DESIGN METHODS ANALYSIS OF SEISMIC INTERACTIONS

SOI FOUNDATION BRIDGESOIL - FOUNDATION - BRIDGE STRUCTURES FORSTRUCTURES FOR

DIFFERENT FOUNDATIONSDIFFERENT FOUNDATIONS

Boris Folić and Radomir FolićF lt f T h i l S i N i SADFaculty of Technical Sciences Novi SAD

INTRODUCTION• The effects of earthquake regarding soil-

t t i t ti (SSI) l tstructures interactions (SSI) are complex to cover. Therefore, researching of earthquake induced vibrations on soil-foundation-structure systems is particularly complex in y p y pfoundation on pile/pile groups

• The damage caused to foundation of• The damage caused to foundation of bridges in eartquakes has emphasized the i t f d t di SSIimportance of understeding SSI.

The analysis of Soil-Structure Interactions (SSI) induced by seismic actions deals with the following

questions:• How does the interplay between soil, foundation and

t t ff t th d f th t t ?structure affect the respond of the structure?• Can the foundation (F) transmit safely the inertial

loads from the super-structure into the groundloads from the super structure into the ground without excessive settlement and deformation?

• Can SSI be foreseen and introduced in the design of t t d fi i ti f t t l i ti lstructures, defining actions of structural inertial

forces to the pile head, and wave-induced ground displacements in the embedded part?p p

• Will the axial forces of the pile induced by the earthquake caused soil degradation around the pile and its tip?and its tip?

The phenomenon of interactionp• Structures founded on rock are considered to be

fixed-base structures.• When the soil is observed separately without the

structure, the influence of the soil on the characteristics of seismic waves moving from the bedcharacteristics of seismic waves moving from the bed rock toward the soil surface can be determined, the resulting record of acceleration obtained for the soil gsurface is called free-field motion.

• To obtain the record the soil must be mathematically modelled in a proper way The most frequent case ofmodelled in a proper way. The most frequent case of horizontally layered soil can be modelled by a simple one-dimensional system.one dimensional system.

•If the ground motions due to earthquake in the bed rock having layers of soil above are known, the g yfree-field motions can be determined by treating the soil as a structure with known motions in the support. •Using an adequate discretised model that g qcorresponds to the geometry and arrangement of soil layers, and observing seismic motions as displacements of stiff support, the response on the soil surface can be obtained starting from the equation of motion of the system, through direct integration (in frequency domain as is the most ffi i t) i ti hi tefficient), i.e. a time-history.

• The obtained record (accelerogram) describes free-fi ld ti i l h th t t i b iltfield motions in place where the structure is built.

• Through generating accelerograms can be described the contribution of more than one possible earthquake by varying the frequency contains. A set od artificial accelerograms is better than a set of real ones for it enables better usage of the techniques. Accelerograms can be scaled, i.e. its ordinates can be multiplied by a corresponding scale factor, which according to EN 1998/2 can be from 0.5 to 2, in order to adjust them to the problem in question.

Two physical phenomena describe the interaction between the structure, foundation and soil:,•Kinematic interaction results from the presence of stiff foundation structure within or on the soil causing th diff i ti b t th f d ti dthe difference in motion between the foundation and the surrounding soil. The phenomenon is analogue to the problem of modification of seismic waves dueto the problem of modification of seismic waves due to soil influence and it is described and resolved in a similar way.y•Inertial interaction causes foundation displacements in relation to the surrounding soil due t th ti f i ti l f d l d i thto the action of inertial forces developed in the structure as a result of its oscillations, which increases forces and moments in the foundationsincreases forces and moments in the foundations.

• The effect of these phenomena is usually described by a complex transfer function (TF) relating the motion of soil and foundation or by arelating the motion of soil and foundation, or by a complex function of impedance that quantifies the stiffness and damping so characteristic for the soil-stiffness and damping so characteristic for the soilfoundation interaction.

• Both functions are due to final stiffness and damping of the surrounding soil. In the assumption of perfectly stiff soil, the stiffness of soil is infinite, the amplitude of TF is 1 and the phase 0 whichthe amplitude of TF is 1, and the phase 0, which means the motions of the foundation and the soil are identical.are identical.

• Impedance function has an infinitely big real part, while the imaginary part is zero. p , g y p

• It is best to create one model that includes both the soil and the structure, because it takes into account the separate influence of the soil on seismic motions as well as the joint soil-structure actionaction.

• When there is a record for a significantly different soil type in comparison to the one undersoil type in comparison to the one under consideration, a separate analysis of soil influences on seismic waves is conducted in twoinfluences on seismic waves is conducted in two successive steps. The first determines the bed rock motion from the given record through the inverse g g(downward) analysis. Then from the obtained record for the bed rock through the direct (upward) analysis we obtain the record for soil surface.

METHODS OF SSI ANALYSIS•Finite Elements Method, Fininte

•Substructure Method-Soil +Foundations,

diference•Direct Method

Soil Foundations +Structure

•Frequency DomainDirect Method•Time Domain AnalysisLinear Analysis

•Frequency Domain AnalysisNon Linear Analysis•Linear Analysis

Problems: Sizes of h d l t

•Non-Linear Analysis•Boundary Elem.

mesh and elements &how to model damping ( t d di ti )

Method

(mat and radiation)

DYNAMIC EQUATIONTime domain• Linear analysis

Frequency domain•Linear analysis (LA)

• Direct integration method

• Modal analysis

•Equivalent LA•Non-linear analysis – hybrid method• Modal analysis

• Non-linear analysisDamping is the same

methodDifferent material damping can be set in all elements, through

di ti d i b tlDamping is the same in all elements; reflexion of waves against the mesh

radiation damping can be correctly taken into account by applying adequate boundaries applicable f b t t th dagainst the mesh

boundary of FE led to unreal systems

for substructure methodBy Fourier transformation a system of linear algebraic equations is y

responseg q

obtained with complex coefficients.

•According to EN 1998-5 SSI shall be introduced into design of the following:

) St t ith P δ (2nd d ) l i ifi t la) Structures with P-δ (2nd order) play significant role;b) Structures with massive or deep-seated

foundations (bridge piers caissons and silos);foundations (bridge piers, caissons, and silos);c) Slender tall structures (towers and chimneys);d) Structures supported on very soft soils withd) Structures supported on very soft soils, with

average shear wave velocity vs,max<100 m/s, ground type S1,yp ,The effects of SSI on pile shall be assessed for all structures to resist the following two types of action

ff teffects: a) Inertia forces from the super-structure combined with static loads Inertia developed in structure (S) causestatic loads. Inertia developed in structure (S) cause

displacement of the foundations (F) relative to the free field. Frequency dependent F impendance funcions are introduced to describe the flexibility of the F support, as well as the radiation damping associate with soil-F interaction In the absence of large rigid F slabs or ofinteraction. In the absence of large, rigid F slabs or of deep embedment, inertial interaction tend to be more importantimportant. b) Kinematic forces arising from the deformation of the surrounding soil due to the passage of seismic wavessurrounding soil due to the passage of seismic waves. Stiff, slab-like or deeply embedded F elements couse F motions to be different from free – field motions because of wave-scatering phenomena, wave – scatering phenomena, wave inclination or embedment.

Elements of Seismic Reesponse Analysis including SSIAnalysis including SSI

(adopted after J. Jonson 2003.)• Free Field Ground Motion SpecificationFree Field Ground Motion SpecificationControl pointControl motion (PGA and Response spectrum)Control motion (PGA and Response spectrum)Spatial variation of motion (wave propag. mech.)Magnitude durationMagnitude, durationModel of soils and structures

Soil Properties• Soil PropertiesNominal properties (low and high strain)V i biliVariability

Continued

• SSI ParametersKinematic interactione a c e ac oFoundation impedancesStructural modelsStructural modelsImportant features (torsion, deck flexibility, ...)Variability (frequency and mode shapes, damping)Non-linear behaviour

• SSI AnalysisInterpretation of responsesInterpretation of responses

PILES• The seismically deforming soil imposes

motion on the foundation and the entiremotion on the foundation and the entire structure. Due to their flexural rigidity the embedded piles tend to resist andembedded piles tend to resist and become stressed reflecting and scattering the seismic wavesthe seismic waves.

• To completely understand the seismic b h i f il il t t tbehaviour of a soil-pile-structure system it is necessary to conduct three analyses:

• 1 Soil Response Analysis – gives a realistic picture of the seismic environment during the designof the seismic environment during the design earthquake. It defines the seismic excitation and provides information for assessing possible loss of p g pstrength resulting fro pore-water pressure build-up in the saturated liquefied cohesionless layers.

• 2 Kinematic Pile Response Analysis – provides the response of the piled foundation in the absence

f i ti f f th t tof inertia forces from the super-structure.• 3 Inertial Soil-Structure Interaction Analysis –

t d t i th d i f thserves to determine the dynamic response of the super-structure and the loads imposed on the foundation by the responsefoundation by the response.

When stages 1&2 are performed correctly, the analysis is exact for linear soil, pile, and structure, but as an engineering g gapproximation can be used in moderately-nonlinear systemsnonlinear systems.

To determine and describe precisely the role of thi i t ti it i t l t ththis interaction it is necessary to evaluate the inelastic behaviour of the super-structure.

• In embedded or piled foundations, even in the absence of a super-structure is calledabsence of a super-structure, is called kinematic interaction and it originates from the

i i f fi ld tt f di l tseismic free-field pattern of displacements imposed onto the foundation.

• The embedded foundation is rigid and diffracts the 1D seismic waves because itsdiffracts the 1D seismic waves because its motion is incompatible with the free-field

ti th f th fi ld bmotion, therefore, the wave field becomes more complicated. p

Afer Lok, Pestana and Seed (2000)

Incident seismic waves are scattered and the seismic excitation affecting the structure baseseismic excitation affecting the structure base differs from the free-field motion, like in the embedded foundation However pilesembedded foundation. However, piles experience bending, axial and shearing stresses, in function to their overall rigidity in relation to the soil. The relationship between psoil and piles is also affected by the kinematic constants imposed at the head of the piles fromconstants imposed at the head of the piles from the cap and the super-structure.

Aft M dAfter Meymond,1998

After Gazetas, 1993

Substructure methodsFor seismic SPSuperst.InteractionInteraction

• The behaviour depend primarily on the type and stiffness of the soil, the relative frequency of the , q ymotion, the pile-cap or pile-head boundary conditions, the type of incident seismic waves, and the overall yp ,relative rigidity of the pile with respect to the soil.

• Piles used to be designed to transmit safely only thePiles used to be designed to transmit safely only the inertia loads due to oscillation of the super-structure. Pile flexural failures, can be associated with thePile flexural failures, can be associated with the presence of strong discontinuities in strength and stiffness of the soil profile. Relatively large curvaturesstiffness of the soil profile. Relatively large curvatures imposed by the surrounding soil due to propagating seismic waves is the most likely cause of the damage.seismic waves is the most likely cause of the damage.

After Dowrick (2005)

Analytical models for dynamic interactionAnalytical models for dynamic interactionin the case of rigid and pile foundations, after Japanese SCE (2000)

After Murono and Nishimra, 2000

After Muronoand Nishimra, 2000

Simplified analitycal model for pile group foundation (a); horizontal force vs. horizontal desplacement (b); vertical force vs. verical displacement (c); bending moment vs. cuvature of piles (d), relationsmoment vs. cuvature of piles (d), relations

After Bakhash, et al. (2002)

Approach is based onGreen`s function f l i f hformulaion for the linear pile analysis. Hiperbolic model ofHiperbolic model of soil is used to definethe nonlinear stress-Strain relationship of the soil.

Maheshwari, Watanabe (2000)

The separation Winkler soil model with interface element is used for model gap formulation.

After Maheshwari, W b (2000)Watanabe (2000)

Afer Lok, Pestana and Seed (2000)

(a) soil-grouped piles system b) sliced elements Aftier Tahighi andKonagai (2006)Assumptions for evaluation of equivalent upright beam Konagai (2006)

Elasto-plastic soil elem-pent is expressed as a Winkler hipothesis model Using a uniaxial meterialUsing a uniaxial meterialAnd zero-length element

Aftier Tahighi andKonagai (2006)g ( )

Aftier Tahighi andKonagai (2006)

After Konagai, et al 2003et al. 2003

Pile group

In the pushover analysis, superp y pstructures and pile foundationAre modeled as a overall t t l t hi h i l dstructural system, which includes

nonlinear properties of both the subgrade and structures

After Japan Code

subgrade and structures.

te Japa Code(2002)

Elasto-plastic model of pile foundation ground resistance.

After Japan Code(2002)

Example

Quasi 3DQuasi 3DModel SPAfter Wu,1994Cai et al 2000Cai et al. 2000nonlinear, used inBalendra (2005)

After Balendra, te a e d a,(2005)

After Balendra, (2005)

After Balendra,(2005)

After Balendra,(2005)

• CONCLUSION• The FEM is convenience tool to study theThe FEM is convenience tool to study the

effects of various variables on the kinematic (K) transfer function (TF) as well as inertialtransfer function (TF) as well as inertial impedance function (IF).

• Numerical model for dynamic SPSI (quantifying• Numerical model for dynamic SPSI (quantifying KTF) often were developed using FEM software ABAQUS or Plaxis In Balendro (2005) identifiesABAQUS or Plaxis. In Balendro (2005) identifies the conditions under which soil nonlinearity, soil

pile separation (gapping) and pile diameter– pile separation (gapping) and pile diameter effects become important in the treatment if kinematic and inertial effectskinematic and inertial effects.

Kinematic interaction•Ground motion intensity does not change the value TF i li il di Whil i iTF in nonlinear soil medium. While an increase in input motion intensity decreases the soil stiffness and increases the hystetic damping in the soil;and increases the hystetic damping in the soil; hence TF is not affected. The influence of the of the pile diameter on TF is significant. •Separation between soil and pile has no effects in the transfer of a pile embedded in an elastic mediummedium.•Maximum bending moment envelope along the pile increase with pile with both for rigid and flexibleincrease with pile with both for rigid and flexible piles.•Soil–pile separation increases the normal stress p palong the lower half of a flexible pile.

Inertial interaction•For flexible piles in an elastic soil medium the•For flexible piles in an elastic soil medium, the real part of the IF is nearly constant and does not change much with pile diameter. For the rigid g p gpiles, the real part of the IF reduces with increasing frequency.S il il ti d th i i d•Soil-pile separation reduces the imaginary and

real part of the IF, as well as increases the normal stress along the pilestress along the pile.•Nonlinearity does not affect the normal stress along the pile.g p•The advances in computer technology justify the use of rigorous SPSI anaysis for important b idbridges.