BICOL UNIVERSITY
COLLEGE OF ENGINEERING
CIVIL ENGINEERING DEPARTMENT
CE 322
GEOTECHNICAL ENGINEERING
(SOIL MECHANICS)
SECOND SEMESTER, AY 2024-2025
PROBLEM SET NO. 5
CHRISTIAN JAY B. RAMOS
2022-9504-95780
BSCE – 3C
ENGR. ANNA G. BILARO, MSCE
PROFESSOR
Christian Jay B. Ramos | CE 3C Lesson 5: Solved Problems
7.1 A permeable soil layer is underlain by an impervious layer as
shown in Figure 7.32. Knowing that k = 4.8×10 -3 cm/sec for the
permeable layer, calculate the rate of seepage through this layer in
3
m /hr/m width. Given: H = 4.2 m and α = 6 °.
Solution:
Christian Jay B. Ramos | CE 3C Lesson 5: Solved Problems
7.2 Find the rate of flow in m 3 / sec /m (at right angles to the cross
section shown in Figure 7.33) through the permeable soil layer. Given:
H = 4 m, H 1 = 2 m, h = 2.75 m, S = 30 m, α = 14°, and k = 0.075
cm/sec.
Solution:
Christian Jay B. Ramos | CE 3C Lesson 5: Solved Problems
7.3 The results of a constant-head permeability test for a fine sand
sample having a diameter of 150 mm and a length of 300 mm are as
follows (refer to Figure 7.5):
Constant-head difference = 500 mm
Water collected in 5 min = 350 cm3
Void ratio of sand = 0.61
Determine:
a. Hydraulic conductivity, k (cm/sec)
b. Seepage velocity
Solution:
Christian Jay B. Ramos | CE 3C Lesson 5: Solved Problems
7.4 In a constant-head permeability test, the length of the specimen is
150 mm, and the cross-sectional area is 3167 mm 2 . If k = 0.062
cm/sec and a rate of flow of 160 cm3 /min has to be maintained during
the test, what should be the head difference across the specimen?
Also, determine the discharge velocity under the test conditions.
Solution:
Christian Jay B. Ramos | CE 3C Lesson 5: Solved Problems
7.5 The following data are for a falling-head permeability test:
Length of the soil sample = 150 mm
Area of the soil sample = 1964 mm 2
Area of the standpipe = 25 mm 2
At time t = 0, head difference = 400 mm
At time t = 8 min, head difference = 200 mm
a. Determine the hydraulic conductivity of the soil (cm/sec).
b. What was the head difference at t = 6 min?
Solution:
Christian Jay B. Ramos | CE 3C Lesson 5: Solved Problems
8.1 Refer to the constant-head permeability test arrangement in a two-
layered soil as shown in Figure 8.2. During the test, it was seen that
when a constant head of h1 = 200 mm was maintained, the magnitude
of h2 was 80 mm. If k 1 is 0.004 cm/sec, determine the value of k 2 given
H1 = 100 mm and H2 = 150 mm.
Solution:
Christian Jay B. Ramos | CE 3C Lesson 5: Solved Problems
8.2 Refer to Figure 8.18. Given:
• H1 = 6 m •D=3m
H
• 2 = 1.5 m • D1 = 6 m
draw a flow net. Calculate the seepage loss per meter length of the
sheet pile (at a right angle to the cross section shown).
Solution:
Christian Jay B. Ramos | CE 3C Lesson 5: Solved Problems
8.3 Draw a flow net for the single row of sheet piles driven into a
permeable layer as shown in Figure 8.18. Given:
• H1 = 3 m • D = 1.5 m
• H2 = 0.5 m • D1 = 3.75 m
calculate the seepage loss per meter length of the sheet pile (at right
angles to the cross section shown).
Solution:
Christian Jay B. Ramos | CE 3C Lesson 5: Solved Problems
8.4 Refer to Figure 8.18. Given:
• H1 = 4 m • D1 = 6 m
• H2 = 1.5 m • D = 3.6 m
calculate the seepage loss in m3 /day per meter length of the sheet
pile (at right angles to the cross section shown). Use Figure 8.10.
Solution:
Christian Jay B. Ramos | CE 3C Lesson 5: Solved Problems
8.5 For the hydraulic structure shown in Figure 8.19, draw a flow net for
flow through the permeable layer and calculate the seepage loss in
3
m / day /m .
Solution:
Christian Jay B. Ramos | CE 3C Lesson 4: Solved Problems
6.4 Repeat Problem 6.3 with the following data (use Gs =2.7):
6.3 The results of a standard Proctor test are given in the following table.
a. Determine the maximum dry unit weight of compaction and the optimum moisture
3
content. Given: mold volume=943.3 cm .
b. Determine the void ratio and the degree of saturation at the optimum moisture content.
Given: G s =2.68.
Solution:
Trial Weight Weight Moisture Moist Unit Weight Dry Unit Weight (
3) 3
No. (kg) (kN) Content (%) (kN /m kN /m )
Soil Compaction Curve
17
Dry Unit Weight, γd
16.75
(kN/m3)
16.5
16.25
16
8 10 12 14 16 18 20 22
Moisture Content, w (%)
