The reliable design of piles for earthquake loads is difficult because of the uncertainties involved in determining the design deformation state of the piles. This is partly due to the uncertainties involved in assessing lateral soil-pile interaction, and partly to the complexity of behaviour of pile groups. As indicated in Figures 9.1, 9.4 and 9.5, high bending moments may occur at various locations up the pile. In addition to the locations of high bending moments indicated by these idealized moment diagrams, high stresses may be induced at other depths due to local shear failure of weak layers of soil or due to liquefaction, or due to loss of lateral support from the soil because of scour in waterways or settlement of loose deposits.

The seismic design of piled foundations will include consideration of the vertical and horizontal stresses and the structural integrity of the foundation. Vertical seismic loads in

Punching action Final buildinn profile

Initial building profile

Punching action Final buildinn profile

Initial building profile

Figure 9.1 Interaction of raked piles and pilecap during an earthquake

Figure 9.1 Interaction of raked piles and pilecap during an earthquake individual piles may vary greatly, depending upon their position in relation to the rest of the pile group and to the superstructure (Figure 9.1). Some piles, particularly those at the edges or corners of pile systems, may have to carry large tensile as well as compression forces during earthquakes.

Lack of structural integrity has caused failure of piled foundations in earthquakes, such as that of San Fernando, 1971. Sufficient continuity reinforcement must be provided between the piles and the pile cap, and the piles themselves must obviously be able to develop the required tensile, compression and bending strength. Where plastic hinges are likely to form in concrete piles, suitable confinement reinforcement must be provided, as it is in columns.

As a supplement to the following discussion of piles, the reader is referred to the specialist literature, especially the extensive review of Pender (1993) and the earlier text of Poulos and Davis (1980).

In response to horizontal ground motions, it appears that piles generally follow the formations of the ground, and do not cut through the soil. It also seems that piles are subject to two distinct failure mode zones:

(1) In the upper part of the pile, say the top 10d (d = diameter), the response is affected by the presence of the free soil surface, which permits the soil adjacent to the pile to yield and move upwards in a wedge (Figure 9.2). Also, the upper part of the pile has inertia loads induced in it by the surrounding soil and the structure above.

(2) In the lower part of the pile, the surrounding soil dominates the response, and flexibility or ductility is required to permit the pile to safely conform to the curvatures imposed by the soil deformations.

In the dynamic response analysis of piled foundations for design purposes, because the soil-pile interaction is so complex, it is usual to simplify the structural modelling problem, often as much as in the following opposing options:

(1) Ignore the soil entirely, using only the stiffness of the pile, after having first defined some depth to pile fixity based on soil stiffness.

(2) Ignore the horizontal and rotational stiffness of the pile, using only the stiffness of the soil.

The development of more sophisticated, research-oriented analytical techniques, similar to the shear beam model described in Section 5.2.2, has been along two main lines:

(1) a continuous elastic model (e.g. Gazetas and Dobry, 1984);

(2) a discrete model with lumped masses, springs and dashpots (e.g. Penzien, 1970; Blaney et al., 1976).

Such techniques permit pile stresses as well as stiffness to be estimated. The linear analyses are generally conducted in the frequency domain, pile stiffnesses and damping being expressed in frequency-dependent terms, as discussed in Section 5.3.3. Significant differences between the results of such studies need to be resolved, particularly for the low-frequency properties.

Method (2) above is used for non-linear as well as linear analyses. Some of the non-linear analyses studied that have been done have not been true dynamic earthquake analyses of the shear beam type noted above, but have been of either repeated or quasi-static cyclic loading nature, in which the soil-pile system has been loaded by a horizontal load and perhaps a moment applied at the top. Clearly, such a loading model closely represents wind or wave loads, but for seismic loading it would give better estimates of stiffness than of worst deformations in the pile.

In an example of a full dynamic earthquake response analysis, some light was thrown on the likely behaviour of long piles in deep sensitive clay in a sophisticated non-linear analysis of a bridge described by Penzien (1970). In this case, it was found that if subjected to moderate earthquake loading like that of El Centro in 1940, the piles would have been deformed to their yield curvatures.

In the majority of design projects, pile design and foundation modelling for superstructure analysis will be carried out with reference to (separate) equivalent-static load analyses of the piles. The latter comprise a number of methods which may be divided into three categories:

(1) limiting (or ultimate) loads;

(2) elastic continuum;

(3) non-linear discontinuum (Winkler springs).

Only the elastic continuum method will be considered here.

Considering an elastic pile embedded in an elastic soil and loaded at the pile head, the displacement u and the rotation 9 at the ground surface are given by u = fuHH + fuMM, (9.1)

where H is the applied horizontal load, M is the applied moment, and fuH, fuM, f9H, f9M are flexibility coefficients. From the reciprocal theorem, f9H = fuM.

For a long pile the flexibility coefficients are functions of the ratio of the Young's moduli of the pile and the soil, Poisson's ratio and Young's modulus of the soil, and the pile diameter. For short piles, the pile length is also required in the expressions for the flexibilities.

The flexibility coefficients for a long circular pile are expressed in terms of a modulus ratio:

where Ep is Young's modulus for the pile material, Es is Young's modulus of the soil, z is the depth below ground level, and D is the pile diameter.

The pile head can be loaded with a horizontal shear force, a moment or both. When the shear force is applied to a pile shaft above the ground surface, it is convenient to express the resulting pile head moment in terms of an eccentricity defined in the following alternative ways:

Lateral elastic displacements of a single 'long' pile

Consider the case where the soil modulus increases linearity with depth. The equations for this case are given by Budhu and Davies (1987, 1988), except for those involving Poisson's ratio where a value of v = 0.5 has been adopted by Pender (1993), where resulting simplifications are given below. Young's modulus of the soil and the stiffness ratio are

where m is the rate of increase in Young's modulus with depth. Budhu and Davies give values of m for sands of various densities. These values are intended for static loading of piles, so they are not appropriate for dynamic excitation of piles embedded in liquefiable sands.

The active length of the pile is la = 1.3DK0222. (9.6)

If the pile length is greater than that given by the above equation, then the pile is 'long' and the following equations for the flexibility coefficients can be used:

The location and maximum moment in the pile section are given by

where IMH = aKb, a = °.6 f, and b = °.17 f—° 3. If IMH is greater than 8, a value of 8 is used.

Non-linear lateral displacements of a single 'long' pile

For estimating the effect of local soil failure at the pile-soil interface, Davies and Budhu (1986) proposed a modification factor to be applied to the elastic behaviour model. Thus for a free-head pile, the pile head displacement, rotation and maximum moment are found from uy = IuyuE,

MMy = IMyMME, where Iuy, Iey and IMy are yield influence factors, uE is the elastic pile head displacement from equations (9.1) and (9.7), 0e is the elastic pile head rotation from equations (9.2) and (9.7), and Mme is the maximum elastic pile shaft moment from equation (9.9). For piles in cohesive soils, the yield influence factors are given by h — 14k°32

where

cD3 1000

c being the rate of increase of undrained shear strength with depth (kN/m3). For piles in cohesionless soils, the yield influence factors are h - k0-35

where

KpYD3 1000

in which $ is the friction angle of the sand, Kp = (1 + sin $)/(1 — sin $), and y is the appropriate unit weight of the sand to give the variation of vertical effective stress with depth.

The non-linear response of a pile as given by the above expressions has been calculated by Pender (1993) for the case where the friction angle of the sand is 35°, its unit weight is 10 kN/m3, H/M is 2.3 and the yield moment of the pile is 1575 kNm. The resulting non-linear plots of pile head displacement and rotation, and the maximum moment in the pile, are plotted as functions of the horizontal shear load on the pile head in Figure 9.3.

Lateral capacity of a single 'long' pile

A much used approach for estimating the ultimate lateral capacity of a pile is that of Broms (1964a, 1964b). He proposes a simple method of estimating the maximum lateral load for two cases, that is, in cohesive and cohensionless soils. Broms considers free-head and fixed-head cases and short, intermediate and long piles. The soil reaction and force diagrams for free-head and fixed head piles in the two soil types are illustrated in Figures 9.4 and 9.5. Broms assumed that the ultimate lateral resistance of the pile is developed when the soil yields and plastic hinges develop in the piles. Charts are provided by Broms to aid the calculation. However, the method of Budhu and Davies (1987, 1988) involves simple equations from which to calculate the capacity directly, as described below for long piles.

Referring to Figure 9.4 for cohesive soils, let the ultimate bearing capacity of the soil be 9iu, where ju is the undrained shear strength. For free-head piles the ultimate lateral capacity is

where f is defined by equation (9.4), and the ratio nc is found from

10MV

The position of the yield moment (and the length of pile shaft over which soil failure occurs) is given by

where e0 and fs define the simplified lateral stress regime adopted for the top of the pile (Figure 9.4).

Plastic hinge a /

Soil at failure

Soil reaction

'Elastic' soil i

Soil at failure

'Elastic' soil

'yield

Bending moment

'yield

Bending moment

Soil reaction

Bending moment

Soil reaction

Bending moment

Figure 9.4 Ultimate pressure distribution against a laterally loaded long pile in cohesive soil (adapted from Broms, 1964a): (a) free-head and (b) fixed-head pile. (Reproduced by permission of the American Society of Civil Engineers)

For a fixed-head pile the ultimate lateral capacity will be given by

The above four equations are based on the same assumptions as Broms, with the exception that ec is 0.6 m for Budhu and Davies and 1.5D for Broms. The minimum length of pile shaft required for this solution to be valid is

9suD

Figure 9.5 Ultimate pressure distribution against a laterally loaded long pile in cohesionless soil (adapted from Broms, 1964b): (a) free-head and (b) fixed-head pile. (Reproduced by permission of the American Society of Civil Engineers)

Figure 9.5 Ultimate pressure distribution against a laterally loaded long pile in cohesionless soil (adapted from Broms, 1964b): (a) free-head and (b) fixed-head pile. (Reproduced by permission of the American Society of Civil Engineers)

The above equations give essentially the same prediction for the ultimate lateral capacity as those of Broms (1964a).

The simplified pressure distributions adopted by Broms for cohesionless soils are given in Figure 9.5. It can be seen that Broms assumed that the soil pressure along the pile shaft is controlled by 3Kp, where Kp is the coefficient of passive earth pressure.

Again, following the work of Budhu and Davies, their expression for the ultimate lateral capacity of a free-head pile in cohensionless soil is

3 KpyD4

The position of the yield moment (and the length of pile shaft over which failure occurs) is given by

y 3KpyD

where y is the unit weight of the sand chosen to give the effective vertical stresses (y ' for a saturated sand). For the fixed-head case, the ultimate lateral capacity is

The minimum length of pile shaft required for this long pile solution to be valid is

As with the cohesive soil case, the above equations give essentially the same predictions of pile lateral capacity as those of Broms (1964b).

In the foregoing discussion a number of aspects of pile behaviour have not been considered, such short piles, raking piles, dynamic stiffness of piles, vertical load capacity pile groups and other soil profiles. These all need specific consideration, for which the reader is referred to the literature, in particular Pender (1993) and Budhu and Davies (1987, 1988).

When a structure is to be built on liquefiable ground, there are a number of procedures which may be used to ensure adequate foundation safety, which fall into two categories:

(1) pile foundations; and

(2) soil improvement.

When using piles in liquefiable ground, the piles should be designed for the conditions induced by liquefaction, as the loss of soil support in the liquefied layer may cause large forces in the piles (Nishizawa et al., 1984). Concrete piles should be detailed for strength and ductility as for columns (Section 10.3.3). However, sole reliance on piles should be practised with caution, because of the difficulty of determining the location and thickness of potential liquefaction layers. In many cases, it will be appropriate to combine piling with a degree of soil improvement to reduce the probability of liquefaction occurring. A range if issues related to the design of piles in liquefiable ground are discussed by Berrill and Yasuda (2002).

In the latter part of the twentieth century, a number of techniques were developed to improve the properties of liquefiable ground. They can be divided into two main categories: densification techniques and reinforcement techniques (Kramer, 1996). These techniques are briefly discussed below.

Densification increases the strength and stiffness of the soil, and reduces the tendency to generate excess porewater pressures under cyclic loading. It is thus one of the most effective and commonly used soil improvements methods. A number of methods are used to carry it out.

Vibro techniques use probes in the soil which vibrate horizontally (vibroflotation) or vertically (vibro rod). These techniques are most effective in granular deposits with fine contents less than 20% and clay contents less than 3%.

Ohsaki (1970) reported on the effectiveness of compaction using the vibroflotation technique in preventing liquefaction in the Tokachioki earthquake of 1968, which caused liquefaction at similar uncompacted nearby sites.

Dynamic compaction is effected by repeatedly dropping a heavy weight from a crane on to the ground surface in a grid pattern. It is effective to depths of 9-12 m. Because of its secondary effects of noise, transmission of vibration to nearby sites and dust problems on dry sites, dynamic compaction is sometimes unacceptable in urban areas. Another, more violent, method of using energy to cause compaction is blasting, which is effective in similar soil conditions to vibro techniques, but its use is clearly limited to remote sites.

Compaction grouting is carried out by injecting into the ground under pressure a low slump grout. A highly viscous grout forms intact bulbs or columns which densify the surrounding soil by displacement. It is at its most effective when the soil is softest and weakest. Compaction grouting is a very adaptable technique as it can be used to any depth and in all soil types.

In general, it is insufficient to densify the soils solely in the area vertically below the foundations. To minimize post-earthquake settlement of a structure on liquefiable soils, the area densified needs to be extended to a zone within an angle of 30-45° away from the base of the structure (Iai et al., 1988), as shown in Figure 9.6.

The strength and stiffness of a soil deposit can sometimes be improved by installing in it discrete elements of other materials, such as concrete, steel, timber or dense gravel. For countering liquefaction these elements are generally in the form of piles.

Stone columns are made of either fine or coarse gravels. One way of installing them is the Franki method, in which a steel casing, initially closed at the bottom by a gravel

Structure

Ground surface

Liquefiable soil

Liquefiable soil

Zone of soil improvement

BC to AD

Figure 9.6 Zone of densification of potentially liquefiable soil required beneath and surrounding a structure plug, is driven to the required depth, and gravel is placed in it as it is withdrawn. The resulting stone columns improve the soil deposit in four or more ways. First, the deposit is improved through the high density, stiffness and strength of the gravel and in this sense the soil is reinforced. Secondly, the stone columns provide drainage routes that inhibit the development of excess porewater pressures. Seed and Booker (1977) describe a design procedure for the use of gravel drains in liquefiable sand. The spacing of the drains is governed by the length of drainage path and the corresponding time required to permit safe dissipation of pore-pressure build-up. Thirdly, the processes used for installing the gravel densify the surrounding soil by both vibration and lateral displacement. Fourthly, as a result of the installation, the lateral stresses are increased in the soil surrounding the columns.

At the time of writing, the NEESR Grand Challenge project, 'Seismic Risk Management for Ports', was having promising results with testing the use of prefabricated vertical drains and colloidal silica grouting for mitigating liquefaction hazards. For more information, visit http://www.neesgc.gatech.edu.

As compaction piles (usually of prestressed concrete or timber) are displacement piles, they improve the soil in the third and fourth ways discussed above for stone columns. In addition, the lateral strength of the piles helps suppress horizontal displacements of the soil. As compaction piles densify the soil within a distance from themselves of 7-12 pile diameters (Kishida, 1967), to be effective they need to be installed in a grid pattern. Between them relative densities of up to 75-80% are mostly achieved (Solymar and Reed, 1986).

While the above two main methods of designing foundations for liquefiable sites (i.e. piles and soil improvements) are sometimes used individually, they often need to be used at the same time. For example, dynamic compaction is sometimes part of site preparatory work prior to filing. Further, it is important to be aware that the effectiveness of soil improvement techniques may be difficult to accurately predict for a given site. Thus, it is advisable to construct test sections before commencing work, or even before finally selecting the techniques to be used.

Additional information on the above techniques soil improvement techniques should be sought in the literature (e.g. Kramer, 1996).

Further advice on seismic foundation design is given in the specialist literature, such as Bhattacharya (2007), Kramer (1996), Pender (1993, 1996), Taylor and Williams (1979) and Zeevaert (1983).

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