2021

Soil Mechanics II and Exercises

Final Exam

July 28, 2021 (Wed.) 10:00–12:00 Kyotsu 4 Lecture Room + Online
Attention: The exam consists of five questions.
 Use of non-programmable calculators are permitted. However, programmable calculators andcalculator functions of mobile phones are prohibited.
 Wherever necessary, specify the units in your answers.
[In-class participants]
 Five answer sheets are provided. 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 thefront page of an answer sheet is insufficient to complete your answer, use the back page of thesame answer sheet after clearly indicating your intent.
[Online participants]
 You must keep your camera ON throughout Zoom connection during the exam.
 You must finish writing at 12:00 and complete submitting the answer sheets via PandA by 12:10.
Your submission will not be accepted after the deadline regardless of any reason. Give yourself
ample time to get through PandA for submitting the answer sheets.
 You may answer a major question over multiple answer sheets but do not answer multiple major
questions on the same answer sheet. You must indicate your name and student ID on all the sheets.
 Any suspicious behavior through camera will result in failed credit of the course and serious
penalties.

[Question 1] Answer the following questions regarding the stress in ground and soil consolidation.
(1) A circular tank with a radius R = 2.0 m is planned to place on the sandy ground whose bulk unit
weight γt = 16.0 kN/m3. To determine how deep should a borehole be drilled for sample collection,
the guideline of ASCE (1972) is followed. By knowing that the circular foundation will exert auniform pressure q = 160 kN/m2 on the sandy ground surface and the water table is sufficiently
far, the required minimum depth of boring is approximated as follows:i.

Estimate depth D1 at which Δσ/q = 0.1 where Δσ is the increase in vertical stress at depth
D1 and q is the net stress on the foundation.
ii. Estimate depth D2 at which Δσ/σ′o = 0.05 where Δσ is the increase in vertical stress at depth
D2 and σ′o is the effective overburden pressure at depth D2.
iii. Choose the smaller of D1 and D2.
Assuming that the ground is a semi-infinite elastic body, the vertical stress Δσ below the center ofa uniformly distributed pressure q on a circular area of radius R at depth z is determined by Eq.
(1) for which Table 1 may be used in estimation.
- 1 -32  1  q  1  
2 
1  z R   

Table 1: The variation of Δσ/q with z/R [Eq. (1)]
z/R
Δσ/q
z/R
Δσ/q0
0.0
1
2.5
0.200
2
0.1
0.999
3.0
0.146
0.2
0.992
3.5
0.111
z/R 4
0.40.949
4.00.087
6
0.8
0.756
4.5
0.070
1.0
0.646
5.0
0.057
80
1.5
0.424
5.5
0.048
2.0
0.284
6.0
0.040

Eq. (1)qR
z0.5

Δσ/q1

Δσ(2) After completion of borehole drilling, a homogeneous and saturated 2-m-thick layer of normallyconsolidated clay was unexpectedly found between depths of 5.0~7.0 m. Laboratory tests on aclay sample showed that the saturated unit weight of clay γsat = 19.0 kN/m3, the initial void ratio
e0 = 0.5 and the compression index Cc = 0.75. Given the unit weight of water γw = 9.8 kN/m3, findthe consolidation settlement of 575a circular tank if the groundwater level is located at the samelevel as a clay layer as shown in Figure 1. Note that, immediate settlement of ground can beneglected and the stress state at the middle of the clay layer can be used in calculation of onedimensional consolidation settlement.

Figure 1- 2 -[Question 2] Answer the following questions.
(1) An unconfined compression test was conducted on a sample taken from a clay ground. In theunconfined compression test, although no confining pressure is applied, the effective stress of thespecimen is equal to the effective stress in the ground.
(1-1) Describe how the pore water pressure changes before and after the sample was taken from theground.
(1-2) In order to maintain the effective stress of the specimen equal to the effective stress in theground, describe the conditions under which the specimen should be stored, focusing on thevoid ratio.
(2) Derive the Mohr-Coulomb failure criterion using the maximum principal stressprincipal stress , the cohesion , and the internal friction angle .

, the minimum(3) A consolidated undrained triaxial compression test was conducted on a clay sample with aconfining pressureof 100 kN/m2. At failure, the axial stresswas 196 kN/m2 and the excess
pore water pressure
was 57.0 kN/m2.
and Skempton’s pore pressure coefficient .
(3-1) Determine the mean effective stress(3-2) Determine the stress ratio at failureof the clay.
(3-3) Next, if the same clay sample is used in a consolidated drained triaxial compression test witha confining pressureof 100 kN/m2, determine the mean effective stressand the axial
differential stressexpected at failure.
(3-4) Draw the effective stress paths in the ′plane for the above consolidated drained triaxial
compression test and the consolidated undrained triaxial compression test.
(3-5) Draw the relationship between the volumetric strain
and axial strain
expected in theconsolidated drained triaxial compression test.

- 3 -[Question 3] Answer all the following questions.
Figure 2 represents a rigid retaining wall of height 4 m with a sand backfill. The groundwater tablechanges with rainfall, and the current depth is m (04) from the backfill surface. The earthpressure acting on the retaining wall can be assumed as Rankine earth pressure. There is no friction
between the retaining wall and the sand backfill. The wet unit weight of sandis 15 kN/m3. The
saturated unit weight of sandis 19 kN/m3. The unit weight of water
is simply 10 kN/m3. Theinternal friction angle ′ is 30 degrees, and the cohesion ′ is 0 kN/m2.
(1) Draw the pore water pressure profile acting on the back side of the retaining wall per unit length(perpendicular to the section) through the depth .
(2) Find the resultant force of the pore water pressure acting on the back side of the retaining wall perunit length (perpendicular to the section) through the depth .
(3) Draw the earth pressure profile acting on the back side of the retaining wall per unit length(perpendicular to the section) through the depth .
(4) Find the resultant force of the earth pressure acting on the back side of the retaining wall per unit
length (perpendicular to the section) through the depth .
(5) Find the resistance force of friction along the base of the retaining wall per unit length(perpendicular to the section). The unit weight of retaining wall is 25 kN/m3, the width of retaining
wall is 2m, and the friction coefficient is 0.3.
(6) Investigate the sliding of the retaining wall when the groundwater table changes with rainfall. The
factor of safety can be assumed to be 1.

Retaining wallz= 15 kN/m3= 19 kN/m3= 10 kN/m3′ = 30 degrees′ = 0 kN/m2

Figure 2- 4 -4m

[Question 4] Answer the following questions.
(1) Describe the reason within 30 words why the bearing capacity of the ground needs to be estimated.
(2) Draw failure mechanism of the ground for the derivation of the Terzaghi’s bearing capacityequation.
(3) Draw the distribution of axial force on a pile that negative friction appears.

[Question 5](1) Answer the following questions regarding the slope stability.
(1-1)

Figure 3 shows an infinite slope. Consider a sliding surface at depth Hf as shown in Figure 3 that isparallel to the slope surface. From the balance of the forces acting on the soil area abcd between theground surface and the sliding surface, find the safety factor, F against the sliding failure. 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 andleft sides of this area abcd. Assume that the groundwater table is well below the sliding surface. If theshear strength along the sliding surface is governed by the Mohr-Coulomb failure criterion ( = c +tan), formulate the safety factor, F for the assumed failure, in terms of c, t, Hf, , .
(1-2)

In order to increase the safety factor, F against the sliding failure in (1-1), ground anchors are installed
into the slope as shown in Figure 4. The ground anchors are installed at an angle  from the horizontal
plane, and its installation interval is L (a ground anchor is installed at the area abcd). The tension ofeach anchor is T. Ground anchors are installed to achieve the following two objectives: (1) Increase
the normal force acting on the sliding surface (clamping effect), and (2) Increase the resistance force
against the sliding of slope (straining effect). Formulate the safety factor, F by considering both twoeffects, in terms of c, t, Hf, , L, , T. Here, neglect the stiffness of the ground anchors.

bLaEHfNSt, c

ETc

dTTW

Figure 3

Figure 4- 5 -(2) Answer the following questions regarding the wave propagation and liquefaction.
(2-1)

An undrained cyclic torsional shear test was performed on saturated loose sand with a constant shear
stress ratio for which liquefaction occurred at a certain number of repetitions was judged. Draw theschematic view of the experimental results on all five graphs shown in Figure 5.

(2-2)

When evaluating the liquefaction characteristics of a sand, a series of experiments (e.g. hollow
torsional test, triaxial test) is performed with different shear stress ratios on the same sand. Explain thereason for this by illustrating the "liquefaction strength curve" obtained from a series of experiments.

(2-3)

Explain the reason why the ground liquefies during an earthquake. Underline three places in your

Number of cycles Nc

Excess pore water pressure ratiou 'cShear strain 

Number of cycles vs Shear stressDA = 7.5%
Number of cycles Nc

Shear stress dShear stress danswer where you think they are important.

Effective mean principal stress 'c

Effective mean principal stress vs Shear stress

Shear stress dNumber of cycles vs Shear strainu 'c = 1

Number of cycles Nc
Number of cycles vs Excess pore water pressure ratio

Figure 5- 6 -Shear strain 

Shear strain vs Shear stress