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Bearing capacity of shallow foundation

Q1) Explain the design criteria of shallow foundations and methods of determining bearing capacity.

A1) INTRODUCTION AND DESIGN CRITERIA

Bearing capability of the foundation is that the most average intensity of applied pressure that a finite loaded space will carry before underlying material fails in shear

The criteria for the determination of bearing capacity of a foundation have supported the wants for the steadiness of the muse. These are declared as follows:

Shear failure of the foundation or bearing capacity failure, because it is usually called, shall not occur. (This is related to plastic flow of the soil material beneath the foundation, and lateral expulsion of the soil from underneath the footing of the foundation); and,

The probable settlements, differential as well as total, of the muse, should be restricted to safe, tolerable, or acceptable magnitudes. In different words, the anticipated settlement beneath the applied pressure on the foundation mustn't be harmful to the steadiness of the structure

These 2 criteria are referred to as the shear strength criterion, and settlement criterion, respectively. These are freelance criteria and thus need an independent investigation. The design value of the safe bearing capacity obviously will be the smaller of the two values obtained from these 2 criteria

METHODS OF DETERMINING BEARING CAPACITY

The following ways are accessible for the determination of the bearing capacity of a foundation

Bearing capacity tables in numerous building codes

Analytical methods

Plate bearing tests

Penetration tests

Model tests and model tests

Laboratory tests

Bearing capacity tables are evolved by bound agencies and incorporated in building codes. they're principally supported by past expertise and a few investigations

Variety of analytical approaches, based on the work of Rankine, Fellenius, Housel, Prandtl, Terzaghi, Meyerhof. Skempton, Hansen, and Bella could also be used Plate bearing tests are load tests conducted within the field on a plate. These involve effort and expense.

There are also certain limitations to their use. Penetration tests are conducted with devices known as Penetrometers, which measure the resistance of soil to penetration. This is correlated to bearing capacity.

Model and prototype tests are very cumbersome and costly and are not usually practicable. Housel's approach is based on model tests.

Simple laboratory tests may be useful in arriving at bearing capacity, especially of pure clays.

Q2) Explain factors affecting bearing capacity and explain various terms used in bearing capacity.

A2) FACTOR AFFECTING BEARING CAPACITY

Soil strength

Foundation depth

Foundation width

Soil weight and surcharge

Spacing between foundation

Earthquake and dynamic mode

Frost action

Subsurface voids

VARIOUS TERMS RELATED TO BEARING CAPACITY

Various terms involving bearing capability

Ultimate bearing capacity (UBC),

Net bearing capacity (NBC),

Safe Bearing capacity (SBC),

Unit sol pressure,

Allowable soil pressure,

Ultimate bearing capacity (UBC)

DEFINITION- it's outlined because the minimum gross pressure intensity at the bottom of the muse at that the soil fails in sheer

Net bearing capacity (NBC),

In the ultimate B.C. (UBC) - surcharge result

q u n = q u –q

q u n = c N C + q (N q -1 ) + 0.5 BN q

Safe Bearing capacity (SBC),

Foundation ought to be designed for pressure Intensity a lot smaller than the last word Bearing capability (UBC) to produce an appropriate issue of safety. F r

SBC for footing placed at depth Dr

q F = q u n /F s+ Df

If surcharge q =

Df isn't effective (if removed thanks to erosion).

q f = q u n / Fs

Foundation pressure are generally surface intensities or net pressure for foundation below the ground surface appropriate overburden surcharge must be considered as additional pressure if it is known to be permanent

Safe soil pressure, q f = q u n /Fs + D f

Unit soil pressure

it's the applied pressure that produces an average unit settlement of the foundation known as tolerable settlement

Allowable soil pressure

It is the maximum net intensity of loading that can be imposed on the soil with no possibility of shear failure or the possibility of excessive settlement

Hence it is the smaller of the net safe bearing capacity and safe bearing pressure

Q3) Explain various modes of failure.

A3) Modes of failure

1. General shear failure

2. Local shear failure

3. Punching shear failure

1. GENERAL SHEAR FAILURE

WHAT ARE THE COMPONENTS IN CONTRIBUTING THE BEARING CAPACITY OF SHALLOW FOUNDATION? - CivilBlog.Org

Fig no General shear failure

Dense sand, stiff and hard clays

Io >85 , N > 30 ,

> 36

The triaxial test shows pronounced peak and failure at small strain

Base failure occurs at very small vertical strain accompanied by large lateral strain with surface heave

The sinking of baseless than 7% base width

Failure zone is well defined

In the load settlement curve, failure load is well defined and peak load is the ultimate load

2. LOCAL SHEAR FAILURE

a) General Shear Failure, (b) Local Shear Failure. (c) Punching Shear... | Download Scientific Diagram

Fig Local shear failure

Loose and medium sands medium to soft clay

Io = 15 - 65 , N = 10 -30 ,

< 30

No peak and failure at large strains

It occurs at large vertical strain and very small lateral strain with no surface heave

Sinking may range from 15 - 20 % base width

Failure zone is difficult to define

From the land settlement graph, the first indication of failure is large deformation in the soil in the early stage of loading which is difficult to distinguish during an incremental load test.

PUNCHING SHEAR FAILURE

General Local and Punching Shear Failure | Civil Engineering Terms

Fig no. Punching shear failure

Very loose and soft saturated clay

Io < 15 , N < 10

Failure with heavy compression

No lateral strain only large vertical strain

Sinking may ranges from > 20% base width

Failure is by sinking and indicate no-slip planes

Load settlement curves indicate failure at very small loads and excessive settlement

Q4) Explain various types of shallow foundations.

A4) SHALLOW FOUNDATION AND TYPE OF SHALLOW FOUNDATION

Depend upon the ratio of D (depth) and W (width) foundation is classified as under

1. Shallow foundation = D/W >1

2. Deep foundation = D/W <1

Type of shallow foundation

A shallow foundation is classified according to the distribution of load on the soil as shown below

footing - concentrated load over a small area

Continuous wall - strip footing to wall

Combined footing - 1. Rectangular footing or trapezoidal footing

2. Cantilever strap or pump handle footing

3. Raft footing

Spread footing - 1. Spread footing

2. Sloped footing

3. Grillage footing

Trapezoidal Footing Formula - Detailed Explanation with Figure – Civilology

Trapezoidal footing

Builder's Engineer: Combined Rectangular Footing.

Combined footing

Raft Foundation — Design Requirements and Applicability

Mat foundation

Strap footing - Wikipedia

Strap footing

SPREAD FOOTING

It is the foremost common variety of shallow foundation wants to transmit the load of wall or isolated column.

The bottom of the wall of the column is enlarged or unfold to distribute the load over an outsized space

To cut back the intensity of load unfold footing doesn't directly rest on the soil. Usually, fifteen to thirty cm thick lean concrete of combine (1:4:8) known as foundation concrete is initially laid, as a base course to hide little pockets in the foundation and to supply a level surface for giving birth spread footing.

WHAT ARE DIFFERENT TYPES OF FOOTINGS? - CivilBlog.Org

Spread footing

Over this foundation concrete, unfold footing rests. If a load of wall footing is high and if there chance of differential settlement, then rather than providing plain foundation concrete, providing steel reinforcement

1. If the projection of footing on the far side wall is excessive, the footing could crack thanks to soil reaction within the cantilever portion. Hence, the stepped foundation is provided.

2 If thickness "t" of footing is a smaller amount, the wall could clock in the footing.

3. Depth of foundation (D) ought to be adequate offer necessary safe bearing capability. Minimum depth of the foundation of ninety cm is provided

4. Explain the mat or raft foundation and contact pressure between rigid and flexible footing.

MAT OR RAFT FOUNDATION

When the undersoil is weak or has a low bearing capability and column hundreds as significant, a mat foundation is provided to transfer the column lands to the underlying soil. Mat foundation or foundation may be a thick ferroconcrete block supporting a variety of columns and transmission the masses to the soil.

Types of mat foundation

1. Flat plate met

2. Plate thickened under the column

3. Plate with pedestal

4. Piled raft

Common types of mat foundations, (a) Flat plate; (b) Plate thickened... | Download Scientific Diagram

Types of mat foundation

(a) Flat plate mat

It is appropriate for fewer compressible soil and comparatively lightweight hundreds with nearer and uniform column spacing

(b) Pate thickened below columns

It is appropriate for heavily loaded columns and provides safety from diagonal shear and negative moments

Pedestals square measure provided at the base of columns higher than slab associated serve the same purpose as kind (b)

(d) Piled raft

When soil is incredibly compressible and geological formation is high, this ruft reduces the settlement and might management buoyancy.

CONTACT PRESSURE UNDER RIGID AND FLEXIBLE FOOTING

The pressure transmitted from the bottom of a foundation to the soil is termed the contact pressure.

This depends on the rigidity of the inspiration structure and also the nature of the soil.

The pressure of a thick compressible layer like soft clay beneath a versatile foundation presents a bowl formed settlement profile with a lot of settlement at the center and virtually zero at the sting.

But the pressure distribution is uniform. This is often the traditional distribution pattern employed in the calculation of stresses and settlements

An extremely rigid footing on identical clay can settle uniform quantity across its breath

Thus the compressible cohesive therefore soil beneath a rigid footing needs to transmit high contact pressure close to the sides than at the center so on maintain regular settlements

For a versatile foundation resting on a non-cohesive soil, the distribution of contact pressure is uniform, however, the sides of the inspiration expertise an outsized settlement attributable to lack of confining pressure at the sides, the inspiration settles a lot of more settlement

Definition of Upward Soil Pressure | Chegg.com

Fig no Flexible and soil footing on cohesive soil

The settlement of a rigid footing on sand layer is uniform and make contact with pressure will increase from zero at the sting to a most at the center

In follow, no foundation is utterly versatile nor infinitely rigid, and thence the particular distribution of contact pressure is somewhere between the intense values.

Sufficient accuracy within the calculation of stresses and displacements will be obtained by forwarding a consistent distribution of contact pressure.

Q6) Explain the Terzaghi’s theory of bearing capacity.

A6) TERZAGHI THEORY OF BEARING CAPACITY

Terzaghi’s analysis although not rigorous permits the USA to work out the final bearing capability of shallow strip footing with a rough base.

Assumptions concerned within the Terzaghi theory

1 The footing is rough (This is a common actual field condition)

2. It is shallow i.e. its depth below the surface isn't greater than the dimension.

3. The shear strength of the soil between the bottom level and also the bottom footing is neglected and this soil is taken into account solely as a surcharge imposing uniform pressure on the horizontal plane at foundation level.

4. General shear failure is assumed which the degree of the soil before and when failure is unchanged.

5. A wedge of soil forthwith below the bottom in a state of elastic equilibrium LE. it's half and parcel of the footing.

6. Passive pressure Pp consists of 3 parts which might be calculated on an individual basis and intercalary though the essential surfaces for these parts aren't identical.

7. Failure zones don't extend on top of the horizontal plane through the bottom of the footing i.e. the shear resistance of soil on top of the bottom is neglected and also the impact of soil around the footing is taken into account akin to a surcharge q=YD.

8. The footing is continuous. This makes the matter a two dimensional one. For isolated footings, however, Terzaghi's future counseled some correction factors to be applied to tie bearing capability values figured out for continuous footing.

Based on these assumptions, the last word bearing capability ratio is figured out as mentioned below:

Derivation of equation for bearing capacity

On the application of load intensity alphabetic character on the footing, the soil wedge bedrock tends to maneuver downward with lateral displacement of zone three and a couple of .but this lateral displacement is resisted by the forces functioning on the planes CB and CA

soil Bearing Capacity and Calculation of Bearing Capacity

Fig no Terzaghis equation

1. Cohesion c acting on the surfaces CB and CA

2. The resultant of passive pressure Pp. creating associate angle o with the traditional to the surfaces CB and CA. Now, when the surface AC associated BC build an angle o with the horizontal, then the passive pressure P would act vertically upward. At failure, the downward and therefore the upward forces on the wedge ACB of unit length should be equal. Additionally, during this position, the building load alphabetic character can represent the final word bearing capability of the soil, and therefore may be substituted by q u r. Hence, the downward forces per m run.

1. qu l t

2. The load of the wedge ACB =1/2 B (height of )= ½ B B/2

3. Tan = ¼ B2 tan

The upward forces are: (1) the passive pressures Pp on every of the surface AC and BC i.e. 2 Pp: and (2) the upward element of cohesion is, acting on CA and CB

= 2 CA c sin = 2 ((B/2)/ Cos ) c sin = Bc tan

Equating downward and upward forces, we get

q u l t .B + ¼ B2 Tan = 2 Pp + B .c tan

q u l t B = 2 Pp + bc tan - ¼ B2 tan

The total passive pressure Pp encompass the subsequent

Passive pressure because of the load of the soil shear zone ACFG. It depends upon

and therefore is written as Pp.it acts joined third distance from C on CA or CB

Passive pressure due to soil cohesion, acting at the midpoint of CA or CH. It depends upon c, and thence is written as Pp(c)

Passive pressure attributable to a surcharge (q), working at the middle purpose of CA or CB. Since it depends on g. allow us to write it as Pp(q)

Equation becomes

q u l t B = 2 [Pp() + Pp(c) + Pp(q)] + Bc tan - ¼ B2tan

Since the term (2 Pp() – ¼ B2 tan ) depends on

Let us express it as N. B2

2 Pp () – ¼ B2 tan = (N) B2/2

2 P p(c) + Bc tan = N c Bc

2 Pp(q) = N q B Df

Where N, Nc and N q are dimensionless bearing capability factors, counting on The Equation then becomes:

C= cohesion

D = depth of the foundation

= unit weight of soil

Tethagi gave the subsequent expression for the bearing capability face

N q = 2 / [2 Cos 2 (45+ /2)]

N c = (N q-1) cot

And

N = tan /2 [(K p y /cos2)-1]

Kp = Passive earth pressure constant depends upon

The values of Nat = 0, 34, 45, are 0, 35, 297.5

Limitations of Terzaghi's Theory

Because the son compression

changes: slight downward movement of footing might not develop the plastic zones

2 Error thanks to the assumption that P, consists of 3 parts, which might be calculated severally and supplementary is little and on the safe aspect.

3 Error thanks to the assumption that failure zones don't extend on top of the horizontal plane through the base of footing and surcharge load. q = y D, isn't true as a result of surcharge load will increase with depth of foundation and thus the speculation is appropriate for shallow foundation only

Q7) What is Meyerhofs analysis?

A7) MEYERHOF ANALYSIS

He extended the analysis of plastic equilibrium of a surface footing to shallow and deep foundations.

It yields the bearing capability of strip footing on a rough base.

It differs from Terzaghi's equation as

It involves the lateral stress constant that ranges between the active and passive values, betting on unit weight, angle of friction, and deformation condition

The shear zone extends higher than the bottom level Angle of wedge

is bigger than

=45+/2

4.5: MEYERHOF'S BEARING CAPACITY THEORY | Engineering360

In Meyerhof's analysis, abd is that the elastic zone, bde is that the radial shear zone and befg are that the zone of mixed shear within which she varies between radial and plane shear relying for the most part upon the depth and roughness of foundation.

The plastic equilibrium in these zones will be established from the boundary conditions ranging from the muse shaft.

To alter the analysis, Meyerhof's introduced a parameter 'B' the angle to define line b to f, wherever the assumed boundary failure slip line intersects the soil surface,

The resultant roll in the wedge of soil bfg is painted by the conventional and tangential stresses Po and So on bf.

Plane bf is termed because the equivalent free surface and P o and so are eliminated because of the equivalent free surface stresses.

Angle B will increase with depth and becomes 90° for a deep foundation.

Though Terzaghi's analysis differs from Otto Fritz Meyerhof, Terzaghi's general equation will be used with Meyerhof's bearing capability factors.

Bearing capability values obtained are on

the point of experimental values and lie between general shear and native shear values of Terzaghi equation for shallow foundation (D, s B), however up to abundant higher for deep foundations

Hence Meyerhof recommended the employment of a reduced price of zero. When tan

=0.85 tan

for deep foundation

Q8) Explain Brinch Hansen Analysis.

A8) BRINCH HANSEN ANALYSIS

It takes under consideration the influence of depth dc", form shape of base S, and inclination of loading.

UBC is expressed within the general kind as

q u = c N c s c dc Ic + q N q S q d q I q + 0.5 B N s d I

And is in shut agreement with the expected result for cohesive soil

Factors Nc Nq N

values area unit is somewhat smaller than corresponding Terzaghi values.

Increase exhaustive shows an important increase in bearing capability N issue

Here N q = tan 2 [(45 +)] e tan

N c = (N q -1) cot

N = 1.8 (Nq-1) tan

Vesic Analysis: it's just like Hansen's equation only there's a slight distinction in the worth of N, and variation on some of Hansen's inclination, form and depth factors.

Vesic's formula for N states

N = 2 (N c +1) tan

Hansen's and Vesic's bearing capability factors area unit satisfactory for non-cohesive likewise as cohesive soils.

	N c	N q	N y	N y (versis)
0	5.14	1	0.0	-
5	6.48	1.57	0.09	0.45
10	8.34	2.47	0.47	1.22
15	10.97	3.94	1.42	2.65
20	14.83	6.4	3.54	5.39
25	20.72	10.66	8.11	10.88
30	30.14	18.4	18.08	22.4
35	46.13	33.29	40.69	48.03
40	75.32	64.18	95.41	109.41
45	133.89	134.85	240.85	271.76
50	266.89	318.96	681.84	762.89

B = form issue to account for the impact of the form of foundation in developing failure surface.

d = Depth issue to account for embedment depth and therefore the further cut resistance within the prime soil

i = Inclination issue to account for each horizontal and vertical part of foundation hundreds.

S FACTOR

		Sc	Sq	Sf
A	Strips	1	1	1
B	Rectangular	1 + 0.2 B/L	1 + 0.2 B/L	1- 0.4 B/L
C	Square	1.3	1.2	0.8
D	Circle	1.3	1.2	0.6

d FACTOR

d c = 1+ 0.2 ∆f/B (√N Q )

d q = 1 for < 10

d q = 1+ 0.1 ∆f/B (√NQ )

Where

N Q = tan² ( 45+ /2 )

Q9) Explain modes of settlement in the shallow foundation.

A9) SETTLEMENT OF SHALLOW FOUNDATION

Causes of settlement

1. Lowering of geological formation and dewatering may end up in shrinkage of soil and increment of stresses in soil.

2. Static countless foundations will cause elastic compression or plastic flow in a static short amount of your time and may result in consolidation settlement over a protracted amount of your time.

3. Dynamic loading will cause shocks and vibrations leading to compaction of soil and in fine saturated sands and silts, physical change might occur throughout earthquakes.

4. Throughout major construction activities in close areas like deep excavations, pile driving, mining activities or heavily loaded structures may lead to a settlement.

5. Other causes like the collapse of pipe conduits, erosion of undersoil, or submersion resulting in the collapse of soil structures may cause settlement of foundations

ALLOWABLE SETTLEMENT

The settlement will cause untoward cracks in exterior masonry walls and interior plaster walls of buildings it will cause a structure to tilt which can become noticeable in high buildings, resulting in its failure.

However, settlements are often totally different pattern under different conditions and also the result caused on the structure can itself rely upon the kind of settlement. Uniform settlement doesn't cause structural harm. However excessive settlement could harm utilities like water system, sewage, electric, phone, etc.

A structure with an awfully rigid raft or mat foundation can expertise uniform settlement. Differential settlement when exceeds the permissible limits, the building could fail structurally in many ways.

Average settlements starting from twenty metric linear units to three hundred metric linear units are permissible betting on the style of soil. Structure or style of construction,

Different building codes have such that permissible limits of settlement and angular distortion

Basically, the settlement has 2 types

Differential settlement

Immediate settlement

COMPONENTS OF SETTLEMENT AND ITS ESTIMATION

While analyzing the settlement of foundation 2 aspects are needed to be studied:

The time needed to achieve a total settlement.

What is going to be the total settlement?

As way as the time needed to achieve total settlement is can depend

Whether it's cohesionless soil or cohesive soil.

Drainage conditions.

Thickness of strata

The settlement is a combination of 2 parts

Time independent compression is known as immediate compression /immediate settlement or elastic settlement.

Time dependant compression, known as consolidation

As way as compression for soil and compression of water thinks about, it's negligible. Thus, the reduction in the volume of a saturated soil sample is especially thanks to the escape of water.

In the case of part saturated soil, there'll not be any flow of water, however, because of compressible air, there'll be a considerable reduction in volume.

In the gift study, time-dependent compression of partially saturated soil is on the far side of the scope of this book, and only time-dependent compression just in case of saturated soil is taken into account

Once the load is applied on saturated cohesive soil, initially, the entire load is taken by pore water, and later on, because of gradual escape/seepage of water, the load is transferred to the soil.

Definition -This method of gradual load transfer from pore water to soil Skeleton, and gradual compression is termed consolidation

The settlement because of consolidation will be divided into 2 elements

Types of settlement

Primary consolidation settlement

Secondary consolidation settlement

Primary consolidation settlement (S c)

Primary consolidation settlement (Sc) is that the settlement resulted because of resistance to the flow of water beneath the evoked hydraulic gradient.

Secondary consolidation settlement (Ss)

Secondary consolidation settlement (S s) is because of plastic deformation of soil at zero excess pore water pressure

Mathematically S = total settlement = SI +Sc +Ss

If the load is applied on saturated non-cohesive soil, where drainage is not permitted, less compression/settlement will take for the following reasons:

Water is highly incompressible

Modulus of chastity of sand is less

Q10) Explain Differential settlement and immediate settlement.

A10) DIFFERENTIAL SETTLEMENT

If a part of the structure settles more than the other part, the difference between the two settlements called as differential settlement

This different a lot of harmful than the settlement of structure, because, it induces serious stresses in structure leading to cracks in the structure. It is so. essential to regulate differential settlement

differential settlement" - Google Search | Floor plans, The originals, Positivity

Fig no Differential settlements

As shown in fig, let footing of column A settle by quantity

1 and column B by

2, from the initial footing level

Then differential settlement =

The ratio of different settlement between the 2 footings and distance between the 2 columns is called angular distortion

Angular distortion = differential settlements / distance between 2 column

= / l = /l

This angular distortion causes a lot of injury to the structure.

It is troublesome to see a differential settlement than to see a total settlement. Usually, the differential settlement is regarding fifty to seventy-fifth of the total settlement

Therefore, if the total settlement is controlled, it'll mechanically management the differential settlement.

Limits of most settlement and most differential settlement as per I.S. 1904 (1975)

Settlement of raft foundations is an additional uniform than that of isolated footings. Hence, the additional settlement is allowable for raft foundations change for isolated footing.

A) Causes of differential settlement

little pockets of soft soil like clay, peat, mud, and organic matter

The equal intensity of loading on the foundation.

Overlapping of stresses from contiguous structures

Unequal swelling, softening and drying of the soil.

The difference in compressibility of the underlying soil

Tilting of a rigid base.

(B) Methods to reduce differential settlement

Preloading or pre compaction to scale back compressibility

Decreasing the effective load by Post for effect.

Increasing the depth of foundation in sandy soil

Use of piles

Soil stabilization techniques, soil reinforcement, etc

IMMEDIATE SETTLEMENT

It can be found out by

Carrying out a field test

Carrying out laboratory test and

Using relations based on the theory of elasticity

Janbu, Bjerrum, and Kjaernsli (1966) have planned the subsequent equation for computing the immediate settlement.

S I = [(1- 2)/E s]

Where the modulus of clay town E s is computed from

Es = ( / (

And and taken from the graph

When completely different clay layers exist, having completely different values of E, by victimization the principle of superposition computations may be plane. This price of S, once accessorial to S, would offer the whole settlement for such soils.

Immediate settlement (si) may also be distinguished by the use of the following equation as counseled in IS 8009 half I 1976

S I = q B [(1- 2) I w / E s]

Where

q = Intensity of contact pressure

B = Least lateral dimension of footing

E s = Modulus of the physical property of soil

I w = Influence issue

= 0.88 for rigid circular footing

= 0.82 for rigid sq. footing

= 1.06 for rigid rectangular footing with L/B

= 1.5

= 1.70 for rigid rectangular footing, with LSB

= 5

The values of influence clotting factor area unit urged in IS code I S: 8009 half I, 1976. Per this code, the entire settlement of a rigid footing is taken as zero.8 times the settlement at the middle of a versatile foundation,

This equation is base on the belief that the load is performing at ground level i.e. impact of depth of footing below GL and depth of exhausting strata below footing isn't thought-about. This can be taken under consideration within the equation explicit in the previous paragraph.

It's tough to see the worth of u and additionally modulus of physical property E, this will be seen by really concluding 2 or a lot of a number of plate load tests, mistreatment different sizes of plates; either sq. or circular plates.

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