## Stress and deformation analysis

### SIGMA/W is a powerful finite element software product for modeling stress and deformation in earth and structural materials. SIGMA/W analyses may range from simple linear elastic simulations to soil-structure interaction problems with nonlinear material models.

Many constitutive soil models enable you to represent a wide range of soils or structural materials. In addition, SIGMA/W models pore-water pressure generation and dissipation in response to external loads. With SIGMA/W you can analyze almost any stress or deformation problem you will encounter.

### Stress History

In Situ stresses can be established with gravity activation or the K0 procedure, which both consider the volumetric water content function to determine effective stress in the unsaturated zone. The at-rest earth pressure coefficient may be defined in all material models.

### Coupled Consolidation

The coupled stress and pore-water pressure formulation can handle complex analyses with saturated or unsaturated soils. This is useful for construction sequences involving fill placement, excavation, and soil-structure interaction.

### Load-Deformation

Unloading or loading activities can be simply and accurately modelled, including submerged fill placement, dam and tailings embankment construction, deep excavations, and open pit mine construction. Pore-water pressure changes can be incorporated by defining the initial and final water conditions.

### Stress Redistribution

The stress redistribution algorithm is capable of doing stress correction for any material model with a failure criteria. Strength Reduction Stability is also available as an alternative to the limit equilibrium stability method.

### Bangkok Wick Drain

Before construction of a new airport in Bangkok, Thailand, full-scale test embankments were constructed on the site to study the effectiveness of prefabricated vertical drains (PVDs) for accelerating the consolidation and dissipation of the excess pore-pressures resulting from fill placement.

Download the GeoStudio data files(1) (2) (3)

Read the analysis details

### Cubzac-les-Ponts, France

In the 1970’s, a series of test embankments were constructed on soft clay at Cubzac-les-Ponts in France. These full-scale field tests were well-instrumented and are well-documented, and consequently provide an excellent case history. Two of the embankments are the subject of this article.

Download the GeoStudio data files (1) (2)

Read the analysis details

### Excavation Below Watertable

The primary objective of this example is to consider the change in pore-water pressure during an excavation below the watertable, particularly the potential for negative pore-water pressures to form. A secondary objective of the example is to demonstrate the use of a moving hydraulic boundary condition on the excavation face.

### Braced Deep Excavation

Halim and Wong's paper in *Underground Singapore 2005* presents six case histories where deflections of the shoring walls were measured during construction. The case histories show that GeoStudio has the capabilities to model the behavior of deep shored excavations in soft ground.

Draw the regions in your domain using CAD-like drawing tools, including drawing polygon and circular regions, coordinate import, copy-paste geometric items, length and angle feedback, region splitting and merging, and direct keyboard entry of coordinates, lengths, and angles. Alternatively, import AutoCAD DWG or DXF files directly into GeoStudio to create your domain geometry.

Define the material properties for your analysis, assign them to regions on the domain, and then define your initial pore-water pressure conditions. Select the constitutive model and define the material response type as drained or undrained. Define the initial pore-water pressure conditions for transient scenarios using results from other SEEP/W or SIGMA/W analyses, defined spatial functions or draw an initial water table.

Define stress/strain boundary conditions to simulate stress and fluid pressure conditions or displacement/force conditions to be placed on the domain. Hydraulic boundary conditions can also be added to simulate total head, pressure head, pore-water pressure, water flux (q), water rate (Q), and climatic conditions. Time-varying loading and hydraulic functions can be defined to simulate changing conditions over the duration of a transient analysis. Structural beams and bars can also be applied to the model domain.

When the Solver is finished, the Y-total stress contours are displayed, with displacement results displayed as either a deformed mesh or vector arrows. Many other contour options are available in the Draw Contours window, including pore-water pressure, material properties, water flow, and gradients. Contour legends and properties can also be modified. Labels can be added to contour lines in Results View. Plastic states may also be viewed on the domain.

Interactively select any node or gauss region to view result information, including resulting displacement, pore-water pressure, material properties, and more. Draw Mohr Circles to review the stress/strain state of any node or gauss region. Display plots of computed results over the x- or y-direction or create time-varying plots of results in transient analyses, such as displacements, pore-water pressure, total or effective stresses, and more. Generate reports of the definition and results, and export into other applications such as Microsoft Excel for further analysis.

## The power of integration

### SIGMA/W offers simple but powerful analytical capabilities when used in combination with other GeoStudio products.

### SIGMA/W stresses in SLOPE/W

There are many geotechnical cases where it is desirable to not only perform a deformation analysis, but also to look at stability. In other instances, a SLOPE/W limit equilibrium stability analysis alone is inadequate. For cases like this, the SIGMA/W computed stresses can be used in SLOPE/W to compute the safety factors, or a Strength Reduction Stability analysis can be computed in SIGMA/W and compared to the SLOPE/W results.

### SIGMA/W pore-water pressures in SLOPE/W

Simulating the placement of fill in SIGMA/W, for example, may create excess pore-water pressures in the foundation. These SIGMA/W excess pore-water pressures can be used in SLOPE/W to analyze the stability during construction and at the end of construction. This could help with designing sub-surface draining or staging the loading.

### SEEP/W results in SIGMA/W

SEEP/W pore-water pressures can be used by SIGMA/W to simulate in situ effective stresses. Combine SEEP/W and SIGMA/W to simulate complex hydro-mechanical coupling in both saturated and unsaturated soils.

### SIGMA/W pore-water pressures in SEEP/W

Excess pore-water pressures generated during any kind of loading (for example, fill placement) can be used in SEEP/W to study how long it will take for the excess pore-water pressure to dissipate. This can help with specifying the rate of loading.

### SIGMA/W stresses in QUAKE/W

Establishing in situ static stresses can be done simplistically in QUAKE/W. Alternatively, you can use the load sequencing and non-linear constitutive soil models in SIGMA/W to improve the estimation of the static stress conditions, and then use them as the initial static stresses in a QUAKE/W dynamic analysis.

### QUAKE/W results in SIGMA/W

Stress results from QUAKE/W can be used in a SIGMA/W stress redistribution analysis.