2017
Soil Mechanics I and Exercises Midterm Exam
2017/11/21 (Tue) 13:00-14:00
W2 Lecture roomAttention:

The exam consists of two questions for which you are provided with two answer sheets. Write down yourname and student 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 scientific calculators are permitted.
However, programmable calculators and calculator functions of mobile phones are prohibited. Anyattempts at cheating on the exam will result in failed credit of the course and serious penalties.

Wherever necessary, specify the units in your answers.

[Question 1]
An embankment is constructed from the soil excavated from a borrow pit. After compaction, the total volume ofthis embankment is 20,000 m3. The soil taken from the borrow pit was investigated and the results obtained atnatural soil conditions are as follows:
Bulk density: 1.80 t/m3
Water content: 15.0%
Specific gravity of soil particles: 2.70
Maximum dry density: 1.90 t/m3, Optimum water content: 17.0 %From the above results of compaction test, water is sprayed during the construction of the embankment to meet theoptimum water content condition in which the dry density reaches 90.0% of the maximum dry density (i.e., degreeof compaction = 90.0%). Answer the following questions using the density of water 1.00 t/m3.

1) Find the void ratio, degree of saturation and dry density of the soil in the borrow pit at natural conditions.
2) Find the volume and mass of the soil to be excavated from the borrow pit at natural conditions.
3) Find the mass of water per 1 m3 of soil that is necessary to spray in the borrow pit at natural conditions.
4) Find the degree of saturation of the embankment after the completion of compaction.

[Question 2]
A sheet pile wall was installed in a fully saturated permeable soil as shown in the figure. Here, e is the void ratio ofthe permeable soil, Gs is the specific gravity of the soil particles, D is the depth of the sheet pile, and γw is the unit
weight of water. Answer the following questions.

(1) While the water level to the right side of the sheet pile stays at the ground level, the water level to the left
side raises and produces failure of the ground when it reaches a height of h. Assuming that the groundfailure area is pqrs:
1) What is this phenomenon called?
2) If the total head at point p is hp, express the pressure head and the pore water pressure at the same point
p as functions of hp and other given data. For this, assume that the datum for the elevation head islocated at the ground surface.
3) Assume that u1, the pore water pressure at point p obtained in 2), acts uniformly on pq, the bottom sideof the ground failure area. Express the effective stress at pq as a function of hp and other given data.
4) Considering an upward flow from the bottom side, pq, to the ground surface rs. The critical hydraulicgradient can be defined as hp/D. Express hp/D as a function of e and Gs.
(2) The figure shows the flownet in the permeable ground just before failure. The flownet is drawn so thateach element surrounded by streamlines and equipotential lines approximates a square.
1) Assume that the hydraulic conductivity of the permeable ground is k. For the given flownet, obtain thedischarge Q for the entire permeable soil, per unit width, per unit of time, just before failure, as afunction of the given data.
2) Using the flownet, the total head at each equipotential line can be expressed as a function of h. Express
hp, the total head at point p, as a function of h.
3) Assume that the water pressure is linearly distributed between points p and q. If u2 is the average porewater pressure acting on pq, express the difference between u2 and u1 as a function of h and γw.