Mathematical philosophy for formula evolution and selection.
THEK Systems Methods Ecosystem
SOIL SPRING MODEL SSM · Modelo de Resorte de Suelo
Validated empirical correlations for estimating the soil spring coefficient Ke in clay soils directly from the unconfined compressive strength qu.
FGET → NFF → ESPP → SSM
An integrated methodological architecture
SSM belongs to the THEK ecosystem of methods for complex systems. Each level has a precise role: theory, modelling, elastic-point identification, and geotechnical application.
Hierarchical modelling methodology through coefficient nesting.
Protocol for identifying the elastic yield point on the stress-strain curve.
Applied correlations for calculating Ke in clay soils.
Engineering problem
Estimating Ke without relying exclusively on plate load testing
SSM transforms a parameter traditionally associated with costly in-situ testing into a quantity directly computable from a standard laboratory test.
Accessible
Uses the unconfined compression test, available in conventional soil laboratories.
Applicable
Provides Ke values ready for preliminary mat and slab modelling.
Traceable
The Ke–qu relationship remains explicit, interpretable, and verifiable.
SSM correlations
Four equations for clay soils
Ke is expressed in kg/cm³ and qu in kg/cm².
Ke = 7.0193 qu − 2.1188
qu > 0.75 · Ke ≈ 4.00–8.00 kg/cm³Ke = 3.7052 qu + 0.3684
0.25 ≤ qu ≤ 0.75 · Ke ≈ 1.30–4.00 kg/cm³Ke = 3.6367 qu + 0.277
qu < 0.25 · Ke ≈ 0.49–1.30 kg/cm³Ke = 5.0805 qu − 0.1931
Applicable as a unified general estimate for clay soils.Model verification
Three independent verification lines
Jiménez Salas (1980)
Comparison with widely used reference ranges for the coefficient of subgrade reaction.
Plate load tests
Dimensional and order-of-magnitude consistency with values obtained in situ.
SAP2000
Documented application to a five-story mat foundation model.
Applications
From the laboratory to the structural model
Preliminary sizing
Initial soil-stiffness estimation before the final geotechnical study.
Mat foundations
Preliminary spring modelling for slabs and mat foundations.
Soil scenarios
Response comparison for soft, intermediate, and stiff soils.
Projects without plate tests
Technical alternative for sites with cost or access restrictions.
INTERNATIONAL COLLABORATION
Collaboration, courses, cooperation, and exchanges
THEK Research Institute welcomes proposals from universities, companies, laboratories, professional organizations, and public institutions interested in applying, validating, teaching, or extending SSM and the broader THEK methods ecosystem.
Scientific collaboration
Joint research, independent validation, publications, and development of new correlations.
Propose collaborationCourses and training
Institutional courses on SSM, ESPP, soil-structure interaction, SAP2000 modelling, and the FGET–NFF architecture.
Request a courseTechnical cooperation
Method application in projects, comparative studies, foundation analysis, and methodological transfer.
Request cooperationAcademic exchanges
Seminars, keynote lectures, visiting researcher activities, university–industry cooperation, and knowledge exchange.
Propose an exchangeScientific SEO · Technical queries
Frequently asked questions about SSM
What is the Soil Spring Model (SSM)?
It is a set of four validated empirical correlations for estimating the soil spring coefficient Ke in clay soils from the unconfined compressive strength qu.
How is Ke calculated with SSM?
The engineer selects the correlation corresponding to the clay condition and enters the qu value obtained from the unconfined compression test. The initial result is expressed in kg/cm³ and can be converted to T/m³ or nodal spring stiffness.
How are ESPP and SSM connected?
ESPP identifies the elastic yield point on the stress-strain curve and provides Ke. SSM correlates those Ke values with qu for practical engineering use.
What projects can use SSM?
SSM can support preliminary sizing, initial mat-foundation modelling, soil-structure interaction analysis, and preliminary studies when plate load testing is unavailable.
Where can the paper and annexes be downloaded?
The English and Spanish versions and supplementary annexes are available in the official Zenodo record for SSM.
Open Science · CC BY 4.0
Download the paper, language versions, and annexes
The official Zenodo record includes the English version, the Spanish version, and the supplementary SSM materials.
Open Science · Academic identity
Publication and scientific profiles
Access the official DOI record, the academic dissemination page, and the author’s scientific identity profiles.
THEK ecosystem