2015
Soil Mechanics I and Exercises Final Exam
2016/1/26 (Tue.) 13:00-15:00 W2 Lecture room
Attention: The exam consists of four questions for which you are provided with five answer
sheets. Write down your name and ID number on every answer sheet. Use the firstanswer sheet to answer [Question 1], the second and third to answer [Question 2],
the fourth one to answer [Question 3], and the fifth answer sheet for [Question 4]. If
the space provided in any answer sheet is insufficient, use the back page after clearlymentioning so (for example, “continued on back page”).
 In addition to personal writing instruments, non-programmable calculators arepermitted, but programmable calculators and all types of mobile phones areprohibited. Any attempts at cheating on the exam will result in failed credit of thecourse and serious penalties.
 Wherever necessary, specify the units in your answers.
[Question 1] Answer the following questions regarding the index properties of soils(1) A cylindrical specimen of clay sampled from the ground has the following dimensions: 5 cmin diameter and 10 cm in height. The mass of the specimen before and after completely
removing all soil moisture using an oven dry is 323.85 g and 235.55 g, respectively. The resultof the specific gravity test reports the density of soil particle ρs = 2.68 g/cm3. Use ρw = 1.00
g/cm3 as water density and determine the following values.
1.

Bulk density ρt2.

Water content w (%）

3.

Dry density ρd4.

Void ratio e

5.

Degree of saturation Sr (%)(2) The dry density of a sandy soil measured in the field was ρd = 1.58 g/cm3. This sand was
taken to the laboratory where the maximum dry density ρdmax = 1.72 g/cm3 and the minimum
dry density ρdmin = 1.43 g/cm3 were obtained. Determine the relative density Dr（%）of thesand at the field.
(3) Explain each technical term listed below using approximately 3 lines for each one. Figures
may be used if necessary.
1. Particle size distribution curve

2. Plasticity index

3. Optimum water content

[Question 2] Answer the following questions for the concrete dam built on top of a sandy soil
shown in Figure 2-1. The hydraulic conductivity of the sand is 4.0 × 10-4 m/s and the unit weightof water is γw = 9.81 kN/m3. Use the second page of the answer sheets to answer parts (1) and (4),but use the third page of the answer sheets to answer parts (2) and (3).
(1) Explain the following concepts:
1) Darcy’s Law

2) Quicksand phenomenon

3) Critical hydraulic gradient(2) Draw the flow net that represents the flow of water under the dam. Use Figure 2-2 in the third
page of the answer sheets for this. Calculate the flow rate of the water leakage under the dam,
per unit of width (perpendicular to the paper).
(3) Find the hydrostatic pressure head acting on point A, located on the upstream side of the baseof the dam. Also, plot the distribution diagram of the uplift pressure acting on the base of thedam (a schematic diagram is fine). Use Figure 2-3 in the third page of the answer sheets forthis.
(4) From your analysis, explain the effects due to the construction of the sheet pile.

Figure 2-1. Concrete dam built on top of a sandy soil

[Question 3] A certain structure was designed to be constructed on top of an inactive verticalfault, with one half of said structure resting on top of each side of the fault. By design, a 40 m gap
was considered so the structure would not produce any stress in the middle of the fault zone
(Figure 3-1).
As the engineer in charge, you have been tasked with predicting two important parameters forthis structure: the total consolidation settlement, and the differential settlement after 5 years.
To do so, you need to work under the following assumptions:i.

The clay on both sides of the fault is the same, fully saturated, and normally consolidated(Unit weight of the saturated clay, γsat = 16.2 kN/m3)ii.

The sand that overlays the clay is incompressible, fully saturated, provides full drainage,and the water table lays on its surface (Unit weight of the saturated sand, γsat = 19.0 kN/m3;
Unit weight of water, γw = 9.81 kN/m3)

iii. The bedrock is incompressible and impermeable
iv. The structure can be represented by a distributed load p = 350 kN/m2 on both sides of thefault (Figure 3-2)v.

The settlement on both sides of the fault is different and can be calculated independently

vi. Terzaghi’s theory of one-dimensional vertical consolidation is fully applicable
To better understand the clay, you took samples at the middle of the clay layers, and run aconsolidation test in the laboratory. The samples were 2.5 cm tall, drained on both ends, and took
142 seconds to reach 50% of consolidation. The obtained coefficient of compression was Cc =0.55. The initial void ratios were e = 2.0 (for the sample taken at the middle of the h = 33.0 claylayer), and e = 2.2 (for the sample taken at the middle of the 14.7 m clay layer).
With this information in mind, answer the following questions:(1) From the laboratory test, calculate the coefficient of consolidation of the clay, cv.
(2) Calculate the total consolidation of the clay layer located left to the fault (h = 33.0 m) andalso of the clay layer located right to the fault (h = 14.7 m)(3) Calculate the settlement that will occur, on each side of the fault, five years after thestructure is constructed(4) The difference between the two settlement values that you obtained in (3), divided over thegap distance (L = 40.0 m) is called differential settlement. This value should be less than
1/500. Calculate the differential settlement for this particular case, and conclude if it’s
acceptable or not.

Structure to be constructed
LeftRightSideSideGap, 40.0 m
2.5 m

SandSand

2.5 m

Clay

14.7 mClay33.0 m

Bedrock
Bedrock
Inactive Vertical FaultFigure 3-1. Structure to be constructed on top of an inactive vertical fault

LeftRight2Side2

p = 350 kN/m
2.5 m

Side

p = 350 kN/m

SandSand

2.5 m

Clay

14.7 mClay

33.0 mBedrock
Bedrock
Inactive Vertical Fault
Figure 3-2. Load diagram

Average degree of consolidation vs. time factor (for this problem, assume Tv ± 0.001):
U (%)

010202530

3540

4550

60

70

80

90

Tv

0.000

0.008

0.031

0.049

0.071

0.096

0.126

0.159

0.197

0.286

0.403

0.567

0.848

[Question 4] Answer the following questions(1) The state of stress of a soil element in the ground is given in the figure below. Draw thecorresponding Mohr’s stress circle (show the coordinate of the center and radius of the Mohr’sstress circle). Also, find the maximum principal stress, the minimum principal stress as wellas the direction of each principal plane.

Unit:(2) Consolidated-undrained ( CU ) triaxial compression test of a normally consolidated clay insaturated condition under the confining pressure σ3 = 300 kN/m2 was undertaken. Answer
the following questions if the axial stress σ1 and pore water pressure uw measured at failure
were σ1 = 900 kN/m2，uw = 100 kN/m2.
1. Draw the Mohr’s stress circles for total stress and effective stress at failure.
2. By assuming that the Mohr-Coulomb failure criterion is satisfied, determine the internal
friction angle ϕ' based on the effective stress of this clay. Note that cohesion c'= 0 can be
regarded for normally consolidated clays.
3. Find the orientation of the failure plane measured from the maximum principal plane aswell as the normal stress and shear stress acting on the failure plane.
(3) Explain the reason why the shear strength of a densely compacted and saturated sandobtained from the consolidated-undrained (CU) triaxial compression test is greater than thatobtained from the consolidated-drained (CD) test.