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NPTEL – ADVANCED FOUNDATION ENGINEERING-I

Module 8

Lecture 30

PILE FOUNDATIONS

Topics

1.1 LOAD TRANSFER MECHANISM 1.2 EQUATIONS FOR ESTIMATING PILE CAPACITY

Point Bearing Capacity, 𝑸𝑸𝒑𝒑 Frictional Resistance, 𝑸𝑸𝒔𝒔

1.3 MEYERHOF’S METHODS ESTIMATION OF 𝑸𝑸𝒑𝒑 Sand Clay (𝝓𝝓 = 𝟎𝟎 𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜)

1.4 VESIC’S METHOD-ESTIMATION OF 𝑸𝑸𝒑𝒑 1.5 JANBU’S METHOD-ESTIMATION OF 𝑸𝑸𝒑𝒑 1.6 COYLE AND CASTELLO’S METHOD-ESTIMATION OF 𝑸𝑸𝒑𝒑 IN

SAND

1.7 FRICTIONAL RESISTANCE (𝑸𝑸𝒔𝒔) IN SAND


LOAD TRANSFER MECHANISM The load transfer mechanism from a pile to the soil is complicated. To understand it, consider a pile of length L, as shown in figure 8.8a. The load on the pile is gradually increased from zero to 𝑄𝑄(z=0) at the ground surface. Part of this load will be resisted by the side friction developed along the shaft, 𝑄𝑄1, and part by the soil below the tip of the pile, 𝑄𝑄2. Now, how are 𝑄𝑄1 and 𝑄𝑄2 related to the total load? If measurements are made to obtain the load carried by the pile shaft 𝑄𝑄(𝑧𝑧), at any depth z, the nature of variation will be like that shown in curve 1 of figure 8.8b. The frictional resistance per unit area, 𝑓𝑓(𝑧𝑧), at any depth z may be determined as 𝑓𝑓(𝑧𝑧) = ∆𝑄𝑄(𝑧𝑧)

(𝑝𝑝)(∆𝑧𝑧) [8.7]

Where 𝑝𝑝 = perimeter of the pile cross section Figure 8.8c shows the variation of 𝑓𝑓(𝑧𝑧) with depth.

Figure 8.8 Load transfer mechanism for piles


If the load Q at the ground surface is gradually increased, maximum frictional resistance along the pile shaft will be fully mobilized when the relative displacement between the soil and the pile is about 0.2-0.3 in. (5-10 mm) irrespective of pile size and length L. however, the maximum point resistance 𝑄𝑄2 = 𝑄𝑄𝑝𝑝 will not be mobilized until the pile tip has moved about 10%-25% o the pile with width (or diameter). The lower limit applies to driven piles and the upper limit to bored piles. At ultimate load (figure 8. 8d and curve 2 in figure 8. 8b), 𝑄𝑄(𝑧𝑧=0) = 𝑄𝑄𝑢𝑢 . Thus 𝑄𝑄1 = 𝑄𝑄𝑠𝑠 And 𝑄𝑄2 = 𝑄𝑄𝑝𝑝 The preceding explanation indicates that 𝑄𝑄𝑠𝑠 (or the unit skin friction, f, along the pile shaft) is developed at a much smaller pile displacement compared to the point resistance, 𝑄𝑄𝑝𝑝 . This condition can be seen in Vesic’s (1970) pile-load results in granular soil, shown in figure 8. 9. Note that these results are for pile piles in dense sand.

Figure 8.9 Relative magnitude of point load transferred at various stages of pile loading

(redrawn after Vesic, 1970) At ultimate load, the failure surface in the soil at the pile tip (bearing capacity failure caused by 𝑄𝑄𝑝𝑝) is like that shown in figure 8. 8e. Note that the foundations are deep foundations and that the soil fails mostly in a punching mode, as illustrated previously in figure 8.1c and 8.3 (from chapter 3). That is, a triangular zone I, is developed at the pile tip, which is pushed downward without producing any other visible slip surface. In dense


sands and stiff clayey soils, a radial shear zone, II, may partially develop. Hence the load displacement curves of piles will resemble those shown in figure 8. 1c (from chapter 3). Figure 8. 10 shows the field load-transfer curves reported by Woo and Juang (1995) on a bored concrete pile (drilled shaft) in Taiwan. The pile was 41.7 m long.

Figure 8.10 Load transfer curves for a pile as obtained by Woo and Juang (1975)

The subsoil conditions where the pile was bored were as follows:

Depth below ground surface (m) Unified soil classification

0-3.7 SM

3.7-6.0 GP-GM

6.0-9.0 GM-SM

9.0-12.0 GM-SM

12.0-18.0 SM

18.0-20.0 CL-ML

20.0-33.0 ML/SM

33.0-39.0 GP-GM

39.0-41.7 GP-SM/GM


EQUATIONS FOR ESTIMATING PILE CAPACITY The ultimate load-carrying of a pile is given by a simple equation as the sum of the load carried at the pile point plus the total frictional resistance (skin friction) derived from the soil-pile interface (figure 8. 11a), or 𝑄𝑄𝑢𝑢 = 𝑄𝑄𝑝𝑝 + 𝑄𝑄𝑠𝑠 [8.8]

Figure 8.11 Ultimate load-carrying capacity of pile

Where 𝑄𝑄𝑢𝑢 = ultimate pile capacity 𝑄𝑄𝑝𝑝 = load − carrying capacity of the pile point 𝑄𝑄𝑠𝑠 = frictional resistance Numerous published studies cover the determination of the values of 𝑄𝑄𝑝𝑝and 𝑄𝑄𝑠𝑠. Excellent reviews of many of these investigations have been provided by Vesic (1977), Meyerhof (1976), and Coyle and Castello (1981). These studies provide insight into the problem of determining ultimate pile capacity. Point Bearing Capacity, 𝑸𝑸𝒑𝒑 The ultimate bearing capacity of shallow foundations was discussed in chapter 3. According to Terzaghi’s equations, 𝑞𝑞𝑢𝑢 = 1.3𝑐𝑐𝑁𝑁𝑐𝑐 + 𝑞𝑞𝑁𝑁𝑞𝑞 + 0.4𝛾𝛾𝐵𝐵𝑁𝑁𝛾𝛾 (for shallow square foundations)


And 𝑞𝑞𝑢𝑢 = 1.3𝑐𝑐𝑁𝑁𝑐𝑐 + 𝑞𝑞𝑁𝑁𝑞𝑞 + 0.3𝛾𝛾𝐵𝐵𝑁𝑁𝛾𝛾 (for shallow circular foundations) Similarly, the general bearing capacity equation for shallow foundations was given in chapter 3 (for vertical loading) as 𝑞𝑞𝑢𝑢 = 𝑐𝑐𝑁𝑁𝑐𝑐𝐹𝐹𝑐𝑐𝑠𝑠𝐹𝐹𝑐𝑐𝑐𝑐 + 𝑞𝑞𝑁𝑁𝑞𝑞𝐹𝐹𝑞𝑞𝑠𝑠𝐹𝐹𝑞𝑞𝑐𝑐 + 1

2𝛾𝛾𝐵𝐵𝑁𝑁𝛾𝛾𝐹𝐹𝛾𝛾𝑠𝑠𝐹𝐹𝛾𝛾𝑐𝑐 Hence, in general, the ultimate load-bearing capacity may be expressed as 𝑞𝑞𝑢𝑢 = 𝑐𝑐𝑁𝑁𝑐𝑐∗ + 𝑞𝑞𝑁𝑁𝑞𝑞∗ + 𝛾𝛾𝐵𝐵𝑁𝑁𝛾𝛾∗ [8.9a] Where 𝑁𝑁𝑐𝑐∗,𝑁𝑁𝑞𝑞∗, and 𝑁𝑁𝛾𝛾∗ are the bearing capacity factors that include the necessary shape and depth factors Pile foundations are deep. However, the ultimate resistance per unit area developed at the pile tip, 𝑞𝑞𝑝𝑝 , may be expressed by an equation similar in form to that shown in equation (9a), although the values of 𝑁𝑁𝑐𝑐∗,𝑁𝑁𝑞𝑞∗, and 𝑁𝑁𝛾𝛾∗ will change. The notation used in this chapter for the width of a pile is D. hence substituting D for B in equation (9a) gives 𝑞𝑞𝑢𝑢 = 𝑞𝑞𝑝𝑝 = 𝑐𝑐𝑁𝑁𝑐𝑐∗ + 𝑞𝑞𝑁𝑁𝑞𝑞∗ + 𝛾𝛾𝐷𝐷𝑁𝑁𝛾𝛾∗ [8.9b] Because the width D of a pile is relatively small, the term 𝛾𝛾𝐷𝐷𝑁𝑁𝛾𝛾∗ may be dropped from the right side of the preceding equation without introducing a serious error, or 𝑞𝑞𝑝𝑝 = 𝑐𝑐𝑁𝑁𝑐𝑐∗ + 𝑞𝑞′𝑁𝑁𝑞𝑞∗ [8.10] Note that the term q has been replaced by q’ in equation (10) to signify effective vertical stress. Hence the point bearing of piles is 𝑄𝑄𝑝𝑝 = 𝐴𝐴𝑝𝑝𝑞𝑞𝑝𝑝 = 𝐴𝐴𝑝𝑝� 𝑐𝑐𝑁𝑁𝑐𝑐∗ + 𝑞𝑞′𝑁𝑁𝑞𝑞∗� [8.11] Where 𝐴𝐴𝑝𝑝 = area of pile tip 𝑐𝑐 = cohesion of the soil supporting the pile tip 𝑞𝑞𝑝𝑝 = unit point resistance 𝑞𝑞′ = effective vertical stress at the level of the pile tip 𝑁𝑁𝑐𝑐∗ + 𝑁𝑁𝑞𝑞∗ = the bearing capacity factors


Frictional Resistance, 𝑸𝑸𝒔𝒔 The frictional or skin resistance of a pile may be written as 𝑄𝑄𝑠𝑠 = Σ 𝑝𝑝 Δ𝐿𝐿𝑓𝑓 [8.12] Where 𝑝𝑝 = perimeter of the pile section Δ𝐿𝐿 = incremental pile length over which 𝑝𝑝 and 𝑓𝑓 are taken constant 𝑓𝑓 = unit friction resistance at any depth 𝑧𝑧 There are several methods for estimating 𝑄𝑄𝑝𝑝 and 𝑄𝑄𝑠𝑠. They are discussed in the following sections. It needs to be reemphasized that, in the field, for full mobilization of the point resistance (𝑄𝑄𝑝𝑝), the pile tip must go through a displacement of 10 to 25% of the pile width (or diameter). MEYERHOF’S METHODS ESTIMATION OF 𝑸𝑸𝒑𝒑 Sand The point bearing capacity, 𝑞𝑞𝑝𝑝 , of a pile in sand generally increases with the depth of embedment in the bearing stratum and reaches a maximum value at an embedment ratio of 𝐿𝐿𝑏𝑏/𝐷𝐷 = (𝐿𝐿𝑏𝑏/𝐷𝐷)𝑐𝑐𝑐𝑐 . Note that, in a homogeneous soil 𝐿𝐿𝑏𝑏 is equal to the actual emebedment length of the pile, L ( figure 8. 11a). However, in figure 8. 6b, where a pile has penetrated into a bearing stratum, 𝐿𝐿𝑏𝑏 < 𝐿𝐿. Beyond the critical embedment ratio, (𝐿𝐿𝑏𝑏/𝐷𝐷)𝑐𝑐𝑐𝑐 , the value of 𝑞𝑞𝑝𝑝 remains constant (𝑞𝑞𝑝𝑝 = 𝑞𝑞1). That is, as shown in figure 8. 12 for the case of a homogeneous soil, 𝐿𝐿 = 𝐿𝐿𝑏𝑏 . The variation of (𝐿𝐿𝑏𝑏/𝐷𝐷)𝑐𝑐𝑐𝑐 with the soil friction angle is shown in figure 8.13. Note that that the broken curve is for the determination of 𝑁𝑁𝑐𝑐∗ and that the solid curve is for the determination of 𝑁𝑁𝑞𝑞∗. According to Meyerhof (1976), the bearing capacity factors increase with 𝐿𝐿𝑏𝑏/𝐷𝐷 and reach a maximum value at 𝐿𝐿𝑏𝑏/𝐷𝐷 ≈ 0.5(𝐿𝐿𝑏𝑏/𝐷𝐷)𝑐𝑐𝑐𝑐 . figure 8.13 indicates that (𝐿𝐿𝑏𝑏/𝐷𝐷)𝑐𝑐𝑐𝑐 for 𝜙𝜙 = 45° is about 25 and that is decreases with the decrease of the friction angle, 𝜙𝜙. In most cases the magnitude of 𝐿𝐿𝑏𝑏/𝐷𝐷 for piles is greater than 0.5(𝐿𝐿𝑏𝑏/𝐷𝐷)𝑐𝑐𝑐𝑐 so the maximum values of 𝑁𝑁𝑐𝑐∗ and 𝑁𝑁𝑞𝑞∗ will apply for calculation of 𝑞𝑞𝑝𝑝 for all piles. The variation of these maximum values of 𝑁𝑁𝑐𝑐∗ and 𝑁𝑁𝑞𝑞∗ with friction angle, 𝜙𝜙, is shown in figure 8. 14.


Figure 8.12 Nature of variation of unit point resistance in a homogeneous sand

Figure 8.13 Variation of (𝐿𝐿𝑏𝑏/𝐷𝐷)𝑐𝑐𝑐𝑐 with soil friction angle (after Meyerhof, 1976)

For piles in sand, 𝑐𝑐 = 0, and equation (11) simplifies to 𝑄𝑄𝑝𝑝 = 𝐴𝐴𝑝𝑝𝑞𝑞𝑝𝑝 = 𝐴𝐴𝑝𝑝𝑞𝑞′𝑁𝑁𝑞𝑞∗ (Figure 8.14) [13]


Figure 8.14 Variation of the maximum values of 𝑁𝑁𝑐𝑐∗ and 𝑁𝑁𝑞𝑞∗ with soil friction angle 𝜙𝜙

(after Meyerhof, 1976) However, 𝑄𝑄𝑝𝑝 should not exceed the limiting value, or 𝐴𝐴𝑝𝑝𝑞𝑞1, so 𝑄𝑄𝑝𝑝 = 𝐴𝐴𝑝𝑝𝑞𝑞′𝑁𝑁𝑞𝑞∗ ≤ 𝐴𝐴𝑝𝑝𝑞𝑞1 [8.14] The limiting point resistance is 𝑞𝑞1(kN/m2) = 50𝑁𝑁𝑞𝑞∗ tan𝜙𝜙 [8.15] Where 𝜙𝜙 = soil friction angle in the bearing stratum In English units, equation (15) becomes 𝑞𝑞1(lb/ft2) = 1000𝑁𝑁q

∗ tan𝜙𝜙 [8.16] Based on field observations, Meyerhof (1976) also suggested that the ultimate point resistance, 𝑞𝑞𝑝𝑝 , in a homogeneous granular soil (𝐿𝐿 = 𝐿𝐿𝑏𝑏) may be obtained from standard penetration numbers as 𝑞𝑞𝑝𝑝(kN/m2) = 40 𝑁𝑁cor 𝐿𝐿/𝐷𝐷 ≤ 400𝑁𝑁cor [8.17]


Where 𝑁𝑁cor = average corrected standard penetration number near the pile point (about 10𝐷𝐷 above and 4𝐷𝐷 below the pile point) In English units, 𝑞𝑞𝑏𝑏(lb/ft2) = 800 𝑁𝑁cor 𝐿𝐿/𝐷𝐷 ≤ 8000𝑁𝑁cor [8.18] Clay (𝝓𝝓 = 𝟎𝟎 𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜𝐜) For piles in saturated clays in undrained conditions (𝜙𝜙 = 0). 𝑄𝑄𝑝𝑝 = 𝑁𝑁𝑐𝑐∗𝑐𝑐𝑢𝑢𝐴𝐴𝑝𝑝 = 9𝑐𝑐𝑢𝑢𝐴𝐴𝑝𝑝 [8.19] Where 𝑐𝑐𝑢𝑢 = undrained cohesion of the soil below the pile tip VESIC’S METHOD-ESTIMATION OF 𝑸𝑸𝒑𝒑 Vesic (1977) proposed a method for estimating the pile point bearing capacity based on the theory of expansion of cavities. According to this theory, based on effective stress parameters. 𝑄𝑄𝑝𝑝 = 𝐴𝐴𝑝𝑝𝑞𝑞𝑝𝑝 = 𝐴𝐴𝑝𝑝(𝑐𝑐𝑁𝑁𝑐𝑐∗ + 𝜎𝜎 ′0𝑁𝑁𝜎𝜎∗) [8.20] Where 𝜎𝜎 ′0 = mean normal ground stress (effective)at the level of the pile point. = �1+2𝐾𝐾0

3� 𝑞𝑞′ [8.21]

𝐾𝐾0 = earth pressure coefficient at rest = 1 − sin𝜙𝜙 [8.22] 𝑁𝑁𝑐𝑐∗,𝑁𝑁𝜎𝜎∗ = bearing capacity factors Note that equation (20) is a mobilization of equation (11) with 𝑁𝑁𝜎𝜎∗ = 3𝑁𝑁𝑞𝑞∗

(1+2𝐾𝐾0) [8.23]

The relation for 𝑁𝑁𝑐𝑐∗ given in equation (20) may be expressed as


𝑁𝑁𝑐𝑐∗ = �𝑁𝑁𝑞𝑞∗ − 1� cot𝜙𝜙 [8.24] According to Vesic’s theory, 𝑁𝑁𝜎𝜎∗ = 𝑓𝑓(𝐼𝐼𝑐𝑐𝑐𝑐 ) Where 𝐼𝐼𝑐𝑐𝑐𝑐 = reduced rigidity index for the soil [8.25] However, 𝐼𝐼𝑐𝑐𝑐𝑐 = 𝐼𝐼𝑐𝑐

1+𝐼𝐼𝑐𝑐Δ [8.26]

Where 𝐼𝐼𝑐𝑐 = rigidity index = 𝐸𝐸𝑠𝑠

2�1+μs�(c+q ′ tan 𝜙𝜙)= Gs

c+q ′ tan ϕ [8.27]

𝐸𝐸𝑠𝑠 = modulus of elasticity of soil 𝜇𝜇𝑠𝑠 = Poisson′s ratio of soil 𝐺𝐺𝑠𝑠 = shear modulus of soil Δ = average volumatric strain in the plastic zone below the pile point For conditions of no volume change (dense sand or saturated clay), Δ = 0, so 𝐼𝐼𝑐𝑐 = 𝐼𝐼𝑐𝑐𝑐𝑐 [8.28] Table D.6 (Appendix D) gives the values of 𝑁𝑁𝑐𝑐∗ and 𝑁𝑁𝜎𝜎∗ for various values of the soil friction angle (𝜙𝜙) and 𝐼𝐼𝑐𝑐𝑐𝑐 . For 𝜙𝜙 = 0 (undrained condition), 𝑁𝑁𝑐𝑐∗ = 4

3(In 𝐼𝐼𝑐𝑐𝑐𝑐 + 1) + 𝜋𝜋

2+ 1 [8.29]


The values of 𝐼𝐼𝑐𝑐 can be estimated from laboratory consolidation and triaxial tests corresponding to the proper stress levels. However, for preliminary use the following values are recommended:

Soil type 𝐼𝐼𝑐𝑐

Sand 70-150

Silts and clays (drained condition) 50-100

Clays (udrained condition) 100-200 JANBU’S METHOD-ESTIMATION OF 𝑸𝑸𝒑𝒑 Janbu (1976) proposed calculating 𝑄𝑄𝑝𝑝 as follows: 𝑄𝑄𝑝𝑝 = 𝐴𝐴𝑝𝑝(𝑐𝑐𝑁𝑁𝑐𝑐∗ + 𝑞𝑞′𝑁𝑁𝑞𝑞∗) [8.30] Note that equation (30) has the same form as equation (11). The bearing capacity factors 𝑁𝑁𝑐𝑐∗ and 𝑁𝑁𝑞𝑞∗ are calculated by assuming a failure surface in soil at the pile tip similar to that shown in the insert of figure 8. 15. The bearing capacity relationships then are


Figure 8.15 Janbu’s bearing capacity factors

𝑁𝑁𝑞𝑞∗ = (tan𝜙𝜙 + �1 + tan2 𝜙𝜙)2(e2η′ tan 𝜙𝜙) [8.31] (The angle 𝜂𝜂′ is defined in the insert of figure 8.15. 𝑁𝑁𝑐𝑐∗ = �𝑁𝑁𝑞𝑞∗ − 1� cot𝜙𝜙 [8.32] Figure 8. 15 shows the variation of 𝑁𝑁𝑞𝑞∗ and 𝑁𝑁𝑐𝑐∗ with 𝜙𝜙 and 𝜂𝜂′. The angle 𝜂𝜂′ may vary from about 70° in soft clays to about 105° in dense sandy soils. Regardless of the theoretical procedure used to calculate 𝑄𝑄𝑝𝑝 , its full magnitude cannot be realized until the pile tip has penetrated at least 10%-25% of the width of the pile. This depth is critical in the case of sand.


COYLE AND CASTELLO’S METHOD-ESTIMATION OF 𝑸𝑸𝒑𝒑 IN SAND Coyle and Castello (1981) analyzed twenty-four large-scale field load tests of driven piles in sand. Based on the test results, they suggested that, in sand, 𝑄𝑄𝑝𝑝 = 𝑞𝑞′𝑁𝑁𝑞𝑞∗𝐴𝐴𝑝𝑝 [8.33] Where 𝑞𝑞′ = effective vertical stress at the pile tip 𝑁𝑁𝑞𝑞∗ = bearing capacity factor Figure 8. 16 sows the variation of 𝑁𝑁𝑞𝑞∗ with 𝐿𝐿/D and the soil friction angle, 𝜙𝜙.

Figure 8.16 Variation o f 𝑁𝑁𝑞𝑞∗ with 𝐿𝐿/𝐷𝐷 (redrawn after Coyle and Castello, 1981)

FRICTIONAL RESISTANCE (𝑸𝑸𝒔𝒔) IN SAND It was pointed out in equation (12) that the frictional resistance (𝑄𝑄𝑠𝑠) can be expressed as 𝑄𝑄𝑠𝑠 = Σ 𝑝𝑝 Δ 𝐿𝐿𝑓𝑓 The unit frictional resistance, f, is hard to estimate. In making an estimation of f, several important factors must be kept in mind. They are as follows:


1. The nature of pile installation. For driven piles in sand, the vibration caused

during pile driving helps densify the soil around the pile. Figure 8. 17 shows the contours of the soil friction angle, 𝜙𝜙, around a driven pile (Meyerhof, 1961). Note that, in this case, the original soil friction angle of the sand was 32°. The zone of sand densification is about 2.5 times the pile diameter surrounding the pile.

Figure 8.17 Compaction of sand near driven piles (after Meyerhof, 1961)

Figure 8.18 Unit frictional resistances for piles in sand


2. It has been observed that the nature of variation of f in the field is approximately as shown in figure 8. 18. The unit skin friction increases with depth more or less linearly to a depth of L’ and remains constant thereafter. The magnitude of the critical depth L’ may be 15 to 20 pile diameters. A conservative estimate would be 𝐿𝐿′ ≈ 15𝐷𝐷 [8.34]

3. At similar depths, the unit skin friction in loose sand is higher for a high displacement pile as compared to a low-displacement pile.

4. At similar depth, bored, or jetted, piles will have a lower unit skin friction as compared to driven piles.

Considering the above factors, an approximate relationship for f can be given as follows (figure 8. 18): For 𝑧𝑧 = 0 to 𝐿𝐿′ 𝑓𝑓 = 𝐾𝐾𝜎𝜎′𝑣𝑣 tan 𝛿𝛿 [8.35a] And for 𝑧𝑧 = " to 𝐿𝐿 𝑓𝑓 = 𝑓𝑓𝑧𝑧=𝐿𝐿′ [8.35b] Where 𝐾𝐾 = effective earth coefficient 𝜎𝜎′𝑣𝑣 = effective vertical stress at the depth under consideration 𝛿𝛿 = soil − pile friction angle In reality, the magnitude of K varies with depth. It is approximately equal to the Rankine passive earth pressure coefficient, 𝐾𝐾𝑝𝑝 , at the top of the pile and may be less than the at-rest pressure coefficient, 𝐾𝐾0, at a greater depth. Based on the presently available results, the following average values of K are recommended for use in equation (35):

Pile type 𝐾𝐾

Bored or jetted ≈ 𝐾𝐾0 = 1 − sin𝜙𝜙

Low-displacement driven ≈ 𝐾𝐾0 = 1 − sin𝜙𝜙 to 1.4𝐾𝐾𝑜𝑜= 1.4(1 − sin𝜙𝜙)

High-displacement driven ≈ 𝐾𝐾0 = 1 − sin𝜙𝜙 to 1.8𝐾𝐾𝑜𝑜= 1.8(1 − sin𝜙𝜙)


The values of 𝛿𝛿 from various investigations appear to be in the range of 0.5𝜙𝜙 to 0.8𝜙𝜙. Judgment must be used in choosing the value of 𝛿𝛿. For high displacement driven piles, Bhusan (1982) recommended 𝐾𝐾 tan 𝛿𝛿 = 0.18 + 0.0065𝐷𝐷𝑐𝑐 [8.36] And 𝐾𝐾 = 0.5 + 0.008𝐷𝐷𝑐𝑐 [8.37] Where 𝐷𝐷𝑐𝑐 = relative density (%) Meyerhof (1976) also indicated that the average unit frictional resistance, 𝑓𝑓𝑎𝑎𝑣𝑣 , for high-displacement driven piles may be obtained from average corrected standard penetration resistance values as 𝑓𝑓𝑎𝑎𝑣𝑣 = (kN/m2) = 2N�cor [8.38] Where N�cor = average corrected value of standard penetration resistance In English units equation (38) becomes 𝑓𝑓𝑎𝑎𝑣𝑣 (lb/ft2) = 40N�cor [8.39] For low displacement driven piles 𝑓𝑓𝑎𝑎𝑣𝑣 (kN/m2) = N�cor [8.40] And 𝑓𝑓𝑎𝑎𝑣𝑣 (lb/ft2) = 20N�cor [8.41] Thus 𝑄𝑄𝑠𝑠 = 𝑝𝑝𝐿𝐿𝑓𝑓𝑎𝑎𝑣𝑣 [8.42] Coyle and Castello (1981), in conjunction with the material presented in section 10, proposed that


𝑄𝑄𝑠𝑠 = 𝑓𝑓𝑎𝑎𝑣𝑣𝑝𝑝𝐿𝐿 = (𝐾𝐾𝜎𝜎�′𝑣𝑣 tan 𝛿𝛿)𝑝𝑝𝐿𝐿 [8.43] Where 𝜎𝜎�′ = average effective overburden pressure 𝛿𝛿 = soil − pile friction angle = 0.8𝜙𝜙 The lateral earth pressure coefficient 𝐾𝐾, which was determined from field observations, is shown in figure 8.19. Thus, if figure 8. 19 is used, 𝑄𝑄𝑠𝑠 = 𝐾𝐾𝜎𝜎�′𝑣𝑣 tan(0.8𝜙𝜙)𝑝𝑝𝐿𝐿 [8.44]

Figure 8.19 Variation of 𝐾𝐾 with 𝐿𝐿/𝐷𝐷 (redrawn after Coyle and Castello, 1981)

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