Drained cavity expansion analysis with a unified state parameter model for clay and sand

This paper presents an analytical solution for drained expansion in both spherical and cylindrical cavities with a unified state parameter model for clay and sand (CASM). The solution developed here provides the stress and strain fields during the expansion of a cavity from an initial to an arbitrary final radius. Small strains are assumed for the elastic region and large strains are applied to soil in the plastic region by using logarithmic strain definitions. Since its development, the unified CASM model has been demonstrated by many researchers to be able to capture the overall soil behaviour for both clay and sand under both drained and undrained loading conditions. In this study, the CASM model is used to model soil behaviour whilst a drained cavity expansion solution is developed with the aid of an auxiliary variable. This is an extension of the undrained solution presented by the authors in 2017. The parametric study investigates the effects of various model constants including the stress-state coefficient and the spacing ratio on soil stress paths and cavity expansion curves. Both London clay and Ticino sand are modelled under various initial stress conditions and initial state parameters. The newly developed analytical solution highlights the potential applications in geotechnical practice (e.g., for the interpretation of cone penetration test data) and also provides useful benchmarks for numerical simulations of cavity expansion problems in critical state soils.

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Effects of fines on liquefaction behaviour in well-graded materials

Canadian Geotechnical Journal ◽

10.1139/cgj-2017-0016 ◽

2017 ◽

Vol 54 (10) ◽

pp. 1460-1471 ◽

Cited By ~ 9

Author(s):

Katherine A. Kwa ◽

David W. Airey

Keyword(s):

Critical State ◽

Soil Mechanics ◽

State Parameter ◽

Triaxial Tests ◽

Particle Sizes ◽

Graded Materials ◽

Fines Content ◽

Cyclic Resistance ◽

Wide Range ◽

Soil Behaviour

This study uses a critical state soil mechanics perspective to understand the mechanics behind the liquefaction of metallic ores during transport by ship. These metallic ores are transported at relatively low densities and have variable gradings containing a wide range of particle sizes and fines contents. The effect of the fines content on the location of the critical state line (CSL) and the cyclic liquefaction behaviour of well-graded materials was investigated by performing saturated, standard drained and undrained monotonic and compression-only cyclic triaxial tests. Samples were prepared at four different gradings containing particle sizes from 9.5 mm to 2 μm with fines (<75 μm) contents of 18%, 28%, 40%, and 60%. In the e versus log[Formula: see text] plane, where e is void ratio and [Formula: see text] is mean effective stress, the CSLs shifted upwards approximately parallel to one another as the fines content was increased. Transitional soil behaviour was observed in samples containing 28%, 40%, and 60% fines. A sample’s cyclic resistance to liquefaction depended on a combination of its density and state parameter, which were both related to the fines content. Samples with the same densities were more resistant to cyclic failure if they contained higher fines contents. The state parameter provided a useful prediction for general behavioural trends of all fines contents studied.

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Analytical Solution of a Borehole Problem Using Strain Gradient Plasticity

Journal of Engineering Materials and Technology ◽

10.1115/1.1480408 ◽

2002 ◽

Vol 124 (3) ◽

pp. 365-370 ◽

Cited By ~ 12

Author(s):

X.-L. Gao

Keyword(s):

Analytical Solution ◽

Strain Gradient ◽

Plastic Region ◽

Yield Condition ◽

Plasticity Theory ◽

Strain Gradient Plasticity ◽

Spatial Gradient ◽

Gradient Plasticity ◽

Present Solution ◽

Classical Plasticity

An analytical solution is presented for the borehole problem of an elasto-plastic plane strain body containing a traction-free circular hole and subjected to uniform far field stress. A strain gradient plasticity theory is used to describe the constitutive behavior of the material undergoing plastic deformations, whereas the generalized Hooke’s law is invoked to represent the material response in the elastic region. This gradient plasticity theory introduces a higher-order spatial gradient of the effective plastic strain into the yield condition to account for the nonlocal interactions among material points, while leaving other relations in classical plasticity unaltered. The solution gives explicit expressions for the stress, strain, and displacement components. The hole radius enters these expressions not only in nondimensional forms but also with its own dimensional identity, unlike classical plasticity-based solutions. As a result, the current solution can capture the size effect in a quantitative manner. The classical plasticity-based solution of the borehole problem is obtained as a special case of the present solution. Numerical results for the plastic region radius and the stress concentration factor are provided to illustrate the application and significance of the newly derived solution.

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A numerical solution of cavity expansion problem in sand based directly on experimental stress-strain curves

Canadian Geotechnical Journal ◽

10.1139/t98-028 ◽

1998 ◽

Vol 35 (4) ◽

pp. 541-559 ◽

Cited By ~ 18

Author(s):

Branko Ladanyi ◽

Adolfo Foriero

Keyword(s):

Numerical Solution ◽

Strain Path ◽

Shear Resistance ◽

Cavity Expansion ◽

Large Strains ◽

Volume Changes ◽

Stress Strain ◽

Stress Variation ◽

Cylindrical Cavity Expansion ◽

State Of Stress

A numerical solution of a spherical and cylindrical cavity expansion problem in sand is presented herein. The underlying theory is unbiased in that it is based directly on experimentally determined stress-strain curves. The solution makes it possible to follow the continuous variation of strains, stresses, and volume changes produced by cavity expansion. It essentially uses the "strain path" approach to determine the state of stress around the cavity, taking into account large strains and the effect of spherical stress variation on the mobilized shear resistance and the associated volume strains. A limited comparison with experimental data shows a reasonable agreement between theory and measurements.Key words: cavities, expansion, sand, stress-strain curves, numerical solution.

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Modified state parameter for characterizing static liquefaction of sand with fines

Canadian Geotechnical Journal ◽

10.1139/t08-122 ◽

2009 ◽

Vol 46 (3) ◽

pp. 281-295 ◽

Cited By ~ 67

Author(s):

D. C. Bobei ◽

S. R. Lo ◽

D. Wanatowski ◽

C. T. Gnanendran ◽

M. M. Rahman

Keyword(s):

Critical State ◽

Volumetric Strain ◽

State Parameter ◽

Confining Pressure ◽

Log P ◽

Test Results ◽

Static Liquefaction ◽

Isotropic Consolidation ◽

Failure Line ◽

Soil Behaviour

An experimental study was carried out to investigate the static liquefaction behaviour of sand with a small amount of plastic and nonplastic fines. Five series of tests were conducted in drained and undrained conditions. The drained test results indicate not only that the failure line coincides with the critical state, but also that the development of volumetric strain during shearing was not sensitive to the initial confining pressure. In both isotropically and anisotropically consolidated undrained tests, a so-called “reverse behaviour” was consistently observed. The results were also interpreted in the critical state framework. The critical and steady state (CS/SS) data were found to trace along the same curve in e–log( p′) space, irrespective of the stress history and effective stress paths. A comparison between the isotropic consolidation line (ICL) and critical state (CS) curve showed that a small amount of fines can significantly change the shape and position of the ICL relative to the CS curve. Furthermore, the soil behaviour manifested in both drained and undrained shearing led to the development of a modified state parameter.

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A rigorous semi-analytical solution for undrained cylindrical cavity expansion in critical state soils

International Journal for Numerical and Analytical Methods in Geomechanics ◽

10.1002/nag.2529 ◽

2016 ◽

Vol 40 (15) ◽

pp. 2137-2160 ◽

Cited By ~ 15

Author(s):

Apostolos Vrakas

Keyword(s):

Analytical Solution ◽

Cylindrical Cavity ◽

Critical State ◽

Cavity Expansion ◽

Cylindrical Cavity Expansion

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Fisher information of accelerated two-qubit systems

International Journal of Modern Physics B ◽

10.1142/s0217979218500509 ◽

2018 ◽

Vol 32 (05) ◽

pp. 1850050 ◽

Cited By ~ 9

Author(s):

N. Metwally

Keyword(s):

Analytical Solution ◽

Fisher Information ◽

General State ◽

Initial State ◽

Werner State ◽

Pure States ◽

X State ◽

Different Parts ◽

Degree Of Entanglement

In this paper, Fisher information for an accelerated system initially prepared in the X-state is discussed. An analytical solution, which consists of three parts: classical, the average over all pure states and a mixture of pure states, is derived for the general state and for Werner state. It is shown that the Unruh acceleration has a depleting effect on the Fisher information. This depletion depends on the degree of entanglement of the initial state settings. For the X-state, for some intervals of Unruh acceleration, the Fisher information remains constant, irrespective to the Unruh acceleration. In general, the possibility of estimating the state’s parameters decreases as the acceleration increases. However, the precision of estimation can be maximized for certain values of the Unruh acceleration. We also investigate the contribution of the different parts of the Fisher information on the dynamics of the total Fisher information.

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Verifying the Movable Elastoplastic Boundary Method by Using Galin’s Problem

Journal of Physics Conference Series ◽

10.1088/1742-6596/2095/1/012087 ◽

2021 ◽

Vol 2095 (1) ◽

pp. 012087

Author(s):

V.I. Bukhalov

Keyword(s):

Analytical Solution ◽

Perturbation Method ◽

Biaxial Tension ◽

Plastic Region ◽

Elastoplastic Problem ◽

Kirsch Problem ◽

The World ◽

Elastoplastic Region ◽

Elastoplastic Boundary

Abstract Galin’s solution for the problem of biaxial tension of a plate with a hole completely covered by the plastic region appears to be a pearl recognized by the world scientific community. This solution serves as a test for all sorts of approximate approaches to solving elastoplastic problems, including the semi-analytical iterative method being developed by the author, focused on solving more complex problems such as the Kirsch problem in the elastoplastic formulation. The proposed iterative approach for a semi-analytical solution involves an explicit analytical expression for stresses in the plastic region and an iterative numerical solution in the elastic region with a refined border. The paper shows the convergence of the results based on the iterative procedure for the elastoplastic region boundary approaching its analytical position, which follows from the analytical solution of Galin’s elastoplastic problem. Consideration has also been given to obtaining results on the determination of the boundary between the elastic and plastic regions using a competing approximate perturbation method. The advantage of the proposed method lays in not limited modifications in parameters due to the requirement for small differences while formulating a problem from the axisymmetric case as seen in the perturbation method.

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The Non-Stationary Dynamic Analytical Solution of a Spherical/Cylindrical Cavity Expansion

Journal of Applied Mechanics ◽

10.1115/1.4048040 ◽

2020 ◽

Vol 87 (11) ◽

Author(s):

V. R. Feldgun ◽

D. Z. Yankelevsky

Keyword(s):

Analytical Solution ◽

General Solution ◽

Cylindrical Cavity ◽

Constant Velocity ◽

Present Model ◽

Elastic Region ◽

Cavity Expansion ◽

Special Cases ◽

Significant Difference ◽

Cavity Boundary

Abstract A review of the pertinent literature related to the dynamic expansion of a spherical/cylindrical cavity shows that all the solutions with kinematic boundary conditions deal with a constant velocity at the cavity boundary. This paper develops a new general solution of the nonstationary dynamic problem of cavity expansion, which allows the application of time-dependent motion conditions at the cavity boundary. This solution can be used, for example, in the development of approximate approaches for projectiles penetrating with a non-constant velocity into different targets. Due to the complexity of the nonlinear nonstationary problem, an analytical solution of the problem may be developed if simplified constitutive relationships are used. In the present model, a simplified material model with a locked equation of state and a linear shear failure relationship is implemented. This solution may be applied to different materials such as concrete, soil, and rock. Special cases of the newly developed nonstationary solution are compared with different spherical and cylindrical cavity expansions solutions reported in the literature, and a good agreement is obtained. The capability of the present model is demonstrated in a following investigation of representative cases of cavity expansion with zero, constant, and variable acceleration of the cavity boundary. A significant difference in the stress variation for the different cases is shown. Along with the general solution which deals with an elastic–plastic region, a simplified solution which disregards the contribution of the elastic region is presented and the evaluation of the elastic region effect may be assessed.

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Estimating the undrained strength of sand: a theoretical framework

Canadian Geotechnical Journal ◽

10.1139/t95-082 ◽

1995 ◽

Vol 32 (5) ◽

pp. 859-870 ◽

Cited By ~ 44

Author(s):

Catherine E. Fear ◽

Peter K. Robertson

Keyword(s):

Shear Wave ◽

Wave Velocity ◽

Shear Wave Velocity ◽

Void Ratio ◽

Triaxial Compression ◽

State Parameter ◽

In Situ Tests ◽

Initial State ◽

Undrained Strength

A framework for estimating the ultimate undrained steady state shear strength of sand (Su) from in situ tests, which combines the theory of critical state soil mechanics with shear wave velocity measurements, is presented. For a particular direction of undrained loading, samples of a given sand at a constant void ratio will reach the same Su, despite the magnitude of the initial effective confining stresses. Unique Su/p′ or [Formula: see text] ratios for a given direction of loading exist for a particular sand only if state parameter is constant throughout the deposit. Normalized shear wave velocity, Vs1, can be correlated with void ratio and is therefore used to estimate Su for a given initial state and direction of loading. Strengths in triaxial compression are examined in this paper; however, the same framework can be used to estimate strengths under other directions of loading. The Su–Vs1 relationship is shown to be relatively sensitive and should be used more as a screening tool rather than an accurate means of predicting Su. Vs1 is converted to equivalent values of SPT (N1)60 and CPT qc1, and the results are compared with the current methods of estimating Su. Key words : in situ testing, liquefaction, sand, undrained strength.

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