KATAI 2D
An open-formulation, verification-driven finite element platform for two-dimensional geotechnical analysis under plane-strain and axisymmetric conditions.
- Status
- Active development
- Role
- Project lead and author
- Built with
- C, C++, Finite element method
- DOI
- 10.5281/zenodo.20692282
- Website
- kataigeo.com
- Updated
KATAI 2D is a two-dimensional finite element platform for geotechnical analysis. It is built around one commitment: the formulation is stated openly and every capability is verified against published theory before it ships.
The distinction matters because geotechnical software is usually consumed as a black box. An engineer supplies parameters, receives a settlement or a factor of safety, and has no practical way to establish whether the number follows from the model they think they specified. KATAI 2D is written so that the path from governing equation to printed result is inspectable at every step, and so that the claim “this is correct” is backed by a test rather than by a brochure.
ScopePermalink to “Scope”
| Capability | Coverage |
|---|---|
| Idealisations | Plane strain, axisymmetric |
| Analysis types | Deformation, stability, groundwater flow, consolidation |
| Elements | 6-node and 15-node triangles (quadratic and quartic interpolation) |
| Constitutive models | Linear elastic; Mohr-Coulomb; Hardening Soil, optionally with small-strain stiffness (HS small) |
| Initial state | K₀ procedure, gravity loading |
| Nonlinear analysis | Plastic analysis, strength-reduction factor of safety |
| Construction sequence | Multi-phase staged construction |
The fifteen-node triangle is included deliberately. Lower-order elements lock in near-incompressible plastic flow, and collapse loads computed with them are systematically high. Where a limit load is the answer being sought, element choice is not a performance preference — it changes the result, and the platform is explicit about that.
Constitutive modelsPermalink to “Constitutive models”
Three models are implemented, in increasing order of what they ask of the user:
- Linear elastic — for verification work and for stiff structural elements, not for soil at working loads.
- Mohr-Coulomb — implemented with exact return mapping in principal stress space, so the edges and the apex of the yield pyramid are handled in closed form rather than smoothed away. The criterion itself is best understood through the Mohr circle it is drawn from.
- Hardening Soil, with optional small-strain stiffness — for problems where unloading–reloading stiffness and the strain-dependence of stiffness at small strains govern the answer, which is most excavation and retaining-wall problems.
SolverPermalink to “Solver”
A sparse direct solver with pattern-aware factorisation and parallel assembly. Staged and time-dependent analyses reuse the sparsity pattern between phases and between time steps, which is where most of the cost sits in a multi-phase run: the pattern is established once and the numerical factorisation is repeated against it.
Direct rather than iterative is a deliberate choice for problems of this size. It removes an entire class of question — whether a result reflects the model or the convergence tolerance of the linear solver — from the interpretation of a run.
VerificationPermalink to “Verification”
Every capability is locked to published theory and checked against closed-form solutions before release. An automated suite runs on every build; at the current version all 89 checks pass, with results matched to analytical solutions at stated tolerances:
- Prandtl bearing capacity, to within 1.1%
- Terzaghi one-dimensional consolidation, to below 2%
Stating the tolerance alongside the benchmark is the part that matters. A verification claim without a number is a marketing claim. The full protocol, benchmark by benchmark, is documented in the scientific manual below.
Documentation and citationPermalink to “Documentation and citation”
The scientific manual documents the theoretical foundations, numerical methods, element families, constitutive models, solvers, groundwater flow and consolidation theory, together with the verification protocol. It is archived on Zenodo under CC-BY-4.0 and has a permanent identifier:
Küçükkarakurt, F. (2026). KATAI 2D — Scientific Manual (Version 0.2). Zenodo. https://doi.org/10.5281/zenodo.20692282
StatusPermalink to “Status”
Version 0.2, in active development. The software is not yet publicly available and the licence has not been announced. Early access registration is open at kataigeo.com and carries no payment or commitment.