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3. The following convergence measurements (U) have been made in a 4.6-m-diameter circular vertical shaft in good quality granitic rock mass (Em = 40 GPa, ν = 0.2): θ (deg) U (mm) 0 2.25 45 2.39 90 1.50 135 1.00
a) Derive the equations that relate convergence to in situ stress.
b) The angle θ is measured (clockwise) with respect to the x-axis, which is oriented 30 degrees clockwise from True North. What is the orientation of the maximum principal stress with respect to True North?
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- Q#5: From the Tri –axial test, determine the effective normal stress on the plane of Maximum shear stress. Explain why the shear failure occurred along the plane with angle 54.73 and not along the plane of maximum shear stress. Take σ’1 = 552, σ’3 = 276, ø’ = 19.45?SITUATION 5: A sand sample is subjected to direct shear testing at it's (in - situ) water content. Two tests are performed. For one of the tests, the sample shears at a stress of 400 kPa when the normal stress is 600 kPa. From these data, 15. Determine the value of the apparent cohesion. c. 230 kPa d. 221 kPa а. 100 kPa b. 179 КРа 16. Determine the corresponding angle of internal friction. a. 22.65 degrees b. 26.57 degrees c. 32.54 degrees d. 18.43 degreesa. A shear vane test, done on a deposit of soft alluvial clay required a torque of 67.5 Nm. The dimensions of the vane were: D = 75 mm; H= 150 mm. What is the value for the undrained %3D shear strength of this clay soil?. 160 KN lun?
- '2\ Answer T for true statements or F for false ones: 1. Intact rock: solid rock sample containing cracks on eye naked. 2. Rock Mass: contains rock samples and crack surfaces on eye naked. 3. The rock sample will break if the applied force is vertical and associated with shear. 4. Unit weight (y) = gm./cm³. 5. Void Ratio (e) = Vs/Vv. 6. In point load test if the rock is fresh, ot= 5 * I, (50) 7. Brazilian Test provides tensile strength values closer to reality than Point Load Test. 8. Schmidt Hammer Test gives direct values for strength. 9. As more the surface is rough its strength for slipping decreases. 10.Fracture Intercept is the measured distance between irregular fractures !!a. For the soil element shown in the figure, the magnitudes of the stresses are kN kN Ox = 70 KN Oy = 265 Try = 75 0 = 32°, draw Mohr's circle to m2' determine • Normal and shear stresses on plane BD • Magnitude of Principal Stresses • Maximum shear stress and draw angle of maximum shear stress on the soil element shown b. If the soil element shown in above figure was extracted 17m below the ground surface with y = 15, C = 1000 Pa and Ø = 22°, whether the soil will be kN safe against shear failure? Oy Tyx Txy Ox Txy B. A Tyx1. Triaxial compression tests are done on quartzite rocks, the results are shown below. (0₁+03)/2 -964.25 14500 19575 23200 29000 43210 63075 psi (01-03)/2 964.25 14500 18850 21750 26100 35960 48575 psi Comment on the applicability of each of the Mohr-Coulomb, Griffith, and Hoek-Brown criteria for the testing results.
- The location of trial failure surface on a slope is shown in Figure and the stress components for each slice are listed in Table. Slice Shearing component _(kN.m·') -0.280 -0.227 0.383 3.214 6.543 8.368 9.792 Normal component (kŇ.m*) 1.911 7.745 13.139 16.344 17.625 16.718 12.125 0.486 Length of trial failure surface=11m Soil friction angle 6° Cohesion, c=28kPa No. 1 3 4 6. 4.228 Trial Fallure Surface (a) Compute the driving stress. (b) Compute the stabilizing stress. (c) Analyze the safety of the slope.Calculate and plot the stress distribution with depth at a point 6.0 m from the corner (along the longest side) of a rectangularly loaded area 18 × 24 m with a uniform pressure of 175 kPa. Perform the calculation using the Boussinesq theoryand the 2:1 method. Comment on the results.When plotting stress distribution with depth, make sure the vertical axis (i.e. depth) increases downwards. Use z=0, 1, 5, 10, 15, 35, 50, and 100 m. Equations that may be helpful are attached.H.W For the stressed soil element shown in Figure, determine: a. Major principal stress (0₁) and minor principal stress (03) b. Angle between horizonal plane (DC) on the soil element and major principal plane c. Normal and shear stresses on the plane AE Use the theoretical(equations) method and the pole method. 100 kN/m² D + A 500 kN/m² B=15 E C 500 kN/m² 100 kN/m² B
- For studying rock porosity change affecting by the pressure, use Newman correlation to calculate the pore volume (isothermal) compressibility, cf, for sandstones as below (Eqn. 2.2 - which is attached). I have also attached my results for part a. I need help with part B. It is using the formula: c = -1/v * dV/dp where v = volume, c = compressibility values calculated in part a, and p is pressure. I am mostly confused on how to compute the change in volume. (a) Calculate cf for 5 different phi (porosity) = 0.02, 0.05, 0.1, 0.15, 0.2 I have already completed this portion and it is attached with the answers needed for part b highlighted in yellow in the uploaded figure. (b) Estimate dV/V for these five cases of phi (porosity), if initial reservoir is 3250 psia and the current reservoir pressure is 1500 psia.A direct shear test, when conducted on a remolded sample of sand, gave the following observations at the time of failure: Normal load = 288 N; shear load = 173 N. The cross-sectional area of the sample = 36 cm2. Determine the major principal stress in kPa. a.174.6 b.246.5 c.163.5 d.146.9Q: An axial compressive load of 4000N was conducted on body of rock has a cross section 0.05 m by 0.03m. Calculate the magnitude of normal and shear stresses on a plane, where the normal stress is inclined at 70° to the axis of the block
