How to Estimate the Load Capacity of Piles? (Formulae) | Soil Engineering

The following article will guide you to learn about how to estimate the load capacity of piles with the help of static and dynamic formulae’s.

Static Formulae for Estimating the Load Capacity of Piles:

Static formulae give the static resistance offered by the soil/rock at the base and along the surface of the pile to the loads applied on the pile.

Basic Principle:

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.

Figure 20.12 shows the value of N_q as a function of ɸ, applicable for driven piles as recommended by IS:2911 (Part 1/ Sec I and Sec III)-1979.

Figure 20.13 shows the value of N_q as a function of 0 applicable for bored piles as recommended by IS – 2911 (Part 1/ Sec II and Sec IV)-1979.

Both the charts of N_q are based on Berezantsev’s curves for d/B of 20 up to ɸ = 35° and Vesic’s curves for ɸ > 35°. Berezantsev’s curves for N_q are shown in Fig. 20.14.

The value of lateral pressure efficient K depends upon the method of construction of the driven pile or the bored pile, as shown in Table 20.4.

The above static formula is applicable for driven cast in-situ piles. In the case of bored piles, the same formula can be used, but the value of ɸ should be reduced by 3° to account for the loosening of the sand due to drilling of the hole. Also K = 1 – sinɸ for bored piles. This value varies from 0.3 to 0.75 for bored piles.

The unit point-bearing resistance of bored piles is generally about half to one-third of that of driven piles. Bored cast in-situ piles with an enlarged base show a point-bearing resistance of about 1.5-2 times that of a pile without the enlargement.

Static Formula as per IS Code for Piles in Clay:

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

Q_u = cN_cA_p + αc̅A_s …(20.12)

where c is the cohesion at the pile tip in kgf/cm²; N_c the bearing capacity factor, equal to 9 for piles; A_p the cross- sectional area of pile toe in cm²; α the reduction factor also called shear mobilization factor or adhesion factor; c̅ the average cohesion over the pile length in kg/cm²; and A_s the surface area of pile shaft in cm². The value of α as recommended by IS:2911 (Part I)-1979 is given in Table 20.5.

Meyerhof’s Method for the Load Capacity of Pile:

Meyerhof suggested the following methods for estimation of load capacity of the piles for cohesionless soils and cohesive soils.

For piles in cohesionless soils, the point-bearing resistance of a pile increases with the depth in sands and reaches its maximum value at the critical embedment ratio. The critical embedment ratio (L/d)_cr typically ranges from 15 d for loose- to medium-dense sands to 20 d for dense sands. The point-bearing capacity is given by –

Q_p = A_p q N_q …(20.13)

The correlation of the point-bearing resistance with the SPT N value of cohesionless soils is given by –

Q_p = A_p x 0.4N(L/d) …(20.14)

where N is the average SPT N value over the depth 10 d above and 4 d below the pile toe.

For saturated clays, the total point-bearing resistance as per Meyerhof’s method is given by –

Q_p = A_pC_uN_c …(20.15)

where N_c= 9.

Janbu’s Method:

As per Janbu’s method, the point-bearing capacity of a pile is given by –

Goodman Method for Point Load Capacity of Piles Resting on Rock:

Goodman (1980) gave the following equation to compute the load capacity of piles resting on rock –

where q_u is the unconfined compressive strength of rock and ɸ is the effective friction angle of rock.

The design value of q_u shall be obtained by dividing the lab q_u by a factor of 5 to account for distributed fractures in the rock, which are not reflected by compression tests on small samples –

Typical values of q_u and ɸ for different types of rock are given in Table 20.6.

Dynamic Formulae for Estimating the Load Capacity of Piles:

Dynamic formulae have been developed as a means to estimate the load capacity of driven piles based on the resist­ance offered by the soil/rock during pile driving.

i Ultimate Load Capacity:

It is the maximum load which a pile or pile shaft can carry before failure of ground, when the soil fails by shear as evidenced from the load-settlement curves, or failure of the pile.

ii. Working Load:

It is the load assigned to a pile according to design.

Principle of Dynamic Formulae:

Dynamic formulae are based on the law governing the impact of elastic bodies. Dynamic formulae used for the estimation of ultimate load capacity of driven piles are based on the simple principle that the energy imparted on the pile during driving is equal to the work done in causing penetration of the pile per blow. Thus,

Wh = Q_uS …(20.23)

where W is the weight of the hammer, h is the height of fall of the hammer, Q_u is the ultimate load capacity of the pile, which is actually the ultimate resistance offered by the soil supporting the pile, and S is the penetration of the pile per blow, also known as set (from the word “permanent set” in the stress strain theory).

Thus, the load-carrying capacity of driven piles can be estimated on the basis of data obtained during the driving of the pile. The formulae used are, therefore, known as dynamic formulae. As dynamic formulae use the data obtained during the driving of the pile for the estimation of load capacity, they are applicable or useful only for driven piles.

The penetration of the pile during driving under each blow of the hammer depends on the load resistance capacity of the soil into which the pile is driven. The greater is the penetration of the pile per blow, the lesser will be the load resistance capacity of the soil.

Dynamic formulae have been developed on the basis of this principle, considering additional factors such as:

1. Elastic compression of the pile.

2. Additional pressure used for driving the pile as in the case of a double-acting steam hammer.

As the input energy is used to estimate the load capacity based on the penetration of the pile per blow, the loss of energy in applying each blow should be subtracted from the total input energy of Eq. (20.23). Otherwise, dynamic formulae would overestimate the load capacity. The loss of energy in each blow can be due to the inefficient hammer or hammer blow. Also, only that part of input energy which causes penetration of the pile should be used to estimate the load capacity. For example, part of the input energy used for elastic compression of the pile should be deducted before equating it to the work done.

Types of Dynamic Formulae:

The following are some important dynamic formulae:

1. Engineering News formula.

2. Hiley’s formula.

3. Danish formula.

Engineering News formula is the simplest and most popular dynamic formula for the estimation of load capacity. Hiley’s formula has been developed later to overcome some of the limitations of Engineering News formula.

1. Engineering News Formula:

This formula was first published in 1888 in Engineering News record and, hence, got its name. As per Engineering News formula, the ultimate load capacity of driven piles is given by –

where W is the weight of the hammer, h is the height of fall of the hammer in cm, % is the efficiency of the hammer, S is the set or penetration of the pile per blow, usually taken as the average penetration of the pile for the last 5-10 blows, C is the empirical constant to account for reduction in theoretical set due to energy loss, that is, 2.5 cm for drop hammer and 0.25 cm for stream hammer.

The value of ƞ_h is given in Table 20.7 for different types of hammers. A factor of safety of 6 is used to determine the safe load. The high value of factor of safety reflects the degree of uncertainty associated with the formula.

Modified Engineering News Formula:

The Engineering News formula has been modified to consider the energy losses in the hammer blow due to the impact as given by –

where e is the coefficient of restitution of the pile and P is the weight of the pile.

2. Hiley’s Formula:

The energy losses in the application of a hammer blow are not completely considered in the Engineering News formula. Hiley’s formula is developed to compute the ultimate load capacity of driven piles, considering various energy losses. Hiley’s formula is recommended by IS – 2911 (Part I)-1984 for the determination of ultimate load capacity of piles. As per this code, the modified Hiley’s formula is given by –

when driving without a dolly or helmet and a cushion of 2.5-cm thickness –

c = 1.77Q_u /A …(20.28b)

when driving with a short dolly or helmet and a cushion of up to 7.5-cm thickness –

where Q_u is the ultimate load capacity of the driven pile in t; W is the weight of the hammer or ram in t; h is the height of free fall of the hammer or ram in cm; ƞ is the efficiency of the hammer blow; S is the final set or penetration of the pile per blow in cm; C is the temporary elastic compressing of (a) dolly and packing (C₁) and (b) pile (C₂) and ground (C₃); P is the weight of the pile, anvil, helmet, and follower in t; e is the coefficient of restitution between the pile and the hammer or ram; 1 is the length of the pile in m; and A is the cross-sectional area of the pile in cm².

Dolly is a cushion of hard wood or other material placed on the top of the casing to receive the blows of the hammer. Helmet is a temporary steel cap placed on the top of the pile to distribute the blow over the cross section of the pile and prevent the head of the pile from damage. The upper portion of the helmet is known as dolly and is designed to hold in position a pad, block, or packing or other resilient material for preventing or absorbing shock from the hammer blow. Follower is an extension piece used to transmit the hammer blows on to the pile head. Follower is used when the pile is driven below the pile frame leaders out of reach of the hammer. Follower is also known as a long dolly.

When the pile finds refusal during driving, P should be substituted by 0.5 P in Eqs. (20.27) and (20.28). The values of e for RCC piles as recommended by IS – 2911 (Part I/Sec I and III)-1979 (R 1997) are given in Table 20.8. As it may be observed, Hiley’s formula contains the unknown Q_u on both sides of the equation and has to be solved for Q_u by trial and error. A factor of safety of 2.5 is used on the ultimate load to compute the allowable load.

Modified Hiley’s formula is superior to the Engineering News formula, as it takes into account the energy losses during pile driving. The efficiency of the hammer is usually provided by the manufacturer. The usual value of effi­ciency is given in Table 20.9 for different types of hammers.

3. Danish Formula:

The ultimate load capacity of the pile as per Danish formula is given by –

where W is the weight of hammer; h the height of fall of the hammer; ƞ_h the efficiency of hammer; S the final set per blow; and C the elastic compression of the pile given by –

Where I is the length of the pile; A the cross-sectional area of the pile; and E the modulus of elasticity of pile material. A factor of safety of 3 to 4 is used to determine the allowable load from the ultimate load.

Limitations of Dynamic Formulae:

Following are the limitations of the dynamic formic formulae:

1. Ultimate load computed from dynamic formulae represents the resistance of the ground to pile driving but not the static load capacity of the pile. When piles are driven through saturated fine sand, the pore pressure devel­oped reduces the load capacity of the pile by as much as 44% in the Engineering News formula. Thus, dynamic formulae are suitable only for coarse sands, where pore water drains out without development of pore pressure.

2. When piles are driven through cohesive soils, the skin friction resistance is reduced and the end-bearing resist­ance is increased. Thus, dynamic formulae do not represent static load capacity for cohesive soils and, hence, are not suitable for such soils.

3. There is uncertainty over the relationship between the dynamic and the static resistance of the soil.

4. The law of impact used in dynamic formulae for the computation of load capacity is not strictly valid for piles subjected to the restraining influence of the soil.

5. The group action and reduced efficiency of the pile group, compared with the sum of individual load capacity of the piles in the group, are not accounted for in dynamic formulae.

6. In the Engineering News formula, the weight of the pile and, hence, its inertia effect are not considered.

7. It is difficult to estimate the energy losses due to vibrations and damage to the dolly or packing accurately and, consequently, it results in errors in the computed load capacity of the pile.