A group of friction piles is shown in figure. The total load on the pile less the soil displaced by the footing is 1800kN. The clay is 16m thick. Ground water table is located 2m below the clay surface.
1. Compute for the effective pressure the mid height of the consolidating clay layer, in kPa.
A. 186.4
B. 174.8
C. 147.6
D. 163.5
2. Compute for the compression index of the clay.
A. 0.297
B. 0.245
C. 0.325
D. 0.288
3. What is the approximate settlement of the foundation?
A. 150 mm
B. 168 mm
C. 214 mm
D. 198 mm
Solution:
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A test is set-up as shown. A cylindrical mold 4” in diameter is filled with silt to height H1 = 0.2 ft, whose coefficient of permeability k1 = 6.1 x 10-4 ft/min.
A second coaxial mold is placed on top of the first mold whose inside diameter is d=1.5” and whose height is H2 = 0.30 ft. Its thickness is negligible. The inside of this second mold is filled with the same silt, but the annular ring outside the small tube and outer tube is filled with sand whose coefficient of permeability is k2 = 2.5 x 10-3 ft/min.
The test set-up is a permeameter of constant head. Water is placed in the mold and maintained at a level h=1.4ft. above the level of the outlet. It may be considered that the system consists of a fictitious soil of thickness H=H1 + H2 and coefficient of permeability kf.
The following general equations may be useful:
kv eq = H/[(H1/kv1) + (H2/kv2) + … + (Hn/kvn)]
kv eq = (1/H)[kh1H1 + kh2H2 + … + khnHn]
1. What is the total flow of water in ft3/min?
A. 2.148 x 10-4
B. 3.521 x 10-4
C. 2.554 x 10-4
D. 2.874 x 10-4
2. What is the equivalent coefficient of permeability, kf, in ft/min?
A. 1.045 x 10-3
B. 1.563 x 10-3
C. 1.874 x 10-3
D. 1.245 x 10-3
3. What is the total amount of water that percolated after 30minutes?D. 325.32 cm3
A. 217.12 cm3
B. 187.54 cm3
C. 256.32 cm3
D. 325.32 cm3
Solution:
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A cut slope was excavated in a saturated clay. The slope made an angle of 60° with the horizontal. When slope failure occurs, distance BC is 8m. Given: Stability number, m=0.185: γ=17 kN/m3; cu = 20kPa.
1. What is the stability factor?
A. 6.32
B. 5.41
C. 4.57
D. 9.36
2. Determine the critical depth of cut in meters.
A. 7.52
B. 6.36
C. 6.87
D. 5.21
3. What is the angle of failure plane in degrees?
A. 19.5
B. 25.4
C. 22.5
D. 28.6
Solution:
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A 4-meter thick sand layer is overlying a very thick dense clay layer. The water table is 2.5m below the ground (sand) surface. The sand have void ratio of 52% and the degree of saturation above water table is 37%. The clay has moisture content of 42%. Assume specific gravity of solids for both sand and clay equal to 2.65.
1. Compute for the value of the unit weight of sand above water table.
A. 18.8 kN/m3
B. 18.3 kN/m3
C. 19.3 kN/m3
D. 17.5 kN/m3
2. Compute for the value of the total stress at a depth of 10m from the ground surface, in kPa.
A. 174.5
B. 181.4
C. 196.3
D. 186.7
3. Compute for the value of the effective stress at a depth of 10m from the ground surface, in kPa.
A. 98.6
B. 132.4
C. 124.5
D. 107.8
Solution:
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Two pressurized tanks A & B are connected at the bottom by 140mm-diameter short pipe as shown in figure. The coefficients of velocity and contraction of the short pipe are 0.92 and 0.86, respectively.
1. What is the flow through the pipe in m3/s?
A. 0.214
B. 0.115
C. 0.187
D. 0.231
2. What is the head lost in meters?
A. 0.85
B. 0.53
C. 1.71
D. 1.32
3. What is the power lost in horsepower?
A. 2.59
B. 1.93
C. 2.98
D. 1.45
Solution:
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An open-top cylindrical tank 1 meter in diameter is 2.80m tall. The tank floats in water with a draft of 2.30 meters. Unit weight of lead is 110 kN/m3.
1. What is the weight of tank in KiloNewtons?
A. 19.54
B. 21.57
C. 15.24
D. 17.72
2. How much lead (in KiloNewtons) must be fastened to the outside bottom of the tank in order make it completely submerged in water?
A. 100m
B. 120m
C. 150m
D. 80m
3. How much lead (in KiloNewtons) must be place inside the tank in order make it completely submerged in water?
A. 4.87
B. 4.21
C. 3.85
D. 3.24
Solution:
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Dry soil is mixed with 17% by weight with water and then compacted. The moist soil has a volume of 1 x 10-3 m3 and a mass of 1.6kg. The soil solids have specific gravity of 2.70.
Determine the following:
1. What is the dry unit weight of the soil in kN/m3?
A. 14.25
B. 13.42
C. 12.54
D. 15.63
2. What is the void ratio of the soil?
A. 97.4%
B. 86.35%
C. 95.85%
D. 92.54%
3. What is the degree of saturation of the soil?
A. 32.21%
B. 25.87%
C. 47.12%
D. 52.32%
Solution:
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A 600-mm non-rigid pipe takes water from a large reservoir. The velocity of flow in the pipe is 2.5 m/s. The flow is suddenly stopped by a quick-closing valve situated 400 m from the reservoir. The pipe is 20mm thick and modulus of elasticity of pipe material is 1.4 x 1011Pa. Bulk modulus of elasticity of water is 2.2 x 109Pa.
1. Compute for the value of the celerity of pressure wave in m/s.
A. 1532
B. 1223
C. 1142
D. 1358
2. Compute for the time for the pressure wave to travel round trip along the pipe.
A. 0.74sec
B. 0.96sec
C. 0.85sec
D. 0.65sec
3. What is the maximum water hammer pressure developed on the pipe due to instantaneous closure of the valve?
A. 3057 kPa
B. 3185 kPa
C. 3263 kPa
D. 3321 kPa
Solution:
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A pump draws 20 liters per second of water from reservoir C and lifts it to reservoir D as shown. The head lost from C to 1 is three times the velocity head in the 150-mm suction line and the head lost from 2 to D is fifteen times the velocity head in the 100-mm discharge line.
1. What is the power delivered by the pump to the system?
A. 62.6 horsepower
B. 64.5 horsepower
C. 75.6 horsepower
D. 87.4 horsepower
2. What is the pressure head at point 1 in meters of water?
A. 32.56m
B. 48.57m
C. 19.74m
D. 15.23m
3. What is the pressure head at point 2 in meters of water?
A. 187.56m
B. 264.63m
C. 321.27m
D. 242.33m
Solution:
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A closed conical tank, upright is position, has a bottom radius of 30cm and a height of 65cm.
1. What is the total volume of the tank in cubic meter?
A. 0.0541
B. 0.0963
C. 0.0852
D. 0.0613
2. If the tank contains 0.022m3 of water, how much water is required to fill the tank?
A. 0.0236m3
B. 0.0147m3
C. 0.0586m3
D. 0.0393m3
3. If the tank contains 0.022m3 of water, what is the depth of water in the tank?
A. 0.09m
B. 0.05m
C. 0.08m
D. 0.12m
Solution:
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A 10-m wide rectangular channel have a flow of 17.6 m3/s when the depth of flow is 1.20m. Use n= 0.014.
1. Compute for the value of the minimum specific energy in meter.
A. 1.32m
B. 1.02m
C. 0.85m
D. 1.63m
2. What is the normal slope?
A. 0.00055
B. 0.00022
C. 0.00044
D. 0.00033
3. What is the average boundary shearing stress in Pa?
A. 4.18Pa
B. 6.85Pa
C. 25.87Pa
D. 102.45Pa
Solution:
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A triaxial test is conducted on a clay specimen and the following results were obtained: cohesion = 32kPa, angle of internal friction = 28°, shearing stress at failure plane = 61 kPa.
1. What is the maximum normal stress in kPa?
A. 114
B. 69
C. 147
D. 156
2. What is the confining stress in kPa?
A. 23.6
B. 17.8
C. 11.2
D. 32.7
3. What is the normal stress at failure plane?
A. 60.2
B. 54.5
C. 45.3
D. 72.8
Solution:
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A 4.2m thick layer of sand is underlain by a layer of clay. The water table is 2m below the ground (sand) surface. For sand, Gs = 2.65 and the average void ratio is 0.52. The sand above water table has a degree of saturation of 0.37. The saturated nit weight of the clay layer is 20.2 kN/m3.
1. Determine the unit weight of sand above water table in kN/m3
A. 17.86
B. 20.46
C. 10.65
D. 18.35
2. Determine the total stress at a point 10m below the ground.
A. 199 kPa
B. 123 kPa
C. 232 kPa
D. 167 kPa
3. Determine the effective stress at a point 10m below the ground.
A. 134.5 kPa
B. 120.4 kPa
C. 156.9 kPa
D. 111.1 kPa
Solution:
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A confined aquifer is shown. This aquifer has a source of recharge located as shown. The hydraulic conductivity of the aquifer is 40m/day with porosity of 25%. The piezometric (head) surface in the two observation wells 1250m apart are at elevation 65m and 60m, respectively from the common datum. The aquifer has an average thickness of 25m and an average width of 4km.
1. Determine the nearest value to the rate of flow of water through the aquifer, in cubic meters per day.
A. 14,000
B. 16,000
C. 18,000
D. 15,000
2. Determine the nearest value to the seepage velocity in m/day.
A. 0.76
B. 0.42
C. 0.54
D. 0.64
3. Determine the nearest value to the time of travel from the head of aquifer to a point 3.4km downstream, in days.
A. 4876
B. 6325
C. 5313
D. 5874
Solution:
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A soil sample taken from subgrade have a density of 1900 kg/m3 with moisture content of 11%. Laboratory tests reveals that the soil solids have density of 2660 kg/m3 and the maximum and minimum void ratios of the soil mass are 0.63 and 0.44, repectively.
1. Determine the nearest value to the dry unit weight of the soil in kN/m3.
A. 17.4
B. 16.8
C. 16.1
D. 18.3
2. Determine the relative density of the sample.
A. 0.554
B. 0.654
C. 0.425
D. 0.722
3. Determine the relative density of the sample.
A. 0.63
B. 0.54
C. 0.40
D. 0.48
Solution:
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A 3-m square plate is immersed in water in a vertical position such that the two edges of the square are horizontal. The immersion is such that the center of pressure on the plate is 10cm from its center of gravity.
1. Determine the distance from the water surface to the center of pressure.
A. 6.5m
B. 6.75m
C. 7.5m
D. 6m
2. Determine the distance from the water surface to the center of pressure.
A. 7.6m
B. 7.5m
C. 6.6m
D. 6.5m
3. Determine the distance from the water surface to the center of pressure.
A. 662 kN
B. 612 kN
C. 856 kN
D. 587 kN
Solution:
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A conical tank with lower base radius of 35cm and 65cm tall contains 0.025m3 of water.
1. What is the total volume of the tank in m3?
A. 0.0912
B. 0.0732
C. 0.0834
D. 0.0891
2. What is the depth of water in the tank in meters?
A. 0.0672
B. 0.0789
C. 0.0728
D. 0.0842
3. How much water must be added to fill the tank in m3?
A. 0.0482
B. 0.0583
C. 0.0641
D. 0.06621
Solution:
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A calibration test of a 0.00785-m2 circular sharp-edged orifice in a vertical side of a large tank showed a discharge of 22,300 N of water in 1minute & 40 seconds at a constant head of 1.20m. Measurement of the jet showed that it traveled 1.92m horizontally while dropping 0.8m.
1. Determine the coefficient of discharge.
A. 0.621
B. 0.597
C. 0.649
D. 0.721
2. Determine the coefficient of velocity.
A. 0.84
B. 0.93
C. 0.74
D. 0.98
3. Determine the coefficient of contraction.
A. 0.77
B. 0.97
C. 0.61
D. 0.67
Solution:
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A 1.6kg soil specimen have a volume of 1 x 10-3 m3 and moisture content of 12%. Specific gravity of soil solids is 2.5.
1. What is the dry density of this soil in kg/m3?
A. 1356
B. 1567
C. 1429
D. 1632
2. What is the void ratio of this soil?
A. 85%
B. 78%
C. 75%
D. 72%
3. What is the degree of saturation?
A. 40%
B. 35%
C. 30%
D. 45%
Solution:
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Water is flowing in a 200-mm diameter rigid pipe that is 650m long. The increase in pressure caused by instantaneous closure of the valve near the exit is 700kPa. Bulk modulus of elasticity of water is 2.07 x 109 Pa.
1. What is the celerity of pressure wave in m/s?
A. 1439
B. 1621
C. 1256
D. 1176
2. What is the maximum discharge in m3/s?
A. 0.0188
B. 0.0279
C. 0.0232
D. 0.0153
3. What water hammer pressure is expected if the valve is closed in 3 seconds?
A. 289kPa
B. 187kPa
C. 342kPa
D. 211kPa
Solution:
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Given the following laboratory result of a sub grade material:
γdmax = 1.735 g/cc Wet weight = 2200 g
MCmax = 15.75% Dry weight = 1879 g
Volume of soil = 1130 cc
1. Determine the dry unit weight of the soil in grams/cc.
A. 1.66
B. 1.95
C. 1.82
D. 1.54
2. Determine the moisture content in percent.
A. 15.4%
B. 17.1%
C. 21.8%
D. 19.3%
3. Determine the percent compaction and indicate whether it is adequate as subgrade material.
A. >95.6% yes
B. <93%, no
C. <95.6%, no
D. >93% yes
Solution:
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In a triaxial test on a cohesionless soil, the soil fails when the deviator stress is 250kPa and the angle of failure plane is 60° with the horizontal.
1. What is the normal stress at failure in kPa?
A. 123.7
B. 145.9
C. 154.2
D. 187.5
2. What is the shearing stress at failure in kPa?
A. 108.3
B. 112.8
C. 132.5
D. 124.4
3. What is the confining pressure in kPa?
A. 100
B. 125
C. 130
D. 115
Solution:
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A clay sample has a plastic limit of 8% and liquid limit 58%
1. Which of the following is measured by plastic limit and liquid limit?
A. Liquidity index
B. Water content
C. Plasticity index
D. Shrinkage index
2. Determine the plasticity index of the clay.
A. 55
B. 45
C. 35
D. 50
3. Determine the liquidity index if the natural moisture content is 30%
A. 0.44
B. 0.54
C. 0.36
D. 0.61
Solution:
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The grain-size curves for soils A and B. It is required to classify the soils according to the Unified Soil Classification System. Use the attached USCS-54.
1. Which of the following classifies soil A?
A. SW
B. SP
C. GP
D. GW
2. Which of the following classifies soil B?
A. GP
B. SC
C. SP
D. GC
3. Which of the following classifies soil C?
A. SP
B. SC
C. SM
D. SW
|
SIEVE ANALYSIS
|
| Sieve
No. |
Diameter
Mm |
Percent Passing |
| Soil A |
Soil B |
Soil C |
| 4 |
4.760 |
90 |
100 |
95 |
| 8 |
2.380 |
60 |
96 |
82 |
| 10 |
2.000 |
54 |
95 |
78 |
| 20 |
0.850 |
31 |
87 |
60 |
| 40 |
0.425 |
20 |
65 |
30 |
| 60 |
0.250 |
14 |
42 |
14 |
| 100 |
0.150 |
9 |
15 |
10 |
| 200 |
0.074 |
4 |
0 |
8 |
| |
LL |
|
|
40% |
| |
PL |
|
|
15% |
Solution:
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A dense silt layer has the following properties: void ratio = 0.50, effective diameter d10 = 10 μm, capillary constant C =0.20cm2. Free ground water level is 8.0 m below the ground surface.
1. Find the height of capillary rise the silt. Capillary rise is given as h = C/(exd10)
A. 3m
B. 2m
C. 4m
D. 5m
2. Find the vertical effective stress in kPa at 6m depth. Assume unit weight of solids=26.4 kN/m3 and that the soil above the capillary action rise and ground surface is partially saturated at 50%.
A. 145.6
B. 138.3
C. 118.7
D. 126.2
3. What is the savings in lining (per meter length of canal) if the most efficient section is used for the same discharge and slope.
A. 205
B. 267
C. 224
D. 238
Solution:
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A cylindrical mold 5” in diameter is filled with silt to height H1 = 0.2 ft, whose coefficient of permeability k1 = 3.6 x 10-4 ft/min.
A second coaxial mold is placed on top of the first mold whose inside diameter is d = 1.5” and whose height is H2 = 0.40 ft. Its thickness is negligible. The inside of this second mold is filled with the same silt, but the annular ring outside the small tube and outer tube is filled with sand whose coefficient of permeability is k2 = 2.7×10-3 ft/min.
The test set-up is permeameter of constant head. Water is placed in the mold and maintained at a level h=1.6 ft. above the level of the outlet. It may be considered that the system consists of a fictitious soil of thickness H = H1 + H2 and coefficient of permeability kf.
The following general equations may be useful:
1. What is the total flow of water in ft3/min?
A. 2.47×10-4 ft3/min
B. 1.85×10-4 ft3/min
C. 3.54×10-4 ft3/min
D. 2.94×10-4 ft3/min
2. What is the equivalent coefficient of permeability, kf, in ft/min?
A. 9.632×10-4 ft/min
B. 7.442×10-4 ft/min
C. 8.083×10-4 ft/min
D. 5.452×10-4 ft/min
3. What is the total amount of water that percolated after 45 minutes?
A. 315 cc
B. 236 cc
C. 375 cc
D. 458 cc
Solution:
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A rectangular canal 5.7m wide and 1.4m deep has a roughness coefficient of 0.013 and is laid on a slope of 0.002
1. Determine the capacity of the canal when flowing full.
A. 22.56 m3/s
B. 26.32 m3/s
C. 29.87 m3/s
D. 32.12 m3/s
2. What is the savings in excavation volume (per meter length of canal) if the most efficient section is used for he same discharge and slope.
A. 0.243 m3
B. 0.654 m3
C. 0..421 m3
D. 0.331 m3
3. What is the savings in lining (per meter length of canal) if the most efficient section is used for the same discharge and slope.
A. 0.812 m2
B. 0.332 m2
C. 0.532 m2
D. 0.632 m2
Solution:
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The pump shown draws 25 liters per second of water from reservoir A and lifts it to reservoir B. The head lost from A to 1 is three times the velocity head in the 150-mm pipe and from 2 to B is ten times the velocity head in the 100-mm pipe.
1. What is the nearest value to the power output of the pump in kilowatts?
A. 78.3
B. 69.6
C. 54.1
D. 60.2
2. What is the nearest value to the pressure at point 1 in kilopascals?
A. 154.2
B. 168.9
C. 230.4
D. 192.2
3. What is the nearest value to the pressure at point 2 in kilopascals?
A. 2596
B. 2678
C. 2134
D. 3112
Solution:
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An open cylindrical tank 30 cm in diameter and 80cm tall is filled with water and revolved about its own vertical axis at constant angular speed.
1. What angular speed will cause 1.4 liters of water to spill?
A. 45.5 rpm
B. 87.2 rpm
C. 65.2 rpm
D. 56.1 rpm
2. What will be the depth of water in the tank when it is brought to rest from an angular speed of 240 rpm?
A. 0.438 m
B. 0.672 m
C. 0.321 m
D. 0.552 m
3. What angular speed will just zero the pressure at the bottom?
A. 269.3 rpm
B. 252.2 rpm
C. 189.4 rpm
D. 298.3 rpm
Solution:
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A solid block having a specific gravity of 3.47 is placed in a cylinder containing mercury having a specific gravity of 13.6.
1. What part (percent) of the block is floating above the mercury level?
A. 65.45%
B. 54.32%
C. 74.49%
D. 25.51%
2. If the volume of the block is 0.018m3, what is the weight of the block?
A. 874.3 N
B. 561.1 N
C. 612.7 N
D. 678.2 N
3. If the volume of the block is 0.018 m3, what downward force is required to make it completely submerged in mercury?
A. 1789 N
B. 1932 N
C. 1456 N
D. 2112 N
Solution:
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A cantilever sheet-pile 8.2m long supports a 5-m high dry sand with dry density of 1.19 g/cc and angle of shearing resistance of 34°. The pile is embedded to a depth of 3.2m. The water table is at the bottom of the sheet pile.
1. What is the maximum active force that can act on the sheet-pile in kN?
A. 158
B. 324
C. 111
D. 211
2. What is the maximum passive resistance that can act on the sheet-pile in kN?
A. 211
B. 111
C. 158
D. 324
3. What passive resistance must be mobilized for stability?
A. 427
B. 262
C. 317
D. 285
Solution:
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A pre-stressed concrete pile, 350mm x 350mm in cross-section and 10m long, is to be driven in a clayey soil. The unconfined compression shear strength, qu of the soil is 110 kPa. Use Nc = 9 and α = 0.76, γ = 16 kN/m3.
1. What is the end bearing capacity of pile in kN.
A. 50.42
B. 78.62
C. 60.64
D. 80.65
2. Compute the skin friction in kN develop along the shaft of the pile.
A. 585.2
B. 635.8
C. 456.2
D. 863.2
3. Compute the capacity of the pile using a factor of safety of 2.
A. 323
B. 358
C. 253
D. 471
Solution:
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A soil sample having a volume of 1 x 10-3 m3 has a mass of 1950 grams and moisture content of 10%. The specific gravity of soil is 2.66
1. What is the nearest value of the dry density of the soil in kg/m3?
A. 1714
B. 1773
C. 1824
D. 1597
2. What is the nearest value to the void ratio in percent?
A. 50.1
B. 76.2
C. 42.5
D. 64.2
3. What is the nearest value to the degree of saturation in percent?
A. 74.2
B. 47.2
C. 53.1
D. 63.5
Solution:
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A confined aquifer is shown. This aquifer has a source of recharge located as shown. The hydraulic conductivity of the aquifer is 40 m/day with a porosity of 25%. The piezometric (head) surface in the two observation wells 1375m apart are at elevation 65m and 60m, respectively from the common datum. The aquifer has a average thickness of 25m and an average width of 4km.
1. Determine the nearest value to the rate of flow of water through the aquifer, in cubic meters per day.
A. 13,221
B. 12,875
C. 15,652
D. 14,546
2. Determine the nearest value to the seepage velocity in m/day.
A. 0.324
B. 0.475
C. 0.582
D. 0.146
3. Determine the nearest value to the time of travel from the head of aquifer to a point 4km downstream, in days.
A. 5427
B. 7624
C. 6875
D. 8725
Solution:
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A granular soil sample taken from the field has a density of 1600 kg/m3. In a laboratory test, it was found out that the density of soil solids is 2600 kg/m3, the moisture content is 11.5%, and the void ratios at its densest and loosest states are 0.43 and 0.62, respectively. Determine the following:
1. The dry density in kg/m3.
A. 1532
B. 1814
C. 1704
D. 1652
2. The void ratio.
A. 0.56
B. 0.51
C. 0.36
D. 0.62
3. The relative density of the granular soil in percent.
A. 31
B. 65
C. 87
D. 51
Solution:
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