Geol 542: Advanced Structural Geology
Fall 2011
Problem Set #6: Experimental Determination of Rock Strength
1. The attached figure shows a plot of the strain data collected on a cylindrical sample of Berea sandstone during a
constant strain rate, uniaxial compression test. The actual data are shown in the attached Table. Note the first
lateral strain is a negative number (negative stresses/strains are compressional/contractional). Use an Excel
spreadsheet to tabulate the data and answer the following questions. In all graphs that you plot, use the
absolute value of the axial stress (i.e., plot axial stress as a positive number).
a) Use the data to determine the Poisson's ratio, , of the sample at each load step. Print out and include your
Excel spreadsheet table.
(8)
b) Make a plot of your calculated values of  as a function of the load (i.e., axial stress).
(4)
c) What is happening at the very start of the experiment (i.e., in the first load increment) to give such an unusual 
value? Hint: think about what happens to most rocks at the very start of a rock compression test.
(4)
d) Now make a plot of axial stress vs axial strain (i.e., you will be recreating one of the curves on the attached
graph). Calculate the Young’s modulus E for each increment of loading (i.e., slope of line) and plot it on a
separate graph as a function of loading. Include a table showing your calculated values of E. To calculate E, use
the formula (yj – yi) / (xj – xi), where (xi, yi) and (xj, yj) are consecutive points on the graph.
(8)
e) Based on your two charts in question (d), comment on whether this sandstone can be considered to behave in a
linear elastic manner as it deforms. Make sure you comment on the expected nature of Young’s modulus for a
linear elastic material. In explaining your range of values of E, be sure to compare your stress vs strain curve
with the expected shape of this curve for most rocks, how this translates into what is physically happening
within the rock during different stages of the experiment, and why this affects your calculated values of E. (6)
f) Do the values of the Poisson’s ratio you calculated make sense based on what you know about this parameter
and how it describes the behavior of elastic materials?
(2)
g) Explain why there is such variability in the calculated  values during the course of the experiment. Again, think
about how the changes that occur in the stress vs strain graph relate to the deformation occurring within the
sample. Remember, Poisson's ratio is only truly valid for strains within the elastic limits of a material.
(8)
h) What do we call the point along the stress vs strain curve where the behavior begins to be no longer elastic, and
what is the value of the stress at this point?
(4)
i) What do we call the maximum point on this particular stress vs strain graph?
(2)
j) Why do the lateral strains suddenly increase rapidly as the axial strain reaches around -2.3 millistrains? Explain
what is physically happening in the rock at this point. Hint: think about how deformation progresses in a
uniaxial experiment.
(4)
k) Was this experiment conducted in a soft or stiff testing machine? Explain your reasoning.
(2)
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Geol 542: Advanced Structural Geology
Fall 2011