The Foundation Engineering Handbook Chapter 8

The Foundation Engineering Handbook Chapter 8 Geotechnical earthquake engineering can be defined as that subspecialty within the field of geotechnical engineering that deals with the design and construction of projects in order to resist the effects of earthquakes. Geotechnical earthquake engineering requires an understanding of basic geotechnical principles as well as an understanding of geology, seismology, and earthquake engineering. In a broad sense, seismology can be defined as the study of earthquakes. This would include the internal behavior of the earth and the nature of seismic waves generated by the earthquake.

Design of Laterally Loaded Piles

Manjriker Gunaratne CONTENTS

8.3.2.2 Lateral Pressure-Deflection (p-y) Method of Analysis 348

8.3.2.3 Synthesis of p-y Curves Based on Pile Instrumentation 350

8.5 Load and Resistance Factor Design for Laterally Loaded Piles 3568.6 Effect of Pile Jetting on the Lateral Load Capacity 3568.7 Effect of Preaugering on the Lateral Load Capacity 360

8.1 Introduction

Single piles such as sign-posts and lamp-posts and pile groups that support bridge piers andoffshore construction operations are constantly subjected to significant natural lateral loads(such as wind loads and wave actions) (Figure 8.1) Lateral loads can be also introduced onpiles due to artificial causes like ship impacts Therefore, the lateral load capacity is certainly

a significant attribute in the design of piles under certain construction situations

Unlike in the case of axial load capacity, the lateral load capacity must be determined byconsidering two different failure mechanisms: (1) structural failure of the pile due to yielding

of pile material or shear failure of the confining soil due to yielding of soil, and (2) pile

becoming dysfunctional due to excessive lateral deflections Although passive failure of theconfining soil is a potential failure mode, such failure occurs only at relatively large

deflections which generally exceed the tolerable movements

FIGURE 8.1

Laterally loaded pile.

One realizes that “short” piles embedded in relatively stiffer ground would possibly fail due toyielding of the soil while “long” piles embedded in relatively softer ground would produceexcessive deflections In view of the above conditions, this chapter is organized to analyzeseparately, the two distinct issues presented above Hence the discussion will deal with twomain issues: (1) lateral pile capacity from strength considerations, and (2) lateral pile capacitybased on deflection limitations

On the other hand, piles subjected to both axial and lateral loading must be designed forstructural resistance of the piles as beam-columns

8.2 Lateral Load Capacity Based on Strength8.2.1 Ultimate Lateral Resistance of Piles

Broms (1964a,b) produced simplified solutions for the ultimate lateral load capacity of piles

by considering both the ultimate strength of the bearing ground and the yield stress of the pilematerial For simplicity, the Broms (1964a,b) solutions are presented separately for differentsoil types, namely, cohesive soils and cohesionless soils

8.2.1.1 Piles in Homogeneous Cohesive Soils

When a pile is founded in a predominantly fine-grained soil, the most critical design case isthe case where soil is in an undrained situation The maximum load that can be applied on thepile depends on the the following factors:

1 Fixity conditions at the top (i.e., free piles or fixed piles) Most single piles can be

considered as free piles under lateral loading whereas piles clustered in a group by a pilecap must be analyzed as fixed piles

2 Relative stiffness of the pile compared to the surrounding soil If the deformation

conditions are such that the soil yields before the pile material then the pile is classified as a

“short” pile Similarly, if the pile material yields first, then the pile is considered a “long”pile

8.2.1.1.1 Unrestrained or Free-Head Piles

Figure 8.2 andFigure 8.3illustrate the respective failure mechanisms that Broms (1964a,b)assumed for “short” and “long” piles, respectively

The ultimate lateral resistance Pucan be directly determined fromFigure 8.4(a)and (b)

based on the geometrical properties and the undrained soil strength For short piles, Mmax, g,

Pu, and f can be determined from Equations (8.1) to (8.4).

FIGURE 8.2

Deflection, soil reaction, and bending moment distributions for laterally loaded short piles in cohesive

soil (From Broms, B., 1964a, J Soil Mech Found Div., ASCE, 90(SM3):27–56 With

L=g+1.5D+f

(8.4)

8.2.1.1.2 Restrained or Fixed-Head Piles

According to the Broms (1964a) formulations, restrained piles can reach their ultimate

capacity through three separate mechanisms giving rise to (1) short piles, (2) long piles, and

(3) intermediate piles These failure mechanisms assumed by Broms (1964a) for restrainedpiles are illustrated in Figure 8.5(a)–(c) The assumption that leads to the analytical solutions

is that the moment generated on the pile top can be provided by the pile cap to restrain the pilewith the boundary condition at the top (i.e., no rotation)

FIGURE 8.3

Failure mechanism for laterally loaded long piles in cohesive soil (From Broms, B., 1964a, J Soil

Mech Found Div., ASCE, 90(SM3):27−56 With permission.)

The ultimate lateral load, Pu, of short piles can be directly obtained fromFigure 8.4(a) Thereader would notice that this condition is presented through a single curve in Figure 8.4(a)due

to the insignificance of the e parameter Mmaxand KPucan also be determined using the

For long piles, the ultimate lateral load, Pu, can be found fromFigure 8.4(b) Then, the

following equations can be used to determine/and hence the location of pile yielding:

(8.7)

On the other hand, for “intermediate” piles where yielding occurs at the top (Figure 8.5b), thebasic shear moment and total length consideration in Equations (8.1), (8.4), and (8.8) can be

used to obtain Pu:

FIGURE 8.4

Ultimate lateral resistance of piles in cohesive soils: (a) short piles and (b) long piles (From Broms,

B., 1964a, J Soil Mech Found Div., ASCE, 90(SM3):27–56 With permission.)

Page 332

FIGURE 8.5

Failure mechanisms for laterally loaded restrained piles in cohesive soils: (a) short piles, (b)

intermediate piles and (c) long piles (From Broms, B., 1964a, J Soil Mech Found Div.,

ASCE, 90(SM3):27–56 With permission.)

top to keep it from rotating The yield strength of steel is 300 MPa The CPT test results (qc)

for the site are also plotted inFigure 8.6(a) The Atterberg limits for the clay are: LL=60 and PL=25 and the saturated unit weight of clay is 17.5 kN/m3

FIGURE 8.6

(a) Illustration for Example 8.1 (b) HP section.

From steel section tables and Figure 8.6(b)

where PI is the plasticity index of the soil

One obtains the following suprofile for PI=35:

Su=(1/13.16)[(4.7+0.04z)+0.001{(9.8z)(l−0.5)−(17.5–9.8)z}]

=0.357+0.0028z MPa

suranges along the length of the pile from 357 to 385 kPa showing the linear trend with depththat is typical for clays Due to its relatively narrow range, it can be reasonably averagedalong the pile depth to be about 371 kPa

But cuD2=24.314 kN, and hence Pu=8.22 MN

Thus, if the pile does not yield, it can take 8.22 MN before the soil fails

In order to check the maximum moment in the pile, Equation (8.6) can be applied

Mmax=Pu(0.5L+0.75D)=8.22(0.5×10+0.75×0.256) MNm=42.68 MNm

But My=213.3 kN m Hence the pile would yield long before the clay, and the pile has to bereanalyzed as a long pile

FromFigure 8.4(b),

Hence, the ultimate lateral load that can be applied on the given pile is about 600 kN.

8.2.1.2 Piles in Cohesionless Soils

Based on a number of assumptions, Broms (1964b) formulated analytical methodologies todetermine the ultimate lateral load capacity of a pile in cohesionless soils as well The mostsignificant assumptions were: (1) negligible active earth pressure on the back of the pile due

to forward movement of the pile bottom, and (2) tripling of passive earth pressure along thetop front of the pile Hence

(8.9)

angle of internal friction (effective stress)

8.2.1.2.1 Free-Head Piles

By following terminology similar to that in the case of cohesive soils, the failure mechanisms

of short and long piles are illustrated in Figure 8.7andFigure 8.8, respectively

The ultimate lateral load for short piles can be estimated fromFigure 8.9(a)or the

FIGURE 8.7

Failure mechanism for laterally loaded short pile in cohesionless soil (From Broms, B., 1964b, J Soil

Mech Found Div., ASCE, 90(SM3):123–156 With permission.)

FIGURE 8.8

Failure mechanism for laterally loaded long piles in cohesionless soil (From Broms, B., 1964b, J Soil

Mech Found Div., ASCE, 90(SM3):123–156 With permission.)

If the Mmaxvalue computed from Equation (8.12) is larger than Myieldfor the pile material,

then obviously the pile behaves as a long pile and the actual ultimate lateral load Pucan be

computed from Equations (8.11) and (8.12) by setting Mmax=Myield

On the other hand, Figure 8.9(b)enables one to determine the ultimate lateral load for longpiles directly

8.2.1.2.2 Restrained or Fixed-Head Piles

For restrained short piles, consideration of horizontal equilibrium inFigure 8.10(a)yields

(8.15)

The above solution only applies if the moment Mmaxat a depth of f computed

is less than Myieldfor the pile material

FIGURE 8.9

Ultimate lateral resistance of piles in cohesionless soils: (a) short piles, (b) long piles (From Broms,

B., 1964b, J Soil Mech Found Div., ASCE, 90(SM3):123–156 With permission.)

Finally, if the above Mmaxis larger than Myield, then the failure mechanism inFigure 8.10(c)

applies Thus, the ultimate lateral load can be computed from the following equation or itsnondimensional form in Figure 8.9(b)

(8.16)

Page 338

FIGURE 8.10

Failure mechanisms for restrained piles in cohesionless soils: (a) short piles, (b) intermediate piles,

and (c) long piles (From Broms, B., 1964b, J Soil Mech Found Div., ASCE, 90(SM3):

123–156 With permission.)

8.3 Lateral Load Capacity Based on Deflections

The maximum permissible ground line deflection must be compared with the lateral

deflection of a laterally loaded pile to fulfill one important criterion of the design procedure

A number of commonly adopted methods to determine the lateral deflection are discussed inthe ensuing sections

8.3.1 Linear Elastic Method

A laterally loaded pile can be idealized as an infinitely long cylinder laterally deforming in aninfinite elastic medium (Pyke and Beikae, 1984) with the horizontal deformation governed bythe following equation:

P=k h y

(8.17)

But, from distributed load vs moment relations,

(8.18)

where B is the width of pile and E P I is the pile stiffness.

Then the equation governing the lateral deformation can be expressed by combining (8.17)and (8.18) as

Broms (1964a,b) showed that a laterally loaded pile behaves as an infinitely stiff member

when the coefficient βis less than 2 Further, when β L≥4, it was shown to behave as an

infinitely long member in which failure occurs when the maximum bending moment exceedsthe yield resistance of the pile section

For the simple situation where khcan be assumed constant along the pile depth, Hetenyi(1946) derived the following closed-form solutions:

8.3.1.1 Free-Headed Piles

8.3.1.1.1 Case (1): Lateral Deformation due to Load H

The following expressions can be used in conjunction withFigure 8.11, for a pile of width d.

Horizontal displacement

(8.21a)

The influence factors K ΔH , K θH , K MH , and K VHare given inTable 8.1.

8.3.1.1.2 Case (2): Lateral Deformation due to Moment M

The following expressions can be used withFigure 8.12

3.0 0.125 0.6459 0.8919 0.2508 0.3829 −0.3854 0.6433 0.8913 0.2514 3.0 0.25 0.3515 0.6698 0.3184 0.0141 −0.0184 0.3493 0.6684 0.3202 3.0 0.375 0.1444 0.4394 0.285 −0.1664 0.1607 0.1429 0.436 0.2887 3.0 0.5 0.0164 0.2528 0.2091 −0.2223 0.2162 0.0168 0.2458 0.215 3.0 0.625 −0.0529 0.1271 0.1272 −0.2057 0.2011 −0.0489 0.1148 0.1353 3.0 0.75 −0.0861 0.0584 0.0594 −0.1519 0.1524 −0.0763 0.0396 0.0684 3.0 0.875 −0.1021 0.0321 0.0154 −0.0807 0.0916 −0.0839 0.0069 0.0225

4.0 0.1250 0.5323 0.8247 0.2907 0.2411 −0.2409 0.5344 0.8229 0.2910 4.0 0.2500 0.1979 0.5101 0.3093 −0.1108 0.1136 0.2010 0.5082 0.3090 4.0 0.3750 0.0140 0.2403 0.2226 −0.2055 0.2118 0.0178 0.2397 0.2200 4.0 0.5000 −0.0590 0.0682 0.1243 −0.1758 0.1858 −0.0558 0.0720 0.1176 4.0 0.6250 −0.0687 −0.0176 0.0529 −0.1084 0.1200 −0.0696 −0.0043 0.0406 4.0 0.7500 −0.0505 −0.0488 0.0147 −0.0475 0.0538 −0.0616 −0.0206 −0.0025 4.0 0.8750 −0.0239 −0.0552 0.0014 −0.0101 −0.0033 −0.0535 −0.0096 −0.0148 4.0 1.0000 0.0038 −0.0555 −0 0.0000 −0.0555 −0.0517 −0.0000 −0

5.0 0.1250 0.4342 0.7476 0.3131 0.1206 −0.1210 0.4343 0.7472 0.3133 5.0 0.2500 0.0901 0.3628 0.2716 −0.1817 0.1818 0.0907 0.3620 0.2720 5.0 0.3750 −0.0466 0.1013 0.1461 −0.1919 0.1930 −0.0455 0.1002 0.1461 5.0 0.5000 −0.0671 −0.0157 0.0494 −0.1133 0.1163 −0.0654 −0.0161 0.0482 5.0 0.6250 −0.0456 −0.0435 0.0026 −0.0412 0.0461 −0.0444 −0.0409 −0.0012 5.0 0.7500 −0.0197 −0.0369 −0.0088 −0.0008 0.0055 −0.0221 −0.0276 −0.0159 5.0 0.8750 0.0002 −0.0279 −0.0044 0.0108 −0.0139 −0.0110 −0.0086 −0.0125

5.0 1.0000 0.0167 −0.0259 −0 0.0000 −0.0259 −0.0091 −0.0000 −0

8.3.1.2 Fixed-Headed Piles

Due to the elastic nature of the solution, lateral deformation of the fixed-headed piles can behandled by superimposing the deformations caused by: (1) the known deforming lateral forceand the unknown restraining pile head moment, or (2) the known deforming moment and theunknown restraining pile head moment Then, by setting the pile head rotation to zero (forfixed end conditions), the unknown restraining moment and hence the resultant solution can

be determined

Example 8.2

The 300mm wide steel pile shown inFigure 8.13is one member of a group held together

by a pile cap that exerts a lateral load of 8 kN on the given pile and a certain magnitude of amoment required to restrain the rotation at the top It is given that the coefficient of

Then, determine the lateral displacement and the slope due to a force 8 kN (Equation 8.21)

If the restraining moment needed at the top is M, then the lateral displacement and the slope due to M are evaluated as follows (Equation 8.22):

For restrained rotation at the top,

0.056M+0.219=0; M=−3.93 kN m

Then ΔM=0.108m

Hence, the total lateral displacement is ΔM+ΔH=0.216 m

8.3.2 Nonlinear Methods

Several nonlinear numerical methods have become popular nowadays due to the availability

of superior computational capabilities Of them the most widely used ones are the stiffness

matrix method of analysis and the lateral force-deflection (p−y) approach.

8.3.2.1 Stiffness Matrix Analysis Method

This method is also known as the finite element method due to the similarity in the basicformulation of the conventional finite element method and the stiffness matrix analysis

method First, the pile is discretized into a number of one-dimensional (beam) elements

Figure 8.14 shows a typical discretization of a pile in preparation for load-deflection analysis.The following notation applies toFigure 8.14:

1, 2,…,N (in bold)—node number

P i (i even)—internal lateral forces on pile elements concentrated (lumped) at the

nodes

FIGURE 8.14

Stiffness matrix method of analyzing laterally loaded piles.

P i (i odd)—internal moments on pile elements concentrated (lumped) at the nodes

X i (i even)—nodal deflection of each pile element

X i (i odd)—nodal rotation of each pile element

K j—lateral soil resistance represented by an equivalent spring stiffness (kN/m)

Based on slope-deflection relations in structural analysis, the following stiffness relationcan be written for a free pile element (i.e., 1,2):

(8.23)

where EI is the stiffness of the pile and L is the length of each pile element.

If the pile is assumed to be a beam on an elastic foundation, then the modulus of lateral

subgrade reaction kh at any depth can be related to the lateral pile deflection at that depth bythe following expression:

p=khy

(8.24)

Hence the spring stiffness K jcan be expressed conveniently in terms of the modulus of lateral

subgrade reaction kh as follows:

For buried nodes: