The field unit weight of the soil sample is 1960 kg/m3 and the unit weight of the soil particle is 2700 kg/m3. If the emax = 0.69 and emin = 0.44.
1) Compute the dry unit weight in kN/m3 if the water content is 11%.
2) Compute the void ratio of the soil sample.
3) Compute the relative density of the soil sample.
Solution:
A 0.30m. x 0.30m concrete pile 22m. long is driven in a clayey soil having an unconfined compressive strength of 110 kN/m2. The unit weight of clayey soil is 18 kN/m3. Frictional constant is 0.76 due to skin friction. Assume a factor of safety equal to 2.0 and a bearing capacity factor Nc = 9.
1) Compute the capacity of pile due to skin friction only.
2) Compute the end bearing capacity of pile.
3) Compute the design capacity of the concrete pile.
Solution:
A cohesive soil specimen has a shearing resistance equal to 28° and cohesion of 30 kPa. If the maximum shearing stress of the soil sample is equal to 70 kPa.
1) Compute the lateral pressure in the cell for a failure to occur.
2) Compute the maximum principal stress to cause failure.
3) Compute the normal stress at the point of maximum shear.
Solution:
The laboratory apparatus shown in the figure maintains a constant head in both the upper and lower reservoirs. The soil sample is a silty sand with a hydraulic conductivity K = 5 x 10-3 cm/sec. and a moisture content of 18.5%. Specific gravity of soil sample is 2.70.
1) Compute the seepage velocity in cm/sec.
2) Determine the time required for the plug of colored water to pass through the soil. Assume also that the colored water has the same unit weight and viscosity as plain water.
3) Compute the discharge of water.
Solution:
A pile group consist of 12 piles with a diameter of 0.30 m. and a pile length of 12m. is shown in the figure. The piles are spaced in a 3 pile by 4 pile rectangular configuration with a pile spacing of 0.60m. center to center of piles. The piles are driven into clay that has the given characteristics.
1) Determine the allowable load on the pile group considering that the piles act individually. Use bearing capacity factor of Nc = 9 an F.S. = 3.
2) Determine the allowable load on the piles considering group action.
3) What would be the minimum pile spacing to achieve 100% efficiency?
Solution:
The following data shows the results of the Liquid Limit, and Plastic Limit test.
1) Liquid Limit
| TEST NO. | 1 | 2 | 3 | 4 |
|
No. of Blows |
35 | 21 | 16 | 11 |
|
Wt. of Wet Soil + Container |
22.46g | 21.33g | 21.29g | 26.12g |
|
Wt. of dry Soil + Container |
19.44g | 18.75g | 18.78g | 22.10g |
|
Wt. of Container |
12.76g | 13.06g | 13.26g | 13.27g |
2) Plastic Limit
| TEST NO. | 1 | 2 |
|
Wt. of Wet Soil + Container |
22.10g | 21.77g |
|
Wt. of dry Soil + Container |
20.42g | 22.10g |
|
Wt. of Container |
13.07g | 13.18g |
3) Natural water content
| TEST NO. | 1 | 2 |
|
Wt. of Wet Soil + Container |
17.94g | 17.39g |
|
Wt. of dry Soil + Container |
14.84g | 14.36g |
|
Wt. of Container |
7.84g | 7.5g |
1) Compute the liquid limit.
2) Compute the plastic limit.
3) Compute the liquidity index.
Solution:
1) Liquid Limit
| TEST NO. | 1 | 2 | 3 | 4 |
|
No. of Blows |
35 | 21 | 16 | 11 |
|
Wt. of Wet Soil + Container |
22.46g | 21.33g | 21.29g | 26.12g |
|
Wt. of dry Soil + Container |
19.44g | 18.75g | 18.78g | 22.10g |
|
Wt. of Container |
12.76g | 13.06g | 13.26g | 13.27g |
| TEST NO. | Wt. of H2O | Wt. of Dry Soil | Water Content | No. of Blows |
| 1 | 22.46-19.44=3.02 | 19.44-12.76=6.68 | 3.02/6.68 (100)=45.21 | 35 |
| 2 | 21.33-18.75=2.58 | 18.75-13.06=5.69 | 258/5.69 (100)=45.34 | 21 |
| 3 | 21.29-18.78=2.51 | 18.78-13.26=5.52 | 2.51/5.52 (100)=45.47 | 16 |
| 4 | 26.12-22.10=4.02 | 22.10-13.27=8.83 | 4.02/8.83 (100)=45.53 | 11 |
Liquid limit = 45.30% from table
2) Plastic Limit
| TEST NO. | 1 | 2 |
|
Wt. of Wet Soil + Container |
22.10g | 21.77g |
|
Wt. of dry Soil + Container |
20.42g | 22.10g |
|
Wt. of Container |
13.07g | 13.18g |
| TEST NO. | Wt. of H2O | Wt. of Dry Soil | Water Content |
| 1 | 22.10-20.42=1.68 | 20.42-13.07=7.35 | 1.68/7.35 (100) = 22.86% |
| 2 | 21.33-18.75=2.58 | 18.75-13.06=5.69 | 1.58/7.01 (100)=22.54% |
Average water content = (22.86+22.54) /2
Average water content = 22.7%
Plastic limit = 22.7%
3) Liquidity index
| TEST NO. | 1 | 2 |
|
Wt. of Wet Soil + Container |
17.94g | 17.39g |
|
Wt. of dry Soil + Container |
14.84g | 14.36g |
|
Wt. of Container |
7.84g | 7.5g |
| TEST NO. | Wt. of H2O | Wt. of Dry Soil | Water Content |
| 1 | 17.94-14.84=3.1 | 14.84-7.84=7.0 | 31/7.0 (100)=44.29% |
| 2 | 17.39-14.36=3.03 | 14.36-7.5=6.86 | 3.03/6.86 (100)=44.17% |
Average water content = (44.29 + 44.17)/2
Average water content = 44.23%
Natural water content = 44.23%
Liquidity index = (ω – PL)/LL – PL
L.I. = (44.23 – 22.7)/45.30 – 22.7
L.I. = 0.952
From the given data, shows a sieve analysis of soil samples A,B and C.
|
SOIL SAMPLE |
||||
| SIEVE NO. | DIAM. (MM) | A | B | C |
| #4 | 4.760 | 100 | 100 | 100 |
| #8 | 2.380 | 97 | 90 | 100 |
| #10 | 2.000 | 92 | 77 | 78 |
| #20 | 0.840 | 87 | 59 | 92 |
| #40 | 0.420 | 53 | 51 | 84 |
| #60 | 0.250 | 42 | 42 | 79 |
| #100 | 0.149 | 26 | 35 | 70 |
| #200 | 0.074 | 17 | 33 | 63 |
| Characteristics of -40 fraction | ||||
| LL | 35 | 46 | 47 | |
| PL | 20 | 29 | 24 | |
1) Classify soil A using AASHTO Method.
2) Classify soil B using AASHTO Method.
3) Classify soil C using AASHTO Method.
Solution:
A vat holding paint (sp.gr. = 0.80) is 8m. long and 4m. deep and has a trapezoidal cross section 3m. wide at the bottom and 5m. wide at the top.
1) Compute the weight of the paint.
2) Compute the force on the bottom of the vat.
3) Compute the force on the trapezoidal end panel.
Solution:
Two open cylindrical tanks are connected by an orifice having a cross sectional area of 0.004 m2. Tank A is 8m. in diam. and its water level is 10m. above that of B whose diameter is 5m. If the coeff. Of discharge is 0.60.
1) Find the discharge flowing in the orifice.
2) How long will it be before the water surfaces are at the same level?
3) How soon after will the water surfaces be 4m. apart?
Solution:
A reservoir of glycerine (glyc) has a mass of 1200 kg and a volume of 0.952 m3.
1) Compute the glycerine weight in kN.
2) Compute the mass density.
3) Compute the specific weight.
Solution:
A retaining wall 6m. high is supporting a horizontal backfill having a dry unit weight of 1600 kg/m3. The cohesionless soil has an angle of friction of 32° and a void ratio of 0.68.
1) Compute the Rankine active force on the wall.
2) Compute the Rankine active force on the wall if water logging occurs at a depth of 3.5m. from the ground surface.
3) Compute the location of the resultant active force from the bottom.
Solution:
Two footings rest in a layer of sand 2.7 m. thick. The bottom of the footing are 0.90m. below the ground surface. Beneath the sand layer is a 1.8m. clay layer. Beneath the clay layer is hard pan. The water table is at a depth of 1.8m. below the ground surface. Void ration of clay is 1.03.
1) Compute the stress increase at the center of clay layer assume that the pressure beneath the footing is spread at an angle of 2 vertical to 1 horizontal.
2) Determine the size of footing B so that the settlement in the clay layer is the same beneath footings A and B. Footing A is 1.5m. square.
3) Determine the settlement beneath footing A.
Solution:
A cohesionless soil has a friction angle of 30° and deviator stress of failure of 400 kPa.
1) Find the angle that the failure plane makes with the major principal plane.
2) Find the confining pressure.
3) Find shear stress at the point on the failure plane.
Solution:
A 0.36m. square prestressed concrete pile is to be driven in a clayey soil as shown in the figure. The design capacity of the pie is 360 kN, with a factor of safety of 2.
1) Compute the end bearing capacity of the pile.
2) Compute the skin friction expected to develop along the shaft of the pile.
3) Compute the length of the pile if α = 0.76.
Solution:
A 7m. deep braced cut in sand is shown. In the plan, the struts are placed at a spacing of 2m. center to center. Using Peck’s empirical pressure diagram, compute the following:
1) Strut load at level A
2) Strut load at level C
3) Strut load at level B
Solution:
A reservoir with a 3400 m2 area is underlain by layers of stratified soils as depicted in the figure.
1) Compute the average coefficient of permeability in m/hour.
2) Compute the interstitial velocity of water moving through the soil if it has a void ratio of 0.60. Express in cm/sec.
3) Compute the water loss from the reservoir in one year in cu.m. assuming that the pore pressure at the bottom sand layer is zero.
Solution:
Two reservoirs A and B have elevations of 250 m and 100m respectively. It is connected by a pipe having a diameter of 25 mm Ø and a length of 100m. A turbine is installed at point in between reservoirs A and B. If C = 120, compute the following if the discharge flowing in the pipe is 150 liters/sec.
1) Head loss of pipe due to friction.
2) The head extracted by the turbine.
3) The power generated by the turbine.
Solution:
A square plate having one of its side equal to 3.5 m. is immerse in a water surface in a vertical position such that the two edges of the square would be horizontal in order that the center of pressure shall be 12cm. from the center of gravity.
1) How far below the water surface should the upper plate be submerged?
2) What is the distance of the center of pressure from the water surface?
3) Determine the hydrostatic force acting on the plate at this position.
Solution:
A discharge of 750 liters/sec. flows through a pipe having a diameter of 400 mm Ø. Length of 65m. long, compute the head loss of the pipeline using:
1) Mannings Equation with n=0.013
2) Darcy Weishback formula with f = 0.012.
3) Hazen Williams Formula with C = 100.
Solution:
A stone weighs 468 N in air. When submerged in water if weighs 298N.
1) Find the volume of the stone.
2) Find the specific weight of the stone.
3) Find the specific gravity of the stone
Solution:
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