Decomposition of Dynamic py Curves Considering Liquefaction during Earthquakes

Abstract: There is an established fact known that, there is a relation between the p-y resistance of piles and liquefaction formation. To investigate this fact, a single pile foundation in liquefiable soils composed of liquefiable sand and overlying soft clay was subjected to sinusoidal shaking motions will be tested. That is the basic purpose of this study was to analyze and construct a p-y curve of liquefied soil under different shaking loading conditions companied with the effects of several key design parameters were undertaken to understand the effect of pile characteristic and pore water pressure response in the zones of responding area.


INTRODUCTION
All the accumulate damaged on the pile foundations was caused by soil liquefaction during earthquakes (Abdoun and Dobry, 2002;Boulanger et al., 1999).Most of that damage is a companion to the movement of the ground, which induced by this phenomenon.Trial prediction to address the p and y behavior had been done by Kagawa et al. (1994), Tokimatsu and Asaka (1998), Cubrinovski et al. (2006), Chen et al. (2007) and Yuan et al. (2010).These trial prediction was helpful by giving results which made other researchers to find the explanation of pore pressure response influences around a pile and its effect on dynamic p-y behavior, this study will be focused on p-y curves (shape, changing behavior, magnitude and developing) at various levels of pore water pressure ratio (r u ) under different shaking loading magnitude and shaping.In the next sections, simulation, protocol and results are presented.

NUMERICAL MODELING OF SHAKE-TABLE TEST SYSTEM
An open source, object-oriented nonlinear finite element analysis framework OpenSees (Mazzoni et al., 2009), is employed throughout the study to model geotechnical systems and simulate their response under seismic loads (http://opensees.berkeley.edu).A twophase (fluid and solid) fully-coupled finite element formulation is adapted based on Biot (1955) theory and the saturated soil is modeled as porous media.A simplified numerical modeling of this theory, known as u-p formulation, was implemented to simulate dynamic response of soil-pile interaction in lateral spreading sand stratums and is expressed in the following matrix form (Chen et al., 1998): A simplified numerical modeling of this theory, known as u-p formulation (Zienkiewicz and Shiomi, 1984;Chan, 1988), is implemented to simulate the dynamic response of saturated sand.The solid-fluid fully coupled 3D 20-8 node elements (brickUP) are used to model the saturated soil (Parra, 1996;Yang and Elgamal, 2004;Elgamal et al., 2002Elgamal et al., , 2003;;Yang et al., 2003).This element is a hexahedral linear isoparametric one with dependent excess pore pressure based on the Biot's theory of porous materials, where twenty nodes represent the solid translational degrees of freedom, with the eight-corner nodes also describing the fluid pressure (Lu, 2006).The clay soil domain is expressed Clay is modeled as a nonlinear hysteretic material (Parra, 1996;Yang and Elgamal, 2004;Yang et al., 2003) with a Von Mises multi-surface kinematic plasticity model (Iwan, 1967;Mroz, 1967).This model emphasizes on the reproduction of soil hysteretic Elasto-plastic shear response, including permanent deformation and the plasticity is exhibited only in the deviatoric stress-strain response (Kondner, 1963).

Model design and layouts:
In the 3D model, there is circle reinforced concrete pile-column.The pile is 0.2 m in diameter and 1.92 m in length with Young modulus equal to 2.08×10 4 (MPa) is tested to simulate the response of pile foundation subjected to soil liquefaction under nearly harmonic base excitations with dynamic sine wave.A rigid mass of 240 kg is set and fixed on the pile head as the superstructure.The soil profiles used in the test consist of two horizontal soil strata.The underlying stratum with 1.2 m thickness is modeled as saturated sand with the upper "model clay" stratum with 0.3 m thickness being weaker reconstituted silty clay.The sand stratum in each model is constructed by the sedimentation method (sand deposition in water).Water table level is located at 0.3 m near the soil interface between clay stratum and liquefiable sand stratum.
In the 3D model, the pile and column are modeled as 3D elastic beam-column elements available in FE model.
Mesh for the 3D FEM modeling is shown in Fig. 1.Length in the longitudinal direction is 3.8 m, while that in transversal direction (in this mesh configuration) is 1.5 m.
The detailed characteristics of the constitutive model for sand and clay and pile for the linear beam elements are defined in Table 1 and 2 (Al-Maula Baydaa, 2013).

Numerical modeling:
Events used in the test: The test program was listed in Table 3.The suite of shaking events began with lowlevel shaking and then successively progressed through very strong motions (0.5 g 1 Hz) to cause soil liquefaction.

RESULTS AND INTERPRETATION
Parametric study: Pile characteristic effects (Pile diameter): Effect of pile diameter on soil-pile interaction at different depths is presented in Fig. 2 to 4. The lateral displacement significantly decreases with using larger diameter pile.The magnitude of lateral acceleration of pile greatly influenced by pile diameter, resulting in the decrease of y at pile head and 0.4 m depth as pile diameter increases from 0.1 m to 0.3 m (Fig. 2 to 4).
The effectiveness of pile diameter in reducing liquefaction-induce lateral displacement can further be improved by enlarging the pile diameter to provide a larger surrounding area and thus, more resistance to hold the ground deformation during an earthquake.
It could be observed that the computed soil displacements around the pile perimeter always increase gradually until they suddenly enlarge at about 3 to 5 Sec and still show higher oscillation during the shaking, which is consistent with the trend of pile bending moments on the pile.The magnitude of lateral

Pile characteristic effects (Pile stiffness):
The representative elastic moduli of pile Ep (i.e., 1.0×10 4 MPa and 4.0×10 4 MPa) are chosen where Es equal to 16.6 MPa for medium-dense sand.Figure 5 shows the effect of pile stiffness ratio as Ep/Es equal to 600 and 2400 on the lateral pile displacements.The maximum pile displacements are around 0.02 mm (Fig. 5).It is observed that the increasing pile stiffness seems to have limited effects on reducing the pile deformations (p and y).While pile acceleration time history response had anther behavior, with the stiffness ratio increases, the pile acceleration response decreases, specially at shallow depth more than at deeper depth (1.2) m, again Fig. 6 shows a smaller stiffness ratio; pile more prone to maximum bending moment.
Pore water pressure ratio Development (r u ): As mentioned earlier the basic aim of this study was to specify p-y curves at levels of r u less than 1.0.To generate these curves, numerical simulation using OpenSeesPL will be applied to constructed these curves.
Results from the numerical p and y time histories at a depth of 0.5, 0.9 and 1.2 m are presented in Fig. 7 for event A and E earthquake event.The upper sand layer liquefied early in shaking for both events as shown in Fig. 7a and b.In event E, for early stages liquefaction take place, with produce a basic resistance (p) with larger relative displacements (y) >0.5 mm at 0.5 m depth with generated high pore pressure ratios in event E except event A, where there is no sing for liquefaction.
Figure 8 show the relationships of (y, p and r u ) as a peak value in events A to E as well as at 0.2 m pile diameter as a dynamic p-y curves as shown together in Fig. 8.The relationships of y and p and at different r u show that the motion amplitude has a significant effect on the relative displacement at specific pore pressure ratio.
The lateral resistance (p) decreases with increasing relative displacement (y) (Fig. 8), which makes the p-y curves softening.No matter of whether the pile pushes the soil or vise versa.The increase in lateral resistance (P) has a relation with the decrease in average pore pressure Fig. 8.The higher the lateral resistance is, during the early stage of liquefaction.This result confirm that the motion (amplitude and shaping) has a significant effect on the pore pressure reduction and the p-y behavior during liquefaction, this finding agree with the results of Fig. 8 for different earthquake amplitude.
The effect of pore pressure ratio on p-y behavior is illustrated in Fig. 9 by the curve fit for p and y (Peak value) for depth 0.5 m.The p values progressively decrease relative to y.

CONCLUSION
Numerical tests were performed using pilesupported structures founded in medium-dense (Dr ≈ 58%) sand profile and subjected to a range of earthquake input motions.Soil-pile interaction was investigated in terms of the dynamic p-y curves through under variation of r u .
Results are presented to document the construction p-y curves under dynamic pore pressures developed using empirical curve fitting.The empirical fitting p-y curves at various levels of r u are presented.In general, it can come to conclude that the increase in the pile diameter has an importance of substrate with little deformation of the soil during the liquefaction process, as well as an increase of soil resistance.
As summarized to the effect of pile characteristics under different cases.Note that the moment on the pile in the sand gradually increases from the bottom to the top in 600 to 2400 ratio and 0.1 to 0.3 diameters.The moment on the pile is larger in larger ratio and diameter.The time when the maximum moment occurs agrees well with the peak sand displacement in all pile characteristics effects.
-displacement matrix ′ = Effective stress tensor which is determined by soil constitutive model Q = Discrete gradient operator coupling solid and fluid phases p = Pore pressure vector S = Compressibility matrix H = Permeability matrix Vectors f u and f p represent the effects of body forces and prescribed boundary conditions for solidfluid mixture and fluid phase respectively.

Fig. 1 :
Fig. 1: Finite element modeling by 20-node brick element without considering excess pore pressure.Clay is modeled as a nonlinear hysteretic material(Parra, 1996;Yang and Elgamal, 2004;Yang et al., 2003) with a Von Mises multi-surface kinematic plasticity model(Iwan, 1967;Mroz, 1967).This model emphasizes on the reproduction of soil hysteretic Elasto-plastic shear response, including permanent deformation and the plasticity is exhibited only in the deviatoric stress-strain response(Kondner, 1963).

Fig. 8 :
Fig. 8: Curve fitting of p-y curve for different pore pressure ratio at 0.5 m depth under Sine wave (0.1g-0.5 g 1 Hz)

Table 3 :
Suite of shaking events