2012

Soil Mechanics I and Exercises

Midterm Examination

2012/11/20 (Tue) 13:00~14:00 Kyotsu 155・Kyotsu 1・Kyotsu 3・W2 Lecture room
Attention:●There are two questions and two answer sheets. Write down your name and ID number on bothof those answer sheets. Use one answer sheet for one question and answer in sequence from【Question 1】. If the front side of the answer sheet is not sufficient for answering that question,
mention that and use the back side of that answer sheet.

●Carrying any personal belongings is prohibited. For any mischievous act, you will not be entitledto get the credit of this subject.

●Wherever necessary, show the units in your answers.

【Question 1】Answer the following questions related to soil index properties.
(1)

Figure 1 shows the ground conditions at a site of concern. The density of water is w = 1,000 kg/m3 andgravitational acceleration is g = 9.8 m/s2.

Unsaturated layer
Depth (m)(water content, w =20%)

Saturated layer(water content, w = 50%)

AFig. 1 Ground conditions
1. A core of saturated soil sampled from soil layer below the water table (saturated layer) had thewater content, w = 50% and the wet bulk density, t=1,750 kg/m3. Find the void ratio (e) and thedensity of soil solids (s).
2. If the water content of the soil ground above the water table (unsaturated layer) was 20%, then findthe wet bulk density of the soil ground above the water table. Assume that there is no change in thevoid ratio and the density of soil solids throughout the depth of the soil ground. For theseparameters, use the values obtained in the previous question (1).
3. Find the total vertical stress, the pore water pressure and the effective vertical stress at the location
A shown in Fig. 1.

(2) What are the effects of the following factors on the soil compaction behavior (the optimum moisture content,
the maximum dry density)? Also, explain the reasons. If necessary, draw the figures.
1. Increment in the compaction energy.
2. Increment in the uniformity coefficient (soil having good grain size distribution curve).

【Question 2】Answer the following questions related to the permeability of soils.
(1)

The constant head permeability test under the condition of the difference in the total head, h=20cm isconducted as shown in Fig. 2. The length of the sand specimen is 20cm. ① Find the critical hydraulic

D=20cmhgradient, ic. ② Find the necessary difference in the total head, h for the occurrence of quicksand.

sand：Gs = 2.67
e = 0.72

Fig. 2(2)Consider the specimen consisting of two types of layers in parallel series, where two different soil layers
are connected in series and the independent single soil layer are filled in as shown in Fig. 3. The lateralboundary of the layer is assumed to be impermeable. The thickness of the individual layers in series on theleft-hand side is H1 and H2 with the width of L1. The thickness of the single layer on the right-hand side is
H1+H2 with the width of L2. The values of the coefficient of permeability of the corresponding layers are
assumed to be k1, k2 and k3 as shown in Fig. 3. By assuming that the water flows uniformly in the soil
specimen in the vertical direction, find the equivalent coefficient of permeability, kv for this soil specimen
consisting of three different soils.
Let us set that H1 =L1 =20cm, H2 =L2 =10cm, k1 =2.0x10-2cm/s, k2 =5.0x10-4cm/s, k3 =1.0x10-3cm/s. Whenthe difference in total head of 30cm is applied between the top and the bottom of the specimen, find thetotal volume of water in a unit width (perpendicular to the figure) of 1cm flowing in the specimen in anhour.

kv
H1

k1

H2

k2

k3

L1Fig. 3L2

2013 Soil Mechanics I and Exercise

Mid-term Examination

2013/11/26 (Tue.) 13:00～14:00

Room: W2

Attention:


There are two questions and two answer sheets. Write down your name and ID number on every
answer sheet. Use one answer sheet per question, and answer them in sequence starting fromQuestion【1】. If the front side of an answer sheet is not enough for answering one specific question,
you can use the back side of the same answer sheet, after clearly mentioning so. All questions bearequal mark.

Non-programmable calculators are permitted, but calculators that have programming functions and alltypes of mobile phones are prohibited. In addition, rulers are permitted to draw straight lines andmeasure distances.

If you behave maliciously during the exam, you will not be entitled to get any credit on this subject.

Wherever necessary, show the units in your answers.

【1】 In order to construct an embankment for the express way, a test embankment shown in Fig. 1 is made by bringing
the soil from the excavation site. This test embankment is assumed to have the dry density of d = 1.6 g/cm3. The
upper and lower surfaces of this embankment are rectangular in shape having dimensions: A = 8 m, B = 12 m, a =2 m, b = 6 m, h = 2.5 m. The soil at the excavation site has soil particle density, s = 2.5 g/cm3 (i.e., specificgravity, Gs = 2.5), water content, w = 20%, and bulk density,t = 1.8 g/cm3. At this condition, calculate thefollowing parameters:(1) Dry density of the soil at the excavation site.
(2) Void ratio of the soil at the excavation site.
(3) Degree of saturation of the soil at the excavation site.
(4) Total weight of the soil to be excavated from the excavation site.
(5) Total volume of the soil to be excavated from the excavation site.

aabbhhAABBFig. 1

【2】Answer the following questions related to soil permeability and flow of water through soils.
(1) In the following graphic (not to scale), Layer 1 is an isotropic soil with a hydraulic conductivity of k = 4.0 × 10-4m/s. Layer 2 is an impermeable rock. A retaining structure, which can be considered of infinite length in thedirection perpendicular to the graphic for the purpose of this analysis, was installed to allow for the creation of adry space next to a lake of 20 m depth, required for the future construction of certain civil structures. To keep thisdry space adequately devoid of water, heavy duty pumps with a pumping capacity of 400 liters per minute will be
installed in this area.
With this information in mind, answer questions (a) through (d):40 mArea for future

5m
Lake

construction works

20 m

Pump

Retaining Structure

10 m

Layer 1: Sandy Soil

20 m

40 m

NOTE: Graphic NOT to scale
Layer 2: Impermeable Rock(a) Calculate the rate of seepage under the retaining structure.
(b) Calculate the maximum allowed spacing between pumps, in meters, in the direction perpendicular to thegraphic, to account for all this seepage.
(c) Calculate the uplift force at the base of the retaining structure per meter of length (in the direction
perpendicular to the graphic). Assume water density as ρw = 1000 kg/m3, and gravitational acceleration as g =9.8 m/s2.
(d) Calculate the required minimum density ρ of the retaining structure if we want to assure that the flotationfactor of safety, defined as

Weight of structure
Uplift force, is equal or greater than 3.0.

(2) In five lines or less (you can include graphics if necessary) explain:(a) the mechanism of quicksand, and(b) how to calculate the quicksand critical hydraulic gradient.

2014

Soil Mechanics I and Exercises Midterm Exam
2014/12/2 (Tue) 13:00-14:00 W2 Lecture room

Attention: There are two answer sheets for two questions including sub-questions. Write down
your name and student ID number on both answer sheets. Use one answer sheet forone question and answer them in the same order as the questions are posed, startingfrom [Question 1]. If the space provided in the answer sheet is insufficient, use theback page after clearly mentioning so (for example, “continued on back page”).
 In addition to writing utensils, scientific calculators are allowed on the exam.
However, programmable calculators or mobile phone calculators/applications areabsolutely not permitted. Any attempts at cheating 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 to the following questions related to the physical properties of soil.
(1) Sieve analysis of Silica sand no.6 was conducted. Based on the particle size
distribution curve shown in Figure 1, find the average particle diameter D50 (the soil
diameter at which 50% of the soil weight is finer) and the uniformity coefficient Uc
associated with the slope of the grading curve.

Silica sand no.6

Percent finer by weight (%)

1005000.01

0.1

110Grain size (mm)Figure 1 Particle size distribution curve(2) The minimum and maximum dry density of the same silica sand No. 6 are ρmin =1.241 g/cm3 and ρmax = 1.556 g/cm3, respectively. Using the soil particle density ρs =

2.643 g/cm3 and the water density ρw = 1.000 g/cm3, answer the sub-questions
below:(a) The void ratio in the loosest state at which the minimum dry density is obtained
is defined as the maximum void ratio emax while the void ratio in the densest
state at which the maximum dry density is obtained is defined as theminimum void ratio emin. Determine emax and emin.
(b) This sand is compacted under water content w = 10% to achieve a relativedensity Dr = 35%. Calculate the total density ρt under these conditions. Herein,
Dr is defined by the following expression.
݁௠௔௫ െ ݁‫ܦ‬௥ ൌ݁௠௔௫ െ ݁௠௜௡(c) In regard to (b), determine the degree of saturation Sr after the compaction.
(d) For the silica sand no.6 that was compacted under water content w = 10%,
obtain the dry density ρdsat on the zero-air-void curve that is defined as the stateof full water saturation (Sr = 100%) when pore air in the voids is completelyexpelled.
(3) Describe the meaning of liquid limit wL, plastic limit wP and plasticity index IP. In
addition, explain which aspects of soil properties are understood by knowing thesevalues.
[Question 2] Answer the following questions related to the permeability of soils.
1) Briefly explain the terms given below. Schematic diagrams can be used to aid inyour explanations.
(a) Constant head permeability test(b) Quick sand2) The soil specimen shown in Figure 2 was prepared by setting impermeableboundaries along both left and right sides of a partitioned block consisting of 2
layers of soil arranged in series and 1 layer of soil connected in parallel. The
individual layers in series on the left-hand side have a width L1 and a thickness H1and H2 respectively, with individual coefficients of permeability k1 and k2. The
single layer on the right-hand side has a width L2 with thickness H1 + H2, and its
coefficient of permeability is assumed to be k3. By considering this a steady-state
permeability problem where the water flows uniformly in the soil specimen alongthe vertical direction, find the equivalent coefficient of permeability kv for this soil
specimen consisting of three different layers of soil.
3) Assume that H1 = L1 = 30 cm, H2 = L2 = 20 cm, k1 = 2.010-2 cm/s, k2 = 5.010-4cm/s, k3 = 1.010-3 cm/s. When a difference in total head h = 40 cm is applied
between the top and the bottom of the specimen, calculate the total volume of waterin a unit width (perpendicular to the figure) of 1 cm flowing through the specimen
in an hour.

Figure 2