Weight-Volume Relationships

P a g e | 3‐1 Chapter 3 Weight-Volume Relationships 1. A given volume of soil in natural occurrence consists of (a) solid particles only. (b) void spaces occupied by air and/or water. (c) solid particles and void spaces. (d) solid particles and void spaces occupied by air and/or water. 2. A fully saturated soil is generally a (a) one-phase system consisting of soil solids. (b) two-phase system consisting of soil solids and air. (c) two-phase system consisting of soil solids and water. (d) three-phase system consisting of soil solids, water and air. 3. A partially saturated soil is (a) dry soil. (b) moist soil. (c) saturated soil. (d) submerged soil. 4. Which of the following is not a volume relationship? (a) Void ratio (b) Porosity (c) Degree of saturation (d) Water content 5. Porosity of a soil is defined as (a) the ratio of volume of voids to the volume of solids. (b) the ratio of volume of voids to the total volume. (c) the volume of water to the volume of voids. (d) The weight of water to the weight of solids. 6. Which of the following is not represented as a percentage? (a) Void ratio (b) Porosity (c) Degree of saturation (d) Water content 7. Select the incorrect statement. (a) Void ratio can be greater than unity. (b) Porosity lies between 0 and 100%. (c) Degree of saturation lies between 0 and 100%. (d) Water content is always less than 100%. 8. If void ratio of a soil is 0.2, then its porosity will be (a) 16.7 %. (b) 20.0 %. (c) 25.0 %. (d) none of the above. P a g e | 3‐2 9. If the specific gravity of soil solids is 2.67, and water content is 32% for a given soil, its void ratio will be (a) 0.12. (b) 0.85. (c) 1.00. (d) none of the above. 10. The dry unit weight γd is related to the moist unit weight γ and moisture content w as γ (a) γ d = 1+ w (b) γ d = γ (1 + w) γ (c) γ d = d 1− w (d) γ d = γ (1 + w) 11. The void ratio e, degree of saturation S, water content w and specific gravity Gs are related as (a) Sw = eGs (b) SGs = we (c) Se = wGs (d) Sew = Gs 12. Dense uniform sand can have a void ratio of (a) 0.1. (b) 0.5. (c) 1.0. (d) 1.2. 13. In its natural state, a moist soil has a volume of 0.33 ft3 and weighs 39.93 lb. The ovendried weight of the soil is 34.54 lb. If Gs = 2.67, what will be the volume of soil solids? (a) 207.0 ft3 (b) 20.7 ft3 (c) 2.07 ft3 (d) 0.207 ft3 14. A representative soil specimen collected from the field weighs 1.9 kN and has a volume of 0.12 m3. The water content as determined in the laboratory is 13.5%. What will be the dry unit weight of the soil? (a) 13.9 kN/m3 (b) 15.8 kN/m3 (c) 17.9 kN/m3 (d) None of the above 15. The term ‘relative density’ is commonly used to indicate (a) density of granular soil with respect to density of water. (b) in situ denseness of granular soil. (c) in situ looseness of granular soil. (d) (a) or (b). P a g e | 3‐3 16. If e = in situ void ratio of soil, emax = void ratio of the soil in the loosest state, and emin = void ratio in the densest state, then the relative density Dr is defined as e −e (a) Dr = max min emax − e e −e (b) Dr = max emax − emin e − emax (c) Dr = emax − emin e −e (d) Dr = max min e − emax 17. The relative density of dense granular soils ranges from (a) 15 to 50%. (b) 50 to 70%. (c) 70 to 85%. (d) 85 to 100%. 18. A granular soil deposit is in loose condition. Which of the following cannot be its relative density? (a) 25% (b) 35% (c) 45% (d) 55% 19. The minimum and maximum void ratios for granular soils does not depend on (a) grain size. (b) mineral composition. (c) grain shape. (d) fine contents. 20. For a given sand and fine mixture, the maximum and minimum void ratios (a) decrease with increase in the volume of fines. (b) increase with increase in the volume of fines. (c) first increase then decrease with increase in the volume of fines. (d) first decrease then increase with increase in the volume of fines. 21. For clean sand samples, emax and emin are related as (a) emax ≈ 0.5 emin (b) emax ≈ emin (c) emax ≈ 1.6 emin (d) emax ≈ 2 emin P a g e | 3‐4 Answers, Hints and Discussion 1. (d) 2. (c) Discussion: (b) is correct for dry soil, and (d) for partially saturated soil. A soil does not exist practically as a one-phase system consisting of soil solids only. 3. (b) 4. (d) Discussion and Hint: Water content is a weight relationship; see Eq. (3.8). 5. (b) Discussion: (a), (c) and (d) are correct for void ratio, degree of saturation and water content, respectively. See Eqs. (3.3), (3.5) and (3.8). 6. (a) 7. (d) 8. (a) Discussion: Eq. (3.7): . . 0.167 or 16.7%. 9. (b) Discussion: S = 100% for saturated soils. Eq. (3.19): 0.32 2.67 0.85. 10. (a) 11. (c) 12. (b) Hint: See Table 3.2. 13. (d) Discussion: Eq. (3.15): Vs = Ws 34.54 = = 0.207 ft 3 Gsγ w (2.67)(62.4) 14. (a) Discussion: Eq. (3.9): . 15. (d) 16. (b) 17. (c) Hint: See Table 3.3. 18. (d) 19. (b) 20. (d) 21. (c) Hint: See Eq. (3.39). . 15.8 kN/m ; Eq. (3.12): . . 13.9 /