Soil Mechanics I and Exercises [Midterm Exam]
November 21, 2023 (Tue.) 13:15–14:15 @W2 Lecture RoomNotes:
The examination consists of two questions for which you are provided with two answer sheets andone graph.

Write down your name and student ID number on every sheet. Use one answer sheet per question
and answer them in sequence, starting from [Question 1]. If the front page of an answer sheet isinsufficient to complete your answer, continue your answer on the back side of the same sheet ofpaper, and be careful not to spread the answer to a single question across multiple sheets of paper.

In addition to personal writing instruments, use of non-programmable calculators and rulers arepermitted. However, programmable calculators and calculator functions of mobile phones areprohibited.

Wherever necessary, specify the units in your answers.

Any attempt at cheating on the exam will result in failed credit of the course and serious penalties.

- 1 -[Question 1]
1) Express each of the following indices using the parameters given inMass

VolumeFigure 1 and the gravitational acceleration g.

Air(1) Soil particle density
Water(2) Void ratio(3) Degree of saturation

Soil (particles)(4) Gravimetric water content(5) Wet unit weight

Figure 12) Answer the following questions.
(1) Soil A having a gravimetric water content of 25.0% and Soil B having that of 40.0% are mixed to obtain
Soil M having that of 30.0%. Find the mass of Soil B to be mixed for 100 g of Soil A.
(2) A mold with a volume of 100 cm3 was filled with Soil M to a wet density ρt of 1.70 g/cm3 while maintaining
a water content of 30.0%. Then, the specimen was saturated by water percolation. Find the volume of waterrequired for the saturation. Assume that the soil particle density ρs of both soils is 2.60 Mg/m3 (g/cm3) andthe density of water is 1.00 Mg/m3 (g/cm3).
(3) After (2), the specimen was compressed while maintaining saturation and allowing drainage to achieve thedry density ρd of 1.40 g/cm3. Find the amount of drainage during the compression.
3) Figure 2 shows the results of a sieve analysis conducted on Soil C. Answer
the following questions.
(1) Draw the particle size distribution curve for Soil C on a separate

Aperture
width ofeach sieve

Dry mass ofsoil remainedon each sieve

9.50 mm0g

4.75 mm

120 g

2.00 mm

240 g

0.850 mm

180 g(3) Soil D is obtained by mixing fractions of 0.425–2.00 mm of Soil C

0.425 mm160 g

only. The standard Proctor tests are conducted on Soil C and Soil

0.250 mm

120 g

D. Explain which soil would be expected to have the higher

0.106 mm

80 g

maximum dry density with a brief reason.

0.075 mm

40 gsheet.
(2) Based on the graph obtained in (1), determine the fines content Fc
and the coefficient of uniformity Uc of Soil C.

60 gFigure 2- 2 -[Question 2]
1) A constant head permeability test for a soil sample is shown in Fig. 3. The cross-sectional area, height andhydraulic conductivity of the soil sample are A, L, and k, respectively. The discharge velocity in the soil sample
is v. The difference in water level between the upstream and downstream sides is H.

Fig. 3. Constant head permeability test.
(1) Write the equation of Darcy’s law using the quantities shown in the figure.
(2) Express the flow rate, q (volume of water flow per unit time), through any horizontal cross section in thesoil sample, using the quantities shown in the figure.
(3) After time T, the total volume of water collected in the container on the right side is Q. Express the hydraulicconductivity of the soil sample, k, using the above quantities and the quantities shown in the figure.
2) A geo-engineering company invented a new “Dual-Sample Permeability Testing Device” as shown in Fig. 4. In
this device, two soil samples are placed at the left and right sides. A screen is placed at top and bottom of the soil
samples to retain the soil while allowing water to flow through. For Sample 1 on the left side, it has permeability,
cross-sectional area, and length of k1, A1, L1, respectively. For Sample 2 on the right side, the permeability, crosssectional area, and length are denoted by k2, A2, L2, respectively. For all questions below, use L1 = 50 cm, A1 =1,000 cm2, L2 = 40 cm, A2 = 1,000 cm2. The unit weight of water is 9.8 kN/m3. Assume the flow in the soil samples
is one-dimensional flow along the vertical direction.

Fig. 4. Setup of the dual-sample permeability test.
- 3 -(1) Two types of sand are used as soil samples and the saturated unit weights of the two sands are γ1sat = 18kN/m3 and γ2sat = 19 kN/m3, respectively. A constant head test has been conducted with H1 = 50 cm and H2= 25 cm. H1 and H2 are kept constant during the test and a steady state flow is maintained. The water levelin the tube, h, is also found to be constant during the test at h = 70 cm. The discharge flow rate throughSample 2 (denoted by q) is measured to be q = 1 cm3/sec. Point A and B in the figure are located at themiddle of Sample 1 and Sample 2, respectively. Answer the following questions.
1. Find the hydraulic conductivity of the two samples, k1 and k2.
2. Find the elevation head, pressure head, and piezometric head (total head) at Point A.
3. Find the elevation head, pressure head, and piezometric head (total head) at Point B.
4. Find the vertical total stress, σA, pore water pressure, uA, and vertical effective stress, 𝜎 , at Point A.
5. Find the vertical total stress, σB, pore water pressure, uB, and vertical effective stress, 𝜎 , at Point B.
(2) Briefly explain the condition of quicksand.
(3) For the same soil samples described above, if the water level above Sample 2 (i.e., H2) does not change but
the water level above Sample 1 (i.e., H1) is gradually raised, determine the value of H1 when the soil inSample 2 becomes quicksand.
(4) To confirm the performance of the device, another constant head test is conducted in which the same sandwas used for both samples (i.e., k1 = k2). The values of H1, and H2 remained constant as same as previously
stated (H1 = 50 cm, H2 = 25 cm). The only measured value in this test is h and the discharge flow rate q is
not measured. Find the measured value of h.

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