Pile Design

Piled Foundations The Purpose of a Piled Foundation As indicated in previous notes, all structures must be designed to carry loads and these must ultimately be transmitted into the ground. It is also important that this is done as efficiently as possible. Where a competent founding stratum is encountered at relatively shallow depths, spread footings tend to be very cost effective. This is because their construction simply entails the excavation of a trench or shaft which is subsequently filled with either mass or reinforced concrete. Construction of piled foundations is generally more costly because it requires the use of specialist equipment and rates of production are slower than for spread footing construction. Where a suitable founding stratum cannot be found at shallow depth (generally a depth of less than about 2.5 to 3.0 metres), the cost of excavating to this stratum can rapidly increase with the result that it becomes more cost effective to use piles. How Piles Carry Load

Foundation Load

Friction develops between pile and soil:

Foundation Load

Pile Material fails in compression under applied load

Skin Friction

Compression develops between pile and soil: End Bearing a) Soil Failure

b) Failure of Pile Material

Figure 1 – Load Carrying Mechanisms in Piled Foundations

Figure 1 shows in general how piles carry load. The foundation load is transmitted into the head of the pile as shown, which can lead to two possible types of failure: a) Soil Failure Where soil failure occurs the pile does not actually fail structurally but moves downwards under the applied load. This movement is resisted by friction at the interface between the pile and the soil (which is termed “skin friction”) and by compression at the base of the pile (which is termed “end bearing”). b) Failure of the Pile Material The second possible failure mechanism involves an actual structural failure of the pile. It is actually quite easy to check whether this will happen. This is done by dividing the applied foundation load by the cross sectional area of the pile to find the imposed stress. If the value obtained is greater than the strength of the pile material, a structural failure will occur. The application of geotechnical engineering to pile design is specifically concerned with soil failure rather than failure of the pile material. Unit Skin Friction, fs The amount of skin friction that will be developed for a given pile is generally evaluated first in terms of the Unit Skin Friction, f s. (Units kN/m2 or kPa) The Unit Skin Friction is defined as the friction per unit area between the soil and the pile surface. This will usually vary at different locations on the pile. Evaluation of the unit skin friction is a key factor in pile design. (Note: sometimes the skin friction will actually be calculated as a cohesion value. In such cases the term “skin friction” is still generally used)

Total Skin Friction, Fs In order to find the total load that the pile can carry in skin friction, it is necessary to multiply the Unit Skin Friction by the area over which this acts. This will give the total skin friction force that is generated, F s, (units kN) so that: Fs = f s x A s

Where:

(1)

fs

is the average unit skin friction over the vertical surface of the pile

As

is the total area of the vertical surface of the pile

A s =π d L

And: Where:

d

is the pile diameter

L

is the pile length

(2)

Note that equation (1) is also sometimes written in an integral form similar to: L

Fs = ∫ π d f s x dx

(3)

0

Unit End Bearing, qb The amount of end bearing that will be developed for a given pile is generally evaluated first in terms of the Unit End Bearing, q b. (Units kN/m2 or kPa) The Unit End Bearing is defined as the compression resistance per unit area between the soil and the end of the pile. Evaluation of the unit end bearing is also a key factor in pile design. Total End Bearing, QB In order to find the total load that the pile can carry in end bearing, it is necessary to multiply the Unit End Bearing by the area over which this acts. This will give the total end bearing force that is generated, Q B, (units kN) so that: Q B = qb x A B

Where:

And:

qb

is unit end bearing over the base of the pile

AB

is the total area of the vertical surface of the pile AB = π

d2 4

(4)

(5)

Note that equation (4) is also sometimes written in an integral form similar to: r

Fs = ∫ 0

r2 qb π dr 4

(6)

Ultimate Pile Capacity The Ultimate Pile Capacity is the maximum load which can be carried by the pile. For a soil failure this is obtained simply by adding together the total skin friction and the total end bearing so that: Pult =Fs + Q B = f s x A s + qb x A B

Where:

Pult

(7)

is the ultimate pile capacity in compression (Units, kN)

Ultimate Limit State and Serviceability Limit State – Factors of Safety The Ultimate Pile Capacity defined above represents the absolute maximum load that the pile can carry, that is the load at which the pile fails. Real piles cannot be designed to carry the full ultimate load as given in equation (7) as this provides no margin of safety against failure. If the pile is loaded up to its Pult value, it will fail. Consequently, in order to provide a factor of safety against failure, we need to reduce the load which is applied to the pile by applying a factor of safety to the ultimate pile capacity. Having provided a sufficient factor of safety to the ultimate pile capacity, we obtain the value of the load which we can safely apply to the pile. This is called the Allowable Pile Capacity, P all, or the Design Capacity. There are two different ways in which the required factor of safety can be applied:

1. Factor of safety applied to Total Ultimate Capacity In this case, the factor of safety is applied to the total combined value of the ultimate skin friction plus the ultimate end bearing. The actual factor of safety used here is an important factor in the pile design and can vary depending on the particular site conditions and experience. Typically, it might be specified that:

Pall =

Fs + Q B 2.5

(8)

2. Separate Factors of Safety applied separately to Ultimate Skin Friction and Ultimate End Bearing In this case two separate factors of safety are specified – one for the skin friction and one for the end bearing. Again, the actual factors of safety used will be important elements in the design and will depend on the particular site conditions and experience. Typically; Pall =

Q B Fs + 3.0 1.2

(9)

Both equations (8) and (9) must be applied in determining the allowable pile capacity – the final value will be the lower of the two values obtained from equations (8) and (9), so that:

Pall

is the lower of

Q B + Fs 2.5

or

Q B Fs + 3.0 1.2

(10)

Remembering that the actual values of the safety factors given here may be adjusted but that the calculation will follow the general principal given here. Why are there two ways of applying safety factors to determine allowable pile capacity? It may seem unusual that there are two ways to apply safety factors as given in equations (8) and (9). The logic behind this can be understood by considering the typical loadsettlement behaviour of piles. This is illustrated in Figure 2 for a pile in London Clay (performance of piles in sands or gravels may be slightly different to this but the same general principles apply). Three curves are shown in Figure 2 – one illustrates the load settlement behaviour for the pile as a whole and the other two shows how the load is shared between load carried on the shaft of the pile (skin friction) and on the base of the pile (end bearing). Analysis of Figure 2 shows that: 1. As the pile is first loaded, most of the load is taken in skin friction and very little in end bearing. As the amount of load taken in this way increases, very little settlement of the pile occurs.

2. Once the skin friction has reached its maximum value, no more load can be carried in this way and any additional pile load then begins to be carried in end bearing. 3. Once end bearing becomes the predominant mechanism by which the load is carried, the rate of pile settlement increases much more rapidly.

(After Simons and Menzies) Figure 2 – Load-Settlement curve for long pile in London Clay Understanding this load carrying mechanism suggests that in order to limit pile settlements it is necessary to adjust the proportions of load carried in skin friction and end bearing. This is because any load applied at the pile head will be carried first in skin friction and then in end bearing. In settlement terms, pile settlements will be very small until the applied load exceeds the available skin friction, after which they will begin to increase rapidly as the load begins to be carried in end bearing. Consequently, one of the best ways of limiting pile settlement is by applying a factor of safety to the skin friction. Summarising; Equation (8) provides control against overall failure – the collapse limit state. Equation (9) provides settlement control – the serviceability limit state.

Calculation of Unit Skin Friction in Piles As illustrated in Figure 2, movement must occur along the shaft in order for a force to be generated (the process is called mobilisation of the force). This force, once generated, will resist the load applied at the pile head. Intuitively, the two factors which might be expected to control movements along the shaft of the pile will be: 1. How much the soil “squeezes” the pile 2. The strength of the bond between the soil and the pile material The first of these will be a function of the normal stress exerted by the soil on the pile; the second will be a function of the soil strength. Again, it is intuitively reasonable that any method for calculating the unit skin friction should take both of these into account. There are three main methods which are generally used to calculate the unit skin friction at any point on a pile: 1.

The α Method (after Tomlinson)

2.

The β Method (after Burland)

3.

The λ Method (after Vijayvergiya and Focht)

The α Method (after Tomlinson) The α Method is used in clay soils and suggests that the unit skin friction at any point on the pile can be calculated as: fs = α Cu

Where:

(11)

α

is a coefficient which depends on the type of clay and its strength, the method of installation and the pile material

Cu

is the undrained cohesive strength of the clay

The choice of the α value to be used is a major factor in the pie design and is generally a question of judgement based on local experience, the characteristics of the particular clay, the method of construction of the pile and the findings from any available pile test data. Figure 3 shows typical suggested design curves for α values from a variety of authors.

(After Bowles) Figure 3 – Some suggested α values for Pile Design If we consider the α Method in terms of our originally intuitive assessment, it clearly takes the soil strength into account but does not make any allowance for how much the surrounding ground tends to “squeeze” the pile. A further factor to consider is that the method only considers the undrained (short term) soil strength. Soil mechanics theory suggests that the soil strength will change over time, but the α Method does not make any allowance for this. Despite these limitations, the α Method is the most widely method of calculating skin friction for piles in clay. The fact that it uses undrained soil parameters means that it is also known as the “Total Stress Approach.” The λ Method (after Vijayvergiya and Focht) The λ Method is also used for calculation of skin friction in clays. This method is based on the back-analysis of field test results on driven piles in clay soils and has been used quite widely in the design of offshore piles. In this case the unit skin friction is given as:

(

f s = λ q + 2C u

Where:

)

(12)

q

is the effective overburden to the average depth of the pile section considered

λ

is a coefficient which is obtained from Figure 4

(After Bowles) Figure 4 – Values of λ coefficient – after Vijayvergiya and Focht Again, considering the original intuitive idea, this seems an improvement on the α method in that it takes account both of the soil strength and, indirectly, of the extent to which the soil is squeezing the pile (the horizontal effective stress is a measure of this and is itself a function of the vertical effective stress). The main drawback of the λ Method is that because it is empirical, it can only be applied under the same circumstances under which the λ value has been derived. In particular this means that it can only be applied in the case of driven piles. The β Method (after Burland) By making a series of fairly simple assumptions, Burland derived the following equation to calculate the unit skin friction in sands and gravels: f s =K q tan δ

(13)

Where:

K

is a lateral earth coefficient which is selected by the Designer

q

as before, is the effective overburden to the average depth of the pile section considered

δ

is the angle of friction between the soil and the pile

The value of K is often taken as the coefficient of lateral earth pressure at rest, i.e. K =K 0 =1 − sin φ'

(14)

The value of δ will be a function of the soil strength, φ’, the method of pile

installation and the pile material. δ is often taken as 0.5 to 0.75 φ’, although some designers may take the value directly as φ’. By writing:

β = K tan δ

(15)

And then substituting this into equation (13) gives the simplest form of Burland’s equation as: fs = β q

(16)

Returning again to the original intuitive idea, equation (16) actually considers both the soil strength (β is a function of soil strength, φ’) and the extent to which the soil “squeezes” the pile (which is measured indirectly through q ). The β method also actually considers the long term strength of the pile as the calculation is carried out using drained parameters. For this reason it is also known as the “Effective Stress Approach”.

Unit End Bearing Calculation of Unit End Bearing in Clays If a pile is simply thought of as a deep foundation, it is reasonable to assume that its base capacity can be determined using an approach similar to that for a shallow foundation. Terzaghi’s equation for a shallow foundation is: qult = cNC + q Nq + 0.5γ BNγ

(17)

Under undrained conditions for a clay soil, φ’ = 0 and Nq = 1. Consequently, the first term is much greater than the second and third terms, which are hence generally ignored, so that for a piled foundation: qb = cN C

(18)

Skempton considered the variation of Nc values for foundations, as shown in Figure 5. Piles are by definition long slender members so that the D/B value will be high; usually very much greater than 4, so that Nc = 9 and assuming a total stress approach equation (18) can be re-written as: qb = 9CU

(19)

Figure 5 – Variation of Nc values with depth for foundation in Clay Calculation of Unit End Bearing in Sand and Gravel Adopting a similar approach to that outlined above for clays, this time the first and third parameters in equation (17) become insignificant (since C = 0), so that: qb = q N q

Where

q

is the vertical effective stress at the toe of the pile.

(20)

The value of Nq used in equation (20) will be different to that used in the design of shallow foundations. A number of authors have suggested Nq values for pile design. The most common values used currently are those suggested by Berezantzev, which are shown in Figure 6.

(After Simons and Menzies) Figure 6 – Berezantsev’s Values of Nq for Pile Design

Procedure for Carrying out a Pile Design Having developed the theory, pile design follows a fairy standard procedure as outlined below: 1. Determine the most appropriate method for pile design: Calculation of skin friction will use equation (11), (12) or (13) Calculation of end bearing will use equation (19) or (20) 2. Divide the total length of the pile up into a series of vertical elements For example, a 12 metre long pile might be divided into 4 No. 3 metre long elements. 3. Calculate the skin friction for each pile element This is done by calculating the unit skin friction for each element and multiplying this by the surface area of that element.

4. The total skin friction, Fs, equals the sum of the values for each of the individual pile elements. 5. Calculate the unit end bearing for the pile This is calculated at the toe level of the pile 6. The total end bearing, QB, equals the unit end bearing multiplied by the cross sectional area of the pile base. 7. The Allowable Pile Capacity can then be calculated by applying the relevant factors of safety to Fs and QB. This requires the use of equation (10)