2021

Soil Mechanics II and Exercises Midterm Exam

2021/6/9 (Wed.)

Test time 8:45-10:15, Submission by 10:30 on PandA

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[Question 1] Answer all the following questions(1) In Terzaghi's one-dimensional consolidation theory, it is assumed that the soil is fully saturated, and thesolid particles and water are incompressible. Show the equation used for the derivation along with thereason why Terzaghi's one-dimensional consolidation equation cannot be derived without theseassumptions.
(2) Sand drain method is a soil improvement method for soft ground.
(2-1)

Explain the sand drain method by graphics.

(2-2)

Explain the principle of the soil improvement by the sand drain method through the mathematicaldefinition of a time factor.

(3) Kögler proposed an extremely simple formula by which the vertical stress in the ground is approximatedwhen a uniformly distributed load is acting on a rectangular foundation. This approximation formula isbased on the simple assumption that the distribution of vertical stress on the horizontal plane in the groundis uniformly distributed within a closed region. As shown in Fig. 1, when a rectangular load p [kN/m2](width: B, length: L) acts on the ground surface, the following equation can be obtained from theequilibrium condition by applying Kögler's assumption.
- 1 -∆𝜎𝑝A

Eq. (1)(3-1)

Using symbols shown in Fig. 1, complete Eq. (1) by the equation that should replace the term (A).

(3-2)

Based on Kögler's assumption, find the final consolidation settlement induced by the structural load pshown in Fig. 2. Here, it is assumed that the consolidation settlement of the clay layer can becalculated from the change in the effective overburden pressure at the center of the clay layer, and = /4. The unit weight of water is 9.8 kN/m3, and the consolidation settlement of sandy layers can beignored.
(4) The vertical stress generated in an elastic ground by a trapezoidal strip load (Fig. 3), such as a levee or aroad embankment, is calculated according to the following equation, given by Osterberg.
𝜎𝑝 𝑎 𝑏𝜃𝜋 𝑎𝜃𝑏𝜃𝑎𝐼 ∙𝑝

Fig. 4 shows one such case when a triangular strip load acts on an elastic ground. Calculate the verticalstress increment at points A and B. You may use the chart shown in Fig. 5 to find the solution.
p = 100 kN/m2

BLzp

sat = 20 kN/m34m

sat = 16 kN/m3
Clay layere0 = 2.1(Normalconsolidation) Cc = 0.426m

Sandy layerz

B=L=8mSandy layer

Fig. 1

Fig. 2

p = 100 kN/m2
4m

4m
4m2m
BFig. 3

AFig. 4- 2 -Fig. 5- 3 -[Question 2] Answer the following questions.
(1) Fill in the blanks in the following sentences with appropriate words forSoil dilatancy is defined as the change in volume caused bycompression tests, the volume of loose soil tends toIn the case of⑥soils and⑤③①to⑧. In the case of.
②, while the volume of dense soil tends totriaxial④.

triaxial compression test, the volume change of the specimen is negligible, and instead,is generated due to the dilatancy characteristics. The value of⑧①⑥tends to be⑦in loose

in dense soils.

(2) In triaxial compression tests, the principal stresses are controlled. Describe why the triaxial compression test
can evaluate the shear strength of a soil even though the shear stress is zero on the principal planes.
(3) A consolidated undrained triaxial compression test was conducted on a sample of normally consolidated clay
after isotropic consolidation with a confining pressure of 200 kN/m2. At failure, the deviator stress 𝑞 was 225
kN/m2 and the excess pore water pressure 𝑢 was 95 kN/m2.
(3-1) Determine the mean effective stress at failure 𝑝′, Skempton's pore pressure coefficient 𝐴 , and the failure
stress ratio 𝑀 .
(3-2) Draw the total stress path of this test in the 𝑝𝑞 plane and the expected effective stress path in the 𝑝′

𝑞 plane.
(3-3) Assuming that the cohesion 𝑐′ is zero, find the internal friction angle 𝜙′ of this clay.
(4) Using the same sample as in (3), uniaxial compression test was conducted, and the uniaxial compressive strength𝑞 was 90 kN/m2.
(4-1) Furthermore, an unconsolidated undrained triaxial compression test is conducted on the same specimen asin (3) with a confining pressure of 100 kN/m2. Determine the estimated undrained shear strength 𝑐 .
(4-2) Draw Mohr’s stress circle at failure for the test (4-1).
(4-3) In general, excess pore water pressure is not measured in the unconsolidated undrained triaxial compression
test. However, the excess pore water pressure at failure can be estimated using the Mohr-Coulomb failure
criterion. Find the value of pore water pressure at failure estimated for the test (4-1).

- 4 -【3】 Answer the following questions.
(1) As shown in Fig. 6, a rigid retaining wall with the heigh of 𝐻 retains a flat backfill. The relationship between
the displacement 𝑢 of the retaining wall and the earth pressure 𝑝 that acts on that wall can be drawn.
(1-1) Indicate the terminologies for which three representative earth pressures of 𝑝 , 𝑝 and 𝑝 are defined.
(1-2) In general, 𝑝𝑝𝑝 as shown in the figure. Explain the reason briefly.

(1-3) The magnitude of displacement when 𝑝

𝑝 is generally less than that when 𝑝

𝑝 as shown in thefigure. Explain the reason briefly.
Earth pressurepOutwards(‐)u(+)
uthe backfill

Towards thebackfill

pp

Retaining wallu (‐)

Heightu (+)
Backfill soil

p0pau
Displacement

Fig. 6(2) After installation of rigid sheet pile into a level ground in Fig. 7 (a), the left-side ground is excavated in Fig.

7 (b). Under the condition of (b), either active or passive state in the ground near the sheet pile can beassumed. Here, the unit weight of the ground is 𝛾, the internal friction angle is 𝜙′, and the cohesion can beneglected.
(2-1) At depth z of point A, schematize Mohr’s stress circles upon the conditions of (a) and (b).
(2-2) At depth z of point B, schematize Mohr’s stress circles upon the conditions of (a) and (b).
(2-3) Coulomb’s earth pressure along the left side of the sheet pile associated with (b) is discussed. Draw therigid wedge and the forces acting on the wedge.
(2-4) Coulomb’s earth pressure along the right side of the sheet pile associated with (b) is discussed. Draw therigid wedge and the forces acting on the wedge.
Sheet pile wall

Sheet pile wallDepthADepthBA(a) Installation of sheet pile
before excavation

B(b) After excavation

Fig. 7- 5 -