kinematic interaction - Dottorato di Ricerca in Ingegneria Geotecnica

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DOTTORATO DI RICERCA
IN INGEGNERIA GEOTECNICA
XXII CICLO
Consorzio tra:
Università di Napoli Federico II, Università di Napoli Parthenope,
Seconda Università di Napoli, Università di Salerno, Università del Sannio
SEISMIC SOIL-STRUCTURE INTERACTION FOR
PILE SUPPORTED SYSTEMS
Dottorando: ing. Raffaele Di Laora
Tutore: prof. ing. Alessandro Mandolini
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
AIM OF THE THESIS
TO BETTER UNDERSTAND THE MATHEMATICAL AND PHYSICAL MEANING OF
KINEMATIC INTERACTION
TO PROVIDE SIMPLIFIED FORMULAS FOR EVALUATING ITS EFFECTS IN TERMS OF
BENDING MOMENTS (INTERFACE AND PILE HEAD)
TO FIND SIMPLY RULES TO ESTIMATE THE IMPORTANCE OF “FILTERING EFFECT”
EXERTED BY PILES ON FOUNDATION INPUT MOTION
TO INVESTIGATE THE RELATIVE IMPORTANCE OF KINEMATIC VS. INERTIAL
INTERACTION
TO PROVIDE A CRITERION TO COMBINE INERTIAL AND KINEMATIC MAXIMUM
EFFECTS
SEISMIC SOIL-STRUCTURE INTERACTION
FR PILE SUPPORTED SYSTEMS
SOIL-STRUCTURE INTERACTION
M u(t)  Cu(t)   K u(t)  M  I s(t)

M u(t)   K *u(t)  M  I s(t)
Msoil uKI    K *uKI   Msoil ub (t )

M uII    K *uII   Mstructure uKI (t )  ub (t )
ONLY IN ELASTICITY
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
SOIL-STRUCTURE INTERACTION
M u(t)  Cu(t)   K u(t)  M  I s(t)

M u(t)   K *u(t)  M  I s(t)
Msoil uKI    K *uKI   Msoil ub (t )
M uII    K *uII   Mstructure uKI (t )  ub (t )
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
SOIL-STRUCTURE INTERACTION
ONE COULD ALSO DEFINE KINEMATIC INTERACTION IN A DIFFERENT WAY.
FOR EXAMPLE, KINEMATIC INTERACTION COULD BE THE PHENOMENON
GENERATED, UNDER SEISMIC MOTION, WHEN ONLY SOIL AND PILES ARE PRESENT,
WITHOUT ANY RESTRAINT AND STRUCTURE.
IN THIS WAY, KINEMATIC INTERACTION HAVE SENSE ALSO, FOR EXAMPLE, IN
PLASTICITY.
UNFORTUNATELY, SUMMING THIS KINEMATIC INTERACTION TO THE INERTIAL ONE,
ONE DOESN’T OBTAIN THE COMPLETE INTERACTION. THEN:
KINEMATIC INTERACTION HAVE SENSE ONLY WITH REFERENCE TO ELASTICITY
HYPOTHESIS AND RIGID RESTRAINT AT PILE HEAD
SIMPLIFIED FORMULAS
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
DOBRY & O’ROURKE (1983)
M  1,86E p  I p 
3/ 4
G1 1/ 4  1  F
1  c 1  c 

F
1  c   c  1  c  c 
4
1
3
2
1/ 4
G 
c   2 
 G1 
MYLONAKIS (2001)
 p

 1



 
2
 c  c  1 3  Ek1
   p



 h1  

1
c
c

1

1



 
d

 


h 
2c 4  1 
d



1/ 4



p
p
/ 1 
/ 1 
0
NIKOLAOU ET AL. (2001)
 Ep 
3 L
M max (  )  0.042c d   

 d   E1 
0.3
0.65
 V2 
 
 V1 
0.5
M max ( t )  M max (  ) 
KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
NUMERICAL ANALYSES
HYPOTESES:
• LINEAR ELASTIC BEHAVIOUR OF PILES AND SOIL
• BOUNDARY CONDITIONS: VERTICAL DISPLACEMENT RESTRAINED
• MODAL DAMPING (10% FOR ALL MODES)
• SOLUTION METHOD: MODE SUPERPOSITION
• FREQUENCY DOMAIN ANALYSIS
• FINITE ELEMENTS: 8-NODE BRICKS (ISOPARAMETRIC)
KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
FREQUENCY DOMAIN ANALYSYS
ADVANTAGES OF FREQUENCY DOMAIN ANALYSES:
• MORE ACCURATE
• VERY QUICK (ABOUT 100-200 TIMES FASTER)
A FREQUENCY DOMAIN ANALYSIS IS PERFORMED:
• PERFORMING A MODAL ANALYSIS EXTRACTING A CERTAIN NUMBER OF MODES;
• APPLYING A UNIT ACCELERATION AT BEDROCK VARIABLE WITH FREQUENCY;
• READING THE STEADY-STATE RESPONSE IN TERMS OF THE VARIOUS
PARAMETERS OF INTEREST (DISPLACEMENT, STRESS AND SO ON);
• MULTIPLYING THE STEADY-STATE RESPONSE BY THE FOURIER TRANSFORM OF
THE BEDROCK SIGNAL
• PERFORM A INVERSE FOURIER TRANSFORM TO OBTAIN THE RESULTS IN THE
TIME DOMAIN
KINEMATIC INTERACTION
2
Acceleration [m/s ]
2.5
Maximum acceleration [m/s 2]
1.3
0
0.0
-2.5
4
6
Time [s]
8
10
ACCELERATION TIME HISTORY AT SURFACE
2
15.0
5.0
2
3
Structural period [s]
MAXIMUM
ACCELERATION
AGAINST
DEPTH
30
0.0
1
15
ANSYS
EERA
25
ANSYS
EERA
0
2
20
ACCELERATION
SPECTRUM AT SURFACE
10.0
5
10
Depth [m]
2
1
0
ANSYS
EERA
-1.3
0
Spectral acceleration [m/s ]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
COMPARISON WITH EERA
4
HOMOGENEOUS SOIL Vs = 400 m/s
RIGID BEDROCK DEPTH : 30 m
INPUT SIGNAL: TOLMEZZO
DAMPING b = 10%
3
KINEMATIC INTERACTION
Bending moment [kNm]
Bending moment [kNm]
0
10
20
30
0
40
1
2
3
4
5
0
0
2.7 m
3
4
1
2
0.6 m
10
HOMOGENEOUS
SOIL
5
Depth [m]
1.8 m
5
Depth [m]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
GROUP EFFECTS
HOMOGENEOUS
SOIL
Vs = 400 m/s
10
Vs = 100 m/s
15
15
pile n. 1
pile n. 2
pile n. 3
pile n. 4
20
20
pile n. 1
pile n. 2
pile n. 3
pile n. 4
NO DIFFERENCE
AMONG PILES OF
THE SAME GROUP
KINEMATIC INTERACTION
Bending moment [kNm]
0
20
40
60
80
100
0
AGAIN, LITTLE DIFFERENCE
BETWEEN SINGLE PILE AND PILE IN
A GROUP
5
Depth [m]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
2-LAYERS SOIL
Vs1 =
100 m/s
BENDING MOMENTS MUCH LARGER
WITH RESPECT TO HOMOGENEOUS
SOIL
10
Vs2 =
400 m/s
FAR FROM THE INTERFACE PILE
DEFORMATIONS ARE EQUAL TO SOIL
DEFORMATIONS
15
pile n. 1
single pile
FF curvature
20
THE INTERFACE IS ONLY A
SINGULARITY AND ITS EFFECTS VANISH
WITH DISTANCE
KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PARAMETRIC STUDY N. 1
FIXED PARAMETERS
L=
d=
H=
E1 =
gp =
gs1 =
gs2 =
βp =
βs1 =
βs2 =
νp =
νs1 =
νs2 =
24 m
1m
30 m
50 MPa
25 kN/m3
16 kN/m3
18 or 20 kN/m3
0.1
0.1
0.1
0.2
0.3
0.3
VARIABLE PARAMETERS
SIGNALS
Ep/E1
Vs2/Vs1
h1/d
BORGO CERRETO
300
1.5
2
STURNO
1000
2
4
NOCERA UMBRA
10000
3
8
6
16
TOLMEZZO
SAN ROCCO
TARCENTO
288 CASES
KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PARAMETRIC STUDY N. 2
FIXED PARAMETERS
H=
30 m
d=
0.5 m
Ep =
gp =
30 GPa
25 kN/m3
gs1 =
VARIABLE PARAMETERS
Ep/E1
Vs2/Vs1
h1/d
L/d
BORGO CERRETO
150
1.5
4
24
16 kN/m3
STURNO
666
2
8
40
gs2 =
1.8 or 2.0 kN/m3
NOCERA UMBRA
1500
3
16
βp =
0.1
TOLMEZZO
βs1 =
0.1
SAN ROCCO
βs2 =
0.1
TARCENTO
νp =
0.2
νs1 =
0.3
νs2 =
0.3
SIGNALS
324 CASES
KINEMATIC INTERACTION
soil layer 1
soil layer 1
soil layer 2
PILE CAP
soil layer 2
30
Bending moment at pile cap [kNm]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
RESULTS – EFFECT OF DEPTH OF INTERFACE
BORGO
CERRETO
STURNO
H 1 < LA
25
H 1 > LA
20
15
NOCERA
UMBRA
TOLMEZZO
10
SAN ROCCO
4
5
8
TARCENTO
16
2
0
0
5
10
15
20
25
h1/d
E1 = 50 MPa, Vs2/Vs1=1.5, Ep/E1 = 300, d = 1 m
LA = 1.5 d (Ep/E1)0.25
WHEN H1 < LA BENDING
MOMENT AT PILE CAP
INCREASES WHEN INCREASING
H1. THIS IS NOT DUE TO AN
INCREASE IN SURFACE
ACCELERATION, BUT THE
CONSTRAINT APPLIED BY
STIFFER LAYER LIMITS
DEFORMATIONS THE MORE IT IS
CLOSE TO THE PILE HEAD
(RESTRAINED)
WHEN H1 > LA eP DEPENDS ONLY
ON THE ACCELERATION AT
SURFACE, THE SHEAR WAVE
VELOCITY OF THE FIRST LAYER,
AND THE DIAMETER OF THE
30
PILE. THE SECOND LAYER
AFFECTS THE ACCELERATION AT
SURFACE.
KINEMATIC INTERACTION
INTERFACE
40
Bending moment at interface [kNm]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
RESULTS – EFFECT OF DEPTH OF INTERFACE
16
H 1 < LA
30
H 1 > LA
STURNO
25
NOCERA
UMBRA
8
20
WHEN H1 < LA BENDING
MOMENT AT INTERFACE CAN
DECREASE OR INCREASE
BECAUSE OF THE INTERACTION
WITH CAP RESTRAINT, BUT
ALWAYS SMALLER THAN IN THE
CASE IN WHICH H1 = LA
BORGO
CERRETO
35
TOLMEZZO
15
SAN ROCCO
WHEN H1 > LA IT INCREASES UP
TO A CERTAIN DISTANCE FROM
PILE TOE, THEN IN DECREASES.
2
10
4
TARCENTO
5
0
0
5
10
15
20
25
h1/d
E1 = 50 MPa, Vs2/Vs1=1.5, Ep/E1 = 300, d = 1 m
LA = 1.5 d (Ep/E1)0.25
30
KINEMATIC INTERACTION
80
Bending moment at interface [kNm]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
RESULTS – EFFECT OF STIFFNESS CONTRAST
6
70
GENERALLY, INCREASING
STIFFNESS CONTRAST PILE
BENDING MOMENT INCREASES
BORGO
CERRETO
3
60
STURNO
2
50
NOCERA
UMBRA
1.5
40
TOLMEZZO
30
SAN ROCCO
ONLY WHEN H1 > LA IT IS
ALWAYS TRUE.
20
TARCENTO
10
0
0.0
1.5
3.0
4.5
6.0
7.5
9.0
10.5
Vs2/Vs1
E1 = 50 MPa, h1/d = 16, Ep/E1 = 300, d = 1 m
12.0
KINEMATIC INTERACTION
WHEN H1 < LA MOMENT AT
INTERFACE CAN DECREASE
WITH INCREASING STIFFNESS
CONTRAST, BECAUSE EVEN IF
SOIL SHEAR STRAINS
GENERALLY INCREASES,
TRANSMISSBILITY DROPS DUE
TO INTERFERENCE BETWEEN
CAP AND STIFFER LAYER
RESTRAINTS
300
Bending moment at interface [kNm]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
RESULTS – EFFECT OF STIFFNESS CONTRAST
1.5
BORGO
CERRETO
STURNO
250
2
200
NOCERA
UMBRA
TOLMEZZO
150
3
100
SAN ROCCO
6
TARCENTO
50
0
0.0
1.5
3.0
4.5
6.0
7.5
9.0
10.5
12.0
Vs2/Vs1
E1 = 50 MPa, h1/d = 4, Ep/E1 = 10000, d = 1 m
BENDING MOMENT AT PILE
CAP DEPENDS ON SURFACE
ACCELERATIONS
KINEMATIC INTERACTION
BENDING MOMENT ALWAYS
INCREASES WHEN INCREASING
STIFFNESS RATIO BOTH AT
PILE CAP AND AT INTERFACE.
1.5
BORGO
CERRETO
300
e p at interface (x 10 4)
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
RESULTS – EFFECT OF PILE-SOIL STIFFNESS RATIO
STURNO
1000
1.0
NOCERA
UMBRA
10000
0.5
TOLMEZZO
SAN ROCCO
TARCENTO
0.0
0
5000
10000
15000
20000
Ep /E1
Es = 50 MPa, h1/d = 16, Vs2/Vs1 = 2, d = 1 m
IF Ep/E1 INCREASES BECAUSE
OF AN INCREASE IN Ep WITH
E1 CONSTANT, FREE FIELD
SHEAR STRAINS REMAIN
CONSTANT, RESULTING IN
SMALLER STRAINS IN THE PILE
DUE TO ITS GREATER
STIFFNESS, BUT THEY
DECREASE LESS THAN
LINEARLY INCREASING
STIFFNESS RATIO.
KINEMATIC INTERACTION
3000
Bending moment at interface [kNm]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
RESULTS – EFFECT OF PILE-SOIL STIFFNESS RATIO
10000
NOCERA
UMBRA
2500
TOLMEZZO
2000
SAN ROCCO
1500
TARCENTO
1000
1000
STURNO
THIS IS ALSO EVIDENT IF EP IS
CONSTANT AND E1
DECREASES, BECAUSE THE
SOIL STRAINS INCREASE.
300
BORGO
CERRETO
500
0
0
5000
10000
15000
AS BENDING MOMENT IS
PROPORTIONAL TO PILE
BENDING STRAIN AND ITS
YOUNG MODULUS, IT
INCREASES WITH INCREASING
STIFFNESS RATIO.
20000
Ep /E1
Es = 50 MPa, h1/d = 16, Vs2/Vs1 = 2, d = 1 m
KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
EFFECT OF DIAMETER AND LENGHT
IF THE INTERFACE IS LOCATED OUTSIDE THE ACTIVE LENGTH OF THE PILE,
BENDING MOMENTS VARY CUBICALLY AGAINST PILE DIAMETER
THIS IS DUE TO THE FACT THAT THE PILE BENDING STRAIN AT OUTER FIBER IS
NOT DEPENDENT ON PILE DIAMETER. OF COURSE ITS INCREMENT INCREASES THE
ACTIVE LENGTH AND THE INTERFACE CAN LOCATE INSIDE THAT, SO THE εp CAN
REDUCE.
THE SAME HAPPENS FOR THE PILE LENGTH: IF THE INTERFACE REMAINS OUTSIDE
THE ACTIVE LENGTH, THE εp IN NOT SENSITIVE TO IT, BUT IF THE LENGTH
DECREASES, THE PART OF PILE EMBEDDED IN THE SECOND LAYER CAN BECAME
TOO SHORT AND RESULT TO A LOWER PILE BENDING STRAIN DUE TO A LOWER
CONSTRAINT OF THE STIFFER LAYER.
KINEMATIC INTERACTION
3.0
2.5
e p (x 10 -4)
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
SIMPLIFIED EVALUATION OF INTERFACE MOMENTS
2.0
Ep = 50 GPa ; h1/d = 16
1.5
Ep = 15 GPa ; h1/d = 8
y = 0.256x
1.0
2
R = 0.904
Ep = 15 GPa ; h1/d = 16
Ep = 30 GPa ; h1/d = 16
0.5
0.0
0
5
10
g 1(Vs2/Vs1)0.5(Ep /E1)-0.25 (x 10-4)
H1 > L A
LA = 1.5 d (Ep/E1)0.25
15
20
KINEMATIC INTERACTION
3.0
2.5
Ep = 500 GPa ; h1/d = 16
e p (x 10 -4)
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
SIMPLIFIED EVALUATION OF INTERFACE MOMENTS
2.0
Ep = 50 GPa ; h1/d = 8
Ep = 50 GPa ; h1/d = 16
1.5
Ep = 15 GPa ; h1/d = 8
1.0
Ep = 15 GPa ; h1/d = 16
Ep = 30 GPa ; h1/d = 8
0.5
Ep = 30 GPa ; h1/d = 16
0.0
0
5
10
15
g 1(Vs2/Vs1)0.5(Ep /E1)-0.25(h1/La)n (x 10-4)
H1 > 0.8 LA
20
KINEMATIC INTERACTION
ALTERNATIVELY, INSTEAD OF γ1, IT CAN BE REPLACED THE QUANTITY (γ1- γ2)
3.0
2.5
Ep = 500 GPa ; h1/d = 16
e p (x 10 -4)
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
SIMPLIFIED EVALUATION OF INTERFACE MOMENTS
2.0
Ep = 50 GPa ; h1/d = 8
y = 0.296x
1.5
R2 = 0.939
1.0
Ep = 50 GPa ; h1/d = 16
Ep = 15 GPa ; h1/d = 8
Ep = 15 GPa ; h1/d = 16
Ep = 30 GPa ; h1/d = 8
0.5
Ep = 30 GPa ; h1/d = 16
0.0
0
5
10
15
(g 1-g 2)(Vs2/Vs1)0.5(Ep /E1)-0.25(h1/La)n (x 10-4)
20
KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
SIMPLIFIED EVALUATION OF INTERFACE MOMENTS
APPARENTLY, THE LAST FORMULATION HAS A DRAWBACK WITH RESPECT TO THE
PREVIOUS ONE:
WITH REFERENCE TO AN HOMOGENEOUS SOIL, (γ1- γ2) TENDS TO 0, AND NO
BENDING MOMENT IS PREDICTED ALONG THE PILE, IN CONTRAST WITH THE
EVIDENCE.
ACTUALLY, EVEN IF THE PREVIOUS FORMULATION PREDICTS A NON-ZERO MOMENT
IN THIS CASE, ITS NUMERICAL VALUE IS EVIDENTLY WRONG, BECAUSE IT BECOMES:
 Ep 
p  

 Es 
0.25
THAT IS INCORRECT.
THE INTERFACE ACTS AS A FURTHER “SOURCE OF BENDING MOMENT”, RULED BY
OTHER PARAMETERS, AND THIS MOMENT ADDS TO THE MOMENT ACTING WHEN
THE PILE IS EMBEDDED IN AN HOMOGENEOUS SOIL; THIS MECHANISM IS RULED BY
DIFFERENT PARAMETERS (FOR EXAMPLE THE BENDING STRAIN IS PROPORTIONAL
TO THE DIAMETER).
IT IS EVIDENT THAT, WHEN THE STIFFNESS CONTRAST IS SHARP, THE INTERFACE
PRACTICALLY BECOMES THE UNIQUE “SOURCE OF BENDING MOMENT” , AND
(γ1- γ2) TENDS TO γ2.
KINEMATIC INTERACTION
ACCORDING TO THE SPEAKER, PILE BENDING STRAIN DEPENDS ALSO ON SOIL
SHEAR STRAINS AROUND THE INTERFACE
3.0
2.5
Ep = 500 GPa ; h1/d = 16
e p (x 10 -4)
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
SIMPLIFIED EVALUATION OF INTERFACE MOMENTS
2.0
Ep = 50 GPa ; h1/d = 8
y = 0.324x
R2 = 0.965
1.5
1.0
Ep = 50 GPa ; h1/d = 16
Ep = 15 GPa ; h1/d = 8
Ep = 15 GPa ; h1/d = 16
Ep = 30 GPa ; h1/d = 8
0.5
Ep = 30 GPa ; h1/d = 16
0.0
0
5
10
15
(g 1* -g 2* )(Vs2/Vs1)0.5(Ep /E1)-0.25(h1/La)n (x 10-4)
γ1* = γ1(h1-d)
γ2* = γ2(h1+d)
20
KINEMATIC INTERACTION
WHEN H1 < LA, NO CORRELATION EXISTS BETWEEN PILE BENDING STRAIN AND
FREE FIELD SHEAR STRAIN
0.5
Ep = 15 GPa ; h1/d = 2
0.4
e p (x 10 -4)
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
SIMPLIFIED EVALUATION OF INTERFACE MOMENTS
Ep = 50 GPa ; h1/d = 2
Ep = 500 GPa ; h1/d = 2
0.3
0.2
0.1
0.0
0.0
1.0
2.0
3.0
g 1 (x 10-4)
THE STRAINS (BOTH FREE-FIELD AND PILE) ARE VERY SMALL
THE EFFECT OF THE PILE STIFFNESS IS LIMITED. THE PILE, IN FACT, HAS NO
SPACE TO DEFORM (ONLY 2 DIAMETERS), BECAUSE CONSTRAINED, AND THEN IT
IS ANYWAY RIGID, REGARDLESS OF ITS YOUNG MODULUS
KINEMATIC INTERACTION
WHEN H1 > LA, PILE FOLLOWS FREE-FIELD ALSO IN 2-LAYERS SOILS
PILE CURVATURE AT PILE CAP IS EQUAL TO FREE-FIELD SOIL CURVATURE
3.0
2.5
e p (x 10 -4)
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
SIMPLIFIED EVALUATION OF PILE CAP MOMENTS
2.0
y = 0.994x
Ep = 50 GPa ; h1/d = 16
2
1.5
R = 0.994
Ep = 15 GPa ; h1/d = 8
1.0
Ep = 15 GPa ; h1/d = 16
Ep = 30 GPa ; h1/d = 8
0.5
Ep = 30 GPa ; h1/d = 16
0.0
0.0
0.5
1.0
1.5
2.0
2.5
g ' r (x 10-4)
' 
a ff
Vs12
NO SEISMIC LOCAL RESPONSE ANALYSIS REQUIRED!
3.0
KINEMATIC INTERACTION
3.0
2.5
soil layer 1
L/d = 24
e p (x 10 -4)
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
SIMPLIFIED EVALUATION OF PILE CAP MOMENTS
2.0
L/d = 40
L/d = 40 ; V s2 = variable
1.5
1.0
0.5
y = 0.994x
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
a ff r / V s12 (x 10-4)
WHEN H1 > LA, PILE BENDING STRAIN AT PILE CAP IS NOT DEPENDENT ON
PILE SLENDERNESS
THE PILE FOLLOWS THE SOIL ALSO IF THERE ARE MORE THAN TWO
LAYERS BELOW THE INTERFACE
KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
MODIFY OF THE FOUNDATION INPUT MOTION
KINEMATIC INTERACTION BETWEEN SOIL AND PILES RESULTS IN TWO
“KINEMATIC” EFFECTS:
MODIFY OF THE SEISMIC SIGNAL AT THE BASE OF THE SUPERSTRUCTURE
A ROTATIONAL COMPONENT OF MOTION RISES (IMPORTANT OLY FOR VERY
TALL STRUCTURES)
THE IMPORTANCE OF THE “FILTERING EFFECT” EXERTED BY THE PILES
DEPENDS ON VARIOUS PARAMETERS; WITH REFERENCE TO TWO-LAYERS SOIL
DEPOSITS, THE PRIMARY VARIABLES INFLUENCING THE PHENOMENON ARE, IN
ANALOGY WITH BENDING MOMENTS:
THE STIFFNESS CONTRAST
THE DEPTH OF THE INTERFACE
THE STIFFNESS RATIO BETWEEN PILE AND SOIL
THE FREQUENCY OF EXCITATION
KINEMATIC INTERACTION
12
10
pile
8
Ampli
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
MODIFY OF THE FOUNDATION INPUT MOTION
free field
6
4
2
0
0
1
2
3
w /w 1
d = 0.5 m, h1/d = 16, Vs2/Vs1 = 3, Ep/Es1 = 1500
GENERALLY PILES EXERT A FILTERING EFFECT, CUTTING ONLY HIGH
FREQUENCIES
4
KINEMATIC INTERACTION
12
10
pile
8
Ampli
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
MODIFY OF THE FOUNDATION INPUT MOTION
free field
6
4
2
0
0
1
2
3
4
w /w 1
d = 1 m, h1/d = 2, Vs2/Vs1 = 6, Ep/Es1 = 10000
IN EXTREME CASES, FILTERING EFFECT IS VERY IMPORTANT ALSO FOR LOW
FREQUENCIES (IN CONTRAST WITH GAZETAS, 1984)
KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
MODIFY OF THE FOUNDATION INPUT MOTION
THE FOUNDATION AND FREE-FIELD MOTION TEND TO BE MORE AND MORE DIFFERENT:
INCREASING THE STIFFNESS RATIO
INCREASING THE STIFFNESS CONTRAST
INCREASING THE IMPORTANCE OF HIGH FREQUENCIES OF THE BEDROCK SIGNAL
DECREASING THE VALUE OF h1/LA
KINEMATIC INTERACTION
ANALYSING THE RESULTS OF THE TWO PARAMETRIC STUDIES, LOOKING AT FREE
FIELD AND FOUNDATION SIGNALS (612 x 2 = 1224 SPECTRA), IT FOLLOWS THAT
IN VERY RARE CASES IN WHICH THE FOLLOWING CONDITIONS:
h1 < L A
Vs2/Vs1 > 3
Ep/Es1 ≥ 10000
ARE CONTEMPORARY PRESENT, IT IS POSSIBLE TO NEGLECT THE FILTERING EFFECT
(WITHOUT A TOO LARGE CONSERVATISM) ONLY FOR STRUCTURAL PERIODS T1 > 0.5 s
25
25
20
20
15
15
free field
BORGO CERRETO
10
5
0
0
1
2
T [s]
3
free field
10
5
0
pile
Sa [m/s2]
pile
Sa [m/s2]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
MODIFY OF THE FOUNDATION INPUT MOTION
4
STURNO
0
1
2
T [s]
d = 1 m, h1/d = 2, Vs2/Vs1 = 6, Ep/Es1 = 10000
3
4
KINEMATIC INTERACTION
IN OTHER (FREQUENT) CASES, IT IS POSSIBLE TO NEGLECT THE FILTERING EFFECT
EXERTED BY THE PILES ONLY WHEN THE STRUCTURAL PERIOD IS GREATER THAN 0.3 s
10
10
8
8
pile
6
Sa [m/s2]
Sa [m/s2]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
MODIFY OF THE FOUNDATION INPUT MOTION
free field
BORGO CERRETO
4
6
2
0
0
1
2
T [s]
3
4
free field
4
2
0
pile
STURNO
0
1
2
T [s]
d = 1 m, h1/d = 16, Vs2/Vs1 = 6, Ep/Es1 = 1000
3
4
KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
MODIFY OF THE FOUNDATION INPUT MOTION
IT’S IMPORTANT TO CLARIFY THAT THE ANALYSES HAVE BEEN
UNDERTAKEN CONSIDERING THE SUPERSTRUCTURE AS A SDOF SYSTEM.
THESE CONCLUSIONS CAN BE CONSIDERED STILL VALID IF THE
STRUCTURE (THE REAL MDOF SYSTEM) IS REGULAR, SO THE
CONTRIBUTION OF THE OTHER MODES (CHARACTERISED BY HIGHER
FREQUENCIES) IS NOT SIGNIFICANT
MOREOVER, THE ANALYSES ARE ELASTIC; IT IS EVIDENT THAT NON
LINEARITY CAN INCREASE THIS DIFFERENCE, FOR EXAMPLE, INCREASING
THE STIFFNESS RATIO.
IT’S ANYWAY IMPORTANT TO KEEP IN MIND THAT REFERRING TO FREEFIELD MOTION FOR INERTIAL INTERACTION ANALYSES IS ALWAYS
CONSERVATIVE.
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
KINEMATIC INTERACTION
IT HAS BEEN HIGHLIGHTED THE ROLE PLAYED BY THE DIFFERENT PARAMETERS
THAT HAVE A SIGNIFICANT INFLUENCE ON KINEMATIC INTERACTION
SIMPLIFIED FORMULAS HAVE BEEN PROPOSED TO SIMPLY EVALUATE KINEMATIC
BENDING MOMENT AT INTERFACE AND PILE HEAD WHEN INTERFACE IS LOCATED
BEYOND THE ACTIVE LENGTH OF THE PILE
IN THE CASES IN WHICH H1 < LA ONE CAN ESTIMATE (CONSERVATIVELY) THESE
MOMENTS PLACING THE INTERFACE AT A DEPTH EQUAL TO THE ACTIVE LENGHT
IT HAS BEEN FOUND A CRITERION TO ESTABLISH IN WHICH CASES IT IS POSSIBLE
TO NEGLECT THE FILTERING EFFECT EXERTED BY PILES
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
KINEMATIC VS. INERTIAL INTERACTION
RECENT ITALIAN CODES IMPOSE TO EVALUATE THE EFFECTS OF KINEMATIC
INTERACTION ONLY UNDER CERTAIN CONDITIONS, BUT REGARDINGLESS OF THE
AMOUNT AND THE DISTRIBUTION OF MASSES OF THE STRUCTURE.
IT IS EVIDENT THAT IT SHOULD BE ALLOWABLE TO NEGLECT KINEMATIC INTERACTION
WHEN ITS EFFECTS ARE NEGLIGIBLE WITH RESPECT TO INERTIAL ONES; FOR THIS
REASON THE CODES INDICATIONS APPEARS TO BE INCOMPLETE, AS THE INERTIAL
EFFECTS ARE PROPORTIONAL TO THE STRUCTURE MASS, WHILE KINEMATIC ONES ARE
EVIDENTLY NOT DEPENDENT ON IT.
TO INVESTIGATE THE RELATIVE IMPORTANCE OF INERTIAL VS. KINEMATIC
INTERACTION (AND THEN TO VERIFY THE VERACITY OF THE INDICATIONS OF THE
CODES), ONCE IT HAS BEEN ESTIMATED THE EFFECTS OF THE LATTER THROUGH THE
FORMULAS PROPOSED, IT HAS BEEN BUILT A SIMPLE TOOL FOR EVALUATING THE
FOUNDATION IMPEDANCE AND THE RESULTING INERTIAL EFFECTS AT PILES TOP.
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
KINEMATIC VS. INERTIAL INTERACTION



















Cuu
Cu
Cu
C
0
2 ,1
uu
Cuu
u2,1Cu
0
 Cu
 C
0
2 ,1
u
0
2 ,1

.......
.......
nn ,1
uu
Cuu

 unn ,1Cu
0
1
0
nn ,1

0
0
1
0
0
nn ,1
vv
nn ,2
uu
nn ,2
u
nn ,2
u
nn ,2

0
0
1
d1,G
0
0
0
1
0
d 2 ,G
nn ,1
u
Cu

C
Cvv
0
0
Cuu
0
Cu
 Cvv
0
.......
.......

 C
0
Cu
C
0
.......

0
0
 Cvv
0
0
Cvv
.......
0
0
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
1
0
0
1
0
0
.......
1
0
0
0
0
0
1
d1,G
0
1
d 2 ,G
.......
0
1
d nn ,G
0
0
0
 Cuu
0
 Cu
 Cu
1,2
uu
1,2
u
1,2
u
1,2

1,2
vv
2 ,1
vv
Cuu

Cu


Cu
C

Cvv
nn ,2
vv
Cvv
  T1   0 
  

 M 1   0 
  N1   0 
  

 .   . 
 .   . 
  

 .   . 
 .    . 
  

 .   . 
  

 .   . 
 .   . 
  

  uG   H PG 
  G   M PG 

RANDOLPH’S EXPRESSIONS FOR BOTH PILE-SOIL COMPLIANCES AND INTERACTION
COEFFICIENTS
HOMOGENEOUS SOIL
r=
L=
s=
n=
Ep =
0.3 m
20 m
1.8 m
9
30 GPa
Es =
γ=
aff =
m=
T=
Hstr =
30 MPa
16 kN/m3
1.1 m/s2
500 t
0.5 s
0m
INERTIAL VS. KINEMATIC INTERACTION
80
A
B
25
D
C
RATIO FOR PILE A
RATIO FOR PILE B
RATIO FOR PILE C
RATIO FOR PILE D
70
KINEMATIC
60
20
50
15
40
30
10
20
5
10
0
0
0
10
20
30
Ep [GPa]
40
50
60
Kinematic moment at pile top [kNm]
30
Ratio inertial/kinematic moment [-]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
EFFECT OF PILE YOUNG MODULUS
INERTIAL VS. KINEMATIC INTERACTION
150
A
C
B
D
RATIO FOR PILE A
RATIO FOR PILE B
RATIO FOR PILE C
RATIO FOR PILE D
KINEMATIC
100
100
50
50
0
0
200
400
600
800
Es [MPa]
D
C
B
1000
0
1200
Kinematic moment at pile top [kNm]
150
Ratio inertial/kinematic moment [-]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
EFFECT OF SOIL YOUNG MODULUS
INERTIAL VS. KINEMATIC INTERACTION
200
KINEMATIC (INTERFACE)
VS2/VS1 = 3
Bending moment [kNm]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
EFFECT OF SOIL YOUNG MODULUS
KINEMATIC (PILE HEAD)
INERTIAL PILE A (PILE HEAD)
150
100
A
B
C
D
50
0
0
200
400
600
800
1000
Es1 [MPa]
C
B
A
1200
INERTIAL VS. KINEMATIC INTERACTION
2500
A
B
35
C
30
D
RATIO FOR PILE A
RATIO FOR PILE B
RATIO FOR PILE C
RATIO FOR PILE D
2000
KINEMATIC
25
1500
20
1000
15
10
500
5
0
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Pile radius [m]
0.7
0.8
0.9
1.0
Kinematic moment at pile top [kNm]
40
Ratio inertial/kinematic moment [-]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
EFFECT OF PILE RADIUS
INERTIAL VS. KINEMATIC INTERACTION
100
A
B
D
C
RATIO FOR PILE A
RATIO FOR PILE B
RATIO FOR PILE C
RATIO FOR PILE D
80
KINEMATIC
10
60
40
5
20
0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Pile spacing s/d [-]
8.0
0
9.0 10.0 11.0 12.0
Kinematic moment at pile top [kNm]
15
Ratio inertial/kinematic moment [-]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
EFFECT OF PILE SPACING
INERTIAL VS. KINEMATIC INTERACTION
50
9
RATIO FOR CENTRAL PILE
8
RATIO FOR CORNER PILE
7
KINEMATIC
40
6
30
5
4
20
3
9
25
2
10
49
1
0
0
0
10
20
30
Number of piles [-]
40
50
60
Bending moment at pile top [kNm]
10
Ratio inertial/kinematic moment [-]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
EFFECT OF NUMBER OF PILES
INERTIAL VS. KINEMATIC INTERACTION
100
10
RATIO FOR PILE A
RATIO FOR PILE B
RATIO FOR PILE C
RATIO FOR PILE D
80
KINEMATIC
A
5
B
60
C
0
D
40
-5
20
-10
-15
0
0
5
10
M / H [m]
15
20
Kinematic moment at pile top [kNm]
15
Ratio inertial/kinematic moment [-]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
EFFECT OF M / H
INERTIAL VS. KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS
IN GENERAL, TIME HISTORIES OF KINEMATIC AND INERTIAL STRESSES ARE OUTOF-PHASE.
IF KINEMATIC AND/OR INERTIAL EFFECTS ARE ESTIMATED ONLY WITH
REFERENCE TO THEIR MAXIMA, IT RISES A PROBLEM: HOW TO COMBINE THEM?
SUMMING THEIR MAXIMA, IN FACT, CAN BE TOO OVERCONSERVATIVE.
IS IT POSSIBLE TO EVALUATE THE PHASE LAG A PRIORI?
INERTIAL VS. KINEMATIC INTERACTION
KS    H I  KS  I  
-6.28
-9.42
 H AP  IS   H I  A   I  
ACCELERATION
STRESS
-12.56
0
 Phase  H I  A    Phase  I  
2
3
4
5
6
7
w /w 1 [-]
PhaseH I  A    PhaseH I KS  
Phase  IS    Phase  H AP  IS   
1
3.14
PhaseKS    PhaseH I KS    PhaseI  
0
STRESS
ACCELERATION
1.57
-1.57
INERTIAL
0.00
PhaseIS   PhaseKS    PhaseH APIS  
PhaseIS   PhaseKS      PhaseH I  AS  
-3.14
0.0
0.5
1.0
1.5
2.0
w /w st [-]
(IF THE MOMENT DUE TO RAFT
ROTATION PREVAILS)
Acceleration phase [rad]
IS    H AP  IS   AP    H AP  IS   A   
KINEMATIC
-3.14
Phase [rad]
A   H I  A  I  
0.00
Stress phase [rad]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS
INERTIAL VS. KINEMATIC INTERACTION
3.14
IS IMPORTANT TO NOTICE THAT
THE PHASE LAG OF EACH
HARMONIC IS INDEPENDENT OF
KINEMATIC INTERACTION,
DEPENDS ONLY ON THE
INERTIAL ONE, THROUGH THE
STRUCTURAL PERIOD
Phase [rad]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS
1.57
x =
5%
0.00
0.0
0.5
1.0
1.5
2.0
w /w st [-]
NEVERTHLESS, THE PHASE LAG
DEPENDS ALSO ON
INTERACTION, BECAUSE IT
DEPEND ON WHERE ARE
PREVALENT HARMONICS OF THE
SURFACE FREE-FIELD SIGNAL
(RIGOROUSLY FOUNDATION
MOTION).
ONE CAN JUDGE A PRIORI THE PHASE LAG BETWEEN
KINEMATIC AND INERTIAL INTERACTION
PERFORMING A FREE-FIELD ANALYSIS
LOOKING AT THE FOURIER SPECTRA OF SURFACE
SIGNAL
COMPARING IT WITH THE STRUCTURAL PERIOD
INERTIAL VS. KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS
NUMERICAL ANALYSES
Esoil[Mpa]
wsoil [Hz]
wstr (with SSI) [Hz]
A
30
0.71
1.45
B
120
1.42
1.45
C
120
1.42
1.02
D
120
1.42
0.72
HYPOTESES:
• LINEAR ELASTIC BEHAVIOUR OF PILES AND SOIL
• BOUNDARY CONDITIONS: VERTICAL DISPLACEMENT RESTRAINED
• MODAL DAMPING (10% FOR ALL MODES)
• SOLUTION METHOD: MODE SUPERPOSITION
• FREQUENCY DOMAIN ANALYSIS
• FINITE ELEMENTS: 8-NODE BRICKS (ISOPARAMETRIC)
INERTIAL VS. KINEMATIC INTERACTION
IN THE CASES SHOWN IN THE FIGURES
THE MOMENT DUE TO RAFT ROTATION
PREVAILS
Fourier Amplitude [m/s]
2.5
2.0
1.5
E1 = 120 MPa
STURNO SIGNAL
1.0
E1 = 30 MPa
0.5
0.0
0
2
4
6
8
10
w [Hz]
2.0
Fourier Amplitude [m/s]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS
1.5
E1 = 120 MPa
1.0
TOLMEZZO SIGNAL
E1 = 30 MPa
0.5
0.0
0
2
4
6
w [Hz]
8
10
LOOKING AT THE SURFACE FOURIER
SPECTRUM WITH REFERENCE, FOR
ISTANCE, TO CASE A – STURNO SIGNAL,
IT CAN BE NOTICED THAT
PREDOMINANT HARMONICS HAVE
LOWER FREQUENCIES (WITH RESPECT
TO THE STRUCTURE). FOLLOWING THIS
METHOD, THEN, KINEMATIC AND
INERTIAL EFFECTS HAVE TO BE OUTOF-PHASE.
IN THE CASE B – TOLMEZZO SIGNAL,
PREDOMINANT HARMONIC OF THE
SURFACE FREE FIELD SIGNAL ARE CLOSE
TO THE STRUCTURE FREQUENCY (THAT
IS EQUAL TO THE GROUND ONE→
RESONANCE). THERE SHOULD BE A
PHASE LAG EQUAL TO 90°.
INERTIAL VS. KINEMATIC INTERACTION
Pile stress [kPa]
1500
CASE A – STURNO
1000
500
0
TOTAL
-500
KINEMATIC
-1000
INERTIAL
-1500
0
1
2
3
4
5
6
1500
Pile stress [kPa]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS
7
8
9
10
11
12
13
14
15
Time [s]
CASE B – TOLMEZZO
1000
500
0
TOTAL
-500
KINEMATIC
-1000
INERTIAL
-1500
0
1
2
3
4
5
6
7
8
Time [s]
9
10
11
12
13
14
15
INERTIAL VS. KINEMATIC INTERACTION
Fourier Amplitude [m/s]
2.0
1.5
E1 = 120 MPa
1.0
TOLMEZZO SIGNAL
E1 = 30 MPa
0.5
0.0
0
2
4
6
8
10
w [Hz]
2.0
Fourier Amplitude [m/s]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS
1.5
E1 = 120 MPa
1.0
TOLMEZZO SIGNAL
E1 = 30 MPa
0.5
0.0
0
2
4
6
w [Hz]
8
10
IN THE CASES, FOR ISTANCE, OF
TOLMEZZO SIGNAL, MOVING THE
STRUCTURE FREQUENCY ON THE LEFT
OF THE PREDOMINANT HARMONICS OF
THE SURFACE FOURIER SPECTRUM
(CASES C AND D), IT IS EXPECTED THAT
KINEMATIC AND INERTIAL INTERACTION
ARE IN-PHASE
INERTIAL VS. KINEMATIC INTERACTION
Pile stress [kPa]
1500
1000
500
0
-500
TOTAL
KINEMATIC
-1000
INERTIAL
-1500
0
1
2
3
4
5
6
1500
Pile stress [kPa]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS
7
8
9
10
11
12
13
14
15
9
10
11
12
13
14
15
Time [s]
1000
500
0
-500
TOTAL
KINEMATIC
-1000
INERTIAL
-1500
0
1
2
3
4
5
6
7
8
Time [s]
INERTIAL VS. KINEMATIC INTERACTION
Fourier Amplitude [m/s]
2.5
2.0
1.5
STARTING FROM CASE A,
DECREASING THE STRUCTURE
HEIGHT UNTIL 5 METERS, THE
BENDING MOMENT DUE TO RAFT
TRANSLATION PREVAILS, AND THEN
KINEMATIC AND INERTIAL
INTERACTION HAVE TO BE IN-PHASE.
E1 = 120 MPa
STURNO SIGNAL
1.0
E1 = 30 MPa
0.5
0.0
0
2
4
6
8
10
w [Hz]
2000
Pile stress [kPa]
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS
1500
TOTAL
1000
KINEMATIC
INERTIAL
500
0
-500
-1000
-1500
-2000
0
1
2
3
4
5
6
7
8
Time [s]
9
10
11
12
13
14
15
INERTIAL VS. KINEMATIC INTERACTION
SEISMIC SOIL-STRUCTURE INTERACTION
FOR PILE SUPPORTED SYSTEMS
PHASE LAG BETWEEN KINEMATIC AND INERTIAL EFFECTS
ACCORDING TO WHAT IS WRITTEN ABOVE, THE PHASE LAG DECREASES (FIXING
OTHER CONDITIONS):
- DECREASING THE FREQUENCY OF THE STRUCTURE;
- INCREASING THE FREQUENCY OF THE SOIL;
- MOVING THE FREQUENCY CONTENT OF INPUT SIGNAL TO HIGHER FREQUENCIES.
IF THE BENDING MOMENT DUE TO RAFT TRANSLATION PREVAILS, OPPOSITE
CONCLUSIONS HAVE TO BE DERIVED; IN THIS CASE, THE THREE CONDITIONS ABOVE
HAVE TO INCREASE THE PHASE LAG.
BASING ON THE DESCRIBED METHOD, IN DESIGN IT IS POSSIBLE TO COMBINE
MAXIMUM KINEMATIC AND INERTIAL EFFECTS IN THE FOLLOWING WAY:
- IN THE CASE THEY ARE IN-PHASE, SUM THE MAXIMA;
- IF THE PHASE LAG IS APPROXIMATELY 180°, TAKE THE MAXIMUM BETWEEN THE
KINEMATIC AND THE INERTIAL CONTRIBUTION;
- IN THE RARE CASE IN WHICH THE PHASE LAG IS ABOUT 90°, IT IS STILL LICIT TO
SUM MAXIMUM EFFECTS WITHOUT COMMITTING LARGE ERRORS; IT IS WORTHY
NOTING THAT IN THIS CASE INERTIAL INTERACTION IS PARTICULARLY IMPORTANT
BECAUSE OF THE RESONANCE BETWEEN FOUNDATION INPUT MOTION AND
STRUCTURE.
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