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13th World Conference on Earthquake Engineering Vancouver, B.C., Canada
August 1-6, 2004 Paper No. 1380
STIFFNESS AND DAMPING OF SOIL-PILE SYSTEM IN
LIQUEFACTION PROCESS
Hatsukazu MIZUNO1 and Tsutomu HIRADE 2
SUMMARY Large-scale and medium-scale shaking table tests of soil-pile system are presented. The objectives of the tests were to clarify dynamic behavior of pile-soil system, and to evaluate change of soil properties, especially stiffness and damping in liquefaction process. A model of piles and basement (pile cap) was set up in saturated sand in a shear box in both of the tests. An oscillator in large-scale tests and a hydraulic servo actuator in medium-scale tests were used for determining stiffness and damping in liquefaction and after liquefaction. In large-scale tests, after table excitation, in dissipation stages of excess pore water pressures, the oscillator excited the pile cap in sweep mode. In medium-scale tests, during shaking table excitation, the actuator excited the pile cap. During the tests accelerations, excess water pore pressures, and displacements at the pile cap and on the soil surface were determined. Soil deformations in liquefaction process also measured directly by a glass fiber measurement apparatus. On the basis of these tests, stiffness and damping at pile head are examined in uplift stages and dissipation stages of excess pore pressures in liquefaction process.
INTRODUCTION Dynamic behavior of soil-pile system in liquefaction process is much affected by change of physical properties of the soil, especially stiffness and damping. Several cases of previous damage to piles during earthquakes related with soil liquefaction. A lot of cases of damage to piles due to liquefaction and lateral spread of the soil were reported in the 1995 Hyougoken-Nanbu (Kobe) earthquake. The objectives of the paper are to clarify dynamic behavior of pile-soil system in liquefaction process, and to evaluate change of soil properties, especially stiffness and damping, and change of coefficients of horizontal subgrade reaction in piles by combination of large-scale and medium-scale shaking table tests, oscillator tests and hydraulic servo actuator tests.
LARGE-SCALE SHAKING TABLE TESTS
1 Research Coordinator, Japan Association for Building Research Promotion, Tokyo, Japan, Email [email protected] 2 Senior research Engineer, Building Research Institute, Tsukuba, Japan, E-mail [email protected]
Stiffness and damping in dissipation process of excess pore pressures of the soil are examined on the basis of the large-scale shaking table tests and oscillator tests.
Figure 1 shows the test setup including sensor distribution in a big shear box on NIED (National Institute of Earth Science and Disaster Prevention) shaking table. Height, length and width of a big shear box at NIED were about 6m, 11.6m and 3m. The soil model was prepared by pouring sand into water through vibrating screen in water. In the tests, the model soil in the box was reused several times by injecting pressurized water from the bottom of the box, and thereby boiling the liquefied and settled soil. Mechanical conditions at pile head and pile tip are fixed and hinged, respectively. The fundamental natural frequency of the building model was adjusted to 5Hz in base-fixed condition. One important point of these works is the oscillator tests during and after table shaking [2,3]. The shaking table tests were done to clarify dynamic behavior of soil and pile in liquefaction process, especially in dissipation process of excess water pressures. The oscillator tests during and after the table shaking were done to determine the relation between excess pore pressures and subgrade reaction coefficients of pile, and to evaluate the stiffness and damping of soil-pile system. Figure 2 shows dissipation process of excess pore pressure on G-4 line after Test 1-4, 150gal earthquake excitation by the table. For the duration of T1, T2, T3, T4 and T5 in the figure, unbalanced mass type
Figure 2. Oscillator tests in dissipation process
1,100
6001,100 700
1 ,100
1,000
500
500 500
550
2,000 3,200 2,100 2,500
1 ,550
G-1G-4
NIED・Disp. M eter in S oil
NIRE・A coustic Tomography M icrophone & Bender Element
Velocity M easurem ents of P & S Waves
AIST・Resistivity M easurem ent
DP RI, Kyoto U niv.・Optical Fiber
G -2
G-3
800
4,000
P-1 G-2
1,600
Base
G-1 G-3
Excess Pore P ressure D isp. M eter
S train Gauge Earth P ressure A ccelerometers Accelerometers
Rotation Angle
G-4
200
270
630
3,950
(@200x20)
600 600
600
N IE D・Disp. Meter in Soil
Figure 1 Test Setup
oscillator excited the base on piles by increasing and decreasing frequencies (sweep up and sweep down). Eccentric mass was adjusted to 100kgfcm. Dynamic forces by the oscillator had almost no influence on the dissipation process of excess pore pressures as shown in the figure. Figures 3 and 4 present average excess pore pressures on G4 line and on pile (P1) for the duration of T1, T2, T3, T4 and T5, respectively. The straight line in the figures corresponds to the overburden pressures.
Figure 5 shows displacement transfer characteristics of the excited base derived from base acceleration. The values in parenthesis represent the excess pore pressure ratio derived from the average value of the excess pore pressures on P-1 line of the pile. The values of the excess pore ratios change from 1.0 to 0.7. Peak frequencies and peak values decrease from the duration of T1 to the duration of T5. That indicates change of properties of saturated soil. Peak frequencies derived from phase characteristics in the figure are 4.6Hz, 6.1 Hz, 7.4 Hz, 8.4 Hz and 9.0 Hz, respectively, and moves from lower frequencies to higher frequencies with progress of pressure dissipation. Peaks near to 5 Hz are considered influence of fundamental natural frequency of model soil
Figure 3 Pore Pressures on G-4 Line
0
5
10
15
20
25
30
35
40
40 80 1 20 160 200 240 280 320 3 60
(s)
kPa
G .L.-3.75m G .L.-2.55m
G .L.-1.35m G .L.-0.55m
T1 T2 T4 T3 T5
Average Pore Pressure at Pile Surface (P1)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 10 20 30 40
w.p. (kPa)
Height (m
)
T1
T2
T3
T4
T5
σ'
Average Pore Pressure at G 4 Point (Soil)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 10 20 30 40w.p. (kPa)
Height (m
)
T1
T2
T3
T4
T5
σ'
Figure 4 Pore Pressures on Pile P1
Figure 2 Oscillator Tests in Dissipation Process
0
0.1
0.2
0.3
0.4
0.5
0.6
0 1 2 3 4 5 6 7 8 9 10 11
Hz
Spe
ctral R
atio(cm/to
nf)
T1(0.69) T2(0.45)
T3(0.31) T4(0.24)
T5(0.15)
-180
-135
-90
-45
0
45
90
135
180
0 1 2 3 4 5 6 7 8 9 10 11Hz
Phase angle(deg.)
T1(0.69) T2(0.45)
T3(0.31) T4(0.24)
T5(0.15)
Figure 5 Transfer Function of Base Displacement
Figure 6 illustrates displacement natural modes derived from accelerations at peak frequencies on the pile, P-1. Model soil is confirmed to vibrate in fundamental natural modes in dissipation process of excess pore pressures. Figure 7 shows distribution of pile bending moments at peak frequencies. The points of maximum bending moments in the soil move from the height about 1 meter to the height about 2 meters during the progress of pore water pressure dissipation. Figure 8 presents horizontal impedances derived from base displacements. Real parts and imaginary parts of the impedance correspond to stiffness and damping of base-pile-soil system. At T1 stage with the average excess pore ratio 0.69, stiffness and damping are both very small or near to zero at all frequencies. It is important that damping is very small at the higher excess pore pressure ratios from seismic design viewpoint. As the excess pore pressures dissipate, stiffness increases, and fundamental natural frequencies of model soil come into being again near to the frequency 6Hz. It is pointed out that damping also increases with peaks in real parts around 6 Hz.
MEDIUM-SCALE SHAKING TABLE TESTS Shaking Table Tests and Hydraulic Servo Actuator Tests Stiffness and damping in uplift (rapidly increasing) process of excess pore pressures of the soil are examined on the basis of the medium-scale shaking table tests and hydraulic servo actuator tests. Figure 9 shows the test setup including sensor distribution in a shear box on BRI (Building research
Figure 8 Dynamic Impedance (Horizontal)
-60
-40
-20
0
20
40
60
0 1 2 3 4 5 6 7 8 9 10 11
Hz
Real
T1(4.6Hz)
T2(6.1Hz)
T3(7.4Hz)
T4(8.4Hz)
T5(9.0Hz)
-60
-40
-20
0
20
40
60
0 1 2 3 4 5 6 7 8 9 10 11
Hz
Imag.
T1(4.6Hz)
T2(6.1Hz)
T3(7.4Hz)
T4(8.4Hz)
T5(9.0Hz)
0
0.5
1
1.5
2
2.5
3
3.5
4
-0.1 0 0.1 0.2 0.3 0.4
(cm /tonf)
Height (m
)
T1(4.6Hz)
T2(6.1Hz)
T3(7.4Hz)
T4(8.4Hz)
T5(9.0Hz)0
0.5
1
1.5
2
2.5
3
3.5
4
-0.002 -0.001 0.000 0.001 0.002 0.003
(tm /tonf)
Height(m)
4.6Hz,0.69
6.1Hz,0.45
7.4Hz,0.31
8.4Hz,0.24
9.0Hz,0.15
Figure 6 Displacement Modes of Pile (cm/tonf)
Figure 7 Pile Bending Moment
Institute) shaking table. Height, length and width of the shear box are 1.0 m, 3.5m and 0.8m by inside measurement, respectively. The shear box is composed of eighteen layers of aluminum square pipe frames. The box is lined with rubber membrane for waterproofing. Two model piles are made of steel, and their width and thickness are 8 cm and 4.5 cm, respectively. The boundary conditions at the heads and the tips of the piles are rotation-constrained and hinged, respectively. Model soils were made of Nikko silica sand No. 5.under the condition of keeping water depth 30 cm after the piles were installed. The steel base was installed on the heads of the piles. Table 1 summarizes physical properties of the test sand, and Figure 10 shows its grain size accumulation curve.
(@54.4x18)
500
250 Base
G-2
Pore Pressure Meter
Displacement Meter
Strain Gage
Pressure Meter
Accelerometer
G-3 G-1
3,500
1,000 1,200
600
150 150
P-2 P-1
400
935
980
Glass-fiber-based
Displacement meter
200
200
400
Actuator
Figure 9 Test Setup
Measuring sensors are also shown in Figure9. Accelerometers and pore pressure meters were installed on G-1 line, and pore pressure meters on G-3 line. Accelerometers and pore pressure meters were installed on an outside face of the pile P-1, and pressure meters on the both sides of P-1. Strain gages were set on the both sides of the pile P-2. Soil deformations and displacements were measured directly by a glass-fiber-based displacement meter and LASER type displacement meters. The LASER type meters were applied to relative displacements between the shaking table and the base, and between the soil surface on G-1 line and the soil surface on the glass-fiber-based displacement meter.
Table 1 Physical properties of Sand
Figure 10 Grain Size Accumulation Curve
Soil Particle Density ρ s(g/ cm3
) 2.699
Coarse Sand Fraction 0.425～1mm (%) 80.2Fine Sand Fraction 75μ m～0.425mm (% 18.2Silt Fraction 5～75μ m (%) 1.6
Uniformity Coefficient Uc 1.76
Curvature Coefficient Uc' 1.07
D50 (mm) 0.575
Maximum Dry Density ρ dm ax(g/ cm3
) 1.626
Minimum Dry Density ρ dm in(g/ cm3
) 1.304
Minimum Void Ratio em in 0.66
Maximum Void Ratio em ax 1.07
G rain size accum ulation curve
0
20
40
60
80
100
0.01 0.1 1 10
G rain size (m m )Perc
enta
ge fin
er (%
)
Density
(gf/ cm3
)
Relat iveDensity
(%)
Average Sett lementfrom Init ial SoilSurface (mm)
ActuatorDisplacement
(Stat ic and Dynamic,1Hz)
Case1* - 1 1.372 25.0
Static Displacement1mm
- 2 1.372 25.0 35.4Sin3Hz
LiquefactionMax. Acceleration 100gal
Target Displacement10mm
- 3 1.426 43.2 110.9Sin3Hz
ReliquefactionMax. Acceleration 300gal
Target Displacement5mm
Case2- 1 1.379 27.3
Static Displacement1mm
- 2 1.379 27.3 64.9Sin3Hz
LiquefactionMax. Acceleration 100gal
Target Displacement10mm
- 3 1.481 60.5 112.5Sin3Hz
ReliquefactionMax. Acceleration 300gal
Target Displacement3～5～3mm
Case3- 1 1.376 26.3
Static Displacement1mm
- 2 1.376 26.3 74.9Sin3Hz
LiquefactionMax. Acceleration 100gal
Target Displacement18mm
- 3 1.496 64.7 115.2Sin3Hz
ReliquefactionMax. Acceleration 300gal
Target Displacement0～5mm
Case4- 1 1.358 20.0
Static Displacement1mm
- 2 1.358 20.0 86.9Sin3Hz
LiquefactionMax. Acceleration 100gal
Target Displacement25mm
- 3 1.497 65.0 143.6Sin3Hz
ReliquefactionMax. Acceleration 300gal
Target Displacement10mm
＊Displacement and reaction data were not measured.
Case Table Excitat ion
Table 2 Test Conditions, Densities and Settlements
The tests were carried out as follows. At first the table was excited in sinusoidal vibration at a frequency 3 Hz. After accelerations at the table reached a target level, and when the excess pore pressures monitored in the soil arrived at an uplift stage of the pore pressures, forced displacements were applied to the base in sinusoidal vibration at a frequency 1 Hz to target displacements by a hydraulic servo actuator. After confirming dissipation of the pressures in the soil, the actuator was stopped, and then the table was stopped. Table 2 summarizes the tests, and includes relative density of the soil, excitation conditions of the shaking table and the hydraulic servo actuator. Initial relative densities of the soil were from 20 percents to 27 percents. After liquefaction, the table was excited by larger accelerations, and the soil was liquefied again. Outline of Test Example Excess pore pressures and accelerations on G-1 line, accelerations of the table and the base, and displacements and loads of the actuator in Case 4-2 are shown in Figure 11. Excess pore pressures in the lower of the soil decreased rapidly after reaching the peak. Pore pressures in the middle and upper of the soil keep higher level after the peaks of the pressures. An incline is recognized on baseline of accelerations in the soil. That is considered due to slants of the accelerometers. Before the actuator moved during excitation of the table, the loads of the actuator increased gradually due to push and pull of the soil by shaking the table. Fourier Spectrum of the actuator loads in Figure 12 indicates a peak at a frequency 1 Hz, and another peak at a frequency 3Hz
-1
0
1
2
3
4
5
6
0 50 100 150
(s)
(kPa)
G 1 G .L.-900
-0.5
0
0.5
1
1.5
2
2.5
3
0 50 100 150
(s)
(kPa)
G 1 G .L.-420
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 50 100 150
(s)
(kPa)
G 1 G .L.-180
-500
-400
-300
-200
-100
0
100
0 50 100 150
(s)
(gal)
G 1 G .L.-180
-200
-150
-100
-50
0
50
100
150
0 50 100 150
(s)
(gal)
G 1 G .L.-420
-150
-100
-50
0
50
100
150
0 50 100 150
(s)
(gal)
G 1 G .L.-935
-250
-200
-150
-100
-50
0
50
100
150
200
250
0 50 100 150
(s)
(gal)
Base Acc.
-200
-150
-100
-50
0
50
100
150
200
0 50 100 150(s)
(kgf)
Load
-30
-20
-10
0
10
20
30
0 50 100 150(s)
(mm)
D isp. Act.
Figure 11 Excess Pore Pressures and Accelerations on G-1 line, Accelerations of the Table and the Base and Displacements and Loads of the Actuator (Case 4-2)
0
500
1000
1500
2000
2500
3000
0 1 2 3 4 5
(H z)
Fourier spectra
Behavior of Piles and Soil Measurement data include components of the frequency 3Hz due to excitation of the table and the frequency 1Hz due to forced displacements of the base by the actuator. Hereafter, examinations are focused on separated data by FFT except for excess pore pressure. Case 2-2 Figure 13 shows uplift of excess pore pressures, displacements and loads of the actuator. The actuator applied to the base about 97 seconds. Figure 14 presents relation between displacement and loads of the actuator from 97.24 seconds to 104.24 seconds. Stiffness degrades with time and with progress of liquefaction. Figures 15 shows bending moments of the pile, and excess pore pressures and their ratios on G-1 line. Maximum points of pile bending moments move to the lower with progress of liquefaction. Ratios of excess pore pressures in the lower of the soil are about 0.4. Figure 16 indicate deformations and shear forces derived from approximated bending moments of the pile by spline function. Larger shear forces are found at the lower of the pile.
Figure 12 Fourier Spectrum of Actuator Loads
97.24-104.24(s)
-40
-30
-20
-10
0
10
20
30
40
-15 -10 -5 0 5 10 15
(mm)
(kgf)
Load
0
1
2
3
4
95 100 105 110 115(s)
(kPa)
G 3 G.L.-900
-40
-30
-20
-10
0
10
20
30
40
95 100 105 110 115
(s)
(mm)
Disp. Act.
Actuator displacement starts
-40
-30
-20
-10
0
10
20
30
40
95 100 105 110 115
(s)
(kgf)
Load
Figure 13 Uplift of Excess Pore Pressures, Displacements and Load of Actuator
Figure 14 Load-Displacement Relation of Actuator
Case 4-2 Figure 17,18, 19 and 20 similarly present results of Case 4-2. Forced displacements were applied to the base by the actuator from about 57 seconds to about 105 seconds. Displacements are 0.4cm at the first stage, and increase to about 2cm from about 64 seconds. From relation between displacement and loads of the actuator from 56.0 to 62.99 seconds shown in Figure 17, stiffness of the soil degrades rapidly. Excess pore pressure ratios reach 0.7 except for those in the lowest of the soil, as shown in Figure 18. Compared with Case 2-2, liquefaction of Case4-2 more proceeds. The pile deforms more near to the pile tip, and shear forces of the pile have constant distribution in the middle and the upper of the soil, as shown in Figure 19.
G -1
0
20
40
60
80
100
0 2 4 6 8 10
Excess pore pressure (KPa)
Hight (cm)
98.18(s)
99.15(s)
100.14(s)
101.12(s)
102.11(s)
103.11(s)
104.11(s)
γ*Z
G -1
0
20
40
60
80
100
0 0.2 0.4 0.6 0.8 1
Excess pore pressure ratioHight(cm)
98.18(s)
99.15(s)
100.14(s)
101.12(s)
102.11(s)
103.11(s)
104.11(s)
0
10
20
30
40
50
60
70
80
90
100
-40 -20 0 20 40 60
(Nm )
Hight (cm)
98.18(s)
99.15(s)
100.14(s)
101.12(s)
102.11(s)
103.11(s)
104.11(s)
Figure 15 Pile Bending Moment, Excess Pore Pressure and Ratios of Excess Pore Pressure (Case 2-2)
0
10
20
30
40
50
60
70
80
90
100
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4
(cm )
Height (cm)
98.18
99.15
100.14
101.12
102.11
0
10
20
30
40
50
60
70
80
90
100
-1 -0.5 0 0.5 1 1.5 2 2.5Q (N)
Height (cm)
98.18
99.15
100.14
101.12
102.11
Figure 16 Displacement and Shear Forces of Pile (Case2-2)
-1
0
1
2
3
4
5
6
50 55 60 65 70(s)
(kPa)
G 1 G .L.-900
-30
-20
-10
0
10
20
30
50 55 60 65 70(s)
(mm)
Disp. Act.
Actuator displacement starts
-20
-15
-10
-5
0
5
10
15
20
50 55 60 65 70(s)
(kgf)
Load
Figure 17 Uplift of Excess Pore Pressures, Displacements and Loads of Actuator (Case4-2)
56.0-62.99(s)
-6
-4
-2
0
2
4
6
-6 -4 -2 0 2 4 6
(m m )
(kgf)
Load
Hysterisis loop of high damping ratio
Figure 18 Displacement – Load Relative of Actuator (Case4-2)
0
10
20
30
40
50
60
70
80
90
100
-10 0 10 20(Nm )
Height (cm)
57.83(s)
58.81(s)
59.77(s)
60.76(s)
61.76(s)
62.76(s)
G -1
0
20
40
60
80
100
0 2 4 6 8
Excess pore pressure (Kpa)
Height (cm)
57.83(s)
58.81(s)
59.77(s)
60.76(s)
61.76(s)
62.76(s)
γ*Z
G -1
0
20
40
60
80
100
0 0.2 0.4 0.6 0.8 1
Excess pore pressure ratio
Height (cm)
57.83(s)
58.81(s)
59.77(s)
60.76(s)
61.76(s)
62.76(s)
Figure 19 Pile Bending Moment, Excess Pore Pressure and Ratios of Excess Pore Pressure (Case 4-2)
0
10
20
30
40
50
60
70
80
90
100
-0.1 0 0.1 0.2 0.3 0.4 0.5
(cm )
Height (cm)
57.83
58.81
59.77
60.76
61.76
0
10
20
30
40
50
60
70
80
90
100
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6Q (N)
Height (cm)
57.83
58.81
59.77
60.76
61.76
Figure 20 Displacement and Shear Forces of Pile (Case 4-2)
Stiffness and Damping at Pile Head Figure 21 summarizes the relations of load vs. displacement, stiffness vs. displacement and load vs. average excess pore pressure at the pile head on plus and minus peaks of load vs. displacement relation of the actuator in Case 2-2 and Case 4-2. The figure presents the data in eight cycles from starting time of forced displacements by the actuator.
0
5
10
15
20
25
30
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Displacem ent (cm )
Load at Pile Head (kgf) kg
0
0.5
1
1.5
2
2.5
3
3.5
0 0.2 0.4 0.6 0.8 1
Displacem ent (cm )
Load at Pile Head (kgf) kg
0
20
40
60
80
100
120
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Displacem ent (ｃm )
Stiffness at Pile Head
(kgf/cm)
kg/cm
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1
Displacem ent (cm )
Stiffness at Pile Head
(kgf/cm)
kg/cm
0
5
10
15
20
25
30
0.0 0.2 0.4 0.6 0.8 1.0
Excess Pore P ressure Ratio
Load at Pile Head (kg
f) kg
0
0.5
1
1.5
2
2.5
3
3.5
0 0.2 0.4 0.6 0.8 1
Excess Pore Pressure Ratio
Load at Pile
Head (kg
f)
kg
0
20
40
60
80
100
120
0.0 0.2 0.4 0.6 0.8 1.0
Excess Pore Pressure Ratio
Stiffness at Pile Head
(kgf/cm)
kg/cm
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1
Excess Pore Pressure Ratio
Stiffness at Pile
Head
(kgf/cm)
kg/cm
Figure 21 Load - Displacement Relation, Stiffness - Displacement Relation, Load - Excess Pore Pressure Relation and Stiffness-Excess Pore Pressure Relation.
Case 2-2 Case 4-2
In load vs. displacement relation, load decrease due to liquefaction is recognized. Particularly in Case 4-2, the loads at the pile head become near to zero when the pile head displacements are about 0.4cm. After increasing the displacements at the pile head, as shown in Figure 17, the loads at the pile head increase. Damping is tried to evaluate by a simple method. Energy dissipation in half cycle is derived from the area closed by curve in half cycle and the axis of ordinates. Strain energy in one cycle is derived from the triangle area closed by the maximum displacement point, a vertical line from the maximum displacement point and the origin. Figure 22 presents relationships of damping ratio vs. pile head displacement, and relationships of damping ratio vs. average excess pore pressure in Case 2-2 and Case 4-2. In Case 4-2, damping ratios are very large near to the displacement 0.4cm. At that time, the loops of load vs. displacement incline almost to a horizontal line, as shown in Figure 18. This point has possibility of limitation in the evaluation method. More examinations are needed.
In Case 2-2,damping ratios are evaluated from 20 to 30 percents in the excess pore pressure ratios smaller than 0.7, and at the displacements smaller than 1.2cm. In Case 4-2, damping ratios are evaluated from 30 to 40 percents in the excess pore pressure ratios smaller than 0.5, and at the displacements smaller than 0.4cm. Relationships between Shear Stress and Shear Strain in the Soil
0
5
10
15
20
25
30
35
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Displacem ent (cm )
Dam
ping Ratio (%)
%
0
50
100
150
200
250
300
350
400
0 0.2 0.4 0.6 0.8 1
Displacem ent (cm )
Damping Ratio (％
) %
0
5
10
15
20
25
30
35
0.0 0.2 0.4 0.6 0.8 1.0
Excess Pore Pressure R atio
Damping R
atio (%)
%
0
50
100
150
200
250
300
350
400
0 0.2 0.4 0.6 0.8 1
Excess Pore Pressure Ratio
Damping Ratio (％
) %
Figure 22 Damping Ratio - Displacement Relation and Damping Ratio - Excess Pore Pressure Relation.
Case 2-2 Case 4-2
The above-mentioned stiffness degrading at pile head is derived from decrease of soil stiffness at uplift stage of the excess pore pressures. Relationships of shear stress and shear strain are examined. Shear strains of the soil are calculated by summing the values evaluated from multiplying the average of adjacent two accelerations on G-1 line by density of the soil there. Shear strains are computed as the values derived from dividing relative displacements of adjacent two points on G-1 line by the thickness among the adjacent two points. Adopted displacements are computed by integrating accelerations double. Figures 23 and 24 present the relation ships of shear stress and shear strain on G-1 line in Case 2-2 from 97.97 sec. to 100.97 sec. and Case 4-2 from 57.03 sec. to 63.26 sec., respectively. In Case 2-2 that an average excess pore pressure ratio is 0.65, stiffness degrading at the lower of the soil is small. In Case 4-2 that an average excess pore pressure ratio reaches 0.7, stiffness degrading is large in the whole of the soil.
97.97-102.97(s)
-1.5
-1
-0.5
0
0.5
1
1.5
-0.040 -0.020 0.000 0.020 0.040
Shear Strain
Shear Stress(kN/m2)
18-30cm 97.97-102.97(s)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-0.010 -0.005 0.000 0.005 0.010
Shear Strain
Shear Stress(kN/m2)
30-42cm
97.97-102.97(s)
-3
-2
-1
0
1
2
3
-0.0010 -0.0005 0.0000 0.0005 0.0010
Shear Strain
Shear Stress(kN/m2)
72-93.5cm
Figure 23 Relation Between Shear Stress and Shear Strain (Case 2-2, G-1 Line)
97.97-102.97(s)
-3
-2
-1
0
1
2
3
-0.002 -0.001 -0.001 0.000 0.001 0.001 0.002
Shear Strain
Shear Stress(kN/m2) 54-72cm97.97-102.97(s)
-3
-2
-1
0
1
2
3
-0.003 -0.002 -0.001 0.000 0.001 0.002 0.003
Shear Strain
Shear Stress(kN/m2)
42-54cm
0
10
20
30
40
50
60
70
80
90
100
-10 0 10 20 30 40 50
kh(N/m3)
Height (cm)
98.18
99.15
100.14
101.12
102.11
0
10
20
30
40
50
60
70
80
90
100
-10 0 10 20 30 40 50
kh(N/m3)
Height (cm)
57.83
58.81
59.77
60.76
61.76
Figure 25 Change in Coefficient of Subgrade Reaction
Coefficient of Subgrade Reaction (Case4-2) Coefficient of Subgrade Reaction (Case2-2)
57.03-63.26(s)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-0.04 -0.02 0.00 0.02 0.04
Shear Strain
Shear Stress(kN/m2)
18-30cm57.03-63.26(s)
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03
Shear Strain
Shear Stress(kN/m2)
30-42cm
57.03-63.26(s)
-1.5
-1
-0.5
0
0.5
1
1.5
-0.02 -0.01 0.00 0.01 0.02
Shear Strain
Shear Stress(kN/m2)
42-54cm57.03-63.26(s)
-1.5
-1
-0.5
0
0.5
1
1.5
-0.02 -0.01 0.00 0.01 0.02
Shear StrainShear Stress(kN/m2)
54-72cm
57.03-63.26(s)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-0.004 -0.002 0.000 0.002 0.004
Shear Strain
Shear Stress(kN/m2)
72-93.5cm
Figure 24 Relation Between Shear Stress and Shear Strain (Case 4-2, G-1
Degrading of stiffness at the pile head is derived from degrading of soil stiffness. Through examining relations of shear stress vs. shear strain in the soil at some heights of the soils in Cases 2-2 and 4-2, coefficients of horizontal subgrade reaction in the pile are derived at an uplift stage of excess pore pressures. The coefficients are calculated from subgrade reactions by differentiating shear forces of the pile, and from relative displacement of the pile. Figure 25 presents the coefficients of subgrade reaction in the pile. With progress of liquefaction, the coefficients in the upper of the soil gradually decrease, and reactions of the soil also decrease. In Case 4-2, where excess pore pressure ratios reach 0.7, the coefficients become almost zero at almost all heights of the soil.
CONCLUDING REMARKS 1. Combination of shaking table tests and oscillator tests or actuator tests is an effective tool for clarifying dynamic behavior and the change of saturated soil properties in liquefaction process from viewpoint of soil-structure interaction 2. The oscillator tests in large-scale shaking table tests can clarify some change of soil properties, especially stiffness and damping in dissipation process of excess pore water pressures. When average pore pressure ratio is high, stiffness and damping of soil are very small. With progress of the dissipation from the lower part to higher part of the soil, stiffness and damping of the soil both increase, and the fundamental natural frequency of the soil becomes recognized. 3. The hydraulic servo actuator tests in medium-scale shaking table tests can determine change of stiffness and damping, and those at pile head at uplift stages of excess pore water pressure. Damping ratios at pile head are profoundly affected by excess pore pressure distribution in the soil and displacements at pile head, and evaluated approximately from 20 to 40 percents at uplift stages of excess pore water pressures.
REFERENCES 1. Mizuno H., “Pile Damage During Earthquakes in Japan (1923-1983),” Geotechnical Special Publication,
No.11, ASCE, Dynamic Responses of Pile Foundation – Experiment, Analysis and Observation, pp53-78, April, 198
2. Mizuno H., Hirade T. and Iiba M. ”Dynamic Behavior of Pile Foundation – Dynamic Characteristic Determination by Oscillator Tests.” Proceedings of The Third Seminar of “Enhancement of Earthquake Performance of Infrastructures Based on Investigation into Fracturing Process”, pp253-258, February 2002 (in Japanese)
3. Mizuno H. and Hirade T. “Stiffness and Damping of Soil-Pile System in Liquefaction Process.” Proceedings of the Eight U.S. Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures Against Liquefaction Technical Report MCEER-03-0003, pp 559-570, June 30, 2003, Multidisciplinary Center for Earthquake Engineering Center Research (This workshop was held December 16-18, 2002 at Edmont Hotel, Tokyo)
Coefficients of Reaction Subgrade
