in a Soil
2.1
A soil profile is shown in Figure 2.25. Calculate the values of , u,
and at points A, B, C, and D. Plot the variation of , u, and
with depth. We are given the values in the table.
Layer No.
Thickness (m)
I
II
III
H1
H2
H3
2
3
7
Unit weight (kN/m3 )
gdry
gsat
gsat
15
17.8
18.6
L
a
y
e
r
I
Dry sand
H1
Figure 2.25
2.2
2.3
2.4
Repeat Problem 2.1 with the following:
Layer No.
Thickness (m)
I
II
III
H1 = 4
H2 = 3
H3 = 5
Soil parameters
e = 0.45, Gs = 2.68
e = 0.7, Gs = 2.5
e = 0.81, Gs = 2.75
Refer to the soil profile shown in Figure 2.26. Given H1 = 4 m and
H2 = 3 m. If the ground water table rises to 2 m below the ground surface,
what will be the net change in effective stress at the bottom of the clay
layer?
Refer to Figure 2.3a, in which there is an upward seepage of the water.
Given: H1 = 0.5 m, H2 = 2 m, h = 0.5 m, void ratio e = 0.55, Gs = 2.68,
a. Calculate the total stress, pore water pressure, and effective stress at C.
(Note: z = 0.7 m.)
b. What is the upward seepage force per unit volume of soil?
2.5
2.6
2.7
2.8
2.9
In Problem 2.4, what is the rate of upward seepage of water? Given: hydraulic
conductivity of soil, k = 0.13 cm/sec, and area of tank = 0.52 m2. Give your
answer in m3/min.
A sand has Gs = 2.66. Calculate the hydraulic gradient that will cause boiling for
e = 0.35, 0.45, 0.55, 0.7, and 0.8. Plot a graph for icr versus e.
A 8 m-thick layer of stiff saturated clay is underlain by a layer of sand
(Figure 2.27). The sand is under artesian pressure. Calculate the maximum depth of cut, H, that can be made in the clay.
Refer to Figure 2.11. Given P = 30 kN, determine the vertical stress increase
at a point with x = 5 m, y = 4 m, and z = 6 m. Use Boussinesq’s solution.
Solve Problem 2.8 using Westergaard solution. Given s = 0.3.
Figure 2.26
Figure 2.27 L a y e r of saturated clay underlain by layer of sand
2.10 Point loads of magnitude 9, 18, and 27 kN act at A, B, and C,
respectively (Figure 2.28). Determine the increase in vertical
stress at a depth of 3 m below point D. Use Boussinesq’s
equation.
2.11 Solve Problem 2.10 using Westergaard solution. Use s = 0.4
2.12 Refer to Figure 2.13. The magnitude of the line load q is 60 kN/m.
Calculate
and plot the variation of the vertical stress increase, , between
the limits of x = - 10 m and x = + 10 m, given z = 4 m.
2.13 Refer to Figure 2.29. Determine the vertical stress increase, , at
point A
with the following values:
q1 = 100 kN/m
x1 = 3 m Z = 2 m
q2 = 200 kN/m
x2 =2 m
2.14 Repeat Problem 6.13 with the following values:
z = 2.5 m
q1 = 100 kN/m
x1 = 3 m
q2 = 260 kN/m
x2 = 2.5 m
2.15 Figure 2.30 shows a line load of limited length. Given q = 200 kN/m, L
= 5 m,
x = 4 m. Determine the vertical stress increase at a point with
coordinates
x = 1 m, y = 3 m, z = 5 m.
2.16 Refer to Figure 2.17. Given B = 5 m, q = 40 kN/m2, x = 1.5 m, and
z = 2 m, determine the vertical stress increase, , at point A.
Figure 2.28
Figure 2.29 Stress at a point due to two line loads
2.17 Repeat Problem 2.16 for q = 700 kN/m2, B = 2 m, x = 2 m, and z = 2.5 m.
2.18 Consider a circularly loaded flexible area on the ground surface. Given:
radius of the circular area =R =3 m; uniformly distributed load = q =
250 kN/m2. Calculate the vertical stress increase at a point located 5 m (z)
below the ground surface (immediately below the center of the circular area).
2.19 Repeat Problem 2.18 with the following: R = 5 m, q = 300 kN/m2, and z = 6 m.
Figure 2.30
Figure 2.31
2.20 The plan of a flexible rectangular loaded area is shown in Figure
2.31. The uniformly distributed load on the flexible area (q) is 400
kN/m2. Determine the increase in the vertical stress ( ) at a
depth of z = 5 m below using influence factors method and Newmark
Chart method.
a. Point A
b. Point B
c. Point C
2.21 Refer to Figure 2.32. The circular flexible area is uniformly loaded.
Given:
q = 320 kN/m2. Determine the vertical stress increase at
point A.
2.22 Refer to Figure 2.33. The flexible area is uniformly loaded. Given: q =
300 kN/m2. Determine the vertical stress increase at
point A.
Figure 2.32
Figure 2.33
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