Shallow Foundation & Bearing Capacity
Bearing Capacity
It is the load carrying capacity of the soil.
- Ultimate bearing capacity or Gross bearing capacity (qu)
It is the least gross pressure which will cause shear failure of the supporting soil immediately below the footing.
- Net ultimate bearing capacity (qun ):
It is the net pressure that can be applied to the footing by external loads that will just initiate failure in the underlying soil. It is equal to ultimate bearing capacity minus the stress due to the weight of the footing and any soil or surcharge directly above it. Assuming the density of the footing (concrete) and soil ( γ) are close enough to be considered equal, then
Where, Df is the depth of footing
- Safe bearing capacity:
It is the bearing capacity after applying the factor of safety (FS). These are of two types,
Safe net bearing capacity (qns):
It is the net soil pressure which can be safety applied to the soil considering only shear failure. It is given by,
Safe gross bearing capacity (qs ):
It is the maximum gross pressure which the soil can carry safely without shear failure. It is given by,
Allowable Bearing Pressure:
It is the maximum soil pressure without any shear failure or settlement failure
where, qs = Safe bearing capacity.
Method to determine bearing capacity
(i) Rankines Method (∅ - soil)
or
(ii) Bells Theory (C - ∅)
where, Nc and Nq are bearing capacity factors.
For pure clays → C = 4, q = 1
(iii) Fellinious Method: (C-soil)
- The failure is assumed to take place by slip and the consequent heaving of a mass of soil is on one side.
- Location of Critical circle
(iv) Prandtl Method: (C - ∅)
For strip footing
For C-soil
(v) Terzaghi Method (C - ∅)
Assumptions
S – Strip footing, S – Shallow foundation, G – General shear failure, H – Horizontal ground, R – Rough base
For strip footing
For square footing
For rectangular footing
For circular footing
where,
D = Dia of circular footing
CNc → Contribution due to constant component of shear strength of soil.
→ Contribution due to surcharge above the footing
→ Contribution due to bearing capacity due to self weight of soil.
Bearing capacity factors
where, = influence factor
For C-soil:
NC = 5.7, Nq = 1, Nγ = 0
(vi) Skemptons Method (c-soil)
This method gives net ultimate value of bearing capacity.
Applicable for purely cohesive soils only.
For strip footing.
For circular and square footing.
Values of NC
- at the surface.
Then NC = 5 For strip footing
NC = 6.0 For square and circular footing.
where Df = Depth of foundation. - If
for strip footing
For square and circular footing.
B =D in case of circular footing.
for rectangular footing - if NC =7.5
for strip footing
NC = 9.0 for circular, square and rectangular footing.
(vii) Meyorhoff's Method → (C - ∅ soil)
(viii) IS code:
Effect of Water Table on Bearing Capacity of Soil
where and are water table correction factor.
when
If they
If they
If water table rise to G.L
and
Plate Load Test
1. Significant only for cohesionless.
2. Short duration test hence only results in immediate settlement.
(i) (ii)
..for ∅=soil … for C-soil
If plate load test carried at foundation level then
(iii)
(iv)
… for dense sand. … for clays
(v)
… for silts.
where,
quf =Ultimate bearing capacity of foundation
qup = Ultimate bearing capacity of plate
Sf = Settlement of foundations
Sp = Settlement of plate
Bf = Width of foundation in m
Bp = Width of plate in m
Housels Approach
where, Qp = Allowable load on plate m and n are constant
P = Perimeter Ap = Area of plate
Af = Area of foundation
Standard Penetration Test
Significant for Granular Soils
(i) and
where, N1 = Overburden pressure correction
N0 = Observed value of S.P.T. number.
= Effective overburden pressure at the level of test in kM/m2.
(ii) For Saturated fine sand and silt, when N1 > 15
where, N2 = Dilatancy correction or water table correction.
related to N value using peck Henson curve or (code method)
- Teng's formula relate N value with reading capacity of granular soil.
Pecks Equation
Dw = depth of water table below G.L
Df = Depth of foundation
B = Width of foundation
N = Avg. corrected S.P.T. no.
S = Permissible settlement of foundation
Cw = Water table correction factor
qa net = Net allowable bearing pressure.
Teng's Equations
Cw =Water table correction factor
Dw = Depth of water table below foundation level
B = Width of foundation
Cd =Depth correction factor
S = Permissible settlement in 'mm'.
I.S Code Method
qns =Net safe bearing pressure in kN/m2
B = Width in meter.
S = Settlement in 'mm'.
I.S. Code Formula for Raft:
Cw : Same as of peck Henson.
Meyer-Hoffs Equation
where, qns = Net safe bearing capacity in kN/m2.
B < 1.2 m
B ≥ 1.2 m (where qns is in kN/m2.
Cone Penetrations Test
(i)
where, = Static cone resistance in kg/cm2
c = Compressibility coefficient
= Initial effective over burden pressure in kg/cm2.
(ii)
where, 'S' = Settlement.
(iii) B > 1.2 m.
where, qns = Net safe bearing pressure in kN/m2.
(iv) B < 1.2 m.
where, Rw = Water table correction factor.
Deep Foundation
Bearing capacity of piles
The ultimate bearing capacity of a pile is the maximum load which it can carry without failure or excessive settlement of the ground. The bearing capacity also depends on the methods of installation
A. Analytical Method
(i) Qup = Qeb + Qsf
(ii) Qup = qbAb + qsAs
where,
Qup = Ultimate load on pile
Qeb = End bearing capacity
Qsf = Skin friction
qb = End bearing resistance of unit area.
qs = Skin friction resistance of unit area.
Ab = Braking area
As = Surface area
(iii) qb ∼ 9C
where, C = Unit Cohesion at base of pile for clays
(iv)
where, α = Adhesion factor
Unit adhesion between pile and soil.
Average Cohesion over depth of pile.
(v)
where, Fs = Factor of safety.
(vi)
F1 = 3 and F2 = 2
(vii) For Pure Clays
B. Dynamic Approach
Dynamic methods are suitable for dense cohesionless soil only.
(i) Engineering News Records Formula
(a)
(b)
where,
Qup = Ultimate load on pile
Qap = Allowable load on pile
W = Weight of hammer in kg.
H = Height of fall of hammer in cm.
S = Final set (Average penetration of pile per blow of hammer for last five blows in cm)
C = Constant
= 2.5 cm → for drop hammer
= 0.25 cm → for steam hammer (single acting or double acting)
(c) for drop hammer
(d) For single Acting Stream Hammer
(e) For Double Acting Stream Hammer
where P = Stream pressure
and a = Area of hammer on which pressure acts.
(ii) Hiley Formula (I.S. Formula)
where, Fs = Factor of safety = 3
ηh = Efficiency of hammer
ηb = Efficiency of blow.
ηh = 0.75 to 0.85 for single acting steam hammer
ηh = 0.75 to 0.80 for double acting steam hammer
ηh = 1 for drop hammer.
where, w = Weight of hammer in kg.
p = Weight of pile + pile cap
e = Coefficient of restitutions
= 0.25 for wooden pile and cast iron hammer
= 0.4 for concrete pile and cast iron hammer
= 0.55 for steel piles and cast iron hammer
S = Final set or penetrations per blow
C = Total elastic compression of pile, pile cap and soil
H = Height of fall of hammer.
C. Field Method
(i) Use of Standard Penetrations Data
where, N = Corrected S.P.T Number
Average corrected S.P.T number for entire pile length
Fs = Factor of safety
= 4 → For driven pile
= 2.5 → for bored pile.
(ii) Cone penetration test
where, qc = static cone resistance of the base of pile in kg/cm2
qc = average cone resistance over depth of pile in kg/cm2
Area of bulb (m)2
Under-Reamed Pile
An 'under-reamed' pile is one with an enlarged base or a bulb; the bulb is called 'under-ream'.
Under-reamed piles are cast-in-situ piles, which may be installed both in sandy and in clayey soils. The ratio of bulb size to the pile shaft size may be 2 to 3; usually a value of 2.5 is used.
where, bu = dia of bulb, Spacing = 1.5 bu.
Negative Skin Friction
(i) For Cohesive sol
Qnf = Perimeter. L1αC for Cohesive soil.
where, Qnf = Total negative skin frictions
where, Fs = Factor of safety.
(ii) For cohesionless soils
Qnf = P x force per unit surface length of pile
(friction force = μH)
Where γ = unit weight of soil.
K = Earth pressure coefficient (Ka < K < Kp)
δ = Angle of wall friction. (φ/2<δ<φ)
Group Action of Pile
The ultimate load carrying capacity of the pile group is finally chosen as the smaller of the
(i) Ultimate load carrying capacity of n pile (n Qup)
and (ii) Ultimate load carrying capacity of the single large equivalent (block) pile (Qug).
To determine design load or allowable load, apply a suitable factor of safety.
(i) Group Efficiency (ηg)
Qug = Ultimate load capacity of pile group
Qup = Ultimate load on single pile
For sandy soil → ηg > 1
For clay soil → ηg < 1 and ηg > 1
Minimum number of pile for group = 3.
Qug = qbAb + qsAs
where qb = 9C for clays
- For Square Group
Size of group, B = (n – 1) S + D
where, η = Total number of pile if size of group is x.x
They η = x2
- Qug = η.Qup
- where, Qug = Allowable load on pile group.
where, Sr = Group settlement ratio
Sg = Settlement of pile group
Si = Settlement of individual pile.
(ii) When Piles are Embended on a Uniform Clay
(iii) In case of Sand
where, B = Size of pile group in meter.
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