2020

Soil Mechanics II and Exercises Midterm Exam

2020/6/10 (Wed.) Test time 8:45-10:15, Submission time via PandA 10:30
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[Question 1] Answer all the following questions(1) In Terzaghi's one-dimensional consolidation theory, the time required for consolidation is influenced by
the thickness of consolidation layer H and the distance to the drainage edge (drainage distance). Here,
explain the reason why the times for consolidation in the layer of thickness H with single-sided drainage
condition and in the layer of thickness 2H with both-sided drainage condition become same.
(2) Answer the following questions about the stress generated in an elastic ground(2-1)

Explain why the Boussinesq stress solution obtained for a semi-infinite linear elastic body is usefulfor estimating the stress in the ground even though the ground is not elastic.

(2-2)

As shown in Fig. 1, a square-shaped building with a central courtyard is constructed on the surface ofa semi-infinite linear elastic ground, and its weight is 100 kN/m2. Calculate the vertical stressincrement at a depth of 10 m below the center of courtyard (Point A). Here, the vertical stress at thepoint below the corner increased in an elastic ground by a rectangular uniform load p of dimensions
B and L is calculated according to the Eq. (1). You may use the chart shown in Fig. 2 to find thesolution.

𝜎(2-3)𝐼 ∙𝑝

1
2𝜋 1𝑚𝑚𝑛 2𝑚1𝑛 √1𝑛𝑚𝑛

sin𝑚𝑛√1𝑚 √1𝑛∙𝑝Eq. (1)As shown in Fig. 3, when the uniformly distributed strip load p acts on the surface of a semi-infinite
linear elastic ground, the magnitude of the principal stresses are equal on the circumference passing
through both ends of the load, and the direction of the maximum principal stress is the direction of thestraight line connecting points D and A. Explain the reason why. Here, the stresses on thiscircumference can be expressed by Eqs. (2) to (4) as follows.
- 1 -𝜎𝑝𝜃𝜋𝜃sin 𝜃𝜃 cos 𝜃𝜃𝑝2𝛽𝜋

sin 2𝛽 cos 2𝛼

Eq. (2)𝜎𝑝𝜃𝜋𝜃sin 𝜃𝜃 cos 𝜃𝜃𝑝2𝛽𝜋

sin 2𝛽 cos 2𝛼

Eq. (3)𝜏𝑝sin 𝜃𝜋𝜃 sin 𝜃𝜃𝑝sin 2𝛼 sin 2𝛽𝜋

40 m

20 m
A40 m
20 m

Fig. 1

Square-shaped building with a central courtyard

Fig. 2

Influence factor Iz- 2 -Eq. (4)DpBC

x




Az

Fig. 3

A circumference having same magnitude of principal stresses- 3 -[Question 2] After completing an isotropic consolidation pressure to the mean effective stress p′o, a consolidated
undrained (CU ) triaxial compression test was conducted with constant confining pressure on a saturated
normally consolidated clay (assuming cohesion 𝑐′ = 0). Using experimental data of the two samples tested under
the condition, the values of p′o were 200 kN/m2 (Test1) and 300 kN/m2 (Test 2), the effective stress path in thep′ - q plane shown in Fig. 4 was obtained. Herein, σ1 is the major principal stress, σ3 is the minor principal stress,
σ′1 is the major effective principal stress, σ′3 is the minor effective principal stress and pf is the mean total stressat failure.

Fig. 4Table 1 shows the results of the mean effective stress p′f and the deviator stress qf obtained at the time of failurein each specimen.
Table 1
2

Test

p′o (kN/m )p′f (kN/m2)

qf (kN/m2)

1200

99

93

2300

147

134

Assume that the material properties of the samples used for each test are the same. Answer the followingquestions.
(1) Calculate the pore water pressure at failure uf in each test and find the average value of the Skempton’spore pressure coefficient at failure Af.
(2) Based on the experimental result, find the average of the slope of the failure line (stress ratio at failure), M.
(3) Draw the effective stress Mohr’s circle at failure for triaxial compression test and derive the relationshipbetween the slope of the failure line M in the p′-q plane and the angle of internal friction 𝜙′, and then findthe average 𝜙′ from the tests.
(4) Based on the above results, determine the average shear strength ratio (cu / p′o) from the undrained shear
strength cu of this saturated normally consolidated clay.
(5) Regarding the experimental result of the same sample subjected to the isotropic consolidation pressure p′o= 400 kN/m2 under the same condition of CU test, draw the relationship among the failure line, theeffective stress path and the total stress path in the p - q plane (q = σ1 - σ3, p = (σ1 + 2σ3) / 3). Specify theestimated values of M, p′o, p′f, pf, qfanduf- 4 -in the figure.

[Question 3] Answer all the following questions(1) Fig. 5 represents a retaining wall of height H. Let the frictional angle, the cohesion, and the unit weight ofthe soil behind the wall be , c, and , respectively. Draw a graphic showing the three types of representative
earth pressure that act on the retaining wall, taking the displacement of the retaining wall () along thehorizontal axis and the earth pressure along the vertical axis. Refer to the figure for the direction of
displacement of the retaining wall.
(2) Based on Coulomb’s earth pressure theory, determine the earth pressure acting on the retaining wall when
it moves towards the soil side ( - direction). 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 theretaining wall and the soil. Show the force polygon diagram using the forces that act on the soil wedge
shown in the figure. Use appropriate symbols for the forces shown in the force polygon diagram and explain
each of those forces. Assume that the ground water table lies far below the retaining wall.
(3) Based on Coulomb’s earth pressure theory mentioned in (2), briefly explain the procedure of determining
the earth pressure acting on the retaining wall when it moves towards the soil side ( - direction).
(4) 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 rightward towards the soil ( +direction). Also, show the earth pressure distribution along the height (H) of the retaining wall. For this,assume that the friction between the retaining wall and the soil behind is zero and that the ground watertable lies far below the retaining wall.
(5) Explain the difference in the magnitudes of the active resultant earth pressure (resultant of the earth pressure
and the water pressure) when the ground water table behind the retaining wall (i) lies at the bottom surfaceof the retaining wall and (ii) is rising up to the ground surface. Focus your answer on the difference in theearth pressure and the water pressure under those two conditions. Assume the unit weight of water as w.

Displacement of the retaining wall(5) Ground water table risingup to the ground surfacecHFig. 5- 5 -