Verification
Verification asks whether the equations are solved correctly; validation asks whether they are the right equations. These articles are about the first question — building benchmark suites against closed-form solutions, choosing defensible tolerances, and treating every release as something that has to earn trust again.
7 articles
Hoek-Brown tunnel: the closed-form ground reaction curve
A circular tunnel in Hoek-Brown rock, derived in closed form from radial equilibrium and solved in KATAI 2D: plastic radius, wall closure, every number given.
Reproducing a PLAXIS 2D benchmark to within 0.03%
A rigid strip footing on an elastic layer, solved in KATAI 2D against the published PLAXIS 2D value: every input, formula and convergence band stated.
Geotechnical FEM verification: the KATAI 2D benchmark suite
How an open-source geotechnical finite element engine is verified: closed-form solutions, published benchmarks and the results, with every tolerance stated.
Strength reduction: what the factor of safety reduces
A factor of safety of 1.990 means the slope stands on c of 2.5129 kPa and phi of 17.43 degrees — worked on a slope whose closed form checks the method.
Grid Convergence Index: an error bar on a FEM result
Three meshes turn a finite element answer into an answer plus an uncertainty — observed order 1.8171, extrapolated 15.2067, fine-grid band 0.27%.
Floating point: why two runs of one model disagree
Floating-point addition is not associative. Summing the same thousand contributions in another order moves the answer by 360 units in the last place.
Terzaghi consolidation: the series and its approximations
The two formulas every textbook gives for the degree of consolidation are approximations to one Fourier series. Here is the series, and where each one fails.
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Related topics
Geotechnical FEM
Finite element modelling for geotechnical problems: element families, plane-strain and axisymmetric idealisation, staged construction and solver behaviour.
Numerical Methods
The numerical machinery underneath engineering analysis: sparse direct solvers, Newton iteration, quadrature, conditioning and floating-point behaviour.
Engineering Software
Building engineering software engineers can trust: replacing spreadsheets with tested tools, reproducible calculations, versioning and documenting assumptions.
Consolidation & Flow
Groundwater flow and consolidation: Terzaghi and Biot theory, coupled formulations, time integration, drainage boundaries and pore pressure dissipation.