Drivability — MADEP CPT Interpreter

Scope and positioning

1. Scope: design, drivability, vibration and execution

Following the course chapter (§2), four different engineering questions surround a driven element, and no single equation answers them all:

Permanent design — what geotechnical resistance and serviceability must the completed pile or wall provide? A Eurocode 7 problem, handled by the retaining-wall, soldier-pile and pile-capacity chapters.
Installation drivability — can the selected element and plant penetrate the actual profile without refusal, instability or unacceptable pile stress? This chapter.
Vibration emission and reception — what vibration reaches the neighbours? The vibration chapter.
Execution verification — how are the predictions checked and updated on site? Instrumented trial and trigger-action plan (vibration chapter §7–8).

Non-normative status (PLAN D10; course §3.3, §7.1, §18.5). The drivability models are empirical research equations. Attaching a familiar factor such as 1.35 or 1.50 does not make them Eurocode compliant, and applying the permanent-design strength factors backwards to an installation resistance is unsafe for machine selection (a lower design strength makes the pile look easier to drive). The route therefore uses an upper-bound resistance profile and a transparent equipment reserve multiplier m_R; no partial factor appears anywhere in srd-from-cpt.js, vibratory-drivability.js or impact-wave-equation.js. Results must be confirmed by an instrumented trial.

Resistance profile

2. CPT → static resistance to driving

buildDrivingResistanceProfile resamples the CPT of the active sounding on a uniform grid of dz = 0.10 m below the driving platform (the same datum shift as the wall design; the CPT ground-level offset is honoured and reported). q_c is read in MPa and converted to kPa; the shaft stress of interval j is taken at its centre, the toe value at z_j. Rows with a missing f_s use f_s = R_f,assumed·q_c (default 1 %) with a note; depths beyond the CPT hold the last value (note emitted); an optional arithmetic averaging window ± w around the toe is available (default 0 = point value, as in the course).

Reference method (course §7.2 “static reference unit resistance”) — an illustrative upper-bound screen, not a pile design method; the user factors default to 1:

q_s(z) = f_toe·f_SRD·q_c(z), τ_s(z) = f_shaft·f_SRD·f_s(z)

FR(z) = 100·f_s/q_c (percentage number)

Alm & Hamre (2001) — friction-fatigue model, coefficients transcribed from the ISSMGE open-access paper (15th ICSMGE Istanbul, pp. 1297–1302) and cross-checked against the OPILE and groundhog documentation. p₀′ = effective overburden at the interval centre (from the layer unit weights and a single water table unless σ′_v0[] is supplied; floor 1 kPa), p_a = 100 kPa, p = tip penetration, δ = constant-volume interface friction angle (per-layer input; module default 29°, not from the paper):

τ_i(p) = f_s,res + (f_s,i − f_s,res)·exp[−k·(p − z_i)] (eq. 1, friction fatigue)

clay: f_s,i = f_s(CPT), f_s,res = 0.004·q_T·(1 − 0.0025·q_T/p₀′) (eq. 2)

sand: f_s,i = K·p₀′·tan δ, K·p₀′ = 0.0132·q_T·(p₀′/p_a)^0.13, f_s,res = 0.2·f_s,i (eq. 3, 4)

k = (q_T/p₀′)^0.5 / 80 (eq. 5)

sand: q_tip = 0.15·q_T·(q_T/p₀′)^0.2; clay: q_tip = 0.6·q_T (eq. 6)

0 ≤ f_s,res ≤ f_s,i (clip); intervals outside the layer list → sand, δ = 29° (note)

q_c is used where the paper writes q_T (no pore-pressure correction is applied).
The sand friction is calibrated for outside friction only; for open elements with inside friction the paper's recommendation — 50 % on both faces — is available (insideFriction: 'half-both'). Unplugged piles are assumed.
The paper's ×1.25 for an upper-bound profile is the srdFactor option (applied to all unit resistances, note emitted).
In the app the layer soil class comes from the interpreted CPT layer type (clay/peat → clay, otherwise sand for Alm & Hamre; silt is a separate class only for the Smith damping).

Integration at every trial toe depth z_j (P = outer + inner contact perimeter, A_toe = toe area × plug ratio, interlock resistance in kN per metre embedded):

R_shaft(z_j) = Σ_{i ≤ j} τ_i(z_j)·P·dz (Alm & Hamre: τ_i depends on the tip position)

R_interlock(z_j) = r_interlock·z_j (course §6.5: not derivable from CPT — experience / trial)

R_toe(z_j) = q_s(z_j)·A_toe

R_static(z_j) = R_shaft + R_interlock + R_toe

Element geometry

3. Driven element from the wall section

The geometry comes from the catalogue section selected for the wall design (drivenElement in the drivability panel; SI properties from section-properties.js):

Element	Toe area	Contact perimeter	Interlock	Mass
Sheet pile, single	A (m²/m) × b — steel area at the toe plane	developed perimeter ≈ 2·A/t per metre of wall × b (both faces of the developed section — a documented approximation)	two free interlocks: 2 × r_interlock	mass per single pile
Sheet pile, pair	A × 2b	2·A/t × 2b	one free interlock: 1 × r_interlock	2 × mass per pile
H-pile, unplugged (default)	steel area A	2b (flange faces) + 2h (web cavities)	0	catalogue kg/m
H-pile, plugged	box area b·h	box perimeter 2(b + h)	0	catalogue kg/m

The steel area A_s (for the stress screen and the wave-equation impedance) is always the steel area. The target depth defaults to the retained height + over-excavation + provided embedment of the wall design; the modelled pile length is the target depth + 0.5 m of stick-up. For the vibratory run the pile mass (mass per metre × pile length) is added to the vibrator's dynamic mass unless switched off.

Vibrodriving

4. Vibratory force-envelope method (Hypervib1-type)

For every trial toe depth z_j ≤ target, runVibratoryDrivability finds the smallest peak centrifugal force F_c for which the peak downward force F_c + W_eff is at least m_R times the vibratory driving resistance R_drive(F_c). Because the driving resistance itself depends on F_c through the pile acceleration (higher acceleration → more degradation), the root is found by bisection with an inner acceleration iteration. Units kN, kPa, m, kg, Hz, g = 9.81 m/s².

Degradation (course §5.2, §7.3; Holeyman 2002 eq. 18) — FR as a percentage number, Λ the liquefaction factor (default 6, clipped to the published 4–10 range with a note):

χ_i = (1 − 1/Λ)·exp(−1/FR_i) + 1/Λ (FR = 0 → χ = 1/Λ)

q_l = χ·q_s, τ_l = χ·τ_s (fully degraded, “liquefied”)

Acceleration-dependent resistance (course §7.5–7.6; Holeyman 2002 eq. 19), iterated to convergence (tolerance 0.01 on |Δa|/max(a, 0.01g), at most 50 iterations):

α = a/g

q_d = (q_s − q_l)·e^−α + q_l, τ_d = (τ_s − τ_l)·e^−α + τ_l

R_s = Σ τ_d,i·P·dz, R_b = q_d,toe·A_toe, R_drive = R_s + R_b + R_interlock

a = max[0, 1000·(F_c − δ_H·R_s) / M_dyn] (δ_H = 0 → free acceleration, optimistic baseline)

Force envelope and root (course §4.4, §8; Holeyman 2002 §5.2 force-equilibrium class):

W_eff = M_dyn·g/1000 + F_crowd − T_line [kN]

G(F_c) = F_c + W_eff − m_R·R_drive(F_c) ≥ 0

F_c,min = smallest F_c with G ≥ 0 — bisection on [0, m_R·R_static + 1], 64 halvings (G is monotone because R_drive decreases with α)

reported for m_R (default 1.0) and always for m_R = 1.25, each with its governing depth (max over the depths)

Conversion to a machine requirement at the operating frequency f, and the preliminary stress screen (course §4, §8.7–8.8):

ω = 2πf; M_e = 1000·F_c/ω² [kg·m]

s₀ = M_e/M_dyn [m]; A_pp = 2·s₀

α_req = 1000·F_c/(M_dyn·g)

σ_screen = (F_c + W_eff)/A_s (uniform axial stress; not computed when A_s is unknown)

A candidate machine (catalogue or custom F_c, or M_e·ω²/1000) is checked at every depth: the worst margins G(m_R = 1) and G(1.25), α, R_drive and the machine conversion at that force; the force-envelope curve G(F_c) is plotted at the governing depth up to 1.4 × the largest force of interest.

Provenance and verification status (agent report §2.1)

Verified verbatim: χ (eq. 18a/b), the acceleration interpolation q_d = (q_s − q_l)e^−α + q_l (eq. 19a/b), FR as a percentage and “Λ chosen in the range of 4 to 10” — Holeyman, A. (2002) Soil behavior under vibratory driving, keynote TransVib 2002, pp. 14–15 (open PDF).
Verified as a model class: The inequality F_c + W_eff > R_drive is the “force equilibrium model” class (Jonker 1987; Warrington 1989) reviewed in the same keynote §5.2 and in course §4.4.
Course only: The δ_H shaft-reaction reduction of the free acceleration and the m_R reserve multiplier. The keynote describes Hypervib1 as an “iterative procedure to identify the coexisting acceleration and soil resistance” without giving δ_H; Van Rompaey, Legrand & Holeyman (1995) and Holeyman & Whenham (2017) are paywalled and were not checked in full (the 2017 abstract confirms the Λ nomenclature).
Numerical parity: Course §8 worked example reproduced to better than 4 significant figures: χ = 0.473233, R_static = 252.794 kN, W_eff = 36.582 kN, α(125 kN) = 5.7919, q_d = 1424.522 kPa, R_drive = 120.037 kN, G(1.25) = 11.536 kN, F_c,min = 85.574 / 113.809 kN, M_e = 2.5847 kg·m, s₀ = 1.175 mm, σ = 24.3 MPa, and the seven §8.9 sensitivities.

Limitations. It does not predict the penetration rate, and it does not check amplitude under load, clamp capacity, power, wave stress or ground vibration (course §7.10) — those are separate checks. δ_H = 0 is an optimistic baseline that should be calibrated against the measured amplitude of a trial (course §15.8). One FR per interval is used for both shaft and toe; no plug mass is modelled.

Impact driving

5. Smith (1960) one-dimensional wave equation

runImpactDrivability simulates one hammer blow at each trial toe depth (every 0.5 m to the target in the app) on a lumped-mass chain: ram → hammer cushion → helmet → (pile cushion) → N pile segments, each a mass joined by a spring; the soil along the shaft and at the toe acts through elasto-plastic springs (quake q, ultimate R_u) with Smith damping. Smith's paper itself is paywalled and was not read; the formulation follows the GRLWEAP descriptions cited below.

Model and defaults

Hammer: Ram impact velocity v₀ = √(2·g·h·η) with h = rated energy/(m_ram·g) when no stroke is given (GRLWEAP procedure). Efficiency η by class: hydraulic 0.80, diesel 0.80, hydraulic/diesel with internal energy monitoring 0.95, single-acting air/steam 0.67, double-acting air/steam or hydraulic 0.50; drop hammers 0.50 is a placeholder (not in the fetched source — set explicitly). Diesel hammers are modelled as an equivalent free-fall ram of the rated energy; combustion, pre-compression and the impact block are not modelled (note emitted).
Cushions: Compression-only springs: loading stiffness k, unloading stiffness k/e² with the coefficient of restitution e (Smith 1960; default e = 0.8 hammer cushion, 0.5 pile cushion). App defaults: helmet 1500 kg, hammer cushion 2.5·10⁶ kN/m; the module falls back to a near-rigid contact of 10 × the pile segment stiffness when no cushion stiffness is given (note emitted).
Pile: Uniform steel section: E = 210·10⁶ kPa, ρ = 7850 kg/m³, segments of 1.0 m (L/N), m_seg = ρ·A·L_seg, k_pile = E·A/L_seg, c = √(E/ρ), impedance Z = E·A/c; pile springs linear and tension-capable (continuous pile).
Quakes: Shaft 2.5 mm; toe 2.5 mm, or D/120 (very dense/hard) … D/60 (softer/loose) for displacement piles — Rausche, GRLWEAP Fundamentals (PDCA) slides 38–40; FHWA GEC-12 Vol. II §12.5.
Smith damping: Shaft: clay 0.65 s/m (0.20 s/ft), sand 0.16 s/m (0.05 s/ft), silt 0.40 s/m (intermediate); toe, all soils 0.50 s/m (0.15 s/ft) — GRLWEAP slide 42; GEC-12 §12.8. The app assigns the shaft value per CPT layer class and maps it to segments by resistance weighting.
Refusal: Labelled at ≥ 250 blows/0.25 m (set ≤ 1 mm) by default; the FHWA GEC-12 Vol. II §17.2 practical refusal of 10 blows/inch ≈ 98 blows/0.25 m is quoted alongside.

Soil springs at pile mass i (u displacement, v velocity, u_P plastic displacement), Smith damping R_dyn = R_static·(1 + J·v):

shaft (two-way): R_s = k_s·(u − u_P), k_s = R_u/q_shaft, |R_s| ≤ R_u (u_P updated on yield); R = R_s·max[0, 1 + J_s·v·sign(R_s)]

toe (compression-only): R_t = k_t·(u − u_P,toe) ∈ [0, R_u,toe], k_t = R_u,toe/q_toe; R = R_t·(1 + J_t·max(0, v))

the damping product is clipped at zero when the static and damping terms oppose — a numerical safeguard, not part of Smith's paper

Explicit central-difference (leap-frog) integration with an automatic time step; the run stops when the ram has separated, the toe has not advanced for 6·L/c and the pile has lost its kinetic energy (or all soil springs are unloaded), or after 40·L/c without further toe advance:

Δt = min(0.5·L_seg/c, 0.1/ω_max), ω_max = max √[k·(1/m_i + 1/m_i+1)] (energy error ∝ (ωΔt)²; set within 0.5 % of a refined run)

v_n+½ = v_n−½ + a_n·Δt, u_n+1 = u_n + v_n+½·Δt

set = u_P,toe (= D_max,toe − q_toe, Smith 1960); blows per 0.25 m = 0.25/set

σ_c,max = max(F_segment, F_top)/A, σ_t,max = max(−F_segment)/A

ENTHRU = ∫ F_{top spring}·v_{pile top} dt (energy transmitted into the pile)

energy audit: E_ram,0 = E_ram + E_kin,others + E_strain + W_cushion + W_contact + W_soil + imbalance

Bearing graph. At the final depth the shaft and toe resistances are scaled together in 12 steps up to 3 × R_static and the blow count, set, stresses and ENTHRU are tabulated against R_u — the classical bearing graph, keeping the shaft/toe split of that depth.

Simplifications (documented in the module header). No gravity or static pre-equilibrium (self-weight ≪ driving forces); no residual stresses between blows; no splices or slacks; no pile-cap impedance change; no plug mass; single blow per depth; uniform pile section; set = D_max − q ignores the residual elastic compression. The SRD profile of §2 (upper bound) is the resistance input.

Static push-in

5b. Static push-in (press-in) — quasi-static force balance

For an element pushed in with a static force — excavator crowd through a driving cap, or the rated force of a press-in machine — runPushIn (push-in.js) answers "how deep does it go" with the force balance at every trial toe depth:

F_push + W(z) ≥ m_R·R_static(z), R_static = R_shaft + R_toe + R_interlock (§2 profile, no dynamic degradation)

W(z) = m′·g·z (element self-weight over the embedded length; optional)

refusal = first z with F_push + W < m_R·R_static; F_required(target) = max_{z ≤ target} [m_R·R_static(z) − W(z)]

Reported for m_R = 1.0 and 1.25 (equipment reserve, not a partial factor), with the governing depth, the margin at the target, the per-depth table, the depth chart (R_static, F_required, F_push, refusal marker) and the outcome marker on the section.

Assumptions. Quasi-static (no rate effects, no set-up between strokes, no plug model beyond the element's toe-area choice); the static profile is the upper envelope of §2 — the right basis for "will it get there", too high for capacity. The Alm & Hamre option with friction fatigue is the usual press-in basis (White & Deeks 2007: press-in force ≈ static CPT-based capacity with friction fatigue). A press-in machine needs its reaction (installed elements or ballast); an excavator can push only what its weight and boom geometry allow — typically not more than 30–50 % of its operating weight through the boom. Obstructions and layers with q_c > 30 MPa refuse pressing regardless of the balance; pre-drilling or vibratory assistance is the usual answer (course §14).

Equipment data

6. Hammer catalogue policy

hammer-catalog.js is pure data. Only verified rows are exported: every row carries the URL that was actually fetched on the stated date (2026-08-29) and a source note; rows whose datasheet could not be retrieved are omitted, and fields a source did not state are null — the UI then asks the user, never guesses. A “custom” entry is always offered.

Rows	Source fetched	Verified fields
ICE 28RF	Dieseko specification sheet (TWF mirror) + Dieseko product page	0–28 kgm, 2300 rpm, 0–1600 kN, dynamic mass 3900 kg (5400 with 200TU clamp), total 5900 kg, amplitude 14/10.4 mm, line pull 400 kN, pull-down 150 kN
ICE 14RF, ICE 815C, PVE 23VMA	Dieseko product pages	moment, force, rpm only — dynamic mass `null` (datasheets behind a form)
ABI MRZV 20VV / 30VV	ABI “Technical Data MRZV VV” sheet (A E Yates)	moment, dynamic mass 2810 / 3995 kg, nominal and max rpm, forces, total mass (the sheet's “100 kN” for the 20VV is an evident misprint for 1000 kN, noted)
Junttan HHK 5A, 5/6A, 7A, 7/9A	Junttan data sheets 05/2011	ram 5000 / 6000 / 7000 / 9000 kg, 59 / 71 / 82 / 106 kJ, 1.2 m stroke, 40–100 bpm, total mass
IHC S-70 … S-280	IHC Hydrohammer onshore brochure IHC02-30-11.12 (mirror) + PDI hammer database cross-check	ram, max net energy, blow rate, total mass
Delmag D30-32, D46-32	Pileco / piledrivershop specification sheets	ram 3000 / 4600 kg, 48.1–95.1 / 71–166 kJ (pump settings), blow rate, total mass; PDI database values noted where they differ

vibratoryConsistency() checks F_c ≈ M_e·(2πf)²/1000 for every vibratory row against the stated force (all within 1.5 %). Impact rows carry the GRLWEAP class efficiency as efficiencyDefault (0.80 for all listed hydraulic and diesel hammers). For a vibratory catalogue row the app uses the dynamic mass with clamp when published and the maximum eccentric moment; for a custom machine the user supplies F_c or M_e.

Data sheet → model

7. Data-sheet input and achievable depth

A supplier sheet describes a machine (centrifugal force, rpm range, amplitude, mass, oil flow, working pressure, motor power, carrier class). The force-envelope model needs the mechanics: eccentric moment M_e, operating frequency f, attached (vibrating) mass M_dyn and the static downforce. vibrator-datasheet.js translates one into the other with the relations of course §4.1–4.3 and records, for every derived number, which sheet value it came from. Blanks are derived; nothing is guessed silently.

Sheet line	Model quantity	Relation
Centrifugal force F_c (kN) — printed at the maximum rpm unless stated otherwise	Eccentric moment M_e	M_e = 1000·F_c/ω_max², ω = 2π·rpm/60 (course §4.1). A printed M_e takes precedence; a >10 % mismatch with the force is flagged.
Frequency range (rpm)	Operating frequency f; force at f	F_c(f) = M_e·(2πf)²/1000 — a fixed-moment machine loses force quadratically below its maximum rpm (205 kN at 2900 rpm is 140 kN at 2400 rpm). The check uses the maximum rpm unless an operating rpm is entered.
Amplitude (mm)	Vibrating mass M_dyn (when not printed)	Peak-to-peak: M_dyn = 2000·M_e/A_pp; single: M_dyn = 1000·M_e/s₀ (course §4.2). Dieseko/ICE, PVE and ABI print the peak-to-peak free amplitude (ICE 28RF: 2·28/3900 = 14.4 mm ≈ sheet 14 mm; with the 200TU clamp 2·28/5400 = 10.4 mm = sheet). The convention is an input; a stated mass is checked against the amplitude.
Vibrating mass / total mass (kg)	M_dyn; static weight of the isolated part	W_static = (M_total − M_dyn)·g — the suppressor housing rests on the pile through its springs and is added to the crowd (course §4.3, W_transmitted); a crane line carrying part of the weight is entered as line pull.
Oil flow, working pressure, motor power, carrier class	Carrier check (not part of the force envelope)	Hydraulic power P = p·Q/600 kW, reported at the working point and at the sheet maxima. The carrier must be inside the class range, deliver at least the working flow and pressure, and not exceed the machine maxima without a limiter / relief. Course §4.6: real power demand depends on the phase between force and velocity — the sheet values and a trial are the only reliable basis.

Achievable depth. With a machine described (data sheet, catalogue row or a custom F_c / M_e) the runner adds the element mass to M_dyn, evaluates the margin G(z) = F_c + W_eff − m_R·R_drive(z) at every trial toe depth from the platform down, and reports the first depth at which the envelope closes (G < 0) as the predicted refusal — the machine cannot pass it, whatever the margin further down (course §4.4: the inequality identifies whether motion is mechanically possible; it does not give the penetration rate). Three outcomes are reported and drawn on the section:

Reaches target (green): G ≥ 0 down to the target with the 1.25 equipment reserve.
Marginal (amber): G ≥ 0 at m_R = 1.0 but the 1.25 reserve is lost below the depth shown — plan a trial pile and a fallback (heavier head, crowd, pre-drilling).
Refusal (red): G < 0 at the depth shown; the achievable depth is the last open trial depth (0.1 m steps). The shortfall to the target is printed.

The minimum vibrator card is the inverse question: the smallest F_c (and its M_e, attached amplitude and acceleration at the chosen frequency and mass) for which the envelope stays open to the target — the specification to send to suppliers (course §7.9).

Plate compactors. An excavator compactor sheet (e.g. SAES HST) lists the same quantities but the machine has no clamp: the element is not rigidly attached, so the attached-mass assumption (M_dyn includes the element) is optimistic. Use such a sheet for light trench sheets driven through a driving cap only, and expect a trial to govern. Amplitude under load, clamp grip, pile stress, resonance and ground vibration remain the separate checks of course §7.10.

Outputs and limitations

8. Reported results and documented limitations

Profile: z, q_toe, τ_shaft, FR, cumulative shaft, interlock, toe and R_static at every trial depth, with every assumption as a note (held values beyond the CPT, assumed f_s, factors, unplugged assumption).
Vibratory: per depth R_static, R_liquefied, χ_toe, R_s, R_b, R_drive, α, q_d, τ_d, F_c,min(m_R) and F_c,min(1.25); the governing depths; M_e, s₀, A_pp, α_req, σ_screen at the required, the 1.25-reserve and the candidate force; the candidate check; the force-envelope curve.
Impact: per depth R_static, R_shaft, R_toe, set, blows/0.25 m, refusal flag, σ_c,max, σ_t,max, ENTHRU, maximum toe displacement and top force, the energy audit; the hammer (η, stroke, v₀, E_kin), the pile model (segments, c, Z) and the bearing graph.
All model outputs are plain numbers (worker-transferable); invalid input returns ok: false with notes, never throws.
The two drivability models are not linked to the vibration prediction; the link is the instrumented trial (course preface).
Extraction, offshore piles, obstructions, very long elastic piles and pore-pressure / liquefaction effects are outside the hand methods (course §1.2).
The hand methods cannot give an exact vibrator force from q_c, f_s, length and embedment alone (course §1.3): geometry and toe condition, masses, frequency, moment, downforce, inner/outer contact, interlocks, groundwater, actual amplitude and power all matter — hence the explicit reserve multiplier and the trial.

References

9. Reference basis

Alm, T. & Hamre, L. (2001). Soil model for pile driveability predictions based on CPT interpretations. Proc. 15th ICSMGE, Istanbul, pp. 1297–1302 (ISSMGE open-access PDF) — friction-fatigue SRD model, coefficients verified verbatim.
Holeyman, A. (2002). Soil behaviour under vibratory driving. Keynote, TransVib 2002 (Louvain-la-Neuve; Balkema), pp. 14–15 — χ (eq. 18), acceleration interpolation (eq. 19), FR in percent, Λ ∈ [4, 10], force-equilibrium model class (§5.2), Hypervib1 (§5.5.1).
Van Rompaey, D., Legrand, C. & Holeyman, A. (1995). A prediction method for the installation of vibratory driven piles. WIT Trans. Built Env. 14 (Proc. 7th Int. Conf. Soil Dynamics and Earthquake Engineering, Chania, 1995), 533–542, WIT Press e-library — original Hypervib1 formulation.
Holeyman, A. & Whenham, V. (2017). Critical review of the Hypervib1 model to assess pile vibro-drivability. Geotech. Geol. Eng. 35, 1933–1951, doi 10.1007/s10706-017-0218-8 — Λ nomenclature confirmed from the abstract.
Smith, E.A.L. (1960). Pile-driving analysis by the wave equation. ASCE J. Soil Mech. Found. Div. 86(SM4), 35–61, doi 10.1061/JSFEAQ.0000281 — lumped-mass model, quake, damping R(1 + Jv), cushion restitution, set = D_max − q (citation confirmed; full text paywalled).
Rausche, F. GRLWEAP Fundamentals (PDCA) — ram velocity √(2ghη) (slide 17), efficiencies (slide 28), quakes (slides 38–40), damping (slides 41–42). GRL (2007). Hammer Types, Efficiencies and Models in GRLWEAP. Rausche, Liang, Allin & Rancman (2004). Applications and correlations of the wave equation analysis program GRLWEAP.
FHWA GEC-12, NHI-16-009 Vol. II (2016). Design and Construction of Driven Pile Foundations — §12.5, §12.8 quake and damping defaults, §17.2 practical / absolute refusal.
Course text: Manual Design of Vibratory Pile Installation (edition 1.0) — §2 the four calculations, §4 vibrator mechanics, §5–7 CPT model and force envelope, §8 worked example (reproduced), §18 common errors.
Manufacturer data as listed per catalogue row (Dieseko/ICE/PVE, ABI, Junttan, IHC Hydrohammer, Delmag) with the PDI hammer database as cross-check.
NBN EN 12699:2015 / NBN EN 12063 — execution standards for driven displacement piles and sheet-pile walls (the execution specification the drivability screen feeds; not implemented as a check).

Every equation on this page is transcribed from srd-from-cpt.js, vibratory-drivability.js and impact-wave-equation.js; the verification status of each source is that of worklog/agent-drivability-report.md. The three Node scripts verify_srd_profile.mjs, verify_drivability_vibratory.mjs and verify_drivability_impact.mjs (171 checks) are run by npm run verify:drivability.