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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A tri-axial test is conducted on a sand sample. The normal and shearing stresses on failure plane are 475 kPa and 350 kPa, respectively.
1. Determine the angle of shearing resistance.
A. 32.3°
B. 59.1°
C. 61.2°
D. 63.2°
2. Determine the angle that the failure plane makes with the horizontal.
A. 57.3°
B. 59.1°
C. 61.2°
D. 63.2°
3. What is the plunger stress in kPa?
A. 632.4
B. 869.5
C. 798.3
D. 812.7
Solution:
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A vertical tank having a horizontal cross-sectional area of 0.4 square meter has 0.0003m2 orifice at its bottom. The initial head on the orifice is h1 = 1.2m. It takes 312 second for the water level to drop from 1.2m to 0.6m.
1. What is the coefficient of discharge?
A. 0.65
B. 0.62
C. 0.68
D. 0.72
2. If C = 0.6, how long will it take for the water level to drop from 1.2m to 0.8m?
A. 202 s
B. 256 s
C. 185 s
D. 231 s
3. If C = 0.6, what is the head on the orifice after 240?
A. 0.52 m
B. 0.43 m
C. 0.85 m
D. 0.73 m
Solution:
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Water flows at the rate of 0.8 m3/s in a 900-m long pipe with a total head lost of 4m. Solve for the pipe diameter in mm by:
1. Darcy-Weisbach formula using f = 0.018.
A. 735
B. 715
C. 812
D. 793
2. Manning’s formula using n = 0.014.
A. 812
B. 735
C. 715
D. 793
3. Hazen-William’s formula using C1 = 130.
A. 812
B. 793
C. 735
D. 715
Solution:
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The elasticity and dimensions of a pipe leading from a reservoir are such that the celerity of pressure wave is 975m/s. The pipe has a length of 610m and a diameter of 1.2m. The flow is initially 0.85 m3/s.
1. What is the water hammer pressure for instantaneous valve closure?
A. 612.52 kPa
B. 731.25 kPa
C. 610.36 kPa
D. 680.74 kPa
2. What is the approximate water hammer pressure at the valve if it is closure in 4 s?
A. 188.8 kPa
B. 209.5 kPa
C. 212.1 kPa
D. 225.3 kPa
3. What pressure is expected when the discharge drops almost instantly from 0.85 m3/s to 0.28 m3/s?
A. 462.8 kPa
B. 550.5 kPa
C. 487.5 kPa
D. 510.2 kPa
Solution:
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A piece of metal weighs 250 N in air and 240 N in water.
1. Determine the volume of the piece of metal in cubic meter.
A. 0.0112
B. 0.0125
C. 0.0136
D. 0.0187
2. What is the unit weight of the metal in kN/m3?
A. 28
B. 25.74
C. 18.72
D. 31.22
3. What is the specific gravity of the metal?
A. 2.85
B. 2.62
C. 3.18
D. 1.91
Solution:
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A sheet pile 10.5 m in length is to retain a 7.3 m deep of soil with friction angle of 31°and unit weight of 17.5kN/m3. It is anchored to a depth of 1.2m below the top of the pile. The anchors are spaced 3m.
1. Find the total active force on the wall per meter width.
A. 279.9 kN
B. 308.8 kN
C. 358.4 kN
D. 421.2 kN
2. What percentage of the total passive resistance is utilized by the wall?
A. 77.7%
B. 65.3%
C. 95.5%
D. 84.5%
3. Determine the tension on the anchor.
A. 321.4 kN
B. 187.5 kN
C. 273.8 kN
D. 91.3 kN
Solution:
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Two footings rest in a layer of sand 2.7m thick. The bottoms of the footings are 0.90m below the ground surface. Beneath the sand layer is a 1.8m thick clay layer. Underneath the clay layer is solid surface. Beneath the sand layer is at a depth of 1.8m below the ground surface.
1. Compute the stress increase in kPa below footing A (1.5m x 1.5m) at the center of the clay layer. Assume that the settlement in the clay layer is the same beneath footings A and B.
A. 28.32
B. 20.14
C. 25.87
D. 22.68
2. Determine the size of footing B so that the settlement in the clay layer is the same beneath footings A and B.
A. 3.2m x 3.2m
B. 2.4m x 2.4m
C. 3.6m x 3.6m
D. 3.8m x 3.8m
3. Determine the settlement in mm beneath footing A.
A. 42.3mm
B. 34.2mm
C. 69.8mm
D. 57.4mm
Solution:
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A pre-stressed concrete pile, 300mm x 300 mm in cross-section, is to be driven in a clayey soil (γ = 18.5 kN/m3) as shown. The design pile has a design capacity of 450 kN. Use factor of safety of 2. The unconfined compression shear strength, qu, of the soil is 110 kPa. Use Nc = 9.
1. What is the end bearing capacity of pile in kN.
A. 44.6
B. 58.6
C. 62.7
D. 75.4
2. Compute the skin friction in kN expected to develop along the shaft of the pile.
A. 855.5
B. 963.2
C. 754.2
D. 689.1
3. Compute the length of the pile if frictional constant α = 0.6.
A. 14.5 m
B. 28.4 m
C. 21.6 m
D. 18.5 m
Solution:
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A 5-m thick sand layer overlies a very thick layer of clay. The sand has void ratio of 0.52 and specific gravity of solids of 2.62. The clay has moisture content of 42% and specific gravity of solids of 2.65. The water table is 3m below the sand (ground) surface. The sand above water table is 30% saturated.
1. Find the total active force on the wall per meter width.
A. 16.85 kN/m3
B. 18.21 kN/m3
C. 17.47 kN/m3
D. 17.04 kN/m3
2. Determine the total stress 10m below the ground surface.
A. 214.5 kPa
B. 154.8 kPa
C. 181.6 kPa
D. 112.9 kPa
3. Determine the effective stress 10m below the ground surface.
A. 112.9 kPa
B. 181.6 kPa
C. 154.8 kPa
D. 214.5 kPa
Solution:
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Water flows at the rate of 2m/s in a 2.5-km long 600-mm pipe that is 20mm thick. Bulk modulus of elasticity of water, EB = 2.2 x 109 Pa. Modulus of elasticity of pipe material is E = 1.4 x 1011 Pa. Density of water is 998 kg/m3.
1. Calculate the nearest value to the velocity of pressure (sound) wave in m/s.
A. 1087
B. 975
C. 1563
D. 1224
2. If a valve at the end of the pipe is closed, determine the maximum time of closure that can be considered as instantaneous closure.
A. 2.1 s
B. 4.1 s
C. 3.2 s
D. 5.2 s
3. Calculate the rise in pressure near the valve due to instantaneous closure of the valve.
A. 2145 kPa
B. 3254 kPa
C. 2443 kPa
D. 2864 kPa
Solution:
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The solid steel ball shown is submerged between the interface of two liquids. The ball has a diameter of 225mm and specific gravity of 7.4.
1. Determine the weight of the ball in Newtons.
A. 485
B. 433
C. 402
D. 387
2. Determine the buoyant force acting on the ball in Newtons.
A. 44
B. 87
C. 79
D. 35
3. Determine the tension in the rope in Newtons.
A. 354
B. 398
C. 315
D. 371
Solution:
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The tank shown is 3m wide into the paper. Neglect atmospheric pressure. Unit weight of water is 9.79 kN.m3.
1. Determine the nearest value to the vertical component of the total hydrostatic force on the quarter-circle panel AB, in kilo Newton.
A. 1485
B. 1365
C. 1658
D. 1505
2. Determine the nearest value to the resultant hydrostatic force acting on the quarter-circle panel AB, in kilo Newton.
A. 1164
B. 955
C. 1234
D. 1321
3. Calculate the nearest value to the angle that the resultant hydrostatic force makes with the horizontal, in degrees.
A. 39.7
B. 56.3
C. 48.1
D. 50.6
Solution:
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Water flow at the rate of 1.2 m3/s at a depth of 1.5m in a 10-m wide irrigation canal. Assume uniform flow and use n = 0.035.
1. Calculate the nearest value to the specific energy in Joule/Newton.
A. 1.5124
B. 1.5087
C. 1.5003
D. 1.5024
2. Determine the slope of the channel bed in meter per kilometer.
A. 0.0064785
B. 0.000064785
C. 0.0000064785
D. 0.064785
3. Determine the boundary shearing stress at the walls in Pa.
A. 0.00733
B. 0.0733
C. 0.0007333
D. 0.733
Solution:
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The following data were obtained from a tri-axial test on a cohesive soil:
Maximum shearing stress at failure plane = 65 kPa
Angle of friction = 28°
Cohesion = 31 kPa
1. Determine the plunger (deviator) stress in kPa.
A. 196.32
B. 214.57
C. 187.63
D. 147.23
2. Determine the minimum normal stress (confining pressure), in kPa.
A. 32.14
B. 18.54
C. 24.89
D. 85.42
3. Determine the normal stress on the plane of maximum shear, in kPa.
A. 98.51
B. 59.36
C. 68.47
D. 85.42
Solution:
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