KATAI 2D 0.9.0 · Open source · Apache‑2.0 · Free
KATAI 2D is open-source finite element software for soil, rock, structures and groundwater: excavations, foundations, slopes, consolidation, seepage and earthquake response in one staged model. Seven constitutive models. 69 verification cases against closed-form solutions and published benchmarks — every one with its input file in the repository, so that any number on this site can be rerun on your machine.
No licence key, no dongle, no account. Windows x64 — a self-contained command line and a Python package. Free for commercial and academic use.
> katai solve kv-slp-001-griffiths-lane-slope.k2d phase 1/1: Initial phase phase 1/1: ok max|u| = 3.083640e-01 m FoS = 1.010 warning K2D-A005 Griffiths-Lane soil: Strength reduction with a non-associated flow rule (material "Griffiths-Lane soil": phi = 19.6 deg, psi = 0 deg): the factor of safety depends on the mesh and falls as the mesh is refined, because the shear band narrows with the elements. … solved 1 phase(s) in 8.17 s
The same method from the command line, on a second Griffiths & Lane slope whose published factor is ≈ 0.99. The warning is the house style: a number that must be qualified is qualified where it is produced, not in a footnote.
Why KATAI 2D
Geotechnical software is trusted with decisions that cannot be tested at full scale. The question is not whether a program produces a result, but what stands behind it.
No capability ships until it reproduces an answer known independently of the program: Prandtl, Terzaghi, Charny, Cox, Griffiths & Lane, Hoek–Brown closed forms. 69 cases, each with its source, its tolerance band and its measured deviation.
The source is public, the formulation is written down equation by equation, and the input is a plain text file with a published schema. When a reviewer asks how a number was obtained, there is an answer.
A load drawn off the mesh, an analysis undefined for a material, a result that depends on the mesh — each produces a stable diagnostic, not a plausible wrong number. 37 codes; no input is ever dropped in silence.
Initial stress, staged excavation, anchors, dewatering, consolidation, a factor of safety, an earthquake — phases of one project on one mesh, with stresses and pore pressures carried from each into the next.
A model is a dozen lines of Python; results come back as NumPy arrays; a parametric study is a loop. The command line has documented exit codes and runs anywhere a script can.
Apache-2.0: commercial work, teaching, research, proprietary tools built on top. No licence server, no seat count, no expiry — and an analysis archived today can be rerun bit for bit in ten years.
Measured, not claimed
Eight of the 69 verification cases. Each number is the measured deviation from a solution that exists independently of the program, on an input file you can download.
Stated as the record states it: not every case is this tight. A circular footing over-predicts its collapse load by +3.7%, and a strength-reduction factor of safety with non-associated flow moves by about 4% over a fourfold mesh refinement. Those numbers are in the same table as the ones above.
Applications
Seven problem types, one engine. Each page states how the analysis is formulated, what the program does, and the benchmark it is verified against.
Factor of safety by φ–c reduction; the failure mechanism is found, not assumed.
FoS 1.384 vs 1.380 charted Formulation and benchmarks → ApplicationWalls, prestressed anchors, struts and interfaces through a real construction sequence.
beam moments +0.00% vs theory Formulation and benchmarks → ApplicationStrip, circular and piled foundations — settlement, load–displacement, limit load.
Prandtl N_c: +0.6% Formulation and benchmarks → ApplicationStaged fill on soft ground: excess pore pressure, settlement and creep through time.
|ΔU| ≤ 0.0061 vs Terzaghi Formulation and benchmarks → ApplicationConfined and free-surface flow, wells, drains and barriers — coupled to the soil.
dam discharge +1.02% Formulation and benchmarks → ApplicationEarthquake records through layered ground, with absorbing boundaries and spectra.
resonant |a|: −0.2% Formulation and benchmarks → ApplicationThe generalised Hoek–Brown criterion, verified around a deep tunnel.
tunnel σ_r: 0.59% / 0.72% Formulation and benchmarks → OverviewEvery analysis is a phase of one project, so excavation, dewatering, consolidation and stability share one mesh and one stress history.
All applications →Constitutive models
Seven models including Linear Elastic, each with drained, undrained (A), (B), (C) and non-porous behaviour. Every one is documented with its governing equations and verified on a problem with a known answer.
Elastic–perfectly plastic with friction, cohesion, dilatancy, a tension cut-off and a dilatancy cut-off. The model of the limit-load benchmarks.
Prandtl N_c +0.6% Equations and parameters → ModelStress-dependent stiffness, hyperbolic shear hardening, a compression cap and a distinct unloading stiffness.
oedometer −0.93% Equations and parameters → ModelHardening Soil with stiffness that decays from G₀ with shear strain — for movements behind walls and under rafts.
unloading heave −0.30% Equations and parameters → ModelLogarithmic compression with a pre-consolidation memory, for normally consolidated clay, silt and peat.
primary loading −0.01% Equations and parameters → ModelSoft Soil with time-dependent secondary compression: settlement that continues at constant effective stress.
creep law +1.81% Equations and parameters → ModelThe generalised 2002 criterion for rock masses, entered as σci, mi, GSI and D — no c′/φ′ fit.
tunnel 0.59% / 0.72% Equations and parameters →Python
No input file is required to get started: build the model in Python, run it, and read the answer back. Every object is created in one call and handed back as a handle, and phases switch those handles on and off — which is the whole of staged construction. Materials, geometry, walls, anchors, geogrids, piles, interfaces, groundwater and every phase type are reachable from the same surface, over the same input contract the CLI and the file use.
import katai
prj = katai.Project("Anchored excavation", mesh_size=2.0, auto_refine=False)
# one soil, Mohr-Coulomb: kN, m, day -- units are fixed and stated
sand = prj.materials.mohr_coulomb("Berlin sand", E=3.0e4, nu=0.3,
c=5.0, phi=32.0, gamma=19.0)
# ground, split so the pit can be dug out of it later
prj.geometry.rectangle(0, 0, 30, 12, material=sand, name="Below formation")
pit = prj.geometry.rectangle(0, 12, 12, 20, material=sand, name="Pit")
prj.geometry.rectangle(12, 12, 30, 20, material=sand, name="Retained ground")
# a diaphragm wall with an interface on each face, and a prestressed anchor
wall = prj.structures.plate((12, 20), (12, 6), EA=1.2e7, EI=1.0e5, w=5.0,
interfaces="both", name="Diaphragm wall")
anchor = prj.structures.anchor((12, 18), (20, 14), EA=2.0e5, spacing=2.5,
prestress=300.0, name="Anchor row 1")
# staging: handles are what phases switch on and off
prj.initial(procedure="k0", exclude=[anchor])
prj.phases.plastic("Excavate to formation", activate=[anchor], deactivate=[pit])
job = prj.run()
print(katai.summary(job, prj)) === Excavate to formation =======================================
status converged
max |u| 4.329029e-02 m
diagnostics
NOTE K2D-A004
A structural element ends on a supported node. The reported
reactions are the soil's contribution only; the element's own
end force at that support is not included in this build.
extremes min at max at
|u| [ m] 0 (0, 16) 0.04329 (3, 12)
u_y [ m] -0.00089196 (30, 18) 0.043216 (3, 12)
sig'_yy [kPa] -376.15 (30, 0) 5.888 (10, 12)
structural forces (envelope |max|)
Anchor row 1 anchor N 195.4 kN/m
Diaphragm wall plate N 325.7 kN/m M 58.33 kNm/m katai.Refusal carries the message verbatim and the stable K2D-*
codes, so a script branches on the reason instead of parsing prose.
prj.save("job.k2d") at any point, and the same analysis opens in the GUI or
runs under katai solve — the test suite pins a scripted case byte-for-byte
against its checked-in file.
for loop.
Install
Two front ends, one contract. The command line is a single self-contained executable;
the Python wheel ships the katai package and the same command line.
No licence key, no administrator rights, no dependencies.
> irm https://raw.githubusercontent.com/fkkarakurt/katai2d/main/install.ps1 | iex # open a NEW terminal, then: > katai info KATAI 2D 0.9.0 (2026-08-31) .k2d project file version: 18 .res results file version: 9 linear solver backend: eigen
The installer downloads the latest release, verifies its SHA‑256 and puts
katai on your PATH.
> pip install katai2d-0.9.0-cp312-abi3-win_amd64.whl > python -c "import katai; print(katai.__version__)" 0.9.0 > katai info KATAI 2D 0.9.0 (2026-08-31) .k2d project file version: 18 .res results file version: 9 linear solver backend: eigen
One abi3 wheel serves every CPython ≥ 3.12 on Windows x64, from Releases.
In development
The engine is open source today. On top of it, a modelling, meshing and reporting application is being built for engineers who would rather draw a section than script it. Real screenshots from the working build below. It is a separate track and not part of the open-source release.
Soil rarely stands alone. Add the structural elements of a real project and build it in the sequence it is actually constructed.
Contours on the mesh, with a legend keyed to the true value range, phase by phase.
When the ground cannot carry a load the program says what fraction it did carry, that this fraction is the limit load, and what to change.
Scope
A capability that is not verified is not in the product. The left column is in the open-source release now, each item with its oracle in the suite; the right column is stated openly instead of implied.
.k2d contract, with a JSON Schemapip install katai2d from PyPI — planned; the wheel ships from Releases todayThe gaps are on the roadmap, not hidden — and nothing lands without the same verification rule: a closed-form solution, an independent computation path, or a published benchmark.
Citation
KATAI 2D is archived with a persistent DOI, so a result computed with it can be referenced the way any other method is. If you use it in a paper, a thesis or an expert report, please cite the software — and, where a specific number matters, the primary source the verification matrix names for that case.
Resolves to the archived record on Zenodo. A CITATION.cff ships in the
repository, so GitHub’s “Cite this repository” button produces the same entry.
@software{katai2d,
author = {Küçükkarakurt, Fatih},
title = {{KATAI 2D}: an open-source, verification-first
finite element engine for geotechnical engineering},
year = {2026},
publisher = {Zenodo},
doi = {10.5281/zenodo.20692282},
url = {https://doi.org/10.5281/zenodo.20692282},
note = {Source: https://github.com/fkkarakurt/katai2d}
} Kucukkarakurt, F. (2026). KATAI 2D: an open-source, verification-first finite element engine for geotechnical engineering [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.20692282
Citing a number rather than the program? Every verified quantity in the matrix carries its own reference — Prandtl, Giroud, Charny, Terzaghi, Griffiths & Lane, Kramer and the rest are listed with their bibliography on the verification page, and the same bibliography is generated into the repository so it can never drift from the tests that use it.
About
KATAI Geotechnical Engineering develops KATAI 2D, a finite element engine for soil and soil–structure analysis. We build computational geotechnics the way we believe engineering software should be built: on established theory, with readable source, and with every result verified against a known solution before it ships. The engine, its command line and its Python package are open source under Apache‑2.0.
Our aim is a tool a practising engineer can trust and a researcher can scrutinise — accurate enough to rely on, transparent enough to defend in a review, an expert report or a paper.
KATAI 2D is designed and written by Fatih Küçükkarakurt, who also maintains its formulation notes and verification record. Work, writing and contact details are at fkkarakurt.com.
FAQ
KATAI 2D is free, open-source finite element software for geotechnical engineering. It analyses deformation, stability, groundwater flow, consolidation and seismic response of soil, rock and soil–structure systems in two dimensions — plane strain and axisymmetry — and is driven from a command line, from Python, or from a plain text project file. Its distinguishing principle is verification: every capability is pinned to a closed-form solution, an independent computation path or a published benchmark, and the record of 69 such cases ships with the source.
Yes. The engine, the katai command line and the Python package are open source under the Apache License 2.0, which permits commercial use, modification and redistribution without fee. There is no licence key, no dongle, no node-locking, no account and no time limit.
Seven: Linear Elastic; Mohr–Coulomb with a tension cut-off and a dilatancy cut-off; Hardening Soil; HS small (Hardening Soil with small-strain stiffness); Soft Soil; Soft Soil Creep; and the generalised Hoek–Brown criterion (2002) for rock, entered as σci, mi, GSI and D. Each soil model can be drained, undrained (A), (B) or (C), or non-porous.
Three-dimensional analysis (it is two-dimensional by design); liquefaction and cyclic pore-pressure generation; suction-dependent strength of unsaturated soil; large-deformation (updated mesh) analysis; discrete jointed rock. Released binaries are for Windows x64 only, and the open-source release has no graphical interface. These limits are stated on the features page rather than left to be discovered.
On problems with exact or published answers, measured on the input files that ship in the repository: Prandtl’s bearing capacity factor +0.6%; the Davis & Booker footing +1.4%; the Cox circular footing +3.7%; the Giroud rigid footing +1.1%; the Charny dam discharge +1.02%; Terzaghi consolidation −1.2% to −0.4%; resonance of a soil column −0.6% and −0.2%; a Hoek–Brown tunnel 0.59% and 0.72%; beam deflection −0.000%. The full record of 69 cases, with every tolerance band, is on the verification page.
For the command line, run one line in PowerShell: irm https://raw.githubusercontent.com/fkkarakurt/katai2d/main/install.ps1 | iex — it downloads the latest release, verifies its SHA-256 and puts katai on your PATH, without administrator rights. For Python, download the wheel from the GitHub releases page and pip install it; one wheel serves every CPython from 3.12 onwards. Publication on PyPI is planned.
Not in the open-source release, which is a command line and a Python package. A desktop application with drawing, meshing, staged construction, result contours, force diagrams and report generation is in development on the same engine as a separate track; real screenshots are on the desktop page, and there is a list to join for the preview.
Cite the software through its archived record: Küçükkarakurt, F. (2026). KATAI 2D: an open-source, verification-first finite element engine for geotechnical engineering. Zenodo. https://doi.org/10.5281/zenodo.20692282. A CITATION.cff file ships in the repository, so GitHub’s “Cite this repository” button produces the same entry. Where a specific number matters, cite also the primary source the verification matrix names for that case.