This document discusses stresses within soil masses. It defines types of stresses such as geostatic stress from the mass of overlying soil and stresses from surface loads. It also discusses concepts of total stress, effective stress, and pore water pressure. For saturated soils, the effective stress is defined as the total stress minus the pore water pressure. Equations are provided to calculate vertical stresses, stresses in layered soils, and stresses in saturated soils both with and without seepage. An example calculation is given to determine the effective stress at a certain depth below the water table for a sand layer.

1. Hydraulic and strength properties of
soils
Lecture
3
Elias A. 1

2. •Concept of effective stress
•Permeability
•Shear characteristics of soils
•Coulomb’s equation for shear strength
•Determination of shear strengths of soils
2

3. STRESSES WITHIN SOIL MASS
3

4. Stresses within the soil
Types of stresses:
• 1- Geostatic stress: Sub Surface Stresses cause by mass of
soil (self weight)
• A. vertical stress
• B. horizontal stress
• 2. Stress distribution in soils due to surface load
a) Stress Caused by a Point Load
b) Vertical Stress Caused by a Line Load
c) Vertical Stress Caused by a Strip Load
d) Vertical Stress Due to Embankment Loading
e) Vertical Stress below the Center of a uniformly Loaded
Circular Area
f) Vertical Stress at any Point below a uniformly Loaded
Circular Area
g) Vertical Stress Caused by a Rectangular Loaded Area
4

5. 5

6. 6

7. 7

8. Geostaticstress/Stressduetoselfweight
σz = ϒ × Z
8
The vertical stress on element A can be determined simply from
the mass of the overlying material.
If ϒ represents the unit weight of the soil, the vertical stress is

9. 9
Stressduetoself weight
Stressesin aLayeredDeposit
Thestressesin a depositconsisting of layersof
soil having different densitiesmaybedeterminedas
z  1 h12 h2 ......n hn   i hi
V
e
rtical stre
ssat depth z1
σz1 = y1 ∗h1
Vertical stressat depthz2
σz2 = y1 ∗ h1 + y2 ∗ h2
Vertical stressat depthz3
ϒ1 ∗ ℎ1 + ϒ2 ∗ ℎ2 + ϒ3 ∗ ℎ3

10. 10
Stressduetoself weight
With uniform surchargeoninfinite land surface
Conversionlandsurface

11. 11
Stressduetoself weight
Vertical Stresses
Vertical stressesdueto self weight increase
with depth,
Thereare 3typesof geostatic stresses:
a.Total Stress,σtotal
b.EffectiveStress,σ'
c.PoreWaterPressure,u
σz = ϒ ∗ z

12. 12
Stressduetoself weight
Total vertical stress
Considerasoil masshaving ahorizontal surface
andwith thewater tableat surface level.The
total vertical stress at depthz is equal tothe
weight ofall material (solids+ water) per
unit areaabovethat depth ,i.e
σztota = ϒsat ∗ z

13. 13
Porewaterpressure
If the pores of asoil massarefilled with water
and if apressureinducedinto theporewater,tries
toseparatethegrains,this pressureis termedaspore
waterpressure
Theporewaterpressureat anydepthwill be
hydrostaticsincethevoid spacebetweenthesolid
particlesiscontinuous,thereforeat depthz:
u = ϒw ∗ z
Stressduetoself weight

14. NB: the effective stress is not the actual grain-to-grain contact stress,
but the average intergranular stress on a plane area within the soil
mass
14
σ’ = σ − u
z ztota
Stressduetoself weight
Effective vertical stress due to self weight of soil
The pressure transmitted through grain to grain at the
contact points through a soil mass is termed as effective
pressure.
The difference between the total stress (σztotal ) and the
pore pressure (u) in a saturated soil has been defined by
Terzaghi as the effective stress ( σ’z).

15. 15
Stressesin SaturatedSoil
If water is seeping, the effective stress at any point
in a soil mass will differ from that in the static
case.
It will increase or decrease, depending on the
direction of seepage.
The increasing in effective pressure due to the
flow of water through the pores of the soil is
known as seepage pressure.
Stressduetoself weight

16. 16
Stressduetoself weight
Stresses in Saturated Soil without Seepage
A column of saturated soil mass with no seepage of water in any direction
The total stress at the elevation of
point A can be obtained from the
saturated unit weight of the
soil and the unit weight of water
above it. Thus,

17. 17
Stressduetoself weight
Stressesin Saturated Soil without Seepage
σz = ϒw H + (HA − H)ϒsat
where
σz = total stress at the
elevation of point A
ϒsat = saturated unit weight
of thesoil
HA= distance between point A
and the water table

18. 18
Stressduetoself weight
Stressesin SaturatedSoil without Seepage
Stressat pointA,
• Total stress: σ𝐴 = ϒ𝑤𝐻1
• Porewaterpressure: UA = ϒ𝑤𝐻1
• Effectivestress:
• StressatpointB,
σ′ = σ𝐴 − 𝑈𝐴

19. 19

20. 20

21. Exercise:
A uniform layer of sand 10 m deep overlays bedrock. The water table
is located 2 m below the surface of the sand which is found to have a
voids ratio e = 0.7.
Assuming that the soil particles have a specific gravity Gs = 2.7
calculate the effective stress at a depth 5 m below the surface.
21

22. 22

23. 23

24. 24

25. 25

26. 26
lecture 4- permeability.pptx