## Stress-deformation analysis

### SIGMA/W performs stress and deformation analyses of geotechnical, civil and mining works. It can perform a simple linear elastic deformation analysis or a highly sophisticated soil-structure interaction analysis with non-linear material models and coupling to seepage analysis.

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.

### Construction Sequence

GeoStudio's Analysis Tree models even the most complex construction sequences. Analyses are added to the Tree, forming a Parent-Child relationship in which each new analysis represents a part of the construction sequence.

### Coupled Consolidation

The coupled stress and pore-water pressure formulation can be used to model construction sequencing involving fill placement, excavation, and soil-structure interaction.

### SLOPE/W Integration

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

Stress redistribution analysis is 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.

### 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.

### 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.

### 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. Define materials using total stress parameters, effective drained parameters or effective parameters with pore-water pressure changes included. 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) and water rate (Q) 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. You can display other contours of almost any parameter including pore-water pressure, material properties, water flow, and gradients, using the Draw Contours window. Contour legends and properties can also be modified. Labels can be added to contour lines for display in Results View. Liquefaction zones following an earthquake can also be displayed.

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.

### 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.

**SIGMA/W coupled with SEEP/W**

SIGMA/W essentially solves equations of equilibrium while SEEP/W solves equations of continuity. A consolidation analysis solves both sets of equations simultaneously and results in both deformation and pore-water pressure changes with time. Running SIGMA/W and SEEP/W at the same time makes it possible to do fully coupled consolidation analyses.

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

Excess pore-water pressures generated during any kind of loading (fill placement, for example) can be taken into 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 insitu 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 and liquefaction results from QUAKE/W can be used in a SIGMA/W stress redistribution analysis.

**QUAKE/W results in SEEP/W-SIGMA/W Consolidation **

The dissipation of excess pore-water pressures generated during earthquake shaking may lead to some consolidation after the earthquake. Using the QUAKE/W computed pore-water pressures in a SEEP/W-SIGMA/W coupled analysis makes it possible to look at the deformation that may occur as a result of the post-earthquake consolidation.