Stress-Strain Relationship in Soil

Adam Stock, Civil Engineering, 2012,
STEP scholar
Mentor: Professor Huabei Liu, Civil
Engineering, The City College of New
York

Education
• My first year of college I traveled abroad to Israel where I spent the
year studying Jewish law, scholarly works and culture
• My formal college education began at Yeshiva University where I
spent 2 years studying math and science
• I transferred to City College in Fall 2009 to begin my Civil Engineering
studies

Experience
• This has been my first experience in the research world, and it has
taught me several important lessons already. But mainly I am using it
to help me determine the path I want to take once I graduate from
college.
• I am hoping next to become involved in a large scale construction
project to really learn how engineering is applied during the
construction period.
• During the Summer 2009 I interned for a small scale
engineer/contractor in Los Angeles, California.

Abstract
For every material there a maximum amount of stress or pressure
that can be withstood until failure occurs, this is called the ductility
of the material. Each type of soil would have a different ductility
value. Currently there is no formula to determine the ductility of a
soil, sample soil must be tested in a laboratory to determine its
strength.
Therefore we have been analyzing test results on the stress-strain
relationship in soil in order to see if we can determine an equation
that would simplify the process of determining the ductility of a soil.

Project Description
Goals
• To determine if there is a correlation between the stress‐strain
relationship, soil type and the point of failure of a material
• If there is a relationship: to create an algorithm that would make it
possible to determine the ductility of a soil using pure mathematics
Procedure
‣ Search Engineering databases for relevant data. We were looking for
either dry or saturated and drained Triaxial tests.
‣ Extract the relevant data and convert it into the form required for
proper analysis
‣ Compare the data to determine if there is indeed a correlation

Background
• What is a Triaxial test
• A triaxial test tests the shear strength of material. The principal
behind the test is that axial load can be different from the shear
load, allowing one to measure the stress‐strain relationship
• There are three types of triaxial test: Unsaturated; Saturated
drained; and Saturated undrained. For this project we were only
searching for the unsaturated and the saturated drained results.
The figure to the left depicts
the loading applied during a
triaxial test.

Research
• In this project there were no experiments performed to compile the
data. Rather the data was extracted from published articles contained
in the American Society for Civil Engineers database.
• The searches focused on finding any articles that contained stressstrain
relationship data that was compiled using the accepted triaxial
tests.
• Any relevant graphs or charts were filed away to be analyzed later.

Data
• The graph to the left exemplifies the
stress‐strain relationship graph.
• The table shows how stress‐strain data
can be broken down into several
categories.
• Both Images were taken from Prakasha
and Chandrasekaran’s paper entitled
“Behavior of Marine Sand‐Clay
Mixtures under Static and Cyclic
Triaxial Shear.”

Analysis
• Once the data is collected the relevant data needs to be extracted:
– Type of Soil
– Void Ration (e 0
)
– Confining Stress (σ 0
/σ 3
)
– Max Stress (q)
– Corresponding Axial Strain
• Next half the value of the max stress and the corresponding axial strain need to
determined.
• The max modulus is then computed as the max stress divided by its corresponding
strain. Likewise the midpoint modulus is computed the same way.
• Many times since the data is not easily accessible from the papers, the graphs need to
be digitized using special software that turns the graphs into easy to use Microsoft
Excel data.

Interpretation
• Once all the required data has been extracted and analyzed it must
also be interpreted.
• We will be looking to see if there is any correlation between soil type,
density and the rupture point.
• The first step would be to plot the data
• Next we would check to see if there is an
equation that could be used to it the data
• Lastly, we would have to check to see how
strong the correlation is to that equation

Results
• This research is still on going and results have not yet been
obtained
• So far we have a lot of data stored away, however we would
ideally like to have more data before analyzing the data we have
and making a conclusion
• Hopefully very soon we will be able to create an algorithm that
will allow us to easily compute the failure point of soil materials

Acknowledgements
I would like to thank Professor Huabei Liu for his help and guidance
throughout the project