Test 16 - Stability of Infinite Slopes

Question 1 ప్రశ్న 1

Which description most accurately represents the assumptions of classical infinite-slope stability analysis?

A The slope has a finite height, and failure must always occur along a circular surface passing through its toe. B The slope extends sufficiently far with an approximately uniform profile, and the potential translational failure plane is parallel to the ground surface. C The slope is assumed to resist movement entirely through passive earth pressure at its toe. D The failure surface must be vertical, and all shear stresses are assumed to be zero.

Question 2 ప్రశ్న 2

A dry homogeneous infinite slope has inclination beta = 30 degrees and soil unit weight gamma = 20 kN/m3. A potential failure plane lies at a vertical depth z = 4 m below the surface. What are the normal stress and downslope shear stress on the plane? Take cos(30 degrees) = 0.8660 and sin(30 degrees) = 0.5.

A 60.0 kPa and 34.6 kPa. B 80.0 kPa and 40.0 kPa. C 69.3 kPa and 20.0 kPa. D 40.0 kPa and 69.3 kPa.

Question 3 ప్రశ్న 3

A dry infinite slope consists of cohesionless sand with effective friction angle phi' = 30 degrees and slope inclination beta = 20 degrees. What is its factor of safety against translational sliding? Take tan(30 degrees) = 0.5774 and tan(20 degrees) = 0.3640.

A 0.63. B 1.00. C 1.27. D 1.59.

Question 4 ప్రశ్న 4

For a dry cohesionless infinite slope, the effective friction angle is phi' = 32 degrees. At what slope inclination beta does the classical infinite-slope model predict limiting equilibrium with factor of safety equal to unity?

A 16 degrees. B 45 degrees. C 32 degrees. D 58 degrees.

Question 5 ప్రశ్న 5

A dry infinite slope has vertical failure-plane depth z = 3 m, gamma = 20 kN/m3, effective cohesion c' = 12 kPa, effective friction angle phi' = 30 degrees and slope angle beta = 30 degrees. What is the factor of safety? Use sin(30 degrees) = 0.5, cos(30 degrees) = 0.8660 and tan(30 degrees) = 0.57735.

A 1.00. B 1.46. C 1.92. D 2.31.

Question 6 ప్రశ్న 6

A dry infinite slope consists of an ideal purely cohesive soil with cohesion c = 10 kPa and friction angle phi = 0 degrees. The slope angle is 30 degrees, gamma = 20 kN/m3 and the potential failure plane is 2 m below the surface vertically. What is the factor of safety?

A 0.58. B 1.00. C 1.15. D 1.73.

Question 7 ప్రశ్న 7

A dry infinite slope has gamma = 20 kN/m3, c' = 10 kPa, beta = 30 degrees and phi' = 20 degrees. Assuming constant strength parameters and a slip plane parallel to the slope, what is the approximate critical vertical depth at which FS = 1? Take sin(30 degrees)cos(30 degrees) = 0.4330, cos²(30 degrees) = 0.75 and tan(20 degrees) = 0.3640.

A 1.56 m. B 2.40 m. C 3.12 m. D 6.25 m.

Question 8 ప్రశ్న 8

For a dry homogeneous infinite slope with constant positive effective cohesion c', constant phi', gamma and beta, how does its calculated factor of safety change as the vertical depth of the potential failure plane increases?

A It necessarily increases because the weight of soil increases with depth. B It remains constant for every cohesive soil because all stress components increase proportionately. C It becomes independent of friction angle at large depths. D It decreases toward tan(phi')/tan(beta), because the relative contribution of cohesion becomes smaller with increasing depth.

Question 9 ప్రశ్న 9

A dry infinite slope has gamma = 20 kN/m3, vertical slip-plane depth z = 3 m, beta = 30 degrees and phi' = 25 degrees. What minimum effective cohesion is required to obtain FS = 1.50 on that plane? Use sin(30 degrees)cos(30 degrees) = 0.4330, cos²(30 degrees) = 0.75 and tan(25 degrees) = 0.4663.

A 9.0 kPa. B 18.0 kPa. C 26.0 kPa. D 39.0 kPa.

Question 10 ప్రశ్న 10

A dry cohesionless infinite slope must satisfy a specified minimum factor of safety of 1.50. Its friction angle is such that tan(phi') = 0.60. What is the maximum permissible slope angle beta under this criterion? Take arctan(0.40) = 21.8 degrees.

A 21.8 degrees. B 30.0 degrees. C 36.9 degrees. D 45.0 degrees.

Question 11 ప్రశ్న 11

A cohesionless infinite slope is fully submerged under static hydrostatic conditions, with balancing external water pressure and no seepage forces. If tan(phi') = 0.60 and tan(beta) = 0.40, what is its ideal factor of safety?

A 0.50. B 0.75. C 1.50. D 3.00.

Question 12 ప్రశ్న 12

A fully submerged homogeneous infinite slope has no seepage and is subjected to balanced hydrostatic water pressures. Its submerged unit weight is gamma' = 10 kN/m3, effective cohesion c' = 6 kPa, phi' = 30 degrees and beta = 30 degrees. For a potential plane 3 m below the ground surface vertically, what is the approximate factor of safety? Take tan(30 degrees) = 0.57735.

A 0.73. B 1.00. C 2.00. D 1.46.

Question 13 ప్రశ్న 13

A cohesionless infinite slope has steady saturated seepage parallel to the slope surface, with the seepage surface at ground level. Given gamma_sat = 20 kN/m3, gamma_w = 10 kN/m3, phi' = 30 degrees and beta = 20 degrees, calculate the factor of safety. Use tan(30 degrees) = 0.5774 and tan(20 degrees) = 0.3640.

A 0.40. B 0.79. C 1.59. D 3.17.

Question 14 ప్రశ్న 14

A saturated infinite slope has steady seepage parallel to its surface, with the seepage surface at ground level. The slope angle is beta = 30 degrees and the potential slip plane is at vertical depth z = 3 m. If gamma_w = 10 kN/m3, what is the pore-water pressure on the plane under the standard parallel-seepage idealization?

A 15.0 kPa. B 30.0 kPa. C 22.5 kPa. D 40.0 kPa.

Question 15 ప్రశ్న 15

A saturated infinite slope has gamma_sat = 20 kN/m3, gamma_w = 10 kN/m3 and beta = 30 degrees. The water table is at the ground surface and seepage is parallel to the slope. At a vertical depth of 4 m, what are the total normal stress, effective normal stress and downslope driving shear stress on a parallel failure plane?

A 60.0 kPa, 30.0 kPa and 34.6 kPa, respectively. B 80.0 kPa, 40.0 kPa and 20.0 kPa, respectively. C 60.0 kPa, 60.0 kPa and 34.6 kPa, respectively. D 30.0 kPa, 60.0 kPa and 17.3 kPa, respectively.

Question 16 ప్రశ్న 16

A saturated infinite slope has steady seepage parallel to the surface with groundwater at ground level. Given gamma_sat = 20 kN/m3, gamma_w = 10 kN/m3, c' = 10 kPa, phi' = 30 degrees, beta = 30 degrees and vertical failure-plane depth z = 2 m, what is the approximate factor of safety?

A 0.58. B 0.75. C 1.58. D 1.08.

Question 17 ప్రశ్న 17

Consider the same cohesionless infinite slope with tan(phi') = 0.60, tan(beta) = 0.40, gamma_sat = 20 kN/m3 and gamma_w = 10 kN/m3. Compare Case I, fully submerged with balanced hydrostatic water pressure and no seepage, with Case II, saturated seepage parallel to the slope with the seepage surface at ground level. What are the ideal factors of safety for Cases I and II, respectively?

A 0.75 and 1.50. B 1.50 and 0.75. C 1.50 and 1.50. D 0.50 and 0.50.

Question 18 ప్రశ్న 18

A cohesionless infinite slope has steady seepage parallel to the surface and the seepage surface at ground level. The ratio gamma'/gamma_sat is 0.50, and tan(phi') = 0.80. What is the limiting slope inclination beta for FS = 1.0? Take arctan(0.40) = 21.8 degrees.

A 11.3 degrees. B 18.4 degrees. C 21.8 degrees. D 38.7 degrees.

Question 19 ప్రశ్న 19

A saturated infinite slope has a potential failure plane at vertical depth z = 3 m, beta = 30 degrees, gamma_sat = 20 kN/m3 and measured pore-water pressure u = 15 kPa on the plane. Assume c' = 8 kPa and tan(phi') = 0.50. Using the measured pore pressure in an effective-stress analysis, what is the factor of safety?

A 0.89. B 1.15. C 1.46. D 1.73.

Question 20 ప్రశ్న 20

For an infinite slope, total normal stress on a potential plane is 45 kPa and the driving shear stress is 25.98 kPa. Its effective cohesion is 10 kPa, and tan(phi') = 0.50. What pore-water pressure would reduce the factor of safety to exactly 1.0, assuming all other quantities remain unchanged?

A 5.00 kPa. B 10.00 kPa. C 20.00 kPa. D 13.04 kPa.

Question 21 ప్రశ్న 21

At a potential failure plane, the driving shear stress remains 25 kPa and the effective friction parameter tan(phi') = 0.50. The total normal stress and effective cohesion remain unchanged, but positive pore-water pressure increases by 10 kPa. By how much does the calculated factor of safety decrease?

A 0.10. B 0.20. C 0.40. D 0.50.

Question 22 ప్రశ్న 22

A dry infinite slope has beta = 30 degrees, phi' = 30 degrees, c' = 10 kPa and gamma = 20 kN/m3. Two potential sliding planes are located at vertical depths of 2 m and 4 m. Assuming homogeneous soil and no other loads, which plane has the lower factor of safety, and what is its approximate value?

A The 2 m plane, with FS = 1.29. B The 2 m plane, with FS = 1.58. C The 4 m plane, with FS = 1.29. D Both planes have FS = 1.00.

Question 23 ప్రశ్న 23

An unsaturated soil slope derives part of its apparent shear resistance from matric suction. During prolonged rainfall, infiltration increases its water content and reduces matric suction. Which interpretation is technically most appropriate?

A Loss of suction-related apparent strength can reduce stability, and the changing pore-pressure conditions should be evaluated rather than treating suction contribution as permanent cohesion. B Infiltration always increases the effective friction angle by the same amount as the water-content increase. C The reduction of matric suction cannot influence slope stability because suction has no relationship to shear strength. D Rainfall necessarily makes the soil fully hydrostatically submerged without any seepage gradients.

Question 24 ప్రశ్న 24

A dry infinite slope has inclination beta = 30 degrees and gamma = 20 kN/m3. A potential sliding plane parallel to the slope lies at a perpendicular distance d = 2 m measured normal to the slope surface, rather than at a vertical depth of 2 m. What are the normal stress and downslope shear stress due to soil self-weight on that plane?

A 30.0 kPa and 17.3 kPa. B 40.0 kPa and 20.0 kPa. C 60.0 kPa and 34.6 kPa. D 34.6 kPa and 20.0 kPa.

Question 25 ప్రశ్న 25

A saturated infinite slope has steady seepage parallel to the surface with the seepage surface at ground level. The slope has beta = 30 degrees, phi' = 30 degrees, gamma_sat = 20 kN/m3, gamma_w = 10 kN/m3 and vertical failure-plane depth z = 2 m. What effective cohesion c' is required to achieve FS = 1.50 on the specified plane? Use sin(30 degrees)cos(30 degrees) = 0.4330.

A 8.66 kPa. B 17.32 kPa. C 25.98 kPa. D 34.64 kPa.

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