2013 Soil Mechanics II and Exercise - Final Exam
2013/07/31 (Wed) 10:00～12:00

Room: Kyotsu-4

Attention:


There are five questions and 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 side of an answer sheet is not enough for answering one specific question,
you can use the back side of the same answer sheet, after clearly mentioning so. All questions bearequal mark.



Non-programmable calculators are permitted, but calculators that have programming functions and alltypes of mobile phones are prohibited.



If you behave maliciously during the exam, you will not be entitled to get any credit on this subject.

Wherever necessary, show the units in your answers.

【1】Answer the followings questions regarding consolidation of clayey soil ground:(1) A clay layer of thickness H lies above an impermeable rock layer. Assume that the ground water level coincides
with the ground surface. After the rapid application of a load over the clay layer, the consolidation process can beanalyzed based on Terzaghi’s one dimensional consolidation equation shown below:∂𝑢∂2 𝑢= 𝑐𝑣 2∂𝑡∂𝑧(1)Here, u: excess pore water pressure (= pore water pressure – hydrostatic pore water pressure), 𝑐𝑣 : consolidation
coefficient, t: time, and z: coordinate along the depth direction.
(a) If the upper surface of the clay layer (i.e., the ground surface) is represented as z = 0, and the lower surface ofthe clay layer (i.e., the upper surface of the impermeable rock layer) as z = H, then write the boundary
condition for the upper surface of the clay layer (z = 0).
(b) Write down the boundary condition for the lower surface of the clay layer (z = H). [Hint: Think about thecondition where the flow rate becomes zero in Darcy’s Law.](2) If immediately after the rapid application of the load, the excess pore water pressure (u) is equal to 𝑢0 [i.e.,𝑢 = 𝑢0 (constant)] then, considering this as the initial condition, find the solution of the consolidation equation
shown above.
(3) Sand drain is one of the ground improvement methods used for accelerating the consolidation of soft ground.
Explain the principles behind this method.

【2】Answer the following questions:(1) Triaxial tests of soil specimens are generally performed in two consecutive steps: a consolidation followed byshearing. Based on the drainage conditions during these steps, the triaxial tests are classified in three types. What
are those types? Mention the drainage condition, and the principal stresses in terms of the total stress and theeffective stress, at each step for the three test types.
(2) What is an unconfined compression test and which triaxial test resembles it better? If the maximum value of thecompressive stress obtained from this test is qu, then show the shear strength of this test specimen using a Mohr’s
stress circle.
Also, comment on why the unconfined compressive strength is used in the case of short term stability analysis.
(3) A saturated sand specimen was tested under drained conditions. The specimen failed at a deviator stress (𝜎1 −𝜎3 ) of 360 kPa when the cell pressure (𝜎3 ) was 100 kPa. Assume 𝑐  = 0 for this sand specimen.
(i)

Find the value of the effective internal friction angle,  .

(ii)

What would the value of the deviator stress be if another identical specimen is tested under a cellpressure of 200 kPa?

(iii)

Represent the above two tests with Mohr’s stress circles and Mohr-Coulomb failure envelopes.

【3】Answer the following questions:(1) The figure below represents a retaining wall of height H. Let the frictional angle, the cohesion, and the unit
weight of the soil behind the wall be , c, and , respectively. Draw a graphic showing the three types ofrepresentative earth pressure that act on the retaining wall, taking the displacement of the retaining wall ()along the horizontal 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 iszero. Also, assume that the surface of the wall is smooth and, hence, there is no friction between the retaining
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 theearth 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 the soil,c, was not equal to zero. Under this new condition, and based on Rankine’s earth pressure theory, obtain theearth pressure that acts on the retaining wall when it moves away from the soil ( direction).
Also, show the earth pressure distribution along the height (H) of the retaining wall. For this, assume that thefriction between the retaining wall and the soil behind is zero and that the ground water table lies far below theretaining wall.
(5) Explain the difference in the magnitudes of the active resultant earth pressure (resultant of the earth pressure andthe water pressure) when the ground water table behind the retaining wall (i) lies at the bottom surface of theretaining wall and (ii) is rising up to the ground surface. Focus your answer on the difference in the earthpressure and the water pressure under those two conditions. Assume the unit weight of water as w.

Displacementof the retaining wall
擁壁の変位





(4)で地下水位が(5)
Ground water rising
上がった場合up to the ground surface

 , , cH【4】Answer the following questions about foundation design:(1) The following figure represents a strip (long) footing.
Load, Q

Footing depth, Df

Unit weight: 𝛾𝑡(1)Saturated unit weight: 𝛾𝑠𝑎𝑡(1)Cohesion: 𝑐(1)Angle of internal friction: 𝜙(1)Layer 1

Layer 2

Footing width, B

Unit weight: 𝛾𝑡(2)Saturated unit weight: 𝛾𝑠𝑎𝑡(2)Cohesion: 𝑐(2)Angle of internal friction: 𝜙(2)(a) Using the parameters shown in the abovefigure, explain the difference between shallow and deep foundation.
(b) Using the bearing capacity factors, Nc, N, and Nq, the ultimate soil-bearing capacity, qu, can be calculatedusing Terzaghi’s bearing capacity equation as follow:

1qu  Q / B    Nc    BN    D f Nq
 
 
2 
Assuming that the water table is located far below the footing, indicate what soil parameters correspond to ,, and  in the previous equation.
(c) By introducing the factor of safety, FS, in the above equation, derive the equation corresponding to theallowable bearing capacity, qallowable.
(d) As shown in the following figure, assume that the water table has risen to a depth of hw below the groundsurface. If Terzaghi’s ultimate bearing capacity equation is represented this time as:1qu  Q / B    Nc    BN    Nq
 
 
2 
indicate what soil parameters correspond to , , and . Use 𝛾𝑤 as the unit weight of water.
Load, Q

Unit weight: 𝛾𝑡(1)Saturated unit weight: 𝛾𝑠𝑎𝑡(1)Cohesion: 𝑐(1)Angle of internal friction: 𝜙(1)hw
Footing depth, Df

Layer 1

Layer 2

Footing width, B(2) Explain the following concepts using figures:
・ Local shear failure and general shear failure
・ Negative skin friction

Unit weight: 𝛾𝑡(2)Saturated unit weight: 𝛾𝑠𝑎𝑡(2)Cohesion: 𝑐(2)Angle of internal friction: 𝜙(2)

【5】Answer the following questions:(1) As shown in the figure below, the ground water table lies at a depth z0 from the ground surface. Assume a steadyseepage flow with the flow parallel to the slope surface. Fill up the blank squares ① ～ ⑦ with the appropriate
expressions, and also answer questions (a) and (b).


b

D

A'

z

t

sat

z0

B'

T

A

L
W



B

z-z0

(z-z0)cos2

C(z-z0)cos

すべり面
Failure surfaces

Let the unit weight of the soil above the ground water table be  t . Similarly, let the saturated unit weight of the soil
below the ground water table be  sat . The flow net is as shown in the figure above, with flow lines parallel to theground surface, and equipotential lines perpendicular to the ground surface and the failure surface. On the shown
flow net, the points C and D lying on the same equipotential line have equal total water heads. If the potential waterhead and the pressure water head are represented by he and h p , respectively, then the total water heads at points C
and D can be written as:

he (C )  hp (C )  he ( D)  hp ( D)
Therefore, the pressure water head at point C, hp  C  can be written as:

hp (C )  he ( D)  he (C )  hp ( D)  (z  z0 )cos2 
Following the above equation, the pore water pressure, u, that acts on the failure surface can be written as:u  hp (C )   w   w ( z  z0 )cos2①

(1)Here,  w is the unit weight of water. Next, we will calculate the normal stress, , and the shear stress,  that act on
the bottom surface of the sliding soil mass (A′ ABB′) that has a width of b, as shown in above figure. To do so, wewill first calculate the weight of the sliding soil mass, W. The weight of the sliding soil mass (A′ ABB ′) is written as:

W   t z0   sat ( z  ②z0 ) b(2)

The length of the bottom of the sliding soil mass, AB is expressed as:

AB =

③

(3)

Using equations (2) and (3),  and  mentioned above are calculated as shown in Equations (4) and (5). Here, L and
T are the vertical (normal) and parallel (shear) components of W (weight of sliding soil) that act at the bottom
surface of the sliding soil mass.

  L / AB   t z0   sat ( z ④z0 ) cos 2 (4)  T / AB   t z0   sat ( z ⑤z0 ) cos  sin (5)From Equations (1) and (4), the effective normal stress that acts on the failure surface is given by:2
 '    u   t z0   '( z  z⑥0 ) cos (6)Here,     sat   w : Submerged unit weight of the soil mass.
If the cohesion and the angle of internal frictional of the soil is represented by 𝑐  and   , then the shear strength,

s, of the soil can be represented by s  c    tan   . Now, the factor of safety, Fs can be obtained as shown below
using the results of equations (5) and (6):c '  t z0   '( z  z0 ) cos 2  tan  'Fs  
 t z0   sat ( z ⑦z0 ) cos  sin s(7)(a) Find the factor of safety when the ground water table lies on the ground surface. At this condition, also find thecritical height, 𝐻𝑐 , for which the soil mass starts to slide.
(b) Find the factor of safety when c  0 , and the ground water table lies far below the failure surface (     t ，

 sat   t ).
(2) In five lines or less, explain the mechanism of soil liquefaction. In addition to that, list five countermeasures againstliquefaction, briefly indicating the principles behind them (i.e., why do they work).

2014 Soil Mechanics II and Exercises Final Exam
2014/07/30 (Wed)10:00~12:00

Room : Kyotsu-4

Attention:


There are five questions and 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 side of an answer sheet is not enough for answering one specific question, you can use
the back side of the same answer sheet, after clearly mentioning so.

Non-programmable calculators are permitted, but calculators that have programming functions andall types of mobile phones are prohibited.



If you behave maliciously during the exam, you will not be entitled to get any credit on this subject.

Wherever necessary, show the units in your answers.

【1】In regards with the consolidation of clayey soil ground, answer the following questions:
As shown in Fig. 1-1, the horizontally layered soil ground consists of a sand layer (5 m thick), a fully
saturated clay layer (3 m thick) and an impermeable layer. Ground water table lies on the upper boundaryof saturated clay layer. Bulk unit weight of sand layer, t=20.0 kN/m3. From the depth of GL-6.5 m, sample
of saturated clay was obtained and one dimensional consolidation test was done. From the test, saturated
unit weight, sat=23.1 kN/m3, compression index, Cc=1.0, swelling index, Cs=0.10, maximum past pressure,py=120 kN/m2, and initial void ratio, e0=2.78 were obtained.
In order to construct a building of reinforced concrete, the soil ground is excavated up to 3 m depth. Let theheight and the equivalent surcharge load of each floor including basement of that building be 3 m and 9
kN/m2, respectively. Assume that the saturated clay layer was in normally consolidated state before the
excavation. At this condition, answer the questions below.
Here onward, consider that the base of the excavation is wide enough and consolidation due to surcharge
load of reinforced concrete building is one dimensional. In addition, the amount of deformation of clay
layer is approximated as the representative strain value at the center of the clay layer. Take unit weight ofwater as 9.81 kN/m3.
(1) If 3 m of the sand layer is excavated, then determine the vertical displacement (expansion or swell) at thebottom surface of this excavation. Consider the vertical swell at the bottom surface of excavation is dueto the swell of clay layer only. Here, swell (or expansion) of the sand layer neglected.
(2) Now, from the condition of (1), 10-floor building [one basement and 9 other floors above the ground] isconstructed. At this condition, determine the final settlement of the bottom surface of the excavation incomparison to its initial condition before the excavation. [Hint: Settlement of normally consolidated clay
= Final settlement].
(3) When 10-floor building [one basement and 9 other floors above the ground] is constructed, consolidation
continues up to 90% of its final settlement. Determine the time taken to reach 90% of final settlement.
Take time factor, Tv=0.848 for 90% degree of consolidation (U=90%) and consolidation coefficient,
cv=80 cm2/day. Here, the consolidation settlement is considered to be only due normal consolidation.
(4) Determine total number of floors that is possible to be included in the building so that there occurs noconsolidation settlement in comparison to its initial condition which is before the excavation.

(5) Time dependent consolidation process that takes place within the saturated clay layer can be analyzed byusing Terzaghi’s one dimensional consolidation equation. Write down the equation of Terzaghi’s one
dimensional consolidation. Explain the symbols (parameters) used in that equation.
In addition, referring to Fig. 1-1, write down the boundary conditions at the upper boundary (drain
condition) and lower boundary (undrain condition) of saturated clay layer.

1st floor

Sand layer

Basement-1

Saturated clay layer

Impermeable layer
Fig. 1-1【2】In regard with failure criterion of soil, answer the following questions:(1) Undrained triaxial compression test was conducted for a normally consolidated saturated clay specimen.
Confining pressure at the end of consolidation was 100 kN/m2. Deviator stress and excess pore waterpressure measured at failure during undrained shearing were 200 kN/m2 and 80 kN/m2, respectively.
Taking the value of cohesion as zero, answer the following questions:(a) Plot Mohr’s stress circles (total as well as effective) along with Mohr-Coulomb’s failure line. In theplot, show the values of major and minor principal stresses also.
(b) In reference to effective stress plot, find the internal friction angle of this soil specimen.
(c) In reference to (b), determine failure angle that the failure plane makes with major principal plane.
(d) In reference to (b) and (c), determine the normal and shear stresses that act on the failure plane.
(e) Plot total stress path and effective stress path in p, p-q space for this test showing the values of p, p
and q at the start and failure states of shearing. [Here, p: mean total stress, p: mean effective stress,
q: deviator stress].
(f) Determine pore water pressure coefficient, Af at failure.
(2) Three direct shear box tests were conducted for the dry sand under constant stress condition. Let thenormal forces applied at each test be N1, N2 and N3 [N1 > N2 > N3]. Answer the following questions:(a) How do you obtain the strength parameter of this sand? Explain in brief with graphs.
(b) Depending on the void ratio, behavior of graphs of volume change with change in horizontal
displacement varies. Draw graphs and comment on this matter.
(3) Explain briefly Sensitivity and Quick clay in regards with clayey soil.

【3】Answer the following questions:(1) In reference to Fig. 3-1, draw a graph showing the relationship between the displacement {u(-) and u(+)}
of the retaining wall and the earth pressure, P that acts on that wall. Also, within the graph, indicate the

(+)
変位u
u(+)

よう壁

u

Retaining wall

displacement

変位u (-)(-)

Failure
すべり面
plane



よう壁

displacement

Retaining wall

earth pressures which represent equivalent active and passive earth pressures.

a)a）主働状態
Active state

Failure
すべり面
plane


b)
Passive stateb）受働状態

Fig. 3-1(2) Explain the conditions at which Rankine’s earth pressure theory and Coulomb’s earth pressure theory
become equal.
(3) Retaining wall of height, H is constructed on the horizontal soil ground (unit weight, ) as shown in Fig.
3-2. Explain the active earth pressure that is calculated based on Coulomb’s earth pressure theory using
Force Polygon diagram. Take  as the friction angle that acts between the retaining wall and the soil
behind the wall.
In the Force Polygon diagram, indicate all the force vectors. Also, explain the component of each of

Retaining wall

よう壁

Height, H
高さ H

those force vectors.



Failure plane
すべり面
Unit weight of soil behind the wall: Friction angle between the retaining wall and
裏込め土の単位体積重量
the soil behind the wall:  
裏込め土とよう壁の摩擦角
Internal friction angle of soil behind the
裏込め土の内部摩擦角
retaining wall: Fig. 3-2(4) As shown in Fig. 3-3, it is thought to set up a freely supported sheet pile after the excavation of a soil
ground. Let H1 be the excavation depth from the soil ground surface and H2 be the depth from the
excavated surface to the base of the sheet pile.
At this condition, calculate the resultant earth pressure, P2 that acts on excavation side.
Also, calculate the position, h2 at which this resultant force P2 acts.
Take unit weight, cohesion and internal friction angle of the soil ground as , 0 and , respectively.

Ground surface

地表面

Freely supported
sheet
pile
自由支持矢板H1

h1

Excavated
掘削面 surface

合力P1

h2
H2

Resultant earthpressure

合力P2

Resultant earthpressure

Fig. 3-3(5) In regards with earth pressure distribution along the freely supported sheep pile as shown in Fig. 3-3,
draw the graphs of earth pressure distribution along the excavated side and retaining side of the sheet
pile. While drawing the graphs, compare the distribution of earth pressure for the conditions whencohesion of the soil is equal to c and zero, respectively. Also, comment on this matter.
【4】Answer the following questions:(1) In relation with slope stability, answer the following questions:
Fellenius method (Sweden method) is one of the slope stability analysis methods where failure plane isassumed to be a circular arc and the failing soil mass is divided into n number of slices. During thismethod following three conditions are considered; a) the condition of equilibrium of forces along thedirection perpendicular to the failure plane, b) the condition of equilibrium of sliding moment andresisting moment around the center of circular arc, and (c) the conditional factor of safety (FS) withrespect to Mohr-Coulomb failure condition.
Now, for the condition where pore water pressure is developed within the slope due to rain fall, write
down the conditional equations (a)~(c) mentioned above. From these conditional equations, derivefollowing calculation equation of slope stability factor.
∑






1

Here, in regards with ith slice:
Internal friction angle of soil=i, cohesion=0, sloping angle of the failure plane=i, self-weight of theslice=Wi, pore water pressure=Ui.
Summation represents the summation of all the slices divided for the sliding soil mass above the failure
plane.

(2) Considering the equation (1), explain why landslides are more likely to occur when it rains.
(3) Regarding the liquefaction of soil ground, answer the following questions:(a) Explain general mechanism of liquefaction.
(b) List three countermeasures against liquefaction and explain the principles behind them.
【5】If B=foundation width, Df=depth of foundation from the ground surface for a strip foundation, answer thefollowing questions:(1) In order to derive Terzaghi’s general bearing capacity equation, correctly draw the failure pattern offoundation ground that is assumed by Terzaghi and explain it.
(2) Terzaghi’s bearing capacity equation consists of three terms. Write down Terzaghi’s bearing capacity
equation and explain the meaning of each of those terms.
(3) In regard with the equation expressed in (2), derive the allowed bearing capacity, qa if factor of safety isF.