Permafrost Thawing and Deformations

Size: px

Start display at page:

Download "Permafrost Thawing and Deformations"

Kristina Allen
5 years ago
Views:

1 1 Introduction Permafrost Thawing and Deformations There is a huge interest in the effects of global warming on permafrost regions. One aspect of this is what degree of deformation may be expected if historically frozen permafrost soils start to thaw. This process can now be modeled by coupling TEMP/W transient results with a load/deformation SIGMA/W analysis in which the soil properties in an elastic-plastic constitutive model are applied via a user Add-In model which adjusts the soil cohesion in the frozen and unfrozen zones. This paper discusses how this is accomplished. 2 Analysis Geometry For this example analysis a simple 2:1 slope comprised of a homogeneous soil is considered as shown below. It is assumed that the slope is in a historical permafrost region with a starting uniform soil temperature of -1 C, and is about to be subjected to a 20 year warming period in which the mean annual surface temperature increases linearly over 20 years from a value of -1 to +5 C Elevation - m Distance - m Figure 1 Example geometry, 2:1 homogeneous slope 3 Project File Analyses There are three analyses in this project file as shown below. The first is a transient TEMP/W analysis in which the thermal profile is modeled for a period of 20 years subject to the warming ground surface boundary condition. The second is an in-situ stress analysis which establishes the stress state in the ground prior to thawing. The final analysis is a SIGMA/W load-deformation analysis in which the ground temperatures from TEMP/W are used to update the soil strength throughout the 20 year period. The 3 rd analysis is indented from the insitu analysis which TEMP and SIGMA Example File: Permafrost thawing and deformation (pdf)(gsz) Page 1 of 9

2 indicates that it is a child analysis and inherits data from its parent. In this case, it inherits the initial stress state. Figure 2 Screen capture of project file analyses 4 Thermal Results The slope material was given a uniform activation temperature of -1C as a starting thermal condition. The soil thermal properties were chosen as shown below. The time units in this image are shown as t but in this case their meaning is years. TEMP and SIGMA Example File: Permafrost thawing and deformation (pdf)(gsz) Page 2 of 9

Figure 3 Thermal properties applied to slope The following function was then applied to the entire ground slope over the duration of the 20 year analysis.

3 Figure 3 Thermal properties applied to slope The following function was then applied to the entire ground slope over the duration of the 20 year analysis. This may not be a realistic assumed warming trend based on global warming predictions alone. It is used to help demonstrate the mechanism of linking deformation to thawing analyses. TEMP and SIGMA Example File: Permafrost thawing and deformation (pdf)(gsz) Page 3 of 9

4 5 Average temperature increase over time 4 Temperature ( C) Time (t) Figure 4 Thermal heating boundary applied to ground surface Screen captures of the ground thawing taken at 4 year intervals are shown in the following figure. The blue, dashed line is the zero degree isotherm. It is clear that the permafrost zone is shrinking over time. You can see that the permafrost zone is shrinking over time as the influence of the ground surface takes affect. Elapsed Time: 4 years Elapsed Time: 8 years Figure 5 Thawing at 4 year intervals TEMP and SIGMA Example File: Permafrost thawing and deformation (pdf)(gsz) Page 4 of 9

5 Elapsed Time: 12 years Elapsed Time: 16 years Elapsed Time: 20 years Figure 6 Thawing at 4 year intervals 5 Deformation Modeling The figure below shows the material model assumed for the soil in the load-deformation analysis. In this case an Add-In user written constitutive model is chosen in which the soil will behave as an elastic-plastic material with a Von-Mises failure criteria. The Add-In model is written to read previously solved data from the TEMP/W thermal analysis. The soil cohesion is then adjusted based on ground temperatures. TEMP and SIGMA Example File: Permafrost thawing and deformation (pdf)(gsz) Page 5 of 9

Figure 7 Deformation material model properties GEO-STUDIO Add-Ins can include a list of input parameters that the user needs to vary in the analysis.

6 Figure 7 Deformation material model properties GEO-STUDIO Add-Ins can include a list of input parameters that the user needs to vary in the analysis. The list of parameters in this Add-In are shown in the list box at the bottom part of this figure. The user is asked for the frozen Cohesion, the thawed Cohesion, the modulus, E, a Poisson ratio, and instructions related to whether or not the current analysis will include freezing and if so, which other analysis in the project file it should request temperature data from. You can see that the analysis is linked to the TEMP/W analysis titled 1 Transient thawing analysis. This Add-In is a library file (*.dll) that was compiled in C# and is stored in the default or user specified Add-In folder where both GeoStudio Define and Solve can access it. Once the file is compiled as a library, it can be shared and used by anyone. It is not necessary to compile the file in C#. Alternately, Fortran, C++, VisualBasic or an.net language could be used. The capability of Add-In to deal with unique scenarios is really limited by the imagination and programming capability of the user. One unique aspect of Add-Ins is that the user can write back custom output data to GeoStudio that will subsequently be available in Contour for graphing or contouring. In this project the TEMP and SIGMA Example File: Permafrost thawing and deformation (pdf)(gsz) Page 6 of 9

7 Add-In model will write out the applied cohesion value and temperature at each Gauss point in the deformation analysis. In this way, the cohesion strength contours can be compared with the cumulative deformation as shown in the following sequence of images. Added to these images is some dynamic sketch text. This text is linked directly to the results at each viewed time step. X-Displacement: m Y-Displacement: m Elapsed Time: 4 years X-Displacement: m Y-Displacement: m X-Displacement: m Y-Displacement: m Elapsed Time: 8 years X-Displacement: m Y-Displacement: m Figure 8 Temperatures and displacements at 4 year intervals TEMP and SIGMA Example File: Permafrost thawing and deformation (pdf)(gsz) Page 7 of 9

8 X-Displacement: m Y-Displacement: m Elapsed Time: 12 years X-Displacement: m Y-Displacement: m X-Displacement: m Y-Displacement: m Elapsed Time: 16 years X-Displacement: m Y-Displacement: m X-Displacement: m Y-Displacement: m Elapsed Time: 20 years X-Displacement: m Y-Displacement: m Figure 9 Temperatures and displacements at 4 year intervals TEMP and SIGMA Example File: Permafrost thawing and deformation (pdf)(gsz) Page 8 of 9

9 The final image shows the crest and toe settlement and heave over time. It is clear that during early thawing the depth of weaker ground is not sufficient to cause much movement. At later times, when the thaw depth is greater, there is enough locked in stress that is released during thawing to cause significant downward movement of the slope Slope movements Y-Displacement (m) Time (years) Crest Settlement : (13.125, 20) Toe Heave : Node 374 (35, 10) Figure 10 Graph of toe and crest movement TEMP and SIGMA Example File: Permafrost thawing and deformation (pdf)(gsz) Page 9 of 9

Hyperbolic Soil Bearing Capacity

1 Introduction Hyperbolic Soil Bearing Capacity This example involves analyzing the bearing capacity of a round footing. The example is useful for illustrating several SIGMA/W features and procedures,