Unit2
Bearing capacity of shallow foundation
Q1) Explain the design criteria of shallow foundations and methods of determining bearing capacity.
A1) INTRODUCTION AND DESIGN CRITERIA
METHODS OF DETERMINING BEARING CAPACITY
Q2) Explain factors affecting bearing capacity and explain various terms used in bearing capacity.
A2) FACTOR AFFECTING BEARING CAPACITY
VARIOUS TERMS RELATED TO BEARING CAPACITY
Various terms involving bearing capability
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),
SBC for footing placed at depth Dr
q F = q u n /F s+ Df
q f = q u n / Fs
Safe soil pressure, q f = q u n /Fs + D f
Unit soil pressure
Allowable soil 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
Fig no General shear failure
2. LOCAL SHEAR FAILURE
Fig Local shear failure
PUNCHING SHEAR FAILURE
Fig no. Punching shear failure
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
2. Cantilever strap or pump handle footing
3. Raft footing
2. Sloped footing
3. Grillage footing
Trapezoidal footing
Combined footing
Mat foundation
Strap footing
SPREAD FOOTING
Spread footing
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
Types of mat foundation
1. Flat plate met
2. Plate thickened under the column
3. Plate with pedestal
4. Piled raft
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
(c) Plate with pedestal
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.
Fig no Flexible and soil footing on cohesive soil
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
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
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 q1) 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
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
It differs from Terzaghi's equation as
=45+/2
Q8) Explain Brinch Hansen Analysis.
A8) BRINCH HANSEN ANALYSIS
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
Here N q = tan 2 [(45 +)] e tan
N c = (N q 1) cot
N = 1.8 (Nq1) 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 noncohesive 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
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:
As way as the time needed to achieve total settlement is can depend
The settlement is a combination of 2 parts
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, timedependent compression of partially saturated soil is on the far side of the scope of this book, and only timedependent 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 (Sc) is that the settlement resulted because of resistance to the flow of water beneath the evoked hydraulic gradient.
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 noncohesive 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
Fig no Differential settlements
Then differential settlement =
= / l = /l
This angular distortion causes a lot of injury to the structure.
A) Causes of differential settlement
(B) Methods to reduce differential settlement
IMMEDIATE SETTLEMENT
It can be found out by
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.
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 thoughtabout. This can be taken under consideration within the equation explicit in the previous paragraph.