Soil Spring Model (SSM)

Validated Empirical Correlations for Soil Spring Coefficient Estimation in Clay Soils

The Soil Spring Model (SSM) introduces a practical and validated methodology for estimating the soil spring coefficient Ke in clay soils directly from the unconfined compressive strength qu.

The model consists of four validated empirical correlations derived from the analysis of 3,000 selected unconfined compression tests, obtained from a historical database of approximately 8,500 laboratory records from the “Dr. Arnaldo Ruffilli” Soil and Rock Laboratory at the Universidad de Guayaquil, Ecuador.

Engineering Problem Addressed

The SSM addresses a recurring problem in soil-structure interaction analysis: the difficulty and cost of determining Ke through in-situ plate load tests.

By relating Ke to qu, a parameter obtained from a widely available laboratory test, the proposed correlations provide civil, structural, and geotechnical engineers with a:

• Direct methodology
• Economical alternative
• Technically grounded procedure
• Practical tool for structural modeling

Scope of the Model

The equations cover:

• Stiff clays
• Moderately compact clays
• Soft clays
• A general correlation for clay soils

The model can be used when a unified preliminary estimate of Ke is required.

Model Verification

The consistency of the SSM was assessed through:

• Comparison with the reference ranges reported by Jimenez Salas
• Compatibility with values obtained from plate load tests
• Complete dimensional verification
• Structural verification through a SAP2000 model
• Application to a five-story building supported on a mat foundation

Elastic Spring Point Protocol (ESPP)

The procedure for obtaining Ke from the stress-strain curve is based on identifying the elastic yield point, where the initial high slope of the curve changes and the soil begins to lose its proportional elastic behavior.

Ke is calculated as the stress at this point divided by the corresponding deformation.

This procedure constitutes the Elastic Spring Point Protocol (ESPP), developed by M.Sc. (TUM) Marcelo Moncayo Theurer.

FGET, NFF, ESPP and SSM Architecture

The SSM represents the first documented empirical application of the Nested Formula Framework (NFF), developed under the Formula Genomics and Evolution Theory (FGET).

Within this conceptual architecture:

• FGET provides the mathematical philosophy.
• NFF provides the hierarchical modeling methodology.
• ESPP identifies the elastic spring point from the laboratory stress-strain curve.
• SSM provides the applied empirical correlations for engineering use.

Practical Applications

The proposed model is intended for:

• Soil-structure interaction analysis
• Mat foundation modeling
• Seismic-resistant design
• Preliminary foundation sizing
• Geotechnical feasibility studies
• Projects without plate load tests
• Sites where direct testing is logistically difficult or economically impractical

The SSM transforms standard laboratory information into a practical engineering parameter that can be incorporated directly into structural analysis and preliminary foundation design.