Shared notation, governing equations, and modelling assumptions.

1.1 Coverage

The documentation covers the implemented interpretation workflow: CPT file parsing for GEF, Excel, and CSV sources, per-point CPT classification, layer detection, layer parameter assignment, stiffness derivation, and experimental m-fitting. It is intended as the full technical account of Stages 1 to 5 rather than a short product summary.

Where the application contains an engineering simplification, the simplification is stated explicitly. The purpose is not to replace engineering judgement, but to make the implemented mathematics auditable and readable.

• Classification and boundary logic are documented separately from parameter assignment.
• Stage 6 uses the interpreted CPT state produced by the earlier stages rather than reclassifying the profile independently.
• The notation follows geotechnical convention with compression positive and depth measured downward.

1.2 Layer quantities carried into engineering use

Per interpreted layer, the application carries the quantities needed by the engineering modules:

Geometry, load combination, hydraulic scenario, and optional Stage 5 tuning are then applied on top of those layer values. The Stage 6 analyses do not reclassify the profile — they consume the interpreted layer model directly.

2.1 Effective stress convention

Compression is taken as positive throughout the engineering modules. Depth z is measured downward from ground level. Elevation values are interpreted in Belgian TAW convention where relevant. The in-situ effective-stress profile is reconstructed from the active groundwater level and the interpreted unit weights.

Only the normal stress components are shifted by pore pressure — the shear components are unaffected. Above the phreatic level the dry unit weight γ is used; below it, γ_sat is used. Compression-positive effective stress is the natural convention for Mohr-Coulomb evaluation and geostatic interpretation, and all later normal/effective distinctions in the deformation route follow from this sign rule.

• z is depth below ground level [m]; z_w is the phreatic level depth below ground [m].
• γ is the unit weight above the phreatic level; γ_sat below; γ_w is the unit weight of water.
• Δz_i is the thickness contribution of layer i; γ_i is the unit weight selected for that layer's position relative to the phreatic level.

2.2 Hydraulic head convention

The seepage route solves for total head, from which pore pressure is derived:

This convention is consistent with the current Stage 6 seepage and coupling logic.

2.3 Plane strain and small strain

The public deformation route uses plane strain on a two-dimensional section and assumes small strain:

The geometry is therefore not updated during the current equilibrium iterations.

3.1 Vector convention and engineering shear

All six-component tensor quantities in the deformation route use the Voigt-6 convention with engineering shear strain (γ = 2ε). The order is [xx, yy, zz, xy, yz, zx] for stress and strain; the engineering shear factor lets the stress-strain relation read linearly as σ = D ε in the shear block.

3.2 Isotropic linear-elastic stiffness

3.3 Plane-strain reduction

For plane strain ε_zz = γ_yz = γ_zx = 0. The reduced 3×3 elastic matrix, acting on plane strains [ε_xx, ε_yy, γ_xy], is the xx/yy/xy block of D_e:

The out-of-plane effective stress σ′_zz is not constrained to a single elastic closed form in plastic runs: σ′_zz becomes an internal state variable and its K₀-controlled initialization is preserved through the Stage 2 return map.

3.1 Raw CPT quantities

The interpretation chain starts from depth, cone resistance q_c, sleeve friction f_s, and optionally pore pressure u₂. The friction ratio is central enough to record at the top:

Supported file structures and column mapping

GEF files declare their physical quantities through #COLUMNINFO lines. The application reads the quantity identifier and maps it to the relevant column index; column order is therefore never assumed.

• GEF quantity 1: penetration length.
• GEF quantity 2: q_c.
• GEF quantity 3: f_s.
• GEF quantity 4: R_f.
• GEF quantity 6: u₂.
• GEF quantity 11: corrected depth, used before quantity 1 when both are present.

Excel workbooks are read from a Data sheet and, when present, a Header sheet. The Data sheet may contain depth, q_c, f_s, and R_f; the Header sheet can provide project, test, location, date, water level, surface level, coordinates, and the net area ratio. CSV files are the reduced-input route — they must contain headers depth and qc; fs and rf are optional. Comma, semicolon, and tab delimiters are detected automatically.

Unit conversion and row filtering

The parser converts q_c and f_s to MPa based on the declared GEF unit string or the Excel/CSV column header. Headers containing MPa are used directly; kPa is divided by 1000; Pa is divided by 1 000 000. If the unit declaration is absent or ambiguous, a heuristic fallback is used so the file remains workable, but explicit unit labels are strongly recommended.

• Depth is expected in metres below surface; rows with z < 0 are discarded.
• Rows with q_c < 0.02 MPa are treated as cone-not-engaged and discarded.
• All-zero rows appended by logging software are discarded.
• R_f is optional; when absent or invalid, the app computes it from f_s and q_c via the equation above.

Water table, elevation, and TAW metadata

The phreatic level is taken from the GEF measurement variables or the Excel Header field Waterniveau when available; otherwise a default depth below surface is assigned. Surface elevation is read from the GEF ZID header, the Excel Header field Grondniveau, or entered manually.

When surface elevation is present, all depth values can be expressed relative to TAW as well as depth below surface.

3.2 Classification is not parameter assignment

This is one of the most important design choices in the app. Robertson, CUR, NEN 6740, and NEN Tabel 3 all appear in the workflow, but they do not all serve the same purpose. The classification stage creates a rationalized soil interpretation; the parameter stage maps the final layer to engineering properties.

Robertson (1990) — normalized SBT / I_c

Robertson uses a normalized q_t–F_r framework. Because final layer unit weights are not yet available at Stage 2, the route uses a preliminary stress estimate with fixed γ = 17 kN/m³ above the water table and γ_sat = 18 kN/m³ below.

The result is mapped into the app's broad families: Gravel, Sand, Silty sand, Sandy clay, Clay, and Peat / organic. Sensitive fine-grained soil is not inferred separately from I_c alone.

Robertson (2016) — iterative Q_tn

Robertson 2016 keeps the same SBT / I_c family mapping but replaces the fixed-stress-exponent cone normalization with an iterative Q_tn formulation. The exponent n varies with the inferred soil behaviour and is solved iteratively. This route is preferred when the input is a CPTu, but the implementation does not require measured u₂.

CUR 3 layers — broad q_c–R_f zoning

The CUR 3 layers route is a direct q_c–R_f zoning rule based on the published broad chart with four material fields: Sand, Silt, Clay, and Peat. It is a boundary-generation method, not a detailed parameter catalogue. No stress correction is applied to q_c before classification.

The chart field "Silt" is carried internally as the app's intermediate family (CUR3 silt) so that the downstream parameter workflow remains stable.

NEN 6740 — stress-dependent material classification

NEN 6740 uses a stress-corrected cone resistance and a graphical chart with fourteen material areas. The app evaluates the published Deltares stress correction and then applies a transparent representative-area rule that selects the nearest material area from a digitized fourteen-material set.

The 0.67 exponent is the documented Deltares implementation of the published NEN route. The 0.34 coefficient is not a normative NEN constant; it is the regression-fit semilog projection used by the app to deterministically reproduce the graphical chart.

NEN Tabel 3 — direct subtype classification

The NEN Tabel 3 route uses raw q_c and R_f and returns a detailed subtype together with the characteristic parameter row used later in the workflow. Because the table contains overlapping q_c–R_f envelopes, the app evaluates rows deterministically in table order: grind, zand, leem, klei, then veen. q_c lower bounds are inclusive and upper bounds exclusive; the open R_f bands < 1 and > 6 remain strict, while the bounded intervals are treated as closed. For this method, raw boundary logic follows the detailed subtype result rather than only the broad family.

3.3 q_c-to-E_oed,i correlation and α methods

The first stiffness step converts the representative cone resistance into an oedometric modulus through one of two α correlations selected in the Stage 4 UI: Method A — Sanglerat literature (fixed α per behavioural soil type) or Method B — SB260-21-6.4.10 (q_c-graded family rules). Method A and Method B are alternative routes; they produce different α — and hence different E_oed,i — for the same layer. The result E_oed,i is a CPT-derived stiffness at the layer's in-situ stress level, before the Hardening Soil reference-stress correction.

Method A — Sanglerat fixed α by behavioural type. Method A applies a fixed Sanglerat-style α default keyed to the broad layer type, so a single α applies to the whole layer regardless of q_c.

Method B — SB260-21-6.4.10 by family, keyed to the EC7 subtype. Method B applies the Tabel 21-6-5 rules, structured around three families: cohesive (klei, leem, veen), transition / overgangsgronden (the (zh) and (lh) subtype variants), and granular / zandgronden (zand, grind, grind (kh)). The family is selected from the EC7 subtype string first, falling back to the broad type when no subtype is set.

• Method A and Method B are not interchangeable: Method A is Sanglerat literature, with high α for granular soils (Sand = 13, Gravel = 15). Method B is SB260 with E_s = 4q_c in the granular family, which gives much smaller effective α (e.g. α = 4 for q_c ≤ 10 MPa).
• The (zh) suffix on klei / leem and (lh) suffix on zand route to the transition family. The (kh) suffix on grind routes to the granular family.
• For peat, water content w is not available in the app, so Method B uses the SB260 default α = 1.5.
• For the full implemented α reference table — every family, q_c band, and modulus formula — see Stage 4 §4.2 of the workflow specification.

3.4 Effective stress at layer midpoint

The reference-stress correction below uses the effective vertical stress at layer midpoint as the in-situ anchor. Above the water table γ is used; below it, γ_sat is used. Pore pressure is hydrostatic.

The phreatic level therefore directly affects the reference stiffness correction in the next subsection.

3.5 Reference-stress correction (shared by Methods A and B)

Both Method A and Method B apply the same Hardening Soil reference-stress correction to convert the in-situ E_oed,i from §3.3 into the reference-stress quantity E_oed,ref at p_ref = 100 kPa. The cohesion-corrected form is used so the correction stays well-behaved in cohesive layers where σ′_v0 can be small relative to c′ cot φ′. Methods A and B differ only in how E_50,ref and E_ur,ref are derived from this shared E_oed,ref; the depth correction itself is identical in both routes.

The stress-exponent default uses the CUR 2003-7 binary: m = 0.5 for granular soils (Sand, Silty sand, Gravel) and m = 1.0 for cohesive soils — klei en leem (Clay, Soft clay, Sandy clay, Peat / organic). The grouping of "klei en leem" includes Sandy clay (leem), so leem is treated as cohesive in both the stress-exponent and the family-rule defaults. Stage 5 m-fitting can override m per layer when site-specific evidence supports a different value.

Sources: CUR 2003-7 (m binary, ν_ur); Schanz, Vermeer & Bonnier (1999) (HS reference-stress correction); SB260-21-6.4.10 (cohesion-corrected denominator form); PLAXIS 2D Material Models Manual (ψ_unsat).

3.6 Method A — CUR 2003-7 stiffness ratios

Method A takes the shared E_oed,ref from §3.5 and applies the CUR 2003-7 family rule to derive E_50,ref. E_ur,ref is taken as three times E_50,ref. The family rule treats klei and leem together, so Sandy clay (leem) is in the cohesive set with the 1.25 factor; for granular soils E_50,ref is set equal to E_oed,ref.

Sources: CUR 2003-7 (E₅₀/E_oed ratio); aGEO (E_ur,ref = 3 E_50,ref); Jáky / EN 1997-1 (K_0,nc).

3.7 Method B — E_50,ref = E_oed,ref

Method B takes the shared E_oed,ref from §3.5 and sets E_50,ref equal to E_oed,ref for all soils. E_ur,ref remains three times the selected E_50,ref.

This gives a single consistent reference stiffness and is sometimes preferred in practice when the engineer wants to avoid the cohesive-soil E₅₀/E_oed split.

3.8 Hydraulic conductivity basis

The app uses indicative hydraulic conductivity values tied to Belgian and USDA-style texture classes, with OVAM 2002 (Tabel 2-44) and De Smedt / VUB 2005 (Tabel 2-45) as the principal reference sources for the I/RA/11461.15.066/JSW guideline. The representative value is treated as a geometric-mean estimate within the adopted class range rather than a deterministic measurement.

Anisotropy is introduced through a k_h/k_v ratio. Sand and gravel are taken as isotropic. Cohesive soils (Clay, Sandy clay / leem, Peat) are taken as k_h/k_v = 3. Silty sand ("fijn zand") sits between the two regimes, and the engineer selects between two anisotropy methods in the Stage 4 UI:

• Method A — OVAM / I/RA/11461 (default). Conservative Belgian engineering practice value. Silty sand is grouped with the fine soils, k_h/k_v = 3.
• Method B — Bear (1979) academic. Literature-typical intermediate value for fine / silty sand, k_h/k_v = 2. Reflects the partly-cohesive nature of silty sand without lumping it fully with cohesive soils.

In-situ measurement takes priority over the indicative table values when available. The engineer can override k_h and k_h/k_v per layer.

3.9 Experimental m-fitting

Stage 5 fits the Hardening Soil stress exponent m to the pointwise CPT-derived E_oed,i values inside one layer. The oedometer law of the Hardening Soil model is linear in logarithmic form, so an OLS regression on (ln(stress ratio), ln(E_oed,i)) pairs gives both m and E_oed,ref directly:

The fit is experimental and remains an engineer preview: the routine never overrides the CUR 2003-7 default automatically. The interface shows the default line, the fitted line, and the point cloud; the engineer may still adjust the previewed m before acceptance, and accepting the fit overrides m only — the reference stiffness is then recomputed from the accepted m.

4.1 Governing PDE

The seepage route is a steady-state saturated-flow problem:

For isotropic homogeneous soil this reduces to Laplace’s equation. In the app, the heterogeneous anisotropic form is preserved because material zones carry their own conductivity values.

4.2 Boundary classes

The public seepage route distinguishes prescribed head, no-flow, and seepage-face boundaries. In the current workflow these are applied to the outer section boundary rather than arbitrary interior edges.

4.3 Free-surface interpretation

Unconfined flow is nonlinear because the active saturated domain is itself part of the solution. The current public route therefore uses an iterative free-surface / seepage-face interpretation rather than a one-shot confined-flow solve.

5.1 Global equilibrium

The deformation route is written in residual form:

5.2 Geostatic preparation

The initial stress state is prepared by a linear gravity step and a K_0,nc-controlled confinement reconstruction. Optionally, the seeded predictor may then be corrected by a plastic self-weight equilibration phase before the service-load step starts.

5.3 Constitutive staging

The current public deformation route supports three constitutive interpretations:

• Linear elastic for baseline screening.
• Stage 1 reduced stiffness as a pseudo-plastic exceedance route.
• Stage 2 exact Mohr-Coulomb elastoplasticity as the current default plastic route.

The shipped Stage 2 route stores plastic strain and uses an exact Mohr-Coulomb active-set return with shear face, shear edge, apex, tension-face, mixed shear-tension, and triple tension-point branches in principal effective stress space.

6.1 Yield function in principal stress space

Using compression-positive effective principal stresses ordered σ₁ ≥ σ₂ ≥ σ₃, the Mohr-Coulomb criterion in its critical form reads:

For the exact multisurface treatment, three pair-wise surfaces F_ij (index pair ij ∈ {12, 13, 23}) are retained simultaneously. F₁₃ governs on the ordered face; F₁₂ and F₂₃ pick up the σ₁=σ₂ and σ₂=σ₃ edges respectively.

6.2 Non-associated flow rule

Plastic flow follows a plastic potential G built with the dilatancy angle ψ′ ≤ φ′. The flow is non-associated when ψ′ ≠ φ′; for dilatant soils ψ′ > 0 introduces a volumetric plastic strain component.

6.3 Return mapping and algorithmic tangent

Because F is piecewise linear in stress, the return map closes in a single linear step on each active branch. The return equation and the algorithmic consistent tangent follow the Simo–Taylor form:

The unsymmetric D_ep is preserved by default in the shipped Stage 2 route. Symmetrization is offered as a convenience option but is theoretically a projection and loses accuracy on active-set transitions.

6.4 Strength reduction (c-φ reduction)

The safety-by-c-φ-reduction route divides the strength parameters by a common multiplier Σ_Msf and searches for the critical value at which equilibrium fails to close:

Reported factor of safety is the highest converged lower bound. The upper bound (first non-converging multiplier) and the bracket are reported alongside so the engineer can judge the numerical uncertainty on the critical state.