Grey Relational Analysis of Steel Pipe Support Pile Vibration Driving Displacement in Lake-Phase Sedimentary Soil

Literature Overview

The study by Shi Linfeng and colleagues, published in the Journal of Shandong University of Science and Technology (Natural Science) in 2019 (Vol. 38, No. 1, pp. 32-39), investigates the displacement behavior of steel pipe support piles during high-frequency vibration driving in lake-phase sedimentary soil layers. The research is grounded in a deep foundation pit engineering project and employs three-dimensional dynamic finite element analysis combined with orthogonal analysis and grey relational analysis to identify the most influential process parameters. This work is particularly relevant to engineers working on urban foundation pit support systems where steel pipe piles are commonly used in soft, water-rich geological conditions.

Geological Context and Engineering Challenges

Lake-phase sedimentary soils present unique challenges for pile driving operations. These soils are characterized by:

• High water content and low shear strength
• Layered structure with alternating soft and slightly stiff layers
• Sensitive response to dynamic loading
• Potential for excessive pile displacement or refusal

The steel pipe support piles used in deep foundation pit projects must be driven to specified depths while maintaining adequate structural integrity and alignment. Excessive displacement during driving can lead to structural deformation of the pile wall, affecting both the pile's load-bearing capacity and the overall stability of the foundation pit support system.

Methodology: Dynamic FEM and Grey Relational Analysis

Three-Dimensional Dynamic Finite Element Model

The authors constructed a three-dimensional dynamic finite element model to simulate the vibration driving process. The model captures the coupled interaction between the vibrating pile, the surrounding soil mass, and the dynamic loading applied by the vibratory hammer. Key modeling considerations include:

• Soil constitutive model selection appropriate for dynamic loading conditions
• Pile-soil interface modeling with appropriate friction and adhesion parameters
• Damping mechanisms representing energy dissipation in both soil and pile materials
• Boundary conditions that minimize wave reflection artifacts

Orthogonal Analysis for Parameter Screening

Orthogonal experimental design was employed to systematically vary the following factors:

The orthogonal array enables the evaluation of each factor's effect with a minimal number of simulations, providing efficient screening of influential parameters.

Grey Relational Analysis for Sensitivity Ranking

Grey relational analysis (GRA) was applied to quantify the degree of association between each process parameter and the pile displacement response. The GRA approach is particularly suitable for this application because:

• It handles systems with incomplete or partially known information
• It provides a quantitative measure of parameter influence
• It does not require assumptions about the statistical distribution of data

Results and Parameter Sensitivity

The grey relational analysis yielded the following sensitivity ranking:

The optimized process parameters for lake-phase sedimentary soil conditions are:

Engineering Practice Integration

Pile Design Considerations

The optimal pile diameter of 0.83 m aligns with common practice for deep foundation pit support in soft ground conditions. However, the study provides quantitative justification for this dimension rather than relying solely on empirical rules. The pile diameter directly affects:

• The bearing area and soil-pile interaction
• The mass of the vibrating system
• The stress concentration at pile-soil interface

Vibration Hammer Selection

The optimized excitation force of 1,875 kN and frequency of 20 Hz provide specific guidance for vibratory hammer selection. In practice, hammer specifications must be matched to:

• Pile mass and driving resistance
• Soil penetration characteristics
• Energy transfer efficiency

The frequency of 20 Hz falls within the typical range for medium-to-large vibratory hammers used in steel pipe pile driving. Lower frequencies generally provide better energy transfer for larger piles, while higher frequencies may be more effective for smaller diameter piles or stiffer soils.

Soil Parameter Characterization

The dynamic elastic modulus of the soil emerges as the least influential parameter, which has important implications for site investigation requirements. This finding suggests that:

• The displacement response is more sensitive to equipment parameters than to soil stiffness
• Reasonable estimates of soil dynamic properties may suffice for design purposes
• The primary focus of site characterization should be on soil density and cohesion rather than precise elastic modulus determination

Quality Control Implications

For steel pipe piles used as foundation pit support, the driving process quality directly affects the structural performance of the support system. The following quality control measures are recommended based on the study's findings:

1. Pre-driving survey: Document soil conditions at each pile location to identify potential variation zones
2. Real-time monitoring: Measure pile displacement and driving force during installation
3. Post-driving inspection: Verify pile alignment and structural integrity through non-destructive testing
4. Process parameter logging: Record all driving parameters for traceability and future optimization

Key Questions and Reflections

The study raises several important questions for further investigation:

• How does the optimized parameter set perform under varying groundwater conditions?
• What is the effect of pile driving sequence on displacement behavior in adjacent piles?
• Can the methodology be extended to consider cumulative effects of multiple driving operations?

The grey relational degree of 0.79 for vibration excitation force indicates that force control is the primary lever for managing pile displacement. This has direct implications for hammer selection and operation: engineers should prioritize force control over frequency adjustment when optimizing the driving process.

Study Insights and Outlook

This research demonstrates the value of combining numerical simulation with systematic parameter analysis for optimizing construction processes. The grey relational analysis approach provides a practical tool for parameter sensitivity ranking that does not require extensive statistical assumptions. For practitioners in foundation engineering, the study offers actionable guidance for vibration driving optimization in challenging geological conditions. The methodology can be extended to other construction scenarios involving dynamic loading of steel pipe piles, including offshore platform foundations, marine bridge piers, and industrial equipment foundations.