2022 Soil Mechanics II and Exercises Final Exam
July 27, 2022 (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.
 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) The ground shown in Fig. 1 consists of a 10 m-thick layer of soft clay deposited over an impermeable
bedrock. Coefficient of volume compressibility (mv) and coefficient of consolidation (cv) of this clay layer
are 3.0×10-4 m2/kN and 2.0×10-2 m2/day, respectively. Consider the construction of a structure on theground surface with a rectangular spread foundation of 20 m long and 10 m wide. The rectangularfoundation will exert a uniform pressure q = 100 kN/m2 on the ground surface. Assume that therepresentative value of the stress in the ground can be taken at the center of the clay layer (i.e., at a depthof 5 m). Also, the stress increment in the clay layer due to the construction of the structure can bedetermined by the elasticity theory, using the stress increment in the ground below the center of thestructure.
(1-1) Find the stress increment at the depth of 5 m below the center of the structure after its construction.
Fig. 2 may be used.
(1-2) Find the consolidation settlement of the structure.
(1-3) Find the time required for the clay layer to reach 90% degree of consolidation (time factor Tv = 0.848).
(1-4) The sand drain method was adopted to shorten the time required for consolidation. As shown in Fig.
3, a square-shaped pattern was chosen for a sand pile diameter of dw = 0.4 m with an interval between
sand piles of d = 2.13 m. Calculate the effective diameter de of a circle whose cross-sectional area
equals the area of the square in which water is collected.
(1-5) Find the time required for the clay layer with sand drains to reach an average of 90% degree ofconsolidation from the diagram representing the theoretical solution of Barron (Fig. 4). It is assumed
that coefficients of consolidation for vertical and horizontal drainages are same (cv = ch).
(2) Fig. 5 shows schematically the Boussinesq’s and Strohschneider's theories for determining the verticalstress increment in the ground when a concentrated load Q acts on the ground surface. In Boussinesq'stheory, which assumes that the ground is a semi-infinite elastic body, the stresses near the ground surface
spread out infinitely along the lateral directions. In reality, however, as in Strohschneider's theory, thestress distribution in the ground is limited within a certain closed region, and no stresses occur outside ofit. Explain why Boussinesq's theory differs from the actual stress distribution.

1dClayddmv = 3.0×10-4 m2/kN-210 m2

cv = 2.0×10 m /dayddedw

Impermeable bedrock

Fig. 1

Fig. 3Fig. 22

Qz

Boussinesq

Fig. 4zz

Strohschneider

Fig. 5[Question 2] Answer all the following questions.
A CU triaxial compression test was conducted on a saturated clay under normal consolidation state. The
cohesion c' of the normally consolidated clay can be considered as zero. The specimen was first isotopicallyconsolidated at 200 kN/m2 and the confining pressure was kept constant during the test. At failure, the axialstress 𝜎 was 400 kN/m2 with pore water pressure uw of 100 kN/m2. Two additional tests were conducted on
the same clay. These extra tests were CD direct shear and the clay was in an over-consolidated state. At failure,
the applied normal stress in the first test was 10 kN/m2 and the measured shear stress was 22.7 kN/m2; in thesecond test the applied normal stress was 50 kN/m2 and the measured shear stress was 33.4 kN/m2.
(1) Find the effective shear strength parameters (cohesion c' and internal friction angle ϕ') of the clay fromthe CU triaxial compression test and CD direct shear tests, respectively.
(2) Find the pre-consolidation pressure of the clay.
(3) Calculate the Skempton's pore pressure coefficient 𝐴 in the CU triaxial compression test.
(4) Another CD triaxial compression test on the same clay was conducted by keeping the effective meanstress (𝑝 ) to be constant during the test. The 𝑝 is the average of all the three effective principal stresses
and the clay was in a normally-consolidated state. The test started with an isotropic confining pressure of
200 kN/m2. In order to keep 𝑝 constant, the axial stress was increased while the radial stress wasreduced during the test. Calculate the axial stress and radial stress at failure for the test, then draw theeffective stress path in p'-q plane.
Note: you may solve (1) and (2) either analytically or graphically. However, if you use graphical approach,please ensure the accuracy. Points may be deducted for inaccurate solution.

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[Question 3] Answer all the following questions.
(1) Describe the significance and/or the purpose of studying earth pressure within 30 words.
(2) Fig. 6 represents a retaining wall of height H where the groundwater level lies at its bottom. Let thefrictional angle, the cohesion, and the unit weight of the soil behind the wall be , c, and , respectively.
Based on Coulomb’s earth pressure theory, determine the earth pressures acting on the retaining wall when
it moves rightward and leftward. Show the force polygon diagrams using the forces that act on the soil
wedge shown in the figure. Use appropriate symbols for the forces shown in the force polygon diagramsand explain each of those forces. Assume that the cohesion, c, of the soil behind the retaining wall is zero.
Also, assume that the surface of the wall is smooth and, hence, there is no friction between the retaining
wall and the soil.
(3) While reassessing the conditions of the soil behind the retaining wall, it was found that the cohesion of thesoil, c, was not equal to zero. Under this new condition, and based on Rankine’s earth pressure theory,
obtain the earth pressure that acts on the retaining wall when it moves leftward. Use Mohr’s stress circle
for the calculation of the earth pressure. Also, show the earth pressure distribution along the height (H) of
the retaining wall.
(4) Explain the difference in the magnitudes of the active resultant earth pressure (resultant of the earthpressure and the water pressure) when the groundwater level behind the retaining wall (i) lies at the bottom
surface of the retaining wall and (ii) rises to the ground surface. Focus your answer on the difference inthe earth pressure and the water pressure under those two conditions. Assume the unit weight of water as
w and the cohesion, c, of the soil behind the retaining wall is zero. Also, assume that the active earthpressure p at the depth of z can be expressed as p＝Kaz when the groundwater level lies at the bottom
surface of the retaining wall.

Fig. 64

[Question 4] A strip footing with a width B is constructed on the ground with the surcharge load q. According
to Terzaghi, when the ground reaches the ultimate bearing capacity, the slip line will develop, which divides
the ground into regions I, II and III as shown in Fig. 7. Let the region bounded by the ground surface and theslip line be defined by the maximum width W and the maximum depth H. Herein, the shape of region II isexpressed by the logarithmic spiral r = ½Bexp(θtanϕ)/cosϕ using the internal friction angle ϕ of the groundand the angle θ. The ground possesses cohesion c of 80 kN/m2, internal friction angle ϕ of 30º and bulk unit
weight γt of 17 kN/m3. The width B of the strip foundation is 1 m and the surface load q is 10 kN/m2. Assume
that the effects of groundwater are negligible, answer the following questions.

Fig. 7(1) Find W/B(2) Find H/B(3) Explain the benefit of knowing W and H in design andconstruction of foundation(4) Calculate the ultimate bearing capacity using the bearing
capacity factors showing on Fig. 8(5) Find the allowable bearing capacity with a safety factor of 3Fig. 85

[Question 5] Answer the following questions.
(1) According to the Fellenius method of stability analysis, a sliding soil mass with underground water isdivided into 𝑛 slices as show in Fig. 9. For any 𝑖th slice counted from the right of a circular arc withradius 𝑟 and center at point O, let the width be 𝑏 , the height be 𝐻 , the length of the base be 𝑙 , theangle of inclination be 𝛼 , the effective cohesion be 𝑐′ , and effective angle of internal friction be 𝜙′ .
Also, the weight of slide is 𝑊 , the forces acting on the right and left sides of the slice are 𝐸 and 𝐸 .
Along the base of slice, 𝑃 (sum of effective normal force 𝑃′ and force 𝑢 𝑙 with pore water pressure𝑢 ) denotes the normal force and 𝑆 denotes the shear force. In the Fellenius method, the resultant forces
acting on the left and right sides of the slice are assumed to be parallel to the sliding plane.
(1-1) Show the equilibrium equation of force in the direction perpendicular to the base of the 𝑖th slice.
(1-2) In regard to the factor of safety 𝐹 , show the equation by which the failure criterion (slidingcondition) of the 𝑖th slice is described.
(1-3) Show the equation of equilibrium for which the balance of moments on the whole sliding soil mass
about point O is taken.
(1-4) Determine the factor of safety 𝐹 for the soil mass against sliding along the circular slip surface
using the above equations.
(1-5) Explain the stability of slope when the ground water level rises due to rainfall using 𝐹 in (1-4).

𝑃𝑃′𝑢𝑙Fig. 9 Sliding soil mass
(2) Answer the following questions regarding soil dynamics and liquefaction.
(2-1) Show two geotechnical conditions that affect the amplification of earthquake ground motion andexplain the effect of the geotechnical conditions on the amplification respectively.
(2-2) Show three principles of liquefaction countermeasure and explain the liquefaction-triggering factor
that the countermeasure targets respectively.

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