Page 1 of 5 pages FINAL EXAM IN GEO-3104 Exam in : GEO-3104 Advanced Structural Geology Date : 28-02-2013 Time : 9.00 12.00 Place : Aud.Max. Approved remedies : Ruler (linjal), Compasses (passer), Protractor (vinkelmåler), Pocket-calculator (lommekalkulator), Ordbok (engelsk-norsk) The exam contains 5 pages including this cover page Contact person: H. Stunitz, 40 60 87 10
Page 2 of 5 pages Question 1: a) Draw one or several diagram(s) to illustrate the terms: fold wavelength, fold amplitude, hinge line, axial plane, inflection line. b) Draw one or two diagram(s) to illustrate the difference between buckling by flexural shear and orthogonal flexure. c) Pre-existing lineations will have characteristic distributions in the stereographic projection after folding. What is the difference in the distribution of lineations between passive shear folding and buckling by flexural shear? Question 2: a) For two planes in a rock, the following stress conditions (σ n, σ s, angle θ between plane normal and σ 1 ) are given: σ n σ s θ [MPa] [MPa] ( ) Plane 1 350 250 45 Plane 2 540 160 20 b) Determine the maximum and minimum stresses (σ 1 and σ 3 ), the maximum shear stress (σ s ), and the mean stress (σ mean ) for this case. c) Byerlee s rule says that the typical rock friction coefficient is μ = 0.6. For a given rock, the stress state is determined to be σ 1 = 200 MPa and σ 3 = 800 MPa. Some pre-existing surfaces in the rock can be moved by such a stress condition without making new fractures. What is the range of angles between σ 1 and the moving surfaces in such a rock? Use a Mohr circle construction for solving the problem. Show all your work. d) For a rock the Coulomb failure criterion is given by: σ s = 150 + 0.466 σ n The stress state for the rock is given by: σ 1 = 800 MPa; σ 3 = 200 MPa. How much pore fluid pressure do you need for shear failure to occur? Without pore pressure, how much
do you have to increase the differential stress (at the given σ 3 ) for shear failure to occur? Use a Mohr circle construction for solving the problem and show your work. Question 3: Page 3 of 5 pages The figure 1 below shows 5 stages of the progressive deformation of a circle to an ellipse by simple shear. The circle and the lines have been generated by drawing them on a deck of cards and shearing the card deck. (a) For the ellipse 4, determine the long and short axes of the ellipse and the angle of the long axis with respect to the shear plane. Calculate the shear strain using the equations: γ = 2 / tan (2Θ) and/or γ = (R-1) / R (b) In ellipse 4, find the two lines of no instantaneous line length change and label them (use the letters for lines given in the undeformed state of the circle in the diagram). (c) One of the 2 lines displayed no change in length throughout the deformation history. Which one is it? Why did it not change length? (d) Define and label the instantaneous shortening and instantaneous elongation sectors with "s" and "e" in the ellipse of stage 4. (e) What is the difference between the shortening and elongation histories of lines G - G and H - H through stages 1 to 5? Make a simple table of the elongation (e) or shortening (s) for each step.
Fig. 1 Page 4 of 5 pages
Question 4 Page 5 of 5 pages In your field area you find folds that have formed in single layers. You have measured the layer thickness and the fold wavelength in 12 of the folds and have prepared the plot below (Fig. 2). (a) Using the Biot-Ramberg relationship: L 0 = 2πh (η L /6η M ) 1/3 determine the average viscosity contrast between layers and matrix. Fig. 2 (b) In ptygmatic folds the initial wavelength is often measured by measuring the curved layer length between the inflection points of the folds. Explain why the Biot-Ramberg analysis works best with single layers and with such ptygmatic folds. Question 5 Explain briefly the differences between the following terms: a.) Dislocation glide - dislocation creep b.) Dynamic recrystallization static recrystallization c.) Diffusion creep dislocation creep