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ASM-1 stress & displacement.pptx.PDF
1. L. D. COLLEGE OF ENGINEERING,
AHMEDABAD
APPLIED MECHANICS
A presentation on
Stresses & Displacements in Soil
Guided by
Prof. Priti Mehta
SUBJECT CODE: 3714312
Presented by
ADITYA H. PATEL (7143001)
JAYDEEPSINH CHHANIYARA (714002)
2. Table of Content
• Introduction
• Concentrated Force : Boussinesq Theory
• Westergard’s Analysis
• Comparison between boussinesq & Westergard’s theory
• Newmark’s Influence Chart
• Contact Pressure
3. INTRODUCTION
Stresses in Soil:
• Vertical Stress: This is the stress exerted on soil particles due
to the weight of overlying soil or structures. It's affected by the
self-weight of soil layers and any additional applied loads.
• Lateral Stress: The pressure exerted sideways on soil particles
due to external forces or confinement. This stress is crucial in
retaining wall design, excavation support, and tunneling.
• Shear Stress: It's the stress that causes one layer of soil to slide
over another. Shear stresses are essential in understanding
soil stability and failure mechanisms.
4. INTRODUCTION
Displacement in Soil:
• Settlement: Vertical downward movement of the soil due
to compression or consolidation. It often occurs when a
load is applied to the soil, causing it to compact.
• Lateral Displacement: Sideways movement of soil due to
various factors like slope instability, lateral earth pressure,
or seismic activity.
• Expansion or Contraction: Soil can expand or contract
due to changes in moisture content, causing horizontal
movements.
5. STRESSES DUE TO SELF WEIGHT
Stresses due to self weight are sometimes known as geostatic stresses. Let us take
the soil mass to be bounded by the horizontal plane (ground surface) xy, and the z-
axis be directed downwards. Under this condition, the soil mass is said to be semi-
infinite. Where there is no external loading, the ground plane becomes a
principal plane since it is devoid of any shear loading. From the symmetry and
the orthogonality of principal planes, one can conclude that all the horizontal and
vertical planes will be devoid of shear stresses, so that within the soil mass, tXY =
tXZ = tYZ = 0. Substituting this in the equilibrium equations (Eq. 12.4), we get sZ =
g z ...(13.1) where g = unit weight of soil and sZ = vertical stress at a point within
and soil mass, situated at a depth z below the ground surfaces
6. CONCENTRATED FORCE : BOUSSINESQ
EQUATIONS
Boussinesq (1885) solved the problem of stress distribution in
soils due to a concentrated load acting at the ground surface.
ASSUMPTIONS-
1. The soil mass is an elastic medium, for which the modulus of
elasticity E is constant.
2. The soil mass is homogeneous, that is, all its constituent parts or
elements are similar and it has identical properties at every point in it in
identical directions.
3. The soil mass is isotropic, that is, it has identical elastic properties in
all directions through any point of it.
4. The soil mass is semi-infinite, that is, it extends infinitely in all
directions below a level surface.
7. In the cylindrical co-ordinates the
corresponding vertical stress σz and
tangential stress τ rz are given by
8. It should be emphasized that although both the vertical normal
stress and shearing stress are independent of the elastic constants
(E and m) they are very much dependent on the assumptions of
linear elasticity.
Equation may be written as:-
9. WESTERGAARD’S ANALYSIS
Westergaard (1938) also solved
the problem of pressure
distribution in soil under point
load, assuming the soil to be an
elastic medium of semi-infinite
extent but containing
numerous, closely spaced,
horizontal sheets of negligible
thickness of an infinite rigid
material which permits only
downward deformation on the
mass as a whole without
allowing it to undergo any
lateral strain.
12. NEWMARK’S INFLUENCE CHART
A more accurate method of determining the vertical stress
at any point under a uniformly loaded area of any shape
is with the help of influence chart or influence diagram
originally suggested by Newmark (1942).
A chart, consisting of number of circles and radiating
lines, is so prepared that the influence of each area unit
(formed in the shape of a sector between two concentric
circles and two adjacent radial lines) is the same at the
centre of the circles, i.e., each area unit causes the equal
vertical stress at the centre of the diagram.
13. Let a uniformly loaded
circular area of radius r1 cm
be divided into 20 sectors (area
units). If q is the intensity of
loading, and σz is the vertical
pressure at a depth z below the
centre of the area, each unit
such as OA1 B1 exerts a
pressure equal to σZ/20 at the
centre.
14. CONTACT PRESSURE
Contact pressure is defined as the vertical pressure acting
at the surface of contact between the base of a footing and
the underlying soil mass.
The actual contact pressure distribution, however,
depends upon the flexural rigidity of the footing and the
elastic properties of the subgrade.
If the footing in flexible, the distribution of contact
pressure is uniform irrespective of the type of the
subgrade or under-soil material. If the footing is perfectly
rigid, the contact pressure distribution depends upon the
type of the subgrade.
