50

because of its empirical character. For other types of piles, such as bored piles, lower bearing capacities must be expected. It may be clear that the pile point resistance can be computed for each depth in the cone penetration graph (not only for one specific depth). If this is done one gets a picture of the pile point resistance derived from the cone penetration graph as indicated in figure 38. This resembles the outcome of the test performed by Geuze and earlier tests. For different size of pile point a different pile point resistance curve will be obtained.

20

ϕ= 0

o

ϕ= 3

5 oϕ

= 25 oϕ

= 30 o

10

23

15

10

5

n x diameter

ϕ= 4

0 o

Figure 38 Figure I Theoretical slip surfaces caused by

penetration of a cone or a pile point The Koppejan method (State of the Art 2006) In The Netherlands a calculation method for the pile point resistance (method of Koppejan) has been developed based on the similarity of the soil behaviour of the penetration of a cone in a Dutch cone penetration test and the penetration of a pile during pile installation. It is assumed that during penetration a failure surface pattern develops around a penetrating cone as well as around a vertically downward moving pile point (figure I). In contrary to the failure surfaces below a shallow foundation where the failure surfaces reach the surface, the failure surfaces near a cone or pile point extend upwards to the CPT rod or the pile shaft. For the calculation method it is assumed that on the average the slip surfaces extend 4 pile diameters (4D) downwards and 8 pile diameters (8D) upwards. The influence zone for a cone with a diameter of 36 mm is therefore 150 mm below and 300 mm above the cone point. The measured cone resistance at a certain depth is therefore influenced by the soil strength over a height of 450 mm.

51

The method of Koppejan for the calculation of the point resistance is mainly empirical and usually gives a good approximation of the real pile point resistance. Subsequently the calculation method will be explained by means of an example. The empirical method consists of a sequence of steps which are elucidated hereafter: - if the cone resistance progressively increases below the pile point, the influence zone is

limited to 0.7D - the contribution to the point resistance of the qc values recorded in the influence zone below

the pile point, is the lowest average qc value (qc,0) of minimal 0.7D and maximal 4D below the point, both in a downward (qc1) and in an upward direction (qc2), whereby the used qc values to determine qc2 must never be higher than the previous value in the upward direction; the average point resistance below the pile point is then qc,0 = ½ (qc1 + qc2)

- the contribution to the point resistance of the influence zone above the pile point is determined by the average qc value (qc,b) over a distance of 8d, whereby in the same way as for qc2 the qc value used for determining qc,b must never be higher than the previous one starting with the last value of the qc2 trajectory. For continuous flight auger piles there is an exception the start of the qc;b trajectory should also be lower than 2 MN/m2

. - the maximum point resistance qmax and the ultimate point resistance qu is then determined as

follows:

2qq

q b;c0;cmax

+= (13)

ppu qq α= (14)

where qmax [kN/m2] maximum point resistance qu [kN/m2] ultimate point resistance, with qu < 15000 kN/m2 (based on

empirical data) αp [-] pile class factor see table I Example: A precast pile with a shaft width of 0.40 m is driven to a depth of 6.8 m (see figure II). This pile has an equivalent shaft diameter of:

m45.044.0D 2eq =

π×=

For this foundation level the following cone penetration resistance are determined using the graph in figure II: - qc1 = 8000 kN/m2 - qc2 = 3000 kN/m2 - qc,b = 1500 kN/m2. The ultimate point resistance for a depth of 6.8 m becomes:

)m/kN35002

15002

30008000

q 2max =

++

=

2maxpu m/kN350035000.1qq =×=α=

52

The ultimate pile point resistance is obtained by multiplying the ultimate point resistance with the point area (0.16 m2 for a square pile with a width of 0.4 m):

AqQ uu = (15)

kN5604.03500Q 2u =×=

where qu [kN/m2] ultimate point resistance stress Qut [kN] ultimate point resistance force A [m2] point area. From Dutch engineering practice it is known that the ultimate bearing capacity of the Koppejan method can be safely used in all situations. In figure III an example of the application of Koppejan method is given where the van der Veen method would have given an overestimation. If the pile point level approaches (<4Deq) the bottom of a layer with high cone penetration values the physical mechanism of punch trough can occur, instead of the type of theoretical failure mechanism given in figure I. The Koppejan method takes good care of this punch trough mechanism. In figure III the resulting dramatically reduction of the bearing capacity for pile point levels near the bottom of the soil layer with high cone penetration resistance values are shown.

lll

lll

0 5 10 MN/m2cone resistance

dept

h in m

5

10

15

4d = 1.80

8d = 3.60 m

6.8

Figure II Example of method of Koppejan for of the determination of the point resistance with the results of a CPT

Figure III Point resistance for a precast 0.29x0.29m2 pile according to Koppejan method (fat line is CPT)

cone resistance

depth

in m

6.8

53

Influence of pile type The pile type and the construction method have significant influence on the ultimate bearing capacity of a pile point. Driving a precast pile in a sand layer leads to densification, resulting in an increase of the angle of internal friction (φ'). Densification also leads to higher horizontal effective stresses on the pile. Both these factors have a positive influence on the ultimate bearing capacity as Coulomb law states τf=σ’tanφ‘. A bored pile can result in a stress relaxation as soil will move toward the excavated space in which the pile is created. Beside stress relaxation, loosening may occur too. Due to the stress relaxation and possible loosening of the packing of the soil, this pile type will have a lower ultimate point bearing capacity than the driven pile. In table I for some pile types the influences of the previous described factors are expressed in a pile class factor (αp). The factors are based on Dutch experience in Dutch sand layers. Pile type Friction factor (αp) in Dutch sand layers

[-] driven straight sided piles 1.0 steel sections and open pipe piles 1.0 continuous flight auger piles 0.8 bored pile 0.5 Tabel I Pile class factors Influence of the shape of the pile base The ultimate point resistance is influenced by the shape of the pile base. The soil surrounding a driven pile with an enlarged base will exhibit a lower effective stress level than surrounding soil a driven pile with a normal shaped base. Lower effective stress results in a lower ultimate point resistance. In figure IV the cause for this mechanism is illustrated by showing a (exaggerated) gap above the enlargement. The ultimate point resistance can be written as follows:

maxpu qq βα= (16) where: qu [kPa] ultimate point resistance, with qu < 15 kN/m2 (based on empirical data) β [-] is the factor that takes in account the influence of the shape of the pile base, see

figure V and VI. p

b

a

C

Figure IV Driven precast concrete pile with an enlarged base

54

The pile base shape factor β can be determined using figure VI. The graph in this figure shows the relations between the effective height of the pile base (H), its equivalent diameter (Deq), and the diameter of the pile shaft (deq) (figure V).

Figure V Shape of the pile base (1) β = 1.0 (2) β = 0.9 (3) β = 0.8 (4) β = 0.7 (5) β = 0.6

2eq

2eq

2

1

dD

AA

=

Figure VI Pile base shape factor β Influence of the shape of the pile cross section The shape of a cross section has influence on the pile point resistance. A round and a square shape result in a higher ultimate bearing capacity than other shapes. This influence is taken in account by using a for shape factor (s) which can be determined by:

φ′+

φ′+

=sin1

rsin1

s (17)

where: φ' [°] the effective angle of internal friction. In case of a pile in a densely packed sand

layer this can be taken φ' = 40° r [-] ratio b/a; for round pile r = 1

pile point level

pile point level

pile point level

55

b [m] the longest side of a rectangular cross section of pile point a [m] the shortest side of a rectangular cross section of pile point The ultimate pile point resistance finally can be rewritten as follows:

maxpu qsq αβ= (18) where: qu [kPa] ultimate point resistance, with qu < 15000kN/m2 C. Pile driving formulae A third type of method for determining the bearing capacity of a point bearing pile uses pile driving formula. The principle is to measure the vertical displacement of the pile due to the action of the driving hammer. This is mostly done by counting the numbers of blows needed for a certain penetration distance e.g. 0.25 m. In soft soil layers this number is very low. When the pile point encounters a hard layer the number becomes higher. A high number indicates a soil layer with a good bearing capacity. In figure VII an example is given of a pile driving record with 0.25 m intervals. All through many very complex/advanced formulae exist these formulae are unreliable and not suitable for design purposes. Sometimes a factor 10 exist between the different predictions made by the various methods. In practice the registration of the number of blows as function of the pile penetration has proven to be very useful for quality control. Actually in engineering practise there is only a limited amount of CPT’s available (for example c.t.c. 15 m and not one CPT for every pile). The dimensions of the piles in between CPT locations are often designed using interpolated CPT values. Figure VII Pile driving record

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

-11

-12

-13

-13

-14

10Cone resistance(MPa)

GL = NAP - 1,25 m

Number of blows per 0,25 m

56

To be able to check whether a proper pile tip level is reached (geology can be different in between the CPT locations), the following procedure should be followed: − pile driving should start at the location of a CPT (distance to a CPT as small as possible) It is

recommended to start at the location with the deepest pile point levels − for a pile at the location of a CPT the pile driving record should be registered for the total pile

length − the pile driving record should match the CPT graph; in that case the recorded blow count can

be used as a guideline for the piles, which are driven between CPT locations − for piles, driven within a distance of 5 times the pile diameter to a previously driven pile a

higher blow count has to be recorded than the one of the previously driven pile D. Calculation by theory The ultimate bearing capacity of a pile is reached when the soil underneath the point is pushed away along continuous failure lines. The critical load on the pile tip is in equilibrium with the shear resistance mobilized in the failure lines (in fact rupture surfaces). This equilibrium is indicated in figure 34. The shear resistance depends on the shear strength characteristics of the soil. If it is a homogeneous soil the shear strength τf is equal to:

φ′σ′+′=τ tanc nf in which c’ and φ’ are the effective cohesion and the effective angle of internal friction. If the shape of the failure line could be determined, it would be possible to calculate the ultimate bearing capacity of the pile point if c’ and φ’ are known. In another words: to determine the ultimate bearing capacity c’ and φ’ have to be determined as well as the location of the failure line. It is how ever not so easy to take an undisturbed soil sample from deep layers especially if the consists of sand. Special equipment is necessary to take the sample and keep it intact for use in the triaxial apparatus. This is the first difficulty, although it may be overcome.

63

It should be mentioned that values as low as 20 kN/m2 have sometimes been found in certain types of sands. One must how ever be extremely careful when using average values. If no other data is available, a high factor of safety should be used, especially in case of tension piles. In sand the friction along tension piles may be much lower than in case of compression piles. This is illustrated in figure 40 which gives the measured skin friction the tubes of a cone penetrometer, both in a downward and upward direction (push and pull). in clay the difference is less pronounced.

Figure 40

C. Field tests The positive skin friction can also determined using the results of Cone Penetration Tests (CPT’s). Originally CPT’s were carried out with a mechanical mantle cone. In 1952 a friction sleeve was introduced to measure the so called local friction. Begemann established that the ratio of local friction and cone resistance, the friction ratio, is related to the soil type. Nowadays CPT’s are carried out with an electrical friction sleeve cone. The friction ratios of local friction and cone resistance measured with this equipment range from approx. 1% for fine sand to approx. 4% for clay. The friction ratio of peat can be as high as 10%.

64

It should be noted that with the mechanical cone the cone resistance and local friction are discontinuously recorded at 200 mm intervals. With the electrical cone recording of data is semi-continuous with extremely short time/depth intervals. Furthermore, the shape of the mechanical cone is not the same as the shape of the electrical cone, as can be seen in figure 41. The recorded cone resistance and local friction with the two cones at a certain depth are therefore not exactly the same. The friction ratio for fine sand determined with the mechanical cone can be around 2%, while the friction ratio determined with the electrical cone usually not exceeds 1.3% as determined with the electrical cone. Differences in friction ratios determined with the two types of cone are much smaller for clay and peat.

Figure 41 Mechanical (left) and Electrical cone (right) The positive skin friction can be derived from the measured local friction. However, it appears that the cone resistance can generally more accurately be determined than the local friction. For the calculation of the positive skin friction the recorded cone resistances are therefore used. The calculation is similar to the determination of the pile point resistance. The positive skin friction is determined as follows:

friction sleeve

cone

friction sleeve

cone

65

css qq α= where: qs [kN/m2] ultimate unit positive skin friction. αs [-] friction factor see table II with Dutch experience qc [kN/m2] recorded cone resistance, where by values higher than 15000 kN/m2

that occur over a depth range more than 1 m have been limited tot 15000 kN/m2 and values higher than 12000 kN/m2 that occur over a depth range of less than 1 m have been limited to 12000 kN/m2.

Pile type Friction factor (αs) in Dutch sand layers1)

[-] driven straight sided precast concrete pile and close ended steel pipe piles

0.010

steel sections, open pipe piles, continuous flight auger piles and bored piles

0.006

Table II Maximum values of αs in sand and gravely sand where 1) The values are valid for very fine to coarse sand, (105 µm <Median<600 µm). For very

coarse sand with M> 600 µm and gravel with a M> 2 mm, reduction factors of 0.75 and 0.5 respectively must be applied to αs.

The value of αs in table II can safely used for clay and silt, in reality values for clay and silt layers will be higher. In peat the positive skin friction should be neglected because of is unreliable nature and there are extremely large deformations needed to mobilise this the ultimate skin friction. The ultimate positive skin friction for a pile is given by:

lCqFl

0s ∆××= ∑+

where: F+ [kN] positive skin friction l [m] length of pile in soil that contributes to positive skin friction C [m] circumference of pile shaft. Safety factors The current engineering practise in the Netherlands for compression piles, the pile point is always calculated using the Koppejan method and the shaft resistance is also calculated by using the cone resistance. The factor of safety is for both the same value and it depends on:

1. The amount of soil investigations (the number of CPT’s): 2. The type of structure and the number of piles: is the construction stiff and strong enough

to redistribute the load if one of the piles is failing? 3. The heterogeneity of the soil. 4. Type of load: constant or variable load.

66

For compression piles the range of the safety factor Fs generally in the range of 2-2.5. In very special situations when all above 4 components are very favourable it can be even less than 2. This lecture note considers compression piles. Tension piles behave totally different and one should not apply the calculation method, friction factors and safety factors for compression piles for the design of tension piles. Some examples of the differences in behaviour of compression piles and tension piles:

1. Due to the progressive (brittle) type of failure during tension conditions the factor of safety has to be taken higher ranging form 2.5 for static load up to 3.75 piles where the load alternates form full compression to full tension.

2. The friction factor for tension (αt) is about 30% lower then the friction factor for compression (αs).

3. In case of simultaneous loaded piles in a pile group the tension capacity is significantly lower than for a single tension pile because the effective stress in between de piles is reduced due to the upward movement of the piles in tension conditions. Furthermore, exhibit pile groups a physical upper limit of the group capacity equal to the weight of the soil in between the piles of the group.

D. Calculation by theory A fourth, maybe the best method, to compute the bearing capacity of a friction pile is by theory using the so-called slip method. In this method the maximum friction along the pile is:

∂ ′σ ′+′=τ tana hpf (21)

where:

pfτ [kN/m2] the maximum friction between pile and soil

hσ′ [kN/m2] the effective horizontal stress exerted by the soil to the pile at any depth ∂′ [°] the angle of friction between pile material and soil a' [kN/m2] the adhesion between pile material and soil. This friction is developed if the loaded pile moves downwards a little relative to the surrounding soil. This friction is called positive. Negative friction also exists and will be discussed hereafter. The friction F in a layer of a small height dh is:

pfcAF τ×= (22)

AdhAc ×= where: AC [m2] the surface of the pile in contact with the soil over the height dh A [m2] the unit area of the cross section of the pile. The total friction Ft is obtained by taking the sum of the friction F in each layer dh of the total height (depth) h of contact between pile and soil.