Sci 1310
Sci 1310
Sci 1310
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The art of selecting, designing, and constructing the elements that transfer the weight
(Weight may also include horizontal loads in addition to vertical loads) of a structure to the
underlying soil or rock. A foundation is interfacing element between the superstructure and the
underlying soil or rock. The loads transmitted by the foundation to the underling soil must not
cause soil shear failure or damaging settlement of the superstructure.
The term “foundation engineering” is used to include the design of foundations for buildings
and other structures and also for such non foundation problems as designs of retaining walls,
bulkheads, cofferdams, tunnels, and earth dams, as well as the design of natural slopes,
dewatering of soils, and stabilization of soils mechanically and chemically.
The geotechnical engineer is responsible for all geotechnical requirements of all types of
structures. For any construction project, the geotechnical engineer‟s responsibilities include:
developing a soil exploration plan;
preparing the Preliminary Geotechnical Report (PGR) to assist in the selection of
foundation type and to perform a preliminary seismic analysis/evaluation;
identifying the proposed boring locations and anticipated foundation type;
Assisting the Construction engineers by preparing pile driving criteria, reviewing pile
installation plans and determining acceptance of as-built piles.
Also assisting bridge designer in determining pile production lengths based on field
load tests.
PROPERTIES OF FOUNDATION
Strength: Load bearing capacities: Crystalline rocks (very strong - 12,000 ),
sedimentary rocks (intermediate - 6,000 ) and other types of soils (relatively lower -
2,000 to 3,000 )
Stable under loads (creep, shrinkage and swelling)
Drainage characteristics: Porosity and permeability
Soil property estimation: Subsurface exploration (test pits - less than 8 ft in depth;
borings - greater than 8 ft) - Estimate level of water table - Testing of soil sample
in laboratory for various properties: Particle size distribution, Liquid limit, Plastic limit, Water
content, Permeability, Shrinkage/ swelling, Shear/compressive strength, Consolidation (creep
and settlement)
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CONSTRUCTION OF FOUNDATIONS
Some amount of excavation required for every building - Top soil consisting of organic
matter is removed - Below the region of soil erosion (by water and wind) & below the
level of permafrost - To the required depth at which the bearing capacity necessary for
the building is met - A variety of machines used for excavation - The sides of
excavation too be protected from caving in by benching, sheeting (soldier beams and
lagging, sheet piles, slurry walls, etc.) or bracing (cross-slot, rakers or tiebacks) - De-
watering using well-points & sumps, and watertight barriers - Mixing the soil by
rotating paddles
Bulldozers, Shovel dozers, Back hoes ,Bucket loaders, Scrapers, Trenching machines
Power shovels, Tractor-mounted rippers, Pneumatic hammers, Drop balls, Hydraulic
splitters and Blasting.
Purpose of Foundation:
All engineering structures are provided with foundations at the base to fulfill the following
objectives and purposes;
i. To distribute the load of the structure over a large bearing area so as to bring intensity
of loading within the safe bearing capacity of the soil lying underneath.
ii. To load the bearing surface at a uniform rate so as to prevent unequal settlement.
iii. To prevent the lateral movement of the supporting material.
iv. To secure a level and firm bed for building operations.
v. To increase the stability of the structure as a whole.
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1. Presence of Loose Fill
Often one encounters pockets of loose fill of recently dumped soil or construction waste at or
near the ground surface. Foundations should be placed below such loose fills.
2. Depth of Water Table
Wherein possible, shallow foundations are not placed below the ground water level to avoid
expensive de-watering costs during foundation construction.
3. Lateral Variability
Usually all foundations are placed at the same Df. there are soil profiles that calls for a
different Dffor different footings. For example, consider a profile in which rock exist at
shallow depth and is gently sloping in some direction. In an attempt to take advantage of the
high allowable soil pressure associated with placing the foundation on rock, we will have a
different Df for each footings so that each can be placed on the rock.
4. Zones of Volume Change
In cold regions where temperature changes cause soil near the ground surface to go through
cycles of freezing and thawing with consequent changes in soil volume, foundation are placed
below the zone so affected.Similarly in swelling soils, there is a zone that undergoes volume
change due to wetting and drying cycles. Df is selected such that it is more than the thickness
of this zone.
5. Scour
When shallow foundations are designed to be placed below the river bed for river crossing
structures, one must recognize that the elevation of the river bed changes on account of scour
that occurs when the water flows at high velocity such as during floods.
Soil Exploration
The knowledge of subsoil conditions at a site is a prerequisite for safe and economical design
of substructure elements. The field and laboratory studies carried out for obtaining the
necessary information about the surface and subsurface features of the proposed area including
the position of the ground water table, are termed as soil exploration or site investigation.
The primary objectives of soil exploration are
Determination of the nature of the deposits of soil.
Determination of the depth and thickness of the various soil strata and their extent in
the horizontal direction.
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The location of ground water table (GWT).
Obtaining soil and rock samples from the various strata.
The determination of the engineering properties of the soil and rock strata that affect
the performance of the structure.
Determination of the in-situ properties by performing field tests.
Phase I. Collection of available information such as a site plan, type, size, and importance of
the structure, loading conditions, previous geotechnical reports, topographic maps, air
photographs, geologic maps, hydrological information and newspaper clippings.
Phase II. Preliminary reconnaissance or a site visit to provide a general picture of the
topography and geology of the site. It is necessary that you take with you on the site visit all
the information gathered in Phase I to compare with the current conditions of the site. Here
visual inspection is done to gather information on topography, soil stratification, vegetation,
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water marks, ground water level, and type of construction nearby.
Phase III. Detailed soils exploration. Here we make a detailed planning for soil exploration in
the form trial pits or borings, their spacing and depth. Accordingly, the soil exploration is
carried out. The details of the soils encountered, the type of field tests adopted and the type of
sampling done, presence of water table if met with are recorded in the form of bore log. The
soil samples are properly labeled and sent to laboratory for evaluation of their physical and
engineering properties.
Phase IV. Write a report. The report must contain a clear description of the soils at the site,
methods of exploration, soil profile, test methods and results, and the location of the
groundwater. This should include information and/or explanations of any unusual soil,
waterbearing stratum, and soil and groundwater condition that may be troublesome during
construction.
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The methods available for soil exploration may be classified as follows
Direct methods ... Test pits, trial pits or trenches
Semi-direct methods ... Borings
Indirect methods ... Soundings or penetration tests and geophysical methods
Advantages
i) Cost effective
ii) Provide detailed information of stratigraphy
iii) Large quantities of disturbed soils are available for testing
iv) Large blocks of undisturbed samples can be carved out from the pits
v) Field tests can be conducted at the bottom of the pits
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Disadvantages
i) Depth limited to about 6m
ii) Deep pits uneconomical
iii) Excavation below groundwater and into rock difficult and
costly iv)Too many pits may scar site and require backfill soils.
Limitations
i) Undisturbed sampling is difficult ii) Collapse in granular soils or below ground water table
Boring: Making or drilling bore holes into the ground with a view to obtaining soil or rock
samples from specified or known depths is called „boring‟
The common methods of advancing bore holes are: Auger boring, Wash boring, rotary boring
and Percussion boring.
Exploratory borings
Boring is carried out in the relatively soft and uncemented ground (engineering „soil‟) which is
normally found close to ground surface. The techniques used vary widely across the world.
General guidelines for location and depth of bore holes Boreholes are generally located at
The building corners The centre of the site
Where heavily loaded columns or machinery pads are proposed.
At least one boring should be taken to a deeper stratum, probably up to the bedrock if
practicable other borings may be taken at least to significant stress level.
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Spacing of Bore Holes – Codal Recommendations
For a small building one bore hole or test pit at the centre can give necessary data
For a building covering not more than 4000 sq.m, one bore hole or test pit at each
corner and one at centre is adequate.
For a large project, the number will depend on its geological features and variation of
strata. Generally a grid of 50 m spacing should be used with a combination of bore
holes and sounding tests.
Depth of Investigation
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5. In very stiff clays, borings should penetrate 5-7 m to prove that the thickness of the stratum
is adequate.
6. Borings must penetrate below any fills or very soft deposits below the proposed structure.
7. The minimum depth of boreholes should be 6 m unless bedrock or very dense material is
encountered.
Significant depth The investigation shall be carried out to the point at which the vertical stress
due to proposed structure is equal to or less than 10% of original effective stress at the point
before the structure is constructed – significant depth
Methods of borings i) Auger boring – preferred for shallow depths , low ground water table
ii) Wash boring: high water table, deeper soil deposit iii) Rotary drilling: high quality boring,
also for rock drilling iv) Percussion drilling: fast drilling, not taking samples, gravel
Auger boring:-Augers are used in cohesive and other soft soils above water table. They may
either be operated manually or mechanically. Hands augers are used up to a depth up to 6 m.
mechanically operated augers are used for greater depths and they can also be used in gravelly
soils. Augers are of two types: (a) spiral auger and (b) post-hole auger.
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Hand Augers Sand pump
Samples recovered from the soil brought up by the augers are badly disturbed and are useful for
identification purposes only. Auger boring is fairly satisfactory bore explorations at shallow
depths and for exploratory borrow pits.
Auger and shell boring:- cylindrical augers and shells with cutting edge or teeth at lower end
can be used for making deep borings. Hand operated rigs are used for depths up to 25 m and
mechanized rigs up to 50 m. Augers are suitable for soft to stiff clays, shells for very stiff and
hard clays, and shells or sand pumps for sandy soils. Small boulders, thin soft strata or rock or
cemented gravel can be broken by chisel bits attached to drill rods. The hole usually requires a
casing.
Wash boring:-Wash boring is a fast and simple method for advancing holes in all types of soils.
Boulders and rock cannot be penetrated by this method. The method consists of first driving a
casing through which a hollow drilled rod with a sharp chisel or chopping bit at the lower end is
inserted. Water is forced under pressure through the drill rod which is alternativety raised and
dropped, and also rotated. The resulting chopping and jetting action of the bit and water
disintegrates the soil. The cuttings are forced up to the ground surface in the form of soil-water
slurry through the annular space between the drill rod and the casing. The change in soil
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stratification could be guessed from the rate of progress and colour of wash water. The samples
recovered from the wash water are almost valueless for interpreting the correct geo-technical
properties of soil.
Percussion drilling:-In this method, soil and rock formations are broken by repeated blows of
heavy chiesel or bit suspended by a cable or drill rod. Water is added to the hole during boring, if
not already present and the slurry of pulverised material is bailed out at intervals. The method is
suitable for advancing a hole in all types of solis, boulders and rock. The formations, however,
get disturbed by the impact.
Rotary boring:- Rotary boring or rotary drilling is a very fast method of advancing hole in both
rocks and soils. A drill bit, fixed to the lower end of the drill rods, is rotated by a suitable chuck,
and is always kept in firm contact with the bottom of the hole. A drilling mud, usually a water
solution of bentonite, with or without other admixtures, is continuously forced down to the
hollow drill rods. The mud returning upwards brings the cuttings to the surface. The method is
also known as mud rotary drilling and the hole usually requires no casing.
Rotary core barrels, provided with commercial diamond-studded bits or a steel bit with shots, are
also used for rotary drilling and simultaneously obtaining the rock cores or samples. The method
is them also known as core boring or core drilling. Water 15 circulated down drill rods during
boring.
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Wash boring
Disturbed but representative samples can generally be used for v Grain-size analysis v
Determination of liquid and plastic limits, Specific gravity of soil solids, Organic content
determination and Soil classification
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Undisturbed samples must be used for -- Consolidation test, Hydraulic conductivity test and
Shear strength test
There is an increasing variety of plant, sampling methods and tools, with particular advantages in
cost, quality of sampling, speed of operation, use in conditions of limited access or headroom,
etc., and the choice of rig is affected by the likely soil conditions to be encountered.
Spacing of Borings
Type of project Spacing (m)
Multistory buildings 10 – 30
One-story industrial plants 20 – 60
Highways 250 – 500
Residential subdivision 250 – 500
Dams and dikes 40 – 80
Soil Sampling
Need for sampling: -Sampling is carried out in order that soil and rock description, and
laboratory testing can be carried out.
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Type of soil samples
Non-Representative samples:-Non-Representative soil samples are those in which neither the
in-situ soil structure, moisture content nor the soil particles are preserved.
• They are not representative
• They cannot be used for any tests as the soil particles either gets mixed up or some particles
may be lost.
• e.g., Samples that are obtained through wash boring or percussion drilling.
Disturbed soil samples:- Disturbed soil samples are those in which the in-situ soil structure and
moisture content are lost, but the soil particles are intact.
• They are representative
• They can be used for grain size analysis, liquid and plastic limit, specific gravity, compaction
tests, moisture content, organic content determination and soil classification test performed in the
lab
• e.g., obtained through cuttings while auguring, grab, split spoon (SPT), etc.
Undisturbed soil samples:-Undisturbed soil samples are those in which the in-situ soil
structure and moisture content are preserved.
• They are representative and also intact
• These are used for consolidation, permeability or shear strengths test (Engineering properties) •
More complex jobs or where clay exist
• In sand is very difficult to obtain undisturbed sample
• Obtained by using Shelby tube (thin wall), piston sampler, surface (box), vacuum, freezing,
etc.,
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Inside wall friction
Design of non-return value
Method of applying force
sizes of sampling tubes
𝑫𝒔−𝑫𝒄
Inside clearance ratio Ci = 𝑿𝟏𝟎𝟎 %
𝑫𝒄
The soil is under great stress as it enters the sampler and has a tendency to laterally expand.
The inside clearance should be large enough to allow a part of lateral expansion to take place, but
it should not be so large that it permits excessive deformations and causes disturbances of the
sample.
For good sampling process, the inside clearance ratio should be within 0.5 to 3 %.
For sands silts and clays, the ratio should be 0.5 % and for stiff and hard clays (below water
table), it should be 1.5 %.
For stiff expansive type of clays, it should be 3.0 %.
𝟐 𝟐
𝑫 −𝑫 𝒄
Area ratio Ar = 𝑫𝟐𝒄
X 100%
−𝑫𝒓
Outside clearance ratio Co =𝑫𝒘 𝒙 𝟏𝟎𝟎%
𝑫𝒓
For good sampling process, the ratio should be within 0-2 %. Minimum inside diameter = =
75mm.
The length (L) should be at least equal to (the intended length + 100mm) for residual soils.
The tube should be uniform and should not have any protrusions or irregularities. The inside of
the tube should be clean and smooth.
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Where, L is the length of the sample within the tube, H is the depth of penetration of the
sampling tube. It represents the disturbance of the soil sample. For good sampling the recovery
ratio should be 96 to 98 %. Wall friction can be reduced by suitable inside clearance, smooth
finish and oiling. The non-returned wall should have large orifice to allow air and water to
escape
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Penetration Tests
These tests involve the measurement of the resistance to penetration of a sampling spoon, a cone
or other shaped tools under dynamic or static loadings. The resistance is empirically correlated
with some of the engineering properties of soil as density index, consistency, bearing capacity,
etc., These tests are useful for general exploration of erratic soil profiles, for finding depth to bed
rock or hard stratum, and to have an approximate indication of the strength and other properties
of soils, particularly the cohesionless soils, from which it is difficult to obtain undisturbed
samples. The two commonly used tests are the standard penetration test and the cone penetration
test.
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It is further driven through 3cm
The number of blows required to drive the sampler 30cm beyond the seating drive is
termed as penetration resistance N.
In very fine silty saturated sand an apparent increase in resistance occurs
For overburden pressure on the value of N(Terzaghi and Peck)
No = 15+ 1 (N-15)
2
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Soil investigation is required for the following purposes –
To know the allowable bearing capacity of foundation for proposed building.
To know the depth and type of foundation for the proposed building.
To know the allowable passive resistance for the foundation of proposed building.
To know the type, grading and nature of soil.
To know the ground water level.
Methods of soil investigation
Test pits: This is done to collect soil samples for detail analysis. In this method several pits are
dug by hand or excavator. The depth of pit is below 5 feet so that one can have visual inspection.
Several samples are collected from the pit of both disturbed and undisturbed soil.
Probing: In this method a 25 mm or 40 mm diameter steel bar is driven into the ground till solid
soil strata is found. It is normally driven by hammer. The penetration and withdrawal of the steel
rod is closely observed to know the nature of soil layer.
Boring: In this method several bore holes are made for the purpose of collecting soil sample
from below the ground. Then the collected sample is analyzed for preparing the soil report.
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Typical steps of soil investigation
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(5) Lack of appreciation that advances in structural design can accommodate relatively high
settlements.
(6) Under-estimation of the importance of the designer, at least, visiting the site during the
investigation or dismissal of trial pits as unscientific or out-dated.
Sequence of report
Foundation reports follow the normal sequence of items of engineering reports in having a title,
contents list, and synopsis, and introduction, body of the report, conclusions and
recommendations. Lengthy descriptions of tests and similar matters are best dealt with in
appendices and the test results tabulated in the body of the report. The client tends to read the
synopsis and recommendations; the main and sub-contractors concentrate on the body of the
report and the design office on its conclusions and recommendations.
Site description
This, as far as possible, should be given on small-scale plans showing site location, access and
surrounding area. The proposed position of the buildings and access roads should be shown. The
site plan should also show the general layout and surface features, note presence of existing
buildings, old foundations and previous usage, services, vegetation, surface water, any
subsidence or unstable slopes, etc.
Written description of the site exposure (for wind speed regulations) should be given together
with records of any flooding, erosion and other geographical and hydrographic information.
Geological maps and sections should, when they are necessary, be provided, noting mines,
shafts, quarries, swallow holes and other geological features affecting design and construction.
Photographs taken on the site, preferably color ones, can be very helpful and should be
supplemented by aerial photographs if considered necessary.
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The ground investigation
(1) Background study and location of holes. This should give a full account of the desk-top
study, examination of old records, information from local authorities, public utilities and the
like, and the field survey. It should detail the position and depth of trial pits and boreholes,
equipment used and in situ testing and information.
(2) Boreholes, trial pits and soil profiles. This section will be mainly a visual presentation of the
logs and profiles together with colour photographs of the trial pits.Where possible, written
information should be given in note form on the soil profiles.
(3) Soil tests. This should list the site and laboratory tests drawing attention to any unusual,
unexpected or special results. The results of the tests should be tabulated, for ease of reference,
and diagrams of such information as particle size distribution, pressure–void ratio curves and
Mohr‟s circles should be given.
Results
This must give details of ground conditions, previous use of site, present conditions, groundwater
and drainage pattern
The tests must give adequate information to determine the soil‟s bearing capacity, settlement
characteristics, behavior during and after foundation construction and, where necessary, its
chemical make-up and condition
Recommendations This is both comment on the facts and also opinions based on experience;
the difference should be made clear. Since the discussion is usually a major part of the report it
should be broken down into sections for ease of reference and readability.
The final section should give firm recommendations on the foundation type or types to be
adopted
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To know the nature of each stratum and engineering properties of the soil and rock,
which may affect the design and mode of construction of proposed structure and
foundation.
To foresee and provide against difficulties that may arise during construction due to
ground and other local conditions.
To find out the sources of construction material and selection of sites for disposal of
water or surplus material.
To investigate the occurrence or causes of all natural and man made changes in
conditions and the results arising from such changes.
To ensure the safety of surrounding existing structures.
To design for the failed structures or remedial measures for the structures deemed to be
unsafe.
To locate the ground water level and possible corrosive effect of soil and water on
foundation material.
Methods of site exploration
Geophysical exploration may be used with advantage to locate boundaries between different
elements of the subsoil as these procedures are based on the fact that the gravitational, magnetic,
electrical, radioactive or elastic properties of the different elements of the subsoil may be
different. Differences in the gravitational, magnetic and radioactive properties of deposits near
the surface of the earth are seldom large enough to permit the use of these properties in
exploration work for civil engineering projects. However, the resistivity method based on the
electrical properties and the seismic refraction methods based on the elastic properties of the
deposits have been used widely in large civil engineering projects. Different methods of
geophysical explorations
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Electrical resistivity method
Electrical resistivity method is based on the difference in the electrical conductivity or the
electrical resistivity of different soils. Resistivity is defined as resistance in ohms between the
opposite phases of a unit cube of a material.
𝐑𝐀
𝛒=
𝐋
𝜌 is resistivity in ohm-cm, R is resistance in ohms, A is the cross sectional area (cm 2), L is
length of the conductor (cm).
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Applications of resistivity soundings are:
Characterize subsurface hydrogeology, Determine depth to bedrock/overburden thickness,
Determine depth to groundwater, Map stratigraphy, clay aquitards, salt-water intrusion and
vertical extent of certain types of soil and groundwater contamination .Estimate landfill thickness
Seismic Method
Seismic refraction is a geophysical method used for investigating subsurface ground conditions
utilizing surface-sourced seismic waves. The methods depend on the fact that seismic waves
have differing velocities in different types of soil (or rock): in addition, the waves are refracted
when they cross the boundary between different types (or conditions) of soil or rock. The
methods enable the general soil types and the approximate depth to strata boundaries, or to
bedrock, to be determined.
Operation
Pulses of low frequency seismic energy are emitted by a seismic source such as a hammer-plate,
weight drop or buffalo gun. The type of source is dependent on local ground conditions and
required depth penetration. Explosives are best for deeper applications but are constrained by
environmental regulations.
The seismic waves propagate downward through the ground until they are reflected or refracted
off subsurface layers. Refracted waves are detected by arrays of 24 or 48 geophones spaced at
regular intervals of 1 - 10 metres, depending on the desired depth penetration of the survey.
Sources are positioned at each end of the geophone array to produce forward and reverse wave
arrivals along the array. Additional sources may be used at intermediate or off-line positions for
full coverage at all geophone positions.
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A geophone is a device that converts ground movement (velocity) into voltage, which may be
recorded at a recording station. The deviation of this measured voltage from the base line is
called the seismic response and is analyzed for structure of the earth.
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APPLICATIONS
Measures Bedrock Depth & Overburden Thickness
Determines Rip ability Parameters
Investigates Pipeline Routes
Locates Geological Structures
Evaluates Sand & Gravel Deposits
Defines Ancient Landfill Sites
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Boring Log
During soil exploration all suitable details are recorded and presented in a boring log. Additional
information consisting mainly of lab and field test result is added to complete the boring log.
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6. Description of subsoil conditions as determined from the soil and rock samples collected
7. Ground water table as observed from the boreholes
8. Details of foundation recommendations and alternatives
9. Any anticipated construction problems
10. Limitations of the investigation
The following graphic presentations also need to be attached to the soil exploration
report:
The boring log is the graphic representation of the details gathered from each bore hole.
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SCHOOL OF BUILDING AND ENVIRONMENT
DEPARTMENT OF CIVIL ENGINEERING
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BEARING CAPACITY OF SOIL
Bearing capacity is the power of foundation soil to hold the forces from the
superstructure without undergoing shear failure or excessive settlement. Foundation soil
is that portion of ground which is subjected to additional stresses when foundation and
superstructure are constructed on the ground. The following are a few important
terminologies related to bearing capacity of soil.
Ultimate Bearing Capacity (qf) : It is the maximum pressure that afoundation soil can
withstand without undergoing shear failure.
Net ultimate Bearing Capacity (qn) : It is the maximum extra pressure(in addition to
initial overburden pressure) that a foundation soil can withstand without undergoing
shear failure.
qn = qf - qo
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Here, qo represents the overburden pressure at foundation level and is equal to D for
level ground without surcharge where the unit weight of soil is and D is the depth to
foundation bottom from Ground Level.
Safe Bearing Capacity (qs): It is the safe extra load the foundation soil is subjected to
in addition to initial overburden pressure.
Allowable Bearing Pressure (qa) : It is the maximum pressure the foundation soil is
subjected to considering both shear failure and settlement.
Foundation is that part of the structure which is in direct contact with soil. Foundation
transfers the forces and moments from the super structure to the soil below such that the
stresses in soil are within permissible limits and it provides stability against sliding and
overturning to the super structure. It is a transition between the super structure and
foundation soil. The job of a geotechnical engineer is to ensure that both foundation and
soil below are safe against failure and do not experience excessive settlement. Footing
and foundation are synonymous.
Depending on the stiffness of foundation soil and depth of foundation, the following
are the modes of shear failure experienced by the foundation soil.
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Shear failure in foundation soil P – curve in different foundation soils
2. Dense or stiff soil that undergoes low compressibility experiences this failure.
8. State of plastic equilibrium is reached initially at the footing edge and spreads
gradually downwards and outwards.
considerable ( >36o) and large N (N > 30) having high relative density (ID> 70%).
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Local Shear Failure
This type of failure is seen in relatively loose and soft soil. The following are some
characteristics of general shear failure.
1. A significant compression of soil below the footing and partial development of
plastic equilibrium is observed.
3. Failure surface does not reach the ground surface and slight bulging of soil around
the footing is observed.
with considerably low ( <28o) and low N (N < 5) having low relative density (I D>
20%).
The below figure presents the conditions for different failure modes in sandy soil
carrying circular footing based on the contributions from Vesic (1963 & 1973)
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Modes of failure at different Relative densities & depths of foundations
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Terzaghi’s bearing Capacity Theory
Terzaghi (1943) was the first to propose a comprehensive theory for evaluating the
safe bearing capacity of shallow foundation with rough base.
Assumptions
1. Soil is homogeneous and Isotropic.
3. The footing is of strip footing type with rough base. It is essentially a two
dimensional plane strain problem.
4. Elastic zone has straight boundaries inclined at an angle equal to the horizontal.
5. Failure zone is not extended above, beyond the base of the footing. Shear
resistance of soil above the base of footing is neglected.
3. The properties of foundation soil do not change during the shear failure
Limitations
1. The theory is applicable to shallow foundations
2. As the soil compresses, increases which is not considered. Hence fully plastic zone
may not develop at the assumed.
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Terzaghi’s concept of Footing with five distinct failure zones in foundation soil
Concept
3. All points need not experience limit equilibrium condition at different loads.
4. Method of superstition is not acceptable in plastic conditions as the ground is near
failure zone.
qn=cNc+γDNq+0.5γBNg-γD
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Safe bearing capacity,
qs=[cNc+γD(Nq-1)+0.5γBNγ] 1/F + γD
Circular footing
Rectangular footing
Shape sc sq s
Strip 1 1 1
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Local shear failure
The equation for bearing capacity explained above is applicable for soil experiencing
general shear failure. If a soil is relatively loose and soft, it fails in local shear failure.
Such a failure is accounted in bearing capacity equation by reducing the magnitudes
of strength parameters c and as follows.
c = ׀2/3 c
Table summarizes the bearing capacity factors to be used under different situations. If
Φ is less than 36o and more than 28o, it is not sure whether the failure is of general or
local shear type. In such situations, linear interpolation can be made and the region is
called mixed zone.
Bearing capacity factors in zones of local, mixed and general shear conditions.
o o o o
Φ< 28 28 < Φ< 36 Φ> 36
1 1 1
N ,N ,N m m m
Nc, Nq, Nγ
c q γ Nc , Nq , Nγ
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Ultimate bearing capacity with the effect of water table is given by,
1. 0.5<Rw1<1
2. When water table is at the ground level (Zw1 = 0), Rw1 = 0.5
3. When water table is at the base of foundation (Zw1 = D), Rw1 = 1
4. At any other intermediate level, Rw1 lies between 0.5 and 1
Rw2 = ½ (1+Zw2)
𝑫
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where ZW2 is the depth of water table from foundation level.
1. 0.5<Rw2<1
2. When water table is at the base of foundation (Zw2 = 0), Rw2 = 0.5
3. When water table is at a depth B and beyond from the base of foundation
(Zw2>= B), Rw2 = 1
4. At any other intermediate level, Rw2 lies between 0.5 and 1
The bearing capacity equation is developed with the idealization that the load on
the foundation is concentric. However, the forces on the foundation may be eccentric or
foundation may be subjected to additional moment. In such situations, the width of
foundation B shall be considered as follows.
B1= B -2e
12
If the loads are eccentric in both the directions, then
Further, area of foundation to be considered for safe load carried by foundation is not
the actual area, but the effective area as follows.
A1= B1 X L1
1 1 1
In the calculation of bearing capacity, width to be considered is B where B < L .
Hence the effect of provision of eccentric footing is to reduce the bearing capacity
and load carrying capacity of footing.
Factor of Safety
It is the factor of ignorance about the soil under consideration. It depends on many
factors such as,
1. Type of soil
2. Method of exploration
13
Typical factors of safety for bearing capacity calculation in different situations
Density of soil: In geotechnical engineering, one deals with several densities such as
dry density, bulk density, saturated density and submerged density. There will always
be a doubt in the students mind as to which density to use in a particular case. In case of
Bearing capacity problems, the following methodology may be adopted.
1. Always use dry density as it does not change with season and it is
always smaller than bulk or saturated density.
2. If only one density is specified in the problem, assume it as dry density and
use.
14
4. If water table is some where in between, use equivalent density as follows.
In the case shown in Fig. 7a, eq should be used for the second
term and sat for the third term. In the case shown in Fig. 7b, d should be
used for second term and eq for the third term.
g=( g1 D1 + g2 D2) / (D1+D2)
D1
D D
2
B B
Bearing capacity of soil depends on many factors. The following are some important
ones.
1. Type of soil
4. Depth of foundation
5. Mode of failure
6. Size of footing
7. Shape of footing
Here, the bearing capacity factors are given by the following expressions which depend
on .
N q=(eptanf) tan2(45+f/2)
Ng=1.5(N q-1) tanf
Equations are available for shape factors (sc, sq, s ), depth factors (dc, dq, d ) and load
inclination factors (ic, iq, i ). The effects of these factors are to reduce the bearing
capacity.
Field Tests are performed in the field. You have understood the advantages of field tests
over laboratory tests for obtaining the desired property of soil. The biggest advantages
are that there is no need to extract soil sample and the conditions during testing are
identical to the actual situation.
16
Plate Load Test
Sand Bags
Platform
for loading
Dial Gauge
Testing Plate
· Labourious
· Time consuming
· Heavy equipment to be carried to field
· Short duration behavior
4. Dial gauges, at least 2, of required accuracy (0.002 mm) are placed on plate
on plate at corners to measure the vertical deflection.
17
6. Loading is provided either as gravity loading or as reaction loading. For smaller
loads gravity loading is acceptable where sand bags apply the load. In reaction
loading, a reaction truss or beam is anchored to the ground. A hydraulic jack
applies the reaction load.
7. At every applied load, the plate settles gradually. The dial gauge readings are
recorded after the settlement reduces to least count of gauge (0.002 mm) &
average settlement of 2 or more gauges is recorded.
9. Red curve indicates the general shear failure & the blue one indicates the local
or punching shear failure.
10. The maximum load at which the shear failure occurs gives the ultimate
bearing capacity of soil.
1. It provides the allowable bearing pressure at the location considering both shear
failure and settlement.
3. The loading techniques and other arrangements for field testing are
identical to the actual conditions in the field.
1. The test results reflect the behaviour of soil below the plate (for a distance of
~2Bp), not that of actual footing which is generally very large.
2. It is essentially a short duration test. Hence, it does not reflect the long term
consolidation settlement of clayey soil.
18
Standard Penetration Test
65 kg Hammer
750
Tripod
mm
5. Split spoon sampler is placed vertically in the hole, allowed to freely settle under
its own weight or with blows for first 150 mm which is called seating drive.
6. The number of blows required for the next 300 mm penetration into the
ground is the standard penetration number N
19
7. Apply the desired corrections (such as corrections for overburden pressure,
saturated fine silt and energy)
2. Cone Penetration Test can either be Static Cone Penetration Test or Dynamic Cone
Penetration Test.
20
3. Continuous record of penetration resistance with depth is achieved.
2 o
4. Consists of a cone 36 mm dia (1000 mm ) and 60 vertex angle.
5. Cone is carried at the lower end of steel rod that passes through steel tube of 36
mm dia.
6. Either the cone, or the tube or both can be forced in to the soil by jacks.
Fig. 7.9 : typical set up for Static Cone Penetration test assembly
21
Advantages of SCPT are
It is the bearing capacity that can be presumed in the absence of data based on visual
identification at the site. National Building Code of India (1983) lists the values of presumptive
SBC in kPa for different soils as presented below.
A : Rocks
Sl Description SBC
(kPa)
No
1 Rocks (hard) without laminations and defects. For e.g. 3240
granite,
condition
3 Residual deposits of shattered and broken bed rocks and hard 880
22
B : Cohesionless Soils
Sl Description SBC
(kPa)
No
1 Gravel, sand and gravel, compact and offering resistance to 440
sand, dry
6 Fine sand, loose and dry 100
C : Cohesive Soils
Sl Description SBC
(kPa)
No
1 Soft shale, hard or stiff clay in deep bed, dry 440
2 Medium clay readily indented with a thumb nail 245
3 Moist clay and sand clay mixture which can be indented with 150
the thumb
6 Black cotton soil or other shrinkable or expansive clay in dry 130 - 160
23
Note :
1. Use d for all cases without water. Use sat for calculations with water. If simply
density is mentioned use accordingly.
C=0
F = 2.5
D = 0.9 m
Nc = 25
Nq = 34
N = 32
qs =P/A = [1.3cNc+γD(N q-1)RW1+0.4γBNg RW2]
B = 1.21 m
24
o 3
2. What will be the net ultimate bearing capacity of sand having = 36 and 𝛾d = 19 kN/m for
(i) 1.5 m strip foundation and (ii) 1.5 m X 1.5 m square footing. The footings are placed at a
depth of 1.5 m below ground level. Assume F = 2.5. Use Terzaghi’ s equations. (Aug 2003)
Nc Nq N
o
35 57.8 41.4 42.4
o
40 95.7 81.3 100.4
o
By linear interpolation Nc = 65.38, Nq = 49.38, Nγ = 54 at = 36
Data
B = 1.5 m
D = 1.5 m
3
𝛾d = 19 kN/m
Strip Footing
qn = 2148.33 kPa
Square Footing
qn=1.3cNc+𝛾D(N q-1)+0.4𝛾BN𝛾
qn = 1994.43 kPa
25
3. A square footing 2.5 m X 2.5 m is built on a homogeneous bed of sand of density 19
kN/m3 having an angle of shearing resistance of 36o. The depth of foundation is 1.5 m below the
ground surface. Calculate the safe load that can be applied on the footing with a factor of safety
of 3. Take bearing capacity factors as Nc= 27, Nq = 30, N = 35. (Feb 2004)
Data
C=0F=3
B = 2.5 m
D = 1.5 m
3
𝛾d = 19 kN/m
Nc = 27 Nq = 30 N𝛾 = 35
qs= P/A = 1.3cNc+𝛾D(N q-1)RW1+0.4gBN𝛾 RW2
Safe load, P = qs*B*B = 3285.4 kN
4. A strip footing 2 m wide carries a load intensity of 400 kPa at a depth of 1.2
3
m in sand. The saturated unit weight of sand is 19.5 kN/m and unit weight above water table
3 o
is 16.8 kN/m . If c = 0 and = 35 , determine the factor of safety with respect to shear failure
for the following locations of water table.
26
Using Terzaghi’ s equation, take Nq = 41.4 and N𝛾 = 42.4. (Feb 2005)
Data
o
C = 0 and C = 35
B=2m
D = 1.2 m
Nc = 0
Nq = 41.4
N𝛾 = 42.4
RW1 = RW2 = 1
3
𝛾𝑠𝑎𝑡 = 16.8 kN/m
F = 4.02
F = 3.227
c. Water table is 2.5 m below Ground Level
27
400 16.8X1.2 X 40.4 X1 0.5X17.745X 2 X 42.4 X 0.8251/F16.8X1.2
F = 3.779
F = 2.353
5. A square footing located at a depth of 1.3 m below ground has to carry a safe load of 800
kN. Find the size of footing if the desired factor of safety is 3.
Use Terzaghi’ s analysis for general shear failure. Take c = 8 kPa, Nc = 37.2, Nq =
22.5, N = 19.7. (Aug 2005)
3
𝛾d = 18 kN/m (Assumed)
c = 8 kPa
F=3
D = 1.3 m
Nc = 37.2
Nq = 22.5
N = 19.7
P = 800 kN
RW1 = RW2 = 1
B = 1.436 m
28
3
6. A square footing 2.8 m X 2.8 m is built on a homogeneous bed of sand of density 18 kN/m
o
and = 36 . If the depth of foundation is 1.8 m, determine the safe load that can be applied on
the footing. Take F = 2.5, Nc = 27, Nq = 36, N𝛾 = 35. (Feb 2007)
Data
3
𝛾 = 18 kN/m c = 0
(sand) F = 2.5
B = 2.8 m
D = 1.8 m
Nc = 27
Nq = 36
N𝛾 = 35
P=?
RW1 = RW2 = 1
P = qs*B*B = 6023 kN
7. A strip footing 1 m wide and a square footing 1 m side are placed at a depth of 1 m below
o
the ground surface. The foundation soil has cohesion of 10 kPa, angle of friction of 26 and
3
unit weight of 18 kN/m . Taking bearing capacity factor from the following table, calculate
the safe bearing capacity using Terzaghi’ s theory. Use factor of safety of 3. (July 2008)
Nc Nq N
o
15 12.9 4.4 2.5
o
20 17.7 7.0 5.0
o
25 25.1 12.7 9.7
29
o
As = 28 , the ground experiences local shear failure C’ =
(2/3)X10 = 6.67 kPa
o
tan ’ = (2/3) X tan’ = 18.01
c q
By linear interpolation, N ’ =15.79, N ’ =5.97, N ’ =4.01
B=1m
D=1m
3
𝛾𝑠𝑎𝑡t = 18 kN/m
Strip footing
Square footing
30
8. A square footing placed at a depth of 1 m is required to carry a load of 1000kN. Find the
o 3
required size of footing given the following data. C = 10 kPa, = 38 , = 19 kN/m , Nc =
61.35, Nq = 48.93, N𝛾 = 74.03 and F = 3. Assume water table is at the base of footing. (July
2007)
Data
o
C = 10 kPa = 38
B=?
3
D = 1 m = 19 kN/m
Nc = 61.35
Nq = 48.93
N𝛾 = 74.03
F=3
RW1 = 1
RW2 = 0.5
P P
qs= A=B 2= 1.3cNc+𝛾D(N q-1)R W1+0.4𝛾BN𝛾 RW21/F+gD
B3+6.14B2-3.56=0
B = 0.72 m
SETTLEMENT.
The vertical downward movement of the base of a structure is called settlement and its effect upon
the structure depends on its magnitude, its uniformity, the length of the time over which it takes
place, and the nature of the structure itself. Settlement has got several implications on a foundation.
31
Appearance of structures Settlement affects the appearance of structures. If a structure settles
excessively, its aesthetic is impaired. It causes doors and windows to distort, walls and plasters to
crack and the structure to tilt.
Utility of Structures – Settlement interfere the utility of structures in many ways. If settlement is
excessive overhead cranes do not operate correctly, machinery may go out of plumb and tracking
units such as radar become inaccurate.
Damage to the Structure – If the settlement is severe, it may lead to the complete collapse of the
structure even though the factor of safety against shear failure is high.
All foundations settleto some extent as the earth materials around and beneath them adjust to loads of
the building. Foundations on bedrock settle a negligible amount. Foundations in other types of soil
may settle much more. Foundations in clay settle more. Where foundation settlement occurs at
roughly the same rate throughout all portions of a building, it is termed uniform settlement.
Settlement that occurs at differing rates between different portions of a building is termed differential
settlement.
When all parts of a building rest on the same kind of soil, and the loads on the building and the design
of its structural system are uniform throughout, differential settlement is normally not a concern.
However where soils, loads, or structural systems differ between parts of a building, different parts of
the building structure may settle by substantially different amounts, the frame of the building may
become distorted, floors may slope, walls and glass may crack, and doors and windows may not work
properly. Figure 1 shows the details of settlement.
32
Settlement deals with the sinking of structure due to compression of soil. As per IS code, the
following types of settlements are reported:
1. Total settlement: - it is combination of initial and consolidation settlement Elastic settlement/
initial settlement: - initial/elastic settlement is the settlement caused due to elastic properties of
the soil due to applied load. Consolidation settlement - Primary consolidation: - is the
consolidation occurs due to the expulsion of air from the voids. Secondary/creep:- is the
consolidation due to expulsion of water from the voids.
2. Differential settlement/ angular distortion: - it is the difference in settlement between two
points below the footing.
3. Time dependent settlement: -for sands, settlement is called immediate settlement as it is the
major settlement, there being no or very less consolidation settlement. For clays, we talk about
initial or elastic settlements and not immediate settlements.
Foundation settlement is the shifting of the foundation (and the structure built upon it) into the soil.
This can cause damage to the structure. Whether the soil is moist or dry is central to predicting the
amount of settlement to expect in a given foundation. Areas with moist soils will have more
foundation settlement than dry areas. The idea is that as water is squeezed out from the soil, the
structure will shift according to the empty spaces the water left. The more water, the more shift.
Immediate Settlement
Immediate settlement concerns the initial pressure on the soil under and surrounding the
foundation. It is "immediate" because it occurs during and right after construction. It has nothing
to do with water displacement, but is merely caused by the weight of the structure. In terms of
building foundations, immediate settlement is relatively easy to predict and measure. In many
cases, given the nature of the soil, foundations are constructed with the ability to withstand a
certain amount of shift without damage. Damage usually occurs only in the long term, as the
shift slowly continues over time.
Consolidation
Consolidation settlement is distinguished from immediate settlement both by the duration of the
settlement and by displacement of water. Consolidation is the more worrisome form of
settlement because it is difficult to predict over months or years. Consolidation settlement is the
settling of a foundation, over time, due to pressure exerted by the structure and squeezes out the
water content of the soil, thus compressing it. Expulsion of moisture from the soil usually is a
long-term process.
33
Primary and Secondary Consolidation
Consolidation settlement has two components, primary and secondary. The former deals
explicitly with the settlement caused by soil moisture displacement, and the latter deals with the
elastic settlement after all movable water has been squeezed out of the soil.
Primary consolidation is the most significant and potentially harmful of the two. Primary
consolidation takes quite a bit of time, from weeks to years. Secondary consolidation is the quicker
result of primary consolidation. Once primary has been completed, and all movable water has been
moved, secondary kicks in. Secondary consolidation occurs immediately after primary, and takes far
less time to complete. After secondary consolidation is complete, the structure remains in its
permanent position. As a result, many builders advise a resident in new homes to avoid repairing any
settlement damage until secondary consolidation is complete, which is normally after two years at
most.
The causes of foundation settlement are rarely due to the design (or under-design) of the structure
itself. More commonly, damage is caused as changes occur within the foundation soils that surround
and support the structure
34
(a) (b)
(a) Cracks in your home’s walls and sticking doors and windows are two of the symptoms of
foundation settlement.
(b) Bricks crack when foundation walls sink
Check out these common causes that call for professional evaluation and
foundation repairs.
Do you have foundation cracks, wall cracks, sticking doors and windows and sloping floors?
Foundation cracks due to differential foundation settlement can be caused by several conditions.
Frost heave
Building codes that require at least 30 inches for a building’s footing depth were established to resist
frost heave from ice expansion in the ground during the winter months. The top layer of soil has gone
through these types of changes over the decades and is typically not very compacted.
Soil type
Some soils, like those we have here in the Greater Cincinnati area, are classified as expansive clay.
This type of soil changes volume when its moisture content changes. The soil shrinks in the dry
summer and fall, when the rain quits falling as seen by cracks in ground. When the moisture returns to
the soil during the winter and spring due to higher quantities of rain and snow, the soil swells back to
its previous volume. This type of differential movement can be seen in houses that have cyclical
cracks which open and close, doors rubbing the frames part of the year during the various seasons.
Watering along the exterior house foundation may help control this movement, but should be started
very early in the year.
35
Varying foundation depth
Foundations that are supported at different soil depths are likely to settle differentially. This condition
is typical when a shallow foundation is placed near a deeper basement foundation or on sloping lots.
Water leaks
In older homes, underground waste piping and/or underground downspout piping can crack or break.
When the piping fails; water leaks along the footing, softening the soil, causing the foundation to
settle differentially. After a building has been constructed, some settlement is quite normal.
Differential settlement, however, is when a building’s piers or foundation settles unequally.
Differential settlement can result in damage to the structure, and is therefore, of concern.
2. Poor Compaction
Placement of fill soils is common practice in the development of both commercial and residential
subdivisions. In general, before a foundation can be constructed on a plot, hilltops are cut down and
valleys are filled in order to create buildable lots. Properly placed and compacted fill soils can provide
adequate support for foundations, and are sometimes brought in from off-site locations. When the soil
fills are not adequately compacted, they can compress under a foundation load resulting in settlement
of the structure.
36
3. Changes in Moisture Content
Extreme changes in moisture content within foundation soils can result in damaging settlement.
Excess moisture can saturate foundation soils, which often leads to softening or weakening of clays
and silts. The reduced ability of the soil to support the load results in foundation settlement. Increased
moisture within foundation soils is often a consequence of poor surface drainage around the structure,
leaks in water lines or plumbing, or a raised groundwater table. Soils with high clay contents also
have a tendency to shrink with loss of moisture. As clay soils dry out, they shrink or contract,
resulting in a general decrease in soil volume.
Therefore, settlement damage is often observed in a structure supported on dried-out soil. Drying of
foundation soils is commonly caused by extensive drought-like conditions, maturing trees and
vegetation and leaking subfloor heating, ventilation, and air conditioning systems.
37
4. Maturing Trees and Vegetation
Maturing trees, bushes and other vegetation in close proximity to a home or building are a common
cause of settlement. As trees and other vegetation mature, their demand for water also grows. The
root systems continually expand and can draw moisture from the soil beneath the foundation. Again,
clay-rich soils shrink as they lose moisture, resulting in settlement of overlying structures. Many
home and building owners often state that they did not have a settlement problem until decades after
the structure was built. Foundations closer to the surface are more often affected by soil dehydration
due to tree roots than are deep, basement level foundations. As a general rule, the diameter of a tree's
root system is at least as large as the tree's canopy.
5. Soil Consolidation
Consolidation occurs when the weight of a structure or newly-placed fill soils compress lower, weak
clayey soils. The applied load forces water out of the clay soils, allowing the individual soil particles
to become more densely spaced. Consolidation results in downward movement or settlement of
overlying structures. Settlement caused by consolidation of foundation soils may take weeks, months,
or years to be considered "complete."
As this occurs, the foundation will experience downward movement -- sometimes at an uneven rate.
This leads to cracks and structural damage.
Differential settlement
Differential settlement occurs when the soil beneath the structure expands, contracts or shifts away.
This can be caused by drought conditions, the root systems of maturing trees, flooding, poor drainage,
frost, broken water lines, vibrations from nearby construction or poorly compacted fill soil.
38
Differential settlement can cause cracks in a structure’s foundation and interior walls, as well as
uneven settling of doors and windows. Other signs of differential settlement include tilting chimneys,
exterior stairs that tilt or sink, bulging walls, leaking through openings and sunken slabs. Since soil
settlement tends to be gradual, cracks due to differential settlement tend to be larger at the top,
diminishing to nearly nothing at the bottom. You may also see signs of vertical movement.
The best way to prevent differential settlement is to analyze the soil you are planning to build on, as
well as the surrounding environment. In the ideal situation, the site soils will be non- expansive,
meaning they have little clays or silts. Also ideally, the structure will be laid on undisturbed, native
soil. An engineer can determine the load bearing capacity of the soil and estimate settlement of the
planned structure. Once these calculations have been performed, make amendments to the soil before
construction begins, in order to minimize differential settlement. If it is necessary to build on
disturbed soil or fill, the foundation can be built on piles which extend down to good load bearing
soil.
In conclusion, you now know what differential settlement is, some common causes and signs, what to
do if you suspect that it is an issue with your structure and the best strategies to avoid it in the first
places. If you see cracks in a structure’s foundation and interior walls, uneven settling of doors or
windows, bulging walls, or tilting chimneys or exterior stairs, it is best to contact a structural engineer
and schedule an onsite evaluation.
Aspects of Settlement
(i) Uniform settlement
(ii) Differential settlement
Uniform settlement does not cause harm to the structural stability of the structure.
Differential Settlement:
Different magnitude of settlement at different points underneath a structure;
Supplementary stress and cause harmful effects- cracking; permanent; irreparable
damage; ultimate yield; failure of structure.
39
Definition of Differential Settlement
Differential settlement refers to the unequal settling of a building's piers or foundation that can result
in damage to the structure. The damage occurs when the foundation sinks in different areas at
different times.
Causes
Differential settlement is primarily due to the condition of the soil upon which the structure sits.
Soil has the capacity to expand or contract based upon the temperature or weather conditions. It
can also shift or wash away due to poor drainage, heavy rainfall, soil drying unevenly, or
changes in the water table.
Effects
The settlement causes cracks in a structure's foundation, slab or supporting piers. These cracks
lead to cracks in the building's interior walls and uneven settling of the building's doors,
windows and trim.
Prevention and Solution
The best way to prevent damage from differential settlement is to thoroughly analyze the soil and
make necessary amendments before construction begins. It may be necessary to reinforce the
structure's piers or foundations if a problem occurs after the building has been constructed.
40
Compaction by roller, vibratory roller, vibrofloatation& compaction by preloading, sand drain
provisions to accelerate consideration- long term & immediate settlement shall be minimized
Providing stone column in loose soil, lime sand mix compaction piles, lime clay mix
piles, cement day mix, cement fly ash soil stabilization reduce settlement in soft day for loose sand.
Water loving trees suck water & Moister from soil up to 3m deep ,Selection of foundation & veerendal
systems framed foundation in expansive soils to minimize different settlement
Organize spacing of footings – footing interface problem
Raft foundation – shallow depth
Pile group, Spacing of piles, no of piles in group and palter of pile lay out contribute, Avoid adjacent
are excavation below foundation level, providing storm water discharge channel. Providing apron and
avoiding or taking precautions for soil subsidence due to tunnel or pipe line
Selection of raft or pile, fooling faming or shear wall providing ground beam, grade beam, plinth
beam, continuous linter, reinforced continuous stripes at all opening level, sill level at window bottom,
reinforce brick masonry
Slab on grade like systems compacting in layers the basement fill, lime water treatment in clay below
strip footing.
Total Settlement
Total foundation settlement can be divided into three different components, namely Immediate or
elastic settlement, consolidation settlement and secondary or creep settlement as given below.
S= Si + Sc +Ss
Here, S = Total Settlement SI
= Immediate / Elastic
Settlement SC = Consolidation
Settlement
SS = Secondary Settlement
41
The components of settlement of a foundation are:
1. Immediate settlement
2. Consolidation Settlement, and
3. Secondary compression (creep)
ΔH = ΔHi + U ΔHc + ΔHs
ΔH = total settlement, ΔHc = consolidation settlement, ΔH = secondary
compression, U
= average degree of consolidation. Generally, the final settlement of a foundation is
of interest and U is considered equal to 1 (i.e. 100% consolidation)
1. Immediate Settlement
Immediate settlement takes place as the load is applied or within a time period of about 7
days.
Predominates in cohesion less soils and unsaturated clay
Immediate settlement analysis are used for all fine-grained soils including silts and clays
with a degree of saturation < 90% and for all coarse grained soils with large co-efficient
of permeability (say above 10.2 m/s)
2. Consolidation Settlement (ΔHc)
Consolidation settlements are time dependent and take months to years to develop. The
leaning tower of Pisa in Italy has been undergoing consolidation settlement for over 700
years. The lean is caused by consolidation settlement being greater on one side. This,
however, is an extreme case. The principal settlements for most projects occur in 3 to 10
years.
Dominates in saturated/nearly saturated fine grained soils where consolidation theory
applies. Here we are interested to estimate both consolidation settlement and how long a
time it will take or most of the settlement to occur.
3. Secondary Settlement/Creep (ΔHs)
Occurs under constant effective stress due to continuous rearrangement of clay particles
into a more stable configuration.
Predominates in highly plastic clays and organic clays.
42
(1) Immediate settlement of cohesive soils
Immediate settlement in cohesive soil may be estimated using elastic theory, particularly for saturated
clays, clay shales, and most rocks. The linear theory of elasticity is used to determine the elastic
settlement of the footing on saturated clay.Schleicher (1926) gave the formula for the vertical
settlement under a uniformly distributed flexible area.
1 − µ2
𝑆i = 𝑞𝐵 𝐼𝑤
𝐸
𝑠
Where q = intensity of contact pressure in units of Es (Undrained Modulus of
Elasticity) B = least lateral dimension of contributing base area in units of S i Es=
modulus of elasticity of soil,
μ = Poisson’s ratio of Soil.(0.5 for saturated clay)
Iw= Influence factor
The value of Es can be determined from stress-strain curve obtained from a triaxial
consolidated –undrained test, unconfined compression tests, and in-situ tests like SPT,
CPT, Plate load tests, Pressure meter etc. The value of influence factor I w for s saturated
clay layer of semi- infinite extent can be obtained from the table 3.1
43
For a semi elastic medium,
1 − µ2
𝑆i = 𝑞𝐵 𝐼𝑠
𝐸𝑠
L/B Circle 1 2 5 10
Is 0.73 0.82 1.00 1.22 1.26
of the layer before any excavation or application of load, ∆𝜎′ = vertical stress increment
@ centre of layer, Cs = Compressibility constant.
𝒒
Cs = 𝟏. 𝟓 𝒄
𝝈𝟎
𝑞𝑐 = Static cone resistance, (400 N as per
Meyerhof) N = No of blows.
44
(2) Consolidation settlement computation
Primary settlement, also known as primary consolidation settlement (Sc), is the reduction in volume
of a soil mass caused by the application of a sustained load to the mass and due principally to a
squeezing out of water from the void spaces of the mass and accompanied by a transfer of the load
from the soil water to the soil solids (ASTM D 653). The rate of settlement is controlled by the
permeability of the soil. As a result, in higher permeability cohesion less soils, the settlement occurs
rapidly, and in lower permeability cohesive soils, the process is gradual.
The following equation is used to estimate the primary settlement in normally consolidated
clays or loose granular materials:
′𝝈+ ∆𝝈 ′
Sc = 𝑯𝑪𝒄 𝒍𝒐𝒈 [ 𝒐
′ ]
𝟏𝟎
𝟏+𝒆𝟎 𝝈𝒐
𝝈′ = ef𝒐fective vertical stress at the middle of the layer after excavation, but before loading and
∆𝝈′= increase or change in effective vertical stress due to loading
45
.
Coefficient of Consolidation
It is one of the important properties of consolidation theory that helps in evaluating
consolidation settlement. It is determined from odometer test. The below mentioned
formula is used to determine coefficient of consolidation,
𝐂𝐯 = (Tv H2) / t
Cv = average coefficient of consolidation
t = Time @ which settlement is required
H= distance of the drainage path.
Time rate of settlement
If clay layer is sandwiched between sand layers, pore water could be drained from top as
well as from bottom – double drainage
Drainage is either from top or bottom- single drainage.
The following equation is used to estimate the consolidation settlement in over consolidated clays.
Dense cohessionless materials do not settle significantly and thus do not have to be evaluated using
this equation.
If the increase in vertical stress at the middle of the consolidation layer is such that ( o’ +
o’) exceeds the pre consolidation pressure ( p’) of the consolidating layer, the folwnig
equation should be used:
The increase in vertical stress is caused by the application of a surcharge to the consolidating layer.
Usually the engineered components and waste of a facility will be the surcharge. The entire vertical
stress that will be induced at the middle of each consolidating layer should be used in the calculations.
This vertical stress typically corresponds to the maximum weight of the facility (e.g., when a solid
waste facility is at its maximum waste height or a waste water lagoon is operating at minimum
freeboard).
46
(3) Secondary Settlement (Ss)
Secondary settlement, also known as creep, is the reduction in volume of a soil mass caused by the
application of a sustained load to the mass and due principally to the adjustment of the internal
structure of the soil mass after most of the load has been transferred from the soil water to the soil
solids (ASTM D 653). Due to the absence of pore water pressure, the solid particles are being
rearranged and further compressed as point-to-point contact is experienced.
47
SCHOOL OF BUILDING AND ENVIRONMENT
DEPARTMENT OF CIVIL ENGINEERING
1
SHALLOW FOUNDATION
TYPES OF SHALLOW
FOUNDATIONS
Strip Footing: A strip footing is provided for a load-bearing wall. A strip footing is also
provided for a row of columns which are so closely spaced that their spread footings
overlap or nearly touch each other.
Spread or Isolated Footing: A spread footing (or isolated or pad) footing is provided to
support an individual column. A spread footing is circular, square or rectangular slab of
uniform thickness. Sometimes, it is stepped or hunched to spread the load over a large
area.
Combined Footing: A combined footing supports two columns. It is used when the two
columns are so close to each other that their individual footings would overlap. A
combined footing is also provided when the property line is so close to one column that
a spread footing would be eccentrically loaded when kept entirely within the property
line. By combining it with that of an interior column, the load is evenly distributed. A
combined footing may be rectangular or trapezoidal in plan.
Strap or Cantilever footing: A strap (or cantilever) footing consists of two isolated
footings connected with a structural strap or a lever. The strap connects the two footings
such that they behave as one unit. The strap is designed as a rigid beam.
Mat or Raft Foundations: A mat or raft foundation is a large slab supporting a number
of columns and walls under the entire structure or a large part of the structure. A mat is
required when the allowable soil pressure is low or where the columns and walls are so
close that individual footings would overlap or nearly touch each other.Mat foundations
are useful in reducing the differential settlements on non-homogeneous soils or where
there is a large variation in the loads on individual columns.
2
iii. In case when the soil is stiff or the eccentricity is large, the method does not give
accurate results.
Design steps:
1. AssumeQ1, Q2 and S are known; therefore Σ𝑄 = 𝑄1 + 𝑄2
2. Find the base area of the footings, A= Q/ qna ,whereqna is the allowable soil
pressure.
3. Locate the line of action of the resultant of the column loads measured from one
of the column ,centre of gravity of the load 𝑥 = (Q2 x c/c distance) / Q: the
location of the resultant force Σ𝑄with respect to any pointmay be obtained by
taking moments about that point.
4. For uniform stress distribution, the required length L of the footing is: 𝐿= 2(𝑥 + 𝑏1)
5. The required width B of the footing is: B =Area /L = (Q1+ Q2) / (q all x L)
6. Actual allowable soil pressure
qo= Q/Ao Where Ao= B x
L
3
Design of Combined Footings by Rigid Method (Conventional Method)
The rigid method of design of combined footings assumes that
1. The footing or mat is infinitely rigid; hence, the deflection of the footing or mat does
not influence the pressure distribution,
2. The soil pressure is distributed in a straight line or a plane surface such that the
centroid of the soil pressure coincides with the line of action of the resultant force of all
the loads acting on the foundation.
4
It should be noted here that the end column along the property line may be connected to
the interior column by a rectangular or trapezoidal footing. In such a case no strap is
required and both the columns together will be a combined footing as shown in Fig. b. It
is necessary that the center of area of the footing must coincide with the center of
loading for the pressure to remain uniform.
𝑸 𝑸𝒆𝒙 𝑸𝒆𝒚
𝐪= − 𝑿− 𝒚
𝑨 𝑰𝒚𝒚 𝑰𝒙𝒙
Where 𝑄= Σ 𝑄= total load on the mat
5
A = total area of the mat
x, y = coordinates of any given point on the mat with respect to the x and y axes passing through
the centroid of the area of the mat
𝑒x ,y = eccentricities of the resultant force
Ix ,Iy= moments of inertia of the mat with respect to the x and y axes respectively. To calculate
all the corner column loads, we have to know the coordinates from the origin.
Step 4. The mat is treated as a whole in each of two perpendicular directions. Thus the total
shear force acting on any section cutting across the entire mat is equal to the arithmetic sum of
all forces and reactions (bearing pressure) to the left (or right) of the section. The total bending
moment acting on such a section is equal to the sum of all the moments to the left (or right) of
the section.
And = moment of inertia of the area of the raft respectively about the x and y axis through
the centroid
For the whole area about x and y axis through the centroid.
6
Numerical problems
1.A raft foundation 10m wide and 12m long is to be constructed in a clayey soil having a shear
strength of 12KN/m2 .Unit weight of soil is 16Kn/m3.If the ground surface carries a surcharge of
20KN/m2.Calculate the maximum depth of foundation to ensure a factor of safety of 1.2 against
base failure. Nc for clay is 5.7.
Solution:
Bearing capacity of soil for rectangular footing in cohesive soil is given by
qf = cNc(1+0.3𝐵)+ σ =cNc(1+0.3𝐵)+( D+q)
𝐿 𝐿
7
2. A Trapezoidal footing is to be produced to support two square columns of 30cm and 50cm
sides respectively. Columns are 6meters apart and the safe bearing capacity of the soil is
400KN/m2.The bigger column carries 5000KN and the smaller 3000KN.Design a suitable size of
the footing so that it does not extend beyond the faces of the columns.
Solution:
=a+b= ( 2 )x ((5000+3000)=5.882m……(1)
6.8 4000
(2𝑎+𝑏)
But =(3 𝑎+𝑏 )
(2𝑎 +𝑏)
= ( 3 )x2.65 =1.169......................................... (2)
𝑎+𝑏 6.8
Substituting this values in (1),we get a=( 5.882)= 0.994m and b= 4.889m
5.917
Hence use trapezoidal footing of size a=1m and b=4.9m and L=4.889m
Solution:
L/B = 3/1.5 =2 .From table Iw= 1.52 for flexible footing and 1.22 for rigid footing.
8
Floating Foundation
General Consideration A floating foundation for a building can be defined as a foundation in which the
weight of the building is approximately equal to the full weight which includes water of the soil
removed from the site of the building. With reference to Fig, this principle of flotation may be
explained. Fig. (a) shows a horizontal ground surface with water table at a depth dw below 16the
ground surface. Fig. (b) shows an excavation made in the ground to a depth D where, D > dw and Fig.
(c) shows a structure built in the excavation and completely filling it. If the weight of the building is
equal to the weight of the soil and water removed from
the excavation, then it is clear that the total vertical pressure in the soil below depth D in Fig. (c) is the
same as in Fig. (a) before excavation. Since there is no change in the water level, the neutral pressure
and the effective pressure remain unchanged. If we could move from Fig. (a) to Fig. (c) without
coming across the intermediate case of (b), the building in Fig. (c) would not settle at all, since an
increase in effective vertical pressure cause settlements.
Principle of a floating foundation:
An exact balance of weight removed against weight imposed. The obtained result is zero settlement of
the building
9
Problems to be considered in the Design of a Floating Foundation
The following problems are to be considered during the design and construction stage of a floating
foundation.
1. Excavation
The excavation for the foundation has to be done with care. The sides of the excavation should suitably
be supported by sheet piling, soldier piles and timber lagging or some other standard method.
2. Dewatering
Dewatering will be necessary when excavation has to be taken below the water table level. Care has to
be taken to see that the adjoining structures are not affected due to the lowering of the water table.
3. Critical depth
In Type 2 foundations the shear strength of the soil is low and there is a theoretical limit to the depth to
which an excavation can be made. Terzaghi (1943) has proposed the following equation for computing
the critical depth D
4. Bottom heave
Excavation for foundations reduces the pressure in the soil below the founding depth which results in
the heaving of the bottom of the excavation. Any heave which occurs will be reversed and appear as
settlement during the construction of the foundation and the building. Though heaving of the bottom of
the excavation cannot be avoided it can be minimized to a certain extent. There are three possible
causes of heave:
1. Elastic movement of the soil as the existing overburden pressure is removed.
2. A gradual swelling of soil due to the intake of water if there is some delay in placing the foundation
on the excavated bottom of the foundation.
3. Plastic inward movement of the surrounding soil.
The last movement of the soil can be avoided by providing proper lateral support to the excavated sides
of the trench. Heaving can be minimized by phasing out excavation in narrow trenches and placing the
foundation soon after excavation. It can be minimized by lowering the water table during the
excavation process. Friction piles can also be used to minimize the heave. The piles are driven either
before excavation commences or when the excavation is at half depth and the pile tops are pushed
down to below foundation level. As excavation proceeds, the soil starts to expand but this movement is
resisted by the upper part of the piles which go into tension. The heave is prevented or very much
reduced. It is only a practical and pragmatic approach that would lead to a safe and sound settlement
free floating
10
SCHOOL OF BUILDING AND ENVIRONMENT
DEPARTMENT OF CIVIL ENGINEERING
1
PILE FOUNDATION
A deep foundation is a type of foundation which transfers building loads to the earth farther
down from the surface than a shallow foundation does, to a subsurface layer or a range of
depths.
A pile is a vertical structural element of a deep foundation, driven deep into the ground at the
building site
Fig.1.pile foundation.
2
Fig.2 Classification of piles
Timber piles
Timber piles are made of-tree trunks driven with small end as a point
Maximum length: 35 m; optimum length: 9 - 20m
Max load for usual conditions: 450 kN; optimum load range = 80 - 240 kN
Difficult to splice, vulnerable to damage in hard driving, vulnerable to decay unless treated with
preservatives (If timber is below permanent Water table it will apparently last forever), if
subjected to alternate wetting & drying, the useful life will be short, partly embedded piles or
piles above Water table are susceptible to damage from wood borers and other insects unless
treated.
S
3
Advantages:
Comparatively low initial cost, permanently submerged piles are resistant to decay, easy to
handle, best suited for friction piles in granular material.
Steel piles
Easy to splice, high capacity, small displacement, able to penetrate through light obstructions,
best suited for end bearing on rock, reduce allowable capacity for corrosive locations or provide
corrosion protection.
Disadvantages:
Vulnerable to corrosion.
HP section may be damaged/deflected by major obstruction
Concrete Piles
Precast piles using ordinary reinforcement are designed to resist bending stresses during
picking up & transport to the site & bending moments from lateral loads and to
provide sufficient resistance to vertical loads and any tension forces developed during
driving.
Prestressed piles are formed by tensioning high strength steel prestress cables, and
4
casting the concrete about the cable. When the concrete hardens, the prestress cables are
cut, with the tension force in the cables now producing compressive stress in the concrete
pile. It is common to higher-strength concrete (35 to 55 MPa) in prestressed piles because
of the large initial compressive stresses from prestressing. Prestressing the piles, tend to
counteract any tension stresses during either handling or driving.
Max length: 10 - 15 m for precast, 20 - 30 m for prestressed
Optimum length 10 - 12 m for precast. 18 - 25m prestressed
Loads for usual conditions 900 for precast. 8500 kN for prestressed
Optimum load range: 350 - 3500 kN
Advantages:
1. High load capacities, corrosion resistance can be attained, hard driving possible
2. Cylinder piles in particular are suited for bending resistance.
3. Cast in place concrete piles are formed by drilling a hole in the ground & filling it with
concrete. The hole may be drilled or formed by driving a shell or casing into the ground.
Disadvantages:
1. Concrete piles are considered permanent, however certain soils (usually organic) contain
materials that may form acids that can damage the concrete.
2. Salt water may also adversely react with the concrete unless special precautions are taken
when the mix proportions are designed. Additionally, concrete piles used for marine
structures may undergo abrasion from wave action and floating debris in the water.
3. Difficult to handle unless prestressed, high initial cost, considerable displacement,
prestressed piles are difficult to splice.
4. Alternate freezing thawing can cause concrete damage in any exposed situation.
Composite piles
In general, a composite pile is made up of two or more sections of different materials or different
pile types. The upper portion could be eased cast-in-place concrete combined with a lower
portion of timber, steel H or concrete filled steel pipe pile. These piles have limited application
and arc employed under special conditions.
5
Timber pile Steel pile.
6
2. Types of Piles based on construction methods
May be defined as a reinforced concrete pile which is moulded in circular, square, rectangular or
octagonal form. The precast concrete piles are cast and cured in a casting yard and then
transported to the site for driving. In case space is available, pile can also be cast and cured near
the site of works. They are driven in a similar manner as timber piles with the help of pile
drivers. The diameter of the pile normally varies 1mm 35 cm to 65 cm and their length varies
from 45 in to 30 m.
Cast-in-situ piles
Are those piles which are cast in position inside the ground. Since the cast-in-situ piles is not
subjected to handling or driving stresses, it is not necessary to reinforce the pile in ordinary cases
or in places where the pile is completely submerged in the soil. Reinforcements are necessary to
be provided in a cast-in- situ piles, when the pile acts as a column and is subjected to lateral
forces. Cast- in-situ piles can be divided into two types. In one the metallic shell of the pile is
permanently left in place inside the ground along with the core while in the other type the outer
shell is withdrawn.
7
2. Types of Piles based on installation type.
In simple terms, during the displacement piling method, piles are driven into the ground
pushing the ground out of the way, as you would see in sheet piling. Displacement piling is good
for e.g. contaminated sites where it costs a lot to take the spoil away.
Using the replacement piling method, muck is dug out and replaced with the pile. We can use
far bigger piles using replacement piling.
In end bearing piles, the bottom end of the pile rests on a layer of especially strong soil or
rock. The load of the building is transferred through the pile onto the strong layer
Friction piles
Friction piles work on a different principle .the pile transfer load of the building to the soil
across the full height of the pile by friction.
8
5. Classification based on method of installation:
Bored piles are constructed in pre-bored holes either using a casing or by circulating stabilizing
agent like betonies slurry. The borehole is then filled with concrete after placing the
reinforcement. The advantage of board pile is that there is no damage due to handling and
Small diameter piles-up to 600 mm diameter; large diameter piles-diameter greater than 600
Driven piles may be of concrete, steel or timber. These piles are driven into the soil by the
impact of hammer. Boring is not required for this type of piles. When a pile is driven into
granular soils it densities the soil and increases strength of soil. But when a pile is driven in
saturated clay, the soil instead of being compacted gets remolded with reduction in strength.
It is a type of driven pile. They are constructed by driving a steel casing in to the ground. The
hole is then filled with concrete by placing the reinforcement and the casing is gradually
lifted.
The piles which transfer its load to a hard and relatively incompressible stratum like rock or
dense sand are called end bearing piles. These piles derive its bearing capacity from end
9
bearing at the pile tip.
The piles which do not rest on hard stratum but derives its carrying capacity from skim friction or
adhesion between the pile surface and surrounding soil are called friction piles.
Tension piles are also called uplift piles. These piles are used to anchor down the structures
10
(iv) Compaction piles:
These piles are used to compact loose granular soil to increase its bearing capacity.
Compaction piles do not carry load and hence they can be of weaker material. Sand piles can
These piles are used to provide anchorage against horizontal pull from sheet piling.
(vi) Fender piles and dolphins:
Fender piles and dolphins are used to protect water front structure from impact of any floating
object or ship.
11
Selection of pile foundation
Soil conditions
Loads from structures
Nature of loads
Number of piles to be used
Cost of construction
If hard soil is available at deeper levels of earth, then there is a need of some source that
can transfer the load of the structures on the deep hard soil strata. This source can be said
to be as the deep foundation. Pile foundation is a type of foundation in which pile is
usually used as the source to transfer the load to deep soil levels. Piles are long and
slender members that transfer the load to hard soil ignoring the soil of low bearing
capacity. Transfer of load depends on capacity of pile. There is a need that pile should
be strong enough to transfer the whole load coming on it to underlying hard strata. For
this purpose, pile design is usually given much consideration. Depending on the load, type
of material is usually selected for the piles.
12
Load carrying capacity of pile
The Ultimate load carrying capacity of a pile is defined as the maximum load which can be
carried by a pile and at which the pile continues to sink without further increase in load.
The allowable load is the load which the pile can carry safely which can be determined from
the ultimate load carrying capacity divided by suitable factor of safety
1. Static Analysis
2. Dynamic Analysis
3. Pile Load Testing
4. Correlation with field tests (SPT, CPT etc)(Penetration tests)
Dynamic formulae are used for driven piles. Static formulae are used both for bored and driven
piles. Load testing is the most reliable method to determine the load capacity of the pile in the
field.
They should be performed on all piling projects. However, they are considerably more expensive
than the other methods used to determine pile capacity, and economic considerations sometimes
preclude their use on projects.
Field tests like SPT, CPT are also used to correlate to load carrying capacity particularly for
cohesion less soils.
1. Static method
Based on the assumption that the ultimate bearing capacity Qup of a pile is the sum of the total
ultimate skin friction Rf and the total ultimate point or end bearing resistance Rp
Qup = Rf +Rp or
13
rp=unit point or toe resistance.
A factor of safety of 2.5 or 3 may be adopted for finding the allowable load.
=m c’
rp=point resistance
=CpNc
=9 Cp.
Qup = m c’ As +9 CpAp
2. Dynamic formulae.
As per the Engineering News formula the allowable load of driven pile is given by:
𝑾𝑯
Qa=
𝑭(𝑺+𝑪)
W = Weight of hammer
14
C = Empirical constant
(c = 2.5 cm for drop hammer and 0.25 cm for single acting and double acting hammer)
𝑾𝑯
(1) Drop hammer Qa =
𝟔(𝑺+𝟐.𝟓)
𝑾𝑯
(2) Single acting stream hammer Qa =
𝟔(𝑺+𝟎.𝟐𝟓)
(𝑾+𝒂𝒑)𝑯
(3) Double acting hammer Qa =
𝟔(𝑺+𝟎.𝟐𝟓)
15
a= effective area of piston in square cm.
p= mean effective stream pressure (kg/cm2)
The relation suggested by Hiley for ultimate bearing capacity of the pile is:
𝜼𝒉𝑾𝑯𝜼𝒃
Qu =
(𝑺+𝑪/𝟐)
cp = Compression of pile
cq = Compression of ground
W = Weight of hammer
16
P= Weight of pile
E= Coefficient of restitution
It should be noted that η depends on the coefficient of restitution, which is given in Table 2, η
being obtained from Fig.2. Hammer coefficient is given in Table 1
Hammer K
The load is applied in increments of 20% of the estimated safe load. Hence the failure load
is reached in 8-10 increments.
Settlement is recorded for each Settlement is recorded for each increment until the rate of
17
settlement is less than 0.1 mm/hr.
The ultimate load is said to have reached when the final settlement is more than 10% of the
diameter is more than 10% of the diameter of pile or the settlement keeps on increasing at
constant load. 45
After reaching ultimate load the after reaching ultimate load, the load is released in
decrements of 1/6th of the total load and recovery is measured until full recovery is
measured until full rebounds is established and next unload is done.
After final unload the settlement is measured for 24 hrs to estimate full elastic recovery.
Load settlement curve depends on the type of pile
18
17
19
Distance of anchor piles from test pile – The distance cannot be less than 1.5 m. It should
not be less than 4 times the diameter of test pile for straight pile and not less than 2 times the
diameter of the bell for belled pile.
Load Application – The load is applied in the pile in the following sequence.
o Load applied in increment at the rate of 25 % of working load till working load is reached
o For each load increment maintain the load constant till settlement is 0.1 mm for 5 min as
per IS Code, 0.1 mm for 20 min as per BS Code
o Go for next loading
o When working load is reached hold the load for 24 hr and unload
o Reload from working load to higher loads
o Hold load constant till settlement is 0.1 mm for 5 min as per IS Code, 0.1 mm for 20 min
as per BS Code
o Repeat the process for subsequent load increments
o Go either up to 5/2 times the working load for initial or routine test or to a settlement equal
to 10 % of pile diameter for straight piles and 7.5 % of base diameter for belled pile
20
Pile group.
When several piles are clustered, it is reasonable to expect that the soil pressures produced
from either side friction or point bearing will overlap.
The super-imposed pressure intensity will depend on both the pile load and spacing, and if
sufficiently large the soil will fail in shear or the settlement will be excessive.
The stress intensity from overlapping stressed zones will obviously decrease with increased
pile spacing s; however, large spacing’s are often impractical in a pile cap is cast over the pile
group for the column base and/or to spread the load to the several piles in the group.
Capacity of pile group is the sum of the individual capacities of piles, but it is influenced by the
spacing between the piles.
Piles are driven generally in groups in regular pattern to support the structural loads. The
structural load is applied to the pile cap that distributes the load to individual piles. If piles are
spaced sufficient distance apart, then the capacity of pile group is the sum of the individual
21
capacities of piles. However, if the spacing between piles is too close, the zones of stress around
the pile will overlap and the ultimate load of the group is less than the sum of the individual pile
capacities specially in the case of friction piles, where the efficiency of pile group is much less.
Group action of piles is evaluated by considering the piles to fail as a unit around the perimeter
of the group. Both end bearing and friction piles are considered in evaluating the group capacity.
End bearing pile is evaluated by considering the area enclosed by the perimeter of piles as the
area of footing located at a depth corresponding to the elevation of pile tips. The friction
component of pile support is evaluated by considering the friction that can be mobilized around
the perimeter of the pile group over the length of the piles as shown in figure below:
1. When closely spaced piles are grouped together it is reasonable to expect that the soil as
resistance will overlap.
2. The bearing capacity of pile group may or may not be the sum of the bearing capacity of
individual piles constituting the group.
3. Theory and tests have shown the total bearing capacity Qug of a group of friction piles
particularly in clay may be less than the product of the friction bearing value Qup of
individual pile multiplied by the number of piles in a group.
4. There is no reduction in the case of end bearing piles.
5. For combined end bearing and friction piles only the load carrying capacity of the
frictional portion is reduced.
6. A method of estimating the bearing capacity of a pile group of friction piles is to multiply
the quantity nQup by a reduction factor called the efficiency of pile group.
22
Qug=n.Qup. ηg
n = number of piles
The efficiency of the pile group depends upon the following factors
Characteristics of pile
Spacing of pile
Total number of piles
No of formulae are available for finding the efficiency of pile.
Pile Spacing
The spacing of piles depends upon the method of installing the piles and the type of soil. The
piles can be driven piles or cast-in-situ piles. When the piles are driven there will be greater
overlapping of stresses due to the displacement of soil. If the displacement of soil compacts the
soil in between the piles as in the case of loose sandy soils, the piles may be placed at closer
intervals.
When piles are placed in a group, there is a possibility the pressure isobars of adjacent piles will
overlap each other as shown in Fig. b. The soil is highly stressed in the zones of overlapping of
pressures. With sufficient overlap, either the soil will fail or the pile group will settle excessively
since the combined pressure bulb extends to a considerable depth below the base of the piles. It
is possible to avoid overlap by installing the piles further apart as shown in Fig. c. large spacing
are not recommended sometimes, since this would result in a larger pile cap which would
increase the cost of the foundation.
23
.
The minimum allowable spacing of piles is usually stipulated in building codes. The spacing for
straight uniform diameter piles may vary from 2 to 6 times the diameter of the shaft. For friction
piles, the minimum spacing recommended is 3d where d is the diameter of the pile. For end
bearing piles passing through relatively compressible strata, the spacing of piles shall not be less
than 2.5d.
For end bearing piles passing through compressible strata and resting in stiff clay, the spacing
may be increased to 3.5d. For compaction piles, the spacing may be Id. Typical arrangements of
24
piles in groups are shown in Fig.
Pile installed through compressive soils can experience “down drag” forces or negative
resistance along the shaft, which results from downward movement (settlement) of adjacent
soil. Negative resistance results primarily from consolidation of soft deposits caused by
dewatering or fill placement.
Negative skin friction (NSF) is in fact a downward friction imposed on foundation piles as a
result of subsoil settlement. It needs only few millimeters of relative displacement between the
settling subsoil and the pile shaft surface, which is not uncommon to have relative
displacement at the pile-soil interface more than these values in normal subsoil settlement
problem, to fully mobilize the shaft resistance in either upward or downward directions.
There are five probable, but not limited to, reasons of existence of NSF, namely,
25
c. Consolidation settlement after dissipation of excess pore pressure induced by pile driving,
For individual piles the magnitude of negative friction Qnf may be taken as follows
For cohesive soils =Qnf = p.c.Lf
For granular soils = ½ Lf 2.p.r.K.f
P perimeter of the pile. r- unit weight
o C cohesion
K earth pressure
F-coefficient of friction.
When the fill starts consolidating under its own overburden pressure, it develops a drag on the
surface of the pile. This drag on the surface of the pile is called 'negative friction'. Negative
friction may develop if the fill material is loose cohesion less soil. Negative friction can also
occur when fill is placed over peat or a soft clay stratum as shown in Fig.C.
The superimposed loading on such compressible stratum causes heavy settlement of the fill
with consequent drag on piles.
Negative friction may develop by lowering the ground water which increases the effective
stress causing consolidation of the soil with resultant settlement and friction forces being
developed on the pile.
Negative friction must be allowed when considering the factor of safety on the ultimate carrying
capacity of a pile. The factor of safety, Fs, where negative friction is likely to occur may be
written as
26
(𝑾 + 𝒆Sch𝟐 𝑷)/((𝑾 + 𝑷))
27
Problem 1
(1) A group of 9 piles arranged in a square pattern with diameter and length of each pile as
25cm and 10m respectively, is used as a foundation in soft clay deposit. The unconfined
compressive strength of clay as 120kN/m2 and the pile spacing as 100cm c/c. Find the
load capacity of the group. Assume the bearing capacity factor as (Nc) 9 and adhesion
factor (m) =0.75. Factor of safety of 3.5 may be taken.
Solution
C=120/2 =60kN/m2
Ap= 𝝅𝒅𝟐/𝟒 =0.049m2 rp=
c Nc = 60 X 9
As = 𝝅𝒅𝒍
rf = m c
Qup = 380 kN
rp= 9 c = 60 X 9
As = 4B l= 4X 2.25X 10
rf = c = 60 kN/m2 a
Qug = 8133kN
28
---------------------------------------------------------------------------------------------------------------------
(2). A group of 16 piles of 600mm diameter is arranged in a square pattern with the c/c spacing
of 1.2m. The piles are 10m long and are embedded in soft clay with cohesion of 30kN/m2.
Bearing resistance may be neglected for the piles. Adhesion factor is 0.6. Determine the Ultimate
load capacity of the pile group.
Solution:
As = 𝝅𝒅𝒍 = 𝝅𝑿 𝟎. 𝟔 𝑿 𝟏𝟎 = 18.84 m2
Qug= Asg rf
rf = c = 30 kN/m2
Qug= Asg rf
= 16.8 X 30
= 5040 kN
29
SCHOOL OF BUILDING AND ENVIRONMENT
DEPARTMENT OF CIVIL ENGINEERING
1
Retaining Wall:
Retaining walls are structures that support backfill and allow for a change of grade.
Lateral earth pressure is the force exerted by the soil mass upon an earth-retaining
structure, such as a retaining wall. It is of two types –
i. Active Earth pressure
The soil exerts a push against the wall making the wall to move slightly away from the
backfilled soil mass. This kind of pressure is known as the active earth pressure of the soil.
Sin Ф =
(σV + σH) sin Ф = (σV -
σH) σV sinФ + σH sinФ = (σV -
σH)
σH (1+ sinФ) = σV (1- sinФ)
= = Ka
2
ii. Passive earth pressure
The retaining wall is caused to move toward the soil and the soil provides the resistance
which soil develops in response to movement of the structure toward it is called the passive
earth pressure
sinФ = AB/OB
=
(σV + σH) sin Ф = (σH – σV)
σV sinФ + σH sinФ = (σH – σV)
σV (1+ sinФ) = σH (1- sinФ)
= = Kp
3
Rankine’s Theory:
Assumptions
1) The soil mass is semi infinite, homogeneous, dry and cohesionless.
2) The ground surface is a plane which may be horizontal or inclined.
3) The face of the wall in contact with the backfill is vertical and smooth. In other
words, the friction between the wall and the backfill is neglected (This
amounts to ignoring the presence of the wall).
4) The wall yields about the base sufficiently for the active pressure conditions to
develop; if it is the passive case that is under consideration, the wall is taken to be
pushed sufficiently towards the fill for the passive resistance to be fully mobilised
Cohisionless soil
For a total height of H of the wall, the total thrust Pa on the wall per unit length of the
wall, is given by Pa acting at a height of (1/3)H.
4
For a total height of H of the wall, the total thrust Pa on the wall per unit length of the
wall, is given by Pp acting at a height of (1/3)H.
Effect of Submergence
Under submerge or saturated condition, the lateral earth pressure will due to –
a. Lateral earth pressure due to submerged unit weight of the backfill soil
b. Lateral pressure due to pore water
5
H2 = depth of fill above water table (taken to be moist),
= moist unit weight, and
’ or sub = submerged or effective unit weight
q = Uniform surcharge
P1 = Ka q H
P2 = x Ka H x H = Ka H2
Total thrust = P 1 + P2
Acting at a distance of x = [(P1x ) + (P2 x )] / [P1 + P2 ] from the base
6
Effect of inclined submergence
Total thrust, P = x Ka H xH = Ka
H2 Problem:
1. A retaining wall 4m height has a smooth vertical back. The backfill has horizontal surface in
level with top of wall. The unit weight of back fill is 18 kN/m3 and the angle of shear resistance
is 30 degrees. The cohesion is zero. Determine –
i. the magnitude of earth pressure per meter run and the point of application
ii. when the water table is at top with saturated unit weight of 18kN/m3
iii. when the retaining wall has the surcharge of 36kN/m2 with unit weight of 18kN/m3
Given
H = 4m
= 18kN/m3
Ф = 30˚
4m
Ka = = 1/3 P
4/3
Ka
Earth pressure at top =0 H
7
Earth pressure at bottom = Ka H = (1/3) x 18 x 4 = 24 kN/m2
P = x (Ka H) x H
= 0.5 x 24 x 4
= 48 kN/m
Hence earth pressure of 48 kN/m is acting at height of 1.33m from the bottom
sa t = 18 kN/m3
P H/3
Ka subH wH
Ka = 1/3
= 50.13 kN/m2
= (1/2) x 50.13 x 4
= 100.26 kN/m
8
H/3 = 4/3 = 1.33m
Hence earth pressure of 100.26 kN/m is acting at height of 1.33m from the bottom
iii. Retaining wall has the surcharge of 36kN/m2 with unit weight of 18kN/m3
q = 36kN/m2
Ka = 1/3
= 36 kN/m2
P1 = Ka q H = 12 x 4 = 48 kN/m
H/2 = 4/2 = 2m
P2 = Ka H2 = (1/2) x 24 x 4 = 48 kN/m
H/3 = 4/3 = 1.33m
Earth pressure of 48 kN/m is acting at a height of 1.33m from the bottom Total
thrust, P = P1 + P2 = 48 + 48 = 96 kN/m
= [ (48 x 2) + (48x1.33) ] / 96
= 1.66m
9
Total earth pressure of 96kN/m is acting at a height of 1.66m from the bottom
Coulomb’s theory considers the soil behind the wall as a whole instead of as an element
in the soil. If a wall supporting a granular soil were not to be there, the soil will slump
down to its angle of repose or internal friction.
It is therefore reasonable to assume that if the wall only moved forward slightly a rupture
plane would develop somewhere between the wall and the surface of repose.
The triangular mass of soil between this plane of failure and the back of the wall is
referred to as the ‘sliding wedge’.
It is reasoned that, if the retaining wall were suddenly removed, the soil within the sliding
wedge would slump downward.
Therefore, an analysis of the forces acting on the sliding wedge at incipient failure will
reveal the thrust from the lateral earth pressure which is necessary for the wall to
withstand in order to hold the soil mass in place.
However, Coulomb recognised the possibility of the existence of a curved rupture
surface, although he considered a plane surface for the sake of mathematical simplicity.
Assumptions:
1. The soil is isotropic and homogenous
2. The surface of rupture is plane
3. The failure wedge is a rigid body
4. There is a friction between wall and the back fill soil and is known as ‘wall
friction’
5. Back of wall need not be vertical
6. Failure is two dimensional
7. The soil is cohesionless
8. Coulomb’s equation of shear strength is valid
10
Limitations:
Coulomb’s theory is applicable –
o to inclined wall faces
o to a wall with a broken face
o to a sloping backfill curved backfill surface, broken backfill surface
o to concentrated or distributed surcharge loads.
One of the main deficiencies in Coulomb’s theory is that, in general, it does not satisfy
the static equilibrium condition occurring in nature.
The three forces (weight of the sliding wedge, earth pressure and soil reaction on the
rupture surface) acting on the sliding wedge do not meet at a common point, when the
sliding surface is assumed to be planar.
Even the wall friction was not originally considered but was introduced only some time
later.
11
Active earth pressure of cohesionless soil:
A simple case of active earth pressure on an inclined wall face with a uniformly sloping
backfill may be considered first. The backfill consists of homogeneous, elastic and isotropic
cohesionelss soil. A unit length of the wall perpendicular to the plane of the paper is considered.
The forces acting on the sliding wedge are
(i) W, weight of the soil contained in the sliding wedge,
(ii) R, the soil reaction across the plane of sliding,
(iii) the active thrust Pa against the wall
Where,
For a vertical retaining wall a horizontal backfill for which the angle of wall friction =
Hence, substitute = 90° , = 0° and =
For a smooth vertical retaining wall a backfill with horizontal surface, = 90° , = 0° and
= 0. Hence,
12
Passive earth pressure of cohesionless soil:
The passive case differs from the active case in that the obliquity angles at the wall and
on the failure plane are of opposite sign.
Plane failure surface is assumed for the passive case also in the Coulomb theory but the
critical plane is that for which the passive thrust is minimum. The failure plane is at a much
smaller angle to the horizontal than in the active case
Where,
For a vertical retaining wall a horizontal backfill for which the angle of wall friction =
Hence, substitute = 90° , = 0° and =
(or)
13
For a smooth vertical retaining wall a backfill with horizontal surface, = 90° , = 0° and
= 0. Hence,
Culmann’s method permits one to determine graphically the magnitude of the earth
pressure and to locate the most dangerous rupture surface according to Coulomb’s wedge theory.
Active earth pressure:
From the figure, the force triangle may be imagined to the rotated clockwise through an
angle (90° – φ), so as to bring the vector W, parallel to the φ-line; in that case, the reaction, R ,
will be parallel to the rupture surface, and the active thrust, P, parallel to the ψ-line (pressure
line).
14
The Various steps in the procedure are:
1. Draw Φ-line AE at an angle Φ with the horizontal.
2. Choose an arbitrary failure plane AV. Calculate weight of the wedge ABV and plot it as AV
to a convenient scale on the φ-line
3. Similarly lay off on AE distances A1, A2, A3 etc to a suitable scale to represent the weight
of wedges AB1, AB2, AB3, and so on.
4. Lay off AD at an angle equal to (α- δ) to the line AE. The line AD is called pressure line.
5. Draw lines parallel to AD from points V, 1, 2, 3 to intersect the assumed lines AV, A1,
A2, A3 at points V’, l’, 2’, 3’ etc respectively.
6. Join points V’, l’, 2’, 3’ etc by a smooth curve which is the pressure locus.
7. Select the point C’ on pressure locus such that the tangent to the curve is parallel to Φ the -
line AE.
8. Draw CC’ parallel to the pressure line AD. The magnitude of CC’ in its natural units gives
the active pressure Pa.
9. Join AC’ and produce to meet the surface of the backfill at C. AC is the rupture line.
15
Passive earth pressure:
The φ-line is to be drawn through point B at an angle – (φ), i.e., it must be drawn at an
angle φ below the horizontal. On the line, the weights of the arbitrarily assumed sliding wedges
are plotted to a convenient force scale. The position line is drawn through A at an angle – (φ + δ)
(or to the left of the back face AB of the wall).
16
STABILTY OF SLOPES
Introduction:
An exposed ground surface that stands at an angle () with the horizontal is called slope.
Slopes are required in the construction of highway and railway embankments, earth dams,
levees and canals. These are constructed by sloping the lateral faces of the soil because
slopes are generally less expensive than constructing walls. Slopes can be natural or man
made. When the ground surface is not horizontal a component of gravity will try to move
the sloping soil mass downwards. Failure of natural slopes (landslides) and man-made
slopes has resulted in much death and destruction. Some failures are sudden and
catastrophic; others are widespread; some are localized. Civil Engineers are expected to
check the safety of natural and slopes of excavation. Slope stability analysis consists of
determining and comparing the shear stress developed along the potential rupture surface
with the shear strength of the soil. Attention has to be paid to geology, surface drainage,
groundwater, and the shear strength of soils in assessing slope stability.
17
In this chapter, we will discuss simple methods of slope stability analysis from
which one will be able to:
Understand the forces and activities that provoke slope failures. Understand
the effects of seepage on the stability of slopes.
Estimate the stability of slopes with simple geometry for different types of
soils.
Highways
Railways
Earth Dams
River Training works
Intense Rain-Fall
1. Erosion: The wind and flowing water causes erosion of top surface of slope
and makes the slope steep and thereby increase the tangential component of
driving force.
2. Steady Seepage: Seepage forces in the sloping direction add to gravity forces
and make the slope susceptible to instability. The pore water pressure
decrease the shear strength. This condition is critical for the downstream
slope.
18
3. Sudden Drawdown: in this case there is reversal in the direction flow and
results in instability of side slope. Due to sudden drawdown the shear stresses
are more due to saturated unit weight while the shearing resistance decreases
due to pore water pressure that does not dissipate quickly.
4. Rainfall: Long periods of rainfall saturate, soften, and erode soils. Water
enters into existing cracks and may weaken underlying soil layers, leading to
failure, for example, mud slides.
5. Earthquakes: They induce dynamic shear forces. In addition there is sudden
buildup of pore water pressure that reduces available shear strength.
6. External Loading: Additional loads placed on top of the slope increases the
gravitational forces that may cause the slope to fail.
7. Construction activities at the toe of the slope: Excavation at the bottom of
the sloping surface will make the slopes steep and there by increase the
gravitational forces which may result in slope failure
Types of failure
2. Toe failure
3. Base failure
19
Definition of Key Terms
L MECHANICS
A. AMALA RAJU ARUL
Slip or failure
toe of slope
surface
Slip or failure zone: It is a thin zone of soil that reaches the critical state or residual
state and results in movement of the upper soil mass.
Slip plane or failure plane or slip surface or failure surface: It is the surface of
sliding.
Sliding mass: It is the mass of soil within the slip plane and the ground surface.
Slope angle : It is the angle of inclination of a slope to the horizontal. The slope
angle is sometimes referred to as a ratio, for example, 2:1 (horizontal: vertical).
Very soft, saturated foundation soils or ground water generally play a prominent role in
geotechnical failures in general. They are certainly major factors in cut slope stability and in the
stability of fill slopes involving both “internal” and “external” slope failures. The effect of water
on cut and fill slope stability is briefly discussed below.
Importance of Water:
Next to gravity, water is the most important factor in slope stability. The effect of gravity is known,
therefore, water is the key factor in assessing slope stability.
20
Effect of Water on Cohesionless Soils:
In cohesionless soils, water does not affect the angle of internal friction (φ). The effect of water on
cohesionless soils below the water table is to decrease the intergranular (effective) stress between soil
grains (σ'n), which decreases the frictional shearing resistance (τ').
Routine seasonal fluctuations in the ground water table do not usually influence either the amount of
water in the pore spaces between soil grains or the cohesion. The attractive forces between soil particles
prevent water absorption unless external forces such as pile driving, disrupt the grain structure.
However, certain clay minerals do react to the presence of water and cause volume changes of the clay
mass.
An increase in absorbed moisture is a major factor in the decrease in strength of cohesive soils as shown
schematically in Figure below. Water absorbed by clay minerals causes increased water contents that
decrease the cohesion of clayey soils. These effects are amplified if the clay mineral happens to be
expansive, e.g., montmorillonite.
Fills on Clays:
Excess pore water pressures are created when fills are placed on clay or silt. Provided the applied loads
do not cause the undrained shear strength of the clay or silt to be exceeded, as the excess pore water
pressure dissipates consolidation occurs, and the shear strength of the clay or silt increases with time.
For this reason, the factor of safety increases with time under the load of the fill.
Cuts in Clay:
As a cut is made in clay the effective stress is reduced. This reduction will allow the clay to expand and
absorb water, which will lead to a decrease in the clay strength with time. For this reason, the factor of
safety of a cut slope in clay may decrease with time. Cut slopes in clay should be designed by using
effective strength parameters and the effective stresses that will exist in the soil after the cut is made.
Sudden moisture increase in weak rocks can produce a pore pressure increase in trapped pore air
accompanied by local expansion and strength decrease. The "slaking" or sudden disintegration of hard
shales, claystones, and siltstones results from this mechanism. If placed as rock fill, these materials will
tend to disintegrate into a clay soil if water is allowed to percolate through the fill. This transformation
from rock to clay often leads to settlement and/or shear failure of the fill.
21
Types of Slopes
1. Infinite Slopes
2. Finite Slopes
Infinite slopes: They have dimensions that extend over great distances and the soil
mass is inclined to the horizontal.
Infinite Slope
Finite slopes:
A finite slope is one with a base and top surface, the height being limited. The
inclined faces of earth dams, embankments and excavation and the like are all finite
slopes.
22
Factor of safety
Factor of safety of a slope is defined as the ratio of average shear strength (τf ) of
a soil to the average shear stress (τd) developed along the potential failure surface.
τf
FS = τ d
FS = Factor of safety
Shear Strength:-
τ f = c + σ tanϕ
Where, c = cohesion
τ d = c d + σ tanϕ d
cd and ϕd are the cohesion and angle of internal friction that develop along the
potential failure surface.
23
Infinite Slopes:
Infinite slopes have dimensions that extended over great distances and the soil mass is
inclined to the horizontal. If different strata are present strata boundaries are assumed
to be parallel to the surface. Failure is assumed to occur along a plane parallel to the
surface.
A slope that extends for a relatively long distance and has a consistent subsurface profile may be
analyzed as an infinite slope. The failure plane for this case is parallel to the surface of the slope and the
limit equilibrium method can be applied readily.
A typical section or “slice” through the potential failure zone of a slope in a dry cohesionless soil, e.g.,
dry sand, is shown in Figure 6-3, along with its free body diagram. The weight of the slice of width b
and height h having a unit dimension into the page is given by:
where γ is the effective unit weight of the dry soil. For a slope with angle β as shown in Figure below:
The normal (N) and tangential (T) force components of W are determined as follows:
The available shear strength along the failure plane is given by:
24
The factor of safety (FS) is defined as the ratio of available shear strength to strength required to
maintain stability. Thus, the FS will be given by:
For an infinite slope analysis, the FS is independent of the slope depth, h, and depends only on the angle
of internal friction, φ, and the angle of the slope, β. The slope is said to have reached limit equilibrium
when FS=1.0. Also, at a FS = 1.0, the maximum slope angle will be limited to the angle of internal
friction, φ.
If a saturated slope in a c-φ soil has seepage parallel to the surface of the slope as shown in Figure
below, the same limit equilibrium concepts may be applied to determine the FS, which will now depend
on the effective normal force (N'). In the following analysis, effective shear strength parameters, c' and
φ' are used.
From Figure above, the pore water force acting on the base of a typical slice having a unit dimension
into the page is:
where h is any depth less than or equal to the depth of saturation and b is a unit width.
The available frictional strength, S, along the failure plane will depend on φ' and the effective normal
force, N' =N-U, where N is the total normal force. The equation for S is:
25
By substituting W = γsat b h into the above expression and rearranging terms, the FS is given by:
From Equation above it is apparent that for a cohesionless material with parallel seepage, the FS is also
independent of the slope depth, h, just as it is for a dry cohesionless material as given earlier. The
difference is that the FS for the dry material is reduced by the factor γ'/γsat for saturated cohesionless
materials to account for the effect of seepage. For typical soils, this reduction will be about 50 percent in
comparison to dry slopes.
The above analysis can be generalized if the seepage line is assumed to be located at a normalized
height, m, above the failure surface where m =z/h. In this case, the FS is:
and γsat and γm are the saturated and moist unit weights of the soil below and above the seepage line.
The above equation may be readily reformulated to determine the critical depth of the failure surface in
a c'-φ' soil for any seepage condition.
Experience and observations of failures of embankments constructed over relatively deep deposits of
soft soils have shown that when failure occurs, the embankment sinks down, the adjacent ground rises
and the failure surface follows a circular arc as illustrated in Figure below.
26
Concepts and Formulas of Circular Arc Failure of Slope Analysis:
The force driving movement consists of the embankment weight. The driving moment is the
product of the weight of the embankment acting through its center of gravity times the
horizontal distance from the center of gravity to the center of rotation (LW).
The resisting force against movement is the total shear strength acting along the failure arc. The
resisting moment is the product of the resisting force times the radius of the circle (LS).
The factor of safety against slope instability is equal to the ratio of the resisting moment to
driving moment.
Failure takes place when the factor of safety is less than 1, i.e., the driving moment > resisting moment.
A rule of thumb based on simplified bearing capacity theory can be used to make a preliminary
"guestimate" of the factor of safety (FS) against circular arc failure for an embankment built on a clay
foundation without presence of free water. The rule of thumb is as follows:
Where: c = unit cohesion of clay foundation soil (psf); γFill = unit weight fill (pcf); HFill = height of fill
(feet)
Since the rule of thumb assumes that there is no influence from groundwater, c and γ Fill are effective
stress parameters.
There are several available methods that can be used to perform a circular arc stability analysis for an
approach embankment over soft ground. The simplest basic method is known as the Normal or Ordinary
Method of Slices, also known as Fellenius’ method or the Swedish circle method of analysis. The
Ordinary Method of Slices can easily be performed by hand calculations and is also a method by which
the computation of driving and resisting forces is straightforward and easily demonstrated. For this
method, the failure surface is assumed to be the arc of a circle as shown in Figure 6-7 and the factor of
safety against sliding along the failure surface is defined as the ratio of the moment of the total available
resisting forces on the trial failure surface to the net moment of the driving forces due to the
embankment weight, that is:
27
Note that since the method consists of computing the driving and resisting forces along the failure arc,
the moment arm R is the same for both the driving and resisting forces. Thus, the above equation
reduces to:
For slope stability analysis, the mass within the failure surface is divided into vertical slices as shown in
Figures above. A typical vertical slice and its free body diagram is shown in Figure below for the case
where water is not a factor.
28
The following assumptions are then made in the analysis using Ordinary Method of Slices:
1- The available shear strength of the soil can be adequately described by the Mohr-Coulomb equation:
where:
τ = effective shear strength
c = cohesion component of shear strength
(σ - u) tan φ = frictional component of shear strength
σ = total normal stress on the failure surface at the base of a slice due to
the weight of soil and water above the failure surface
u = water uplift pressure against the failure surface
φ = angle of internal friction of soil
tan φ = coefficient of friction along failure surface
3- The factors of safety with respect to cohesion (c) and friction (tan φ) are equal.
4- Shear and normal forces on the sides of each slice are ignored.
5- The water pressure (u) is taken into account by reducing the total weight of the slice by the water
uplift force acting at the base of the slice.
The equation above is expressed in terms of total strength parameters. The equation could easily have
been expressed in terms of effective strength parameters. Therefore, the convention to be used in the
stability analysis, be it total stress or effective stress, should be chosen and specified. In soil problems
involving water, the engineer may compute the normal and tangential forces by using either total soil
weights and boundary water forces (both buoyancy and unbalanced hydrostatic forces) or submerged
(buoyant) soil weights and unbalanced hydrostatic forces. The results are the same. When total weight
and boundary water forces are used, the equilibrium of the entire block is considered. When submerged
29
weights and hydrostatic forces are used, the equilibrium of the mineral skeleton is considered. The total
weight notation is used herein as this method is the simplest to compute.
To compute the factor of safety for an embankment by using the Ordinary Method of Slices, the step-
by-step computational procedure is as follows:
Step 1- Draw a cross-section of the embankment and foundation soil profile on a scale of either 1-inch =
10 feet or 1-inch = 20 feet scale both horizontal and vertical.
Step 3- Divide the circular mass above the failure surface into 10 - 15 vertical slices as illustrated in
Figure below
To simplify computation, locate the vertical sides of the slices so that the bottom of any one slice is
located entirely in a single soil layer or at the intersection of the ground water level and the circle.
Locate the top boundaries of vertical slices at breaks in the slope. The slice widths do not have to be
equal. For convenience assume a one-foot (0.3 m) thick section of embankment. This unit width
simplifies computation of driving and resisting forces.
Also, as shown in figures above the driving and resisting forces of each slice act at the intersection of a
vertical line drawn from the center of gravity of the slice to the failure circle to establish a centroid point
on the circle. Lines (called rays) are then drawn from the center of the circle to the centroid point on the
circular arc. The α angles are then measured from the vertical to each ray.
When the water table is sloping, use Equation 6-16 to calculate the water pressure on the base of the
slice:
To compute WT, use total soil unit weight, γt, both above and below the water table.
Step 5- Compute frictional resisting force for each slice depending on location of ground water table.
Note that the effect of water is to reduce the normal force against the base of the slice and thus reduce
the frictional resisting force. To illustrate this reduction, take the same slice used in Step 4 and compute
the friction resistance force for the slice with no water and then for the ground water table located 5 feet
above the base of the slice.
T is the component of total weight of the slice, WT, acting tangent to the slice base.
T is the driving force due to the weight of both soil and water in the slice.
Step 8- Sum resisting forces and driving forces for all slices and compute factor of safety.
31
Slope stability guidelines for design:
CU triaxial test
with pore water
pressure Use Bishop Method
Long-term measurements or with combination of cohesion
(embankment on soft CD triaxial test. and angle of internal friction
clays and clay cut slopes). Use effective (effective strength parameters
strength from laboratory test).
parameters.
Direct shear or
direct simple shear
test. Slow strain
rate and large Use Bishop, Janbu or Spencer
Existing failure planes deflection needed. Method to duplicate previous
Use residual shear surface.
strength
parameters.
32
Foundation Type of Source of Strength
Remarks
Soil Type Analysis Parameters
Obtain effective friction
angle from charts of
standard penetration Use Bishop Method with an
Granular All types
resistance (SPT) versus effective stress analysis.
friction angle or from
direct shear tests.
Note: Methods recommended represent minimum requirement. More rigorous methods such
as Spencer’s method should be used when a computer program has such capabilities.
Remarks on Safety Factor:
For side slopes of routine highway embankments, a minimum design safety factor of 1.25 as determined
by the Ordinary Method of Slices is used. For slopes that would cause greater damage upon failure,
such as end slopes beneath bridge abutments, major retaining structures, and major roadways such as
regional routes, interstates, etc., the design safety factor should be increased to at least 1.30 to 1.50. For
cut slopes in fine-grained soils, which can lose shear strength with time, a design safety factor of 1.50 is
desirable.
The step-by-step procedure presented in the Circular Arc Failure of Slope Analysis article illustrates
how to compute the factor of safety for one selected circular arc failure surface. The complete analysis
requires that a large number of assumed failure surfaces be checked in order to find the critical one, i.e.,
the surface with the lowest factor of safety.
This task would obviously be a tedious and time consuming operation if done by hand. Therefore a
computer program becomes a valuable tool for performing such computations. Any method for stability
analysis is easily adapted to computer solution. For critical circle methods a grid of possible circle
centers is defined, and a range of radius values established for each. The computer can be directed to
perform stability analyses for each circle center over the range of radii and then to print out all the
safety factors or just the minimum one and its radius. A plot of minimum safety factor for each circle
center in the form of contours can be used to define the location of the most critical circle and the
minimum safety factor as shown in Figure below. The radius of the most critical surface can be used to
locate the intersection points of the circle with the ground surface above and below the slope. This is
useful in identifying structures above and below the slope that may be potentially impacted by slope
instability.
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Figure above shows just one of several ways that computer programs can be used to search for the most
critical failure surface. It is beyond the scope of this manual to discuss these in detail. However, the
following points should be noted as one uses a computer program for locating the most critical failure
surface:
1. Check multiple circle center locations and compare the lowest safety factors. There may be more
than one “local” minimum and a single circle center location may not necessarily locate the
lowest safety factor for the slope.
2. Search all areas of the slope to find the lowest safety factor. The designer may find multiple
areas of the slope where the safety factors are low and comparable. In this case, the designer
should try to identify insignificant failure modes that lead to low safety factors for which the
consequences of failure are small. This is often the case in cohesionless soils, where the lowest
safety factor is found for a shallow failure plane located close the slope face.
3. Review the soil stratigraphy for “secondary” geological features such as thin relatively weak
zones where a slip surface can develop. Often, circular failure surfaces are locally modified by
the presence of such weak zones. Therefore computer software capable of simulating such
failures should be used. Some of the weak zones may be man-made, e.g., when new fills are not
adequately keyed into existing fills for widening projects.
4. Conduct stability analyses to take into account all possible loading and unloading schemes to
which the slope might be subjected during its design life. For example, if the slope has a
detention basin next to it, then it might be prudent to evaluate the effect of water on the slope,
e.g., perform an analysis for a rapid drawdown condition.
5. Use the drained or undrained soil strength parameters as appropriate for the conditions being
analyzed
6. Use stability charts to develop a “feel” for the safety factor that may be anticipated. Stability
charts are discussed in the next section. Such charts may also be used to verify the results of
computer solutions.
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Finite Slopes
A finite slope is one with a base and top surface, the height being limited. The
inclined faces of earth dams, embankments, excavation and the like are all finite
slopes.
c) Repeating the process until the worst slip surface, that is, the one with
minimum margin of safety is found.
Methods:-
II. Total stress analysis for cohesive –frictional (c-ϕ) soil – (Swedish method of
slices or Method of slices)
III. Effective stress analysis for conditions of steady seepage, rapid drawdown and
immediately after construction.
V. Taylor‟s method.
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For simplicity, when analyzing the stability of a finite slope in a homogeneous soil, we need to
make an assumption about the general shape of the surface of potential failure.
Hence most conventional stability analyses of slopes have been made by assuming that the curve of
potential sliding is an arc of a circle.
Culmann’s method assumes that the critical surface of failure is a plane surface passing through the
toe.
Culmann’s analysis is based on the assumption that the failure of a slope occurs along a plane when
the average shearing stress tending to cause the slip is more than the shear strength of the soil.
(a) The angle of the critical failure plane q can be calculated from:
(b) The critical depth of the cut slope can be calculated from:
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Like Culmann’s method, the other methods are
Modes of Failure
i. Slope failure
The surface of sliding passes at some distance below the toe of the slope.
Shallow slope
failure
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Toe Circle all circles for soils with f > 3° & b > 53°
• Slope Circle always for D = 0 & b < 53°
• Midpoint Circle always for D > 4 & b < 53°
Various procedures of stability analysis may, in general, be divided into two major classes:
.
Mass procedure
Method of slices
• In this case, the mass of the soil above the surface of sliding is taken as a unit.
• Most natural slopes and many manmade slopes consist of more than on soil with different properties.
• This procedure is useful when the soil that forms the slope is assumed to be homogeneous. • In this
case the use of mass procedure is inappropriate.
• In the method of slices procedure, the soil above the surface of sliding is divided into a number of
vertical parallel slices.
The stability of each slice is calculated separately.
• It is a general method that can be used for analyzing irregular slopes in non-homogeneous slopes in
which the values of c’ and f’ are not constant and pore water pressure can be taken into consideration.
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cd = g H m
Where
m = S ta bility num be r
H = height of slope
γ = unit we ig h t of soil
Cd = . H. m
It is a general method that can be used for analyzing irregular slopes in non-homogeneous slopes in
which the values of c’ and f ’ are not constant.
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Because the SWEDISH GEOTECHNCIAL COMMISION used this method extensively, it is
sometimes referred to as the SWEDISH Method.
In mass procedure, only the moment equilibrium is satisfied. Here attempt is made to satisfy force
equilibrium.
The soil mass above the trial slip surface is divided into several vertical parallel slices.
The width of the slices needs not to be the same (better to have it equal).
The base of each slice is assumed to be a straight line.
The inclination of the base to the horizontal is a.
The height measured in the center line is h.
The height measured in the center line is h.
The accuracy of calculation increases if the number of slices is increased.
The procedure requires that a series of trial circles are chosen and analyzed in the quest for the
circle with the minimum factor of safety.
Two Methods:
Bishop’s simplified method is probably the most widely used (but it has to be incorporated into
computer programs).
The ordinary method of slices is presented in this chapter as a learning tool only.
It is used rarely now because it is too conservative.
It yields satisfactory results in most cases.
Analyses by more refined methods involving consideration of the forces acting on the sides of
slices show that the Simplified Bishop Method yields answers for factors of safety which are
very close to the correct answer.
The Bishop Simplified Method yields factors of safety which are higher than those obtained with
the Ordinary Method of Slices.
The two methods do not lead to the same critical circle.
The Fs determined by this method is an underestimate (conservative) but the error is unlikely to
exceed 7% and in most cases is less than 2%.
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Stability Number
In a slope the component of the self weight () causes instability and the cohesion contributes to
stability.
The maximum height (Hc) of a slope is directly proportional to unit cohesion (Cu) and inversely
proportional to unit weight ()
Sn = c/(Fc. . H)
Hc= Fc. H
Hc = Critical Height
Fc = Factor of Safety with respect to cohesion
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