Soil Structure Interaction Analysis of a Dry Dock

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Soil Structure Interaction Analysis of a Dry Dock

KAVITHA P1, MUTHU VENKATESH M2, SUNDAAVADIVE!U "

1 Ph.D scholar, Dept. of Ocean Engg., IIT Madras, Chennai – 600036, India2 or!er M.Tech "t#dent, Dept. of Ocean Engg., IIT Madras, Chennai – 600036, India

3 Professor, Dept. of Ocean Engg., IIT Madras, Chennai – 600036, India

Email: oe$3d003%s!ail.iit!.ac.in , &en'ateshpearl%g!ail.co! , rs#n%iit!.ac.in

A#stract$

Pile foundation is one of the most popular forms of deep foundations and is widely used for supporting water front structures in weak soils characterized by low shear strength and high

compressibility and also in good soil formations if structures are subjected to heavy lateral

loadings and moments. The lateral forces are mainly due to berthing forces and lateral earth

pressure due to unstable slope as a result of dredging or siltation etc. Conventionally APguidelines and !esic e"uation are used to analyze the laterally loaded piles. The study of

laterally loaded pile in active soil wedge re"uires a proper assessment of soil structure interaction phenomenon involving the interaction between pile surface and the surrounding soil. Theinstability of soil wedge can occur due to self weight# surcharge load# dredging# siltation and

earth"uake force. The soil structure interaction problem of piles located in active soil wedge has

rarely been approached. $aterally loaded piles are analyzed by methods derived from theclassical beam on elastic foundation mode in which the soil support is appro%imated by a series

of independent elastic spring. The soil spring constants estimated from AP guidelines and !esic

e"uations are not suitable for piles located in active soil wedge. &ence a numerical study is

carried out for on dry dock in site specific soil and in dense sand# in order to study the behaviour of piles in active soil wedge. 'ased on the P() curves plotted for piles located in active soil

wedge# appropriate reduction factor is obtained for AP guidelines for dense sand. Profile of the

active soil wedge determined using P() curve plots from Pla%is results closely matches with thetheoretical soil slip plane. *oil spring constants are estimated from the modified AP curves and

are used to model the dry dock in *taad pro for dense sand in order to validate the results.

(e)*ords+ Dr) Doc', "oil "tr#ct#re Interaction, "oil "pring Constants, cti&e "oil -edge, P/ c#r&es.

1% Intro&uction

The classic form of dry(dock# properly known as graving dock# is a narrow basin#

surrounded by concrete diaphragm walls# closed by gates or by a caisson# into which a vessel

may be floated and the water pumped out# leaving the vessel supported on blocks. The keel blocks as well as the bilge block are placed on the floor of the dock in accordance with the

+docking plan+ of the ship. ,ry(docks are used for the construction# maintenance# and repair of ships# boats# and other watercraft. The diaphragm wall of dry(dock are generally supported by

group of piles behind them connected via a tie beam. The interaction between soil - structure isa critical problem in geotechnical engineering. The effect of soil structure interaction becomes

prominent for heavy structures resting on relatively soft soils. Accurate modeling of soil(

structure interaction is very important in order to obtain realistic solutions of many foundation problems. *eismic behavior of a structure is highly influenced not only by the response of the

superstructure# but also by the response of the foundation and the ground as well. The behavior

mailto:[email protected]





http://en.wikipedia.org/wiki/Caisson_(engineering)



http://en.wikipedia.org/wiki/Caisson_(engineering)




of pile subjected to lateral load due to e%cavation induced soli displacement is a classical

e%ample of non linear soil structure interaction. sually# laterally loaded piles are analyzed by

methods derived directly from the classical /beam on elastic foundation0 mode in which the soilsupport is appro%imated by a series of independent elastic spring.

ig. 1 Picture of a typical ,ry ,ock

2% !aterally !oa&e& Piles In Acti'e Soil (e&)e$

Pile foundation is one of the most popular forms of deep foundations and is widely usedfor supporting water front structures in weak soils characterized by low shear strength and high

compressibility and also in good soil formations if structures are subjected to heavy lateralloadings and moments. The permissible deflection at the pile head and the distribution of the

bending moment along the pile are important information for the structural design of pile

foundation that support lateral loads. 2stimating the ma%imum deflection at the pile head isimportant to satisfy the serviceability re"uirement of the superstructure while the bending

moment is re"uired for the structural design of piles and retaining walls. The lateral forces are

mainly due to berthing forces# and lateral earth pressure due to unstable slope as a result of dredging or siltation etc. The study of laterally loaded pile in active soil wedge re"uires a proper

assessment of soil(structure interaction phenomenon involving the interaction between pile

surface and the surrounding soil. *lope instability is a common problem in these regions# due tothe low shear values of the sediments. The instability of soil wedge can occur due to# self weight#

surcharge load# dredging# siltation# earth"uake force. As a result# failure with large displacements

will take place resulting in lateral forces on piles embedded in such slopes.



ig.3 2%amples of laterally loaded piles located in active soil wedge

$aterally loaded piles can be classified as rigid and fle%ible depending on length4diameter ratios

and relative stiffness of pile(soil system. n case of rigid piles# failure occurs due to yielding of

soil and it is assumed that the pile rotates as a unit about a point in which the passive resistancedevelops in front of the pile above the point of rotation and in the rear portion of the pile below

the point of rotation. &owever# in case of fle%ible piles# formation of a plastic hinge takes place

at certain depth below the ground.

"% P*+ Meto& -f Analysis$

A model describing the P() method of analysis is shown in ig.5. An elevation view of a

pile is shown in ig.5 6a7# with a lateral load Pt an a%ial load P, and a moment M applied at the pile head. The pile is shown as an elastic line in ig. 5 6b7 in a coordinate system with deflection

) and length along the pile. The rock 6soil# usually7 is modeled according to the 8inkler

concept with a number of nonlinear# discrete mechanisms. The mechanisms# shown in the first

"uadrant for convenience# are characterized by a spring and sliding block merely to indicatenonlinearity# and they are described by the p) curves in ig. 5 6c7# where p is the resistance of

the rock and ) is the local deflection. The parameter p refers to the line load from the rock

resistance and is the integral of the unit stresses acting around the circumference of the pile. Anumber of authors have made recommendations for predicting p) curves for different soils.



ig 5. 9odel of $aterally $oaded Pile: 6a7 2levation !iew; 6b7 As 2lastic $ine; 6c7 p(y Curves

.% Pla/is "D*0EM Tool

The finite element modeling and analysis have been carried out using P$A<* 5,# a

special tool for solving geotechnical engineering problems.

.%1 Soil Mo&els

Pla%is 5, has inbuilt soil models. The soil domain is generated by by giving bore hole data at

one or more locations. *ome of the commonly used soil models are#• $inear 2lastic model= stress and strain are linearly proportional# no failure condition.

Tensile stresses allowed.

• 9ohr(Coulomb model = $inear elastic until limit state# perfectly plastic. ailure as per well known c# > parameters. Tensile stresses could be limited. $oading and unloading

modulus are the same.• &ardening *oil 9odel = more versatile. 9C strength parameters. ,ifferent loading and

unloading modulus. *imilar to hyperbolic model. 8ell suited for e%cavation and dredging

problems. * analysis possible. *till# not ade"uate for cyclic4dynamic load analysis.

• or the current work# the linearly elastic perfectly plastic# 9ohr(Coulomb soil model wasused. The 9ohr(Coulomb model re"uires a total of five parameters# which can be

obtained from basic tests on soil samples. The input parameters with their standard units

are listed below:• ϒ : nit 8eight of soil ?k@4m5

• E : )oungBs modulus ?k@4m3

•

ν

: PoissonBs ratio ?no unit

•

ϕ

: riction angle ?degree

• c : Cohesion ?k@4m3



•

ψ

: ,ilatancy angle ?degree

.%2 Structural Eleents

The other elements e%cept soil can be defined using the different structural elements in

Pla%is like the anchors# geo grid# plate# beam and embedded pile. An embedded pile consists of a beam element with embedded interface elements to describe the interaction with the soil at the

pile skin and the pile foot. The material parameters of the embedded pile distinguish between the

parameters of the beam and the parameters of the skin resistance and end bearing. The beam

element is defined as linear elastic and material property as regular beam is assigned to it.

ig . *tiffness of embedded interface element at skin of pile

Plate element is used model diaphragm walls# retaining wall# footings etc#. The plate element can

undergo orthotropic material behavior by varying the value of )oungBs modulus along %(a%is andy(a%is.

.%" Mo&el Descrition an& 3roun& 4on&itions

A uniform soil domain is created in Pla%is using the properties of dense sand given in

table 1. 9ohr(Columb model is used and the soil parameters are assigned as given in table.1. Thesoil domain is DEm long# m wide and 5Fm deep. The water table is assumed to be at 1m below

G.$. The soil model accommodates diaphragm wall and the three rows of piles behind the wall

connected by tie beam. The e%cavation is 1F.Fm deep and is carried out in eight stages and thewhole process is modeled in H phase.

Table 1 *oil parameters used for dense sand

nit 8eight# I sat 3E k@4m5

2lastic modulus# 2 D#EEE k@4m

3

Angle of internal friction# > 5Jo

PoissonBs ratio# K E.3

nitial *ubgrade modulus# L 31JDE k@4m5

The deformed soil mesh and horizontal soil displacement contour are shown in ig J.1 - J.3.The displacement and bending moment profile of the piles at the end of each phase of analysis is



obtained from Pla%is output.These results were further used to study the Pile(soil interaction#

located in the active wedge zone.

ig F. ,eformed soil mesh at the end of phase D



ig.J ,eformed structure 6diaphragm wall and piles7

.%. Mes 3eneration an& 4on'er)ence Analysis$

The geometry of the soil = structure model has to be divided into elements for performing

finite element calculations. P$A<* allows automatic generation of finite element meshes based

on a robust triangulation procedure# which results in /unstructured0 meshes. These meshes maylook disorderly# but the numerical performance of such meshes is usually better than for regular

6structured7 meshes. The mesh generator re"uires a general meshing parameter# which represents

the average element size 6le7. n# P$A<*# this parameter is calculated from the outer geometrydimensions and a Global coarseness is refined. ,istinction is made between five levels of global

coarseness; !ery coarse# coarse# medium# fine and very fine. The diaphragm wall is meshed into

J noded triangular elements with si% degree of freedom per node. The embedded pile is defined

as a 5 node special element. ,ue to e%istence of the embedded pile# 5 e%tra nodes are introducedinside the 1E node tetrahedral soil element. This set of 5 node beam element into a 1E node

tetrahedral element is analyzed as one unit to get the pile(soil interaction. 'eams are composed

of beam elements with three degrees of freedom per node: Two translational degrees of freedom

6u% and uy7 and one rotational degree of freedom 6rotation in the %(y plane:z7. 'endingmoments and a%ial forces are evaluated from the stresses at the stress points.

The soil domain must be fi%ed such that there is no influence of the e%cavation on the soiloutside the domain. The soil domain considered was DEm long# Jm wide and 5Em deep. 9esh

convergence was done by varying the mesh type from very coarse to very fine and the variation

in the bending moment profile of the diaphragm wall was studied. The variation in the meshingtype largely affected the bending moment value at the propped support which is plotted in the

chart below.

Table 3: Comparison of various types of mesh in Pla%is 5,

92*&T)P2

@M.M2$292@T*

@M.M @M,2*

N2$AT!2*O2 ACTMN

!ery coarse 1F 5EH 3

Coarse 51J FJ 1.F

9edium J13 1E555 1

ine 11ED 1HJ E.

!ery fine 3533 5J33E E.F

.%5 !oa& Stein) Proce&ures$

8hen soil plasticity is involved in finite element calculation the e"uation become non(

linear# which means that the problem needs to be solved in a series of calculations steps. ,uringeach calculation step# the e"uilibrium errors in the solution are successively reduced using a

series of iterations. The iteration procedure is based on an accelerated initial stress method. f the

calculation step is of a suitable size then the number of iterations re"uired for e"uilibrium will berelatively small# usually about five to ten. f the step size is too small# then many steps are

re"uired to reach the desired load level and computer time will be e%cessive.



(E.3F (E.3 (E.1F (E.1 (E.EF E

(3E

(1F

(1E

(F

E

Phase 1 Phase 3 Phase 5

Phase Phase F Phase J

Phase Phase D

Dislaceent U/ 67

Det 8 67

ig . ,isplacement of pile 1 after each phase of e%cavation

(5EEE (3FEE (3EEE (1FEE (1EEE (FEE E FEE

(3E

(1F

(1E

(F

E

Phase 1 Phase 3 Phase 5

Phase Phase F Phase J

Phase Phase D

9en&in) oent M:6kN7

Det 8 67

ig D. 'ending moment of pile 1 after each phase of e%cavation

5% STAAD P- Mo&el



n *TAA, PNM# the structure is modeled as NCC moment resisting frame. 'eam

elements were used to model the diaphragm wall# piles and tie beam which are interconnected by

nodes. The soil springs are used to idealize the soil support for pile. The soil is modeled as elasticspring supports spaced at 1 m c4c. The spring constants are estimated using modulus of sub(grade

reaction# Ls. The lateral 2arth pressure and water pressure were estimated theoretically and are

directly applied on the diaphragm wall as linearly varying load. The failure plane of soil isassumed linear# inclined at an angle Q to the horizontal.

5%1 Soil Srin) Stiffness Estiation$

!esic e"uation 6'owels th 2dition7 is used for the determination of modulus of sub(gradereaction and @ewmarks distribution is used for the spring stiffness. 9odulus of subgrade

reaction k s is determined using the following e"uation

−××=

313

C

1

JF.E

s

s

p p

s s

E

I E

1 E

1'

µ

6F.17

'ased on @ewmarkBs distribution the spring stiffness is given as follows.

irst spring (

( ) ( )[ ]31

JP3C

++ −+

nnn ' ' '

1l

6F.37

ntermediate spring

( ) ( )[ ]11

1E13

+− ++

nnn ' ' '

1l

6F.57

'ottom spring (

( ) ( )[ ]31

JP3C

−− −+

nnn ' ' '

1l

6F.78here# ' 8idth of Pile4disphragm wall

2s#2 p )oungs modulus of *oil and Pile

p 9oment of inertia of Pile

l *pacing between two adjacent springs

' n 9odulus of subgrade reaction of n th spring



ig.H sometric view dry dock frame showing differential water pressure load

;% esults an& Discussion$

Comparison of results from Pla%is and *taad pro6!esic e"uation7 are presented in the following

charts:

The results of displacement and bending moment profile from Pla%is 5, and *taad profor the diaphragm wall and piles are compared. *taad pro model# where the soil spring stiffness

is calculated from !esic e"uation is very rigid at the bottom and is over estimating bendingmoment in the structure. Conventional vesic method of estimating soil spring stiffness is not

applicable of piles located in active soil wedge as the lateral soil resistance is very less along the

wedge profile. &ence an alternated method of estimating the soil spring stiffness need todeveloped in order to solve the ** problem of Piles located in active soil wedge.

;%1 Plottin) P*+ 4ur'es fro P!A<IS esults$



The soil resistance 6P7 along the pile shaft is determined from the bending moment

obtained from Pla%is output# using an approach followed by )ang et al. 63EEF7 and ,unnavant

61HDJ7. The bending moment curve of the pile shaft is curve fitted by a cubic polynomialfunction#

M 4 5 a 3 7 2 c d 6J.17

8here# O is the depth and a# b# c and d are constants obtained from curve(fitting processThen distribution of soil resistance along pile shaft is obtained by double differentiating the

above e"uation.

P 4 5 d 2 M8d 2 4 5 6a 274 6J.37

rom the e"uation J.3 soil resistance 6P7 is calculated along pile shaft at 3m interval and is

plotted against the corresponding pile displacement at end of each phase. Thus a family of P()

curves was plotted for each pile at 3m spacing.

E E.E3 E.E E.EJ E.ED E.1 E.13 E.1(1E

E

1E

3E

5E

E

FE

JE

E

DEHE

1EE

11E

13E

(1m (1Fm (1Jm (1Dm (3Em (33m (3m

Pile &islaceent + 67

Soil resistance P 6kN7

ig J.11 amily of P() curves for pile 1 at every 3m depth

;%2 ESTIMATI-N -0 EDU4TI-N 0A4T- 0- API 3UIDE!INES$

The lateral soil resistance(deflection 6P()7 relationships for piles in sandy soil at any specificdepth O can be plotted using the AP guidelines given below.

×

××

××= / P ,

9' P , P

#

# tanh

6J.578here#

• P# = is ultimate lateral bearing capacity of soil at any depth O#

• P#5 C $ C 2 D4 : or C 3;D : 6k@4m7 6J.7

• C1# C3# C5 are empirical constants based on >



• ,( Pile4,(wall thickness

• L( initial modulus of subgrades reaction 6k@4m5 7

• A( factor to account for cyclic or static loading condition.

•AR 65(E.DO4,7 S E.H for static loading

n order to account for the reduction in lateral resistance of soil for piles located in active soil

wedge a reduction factor N is introduced in the AP guidelines as given below

9odified AP formula

×

×××

×××= / p ,

9' < p < , P

#

# tanh

6J.F7'y trial and error method the value of the reduction factor is fi%ed such that the P()

curve obtained from the modified AP formula fits with the one plotted using Pla%is at

appropriate depth.

'y studying the P() curves plotted for each piles and the table for reduction factor# it can be seen

that the active soil wedge plane passes through the pile 1 at (1m depth and touches the surface

just in front of pile 3. According the plane of active soil wedge 6soil slip plane7 is drawn andcompared with the theoretical soil slip plane in ig J.31

ig J.1 Theoretical and actual soil slip plane 6active wedge7



=% 4onclusion

'ased on the above work the following conclusions were drawn:

• The soil spring constants estimated from AP guidelines and !esic e"uations is not

suitable for piles located in active soil wedge.

• &ence proper reduction factor are introduced to modify the AP guidelines P() curves of

pile in sandy soil.

• 'ased on the values of reduction factors obtained it is concluded that the effect of active

soil wedge decreases with increase in distance from the crest of the wedge.

• Profile of the active soil wedge determined using P() curve plots from Pla%is results

closely matches with the theoretical soil slip plane.• The soil spring constants estimated from modified P() curves gave realistic solutions for

*oil(Pile nteraction problem in active soil wedge compared to that of AP and !esic

e"uation.

>% eferences

• Dru#a !al Pra&an 63E137# ,evelopment of P() Curves for 9onopiles in Clay using

inite 2lement 9odel Pla%is 5, oundation# 9aster of science thesis# @orwegian

niversity of *cience and Technology.

•

• Ke +an) an& o#ert !ian) 63E17# 9ethods for ,eriving p( ) Curves from nstrumented

$ateral $oad Tests# Geotechnical Testing ournal# !ol. 5E

•

• Mutukkuara K 63EE7# @on(linear *oil *tructure nteraction of Piles on *loping

Ground# ,octoral of Philosophy thesis# T madras(Chennai

•

• !yon 4% eese 61HH7# Analysis of $aterally $oaded Piles in 8eak Nock# ournal of

Geotechnical and Geoenvironmental 2ngineering.

•

• ?ayanta Ko&ikara et all 63E1E7# Theoretical p( ) Curves for $aterally $oaded *ingle

Piles in

• ndrained Clay sing 'ezier Curves# ournal of Geotechnical and Geoenvironmental

2ngineering# A*C2.

•

• T% +% Po# et all 61HH7# Performance of Two Propped ,iaphragm 8alls in *tiff Nesidual

*oil# ournal of Performance of Constructed acilities.

•



• H% 3% Poulos an& !% T% 4en 61HH7# Pile Nesponse due to 2%cavation(nduced $ateral

*oil 9ovement# ournal of Geotechnical and Geoenvironmental 2ngineering# A*C2.

•

• Prof Antonio 3ens et all 63E157# Pla%is Advanced Cource on Computational

Ceotechnics# Chennai

•

• Aerican Petroleu Institute 6API P 2A7# Necommended Practice for Planning#

,egigning and Constructing i%ed Mffshore Platforms.

Documents

Soil Structure Interaction Analysis of a Dry Dock