Dynamic and Seismic Response of Anchored Pile Walls Under Earthquake Loading

1. Introduction

The problem was modeled using a geometry of 35 m width and 20 m depth. A ground anchor was modeled by a combination of a node-to-node anchor and a geotextile element. The geotextile simulates the grout body, while the node-to-node anchor simulates the anchor rod. In reality, a complex three-dimensional state of stress exists around the grout body. Although the precise stress state and soil interaction cannot be fully captured with this 2D model, this approach allows for the estimation of stress distribution, deformations, and global structural stability, assuming the grout body does not slip relative to the soil. With this model, it is not possible to evaluate the pull-out force of the ground anchor.

The pile wall is modeled as a beam. Interfaces around the beam are used to model soil-structure interaction effects. These interfaces are extended 1.0 m under the wall. Interfaces should not be used around the geotextiles representing the grout body.

The excavation is constructed in several stages. The separation between stages is modeled by geometry lines.

The water table is initially below the excavation level. A stepwise rise in the water level was simulated, and its pressure effects on the pile wall and existing building were analyzed. During the excavation stages, water is drained, and no groundwater is present. A schematic view of the analyzed model for the studied section of Gazino Station is shown in Figure 1.

Figure 1. Modeled section.

Figure 1. Modeled section.

2. Material and Methods

2.1. Soil and Interface Properties

The properties of the three soil layers and interface materials were adopted from the PLAXIS Tutorial Manual (Version 8), as shown in Table 1.

2.2. Properties of the Plates

The properties of the structural plate elements—namely the pile wall, pile cap, and building beams—were also adopted from the PLAXIS Tutorial Manual (Version 8), as detailed in Table 2, Table 3 and Table 4.

2.3. Properties of the Anchors

The properties for the anchor rods and grout bodies were assumed from the same source, as shown in Table 5 and Table 6.

3. Steps and Procedures

Plaxis version 8 has been used for this study, all above said properties of materials and plates are filled, the study including three scopes as following:

3.1. Study of Pile Wall Behavior Under Water Pressure

In three stages, the groundwater level was raised starting from the bottom of the excavation and ending with the submersion of the entire pile wall.

3.2. Study of Pile Wall Behavior Under Dynamic Load

In this case, the top of the pile wall will be subjected to dynamic load.

3.3. Study of Pile Wall Behavior Under Earthquake

As part of this, an earthquake recorded by the USGS in 1989 was applied to the basement.

4. Results and Discussion

Using the PLAXIS 8 software, three distinct loading conditions (water pressure, dynamic load, and seismic load) were simulated on the numerical model of the anchored pile wall. The following presents a detailed account of the obtained results along with a comprehensive discussion of their engineering implications.

4.1. Pile Wall Behavior Under Water Pressure

Results

The simulation results revealed a decrease in wall displacement as the groundwater level was progressively raised across three stages. In the initial phase (dry wall), the highest displacement value was recorded. As the lower part of the wall (4 m) became submerged in Phase 4, a reduction in displacement was observed. This decrease became more pronounced in Phase 6 when the wall was fully submerged, as illustrated in Figure 2, which compares the output phases.

Discussion

This initially counter-intuitive behavior is attributed to the increase in Total Lateral Pressure on the wall with the rising water table. The pore water pressure contributes to an increase in the total pressure on the back face of the wall, generating a counteracting reaction and enhancing soil resistance. Additionally, changes in the mechanical properties of saturated soil (such as Young’s modulus and shear strength) may play a role in improving system stability. This finding suggests that, under these modeling assumptions, hydrostatic loading is not a critical factor and may even have a stabilizing effect. However, it is important to note that this conclusion is based on the assumption of no seepage or water flow. A study incorporating steady-state seepage conditions might yield different results, potentially highlighting destabilizing effects from water flow pressures, as it clearly in Figure 1.

Figure 1. Comparison of Output phases.

Figure 1. Comparison of Output phases.

4.2. Pile Wall Behavior Under Dynamic Load

Results:

The application of a concentrated dynamic load at the top of the wall caused a continuous increase in horizontal displacements over the simulation time, with a marked acceleration noted in Phase 3 immediately after load application. The distribution of Plastic Points—areas within the finite element mesh where stresses have reached yield conditions—showed a clear concentration in two key zones:

• The area surrounding the anchor heads.
• There is a zone between the existing building and the pile wall.

In Figure 2, we can see how these plastic points are distributed.

Discussion:

The concentration of plastic points around the anchor heads indicates the development of high-stress concentrations in these regions under dynamic loading. This could be a precursor to potential anchor pull-out failure or exceedance of the bearing capacity of the soil surrounding the grout body. This aligns with the study’s stated limitation that the simplified 2D model cannot accurately evaluate anchor pull-out forces. The significant effect in the zone between the building and the wall reflects the complex dynamic interaction between the existing structure and the retaining wall under external loading, which can lead to response amplification in this area. These results underscore the critical importance of detailed design for anchor connection points and the necessity of analyzing structure-soil-structure interaction when dynamic loads are anticipated.

Figure 2. shows the plastic points.

Figure 2. shows the plastic points.

4.3. Pile Wall Behavior Under Earthquake

Results:

Applying the 1989 USGS-recorded earthquake accelerogram to the model base induced both vertical and horizontal displacements. The maximum vertical displacement occurred at the basement level. The results also showed that displacement values at the top and bottom of the wall were similar for most of the simulation period. However, at a dynamic time of 4.08 seconds, a significant and sudden disparity emerged, with the displacement at the top of the wall becoming substantially greater than at the bottom, as shown in the time-displacement curve in Figure 3.

Discussion:

The pronounced disparity in displacement between the top and bottom at 4.08 seconds suggests the occurrence of a resonant response or a critical moment where the inertial effect of the upper portion of the wall is amplified. This specific time likely coincides with a natural frequency or a significant harmonic of the soil-wall-anchor system, leading to amplified motion at the wall crest. This behavior reveals a potential lack of system ductility or insufficient flexural resistance when subjected to seismic motion with a specific frequency content. This finding highlights the importance of conducting response spectrum analyses and designing retaining walls to accommodate significant seismic deformations without global stability failure, taking into account the unique dynamic characteristics of each site, including soil amplification effects, which is clearly visible in Figure 3.

5. Conclusion

According to the numerical analysis, the anchored pile wall responds critically to dynamic and seismic loads and shows stability under rising groundwater levels. A resonant response was induced by seismic excitation at 4.08 seconds, causing significant displacement at the top of the wall. As a result of dynamic loading, anchors and the existing building were subjected to high stress concentrations. Therefore, seismic and dynamic forces govern the design, not hydrostatic pressure. Optimizing wall stiffness, anchor detailing, and performing dynamic response analyses are recommended. Moreover, controlled deformations are necessary to ensure the safety of adjacent structures. In urban excavations, anchored earth-retaining systems should be designed taking dynamic considerations into account