Question

Three samples of the same depleted reservoir formation were analyzed using conventional tri-axial cell and the results of axial and radial stresses at the point of failure are reported below: (30 Marks)
Sample
Sample         Radial Stress (MPa)           Axial Stress (MPa)

1                        0.358                                            8

2                        1.052                                           10

3                        1.692                                           12
(a) Using graphical representation of Mohr circles determine the value of cohesion and internal friction angle of this formation. You must draw the circles and failure criteria into exact scale and read the values from your plot.
(b) If the confining pressure applied at a certain depth is 2.2 MPa, determine the minimum vertical stress which is required to cause failure of the formation according to Mohr-Coulomb failure criterion. Use both graphical approach and calculations and compare the results.

Answer 1

a) Sanople 1 6, 3+0.358 - 2 358 MPa 620- 353 MPa Sample Tlo 025 1. O25 MPa = Sarople 3 2+1.692 3.692 MPa 692 MPa Failure envelope (b) C .7 MPa 37 5 2. 42 16. 3 4 a C 2. 16 Steps ok corstruction : Draw 3 semi- circles coith the values of samples - 1,2,3 Draw Ibe tangent or all three semi- círcles .Thi's represent the jailure envelope From qure, cohesion, C t MPa internal riction , 6 < 37 2.2MPa 2c tan (45+ ) 3 tan 45+ 2-2 tar (45+3) 2xl. tan (45+3) 15.6 MPa 5.67 2 2 3.4 MPa

Graphically o 45+ 63.5 Oo 2 m a ABG equal 63.5 Since two sides are Y (2x 63.5) 180 53 m A ABD AD Cos 63.5 AD = 2.6 DC lo A BCD, Cos 53 O6 T DC O.G (AD+ DC) = DC 56 O. 4 DC DC = 3.9 6.5 AD + DC - '. Thus centre oL semi - circle Lies at 6.5+2.2 .t MPa Thus draw the semi- circle, cohich qives 15 MPa - 15. - 2. 2 13.5 MPa