Advanced foundation design(nce 011)

ADVANCED FOUNDATION DESIGN(NCE-011)
By- Md Mozaffar Masud
Assistant Professor
Civil Engineering Department
JIT, Barabanki

Soils Investigation
 Determination of surface and subsurface soil
conditions and features in an area of proposed
construction that may influence the design and
construction and address expected post construction
problems.

Soils Investigation contd.
 Required to evaluate an area for the construction of
a project or evaluate local material as a construction
material
 Soil Investigation
 Field Sampling and Testing
 Laboratory Analysis
 Report preparation
 Planning and evaluation of field work are aided by
knowledge of the mechanics of soil deposit’s
formation

 Soil grains are the result of weathering of bedrock
 physical weathering
granular soil types (gravel, sand, silt)
 chemical weathering
clays
 Soil deposits
 residual- product of weathering the original
bedrock
 transported- moved from their place of origin

 Transportation agents
 Rivers and streams
gravel sand silt deposited as a fn (water
velocity)
 Lakes
clays and silts settling out
 Wind
sand dunes and loess deposits (silt particles)

 Glacier soil deposits
 tills (mixture of gravel sand silt clay)
material that has been shoved forward or
picked up from an advancing glacier
this material is deposited when a glacier stops
or retreats as it melts
 fluvial deposits associated with glaciers
clays from glacier lakes
marine clays deposited from salt water
sorted gravel, sand and silt from glacier streams

Requirement of Soils Investigation
 Field Investigation Techniques
 determine bearing capacity for foundations
 determine water resources
 find aggregate deposits (road construction)
 estimate infiltration and seepage rates
 assess land use capabilities
 Information required
 depth, thickness, properties of each soil layer
 location of groundwater table
 depth to bedrock

 Subsurface Investigation
 Geophysical methods
seismic or electrical-variations in the speed of sound
waves or electrical resistivity of soil formations
 Test pits or trenches
shallow depths only
 Hand Augers
shallow depths only
 Boring test holes and sampling with drill rigs
principal method for detailed soil investigations

GEOPHYSICAL METHOD
 Although boring and test pits provide definite results but they are
time consuming and expensive.
 Subsurface conditions are known only at the bore or test pit
location.
 The subsurface conditions between the boring need to be
interpolated or estimated.
 Geophysical methods are more quick and cheaper.
 They provide thorough coverage of the entire area.
 results of Geophysical testing however are less definitive and
require subjective interpretation.
 both methods are important. In case geophysical testing in major
in scope, few borings and sampling will be required for accurate
determination of soil properties.
 If boring is major in scope then few geophysical lines will be
required to know the conditions in-between the borings.

Geophysical Techniques Indirect Methods
Ground Penetrating Radar
(GPR)
 Electromagnetic (EM)
 Magnetic
 Utility Locating
 Seismic
 Electrical Resistivity
 Gravity
 Very Low Frequency (VLF)

Geophysical Techniques Indirect Methods
Advantages
Non-Destructive
 Cost Effective
 Provides Preliminary or
Supplemental
Information

Geophysical Equipment
Seismograph Spectrum Analyzer
Portable Analyzer Velocity Recorder

Soil Resistivity Method
Resisitivity (ohm-m) is an electrical property. It is
the reciprocal of conductivity
Arrays of electrodes used to measure changes in
potential.
Evaluate changes in soil types and variations in
pore fluids
Used to map faults, karst features (caves,
sinkholes), stratigraphy, contaminant plumes.

Seismic Refraction Method
0.000
0.005
0.010
0.015
0.020
TravelTime(seconds)
0 10 20 30 40 50
Distance From Source (meters)
Horizontal Soil Layer over Rock

Seismic Refraction Method
Seismic
Testing of
Equipments

Westergaard’s Theory of Stress
 Westergaard developed a solution to determine
distribution of stress due to point load in soils
composed of thin layer of granular material that
partially prevent lateral deformation of the soil.

Westergaard’s Theory of Stress
2/322z
z
r
21
1
z
P

















2/32
2
2z
z
r
a
1
z2
a.P

















• Point Load



22
21
a

 Shallow foundations:
 Where the ratio of embedment depth to min plan
dimension is less or equal to 2.5
 Embedment depth is the depth below the ground surface
where the base of foundation rests.
plain concrete foundation,
stepped reinforced concrete foundation,
 reinforced concrete rectangular foundation
reinforced concrete wall foundation.
Shallow Foundation

Steps in Selection of Foundation Types
 1 Obtain the required information concerning the nature of the
superstructure and the loads to be transmitted to the foundation.
 2. Obtain the subsurface soil conditions.
 3. Explore the possibility of constructing any one of the types of foundation
under the existing conditions by taking into account (i) the bearing
capacity of the soil to carry the required load, and (ii) the adverse effects
on the structure due to differential settlements. Eliminate in this way, the
unsuitable types.
 4. Once one or two types of foundation are selected on the basis of
preliminary studies, make more detailed studies. These studies may require
more accurate determination of loads, subsurface conditions and footing
sizes. It may also be necessary to make more refined estimates of
settlement in order to predict the behavior of the structure.
 5. Estimate the cost of each of the promising types of foundation, and
choose the type that represents the most acceptable compromise between
performance and cost.

Shallow Foundation
The most common (and
cheapest) type of shallow
foundations are SPREAD FOOTINGS

Shallow Foundation
 Strip Footings to support wall loads
 Rectangular and Trapezoidal Footings for two
columns (combined footing) or machine base

Raft or Mat Foundation
 To lower the bearing pressure and reduce
differential settlement on soils with low bearing
capacity or erratic or variable conditions

Ultimate Bearing Capacity, qf
The least pressure that would cause shear
failure of supporting soil immediately below
and adjacent to a foundation

Modes of Failure(General Shear Failure)
on low compressibility
(dense or stiff) soils
plastic equilibrium
throughout support and
adjacent soil masses
heaving on both sides
of foundation
final slip (movement of
soil) on one side only
causing structure to tilt

Modes of Failure (Local Shear Failure)
on highly compressible
soils
only partial development
of plastic equilibrium
only slight heaving on
sides
significant compression of
soil under footing but no
tilting

Modes of Failure (Punching Shear Failure)
on loose, uncompacted
soils
vertical shearing around
edges of footing
high compression of soil
under footing, hence large
settlements
no heaving, no tilting

Assumptions for Terzaghi's Method
 Depth of foundation is less than or equal to its width
 No sliding occurs between foundation and soil (rough
foundation)
 Soil beneath foundation is homogeneous semi
infinite mass
 Mohr-Coulomb model for soil
 General shear failure mode is the governing
mode (but not the only mode)

Assumptions for Terzaghi's Method
 No soil consolidation occurs
 Foundation is very rigid relative to the soil
 Soil above bottom of foundation has no shear
strength; is only a surcharge load against the
overturning load
 Applied load is compressive and applied vertically to
the centroid of the foundation
 No applied moments present

Terzaghi’s Bearing Capacity Equation
Neglecting the shear strength
of the soil above depth D
implies that this soil is a
surcharge: qo= γD
Terzaghi’s general equation:
qf = 0.5γBNγ + cNc + γDNq

Terzaghi's bearing capacity factors for
general shear failure

The General Bearing Capacity Equation.

Other Factors
 For continuous footing,
s = 1
 For perpendicular load,
i = 1
 For level foundation,
b =1
 For level ground,
g =1
 Need to compute factors
 Bearing Capacity Factor N,
 Depth Factor d

General Shear Failure of Footings (Ultimate
Bearing Capacity)
qccf DNSNcSNγBq   )()(5.0
)45(tan 2
2)tan( 
 eNq
)cot()1(  qc NN
)4.1tan()1(   qNN
FOOTING TYPE Sγ Sc
Strip 1.0 1.0
Square 0.8 1.2
Circular 1.6 1.2
Rectangular 1-0.2(B/L) 1+0.2(B/L)
 theory was developed
for strip footings
 To adapt square, circular
and rectangular shapes,
Terzaghi & Peck
developed shape factors
here which are still
widely used today:

Settlement
 Immediate Settlement: Occurs
immediately after the construction.
This is computed using elasticity
theory (Important for Granular soil)
 Primary Consolidation: Due to gradual
dissipation of pore pressure induced
by external loading and consequently
expulsion of water from the soil mass,
hence volume change. (Important for
Inorganic clays)
 Secondary Consolidation: Occurs at
constant effective stress with volume
change due to rearrangement of
particles. (Important for Organic soils)

Elastic Settlement of Rectangular footings

Elastic Settlement [Schmertman Method
(1978)]
𝜌 = ∁1∁2∆𝜎
𝑖=1
𝑛
𝐼𝑧
𝐸
𝑖 ∆𝑍𝑖

Primary Consolidation
 Expulsion of water from soils accompanied by
increase in effective stress and strength
 Amount can be reasonably estimated based on lab
data, but rate is often poorly estimated

Consolidation Settlement
 This method makes use of the results of the conventional
oedometer test where the consolidation parameters of the
soil are measured.
 To compute the stress changes within the soil mass. The stress
changes are computed using a Boussinesq type approach
assuming elasticity.
 The important parameter for consolidation settlement
calculation is the net effective stress change in the soil.
 Usually the settlements are calculated for the soil divided into
a number of sub-layers and the final total settlement is the
sum of individual sub-layer settlements

Secondary Consolidation
 At the end of primary settlement, settlement may
continue to develop due to the plastic deformation
(creep) of the soil.
 The stage of consolidation is called secondary
consolidation.

Deep Foundation
 Deep Foundations are those -
 in which the depth of the foundation is very large
in comparison to its width.
 Which are not constructed by ordinary methods
of open pit excavations.

When Used?
 In cases where -
 The strata of good bearing capacity is not available near
the ground
 The space is restricted to allow for spread footings
 In these cases the foundation of the structure has to be taken
deep with the purpose of attaining a bearing stratum which is
suitable and which ensures stability and durability of a
structure.
 The bearing stratum is not the only case. There may be many
other cases. For example, the foundation for a bridge pier
must be placed below the scour depth, although suitable
bearing stratum may exist at a higher level.

Pile Foundations
 BS8004 defines deep foundation with D>B or D>3m.
 Pile foundation always more expensive than shallow
foundation but will overcome problems of soft
surface soils by transferring load to stronger, deeper
stratum, thereby reducing settlements.
 Pile resistance is comprised of
 end bearing
 shaft friction
 For many piles only one of these components is
important. This is the basis of a simple classification

End Bearing Piles
 End bearing pile
rests on a relative
firm soil . The load
of the structure is
transmitted
through the pile
into this firm soil or
rock because the
base of the pile
bears the load of
the structure, this
type of pile is called
end bearing pile
Piles
Soft Soil
Rock

Types of Pile
 The pile installation procedure varies considerably, and has an
important influence on the subsequent response
 Three categories of piles are classified by method of
installation as below:
 Large displacement piles
They encompass all solid driven piles including precast
concrete piles, steel or concrete tubes closed at the
lower end
 Small displacement piles
They include rolled steel sections such as H-pile and
open-end tubular piles
 Replacement piles
They are formed by machine boring, grabbing or hand-
digging.

Ultimate capacity of axially load single pile
in soil
 Estimated by designer based on soil data and
somewhat empirical procedures. It is common
practice that the pile capacity be verified by pile load
test at an early stage such that design amendment
can be made prior to installation of the project piles.
The satisfactory performance of a pile is, in most
cases, governed by the limiting acceptable
deformation under various loading conditions.
Therefore the settlement should also be checked.

Basic Concept
Qu
W
Qs
Qb
 The ultimate bearing capacity (Qu )of a pile
may be assessed using soil mechanics
principles. The capacity is assumed to be
the sum of skin friction and end-bearing
resistance, i.e
Qu =Qb+Qs-W ……………………….(1)
Where,
Qu is total pile resistance,
Qb is the end bearing resistance and
Qs is side friction resistance
 General behaviour
 Shaft resistance fully mobilized at
small pile movement (<0.01D)
 Base resistance mobilized at large
movement (0.1D)

End Bearing resistance for Bore pile in
granular soils
 Due to the natural of granular soil, the c’ can be assumed
equation to zero. The ultimate end bearing resistance for
bored pile in granular soils may be express in terms of vertical
effective stress, ’v and the bearing capacity factors Nq as :
QB=AB Nq ’v
Nq is generally related to the angle of shearing resistance f’.
For general design purposed, it is suggested that the Nq value
proposed by Berezantze et al (1961) as presented in Figure ??
are used. However, the calculated ultimate base stress should
conservatively be limited to 10Mpa, unless higher values have
been justified by load tests.

Shaft Friction Resistance
 The ultimate shaft friction stress qs for piles may be expressed in terms of mean
vertical effective stress as :
qs =c’+Ksv’tands
qs =b v’ (when c’=0)
Where,
Ks= coefficient of horizontal pressure which depends on the relative density and
state of soil, method of pile installation, and material length and shape of pile. Ks may
be related to the coefficient of earth pressure at rest,
K0=1-sin
Qv’ = mean vertical effective stress
s’ = angle of friction along pile/soil interface
b = shaft friction coefficient
Qs = pLqs
Where p is the perimeter of the pile and L is the total length of the pile

Bored pile in Clays
 The ultimate end bearing resistance for piles in clays
is often related to the undrained shear strength, Cu,
as
qB=NcCu
QB=ABNcCu
where,
Nc= 9 when the location of the pile base below
ground surface exceeds fours times the pile diameter

Bored pile in Clays
 The ultimate shaft friction (qs) for soils in stiff over-
consolidated clays may be estimated on the semi-
empirical method as:
qs=aCu
a is the adhesion factor (range from 0.4 to 0.9)

Design of Pile Groups
 The efficiency of a pile group is the ratio of the ultimate
capacity of the group to the sum of the candidates of
the individual piles.
ɳg = Qug
nQu
Where:
g = Pile group efficiency.
Qug = Ultimate capacity of the pile group.
n = Number of piles in the pile group.
Qu = Ultimate capacity of each pile in the pile group

Design of Pile Groups
 The group efficiency may be less than 1 for a pile
group driven into a compressible cohesive soil, or
into a dense cohesionless soil underlain by a weak
cohesive deposit.
 The group efficiency in cohesionless soils is generally
greater than 1.
 The settlement of a pile group is likely to be many
times greater than that of a single pile carrying the
same load as each pile in the pile group.

Stress Zones from a Single Pile and Pile
Group

Group Capacity in Cohesionless Soils
 The ultimate axial compression capacity of a pile
group driven in a cohesionless soil may be taken as
the sum of the individual capacities, unless underlain
by a weak deposit, jetted, or predrilled.
 If underlain by a weak deposit, the ultimate group
capacity is the lesser of the 1) sum of the individual
pile capacities, or 2) the group capacity against block
failure.
 A minimum center-to-center pile spacing of 3
diameters is recommended.

Group Capacity in Cohesive Soils
 For pile groups in clays with undrained shear strengths
less than 95 kPa (2 ksf), and the cap not in firm contact
with the ground, use a group efficiency ranging from
0.7 for c-t-c spacings of 3 diameters, to 1.0 for c-t-c
spacings of 6 diameters (interpolate in between).
less than 95 kPa (2 ksf), and the cap in firm contact
with the ground, a group efficiency of 1.0 may be used.
greater than 95 kPa (2 ksf), regardless of pile
cap/ground contact, use a group efficiency of 1.0.

Group Capacity in Cohesive Soils
 Calculate the ultimate pile group capacity against block
failure, and use the lesser capacity.
 A center-to-center spacing less than 3 diameters should not
be used
 Short-term group efficiencies in cohesive soils 1 to 2 months
after installation may be as low as 0.4 - 0.8 due to high
driving-induced excess porewater pressures (results in
decreased effective stress).
 Pile groups in clays which are loaded shortly after pile
installation should consider the reduced short-term group
capacity.
 In critical cases, piezometers should be installed to monitor
porewater pressure dissipation with time

Settlement of pile group
 Block failure of pile groups is generally only a design
consideration for pile groups in soft cohesive soils or
in cohesionless soils underlain by a weak cohesive
layer.
 The bearing capacity factor, Nc, for a rectangular pile
group is generally 9.
 However, Nc should be calculated for pile groups
with small pile embedment depths and/or large
widths
Nc = 5 [ 1+D/5B ] [ 1+B/5Z ] ≤ 9

Expansive Soils
 Vertisol Soils, or known as Shrink Swell Soils
 The Soil contracts due to its clay minerals and the
structure of the clay allowing water to be imbedded
in-between the clay layers
 Process is reversible, and causes contraction of the
soil

Characteristics of expansive soils
 The expansive properties of soils depend on the
grain size, mineralogy and water content.
 The 2:1 sheet smectite group include expansive
monmorillonite clay.
 Montmorillonite swell and shrink at different
moisture content

Foundation on expansive soil
 Foundation is the lowest load-bearing part of
engineering infrastructures, typically below ground
level.
 Foundations are affected by engineering properties
and characteristic of the soil.
 Engineering problems and type of foundation
support are vital in construction of foundation.

Foundation on expansive soil contd.
 Foundation on expansive soils is affected by the
behaviour of soil under different moisture content.
 The swelling tendency of expansive soils on
foundation can be quantified by the swell potential
and swelling pressure parameters.
 The major engineering problem of expansive soils on
foundation is shrink-swelling characteristics of the
soil.
 Foundation types that can be utilised on expansive
soils are pile, raft, shallow and caissons foundation.

Engineering problems
 Swelling and shrinking of soil

What can be done?
 Test soil before building
 If expansion is greater then 10 %, it is critical
 Remove soil
 Mix soil with material that does not expand
 Keep consistent soil moisture
 Have strong foundations in buildings that can handle
the changes in volume.

Engineering solutions
 Post-wet and pave the area with bricks or blocks laid
on the plastic membrane.
 Total removal of expansive soils.
 Under pinning with piles.
 Reinforcement of with tie-bars.
 Caissons foundation.

Well Foundation
Well foundation is the most commonly adopted
foundation for major bridges in India. Since then many
major bridges across wide rivers have been founded on
wells.
Well foundation is preferable to pile foundation when
foundation has to resist large lateral forces.
The construction principles of well foundation are similar
to the conventional wells sunk for underground water.
But relatively rigid and engineering behaviour.
Well foundations have been used in India for centuries.
The famous Taj Mahal at Agra stands on well foundation.

Benefits of Well Foundation
 Provides massive and solid foundation.
 Possible to sink well through boulders,logs of wood
found at depth.
 Large section modulus with minimum cross sectional
area is advantageous.
 The strata through which well passes is known
exactly.
 Well raising and stiening is done in steps so
foundation level can be varied.
 Economical to provide it for unstable soil mass

Shapes of well foundations
Wells have different shapes and accordingly
they are named as:-
 Circular well,
 Double D well,
 Twin circular well,
 Double octagonal well,
 Rectangular well.

Types of Well Foundation
Open caisson or well
Box Caisson
Pneumatic Caisson

Types of Well Foundation
 Open caisson or well: The top and bottom of the
caisson is open during construction. It may have any
shape in plan.
 Box caisson: It is open at the top but closed at the
bottom.
 Pneumatic caisson: It has a working chamber at the
bottom of the caisson which is kept dry by forcing
out water under pressure, thus permitting excavation
under dry conditions.

Construction Procedure
 Layout
 Fabrication of cutting edge.
 Well curb.
 Construction of stieining.
 Island construction
 Well Sinking.
 Plugging.
 Sand filling.
 Casting of well cap.

Sinking Operations
 Erect Cutting Edge.
 Erect inside shuttering of curb.
 Fix reinforcement for the curb.
 Erect outside shuttering of curb.
 Concrete the curb and ground it.
 Remove the shuttering.
 Fix reinforcement in steining
 Erect reinforcement for one lift.

Sinking Operations Contd.
 Concrete the steining.
 Dredge inside the well.
 Sink the well in stages.
 Sinking is done by uniform excavation of material.
 Use of water jetting and explosives may be done.
 Normally dewatering should not be done.
 Tilts must be rectified wherever necessary

Precautions
 When two wells sunk near each other, they should
be sunk alternately.
 Least possible area must be disturbed in vicinity.
 In sinking of dumb bell shaped well, excavation must
be done simultaneously.
 Dredged material must not be accumulated near
well.
 In sinking of two wells through sand, timber logs are
provided between steining.
 Care must be taken when cutting edge approaches
junction of strata.

Sinking Well Through Clay Strata
 It is one of the tough situations to face as well
becomes stationary.
 Tilting occurs due to horizontal force by water.
 The well becomes vulnerable to tilt if a step is
provided on outside face of the well steining to
reduce
 It may lead to a very expensive and time-consuming
affair for attempting to make well straight and
vertical.

Measures Adopted
 Remove soil in contact with the outside surface of
the well by grabbing to a certain depth.
 Continue grabbing much below the cutting edge level
of the well.
 Dewatering well results into increasing effective
weight.
 Flushing with jet of water on the outside face of well.
 By Kentledge loading on the well

General Measures for Ease of Sinking.
 Appropriate choice of cutting edge and adoption of proper
detailing.
 The "Angle iron" cutting edge works well when the well passes
through alluvial soil strata without any hard obstruction.
 A "V type" cutting edge is more appropriate in meeting various
obstructive situation provided correct detailing is adopted.
 The inclined plate should be stopped about 25 mm above the
bottom tip of vertical plate.
 Adequate no. of Borelogs must be taken in the location of each
well.
 Presence of very large boulder covering a part of the well at some
depth in the bridge over Brahmaputra at Jogighopa.
 Similar type of problems including sudden change of bed profile are
encountered in various rivers in India.

Types of slopes
 Two Types:
 Natural slopes: Due too natural causes
 Man made slopes: Cutting and embankments
 The slopes whether natural or artificial may be
 Infinite slopes
 Finite slopes

Causes of Failure of Slopes
 The important factors that cause instability in a slope
and lead to failure are:
 Gravitational force
 Force due to seepage water
 Erosion of the surface of slopes due to flowing
water
 sudden lowering of water adjacent to a slope
 Forces due to earthquakes

COMMON FEATURES OF SLOPE STABILITY
ANALYSIS METHODS
 Safety Factor: F = S/Sm where S = shear strength and
Sm = mobilized shear resistance. F = 1: failure, F > 1:
safety
 Shape and location of failure is not known a priori
but assumed (trial and error to find minimum F)
 Static equilibrium (equilibrium of forces and
moments on a sliding mass)
 Two-dimensional analysis

Factors Affecting Slope Failure
 Geological discontinuities
 Effect of Water
 Geotechnical Properties of Material
 Mining Methods
 State of stress
 Geometry slope:
 Temperature
 Erosion
 Seismic effect
 Vegetation

Types of Rock Slope Failure
 Plane failure
 Wedge Failure
 Toppling failure
 Rockfalls
 Rotational Failure

Rock Slope Stability Analysis: Limit
Equilibrium Method
 Planar Failure Analysis
 Sliding analysis of a block
 Plane failure analysis along a discontinuity
 Water is filled in discontinuities
 Tension crack present in the upper slope surface
 Tension crack present in the slope surface
 The tension crack is filled with water with upper slope angle
 Effect of rock bolts
 Wedge Failure Analysis
 Analysis of wedge failure considering only frictional resistance
 Analysis of wedge failure with cohesion and friction angle
 Toppling Failure Analysis
 Kinematics of block toppling failure
 Limit equilibrium analysis for toppling failure
 Stability analysis of flexural toppling

Infinite Slope Analysis
 Translational failures along a single plane failure
surface parallel to slope surface
 The ratio of depth to failure surface to length of
failure zone is relatively small (<10%)
 Applies to surface raveling in granular materials or
slab slides in cohesive materials
 Equilibrium of forces on a slice of the sliding mass
along the failure surface is considered

Infinite Slope Analysis contd.
 F = f(c’, ’, , b, d, u)
 F = (c’/ d) secbcosecb + (tan’/tanb)(1-ru sec2b)
where ru = u/d (different ru for seepage parallel to
slope face, seepage emerging, seepage downward,
etc)
 For Granular Soil: F = (tan’/tanb)(1-ru sec2b) Dry
Granular Soil (ru = 0): F = (tan’/tanb)
 For Cohesive Soil: F decreases with increasing depth
to failure plane; if c is sufficiently large, dc for F = 1
may be large and infinite slope failure may not apply.

Finite Slopes: Plane Failure Surface
 Translational Block Slides along single plane of
weakness or geological interface
 F = c’L + (W cos uL) tan’ / W sin + Fw

Method of Slices
 Assumes that resultant of side forces on each slice
are collinear and act parallel to failure surface and
therefore cancel each other
 F = [cn ln + (Wn cosan - un ln) tann] / Wn sinan
 Undrained analysis: F = [cn ln] / Wn sinan

Side Forces in Method of Slices

Bishop’s Simplified Method
act in horizontal direction and therefore vertical side
force components cancel each other
 F = [cn bn + (Wn - un bn) tann](1/ma) / Wn sinan
 ma = cosan + (sinan tanan)/F
 Undrained analysis: F = [cn ln] / Wn sinan

Wedge Method
 Failure surface consists of two or more planes and
applicable to slope containing several planes of
interfaces and weak layers
 Force equilibrium is satisfied
either acts horizontally or at varying angles from
horizontal (typically up to 15o)

Wedge Analysis
 Equilibrium of
Forces in each
slice is considered
to adjust the
inter-slice forces
and balance them
resulting in a
correct solution.

Machine Foundations
 Machine foundations require a special consideration because they
transmit dynamic loads to soil in addition to static loads due to weight of
foundation, machine and accessories.
 The dynamic load due to operation of the machine is generally small
compared to the static weight of machine and the supporting foundation.
 In a machine foundation the dynamic load is applied repetitively over a
very long period of time but its magnitude is small and therefore the soil
behaviour is essentially elastic, or else deformation will increase with each
cycle of loading and may become unacceptable.
 The amplitude of vibration of a machine at its operating frequency is the
most important
 parameter to be determined in designing a machine foundation, in
addition to the natural frequency of a machine foundation soil system.

Machine Foundations: Block
Foundation
 Block foundation consists of a massive
block of concrete resting directly on soil
or supported on piles or a pedestal
resting on a footing.
 If two or more machines of similar type
are to be installed in a shop, these can
profitably be mounted on one continuous
mat.
 A block foundation has a large mass and,
therefore, a smaller natural frequency.
 The block has large bending and torsional
stiffness and easy to construct. To modify
the block foundation at a later time is
extremely difficult.

Machine foundations: Box or Cassion
Foundation
 However, if a relatively lighter foundation is
desired, a box or a caisson type foundation may
be provided.
 The mass of the foundation is reduced and its
natural frequency increases.
 Box or Caisson foundation consists of a hollow
concrete block (can be used as operational
space) that supports the machine on its top.
Hammers may also be mounted on block
foundations, but their details would be quite
different than those for reciprocating machines.
 It has high static stiffness just like a plate
foundation and is not easily amenable to
alterations at a later date.

Machine foundations: Wall type
Foundation
 Steam turbines have complex foundations
that may consist of a system of walls
columns, beams and slabs.
 This type is usually adopted for very high-
speed machines requiring large operational
space below for connecting pipes and
additional equipment.
 It can be made or either RCC or steel frames.
Although the frame made of steel is easy to
alter at a later date, its behaviour under
dynamic loading is not as good as that of an
RCC frame.
 Each element of such a foundation is
relatively flexible as compared to a rigid
block and box or a caisson-type foundation.

Design Criteria for Machine Foundations
 It should be safe from a bearing capacity failure under static and dynamic
loads,
 The settlement must be less than the prescribed ones,
 The dynamic amplitudes of the machine-foundation-soil system must be
within the prescribed limits under service conditions.
 There should be no resonance, i.e. the natural frequency of the machine-
foundation-soil system should not coincide with the operating frequency
of the machine,
 Preferably, the Centre of gravity of the machine should lie in the same
vertical line as the Centre of gravity of the foundation system.
 When design criteria (iii) to (v) are satisfied then
 the machine itself is not damaged by the vibrations generated,
 the structure in which the machine is housed and adjacent structures do not
suffer any vibration induced damage,
 performance of machines located in its vicinity is not impaired, and
 employees working around the machine are not bothered by the vibrations

Vertical Vibrations of a Machine
Foundation
Vertical Vibrations of a Machine Foundation (a) Actual Case (b)
Equivalent model with damping ( c) Model without damping

Design of Machine Foundation
 In order to calculate the natural frequency and
amplitude of vibrations for a particular machine-
foundation-soil-system, you need to know the local
soil profile and soil characteristics as also the
dynamic loads generated by the machine that are
provided by the manufacturer.
 Empirical
 Elastic half space method
 Linear elastic weightless spring method, and

Empirical Method
 On such design guideline, rather a rule of thumb was the weight of
the foundation should be at least three to five times the weight of
machine being supported.
 There are some empirical formulae available in literature for
estimating the natural frequency, mostly for the vertical mode of
vibration.
 In these formulae, it is assumed that a certain part of the soil,
immediately below the foundation, moves as a rigid body along
with the foundation and is called apparent soil mass or in-phase
mass.
 For example, D.D.Barken in 1962 suggested that the mass of the
vibrating soil should be between 2/3 to 3/2 times the weight of
foundation and machine.
 These guidelines/formulae do not take into account the nature of
subsoil, type of excitation force (harmonic/impact), contact area
and mode of vibration.

Advanced foundation design(nce 011)

Advanced foundation design(nce 011)

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