Stress-Strain Relationship in Soil
Stress-Strain Relationship in Soil
Stress-Strain Relationship in Soil
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Adam Stock, Civil Eng<strong>in</strong>eer<strong>in</strong>g, 2012,<br />
STEP scholar<br />
Mentor: Professor Huabei Liu, Civil<br />
Eng<strong>in</strong>eer<strong>in</strong>g, The City College of New<br />
York
Education<br />
• My first year of college I traveled abroad to Israel where I spent the<br />
year study<strong>in</strong>g Jewish law, scholarly works and culture<br />
• My formal college education began at Yeshiva University where I<br />
spent 2 years study<strong>in</strong>g math and science<br />
• I transferred to City College <strong>in</strong> Fall 2009 to beg<strong>in</strong> my Civil Eng<strong>in</strong>eer<strong>in</strong>g<br />
studies
Experience<br />
• This has been my first experience <strong>in</strong> the research world, and it has<br />
taught me several important lessons already. But ma<strong>in</strong>ly I am us<strong>in</strong>g it<br />
to help me determ<strong>in</strong>e the path I want to take once I graduate from<br />
college.<br />
• I am hop<strong>in</strong>g next to become <strong>in</strong>volved <strong>in</strong> a large scale construction<br />
project to really learn how eng<strong>in</strong>eer<strong>in</strong>g is applied dur<strong>in</strong>g the<br />
construction period.<br />
• Dur<strong>in</strong>g the Summer 2009 I <strong>in</strong>terned for a small scale<br />
eng<strong>in</strong>eer/contractor <strong>in</strong> Los Angeles, California.
Abstract<br />
For every material there a maximum amount of stress or pressure<br />
that can be withstood until failure occurs, this is called the ductility<br />
of the material. Each type of soil would have a different ductility<br />
value. Currently there is no formula to determ<strong>in</strong>e the ductility of a<br />
soil, sample soil must be tested <strong>in</strong> a laboratory to determ<strong>in</strong>e its<br />
strength.<br />
Therefore we have been analyz<strong>in</strong>g test results on the stress-stra<strong>in</strong><br />
relationship <strong>in</strong> soil <strong>in</strong> order to see if we can determ<strong>in</strong>e an equation<br />
that would simplify the process of determ<strong>in</strong><strong>in</strong>g the ductility of a soil.
Project Description<br />
Goals<br />
• To determ<strong>in</strong>e if there is a correlation between the stress‐stra<strong>in</strong><br />
relationship, soil type and the po<strong>in</strong>t of failure of a material<br />
• If there is a relationship: to create an algorithm that would make it<br />
possible to determ<strong>in</strong>e the ductility of a soil us<strong>in</strong>g pure mathematics<br />
Procedure<br />
‣ Search Eng<strong>in</strong>eer<strong>in</strong>g databases for relevant data. We were look<strong>in</strong>g for<br />
either dry or saturated and dra<strong>in</strong>ed Triaxial tests.<br />
‣ Extract the relevant data and convert it <strong>in</strong>to the form required for<br />
proper analysis<br />
‣ Compare the data to determ<strong>in</strong>e if there is <strong>in</strong>deed a correlation
Background<br />
• What is a Triaxial test<br />
• A triaxial test tests the shear strength of material. The pr<strong>in</strong>cipal<br />
beh<strong>in</strong>d the test is that axial load can be different from the shear<br />
load, allow<strong>in</strong>g one to measure the stress‐stra<strong>in</strong> relationship<br />
• There are three types of triaxial test: Unsaturated; Saturated<br />
dra<strong>in</strong>ed; and Saturated undra<strong>in</strong>ed. For this project we were only<br />
search<strong>in</strong>g for the unsaturated and the saturated dra<strong>in</strong>ed results.<br />
The figure to the left depicts<br />
the load<strong>in</strong>g applied dur<strong>in</strong>g a<br />
triaxial test.
Research<br />
• In this project there were no experiments performed to compile the<br />
data. Rather the data was extracted from published articles conta<strong>in</strong>ed<br />
<strong>in</strong> the American Society for Civil Eng<strong>in</strong>eers database.<br />
• The searches focused on f<strong>in</strong>d<strong>in</strong>g any articles that conta<strong>in</strong>ed stressstra<strong>in</strong><br />
relationship data that was compiled us<strong>in</strong>g the accepted triaxial<br />
tests.<br />
• Any relevant graphs or charts were filed away to be analyzed later.
Data<br />
• The graph to the left exemplifies the<br />
stress‐stra<strong>in</strong> relationship graph.<br />
• The table shows how stress‐stra<strong>in</strong> data<br />
can be broken down <strong>in</strong>to several<br />
categories.<br />
• Both Images were taken from Prakasha<br />
and Chandrasekaran’s paper entitled<br />
“Behavior of Mar<strong>in</strong>e Sand‐Clay<br />
Mixtures under Static and Cyclic<br />
Triaxial Shear.”
Analysis<br />
• Once the data is collected the relevant data needs to be extracted:<br />
– Type of <strong>Soil</strong><br />
– Void Ration (e 0<br />
)<br />
– Conf<strong>in</strong><strong>in</strong>g <strong>Stress</strong> (σ 0<br />
/σ 3<br />
)<br />
– Max <strong>Stress</strong> (q)<br />
– Correspond<strong>in</strong>g Axial <strong>Stra<strong>in</strong></strong><br />
• Next half the value of the max stress and the correspond<strong>in</strong>g axial stra<strong>in</strong> need to<br />
determ<strong>in</strong>ed.<br />
• The max modulus is then computed as the max stress divided by its correspond<strong>in</strong>g<br />
stra<strong>in</strong>. Likewise the midpo<strong>in</strong>t modulus is computed the same way.<br />
• Many times s<strong>in</strong>ce the data is not easily accessible from the papers, the graphs need to<br />
be digitized us<strong>in</strong>g special software that turns the graphs <strong>in</strong>to easy to use Microsoft<br />
Excel data.
Interpretation<br />
• Once all the required data has been extracted and analyzed it must<br />
also be <strong>in</strong>terpreted.<br />
• We will be look<strong>in</strong>g to see if there is any correlation between soil type,<br />
density and the rupture po<strong>in</strong>t.<br />
• The first step would be to plot the data<br />
• Next we would check to see if there is an<br />
equation that could be used to it the data<br />
• Lastly, we would have to check to see how<br />
strong the correlation is to that equation
Results<br />
• This research is still on go<strong>in</strong>g and results have not yet been<br />
obta<strong>in</strong>ed<br />
• So far we have a lot of data stored away, however we would<br />
ideally like to have more data before analyz<strong>in</strong>g the data we have<br />
and mak<strong>in</strong>g a conclusion<br />
• Hopefully very soon we will be able to create an algorithm that<br />
will allow us to easily compute the failure po<strong>in</strong>t of soil materials
Acknowledgements<br />
I would like to thank Professor Huabei Liu for his help and guidance<br />
throughout the project