2016

Soil Mechanics II and Exercises

2016/7/27 (Wed) 10:00-12:00

Final Exam

Kyotsu 4 Lecture room

Attention:
The 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 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 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] Answer the following questions:(1) Consider the homogeneous and uniform 10 m thick clay layer lying above the non-artesian gravel layer (fullydrained layer) shown in Figure 1. Herein, the saturated unit weight of the soil is γsat, the unit weight of water is γw,
the coefficient of consolidation is cv, the compression index is Cc, and the initial void ratio of the soil is e0. Let theclay layer carry a uniform load Δp = 100 kN/m2 over a sufficiently large area compared to its thickness. Calculate
the time required for the clay layer to reach an average degree of consolidation U = 90%, and the amount of total
subsidence (final settlement). Upon calculation of the settlement, the groundwater level is assumed to be at thesurface of the clay layer and the representative value of the stress in the ground can be taken at the center of theclay layer (i.e., at a depth of 5 m). The time factor corresponding to U = 90% is Tv = 0.848.

H=10p=100kN/m2

sat=16.5kN/m3，w=9.8kN/m3
cv=2.0×10-3m2/day
Cc=0.8，e0=2.0

Figure 1

Figure 21

(2) In order to reduce the time taken for the consolidation process calculated in (1), sand drains are driven into theclay layer following the layout shown in Figure 2 (diameter of sand drains dw = 0.4 m, length = 10 m into the claylayer, square array at a pitch d = 2.13 m). After their installation, the clay layer is subjected to a uniform load
Δp = 100 kN/m2 over a sufficiently large area compared to its thickness, exactly the same way as indicated in (1).
In this case, calculate the time required for the improved clay layer to reach an average degree of consolidation U= 90%, in accordance to the following procedures. Assume that the flow of water in the ground with sand drains
takes place only in the horizontal direction, toward said sand drains.
1) Take the side length of a square surrounding the center of an installed column of sand drain equal to the pitch,and then calculate the effective diameter de of a circle whose cross-sectional area equals the area of the square inwhich water is collected.
2) Obtain the time factor Th for horizontal drainage that corresponds to an average degree of consolidation U =90% from the diagram representing the theoretical solution of Barron (Figure 3).
3) Find the time required for the clay layer with sand drains to reach an average degree of consolidation U = 90%.
In this case, it is assumed that the coefficient of consolidation of the clay layer is not changed by the installation of
the sand drains, and anisotropic permeability is not accounted for (coefficient of consolidation for horizontal
drainage ch = cv).

0.0n = 20

0.2

n=de/dw

0.4

104

U

6

0.6

2
0.8
1.0

0.0001

0.001

0.01

0.1

1

Th = ch t / de2
Figure 3[Question 2] Answer the following questions:(1) Using a figure (or figures) representing the τ－σ plane, graphically outline the main features of the 3 types offailure criteria (Coulomb's, Mohr’s, and Mohr-Coulomb’s failure criterion) explaining, in general terms, thecharacteristics of each of them.

2(2) Use figures to explain the following terms:
1) Ratio of sensitivity2) Undrained shear strength
3) Dilatancy[Question 3]
As shown in Figure 4, a rigid retaining wall, 4 m high, with a fully smooth vertical back face, retains a flatcohesionless backfill with a uniform surcharge of 10 kN/m2. During dry season, the groundwater table drops
far below the base of the wall and the unit weight of the backfill equals its wet unit weight γt = 15.5 kN/m3.
During rainy season, however, the drain holes become clogged due to a poor design, and the groundwatertable rises to the backfill surface and develops hydrostatic pressure behind the retaining wall, while the unit
weight of the backfill equals its saturated unit weight γsat = 19.0 kN/m3.
Surcharge q = 10 kN/m2

Retaining wall

4m

Groundwater table rose tothe backfill surface
γw = 9.8 kN/m3Cohesionless backfill
γt = 15.5 kN/m3
γsat = 19.0 kN/m3
ϕs = 35°
Collector pipe

Original ground

Groundwater table dropped
far below the base of thewall

OFigure 4Herein, the unit weight of water is γw = 9.8 kN/m3 and the friction angle of the backfill is ϕs = 35°. According
to Rankine active earth pressure, answer the following questions.

3(1) Calculate the total resultant force per unit length of the wall and the corresponding overturning moment
per unit length of the wall about a point O, during dry season.
(2) Calculate the total resultant force per unit length of the wall and the corresponding overturning moment
per unit length of the wall about a point O, during rainy season.
(3) Discuss the importance of drainage system in retaining walls from the view point of their stability.

[Question 4] Answer the following questions:(1) Explain when a foundation is defined as shallow or deep, based on its width, B, and depth, Df(2) Use a graphic to describe the failure mechanism of a shallow strip foundation after Terzaghi’s general
shear failure theory, and include a brief explanation of it(3) Express Terzaghi’s formula to calculate the ultimate bearing capacity, qd, of a shallow strip foundation,and briefly explain each element(4) Explain how to obtain the allowable bearing capacity, qa, of a shallow strip foundation built at a depth Df,
after applying a factor of safety, F, to its ultimate bearing capacity, qd[Question 5] Answer the following questions:(1) Determine the factor of safety, F, of an infinite slope against sliding, along the slip plane located at adepth H. The slope is inclined at an angle β, the cohesion is c, the internal friction angle is ϕ, and the unit
weight of the soil mass is γ. Herein, it is assumed that the level of the groundwater table is sufficiently deep.
(2) Find the critical depth Hc at which the plane failure of the infinite slope mentioned in (1) occurs.
(3) By paying attention to changes in the factor of safety against sliding, explain why landslides are likely tooccur when it rains(4) Explain the mechanism of soil liquefaction at the time of earthquake in the context of the dilatancy ofsoils.

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