Draft:Geotechnical variability

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

Geotechnical variability is a major source of uncertainty in civil engineering projects.

Inherent variability[edit]

Geomaterials are formed and altered by natural processes such as sedimentation, colluvial or glacial actions, weathering, etc., which give rise to variability in the material properties. The differences in engineering properties (e.g. mechanical properties) are most notable across layers of different geologic origins. For example, the engineering properties can be vastly different between a layer of glacial till and its underlying sandstone bedrock.

Even within the same soil layer, the properties are rarely ‘homogeneous’, and substantial variability had been observed through in situ and laboratory tests of soil and rock materials. The inherent variability can have important implications to engineering performance. For example, spatial variations of shear strength and stiffness of a soil layer can lead to differential settlements of foundations embedded in that stratum.

Some components of the variability can be explained and modeled with consideration of the geological origin, while others may be more 'localized' effects. The spatial variations for a certain property () of a soil deposit is usually represented by two components:

   

where is the trend component at location , and is called the residual, or deviation from the trend at that location.

Trend[edit]

Many geotechnical properties (e.g. shear strength, stiffness, etc.) display certain trends both in the vertical and lateral directions. On many occasions, vertical trends observed in soil properties originate from the fact that soil behavior is largely controlled by the effective stress experienced by the soil particles[1][2], which increases with depth due of the weight of the material. For example, this change in confining pressure is closely related to the increase in undrained shear strength with depth for normally consolidated clays. Apart from the stress-dependent effects, the vertical trends of soil strength and stiffness, as observed in various in situ tests (e.g. standard penetration test, vane shear test, cone penetration test), may also be related to other geological processes at the specific region. Likewise, trends in lateral directions can be significant for geotechnical properties, and these can arise from variations in the depositional or other processes such as weathering, fluvial or colluvial processes, etc[3].

The trends may be represented mathematically by linear or polynomial functions. However, considering the inherent variations in the properties and the limited data available, determination of the trend or its polynomial order is also associated with much uncertainty. In general, a higher order polynomial increases the flexibility of the trend function and lead to a better fit to the data[4]. On the other hand, an ever-increasing trend flexibility can lead to overfitting, which means random noise and errors are included in the statistical model, which reduces its predictive power at unsampled locations[5]. Correspondingly, various approaches[6][7] have been proposed to offer rational selection criteria for trend function. A good understanding of geological history at the region is often helpful in determining the trend, but this is not always straightforward.

Coefficient of variation[edit]

The coefficient of variation

Scale of fluctuation[edit]

Measurement error[edit]

Statistical uncertainty[edit]

Transformation uncertainty[edit]

Transformation uncertainty refers to the uncertainty associated with the correlation equation for soil/rock properties. In the geotechnical literature[8], such a correlation equation is called a transformation model. Let be the soil/rock design property of interest and be the measured property. A transformation model is an equation that relates to :

  

where is the prediction value for and is the transformation uncertainty. The transformation uncertainty can be modeled as a random variable with mean value equal to and coefficient of variation (COV) equal to . In the case that is modeled as a lognormal random variable, statistics for can be predicted as follows:

  

The transformation uncertainty is epistemic in its nature because depends on missing factors (e.g., secondary soil/rock properties) that can be known in principle but are unknown in practice.

In geotechnical engineering, direct evaluation of design property during site characterization can be costly and time consuming. In the circumstance where site investigation budget is limited, the transformation model can be used to obtain first-order estimate for based on . A useful reference for transformation models was established by Kulhawy and Mayne (1990)[9].

Examples for clay properties[edit]

Design property Measured property

Predicted value for

mean for [10]

COV for [10]

[11] 1.04 0.55
[12] 1.11 0.53
[13] 1.05 0.49
[14] 2.94 1.90

= undrained shear strength; = preconsolidation stress; = overconsolidation ratio; = effective vertical stress; = total vertical stress; = (corrected) cone resistance; = pore pressure coefficient; = liquidity index; = 1 atmosphere pressure.

Examples for sand properties[edit]

Design property

Measured property

Predicted value for mean for [10] COV for [10]

Examples for rock properties[edit]

Design property

Measured property

Predicted value for mean for [10] COV for [10]

References[edit]

  1. ^ Terzaghi, K., Peck, R. B. & Mesri, G. (1996). Soil Mechanics in Engineering Practice, 3rd ed.. Wiley. 592pp.
  2. ^ Schofield, A. N., & Wroth, C. P. (1968). Critical state soil mechanics. McGraw-Hill. 310pp.
  3. ^ Zhu, H. & Zhang, L. M. (2013). Characterizing geotechnical anisotropic spatial variations using random field theory. Canadian Geotechnical Journal 50 (7), 723–734.
  4. ^ Baecher, G. B. & Christian, J. T. (2003). Reliability and Statistics in Geotechnical Engineering. Wiley. 605pp.
  5. ^ Liu, W. F., Leung, Y. F. & Lo, M. K. (2017). Integrated framework for characterization of spatial variability of geological profiles. Canadian Geotechnical Journal 54(1), 47–58.
  6. ^ Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6): 716–723.
  7. ^ Beck, J.L. (2010). Bayesian system identification based on probability logic. Structural Control and Health Monitoring, 17(7), 825–847.
  8. ^ Phoon, Kok-Kwang; Kulhawy, Fred H (1999-11-22). "Evaluation of geotechnical property variability". Canadian Geotechnical Journal. 36 (4): 625–639. doi:10.1139/t99-039. ISSN 0008-3674.
  9. ^ Kulhawy F.H. and Mayne P.W. Manual on Estimating Soil Properties for Foundation Design, 1990.
  10. ^ a b c d e f Ching, Jianye; Phoon, Kok-Kwang (2014-04-22). "Transformations and correlations among some clay parameters — the global database". Canadian Geotechnical Journal. 51 (6): 663–685. doi:10.1139/cgj-2013-0262. ISSN 0008-3674.
  11. ^ G, Mesri, (1975/04/00). "NEW DESIGN PROCEDURE FOR STABILITY OF SOFT CLAYS". Journal of Geotechnical and Geoenvironmental Engineering. 101 (GT4). ISSN 1090-0241. Check date values in: |date= (help)
  12. ^ M, JAMIOLKOWSKI,; C, Ladd, C; T, Germaine, J; R, LANCELLOTTA, (1985/00/00). "NEW DEVELOPMENTS IN FIELD AND LABORATORY TESTING OF SOILS. PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON SOIL MECHANICS AND FOUNDATION ENGINEERING, SAN FRANCISCO, 12-16 AUGUST 1985". Publication of: Balkema (AA). Check date values in: |date= (help)
  13. ^ "Establishment of generic transformations for geotechnical design parameters". Structural Safety. 35: 52–62. 2012-03-01. doi:10.1016/j.strusafe.2011.12.003. ISSN 0167-4730.
  14. ^ Stas, C. V.; Kulhawy, F. H. (1984-11-01). "Critical Evaluation of Design Methods for Foundations Under Axial Uplift and Compression Loading. Final Report".


Basic editing[edit]

What is the wiki[edit]

The wiki is a database containing documents. Anyone can create documents, and anyone can edit these

There is no inherent structure or permanent links between the documents, e.g. there is not any 'top' page and 'sub' pages. Everything can be freely linked together.

A couple of important things:

  • You cannot damage anything, so do not be afraid to try to do things in the wiki!
  • Some features, like adding images, requires you to log in (more info later)
  • You can edit whatever you like.
  • Any edits can easily be 'undone', so if something gets messed up there is no problem to undo the edits or changes.

Page titles[edit]

  • The first character in the title is not case sensitive, however all of the rest of the characters are:
    • my page and My page are the same document
    • all of the following are different documents:
      • my Page
      • My page
      • MY PAGE
      • (and so on)

Using the wiki and finding information[edit]

As a user, you experience the wiki just like any other web pages. Use links and menus to find information, or use the search field at the top to find things.

The search function looks at page titles, but also at the text inside the pages. If the wiki cannot find something, you will be asked if you would like to create a page.

Creating new pages[edit]

  • Method 1) Search for the title of the page you want. If this document does not exist in the database, then you will be asked if you want to create it.
  • Method 2) Make a link in an existing document. If the document does not exist, then you will be asked if you want to create it when you select the link.

TC304

Basic editing of a page[edit]

Starting the editor[edit]

  • Press 'Edit source' at the top of the page
This will let you edit the entire page (all sections)
  • Or press 'edit source' on any individual section
This will let you edit a single section (and any sub-sections)

The wiki editor will open. This has a menu bar at the top, where you can do basic text formatting by pushing the buttons.

When you are done editing, push the 'Save page' button at the bottom. Alternately, you can use 'Show preview', or if you get cold feet: push Cancel

Simple text format, like bold and italic[edit]

When using the wiki editor, you have a menu bar with buttons. The most important ones:

  • The B button gives bold text
  • The I button gives italic text
  • The A button gives a heading
  • The line button gives a horizontal line

Mark the text you want to be bold (or italic, or a heading) and push the menu button to format the text.

Bullet points and indents[edit]

Using a star (*) at the start of the line makes a bullet point, and a colon (:) makes an indented line.

Push edit to see how the following text is formatted:

  • Bullet 1
  • Bullet 2
This is an indented line
This is another indented line
  • Bullet 3
    • sub bullet
    • sub bullet
This is a double indented line
  • Bullet 4
Note that you can also use text formatting, for example bold if you want!

Paragraphs[edit]

You need to leave a blank line to create a new paragraph.

For an example, click on the 'edit' button for this section and see how this paragraph is formatted.

Notice how the wiki ignores extra blank spaces, and only creates a new paragraph when there is one or more blank lines between the text

Using headings[edit]

The heading button gives you a second level heading. If you want an additional level, you need to add a couple of equal signs (before and after):

==This is formatting for a level 2 heading (and is automatic when you push the heading button)==
===add an equal sign if you want to format a level 3 heading===
====and another if you want to format a level 4 heading===

Note: Level 1 heading is reserved for the title of the page, you cannot use level 1 formatting yourself.

Creating basic links[edit]

You can make links to

Link to another wiki page[edit]

The wiki uses square brackets for links inside the wiki:

  • Double brackets, e.g. [[TC304]] is a link to a another page in the wiki
  • It will look like this: TC304

You can also ask for a different text to be displayed:

Link to a web page[edit]

  • Single brackets, e.g. [http://140.112.12.21/issmge/tc304.htm TC304] is a link to an external web page
TC304 is the text to be displayed, whereas http://140.112.12.21/issmge/tc304.htm is the link
  • It will look like this: TC304

Using images[edit]

IMPORTANT: file names are case sensitive, e.g.

photo.jpg
Photo.jpg
photo.JPG

are three different files

Use the editing buttons to insert an image. Note that this gives an image in its original size.

  • The format is [[File:Example.jpg]] where you have to fill in the file name (exactly)
  • You can also specify scaling for the image: [[File:Example.jpg|300px]]

There are lots and lots of formatting possibilities for images. For advanced formatting you need to edit in the commands yourself. For more detail see: help for image formats