Static vs. Dynamic Analysis - Cantilever and MSE Wall

Permanent retaining systems located in seismic regions must be capable of resisting both static earth pressures and earthquake-induced loading. The response of retaining structures during seismic events depends strongly on wall stiffness, deformation mechanisms, and the ability of the system to redistribute stresses.

Cantilever wall systems, such as sheet pile walls, are generally more susceptible to accumulated permanent deformations during sustained seismic loading because they lack intermediate restraint. In contrast, Mechanically Stabilized Earth (MSE) wall systems tend to perform more favorably during earthquakes due to load sharing between multiple reinforcement layers and the inherent flexibility of the reinforced soil mass.

This article compares the seismic response of a cantilever sheet pile wall and an MSE wall subjected to a horizontal seismic acceleration of 0.1g using several commonly adopted analysis approaches.

Seismic Analysis Methods

The following analysis methods were evaluated using the DeepEX interface:

• Limit Equilibrium Method (LEM) with Mononobe–Okabe seismic earth pressures

• Nonlinear beam-spring analysis with Mononobe–Okabe loading

• Finite Element Method (FEM) with pseudostatic acceleration

• Dynamic FEM analysis using harmonic acceleration loading (4 Hz frequency, 1-second duration)

The Mononobe–Okabe method, developed by Noboru Mononobe and Matsuo Okabe, extends classical Coulomb earth pressure theory to include inertial seismic effects through pseudostatic horizontal and vertical acceleration coefficients.

Cantilever Wall Seismic Response

Figures 1 through 3 compare the predicted wall bending moments and displacements obtained from the different analysis methods.

The LEM, nonlinear beam-spring, and pseudostatic FEM analyses produced relatively similar maximum bending moments. However, the fully dynamic FEM analysis generated time-dependent response variations throughout the loading duration.

The maximum bending moments obtained from the dynamic analysis were approximately 33% greater than those predicted using conventional pseudostatic approaches.

This difference highlights an important limitation of simplified seismic methods: while pseudostatic analyses account for inertial loading, they cannot fully capture:

• Dynamic amplification

• Phase effects

• Wave propagation

• Time-dependent stress redistribution

• Accumulated permanent deformation

Cantilever retaining systems are particularly sensitive to these effects because they rely primarily on passive resistance and flexural stiffness to maintain stability during shaking.

Figure 1: LEM seismic analysis results

Figure 2: Nonlinear seismic analysis results

Figure 3: FEM pseudostatic seismic analysis results

Figure 3a: FEM dynamic analysis results at 0.81 s

Figure 3b: FEM dynamic analysis results at 0.99 s

MSE Wall Seismic Response

Figures 4.a through 4.d compare the seismic performance of the MSE wall using both conventional and advanced numerical methods.

The pseudostatic and dynamic FEM analyses produced relatively similar overall deformation patterns, although the dynamic analysis generated slightly greater reinforcement loads.

The FEM analyses also produced lower reinforcement reactions compared to the simplified stiffness method recommended by AASHTO.

The coherent gravity/coherent earth approach generated significantly larger reinforcement loads compared to all other methods.

These results suggest that the stiffness method provides predictions that are generally more consistent with advanced FEM analysis, while the coherent earth method may produce overly conservative reinforcement demands for some seismic conditions.

Figure 4.a: MSE wall with pseudostatic seismic loading

Figure 4.b: MSE wall with dynamic seismic loading

Figure 4.c: MSE wall with Mononobe–Okabe loading using the coherent earth method

Figure 4.d: MSE wall with Mononobe–Okabe loading using the stiffness method

Dynamic vs. Pseudostatic Analysis

Pseudostatic methods remain widely used because they are computationally efficient and relatively straightforward to apply. However, dynamic FEM analysis provides a more realistic representation of seismic behavior by incorporating:

• Time-dependent acceleration records

• Dynamic stress redistribution

• Soil inertia effects

• Wave propagation

• Damping behavior

• Accumulated displacement response

  
  

For flexible retaining systems such as cantilever sheet pile walls, dynamic effects can significantly increase bending moments and permanent wall displacements relative to pseudostatic predictions.

In contrast, MSE wall systems often exhibit improved seismic performance because reinforcement layers distribute stresses throughout the reinforced soil block, reducing localized deformation demands.

Modeling Recommendations for Seismic Wall Analysis

Accurate seismic retaining wall analysis requires careful consideration of both soil behavior and dynamic loading conditions.

Key modeling recommendations include:

• Evaluate both pseudostatic and dynamic loading scenarios where appropriate

• Consider permanent displacement performance in addition to stability

• Use realistic soil stiffness and damping properties

• Include soil–structure interaction effects

• Evaluate reinforcement load redistribution in MSE systems

• Consider wave frequency and loading duration effects in dynamic analyses

• Compare simplified methods against FEM results for critical structures

For critical infrastructure and high seismic regions, dynamic FEM analysis can provide valuable insight into wall deformation mechanisms and time-dependent structural response.

Conclusion

The comparison between cantilever sheet pile walls and MSE wall systems highlights the importance of selecting appropriate seismic analysis methods for retaining structure design.

While traditional pseudostatic approaches often provide reasonable estimates for overall stability and bending response, dynamic FEM analysis can reveal significantly greater bending moments and time-dependent deformation effects, particularly for flexible cantilever systems.

For MSE walls, both pseudostatic and dynamic FEM analyses showed good agreement with the stiffness method, while the coherent earth approach produced substantially larger reinforcement demands.

These results demonstrate that incorporating dynamic soil–structure interaction effects can improve understanding of retaining wall performance under earthquake loading and help engineers develop safer and more economical seismic designs.

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