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Sanjivani Rural Education Society’s

Sanjivani College of Engineering, Kopargaon, 423603

An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune

Subject: Foundation Engineering

B. Tech. (Civil Engg)

Unit-II: Bearing Capacity & Shallow Foundation

Department of Civil Engineering

Sanjivani College of Engineering, Kopargaon, 423603

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FOUNDATION TYPES

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1. Shallow Foundations

1. D/B ≤ 1 (Terzaghi, 1943); later researchers said D/B

can be up to 3-4.

2. Depth generally less than 3m

2. Deep Foundations

Focus of this course

TYPES OF SHALLOW FOUNDATIONS

1. Square Footings
2. Combined Footings
1. Rectangular Footings
2. Trapezoidal Footings
3. Strip Footings
4. Mat/Raft Footings
5. Floating Foundations

Spread Foundations

• The structural load is literally spread over a broad area under the building.
• Load is spread through a wider bottom part than the load-bearing foundation walls it supports.
• Most commonly used foundation type.

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TYPES OF SHALLOW FOUNDATIONS

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Square Footings

• Square in plan
• Used to support individual columns

TYPES OF SHALLOW FOUNDATIONS

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Strip Footings

• L/B ≥ 5
• To support wall loads

TYPES OF SHALLOW FOUNDATIONS

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Combined Footings

• Rectangular/Trapezoidal
• To support two columns or machine base

Rectangular Footing

Trapezoidal Footing

TYPES OF SHALLOW FOUNDATIONS

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Raft/Mat Footings

• To support a very heavy structure by spreading the contact pressure over a large area.
• For weak soil conditions
• To reduce settlements

TYPES OF SHALLOW FOUNDATIONS

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Floating Foundations

• Weight of the structure is equal to the weight of the soil displaced by foundations
• Net increase of load over the soil is (nearly) zero
• Where deep deposits of weak soil stratum exists

TYPES OF FOUNDATION FAILURE

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1. Due to excessive settlement

Maximum tolerable settlement

• 25.4mm (1”) for square/strip footings
• 50.8mm (2”) for mat footings

2. Due to shear failure in soil

Focus of this chapter

^ϖ DEFENITION

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The term ‘Bearing cpacity of soil‘ is used to indicate the maximum load per unit area which the soil will resist safely without displacement

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By dividing the ultimate bearing power of soil by a factor of safely,the bearing capacity of a soil is obtained……….

BEARING CAPACITY

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– Basic Definitions –

NSL

Foundation Level

Bearing pressure/ contact pressure _{is the contact force per unit} area along the bottom of the foundation.

P₁

P₂

P₁ = Structural/Net load on soil

P₂ = Weight of overburden soil

P = P₁ + P₂ = Total/Gross load supported by soil

BEARING CAPACITY

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Ultimate Bearing Capacity (q_u or q_ult)

The ultimate bearing capacity is the gross pressure at the base of the foundation at which soil fails in shear.

NSL

Foundation Level

P₁

P₂

P₁ = Structural/Net load on soil P₂ = Weight of overburden soil

P = P₁ + P₂ = Total/Gross load supported by soil

– Basic Definitions –

BEARING CAPACITY

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Net Ultimate Bearing Capacity (q_nu)

It is the net increase in pressure at the base of foundation that cause shear failure of the soil. OR

It is the structural load that can be carried by soil without undergoing shear failure.

NSL

P₁

P₂

Foundation Level

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P₁ = Structural/Net load on soil P₂ = Weight of overburden soil P = P₁ + P₂ = Total/Gross load

supported by soil

q_nu = q_u – γ.D_f

γ.D_f = Overburden pressure

– Basic Definitions –

BEARING CAPACITY

Net Safe Bearing Capacity (q_ns)

It is the net pressure which can ‘safely’ be applied to the soil considering only shear failure.

q_ns = q_nu /FOS

NSL

Foundation Level

P₁

FOS - Factor of safety usually taken as 2.00 -3.00

– Basic Definitions –

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BEARING CAPACITY

Gross Safe Bearing Capacity (q_s)

It is the maximum gross pressure which the soil can carry safely without shear failure.

q_s = q_nu / FOS + γ.D_f

NSL

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Foundation Level

P₁

P₂

– Basic Definitions –

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BEARING CAPACITY

Net Allowable Bearing Capacity (q_a or ABC)

It is the maximum pressure which the soil can carry safely without undergoing shear failure and excessive settlement.

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• q_a is used for the design of foundation.

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– Basic Definitions –

TYPES OF SHEAR FAILURE

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General Shear Failure

• Fully developed failure plane
• Sudden or catastrophic failure
• Bulging on ground surface adjacent to the foundation
• Most common type of shear failure
• Occur in relatively strong soils (Dense sand)

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Local Shear Failure

• Failure plane not completely defined
• Sudden jerks at failure
• Small amount of bulging might be observed
• Occur in sand or clay with medium compaction

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Punching Shear Failure

• Foundation sinks into soil like a punch
• Failure surface do not extend up to the ground surface

• Occurs in very loose sands weak clays

SHEAR BASED DESIGN

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– GENERAL COMMENTS –

• Usually only necessary to analyze general shear failure.

• Local and punching shear

failure can usually be

anticipated by settlement analysis.

Punching Shear Failure

Local Shear Failure

General Shear Failure

TERZAGHI'S METHOD

• Since soil cohesion can be difficult to

quantify, conservative values of c ( cohesion) should be used.

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• Frictional strength is more reliable and does not need to be as conservative as cohesion.

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• Terzaghi's method is simple and familiar to many geotechnical engineers; however, it

does not take into account many factors, nor does it consider cases such as rectangular

foundations.

Assumptions For Terzaghi's Method

Depth of foundation is less than or equal to its width

No sliding occurs between foundation and soil( rough foundation)

Soil beneath foundation is

homogeneous semi infinite mass

Mohr-Coulomb model for soil

General shear failure mode is the governing mode(but not the only mode)

Footing is rough

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Assumptions For Terzaghi's Method

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No soil consolidation occurs

Foundation is very rigid relative to the soil.

Soil above bottom of foundation has no shear strength; is only a surcharge load against the overturning load.

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Applied load is compressive and applied vertically to the centroid of the foundation

No applied moments present

Failure Modes for Shallow Foundations

Bearing Capacity

General Shear Failure,

Zones I, II, III,

Dense Sand

Local Shear Failure, Zones I, II,

Medium Dense Sand

Failure Modes, Continued

Bearing Capacity

Punching Failure, Zone I Only, Loose Sand and Soft Clay

Bearing Capacity Analysis

Bearing Capacity

Zone I, Active.

Zones II, Transition.

Zones III, Passive.

Terzaghi B/C Assumptions

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Bearing Capacity

Three zones do exist:

1. Active zone, just below the foundation.
2. Transition zone, between the active and passive zones.
3. Passive zone, near the ground surface, just beside the foundation.

passive

active

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Transition

Terzaghi Bearing Equation for

^{April 5, 2012} Bearing Capacity ₁₀

Strip Footing

q_{u net} = c N_c + γ₁ D (N_q - 1) + 0.5 B γ₂ N_γ

Generalized soil strength : c, φ

(drainage as applicable)

Soil unit weight : γ₂ (total or effective as applicable)

Overburden

γ ₁ D

B

Failure Zone (depth ≈ 2B)

Terzaghi Bearing Equation

Bearing Capacity

^qult ⁼

q_ult = c N_c

q_ult = c N_c + γ₁ D N_q

Cohesion Term

Above F.L.

q_ult = c N_c + γ₁ D N_q + 0.5B γ₂ N_γ

Below F.L.

Terzaghi Bearing Equation

Bearing Capacity

Strip footings: Qu = c Nc + γ D Nq + 0.5 γ B Nγ

Terzaghi's Bearing capacity equations:

Strip footings: Qu = c Nc + γ D Nq + 0.5 γ B Nγ

Square footings: Qu = 1.3 c Nc + γ D Nq + 0.4 γ B Nγ

Circular footings: Qu = 1.3 c Nc + γ D Nq + 0.3 γ B Nγ

Square footings: Qu = 1.3 c Nc + γ D Nq + 0.4 γ B Nγ

N_c, N_q, N_γ are Terzaghi B/C Coefficients, f(φ)

C, φ are the soil shear strength parameters

Based on Terzaghi’s bearing capacity theory, column load P is resisted by shear stresses at edges of three zones under the footing and the overburden pressure, q (=γD) above the footing. The first term in the equation is related to cohesion of the soil. The second term is related to the depth of the footing and overburden pressure. The third term is related to the width of the footing and the length of shear stress area. The bearing capacity factors, Nc, Nq, Nγ, are function of internal friction angle, φ.

Terzaghi's Bearing capacity equations:

Strip footings: Qu = c Nc + qNq + 0.5 γ B Nγ

Square footings: Qu = 1.3 c Nc +q Nq + 0.4 γ B Nγ

Circular footings: Qu = 1.3 c Nc + q Nq + 0.3 γ B Nγ

Where

q=γ D

PRESUMPTIVE BEARING CAPACITY

• Building codes of various organizations in different countries gives the allowable bearing capacity that can be used for

proportioning footings.

• These presumptive bearing capacity values based on experience with other structures already built.
• As presumptive values are based only on

visual classification of surface soils, they are not reliable.

• These values don't consider important

factors affecting the bearing capacity such as the shape, width, depth of footing,

location of water table, strength and compressibility of the soil.

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• Generally these values are conservative and can be used for preliminary design or even for final design of small unimportant

structure.

• IS1904- 1978 recommends that the safe bearing capacity should be calculated on the

basis of the soil test data. But, in absence of such data, the values of safe bearing

capacity can be taken equal to the

presumptive bearing capacity values.

^♣ It is further recommended that for non-

cohesive soils, the values should be reduced by 50% if the water table is above or near base of footing.

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MEYERHOF’S ANALYSIS

^ϖ Assumptions

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Failure zones to extend above base level of the footing.

The logarithmic spiral extends right up to the ground surface.

Meyerhof (1951, 1963 ) proposed an

equation for ultimate bearing capacity of

strip footing which is similar in form to that of Terzaghi but includes shape factors,

depth factors and inclination factors.

Meyerhof's equation is

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VESIC'S BEARING CAPACITY THEORY

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• Vesic(1973) confirmed that the basic nature of failure surfaces in soil as suggested by

Terzaghi as incorrect.

• Developed formulas based on theoretical and experimental findings.
• Vesić retained Terzaghi’s basic format and added additional factors, which produces more accurate bearing capacity values.
• Applies to a much broader range of loading and geometry conditions.

^♣ The bearing capacity formula is re- written as

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SKEMPTON’S ANALYSIS

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^♣ Skempton (1951) based on his investigations of footings on saturated clays observed that

the bearing capacity factor �_C is a function

of ratio D/ B in the case of strip footing and square or circular footings, for Φ = 0

condition.

^♣ Bearing capacity factors in Terzaghi's

equation tends to increase with depth for a cohesive soil.

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FIELD TESTS: DIRECT DETERMINATION OF BEARING CAPACITY OF SOIL

• Plate Load Test
• Vane Shear test
• Dynamic cone penetration
• Field-Density (approximation)
• Field observation
• Previous Knowledge
• Field Sample Collection

PLATE LOAD TEST

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Simplest and widely used field test- plate load test

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A square pit of sides equal to five times the width of test plate is dug up to the required depth.

Test plates are iron plates of size 60cm square for clayey soil 30cm square for sandy soil.

At the centre of the pit, a square hole of size equal to the test plate is dug.The bottom of the test plate should be along the proposed foundation level. (b1/d1=b2/d2)

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• ^{Seat the plate accurately over the} centre of pit and it should be in contact with the soil over the whole area
• ^{A loading post and hydraulic jack} is provided above the test plate.Hydraulic jack support a gravity loading platform. The loading is done with sand bags,concrete blocks.

♣ ^{Load is increased}

in regular

increments of 250kg or 1/5^th of

bearingcapacity

ultimate whichever is less

• Each loading increment is kept in postion until no further measurable settlement occurs. Settlement of the plate is measured by two sensitive dial guage of sensitivity 0.02mm.
• Plot a graph between settlement and load.
• From the graph measure maximum load upto which settlement is proportional

ultimate Bearing capacity of soil = Maximum load/area of test plate

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FACTOR OF SAFETY MAY BE 2 OR 3

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^♣ Safe bearing capacity

METHODS FOR IMPROVING BEARING CAPACITY OF SOIL

Increase the depth of foundation

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By draining the soil

• Water content in soil will decreases its bearing capacity
• By draining sandy soil and gravel by gravity pipe drainage system- improve bearing capacity

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By compacting the soil

^♣ Reduces the open spaces between the individual particles

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By grouting

Cement mortar can be injected under pressure into the subsoil to seal off voids in between subsoil and foundation.

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By confining the soil

• Sheet piles are driven around the structure to form an enclosure
• Which will prevent the movement of soil.

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Chemical treatment

• Chemical solution are injected under pressure into the soil
• Forms a gel and keep soil particles together to form a compact mass.

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By grouting

^♣ Cement mortar can be injected under pressure into the subsoil to seal off voids in between subsoil and foundation.

FIELD TESTS: CALCULATION BASED ON ENGINEERING PROPERTIES

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Shear tests: measuring shear strength of soil

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Triaxial test : measurement of shear strength in all three dimensions

^♣ Consolidation test: expulsion of water under static sustained load.

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Settlement Analysis: analysis of load bearing based on settlement of soil.