2019

Soil Mechanics I and Exercises

Final ExamJanuary 28, 2020 (Tue.) 13:00-15:00 Kyotsu (Joint) 2 Lecture roomAttention:
This 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 per question and answer themin sequence, starting from [Question 1]. If the front page of an answer sheet is insufficient to complete
your answer, use the back page of the same answer sheet after clearly indicating your intent (for example,“continues on the back”).

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]

Answer the following questions.

(1) An embankment was constructed from the soil excavated from an excavation site. After completion, the total
volume of this embankment is 50,000 m3. The soil taken from the excavation site was investigated under its
natural conditions and the following results were obtained:
Bulk density: 1.80 t/m3 (g/cm3) Water content: 13.0 % Specific gravity of soil grains: 2.70
In addition, the following results were obtained from the compaction tests conducted for the excavated soil:
Maximum dry density：1.90 t/m3 (g/cm3)

Optimum water content: 15.0 %From the results of the compaction tests, water is sprayed to reach the optimum water content condition and the drydensity of the embankment is set to be 90.0 % of the maximum dry density (i.e., degree of compaction = 90.0%)
during the construction of the embankment.
Answer the following questions considering the density of water as 1.00 t/m3 (g/cm3).
1) Calculate the void ratio, degree of saturation, and dry density of the soil at the excavation site in its naturalcondition.
2) Calculate the mass and volume and of the soil to be excavated from the excavation site in its natural condition.
3) Calculate the mass of water necessary to be sprayed on 1 m3 of soil in natural condition at the excavation site.
4) Calculate the degree of saturation of the embankment after the completion of compaction.
(2) Briefly explain the following terms using the figures.
1) Particle size distribution curve2) Plasticity chart3) Compaction curve-1-[Question 2]

Answer the following questions on the water flow in saturated soils. Assume that the water flow

is governed by Darcy’s law and steady state condition is established for all cases below.
(1) Determine the flow rate, Q1, when the constant head permeability test is conducted on Soil 1 as shown in Figure
1. The hydraulic conductivity of Soil 1, k1 = 3.0×10-4 m/s, was obtained prior to this permeability test. The
cross-sectional area of the specimen is 1.0×10-2 m2, and the specimen is supported by mesh at the bottom.
(2) Plot the variations of total, potential and pressure heads along the horizontal axis of a graph and label thevertical axis with elevations, under the constant-flow condition shown in Question (1). Assume that the bottom
level of Soil 1 is the datum.

0.2 m

0.3 m

Soil 1

0.2 m

Figure 1

Soil 30.1 m

Soil 20.2 m

Figure 2A second constant head permeability test, with Soil 2 and Soil 3 placed as shown in Figure 2 using thesame permeameter, gives the flow rate, Q2, which is found to be equal to the flow rate, Q1, shown in Question (1).
The hydraulic conductivity of Soil 2, k2, is known, (k2 = 6.0×10-4 m/s), while the hydraulic conductivity of Soil 3,k3, is unknown. The cross-sectional area of the specimen is 1.0×10-2 m2.
(3) Determine the equivalent hydraulic conductivity in the vertical direction, kV, when Soil 2 and Soil 3 shown in
Figure 2 are regarded as one unit layer.
(4) Determine the hydraulic conductivity of Soil 3, k3.
(5) Determine the pressure head at the boundary between Soil 2 and Soil 3.

-2-[Question 3]

Answer the following questions.

Figure 3 shows the cross-section of a ground consisting of an impermeable rock mass overlain by a clay layer anda sand layer, where the groundwater table is located at 3 m below the surface. The thickness of the sand layer andthe clay layer are 6 m and 10 m, respectively. Take the z-axis along the vertical depth for one-dimensional problem.
The distribution of total stress  at a depth z (3Sand layer： =(a)z+z6) in the sand layer is given as(b)

z

(36)

and the total stress  due to the overlying layers in the clay layer becomes,
Clay layer： =(c)z+(d)

As the pore water pressure distribution, u, follows a
Pore water pressure：u =(f)z(6z+(e)16)

relationship, it can be expressed as(g)(3z16)

Therefore, the effective stress ′ of each soil layer can be obtained as follows.
Sand layer：’ =(h)z+(i)(3z6)

Clay layer：’ =(j)z+(k)(6z16)

Figure 3
Assuming that a 4-m high embankment with a total unit weight of soil t = 18.0 kN/m3 is constructedinstantaneously on this ground, answer the following questions.
(1) In the above sentences, fill in the blanks

(a)

～(k)

using t, sat1, sat2, w while describing(e)using suitable terms.
(2) Using sat1 = 20.0 kN/m3, sat2 = 15.0 kN/m3, w = 9.81 kN/m3, find the distributions of effective stress in termsof z in both sand and clay layers at the time immediately after construction of the embankment.
(3) Using the conditions described in (2), show the profiles of total stress, pore water pressure, and effective stress
distribution from the ground surface to the rock mass ( 0z16 ) when sufficient time has elapsed(consolidation is completed) after embankment construction. In the profiles, indicate the values of total stress,
pore water pressure, and effective stress at the ground surface and at the boundary between the sand and claylayers, as well as between the clay layer and the rock mass.
(4) The coefficient of consolidation, Cv, of the clay layer is obtained to be 1.55×10-3 cm2/s. Using Table 1, estimate
the degree of consolidation of this clay layer after 1 year of the construction of the embankment without taking
into account the construction process.

-3-U (%)
05101520Table 1 The degree of consolidation and time factor, Tv, relation
Tv
U (%)
Tv
U (%)
Tv
U (%)
0.000
250.049
500.197750.002300.071
55
0.239
80
0.008
35
0.096
60
0.286
85
0.018
40
0.126
65
0.340
90
0.031
45
0.159
70
0.403
95
100

Tv
0.477
0.567
0.684
0.848
1.129
∞

(5) Before construction of the embankment, oedometer tests on sampling clay were carried out. Then, thefollowing results were obtained: the consolidation yield stress pc is 1.40×102 kN/m2, the compression index Cc
is 2.00×10-1 and the swelling index Cs is 2.00×10-2, respectively. When sufficient time has elapsed(consolidation is completed) after embankment construction, calculate the amount of consolidation settlementof the clay layer. Here, before embankment construction, the initial void ratio of the clay layer is 0.80 regardlessof the depth.

[Question 4]

Answer the following questions.

(1) A consolidated drained triaxial compression test was conducted on the silty soil specimen under the conditionof the constant confining pressure, 3 = 100 kN/m2 after an isotropic consolidation. When the axial stressreached 1 = 500 kN/m2, a failure occurred with a 60° failure surface measured counterclockwise from themaximum principal stress plane as shown in Fig. 4. Answer the following questions.
1) Draw the Mohr’s stress circle at failure and find the normal stress, f and shear stress, f acting on the failuresurface.
2) Assuming the Mohr-Coulomb’s failure criterion holds for a failure of the soil, find the cohesion, c’ and the angleof shear resistance, ’ of this silty soil. (A failure line should be drawn in the figure for question (1) together withc’ and ’).
3) Obtain the maximum stress, max and the maximum stress plane (the angle measured from the maximum principal
stress plane) of this silty soil.
1 = 500 kN/m2

3 = 100 kN/m2

3
f=60°

1Figure 4(2) Explain the following terms. (You may use schematic figures.)
1) Dilatancy2) Sensitivity-4-