Pile Behavior During Liquefaction

The introductory section establishes the critical importance of understanding pile foundation behavior during soil liquefaction, a phenomenon causing significant damage during earthquakes. Pile foundations are particularly vulnerable to lateral loads, with their strength and stiffness significantly reduced during liquefaction. The research focuses on seismic assessment methods, employing both simplified and detailed dynamic analysis. A case study involving a bridge built on pile foundations in liquefiable soil is used to analyze the effects of liquefaction, lateral spreading, and soil-structure interaction during a predicted future earthquake. The abstract highlights the research's aim to study these effects and how they impact the bridge's performance during a seismic event. The vulnerability of pile foundations is a primary concern, specifically the loss of strength and stiffness in liquefied soil. The research methodology includes both simplified and detailed dynamic analysis. The case study of the bridge allows for a practical application of the analysis methods, with the goal of examining the overall impact of these geotechnical issues on the stability and integrity of the bridge structure.

This section reviews existing literature concerning pile loading in liquefiable soils during earthquakes. It describes the complex interaction between soil, pile, and superstructure, which changes throughout an earthquake event. Three cases are outlined showing changes in load distribution—initial inertial loads, the addition of kinematic forces from ground displacement during liquefaction, and the post-liquefaction dominance of kinematic forces due to lateral spreading. The behavior is categorized into cyclic and lateral spreading phases, highlighting the influence of factors such as ground displacements and inertial loads. Several case studies from previous earthquakes (e.g., the 1995 Kobe earthquake, the Yachiyo Bridge, and the Landing Road Bridge) illustrate actual damage patterns and observed pile behaviors under liquefaction conditions. These examples demonstrate the variations in damage features depending on pile stiffness, lateral spreading, and the presence of overlying non-liquefied layers. Experimental studies using shake table and centrifuge tests are also discussed to illustrate the influence of cyclic ground displacement magnitude (rather than extent of liquefaction alone) and the interaction of kinematic and inertial loads on pile response. The relative stiffness of the pile is identified as a key factor influencing damage patterns, with stiff piles experiencing more severe effects due to larger relative displacements.

This section details a simplified analysis method applied to a case study of the Fitzgerald Avenue Twin Bridges in Christchurch, New Zealand. This bridge is a vital lifeline in the event of a disaster, making its seismic assessment critical. The Christchurch City Council proposed a retrofitting plan, including the installation of large-diameter bored piles to improve the foundation's strength. The analysis focuses on identifying key input parameters for a simplified model: magnitude of free-field ground displacement, stiffness degradation due to liquefaction (β), ultimate pressure from the liquefied soil (p_2-max), and inertial load from the superstructure. These parameters are varied parametrically to determine their impact on pile response. The ultimate pressure from the liquefied soil (p_2-max) is evaluated using the undrained or residual strength (S_u) of the sandy soil and empirical correlations with SPT values. The study also examines the influence of soil stiffness degradation (β) on pile behavior. Results from the parametric study are used to demonstrate key features of pile response, specifically focusing on the transition between stiff and flexible pile behavior under combined crust layer and inertial loads. A threshold ground displacement is identified beyond which further increases have minimal impact on the pile response for stiff piles.

The section describes an advanced dynamic analysis using the effective stress principle and a state-concept constitutive model for the soil. This model provides detailed information on free-field ground response, soil-structure interaction, and pile performance which is not possible in simplified analysis. The determination of constitutive model parameters is discussed, highlighting the importance of the dilatancy parameter (S_c) in controlling pore pressure development and liquefaction resistance. Toyoura sand data from previous studies were used as a reference, but key parameters were modified using correlations with SPT blow counts to match conditions for the Fitzgerald Bridge case. The modeling of the non-liquefied base layer is shown to significantly affect the pile response. A comparison is made between analyses using non-linear and equivalent linear stress-strain relationships for the base layer, revealing the impact of base layer modeling on the pile behavior (fixity at the pile tip). Results from the effective stress analysis are compared with those from a more conventional pseudo-static approach, showing similarities in bending moment distribution while noting that the pseudo-static approach can not accurately capture the effects of widespread liquefaction.

The research employs a simplified analysis approach where key input parameters are varied parametrically to identify key features of pile response under liquefaction conditions. The parameters studied include the magnitude of applied free-field ground displacement, the degradation of soil stiffness and strength due to liquefaction (represented by β), and the magnitude of inertial load from the superstructure. By systematically varying these parameters, the study aims to evaluate their effects on soil-pile interaction and to offer practical guidance to designers. The results of this parametric study help determine how variations in these key parameters influence pile behavior. A focus is placed on emphasizing the importance of considering a wide range of values for these input parameters during simplified analysis because of inherent uncertainties in predicting them. The overall goal is to provide designers with insights to improve the accuracy and reliability of their designs.

In contrast to simplified analysis, an advanced analysis method based on the effective stress principle and an advanced constitutive model for soil is used. This approach uses a state-concept interpretation of sand behavior, providing detailed information on free-field ground response, soil-structure interaction, and pile performance. The modeling technique is meticulously described to guide practical application of the effective stress methodology. The study directly evaluates the effects of seismic soil-pile interaction, excess pore water pressure, and soil liquefaction. The advantages and disadvantages of this approach, compared to simplified analysis, are discussed. The advanced analysis offers greater accuracy, but requires more computational resources and expert knowledge. The detailed results obtained provide a more thorough understanding of the complex interaction between the liquefied soil and the pile foundation. The constitutive model's accuracy significantly influences the results, requiring careful selection based on in-situ soil conditions.

This section compares the simplified and advanced analysis methods, highlighting their respective advantages, disadvantages, and areas of applicability. Simplified analyses, while computationally efficient and useful for preliminary assessments, rely on empirical correlations that may introduce uncertainties in predicting soil liquefaction, residual strength, and ground movement magnitude. In contrast, advanced dynamic analysis provides more accurate results by directly evaluating seismic soil-pile interaction and the effects of excess pore water pressure. However, these advanced methods require significant computational resources and specialized expertise. The choice of method depends on the project's requirements, available resources, and the desired level of accuracy. The research emphasizes that, while simplified methods are computationally feasible, a thorough understanding of their limitations and the uncertainties in the input parameters is essential for reliable design.

The case study focuses on the Fitzgerald Avenue Twin Bridges in Christchurch, New Zealand, identified as crucial infrastructure for post-disaster emergency services. To mitigate potential damage during anticipated earthquakes, a structural retrofit plan is in place. This retrofit involves strengthening the existing foundation by installing new large-diameter bored piles, as shown schematically in Figure 3.4. These new piles will be rigidly connected to the existing foundation and superstructure, extending into deeper, non-liquefiable soil strata. The bridges are explicitly identified as a lifeline, and this necessitates a thorough seismic assessment of their foundations to ensure their continued functionality after a significant seismic event. The proposed solution to improve the seismic resilience of the bridge infrastructure focuses on reinforcing the foundation by installing additional piles extending into a deeper, non-liquefiable strata below the liquefiable layer. The location of the new piles is provided schematically to clarify the implementation plan.

A simplified analysis method is applied to assess the pile foundation's behavior under seismic loading. This method utilizes a three-layer soil model, including liquefied, crust, and base layers. Soil springs are represented by bi-linear p-δ relationships, with initial stiffness (k) and ultimate pressure (p_max). The loss of stiffness in liquefied soil layers is captured by a degradation factor (β). The pile is modeled using beam elements, and a tri-linear moment-curvature (M-φ) relationship is used to represent the pile's material behavior. Uncertainty in the ultimate pressure exerted on the piles by the liquefied soil is addressed. The analysis uses the undrained or residual strength of the sandy soils (S_u) from empirical correlations with SPT values, originally proposed by Seed and Harder (1990) and shown in Figure 3.8. The simplified method enables the incorporation of complex soil layering and varying pile diameters throughout the depth, making it a flexible tool for assessing different design parameters.

A parametric study is performed to investigate the influence of key parameters on pile response. The primary parameters varied include: the magnitude of free-field ground displacement, the degradation of soil stiffness due to liquefaction (β), and the ultimate pressure exerted by the liquefied soil (p_2-max). Analyses consider both lateral spreading and cyclic loading scenarios, showing that the chosen liquefied soil properties have a large effect on the response of stiff piles, and that a threshold ground displacement exists for stiff piles undergoing lateral spreading. Increasing loads at the pile head (due to crust layer and inertial loads) shows a transition from stiff to flexible pile behavior. The results demonstrate how these parameters affect soil-pile interaction and highlight the need to consider a wide range of parameter values in design. The analysis considers different p-δ curves for the liquefied soil, including an equivalent linear case without an ultimate pressure limit and cases with ultimate pressure limits based on upper and lower bound values of S_u. This highlights the significance of a rigorous consideration of the ultimate pressure exerted by the liquefied soil and the effect of varying this parameter, showing that using more rigorous p-δ curves is necessary for cases with large relative displacements.

The advanced analysis methodology relies on the effective stress principle and incorporates a sophisticated constitutive model for soil behavior. This model is specifically designed to capture the complexities of sand behavior under dynamic loading, utilizing a state-concept interpretation. The analysis provides detailed insights into free-field ground response, soil-structure interaction, and pile performance under seismic conditions, aspects which are often simplified or approximated in less rigorous methods. The effective stress approach is crucial for accurately representing the influence of pore water pressure on soil strength and stiffness during liquefaction. The use of a state-concept-based constitutive model ensures that the model accurately reflects the non-linear and path-dependent behavior of the soil under cyclic loading conditions. The detailed results generated allow for a comprehensive assessment of the pile foundation’s response during an earthquake event, capturing interactions that might be missed by simplified methods.

Determining the parameters for the constitutive soil model is a crucial aspect of the analysis. Where detailed laboratory tests are unavailable, model parameters are established by adapting parameters from existing studies of Toyoura sand. These parameters are derived from a comprehensive set of torsional tests including monotonic drained p'-constant tests, monotonic undrained tests, and cyclic undrained (liquefaction) tests (Cubrinovski and Ishihara 1998a; 1998b). However, key parameters, especially the dilatancy parameter (S_c), are modified using empirical correlations with the standard penetration test (SPT) blow count (N₁) to reflect the specific conditions of the Fitzgerald Bridge site. Initial void ratios of soil layers are also determined using empirical correlations (Cubrinovski and Ishihara 1999). The use of Toyoura sand as a reference provides a benchmark for comparison, and the adjustments based on SPT data ensure the model appropriately represents the specific soil conditions at the study site. The careful calibration of these parameters is essential to ensure the accuracy and reliability of the simulation results.

The modeling of the non-liquefied base layer plays a significant role in determining the overall pile response. The study compares three analyses with different base layer properties. The first utilizes a base layer with non-linear stress-strain properties, while the other two employ equivalent linear stress-strain relationships with a degraded shear modulus (G) to account for pore pressure build-up and non-linear behavior at large strains. The degradation factor for G was 0.3 and 0.5, representing different levels of soil stiffness reduction. Figure 4.16 presents the stress-strain curves for these three cases, highlighting the differences in behavior. The non-linear model reveals larger ground displacements in the base layer compared to the equivalent linear cases. A detailed comparison of pile tip displacement (approximately 7mm in the non-linear case versus virtually zero in the equivalent linear cases) is provided in Figure 4.19. This highlights the importance of accurate base layer modeling, because assuming pile fixity at the pile tip may lead to unconservative results. The research demonstrates that the choice of base layer model significantly influences the prediction of pile behavior, highlighting the necessity for appropriate selection and validation of these model parameters.

The results from the effective stress analysis are compared to a more conventional pseudo-static approach. The pseudo-static method approximates complex dynamic forces with two static loads: kinematic loads from soil movement acting on soil springs, and inertial loads from the superstructure applied at the pile head. Empirical methods based on SPT blow counts are used to calculate soil spring stiffness, ultimate pressure, and free-field ground displacement. Figure 4.23 compares the pile behavior predicted by both the effective stress analysis and the pseudo-static approach. The bending moment distributions show similarities, though the effective stress analysis predicts a slightly lower bending moment at the liquefied-base layer interface and a flattening of the bending moment above the mid-liquefied layer. This difference stems from the pseudo-static analysis's assumption of a rigid base layer, which contrasts with the more realistic, non-linear behavior captured in the effective stress analysis. The comparison demonstrates that while the pseudo-static approach provides a computationally simpler method, it may not capture all aspects of the dynamic behavior under liquefaction.

This section introduces a novel two-layer finite element analysis technique designed to overcome the limitations of conventional 2D models in simulating 3D effects, particularly in scenarios involving pile groups in liquefied soil. Conventional 2D methods struggle to accurately model the flow of liquefied soil past stiff piles and the influence of pile location within a group. The proposed two-layer model aims to address these limitations by using overlapping 2D finite element meshes with different out-of-plane thicknesses. This approach allows for a more realistic representation of 3D behavior, enabling the model to simulate phenomena such as the unequal lateral displacements of piles within a group, which is a limitation of traditional 2D finite element analysis techniques. The relative contribution of each layer can be adjusted through controlling the out-of-plane thicknesses. The method is particularly effective in cases where lateral ground displacements are significant, a common feature of lateral spreading in liquefied soil.

The two-layer model is initially applied to evaluate the effects of deep soil mixing (DSM) walls on liquefaction remediation. The analysis considers DSM cells of varying sizes (C-5, C-10, and C-20), with the results indicating a strong dependence of pore pressure build-up and ground response on cell size. Figures 5.10, 5.11, and 5.12 show the pore pressure build-up for each cell size, illustrating how closer spacing of DSM walls reduces excess pore pressures and the extent of liquefaction. Figure 5.13 compares excess pore pressure time histories at a depth of 6.5m for all three models, confirming that smaller cells exhibit less liquefaction due to the stiffening effects of the walls. The analysis demonstrates the two-layer model's ability to simulate the interaction between the DSM walls and the soil, and how these walls influence pore pressure distribution and overall soil response during liquefaction. This makes the two layer model suitable for assessing the effectiveness of ground improvement techniques for mitigating liquefaction risk.

The study further demonstrates the application of the two-layer model to simulate pile groups subjected to lateral spreading. Unlike the DSM-wall models, determining appropriate out-of-plane thicknesses for pile groups is not straightforward. The document outlines different approaches to determine this, emphasizing that the approach depends on the pile group geometry and spacing. The most accurate results are achieved when the stiffer layer (containing piles) is modeled as a secondary layer attached to a primary free-field soil layer. The two-layer model is applied to simulate a large-scale shaking table experiment to further demonstrate its capabilities in modeling pile groups. The model accurately reproduces phenomena observed in case histories of damaged piles. The simulation accurately shows different pile deformations based on the pile's location within a group. Conventional 2D models fail to reproduce this effect because all piles in the group are subjected to the same soil displacement.

The concluding remarks summarize key findings on pile foundation behavior in liquefied soil, drawing upon both case histories from past earthquakes and experimental data from shake table and centrifuge tests. The research emphasizes that earthquake loads on piles originate from both soil displacement (kinematic loads) and inertial loads from the superstructure. Liquefaction leads to soil stiffness degradation and increased displacement. Pile response is characterized by two distinct phases: cyclic and lateral spreading. For both phases, the pile response is significantly influenced by pile stiffness, liquefied soil properties, pile fixity (at head and tip), interaction effects within pile groups, and the presence of a non-liquefied crust layer. The most severe damage consistently occurs at the pile head and at interfaces between liquefied and non-liquefied soil layers. The summary effectively integrates observations from field data and experimental results to provide a comprehensive overview of the key factors controlling pile foundation performance during seismic events, emphasizing the complex interactions between the pile, the liquefied soil, and the superstructure.

The concluding section evaluates the performance of simplified and advanced analysis methods. Simplified analysis methods, specifically seismic displacement methods, were reviewed and applied, along with a parametric study to analyze the influence of key parameters (liquefied soil properties, ground displacement, crust load, and inertial load) on pile response. This analysis revealed that the choice of liquefied soil properties is highly significant for stiff piles, and that for stiff piles undergoing lateral spreading a threshold ground displacement exists above which further increases have minimal impact. The two-layer finite element modeling technique is highlighted as a significant advancement in 2D modeling, offering improved capabilities for simulating 3D effects in both liquefaction remediation (using DSM walls) and the analysis of pile groups in laterally spreading soil. This contrasts with the limitations of conventional one-layer models, particularly in modeling soil flow around pile groups and the variation in pile response within a group.

The conclusion provides recommendations for future research to further enhance simplified analysis methods. The focus should not be on refining the models themselves but on more accurately identifying key parameters and developing improved correlations between these parameters and in-situ site investigation data. The research suggests that back-calculation of soil properties (β, p_max, and S_u) from experimental tests and case histories is crucial, advocating for a rigorous and consistent methodology across various data sources. Further detailed investigation is also recommended into the interaction between kinematic loads (from ground displacement) and inertial loads (from the superstructure). This could involve back-calculating loads from experimental tests or employing advanced time history analysis to gain a deeper understanding of the phasing and magnitude of these loads. The overall aim of the recommended future research is to improve the accuracy and reliability of simplified analysis methods by improving the understanding and characterization of key input parameters.