Abstract Effective explicit algorithms for integrating complex elastoplastic constitutive models, such as those belonging to the Cam clay family, are described. These automatically divide applied strain increment into subincrements using an estimate of local error and attempt control global integration in stresses. For a given scheme, number substeps used is function tolerance specified, magnitude imposed increment, non‐linearity relations. The build on work Sloan 1987 but include important...

This paper investigates the undrained stability of a plane strain circular tunnel in clay, where shear strength profile is assumed to increase linearly with depth. Stability solutions for variety geometries and soil conditions are found using rigid-block upper bound methods as well finite element limit analysis (which gives both lower bounds). The latter procedures employ discrete form theorems classical plasticity, use bespoke conic programming scheme solve resulting optimization problems,...

This paper focuses mainly on the stability of a square tunnel in cohesive–frictional soils subjected to surcharge loading. Large-size noncircular tunnels are quickly becoming widespread building technology by virtue development advanced tunneling machines. The loading has been investigated theoretically and numerically, assuming plane strain conditions. Despite importance this problem, previous research subject is very limited. At present, no generally accepted design or analysis method...

In this paper, numerical limit analysis and semianalytical rigid block techniques are used to investigate the effect of tunnel spacing on stability two circular tunnels excavated side by side. The modeled under plane-strain conditions, which implies that they assumed be infinitely long. Bounds obtained using finite-element analysis, formulation is based upper lower bounds theorems classical plasticity. Solutions advanced conic programming schemes solve resulting optimization problems, bound...

A new finite element algorithm for solving elastic and elastoplastic coupled consolidation problems is described. The procedure treats the governing relations as a system of first-order differential equations based on backward Euler Thomas Gladwell schemes with automatic subincrementation prescribed series time increments. increments, which are called coarse steps, serve to start chosen by user. attempts select subincrements such that, given mesh, time-stepping (or temporal discretisation)...

The stability of dual square tunnels in cohesive-frictional soils subjected to surcharge loading has been investigated theoretically and numerically assuming plane strain conditions. From the viewpoint efficient utilization underground space for human activities, noncircular openings should be preferred design stage. Despite importance this issue, previous research on subject is very limited. At present, no generally accepted or analysis method available evaluate multiple tunnels–openings...

This paper investigates the stability of a plane strain rectangular tunnel under undrained conditions, where shear strength profile increases linearly with depth. The tunnels for range geometries and soil conditions is found using rigid-block upper bound methods as well finite element limit analysis (FELA). latter procedures employ discrete form theorems classical plasticity to formulate an optimization problem that solved bespoke conic programming scheme. Rigorous solutions, obtained...

This paper presents an algorithm for controlling the error in non-linear finite element analysis which is caused by use of load steps. In contrast to most recent schemes, proposed technique non-iterative and treats governing load–deflection relations as a system ordinary differential equations. permits equations be integrated adaptively where step size controlled monitoring local truncation error. The latter measured computing difference between two estimates displacement increments each...

This paper investigates the application of high-order elements within framework arbitrary Lagrangian-Eulerian method for analysis elastoplastic problems involving large deformations. The governing equations as well its important aspects such nodal stress recovery and remapping state variables are discussed. efficiency accuracy 6-, 10-, 15-, 21-noded triangular compared two geotechnical engineering problems, namely, behavior an undrained layer soil under a strip footing subjected to...

Estimation of the bearing capacity shallow foundations on layered soil profiles, such as a sand layer finite thickness over clay, is mainly based empirical models resulting from interpretation experimental test results. While it generally accepted that may be applicable to properties and footing geometries outside range tested experimentally, they offer limited insights how assumed failure mechanism affects their application. In particular, contribution overall accounted for via simple...

Summary This paper studies the behaviour of error incurred when numerically integrating elasto‐plastic mechanical relationships a constitutive model for soils using an explicit substepping formulation with automatic control. The correct update all variables involved in numerical integration incremental stress–strain is central to computational performance scheme, and, although often missed literature, (including specific volume) should be explicitly considered algorithmic formulation....

The automatic time-stepping algorithms developed in a companion paper are used to study the behaviour of several problems involving consolidation porous media. aim these analyses is demonstrate that new procedures robust, efficient, and can control global temporal discretization (or time-stepping) error displacements lie near prescribed tolerance. Copyright © 1999 John Wiley & Sons, Ltd.