Question

Determine the ultimate load carrying capacity of a group pile in the following scenarios: a) Piles are 20 m long, 3 by 3 in plan, square in cross section and to be driven into a granular soil b) Piles are 20 m long, 3 by 3 in plan, square in cross section and to be driven into saturated clay soil c) Provide a reflective comment on your results

Answer 1

There are many information not available in the question to find the ultimate capacity of pile only length,area of cross section(As) and area of the surface(Ap) are given so i am giving you the concept of calculating the desired.

The ultimate capacity includes two parts the unit point bearing resistance and the skin resistance.

The unit point-bearing resistance of a pile may be given by –

f_p = cN_c + σ’N_q + 0.5γBN_γ …(20.2)

where c is the unit cohesion of the soil at the pile tip; σ’, the effective overburden pressure at the base of the pile; γ, the density of the soil at the pile tip; B, the width or diameter of the pile; and N_c, N_q, and N_γ, the bearing capacity factors.

The magnitude of the third term, 0.5γBN_γ, in Eq. (20.2) is very small for deep foundations compared with the second term, σ’N_q, and, hence, is neglected. Therefore,

f_p = cN_c +σ’N_q …(20.3)

The total bearing resistance of pile is given by –

Qp = f_pA_p …(20.4)

The total skin friction resistance is given by –

Q_s = f_sA_s …(20.5)

The ultimate load capacity of the pile is given by –

Q_u = f_pA_p + f_sA_s …(20.6)

Piles in Sands:

For pure sands –

Q_u = σ’N_q +f_sA_s …(20.7)

Thus, the point-bearing resistance of piles in granular soils increases proportionately with the increase in the length of the pile. However, when the embedded pile length is more than a critical depth, the point-bearing resistance does not increase further with the increase in the pile length. This is due to the arching action in granular soils. For driven piles in granular soils, the critical depth is found to be equal to 15 D for loose- to medium-dense sands and 20 D for dense sands. The maximum value of unit point-bearing resistance is limited to 11000 kN/m² for silica sand and 5000 kN/m² for calcareous sand. The unit skin friction resistance is given by –

f_s = σ_h tan δ – Kσ̅ tan δ …(20.8)

where σ_h is the average horizontal pressure over the pile length, acting normal to the pile surface, K is the lateral earth pressure coefficient, and 8 is the angle of friction between the pile and the soil. The total skin friction resistance is given by –

Q_s = f_sA_s …(20.9)

As per IS – 2911 (Part I), δ = ɸ, K = 1 – 3 for loose- to medium-dense sand.

The value of σ_h and, hence, the average pressure, cr increases with an increase in depth from the ground level. However, for depth greater than 15-20 times the pile diameter, the value of σ_h is restricted to the maximum value corresponding to the depth equal to 15-20 times the pile diameter. The maximum value of the unit skin friction resistance is about 100 kN/m² for silica sand and 20 kN/m² for calcareous sand.

Piles in Clay:

Piles in clays or cohesive soils carry most of the load by skin friction resistance of the pile shaft. The load-carrying capacity using static formula is computed on the basis of total stress approach taking ɸ_u = 0, assuming undrained conditions. The load capacity is a function of the reduction factor, α. The value of α depends on the undrained shear strength of the soil. The value of α is close to 1 for soft clays with low undrained strength. It decreases with the increase in the stiffness of the clay, and for very stiff clays, it may be as low as 0.3.

However, the skin friction resistance will be more for stiff clays due to higher shear strength. In the case of piles driven in clay, the soil loses some of its shear strength due to the sensitivity by remolding. As time elapses, most of the lost strength is regained by thixotropy. A time gap of minimum 30 days should be maintained from the driving of piles in clay and loading the pile. For the same reason, pile load tests in the case of driven piles in clays should be performed at least 30 days after piles are driven. Static formulae should be taken only as a guide for estimation of load capacity of the piles. It should always be supplemented by pile load tests.

Static Formula as per IS Code for Piles in Sand:

As per IS – 2911 (Part I)-1979, the ultimate load capacity of a pile in granular soil is given by –

where A_p is the cross-sectional area of pile at the bottom; d the diameter of the stem; γ’ the effective unit weight of soil at pile tip at bottom; σ’_p the effective stress at the pile toe; K the coefficient of earth pressure; σ’_si the average effective stress for the layer; A_si the surface area of pile for the ith soil layer; N_γ the bearing capacity factor for general shear as per IS – 6403-1981; and N_q the bearing capacity factor.

The bearing capacity factor, N_q, depends on the method of installation of the pile, that is, driven or bored pile, and on the angle of internal friction of the soil, ɸ

where ɸ_i is the in-situ angle of shearing resistance.