Download CEE 380 Spring 2021 - Homework Assignment #5: Soil Mechanics and Foundation Engineering and more Exercises Geotechnical Engineering in PDF only on Docsity!
UNIVERSITY OF ILLINOIS, URBANA-CHAMPAIGN NAME: _______________
DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING DATE: _______________
CEE 380 Spring 202 1 – Homework Assignment # 5
Due Thursday, April 29
th
NOTE: SHOW YOUR CALCULATIONS IN A CLEAR FORM AND INCLUDE UNITS
- A building with 32 m by 20 m rectangular floor plan will be constructed at a site as shown below. A
surcharge of 600 kPa is estimated to be applied to the ground surface due to the building construction.
Determine the stresses at 10 m below Points A, B, and C. Use Boussinesq, Westergaard, and 2:
method for the evaluation (30 points).
Vertical stress, σv (kPa), 10m below
Point A Point B Point C
Boussinesq
Westergaard
2:1 method
32 m
20 m
16 m 16 m
10 m
10 m
< Plan view >
A
B
C
10 m
Dev
Patel
at
A A
ointA
Pointe
m
1z
l b
b
I
w
I
o Z
to
16
IB
lb e lb
(^20) B
I
B Blak^1
Blue
D
n
lb
y
so
bz
z
me
i (^6)
Lbthe
0
Blue
Io
n H
y
m I 6
480 271 Z^
36 n i
324 198 46.8 (^) If
o Z
2 lmenth^
304.762 304.762^304
q
600hPa
_KNW Bominery Westergaard
G
cent
_138hPa a^ ccb
M
104
20ns
go
Goo
kPa
In
0.135 a
62 b
276hPa 2 wth 208
32M
coz
go.es
a A
81hPa
a e
120hPa 2
city
81
hood
kN
za
o z^
324hPa
z Iom Oz 240hPa^
Ffs
z go
BL
A
120hPa
g
q
y
q
B
kPa 82
208
8
lb
480hPa
B^12 L
121 coz
if
coz 198hPa^ fb
8hPIB
6
36 kPa
304 762hPa^
Ic
cute
_0.
B
135.6hPa
Some
fog
pointA
B csince
Ic
iμ
o
somedepth
6z 2
kPa
2
- A series of four direct shear tests were conducted on a dry sand. The initial size of the specimens
were 50 mm by 50 mm (in horizontal plane) and 20 mm high. The following test results were
reported.
Test Number Vertical stress (kPa) Shear Stress at Failure (kPa)
1 50 35.
2 100 71
3 200 142
4 400 284
Plot the test results in normal stress-shear stress space, draw the best-fit Mohr-Coulomb
failure envelope, and report the friction angle (20 points). [Note: assume that the cohesion
intercept is zero.]
Friction angle (degrees)
they
Mohs
Coulomb
failure
envelope
i
y
o
71mi (^) I
etotonoli
Given
e (^) O
i
T bind
i
tonto
_0.
i
i
Of
ton
4
- You are going to construct a 6 m tall gravity retaining wall as shown in the figure below.
Calculate the resultant force acting on a vertical plane of the wall per unit meter (a) for active
conditions and (b) for passive conditions. Use J w = 10 kN/m
3
(30 points).
a) For active condition,
z (m) σ'v (kPa) KA σ'h (kPa) u (kPa)
Upper layer
3
Lower layer
3
6
Resultant force, PA (kN/m)
b) For passive condition,
z (m) σ'v (kPa) KP σ'h (kPa) u (kPa)
Upper layer
3
Lower layer
3
6
Resultant force, PP (kN/m)
W
A
L
L
3 m
3 m
z (m)
Soil A
J t
= 17 kN/m
3
I ' = 31 q
Soil B
J t
= 19 kN/m
3
I ' = 34 q
H
bm
ka
tongs
ka
_tail 29 so
KA
o
32 KA
ton
28
KAI
U o^
u o
a 17
51 A
51hPa
q 17
5 91 51
o o
o
6h
ka
ou
108 S1 lb 32
q _Kap
μ Vw hw
se
O
52.07 30
(^30) Pressure
diagram
61 78 124.^
PA
3 14.28^114
114
3 16.32 is.is
6
okay
1M
h z
sa o
o O O
SI SI^
o
51
j
s
78 305.89 30
ht qlxkp isg.gr
3
2 3
6h
_q ka^ z
1M
iso
6h
_out
Kpz
Guest 157
108
Isan
180
vw hw^
30 3
o
q
s
(^91 78) 305.
5
5. (Extra credit) See attached the data from the consolidation test performed on the cylindrical
specimen of clay-rich material with initial height of 70 mm, diameter of 47 mm, and void ratio
of 0.39. 500 kPa of all-around pressure was applied to the specimen while the pore pressure on
its two ends was preserved at 0 kPa. Using the information on changes in specimen volume with
time provided in “Consolidation” worksheet, plot the consolidation curve and calculate the
consolidation coefficient for the material (20 points).
6. (Extra credit) See attached the data from conventional triaxial compression tests performed on
the three cylindrical specimens of clay-rich material. Information on the initial dimensions of the
specimens, as well as the applied confining pressure V 3 and initial pore pressure uo, is provided
in “Shearing” worksheet. Using the data on changes in the axial load and pore pressure due to
the axial compression of the specimens, determine the friction angle and cohesion for the material
(at failure). Plot the stress paths in q - p ′ diagram (30 points).
Pp 12
(^3 )
1 3 X159.
t 3 21.07^ t
1
3
Pp 9684
as
