### Integrated into the GeoStudio Suite

SIGMA/W is integrated into the GeoStudio suite, and therefore has access to the GeoStudio features for creating your model, analyzing it, and viewing results.

### Comprehensive Stress-Strain Formulation

SIGMA/W uses a finite element-based formulation for performing stress and deformation analyses of earth structures. Its comprehensive stress-strain formulation makes it possible to analyze both simple and highly complex problems. SIGMA/W can perform a simple linear elastic deformation analysis or a highly sophisticated, nonlinear elastic-plastic analysis, which may involve soil-structure interactions, coupled stress and pore-water pressure response, and the consideration of strength reduction stability. The many constitutive soil models allow you to represent a wide range of soils or structural materials. These features enable SIGMA/W to analyze almost any stress or deformation problem you will encounter in geotechnical, civil, and mining engineering projects.

### Incremental Load Formulation

SIGMA/W is formulated for 1- or 2-dimensional plane strain or axisymmetric problems using a small displacement, small strain, incremental load formulation. For each load step, incremental displacement at each node resulting from the incremental load is computed and added to the displacement at the beginning of the load step to give the total displacement. For soil models with nonlinear material properties, SIGMA/W solves the equations iteratively using the Newton-Raphson technique; soil properties are updated every iteration until a converged solution is achieved. You can simulate the filling and excavation of materials by activating or deactivating finite elements at various stages of the construction process.

### Typical Applications

SIGMA/W can model almost any stress/deformation problem, including:

- Settlement of footings, fluid-filled tanks, or earth structures
- 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 and sloping excavations
- Volume change resulting from pore water pressure change
- Field stresses in hard rock environments
- Staged fill placement and excavation
- Soil-structure interactions, including anchors, soil nails, geosynthetics, pile walls, and more
- Fully-coupled consolidation analysis
- Tailings deposition
- Permanent deformations resulting from strength loss
- Strength reduction stability
- Subsurface drainage design for soft soils
- Closure around a tunnel and stresses in the tunnel lining

### Obtain Converged Solutions for Challenging Problems

SIGMA/W can obtain solutions to complex non-linear problems due to its sophisticated stress update algorithm and robust convergence schemes, which include the Unbalanced Energy and Relative Displacement/Residual Load techniques.

### Saturated-Unsaturated Formulation

SIGMA/W is formulated to handle both saturated and unsaturated soils, which provides greater flexibility for handling coupled engineering problems.

### Coupled Consolidation Analysis

SIGMA/W is capable of handling the same degree of hydraulic non-linearity as SEEP/W, with convergence settings uniquely defined for stress-strain and water flow. This opens the door to solving various classes of problems with a new degree of rigour. For example, SIGMA/W can simulate the complex saturated-unsaturated flow that occurs during staged construction of large tailings dams or zoned dams in which a significant portion of the domain is unsaturated at the onset of construction. In addition, all stress-strain material models can be used in consolidation analyses and the unsaturated response is handled in a consistent manner.

### Model Construction Sequences with Ease

The Analysis Tree in GeoStudio provides a powerful and simple way to model even the most complex construction sequence. Analyses are added to the Tree, forming a Parent-Child relationship in which each new analysis represents a part of the construction sequence and forms the initial condition for the subsequent construction activities.

### In Situ Condition Options

Three methods can be used to establish the in situ stresses in the domain: Gravity Activation; Field Stresses; and the K_{0} Procedure. All material models applied to the domain must have a valid K_{0}, which can be specified or calculated automatically. The calculated option uses the relationship proposed by Jaky (1944) if the soil model has a friction angle, and the relationship from Schmidt (1966) if the soil model has an over-consolidation ratio. This method can model a range of stress histories that can be used as a basis for conducting load-deformation or consolidation analyses.

### Comprehensive Constitutive Model List

SIGMA/W offers a comprehensive list of constitutive models including Isotropic Elastic, Hyperbolic, Mohr-Coulomb, Mohr-Coulomb Hardening/Softening, Modified Cam-Clay, NorSand, Tresca, Tresca Hardening/Softening, Ubiquitous Joint, Ubiquitous Joint Hardening/Softening, and Generalized Hoek Brown.

### Soil Response Types

Materials are assigned as drained or undrained in the material definition for load-deformation analyses. Undrained and drained response types can be combined, making it possible to simulate a free draining material overlying a fully undrained material. Pore-water pressures are calculated for materials designated as undrained. As such, the excess pore-water pressure that develops in a low conductivity geologic unit can now be calculated without doing a consolidation analysis. Undrained behaviour is simulated using effective stress stiffness properties instead of total stress stiffness properties.

In a consolidation analysis, the response type is ignored as all materials are assumed to be consolidating. However, a material option is available to designate a material with 'no change in pore pressure during loading'. This allows the groundwater flow equations to be solved for all materials on the domain, while ensuring that some materials do not respond to loading or unloading.

### Estimate Material Properties for Typical Materials

Material properties, such as the E-Modulus versus Stress function, can be estimated using built-in properties for typical materials. The estimation process requires only fundamental material information such as the soil classification.

### Comprehensive Range of Generalized Boundary Conditions

SIGMA/W supports a comprehensive list of boundary condition options including normal/tangential stress, X-Y stress, hydrostatic pressure, displacement, force, or spring boundaries. In keeping with the entire GeoStudio suite, SIGMA/W makes broad use of generalized functions for boundary condition definition. As such, actual field data over time or user-specified functional relationships can be pasted into SIGMA/W.

### Hydrostatic Stress Boundary for Water Surcharge Loads

The hydrostatic stress boundary provides a convenient approach for modelling the water surcharge load in either an in situ analysis or a transient coupled stress and pore-water pressure analysis. This makes it possible to model problems such as rapid drawdown in a single analysis.

### Soil-Structure Interaction

SIGMA/W’s structural elements can be used to model anchors, nails, tie-backs, wall systems, piles or any other soil-structure interaction problem in geotechnical engineering.

### Integrated with SLOPE/W for Stress-Based Stability Analyses

The stresses and/or pore-water pressures from a SIGMA/W analysis can be used directly in SLOPE/W to do a stress-based stability analysis.

### Stress Redistribution Analysis

The stress redistribution analysis type can be used to conduct a strength reduction slope stability analysis, model stress transfer onto structures such as pile walls installed within failed slopes, or calculate permanent deformations resulting from strength loss due to liquefaction or strain softening.

### Model in 1D, 2D or Axisymmetric View

SIGMA/W includes analysis options for modeling pseudo three-dimensional problems.

### Powerful Graphing Options

Graphing is critical for the interpretation of stress-strain problems. The powerful graphing options in GeoStudio make it possible to plot critical information such as lateral displacement, surface settlements, pore-water pressure versus time, bending moments, shear distribution in structures, and more. New convergence graphs provide insight on the effect of material non-linearity and convergence settings on solve time performance. All of this data can be exported or copy/pasted directly into spreadsheet software.

### View Stresses in a Mohr Circle

A Mohr Circle can be plotted at any gauss point or node to further interrogate the results.

### View Deformed Mesh and Yield Zone

Interpretation of the results is enhanced through the ability to view a deformed mesh, displacement vectors, and the location of the yield zone.

### View Plastic States

SIGMA/W includes the option to view plastic states on the domain. This allows for the visualization of a variety of stress-state conditions including failure, yielding on the cap surface, yielding on the shear surface, and engagement of the tension cut-off surface. This is critical for interpreting results when sophisticated stress-strain material models are employed in an analysis, as it allows for the differentiation between portions of the domain that have failed and those that have yielded.

### Sensitivity Analysis with SIGMA/W

A sensitivity analysis can be readily conducted with SIGMA/W by cloning multiple analyses using the Analysis Tree and then making slight changes to each one.