Lcrit
y
tP
tM Q
Lcrit L
Pile Length
Lcrit
y
tFigure 2-6 Solving for Critical Pile Length
2-1-4 Occurrences of Lateral Loads on Piles
Piles that sustain lateral loads of significant magnitude occur in offshore structures, waterfront structures, bridges, buildings, industrial plants, navigation locks, dams, and retaining walls. Piles can also be used to stabilize slopes against sliding that have either failed or have a low factor of safety. The lateral loads may be derived from earth pressures, wind, waves and currents, earthquakes, impact, moving vehicles, and the eccentric application of axial loads. In numerous cases the loading of the piles cannot be obtained without consideration of the stresses and deformation in the particular superstructure.
Structures where piles are subjected to lateral loading are discussed briefly in the following paragraphs. Some general comments are presented about analytical techniques. The cases that are selected are not comprehensive but are meant to provide examples of the kinds of problems that can be attacked with the methods presented herein. In each of the cases, the assumption is made that the piles are widely spaced and the distribution of loading to each of the piles in a group is neglected.
2-1-4-1 Offshore Platform
A bent from an offshore platform is shown in Figure 2-7(a). A three-dimensional analysis of such a structure is sometimes necessary, but a two-dimensional analysis indicated by the drawing is frequently adequate. The preferred method of analysis of the piles is to take the full interaction into account between the superstructure and the supporting piles. The piles are assumed to be removed and replaced by nonlinear reactions: axial load versus axial movement,
lateral load versus lateral deflection, and moment versus lateral deflection. A simplified method of analyzing a single pile is illustrated in the sketches.
P
tM
tθt
P
tM
tθt
(a) (b) (c) Figure 2-7 Simplified Method of Analyzing a Pile for an Offshore Platform
The second pile is shown in Figure 2-7(b). The assumption is made that the annular void between the jacket leg and the head of the pile was sealed with a flexible gasket, and that the annular space was filled with grout. Thus, in bending the pile and jacket leg will be continuous and have the same curvature.
The sketch in Figure 2-7(c) shows that the stiffness of the braces was neglected and that the rotational restraint at the upper panel point was intermediate between being fully fixed and fully free. The assumption is then made that the resultant force on the bent can be equally divided among the four piles, giving a known value of Pt. The second boundary condition at the top of the pile is the value of the rotational restraint, Mt/St, which is taken as 3.5 EI/h, where EIc
is the combined bending stiffness of the pile and the jacket leg. The p-y curves for the supporting soil can be generated, and the deflection and bending moment along the length of the pile can be computed.
The method is approximate; however, a pile with the approximate geometry can be rapidly modeled by the p-y method. Also, there may be other structures where the pile head is neither completely fixed nor completely free, and the use of rotational restraint as one of the boundary conditions is convenient.
The implementation of the method outlined above is shown by Example 3 provided with LPile and explained in the User’s Manual. In addition to investigating the exact value of Mt/ St, the designer should consider the rotation of the superstructure due principally to the movement
of the piles in the axial direction. This rotation will, of course, affect the boundary conditions at the top of the piles.
2-1-4-2 Breasting Dolphin
An interesting use of a pile under lateral load is as a breasting dolphin. Figure 2-8(a) depicts a vessel with mass m approaching a freestanding pile. The velocity of the vessel is v and its energy on contact would be ½mv2. The deflection of the pile could be computed by finding the area under the load-deflection curve that would equate to the energy of the vessel.
The analyst would be concerned with a number of parameters in the problem. The level of water could vary, requiring a number of solutions. The pile could be tapered to give it the proper strength to sustain the computed bending moment while at the same time making it as flexible as possible.
With the first impact of a vessel, the soil will behave as if it were under static loading (assuming no inertia effects in the soil) and would be relatively stiff. With repeated loading on the pile from berthings, the soil will behave as if under cyclic loading. The appropriate p-y curves would need to be used, depending on the number of applications of load.
A single pile, or a group of piles, could support the primary fendering but the exact types of cushions or fenders to be used between the vessel and the pile need to be selected on the basis of the vessel size and berthing velocity. It should be noted that fenders must be mounted properly above the waterline to prevent damage to the berthing vessels.
Deflection
Load
Breasting Dolphin
m, v
Deflection
Load
Breasting Dolphin
m, v
Figure 2-8 Analysis of a Breasting Dolphin
2-1-4-3 Single-Pile Support for a Bridge
A common design used for the support of a bridge is shown in Figure 2-9. The design provides more space under the bridge in an urban area and may be aesthetically more pleasing than multiple columns.
As may be seen in the sketch, the primary loads that must be sustained by the pile lie in a plane perpendicular to the axis of the bridge.
The loads may be resolved into an axial load, a lateral load, and a moment at the ground surface or, alternately, at the top of the column.
The braking forces are shown properly in a plane parallel to the axis of the bridge and can be large, if heavily loaded trucks are suddenly brought to a stop on a downward-sloping span.
The deflection that may be possible in the direction of the axis of the bridge is probably limited to that allowed by the joints in the bridge deck. Thus, one of the boundary conditions for the piles for such loading could be a limiting deflection.
If it is decided that significant loads can be acting simultaneously in perpendicular planes, two independent solutions can be made, and the resulting bending moments can be added algebraically. Such a procedure would not be perfectly rigorous but should yield results that will be instructive to the designer.
From Dead Loads From Wind and
Other Forces Loads From Traffic
Loads From Braking and Wind Forces
From Dead Loads From Wind and
Other Forces Loads From Traffic
Loads From Braking and Wind Forces
Figure 2-9 Loading On a Single Shaft Supporting a Bridge Deck 2-1-4-4 Pile-Supported Overhead Sign
The sketches in Figure 2-10 show two schemes for piles to support an overhead sign.
Many such structures are used in highways and in other transportation facilities. Similar schemes could be used for the foundation of a tower that supports power lines.
The loadings on the foundation from the wind will be a lateral load and a relatively large moment; a small axial load will result from the dead weight of the superstructure. The lateral load and moment will be variable because the wind will blow intermittently and will gust during a storm. The predominant direction of the wind will vary; these factors should be taken into account in the analysis.
The sketch in Figure 2-10(a) shows a two-pile foundation. The lateral load and axial load will be divided between the two piles, and the moment will be carried principally by tension in one pile and compression in the other. The lateral load will cause each of the piles to deflect, and there will be a bending moment along each pile. In performing the analysis for lateral loading, p-y curves must be derived for the supporting soil with repeated loading being assumed. A factored load must be used, and the degree of fixity of the pile heads must be assessed. The connection between the piles and the cap may be such that the pile heads are essentially free to rotate.
Alternatively, the design may be made so that the pile heads may be assumed to be completely fixed against rotation.
Pile Cap
Column Column
Dead Load Dead Load
Wind Load
Wind Load
Single-Shaft Foundation Two-Shaft
Foundation
(b) (a)
Pile Cap
Column Column
Dead Load Dead Load
Wind Load
Wind Load
Single-Shaft Foundation Two-Shaft
Foundation
(b) (a)
Figure 2-10 Foundation Options for an Overhead Sign Structure
The pile heads, under almost any designs, will likely be partially restrained, or at some point between fixed and free. An interesting exercise is to take a free body of the pile from the bottom of the cap and to analyze its behavior when a shear and a moment are applied at the end of this “stub pile. “ The concrete in this instance will serve a similar function as the soil along the lower portion of the pile. The rotational restraint provided by the concrete can be computed by use of an appropriate model, perhaps by using finite elements. At present, an appropriate analytical technique, when a pile head extends into a concrete cap or mat, is to assume various degrees of pile-head fixity, ranging from completely fixed to completely free, and to design for the worst conditions that results from the computer runs.
The sketch in Figure 2-10(b) shows a structure supported by a single pile. Shown in the figure is a pattern of soil resistance that must result to put the pile into equilibrium. In performing the analyses, the p-y curves must be derived as before but, in this instance, the conditions at the pile head are fully known. The loading will consist of a shear and a relatively large moment, and the pile head will be free to rotate. Because the axial load will be relatively small, studies will probably be necessary to determine the required penetration of the pile so that the tip deflection will be small and the pile will not behave as a “fence post. “
Of the two schemes, selection of the most efficient scheme will depend on a number of conditions. Two considerations are the deflection under the maximum load at the top of the structure and the availability of equipment that can construct the large pile.
2-1-4-5 Use of Piles to Stabilize Slopes
An application for piles that is continuing interest is the stabilizing of slopes that have moved or are judged to be near failure. The sketch in Figure 2-11 illustrates the application. A bored pile is often employed because it can be installed with a minimum of disturbance of the soil near the actual or potential sliding surface.
Figure 2-11 Use of Piles to Stabilize a Slope Failure
The procedures for the design of such a pile are described in some more detail later in this manual. The special treatment accorded to this particular problem is due to its importance and because the technical literature fails to provide much guidance to the designer.
2-1-4-6 Anchor Pile in a Mooring System
The use of a pile as the anchor for a tieback anchor is illustrated in Figure 2-12. A vertical pile is shown in the sketch with the tie rod attached below the top of the pile. The force in the rod can be separated into components; one component indicates the lateral load on the pile and the other the axial load.
The p-y curves are derived with proper attention to soil characteristics with respect to depth below the ground surface. The loading will be sustained and a proper adjustment must be made, if time-related deflection is expected.
The analysis will proceed by considering the loading to be applied at the top of the pile or, preferably, as a distributed load along the upper portion of the pile. In the case of the anchor that is shown, the load is applied at some distance from the top of the pile. The analytical method can deal with the anchor pile by appropriate innovation.
2-1-4-7 Other Uses of Laterally Loaded Piles
Piles under lateral loading occur in many structures or applications other than the ones that were earlier mentioned. Some of these are high-rise buildings that are subjected to forces from wind or from unbalanced earth pressures; pile-supported retaining walls; locks and dams;
waterfront structures such as piers and quay walls; support for overhead pipes and for other facilities found in industrial plants; and bridge abutments.
The method has the potential of analyzing the flexible bulkhead that is shown in Figure 2-12. The sheet piles (or tangent piles if bored piles are used) can be analyzed as a pile, if the p-y curves are modified to reflect the soil resistance versus deflection for a wall, rather than for a pile. Research on the topic has been undertaken (Wang, 1986) and has already been implemented in computer program PYWall from Ensoft, Inc.
Sheet Pile Wall
Anchor Pile (Dead Man) Tie-back
Sheet Pile Wall
Anchor Pile (Dead Man) Tie-back
Figure 2-12 Anchor Pile for a Flexible Bulkhead