- The following data presents the results of triaxial tests performed on a dry samples of cohesionless fine sand from the Frio formation in the Gulf of Mexico Basin:
Confining pressure Pore pressure Peak deviatoric stress [MPa] [MPa] [MPa] 3.4 0 7.1 6.9 0 20.6 10.3 0 29.7

- Plot the maximum principal effective stress as a function of for the three experiments. Fit a line that goes to the intercept (0,0) and calculate the shear strength parameter .
- Replot the data as Mohr circles, calculate the shear angle and plot the shear yield line. Does the shear yield line intersect the Mohr circles?

- The file Triaxial-1500psi-raw.dat (uploaded to Github) contains data from a triaxial test performed on a sandstone in dry conditions ( = 0 psi). is the confining pressure, is the deviatoric stress (), is the axial strain, and is the radial strain.
- Plot deviatoric stress and strains as a function of time (two plots). Mechanical experiments are usually performed at constant strain rate or constant stress rate. Which case is this? What is the rate?
- Plot deviatoric stress as a function of axial strain. Compute loading Young modulus at 25% of the peak stress and the unloading Young moduli for the two unloading cycles. Comment on the difference.
- Plot radial strain versus axial strain and compute loading Poisson ratio.
- Plot deviatoric stress versus volumetric strain. Does the sample contract, dilate, or both? Explain.
- If the shear strength parameter is , what is the of this rock?

- Twelve triaxial tests on cylindrical plugs of Berea Sandstone are reported below (Bernabe and Brace, 1990 - The Brittle-Ductile Transition in Rocks, Geophys. Monogr. Serf. Vp, 56, 91-101). (*) This is the axial stress that a load cell measures inside a pressurized vessel (). For example, the value would be zero for hydrostatic loading (
).
Confining pressure Pore pressure Peak deviatoric stress [MPa] [MPa] [MPa] 10 0 116 50 0 227 20 8 119 45 8 183 60 8 206 75 8 228 50 37 120 50 32 141 90 64 161 90 55 187 130 96 186 130 84 207

- Plot all data points in a versus plot and draw respective Mohr Circles (in Matlab, Python or Excel).
- Fit the data to Mohr-Coulomb criterion to compute unconfined compressive strength and the parameter through a linear regression. Then, calculate the cohesive strength and internal friction coefficient .
- Based on this information, compute the failure angle of the shear fracture you would expect to see in this sample after failure. Draw a sketch indicating the orientation with respect to the axial and radial stress.
- Did pore pressure significantly change the effective stress failure criterion?

Hint: figure out first how to calculate the effective radial and axial stresses.