2020

Soil Mechanics I and Exercises Mid Exam

2020/12/1 (Tue.) Test time 13:00-14:00, Submission time via PandA 14:15
Attention:
The exam consists of two questions. Separate answer sheet for each major question. Write your name andthe question number on all pages. You may answer a major question over multiple answer sheets but do
not answer multiple major questions on the same answer sheet.

Stop writing the answer at 14:00 and submit the answer sheet via PandA by 14:15.

Your submission will not be accepted after the deadline regardless of any reason. Give yourself ample
time to get through Panda for submitting the answer sheet.

If possible, combine all answer sheets in sequence and submit in a single file. When submitting multiple
files for multiple answer sheets, please order them and set the file names in a way that the question
number as well as the page number of answer sheet is understandable.

During the examination, you may consult the lecture materials and reference sources, but carefully
manage your exam time.

Answer sharing and copying is academic dishonest. If the similarities in answers are observed amongexaminees, an extra oral examination may be conducted later for individual investigation.

Wherever necessary, specify the units in your answers.

[Question 1]
1) Fill in the blanks in the following sentences with appropriate words for①to⑧.

Soil compaction is a process by which the soil density is increased by mixing and compacting of soil andwater for the purposes of①， ②， ③. Even if the same soil sample is compacted with the sameenergy, the dry density after compaction varies with the water content. The relationship between the watercontent and the dry density is referred to as “compaction curve”. The water content and the dry density
obtained at the peak position of the curve are called
compacted soil exhibits maximum
water content greater than

④.

and

⑤⑥

at water content less than④⑧

is an indicator for density control in embankment construction,④

which is defined as the ratio of dry density of compacted soil to⑤, respectively. In general, theand minimum⑦at a.

2) (2-1) Specify the range of particle size classified as “fine fraction”.
(2-2) Void ratio of the clay is generally larger than that of the sand. Concisely describe the particle shapeand the particulate structure of the clay, which are considered as possible causes of the large void ratioof clay.
(2-3) List two indices regarding the consistency limits and give a definition for each of which. Symbols
used in the definition formula should be explained (e.g., water content: w = mw/ms, mw: mass of water,
ms: mass of soil particles).

- 1 -3) An embankment with a volume of 20,000 m3 is planned to be constructed. A soil sample of a volume of
1,000 cm3 was taken at the excavation site, and its total mass was 1.60 kg. The soil was compacted toconstruct the embankment with a dry density ρd = 1.71 g/cm3. After the construction, the total density of theembankment was ρt = 2.00 g/cm3. Given the specific gravity of soil Gs = 2.70, the density of water ρw = 1.00
g/cm3, and the gravitational acceleration g = 9.81 m/s2, answer the following questions with three significantdigits.
(3-1) Find the total weight and the water content of the embankment.
(3-2) Find the total density and the dry density of the soil at the excavation site.
(3-3) Find the volume and the weight of the soil to be taken from the excavation site.
(3-4) Find the void ratio and the degree of saturation of the soil at the excavation site.
(3-5) Find the void ratio and the degree of saturation of the soil at the embankment.

[Question 2](1) The equipment for hydraulic conductivity test under constant head
condition consists of two tanks and the connection pipe as shown in thefigure. The water flows vertically down through the cylindrical specimen
whose length and diameter are l and d, respectively. Answer theADfollowing questions assuming that a steady state condition is establishedh1Cin this relatively slow one-dimensional flow for which Darcy’s law canh2

be applied. Moreover, energy loss due to friction and deformation in theBxlh3

tanks and the connection pipe can be ignored. When necessary, report

Datum

numeric answers with three significant digits.
(1-1) Describe the potential head, zA, and the pressure head, pA at point A.
(1-2) Describe the potential head, zB, and the pressure head, pB at point B.
(1-3) Describe the potential head, zC, and the pressure head, pC at point C.

(1-4) Discharge at point D per one hundred seconds is 5.10×101 cm3 when the diameter and the length of thesample are 5 cm and 10 cm, respectively, and the amounts of h1, h2 and h3 are 23, 18, 3 cm for eachlength. Find the hydraulic conductivity, k.
(1-5) Given the gravitational acceleration g = 9.81 m/s2, find theArea Avelocity head in regard to (1-4) and show that the pressure

Equipotential lineshead can be taken to the total head.
Area CArea B(2) The flow net as shown in the figure is described for an isotropic
ground with the hydraulic conductivity of k under the difference ofhead, H, in two-dimensional steady state condition. Answer theFlow channel
i+1yfollowing questions.
(2-1) The number of flow channels is Nf and the number of- 2 -x

Flow linesequipotential drops, which is separated by the potential curves, is Nd. Describe the total discharge perunit second, Q.
(2-2) In the flow net drawn for an isotropic ground, each element surrounded by the flow lines and thepotential lines should be a square. Explain the advantage of using curvilinear squares in the flow net.
(2-3) Let u, v and h(x, y) be the flow velocity in the x and y directions and the total head at any point. Applying
the velocity potential function (or the total head),  = -k･h(x, y)), and Darcy’s law, express u and v andderive the governing equation which is known as Laplace's equation for two-dimensional flow.

- 3 -