Analysis of Laterally Loaded Drilled Shafts and Piles Using

LPILE

Shin-Tower Wang, Ph.D., P.E. Ensoft, Inc./Lymon C. Reese &

AssociatesAustin, Texas

April 3, 2009

Outlines Introduction Basic theory of the p-y curve method

Numerical solution for soil-structure interaction

Characteristic Shape of p-y Curves Available p-y Curve Criteria Common Input Values

Special consideration for large-diameter piers Effect of nonlinear EI on deflection Special features in LPILE

Piles are used in a variety of ways to support super-structures

Drilled Shafts with Lateral Load

PM

Q

Ultimate earth pressure

(strength fully mobilized)

Actual earth pressure

Ultimate earth pressure

(strength fully mobilized)

Actual earth pressure

Methods of Solution

Linearly elastic solution (Poulos and Davis, 1980) emphasizes the condition of continuity although the soil cannot be characterized as a linearly elastic material.

Limit-equilibrium solution (Broms, 1965)

finds the ultimate lateral load at failure, but soil-structure interaction at lesser loads is not addressed.

The p-y method with beam-column model (McClelland, Matlock, Reese, 1958-1975)

has been developed extensively to take into account the soil-structure interaction and nonlinear resistance of soils.

3-D Finite-Element method

Soil Failure Patterns

Wedge Failure

Plane-Strain Failure

Nonlinear Model for Lateral Soil Resistance

EI = pile stiffnessy = pile deflectionx = distance along pilePx = axial load on pile andEpy = slope of secant to p-y curve at point on pileW = distributed lateral loading

02

2

4

4

WyEdx

ydP

dx

ydEI pyx

Differential Equation

Illustration of Numerical Solution Procedure

Epy

x

p

yV

y

p

Epy

p-y Curves Developed From Static-Load Tests on24-in. Diameter Pile.

Characteristic Shape of p-y Curves

a. Initial Linear-elastic section

b. Transition from linear to nonlinear section

c. Yield section into limit state or plasticity failure

a.

b.

c.

p-y Curve Criteria Soft Clay (Matlock, 1970) Stiff Clay

(1). with free water (Reese et al., 1975) (2). Without free water (Reese & Welch, 1975)

Sand (Reese model & API Model) Liquefied Sand (Rollins et al., 2005) c- Soil (Evans and Duncan*, 1982) Strong Rock (Reese & Nyman, 1978) Weak Rock (Reese, 1997)

(* Concept only, not the full model)

Common Input Values Effective Unit Weight Shear Strength

Cohesion, c Friction Angle,

Soil Stiffness, 50

Initial Stiffness of p-y Curve, k Rock Properties, RQD, qu, etc.

Soft Clay

Static Loading

Cyclic Loading

Stiff Clay with Free Water

Static Loading

Cyclic Loading

Stiff Clay without Free Water

Static Loading Cyclic Loading

Sand (Reese Criteria)

Static & Cyclic Coefficients

Liquefied Sand (Rollins et al.)

Rollins model is limited to relative densitiesBetween 45 and 55 percent

Pile diameter = 324 mm

Cemented c- Soil

Use of this p-y curve is not recommended without a load test to establish k

y

p

b/60 3b/80

m

uym

yu

pm

pu

ks

k pk

yk

Pult=Pu( ) + Pu ( c )

Vuggy Limestone

y

p

0.0004b

pu = b su

Es = 2000su

Perform proof test if deflection is in this range

Assume brittle fracture if deflection is in this range

Es = 100su

NOT TO SCALE

0.0024b

Weak Rock

y

p

A

pur

Required rock propertiesUniaxial Compressive Strength, su (from lab tests)RQD (from field investigation records)Rock Mass Modulus (interpreted)krm (from lab tests or estimated)Effective Unit Weight (from lab tests)

Kir

ya

Soil Layering Effects

Georgiadis’ Method for Equivalent Depth (1983)

Georgiadis’ Method for Equivalent Depth (1983)

Pile-Head Conditions:Shear and Moment

Mt

Pt

Qt

Note: Origin of Coordinate System for Pile and Soil Layers is Located at the Pile Head

Layer 1

Layer 2

Layer 3

Pile Length

Distance to Ground Surface

Pile-Head Conditions:Displacement and Slope

Qt

Note: Origin of Coordinate System for Pile and Soil Layers is Located at the Pile Head

Layer 1

Layer 2

Layer 3

Pile Length

Distance to Ground Surface yt

t

Effect of Side Friction and Tip Resistance on Large-Diameter Piers

Contact friction, Fs

Tip rotation bearing, Fb

Contact friction (maybe small)

B

H

Fs

0.2”

Tip rotation bearing, Fb

(need large mobilization)

Fb

0.05B

M

Size Effect

1. For linear elastic portion of the p-y curves the size effect is not significant on initial k values.

2. For ultimate soil resistance Pu is a function of the pile diameter.

3. Most correlation coefficients in current p-y criteria were derived based on pile diameter of 2 ft to 4 ft.

Using service load to check deflection criteria

Using factored load to check bending moment and shear

Uncrack/Crack EI’s

Effect of Nonlinear EI on Deflection

Comparison of pile-head deflections computed for same load using elastic and nonlinear EI values.

It is possible to under-predict pile-head deflections if only elastic EI values are used.

Top Deflection vs. LengthTop Deflection vs. Embedment Depth

LPILE Plus 5.0, (c) 2004 by Ensoft, Inc.

Embedment Depth, meters121110987

Top D

efle

ctio

n, m

0.05

0.045

0.04

0.035

0.03

0.025

0.02

0.015

0.01

0.005

0

Pile Subjected to Lateral Spreading due to Liquefaction of Soils

Slope Stabilized by Drilled Shafts

Fs is derived from p-y curves

Adjust the Passive Earth Pressure Not Over The Bending Capacity

Slope-Stability Analysis with Resistance from vertical piles

Main Window for LRFD

Load CombosUnfactored LoadsFactored Loads

Unfactored Load Definitions

Load Factors, Resistance Factors, and Combinations

Load Summary Report (1)

Load Summary Report (3)

Concrete Properties

Reinforcing Bar Properties

Warning messagefor cage spacingand percent steel

Bar bundling options

Recent Publications by Others Using LPILE

Rollins, K.M., Peterson, K.T., and Weaver, T.J.,”Lateral Load Behavior of Full-Scale Pile Group in Clay”, J. Geotech. & GeoEnviro. Eng. ASCE Vol 124, No.6, June, 1988. Anderson, J.B., Townsend, F.C., and Grajales, B.,”Case History Evaluation of Laterally Loaded Piles”, J. Geotech. & GeoEnvir. Eng. ASCE Vol 129, No.3, March, 2003. Davidson, W.A, McCabe, R.J., and Soydemir, C.,”Below Boston’s new Bridge”, Civil Engineering, Dec. 1998.

Thank You