SHALLOW FOUNDATION

D
SHALLOW FOUNDATION
MADE BY : MISS.DHARA DATTANI
(ME TRANSPORTATAION)
LECTURER AT ATMIYA INSTITUTE OF TECHNOLOGY AND SCIENCE FOR
DIPLOMA STUDIES,RAJKOT.GUJRAT,INDIA.
1
CONTENTS
 Definitions
 Design criteria
 Methods to determine bearing capacity
 Modes of failures
 Effect of eccentric loading
 Settlement of foundation
 Bearing capacity of raft and its factor affecting
 Floating foundation
 Contact pressure
2
Bearing Capacity Of Shallow
Foundation
 * A foundation is required for distributing the loads of the
superstructure on a large area.
 * The foundation should be designed such that
 a) The soil below does not fail in shear
 b) Settlement is within the safe limits.
3
1. FOOTING :
 Lowest part of foundation of the structure that transmits loads directly to soil
2. FOUNDATION
 It is a part of structure that transmits the load of super structure to the ground
3. BEARING CAPACITY
 Load carrying capacity of foundation soil
 Expressed as load per unit area kN/m2
4. GROSS BEARING CAPACITY : (q)
 Total pressure acting on the base of footing including weight of superstructure
,self weight of footing and weight of fill over the footing called as gross bearing
capacity
4
5. NET BEARING CAPACITY : (qN)
 It is defined as gross bearing capacity minus the original overburden pressure
at the foundation level. qn =q-Y *D
6. ULTIMATE BEARING CAPACITY (qu):
 It is defined as the gross pressure at the base of foundation at which the soil
fails in the shear
7. NET ULTIMATE BEARING CAPACITY(qnu) :
 It is defined as a net pressure in excess of the surcharge pressure at which soil
fails in shear. It is equal to gross pressure minus surcharge pressure.
5
qnu = qu – γ ∗ 𝐷
8. NET SAFE BEARING CAPACITY : (qns)
 It is defined as the maximum load per unit area in excess of surcharge pressure
which the foundation soil or bed can carry safely load without risk or shear
failure.
 Where, f= Factor of safety taken as 2 to 5.
9. Safe Bearing Capacity: (qs)
 It is the maximum gross pressure which the soil can carry safely load without
shear failure. It is equal to net bearing capacity plus the original over burden
pressure.
6
qnx=
𝑞𝑛𝑢
𝐹
qs=
𝒒𝒏𝒖
𝑭
+ γ ∗ 𝐷
10. Allowable Bearing Capacity : (qa)
 It is the net loading intensity at which the foundation soil
neither fails in shear nor there is excessive settlement ,to the
structure.
7
2. DESIGN CRITERIA
 For A Satisfactory Performance, A Foundation Must
Be Following Criteria :
1. Location & Depth Criteria
2. Shear or Bearing Failure Criteria
3. Settlement Criteria
8
1 . LOCATION AND DEPTH CRITERIA
 Foundation must be properly located and at a desired depth that its
performance not affected by factors such as,
 Lateral expulsion of soil from beneath the foundation
 Seasonal volume changes caused by freezing and thawing
2. SHEAR OR BEARING FAILURE CRITERIA
 It is associated with plastic flow of the soil material beneath the foundation,
and lateral expulsion of the soil from underneath the foundation.
 A adequate factor of safety is provided to preclude the bearing capacity
failure.
3. SETTLEMENT CRITERIA
 The settlement of the foundation, especially the differential settlement
must be in permissible limits. Excessive settlement may affect the utility
of structure, spoil the appearance of structure and also damages the
structure.
9
Methods of determining the bearing
capacity
 Methods of determining the bearing capacity
10
A) I.S.CODE
METHOD
(I.S.:1904-1978)
BEARING CAPACITY
TABLES IN VARIOUS
BUILDING CODES
B) ANALYTICAL
METHOD
1.PRANDTL’S
ANALYSIS
2. RANKINE’S
ANALYSIS
3. TERZAGI’S
METHOD
4.SKEMPTON THEORY
C) FIELD TEST
METHOD
1. PLATE LOAD TEST
2. SPT
3. SCPT
4. DCPT
5. PRESSURE METER
Prandtl’s Analysis
 This theory is used to determine the ultimate bearing capacity of soil.
 The analysis is based on assumptions that a strip footing placed on ground
surface sinks vertically downwards direction in to soil as failure, like a punch.
 Fig shows failure zones developed below footing
 Zone-1 : immediately under footing subjected with compressive stress.
 Zone -2: exerts pressure on side zones II and III
 Soil in zone II assumed as in plastic equilibrium
 Zone II pushes zone III upwards
11
12
 So prandtls gave an expression for ultimate bearing capacity
for a strip footing using theory of plasticity.
 He assumed curved path of a slip surface of the shape of logarithmic spiral.
 For purely cohesive soils(ø=0),the spiral becomes circular arc and prandtls analysis
gives the equation :
c=cohesion of the soil.
 For cohesion less soil prandtls theory shows that UBC(ultimate bearing capacity)
increases with the width B
 For cohesive soil of strip footing the,
 It is only applicable for footing with perfectly smooth base, but in actual footing have
rough surface so theory does not gives exact results
13
qu=(π+2)c= 5.14*c
qu= 5.14 c + γ ∗ 𝐷
Rankine’s analysis
 Rankine considered the plastic equilibrium of two soil elements ,one below
the footing
 (element-I) and the other just outside the footing (element-II) at the base
level of the foundation
14
 When the load on the footing increases and approaches a value of qu, a state of
plastic equilibrium is reached under the footing i.e. element I is on the verge of
failure. For element I the vertical stress is the major principal stress ( σ1) and
lateral stress is minor principal stress ( σ3 ).on the other hand , for element II, the
lateral stress is major principal and vertical is minor principal stress.
 For the shear failure of element I, element II must fail by lateral thrust from
Element-1,during the state of shear failure the following principal stress relationship
exist,
 Tan2 α + 2c tan α
For cohesionless soil c=0
σ1= σ3 tan2 α
 for element II =
Tan2 α + 2c tan α
σ3 = σv = 𝛾 ∗ 𝐷 Tan2 α
15
 For element I
σ3 = σh = σ1 of the element II
= γ ∗ 𝐷 Tan2 α
σ1= σ3 tan2 α
= γ ∗ 𝐷 Tan2 (Tan2 α)
= γ ∗ 𝐷 Tan4 α
But qu = γ ∗DTan4 α
tan2 α =
1+𝑠𝑖𝑛ø
1−𝑠𝑖𝑛ø
16
qu= γ ∗ 𝐷
1+𝑠𝑖𝑛ø
1−𝑠𝑖𝑛ø
 Minimum depth of foundation obtained by
q= intensity of loading at the base of foundation.
17
Dmin =
q
𝛾
[
1+𝑠𝑖𝑛ø
1−𝑠𝑖𝑛ø
]
MODES OF SHEAR FAILURE
 When horizontal strip footing resisting on the earth surface,
homogeneous soil is subjected to a gradually increasing load,
characteristic load settlement curves are obtained. The load
settlement behaviour is found to be related to the soil
characteristic.
 Three types of failure are considered:
1. GENERAL SHEAR FAILURE
2. LOCAL SHEAR FAILURE
3. PUNCHING SHEAR FAILURE
18
General shear failure
 If the soil properties are such that as the footing is loaded to failure a
slight downward movement of the footing develops the fully plastic zone
due to which the entire soil along a slip surface fails in shear and the soil is
bulges out on the sides of the footing , this type of failure is called General
shear failure.
 It usually occurs in dense sand or stiff clay.

19
Local shear failure
 If the soil properties are such that before the plastic zone are fully developed , large
deformation occur immediately below the footing resulting in the shear failure of the
soil in the potion just below footing is called a Local shear failure
 The local shear failure usually occurs in the case of sand or clayey soils of medium
compaction
20
Punching shear failure
 It occurs when there is a high compression of soil under the
footing,accompanied by shearing in the vertical direction around the
edges of the footing. It is slightly inclined and never reaches to the ground
surface. There is no tilting of the footing.
 It is mainly occurred in loose or soft clay.
21
Terzagi’s bearing capacity theory
 In 1943 terzagi gave an assumption on bearing capacity of soil
Assumptions :
 The footing is long : i.e. L/B ratio is infinite
 The base of footing is rough
 The footing is laid at shallow depth i.e. D<B
 The load on footing is vertical and load is uniformly distributed
 The shear strength of the base is neglected
 Soil above the base is neglected by surcharge pressure
 The shear strength of the soil is governed by mohr-Columbus equation.
22
23TERZAGI ANALYSIS IMAGE OF STRIP FOOTING
 Strip footing of width B subjected to the loading intensity qu to cause failure
 The footing is shallow i.e. the depth D of the footing is equal to or less than width of
the footing
 According to the terzagi the loaded soil fails along the composite surface FGCDE as
shown in fig. this region can be divide into five zones:
 Zone I, called zone of elastic equilibrium(ABC)
 Zone II, called zone of radial shear
 Zone III, called zone of linear shear
 When the base of the footing AB sinks into the ground zone I wedge shaped
immediately beneath the footing is prevented from undergoing any lateral yield by
friction and cohesion between the soil and the base of the footing
 Thus zone I remains in state of elastic equilibrium and it acts as if it were the part of
footing
 Its boundaries assumed as plane surface rising at an angle with the horizontal
24
 Zone II (BCD and ACG) are called the zones
of radial shear, because the lines that
constitute one set of shear pattern are
straight radial lines which radiate from the
outer edges of the base of the footing,
while the lines of the other set are
logarithm spirals with their centres located
at the outer edge of the base of the
footing. Thus the boundaries AC,AG,BC and
BD of these zones are the plane surfaces
while the boundaries CG and CD are the
arcs of a logarithm spiral
 Zone III AFG,BDE are called the zones of
linear shear and are triangular in shape.
These are passive rankine zone with their
boundaries making an angle
with the horizontal
25
45 −
∅
2
 It is assumed that the failure do not extend above the horizontal plane
passing through base of the footing. This implies that the shear resistance
of the soil lying above the horizontal plane passing through the base of
footing is neglected, and the effect of the soil above the plane is taken
equivalent to a surcharge pressure
 The application of the zone surface qu on the footing tends to push the
wedge of soil ABC into the ground with lateral displacement of zones II
and III, but this lateral displacement is resisted by forces on the plane AC
and BC
26
 For ultimate bearing capacity of soil for strip footing
qu=c*Nc+ γ ∗ 𝐷*Nq+0.5 γ*B*N
 Where,
qu= UBC in kN/m2
C= cohesion/m2
γ = unit weight of soil kN/m3
D= depth of footing (m)
B= width of footing(m)
Nc,Nq,Ny = terzagi bearing capacity factors
Nc’,Nq’,Ny’ depends on the angle of shearing resistance( ø )of the soil.
27
 Nq=
𝑎2
2 cos 2 (45+
∅
2
)
a= 𝑒(
3𝜋
4 −
∅
2
) tanø
 Nc= [Nq-1]cotø
 Ny=
𝑡𝑎𝑛∅
2
[
𝐾𝑝
𝑐𝑜𝑠2ø
- 1]
 Kp= passive earth pressure depending upon ø
28
 For cohesiveless soil ø=0
 Nc=1.5π+1=5.7
 Nq=1
 Ny=0
 Thus, for strip footing
 qu=5.7c+ γ*D
 If footing located at ground surface D=0
 qu=5.7c
29
 Equation for local for shear failure for strip footing can be written as
When local shear failure ø<29
qu=
2
3
* C*Nc’+ γ ∗ 𝐷*Nq’+0.5 γ*BN γ’
Nc’,Nq’,Ny’ depends on the angle of shearing resistance( ø )of the soil.
Or equal to ø’
30
 Terzagi gave different equations for different footing
 Square footing:
 qu= 1.3cNc+ γ ∗ 𝐷*Nq+0.4 γ*B*Ny
 B= dimension of side of footing
 Circular footing
 qu= 1.3c*Nc+ γ ∗ 𝐷*Nq+0.3 γ*B*Ny
 B= diameter of footing
Rectangular footing
qu= 1.3cNc ( 1+ 0.3
𝐵
𝐿
) + γ*D*Nq+0.5 γ*B*Nγ ( 1 – 0.2
𝐵
𝐿
)
B= width or diameter
L= length of footing
31
EFFECT OF WATER TABLE ON BEARING
CAPACITY
Terzagi assumed the water table is at greater depth. If the W.T. is located
close to the foundation ,the bearing capacity equation written as follows :
qu=c.Nc+ γ1*D*Nq*Rw1+0.5 γ2*B*N γ*Rw2
Where,
Rw1 and Rw2 are the reduction factors for the water table
γ1= average unit weight of the surcharge soil situated above water table
γ2=avg unit weight of the soil in the wedge zone, situated within the depth
below the footing.
32
33
 Case 1 Water table above the base of footing
 Rw1 = 0.5 [ 1+
𝑍𝑤1
𝐷
]
 Rw2=0.5
 Case 2: Water table below the base of footing
 Rw1 = 1
 Rw2 = 0.5[ 1+
𝑍𝑤2
𝐷
]
 Case 3: when water table at a depth equal to or greater than the width of
footing below the base of foundation
 Rw1=1
 Rw2= 1
34
Skempton’s analysis
 Skempton’s analysis used for purely cohesive soil ø=0
 And for purely saturated soil
 Can be used for shallow footing as well as deep footing
 For pure cohesive soil :
 qu=c*Nc+ γ ∗ 𝐷*Nq+0.5 γ*B*N.. Given by terzagi
 ø=0
 Nq=1
 Nc=0
35
 As per skempton UBC= cNc+ Qu=c*Nc+γ*D
 The Net.U.B.C
 qnu= qu- γ ∗D
 Different shape of footing:
(A) STRIP FOOTING:
Nc=5[1+0.2 [
𝐷
𝐵
]
If Nc value is greater than 7.5 , take Nc=7.5
(B) Square or Circular Footing:
Nc=6[1+0.2 [
𝐷
𝐵
]
If Nc is greater than 9.0 take Nc=9
B= square of footing or dia of footing
36
 Rectangular footing :
 For
𝐷
𝐵
< 2.5
 Nc=5[1+0.2 [
𝐷
𝐵
] +[1+0.2 [
𝐷
𝐵
]
 For
𝐷
𝐵
> 2.5
 Nc=7.5[1+0.2 [
𝐵
𝐿
]
 Where,
 B= width of rectangular footing
 L= Length of rectangular footing
37
I.S. Code Method
 As per the Is-code 6403-1981:
 qnu= cNc*Sc*dc*ic+q(Nq-1)Sq*dq*iq+0.5 γBN γ*S γd γi γW’
 Nc*Sc*dc*ic+q(Nq-1)Sq*dq*iq+0.5 γBN γS γd γ i γ W’
 Where, dc,dq,dγ= depth factors
 Iq,ic,iγ= inclination factors
 Nc,Nq,Nγ= bearing factors recommended by Vesic (1973)
 q= effective pressure at base
 qnu= qu- γ*D
=qu-q
 All notation defined earlier.
38
 When W.t. is at below depth W’=1.0
 If above W’=0.5
 If same size or equal to depth
 W’=0.5[1+
𝑍𝑤2
𝐵
]
39
Settlement of Foundation
 A geotechnical engineer is called upon to predict the magnitude of
settlement and rate of settlement of foundation due to structural loads
 There are mainly three types of settlements
1. Immediate settlement
2. primary consolidation
3. Secondary consolidation
40
Immediate settlement
 When a partially saturated soil mass is subjected to external loads, a
decrease in volume occurs due to expulsion and compression of air in the
voids.
 Decrease in volume of soil mass due to compression of solid particles
called as immediate or initial settlement
41
Primary consolidation (sp)
 After the initial consolidation, further reduction in volume of soil mass due
to expulsion of water from air voids, called as Primary consolidation.
 In fine grained soil, sp occurs for long time where as in coarse grain soil it
takes less time due to high permeability.
42
Secondary consolidation
 The reduction in volume continues at a very slow rate even after the excess
pore water pressure developed by the applied pressure is fully dissipated
and the primary consolidation is complete.
 This reduction in volume called as Secondary consolidation.
 This settlements are important for peats and soft organic clay
 Settlement is expressed as S= si+sc+ss
43
Sources of settlement of foundation
 Elastic compression of the foundation soil, caused by giving rise to immediate
settlement
 Plastic compression of the foundation soil, caused by loads giving rise to
consolidation settlement of fine grained soils
 Repeated lowering and raising of ground water level in granular loose soils
 Under ground erosion may cause cavity in subsoil which collapse and cause
settlement
 Seasonal swelling and shrinkage and expansion of soil
 Vibrations due to pile driving
 Surface erosion
 landslides
44
 Due to some minerals in soil example-non cohesive soil,gypsum,may result
the settlement of foundation and alsoresponsible for the intergranulars
bond of soil
 Frost heave occurs if the structure is not found below the depth of frost
penetration,when thaw occurs the foundation may settle
45
Bearing capacity of Raft
 A mat or raft foundation is a thick reinforced concrete slab which supports
all the load of bearing walls columns of structure etc.
 When raft should be provided?
 Soil pressure is low
 Loads of structure are heavy
 When columns and walls are so close to structure that individual footing
would overlap
 When there is large variation of load in individual columns
 When soil is non homogeneous and also when differential settlements
chances are more.
46
FACTORS AFFECTING BEARING
CAPACITY
 Position of ground water table
 Relative density or angle of shearing resistance
 Width of footing
 Depth of footing
 Unit weight of soil
 Eccentricity of load
47
Floating Foundation
 Floating foundation is defined as foundation in which the weight of the
building is approximately equal to the full weight of soil and water
removed from the site of the building
48
 The principle of floating foundation is explained that a horizontal ground
surface with a horizontal water table at a depth Dw below the ground
surface shows an excavation made in groundto a depth D where D>dw ,fig
shows that structure built in an excavation and completely filling it.
 If the weight of the building is equal to weight of soil and water removed
from the excavation ,then it is evident that the total vertical pressure in the
soil below depth D is same as before excavation
 Since the water level has not changed neutral pressure and effective
pressure are therefore unchanged. Since the settlements caused by an
increase in vertical pressure the building will not settle at all.
49
FLOATING FOUNDATION
Example 1 Example 2
While dealing with floating foundation two type of soil are there:
Soil type -1
Shear failure will not occur but settlements or differential settlements will
occur due to building loads.
Soil type 2 :
Shear strength of foundation is low that the rupture of the soil would occur if
the building were founded at ground level
In absence of strong layer at a reasonable depth, the building can only built
on a floating foundation which reduces the shear stresses to an acceptable
value. Solving this problem solves the settlement problem
51
FLOATING FOUNDATION
 Floating foundation was a necessary innovation in
the development of tall buildings in the wet soil
of Chicago in the 19th century, floating foundation
was developed by John Wellborn Root.
Contact pressure
 A vertical pressure acting at the surface of the contact between the base of
footing and the underlying soil mass.
 In design it is assumed that the load on footing is uniform also the
distribution of contact pressure is uniform
 However this assumption is no always valid, because it depends on elastic
properties of underlying soil mass.
53
Contact pressure on saturated clay
 It shows the qualitative contact pressure distribution under flexible and
rigid footing resting on a saturated clay and subjected to uniformly
distributed load q. when the footing is flexile it deforms into shape of a
bowl, with the maximum deflection at the centre.
 If the footing is rigid the settlement is uniform.
 The contact pressure is more at the centre and maximum deflection at the
edges
54
55
Contact pressure on sand
in this footing edges of flexible footing undergo a large settlement than at
centre.
The soil at the centre is confined and has large modulus of elasticity and
deflects less for the same contact pressure. The contact pressure is uniform.
In case of rigid footing settlement is uniform. the cp increases from zero at
the edges to a maximum at centre.
56
PLATE LOAD TEST
 Plate load test is a field test, used to determine the ultimate bearing
capacity of soil
 the probable settlement under a given load.
 design of shallow foundation.
 For performing this test, the plate is placed at the desired depth, then the
load is applied gradually and the settlement for each increment of load is
recorded.
 At one point a settlement occurs at a rapid rate, the total load up to that
point is calculated and divided by the area of the plate to determine
the ultimate bearing capacity of soil at that depth. The ultimate bearing
capacity is then divided by a safety factor (typically 2.5~3) to determine
the safe bearing capacity
57
Plate load test 58
Plate Load Test Equipment
 The following apparatus is necessary for performing plate load test.
 Test plate
 Hydraulic jack & pump
 Reaction beam or reaction truss
 Dial gauges
 Pressure gauge
 Loading columns
 Necessary equipment for loading platform.
 Tripod, Plumb bob, spirit level etc
59
Plate Load Test Procedure
 The necessary steps to perform plate load test is written below-
 Excavate test pit up to the desired depth. The pit size should be at least 5 times the size
of the test plate (Bp).
 At the center of the pit, a small hole or depression is created. Size of the hole is same as
the size of the steel plate. The bottom level of the hole should correspond to the level of
actual foundation. The depth of the hole is created such that the ratio of the depth to
width of the hole is equal to the ratio of the actual depth to actual width of the
foundation.
 A mild steel plate is used as load bearing plate whose thickness should be at least 25
mm thickness and size may vary from 300 mm to 750 mm. The plate can be square or
circular. Generally, a square plate is used for square footing and a circular plate is used
for circular footing.
 A column is placed at the center of the plate. The load is transferred to the plate
through the centrally placed column.
 The load can be transferred to the column either by gravity loading method or by truss
method.
60
 For gravity loading method a platform is constructed over the column and
load is applied to the platform by means of sandbags or any other dead
loads. The hydraulic jack is placed in between column and loading
platform for the application of gradual loading. This type of loading is
called reaction loading.
 At least two dial gauges should be placed at diagonal corners of the plate
to record the settlement. The gauges are placed on a platform so that it
does not settle with the plate.
 Apply seating load of .7 T/m2 and release before the actual loading starts.
61
Plate Load Test Procedure
 The initial readings are noted.
 The load is then applied through hydraulic jack and increased gradually. The
increment is generally one-fifth of the expected safe bearing capacity or one-
tenth of the ultimate bearing capacity or any other smaller value. The applied
load is noted from pressure gauge.
 The settlement is observed for each increment and from dial gauge. After
increasing the load-settlement should be observed after 1, 4, 10, 20, 40 and 60
minutes and then at hourly intervals until the rate of settlement is less than .02
mm per hour. The readings are noted in tabular form.
 After completing of the collection of data for a particular loading, the next load
increment is applied and readings are noted under new load. This increment
and data collection is repeated until the maximum load is applied. The
maximum load is generally 1.5 times the expected ultimate load or 3 times of
the expected allowable bearing pressure.
62
Plate Load Test Procedure
Limitation of plate load test
 Base plate not less than 30cm not more than 75cm
 Soil should be homogeneous, if not then results are incorrect
 Suitable for cohesionless soil
 It will give immediate settlement
63
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SHALLOW FOUNDATION

  • 1. SHALLOW FOUNDATION MADE BY : MISS.DHARA DATTANI (ME TRANSPORTATAION) LECTURER AT ATMIYA INSTITUTE OF TECHNOLOGY AND SCIENCE FOR DIPLOMA STUDIES,RAJKOT.GUJRAT,INDIA. 1
  • 2. CONTENTS  Definitions  Design criteria  Methods to determine bearing capacity  Modes of failures  Effect of eccentric loading  Settlement of foundation  Bearing capacity of raft and its factor affecting  Floating foundation  Contact pressure 2
  • 3. Bearing Capacity Of Shallow Foundation  * A foundation is required for distributing the loads of the superstructure on a large area.  * The foundation should be designed such that  a) The soil below does not fail in shear  b) Settlement is within the safe limits. 3
  • 4. 1. FOOTING :  Lowest part of foundation of the structure that transmits loads directly to soil 2. FOUNDATION  It is a part of structure that transmits the load of super structure to the ground 3. BEARING CAPACITY  Load carrying capacity of foundation soil  Expressed as load per unit area kN/m2 4. GROSS BEARING CAPACITY : (q)  Total pressure acting on the base of footing including weight of superstructure ,self weight of footing and weight of fill over the footing called as gross bearing capacity 4
  • 5. 5. NET BEARING CAPACITY : (qN)  It is defined as gross bearing capacity minus the original overburden pressure at the foundation level. qn =q-Y *D 6. ULTIMATE BEARING CAPACITY (qu):  It is defined as the gross pressure at the base of foundation at which the soil fails in the shear 7. NET ULTIMATE BEARING CAPACITY(qnu) :  It is defined as a net pressure in excess of the surcharge pressure at which soil fails in shear. It is equal to gross pressure minus surcharge pressure. 5 qnu = qu – γ ∗ 𝐷
  • 6. 8. NET SAFE BEARING CAPACITY : (qns)  It is defined as the maximum load per unit area in excess of surcharge pressure which the foundation soil or bed can carry safely load without risk or shear failure.  Where, f= Factor of safety taken as 2 to 5. 9. Safe Bearing Capacity: (qs)  It is the maximum gross pressure which the soil can carry safely load without shear failure. It is equal to net bearing capacity plus the original over burden pressure. 6 qnx= 𝑞𝑛𝑢 𝐹 qs= 𝒒𝒏𝒖 𝑭 + γ ∗ 𝐷
  • 7. 10. Allowable Bearing Capacity : (qa)  It is the net loading intensity at which the foundation soil neither fails in shear nor there is excessive settlement ,to the structure. 7
  • 8. 2. DESIGN CRITERIA  For A Satisfactory Performance, A Foundation Must Be Following Criteria : 1. Location & Depth Criteria 2. Shear or Bearing Failure Criteria 3. Settlement Criteria 8
  • 9. 1 . LOCATION AND DEPTH CRITERIA  Foundation must be properly located and at a desired depth that its performance not affected by factors such as,  Lateral expulsion of soil from beneath the foundation  Seasonal volume changes caused by freezing and thawing 2. SHEAR OR BEARING FAILURE CRITERIA  It is associated with plastic flow of the soil material beneath the foundation, and lateral expulsion of the soil from underneath the foundation.  A adequate factor of safety is provided to preclude the bearing capacity failure. 3. SETTLEMENT CRITERIA  The settlement of the foundation, especially the differential settlement must be in permissible limits. Excessive settlement may affect the utility of structure, spoil the appearance of structure and also damages the structure. 9
  • 10. Methods of determining the bearing capacity  Methods of determining the bearing capacity 10 A) I.S.CODE METHOD (I.S.:1904-1978) BEARING CAPACITY TABLES IN VARIOUS BUILDING CODES B) ANALYTICAL METHOD 1.PRANDTL’S ANALYSIS 2. RANKINE’S ANALYSIS 3. TERZAGI’S METHOD 4.SKEMPTON THEORY C) FIELD TEST METHOD 1. PLATE LOAD TEST 2. SPT 3. SCPT 4. DCPT 5. PRESSURE METER
  • 11. Prandtl’s Analysis  This theory is used to determine the ultimate bearing capacity of soil.  The analysis is based on assumptions that a strip footing placed on ground surface sinks vertically downwards direction in to soil as failure, like a punch.  Fig shows failure zones developed below footing  Zone-1 : immediately under footing subjected with compressive stress.  Zone -2: exerts pressure on side zones II and III  Soil in zone II assumed as in plastic equilibrium  Zone II pushes zone III upwards 11
  • 12. 12
  • 13.  So prandtls gave an expression for ultimate bearing capacity for a strip footing using theory of plasticity.  He assumed curved path of a slip surface of the shape of logarithmic spiral.  For purely cohesive soils(ø=0),the spiral becomes circular arc and prandtls analysis gives the equation : c=cohesion of the soil.  For cohesion less soil prandtls theory shows that UBC(ultimate bearing capacity) increases with the width B  For cohesive soil of strip footing the,  It is only applicable for footing with perfectly smooth base, but in actual footing have rough surface so theory does not gives exact results 13 qu=(π+2)c= 5.14*c qu= 5.14 c + γ ∗ 𝐷
  • 14. Rankine’s analysis  Rankine considered the plastic equilibrium of two soil elements ,one below the footing  (element-I) and the other just outside the footing (element-II) at the base level of the foundation 14
  • 15.  When the load on the footing increases and approaches a value of qu, a state of plastic equilibrium is reached under the footing i.e. element I is on the verge of failure. For element I the vertical stress is the major principal stress ( σ1) and lateral stress is minor principal stress ( σ3 ).on the other hand , for element II, the lateral stress is major principal and vertical is minor principal stress.  For the shear failure of element I, element II must fail by lateral thrust from Element-1,during the state of shear failure the following principal stress relationship exist,  Tan2 α + 2c tan α For cohesionless soil c=0 σ1= σ3 tan2 α  for element II = Tan2 α + 2c tan α σ3 = σv = 𝛾 ∗ 𝐷 Tan2 α 15
  • 16.  For element I σ3 = σh = σ1 of the element II = γ ∗ 𝐷 Tan2 α σ1= σ3 tan2 α = γ ∗ 𝐷 Tan2 (Tan2 α) = γ ∗ 𝐷 Tan4 α But qu = γ ∗DTan4 α tan2 α = 1+𝑠𝑖𝑛ø 1−𝑠𝑖𝑛ø 16 qu= γ ∗ 𝐷 1+𝑠𝑖𝑛ø 1−𝑠𝑖𝑛ø
  • 17.  Minimum depth of foundation obtained by q= intensity of loading at the base of foundation. 17 Dmin = q 𝛾 [ 1+𝑠𝑖𝑛ø 1−𝑠𝑖𝑛ø ]
  • 18. MODES OF SHEAR FAILURE  When horizontal strip footing resisting on the earth surface, homogeneous soil is subjected to a gradually increasing load, characteristic load settlement curves are obtained. The load settlement behaviour is found to be related to the soil characteristic.  Three types of failure are considered: 1. GENERAL SHEAR FAILURE 2. LOCAL SHEAR FAILURE 3. PUNCHING SHEAR FAILURE 18
  • 19. General shear failure  If the soil properties are such that as the footing is loaded to failure a slight downward movement of the footing develops the fully plastic zone due to which the entire soil along a slip surface fails in shear and the soil is bulges out on the sides of the footing , this type of failure is called General shear failure.  It usually occurs in dense sand or stiff clay.  19
  • 20. Local shear failure  If the soil properties are such that before the plastic zone are fully developed , large deformation occur immediately below the footing resulting in the shear failure of the soil in the potion just below footing is called a Local shear failure  The local shear failure usually occurs in the case of sand or clayey soils of medium compaction 20
  • 21. Punching shear failure  It occurs when there is a high compression of soil under the footing,accompanied by shearing in the vertical direction around the edges of the footing. It is slightly inclined and never reaches to the ground surface. There is no tilting of the footing.  It is mainly occurred in loose or soft clay. 21
  • 22. Terzagi’s bearing capacity theory  In 1943 terzagi gave an assumption on bearing capacity of soil Assumptions :  The footing is long : i.e. L/B ratio is infinite  The base of footing is rough  The footing is laid at shallow depth i.e. D<B  The load on footing is vertical and load is uniformly distributed  The shear strength of the base is neglected  Soil above the base is neglected by surcharge pressure  The shear strength of the soil is governed by mohr-Columbus equation. 22
  • 23. 23TERZAGI ANALYSIS IMAGE OF STRIP FOOTING
  • 24.  Strip footing of width B subjected to the loading intensity qu to cause failure  The footing is shallow i.e. the depth D of the footing is equal to or less than width of the footing  According to the terzagi the loaded soil fails along the composite surface FGCDE as shown in fig. this region can be divide into five zones:  Zone I, called zone of elastic equilibrium(ABC)  Zone II, called zone of radial shear  Zone III, called zone of linear shear  When the base of the footing AB sinks into the ground zone I wedge shaped immediately beneath the footing is prevented from undergoing any lateral yield by friction and cohesion between the soil and the base of the footing  Thus zone I remains in state of elastic equilibrium and it acts as if it were the part of footing  Its boundaries assumed as plane surface rising at an angle with the horizontal 24
  • 25.  Zone II (BCD and ACG) are called the zones of radial shear, because the lines that constitute one set of shear pattern are straight radial lines which radiate from the outer edges of the base of the footing, while the lines of the other set are logarithm spirals with their centres located at the outer edge of the base of the footing. Thus the boundaries AC,AG,BC and BD of these zones are the plane surfaces while the boundaries CG and CD are the arcs of a logarithm spiral  Zone III AFG,BDE are called the zones of linear shear and are triangular in shape. These are passive rankine zone with their boundaries making an angle with the horizontal 25 45 − ∅ 2
  • 26.  It is assumed that the failure do not extend above the horizontal plane passing through base of the footing. This implies that the shear resistance of the soil lying above the horizontal plane passing through the base of footing is neglected, and the effect of the soil above the plane is taken equivalent to a surcharge pressure  The application of the zone surface qu on the footing tends to push the wedge of soil ABC into the ground with lateral displacement of zones II and III, but this lateral displacement is resisted by forces on the plane AC and BC 26
  • 27.  For ultimate bearing capacity of soil for strip footing qu=c*Nc+ γ ∗ 𝐷*Nq+0.5 γ*B*N  Where, qu= UBC in kN/m2 C= cohesion/m2 γ = unit weight of soil kN/m3 D= depth of footing (m) B= width of footing(m) Nc,Nq,Ny = terzagi bearing capacity factors Nc’,Nq’,Ny’ depends on the angle of shearing resistance( ø )of the soil. 27
  • 28.  Nq= 𝑎2 2 cos 2 (45+ ∅ 2 ) a= 𝑒( 3𝜋 4 − ∅ 2 ) tanø  Nc= [Nq-1]cotø  Ny= 𝑡𝑎𝑛∅ 2 [ 𝐾𝑝 𝑐𝑜𝑠2ø - 1]  Kp= passive earth pressure depending upon ø 28
  • 29.  For cohesiveless soil ø=0  Nc=1.5π+1=5.7  Nq=1  Ny=0  Thus, for strip footing  qu=5.7c+ γ*D  If footing located at ground surface D=0  qu=5.7c 29
  • 30.  Equation for local for shear failure for strip footing can be written as When local shear failure ø<29 qu= 2 3 * C*Nc’+ γ ∗ 𝐷*Nq’+0.5 γ*BN γ’ Nc’,Nq’,Ny’ depends on the angle of shearing resistance( ø )of the soil. Or equal to ø’ 30
  • 31.  Terzagi gave different equations for different footing  Square footing:  qu= 1.3cNc+ γ ∗ 𝐷*Nq+0.4 γ*B*Ny  B= dimension of side of footing  Circular footing  qu= 1.3c*Nc+ γ ∗ 𝐷*Nq+0.3 γ*B*Ny  B= diameter of footing Rectangular footing qu= 1.3cNc ( 1+ 0.3 𝐵 𝐿 ) + γ*D*Nq+0.5 γ*B*Nγ ( 1 – 0.2 𝐵 𝐿 ) B= width or diameter L= length of footing 31
  • 32. EFFECT OF WATER TABLE ON BEARING CAPACITY Terzagi assumed the water table is at greater depth. If the W.T. is located close to the foundation ,the bearing capacity equation written as follows : qu=c.Nc+ γ1*D*Nq*Rw1+0.5 γ2*B*N γ*Rw2 Where, Rw1 and Rw2 are the reduction factors for the water table γ1= average unit weight of the surcharge soil situated above water table γ2=avg unit weight of the soil in the wedge zone, situated within the depth below the footing. 32
  • 33. 33
  • 34.  Case 1 Water table above the base of footing  Rw1 = 0.5 [ 1+ 𝑍𝑤1 𝐷 ]  Rw2=0.5  Case 2: Water table below the base of footing  Rw1 = 1  Rw2 = 0.5[ 1+ 𝑍𝑤2 𝐷 ]  Case 3: when water table at a depth equal to or greater than the width of footing below the base of foundation  Rw1=1  Rw2= 1 34
  • 35. Skempton’s analysis  Skempton’s analysis used for purely cohesive soil ø=0  And for purely saturated soil  Can be used for shallow footing as well as deep footing  For pure cohesive soil :  qu=c*Nc+ γ ∗ 𝐷*Nq+0.5 γ*B*N.. Given by terzagi  ø=0  Nq=1  Nc=0 35
  • 36.  As per skempton UBC= cNc+ Qu=c*Nc+γ*D  The Net.U.B.C  qnu= qu- γ ∗D  Different shape of footing: (A) STRIP FOOTING: Nc=5[1+0.2 [ 𝐷 𝐵 ] If Nc value is greater than 7.5 , take Nc=7.5 (B) Square or Circular Footing: Nc=6[1+0.2 [ 𝐷 𝐵 ] If Nc is greater than 9.0 take Nc=9 B= square of footing or dia of footing 36
  • 37.  Rectangular footing :  For 𝐷 𝐵 < 2.5  Nc=5[1+0.2 [ 𝐷 𝐵 ] +[1+0.2 [ 𝐷 𝐵 ]  For 𝐷 𝐵 > 2.5  Nc=7.5[1+0.2 [ 𝐵 𝐿 ]  Where,  B= width of rectangular footing  L= Length of rectangular footing 37
  • 38. I.S. Code Method  As per the Is-code 6403-1981:  qnu= cNc*Sc*dc*ic+q(Nq-1)Sq*dq*iq+0.5 γBN γ*S γd γi γW’  Nc*Sc*dc*ic+q(Nq-1)Sq*dq*iq+0.5 γBN γS γd γ i γ W’  Where, dc,dq,dγ= depth factors  Iq,ic,iγ= inclination factors  Nc,Nq,Nγ= bearing factors recommended by Vesic (1973)  q= effective pressure at base  qnu= qu- γ*D =qu-q  All notation defined earlier. 38
  • 39.  When W.t. is at below depth W’=1.0  If above W’=0.5  If same size or equal to depth  W’=0.5[1+ 𝑍𝑤2 𝐵 ] 39
  • 40. Settlement of Foundation  A geotechnical engineer is called upon to predict the magnitude of settlement and rate of settlement of foundation due to structural loads  There are mainly three types of settlements 1. Immediate settlement 2. primary consolidation 3. Secondary consolidation 40
  • 41. Immediate settlement  When a partially saturated soil mass is subjected to external loads, a decrease in volume occurs due to expulsion and compression of air in the voids.  Decrease in volume of soil mass due to compression of solid particles called as immediate or initial settlement 41
  • 42. Primary consolidation (sp)  After the initial consolidation, further reduction in volume of soil mass due to expulsion of water from air voids, called as Primary consolidation.  In fine grained soil, sp occurs for long time where as in coarse grain soil it takes less time due to high permeability. 42
  • 43. Secondary consolidation  The reduction in volume continues at a very slow rate even after the excess pore water pressure developed by the applied pressure is fully dissipated and the primary consolidation is complete.  This reduction in volume called as Secondary consolidation.  This settlements are important for peats and soft organic clay  Settlement is expressed as S= si+sc+ss 43
  • 44. Sources of settlement of foundation  Elastic compression of the foundation soil, caused by giving rise to immediate settlement  Plastic compression of the foundation soil, caused by loads giving rise to consolidation settlement of fine grained soils  Repeated lowering and raising of ground water level in granular loose soils  Under ground erosion may cause cavity in subsoil which collapse and cause settlement  Seasonal swelling and shrinkage and expansion of soil  Vibrations due to pile driving  Surface erosion  landslides 44
  • 45.  Due to some minerals in soil example-non cohesive soil,gypsum,may result the settlement of foundation and alsoresponsible for the intergranulars bond of soil  Frost heave occurs if the structure is not found below the depth of frost penetration,when thaw occurs the foundation may settle 45
  • 46. Bearing capacity of Raft  A mat or raft foundation is a thick reinforced concrete slab which supports all the load of bearing walls columns of structure etc.  When raft should be provided?  Soil pressure is low  Loads of structure are heavy  When columns and walls are so close to structure that individual footing would overlap  When there is large variation of load in individual columns  When soil is non homogeneous and also when differential settlements chances are more. 46
  • 47. FACTORS AFFECTING BEARING CAPACITY  Position of ground water table  Relative density or angle of shearing resistance  Width of footing  Depth of footing  Unit weight of soil  Eccentricity of load 47
  • 48. Floating Foundation  Floating foundation is defined as foundation in which the weight of the building is approximately equal to the full weight of soil and water removed from the site of the building 48
  • 49.  The principle of floating foundation is explained that a horizontal ground surface with a horizontal water table at a depth Dw below the ground surface shows an excavation made in groundto a depth D where D>dw ,fig shows that structure built in an excavation and completely filling it.  If the weight of the building is equal to weight of soil and water removed from the excavation ,then it is evident that the total vertical pressure in the soil below depth D is same as before excavation  Since the water level has not changed neutral pressure and effective pressure are therefore unchanged. Since the settlements caused by an increase in vertical pressure the building will not settle at all. 49
  • 51. While dealing with floating foundation two type of soil are there: Soil type -1 Shear failure will not occur but settlements or differential settlements will occur due to building loads. Soil type 2 : Shear strength of foundation is low that the rupture of the soil would occur if the building were founded at ground level In absence of strong layer at a reasonable depth, the building can only built on a floating foundation which reduces the shear stresses to an acceptable value. Solving this problem solves the settlement problem 51
  • 52. FLOATING FOUNDATION  Floating foundation was a necessary innovation in the development of tall buildings in the wet soil of Chicago in the 19th century, floating foundation was developed by John Wellborn Root.
  • 53. Contact pressure  A vertical pressure acting at the surface of the contact between the base of footing and the underlying soil mass.  In design it is assumed that the load on footing is uniform also the distribution of contact pressure is uniform  However this assumption is no always valid, because it depends on elastic properties of underlying soil mass. 53
  • 54. Contact pressure on saturated clay  It shows the qualitative contact pressure distribution under flexible and rigid footing resting on a saturated clay and subjected to uniformly distributed load q. when the footing is flexile it deforms into shape of a bowl, with the maximum deflection at the centre.  If the footing is rigid the settlement is uniform.  The contact pressure is more at the centre and maximum deflection at the edges 54
  • 55. 55
  • 56. Contact pressure on sand in this footing edges of flexible footing undergo a large settlement than at centre. The soil at the centre is confined and has large modulus of elasticity and deflects less for the same contact pressure. The contact pressure is uniform. In case of rigid footing settlement is uniform. the cp increases from zero at the edges to a maximum at centre. 56
  • 57. PLATE LOAD TEST  Plate load test is a field test, used to determine the ultimate bearing capacity of soil  the probable settlement under a given load.  design of shallow foundation.  For performing this test, the plate is placed at the desired depth, then the load is applied gradually and the settlement for each increment of load is recorded.  At one point a settlement occurs at a rapid rate, the total load up to that point is calculated and divided by the area of the plate to determine the ultimate bearing capacity of soil at that depth. The ultimate bearing capacity is then divided by a safety factor (typically 2.5~3) to determine the safe bearing capacity 57
  • 59. Plate Load Test Equipment  The following apparatus is necessary for performing plate load test.  Test plate  Hydraulic jack & pump  Reaction beam or reaction truss  Dial gauges  Pressure gauge  Loading columns  Necessary equipment for loading platform.  Tripod, Plumb bob, spirit level etc 59
  • 60. Plate Load Test Procedure  The necessary steps to perform plate load test is written below-  Excavate test pit up to the desired depth. The pit size should be at least 5 times the size of the test plate (Bp).  At the center of the pit, a small hole or depression is created. Size of the hole is same as the size of the steel plate. The bottom level of the hole should correspond to the level of actual foundation. The depth of the hole is created such that the ratio of the depth to width of the hole is equal to the ratio of the actual depth to actual width of the foundation.  A mild steel plate is used as load bearing plate whose thickness should be at least 25 mm thickness and size may vary from 300 mm to 750 mm. The plate can be square or circular. Generally, a square plate is used for square footing and a circular plate is used for circular footing.  A column is placed at the center of the plate. The load is transferred to the plate through the centrally placed column.  The load can be transferred to the column either by gravity loading method or by truss method. 60
  • 61.  For gravity loading method a platform is constructed over the column and load is applied to the platform by means of sandbags or any other dead loads. The hydraulic jack is placed in between column and loading platform for the application of gradual loading. This type of loading is called reaction loading.  At least two dial gauges should be placed at diagonal corners of the plate to record the settlement. The gauges are placed on a platform so that it does not settle with the plate.  Apply seating load of .7 T/m2 and release before the actual loading starts. 61 Plate Load Test Procedure
  • 62.  The initial readings are noted.  The load is then applied through hydraulic jack and increased gradually. The increment is generally one-fifth of the expected safe bearing capacity or one- tenth of the ultimate bearing capacity or any other smaller value. The applied load is noted from pressure gauge.  The settlement is observed for each increment and from dial gauge. After increasing the load-settlement should be observed after 1, 4, 10, 20, 40 and 60 minutes and then at hourly intervals until the rate of settlement is less than .02 mm per hour. The readings are noted in tabular form.  After completing of the collection of data for a particular loading, the next load increment is applied and readings are noted under new load. This increment and data collection is repeated until the maximum load is applied. The maximum load is generally 1.5 times the expected ultimate load or 3 times of the expected allowable bearing pressure. 62 Plate Load Test Procedure
  • 63. Limitation of plate load test  Base plate not less than 30cm not more than 75cm  Soil should be homogeneous, if not then results are incorrect  Suitable for cohesionless soil  It will give immediate settlement 63
  • 64. 64