On the stability of supported excavations

1984 ◽  
Vol 21 (2) ◽  
pp. 338-348 ◽  
Author(s):  
A. M. Britto ◽  
O. Kusakabe
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Plastic Material ◽  
Cohesive Soil ◽  
Perfectly Plastic ◽  
Centrifuge Tests ◽  
Bentonite Slurry ◽  
Undrained Conditions ◽  
Elastic Perfectly Plastic ◽  
The Stability

Unsupported plane strain trenches and axisymmetric shafts cannot be excavated to great depths in a purely cohesive soil. Therefore, it is standard practice to provide some form of support. Timber supports with struts are conventional and quite common. Bentonite slurry support has become more popular in recent years especially in the construction of diaphragm walls. In this paper the effect of rigid lateral support and slurry support on the stability (mode of failure) for both plane strain and axisymmetric excavations are investigated under undrained conditions. When immediate failure is of interest in saturated clays the changes in the water content can be neglected and the soil can be treated as a [Formula: see text] material. For the purposes of the analyses presented here the lateral support is assumed to be rigid and the soil is idealized as an elastic perfectly plastic material with cohesion Cu. The results from upper bound calculations, finite element collapse analyses, and centrifuge tests are presented. The analogy between deep footing failure and base failure of excavation allows the solutions for the footing problem to be interpreted for trench excavations. It is found that slurry support is more effective than rigid lateral support for axisymmetric excavations. The slurry support reduces the amount of surface settlement and also stabilises the trench against base failure. For excavations with rigid lateral support the possibility of base failure is greatly increased. The results are presented in the form of stability charts. Keywords: limit analysis, slurry support, stability number, supported excavation, upper bound solution.

The Upper Bound Approach to Plane Strain Problems Using Linear and Rotational Velocity Fields—Part II: Applications

1986 ◽  
Vol 108 (4) ◽  
pp. 307-316 ◽  
Author(s):  
Betzalel Avitzur ◽  
Waclaw Pachla
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Metal Cutting ◽  
Failure Modes ◽  
Plastic Material ◽  
Rotational Velocity ◽  
Optimization Procedure ◽  
Velocity Fields ◽  
Perfectly Plastic ◽  
Strip Drawing

Following Part I which investigated an upper bound approach to plane strain deformation of a rigid, perfectly plastic material, this Part II considers the same approach as applied to actual forming operations. The processes of drawing and extrusion, of metal cutting and of rolling are analyzed, and explicit equations are developed to calculate the surfaces of velocity discontinuity (shear boundaries), velocity discontinuities, and the upper bound on power for these processes. Both the simple, unielement velocity fields as well as the more complex multielement fields are explored. The upper bound solution is shown to be a function of the independent (input) and pseudoindependent (assumed) process parameters as minimized by an optimization procedure. Rules concerning the assumption of pseudoindependent parameters are presented and the optimization procedure is discussed. Final conclusions lead the way for the application of upper bound analyses to such industrial processes as sheet and strip drawing, extrusion, forging, rolling, leveling, ironing and machining, and to the investigation of such flow failure modes as central bursting, piping and end splitting (alligatoring).

Response and Instability of Sloping Seabed Supporting Small Marine Structures: Wave-Structure-Soil Interaction Analysis

2021 ◽  
pp. 1-20
Author(s):  
Amin Rafiei ◽  
M.S. Rahman ◽  
M.A. Gabr
Keyword(s):  
Interaction Analysis ◽  
Plastic Material ◽  
Wave Structure ◽  
Element Model ◽  
Induced Response ◽  
Perfectly Plastic ◽  
Marine Hydrokinetic ◽  
Elastic Perfectly Plastic ◽  
The Stability ◽  
Wave Induced

Abstract Wave-induced liquefaction in seabed may adversely impact the stability and bearing capacity of the foundation elements of coastal structures. The interaction of wave, seabed, and structure has been studied mostly for only mildly sloping seabed (<5°) using a decoupled approach. However, some of the marine hydrokinetic devices (MHKs) may be built on or anchored to the seabed with significant steepness. The wave-induced response and instantaneous liquefaction within sloping seabed supporting a small structure (representing a small MHK device) are evaluated herein by developing an almost fully coupled finite element model. The effects of coupling approach on the stress response and liquefaction of the seabed soils are investigated. Subsequently, post-liquefaction deformation of seabed soils around the structure is assessed. The poroelasticity equations governing the seabed response coupled with those for other domains are solved simultaneously. For post-liquefaction analysis, the soil is modeled as elastic perfectly plastic material. The development of instantaneously liquefied zones near the foundation is studied in terms of seabed steepness and wave parameters. The changes in the effective stress paths due to the development of liquefied zones are evaluated in view of the soil's critical state. The results indicate that the decoupled solution yields significantly larger stresses and liquefaction zones around the structure. The seabed response and the liquefaction zones become smaller for steeper slopes. The presence of liquefied zones brings the stress state closer to the failure envelope, reduces the confining stresses, and induces larger plastic strains around the foundation element.

The Upper Bound Approach to Plane Strain Problems Using Linear and Rotational Velocity Fields—Part I: Basic Concepts

1986 ◽  
Vol 108 (4) ◽  
pp. 295-306 ◽  
Author(s):  
Betzalel Avitzur ◽  
Waclaw Pachla
Keyword(s):  
Plane Strain ◽  
Upper Bound ◽  
Rotational Motion ◽  
Plastic Material ◽  
Rotational Velocity ◽  
Linear Motion ◽  
Velocity Discontinuity ◽  
Perfectly Plastic ◽  
Plane Strain Deformation ◽  
Strip Drawing

This paper investigates an upper bound approach to plane strain deformation of a rigid, perfectly plastic material. In this approach the deformation region is divided into a finite number of rigid triangular bodies that slide with respect to one another. Neighboring rigid body zones are analyzed in specific cases where the zones are (1) both in rotational motion, (2) one in linear, the other in rotational motion and (3) both in linear motion. Specific equations are presented that describe surfaces of velocity discontinuity (shear boundaries) between the moving bodies, and the velocity discontinuities and shear power losses for each of the three cases. The shape of the surface of velocity discontinuity is uniquely determined by the velocity ratios of neighboring bodies, their relative directions of motion and, where applicable, the positions of their centers of rotation. Where one or both neighboring bodies exhibit rotational motion, the surface of velocity discontinuity is found to be a cylindrical surface. In the case of two neighboring bodies, each with linear motion, the surface of velocity discontinuity is found to be planar. The velocity discontinuity is found to be constant along the entire surface of velocity discontinuity. The characteristics of the surfaces of velocity discontinuity in plane strain deformation are investigated. The upper-bound approach to plane strain problems can be successfully adapted to real metal forming processes, including sheet and strip drawing, extrusion, forging, rolling, leveling, ironing, and machining.

On the Conditions to Prevent Plastic Shakedown of Structures: Part I—Theory

1993 ◽  
Vol 60 (1) ◽  
pp. 15-19 ◽  
Author(s):  
Castrenze Polizzotto
Keyword(s):  
Mechanical Load ◽  
Plastic Material ◽  
Perfectly Plastic ◽  
Shakedown Theory ◽  
Elastic Perfectly Plastic ◽  
Plastic Shakedown ◽  
Steady Load

For a structure of elastic perfectly plastic material subjected to a given cyclic (mechanical and/or kinematical) load and to a steady (mechanical) load, the conditions are established in which plastic shakedown cannot occur whatever the steady load, and thus the structure is safe against the alternating plasticity collapse. Static and kinematic theorems, analogous to those of classical shakedown theory, are presented.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

Analytical Solutions of Crack Tip Plasticity Zone Shape for a Semi-Infinite Crack

2003 ◽  
Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Analytical Solutions ◽  
Yield Criterion ◽  
Plasticity Zone ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Classical Plasticity ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this work, closed-form analytical solutions for the plasticity zone shape at the lip of a semi-infinite crack are developed. The material is assumed isotropic with a linear elastic-perfectly plastic constitution. The solutions have been developed for the cases of plane stress and plane strain. The three crack modes, mode I, II and III have been considered. Finally, prediction of the plasticity zone extent has been performed for both the Von Mises and Tresca yield criterion. Significant differences have been found between the plane stress and plane strain conditions, as well as between the three crack modes’ solutions. Also, significant differences have been found when compared to classical plasticity zone calculations using the Irwin approach.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

Effect of Core Plasticity on the Post-Buckling Behavior of Debonded Sandwich Beams

2000 ◽  
Author(s):  
Bhavani V. Sankar ◽  
Manickam Narayanan ◽  
Abhinav Sharma
Keyword(s):  
Plastic Material ◽  
Maximum Load ◽  
Face Sheet ◽  
Compression Tests ◽  
Element Analysis ◽  
The Core ◽  
Perfectly Plastic ◽  
The Face ◽  
Post Buckling ◽  
Elastic Perfectly Plastic

Abstract Nonlinear finite element analysis was used to simulate compression tests on sandwich composites containing debonded face sheets. The core was modeled as an elastic-perfectly-plastic material, and the face-sheet as elastic isotropic. The effects of core plasticity, face-sheet and core thickness, and debond length on the maximum load the beam can carry were studied. The results indicate that the core plasticity is an important factor that determines the maximum load.

A Compressible Elastic, Perfectly Plastic Wedge

1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
The State ◽  
Hardening Material ◽  
Included Angle ◽  
Elastic Plastic ◽  
Numerical Example ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.

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