Volcanic Ash 2 OUTLINE OF THE EXPERIMENTS 3 STATIC HORIZONTAL LOADING TEST (50 G)

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1 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 5 G. Based on these experiments, two important factors in the seismic design of pile foundations were studied: horizontal static subgrade reaction (K h ) and horizontal dynamic subgrade reaction (K he ). The relationship between these two factors, expressed as K he =αk h, 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 5 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 (K h ) y reaccion dinamica horizontal de la subrasante (K he ). Su relacion, expresada por K he = αk h, 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. 1 INTRODUCTION Current seismic designs (Japan Road Association, 199 and, Ogawa and Ogata, 1997) for pile foundations in Japan require analysis of the seismic behaviour of the pile using the traditional seismic coefficient method, seismic horizontal load-carrying capacity method and the dynamic analysis method. These design methods share the same structural engineering consideration: the provision of a certain degree of deformation capacity under seismic force. However, in assessing the seismic resistance of the ground, the ground spring during an earthquake (dynamic coefficient of horizontal subgrade reaction) is determined largely based on the static spring of the soil, i.e., a soil constant, rather than on ground strength, which can be determined using soil survey results. Since the pile foundation is surrounded by ground, it is generally considered to generate virtually no response vibrations. However, the pile foundation does react to seismic motion, which triggers simultaneous response displacement of the surrounding ground. During an earthquake, seismic force acts on the pile foundation, and the force is transmitted to the superstructure. The response of the superstructure is returned to the ground as inertial force. These forces act differently from earthquake to earthquake because the waveforms of seismic motions are different in each earthquake. For this reason, the seismic behavior of pile foundations is very complicated, and the present seismic design method does not satisfactorily address this

2 complexity. Analysis of the seismic behavior of the pile foundation requires a clear understanding of spring characteristics and other complicated soil factors during an earthquake, such as nonlinear factors. To accurately assess the seismic resistance of pile foundations, this research focused on the spring constant for foundations built in volcanic ash soil, which is widely distributed throughout Hokkaido. A series of centrifuge experiments was conducted to test the static horizontal load and dynamic vibration of single piles under a centrifugal acceleration of 5 G. Elements considered important to the seismic design of pile foundations were examined by comparing the characteristics of the coefficient of dynamic horizontal subgrade reaction of the pile (K he ) with those of the coefficient of static horizontal subgrade reaction (K h ). OUTLINE OF THE EXPERIMENTS could accurately represent conventional steel piles (φ = 5 mm, t = mm) (Table 1). The centrifuge generated a centrifugal acceleration of 5 G. The bearing layer consisted of soil cement, and the embedding depth was three times the length of the pile diameter. The soil used for the experiment was disturbed volcanic ash soil collected from the Lake Shikotsu area, a type of soil that is considered to be unique to Hokkaido. Soil was poured from a set height to ensure that the model ground was of uniform soil quality. For the vibration experiment, strain gauges were installed on the pile. Accelerometers were placed at points far enough from the strain gauges that the behavior of the pile would remain unaffected at the depths of the strain gauge locations. A static horizontal loading test and dynamic loading tests using white noise and sine waves were also conducted. In the dynamic loading tests, a 4-g weight (.4 kg x 5 3 = 5 tf) was installed on the pile head to represent the bridge substructure. The experiments were conducted using a model steel pile on a scale of 1:5 (φ = mm, t =. mm) in a steel container (Figure 1) with internal dimensions of 7 x x 35 mm (L x W x H). The scale was set at 1:5 so that the model pile Accelerome Strain gauge Volcanic Ash Soil Cement Model pile 19ch Weight P1 5ch P 4ch P3 3ch P4 P5 P Figure 1 Experimental container Table 1 Scale factors for the experiment ch 1ch 17ch 3 STATIC HORIZONTAL LOADING TEST (5 G) A static horizontal loading test of the pile was conducted using the multi-cycle strain control method, which employs a horizontal loading device. The loading rate was 3 Notation Unit Scale Experimental size Real size Ground Thickness H g1 m 1/ λ Bearing ground thickness H g m 1/λ.4. Embedding depth L m 1/λ.3 1. Outer diameter D m 1/λ..5 Pile Plate thickness t m 1/λ.. Modulus of elasticity E Tf/m 1.1x 7.1x 7 Geometrical moment of inertia I m 4 1/λ x x -11 Cross-sectional area A m 1/λ.1575x Structure Weight M S Tf 1/λ 3.4x Height H S m 1/λ Vibration acceleration α g λ (1) (.) Note: 1/λ = model/real = 1/5 4.5 mm/min. at the model pile head. Pile displacement was measured using laser displacement gauges, and pile stress was determined with strain gauges. The permissible displacement (δ) for this test was set at.3 mm, which is equal to the permissible displacement of the full-size pile (15 mm) divided by 5 G. This test displacement was used as a criterion for pile displacement. The duration of full virgin load application was approximately 15 min., in compliance with the standard set by the Japanese Geotechnical Society (193). To calculate the static subgrade reaction, the pile foundation was regarded as the beam of the elastic foundation of the skeletal model, and a Winkler spring model was constructed for use in the analysis of the coefficient of subgrade reaction (Figure ). The vertical distribution and the coefficient of subgrade reaction were used as parameters for the trial calculation. This calculation was performed to determine the values

3 that would produce agreement between the experimental distribution of displacement at the pile head and pile stress in the ground and those estimated from the analysis. The static subgrade reaction coefficient (K h ) was defined as the area of the coefficient of subgrade reaction (A) divided by depth (Z), as seen in Figure 3. The coefficient of static subgrade reaction was found to be 5,5 kn/m from the results of the experiments and the analysis carried out by recreating the experimental situations. In making this calculation, it was assumed that the distribution of the coefficient was uniform (Figures 4 and 5). Fitting of bending moment curves was performed using theoretical and experimental values of flexural rigidity of the pile in volcanic ash soil to analyze the vertical distribution of rigidity. In the experimental ground, rigidity 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: - The depths of the peak points of the bending moment were constant with respect to load value. - Displacement at the pile head was approximately 1 mm (% of the pile diameter), yet it did not affect the rigidity of the ground. - Linear representation of the strain value of the pile material was possible. Distance from the pile head (m) Distance from the pile head (m). -. Y =-1.7E X +.39E-3 X:Distance from the pile head Y:Coefficient of subgrade reaction Area (A) 4 Spring value (constant) 4114 Upper layer Lower layer Figure 3 Coefficient of subgrade reaction Depth range of the spring value (upper layer) Depth range of the spring value (lower layer) Theoretical value 4kN/m Theoretical value 5kN/m Theoretical value 55kN/m Theoretical value 55kN/m Experimental value (Load:.1kN) Experimental value (Load:.59kN) Experimental value (Load:.39kN) Experimental value (Load:.5kN). 1.x -3.x -3 3.x -3 δ (m) Figure 4 Distribution of vertical displacement Figure Analytical model Distance from the pile head (m) Theoretical value 4kN/m Theoretical value 5kN/m Theoretical value 55kN/m Theoretical value 55kN/m Experimental value (Load:.1kN) Experimental value (Load:.59kN) Experimental value (Load:.39kN) Experimental value (Load:.5kN) Depth range of the spring value (upper layer) Depth range of the spring value (lower layer) -4.x -3-3.x -3 -.x -3-1.x x -3 M (kn m) Figure 5 Distribution of the vertical bending moment

4 4 COEFFICIENT OF DYNAMIC SUBGRADE REACTION 4.1 Method used for calculation of the coefficient of subgrade reaction In the current specifications for highway bridges, the correction coefficient, α, is used to assess ground rigidity and determine the coefficient of dynamic subgrade reaction rather than the coefficient of static subgrade reaction. In this study, the coefficient of subgrade reaction was calculated using two methods (p-δ and eigenvalue analysis), and then compared with the coefficient of static subgrade reaction to determine the correction coefficient. 4. Analysis of the coefficient of subgrade reaction using the p-δ curve (p-δ method) (1) Calculation using the p-δ method To calculate the coefficient of subgrade reaction caused by interaction between the ground and the pile (K he1 ), the interaction force (p) was divided by relative displacement (δ). Figure shows the process used to make this calculation. The level of vibration was determined based on the assumption that displacement is minimal, i.e., the plasticity of the pile and the ground was not considered. Fourier spectrum of acceleration Bandpass filter Fourier transformation for speed and displacement calculation Third-degree function using the four-point method Ground displacement Strain Relative displacement Bending moment Second-order integral Pile displacement Figure Process of the p-δ method Second derivative Subgrade reaction Recent research studies and analyses have revealed that relative displacement and relative interaction force, both of which are used to calculate the coefficient of dynamic subgrade reaction, change with respect to the number of P1 Strain (µ) 19ch Acceleration (G) ch Voltage (mv) 1ch Acceleration (G) vibrations (i.e., they are frequency dependent). In this study, analysis was performed at the natural frequency of the pile foundation, which best reflects the relative displacement of the pile and the ground, to develop a new method for calculating the coefficient of dynamic subgrade reaction. The coefficient of dynamic subgrade reaction calculated from the interaction force of the pile and the ground was compared with the coefficients of dynamic and static subgrade reaction. () Natural frequency of the pile foundation in volcanic ash soil A sine-wave-based experiment was conducted on the pile foundation by applying the vibration of white noise (a waveform with a frequency of between and 35 Hz) to clarify its natural frequency. The analysis results for the Fourier transformation characteristics and the transfer function indicated that the natural frequency of the pile foundation was between 55 and 5 Hz under the conditions of white noise vibration when the weight was 4 g (Figures 7, and 9). Based on the Fourier transformation characteristics and the transfer function obtained in the sine-wavevibration experiment (Figure ), the natural frequency of the pile foundation in volcanic ash soil was found to be.5 Hz. Acceleration and strain calculated from this frequency value were used for analysis Time (sec) Figure 7 White noise W = 4 g Dyn. Amp. =.4

5 Fourier amplitude ratio g Frequency (Hz) taken at six points, the equation for curve fitting was approximated using a multi-term fifth-degree function. Equation 1, the second derivative of this function, was used to calculate the subgrade reaction. It was hypothesized that the function of the subgrade reaction could be approximated using a curve from the third-degree function. Figure 19ch/17ch Transfer function Dyn. Amp. =.4 Fourier amplitude ratio Figure 9 P1/17ch Transfer function Dyn. Amp. =.4 Fourier amplitude Fourier amplitude Fourier amplitude Fourier amplitude g Frequency (Hz) P ch/17ch P3 ch/17ch Nominal frequency (Hz) 19 ch/17ch P1 ch/17ch Figure Transfer function of the sine wave W = 4 g Dyn. Amp. =.4 (3) Calculation of relative displacement and subgrade reaction To calculate displacement of the pile, the bending moment must be identified from pile strain values after which curve fitting must be performed (Figure 13). Since measurements were 5ch Displacement (m) d M = q( x) dx (1) d y EI = M ( x) dx () The constants of a multi-term second-order integral (Equation ) were assessed by setting the boundary conditions of the deflection angle (θ) and displacement (δ) at the pile s lower end at zero because that end is fixed by soil cement. Due to the limitations of the experimental apparatus, direct measurement of displacement was not possible in the ground. The second-order Fourier integral of the equation for ground acceleration was used to calculate displacement (Figures 11 and 1). For calculations necessary for correcting the displacement axis, bandpassing from 5 to 1, Hz was performed. The coefficient of subgrade reaction could be calculated because the above procedure enables the computation of displacements of the pile and the ground and subgrade reaction. 5ch Acceleration (G) Time (sec) Experimental acceleration Figure 11 Sine wave.5 Hz Dyn. Amp. =.4.x x -4 1.x -4 5.x x -5-1.x x -4 -.x Time (sec) Figure 1 Sine wave.5 Hz Dyn. Amp. =.4

6 . Volcanic ash.5hz D=.4 W=4g. Volcanic ash.5hz D=.4 W=4g sec sec (Maximum shear strain) sec sec -.x -3-1.x x -3.x -3 Pile bending moment (kn m) Figure 13 Distribution of the bending moment at different times (4) Analysis results Dynamic coefficient of the ground The time-history displacement (pile, ground and relative), and the distribution of subgrade reaction and its coefficient are shown in Figures 14 to 1. Curves were determined for approximation based on the distribution of the coefficient of subgrade reaction. A curve that represents the average values of all the curves was identified, and the average value of the curve identified was found to be 1,4 kn/m, from which the value of dynamic spring was estimated Volcanic ash.5hz D=.4 W=4g t=.1 sec -4.x -4 -.x -4..x -4 4.x -4 Pile displacement (m) Figure 14 Pile displacement at different times. -. Volcanic ash.5hz D=.4 W=4g sec sec (Maximum shear strain) sec sec -1.x -4-5.x x -5 1.x -4 Figure 15 Relative displacement of the ground at different times 5 7 t=.1 sec Relative ground displacement (m) t=.1 sec sec sec (Maximum shear strain) sec sec Subgrade reaction of the pile (kn/m) Figure 1 Subgrade reaction of the ground at different times. -. Volcanic ash.5hz D=.4 W=4g x -4 -.x -4..x -4 4.x -4 Figure 17 Relative ground and pile displacement at different times. -. Figure 1 Vertical distribution of the coefficient of subgrade reaction 11 t=.1 sec sec sec (Maximum shear strain) sec sec Relative ground and pile displacement (m) Volcanic ash.5hz D=.4 W=4g Average value of all data Average value of the fitted curve up to.3 m deep Fitted curve of the average value of all data Coefficient of subgrade reaction (kn/m ) Coefficient of dynamic subgrade reaction Estimated average value 14 kn/m

7 Pile displacement For the pile displacement mode, the primary mode is dominant because of the tremendous effect of one mass point (4-g weight). The distribution of bending stress for the pile indicates that a large bending moment originates from a depth of approximately 4 mm, at which the ground shows significant displacement. Looking at the displacement found through curve fitting of the bending distribution and a second-order integral, the displacement of the pile indicates the first vibration mode. Ground displacement It can be seen that the time-history displacement of the ground found by accelerometers placed in the ground does not indicate the first vibration mode as is the case in the displacement of the pile. The low-frequency component is larger than the vibrational component due to the effect of surface waves caused by the use of a fixed container. Therefore, in the dynamic experiment, the ground displacement mode is considered to be high because the surface part is affected by both base vibrations and surface waves due to the effects of the container. 4.3 Analysis of the coefficient of dynamic subgrade reaction using an eigenvalue (eigenvalue analysis) Most research on the dynamic interaction between piles and ground employs methods such as second- and third-order FEM and the Penzien model for experiments and analyses. The specifications for highway bridges, which were revised in March, however, use the normal correction coefficient, α, to assess ground rigidity and determine the coefficient of dynamic subgrade reaction for dynamic and other analyses. By focusing on this correction coefficient, this experiment adopted the use of an analysis model, which was used for both analysis of the coefficient of static subgrade reaction and eigenvalue analysis (mode analysis by free vibration) of the coefficient of dynamic subgrade reaction. The value of the spring coefficients of the pile was set as a parameter to assess the coefficient of dynamic subgrade reaction (K he ) at the natural frequency of the pile foundation obtained from the experiment. The assumptions made for the eigenvalue method are as follows: The pile and the ground are in the linear region. Characteristic frequency (Hz) For analysis of vertical distribution of ground rigidity, the distribution used in the horizontal static subgrade reaction test is utilized. Bending rigidity of the pile is determined based on the bending test, and the conditions of the pile s lower end are constant. The spring coefficients of the pile are from a discrete spring (Winkler) in the analysis model. According to these hypotheses and the eigenvalue method, a coefficient of dynamic subgrade reaction of 1, kn/m was obtained. Figure 19 shows the results of the analysis Figure 19 Computation of the coefficient of dynamic subgrade reaction using the dominant frequency of the ground 4.4 Coefficient of dynamic subgrade reaction: comparison between dynamic reaction and static reaction The coefficient of dynamic subgrade reaction acquired from the dynamic centrifugal experiment was compared with the coefficient of static subgrade reaction. The coefficient of dynamic subgrade reaction is 3.3 times greater in the p-δ method and.3 times greater in the eigenvalue method (Table ). Table Theoretical value based on the analysis Fitted strait line Dominant frequency of volcanic ash.5hz (experimental value) Theoretical coefficient of dynamic subgrade reaction of volcanic ash 1kN/m Comparison of the coefficient of subgrade reaction (volcanic ash) K he 3 Coefficient of dynamic subgrade reaction (kn/m ) 4 α=k he /K h p-δ method (K he1 ) kn/m 1,4.3 Eigenvalue method (K he ) kn/m 1, 3.3 5

8 The same methods were applied to assess silica sand and kaolin clay. The results differed according to soil type (Table 3); thus, the coefficient of dynamic subgrade reaction should not be determined solely from the coefficient of static subgrade reaction. Seismic resistance should be assessed with reference to soil type. Table 3 Comparison of the coefficient of subgrade reaction by soil type Silica sand Kaolin clay Volcanic ash K h KN/m, 4, 5,5 K he1 KN/m 7,4 15,5 1,4 K he KN/m 55,5 13,7 1, K he1 /K h CONCLUSIONS A series of dynamic centrifuge model 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 reaction. The following results were found: 1) The vibration experiment conducted using the centrifuge apparatus roughly clarified the dynamic characteristics of ground and piles by soil type. ) According to the p-δ method, the coefficient of horizontal dynamic subgrade reaction, K he1, is 7,4 kn/m for silica sand, 15,5 kn/m for kaolin clay and 1,4 kn/m for volcanic ash. The coefficient of dynamic subgrade reaction (K he1 ) divided by the coefficient of static subgrade reaction (K h ), α, is 1.4 for silica sand, 3.9 for kaolin clay, and.3 for volcanic ash. 3) The coefficient of dynamic horizontal subgrade reaction changes with respect to strain and frequency. The coefficient of horizontal static subgrade reaction, K he, determined using the eigenvalue method, differs depending on the vibration mode and dominant frequency of the pile (eigenvalue), both of which are affected by soil type. dynamic analysis method are currently used in the design of pile foundations. These methods employ a ground constant to define, in a fairly simple manner, the dynamic subgrade reaction (during an earthquake) of the pile foundation, K he, which is considered to be an important factor in assessing seismic resistance. A series of horizontal dynamic centrifuge model experiments was conducted to analyze the dynamic subgrade reaction of silica sand, kaolin clay and volcanic ash. The results differed according to the soil type due to dynamic interactions between the pile and the ground. To appropriately assess the coefficient of horizontal dynamic subgrade reaction, K he, new concepts are necessary for the creation of seismic designs for pile foundations (Wang et al,, Meymand, 199, Tomisawa et al, 1). Such new seismic designs should address both the soil and response characteristics of the pile and the ground while maintaining the advantages of the current design. In the future, dynamic characteristics according to soil type will be examined in terms of nonlinear characteristics and pile displacement. REFERENCES Japanese Geotechnical Society (193): Horizontal Loading Test Method for Piles and Instruction Manual. (in Japanese) Japan Road Association (199): Reference Concerning Application of "Specifications Concerning Restoration of Highway Bridges Damaged by the Hyogo-ken Nambu Earthquake" (draft). (in Japanese) Japan Road Association (): Specifications for Highway Bridges with Instruction Manual V - Seismic Design Edition, pp.- 1. (in Japanese) Meymand (199): Shaking Table Scale Model Tests of Nonlinear Soil-Pile-Super Structure Interaction in Soft Clay. Ogawa and Ogata (1997): Verification of Vibration Resistance by Dynamic Analysis : Foundation Work, vol. 5, No. 3. (in Japanese) Tomisawa et al (1): Dynamic Horizontal Subgrade Reaction of Pile by Dynamic Centrifuge Model Test, Proceedings of the 5th Academic Lecture Meeting of Japan Society of Civil Engineers. (in Japanese) Wang et al (): Experimental Consideration of Dynamic Interaction between Pile Foundation and Ground Using a Large Shear Soil Layer, Proceedings of the Japan Society of Civil Engineers. (in Japanese) The seismic coefficient method, the seismic horizontal load-carrying capacity method and the