2016
Soil Mechanics I and Exercises Final Exam
2017/1/31 (Tue.) 13:00-15:00 W2 Lecture roomAttention: The exam consists of four questions for which you are provided with four answer sheets.
Write down your name and ID number on every answer sheet. Use one answer sheet perquestion and answer them in sequence, starting from [Question 1]. If the space provided inany answer sheet is insufficient, use the back of the page after clearly mentioning so (forexample, “continues on the back”).
In addition to personal writing instruments, non-programmable calculators are permitted, butprogrammable calculators and all types of mobile phones are prohibited. Any attempts atcheating on the exam will result in failed credit of the course and serious penalties.



Wherever necessary, specify the units in your answers.

[Question 1] Answer the following questions(1) In order to understand the physical properties of a soil extracted from a borrow pit used to build anembankment, a sample of 0.5 m3 was taken and its weight was found to be 8.9 kN. From this soil, asample of 4.0×10-3 kN was taken, oven-dried, and reweighted. The oven-dried weight was 3.48×10-3
kN. Based on a test conducted separately, it was found that the unit weight of soil particles was γs =26.2 kN/m3. Answer the following questions assuming unit weight of water γw = 9.8 kN/m3.
1) Find the water content w (%), the total unit weight γt (kN/m3), and the dry unit weight γd (kN/m3)of this soil
2) Find the void ratio e of this soil
3) Find the degree of saturation Sr (%) of this soil4) This soil is compacted to obtain a dry unit weight of γd = 16.7 kN/m3 for the construction of the30,000 m3 embankment. Determine the weight and the volume of soil needed to be excavatedfrom the borrow pit.
(2) Explain briefly the following terms
1) Relative density2) Optimum water content

[Question 2] Answer the following questions(1) Explain the following terms
1) Total water head
2) Darcy’s law(2) Derive the equation used to calculate the equivalent vertical hydraulic conductivity coefficient kv forthe stratified ground shown in Figure 2.1. Use the hydraulic conductivity coefficients of each layer (k1to k3), as well as their thickness (H1 to H3) in your answer.

Figure 2.1(3) Answer the following questions
1) Figure 2.2 shows a constant head hydraulic conductivity test with water flowing in the upward
direction through the soil column. Plot the vertical distribution of total head, pressure head, andelevation head in the right side of the system, from elevation 0 to 3.6 m. The datum of the system
is located at 0 m.
2) Calculate the vertical effective stress ߪ௩ᇱ at the bottom of the sand layer. Assume that the unit
weight of water is 9.8 kN/m3, and that the physical properties of the sand are those given in
Figure 2.2, where k is the hydraulic conductivity of the sand layer, Gs is the specific gravity of thesoil particles, and e is the void ratio of the soil.
3) Calculate the height of the water table on the left side of the system that would cause the sandcolumn to reach quicksand state.

Figure 2.2

[Question 3] The construction of an embankment represents a surcharge load of q = 90 kN/m2over a wide area, as shown in Figure 3.1. The compression index of the clay layer is Cc = 0.80,
its initial void ratio is e0 = 2.2, and its consolidation index is cv = 10 m2/year. Assume, for thisproblem, that the clay layer is normally consolidated and that its consolidation settlement can becalculated by using the compressive stress at mid-depth (i.e., z = 7 m) as representative for thewhole layer. Similarly, assume that the water pressure distribution in the sand layer does notchange due to the surcharge loading and remains at hydrostatic pressure. If necessary, use Table
3.1, which shows the relationship between the average degree of consolidation U and the time
factor Tv, and Figure 3.2, which represents how dimensionless excess pore water pressure
distribution changes for different values of time factor Tv, at different dimensionless depths
Z = z/h. For this problem, the unit weight of water is γw = 9.8 kN/m3.
(1)

Calculate the total consolidation settlement expected for the clay layer.

(2)

Calculate the consolidation settlement expected for the clay layer after six months.

(3)

Calculate, at mid-depth of the clay later (z = 7 m), the values of pore water pressure(sum of the hydrostatic pressure and the excess pore water pressure) immediately after
the application of the surcharge load, six months later, and at the end of theconsolidation process.
Dimensionless excess pore water pressure u/u0 (= u/q)Time factor

Dimensionless depth Z = z/H

SandClay

Sand

Figure 3.1 Representation of the ground layers
including their values of saturated unit weight(Initial)

Figure 3.2 Distribution of dimensionlessexcess pore water pressure

Table 3.1 Relationship between the average degree of consolidation U and the time factor Tv
Tv

0.05

0.10

0.15

0.20

0.30

0.40

0.50

U

0.252

0.357

0.437

0.504

0.613

0.698

0.764

Tv

0.60

0.70

0.80

0.848

0.90

1.00

U

0.816

0.856

0.887

0.900

0.912

0.931

[Question 4] Answer the following questions(1)

Consider the principal state of stress of a given point in the ground shown in the figure
below. By using Mohr’s stress circle, obtain the normal stress and shear stress acting on
the A-A’ plane that makes an angle 60° anticlockwise from the horizontal plane.

= 240 kN/m2

A= 360 kN/m2

60°A’(2)

Let the cohesion c be zero and the friction angle be 30° for this ground. During theexcavation work being carried out near this point, σy remains constant while σxdecreases until failure occurs. Predict the value of σx at failure using Mohr’s stress circle
and the Mohr-Coulomb failure criterion.

(3)

In regard to (2), find the normal stress and shear stress on the failure plane. Also,
determine the orientation of the failure plane.

(4)

During the consolidated undrained triaxial compression test of a normally consolidated
clay, the value of the positive excess pore water pressure generally rises. Explain thereason from the concept of dilatancy. Herein, the pressure is taken as positive forcompression.