2019 Soil Mechanics II and Exercises Final Exam
July 24, 2019 (Wed.) 10:00–12:00

Kyotsu 4 Lecture roomAttention: The exam consists of five questions for which you are provided with five 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 from [Question 1]. If the front page of an answer sheet is insufficient tocomplete your answer, use the back page of the same answer sheet after clearly indicating yourintent.
 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 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 all the following questions.
(1) A saturated clay layer of thickness H lies above an impermeable rock layer. Assume that the groundwaterlevel coincides with the ground surface. After the rapid application of a load over the clay layer, theconsolidation process is considered. Terzaghi’s one dimensional consolidation equation is given below. Here,u is the excess pore water pressure (= pore water pressure – hydrostatic pore water pressure), cV is thecoefficient of consolidation, t is time, and z is the coordinate along the vertical direction.
u 2u
 cV 2tz(1)(a) Write down the boundary condition for the upper surface of the clay layer (ground surface, z  0 ).
(b) Write down the boundary condition for the lower surface of the clay layer (in contact with the impermeablerock layer, z  H ).
(c) Assuming that the initial pore water pressure u0 is constant regardless of depth, the solution of theconsolidation equation is given by the following equation. Let the horizontal axis represent the excess porewater pressure u , and the vertical one be the depth z. Draw schematic diagrams of excess pore waterpressure for the initial value, during consolidation and at the end of consolidation, respectively.
 2uM u    0 sin  z  exp   M 2Tv  H m0  MMc t2m  1
 , Tv  V2
H2(2)(d) Sand drain is a soil improvement method for soft ground. Explain the change in consolidation behavior byusing this method.

1(2) A uniformly distributed load of q is acting on a rectangular foundation of dimensions a × b as shown inFigure 1.
(a) Assuming the ground as a linear elastic body, find the vertical stress at a depth of z just under the centerof the foundation. The vertical stress  z at a depth of z under the corner of a rectangular ( a × b )distributed load q can be obtained by the following equation.

 z  qI q  m, n  m aznbz(3)a  mzuniformly
distributed qloadb  nzz

z
Figure 1(b) Real soil ground is not elastic. Explain the reason why the solution given in (a) assuming that soil is a linear
elastic body is useful for calculation of stress in soil ground.

[Question 2]
Answer the following questions regarding failure of soil.
(1) Using Mohr’s stress circle, derive the Mohr-Coulomb failure criterion in terms of the principal stresses.
(2) Drained triaxial tests under constant confining pressure were carried out for two samples of the same sand thatwere prepared at different densities. Plot the relationship between volume change and axial strain for the loose
and dense samples, respectively.
(3) Briefly explain the following terminology.
1) Skempton’s pore pressure parameter2) Soil sensitivity ratio2[Question 3]
Answer the following questions based on the theory of retaining walls.
(1) Using a X-Y figure, with horizontal displacement shown in the X axis and earth pressure in the Y axis, show
the different behaviors between active and passive earth pressure acting on a retaining wall.
(2) After applying for all corresponding permits with the local government, a neighborhood association built an
artificial pond so the neighbors could enjoy swimming and sailing during the scorching summer months. If
the unit weight of the reinforced concrete used to build the vertical retaining wall is 𝛾

24 kN/m , calculate

the factor of safety against overturning moment, for the chosen design, at point A. Assume that the friction on
the bottom surface of the retaining wall prevents sliding. A smooth plastering was applied on the vertical wallto create an impermeable barrier against the filtration of water. Note that the water level of the pond does notreach the top of the retaining wall due to the installation of an overflow drainage system.
Overturning of theretaining wall
Overflowdrainagesystem

1m

1m
Neighborhood
artificial pond
γw = 9.8 kN/m34m
Retainingwall

2.5 m

Original ground

AFigure 2(3) After several years of summer fun, and with the corresponding government licenses, the association filled thepond with a horizontal compacted cohesionless backfill so that new houses could be built on the newly
developed area. Assume that the original smooth vertical surface of the retaining wall and the drainage systemwere kept the same, so that no friction occurs between the wall and the backfill, and the water table can only
rise up to the original water level of the pond. Calculate the factor of safety against overturning moment
around point A during both, (i) dry and (ii) rainy seasons. For dry season, assume that the water table drops
far below the base of the wall.
Overturning of theretaining wall
Overflowdrainage
system

1m1m

Compacted
cohesionlessbackfill
γt = 15.5 kN/m3
γsat = 19.0 kN/m3
ϕs = 35°4m
Retainingwall

2.5 m

A

Original groundFigure 33

Water table during
rainy season

[Question 4]
Answer the following questions.
(1) Explain the following two concepts about pile foundations, using figures if necessary.
1) Bearing mechanism of pile foundations
2) Negative friction(2) The ultimate bearing capacity of strip foundations 𝑞 proposed by Terzaghi can be given by the following
equation using the bearing capacity factors 𝑁 , 𝑁 , and 𝑁 :𝑐𝑁𝑞1𝛾𝐵𝑁2𝛾𝐷 𝑁

where 𝑐 is the cohesion, 𝛾 is the unit weight, 𝐵 is the width of the foundation and 𝐷 is the embedded
length of the foundation.
1) Draw the failure slip lines and explain the failure mechanism used by Terzaghi to derive the ultimate bearing
capacity.
2) Derive allowable bearing capacity 𝑞 considering the safety factor 𝐹 .
(3) A strip foundation is installed in the two-layer base ground shown in Figure 4. The ground water table is locatedat a depth ℎ from the ground surface.
1) Describe the ultimate bearing capacity of this foundation using the bearing capacity factors 𝑁 , 𝑁 , and 𝑁 ,and the parameters listed in the table. The unit weight of water is 𝛾 .
2) Select the parameters needed to calculate the bearing capacity factors 𝑁 , 𝑁 , and 𝑁 from the followingtable.

Bulkunit weight

Table
Saturated
unit weight

Soil layer 1𝛾

Soil layer 2𝛾

CohesionInternalfriction angle

𝛾𝑐𝜙𝛾𝑐𝜙Embedded depth 𝐷

Load 𝑄ℎ▽

Soillayer 1
Soillayer 2

Width of foundation 𝐵Figure. 44

[Question 5]
Answer the following questions.
(1) Answer the following questions about slope stability using the method of slices. Assume that the water table
is located deep enough and does not affect the slope stability.
1) According to the Fellenius method of stability analysis, a sliding soil mass is divided into n slices as shownin Figure 5. For any ith slice counted from the left of a circular arc with radius R and center at point O, let theangle of internal friction be i, the cohesion be ci, the length of the base be Li, the angle of inclination be i.
Also, the weight of slide is Wi, the horizontal forces acting on the right and left sides of the slice are Hi andHi+1, the vertical forces acting on the right and left sides of the slice are Vi and Vi+1,respectively. Along thebase of slide, Ni denotes the normal force and Si denotes the shearing force.
In the Fellenius method, the factor of safety Fs for the soil mass against sliding along the circular slip surface
is derived as follows by assuming the forces acting on the both sides of the slice are in equilibrium (theresultant forces acting on the left and right sides of the slice are parallel to the sliding plane)𝐹∑𝑐𝐿∑𝑊 cos 𝜃 tan 𝜙𝑊 sin 𝜃

Eq. (1)

Derive Eq. (1) and show the following three equations.
a)
b)
c)

2)

Equilibrium equation of force in the direction perpendicular to the base of the ith slice
Equation of failure criterion (sliding condition) of the ith slice
Equation of equilibrium for which the balance of moments on the whole sliding soil mass about point
OConsider the slope stability during an earthquake using the seismic coefficient method. In this method,
the ground is assumed to be a rigid body, and the inertial force which is calculated by the acceleration
acting on the ground multiplied by the mass of ground is considered in the static balance equation. Here,
only horizontal earthquake motion is considered because the influence of vertical motion is negligible.
Let the acceleration of gravity, the acceleration acting on the ground, the horizontal seismic coefficient beg, , and kh (= /g), respectively. When the horizontal seismic force kh･Wi acts on the ith slice, show thefactor of safety Fs for the soil mass against sliding along the circular slip surface.

Vi+1
HiWiHi+1

ViNi Si
LiFigure 55i

(2) Answer the following questions about soil liquefaction.
1) Explain the mechanism of soil liquefaction at the time of earthquake in the context of the dilatancy ofsoils. If necessary, you may explain using a figure.
2) Explain the following terms about soil liquefaction. If necessary, you may explain using a figure.
a) Liquefaction strength curveb) Factor of safety against liquefaction

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