and numerical calculation methods are applied in this study. We analysed the mechanism of induced stress interference in a single fracture under different fracture spacings and principal stress ratios. We also investigated the hydraulic fracture morphology and synchronous expansion process under different fracture spacings and principal stress ratios. The results show that the essence of induced stress is the stress increment in the area around the hydraulic fracture. Induced stress had a dual role in the fracturing process. It created favourable ground stress conditions for the diversion of hydraulic fractures and the formation of complex fracture network systems, inhibited fracture expansion in local areas, stopped hydraulic fractures, and prevented the formation of effective fractures. The curves of the maximum principal stress, minimum principal stress, and induced principal stress difference with distance under different fracture lengths, different fracture spacings, and different principal stress ratios were consistent overall. With a small fracture spacing and a small principal stress ratio, intermediate hydraulic fractures were difficult to initiate or arrest soon after initiation, fractures did not expand easily, and the expansion speed of lateral hydraulic fractures was fast. Moreover, with a smaller fracture spacing and a smaller principal stress ratio, hydraulic fractures were more prone to steering, and even new fractures were produced in the minimum principal stress direction, which was beneficial to the fracture network communication in the reservoir. When the local stress and fracture spacing were appropriate, the intermediate fracture could expand normally, which could effectively increase the reservoir permeability.

Cumulative Damage in Fatigue under Multiaxial Stress Conditions

1974 ◽  
Vol 188 (1) ◽  
pp. 423-430 ◽  
Author(s):  
D. L. Mcdiarmid
Keyword(s):  
Experimental Investigation ◽  
Aluminium Alloy ◽  
Principal Stress ◽  
Stress Ratio ◽  
Uniaxial Stress ◽  
Cumulative Damage ◽  
Stress Conditions ◽  
Multiaxial Stress ◽  
Stress Ratios ◽  
Damage Criteria

Previous investigations into cumulative damage fatigue under uniaxial stress are discussed in conjunction with the parameters relevant to the present experimental investigation. The results of two-level block programme tests on 2L65 aluminium alloy at four values of constant principal stress ratio and at several combinations of two different principal stress ratios are presented and discussed with reference to cumulative damage criteria developed for the case of uniaxial fatigue stress.

Assessing the undrained strength cross-anisotropy of three tailings types

2022 ◽  
Vol 12 (1) ◽  
pp. 1-24
Author(s):  
D. Reid ◽  
R. Fanni ◽  
A. Fourie
Keyword(s):  
Principal Stress ◽  
Stress Ratio ◽  
Additional Data ◽  
Layered Materials ◽  
Engineering Practice ◽  
Published Data ◽  
Shear Tests ◽  
Undrained Strength ◽  
Cross Anisotropy ◽  
Current Engineering

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 being despite the very common layering profile seen 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 degrees during undrained shearing. 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.

scholarly journals Determination of the Paleostress Orientations and Magnitudes for Missan Structures, Southeastern Iraq

2018 ◽  
Vol 26 (10) ◽  
pp. 213-233
Author(s):  
Atheer Edan Khalil AL- Hachem ◽  
Mustafa Rasheed Salih Al – Obaidi
Keyword(s):  
Principal Stress ◽  
Graphical Methods ◽  
Principal Stresses ◽  
Unstable Region ◽  
Diagram Method ◽  
Stress Orientations

        The use of  Right dihedral method and Mohr diagram method allow determination of the paleostress orientation and its magnitude in Missan structures, Southeastern Iraq. The principal stress orientations and its magnitudes have been determined by the measure of the striation on the faults planes. The measurement of orientation of the principal stress was deduced by different graphical methods, the horizontal maximum principal stresses (σ1) magnitudes were (3600, 4360,4650, 4750 and 5700) bars, the horizontal  intermediate  principal stresses (σ2) magnitudes   were (1528, 1842,1962.5, 1998.5 and 2390.5) bars and the vertical minimum principal stresses (σ3) magnitudes were (544, 676,725, 753 and 919) bars. This study shows that area is located within the unstable region since the poles of measured faults lie in the area of reactivated faults in Mohr diagram.

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