2016

Soil Mechanics II and Exercises

2016/6/8 (Wed)8:45-10:15

Midterm Exam

Kyotsu 4 Lecture room

Attention:
The exam consists of three questions for which you are provided with three answer sheets. Write down
your name and ID number on every answer sheet. Use one answer sheet per question and answer themin sequence, starting from [Question 1]. If the front page of an answer sheet is insufficient to complete
your answer, use the back page of the same answer sheet after clearly indicating your intent.

Scores for each question are equally weighted.

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] Answer the following questions(1) A saturated clay layer of thickness H lies above an impermeable rock layer. Assume that thegroundwater level coincides with the ground surface. After the rapid application of a load over the claylayer, the consolidation process can be analyzed based on Terzaghi’s one dimensional consolidation
equation. Terzaghi’s consolidation equation is given below where u is the excess pore water pressure (=pore water pressure – hydrostatic pore water pressure), Cv is the coefficient of consolidation, t is thetime, and z is the coordinate along depth direction.

u
 2u
 Cv 2tz(1)(a) The ground with high coefficient of permeability will have higher coefficient of consolidation thanthe ground with low coefficient of permeability; therefore, the period of time needed forconsolidation is shorter. Explain whether the ground with high coefficient of volume compressibility
will need a shorter or longer consolidation time than the ground with low coefficient of volume
compressibility if both grounds have the same value of the coefficient of permeability.
(b) The solution of consolidation equation can be expressed using the time factor Tv. Explain what thetime factor is.

(2) If the upper surface of the clay layer (the ground surface) is represented as z = 0, and the lower surfaceof the clay layer (the upper surface of the impermeable rock layer) as z = H,(a) Write down the boundary condition for the upper surface (z = 0) of the clay layer.
(b) Write down the boundary condition for the lower surface (z = H) of the clay layer (Hint: Thinkabout the condition under which the flow rate becomes zero in Darcy’s law）

(3) In order to solve the consolidation equation, the solution of Eq.(1) is written as follows.．

u  f t  g  z (2)Based on this, find the general solution of the consolidation equation as given in Eq.(1) from theboundary conditions of the upper surface (z = 0) and the lower surface (z = H) of the clay layer.

[Question 2] Answer the following questions
5 cm was taken from a depth of 10 m beneath the(1) An undisturbed clay sample with a diameterground surface, and was subsequently subjected to an unconfined compression test in the laboratory. The
sample failed when the applied axial compression force was

196.35 N. After failure, a new sampleof the same size was prepared from the remaining material by remolding it, and this new remoldedsample failed when the applied axial compression force reached130.90 N. (For this problem,

assume that the change in sample diameter due to vertical stress is negligible).

(a) Draw the Mohr circles for both the undisturbed and the remolded samples, and calculate thevalues of undrained shear strength (and) for both cases.

(b) Calculate the degree of sensitivity for this clay sample(c) If both samples are subjected to Triaxial UU tests, with a confining pressure of

150 kPa,

calculate the axial compressive stresses that would cause them both to fail(d) If a new clay sample from the same clay layer was obtained from a depth of 20 m beneath theground surface, predict the value of undrained shear strength that would be obtained in this case(assume that the clay is normally consolidated, that the clay layer extends from the groundsurface to a depth larger than 20 m, and that the water table is located on the surface, as in thefigure)

10 m
20 m

Original sample (for parts (a), (b), andNew sample (for part (d))

CLAY LAYER

tan ′ that represents(2) The Mohr-Coulomb failure criterion can be described by the equation
the tangent to the Mohr circle in the following figure whereprincipal stresses,

and() are the effective′ is the effective friction angle and ′ is the cohesion based on the concept ofeffective stress. Since the Mohr circle is, by definition, tangent to the aforementioned line, the maximum
value ofat failure can be calculated as a function of(a) Obtain the mentioned function(b) For a normally consolidated soil,, ′, and′.

, , ′0. If

300 kPa and the deviator stress

575 kPa, calculate both the value of the effective friction angle
failure plane′, as well as the angle of the(as shown in the figure below).

′2′

[Question 3] Answer the following questions(1) The figure below represents a retaining wall of height H. Let the frictional angle, the cohesion, and theunit weight of the backfill soil be ϕ, c, and γ, respectively. Draw a diagram showing the three types ofrepresentative earth pressure that act on the retaining wall, taking the displacement of the retaining wall(δ) along the horizontal axis and the earth pressure along the vertical axis. Refer to the figure below 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 wallwhen it moves leftward (δ- direction). Assume that the cohesion, c, of the backfill soil is zero. Also,
assume that the surface of the retaining wall is not smooth; hence, there is friction between the retaining
wall and the backfill soil (interface friction angle α). Show the force polygon diagram using the forcesthat act on the soil wedge shown in the figure. Use appropriate symbols for the forces shown in theforce polygon diagram and clearly describe each of those forces.
(3) While reassessing the conditions of the backfill soil, it was found that the cohesion was not zero. Under
this new condition, and based on Rankine’s earth pressure theory, draw the earth pressure distribution
diagram exerting on the retaining wall of height H when it moves leftward (δ- direction). For this,assume that the friction between the retaining wall and the backfill soil can be ignored and that thegroundwater table lies deep below the retaining wall.
(4) Explain the difference in the magnitudes of the resultant active force (a sum of the forces due to earthpressure and the water pressure) when the groundwater table behind the retaining wall rises up theground surface and lies at the bottom surface of the retaining wall. Focus your answer on the differencein the earth pressure and the water pressure under those two conditions. Assume that the cohesion of thebackfill soil is zero and the unit weight of water is γw. When the groundwater table lies at the bottom
surface of the retaining wall, the active earth pressure p at depth z can be written as p = KA γ z , where KA
is the coefficient of active earth pressure.

Displacementof the retaining wall
擁壁の変位

4) Groundwater table rising((4)で地下水位が上がった場合

up to the ground surface

 , , cH