2020

Soil Mechanics II and Exercises Final Exam

2020/7/29 (Wed.) Test time 10:00-12:00, Submission time via PandA 12:15
Attention:
The exam consists of five 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 12:00 and submit the answer sheet via PandA by 12:15.

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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 similarity in answers are observed among
examinees, an extra oral examination may be conducted later for individual investigation.

Wherever necessary, specify the units in your answers.

[Question 1]
A road embankment passing through a homogeneous and uniform 8-m-thick layer of normally consolidated
clay underlain by a very stiff layer of sand as shown in Figure 1 is considered. The bulk unit weight ofembankment γt is 15.8 kN/m3 and the saturated unit weight of clay γsat is 18.3 kN/m3. For the clay layer, theinitial void ratio eo is 0.9, the compression index Cc is 0.2, the coefficient of consolidation cv is 0.02 m2/day.
Groundwater is at the surface of clay and the pore water is drained on the upper and lower boundaries of theclay layer. The unit weight of water γw is 9.8 kN/m3.
Two stages of embankment construction are proposed. First, the clay layer is preloaded by constructing theembankment of height H1 = 4.0 m, bottom width W = 20.0 m and embankment slope of 1:2. The embankment
remains on the clay layer over a number of days Δt to drain the excess pore water and to cause the consolidation
settlement S2 where S2<S1 where S1 represents the final consolidation settlement of the clay layer due to theembankment of height H1 as depicted in Figure 2. Next, the part of the embankment regarded as preload isremoved; therefore the height of the road embankment becomes H2 = 2.0 m with the same bottom width andembankment slope.
Assume that stress state at the middle of the layer can be used as the representative stress state of the clay layer.
Let the stress increase in the clay layer due to the embankment loading follow the elastic solution of the verticalstress in ground beneath the center of an embankment. Ignore immediate settlement, deformation ofembankment and ground rebound after removal of preload. Construction and removal periods of embankment
are not accounted for calculation. In order to obtain the solutions, Table 1 and Figure 3 may be used. Providedthat the clay layer is deformed only by one-dimensional consolidation, answer the following questions.

- 1 -Figure 1: Ground profile and outline of embankment

Hy

H1
H2
S2

S1

S

Δttt90Figure 2: Effects of preload (H1-H2) on consolidation time (t) and consolidation settlement (S)(1) Calculate the effective vertical stress σ'zo at the middle depth of the clay layer before the construction ofembankment.
(2) Estimate the vertical stress increase Δσ1 applied at the middle depth of the clay layer beneath the center ofthe embankment of height H1.
(3) Find the final settlement S1 induced by Δσ1 using σ'zo at the middle depth of the clay layer.
(4) Estimate the vertical stress increase Δσ2 applied at the middle depth of the clay layer beneath the center ofthe embankment of height H2.
(5) Find the final settlement S2 induced by Δσ2 using σ'zo at the middle depth of the clay layer.
(6) Determine the number of days (t90) when the clay layer reaches an average of 90% degree of consolidation.
(7) In order to allow the embankment of height H1 to settle to S2 by consolidation, how many days (Δt) isrequired to hold the embankment before the removal of preload?
(8) Explain the benefits and limitations of preloading method.

- 2 -Table 1: Relation between average degree of consolidation U and time factor Tv
U (%)

Tv

U (%)

Tv

U (%)

Tv

U (%)

Tv

00.000250.049

500.19775

0.477

50.002

30

0.071

55

0.239

80

0.567

100.008

35

0.096

60

0.286

850.684

150.018

400.126650.340

900.848200.031450.159700.403

95

1.129

100

∞

Figure 3: Influence value for vertical stress determination in ground due to a half-width embankment loading- 3 -[Question 2](1) It is difficult to walk over water, but can walk the top of the soil. Explain this reason.
(2) For soil and steel, explain the difference in volume change when they receive any external force.

[Question 3]
As shown in the Figure 4, an earth retaining wall is installed on the ground composed of a clay layer and a sandlayer. It is planned to excavate the ground on the left side of the earth retaining wall up to 5 m in depth. The watertable at the end of excavation is located at the top of the clay layer.
It is assumed that there is no frictional force between the earth retaining wall and the ground. The clay layer isconsidered to be failed in the undrained condition because the construction period is short. The unit weight of water
is assumed to be 10 kN/m3 for simplicity.
(1) Cohesion of the sand layer 𝑐 and the internal friction angle 𝜙 are 0 kN/m2 and 30°, respectively. Find thecoefficient of active earth pressure of the sand layer.
(2) Undrained shear strength of the clay layer 𝑐 is 35 kN/m2 regardless of depth. Vertical effective stress 𝜎′
applying at the point of the clay layer is 90 kN/m2. Draw two Mohr’s stress circles corresponding to the active
and passive failure states of the clay. Indicate the stress values at the intersection of the Mohr’s stress circle andthe axis of the diagram.
(3) Draw the lateral pressure profile per unit width through the depth (sum of water pressure and soil pressure)acting on the back side of the retaining wall (right side of the retaining wall in the figure) at which

the active

failure state is reached. In addition, find the resultant force of the lateral pressure per unit width and indicate theposition of resultant force measured from the bottom of the earth retaining wall.
(4) Draw the lateral pressure profile per unit width through the depth (sum of water pressure and soil pressure)acting on the front side of the retaining wall (left side of the retaining wall in the figure) at which the passive
failure state is reached. In addition, find the resultant force of the lateral pressure per unit width and indicate theposition of resultant force measured from the bottom of the earth retaining wall.
(5) Investigate the stability of the retaining wall, considering the bottom of the retaining wall as the center of rotation.

Retainingwall
Sand layer
Wet unit weight 18kN/m3

▽

5m

▽
1.5m

Clay layer
Saturated unit weight 18kN/m3

Figure 4- 4 -[Question 4](1) Figure 5 shows a cross-sectional view of the right half of the symmetry plane of the strip foundation. The
ultimate bearing capacity of the strip foundations 𝑞

proposed by Terzaghi can be given by the following

equation, using the bearing capacity factors 𝑁 , 𝑁 , and 𝑁 . Note that 𝛾 is the unit weight, 𝑐 is thecohesion, 𝐵 is the width of the foundation and 𝐷 is the embedded depth of the foundation.
𝑞𝑐𝑁

1𝛾𝐵𝑁
2𝛾𝐷 𝑁1) Draw the failure slip lines assumed by Terzaghi to derive the ultimate bearing capacity. First, draw theFigure 5 (no symbol is required) on your answer sheet, then draw the failure slip lines there. Also,indicate the angles between the slip lines and the ground surface.
2) Add the directions of slip on the slip lines in the figure shown in 1)
3) Each bearing coefficient is a function of the internal friction angle 𝜙. Explain the reason.
4) Explain the reason why the bearing capacity coefficients of other bearing capacity formulas are different
from that of Terzaghi.
5) Let the safety factor be 𝐹 and derive the allowable bearing capacity 𝑞 . In the derivation process, notonly formulate equations, but also state its assumptions.
6) In Figure 5, the groundwater level is much lower than the foundation base. Suppose that the groundwaterlevel gradually rises and reaches the ground surface. Explain how the ultimate bearing capacity changes
during this process, provided that the cohesion 𝑐 and internal friction angle 𝜙 do not change.
𝑄𝐷𝛾, 𝑐, 𝜙

𝐵/2Figure 5(2) Ultimate bearing capacity for local shear failure is usually smaller than that for general shear failure. Explain
the reason.
(3) Describe the principle of countermeasures against negative friction of pile foundation.

- 5 -[Question 5](1) Answer the following questions regarding the slope stability.
Figure 6 shows an infinite slope. Consider a sliding surface at depth Hf as shown in Figure 6 that is parallelto the slope surface. From the balance of the forces acting on the soil area abcd between the ground surface andthe sliding surface, find the safety factor, F for the sliding failure under the conditions 1) to 3) shown below.
Derivation processes of the safety factor must be described. Here, N and S are the normal and tangential forces
acting on the base of the area abcd, respectively. Neglect the balanced forces, E acting on the right and left sidesof this area abcd.
Assume that the groundwater table is well below the sliding surface (Figure 6 (a)). If the shear strength1)

acting on the sliding surface is governed by the Mohr-Coulomb fracture criterion ( = c + tan), thenfind the safety factor, F for the assumed failure.
Due to the rainfall, the groundwater table rose and reached the ground surface (Figure 6 (a)). If the2)seepage flow exists and it flows parallel to the slope surface, find the safety factor, F. Here, the effective
shear strength,  of the soil is  = c’ + ’tan’.
3)

The area including the slope was selected for the dam construction site, and the slope was submerged in
the dam lake (Figure 6 (c)). The water surface of the dam lake is at a very high level so that there is nowater flow in the dam lake, and the difference in water pressures acting on the left and right sides of theregion abcd is negligible. Find the safety factor, F. Then, mention how the slope stability changes in thepresence of the seepage flow and in the hydrostatic condition by comparing the results of 2) and 3),
assuming that the cohesion c’ = 0.

b

LaEHfNSaEcd

EHfWbLt, cFigure 6 (a)NSaEcdE
HfWb

L

sat, 'c'Figure 6 (b)NSsat, 'c'
Ecd
W
Figure 6 (c)(2) Answer the following questions regarding the wave propagation and liquefaction.
1)

As a laboratory test for examining the liquefaction strength of the ground, the cyclic triaxial test under
undrained conditions is often used. How the stress ratio under this experimental condition is expressedby cyclic loads for which an axial stress d is repeatedly applied to an isotropic stress state subjected to aconfining pressure 3? In addition, explain what kind of plane would the shear forces produced during
earthquakes be reproduced in this experiment by using Mohr's stress circles.

2)

Explain about the cyclic mobility of soil

3)

It is well known that the liquefaction of ground occur easily in loosely deposited sandy ground. Explain
reasons why liquefaction is less likely to occur in (1) clay ground and (2) gravel ground.
- 6 -