The ultimate bearing capacity (q_{f}) is the value of bearing stress which causes a sudden catastrophic settlement of the foundation (due to shear failure).
The allowable bearing capacity (q_{a}) is the maximum bearing stress that can be applied to the foundation such that it is safe against instability due to shear failure and the maximum tolerable settlement is not exceeded. The allowable bearing capacity is normally calculated from the ultimate bearing capacity using a factor of safety (F_{s}).
When excavating for a foundation, the stress at founding level is relieved
by the removal of the weight of soil. The net bearing pressure (q_{n})
is the increase in stress on the soil.
q_{n} = q  q_{o}
q_{o} = g D
where D is the founding depth and g is the
unit weight of the soil removed.
Failure mechanisms and derivation of equations  Bearing capacity 
q_{f} = (2 + p) s_{u} = 5.14 s_{u}This equation is based on a weightless soil. Therefore if the soil is noncohesive (c=0) the bearing capacity depends on the surcharge q_{o}. For a footing founded at depth D below the surface, the surcharge q_{o} = gD. Normally for a shallow foundation (D<B), the shear strength of the soil between the surface and the founding depth D is neglected.
radius of the fan r = r_{0} .exp[q.tanf'].
q is the fan angle in radians (between 0 and p/2)
f' is the angle of friction of the soil
r_{o} = B/[2 cos(45+f'/2)]
Upper and lower bound solutions  Failure mechanisms and derivation of equations 
The ultimate load capacity of a footing can be estimated by assuming a failure mechanism and then applying the laws of statics to that mechanism. As the mechanisms considered in an upper bound solution are progressively refined, the calculated collapse load decreases.
As more stress regions are considered in a lower bound solution, the calculated collapse load increases.
Therefore, by progressive refinement of the upper and lower bound solutions,
the exact solution can be approached. For example, Terzaghi's mechanism
gives the exact solution for a strip footing.
Semicircular slip mechanism  Failure mechanisms and derivation of equations 
Circular arc slip mechanism  Failure mechanisms and derivation of equations 
Bearing capacity of shallow foundations  Bearing capacity 
q_{f} =c.N_{c} +q_{o}.N_{q} + ½g.B .N_{g}
For drained loading, calculations are in terms of effective stresses;
f´
is > 0 and N
_{c}, N_{q} and Ng
are all > 0.
For undrained loading, calculations are in terms of total stresses;
the undrained shear strength (s_{u}); N_{q} = 1.0 and Ng
= 0
c = apparent cohesion intercept
q_{o} = g . D (i.e. density x depth)
D = founding depth
B = breadth of foundation
g = unit weight of the soil removed.
Bearing capacity equation (undrained)  Bearing capacity of shallow foundations 
Bearing capacity equation (drained)  Bearing capacity of shallow foundations 
q_{f} =c.N_{c} +q_{o}.N_{q} + ½g.B .N_{g}This equation is applicable only for shallow footings carrying vertical noneccentric loading.
q_{f} = c .N_{c} .s_{c} + q_{o} .N_{q} .s_{q} + ½ g .B .N_{g} .s_{g}Other factors can be used to accommodate depth, inclination of loading, eccentricity of loading, inclination of base and ground. Depth is only significant if it exceeds the breadth.
Bearing capacity factors  Bearing capacity equation (drained) 
Shape factors  Bearing capacity equation (drained) 




square 



circle 



rectangle (B<L)  1+ 0.2(B/L)  1+ 0.2(B/L)  1  0.4(B/L) 
Depth factors  Bearing capacity equation (drained) 
Factor of safety  Bearing capacity of shallow foundations 
Experience has shown that the settlement of a typical foundation on
soft clay is likely to be acceptable if a factor of 2.5 is used. Settlements
on stiff clay may be quite large even though ultimate bearing capacity
is relatively high, and so it may be appropriate to use a factor nearer
3.0.
Presumed bearing values  Bearing capacity 
Category  Types of rocks and soils  Presumed bearing value 
Noncohesive soils  Dense gravel or dense sand and gravel  >600 kN/m² 
Medium dense gravel,
or medium dense sand and gravel 
<200 to 600 kN/m²  
Loose gravel, or loose sand and gravel  <200 kN/m²  
Compact sand  >300 kN/m²  
Medium dense sand  100 to 300 kN/m²  
Loose sand  <100 kN/m² depends on
degree of looseness 

Cohesive soils  Very stiff bolder clays & hard clays  300 to 600 kN/m² 
Stiff clays  150 to 300 kN/m²  
Firm clay  75 to 150 kN/m²  
Soft clays and silts  < 75 kN/m²  
Very soft clay  Not applicable  
Peat  Not applicable  
Made ground  Not applicable 
Presumed bearing values for Keuper Marl
Weathering  Zone  Description  Presumed bearing value 
Fully weathered  IVb  Matrix only  as cohesive soil 
Partially weathered  IVa  Matrix with occasional pellets less than 3mm  125 to 250 kN/m² 
III  Matrix with lithorelitics up to 25mm  250 to 500 kN/m²  
II  Angular blocks of unweathered marl with virtually no matrix  500 to 750 kN/m²  
Unweathered  1  Mudstone (often not fissured)  750 to 1000 kN/m² 
Bearing capacity of piles  Bearing capacity 
For largediameter piles, settlement can be large, therefore a safety factor of 22.5 is usually used on the working load.
Full shaft capacity is mobilised at much smaller displacements than
those related to full base resistance. This is important when determining
the settlement response of a pile. The same overall bearing capacity may
be achieved with a variety of combinations of pile diameter and length.
However, a long slender pile may be shown to be more efficient than a short
stubby pile. Longer piles generate a larger proportion of their full capacity
by skin friction and so their full capacity can be mobilised at much lower
settlements.
The proportions of capacity contributed by skin friction and end bearing
do not just depend on the geometry of the pile. The type of construction
and the sequence of soil layers are important factors.
Driven piles in noncohesive soil  Bearing capacity of piles 
In noncohesive soils, skin friction is low because a low friction 'shell' forms around the pile. Tapered piles overcome this problem since the soil is recompacted on each blow and this gap cannot develop.
Pile capacity can be calculated using soil properties obtained from standard penetration tests or cone penetration tests. The ultimate load must then be divided by a factor of safety to obtain a working load. This factor of safety depends on the maximum tolerable settlement, which in turn depends on both the pile diameter and soil compressibility. For example, a safety factor of 2.5 will usually ensure a pile of diameter less than 600mm in a noncohesive soil will not settle by more than 15mm.
Although the method of installing a pile has a significant effect on
failure load, there are no reliable calculation methods available for quantifying
any effect. Judgement is therefore left to the experience of the engineer.
Ultimate pile capacity  Driven piles in noncohesive soil 
Values of K_{s} and d can be
related to the angle of internal friction (f´)
using the following table according to Broms.
Material  d  K_{s}  

low density  high density  
steel  20°  0.5 
1.0 
concrete  3/4 f´  1.0  2.0 
timber  2/3 f´  1.5  4.0 
It must be noted that, like much of pile design, this is an empirical relationship. Also, from empirical methods it is clear that Q_{s} and Q_{b} both reach peak values somewhere at a depth between 10 and 20 diameters.
It is usually assumed that skin friction never
exceeds 110 kN/m² and base resistance will not exceed 11000 kN/m².
Standard penetration test  Driven piles in noncohesive soil 
Schmertmann (1975) has correlated Nvalues obtained from SPT tests against
effective overburden stress as shown in the figure.
The effective overburden stress = the
weight of material above the base of the borehole  the wight of water
e.g. depth of soil = 5m, depth of water =
4m, unit weight of soil = 20kN/m³,
s'_{v}
= 5m x 20kN/m³  4m x 9.81kN/m³ »
60 kN/m²
Once a value for f´ has been estimated, bearing capacity factors can be determined and used in the usual way.
Meyerhof (1976) produced correlations between base and frictional resistances and Nvalues. It is recommended that Nvalues first be normalised with respect to effective overburden stress:
Normalised N = N_{measured} x 0.77 log(1920/s´_{v})
Pile type  Soil type  Ultimate base resistance

Ultimate shaft resistance

Driven  Gravelly sand
Sand 
but < 400 N 

Sandy silt
Silt 
but < 300 N 

Bored  Gravel and sands 
but < 300 N 
N_{avg} 
Sandy silt
Silt 
but < 300 N 
L = embedded length
d = shaft diameter
N_{avg} = average value along shaft
Cone penetration test  Driven piles in noncohesive soil 
q_{b} = average cone resistance calculated over a depth equal to three pile diameters above to one pile diameter below the base level of the pile.Shaft resistance
Type of pile 

Solid timber )
Precast concrete ) Solid steel driven ) 
0.005  0.012 
Openended steel  0.003  0.008 
Bored piles in noncohesive soil  Bearing capacity of piles 
Driven piles in cohesive soil  Bearing capacity of piles 
For piles driven into stiff clays, a little consolidation takes place, the soil cracks and is heaved up. Lateral vibration of the shaft from each blow of the hammer forms an enlarged hole, which can then fill with groundwater or extruded porewater. This, and 'strain softening', which occurs due to the large strains in the clay as the pile is advanced, lead to a considerable reduction in skin friction compared with the undisturbed shear strength (s_{u}) of the clay. To account for this in design calculations an adhesion factor, a, is introduced. Values of a can be found from empirical data previously recorded. A maximum value (for stiff clays) of 0.45 is recommended.
The ultimate bearing capacity Q_{f} of a driven pile in cohesive
soil can be calculated from:
Q_{f} = Q_{b} + Q_{s}
where the skin friction term is a summation of layer resistances
Q_{s} = S( a
.s_{u}(avg) .A_{s})
and the end bearing term is
Q_{b} = s_{u} .N_{c} .A_{b}
N_{c} = 9.0 for clays and silty clays.
Bored piles in cohesive soil  Bearing capacity of piles 
The mobilisation of full endbearing capacity by largediameter piles
requires much larger displacements than are required to mobilise full skinfriction,
and therefore safety factors of 2.5 to 3.0 may be required to avoid excessive
settlement at working load.
Carrying capacity of piles in layered soil  Bearing capacity of piles 
The base resistance at the pile toe is
q_{p} = q_{2} + (q_{1} q_{2})H / 10B
but
£ q_{1}
where B is the diameter of the pile, H is the thickness between the base of the pile and the top of the weaker layer, q_{2} is the ultimate base resistance in the weak layer, q_{1} is the ultimate base resistance in the strong layer.
Effects of groundwater  Bearing capacity of piles 
Effect on bearing capacity
In cohesive soils, the permeability is so low that any movement of
water is very slow. They do not suffer any reduction in bearing capacity
in the presence of groundwater.
In granular soils, the position of the water table is important. Effective
stresses in saturated sands can be as much as 50% lower than in dry sand;
this affects both the endbearing and skinfriction capacity of the pile.
Effects on construction
When a concrete castinplace pile is being installed and the bottom
of the borehole is below the water table, and there is water in the borehole,
a 'tremie' is used.
With its lower end lowered to the bottom of the borehole, the tremmie is filled with concrete and then slowly raised, allowing concrete to flow from the bottom. As the tremie is raised during the concreting it must be kept below the surface of the concrete in the pile. Before the tremie is withdrawn completely sufficient concrete should be placed to displace all the free water and watery cement. If a tremie is not used and more than a few centimetres of water lie in the bottom of the borehole, separation of the concrete can take place within the pile, leading to a significant reduction in capacity.
A problem can also arise when boring takes place through clays. Site investigations may show that a pile should terminate in a layer of clay. However, due to natural variations in bed levels, there is a risk of boring extending into underlying strata. Unlike the clay, the underlying beds may be permeable and will probably be under a considerable head of water. The 'tapping' of such aquifers can be the cause of difficulties during construction.
Effects on piles in service
The presence of groundwater may lead to corrosion or deterioration
of the pile's fabric.
In the case of steel piles, a mixture of water and air in the
soil provides conditions in which oxidation corrosion of steel can occur;
the presence of normally occurring salts in groundwater may accelerate
the process.
In the case of concrete piles, the presence of salts such as
sulphates or chlorides can result in corrosion of reinforcement, with possible
consequential bursting of the concrete. Therefore, adequate cover must
be provided to the reinforcement, or the reinforcement itself must be protected
in some way. Sulphate attack on the cement compounds in concrete may lead
to the expansion and subsequent cracking. Corrosion problems are minimised
if the concrete has a high cement/aggregate ratio and is well compacted
during placement.