Stresses in a Soil Mass

P a g e | 10‐1 Chapter 10 Stresses in a Soil Mass 1. For the calculation of foundation settlement, which of the following is estimated? (a) Increase of vertical stress in soil (b) Net increase of vertical stress in soil (c) Increase of porewater pressure (d) None of the above 2. The shear stress on a principal plane is (a) zero. (b) non-zero. (c) a non-zero value equal to normal stress. (d) a non-zero value greater than normal stress. 3. Boussinesq (1883) solved the problem of stresses produced at any point as a result of a point load on the surface of infinitely large half-space in (a) homogeneous medium. (b) elastic medium. (c) isotropic medium. (d) all of the above. 4. The vertical normal stress at a point caused by the point load is (a) dependent on the Poisson’s ratio. (b) independent of the Poisson’s ratio. (c) directly proportional to the point load. (d) both (b) and (c). 5. If Δσz = vertical normal stress increase at depth z caused by the point load acting on the ground surface, then (a) Δσ z ∝ z (b) Δσ z ∝ z 3 (c) Δσ z ∝ 1 z (d) Δσ z ∝ 1 z2 6. The vertical normal stress increase caused by a point load of 10 kN acting on the ground surface at a point 1 m vertically below its point of application is (a) 0. (b) 4.775 kN. (c) 5 kN. (d) 10 kN. P a g e | 10‐2 7. If Δσz = vertical normal stress increase at depth z caused by a line load of intensity q per unit length acting on the ground surface, then (a) Δσ z ∝ q 1 (b) Δσ z ∝ z (c) both (a) and (b). (d) none of the above. 8. The vertical stress increase at a depth of 1 m below the centre of the flexible circular area of 2 m diameter subjected to a pressure of 100 kN/m2 is (a) 0 (b) 29.28 kN/m2 (c) 64.65 kN/m2 (d) 91.06 kN/m2 9. The vertical normal stress increase of 10% caused by a flexible strip load takes place at a depth of about (a) 0.5B (b) B (c) 2B (d) 4B where B is the width of the strip load. 10. If N = number of elements in the influence chart for vertical pressure, then the influence value is equal to (a) N (b) 1/N (c) N2 (d) 1/N2 11. If the influence chart developed by Newmark (1942) is used to determine the vertical stress at any point below a uniformly loaded flexible area, then the increase in the pressure at that point is (a) directly proportional to the influence value. (b) directly proportional to the square of the influence value. (c) inversely proportional to the influence value. (d) inversely proportional to the square of the influence value. P a g e | 10‐3 Answers, Hints and Discussion 1. (b) 2. (a) 3. (d) 4. (d) Discussion and Hint: See Eq. (10.13). (a) and (c) are correct for the horizontal normal stresses caused by the point load as observed from Eq. (10.10) and Eq. (10.11). 5. (d) 6. (b) Discussion: Eq. (10.13): ∆ 7. (c) 8. (c) Hint: Use Eq. (10.26). 9. (d) 10. (b) 11. (a) 0.4775 4.775 .