Miscellaneous Problems2

MISCELLANEOUS PROBLEMS 

Soil Bearing Capacity For Shallow Foundations

Situation 1: A long wall footing that is 2 m wide is situated on stiff, saturated clay. The depth of the footing is 1 m. The clay has a unit weight of 18.5 kN/m3 and an undrained shear strength of 110 kPa. Loading is applied rapidly enough that undrained conditions prevail (φ = 0). Use Terzaghi bearing capacity factors and the following bearing capacity formula.

The shape and depth factors are

(

)

(

)

and are embedded of 2 m in a stiff clay (c = 90 kPa, φ = 28°, γ = 17.5 kN/m3). Use α = 1 for soft clay and α = 0.50 for stiff clay. Nc = 9. 7. Which of the following most nearly gives the capacity of the pile group based on single pile failure mode? a. 3432.24 kN c. 3743.52 kN b. 3646.98 kN d. 3826.17 kN 8. Which of the following most nearly gives the capacity of the pile group based on block failure mode? a. 9150.40 kN c. 10167.49 kN b. 8732.91 kN d. 9733.10 kN 9. Which of the following most nearly gives the center-to-center spacing of the piles for an efficiency factor of 1? a. 0.72 m c. 0.61 m b. 0.55 m d. 0.68 m Situation 4: A 0.30 m diameter prestressed concrete pile has been driven 6 m into a dense sand deposit. The soil-pile friction angle is 25°. The unit weight of the prestressed concrete pile is 25 kN/m 3, and the unit weight of the sand is 20 kN/m 3. Assume that the critical depth is 20 times the pile diameter of the pile, and that the horizontal earth pressure coefficient for tension is 1.1. 10.

1.

Which of the following most nearly gives the surcharge on the soil? a. 5.68 kPa c. 8.70 kPa b. 4.80 kPa d. 7.80 kPa Which of the following most nearly gives the ultimate bearing capacity of the soil? a. 656.54 kPa c. 456.67 kPa b. 765.28 kPa d. 698.40 kPa Which of the following most nearly gives the ultimate bearing capacity of the soil per meter length of footing? a. 300 kN/m c. 1000 kN/m b. 600 kN/m d. 1400 kN/m

2.

3.



Pile Foundations

Situation 2: A rigid foundation is supported by friction piles in clay as shown in the following plan and elevation views. The total load on piles reduced by the displaced soil weight, 2000 kN.

Which of the following most nearly gives the weight of the pile? a. 11.20 kN c. 15.10 kN b. 10.60 kN d. 9.87 kN Which of the following most nearly gives the skin friction of the pile described? a. 174.0 kN c. 134.0 kN b. 124.0 kN d. 144.0 kN Which of the following most nearly gives the ultimate pullout load capacity? a. 134.6 kN c. 174.6 kN b. 124.6 kN d. 184.6 kN

11.

12.

Situation 5: A 10 m long precast concrete pile is installed into homogenous sand. The pile cross section is 254 mm x 254 mm. The unit weight of the sand is 18.8 kN/m3. The internal friction angle of the sand is 35°. Consider the critical depth as 15 times the width of the pile. The earth pressure coefficient is 1.6 and the soil-pile friction angle is 0.6φ. 13.

Which of the following most nearly gives the effective vertical pressure at the critical depth? a. 41.70 kPa c. 33.26 kPa b. 71.60 kPa d. 88.11 kPa Which of the following most nearly gives the skin friction capacity along the pile from depth 0 to the critical depth? a. 85.1 kN c. 45.1 kN b. 65.1 kN d. 75.1 kN Which of the following most nearly gives the frictional resistance of the pile in the sand? a. 225.11 kN c. 233.21 kN b. 321.11 kN d. 361.82 kN

14.

15.

17.

 Clay γ=19 kN/m3 eo=0.75 Cc=0.24 w=28%

12.0 m Layer 1

Braced Excavation

Situation 6: A braced cut in sand 7 m deep is shown in figure. In the plan, the struts are placed at spacing 2 m center-to-center. Use Peck’s empirical pressure diagram. 5m

3

Clay γ = 18 kN/m , eo = 1.03, Cc = 0.32, w = 45% 3

Clay γ = 20 kN/m , eo = 0.88 Cc = 0.21 w = 20%

Layer 2

1m

Layer 3

2m

A

B

4.

5.

6.

Which of the following most nearly gives the effective pressure at the midheight clay layer 2? a. 123.67 kPa c. 184.3 kPa b. 119.13 kPa d. 155.1 kPa Which of the following most nearly gives the change in pressure at the midheight of layer 2? a. 22.6 kPa c. 19.1 kPa b. 18.0 kPa d. 12.7 kPa Which of the following most nearly gives the settlement of layer 2? a. 5 mm c. 27 mm b. 35 mm d. 17 mm

Situation 3: A pile group consisting 9 piles, each 0.40 m in diameter, is rranged in a 3 x 3 matrix at a spacing of 1.20 m. The piles penetrate a soft clay (c = 20 kPa, φ = 30°, γ = 17 kN/m3) of thickness 8 m

2m

Sand φ = 30° γ = 17 kN/m3

C 2m

16.

17.

18.

Which of the following most nearly gives the load on strut A? a. 116.01 kN c. 126.55 kN b. 101.42 kN d. 89.20 kN Which of the following most nearly gives the load on strut B? a. 66.95 kN c. 49.20 kN b. 56.30 kN d. 38.67 kN Which of the following most nearly gives the load on strut C? a. 180.90 kN c. 69.20 kN b. 206.24 kN d. 126.85 kN

Situation 7: Figure gives the section of a long braced cut. The sides are supported by steel sheet pile walls with struts and wales. The soil excavated at the site is stiff clay with the following properties c = 800 psf, φ = 0°, γ = 115 pcf. The struts are placed 12 ft apart center-to-center horizontally.

25.

Which of the following most nearly gives the coefficient of active pressure of the soil? a. 0.341 c. 0.248 b. 0.348 d. 0.268 Which of the following most nearly gives the active force per unit length of the wall? a. 50.1 kN/m c. 45.5 kN/m b. 25.4 kN/m d. 65.1 kN/m Which of the following most nearly gives the active force for 15-m width wall? a. 680 kN c. 970 kN b. 380 kN d. 750 kN

26.

27.



Stability of Earth Retaining Structures: Rankine’s Theory of Active Pressure

Situation 10:

19.

A retaining wall is shown.

Which of the following most nearly gives the load on strut C? a. 46.88 kips c. 55.87 kips b. 90.25 kips d. 62.92 kips Which of the following most nearly gives the load on strut B? a. 56.67 kips c. 77.89 kips b. 92.17 kips d. 68.35 kips Which of the following most nearly gives the maximum moment of the sheet pile section? a. 2875 lb-ft/ft c. 4322 lb-ft/ft b. 4699 lb-ft/ft d. 5523 lb-ft/ft

20.

21.

Situation 8: A braced excavation in soft, normally consolidated clay is shown in the figure. The struts are spaced at 1 m center-to-center. 28.

Which of the following most nearly gives the active force of the soil? a. 35 kN/m c. 45 kN/m b. 76 kN/m d. 67 kN/m Which of the following most nearly gives the overturning moment per unit length of the wall? a. 126.7 kNm/m c. 156.7 kNm/m b. 211.3 kNm/m d. 201.56 kNm/m Which of the following most nearly gives the factor of safety against overturning? a. 2.1 c. 1.2 b. 1.9 d. 2.6

4m 1m

29.

A 2m B 2m

Clay c = 24 kPa γ = 20 kN/m3

30.

C 1m



Slope Stability of Finite Slopes

Situation 11: 22.

A slope with the soil properties given is shown.

Which of the following most nearly gives the load on strut A? a. 146.98 kN c. 137.84 kN b. 130.15 kN d. 121.44 kN Which of the following most nearly gives the load on strut B? a. 161.45 kN c. 150.68 kN b. 182.13 kN d. 177.22 kN Which of the following most nearly gives load on strut C? a. 219.66 kN c. 201.72 kN b. 236.30 kN d. 246.50 kN

23.

24.



Stability of Earth Retaining Structures: Coulomb’s Theory of Active Pressure

Situation 9: properties shown.

A gravity retaining wall is holding soil backfill with the

31.

Which of the following most nearly gives the depth factor of the slope? a. 0.67 c. 0.50 b. 0.75 d. 0.33

32.

Which of the following most nearly gives the stability number of the slope given using Taylor chart? a. 5.5 c. 8.4 b. 7.1 d. 9.1 Which of the following most nearly gives the cohesive factor of safety of the stability? a. 2.55 c. 2.10 b. 2.67 d. 2.41

33.



If H = 8 m and β = 20°, which of the following most nearly gives the factor of safety against sliding on the rock surface? a. 1.395 c. 1.524 b. 1.472 d. 1.657

43.

Slope Stability of Finite Slopes With Plane Failure Surface

γ = 18.639 kN/m3

Situation 12: A cut is to be made in a soil having γ = 105 pcf, c = 600 psf, and φ = 15°. The side of the cut slope will make an angle of 45° with the horizontal. Use a factor of safety 3. 34.

Which of the following most nearly gives the value of the critical angle along which the most probable failure will occur? a. 20.35° c. 30.64° b. 25.05° d. 35.78° Which of the following most nearly gives the maximum safe depth of the cut? a. 15.42 ft c. 20.19 ft b. 27.39 ft d. 23.05 ft Which of the following most nearly gives the developed shear stress along the failure plane? a. 247.28 psf c. 205.43 psf b. 220.39 psf d. 192.60 psf

35.

36.

Situation 13: A cut is to be made in a soil having γ = 114 pcf, c = 630 psf, and φ = 20°. The side of the cut slope will make an angle of 40° with the horizontal. Use a factor of safety 1.25.

H β

If β = 30°, which of the following most nearly gives the critical height? a. 11.60 m c. 10.40 m b. 8.47 m d. 13.41 m If H = 6 m, which of the following most nearly gives the maximum angle β so that the slope is stable? a. 35.3° c. 37.5° b. 32.6° d. 29.8°

44.

45.



Which of the following most nearly gives the critical height of embankment? a. 111 ft c. 321 ft b. 221 ft d. 156 ft Which of the following most nearly gives the modified angle of friction? a. 21.76° c. 32.10° b. 19.67° d. 16.23° Which of the following most nearly gives the allowable height of the embankment? a. 128.70 ft c. 155.10 ft b. 133.40 ft d. 167.90 ft

38.

39.



Slope Stability of Infinite Slopes With Seepage

Situation 16: In the figure, there is seepage through the soil and the ground water table coincides with the ground surface. If H = 8 m and β = 20°, which of the following most nearly gives the developed normal stress on the rock surface? a. 120.19 kPa c. 157.32 kPa b. 94.45 kPa d. 131.67 kPa Which of the following most nearly gives the factor of safety against sliding on the rock surface? a. 1.387 c. 0.982 b. 1.150 d. 1.216 Which of the following most nearly gives the developed shear stress on the rock surface? a. 55.47 kPa c. 74.03 kPa b. 47.92 kPa d. 62.51 kPa

46. 37.

Rock Surface

47.

48.

Slope Stability of Finite Slopes With Circular Failure Surface γ = 18.639 kN/m3 c = 18 kPa φ = 25°

Situation 14: Figure shows the details of an embankment made of cohesive soil with φ = 0 and c = 30kN/m2. The unit weight of the soil is 18.9 kN/m3. The weight of the sliding mass is 360 kN acting at an eccentricity of 5.0 m from the centre of rotation. Assume that no tension crack develops. The central angle is 70°.

H

Rock Surface β



Bearing Capacity and Settlement From SPT

Situation 17: A mat foundation measuring 100 ft by 32 ft supports a total load of 5200 tons. Beneath the foundation is sand with a density of 120 pcf. The average standard penetration number from Standard Penetration Test was N = 18. The base of the foundation is located 8 ft below the ground level. The allowable settlement is 2 inches. 40.

Which of the following most nearly gives the sliding moment? a. 1700 kNm c. 1600 kNm b. 1800 kNm d. 1900 kNm Which of the following most nearly gives the restoring moment? a. 2330 kNm c. 2610 kNm b. 3430 kNm d. 2970 kNm Which of the following most nearly gives the factor of safety against sliding? a. 1.65 c. 1.85 b. 1.77 d. 1.90

41.

42.



Slope Stability of Infinite Slopes Without Seepage

Situation 15: An infinite slope is shown in the figure. The shear strength parameters at the interface of soil and rock are c = 18 kPa and φ = 25°.

49.

50.

51.

Which of the following most nearly gives the effective overburden pressure at the base of the foundation? a. 0.71 tons/ft2 c. 0.96 tons/ft2 b. 1.42 tons/ft2 d. 0.48 tons/ft2 Which of the following most nearly gives the allowable bearing capacity for the foundation if the correction factor for overburden pressure is cN = 0.62? a. 2.43 tons/ft2 c. 1.86 tons/ft2 b. 2.12 tons/ft2 d. 2.90 tons/ft2 Which of the following most nearly gives factor of safety against bearing capacity failure? a. 2.27 c. 2.56 b. 2.12 d. 2.75 Prepared by: Engr. Jesus Ray M. Mansayon