# 4.9 Problems

1. 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

1. 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 .
2. 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?

2. 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.
1. 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?
2. 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.
5. If the shear strength parameter is , what is the of this rock?
3. 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
1. Plot all data points in a versus plot and draw respective Mohr Circles (in Matlab, Python or Excel).
2. 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 .