Numerical Evaluation of The Nonlinear Behavior of Soil-Pile Interaction Under The Effect of Coupled Static-Dynamic Loads

Liquefaction of saturated soil layers is one of the most common causes of structural failure during earthquakes. Liquefaction occurs as a result of increasing pore water pressure, whereby the rise in water pressure occurs due to unexpected change in stress state under short-term loading, i.e., shaking during an earthquake. Thus, general failure occurs when the soil softens and eliminates its stiffness against the uplift pressure from the stability of the subsurface structure. In this case, the condition of soil strata is considered undrained because there is not enough time for the excess pore water pressure to dissipate when a sudden load is applied. To represent the non-linear characteristics of saturated sand under seismic motions in Kobe and Ali Algharbi earthquakes, the computational model was simulated using the UBCSAND model. The current study was carried out by adopting three-dimensional-based nite element models that were evaluated by shaking table tests of a single pile model erected in the saturated soil layers. The experimental data were utilized to estimate the liquefaction and seismicity of soil deposits. According to the results obtained from the physical models and simulations, this proposed model accurately simulates the liquefaction phenomenon and soil-pile response. However, there are some differences between the experiment and the computational analyses. Nonetheless, the results showed good agreement with the general trend in terms of deformation, acceleration, and liquefaction ratio. Moreover, the displacement of liqueed soil around the pile was captured by the directions of vectors generated by numerical analysis, which resembled a worldwide circular ow pattern. The results revealed that during the dynamic excitation, increased pore water pressure and subsequent liquefaction caused a signicant reduction in pile frictional resistance. Despite this, positive frictional resistance was noticed through the loose sand layer (near the ground surface) until the soil softened completely. It is worth mentioning that the pile exhibited excessive settlement which may attribute to the considerable reduction, in the end, bearing forces which in turn mobilizing extra end resistance.


Introduction
Several studies have recently focused on the effect of dynamic excitation on the soil-structure behavior. The phenomena of soil uidization have been noticed and considered a major concern when the soil layers are fully saturated. Terzaghi and Peck in 1967, presented a new phenomenon named "spontaneous liquefaction" and they described it as an abrupt loss of a soil strength of the loose sand, which in turn created ow slides owing to a minor disturbance. Mogami and Kubo (1953) reported the same occurrence noted after earthquakes. This phenomenon has been studied extensively since 1964 due to the Niigata earthquake which was de nitely the incident that brought the soil liquefaction to the attention globally. In 1964 and 1995, two larger earthquakes in Niigata and Kope, respectively, demonstrated the magnitude and scope of destruction that soil liquefaction may produce (Robertson and Wride 1998). Therefore, liquefaction was considered as a signi cant design aw for constructions in saturated sand soils i.e., earth dams. Mory et al. (2007), studied the effect of the intense wave loading on a vertical wall and the liquefaction was signi cantly detected at the wall toe. Sakai et al. in 1992, identi ed the liquefaction phenomenon in the sand as a transient phenomenon, and Michallet et al. in 2009 stated that this phenomenon was caused by the trapped air bubbles inside the soil layers. Tzang and Ou in 2006, named this phenomenon as soil uidization and stated that the critical over-pressure (for liquefaction development) is reached when the excess pore water pressure becomes close to the static soil pressure. In fact, the excess pore water pressure develops inside the soil as a result of the cyclic loading of an earthquake. This increase in pore pressure may cause a signi cant reduction in soil strength, thus in turn the soil layer behaves as a liquid-like form. Kenan H. and Maksat O. in 2019, studied seismic excitation of an actual soil layer, they used 29 saturated sand samples and performed a set of laboratory experiments to investigate the seismic loadings. Their results showed that the liquefaction phenomenon is less pronounced at the soil layer in shallow depth. Additionally, even if the produced excess pore pressure is not high enough to induce liquefaction collapse, yet the pressure dissipation produces huge damage due to excessive settlement. Consequently, a failure of saturated sand soils may be attributed to the liquefaction phenomenon and/or excessive settlement. Many researchers (Suzuki H., et al. 2008;Tokimatsu K., et al. 2007; and Tamura S. with Tokimatsu K., 2006) investigated the soil-structure interaction in   saturated soil layers via shaking table tests. Tokimatsu K. et al. in 2004, conducted shaking table tests with large-scale models in dry and saturated soils to study the piles under the kinematic and inertial effect of earthquakes.
The ndings showed that these forces have in uenced the pile stresses if the natural period of the pile exceeds that of the ground.
The above literature showed that a shaking table test might come up with a realistic comprehension of the soilstructure interaction under earthquake excitation. Furthermore, this test is taking less time and is low-cost as compared with full-scale tests of foundation (Altaee and Fellenius 1994). However, because of the different scaling low, developing advanced physical models are not straightforward. According to Altaee and Fellenius (1994), the difference between the results of the 1g physical model and the prototype may be attributed to the nonlinearity of a stress-strain behavior and the initial con ning pressure. Despite the apparent bene ts of shaking table tests, due to scale, the measured response may differ from the large-scale prototype response.
Ongoing researches in numerical modeling are capable of capturing the nonlinear behavior of three-dimensional models of the soil-pile system in varied ground situations (Hussein A. and El Naggar M. 2021). Numerical analysis may be able to take control of some of the drawbacks of the laboratory models, i.e., scaling (Cheng Z. and Jeremí c B. 2009), allowing for the validation of the experiment outputs and intense comprehension of various soil-pile system attributes. Several studies explored the attitude of piles in saturated sand soil using the latest advances in numerical analyses, such as realistic numerical models for soil manner and trustworthy time-domain solvers (

Evaluation Of The Effect Of Stress-strain Reversal During Soil Liquefaction
The majority of studies on the factors that cause saturated sands to liquefy have focused on the horizontal ground, in which a soil particle is supposed to be subjected to entirely reversed cycles of shear forces during an earthquake (Seed and Lee 1966;and Finn et al. 1971). Yoshiaki and Hrnosm in 1975 proposed the term ''R'' which describes the level of stress reversal and is described as the ratio of one direction's maximum shear stress to the other direction's maximum shear stress ( Figure 1). The authors presented the magnitude of stress reversal in terms of the initial shear stress τ 0 and the dynamic shear stress τ d : Robertson and Wride in 1998, stated that if the initial void ratio of a soil layer is greater than the ultimate state line (USL, this term is de ned by Poorooshasb and Consoli 1991), the soil may experience strain softening (SS) under signi cant stresses, after a period of time reaching an optimum state known as a critical or steady-state.
The frequency of an earthquake excitation, which typically ranges from 0 to 15 Hz, reveals that loading cycles are a signi cant parameter affecting the liquefaction attitude of the soil layer (Silva, W.J. 1988). The in uence of loading cycles on liquefaction of granular soils has been studied for a variable frequency ranging from 0.05 to 12 Hz, largely using cyclic triaxial experiments on saturated sand, and failure principles rely on the normal strain and the ratio of excess pore pressure. However, there are con icts to the ndings on the impact of loading frequency on soil liquefaction resistance. Many  . Yoshiaki and Hrnosm in 1975 stated that the degree of stress reversal had a signi cant impact on the initial liquefaction circumstances, but had no effect on the entire liquefaction conditions. Zhenzhen Nong et al. (2020) had concluded the previous studies related to the in uence of loading cycles on the liquefaction phenomenon of granular soils, as shown in Table 1.  The pore pressure ratio is calculated depending on the following equation: Where: (∆P w ) is the difference in excessive pore water pressure, P ' init is the initial effective pressure. reduction factor 'R', which in turn is taken as 0.6 and 0.7 for elements between the pile and loose sand and the pile with dense sand, respectively as recommended by Ghaliba an 2006. In order to capture the precise soil-pile response, the model main parameters were calibrated, as presented in Table 2 and 3. Subsequently, the earthquake duration was scaled by multiplying the original acceleration time to (λ 0.75 ), and then the intended acceleration values were incorporated with the new time set.
Even though the reduced mesh size increases the analytical precision, the calculation time increase as well.
However, because the current models need very ne mesh to capture the behavior of soil-pile interaction under different ground accelerations, tetrahedral elements of 0.04 m length were considered. Elements were distributed as the more zone density at the highly deformed area closed to the pile body, as shown in gure 3. A 4-node tetrahedral element was used to represent the soil layers, each element has four degrees of freedom: three for displacements and one for pore water pressure. The pile body and the pile cap were also discretized in a similar way with the soil elements. The problem was taken as an isotropic-elastic material for pile and pile cap, and isotropic-modi ed UBCSAND model for the loose and dense sand soil layers. In current numerical simulation, the laboratory model was scaled up (η = 2) by adapting Wood (2004) scaling law.  Damping ratio (ξ) 5% 5%

Boundary Conditions And Coupled Effective Stress Analysis Stages
For all sorts of analysis, MIDAS GTS NX offers a variety of boundary conditions. For static computations, this study used a 3-D element model and ground initial conditions. As illustrated in gure 4a, the bottom of the sandbox was set in the x-y-z directions, the front and back faces were xed at the y-direction, and the right and left faces were xed at the x-direction. For dynamic analysis, since the plane wave moves into the soil layers, the boundary condition should be maintained to eliminate wave re ection and to avoid the boundary in uence. Since modeling in nite ground is beyond the bounds of possibility, two methods were employed in these models; one is applying plane free eld elements at the soil box sides, and second, extruding the sides elements in a soil box for a long distance to obtain a wide model box which in turn assist in minimizing the wave re ections. However, the latter mothed was noticed as time-consuming, and no restriction rules are available, therefore, the free eld elements were considered which are less time-consuming with correspond to more reasonable outputs.
The rst stage in the model analysis was achieved by activating the static boundary conditions ( gure 4a) to calculate the total stresses initiated by model self-weight. Then, adding a water table on the soil surface (create phreatic surface) to develop the problem of effecting coupled stresses on saturated soil below the groundwater table. Sequentially, the vertical static load and then the lateral static load were applied on a nonlinear soil constitutive model. Then, switching to the lique able layers by adopting the UBCSAND model and introducing the earthquake input motion. In the later stage, the static boundary was deactivated and switched by the elastic boundary conditions, as shown in gure 4b.

Soil-pile Deformation Due To Liquefaction
The soil deformation around the pile was explored to evaluate the compatibility between the numerical calculations and laboratory testing. To study the mechanism of liquefaction-induced signi cant soil-pile deformation, it is found that the two forms of modeling (using Kope and Ali Algharbi earthquakes) be consistent at the same time with the experiment results. Soil-pile deformation in the laboratory experiments (Hussein and Albusoda 2021) was presented by the vertical and horizontal displacements. Soil-pile deformation from the numerical modeling was further illustrated via MIDAS GTS NX. Figure 5 shows the contour lines and the vectors of the maximum total deformation of soil layers and gure 16 shows the maximum vertical and lateral deformation of the pile, due to applying a couple of static loads (50% of the allowable vertical load and 50% of the allowable horizontal load) with two different ground acceleration (Kope and Ali Algharbi).
Dilatancy is a phenomenon related to dense soil subjected to shearing. In other word, when a dense sand layer experiences shear force, the overall volume of the intended layer increase. This phenomenon was observed by the current numerical model as shown in gure 5. The low liquefaction ratio in a dense sand layer may attribute to the dilation phenomenon which in turn considered as the liquefaction resistance (Madhira and Jaswant 2000). Thus, the phase transition was very noticeable in which the volumetric strain shifted from contraction in a loose sand layer to dilation in the dense sand layer. Pile response during dynamic excitation is highly in uenced by the nonlinearity of soil-pile interaction. The pile distortion during the high-intensity ground acceleration of Kope earthquake (around 0.82g) was clear in gure 6a, this deformation may be attributed to the material nonlinearity, cyclic loads during the high ground acceleration cause soil movement, which in turn affects the pile strength. As the loose soil softens due to liquefaction, the stresses around the pile start to diminish. In other words, as the soil loses its stiffness owing to liquefaction, the pile becomes an unstable column. Thus, the pile friction resistance will begin to deteriorate, and the pile may buckle as a result of existing an axial load on the pile cap. Manish et al. 2017, stated that the degree of pile deformation is controlled by pile's stiffness, depth of the saturated loose sand layer, and the intensity of the ground motion. As for the vertical settlement, it is likely that the pile will drop vertically or incline in one direction as a result of a complex effect of buckling and bending. In this manner instead of the pile is to resist both skin and end bearing resistance, the pile now is only resisting the end bearing, and this phenomenon will de nitely reduce the geotechnical capacity to some extent because the contact surface area of the pile skin to resist the down drag effect has diminished ( gure 16). This will not only cause buckling due to the loss of all-around stresses but will de nitely cause a negative skin friction impact i.e. down drag to the pile if the end bearing is insu cient to cater for the geotechnical in uence from the soil and also from the structural load.
On the other hand, the pile followed the soil motion during Ali Algharbi earthquake without a signi cant buckling or deformation as shown in gure 6b. That may be attributed to the low ground acceleration (around 0.1g), so the pile stiffness was enough to resist the ground shaking. In another word, the loss of skin friction of the pile is lower, due to lower vibration of the ground.
The above results were validated (by using the scaling law of Wood (2004)) by the experiment ndings (Hussein and Albusoda 2021), as shown in gure 7. As predicted by numerical and experimental ndings, the magnitude of the pile settlement increased with higher input acceleration (Kope earthquake). This indicates the considerable in uence of shaking intensity on the soil-pile response as previously noted.
Based on these results, the pile displaced vertically and laterally relative to the surrounding soil during different load increments rather than a smooth 1-D movement as stated by Chian and Madabhushi 2012.

Near And Far-eld Measurements Of Acceleration And Pore Water Pressure In Soil Layers
Excess pore-water pressure is expected to be developed in a liquefying soil layer, along with alleviation in seismic waves. The liquefaction ratio, R u , is calculated by dividing the variation in pore pressure by the soil's initial effective vertical pressure. Figures 8 to 11 show the contour lines of the maximum state of how the water pressure ratio propagates through the soil layers of a different time. The results were in good agreement with the experiment ndings (Hussein Albusoda 2021). Some other observations were also extracted from the MIDAS GTS NX outputs.
As presented in gures 8 and 9, the high-water pressure ratio at the far-eld in the early stages (less than 10 seconds) may attribute to re-orientation of the soil particles away from the pile body during seismic excitation (as shown in gure 5a) which in turn trying to uplift the pile (as shown in gure 7a) giving high excess pore pressure at the far-eld as compared to the elements near the pile at the same depth.
Based on the numerical analysis and experimental data, it appears that at all depths of the saturated sand sample, both the formation of excess pore pressure and the propagation of ground acceleration (Figures 11 and 13) from the model bottom to the surface soil were roughly similar.
The liquefaction phenomenon is generated roughly at a time of reaching the intense shaking (high ground acceleration) followed by pile drag down. Although this situation is not very clear under the effect of the Ali Algharbi earthquake due to low acceleration (around 0.1g), it is signi cantly noticed with the Kope earthquake (around 0.82g), gures 8, 9, 10, 11, and 12.
The current numerical models could capture the liquefaction propagation through the soil layers as shown in gures 10 and 12. In general, some differences were observed between the numerical outputs and the experimental ndings may attribute for instance: to minor changes in the boundary condition that could cause such inconsistencies in the numerical modeling and the laboratory samples. On the other hand, the similarity in the general pattern of acceleration and liquefaction ratio time histories is noted, which is suitable for both modeling post-earthquake response and adequately calculating the movement of the pile embedded in the soil. It is noticed that the ctional resistance in dense sand is higher than of the loose one to some extent as shown in gure 16, which may be attributed to the shorter length of the shear zone in a loose sand layer and less effective weight of the surrounding soil in addition to the high liquefaction ratio which is recorded at shallow depths, as shown in gures 8 and 9. Overall, soil particles lose their shear strength and roughly behave as a slurry as noticed at the end of the laboratory tests, the numerical analyses could capture this behavior by decreasing the frictional resistance signi cantly during the dynamic excitation until it reaches the minimum value at the nal stage.

Conclusion
The results of the proposed model of soil-pile interaction system were in good agreement with the 1g shaking there was some pore pressure buildup, but still not enough to produce liquefaction due to the densi cation of the dense sand. Smaller excess pore pressure in a dense sand layer indicates that some of the soil's shear strength has been preserved, which may provide some restriction to pile movement. In the strain-softening effect, the buildup of pore water pressure becomes negative i.e. dilation as the stress-strain response experiences peak and then ultimate stress. This is part of the element preserved through time history due to the compactness of the sand through time has caused signi cant sand particle densi cation which restricts partly the elevated pore water pressures due to small voids volume.
As seen in gures 10 and 12, this observation suggests that extra pore pressure was rst initiated and developed in faraway from the pile body, resulting in stability of the pile during the 5 and 15 seconds of applying Kope and Ali Algharbi earthquakes respectively. Nonetheless, once the pile began to drop down, it was impeded by the frictional resistance of surrounding soil as it tried to re-orientate the particles away due to controlled dilation ( gure 5). Pile buckling deformation was observed in numerical modeling during the application of high intense acceleration (Kope earthquake), as shown in gure 6a. It is suggested that to eliminate buckling, certain design considerations should be taken to enhance the pile's rigidity. The dimension of the pile can be increased based on the depth of the saturated loose sand and the boundary conditions at the top and bottom of the lique ed layer. Bending and buckling principles are interconnected and should not be considered separately since they will combine during an earthquake to induce pile failure.
The general trend and magnitude of pile displacement under the effect of the Kope earthquake was roughly closed to 1g shaking table and the current numerical model ( gure 5a); However, the existing model slightly overestimated the vertical displacement of a pile under the effect of Ali Algharbi earthquake ( gure 5b). This could address some the inconsistencies between the numerical model and the laboratory test, where these discrepancies may attribute to the general experimental setting-up, scaling law, boundary conditions, the accuracy of the strain gauge sensors, and error tolerance of the analysis control setting-up of the existing numerical model. Despite the variations between the numerical model and 1g shaking test results, the overall response of the soil and pile were compared satisfactorily. Consequently, the existing model can be used to study different criteria or model properties that are not captured in physical modeling, as well as to overcome experimental modeling drawbacks such as restricted or di cult measurements or scaling effects. As a result, the present study uses veri ed numerical models to analyze the shear stress-strain relationship and frictional resistance, which were not addressed in the experimental program.    An undrained cyclic loading response of saturated sand soil under a coupled of static loads (vertical and lateral) and dynamic excitation (Kope earthquake). Figure 15