2. Definition
• The term bearing capacity qualitatively refers to the supporting
power of a soil or rock.
• By the use of theoretical analyses, such as Terzaghi’s analysis,
Skempton analysis, Meyerhof analysis, etc.
• By the use of plate load test results.
• By the use of penetration test results.
• By the use of building codes.
Methods of determining Bearing Capacity
3. Prandtl’s Analysis
ASSUMPTIONS
The following assumptions were made in Prandtl’s analysis.
• The soil is homogeneous and isotropic.
• The soil mass is weight less.
• The shear strength of soil can be expressed by Mohr-coulomb
equation.
• Prandtl assumed the failure zones to be formed as shown in fig.
4. • Zone Ι is bound by two planes inclined at (45+ Φ/2) to the
horizontal and acts as a rigid body.
5. • Zone ΙΙ is bound by two planes inclined at (45 + Φ/2) and (45 -
Φ/2) to the horizontal. The base of this zone is a logarithmic
spiral in section. All radial sectors in this zone are failure
planes.
• Zone ΙΙΙ is bound by two planes inclined at (45 - Φ/2)
horizontal and also acts as a rigid body.
• The problem is essentially two dimensional, i.e., the equation
is derived for a long strip footing.
• The base of the footing is smooth.
6. Prandtl’s Analysis
• Prandtl’s analysis is based on a study of plastic failure in metals
when punched by hard metal punchers (Prandtl, 1920).
• Prandtl (1921) adapted the above study to soil loaded to shear
failure under a relatively rigid foundation. Prandtl’s equation for
ultimate bearing capacity is
7. • It is applicable for 𝑐−Φ soil. But for a cohesion-less soil for which
𝑐=0, gives 𝑞f = 0. Hence the equation fails for cohesion-less soils.
• This anamoly which is due to the assumption that the soil is weight
less was removed by Taylor (1948).
• Prandtl’s equation with Taylor’s correction is
8. Limitations of Prandtl’s Analysis
• In the original Prandtl’s equation, the ultimate bearing capacity reduces
to zero for cohesionless soil.
• The original Prandtl’s equation is applicable only for a footing resting on
surface. Attempts have been made by Taylor to overcome the anomalies
arising due to assumptions (1) and (2) to some extent.
• In the case of a footing resting on purely cohesive soil, Prandtl’s equation
leads to an indeterminate quantity. Only by applying L’ Hospital’s rule the
limiting value Φ → 0 is obtained as 𝑞u =5.148.
• In the original Prandtl’s equation, the size of the footing is not
considered.
9. Analytical method
• Reissner (1924) extended Prandtl's analysis for uniform load q per
unit area acting on the ground surface. He assumed that the shear
pattern is unaltered and gave the bearing capacity expression as
follows.
10. • if Φ=0, the logspiral becomes a circle and Nc is equal to (π+2) ,also
Nq becomes 1. Hence the bearing capacity of such footings
becomes
11. Presumptive bearing capacity
• Building codes of various organizations in different countries gives
the allowable bearing capacity that can be used for proportioning
footings.
• These presumptive bearing capacity values based on experience
with other structures already built.
• As presumptive values are based only on visual classification of
surface soils, they are not reliable.
• These values don't consider important factors affecting the bearing
capacity such as the shape, width, depth of footing, location of
water table, strength and compressibility of the soil.
12. • Generally these values are conservative and can be used for
preliminary design or even for final design of small unimportant
structure.
• IS1904-1978 recommends that the safe bearing capacity should be
calculated on the basis of the soil test data. But, in absence of such
data, the values of safe bearing capacity can be taken equal to the
presumptive bearing capacity values.
• It is further recommended that for non-cohesive soils, the values
should be reduced by 50% if the water table is above or near base of
footing.
13.
14. Meyerhof’s Analysis
Assumptions
• Failure zones to extend above base level of the footing.
• The logarithmic spiral extends right up to the ground surface.
Meyerhof (1951, 1963 ) proposed an equation for ultimate bearing
capacity of strip footing which is similar in form to that of Terzaghi but
includes shape factors, depth factors and inclination factors.
• Meyerhof's equation is
15.
16. • It is further suggested that the value of Φ for the plane strain
condition expected in long rectangular footings can be obtained
from Φtriaxial.
17. Vesic's Bearing Capacity Theory
• Vesic(1973) confirmed that the basic nature of failure surfaces in
soil as suggested by Terzaghi as incorrect.
• Developed formulas based on theoretical and experimental
findings.
• Vesić retained Terzaghi’s basic format and added additional factors,
which produces more accurate bearing capacity values.
• Applies to a much broader range of loading and geometry
conditions.
18. • The bearing capacity formula is re-written as
where
19. Skempton’s Analysis
• Skempton (1951) based on his investigations of footings on
saturated clays observed that the bearing capacity factor 𝑁C is a
function of ratio D/B in the case of strip footing and square or
circular footings, for Φ = 0 condition.
• Bearing capacity factors in Terzaghi's equation tends to increase
with depth for a cohesive soil.
