Experimental Study on Characteristics of Horizontal Dynamic by tjm72505

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									Experimental Study on Characteristics of Horizontal Dynamic
Subgrade Reaction Using a Single-Pile Model
Estudio Experimental sobre las Caracteristicas de la Reaccion
Dinamica Horizontal de la Subrasante Utilizando un Modelo de Pilote
Aislado
Hirofumi Fukushima, Jun’ichi Nishikawa and Kouichi Tomisawa
Geotechnical Division, Civil Engineering Research Institute of Hokkaido




Abstract
The spring constant of a pile foundation was studied to assess the seismic resistance of foundations built in sandy,
clay and volcanic ash soils, the last of which is widely distributed throughout Hokkaido, Japan. Centrifuge
experiments were performed to test the static horizontal load and dynamic vibration of single piles under a
centrifugal acceleration of 50 G. Based on these experiments, two important factors in the seismic design of pile
foundations were studied: horizontal static subgrade reaction (Kh) and horizontal dynamic subgrade reaction (Khe).
The relationship between these two factors, expressed as Khe=αKh, was also studied. It was revealed that α differs
according to soil type, indicating the necessity of including soil type in the assessment of seismic designs for pile
foundations.


Resumen
La constante de resorte de la cimentacion por pilotes fue estudiada para determinar su resistencia sismica en
suelos arenosos, suelos arcillosos y en cenizas volcanicas, las cuales se encuentran extensamente en el area de
Hokkaido, Japon. Ademas, experimentos en centrifuga fueron llevados a cabo para evaluar la carga horizontal
estatica y la vibracion dinamica en pilotes aislados bajo aceleracion centrifuga de 50 g. Con base en estos
experimentos, se estudiaron los factores importantes para el diseno asismico de la cimentacion por pilotes:
reaccion estatica horizontal de la subrasante (Kh) y reaccion dinamica horizontal de la subrasante (Khe). Su
relacion, expresada por Khe = αKh, tambien fue estudiada. Se logro determinar que α depende del tipo de suelo, lo
cual indica la necesidad de incluir el tipo de suelo en la evaluacion de un diseno asismico de cimentaciones por
pilotes.

                                                             rather than on ground strength, which can be
1 INTRODUCTION                                               determined using soil survey results.
                                                                Since the pile foundation is surrounded by
  Current seismic designs (Japan Road                        ground, it is generally considered to generate
Association, 1996 and 2002, Ogawa and Ogata,                 virtually no response vibrations. However, the
1997) for pile foundations in Japan require                  pile foundation does react to seismic motion,
analysis of the seismic behaviour of the pile using          which      triggers     simultaneous       response
the traditional seismic coefficient method,                  displacement of the surrounding ground. During
seismic horizontal load-carrying capacity method             an earthquake, seismic force acts on the pile
and the dynamic analysis method. These design                foundation, and the force is transmitted to the
methods share the same structural engineering                superstructure. The response of the superstructure
consideration: the provision of a certain degree of          is returned to the ground as inertial force. These
deformation capacity under seismic force.                    forces act differently from earthquake to
However, in assessing the seismic resistance of              earthquake because the waveforms of seismic
the ground, the ground spring during an                      motions are different in each earthquake. For this
earthquake (dynamic coefficient of horizontal                reason, the seismic behavior of pile foundations is
subgrade reaction) is determined largely based on            very complicated, and the present seismic design
the static spring of the soil, i.e., a soil constant,        method does not satisfactorily address this
complexity. Analysis of the seismic behavior of                          could accurately represent conventional steel piles
the pile foundation requires a clear understanding                       (φ = 500 mm, t = 10 mm) (Table 1). The
of spring characteristics and other complicated                          centrifuge generated a centrifugal acceleration of
soil factors during an earthquake, such as non-                          50 G. The bearing layer consisted of soil cement,
linear factors.                                                          and the embedding depth was three times the
   To accurately assess the seismic resistance of                        length of the pile diameter. The soil used for the
pile foundations, this research focused on the                           experiment was disturbed volcanic ash soil
spring constant for foundations built in volcanic                        collected from the Lake Shikotsu area, a type of
ash soil, which is widely distributed throughout                         soil that is considered to be unique to Hokkaido.
Hokkaido. A series of centrifuge experiments was                         Soil was poured from a set height to ensure that
conducted to test the static horizontal load and                         the model ground was of uniform soil quality. For
dynamic vibration of single piles under a                                the vibration experiment, strain gauges were
centrifugal acceleration of 50 G.                                        installed on the pile. Accelerometers were placed
   Elements considered important to the seismic                          at points far enough from the strain gauges that
design of pile foundations were examined by                              the behavior of the pile would remain unaffected
comparing the characteristics of the coefficient of                      at the depths of the strain gauge locations. A
dynamic horizontal subgrade reaction of the pile                         static horizontal loading test and dynamic loading
(Khe) with those of the coefficient of static                            tests using white noise and sine waves were also
horizontal subgrade reaction (Kh).                                       conducted. In the dynamic loading tests, a 400-g
                                                                         weight (0.4 kg x 503 = 50 tf) was installed on the
2 OUTLINE OF THE EXPERIMENTS                                             pile head to represent the bridge substructure.

   The experiments were conducted using a model                          3 STATIC HORIZONTAL LOADING TEST
steel pile on a scale of 1:50 (φ = 10 mm, t = 0.2                          (50 G)
mm) in a steel container (Figure 1) with internal
dimensions of 700 x 200 x 350 mm (L x W x H).                                    A static horizontal loading test of the pile was
The scale was set at 1:50 so that the model pile                             conducted using the multi-cycle strain control
                                                                                            method, which employs a horizontal
           Accelerome                                     Model pile                        loading device. The loading rate was
                                    70              19ch
           Strain gauge                                   Weight               10           0.25 mm/min. at the model pile head.
                                    10
                                    30            P1       5ch                              Pile displacement was measured using
                                    30            P2       4ch                              laser displacement gauges, and pile
                                                  P3       3ch                              stress was determined with strain
                                    50
                                                                                            gauges. The permissible displacement
                                                  P4       2ch
                                                                                            (δ) for this test was set at 0.3 mm,
                                                                             300
                                    80                                                      which is equal to the permissible
                                                                                            displacement of the full-size pile (15
      Volcanic                                    P5       1ch
                                                                                            mm) divided by 50 G. This test
      Ash                           90                                                      displacement was used as a criterion
                                    10            P6       17ch                             for pile displacement. The duration of
     Soil Cement                    30                                         40           full virgin load application was
                                                                                            approximately 15 min., in compliance
                                             700                                            with the standard set by the Japanese
Figure 1 Experimental container                                                             Geotechnical Society (1983).
Table 1 Scale factors for the experiment                                                     To calculate the static subgrade
                                                                                            reaction, the pile foundation was
                                                                  Experimental
                                            Notation Unit   Scale
                                                                       size
                                                                                  Real size regarded as the beam of the elastic
   Ground
                        Thickness       g1    H         m    1/ λ     0.300        15.000   foundation of the skeletal model, and a
                Bearing ground thickness      H         m    1/λ      0.040         2.000
                    Embedding depth
                                        g2
                                               L        m    1/λ      0.320        16.000
                                                                                            Winkler spring model was constructed
                     Outer diameter            D        m    1/λ      0.010         0.500   for use in the analysis of the
     Pile
                     Plate thickness           t
                                                    2
                                                        m    1/λ
                                                                  7
                                                                      0.002
                                                                                7
                                                                                    0.010   coefficient of subgrade reaction
                  Modulus of elasticity        E      Tf/m    1      2.1x10        2.1x10
              Geometrical moment of inertia    I4
                                                       m4
                                                            1/λ
                                                                       -11
                                                                  7.3952x10         -11
                                                                                4.6220x10   (Figure 2). The vertical distribution
                   Cross-sectional area        A2
                                                       m2
                                                            1/λ
                                                                       -6
                                                                  6.1575x10       0.01539   and the coefficient of subgrade
                                                        3         -3
  Structure
                          Weight         S    M        Tf   1/λ     0.4x10           50.0   reaction were used as parameters for
                          Height              H         m    1/λ      0.015          0.75
             Vibration acceleration
                                        S
                                               α        g     λ        (1)         (0.020)  the trial calculation. This calculation
  Note: 1/λ = model/real = 1/50                                                             was performed to determine the values
that would produce agreement between the
experimental distribution of displacement at the                                                                                                               Y =-1.067E02 X + 2.398E-03
pile head and pile stress in the ground and those                                                                                               0.00                X:Distance from
estimated from the analysis. The static subgrade                                                                                                                      the pile head
                                                                                                                                                                                         Upper
                                                                                                                                                                    Y:Coefficient of
reaction coefficient (Kh) was defined as the area                                                                                                                     subgrade reaction  layer
of the coefficient of subgrade reaction (A) divided                                                                                             -0.05
by depth (Z), as seen in Figure 3. The coefficient                                                                                                                                          -0.054
of static subgrade reaction was found to be 5,500




                                                                                                              Distance from the pile head (m)
kN/m2 from the results of the experiments and the                                                                                               -0.10
analysis carried out by recreating the experimental
situations. In making this calculation, it was
assumed that the distribution of the coefficient                                                                                                -0.15
was uniform (Figures 4 and 5).
   Fitting of bending moment curves was                                                                                                                                        Spring value                      Lower
performed using theoretical and experimental                                                                                                    -0.20
                                                                                                                                                                               (constant)
                                                                                                                                                                                                                 layer
values of flexural rigidity of the pile in volcanic                                                                                                           Area (A)
ash soil to analyze the vertical distribution of
rigidity. In the experimental ground, rigidity
                                                                                                                                                -0.25
increased at a constant rate in a particular depth
range. After this increase, however, rigidity
became constant. The experimental ground was
thought to be elastic for the following reasons:                                                                                                -0.30
                                                                                                                                                                            120
                                                                                                                                                             0 20 40 60 80100 140
 - The depths of the peak points of the bending
    moment were constant with respect to load
    value.                                                             Figure 3 Coefficient of subgrade reaction
 - Displacement       at the pile head was
                                                       Distance from the pile head (m)




    approximately 1 mm (10% of the pile                                                              0.0

    diameter), yet it did not affect the rigidity of
    the ground.
 - Linear representation of the strain value of the
                                                                                                     -0.1
                                                                                                                                                                                               Depth range of the spring value (upper layer)


    pile material was possible.                                                                                                                                                                Depth range of the spring value (lower layer)


                                                                                                     -0.2
                                                                                                                                                                                                                                 2
                                                                                                                                                                                                Theoretical value 4000kN/m
                                                                                                                                                                                                                           2
                                                                                                                                                                                                Theoretical value 5000kN/m
                                                                                                                                                                                                                           2
                                                                                                                                                                                                Theoretical value 5500kN/m
                                                                                                                                                                                                                           2
                                                                                                                                                                                                Theoretical value 5500kN/m
                                                                                                     -0.3
                                                                                                                                                                                                Experimental value (Load: 0.0128kN)
                                                                                                                                                                                                Experimental value (Load: 0.0259kN)
                                                                                                                                                                                                Experimental value (Load: 0.0396kN)
                                                                                                                                                                                                Experimental value (Load: 0.0526kN)

                                                                                                     -0.4
                                                                                                                                                                                       -3                              -3                            -3
                                                                                                                                                 0.0                       1.0x10                             2.0x10                        3.0x10

                                                                                                                                                                                δ (m)
                                                                Figure 4 Distribution of vertical displacement
                                                                   Distance from the pile head (m)




                                                                                                       0.0



                                                                                                                                                                                                                            Depth range
                                                                                                      -0.1                                                                                                                  of the spring value
                                                                                                                                                                                                                            (upper layer)
                                                                                                                                                                                                                            Depth range
                                                                                                                                                                                                                            of the spring value
                                                                                                                                                                                                                            (lower layer)
                                                                                                      -0.2
                                                                                                                                                                                 2
                                                                                                                                                       Theoretical value 4000kN/m
                                                                                                                                                                                  2
                                                                                                                                                       Theoretical value 5000kN/m
                                                                                                                                                                                  2
                                                                                                                                                       Theoretical value 5500kN/m
                                                                                                                                                                                  2
                                                                                                                                                       Theoretical value 5500kN/m
                                                                                                      -0.3
                                                                                                                                                       Experimental value (Load: 0.0128kN)
                                                                                                                                                       Experimental value (Load: 0.0259kN)
                                                                                                                                                       Experimental value (Load: 0.0396kN)
                                                                                                                                                       Experimental value (Load: 0.0526kN)

                                                                                                      -0.4
                                                                                                                              -3                               -3                 -3                     -3                                         -3
                                                                                                        -4.00x10                                   -3.00x10            -2.00x10               -1.00x10                  0.00              1.00x10

                                                                                                                                                                    M (kN m)
                                                                Figure 5                                                                         Distribution of the vertical bending
Figure 2 Analytical model                                                                                                                        moment
4 COEFFICIENT OF DYNAMIC SUBGRADE                                                        vibrations (i.e., they are frequency dependent). In
  REACTION                                                                               this study, analysis was performed at the natural
                                                                                         frequency of the pile foundation, which best
4.1 Method used for calculation of the                                                   reflects the relative displacement of the pile and
  coefficient of subgrade reaction                                                       the ground, to develop a new method for
  In the current specifications for highway                                              calculating the coefficient of dynamic subgrade
bridges, the correction coefficient, α, is used to                                       reaction. The coefficient of dynamic subgrade
assess ground rigidity and determine the                                                 reaction calculated from the interaction force of
coefficient of dynamic subgrade reaction rather                                          the pile and the ground was compared with the
than the coefficient of static subgrade reaction.                                        coefficients of dynamic and static subgrade
In this study, the coefficient of subgrade reaction                                      reaction.
was calculated using two methods (p-δ  and                                              (2) Natural frequency of the pile foundation in
eigenvalue analysis), and then compared with the                                         volcanic ash soil
coefficient of static subgrade reaction to                                                  A sine-wave-based experiment was conducted
determine the correction coefficient.                                                    on the pile foundation by applying the vibration of
                                                                                         white noise (a waveform with a frequency of
4.2 Analysis of the coefficient of subgrade                                              between 10 and 350 Hz) to clarify its natural
    reaction using the p-δ curve (p-δ method)                                            frequency. The analysis results for the Fourier
(1) Calculation using the p-δ method                                                     transformation characteristics and the transfer
   To calculate the coefficient of subgrade reaction                                     function indicated that the natural frequency of the
caused by interaction between the ground and the                                         pile foundation was between 55 and 85 Hz under
pile (Khe1), the interaction force (p) was divided                                       the conditions of white noise vibration when the
by relative displacement (δ). Figure 6 shows the                                         weight was 400 g (Figures 7, 8 and 9). Based on
process used to make this calculation. The level                                         the Fourier transformation characteristics and the
of vibration was determined based on the                                                 transfer function obtained in the sine-wave-
assumption that displacement is minimal, i.e., the                                       vibration experiment (Figure 10), the natural
plasticity of the pile and the ground was not                                            frequency of the pile foundation in volcanic ash
considered.                                                                              soil was found to be 62.5 Hz. Acceleration and
                                                                                         strain calculated from this frequency value were
Fourier spectrum of        Strain
                                                                                         used for analysis.
acceleration
                                                                                          150
                                                                                          100
Bandpass filter            Bending moment
                                                         P1 Strain ( µ)




                                                                                           50
                                                                                            0
                                                                                          -50
                                                                                         -100
Fourier transformation                                                                   -150
for speed and
displacement calculation                                                                  10
                                                                 19ch Acceleration (G)




                                                                                           8
                                                                                           6
                                                                                           4
                                                                                           2
                                                                                           0
                                                                                          -2
Third-degree function      Second-order     Second                                        -4
                                                                                          -6
using the four-point       integral         derivative                                    -8
                                                                                         -10
method                                                                                    0.5
                                                                                          0.4
                                                             8ch Voltage (mV)




                                                                                          0.3
                                                                                          0.2
                                                                                          0.1
                           Pile             Subgrade                                      0.0
Ground displacement        displacement     reaction
                                                                                         -0.1
                                                                                         -0.2
                                                                                         -0.3
                                                                                         -0.4
                                                                                         -0.5
                                                               21ch Acceleration (G)




                                                                                           10
          Relative displacement                                                             8
                                                                                            6
                                                                                            4
                                                                                            2
                                                                                            0
                                                                                           -2
Figure 6 Process of the p-δ method                                                         -4
                                                                                           -6
                                                                                           -8
                                                                                          -10

   Recent research studies and analyses have                                                    0.0   0.1   0.2   0.3   0.4   0.5   0.6   0.7   0.8   0.9   1.0   1.1   1.2   1.3   1.4

revealed that relative displacement and relative                                                                                     Time (sec)

interaction force, both of which are used to                                             Figure 7 White noise W = 400 g
calculate the coefficient of dynamic subgrade                                                     Dyn. Amp. = 0.4
reaction, change with respect to the number of
                                                                                                                            taken at six points, the equation for curve fitting
 Fourier amplitude ratio



                            50

                                           400 g
                                                                                                                            was approximated using a multi-term fifth-degree
                            40
                                                                                                                            function. Equation 1, the second derivative of this
                                                                                                                            function, was used to calculate the subgrade
                            30


                            20


                            10
                                                                                                                            reaction. It was hypothesized that the function of
                            0                                                                                               the subgrade reaction could be approximated
                                     10                       100
                                                         Frequency (Hz)
                                                                                             1000
                                                                                                                            using a curve from the third-degree function.

Figure 8 19ch/17ch Transfer function                                                                                           d 2M
         Dyn. Amp. = 0.4                                                                                                              = − q ( x)                                                               (1)
                                                                                                                                dx 2
                                                                                                                                  d2y
                                                                                                                               EI 2 = − M ( x)                                                                 (2)
  Fourier amplitude ratio




                            500


                            400
                                           400 g                                                                                   dx
                            300


                            200
                                                                                                                               The constants of a multi-term second-order
                            100
                                                                                                                            integral (Equation 2) were assessed by setting the
                                                                                                                            boundary conditions of the deflection angle (θ)
                                 0

                                      10                       100                            1000
                                                          Frequency (Hz)                                                    and displacement (δ) at the pile’s lower end at
Figure 9 P1/17ch Transfer function                                                                                          zero because that end is fixed by soil cement.
         Dyn. Amp. = 0.4                                                                                                       Due to the limitations of the experimental
                                                                                                                            apparatus, direct measurement of displacement
                             12                                                                                             was not possible in the ground. The second-order
                                                                                                                            Fourier integral of the equation for ground
   Fourier amplitude




                             10                                                 19 ch/17ch

                                 8
                                                                                                                            acceleration was used to calculate displacement
                                 6
                                                                                                                            (Figures 11 and 12). For calculations necessary
                                                                                                                            for correcting the displacement axis, bandpassing
                                 4

                                 2

                                 0
                                                                                                                            from 50 to 1,000 Hz was performed. The
                                     40      50     60        70           80   90           100
                                                                                                                            coefficient of subgrade reaction could be
       Fourier amplitude




                            500

                            400
                                                                                P1 ch/17ch                                  calculated because the above procedure enables
                            300                                                                                             the computation of displacements of the pile and
                            200
                                                                                                                            the ground and subgrade reaction.
                            100                                                                                                                     10
                                                                                                                                                     8
                                                                                                                            5ch Acceleration (G)




                                 0                                                                                                                   6
                                     40      50     60        70           80   90           100                                                     4
                            500                                                                                                                      2
                                                                                                                                                     0
  Fourier amplitude




                            400
                                                                                P2 ch/17ch                                                          -2
                                                                                                                                                    -4
                                                                                                                                                    -6
                            300                                                                                                                     -8
                                                                                                                                                   -10
                            200
                                                                                                                                                         0.0        0.1      0.2        0.3        0.4   0.5    0.6
                            100                                                                                                                                                      Time (sec)
                                 0
                                                                                                                                                                           Experimental acceleration
                                     40      50     60        70           80   90           100
                            500

                                                                                                                            Figure 11 Sine wave 62.5 Hz Dyn. Amp. = 0.4
 Fourier amplitude




                                                                                P3 ch/17ch
                            400


                            300

                            200
                                                                                                                                                         -4
                            100                                                                                              2.0x10-4
                                                                                                                             1.5x10-4
                                                                                                     5ch Displacement (m)




                                 0
                                     40      50     60        70           80   90           100
                                                                                                                             1.0x10-5
                                                                                                                             5.0x10
                                                   Nominal frequency (Hz)                                                        0.0
                                                                                                                                   -5
                                                                                                                            -5.0x10-4
Figure 10 Transfer function of the sine wave                                                                                -1.0x10-4
                                                                                                                            -1.5x10-4
           W = 400 g Dyn. Amp. = 0.4                                                                                        -2.0x10
                                                                                                                                                              0.0    0.1       0.2       0.3       0.4   0.5    0.6
                                                                                                                                                                                      Time (sec)
(3) Calculation of relative displacement and
subgrade reaction
   To calculate displacement of the pile, the                                                                               Figure 12 Sine wave 62.5 Hz Dyn. Amp. = 0.4
bending moment must be identified from pile
strain values after which curve fitting must be
performed (Figure 13). Since measurements were
                                                            Volcanic ash 62.5Hz D=0.4 W=400g                                                                                                                                                             Volcanic ash 62.5Hz D=0.4 W=400g
                             0.00                                                                                                                                                                               0.00
                                                                                                                                                                                                                                                                             7             8                        10        11        12 13 14 15
                                                                                                                                                                                                                                                                                                        9
                                                                                                                                                                                                                                                                             65 4              3                1
                                                                                                                                                                                                                                                                                                    2                                   17 16
                      -0.05                                                                                                                                                                                     -0.05




                                                                                                                                                                                          Container depth (m)
                                                                                                                                                                                                                                                                                                                                   18
                                                              15                              17
Container depth (m)




                                                                           16                                           18
                                                              1413    12             11               10                 9               8             7
                                                                                                  1              2                   3       4         5 6

                      -0.10                                                                                                                                                                                     -0.10

                      -0.15                                                                                                                                                                                     -0.15                                                                                                    ∆ t=0.001 sec
                                                                                                                         ∆ t=0.001 sec

                                                                                                                                                                                                                -0.20                                                                                                     1 - 0.1424 sec
                      -0.20                                                                                               1 - 0.1424 sec                                                                                                                                                                                  5 - 0.1466 sec
                                                                                                                          5 - 0.1466 sec                                                                                                                                                                                 (Maximum shear strain)
                                                                                                                         (Maximum shear strain)                                                                 -0.25                                                                                                     9 - 0.1504 sec
                      -0.25
                                                                                                                          9 - 0.1504 sec                                                                                                                                                                                 18 - 0.1594 sec
                                                                                                                         18 - 0.1594 sec                                                                        -0.30
                      -0.30                                                                                                                                                                                                                                    -1.0                                     0.0                                  1.0                      2.0
                                -3                                 -3                     -3                                                                                   -3
                        -2.0x10                            -1.0x10         0.0      1.0x10                                                                            2.0x10
                                                              Pile bending moment (kN m)                                                                                                                                                                      Subgrade reaction of the pile (kN/m)
  Figure 13 Distribution of the bending moment at                                                                                                                                        Figure 16                                                  Subgrade reaction of the ground at
  different times                                                                                                                                                                                                                                  different times
  (4) Analysis results                                                                                                                                                                                                                                       Volcanic ash 62.5Hz D=0.4 W=400g
    • Dynamic coefficient of the ground                                                                                                                                                                         0.00                                                                                                                        16     15
                                                                                                                                                                                                                                                                                                   18               17

     The time-history displacement (pile, ground
                                                                                                                                                                                                                                                                                  8         9               10                               14
                                                                                                                                                                                                                                                                                                                         11        12      13
                                                                                                                                                                                                                                                                     7
                                                                                                                                                                                                                                                                 6
                                                                                                                                                                                                                                                                         5    4        3




                                                                                                                                                                                        Container depth (m)
                                                                                                                                                                                                                -0.05                                                                                       1

  and relative), and the distribution of subgrade
                                                                                                                                                                                                                                                                                                   2




  reaction and its coefficient are shown in Figures                                                                                                                                                             -0.10
  14 to 18.         Curves were determined for
                                                                                                                                                                                                                                                                                                                    ∆ t=0.001 sec
  approximation based on the distribution of the                                                                                                                                                                -0.15
  coefficient of subgrade reaction. A curve that                                                                                                                                                                                                                                                                    1 - 0.1424 sec
                                                                                                                                                                                                                -0.20
  represents the average values of all the curves was                                                                                                                                                                                                                                                               5 - 0.1466 sec
  identified, and the average value of the curve                                                                                                                                                                -0.25
                                                                                                                                                                                                                                                                                                                    (Maximum shear strain)

  identified was found to be 12,400 kN/m2, from
                                                                                                                                                                                                                                                                                                                    9 - 0.1504 sec
                                                                                                                                                                                                                                                                                                                    18 - 0.1594 sec
  which the value of dynamic spring was estimated.                                                                                                                                                              -0.30
                                                                                                                                                                                                                                                        -4                            -4
                                                                                                                                                                                                                                                                                                        0.0                                       -4             -4
                                                                                                                                                                                                                                              -4.0x10          -2.0x10                                                             2.0x10               4.0x10
                                                              Volcanic ash 62.5Hz D=0.4 W=400g
                                            0.00                                                                                                                                                                                                   Relative ground and pile displacement (m)
                                                                           15        16                          18

                                                                                                                                                                                         Figure 17 Relative ground and pile displacement
                                                                                                  17                                                   7
                                                                           14 13      12     11            10                9           8
                                                                                                                                         4       5 6
                Container depth (m)




                                            -0.05                                                      1        2                3



                                                                                                                                                                                         at different times
                                            -0.10
                                                                                                                                                                                                                                                         Volcanic ash 62.5Hz D=0.4 W=400g
                                            -0.15                                                                                                                                                                                      0.00


                                            -0.20

                                                                                                                                                                                                                                       -0.05
                                                                                                                                                                                                                                                                                           Average value of all data
                                            -0.25
                                                                                                                                                                                                                 Container depth (m)




                                            -0.30
                                                    -4.0x10
                                                            -4
                                                                   -2.0x10
                                                                                        -4
                                                                                                       0.0                            2.0x10
                                                                                                                                                       -4
                                                                                                                                                                 4.0x10
                                                                                                                                                                          -4                                                                                                                            Average value of
                                                                                                                                                                                                                                       -0.10
                                                                                                                                                                                                                                                                                                         the fitted curve
                                                                            Pile displacement (m)                                                                                                                                                                                                       up to 0.30 m deep
  Figure 14 Pile displacement at different times
                                                                 Volcanic ash 62.5Hz D=0.4 W=400g                                                                                                                                      -0.15
                                             0.00                                                               18
                                                                                   17
                                                                                                                11               10               9
                                                                           16 15 14 13       12
                                                                                                                                             7               8
                                                                                    1             2    3    4       5    6
                      Container depth (m)




                                            -0.05
                                                                                                                                                                                                                                                                                                   Fitted curve of
                                                                                                                                                                                                                                       -0.20
                                                                                                                                                                                                                                                                                                the average value of
                                            -0.10
                                                                                                                                                                                                                                                                                                        all data
                                            -0.15                                                                                        ∆ t=0.001 sec                                                                                 -0.25

                                            -0.20                                                                                         1 - 0.1424 sec
                                                                                                                                          5 - 0.1466 sec
                                                                                                                                          (Maximum shear strain)
                                            -0.25                                                                                         9 - 0.1504 sec
                                                                                                                                                                                                                                       -0.30
                                                                                                                                                                                                                                               0    5000 10000 15000 20000 25000 30000 35000 40000 45000 50000
                                                                                                                                         18 - 0.1594 sec                                                                                                                                                                                                  2
                                                                                                                                                                                                                                                                             Coefficient of subgrade reaction (kN/m )
                                            -0.30
                                              -1.0x10
                                                      -4
                                                              -5.0x10
                                                                                -5
                                                                                                           0.0                               5.0x10
                                                                                                                                                                 -5
                                                                                                                                                                          1.0x10
                                                                                                                                                                                   -4                                                              Coefficient of dynamic subgrade reaction
                                                                                                                                                                                                                                                                                        2
                                                                     Relative ground displacement (m)                                                                                                                                              Estimated average value 12400 kN/m
  Figure 15 Relative displacement of the ground at                                                                                                                                       Figure 18 Vertical distribution of the coefficient
            different times                                                                                                                                                                        of subgrade reaction
  •  Pile displacement                                                                    • For analysis of vertical distribution of ground
     For the pile displacement mode, the primary                                            rigidity, the distribution used in the
  mode is dominant because of the tremendous                                                horizontal static subgrade reaction test is
  effect of one mass point (400-g weight). The                                              utilized.
  distribution of bending stress for the pile                                             • Bending rigidity of the pile is determined
  indicates that a large bending moment                                                     based on the bending test, and the conditions
  originates from a depth of approximately 40                                               of the pile’s lower end are constant.
  mm, at which the ground shows significant                                               • The spring coefficients of the pile are from a
  displacement. Looking at the displacement                                                 discrete spring (Winkler) in the analysis
  found through curve fitting of the bending                                                model.
  distribution and a second-order integral, the                                           According to these hypotheses and the
  displacement of the pile indicates the first                                          eigenvalue method, a coefficient of dynamic
  vibration mode.                                                                       subgrade reaction of 18,000 kN/m2 was obtained.
                                                                                        Figure 19 shows the results of the analysis.
  •  Ground displacement
     It can be seen that the time-history                                               85
  displacement of the ground found by                                                               Theoretical value based on the analysis



                                                        Characteristic frequency (Hz)
                                                                                        80          Fitted strait line
  accelerometers placed in the ground does not
                                                                                        75
  indicate the first vibration mode as is the case in                                          Dominant frequency of
  the displacement of the pile.                                                         70      volcanic ash 62.5Hz
     The low-frequency component is larger than                                         65      (experimental value)

  the vibrational component due to the effect of                                        60                                      Theoretical coefficient
  surface waves caused by the use of a fixed                                            55                                      of dynamic subgrade
  container.       Therefore, in the dynamic                                                                                    reaction of volcanic ash
                                                                                        50
  experiment, the ground displacement mode is                                                                                    18000kN/m2
  considered to be high because the surface part is                                     45

  affected by both base vibrations and surface
                                                                                             50

                                                                                             60
                                                                                             70
                                                                                             80 0
                                                                                             90 0
                                                                                             1000




                                                                                                                                  20



                                                                                                                                              30


                                                                                                                                                      40

                                                                                                                                                      50
                                                                                               00

                                                                                               00
                                                                                               0
                                                                                               0

                                                                                               00




                                                                                                                                    00



                                                                                                                                                00


                                                                                                                                                        00

                                                                                                                                                        00
  waves due to the effects of the container.
                                                                                                 0




                                                                                                                                      0



                                                                                                                                                  0


                                                                                                                                                          0

                                                                                                                                                          0
                                                                                                                                                      2
                                                                                               Coefficient of dynamic subgrade reaction (kN/m )

4.3 Analysis of the coefficient of dynamic                                              Figure 19      Computation of the coefficient of
    subgrade reaction using an eigenvalue                                                              dynamic subgrade reaction using the
    (eigenvalue analysis)                                                                              dominant frequency of the ground
  Most research on the dynamic interaction
between piles and ground employs methods such                                           4.4 Coefficient of dynamic subgrade reaction:
as second- and third-order FEM and the Penzien                                             comparison between dynamic reaction
model for experiments and analyses. The                                                    and static reaction
specifications for highway bridges, which were                                            The coefficient of dynamic subgrade reaction
revised in March 2002, however, use the normal                                          acquired from the dynamic centrifugal experiment
correction coefficient, α, to assess ground rigidity                                    was compared with the coefficient of static
and determine the coefficient of dynamic                                                subgrade reaction. The coefficient of dynamic
subgrade reaction for dynamic and other analyses.                                       subgrade reaction is 3.3 times greater in the p-δ
By focusing on this correction coefficient, this                                        method and 2.3 times greater in the eigenvalue
experiment adopted the use of an analysis model,                                        method (Table 2).
which was used for both analysis of the
coefficient of static subgrade reaction and                                             Table 2        Comparison of the coefficient of
eigenvalue analysis (mode analysis by free                                                             subgrade reaction (volcanic ash)
vibration) of the coefficient of dynamic subgrade
reaction. The value of the spring coefficients of                                                                                    Khe         α=Khe/Kh
the pile was set as a parameter to assess the
coefficient of dynamic subgrade reaction (Khe2) at                                            p-δ method (Khe1)
the natural frequency of the pile foundation                                                                                      12,400              2.3
                                                                                                   kN/m2
obtained from the experiment.
  The assumptions made for the eigenvalue                                                Eigenvalue method (Khe2)
                                                                                                                                  18,000              3.3
method are as follows:                                                                            kN/m2
  • The pile and the ground are in the linear
     region.
   The same methods were applied to assess silica    dynamic analysis method are currently used in the
sand and kaolin clay.       The results differed     design of pile foundations.          These methods
according to soil type (Table 3); thus, the          employ a ground constant to define, in a fairly
coefficient of dynamic subgrade reaction should      simple manner, the dynamic subgrade reaction
not be determined solely from the coefficient of     (during an earthquake) of the pile foundation, Khe,
static subgrade reaction.      Seismic resistance    which is considered to be an important factor in
should be assessed with reference to soil type.      assessing seismic resistance.
                                                        A series of horizontal dynamic centrifuge
Table 3        Comparison of the coefficient of      model experiments was conducted to analyze the
               subgrade reaction by soil type        dynamic subgrade reaction of silica sand, kaolin
                    Silica   Kaolin    Volcanic      clay and volcanic ash. The results differed
                    sand      clay       ash         according to the soil type due to dynamic
                                                     interactions between the pile and the ground.
  Kh      KN/m2     20,000    4,000      5,500          To appropriately assess the coefficient of
                                                     horizontal dynamic subgrade reaction, Khe, new
  Khe1    KN/m2     27,400   15,500     12,400       concepts are necessary for the creation of seismic
                                                     designs for pile foundations (Wang et al, 2000,
  Khe2    KN/m2     55,500   13,700     18,000       Meymand, 1998, Tomisawa et al, 2001). Such
                                                     new seismic designs should address both the soil
                                                     and response characteristics of the pile and the
     Khe1/Kh         1.4       3.9        2.3
                                                     ground while maintaining the advantages of the
                                                     current design.
5 CONCLUSIONS                                           In the future, dynamic characteristics according
                                                     to soil type will be examined in terms of non-
  A series of dynamic centrifuge model               linear characteristics and pile displacement.
experiments were conducted in connection with
seismic behavior of the pile foundation to
compare the coefficient of dynamic subgrade
reaction with the coefficient of static subgrade     REFERENCES
reaction. The following results were found:          Japanese Geotechnical Society (1983): “Horizontal
                                                       Loading Test Method for Piles and Instruction
                                                       Manual”. (in Japanese)
1) The vibration experiment conducted using the      Japan      Road     Association   (1996):    Reference
   centrifuge apparatus roughly clarified the          Concerning        Application   of     "Specifications
   dynamic characteristics of ground and piles by      Concerning Restoration of Highway Bridges
   soil type.                                          Damaged by the Hyogo-ken Nambu Earthquake"
2) According to the p-δ method, the coefficient of     (draft). (in Japanese)
                                                     Japan Road Association (2002): “Specifications for
   horizontal dynamic subgrade reaction, Khe1, is      Highway Bridges with Instruction Manual V -
   27,400 kN/m2 for silica sand, 15,500 kN/m2          Seismic Design Edition”, pp.210- 221. (in Japanese)
   for kaolin clay and 12,400 kN/m2 for volcanic     Meymand (1998): “Shaking Table Scale Model Tests
   ash. The coefficient of dynamic subgrade            of Nonlinear Soil-Pile-Super Structure Interaction in
   reaction (Khe1) divided by the coefficient of       Soft Clay”.
   static subgrade reaction (Kh), α, is 1.4 for      Ogawa and Ogata (1997): “Verification of Vibration
                                                       Resistance by Dynamic Analysis”: Foundation Work,
   silica sand, 3.9 for kaolin clay, and 2.3 for       vol. 25, No. 3. (in Japanese)
   volcanic ash.                                     Tomisawa et al (2001): “Dynamic Horizontal Subgrade
3) The coefficient of dynamic horizontal subgrade      Reaction of Pile by Dynamic Centrifuge Model Test”,
   reaction changes with respect to strain and         Proceedings of the 56th Academic Lecture Meeting
   frequency. The coefficient of horizontal static     of Japan Society of Civil Engineers. (in Japanese)
                                                      Wang et al (2000): “Experimental Consideration of
   subgrade reaction, Khe2, determined using the       Dynamic Interaction between Pile Foundation and
   eigenvalue method, differs depending on the         Ground Using a Large Shear Soil Layer”,
   vibration mode and dominant frequency of the        Proceedings of the Japan Society of Civil Engineers.
   pile (eigenvalue), both of which are affected       (in Japanese)
   by soil type.

  The seismic coefficient method, the seismic
horizontal load-carrying capacity method and the

								
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