SIGMA/W

Finite-Element Stress & Deformation Analysis

The following are an integrated suite of five geotechnical software packages being used extensively throughout the world on six continents and in more than 70 countries. They are used by practicing engineers for the analysis and design of a wide variety of structures and by universities for teaching and research. The five state-of-the-art software packages for geotechnical modeling in the Microsoft Windows environment are:

SLOPE/W for slope stability
SEEP/W for groundwater seepage
CTRAN/W for contaminant transport
SIGMA/W for stress and deformation
TEMP/W for geothermal analysis

Features of the Finite-Element Software

SEEP/W, CTRAN/W, SIGMA/W, and TEMP/W are all based on the finite-element method. The CAD-like interface of these products helps to simplify one of the most difficult aspects of using finite-element software: creating the finite-element mesh. You can draw elements individually on the screen or generate elements over a specified region. And you never have to worry about the node and element numbering; as elements are generated, the mesh numbering scheme is sorted for the analysis.
Other features of the finite-element software include:

Four- to eight-noded quadrilateral elements
Three- to six-noded triangular elements
Infinite elements for far-field boundary conditions
Selectable Gaussian integration order
Color shading of elements according to material type
Display of boundary conditions as graphic symbols
Boundary conditions specified as functions for transient analyses
No inherent restrictions on the number of nodes and elements
No restriction on the nodal number difference (bandwidth) in an element

Software Integration

How different products work together

The integration of this geotechnical software allows you to use results from one product as input for another product. For example, a finite-element mesh developed in SEEP/W for a seepage analysis can be imported into SIGMA/W for a stress/deformation analysis. Other examples of integration are:

Pore-water pressure distributions computed by SEEP/W can be used in SLOPE/W for a slope stability analysis.
Pore-water pressures that arise due to external loadings can be computed by SIGMA/W as part of a stress analysis. The dissipation of the load-induced excess pore-water pressures can be analyzed by SEEP/W. SIGMA/W can then compute the deformation resulting from the excess pore-water dissipation.
SLOPE/W can use the SIGMA/W-computed stress-induced excess pore-water pressures in a stability analysis. This makes it possible, for example, to compute the end-of-construction stability conditions in terms of effective stresses.
SIGMA/W-computed finite-element stresses can be used in SLOPE/W to compute stability factors. This new and innovative method makes it possible to assess the overall stability of a slope as well as the local stability factor of each slice.

SIGMA/W analyzes geotechnical stress and deformation problems. The comprehensive formulation of SIGMA/W makes it possible to consider analyses ranging from simple linear-elastic deformation problems to sophisticated effective-stress nonlinear problems with staged applied loadings.

Many computed parameters such as vertical stress can be contoured.

FEATURES AND CAPABILITIES

Constitutive Models

SIGMA/W is formulated for the following elastic and elastic-plastic constitutive soil models:

Linear-Elastic
Anisotropic Linear-Elastic
Non-linear-Elastic
Elastic-Plastic (Tresca & Mohr-Coulomb Failure Criterion)
Strain-Softening (Von Mises Failure Criterion)
Cam-Clay (Critical State)
Modified Cam-Clay (Critical State)

Fill placement or excavation can be modeled by specifying the time step at which to add or remove an element from the analysis.

You can use any combination of these soil models in a stress analysis to represent various types of soils or structural materials.

Analysis Types

Drained total and effective stress
Undrained effective stress
Total stress analysis with pore-water pressures based on total stress changes
Two-dimensional plane strain
Three-dimensional axisymmetric
Volume change (deformation due to changes in pore-water pressure; uncoupled consolidation when integrated with SEEP/W)
In-situ stress analysis

Boundary Conditions

X and Y displacements
X and Y forces
X and Y pressures
X and Y spring constants
Self-weight gravity loading

Stop-Restart Solving

A powerful, stop-restart feature provides for great flexibility in modeling changing boundary conditions. The finite-element processing can be halted at any time and restarted after making changes.

Pore-Water Pressure Parameters

B-Parameter can be specified as a function of pore pressure, and A-Parameter can be specified as a function of deviatoric stress. The B pore-water pressure function makes it possible to consider both saturated and unsaturated conditions.

VIEWING AND PLOTTING

The results can be graphically displayed as a deformed mesh, displacement vectors, contours, graphs, and shading of yield zones. Any stress state can be displayed as a Mohr Circle with the associated stress-orientation diagrams by clicking on any node or element Gauss region. Deformations can be displayed at any magnification.
The computed parameters (such as stress, strain, pore-water pressure, and deformation) can be displayed as contours or graphs. These variables include: Vertical (Y) stress; Horizontal (X) stress; X-Y shear stress; Maximum (major principal) stress; Minimum (minor principal) stress; Maximum shear stress; Mean stress (p), Deviatoric stress (q); Strains; Pore-water pressure; and Material properties. Stress conditions can be contoured and graphed as total or effective stresses. You can contour and graph the computed variables as the total summation for all load steps or the incremental change between any two selected load steps.

Computed parameters can be plotted as a function of space, time, deformation or strain. The total stress, effective stress, or strain state at any node or element Gauss region can be displayed as a Mohr Circle with the associated diagrams.

TYPICAL APPLICATIONS

Deformation

SIGMA/W is ideally suited for computing ground deformations including:

Settlement of footings

Deformation within or underneath an embankment or earth dam
Lateral movement of braced or anchored excavations and surface settlement around the excavation
Floor rebound of open-pit, sloping excavations
Volume changes (uncoupled consolidation or heave) resulting from pore-water pressure changes

Deformations can be plotted as a deformed mesh at a specified magnification.

Soil Structure Interaction

Soil-structure interaction problems can be analyzed by including structural components in the finite-element mesh that have equivalent structural stiffness parameters. Contact between the soil and the structure can be modeled by any of the constitutive soil models or as a special slip surface.

Embankments and Excavations

Fill placement for embankments or removal of earth from excavations can be modeled by indicating the time (load) step at which any element is added to or removed from the analysis. These elements can be specified graphically by clicking on each element or selecting them as a group. During the analysis, these elements are added to or removed from the mesh before each load step.

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Τελευταία Ενημέρωση 27 Ιουλίου 2004 - Last Revised on July 27, 2004

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