Mineral Gypsum volcanic ash Orthoclase Kaolinite Quartz Calcite Dolomite Magnite
SOIL MECHANICS (hand-outs) INDEX PROPERTIES OF SOILS.v1 FILL THE BLACK SPACES BELOW: ------------------------------------------------------------------------------------------Key Notes: 1. _________________is composed of solid, liquid and gases 2. The spaces between the solids are called ________________. 3. Soil mater is commonly called ________________________. 4. If all the voids are filled with water, the so il is ______________ 5. If all the voids are filled with are, the soil is aid to be ________. Physical Properties of Soil The following relationships can be made from the phase diagram shown:
Specific Gravity 2.32 2.56 2.61 2.67 2.72 2.87 5.17
16. DEGREE OF SATURATION (S) is the ratio, often expressed as a percentage, of volume of water to the volume of voids. Formula:
____________ ________________ _____
( ϒ), is the weight of soil per unit volume (bulk 17. UNIT WEIGHT (ϒ unit weight) Formula:
___________ ________________ ______
18. Dry Unit weight: Formula:
____________ ________________ _____
19. Saturated Unit weight: Formula:
____________ ________________ _____
20. Effective or buoyant unit weight is the weight of a saturated 6. 7. 8.
9.
soil, surrounded by water, per unit volume of soil.
Total weight of soil, _____________________ Volume of voids, ________________________ Total Volume, ____________________________
WATER CONTENT (w) is the ratio, often expressed as a percentage, of the weight of water to the weight of solids.
Formula:
____________ ________________ _____
21. RELATIVE DENSITY (Dr) is the index that quantifies the degree of packing between the loosest, and densest possible state of coarse-grained soils. Formula:
____________ ________________ _____
Formula:
____________ ________________ _____
10. VOID RATIO (e) is the ratio of volume of voids space to the volume of solids. Void ratio is usually expressed as a decimal quantity.
Formula:
____________ ________________ _____
Formula:
Designation of Granular Soils
_____________ ________________ ____
11. SPECIFIC VOLUME (V’) is the volume of soil per unit volume of solids.
Designation Very loose Loose Medium dense Dense Very Dense
Formula:
_____________ ________________ ____
12. POROSITY (n) is the ratio of volume of voids to the total volume and is usually expressed as a percentage.
Dr (%) 0 - 15 15 – 35 35 – 70 70 – 85 85 – 100
Formula:
_____________ ________________ ____
13. SPECIFIC GRAVITY (Gs) is the ratio of the weight of the soil solids to the weight of water of equal volume. Formula:
EXERCISES: Prove the following relations: e
22.
n
Density and Unit Weight of Water
23.
S
14. Density of water,
24.
d
25.
sat
_____________ ________________ ____
___________________________ ___________________________
15. Unit weight of water _____________________________
e 1 wGs e Gs
1 e
w
Gs Se
1 e
w
Gs w (1 w)
1 e
PROBLEM SOLVING: -3
3
A moist soil has these values; V=7.08 x 10 m , m = 13.95 kg, w = 9.8% and Gs = 2.66. Determine the density, dry density, void ratio, porosity, degree of saturation and the volume occupied by water, 26. Density: 3 3 3 3 a. 1770.3 kg/m b. 1970.3 kg/m c. 1870.3 kg/m d. 2070.3 kg/m e. NOTA 27. Dry Density: 3 3 3 3 a. 1894.4 kg/m b. 1994.4 kg/m c. 1794.4 kg/m d. 2094.4 kg/m e. NOTA 28. Void Ratio a. 0.58 b. 0.38 c. 0.48 d. 0.68 e. NOTA 29. Porosity: a. 0.234 b. 0.432 c. 0.342 d. 0.324 e. NOTA 30. Degree of Saturation: a. 64.3% b. 34.3% c. 44.3% d. 54.3% e. NOTA 31. Volume occupied by water: 3 3 3 3 a. 0.00125 m b. 0.00225 m c. 0.00325 m d. 0.00425 m e. NOTA The mass of the sample of a saturated soil is 500 grams. The dry mass, after oven drying, is 400 grams. Determine the (a) water content (b) void ratio (c) saturated unit weight (d) effective unit weight. Gs = 2.7 32. Water Content a. 25% b. 20% c. 35% d. 30% e. NOTA 33. Void ratio a. 0.565 b. 0.675 c. 0.575 d. 0.775 e. NOTA 34. Saturated Unit Weight 3 3 3 3 a. 18.77 kN/m b. 19.77 kN/m c. 17.77 kN/m d. 20.77 kN/m e. NOTA 35. Effective Unit wt. 3 3 3 3 a. 9.256 kN/m b. 9.556 kN/m c. 9.756 kN/m d. 9.956 kN/m e. NOTA 3
A soil sample has a bulk unit weight of 19.6 kN/m at a water content of 10%. Determine the void ratio, percentage of air in the voids (air voids) and the degree of saturation of this sample. 36. Void Ratio a. 0.386 b. 0.286 c. 0.422 d. 0.486 e. NOTA 37. Percentage of air in voids (air voids) a. 40% b. 55% c. 45% d. 50% e. NOTA 38. Degree of Saturation a. 55% b. 50% c. 45% d. 405% e. NOTA A saturated silty class encountered in a deep excavation is found to have a water content of 23%. Determine its porosity and bulk unit weight. 39. Porosity a. 0.383 b. 0.325 c. 0.343 d. 0.483 e. NOTA 40. Bulk unit weight 3 3 3 3 a. 19.098 kN/m b. 20.098 kN/m c. 18.098 kN/m d. 21.098 kN/m e. NOTA -4
3
A wet sand sample has a volume of 4.64x10 m and weighs 8N. After oven drying, the weight reduces to 7.5 N. Calculate the water content, void ratio, and the degree of saturation. 41. Water Content a. 26.7% b. 16.7% c. 10.7% d. 6.7% e. NOTA 42. Void Ratio a. 0.44 b. 0.54 c. 0.64 d. 0.34 e. NOTA 43. Degree of saturation a. 22% b. 28% c. 20% d. 32% e. NOTA 3
A sandy soil has a natural water content of 10% and a bulk unit weight of 18.5 kN/m . The void ratios corresponding to the densest and loosest state of this soil are 0.51 and 0.87. Find the relative density and the degree of saturation for this soil. 44. Relative density a. 0.675 b. 0.575 c. 0.555 d. 0.745 e. NOTA 45. Degree of saturation a. 35% b. 37% c. 47% d. 40% e. NOTA
FILL THE BLACK SPACES BELOW: 46. __________________________ OF SOIL Is the determination of the size range of particles present in a soil expressed as a percentage of the total dry weight ( or mass). Two methods are generally used to find the particle-size distribution of soil: (1) sieve analysis – for particle sizes larger than 0.075 mm in diameter, and (2) hydrometer analysis – for particle sizes smaller than 0.075mm in diameter.
57. Gravel
(size limits – ___________________________)
58. Sand
(size limits – ___________________________)
59. Silit and clay
(size limits – ___________________________)
US Standard Sieve sizes Sieve No. Opening (mm) 4 4.750 6 3.350 8 2.360 10 2.000 16 1.180 20 0.850 30 0.600 40 0.425 50 0.300 60 0.250 80 0.180 100 0.150 140 0.106 170 0.066 200 0.075 270 0.053
47. _____________________________ consist of shaking the soil sample through a set of sieves that have progressively smaller openings. To conduct a sieve analysis, one must first oven-dry the soil and then break all lumps into small particles. The soil I then shaken through a stack of sieves with openings of decreasing size from top to bottom. After the soil is shaken, the mass of soil retained on the sieve is determined. 48. _____________________________
is based on the principle of sedimentation of soil grains in water. When a soil specimen is dispersed in water, the particles settle at different velocities, depending on their shape, size and weight.
D
Effective Size (D10)
18 z (Gs 1) wt D
1.
The diameter of the particle size in a distribution curve corresponding to _____________ finer.
Where: 49. D = _____________________________________
2.
Formula:
50. μ = _____________________________________ 51. z =
Uniformity coefficient, Cu _____________ _______________ _____
_____________________________________
1.
Coefficient of gradation (coeff. Of curvature), Cc
52. ϒ w = ____________________________________ Formula:
53. Gs = _____________________________________
___________ ________________ _____
PERCENT RETAINED AND PERCENT FINER Example Problem:
54. %retained on each sieves =
The following are the results of a sieve analysis:
Formula:
U.S. Sieve No.
on each sieve (g)
____________ _______________ ______
55. %finer than (ith) sieve = Formula:
___________ ________________ ______
56. The percentages of gravel, sand, silt and clay particles in a soil can be obtained from the particle size distribution curve. According _________________________________________________ (USCS), the soil has these percentages;
Mass of soil retained
to
4
0
10
21.6
20
49.5
40
102.6
60
89.1
100
95.6
200
60.4
pan
31.2
60. Determine the percent finer than each sieve size and plot a grain size distribution curve.
Tabular Solution: U.S. Sieve No.
Opening (mm)
Mass of soil retained on each sieve (g)
Cumulative Mass
Percent finer (%)
retained above each sieve (g)
4 10 20 40 60 100 200 pan
Determine D10, D30 and D60, from the grain size distribution curve. 61. D10: a. . 0.09 mm b. . 0.185 mm c. 0.41 mm 62. D30 a. 0.185 mm b. 0.09 mm c. 0.41 mm 63. D60 a. 0.09 mm b. 0185 mm c. 0.41 mm
d. . 0.651 mm
e. NOTA
d. 0.651 mm
e. NOTA
d. 0.651 mm
e. NOTA
64. Calculate the Uniformity Coefficient (Cu). a. 4.16 b. 3.56
c. 4.56
d. 5.22
e. NOTA
65. Calculate the Coefficient of Gradation (Cc) a. 0.53 b. 0.93
c. 0.63
d. 0.73
e. NOTA
