Geotechnical FEM
Finite element analysis applied to soil and rock. These articles cover formulation rather than button-pressing: which element families behave well in near-incompressible plasticity, when plane-strain and axisymmetric idealisations diverge, and how staged construction is actually assembled inside a solver.
12 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.
Drucker-Prager: four ways to match Mohr-Coulomb
A cone fitted to a hexagon is right in some directions and wrong in others. Matched at triaxial compression it overstates extension strength by exactly 40%.
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.
Sparse direct solvers: ordering, fill-in and the cost
The same matrix, factorised in two different orders, produces 498501 fill entries or none at all. Ordering is not a tuning parameter — it is most of the cost.
Monopile p-y curves: what PISA was needed to fix
At 35 degrees the API p-y transition sits at 16.96 diameters whatever the diameter. On an 8 m monopile that is 135.67 m, deeper than the pile itself.
Dilatancy angle: what the choice of psi actually costs
Associated flow is convenient and wrong for soil. On one bearing capacity problem it inflates the collapse load from 200.8 to 301.4 kPa — a third more.
Mohr-Coulomb return mapping: the corners and the apex
The single-surface return is three lines of algebra and it produces an inadmissible state. Worked in full, with the principal ordering violated by 37.494 kPa.
The K0 procedure: initial stresses before anything moves
A model starting from the wrong horizontal stress is wrong before the first load. Jaky, elasticity and overconsolidation give 0.429, 0.470 and 0.980 here.
Gauss quadrature in finite elements: how many points
An n-point Gauss rule is exact to degree 2n-1, which decides everything. Under-integrate and the element develops modes that deform at no energy cost at all.
Plane strain vs axisymmetric: the depth the stress reaches
A strip and a circle of the same width put very different loads on the ground below. The 10% contour sits at 1.85B under one and 6.34B under the other.
Terms defined
Related topics
Numerical Methods
The numerical machinery underneath engineering analysis: sparse direct solvers, Newton iteration, quadrature, conditioning and floating-point behaviour.
Constitutive Models
Soil constitutive models: linear elasticity, Mohr-Coulomb, Hardening Soil and small-strain stiffness, including the return-mapping details textbooks omit.
Soil Mechanics
The fundamentals everything else rests on: classification from grading and plasticity, the Mohr circle, and the arithmetic that has to be right first.
Verification
Verification and validation of engineering software: closed-form benchmarks, tolerance selection, regression suites and what makes a result trustworthy.