Rete dei Laboratori Universitari di Ingegneria Sismica (Reluis)

Rete dei Laboratori Universitari di Ingegneria Sismica (Reluis)

Progetto esecutivo 2005 – 2008 (Attuazione Accordo di Programma Quadro DPC-Reluis del 15 Marzo 2005)

Rapporto Scientifico Attività 2 anno

Anno 2007 Report Scientifico - 2° anno - PROGETTO RELUIS Linea n. 6

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Rete dei Laboratori Universitari di Ingegneria Sismica

Progetto esecutivo 2005–2008

Progetto di ricerca N. 6

METODI INNOVATIVI PER LA PROGETTAZIONE DI OPERE DI SOSTEGNO E LA

VALUTAZIONE DELLA STABILITÀ DEI PENDII

Coordinatori: Associazione Geotecnica Italiana A. Burghignoli, M. Jamiolkowski, G. Ricceri, C. Viggiani

6.4 Deep Foundations

Coordinator: Armando Lucio Simonelli

6.4.1 Introduction In this report the research activity carried out during the second year of the RELUIS project on the theme

“Deep Foundation” is accounted for. The main objective of the project is to individuate elements to be introduced in the technical code, regarding the seismic design of deep foundations, with particular attention to the effects of kinematic interaction. In the second year the Research Units (RU) University of Sannio (UNISANNIO), University of Calabria (UNICAL), Second University of Naples (SUN), University of Catania (UNICT) and University of Basilicata (UNIBAS) focused on the numerical modelling of the seismic response of foundation piles, by adopting different approaches. A further activity has been the definition and organization of an experimental activity on pile models, to be performed by the shaking table at the University of Bristol during the third year. In what follows, the research activities carried out by the single Units are briefly illustrated.

• Research activity carried out by SUN • Research activity carried out by UNICAL • Research activity carried out by UNICT • Research activity carried out by UNISANNIO • Research activity carried out by UNIBAS

6.4.2 Research activity carried out by the SUN research unit

6.4.2.1 Introduction Dynamic soil pile interaction is a very complex problem involving a number of factors, such as subsoil

model, soil properties, non linear soil behaviour, seismically induced pore-water pressure, inertial effects and kinematic interaction between soil and pile. Despite these complexities, engineering practice is still based on pseudostatic approaches, thus neglecting the effects of kinematic interaction. By contrast there is extensive research on kinematic interaction and case histories confirming the role of kinematic pile bending moments, including pile damages observed after the earthquake events of Mexico City (1985), Kobe (1995) and Chi Chi (1999).

Studies on this argument have been based on both simplified models (Dobry & O’Rourke, 1983; Nikolau et al., 2001; Mylonakis, 2001; Sica et al. 2007) and more complex analyses in which the subsoil was assumed to be linear-elastic (Bentley & El Naggar, 2000; Aversa & Maiorano, 2006) or non-linear (Wu & Finn; 1997; Maheshwari et al. 2006; Maiorano et al., 2007). Analyses based on simplified approaches have been essentially performed to define approximate analytical solution capable to reproduce kinematic bending moments at the interface between two layers characterized by sharply different shear moduli. On the other hand, studies based on advanced models have been performed to validate the applicability of analytical solutions. Most of these researches have been focused on the single pile problem. Literature on dynamic pile group effects is much less extensive and essentially dedicated to the elementary cases of constant or linearly varying with depth shear modulus.

A number kinematic pile-soil interaction analyses of both single piles and pile groups using the 3D finite element computer program VERSAT-P3D (Wu, 2004) have been performed in order to assess the influence of a number of factors, like the subsoil model and the soil properties (shear wave velocities). Simplified subsoil conditions have been considered: a two layered profile, with different values of the stiffness contrast


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between the two soil layers, in terms of their respective S-waves velocities VS2/VS1. Italian real acceleration time histories have been employed in the analyses (Scassera et al., 2006).

6.4.2.2 Parametric study The study reported in this section is aimed to address a number of fundamental issues of the pile-soil

kinematic interaction. Besides the scope of assessing the suitability of the analytical solutions published in literature is the

development of reference solutions for both bending moments and displacements, and simple rules to predict the effect of kinematic interaction at the pile top.

The kinematic interaction analyses have been performed for pile groups and isolated piles embedded in an ideal subsoil consisting of two layers underlined by a rigid base (Figure 6.4.2.1). Such base is located at a depth H=30 m while the interface between the layers (H1) was located at depths 5, 10, 12, 15, 17, 19 or 20 m. Piles with a length L=20m, a diameter d=0.6m and a Young’s modulus EP=30 GPa were considered; they were installed without changing the in situ stress conditions (wished in place) to model perfectly bored piles. The pile head is fixed against rotation. A 3x3 or alternatively 5x5 pile group was considered. The pile spacing was taken equal to 4 diameters.

L

B

HH1

��

��

��

��

��

��

��

��

��

��

H2VS2

VS1

Figure 6.4.2.1. Cases considered in the parametric study. The shear wave velocity VS1 of the upper layer was taken 50 m/s or 100 m/s, while the ratio of the two

shear wave velocities was set equal to 2 and 4 for both values of VS1. Finally a soil density of 1.94 t/m3 and a coefficient of Poisson ν=0.4 have been assumed.

The resulting profiles can be classified as subsoil type D, and sometimes subsoil type C, according to EN-

1998-1 (2003). It is worth mentioning that Eurocode 8-5 (2003) recognises the importance of kinematic interaction for important structures in regions of moderate to high seismicity, when the ground profile contains consecutive layers of sharply differing stiffness.

The well known relation between the shear wave velocity and the small strain shear modulus G0 is:

( ) ( )0

s

G zV z

ρ=

(1) where ρ is the soil density. Table 1 summarizes the geotechnical parameters: Table 1. Geotechnical parameters of the soils

G01 (kPa) G02 (kPa) VS1 (m/s) VS2 (m/s) ν1 ν2 γ1 (kN/m3) γ2 (kN/m3) VS2/VS1 19368 309888 100 400 0.4 0.4 19 19 4 19368 77472 100 200 0.4 0.4 19 19 2 4842 77472 50 200 0.4 0.4 19 19 4 4842 19368 50 100 0.4 0.4 19 19 2


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The analyses have been performed in the time domain; the input acceleration time histories have been selected from a database of records of Italian seismic events, assembled in the framework of the ReLUIS research programme (Lanzo, 2006). The signals have been scaled to values of ag equal to 0.35g (according to the seismic zonation specified by OPCM 3274, 2003), and have been applied to the base of the subsoil models. Table 2 summarizes the main data (seismic event, magnitude, peak ground acceleration, location of the recording station, distance from the epicentre) of the acceleration time histories used in the analyses.

Table 2. Acceleration time-histories used in the analyses

Name Event Station Mw Distance (km) PGA (g)A-TMZ270 Friuli, 1976 Tolmezzo 6.5 23 0.357 A-STU270 Irpinia, 1980 Sturno 6.9 32 0.320 E-NCB090 Umbria-Marche, 1997 Norcia Umbra 5.5 10 0.382

6.4.2.3 Analysis Results Figure 6.4.2.2 summarises the results obtained for a moderate sized foundations (3x3) in the case of

Tolmezzo (A-TMZ270), VS2/VS1=4, VS1=100m/s and H1=75%L. The diagrams reported in the upper part of this Figure represent the bending moment envelops along the edge piles (A, D, and E) and the central pile (B), while the diagrams in the lower part illustrates the maximum deflection and acceleration profiles along the foundations centre and a near foundation axis (point A in 6.4.2.1).

For comparison the bending moment envelop computed for the single pile has been added to Figures (6.4.2.2a) and (6.4.2.2b). Furthermore, a free-field analysis has been performed by code EERA and the corresponding maximum acceleration profile has been added to the diagrams of Figure (6.4.2.2d).

At the interface depth the bending moment envelops exhibits a pronounced scatter while the pile deflection curves are less affected by the transition from the upper to the lower layer. It may be seen that no significant differences exist between the bending moment profiles of the piles belonging to the group. At the same time the response of these piles is practically coincident with that found for the single pile. In other terms the (kinematic) group effects can be considered negligible, at least in the case of moderate sized and closely spaced pile groups. Such result, and many similar findings that are not presented for lack of space, seem very appealing as they indicate that the kinematic effect of a pile group can be predicted with reasonable accuracy by merely performing a single pile analysis; this implies in turn considerable savings in terms of computational efforts. This result is in agreement with the field measurements on a 12-storey building in Japan carried out by Nikoalu et al (2001) and the analytical studies of Fan et al. (1991) and Kaynia and Mahzooni (1996).

0

5

10

15

20

25

300 100 200 300 400 500

SINGLEPile DPile E

M [kNm]

� �

� � �

z [m]

0

5

10

15

20

25

30

0 100 200 300 400 500

SINGLEPile APile B

M [kNm]

� �

� � �

0

5

10

15

20

25

300 10 20 30 40 50 60

Free Field 2

Asse fondazione

u [mm]

z [m]

0

5

10

15

20

25

30

0.00 0.25 0.50 0.75 1.00 1.25

EERA

Free Field 2

Asse fondazione

a/g

Figure 6.4.2.2. Results in the case of Tolmezzo, VS2/VS1=4, VS1=100, and H1=75%L. The line labelled

Free Field 2 refers to the near foundation vertical axis


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A synthesis of the results obtained in the case of VS1=100 m/s is illustrated in Figure 3, where the maximum bending moments at the interface depth H1 (MINT) and the pile top (MCAP) are plotted against H1. The continuous lines refer to analysis performed for a (3x3), 8d sized pile group, and particularly to pile A belonging to the middle row (see Figure 6.4.4.2), while the dashed lines pertain to the single pile. The following deductions about Figure 6.4.2.3 are worthy of note: (i) the response of the single pile remains practically unchanged in the group whatever the value taken by H1; (ii) the bending moments MINT are strongly affected by the ratio of the two shear wave velocities; (iii) for both Tolmezzo and Norcia Umbra the plot of MINT is more scattered and variable for larger values of VS2/VS1; (iv) the bending moments curves MCAP have e trend of converging for increasing values of H1, where the effect of the interface depth is of minor concern and the bending moment at the pile cap is essentially governed by the elastic properties of the upper layer (su questa frase evidenziata in giallo ho qualche dubbio).

The results found for VS1=50m/s are illustrated in Figure 6.4.2.1 and lead to similar conclusions.

6.4.2.4 analysis results vs. simplified formulas Figures 6.4.2.5 and 6.4.2.6 show the comparison between the bending moments at the interface depth

computed by the finite element analyses and those evaluated by the analytical solutions provided by Nikolau et al. (2001), Dobry and O’Rourke (1983) and Mylonakis (2001). In all the cases a preliminary analysis of the free-field response in the time domain was carried out by code EERA. Once the maximum free-field surface acceleration amax-S was available, this has been employed in eq. (6) to compute the maximum shear strain at the interface γ1, as suggested by Mylonakis (ibidem), and then, again. in eq. (11) to compute the maximum (or characteristic) shear stress at the interface τC, as suggested by Nikolau et al. (ibidem). Both the bending moments expressions provided by Dobry and O’Rourke and Mylonakis have been applied with the above value for g1. Finally, the formula by Nikolau et al. has been applied with the above ‘characteristic’ value for τC , based on the maximum acceleration in the time domain, although the method proposed by Nikaolu et al. provides an approximate expression of the maximum (steady-state) bending moment induced by harmonic excitations and a frequency-to-time reduction factor to convert the steady-state bending strain to the corresponding transient peak value in the time domain; in the case under examination, no reduction factor has been applied giving confidence that this is included in the free-field surface acceleration evaluated in the time-domain analysis.

VS2/VS1=4

VS2/VS1=2

0

200

400

600

800

0 5 10 15 20

MIN

T [kN

m]

TOLMEZZO

VS2/VS1=2

VS2/VS1=4

0

200

400

600

800

0 5 10 15 20

NORCIA UMBRA

VS2/VS1=4

VS2/VS1=20

200

400

600

800

0 5 10 15 20H1 [m]

MC

AP [

kNm

]

VS2/VS1=4

VS2/VS1=20

200

400

600

800

0 5 10 15 20H1 [m]

Figure 6.4.2.3. Maximum Bending moments in the case VS1=100m/s for a (3x3) pile group and the single pile


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VS1=50

VS1=50

0

200

400

600

800

1000

1200

0 5 10 15 20

V2/V1=4

V2/V1=2

MIN

T [kN

m]

TOLMEZZO 1976

VS1=500

200

400

600

800

1000

1200

0 5 10 15 20

V2/V1=4

V2/V1=4

NORCIA UMBRA 1997

VS1=50

0

200

400

600

800

0 5 10 15 20

V2/V1=4

V2/V1=4

H1 [m]

VS1=50

VS1=50

0

200

400

600

800

0 5 10 15 20

V2/V1=4

V2/V1=2

H1 [m]

MC

AP [

kNm

]

Figure 6.4.2.4. Maximum Bending moments in the case VS1=50m/s for a single pile

VS2/VS1=4

0

200

400

600

800

0 5 10 15 20

Dobry e O'Rourke (1983)Nikolau et al. (2001)Mylonakis (2001)

MIN

T [kN

m]

TOLMEZZO

VS2/VS1=4

0

200

400

600

800

0 5 10 15 20

Dobry e O'Rourke (1983)Nikolau et al. (2001)Mylonakis (2001)

NORCIA UMBRA

VS2/VS1=2

0

200

400

600

800

0 5 10 15 20

Nikolau et al. (2001)Dobry & O'Rourke (1983)Mylonakis (2001)

MIN

T [kN

m]

H1 [m]

VS2/VS1=20

200

400

600

800

0 5 10 15 20

Nikolau et al. (2001)Dobry & O'Rourke (1983)Mylonakis (2001)

H1 [m]

Figure 6.4.2.5. Comparison between bending moments predicted by analytical solutions and those evaluated by the finite element analyses for VS1=100m/s.


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VS2/VS1=4

0

200

400

600

800

1000

1200

0 5 10 15 20

Dobty & O'Rourke

Nikolau et al.

Mylonakis (2001)

MIN

T [kN

m]

TOLMEZZO 1976

VS2/VS1=40

200

400

600

800

1000

1200

0 5 10 15 20

Dobry e O'Rourke

Nikolau et al.

Mylonakis (2001)

NORCIA UMBRA 1997

VS2/VS1=4

0

200

400

600

800

1000

1200

0 5 10 15 20

Dobry & O'RourkeNikolau et al.Mylonakis (2001)

MIN

T [kN

m]

H1 [m]

Figure 6.4.2.6. Comparison between bending moments predicted by analytical solutions and those evaluated by the finite element analyses for VS1=50m/s.

The comparisons in Figures 6.4.2.5 and 6.4.2.6 show that: (i) the analytical solutions do not differ

significantly each-other and tend to be conservative; (ii) there are significant discrepancies between the bending moments predicted by the finite element analysis and those evaluated by the closed form expressions, especially for decreasing values of VS1 (or EP/E1) and increasing values of H1, with a maximum of around 120% (assuming as reference solution the bending moment computed by VERSAT); (iii) the curves obtained by the closed form expressions have a trend of increasing for increasing values of the interface depth while those pertaining to the finite element analyses exhibits a somewhat “plateau”.

From the points addressed above there appears that the closed form expression could be applied within reasonable accuracy only for certain depths of the interface between the two layers (H1<50%L) and moderate values of the pile-soil relevant stiffness. By contrast considerable discrepancies are expected for higher values of H1, i.e in the case of end-bearing piles that is quite frequent in engineering practice.

There is therefore the need of further research to define the extent at which the simplified formulas can be considered applicable. Based on the results of the above parametric study, this research unit is actually developing a new criterium for evaluating the kinematic bending moment at the interface depth, that can be considered an extension of the closed form expressions and will form the content of a specific paper.

6.4.3 Research activity carried out by the UNICAL research unit

6.4.3.1 Introduction A method for the analysis of the kinematic interaction of single piles has been developed. The method

permits soil layering effect to be reliably accounted for. The study is conducted in the frequency domain and is limited to linear, viscoelastic behaviour of the soil-pile system. The agreement between the present solution and the results provided by other formulations has been investigated (Cairo, 2007; Cairo & Dente, 2007a, 2007b).

In addition, the method originally developed by Conte & Dente (1988, 1989) for the seismic analysis of piles in layered soils has been reviewed. In this method, the pile is modelled as a linearly elastic beam connected to the surrounding soil by non linear springs and dashpots.

During the second year of research, numerical analyses of a wide range of reference cases, differing for characteristic parameters of the exciting waveform and soil layering conditions have been carried out.


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6.4.3.2 Methods of analysis

SASP - Seismic Analysis of Single Piles (Cairo & Dente)

L

ug(t)=ugeiωt

d

Esj νsj βsj ρsj hj

1

2

j

•••

•••

Figure 6.4.3.1. Single pile in layered soil excited by harmonically propagating waves (Cairo & Dente, 2007a).

Figure 6.4.3.1 shows a pile embedded in a layered soil and excited by harmonically propagating S waves. Each soil layer is modelled as an elastic material of Young’s modulus Es, Poisson’s ratio νs and mass density ρs; the pile is considered to be an elastic cylinder of length L, diameter d, Young’s modulus Ep and mass density ρp. In order to account for the effect of the material damping, Young’s modulus is replaced by its complex counterpart with βs and βp indicating the damping ratio of the soil and pile, respectively. The solution in the frequency domain is extended to the time domain using the Fast Fourier Transform (FFT).

After discretizing the pile by a finite number of one-dimensional elements, the following dynamic equilibrium equation can be written (Cairo & Dente, 2007a):

}{}]){[][]([ 21 fs

tppsp QuMFK =ω−+ −

where [Kp] and [Mp] indicate, respectively, the global stiffness matrix and mass matrix of the pile, }{ t

pu is

the vector containing the nodal horizontal displacements and rotations of the pile, [Fs] denotes the dynamic flexibility matrix of the soil, � is the vibration frequency, and

}{}{][}{ 1 fs

fss

fs PuFQ −= −

with the free-field motion }{ fsu and the corresponding stress field }{ f

sP .

In order to determine [Fs], a procedure based on the dynamic stiffness matrices proposed by Kausel & Roësset (1981) to analyse horizontally layered soils is employed (Cairo & Dente, 2007a). These stiffness matrices can be used to evaluate the free-field soil response, too (Cairo & Dente, 2007a). Once element nodal displacements and rotations of the pile are determined, shear forces and bending moments can be computed.

A computer program, named SASP (Seismic Analysis of Single Piles), has been developed. In order to validate the proposed approach, several comparisons with other existing solutions have been carried out (Cairo, 2007; Cairo e Dente, 2007b).

BDWF - Beam-on-dynamic-Winkler-foundation (Conte & Dente)

The method originally developed by Conte & Dente (1988, 1989) for the seismic analysis of piles in

layered soils is reviewed. In this method, the pile (Figure 6.4.3.2) is modelled as a linearly elastic beam connected to the surrounding soil by non linear springs and dashpots, which provide the interaction forces in the lateral direction. The stiffness of the springs is related to the soil shear modulus updated to the current


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strain level induced by the seismic motion, according to a non linear hysteretic Ramberg-Osgood type model. The radiation damping coefficient is evaluated using simple analytical expression available in the literature (Gazetas & Dobry, 1984).

The non linear response of the soil in free-field condition is achieved by a numerical technique based on the characteristics method, under the assumption of one-dimensional propagation of shear waves (Conte & Dente, 1987).

The method accounts for important effects such as heterogeneity and non linearity of the soil, energy dissipation due to material and radiation damping. In addition, the presence of a superstructure, idealized as a number of masses connected by elastic beams, can be considered to analyse directly the response of the superstructure-pile-soil system in time domain.

Figure 6.4.3.2. Soil-pile system (beam-on-dynamic-Winkler-foundation).

6.4.3.3 Numerical simulations In order to assess the accuracy of SASP, some comparisons with other solutions have been performed.

The displacement and the rotation kinematic factors Iu e Iφ (Figure 6.4.3.3) are calculated and compared with the solution obtained by Mamoon & Banerjee (1990). They express the amplitudes (absolute values) of horizontal displacement and rotation of the pile head, normalized by the amplitude of the free-field ground surface displacement, as a function of the dimensionless frequency a0=ωd/Vs and the direction of propagation of the shear waves ψ. As can be seen, at lower frequencies, the free-head piles follow the movement of the ground while, at higher frequencies, they experience considerably reduced deformations. In addition, a rotational motion arises.

0.0

0.4

0.8

1.2

1.6

0.0 0.2 0.4 0.6 0.8 1.0a 0

I u

Ψ=90°

Ψ=45°(a)


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-0.1

0.0

0.1

0.2

0.0 0.2 0.4 0.6 0.8 1.0a 0

I φ

Mamoon e Banerjee (1990)presente studio

Ψ=90°

Ψ=45°(b)

Figure 6.4.3.3. Kinematic interaction factors (Cairo & Dente, 2007a). The response of a fixed-head pile to transient seismic excitation and embedded in a two layer soil profile

has been investigated. The envelopes of peak moments in the time domain are shown in Figure 6.4.3.4. As can be seen, the maximum bending moment at the layer interface tends to be greater than the maximum bending moment at the pile head.

Several analyses have been performed in this year of activity referring to a fixed-head pile in a two layer soil profile (Figure 6.4.3.5) adopting both SASP and the BDWF. Soil shear stiffness contrast has been changed from 16 to 4 which implies shear wave velocity ratio varying from 4 to 2; the velocity values have been chosen in order to have type D or C subsoils. The analyses have been performed by adopting Italian accelerograms scaled in magnitude to provide a rock peak acceleration consistent with the seismic zone taken into account (0.35g). The results presented in Figure 6.4.3.6 refer to the highest stiffness contrast (Vs2/Vs1=4).

0

4

8

12

16

0 1 2 3

M (MNm)

z (m

)

this study

Nikolaou & Gazetas (1997)

Anderson, Loma Prieta

0

4

8

12

16

0 1 2

M (MNm)

z (m

)

this study

Nikolaou & Gazetas (1997)

JMA, Kobe

Figure 6.4.3.4. Distribution with depth of envelope of moments for seismic excitations (Cairo & Dente, 2007b).


11 / 29

L=20

m

H1=

15 m

H2

d=0.6 m

Vs1

Vs2

Figure 6.4.3.5. Reference scheme adopted for the parameter study.

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800

|M| (kNm)

z (m

)

A-AAL018 A-TMZ270 A-STU000

A-STU270 A-TMZ000 B-BCT000

B-BCT090 C-NCB000 C-NCB090

E-AAL018 E-NCB000 E-NCB090

J-BCT000 J-BCT090 R-NC2000

R-NC2090 R-NCB090 TRT000

S1 D 4

Figure 6.4.3.6. Bending moments along the pile for the two-layer soil profile S1, soil type D and Vs2/Vs1=4. Comparisons between SASP and the proposed BDWF are presented in Figures 6.4.3.7-9, regarding the

three accelerograms that systematically induce the higher bending moments along the pile.


12 / 29

0

2

4

6

8

10

12

14

16

18

20

0 400 800

M (kNm)z

(m)

SASP

BDWF

A-

0

2

4

6

8

10

12

14

16

18

20

0 400 800

M (kNm)

z (m

)

SASP

BDWF

A-STU270

0

2

4

6

8

10

12

14

16

18

20

0 400 800

M (kNm)

z (m

)

SASP

BDWF

A-

Figure 6.4.3.7. Comparison between SASP and the proposed BDWF: scheme S1, soil type D, Vs2/Vs1=2.

0

2

4

6

8

10

12

14

16

18

20

0 400 800

M (kNm)

z (m

)

SASP

BDWF

A-STU000

0

2

4

6

8

10

12

14

16

18

20

0 400 800

M (kNm)

z (m

)

SASP

BDWF

A-STU270

0

2

4

6

8

10

12

14

16

18

20

0 400 800

M (kNm)z

(m)

SASP

BDWF

A-TMZ270



13 / 29

0

2

4

6

8

10

12

14

16

18

20

0 400 800

M (kNm)z

(m)

SASP

BDWF

A-

0

2

4

6

8

10

12

14

16

18

20

0 400 800

M (kNm)

z (m

)

SASP

BDWF

A-STU270

0

2

4

6

8

10

12

14

16

18

20

0 400 800

M (kNm)

z (m

)

SASP

BDWF

A-TMZ270


6.4.4 Research activity carried out by the UNICT research unit

6.4.4.1. Introduction The seismic response of pile foundations is a very complex process involving inertial interaction between

structure and pile foundation, kinematic interaction between piles and soils, and nonlinear response of soils to strong earthquake motions.

Today the seismic evaluation and design of soil-pile interaction is an area of active research and in the last thirty years, mathematical models (Novak, 1974; Novak & Sheta, 1982; Gazetas, 1984; 1991; Kanya & Kausel, 1991; Makris & Gazetas, 1992; Milonakis et al., 1997; Gazetas & Mylonakis, 1998; Nikolaou et al., 2001; and others) and several simplified approaches (El Naggar e Novak, 1994; Abghari & Chai, 1995; Tabesh & Poulos, 2001; Liyanapathirana & Poulos, 2005; Poulos, 2006; ) have been developed for the analysis of single piles or pile groups.

There are two sources of loading of the pile by the earthquake: “inertial” loading of the pile head caused by the lateral forces imposed on the superstructure, and “kinematic” loading along the length of the pile caused by the lateral ground movements developed during the earthquake, assuming zero the inertia of the superstructure.

Part 5 of the Eurocode 8 (2003), in particular, states that piles shall be designed for the following two loading conditions:

a) inertia forces on the superstructure transmitted on the heads of the piles in the form of axial and horizontal forces and moment;

b) soil deformations arising from the passage of seismic waves which impose curvatures and thereby lateral strain on the piles along their whole length.

Analyses to determine the internal forces along the pile, as well as the deflection and rotation at the pile head, shall be based on discrete or continuum models that can reproduce the soil reactions along the pile, with due consideration to the effects of cyclic loading and the magnitude of strains in the soil.

6.4.4.2. Soil - pile interaction model To predict the response of pile-supported structures, the p-y method has been extensively used and

several p-y curves for different soil-pile systems have been proposed, which are mainly based on in-situ pile tests under static or low frequency cyclic loading conditions. The p-y curve approach (load transfer method) is a widely accepted method for predicting pile response under static loads because of its simplicity and practical accuracy.

The p-y method models the bending behaviour of the pile by either finite difference or finite element techniques and models the soil reaction using non linear reaction “springs” (i.e., nonlinear Winkler (1876)


14 / 29

sub-grade springs), which have been derived for static loading in many types of soils empirically or semi-empirically.

The approach with p-y curves is further extended for the dynamic response analysis of pile foundations by adding a dashpot in parallel to the nonlinear spring governed by p-y curve, in order to account for the radiation damping effect.

By accepting Winkler’s foundation assumption (Dobry et al., 1982; Gazetas & Dobry, 1984; Dobry & Gazetas, 1988; Makris & Gazetas, 1992; Gazetas et al., 1992; Kavvadas & Gazetas, 1993), the soil-pile contact is discretized to a number of points where combinations of springs and dashpots represent the soil-pile stiffness and damping at each particular layer.

The p-y method can be extended to earthquake loading conditions if dynamic p-y curves are adopted (Kagawa & Kraft, 1980). The dynamic p-y curves, in fact, allow for the generation of different p-y relationships based on the frequency of loading and soil profile. Substituting dynamic p-y curves in place of traditional static p-y relationships for analysis should result in better estimates of the response of structures also to dynamic loading (Hajialilue-Bonab et al., 2007; Rovithis et al., 2007a; 2007b).

Static lateral loading Several approaches are currently available to analyze the behaviour of piles subjected to lateral load

ranging from complex models, as non linear analysis and 2D or 3D finite element methods, to the use of simplified approaches as limit equilibrium (LE) approach and p-y analysis approach.

The p-y approach for analyzing the response of laterally loaded piles is essentially a modification of the basic Winkler model, where p is the soil pressure per unit length of pile and y is the pile deflection. The soil is represented by a series of non linear p-y curves that vary with depth and soil type.

Researches based on results of field tests on full scale piles suggests to employ non linear p-y relationship (Reese et al., 1974; Reese & Welch, 1975; Reese & Van Impe, 2001; Juirnarongrit & Ashford, 2006), thus a hyperbolic p-y relationship can be adopted:

)z(p

)z(y

)z(E1

)z(y)z(p

lim

p

si

p

+=

(1)

where Esi [FL-2] is the initial modulus of horizontal sub-grade reaction, yp [L] is the pile lateral deflection, p and plim [FL-2] are the mobilized and the ultimate horizontal soil resistance respectively.

Dynamic lateral loading To incorporate the dynamic effects in the framework of a Winkler’s approximation, a conventional and

widely accepted method is to add a dashpot in parallel to the non linear spring governed by p-y curve, in order to account for the radiation damping effect. Thus the soil-pile contact is discretized in a number of points where combinations of springs and dashpots represent the soil-pile stiffness and damping at each particular layer, through the development of a complex stiffness as a function of the frequency content. The complex stiffness has a real part k1 and an imaginary part k2:

y)ikk(kyp 21d +== (2)

where pd is the dynamic value of the reaction p on the p-y curve at depth z [e.g., in N/m] and k the secant modulus to the static p-y curve at pile deflection y.

The real part k1 represents the true stiffness k, the imaginary part of the complex stiffness k2, describes the out of phase component and represents the damping caused by the energy dissipation in the soil element. Because this damping component generally grows with frequency, it can also be defined in terms of the constant of equivalent viscous damping (the dashpot constant) given by c = k2/ω, where ω is the circular frequency of loading equal to 2πf and f the actual frequency of loading [rad/s].

The overall relationship between the dynamic soil resistance and loading frequency for each test can be established in the form of the generic equation (Figure 1):

��

�

��

��

�

�++=n

o2

osd D)z(y

aa)z(p)z(pωκβα pd ≤ plim at depth of p-y curve (3)


15 / 29

where pd is the dynamic value of the reaction p on the p-y curve at depth z; ps is the corresponding reaction on the static p-y curve at depth z [N/m]; ao is the frequency of loading, expressed in dimensionless terms ωro/vs; vs is the propagation velocity of seismic shear waves; ro is the pile radius equals; D is the pile diameter [m]; α, β, κ and n are dimensionless constants defining the dynamic p-y curves. Values are given for various soil types (NCHRP, 2001).

To generate dynamic p-y curves according to equation (3), the corresponding static reaction ps given by equation (1) can be used (Figure 2). The constant α is taken equal to unity to ensure that pd = ps for ω = 0. For large frequencies or displacements, the maximum soil resistance in dynamic conditions is limited to the ultimate static lateral resistance plim of the soil. The dynamic p-y curves are most accurate when ao > 0,02.

Equation (3) can be used directly to represent the dynamic relationship between a soil reaction and a corresponding lateral pile deflection. Thus the total dynamic soil reaction at any depth is represented by a nonlinear spring whose stiffness is frequency dependent.

The approach proposed was employed and implemented in an original computer code. Such code allows the assessment of the lateral response of a single pile (lateral deflection, bending moment and shear force distribution). Using the p-y method the lateral secant stiffness of piles can be developed as functions of lateral deformations through the considered non linear p-y analysis.

��

��

� ��∆��

��

��

� ��

��

��

� ��

� ��∆�� ∆��

�� ∆��

Figure 6.4.4.1. Equivalent stiffness including damping. Figure 6.4.4.2. Dynamic p-y curves.

6.4.4.3. Numerical examples To evaluate the influence and the importance of the inertial effects, numerical analyses have been carried

out on an free-head single pile embedded in a medium clay soil deposit (Figure 3). The pile length is L = 20 m, the diameter D = 1.0 m, the Young’s modulus Ep = 28.500 MPa. The undrained shear strength and the seismic shear waves velocity of soil were considered constant with depth and equal to cu = 70 kPa and vs = 180 m/sec respectively, the mass density of soil was ρ = 1.94 kNsec2/m4.

Ultimate lateral soil resistance according to Broms (1964) is plim = 630 kPa, while the initial modulus of horizontal sub grade reaction is Esi = 25.1 MPa.To estimate inertial loading effects, dynamic p-y curves were developed according to curve parameter constants: α = 1, β = -360, κ = 84 and n = 0.19. The dynamic p-y curves were generated for a range of harmonic loading with varying frequencies at the pile head (0 to 5 Hz).

The results of the numerical analyses are summarized in the Figure 4 in terms of computed distribution of bending moment for a fixed value of the pile head deflection (y = 0,5 cm).


16 / 29

L

F(t)

D

L/D = 20cu = 70 kPaEp = 28.5 MPaEsi = 25.1 MPavs = 180 m/sec

-0.1 0 0.1 0.2 0.3 0.4 0.5

Momento Flettente (MNm)

20

18

16

14

12

10

8

6

4

2

0

Prof

ondi

tà (m

)

-0.1 0 0.1 0.2 0.3 0.4 0.5

p -y statico

2 H z3 H z4 H z5 H z

Figure 6.4.4.3. Pile and soil layout under study. Figure 6.4.4.4. Bending moment distribution.

Analyzing the results obtained it is possible to observe that the values of the bending moment are

frequency dependent. As expected, if inertial effects are ignored and only static condition are considered, the moments along the pile length can be significantly underestimated, being the maximum values in dynamic conditions, for the considered numerical examples, greater than 50 % of the corresponding values in static conditions (Castelli & Maugeri, 2007b).

The passage of seismic waves through the soil imposes lateral movements and curvatures on the pile, generating kinematic bending moments even in absence of a superstructure. To evaluate the effects due to the lateral movements along the pile length independent p-y curves relating soil reaction and relative soil - pile movements can be adopted (Castelli & Maugeri, 2007a). The implementation of the method involves imposing a known free-field soil movement profile. When the expected free-field movement is large enough to cause the ultimate pressure of laterally spreading soils to be fully mobilized, the ultimate pressure, instead of free-field soil movement, may be used. If kinematic effects are ignored and only inertial effects are considered, the maximum moments along the pile length can be underestimated (Maugeri & Castelli, 2007).

6.4.5 Research activity carried out by the SANNIO research unit

6.4.5.1. Introduction In accordance to the project timetable, the research activities carried out by the Operative Unite of the

University of Sannio (UNISANNIO) in the second year of the Reluis project, was focused on two main features: (1) numerical modelling of kinematic interaction occurring at the soil-pile interface by approaches of different complexity; (2) definition and planning of the experimental activities to set up the physical model on the shaking table.

With respect to numerical modelling, a wide parametric study by the simplified “Beam on Dynamic Winkler Foundation” (BDWF) method has been carried out. These analyses were aimed at investigating the kinematic response of single piles by taking into account different seismic inputs, stratigraphic conditions, and mechanical properties of the subsoil. In addition, during the second year of the project UNISANNIO started the numerical modelling by a 3-D continuum approach of the boundary value problem regarding the seismic response of a single pile in a two-layer subsoil. To such a scope, it was adopted the f.e.m. code ABAQUS chosen at the end of the first year of activities as the reference one for advanced dynamic analyses.

As the experimental activities on the shaking table regard, in agreement with the University of Bristol features of the Shear Stack, technical devices, plan of the tests to carry out on the single pile model were defined.


17 / 29

6.4.5.2. Numerical modelling

Simple Analysis based on “Beam on Dynamic Winkler Foundation” (BDWF) model As exhaustively dealt with in the relation of the first-year research activity (see, paragraph on the literature

analysis methods) in the BDWF approach the pile is connected to the soil through continuously-distributed springs (linear or non-linear) and dashpots. The free-field motion is the input excitation of the simplify system of pile, springs and dashpots, at different quotas, estimated to means of calculation codes commonly used for problems of local seismic response (Shake, EERA, etc.).

The parameter of springs (stiffness k) and of dashpots (damping c), generally dependent on frequency, can be determines through theoretical models (Novak et al., 1978; Gazetas e Dobry, 1988; El Naggar e Novak,1995 e 1996) or through calibrations with more rigorous numerical solutions (Kavaddas e Gazetas, 1993; Nikolaou et al., 1995; Mylonakis at al., 1997). The analys method, used by UNISANNIO, is that proposed by Mylonakis et al. (1997). The analyses are performed in the frequency domain, and the results are transformed in the time domain through standard Fourier transformations. Eighteen italian accelerograms have been used as input motion in the analyses. The results are given by an envelopes of maximum kinematic bending moments computed (in time domain) along the pile for each of the 18 accelerograms chosen.

The configuration consist in a single circle fixed-head pile, with a diameter d=0.60 m, in a two-layer soil deposit with different shear wave velocity Vs. The bedrock has been considered at the bottom of the second layer.

To conform with most of the analytical results presented in the literature (Nikolaou et al., 2001; Mylonakis, 2001), the pile has been modelled as a solid elastic cylinder of Young modulus Ep=2.5•107 KPa and density γ=2.5 Mg/m3. For future analysis on dynamic interaction (kinematic + inertial) the super-structure has been modelled with a simple oscillator, with one degree of freedom, with a concentrate mass, m= 60 Mg, at the head of concrete colon with the same diameter of pile.

In all analyses the following parameters remain invariable: thickness of first layer (H1=15 m), pile length (L=20 m) and diameter (d=0.60 m); Soil Poisson’s ratio (ν1 = ν2 = 0.4), soil density (ρ= 1.9 (Mg/m3) and soil material damping (β1 = β2 = 10%). The shear wave velocity of the elastic bedrock has been assumed equal to 1200 m/s.

As stated above, Italian recordings have been used as input motions in the numerical analysis. The accelerograms have been chosen in such a way that their original peak ground accelerations are as close as possible to the reference maximum peak acceleration on soil type A, agR , of the seismic zone in hand. All results shown in this paper refer to the Zone 1 (OPCM 3274 e 3519) of the actual Italian seismic zonation which prescribes agR =0.35g on soil type A. The selected accelerograms have been scaled in amplitude to provide a peak acceleration (PGA) equal to 0.35g, linearly de-convoluted at bedrock level and then propagated upward in the soil to provide the excitation motion of the pile-soil system.

All parameter cases analysed in this study have been listed in Table 1. The analyses have been divide in three groups corresponding to three different geometrical schemes (S1, S2 and S3), with varying thickness H2 of the second layer. For each group, 6 cases have been investigated, corresponding to two different shear wave velocity of first layer V1 and tree different shear wave velocity contrasts between the first and second layer (V2/V1 varies from 2 to 4).

The shear wave velocities of the first and second layers were selected in such a way that subsoil profiles correspond to class C or D of the EC8 classification, on the base of the equivalent shear wave velocity Vs,30 in the upper 30 m of the soil profile (Table 3). In the table the fundamental frequency f1 of the soil profile is also shown.

Selected results are shown in Figures 6.4.5.1 to 6.4.5.6. They represent envelopes of maximum kinematic bending moments computed (in time domain) along the pile for each of the 18 accelerograms chosen for the Zone 1 of the Italian seismic zonation. In particular, Figures 6.4.5.1, 6.4.5.3 and 6.4.5.5 correspond to class D soil profiles while Figures 6.4.5.2, 6.4.5.4 and 6.4.5.6 to class C profiles. In all figures three grey zones have been added corresponding to the range of reinforced concrete pile yielding moments for typical reinforcements of the cross section (8�16, 24�12 and 12�30) and magnitude of the normal load acting within the pile (the pile M-N domain was computed assuming a concrete of class C20/25 with Rck=25 N/mm2 and fck=20N/mm2 and steel rebars with fyk=375 N/mm2 and ftk=450 N/mm2, corresponding to the Italian steel class FeB38K). For each reinforcement the lower limit of the grey zone represent the cross section yielding moment corresponding to zero normal load while the higher one to a normal load equal to 1200 KN.


18 / 29

Table 3 Parameter cases analysed in this study

From the above results several observations may be drawn:

• at the soil layer interface the kinematic bending moment increases dramatically when the shear wave velocity contrast between the second and first layer V2/V1. This happens for both for subsoil types D (Figure 6.4.5.1, 6.4.5.3 and 6.4.5.5) and C (Figure 6.4.5.2, 6.4.5.4 and 6.4.5.6); in the latter case, however, the peak kinematic bending moments at the soil layer interface and pile head are much smaller that those computed for subsoil type D, in the same geometry;

• for subsoil profiles corresponding to class C the computed kinematic bending moments is almost always nearly localized at the soil layer interface, the kinematic bending moment at pile head is 20% and 60% of kinematic bending moment at interface;

• for subsoil profiles corresponding to class D the computed kinematic bending moments is not usually nearly localized at the soil layer interface, in the some case, however, the peak kinematic bending moments is computed at pile head, where all inertial effects will be into account.

• three accelerograms, labelled A-STU000, A-STU270 and A-TMZ270, systematically induce the higher kinematic bending moments along the pile. This could be attributed to the long duration of strong motion even if the dominant frequencies (2.63, 5 and 1.56 Hz, respectively) are not close to the resonant ones (Table 3);

• for subsoil profiles corresponding to class D the computed kinematic bending moments may be well above the yielding moments of the pile cross section computed for typical concrete reinforcements and normal load acting along the pile D=0.6 m. As the analyses have been performed assuming linear elastic behaviour for the pile, the computed kinematic bending moments can be assumed valid until they exceed the pile yielding moment.

• for subsoil profiles corresponding to class C, or worse then it, and shear wave velocity contrasts V2/V1> 2 the computed kinematic bending moments may also be worth of consideration, specially if the concrete pile has low reinforcement.

• as found by Nikolaou et al. (2001) by performing frequency domain analyses by a BDWF model, the maximum pile bending moment at the soil layer interface results slightly affected by soil depth below the pile tip. This statement is confirmed by results shown in Figures from 1 to 6, obtained in the time domain. For a fixed value of shear wave velocity contrast and subsoil class, the maximum kinematic bending moment at the soil layer interface, in fact, results almost unaltered by soil depth below the pile tip, i.e. by the different geometrical scheme S1, S2 ed S3 here investigated.

Analysis based on continuum approach and 3-D geometry

In the numerical methods based on a continuum approach the soil, pile and superstructure are modelled

as a whole. The soil-pile geometry typically is modelled in 3-D. In the II years of research UNISANNIO developed a 3-D model with a single pile in a two-layer soil deposit

(Figure 7). The soil-pile geometry is discretized by f.e.m. techniques and analyzed in the time domain by ABAQUS code. The pre-processing module of ABAQUS code (CAE module) has been used to define the 3-D model. The definition of the model has been very laborious, since it has been necessary to deal with many problems to obtain a finite model suitable to simulation both static and dynamic phases. In particular, the problems concerned: definition of f.e.m. model dimension to obtain an accurate simulation of seismic waves propagation inside; selection of opportune boundary conditions (infinite elements) in order to minimize the reflection of the seismic waves on the border (“box effect”); selection of the kind of element useful to discretize soil and pile; the connection between pile and soil.

Scheme H1 H2 V1 V2 f1 V2/V1 Vs, 30 Soil type(m) (m) (m/s) (m/s) (Hz) (m/s) EC815 15 100 200 1.34 2.0 133

100 300 1.54 3.0 150 DS1 100 400 1.61 4.0 160

150 300 2.00 2.0 200150 400 2.22 2.7 218 C150 600 2.40 4.0 240

15 30 100 200 1.05 2.0 133100 300 1.34 3.0 150 D

S2 100 400 1.51 4.0 160150 300 1.56 2.0 200150 400 1.90 2.7 218 C150 600 2.29 4.0 240

15 6 100 200 1.54 2.0 160100 300 1.64 3.0 169 D

S3 100 400 1.68 4.0 174150 300 2.29 2.0 235150 400 2.39 2.7 245 C150 600 2.47 4.0 255


19 / 29

As just say, 3-D modelling with the CAE model is not much easy, but many benefit can be obtained. In fact define the procedure, it is possible quickly change: the geometric characteristic of the model and the boundary condition and load condition.

In this initial stage of the 3-D modelling, pile and soil linear elastic behaviour has been considered. The model in Figure 6.4.5.7 has been studied, in a second phase it will introduced the non-linerarity of pile and soil.

6.4.5.3. Experimental activities on shaking table In the second year of research activities the experimental feature and technical modality were defined and

the experimental tests on piles models were planned. They were defined in agreement with the colleagues of the Engineering University of Bristol (prof. C. A.

Taylor e prof. D.M. Wood), during a lots of meeting in Bristol, where the experimental activities will be conducted.

As shown in Figure 6.4.5.8, the soil model have the same dimension of the Shear Stack, a special box for geotechnical tests: length 120 cm, breath 50 cm, thickness 80 cm. It will use pile in aluminium with circular pit section, with diameter esternal 20 mm e thickness 70 cm. The layer of soil foundation are in granular materials; in a first step it will use an homogeneous single layer, then it will use two different soil layers(the upper layer uniform sand (Dr=40%), the other layer a granular consolidate materials).

It will be examined different configurations where the pile head is free and also pile head fixed against rotation; in the latter situation it will make a system with a double pendulum, as shown in Figure 8.

As regards the sequences of the tests will use, first of all, a mono-layer prototype in free-filed condition, to control all instruments for deformation measurement, for input application ect. .

At the end of the phase of calibration of the model, 4 configuration of test with bi-layers will study: 1) prototype without pile (free-field), 2) prototype with pile free head, 3) prototype with pile head fixed against rotation; 4) prototype with pile head fixed against rotation with a mass.

Each prototype will submit on a sequence of ten dynamic input (sinusoidal function and real accelerogramms) to define, in the first time, the prototype’s proprieties, and, then, to investigate on the kinematic and inertial interaction of the model.

6.4.6 Research activity carried out by the UNIBAS research unit During the first semester of the second year, attention has been focussed on kinematic interaction. In accordance with the other working groups, a scheme for preliminary parametric analyses has been

selected, in order to investigate the influence of some major factors, such as soil profile and soil properties. As a first step, the behaviour of a single pile in a two-layered compressible medium overlying the bedrock formation has been analysed.

Pile length L and diameter d were respectively assumed to be equal to 20 m and 0,6 m; the pile head was assumed to be restrained from rotating. The overall thickness of the two compressible layers was set equal to 30 m, while the thickness of the upper layer was assumed to vary between 5 and 19 m. Three different values (1; 2; 4) have been assumed for the ratio of shear wave velocities between lower and upper layer, defined as V2/V1.

Some preliminary analyses have been performed, utilising an in-house computer code, which models the subsoil as a set of independent springs, following the classical dynamic Winkler-type approach. An extensive parametric study is in progress. A comparison with the results obtained by other working groups will be carried out; the next step will be the analyses of a (relatively small) group of free-standing piles connected by a rigid cap.


20 / 29

Figure 6.4.5.1. Kinematic bending moments for the two-layer soil profile S1 (H1=15 and H2=15m) and soil type D. From top to bottom: V2/V1=2, 3 and 4

VS1=100 m/s; VS2=200 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)

A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30

VS1=100 m/s; VS2=300 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)

A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30

VS1=100 m/s; VS2=400 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)

A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30

VS1=100 m/s; VS2=200 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)

A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30

VS1=100 m/s; VS2=300 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)

A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30

VS1=100 m/s; VS2=400 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)

A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30


21 / 29

Figure 6.4.5.2. Kinematic bending moments for the two-layer soil profile S1 (H1=15 and H2=15m) and soil type C. From top to bottom: V2/V1=2, 3 and 4

VS1=150 m/s; VS2=400 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)

A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30

VS1=150 m/s; VS2=600 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)

A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30

VS1=150 m/s; VS2=300 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30

VS1=150 m/s; VS2=400 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)

A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30

VS1=150 m/s; VS2=600 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)

A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

R-NCB090 TRT000

8 φ φ φ φ

16

12 φ

φ φ φ 24

12 φ

φ φ φ 30

VS1=150 m/s; VS2=300 m/s

0

2

4

6

8

10

12

14

16

18

20

0 200 400 600 800 1000

M kin (KN*m)

z (m

)A-AAL018 A-STU000

A-STU270 ATMZ000

ATMZ270 B-BCT000

B-BCT090 C-NCB000

C-NCB090 E-AAL108

E-NCB000 E-NCB090

J-BCT000 J-BCT090

R-NC2000 R-NC2090

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Figure 6.4.5.7 F.e.m model analysis 3-D (ABAQUS code)

Figure 6.4.5.8 Scheme of experimental physical model on shaking table

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