2015

Soil Mechanics II and Exercises Midterm Exam

2015/6/10 (Wed.) 8:45-10:15

Kyotsu 4 Lecture roomAttention:
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 them insequence, starting from [Question 1]. If the front page of an answer sheet is insufficient to complete youranswer, 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) Write a flow chart showing the derivation of the one-dimensional consolidation equation from thefollowing four assumptions and conditions:(a) Darcy’s law v = −k ∂uγ w ∂z(b) Continuity equation for the water (mass conservation law)∂v ∂ε=∂z ∂t(c) Effective stress - strain relationship of the soil d ε = mv dσ '(d) Constant total stress∂σ ∂σ ' ∂u=+= 0
∂t
∂t
∂t

where v is pore water velocity, k is coefficient of permeability, γ w is unit weight of water， u isexcess pore water pressure， ε is volumetric strain, mv is coefficient of volume compressibility， σ ' iseffective stress， σ is total stress, t is time and z is the position coordinate.
(2) In the ground condition shown in Figure 1, theγt1=19.0 kN/m3

groundwater level has dropped from 1 m to 5 m as aresult of groundwater pumping over time. Determine theconsolidation settlement S of the clay layer induced by
the groundwater drawdown. It is assumed that the unit
weight of the soil where groundwater level has dropped
is γt1=19.0 kN/m3, same as that above the initial
groundwater level. Also, the unit weight of water issand
砂層 layer γt2=20.0 kN/m

35m 6mclaylayer
粘土層γt3=20.0 kN/m3
e0=2.4mv=4.69 x 10-4 m2/kN

taken as γw=9.81 kN/m3. Stress state at the middle of thelayer can be used as the representative stress state of theclay layer.

1mFigure 110m

(3) According to clay layers having a thickness of H or 2H as depicted in Figure 2 from ① to ⑨, arrange
them in the ascending order of time required to complete one-dimensional consolidation.

cv

2H

cv

2H

④Hcv

2cv

cv

2H

⑤⑥cv

H4cv

H

⑧⑦2H

③②

①

⑨4cv

H4cv

2HPermeable layer
透水層

不透水層Impermeable layer

Figure 2(4) The vertical stress in the ground beneath the corner of a rectangular area caused by a uniformly distributedload q is calculated as follows by Newmark’s equation.

σz()


mn m 2 + n 2 + 2q 
mn−1
+ sin222π  m 2 + 1 n 2 + 1 m 2 + n 2 + 1m + 1 n + 1 ()()

= qf B (m, n)
Now, consider a rectangular load being exerted on the ground surface as shown in Figure 3. Calculate thevertical stress increases ΔσzO and ΔσzG that occur at a depth z=6 m just below points O and G, respectively.
In order to obtain the solutions, Figure 4 may be used.
8m

O2m

q=140 kN/m21m
GFigure 34m2m4m

uniformly
distributed loador

or

or

or

Figure 4[Question 2] Answer the following questions(1) Clay samples in undisturbed and remolded conditions were subjected to unconfined compression tests.
The corresponding values for unconfined compression strength obtained for each one are expressed by 𝑞𝑞𝑢𝑢(undisturbed) and 𝑞𝑞𝑢𝑢𝑢𝑢 (remolded).
1)

Draw the schematic plot of stress-strain relationship obtained from undisturbed and remolded clay
samples. Clearly indicate in the figure the unconfined compression strength for both the undisturbed

2)(𝑞𝑞𝑢𝑢 ) and the remolded (𝑞𝑞𝑢𝑢𝑢𝑢 ) samples.

Express the formula to obtain the degree of sensitivity from the results of this test.

(2) A saturated and normally consolidated clay sample is consolidated to a stress 𝑝𝑝′ , and then subjected to anundrained triaxial compression test. As a result, the deviator stress and the pore water pressure obtained atfailure are 𝑞𝑞𝑓𝑓 and 𝑢𝑢𝑓𝑓 , respectively.
1)

Draw the Mohr’s Circle for total stress. Clearly specify in the figure the major and minor principalstresses.

2)

Draw the Mohr’s Circle for effective stress. Clearly specify in the figure the major and minor
principal stresses.

3)
4)

Express the formula that defines the pore pressure coefficient at failure (𝐴𝐴𝑓𝑓 ).

′− 𝑞𝑞 spaces, where 𝜎𝜎𝑚𝑚 =Draw the expected total and effective stress paths in the 𝜎𝜎𝑚𝑚 − 𝑞𝑞 and 𝜎𝜎𝑚𝑚′(𝜎𝜎1 + 2𝜎𝜎3 )⁄3 and 𝜎𝜎𝑚𝑚= (𝜎𝜎1′ + 2𝜎𝜎3′ )⁄3

[Question 3] Answer the following questions(1) A retaining wall with a vertical back face is shown in Figure 5. Its frictionless face with a height H retains
a horizontal backfill made of dry sand. The unit weight and the internal friction angle of the backfill are γand ϕ, respectively. Once the wall moving outward of the backfill exceeds the limit, a backfill wedge isformed and slips along a failure plane with an angle θ measured from the horizontal. Based on Coulomb’s
earth pressure theory, answer the following questions by considering forces per unit width of the retaining
wall:(a) Draw the vector diagram of forces that act on the backfill wedge sliding along the failure plane.
(b) Determine the resultant force acting on the retaining wall by optimizing it with respective to the angle
θ.

Figure 5