Finite Element Analysis in Geotechnical Engineering

Finite element analysis (FEA / FEM) is one of the main tools modern geotechnical engineers use to predict how ground and structures move and fail together — through excavation, filling, dewatering and long-term consolidation.

If you are new to it, the important idea is simple: the software only solves the problem you define. A converged model can still be wrong if the ground model, drainage assumption, construction sequence or constitutive model is wrong. This guide is written so you can understand what FEM is doing, when to use it, how a credible model is built, which software is commonly used, and what the key terms mean — with Australian practice in mind.

Related Hub reading: Geotechnical Modelling and Analysis, Geotechnical Site Investigation, and Pile Capacity.

Who this guide is for

• Graduates and engineers opening their first PLAXIS, RS2, MIDAS or GeoStudio model
• Reviewers who need to interrogate someone else's FEM report without drowning in jargon
• Designers who already use limit-equilibrium or wall software and want to know what continuum FEM adds

How to use this guide

1. Read What FEM is, When it is worth using, and the worked example first — that gives you the mental model.
2. Use the workflow section as a checklist when you set up or review a real job.
3. Use constitutive models, parameters, software and Australian practice when you are choosing inputs and acceptance criteria.
4. Keep the key terms glossary open while you read manuals, calculation reports or output plots.
5. Before you rely on numbers, run the quality control and common failure modes lists.

What finite element analysis is (in geotechnics)

The finite element method divides soil, rock and structures into a mesh of small elements connected at nodes. The program solves equilibrium for displacements (and often pore pressures) under loads, restraints and construction stages. From those displacements it derives strains, stresses, structural forces and failure mechanisms.

In geotechnics one connected model can represent:

• layered ground and groundwater
• walls, slabs, piles, anchors, props and linings
• interfaces where soil can slip relative to a structure
• excavation, filling, dewatering and support installation in sequence
• short-term undrained response and long-term drained / consolidation behaviour

FEM is most useful when you need answers that closed-form equations struggle with:

• How much will this wall move at stage 4?
• Where does settlement concentrate?
• What happens if the first prop is delayed?
• Which parameter actually controls the design?

A simple mental model

Think of FEM as three layers stacked together:

1. Geometry and stages — what exists, what is dug or filled, and in what order
2. Material behaviour — how each soil/rock/structure zone stresses and strains (the constitutive model)
3. Math solution — the mesh and solver finding a displacement field that satisfies equilibrium (within tolerance)

If layer 1 or 2 is wrong, layer 3 will still give you neat plots.

When FEM is worth using

Use FEM when geometry, construction sequence or interaction drive the decision — not because a licence is available.

Good candidates

• Deep excavations with staged support next to existing buildings or services
• Embankments or fills on soft clay where pore pressure and staged loading matter
• Tunnels and shafts with ground loss, lining forces and surface settlement troughs
• Piled rafts, pile groups and foundations with complex load sharing
• Slopes and retention systems where deformation or progressive failure matters
• Problems linking seepage / dewatering with movement and effective stress
• Seismic, cyclic or dynamic loading assessments

Often unnecessary

• Simple footings on well-understood ground where bearing and settlement equations are adequate
• Preliminary screening where order-of-magnitude checks are enough
• Cases with almost no reliable stiffness or groundwater data — a complex model then amplifies uncertainty rather than reducing it

A useful rule: analysis effort should match risk and data quality.

A worked example: basement next to a neighbour

Imagine a two-level basement beside an existing strip footing. Stiff clay over sand, groundwater near formation level. The design questions are wall deflection, prop forces, basal heave risk and settlement under the neighbour.

A useful FEM story looks like this:

1. Purpose — SLS wall movement and neighbour settlement limits; ULS for basal heave / global stability.
2. Ground model — layers, su or c′–φ′, stiffness (especially unloading stiffness), groundwater and permeability from the investigation.
3. 2D plane strain section — long basement wall; 3D only if corners or openings dominate.
4. Initial stresses — K₀ / OCR and pore pressures before any dig.
5. Stages — install wall → excavate to first prop → install prop → excavate to formation → dewater as planned → cast slabs → long-term drained condition.
6. Outputs to review — wall deflection envelope, prop force vs stage, settlement trough at the neighbour, plastic zones, FoS by φ/c reduction for the deep mechanism.
7. Checks — compare FoS with limit equilibrium; compare movements with experience and trigger levels; sensitivity on Eur, groundwater and first-prop timing.

That sequence is the heart of geotechnical FEM. Everything else in this article supports doing those steps without fooling yourself.

FEM compared with other analysis methods

Method	What it does well	Typical geotech use
Limit equilibrium	Transparent FoS along assumed slip surfaces	Slopes, some retaining checks
Beam–spring / subgrade reaction	Fast soil–structure interaction for walls and beams	Preliminary retention, props
Finite element (FEM)	Irregular geometry, staging, SSI, coupled flow–deformation	Basements, tunnels, embankments, complex foundations
Finite difference (FDM)	Staged excavation, progressive yielding, large strain	Mining, underground openings, dynamics
Discrete element (DEM)	Separate blocks/particles and joint-controlled movement	Jointed rock, granular flow

FEM does not make limit-equilibrium obsolete. For slopes and many global-stability checks, a transparent FoS is still the everyday benchmark. FEM adds deformation, staging and interaction — then you cross-check.

Building a geotechnical FEM model: the workflow

Skip these early steps and you usually get polished but unreliable output.

1. Define the purpose

Write down what the model must decide:

• ULS: collapse, base heave, slope failure, structural overstress
• SLS: wall deflection, settlement, angular distortion, crack risk
• Temporary works vs permanent works
• Groundwater / aquifer interference effects

Different aims need different constitutive models, drainage assumptions and outputs.

2. Assemble the ground model

FEM starts from an engineering geological model: stratigraphy, groundwater, strength, stiffness and variability — built from desk study, boreholes, in situ tests, lab tests and monitoring. See Geotechnical Site Investigation.

Include enough surrounding ground that boundaries do not choke the mechanism. A thin weak layer that controls failure may need to be modelled explicitly even if it is only a fraction of the profile.

3. Choose 2D or 3D

• Plane strain — long walls, embankments, tunnels with roughly constant cross-section
• Axisymmetric — circular footings, shafts, single piles under vertical load
• 3D — corners, irregular excavations, pile groups, tunnel junctions, isolated loaded buildings

A well-built 2D section is often the right first model. Move to 3D when the mechanism is clearly three-dimensional.

4. Geometry, mesh and boundaries

Place far-field boundaries far enough that edge displacements and stresses are near zero for the quantities you care about. Typical restraints: fix the base; restrain horizontal movement on vertical sides; leave the ground surface free unless loaded.

Use a graded mesh: fine near excavation faces, footing edges, tunnel openings and interfaces; coarser farther away. Then refine again — if design-critical movements or forces change materially, keep refining.

5. Initial stresses

Soil behaviour depends on the current stress state. Before construction:

• set pore pressures from the groundwater model
• establish effective vertical stress from unit weights
• set horizontal effective stress via K₀ where ground is level, or gravity switch-on for slopes and complex stratigraphy

Getting K₀ and OCR wrong often produces more error than choosing between two advanced soil models.

6. Staged construction

Model the sequence that will actually be built:

1. initial ground state
2. install wall / piles / improvements
3. excavate or fill in lifts
4. install props, anchors, floors or linings
5. dewater or recharge as planned
6. apply permanent loads
7. long-term consolidation / drained conditions

Activating the final geometry in one step misses temporary peaks in wall moment, prop force and ground movement.

7. Drainage and groundwater

Decide drained, undrained, or coupled consolidation for each stage:

• Undrained — short-term clay response; excess pore pressure develops with loading/unloading
• Drained — long-term effective-stress behaviour
• Coupled / consolidation — time-dependent settlement and strength change as excess pore pressure dissipates

Hydraulic boundaries must match real drainage paths. Assuming free drainage where water cannot escape underestimates pore pressure and time to settle.

8. Soil–structure interaction

Represent walls, slabs and piles with appropriate structural elements, and use interface elements where slip or gap opening matters. Interface strength is usually a reduced fraction of adjacent soil strength. Ignoring interfaces can glue soil to the structure and distort both movements and forces.

Constitutive models: what to use when

A constitutive model is the stress–strain law for soil or rock. More parameters only help if you have data to support them.

Model	Role	Strengths	Limits
Linear elastic	Stiff structural zones or far-field rock	Simple	Poor for soil failure and nonlinear stiffness
Mohr–Coulomb	First-order strength and plastic zones	Familiar c–φ inputs; useful preliminary model	Constant stiffness; limited pre-failure deformation
Hardening Soil (and HS-small)	Excavations, tunnels, serviceability	Stress-dependent stiffness; separate unloading stiffness	Needs good stiffness data
Soft Soil / Cam-Clay family	Soft normally consolidated clays	Compression and critical-state behaviour	Less suited to dense sands / stiff OC clays without care
Hoek–Brown / rock-mass models	Rock mass strength	Confining-stress dependent rock strength	Continuum idealisation; joints may need discrete treatment

Practical selection

• Stability screening and first plastic mechanisms → Mohr–Coulomb is often enough
• Wall deflection, settlement troughs, heave → need realistic stiffness (often Hardening Soil or equivalent)
• Soft clay embankments / consolidation → soft-soil / critical-state models plus coupled flow
• Joint-controlled rock → continuum models may hide the real mechanism

Document why the model was chosen and which parameters control the outputs you will design on.

Key parameters (and why stiffness dominates SLS)

Typical inputs include unit weight, c′ and φ′ (or su), dilatancy ψ, E or E50 / Eur / Eoed, Poisson’s ratio ν, permeability, OCR / preconsolidation pressure, and interface R-values.

For serviceability, stiffness usually matters more than peak strength. Soil stiffness depends on strain level, stress path, drainage and stress history. A modulus taken from a failure-oriented correlation can badly mis-predict movement.

Where parameters are uncertain, run sensitivity studies on the few inputs that move the answer — often Eur, K₀, su profile, groundwater head and prop timing — rather than varying everything.

Stability by strength reduction

In FEM, factor of safety is commonly obtained by φ/c reduction: cohesion and tanφ are reduced until the model can no longer equilibrate or a clear mechanism forms. The reduction factor is the FoS.

Advantages: no assumed circular surface; works for complex geometry; shows a deformation-based mechanism.

Caveats: non-convergence can be numerical; mesh and constitutive model affect FoS; always compare with limit-equilibrium results and explain differences.

Typical applications

Deep basements / retention — staged excavation, wall bending, prop/anchor forces, basal heave and neighbour movement. Australian practice often references AS 4678 for earth-retaining structures, with FEM used to quantify deformation and interaction.

Foundations and piled rafts — settlement profiles, load sharing and interaction. Pile geotechnical design still sits under frameworks such as AS 2159; FEM informs serviceability and group effects rather than replacing code strength thinking.

Embankments on soft ground — staged filling, excess pore pressure, consolidation rate, vertical drains and FoS evolving with time.

Tunnels and shafts — ground loss, lining forces, face support and settlement troughs.

Slopes and reinforced soil — deformation, progressive failure and verification of critical sections alongside limit-equilibrium design.

Geotechnical FEM software commonly used in practice

These are among the most widely used continuum FEM packages in geotechnical consulting. Software choice matters less than the ground model and checks — but starting inside a package your team already reviews is usually wise.

Software	Best starting point	Official link
PLAXIS 2D (Seequent / Bentley)	Everyday 2D deformation, stability, groundwater, consolidation, dynamics	PLAXIS 2D
PLAXIS 3D	Full 3D soil–structure interaction and staged construction	PLAXIS · Bentley PLAXIS 3D
MIDAS GTS NX	2D/3D staging, tunnels, foundations, coupled flow–stress, dynamics	GTS NX
RS2 (Rocscience)	2D soil/rock FEM for excavations, tunnels, slopes (strength reduction)	RS2
RS3 (Rocscience)	3D companion to RS2	RS3
GeoStudio SIGMA/W (Seequent)	2D stress–deformation, consolidation and SSI inside GeoStudio	GeoStudio 2D
GEO5 FEM (Fine)	2D settlement, excavations, slopes, tunnels, walls, groundwater, consolidation	GEO5 FEM

If you are learning, start with a 2D staged excavation or embankment tutorial in whichever package your office uses. Master staging, interfaces, drained/undrained choice and output interpretation before chasing advanced constitutive models.

Australian practice notes

FEM is an analysis tool, not a substitute Australian Standard. Design still needs the relevant code framework (for example AS 4678 for many earth-retaining structures, AS 2159 for piles, project specs and authority requirements).

In practice:

• keep ULS and SLS checks explicit
• apply partial factors / strength reduction consistently with the governing standard — do not mix factoring systems casually inside one model
• use FEM to understand mechanisms, movements and staging; use standards to set acceptance criteria and resistance factors
• for aquifers and drained basements, groundwater modelling may also need regulator expectations (for example aquifer interference assessments in NSW)
• report assumptions so an independent checker can reproduce the logic

Quality control checklist

Before design relies on the output:

1. Confirm geometry against drawings and the ground model (units included).
2. Trace every key parameter to a test, correlation or stated assumption.
3. Verify groundwater and drainage boundaries.
4. Walk through every construction stage against the temporary works method.
5. Check mesh and boundary sensitivity for design-critical outputs.
6. Benchmark against hand calculations, limit equilibrium or published case behaviour.
7. Inspect displacement fields, plastic zones and structural force diagrams for physical sense.
8. Run sensitivity on uncertain drivers.
9. Arrange independent review for high-consequence models.
10. Plan monitoring (inclinometers, survey, piezometers) where the observational method closes the loop.

A green "calculation finished" light is not a verification.

Common failure modes of FEM studies

• Wrong question — detailed deformation model used only to extract a single FoS that limit equilibrium already answered
• Underspecified stiffness — SLS predictions from parameters never measured at the relevant strain level
• Final-state only staging — misses temporary overstress
• Boundaries too close — artificially stiff domain, optimistic movements
• No interfaces — soil glued to wall/pile
• Drained/undrained mismatch — short-term excavation analysed as drained, or long-term settlement as undrained
• Black-box trust — no hand-check, no sensitivity, no mechanism review
• False precision — reporting 12.37 mm settlement as if the ground were known to 0.01 mm

Learning path if you are new to geotechnical FEM

1. Revise effective stress, drained vs undrained behaviour, and basic earth pressure.
2. Rebuild one published tutorial (excavation or embankment) and explain every stage out loud.
3. Change one input at a time (Eur, K₀, water level, prop timing) and write what moved.
4. Cross-check FoS with a limit-equilibrium tool on the same section.
5. Read someone else's calculation report and mark assumptions you would challenge.
6. Only then move to 3D or advanced constitutive models.

Frequently asked questions

Is FEM more accurate than hand calculations?
Not automatically. FEM can represent more of the real problem. Accuracy still depends on investigation data, parameters, staging and review. Hand calculations remain essential benchmarks.

Should every retaining wall use FEM?
No. Many walls are designed efficiently with earth-pressure methods and wall software. Use FEM when movement, neighbours, staging or unusual ground make deformation and interaction important.

Mohr–Coulomb or Hardening Soil?
Use Mohr–Coulomb for first strength/mechanism checks. Use Hardening Soil (or similar) when serviceability movements matter and you have credible stiffness data, especially unloading stiffness.

Why did my safety calculation not converge?
It may be physical failure — or a numerical issue (mesh, step size, constitutive settings, boundary conditions). Inspect the mechanism, refine the mesh, and compare with limit equilibrium before treating non-convergence as a FoS.

What should I put in the report?
Purpose, ground model, constitutive models and parameter sources, stages, drainage assumptions, boundary/mesh notes, key plots, sensitivity, benchmarks, and what would change the recommendation.

Key terms in geotechnical design and FEM analysis

Use this glossary when a report, tutorial or software manual throws a term at you. Terms are grouped by theme. Skim the group that matches what you are doing today; you do not need to memorise all 100 up front.

Safety, limit states and classical checks

1. Limit equilibrium analysis

A classical check that compares the forces or moments trying to cause failure with those resisting it, usually along an assumed slip surface. It remains the everyday benchmark for slopes and many retaining checks, even when FEM is also used.

2. Method of slices

A limit-equilibrium technique that divides the soil mass above a trial slip surface into vertical slices so equilibrium can be assessed slice by slice. Most commercial slope software is built on variants of this idea.

3. Bishop’s simplified method

A widely used circular-slip method of slices that satisfies overall moment equilibrium and is still a default choice for many slope FoS calculations.

4. Spencer’s method

A more rigorous method of slices that satisfies both force and moment equilibrium. It is useful for non-circular and composite slip surfaces.

5. Morgenstern–Price method

Another rigorous limit-equilibrium method for general slip surfaces, with flexible assumptions about interslice forces. Often used when the failure surface is not a simple circle.

6. Factor of safety (FoS)

How much stronger the ground (or system) is than it needs to be for equilibrium: available resistance divided by the resistance required for balance. Values above 1.0 indicate reserve against the mechanism analysed.

7. Critical slip surface

The potential failure surface with the lowest FoS — the one the analysis says is most likely to fail. Finding it usually means searching many trial surfaces.

8. φ/c reduction (strength reduction method)

In FEM, cohesion and tanφ are reduced together until the model can no longer find equilibrium or a clear mechanism forms. The reduction factor is reported as the FoS. It does not require assuming a circular surface in advance.

9. Ultimate limit state (ULS)

The design check against collapse or rupture: bearing failure, slope failure, structural snap-through, or similar. Safety against failure, not comfort of service.

10. Serviceability limit state (SLS)

The design check against excessive movement, cracking, tilt or other performance problems in normal use. In FEM work, SLS often governs wall deflection and settlement.

Foundations, bearing and settlement

11. Allowable bearing pressure

The foundation pressure you may use in design after applying FoS and settlement limits. It is usually the lower of the strength-based and settlement-based values.

12. Ultimate bearing capacity

The pressure that would cause shear failure of the supporting soil under a foundation. It is a strength limit, not a settlement limit.

13. Bearing capacity factors (Nc, Nq, Nγ)

Dimensionless factors in classical bearing-capacity formulas. They depend mainly on the friction angle and scale cohesion, surcharge and self-weight contributions.

14. Shape / depth / inclination factors

Corrections applied to bearing-capacity equations for footing shape, embedment depth and inclined loading. They adjust the ideal strip-footing solution toward real geometry.

15. General shear failure

A clear foundation failure mode with a well-defined slip surface and heave beside the footing. Typical of stronger, denser ground under relatively shallow footings.

16. Local shear failure

Partial plastic yielding under the footing without a fully developed failure surface. Common in intermediate ground where compressibility and strength both matter.

17. Punching shear failure

The footing punches downward into compressible ground with little side heave. Often associated with soft or loose soils and deeper relative embedment.

18. Net / gross bearing pressure

Gross pressure includes the effect of soil displaced by the foundation. Net pressure is the extra pressure beyond the existing overburden at founding level — usually what settlement and net capacity checks use.

19. Contact pressure distribution

How pressure is shared under a footing or raft. Real distributions are often non-uniform because of stiffness of the structure and non-uniform ground.

20. Settlement analysis

Prediction of how much a foundation, embankment or fill will move downward under load, immediately and over time.

21. Immediate (elastic) settlement

Settlement that occurs almost as soon as load is applied, mainly from distortion of the ground. In clay it is often treated as undrained deformation.

22. Consolidation settlement

Time-dependent settlement as water is squeezed from fine-grained soils and excess pore pressure dissipates. It can dominate long-term performance on soft clay.

23. Differential settlement

Uneven settlement between parts of a structure. It often causes more damage than a larger uniform settlement.

24. Angular distortion

Relative settlement between two points divided by the distance between them. A common SLS acceptance measure for buildings and stiff structures.

Earth pressure, retaining and soil–structure interaction

25. Active earth pressure

The minimum lateral soil pressure on a wall when the wall moves away from the soil enough to mobilise active failure. Used for many retaining design cases.

26. Passive earth pressure

The maximum lateral resistance when a wall is pushed into the soil. Passive resistance is valuable but mobilises only at larger movements.

27. At-rest earth pressure (K₀)

Lateral pressure when there is essentially no lateral strain — the natural 'locked-in' horizontal stress state. Critical for initial stress generation in FEM.

28. Rankine theory

Classical earth-pressure theory for smooth vertical walls based on plastic equilibrium in the soil mass. Simple, transparent and still taught as a first check.

29. Coulomb theory

Earth-pressure theory that includes wall friction and a planar failure wedge. It is often closer to real walls than frictionless Rankine assumptions.

30. Earth pressure coefficient (Ka, Kp, K₀)

Ratios of horizontal to vertical effective stress for active (Ka), passive (Kp) and at-rest (K₀) conditions. They convert vertical effective stress into design lateral stress.

31. Surcharge loading

Extra surface load from traffic, stockpiles, cranes or adjacent buildings. It increases earth pressures, bearing demand and settlements and must appear in staged models.

32. Overturning

A retaining structure rotating or toppling under lateral loads. Checked as a ULS stability mode for gravity and cantilever walls.

33. Sliding

A retaining structure sliding horizontally on its base. Resistance comes from base friction, adhesion and any passive resistance in front of the toe.

34. Global stability

Overall stability of the wall–soil system on a deep slip surface, not just local sliding or overturning of the wall stem. FEM strength reduction is often used here alongside limit equilibrium.

35. Embedment depth

How deep a footing, wall toe or pile tip sits below ground or dredge level. Embedment affects capacity, movement and passive resistance.

36. Structural forces (shear, moment, axial)

Internal forces in walls, piles, slabs, anchors and props that structural design must resist. FEM is often used to extract these envelopes through construction stages.

37. Soil–structure interaction (SSI)

How soil and structure deform together and share load. Ignoring SSI can mispredict both ground movement and structural demand.

38. Interface friction / Rinter

The strength (and often stiffness) reduction applied at soil–structure contacts in numerical models. Rinter < 1.0 allows slip and reduces adhesion/friction relative to the adjacent soil.

Drainage, groundwater and construction staging

39. Drained analysis

Analysis where pore pressures are assumed to dissipate freely with loading. Appropriate for long-term conditions and free-draining soils; uses effective-stress strength parameters.

40. Undrained analysis

Short-term analysis with no drainage during loading. Typical for rapid excavation or loading in clay; often uses undrained strength su.

41. Fully coupled flow–deformation

An FEM formulation that solves deformation and groundwater flow together so pore pressure and displacement interact at each step. Needed when timing of consolidation matters.

42. Consolidation analysis

Time-dependent coupled settlement and pore-pressure dissipation under load. Used for embankments, fills and foundations on clay.

43. Steady-state seepage

Long-term groundwater flow where heads no longer change with time. Typical for permanent seepage through or around a structure.

44. Transient (unsteady) seepage

Groundwater flow that changes with time — pumping, rainfall, reservoir drawdown or changing boundary heads.

45. Staged construction

Modelling construction step by step: activate/deactivate soil, supports, loads and water conditions in sequence so stress paths stay realistic.

46. Excavation sequence

The order of digging and installing support in a pit or cut. Prop timing and lift thickness often control wall movement more than wall thickness alone.

47. Initial stress generation

Setting realistic in-situ stresses and pore pressures before any construction stage. Bad initial stresses poison every later result.

48. K₀ procedure

Initialising horizontal effective stress from vertical effective stress using K₀. Common for level ground with horizontal strata; often followed by a plastic nil-step if equilibrium needs cleaning up.

49. Gravity loading (gravity switch-on)

Building initial stresses by applying self-weight in the model. Useful for slopes and non-horizontal stratigraphy where a simple K₀ field is not enough.

FEM model setup: geometry, mesh and boundaries

50. Finite element method (FEM)

A numerical method that splits soil and structures into finite elements, solves for nodal unknowns (usually displacements), and derives stresses, strains and forces for design.

51. Plane strain model

A 2D model assuming zero strain out of plane. Suitable for long walls, embankments and tunnels with roughly constant cross-section.

52. Axisymmetric model

A 2D model of a problem with rotational symmetry about a vertical axis — circular footings, shafts and single piles under centred vertical load.

53. 3D continuum model

A full three-dimensional FEM representation used when geometry or loading varies strongly in all directions.

54. Mesh / discretisation

Breaking the geometry into finite elements for computation. Mesh choice is a modelling decision, not an automatic detail.

55. Mesh refinement (graded mesh)

Using smaller elements where stresses and strains change rapidly, and larger elements farther away. Improves accuracy without wasting compute everywhere.

56. Node

A mesh point where primary unknowns (typically displacements, sometimes pore pressures) are calculated.

57. Element (continuum element)

A small volume or area of soil or rock with an assumed displacement field. Element order and shape affect accuracy near failure and in axisymmetry.

58. Degrees of freedom (DOF)

The independent movements allowed at a node (for example ux, uy, uz). Boundary conditions restrain selected DOFs.

59. Boundary conditions

The supports, rollers, loads and drainage conditions applied at model edges and surfaces. They stand in for the infinite ground outside the mesh.

60. Far-field boundary

A distant model edge placed far enough that it does not artificially stiffen or distort the zone of interest.

Constitutive models and material parameters

61. Constitutive model

The mathematical stress–strain (and often hydraulic/time) law assigned to a material. It is the heart of whether FEM predicts realistic movement and failure.

62. Linear elastic model

Hooke’s law with constant E and ν. Useful for stiff structural parts or far-field zones; too crude for most soil near failure.

63. Mohr–Coulomb model

An elastic–perfectly plastic model with a c–φ failure criterion. The standard first-order soil model for strength and plastic zones.

64. Drucker–Prager model

A smooth plastic yield surface often used as an alternative or approximation to Mohr–Coulomb in continuum plasticity.

65. Hardening Soil (HS) model

An advanced elastoplastic model with stress-dependent stiffness and separate loading and unloading stiffnesses (E50, Eoed, Eur). Common for excavations and serviceability predictions.

66. Modified Cam-Clay (MCC)

A critical-state clay model linking compression, yielding and strength through void ratio and mean effective stress. Suited to soft, near-normally consolidated clays.

67. Critical state

A state of continued shearing at constant volume and constant effective stress — the large-strain 'steady' condition many clay models aim toward.

68. Dilatancy angle (ψ)

Controls plastic volume change during shear. ψ ≈ 0 for many clays at critical state; dense sands may dilate (ψ > 0). Non-associated flow (ψ ≠ φ) is usual for soils.

69. Young’s modulus (E)

Elastic stiffness: axial stress divided by axial strain. In soils it is rarely a single constant — strain level and stress path matter.

70. Poisson’s ratio (ν)

Lateral strain divided by axial strain under uniaxial loading. In undrained saturated clay, ν is often taken near 0.5.

71. Shear modulus (G)

Stiffness in shear: shear stress divided by shear strain. Small-strain G is central to dynamic and low-strain deformation problems.

72. Unloading–reloading stiffness (Eur)

The higher stiffness used when soil is unloaded then reloaded. Excavation heave and wall movement are often sensitive to Eur.

73. Secant stiffness (E50)

Average stiffness to about 50% of peak strength in a drained triaxial test. A core Hardening Soil input.

74. Oedometer stiffness (Eoed)

Confined one-dimensional compression stiffness from an oedometer/consolidation test. Captures primary compression response.

75. Non-associated flow rule

Plastic strain increments are not perpendicular to the yield surface (ψ ≠ φ). More realistic for soils than associated flow, which can overpredict dilation.

76. Yield surface

The stress boundary beyond which permanent (plastic) strains develop. Inside the surface, response is mainly elastic (or hypoelastic).

77. Plasticity / plastic zone

Regions where the soil has yielded and is accumulating irreversible strain. Contours of plastic points help you see mechanisms.

78. Strain hardening / softening

Strength or stiffness increasing with plastic strain (hardening) or decreasing after peak (softening). Softening models need careful mesh and energy control.

79. Large deformation / updated mesh

Analysis that updates geometry as displacements become large — soft soil collapse, large wall movements or progressive failure.

Stress paths, numerics and analysis types

80. Convergence / residual

A measure of how close the numerical solution is to equilibrium. Small residuals mean the step has converged; non-convergence may be physical failure or a numerical issue.

81. Load stepping / iteration

Applying load or excavation in increments and iterating within each step so nonlinear material behaviour can be followed stably.

82. Plastic calculation

A standard elastoplastic FEM stage used to compute deformation and forces under a construction or load phase.

83. Safety calculation

A dedicated FoS analysis, commonly φ/c reduction, run from a reached stress state after plastic staged construction.

84. Dynamic analysis

Time-domain or frequency-domain response to earthquakes, machine vibration or impact. Needs appropriate damping, boundaries and small-strain stiffness.

85. Excess pore pressure

Pore pressure above or below the steady hydrostatic/seepage value caused by undrained loading or unloading. It changes effective stress and temporary strength.

86. Effective stress path

The track of effective stress during loading. Drainage and stress path control whether the soil dilates, contracts, hardens or approaches failure.

87. Principal stresses

The three normal stresses on planes of zero shear (σ1 ≥ σ2 ≥ σ3). Failure criteria and many plots are framed in principal stress space.

88. Deviatoric stress (q)

A scalar measure of shear intensity in the stress state. In triaxial compression it reduces to σ1 − σ3.

89. Mean effective stress (p′)

The average effective stress. It controls volumetric behaviour and stiffness in many advanced soil models.

90. Stress history / OCR in analysis

Accounting for the maximum past effective stress (preconsolidation) relative to today’s stress. OCR strongly affects K₀, stiffness and undrained strength.

Structural elements, checking and reporting

91. Plate / shell element

Structural elements for walls, slabs and linings that carry bending and membrane forces. Used to extract design shear and moment.

92. Beam / embedded beam

Elements for piles, props and beams. Embedded beams interact with the surrounding continuum along their length.

93. Geogrid / membrane element

Tensile reinforcement elements with little or no bending stiffness — geogrids, geotextiles and similar inclusions.

94. Interface element

Thin elements that allow relative shear and normal movement between soil and structure. Essential for realistic SSI.

95. Anchor / strut modelling

Representing prestressed ground anchors or temporary struts as discrete supports with stiffness, prestress and sometimes free length.

96. Groundwater flow boundary

Prescribed head, impermeable boundary, well, drain, recharge or seepage face that controls water entering or leaving the model.

97. Hydraulic head / equipotential

Total hydraulic energy level of groundwater. Equipotentials are lines or surfaces of equal head in a flow net or seepage solution.

98. Sensitivity analysis

Re-running the model with varied inputs — stiffness, strength, groundwater, mesh, boundaries — to see what actually drives the design answer.

99. Model validation / calibration

Checking the model against hand calculations, lab/field benchmarks or monitoring before relying on it for decisions.

100. Post-processing (displacements, stresses, forces)

Reading and plotting outputs: movements, stresses, pore pressures, plastic zones and structural force envelopes for design and review.

Remember

• FEM is only as good as the ground model and the construction sequence you feed it.
• Choose the simplest constitutive model that captures the behaviour you need to decide.
• Stiffness and groundwater usually control serviceability; strength controls collapse.
• Stage the works as they will be built, including temporary support timing.
• Always cross-check with conventional methods and field evidence.
• Document assumptions, factors, and what would change the recommendation.

Before you start a FEM package of work

• Write the design questions and acceptance criteria (movements, FoS, forces) in one page.
• Confirm the investigation can support the chosen constitutive model — especially stiffness and groundwater.
• Agree 2D vs 3D and the representative sections with the design team.
• Lock the temporary works sequence with the contractor where possible.
• Define benchmarking and sensitivity cases up front.
• Decide what will be monitored, and what actions follow if triggers are approached.

Building or reviewing a numerical model and need the site data behind it first? See Geotechnical Site Investigation, Soil Classification, and Geotechnical Modelling and Analysis. All written for Australian practice.