A semi‐analytical solution for displacement‐controlled elliptical cavity expansion in undrained MCC soil

2021 ◽  
Author(s):  
Hang Zhou ◽  
Hanlong Liu ◽  
Zengliang Wang
Keyword(s):  
Analytical Solution ◽  
Cavity Expansion ◽  
Elliptical Cavity

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

2018 ◽  
Vol 55 (7) ◽  
pp. 1029-1040 ◽  
Author(s):  
Pin-Qiang Mo ◽  
Hai-Sui Yu
Keyword(s):  
Analytical Solution ◽  
Plastic Region ◽  
State Parameter ◽  
Auxiliary Variable ◽  
Cavity Expansion ◽  
Large Strains ◽  
Initial State ◽  
Model Soil ◽  
Spacing Ratio ◽  
Soil Behaviour

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.

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

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.

Cavity Expansion in Soil of Finite Radial Extent

2014 ◽  
Vol 553 ◽  
pp. 464-469
Author(s):  
Mohammad Pournaghiazar ◽  
Adrian R. Russell ◽  
Nasser Khalili
Keyword(s):  
Analytical Solution ◽  
Quartz Sand ◽  
Stress Condition ◽  
Constitutive Models ◽  
Solution Procedure ◽  
Cavity Expansion ◽  
Finite Boundary ◽  
Spherical Cavities ◽  
Radial Extent ◽  
Zero Radius

The problem of drained cavity expansion in a soil of finite radial extent is investigated. Spherical cavities expanded from zero radius subjected to a constant stress condition at the finite boundary are considered. The new analytical solution procedure presented enables more advanced constitutive models to be implemented than possible than when using other solution procedures. Cavity expansion results generated for a Sydney quartz sand highlight substantial differences between cavity limit pressures for boundaries of finite and infinite radial extent.

scholarly journals ANALYZING THE SPHERICAL CAVITY EXPANSION PROBLEM IN A MEDIUM WITH MOHR − COULOMB − TRESCA'S PLASTICITY CONDITION

2019 ◽  
Vol 81 (3) ◽  
pp. 292-304 ◽  
Author(s):  
V.L. Kotov ◽  
D.B. Timofeev
Keyword(s):  
Plastic Deformation ◽  
Analytical Solution ◽  
Spherical Cavity ◽  
Yield Criterion ◽  
Closed Form Solution ◽  
Cavity Expansion ◽  
Plasticity Condition ◽  
Rigid Plastic ◽  
Tangential Stresses ◽  
Shockwave Front

An analytical solution of the one-dimensional problem of a spherical cavity expanding at a constant velocity from a point in a space occupied by a plastic medium has been obtained. Impact compressibility of the medium is described using linear Hugoniot's adiabat. Plastic deformation obeys the Mohr - Coulomb yield criterion with constraints on the value of maximum tangential stresses according to Tresca's criterion. In the assumption of rigid-plastic deformation (the elastic precursor being neglected), incompressibility behind the shockwave front and the equality of the propagation velocities of the fronts of the plastic wave and the plane shockwave defined by linear Hugoniot's adiabat, a boundary-value problem for a system of two first-order ordinary differential equations for the dimensionless velocity and stress depending on the self-similar variable is formulated. A closed-form solution of this problem has been obtained in the form of a stationary running wave - a plastic shockwave propagating in an unperturbed half-space. This solution is a generalization of the earlier obtained analytical solution for a medium with the Mohr - Coulomb plasticity condition. The effect of constraining the limiting value of maximal tangential stresses on the distribution of dimensionless stresses behind the shockwave front has been examined. Formulas for determining the range of cavity expansion velocities, within which a simple solution for a medium with Tresca's plasticity condition is applicable, have been derived. The obtained solution can be used for evaluating resistance to high-velocity penetration of rigid strikers into low-strength soil media.

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