Application · Groundwater flow
Seepage with a free surface, and a mass balance you can read.
Water sets the effective stress, and effective stress sets everything else. KATAI 2D solves steady and transient groundwater flow — confined or with a free surface and a seepage face — and hands the pore-pressure field directly to the deformation, consolidation and safety analyses in the same model. On the classical unconfined dam it returns the exact discharge to +1.02% and closes its global mass balance to 8×10−14.
The engineering problem
In unconfined flow the position of the water table is part of the answer. The boundary on which the pressure is zero is not known in advance, and neither is the height at which water breaks out on a downstream face. The problem is nonlinear even when the soil is not.
A seepage solution is also easy to get approximately right and hard to get exactly right. A discharge that is a few percent off looks plausible; a mass balance that does not close shows that the solution is not a solution. The second check costs nothing and is rarely printed.
The formulation
The full statement of what is solved, element by element and model by model, is on the theory and constitutive models pages.
What KATAI 2D does
- Boundary conditions per edge: prescribed head, prescribed flux, closed, or a seepage face that decides for itself where water exits.
- Wells and drains as line elements with a discharge and a minimum head, or a prescribed head; vacuum drains and infiltration wells included.
- Cut-off barriers. A wall or an interface can be impermeable or semi-permeable to cross-flow.
- Anisotropy. Separate horizontal and vertical permeability per material.
- Transient flow for drawdown and filling, and fully coupled flow–deformation when the water level changes faster than the soil can follow.
- One model. The pore pressures of a flow phase are the pore pressures of the deformation phase that follows.
Verified
The numbers, with their sources.
Each row is a case in the generated verification matrix, asserted by an automated test on every build of release 0.9.0.
| Benchmark | Reference | KATAI 2D | Case |
|---|---|---|---|
| Unconfined rectangular dam with a seepage face — discharge | Charny (1951) exact theorem | +1.02% · mass balance 8×10−14 | KV-FLW-001 |
| Column with a prescribed flux — head profile and recovered discharge | Darcy, exact | to 10−9 | KV-FLW-002 |
| Drain line — drawdown and extracted discharge | 1D confined closed form | −0.00% / +0.00% | KV-FLW-003 |
| Flow across a semi-permeable barrier — discharge | series resistance closed form | −0.10% / −0.15% | KV-FLW-004 |
| Axisymmetric ground with a water table — equilibrium residual, tri15 | geostatic identity | 8.1×10−13 | KV-CST-013 |
| Submerged block under the K0 procedure — effective stress | Terzaghi effective stress | ~5×10−13 kPa residual | KV-NUM-003 |
Charny’s theorem is the right test for a free-surface code because it is exact for the discharge even though the free surface itself has no closed form — so a correct discharge cannot be obtained by tuning the surface.
The complete record, with every tolerance band, is on the verification page.
Stated limits
What this analysis does not do, in the same place as what it does. A limit you know about is an engineering judgement; one you find out about later is an error.
- Unsaturated flow is implemented but verified only in its saturated limit. The van Genuchten retention curve, Mualem relative permeability and Bishop’s χ = Se are in the engine and reachable from the input file; the verification record covers the saturated limit of that formulation (KV-STR-008), not the unsaturated regime. Use it knowing which half is pinned to a published solution.
- A semi-permeable interface is refused in a consolidation phase with an explanation, rather than approximated.
- Two-dimensional flow: a well is a line sink per metre out of plane (or a true axisymmetric well in an axisymmetric model).
Questions
Does it find the phreatic surface automatically?
Yes. In unconfined flow the free surface and the exit point on a seepage face are part of the solution. On the Charny dam benchmark the discharge is within +1.02% of the exact value and no node above the free surface is left saturated.
Can seepage results be used directly in a stability or deformation analysis?
Yes, and without export or import: a flow phase and the deformation, consolidation or safety phase that follows are phases of the same model, on the same mesh.
Is unsaturated soil mechanics supported?
Partly, and the record says exactly which part. The retention curve, relative permeability and effective-stress coupling are implemented; they are verified against a published solution only in the saturated limit. Suction-dependent strength models are not in the release.
Related
Other analyses on the same engine.
Consolidation & embankments
Staged fill on soft ground: excess pore pressure, settlement and creep through time.
|ΔU| ≤ 0.0061 vs Terzaghi Read more → ApplicationExcavations & retaining walls
Walls, prestressed anchors, struts and interfaces through a real construction sequence.
beam moments +0.00% vs theory Read more → ApplicationSlope stability
Factor of safety by φ–c reduction; the failure mechanism is found, not assumed.
FoS 1.384 vs 1.380 charted Read more →Install it, run a published benchmark, check the number.
KATAI 2D is free under Apache‑2.0, installs in one line and ships the input files of the benchmarks it is verified against. The fastest way to judge it is to rerun one.