2018

Soil Mechanics II and Exercises Final Exam

2018/8/1 (Wed)10:00-12:00

Kyotsu 2 Lecture room

Attention:•This 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 insequence, starting from [Question 1]. If the front page of any answer sheet is insufficient to complete
your answer, use the back page of the same answer sheet after clearly indicating your intent.

•Scores of all questions are weighted evenly.

•In addition to personal writing instruments, non-programmable calculators are permitted. However,programmable calculators and calculator functions of mobile phones are prohibited. Any attempts atcheating on the exam will result in failed credit of the course and serious penalties.

•Wherever necessary, specify the units in your answers.

[Question 1]
The ground shown in Figure 1 consists of a 10 m-thick layer of soft clay deposited over an impermeable
bedrock. Samples were taken from this clay layer and tested at the laboratory. For a certain set of loadconditions, the following properties that represent this ground were obtained: coefficient of volumetric change
mv = 3.00 × 10-3 m2/kN, and coefficient of permeability k = 1.55 × 10-4 m/day. To answer the following
questions, assume that load conditions at the field are similar to the laboratory ones and also that the clay layer
is completely saturated and deformed only by one-dimensional consolidation.
The groundwater table coincides with the ground surface, and the unit weight of water is 9.8 kN/m3.
(1) Calculate the vertical coefficient of consolidation cv (m2/day) of the clayey soil.
(2) Calculate the time (days) for this soil to reach 90% degree of consolidation (Tv = 0.848) due to verticalloading.
(3) Calculate the settlement (consolidation at the time described in point (2)) when the soil is subject to thesurcharge load ∆p = 60 kN/m2.
(4) The sand drain method was adopted to shorten the time required for consolidation. As shown in Figure 2,
a hexagonal pattern was chosen, with sand pile diameter dw = 0.35 m and distance between sand pile coresd = 2.0 m. Calculate the equivalent sand drain diameter de.
(5) Using Figure 3, find the time required for this clay layer to reach 90% consolidation. For simplicity,
assume the mechanical properties to be the same in both the vertical and horizontal directions (cv = ch).
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ddd-4k = 1.55×10 m/daydeH = 10mmv = 3.00×10-3m2/kN

γw = 9.8kN/m3dw
Impermeable Bedrock

Figure 1

Figure 20.0

U
Degree of Consolidation
UClayn = 200.2

100.4

460.6

20.8
1.00.0001

0.001

0.01

Th = chTt h/ de2

Figure 3

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[Question 2]
Answer the following questions regarding shear strength of soils.
(1) A consolidated undrained triaxial compression test was conducted on a saturated, normally consolidated
clay. The confining pressure, used until the end of consolidation and kept constant during shearing, was
100 kN/m2. The deviator stress measured at failure was 72 kN/m2. The pore water pressure increment
obtained from the beginning of shearing was 64 kN/m2. Answer the following questions, assuming that thecohesion 𝑐𝑐′ is zero.

(a) Draw Mohr’s circles for total stress and effective stress at failure along with the values of the maximum
and minimum principal stresses.
(b) Find the internal friction angle 𝜙𝜙′ of the clay(c) Draw the total stress path and the expected effective stress path in 𝑝𝑝 − 𝑞𝑞 and 𝑝𝑝′ − 𝑞𝑞 planes,respectively. Include the values of 𝑝𝑝′ ，𝑝𝑝，𝑞𝑞 at the beginning of shearing and at failure in the figure.

Herein, 𝑝𝑝 is the mean total stress, 𝑝𝑝′ is the mean effective stress, and 𝑞𝑞 is the deviator stress.

(d) Find the value of Skempton’s pore pressure coefficient at failure 𝐴𝐴𝑓𝑓 .
(e) Find the slope of the critical state line 𝑀𝑀 of the clay.

(2) The three types of triaxial compression tests for soils generally depend on the consolidation process andthe drainage conditions during the shearing process.
(a) Apart from consolidated-undrained triaxial compression test, list the other two test methods.
(b) For each of the test methods answered in (a), schematically draw Mohr’s circles of the total stress andeffective stress at failure for experiments conducted with two different confining pressures.
(c) Describe the characteristics of cohesion and internal friction angle obtained for each test answered in
(a).

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[Question 3]
Consider the retaining wall of height H shown in Figure 4. Let the frictional angle, the cohesion, and the unit
weight of the backfill soil be ϕ, c, and γ, respectively. Answer the following questions.
Displacementof the retaining wall
擁壁の変位
In part (4), the groundwater(4)で地下水位がtablerises to the ground
上がった場合surface

Figure 4(1) Based on Coulomb’s earth pressure theory, determine the earth pressure acting on the retaining wall when

it moves leftward (𝛿𝛿− ) as indicated in the figure. Assume that the cohesion c of the backfill soil is zero andthat the surface of the retaining wall is smooth; hence, there is no friction between the retaining wall andthe backfill soil. Draw the force diagram composing of the forces that act on the soil wedge shown in thefigure. Use appropriate symbols for the forces that appear in the force diagram and clearly explain eachone of those forces.
(2) Under the concept of Coulomb’s earth pressure described in (1), briefly explain the procedure by which

the earth pressure acting on the retaining wall is determined when it displaces in the direction to the left(𝛿𝛿− ) of the figure.
(3) While reassessing the conditions of the backfill soil, it was found that the cohesion was not zero. Under

the concept of Rankine’s earth pressure, obtain the earth pressure that acts on the retaining wall when it
moves in the direction to the left (𝛿𝛿− ) of the figure and draw the earth pressure distribution diagram

exerting on the retaining wall of height H. It is assumed that the friction between the retaining wall andthe backfill soil is zero and that the groundwater table lies sufficiently deep below the retaining wall.
(4) Focusing on the difference in the earth pressure and water pressure, explain the difference in themagnitudes of the resultant active force (a sum of the forces due to earth pressure and the water pressure)when the groundwater table behind the retaining wall rises up to the ground surface and lies at the bottomof the retaining wall. Herein, the unit weight of water is γw.

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[Question 4]
Answer the following questions about bearing capacity of soils.
(1) Draw the failure patterns for the cases of local shear failure and general shear failure for a strip foundation.
Clearly indicate which of the plotted regions are under passive or active condition. Assume that the watertable is located deep enough and does not affect these patterns.
(2) Terzaghi developed the following equation to calculate the bearing capacity of soils, qu. The constants 𝑘𝑘1 ,𝑘𝑘2 , and 𝑘𝑘3 are different for strip, square, and circular foundations, but the expressions (I), (II), and (III)are similar in all three cases.

(𝐼𝐼)𝑞𝑞𝑢𝑢 = 𝑘𝑘1
Type ofFoundation
Strip
SquareCircularConstant forcontribution ofcohesion, 𝑘𝑘1
1.0+ 𝑘𝑘2

1.3(𝐼𝐼𝐼𝐼)+ 𝑘𝑘3

Constant forcontribution ofsurcharge, 𝑘𝑘2
1.0
1.0

1.3(𝐼𝐼𝐼𝐼𝐼𝐼)

Constant forcontribution of unit
weight of soil, 𝑘𝑘3
1.0

1.0

0.8
0.6

Complete down Terzaghi’s equation by indicating the expressions that should replace the terms (I), (II),and (III). Assume that the foundation has a width B and a depth D, and that the characteristics of the soil
are: unit weight γ, cohesion c, and angle of friction ϕ.
(3) The base of a circular footing of diameter B = 2 m rests at a depth D = 1.7 m in a soil with parameters γ =19 kN/m3, γsat = 21 kN/m3, c = 26 kPa, ϕ = 22.5°. Assume that the water table is located deep enough anddoes not affect the bearing capacity of the soil. Determine the ultimate bearing capacity of the soil underthese conditions.
For your analysis you can use the following equations for the bearing capacity factors, where ϕ is inradians:
3𝜋𝜋1𝑁𝑁𝑞𝑞 = 1−sin 𝜙𝜙 exp �� − 𝜙𝜙� tan 𝜙𝜙�
2𝑁𝑁𝑐𝑐 = �𝑁𝑁𝑞𝑞 − 1� cot 𝜙𝜙𝑁𝑁𝛾𝛾 = �𝑁𝑁𝑞𝑞 − 1� tan(1.4𝜙𝜙)(4) If the water table rises and stays at the base of the foundation, calculate the new bearing capacity of thissoil. Use a unit weight of water: γw = 9.8 kN/m3.
(5) If we replace the circular footing with a square one of sides B = 2 m, calculate the new bearing capacity ofthe soil under the same conditions described in (4). Comment on the difference.

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【Question 5】
Answer the following questions.
(1) According to the Fellenius method of stability analysis, a sliding soil mass is divided into n slices as show
in Figure 5. For any ith slice counted from the right of a circular arc with radius r and center at point O, let
the width be bi , the height be hi , the length of the base be li , the angle of inclination be α i , the angleof internal friction be φi and the cohesion be ci . Also, the weight of slide is Wi , the forces acting on theright and left sides of the slice are Ei (the resultant of the horizontal force H i and the vertical force Vi )and Ei +1 (the resultant of the horizontal force H i +1 and the vertical force Vi +1 ). Along the base of slide,Pi denotes the normal force and Si denotes the shearing force.

(a) Show the equilibrium equation of force in the direction perpendicular to the base of the ith slice.
(b) In the Fellenius method, the resultant forces acting on the left and right sides of the slice are assumed tobe parallel to the sliding plane; thus (Vi +1 − Vi ) / ( H i +1 − H i ) =sin α i / cos α i . Rewrite the equation
obtained in (a) by using this expression.
(c) In regard to the factor of safety F , show the equation by which the failure criterion (sliding condition)of the ith slice is described .
(d) Show the equation of equilibrium for which the balance of moments on the whole sliding soil mass
about point O is taken.
(e) Use (b), (c) and (d) to determine the factor of safety F for the soil mass against sliding along thecircular slip surface.

Vi +1

Ei +1
Hi

H i +1hiEi

Figure 5 Sliding soil mass
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Vi(2) The onset mechanisms of liquefaction can be explained as follows.
A loosely deposited sandy ground such as reclaimed land lying deeper than the groundwater level is under（①）condition. When this ground is subjected to （ ②）due to an earthquake,（ ③）of the

sandy ground with respect to the duration time of the earthquake ground motions is small, so the soil
element in the ground becomes almost （ ④decreased by the negative （）condition. At that time when the mean effective stress⑤ ）is nearly zero, liquefaction eventually occurs.

(a) Fill in the blanks ① to ⑤ with the appropriate expressions.
(b) Choose any three of ① ~ ⑤ and present the underlying principle of liquefaction countermeasureassociated with each of which (also show the number ① ~ ⑤).

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