2015

Soil Mechanics II and Exercises Final Exam

2015/7/29 (Wed.) 10:00-12:00

Kyotsu 4 Lecture room

Attention:
The exam consists of five questions for which you are provided with five answer sheets. Write down yourname 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.

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
A thick stratum of saturated clay is deposited above an impermeable bedrock. Assume that the groundwaterlevel coincides with the ground surface. After the immediate application of a load over the clay layer, theconsolidation process can be analyzed based on Terzaghi’s one dimensional consolidation equation. The
consolidation equation expressed in terms of excess pore water pressure (= pore water pressure - hydrostaticpressure) u, coefficient of consolidation Cv, time t, and coordinate along the depth direction z is given below.
∂u∂ 2u= Cv 2
∂t
∂z(1)

The boundary conditions of this equation are taken at the top surface of the clay layer (ground surface) wherez = 0 and at the bottom surface of the clay layer (the top surface of the impermeable bedrock) where z = H. At
the top surface (z = 0) of the clay layer, it is required that,z = 0: u = 0(2)

Furthermore, at the bottom surface of the clay layer (z = H), the impermeable condition is given below as the flowrate becomes zero in Darcy’s law,z = H：

∂u=0.
∂z(3)

1) Considering the excess pore water pressure u = u0 immediately after the rapid increase in load as the initialcondition, obtain the solution of the consolidation equation (1) using the boundary conditions (2) and (3).
2) Sand drain is a soil improvement method used to accelerate the consolidation of soft ground. Explain theprinciples to accelerate the consolidation process by this method.
13) When a distributed strip load is applied over a clayey ground as shown in Fig. 1, the vertical stress σz witha b
respect to the depth z below the ground surface at point C is given by I q  ,  as a function of thez z

variables a/z and b/z, so that:
a b
σ z I q  ,  ・×qq
=z z

(4)

Similar to Eq.(4), express the vertical stress σz with respect to the depth z below the ground surface at points Aand B in association with the function Iq. Herein, the behavior of clayey ground is assumed to be linearly elastic.

abqzACBFigure 1[Question 2] Briefly explain the following concepts. You may use figures and equations if needed.
1)

Mohr-Coulomb failure criterion

2)

Soil dilatancy

3)

Soil sensitivity ratio

4)

Soil undrained shear strength ratio

5)

Skempton’s pore pressure parameter A2

[Question 3] Answer the following questions
1) Consider Rankine’s theory applied to a smooth wall retaining a dry cohesionless soil with friction angle ϕ.
According to Fig. 2, when the soil surface is a horizontal plane, the active pressure σ3 acts on a verticalplane while the vertical pressure σ1 acts on a horizontal plane. The mobilized states of stresses for σ1 and σ3
are shown on Mohr’s stress circle (see Fig. 4) with center at point C touching the failure envelop of the soil
at point D. Herein, p = OC is the mean stress and q = CD is the stress deviator. Find the active earth pressure
coefficient, which is represented by σ3/σ1, in terms of ϕ.
2) According to Fig. 3, when the soil surface slopes at a constant angle i, where i < ϕ, it is assumed that theactive pressure σi acts in a direction parallel to the sloping surface while the vertical pressure σv acts on aplane inclined at an angle i to the horizontal. Since these mobilized stresses are not normal to their respective
planes, they are not principal stresses. The normal and tangential components of σv along its applied surface
are sv and tv, respectively, and are represented by the coordinates of point A while those of σi, which are siand ti, are represented by the coordinates of point Bʹ in Mohr’s stress circle (see Fig. 4). This is brought out
by tracing a line OA in a direction parallel to the sloping surface. Line OA also intersects the Mohr’s stresscircle at point B; therefore OB = OBʹ. Note that Point F divides AB in half. Find the active earth pressure
coefficient, which is represented by σi/σv, in terms of ϕ and i.

Figure 2

Figure 3

Figure 43

[Question 4] Answer the following questions.
1) The following figure (Fig. 5) depicts the stability problem of a long slope with a sliding surface in a weatheredrock layer. The groundwater is present at a depth z0 in the weathered rock layer by rainfall infiltration to theslope. Herein, it is assumed that the flow line is parallel to the slope surface. Let the vertical depth from the slope
surface to the sliding plane be H, the angle of inclination of the slope be β, the unit weight of the soil above thegroundwater level be γt, the unit weight of the soil below the groundwater level be γsat, the cohesion of soil be cʹ,the internal friction angle of soil be ϕʹ, and the unit weight of water be γw. Answer the following questions:

ββz0γtFlow line

H

Weathered rock layer

γsat, cʹ, φʹ, γw

Sliding surface

βFigure 5(1) Find the safety factor against sliding of this slope. Clearly express the following elements.
-

Normal stress σ and shear stress τ acting on the sliding surface-

Pore water pressure u acting on the sliding surface-

Normal effective stress σʹ acting on the sliding surface-Mohr-Coulomb failure criterion(2) It is assumed that the slope fails when the groundwater level reaches the slope surface. Find the depth (thecritical depth Hc) at which sliding failure occurs.

2) Investigation of topographic maps is undertaken due to construction of a highway embankment. It was found thatthe site is located exactly on an old river bed. In addition, the area is often stricken by large earthquakes. Priorto the design, the standard penetration tests were conducted and a borehole profile was obtained as shown in Fig.
6.
(1) Explain how to obtain an N-value. In addition, qualitatively describe the relationship between ground densityand N-value.
(2) Discuss the possibility of liquefaction at the site under the given conditions, such as the topography, seismic
history and also the standard penetration test results shown in Fig. 6.

4

(3) The definition of factor of safety against liquefaction is described below where Rl is the normalized cyclic
resistance ratio (CRR) and L is the normalized cyclic shear stress ratio (CSR). Explain how Rl and L arederived and obtained.
Factor of safety against liquefaction： FL =RlL

(4) The result of the investigation indicates that the liquefaction susceptibility is quite high at the site; therefore,engineering countermeasures are employed before constructing the embankment. Explain about theprinciples of mitigation of the measures against liquefaction that are particularly effective to embankments

3

Relative density

N -value

10

5

7

6

3
1218

11121291324

15
16
17

Dense to medium

7Fine sand10

1434
35
35

2027

21

29

24

Medium25Silty fine sand3419231520292734
16263727282930

11626
13Loose25

Silt mingledwith sand

1040

182255Loose

9Fine sand

128203040

Downhole
water level

84

7104

Depth (m)2Fine sand1N-value00

Very loose

Depth (m)Soil classificationand list three appropriate techniques based on these principles.

2530

Figure 6550

[Question 5]
1) Explain the following concepts with the help of figures.
• General shear failure and local shear failure• Shallow foundation and deep foundation• Negative friction
2) To answer the following questions assume that the strip foundation was built in a homogeneous ground, as
shown in Fig. 7.

Figure 7(1) Express the formula to calculate the bearing capacity of the soil, qd, as a function of Terzaghi’s bearing
capacity factors (Nq, Nc, and Nγ) and the soil parameters indicated in Fig. 5.1. Assume, for this problem,that the groundwater is located deep enough.
(2) Derive the formula of the allowable bearing capacity of the soil, qa, by introducing safety factor, SF, to theformula for the bearing capacity of the soil, qd, as described in (1).
3) To answer the following questions, assume that the strip foundation was built in a ground composed of two
different soil layers, as shown in Fig. 8.

Figure 8(1) Express the formula to calculate the bearing capacity of the soil, qd, making use of Terzaghi’s bearing
capacity equation, Terzaghi’s bearing capacity factors (Nq, Nc, and Nγ), and the soil parameters indicated inFig. 8. Assume, for this problem, that the groundwater is located deep enough.

6(2) From the condition shown in Fig. 8, the groundwater raises until reaching a depth hw, as indicated in Fig.
9. Express the formula to calculate the bearing capacity of the soil, qd, making use of Terzaghi’s bearing
capacity factors (Nq, Nc, and Nγ), and the soil parameters indicated in Fig. 9. Use γw as the unit weight ofwater.

Figure 97