2017
Soil Mechanics I and Exercises Final Exam
2018/1/30 (Tue.) 13:00-15:00 Kyotsu 2 Lecture room
Attention:
This exam consists of four questions for which you are provided with four 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 space provided in any answer sheet is insufficient, use the backof the page after clearly mentioning so (for example, “continues on the back”).

In addition to personal writing instruments, rulers and non-programmable calculators are permitted, butprogrammable calculators and all types of mobile phones are prohibited. Any attempts at cheating on theexam 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) In constructing highway embankments, the test embankment shown in the figure below is built using soil
excavated from a collecting site. The test embankment requires compacted soil with a dry density ρd = 1.8g/cm3. The rectangular planes forming the base and the top of the embankment are flat, horizontal, and havedimensions of A = 16.0 m, B = 20.0 m, and a = 4.0 m, b = 8.0 m, respectively. The height of the embankmentis h = 3.0 m. The soil in the collecting site has soil particle density ρs = 2.7 g/cm3 (specific gravity of soil
particles Gs = 2.7), water content w = 15%, and bulk density ρt = 2.0 g/cm3. Under these conditions, obtainthe following values, assuming unit weight of water ρw = 1.0 g/cm3.
1) Dry density of the soil in the collecting site2) Void ratio of the soil in the test embankment3) Degree of saturation of the soil in the test embankment
4) Dry mass of the test embankment
5) Total mass of soil taken from the collecting site

AB
Figure 1(2) Explain the following technical terms defined in soil mechanics
1) Optimum water content
2) Consistencyhab[Question 2]
Figure 2 (not to scale) represents the cross section of an infinite sloped ground, showing a permeable sand layer
with a density of 1730 kg/m3 and a hydraulic conductivity of 5.3 × 10-5 m/s overlaying an impermeable rocklayer.

Ground surface

Permeable
sand layer

Groundwater table(free surface)

5m

A3m

Impermeablerock layer

B2m

15 m

8°

Figure 2 Cross section of the studied sloped ground(1) Draw a rough flow-net of the water seepage through this system.
(2) Points A and B are located on the groundwater table and separated 15 m horizontally. Calculate the headdifference between these two points.
(3) Calculate the flow rate through the permeable soil per day, per unit of width in a section perpendicular tothe figure.
(4) Some weeks after finishing your analysis, it was found that the total flow rate was not the one calculated in(3), but just 1.20 m3/day (per unit of width in a section perpendicular to the figure), instead. Because of this,you were asked to drill some vertical boreholes to analyze the sand layer, and it was only then that you
found that the previously thought as a single sand layer was actually composed of two parallel sand layers.
Both layers have the same dip (8°) as that of the impermeable rock layer and the ground surface, but thetop sand layer (the one closest to the ground surface) is three times thicker than the bottom one (i.e., youfound in your vertical borehole that the top layer continued down to a depth of 6 m, while the bottom one
continued for the remaining 2 m). You immediately realized that the hydraulic conductivity originallyreported (5.3 × 10-5 m/s) corresponded only to the top layer.
If the groundwater table depth is the same as that shown in Figure 2, calculate the hydraulic conductivity ofthe bottom sand layer (the one closest to the impermeable rock layer) under these circumstances.

[Question 3]
The figure below shows the cross-section of a ground consisting of an impermeable rock mass overlain by a clay
layer and a sand layer, where the groundwater table is located at the ground surface. The thickness of the sandlayer and the clay layer are 4 m and 10 m, respectively. Take the z-axis along the vertical depth for
one-dimensional problem.
The distribution of total stress σ at a depth z in the sand layer is given by its saturated unit weight sat1,Sand layer：σ =(0  z  4 )①and the total stress  due to the overlying layers in the clay layer with saturated unit weight sat2 becomes,
Clay layer：σ=( 4  z  14 )②

As the pore water pressure distribution u follows arelationship; it can be expressed in terms of the③density of water ρw and the gravitational acceleration g, as
Pore water pressure：u =( 0  z  14 )④

Therefore, the effective stress σ′ of each soil layer can be obtained:
Sand layer：σ′ ⑤(0  z  4)

Clay layer：σ′ ⑥( 4  z  14 )Figure 3
Assuming that a 5 m high embankment with a total unit weight of soil γt = 16.0 kN/m3 is constructedinstantaneously on this ground, answer the following questions.
(1) In the above sentences, fill in①～⑥using z, γsat1, γsat2, ρw, g while describing

③

using

suitable terms.
(2) Using γsat1 = 18.0 kN/m3, γsat2 = 16.0 kN/m3, ρw = 1.0 g/cm3, g = 9.8 m/s2, find the distributions of effective
stress in terms of z in both sand and clay layers at the time immediately after construction of theembankment.
(3) Using the conditions described in (2), plot the profiles of total stress, pore water pressure, and effective stress
distribution from the ground surface to the rock mass ( 0  z  14 ) when sufficient time has elapsed(consolidation has 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 sandand clay layers, as well as between the clay layer and the rock mass.

(4) Obtain the increment of effective stress ∆σ′ in the clay layer when sufficient time has elapsed afterembankment construction, and calculate the compressive deformation after completion of consolidation in
the clay layer. Herein, the coefficient of volume change mv of the clay layer is assumed to be 1.0×10-4 m2/kN.
(5) The coefficient of permeability k of the clay layer is 1.0×10-7 m/s. If the amount of compressive deformation
when a time t has elapsed after embankment construction was 4.8×10-2 m, calculate the time t [days] required
to reach such amount of compressive deformation. Refer to the table below showing the variation of degreeof consolidation with time factor.
Degree of consolidation %405060708090

Time factor

0.126

0.197

0.287

0.403

0.567

0.848

[Question 4]
Answer the following questions. Assume that soil failure occurs following the Mohr-Coulomb failure criterion.
(1) The consolidated-drained triaxial test (CD test) was performed on a dense, saturated silty sand, at a confining
stress of. Failure occurred when the axial stress reached

1) Express the values of the normal stressandin terms of the principal stresses
angle of internal friction2) Using the fact that ( ,.

and shear stressin the direction of the surface of failure,, and of the silty sand strength parameters (cohesionand).
) is a point on the failure criterion line, express the Mohr-Coulomb failure

criterion as a function of the principal stresses,, and of the soil strength parameters

3) The following results were obtained in the laboratory. Calculateandand.

for this silty sand:CaseABC(kN/m2)50

100

150(kN/m2)

1723445164) Describe the points to pay attention to when setting the experimental conditions for a CD test on a soil
with relatively low water permeability such as silty sands.
(2) When the consolidated-undrained triaxial test ( CU test) was performed on a saturated, normally consolidated
clay at a confining stress of, the maximum value of the principal stress difference (deviator stress) wasmax .

1) Plot the “strain-deviator stress”, and the “excess pore pressure-axial strain” diagrams for this test. In thelatter diagram, you must clearly specify the sign of the excess pore pressure.
2) From themax

values obtained for several values ofeffective stress are found to be related as′ and, the strength parameters for total and′. Explain why.