2022

Soil Mechanics I and Exercises

2022/11/29 (Tue.) 13:15-14:15

Midterm Exam

Research Bldg. No.9 W2

Attention:
The exam consists of two questions for which you are provided with two answer sheets. Write down yourname and ID number on every answer sheet. Use one answer sheet per question and answer them insequence, starting from [Question 1]. If the front page of an answer sheet is insufficient to complete youranswer, use the back page of the same answer sheet after clearly indicating your intent.

Scores for each question are equally weighted.

In addition to personal writing instruments, non-programmable calculators are permitted. However,programmable calculators and calculator functions of mobile phones are prohibited. Any attempt 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] Using the specific gravity of soil particle Gs = 2.69 and the water density ρw = 1.00 g/cm3, answer
to the following questions. Graphics may be used if necessary.
(1) Particle size distribution curve of the soil is reported in Figure 1. Describe the test apparatuses and themethods used to obtain particle size distribution of soils.

Figure 1 Particle size distribution curve (Edosaki sand)(2) According to Fig. 1, find the average particle size D50 and the uniformity coefficient Uc.
(3) A soil compaction test was conducted for the soil and results are shown below. Draw the compaction curvefor this soil.
Water content w (%)
3

Total density ρt (g/cm )

10.2

12.6

14.3

15.4

17.0

19.8

21.5

1.741.80

1.84

1.90

1.89

1.87

1.84

- 1 -(4) From the definition of the zero-air void curve, express the relationship among the specific gravity of soil
particle Gs, the dry density of soil ρd, the water density ρw, and the water content w. Also, add the zero-airvoid line along with the compaction curve obtained in (3).
(5) Determine the optimum water content and the maximum dry density of the soil from the compaction curve
obtained in (3).
(6) The volumetric water content θ is defined as the ratio of the volume of water to the total volume (Vw/V). In
regard to (5), find θ of this soil under the optimum water content.
(7) This soil is compacted with water content w = 10.0% to achieve the degree of compaction of 90.0%.
Calculate the total density ρt and the degree of saturation Sr after compaction.

[Question 2]
The constant head permeability test on a sand column has been
carried out as shown in the right figure. The cross-sectional areaof the sand column is 1.00×10 [cm2] and Point A is located at adistance of x [m] from the reference plane. Answer thefollowing questions regarding the water flow in the sandcolumn. Assume the sand column is saturated and the waterflow is governed by the Darcy’s law with steady state condition
established for all cases below. Head loss due to friction andshape of pipes can be ignored. The reference plane is shown in
the figure. The unit weight of water is 9.81 [kN/m3] and thegravitational acceleration is 9.81 [m/s2].
First, assume that both sand layers are composed of the same
sand (specific gravity, Gs, is 2.60, void ratio, e, is 0.70 andhydraulic conductivity (coefficient of permeability), kI is 1.0×10-5 [m/s]).
(1) Draw a distribution diagram of the elevation head, pressure head and piezometric head (total head) in the sandlayer. For each hydraulic head, mark its value at the top and bottom of the sand column in the diagram.
(2) Show the pressure head (2 ≤ x ≤ 5), u, in the sand layer as a function of x.
(3) Determine the elevation head, pressure head, and piezometric head at the point A where x = 4.
(4) Determine the hydraulic gradient and flow rate per unit time.
(5) The total stress, , in the sand layer is  = − t x + 5 t +  w (2 ≤ x ≤ 5). Determine the unit weight of the saturated
sand,t, and find the vertical effective stress, ', at the bottom of the sand layer (x = 2).
(6) The drainage port of the upstream tank located 8 m above the reference plane is closed and the water level isgradually raised. Determine the water level (measured from the reference plane) when the sand layer becomesquicksand.
- 2 -Next, the drainage port of the upstream tank is re-opened and fixed at 8 m from the reference plane. Assume thesandy column is composed of two sand layers as shown in the figure. The sand in layer I has specific gravity, Gs, of2.60, void ratio, e, of 0.70 and hydraulic conductivity (coefficient of permeability), kI, of 1.0×10-5 [m/s]. The sandin layer II has specific gravity, Gs, of 2.60, void ratio, e, of 0.80 and hydraulic conductivity (coefficient ofpermeability), kII, of 2.0×10-5 [m/s].
(7) Show the piezometric head, h, of sand layer I (3 ≤ x ≤ 5) as a function of x.
(8) Show the pressure head, u, of sand layer II (2 ≤ x ≤ 3) as a function of x.

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