Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show. Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.

1. 1
Geotechnical Engineering–II [CE-321]
BSc Civil Engineering – 5th Semester
by
Dr. Muhammad Irfan
Assistant Professor
Civil Engg. Dept. – UET Lahore
Email: mirfan1@msn.com
Lecture Handouts: https://groups.google.com/d/forum/geotech-ii_2015session
Lecture # 7
27-Sep-2017

2. 2
STRESS DISTRIBUTION IN SOIL
What causes stress in soil?
Two principle factors causing
stresses in soil.
1. Self weight of soil
2. External loads (Structural loads,
external load, etc.)
v
h


3. 3
Practice Problem #2
Find the total stress, pore water pressure and effective stress of
the soil system at 6m and 16m depths from NSL. Also plot the
stress plots for each down to the bottom of layer B.
+12m
0m
-6m
-20m
WT
Stratum-A
gsat = 1856.7 kg/m3
Stratum-B
gsat = 1952.8 kg/m3
NSL

4. 4
Practice Problem #3
A layer of sand 4.5m deep overlies a thick bed of clay. The
water table is 2m below the top of sand. Above WT the sand
has an average void ratio of 0.52 and average degree of
saturation of 0.37. The clay has a water content of 42%.
Calculate the total stress, effective stress and PWP on a
horizontal plane 9m below the ground surface and draw
pressure distribution diagrams down to this level. Assume the
specific gravity of soil grains equal to 2.65 for both the sand
and clay layer.

5. 5
Practice Problem #4
A layer of sand extends from ground level to a depth of 9m
and overlies a 6m thick layer of clay having very low
permeability. The WT is 6m below the surface of sand. The
saturated unit weight of sand is 19 kN/m3 and that of the clay
is 20 kN/m3. The unit weight of sand above the WT is 16
kN/m3. Over a short period of time, the WT rises by 3m and is
expected to remain permanently at this new level. Determine
the effective vertical stress at depth of 8m and 12m below the
ground level.
a) Immediately after the rise of WT
b) Several years after the rise of WT

6. 6
STRESS DISTRIBUTION IN SOIL
What causes stress in soil?
Two principle factors causing
stresses in soil.
1. Self weight of soil
2. External loads (Structural loads,
external load, etc.)
v
h


7. 7
STRESS DUE TO EXTERNAL LOAD
Contact Pressure
Pressure developed at the
contact point of foundation and
soil.
𝜎 𝑜 =
𝑃
𝐵 ∙ 𝐿
Where,
σo = contact pressure
P = Point load
B x L = Contact area
P
𝝈 𝒐 =
𝑷
𝑩 ∙ 𝑳

8. 8
Stress Distribution in Soil with Depth
• Intensity of stress decreases with depth.
• Intensity of stress decreases radially from the point load.
STRESS DUE TO EXTERNAL LOAD

9. 9
STRESS INCREASE (∆q) DUE TO
EXTERNAL LOAD
Determination of stress due to external load at any
point in soil
1. Approximate (2:1) Method
2. Boussinesq’s Theory
3. Westergaard’s Theory

10. 10
APPROXIMATE METHOD
Use of 2:1 (V:H) stress
distribution.
𝜎 𝑧 =
𝑄
(𝐵 + 𝑧) ∙ (𝐿 + 𝑧)
Where,
σz = Stress at depth ‘z’
Q = Point load
B x L = Footing dimensions
𝝈 𝒛

11. 11
For rectangular foundation
For strip footing
Where,
σz = Stress at depth ‘z’
Q = Point load
B x L = Footing dimensions
𝝈 𝒐 =
𝑸
𝑩𝑳
𝝈 𝒛 =
𝑸
𝑩 + 𝒛 . (𝑳 + 𝒛)
APPROXIMATE METHOD
𝜎 𝑧 =
𝑄
(𝐵 + 𝑧) ∙ (𝐿 + 𝑧)
𝜎 𝑧 =
𝑄
(𝐵 + 𝑧) ∙ 1

12. 12
STRESS INCREASE (∆q) DUE TO
EXTERNAL LOAD
Determination of stress due to external load at any
point in soil
1. Approximate Method
2. Boussinesq’s Theory
3. Westergaard’s Theory

13. 13
Boussinesq’s Theory for Point Load
Q
Boussinesq (1885) solved the problem of stress produced by any point
load on following assumptions;
• The soil mass is elastic, isotropic, homogeneous and semi-infinite.
• The soil mass is weightless.
• The load is a point load acting on the surface.
Q

14. 14
Boussinesq’s Theory for Point Load
Q
 
 
 
  































23
2
2
22
5
2
23
2
2
22
5
2
21
3
2
21
3
2
rL
zx
zLLr
xy
L
zyQ
rL
zy
zLLr
yx
L
zxQ
y
x






5
3
2
3
L
Qz
z

 
22
yxr 
Where,
  2522
3
2
3
zr
zQ



22222
zrzyxL 
 = Poisson’s
ratio

15. 15
Q
  2522
3
5
3
2
3
2
3
zr
zQ
L
Qz
z




The above relationship for
z can be re-written as
   








 2522
1
1
2
3
zrz
Q
z


where
   252
1
1
2
3
zr
IB



QBI
z
Q
2

Independent of all material properties
Boussinesq’s Theory
for Point Load

16. 16
CONCLUDED
REFERENCE MATERIAL
An Introduction to Geotechnical Engineering (2nd Ed.)
Robert D. Holtz & William D. Kovacs
Chapter #10