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Bearing Capacity of Piles

Ultimate bearing capacity of a pile is the maximum load which the pile can carry without shear failure or excessive settlement of the ground. The bearing capacity depends on pile geometry, soil properties and the method of installation. The total ultimate load on a pile is obtained by combining end bearing and skin friction; the allowable or safe load is obtained by applying a suitable factor of safety to the ultimate load.

A. Analytical Method

The analytical (or static) method separates the ultimate resistance of a pile into two components: end bearing at the pile toe and skin friction along the pile shaft.

1. Basic relation

   

   Thus,

   
   

   where:

   • Q_up = Ultimate load on pile
   • Q_eb = End bearing capacity
   • Q_sf = Skin friction capacity
   • q_b = End bearing resistance per unit area
   • q_s = Skin friction resistance per unit area
   • A_b = Bearing area (area of pile base)
   • A_s = Surface area of pile in contact with soil

2. End bearing resistance in clay

   For piles socketed into clay, a commonly used empirical relation is

   q_b ≈ 9 C

   where C is the unit cohesion (undrained shear strength) at the base of the pile.

3. Skin friction (cohesive soils)

   

   where a is the adhesion factor and

   

   a × c̄ = unit adhesion between pile and soil, where c̄ = average cohesion over the depth of pile.

4. Factor of safety

   

   where F_s is the factor of safety applied to obtain the allowable load from the ultimate load.

5. Typical factors of safety

   

   In practice:

   • F₁ = 3 and F₂ = 2 in some approaches.
   • In many designs an overall factor of safety of 2.5 may be adopted depending on conditions.
   • 
   • Typical recommended values for different methods and soils should be used as per relevant codes and experience.

6. Pure clays

   

   For pure clays, end bearing and shaft resistance are commonly related to the undrained shear strength and appropriate adhesion factors. Use of conservative values and code guidance is essential.

B. Dynamic Approach

Dynamic (or pile-driving) formulae estimate the bearing capacity from the energy imparted by hammer blows and the measured set (penetration per blow). These methods are most suitable for driven piles in dense cohesionless soils and for preliminary on-site assessment.

(i) Engineering News formula

This classical relation relates the ultimate and allowable pile capacity to hammer energy, set, and empirical constants.

where:

• Q_up = Ultimate load on pile
• Q_ap = Allowable load on pile
• W = Weight of hammer (kg)
• H = Height of fall of hammer (cm)
• S = Final set (average penetration of pile per blow for last five blows) (cm)
• C = Constant; typical values are 2.5 cm for drop hammer and 0.25 cm for steam hammer (single or double acting)

For drop hammer

For steam hammers

- For single-acting steam hammer:

Q_ap = WH / 6(S + 0.25)

- For double-acting steam hammer:

where P = steam pressure and a = area of hammer on which the pressure acts.

(ii) Hiley formula (I.S. formula)

In the Hiley formula the dynamic resistance is estimated using hammer energy, pile mass and elastic behaviour:

• F_s = factor of safety, commonly taken as 3
• η_h = efficiency of the hammer
• η_b = efficiency of the blow

Typical efficiency ranges:

• η_h = 0.75 to 0.85 for single acting steam hammer
• η_h = 0.75 to 0.80 for double acting steam hammer
• η_h = 1 for drop hammer

where:

• W = weight of hammer (kg)
• P = weight of pile + pile cap (kg)
• e = coefficient of restitution (elastic rebound factor)
• Typical e values: 0.25 for wooden pile & cast-iron hammer; 0.4 for concrete pile & cast-iron hammer; 0.55 for steel piles & cast-iron hammer
• S = final set (penetration per blow)
• C = total elastic compression of pile, cap and soil
• H = height of fall of hammer

C. Field Method

Field methods use in-situ tests and test piles to determine pile capacity. Two common field approaches are the Standard Penetration Test (SPT)-based correlations and the Cone Penetration Test (CPT).

(i) Use of Standard Penetration Test (SPT) data

Empirical correlations relate SPT N-values to unit resistances and hence to pile capacity.

where N = corrected SPT number

N̄ = average corrected SPT number over the pile length

Recommended factors of safety (F_s) depending on pile type:

• F_s = 4 for driven piles
• F_s = 2.5 for bored piles

For non-displacement piles (for example H-piles) empirical relations for unit end bearing and unit skin friction are used. For example:

q_b = 200 N

q_s =

UNDER-REAMED PILE

An under-reamed pile is a cast-in-situ pile with an enlarged base or bulb called an under-ream. Under-reamed piles are used in both sandy and clayey soils where additional end-bearing and uplift resistance are required. The ratio of bulb diameter to shaft diameter is usually between 2 and 3; a typical value used in design is 2.5.

where b_u = diameter of the bulb and typical spacing between bulbs is taken as 1.5 × b_u.

Cone Penetration Test

The static cone penetration test (CPT) provides continuous measurements of cone resistance which can be correlated with pile capacity.

where:

• q_c = static cone resistance at the base (kg/cm²)
• q̄_c = average cone resistance over the depth of the pile (kg/cm²)
• A_b = π/4 × (b_u)² = area of bulb (m²)

Negative Skin Friction 

Negative skin friction (also called downdrag) is a downward shear drag on piles caused by relative downward movement of surrounding compressible soil. It occurs when piles pass through consolidating compressible layers; the settling soil drags the pile downward, increasing the load transferred to the pile. A small relative movement (in the order of 10 mm) between soil and pile may be sufficient for the full negative skin friction to develop.

(i) Negative skin friction in cohesive soils

where:

• F_n = total negative skin friction (downward shear drag)
• P = perimeter of the pile
• L_c = length of pile within the compressible soil layer
• c_a = unit adhesion

Unit adhesion may be expressed as:

where α = adhesion factor and c_u = undrained cohesion of the compressible layer.

(ii) Negative skin friction in cohesionless soils

where:

• k = lateral earth pressure coefficient
• γ = unit weight of soil
• δ = angle of internal friction between pile surface and soil (interface friction angle)

GROUP ACTION OF PILES

When piles are used in groups, interaction between piles affects the total capacity and settlement behaviour. The ultimate load carrying capacity of a pile group is taken as the smaller of:

• the sum of the ultimate capacities of individual piles (n × Q_up), and
• the ultimate capacity of an equivalent single block or footing of the same group dimensions (Q_ug).

For design, apply a suitable factor of safety to the chosen ultimate capacity to obtain allowable loads.

(i) Group efficiency (η_g)

Group efficiency is defined as the ratio:

η_g = Q_ug / (n × Q_up)

where:

• Q_ug = ultimate load capacity of pile group
• Q_up = ultimate load capacity of a single pile

Typical tendencies:

• In sandy soils η_g may be greater than 1 due to beneficial interaction and increased passive resistance at group edges.
• In clayey soils η_g is often less than 1 because of increased settlement and overlap of stress zones, although under certain conditions it may exceed 1.
• Minimum number of piles for group action is generally taken as 3.

Expression for pile group capacity from combined base and skin resistance:

Q_ug = q_b A_b + q_s A_s

where for clays q_b ≈ 9C and A_b = B² (for a square block) and A_s = 4 B L (for a square group of side B and pile embedment L).

For a square pile group:

Size of the group, B = (n - 1)S + D

where n = total number of piles in the group, S = centre-to-centre spacing, and D = pile diameter.

where:

• S_r = group settlement ratio
• S_g = settlement of pile group
• S_i = settlement of an individual pile

(ii) When piles are embedded in a uniform clay

Behaviour of pile groups in uniform clay depends on relative stiffness of piles and surrounding soil; group effects, stress distribution and consolidation must be considered when estimating capacity and settlement.

(iii) In case of sand

where B = size (side) of pile group in metres. For sands the group action depends strongly on spacing, relative density and lateral confinement; empirical and analytical methods are used to evaluate group capacity and settlement.

Designers should always check both individual-pile-based capacity (n × Q_up) and equivalent-block capacity (Q_ug), compare settlements, and apply appropriate factors of safety and code provisions.