Vibration Impact — MADEP CPT Interpreter

Scope and positioning

1. Source–path–receiver

The vibrating or hammered pile is the source; the ground is the path along which the particle velocity reduces with distance through geometric spreading and material damping but can be amplified by layering and resonance; the building and its occupants are the receiver, each with its own criterion. The source strength is not uniquely defined by the vibrator's catalogue force, and CPT data do not define the vibration at a neighbour (course §1.3, §2.3): the predictor below is statistical and must be verified during execution. The drivability model of the drivability chapter and the PPV model are linked only through the instrumented trial.

One framework per receiver function. Each receiver function is tied to one standard, says so in its result (framework, source, quantity), and the wrapper assessReceiver compares the prediction with that single framework. The limits refer to different quantities and locations — SBR-A: the velocity component V_top at the measuring point; DIN 4150-3: the maximum component at the foundation or the horizontal component at the top floor; BS 7385-2: the peak component at the building base — whereas the predictors give the resultant PPV at the ground surface. Comparing a predicted resultant with a component limit is conservative; the notes repeat this.

Source and path

2. Empirical PPV predictors (ppv-prediction.js)

Vibratory piling — TRL 429 (Hiller & Crabb 2000) as reproduced in BS 5228-2:2009+A1:2014 Annex E, Table E.1. Resultant PPV at the ground surface at horizontal distance x from the active pile; k_v carries an exceedance probability (a statistical predictor, not an upper bound), δ_v the operating phase; calibration domain 1 ≤ x ≤ 100 m and 1.2 ≤ W_c ≤ 10.7 kJ per cycle:

v_res = k_v · x^−δ_v [mm/s, x in m]

k_v = 60 (50 % exceedance), 126 (33.3 %), 266 (5 %)

δ_v = 1.4 (steady-state driving), 1.3 (all operations), 1.2 (start-up / run-down)

The app evaluates all nine (phase, probability) pairs for the receiver distance and plots the distance curves. Outside 1–100 m a note says extrapolation is not justified without site data; k_v = 266 is flagged as an approximate 95th-percentile screening envelope, not a maximum. Course §11 values at 30 m (steady 0.513 / 1.078 / 2.275, all 0.721 / 1.514 / 3.196, start-up 1.013 / 2.127 / 4.491 mm/s) are reproduced.

Percussive (impact) piling — BS 5228-2 Annex E, Table E.1 equation with Table E.2 k_p. W is the hammer energy per blow in joules (the app uses rated energy × efficiency), r the slope distance from the pile toe; calibration domain 1 ≤ L ≤ 27 m, 1 ≤ x ≤ 111 m, 1.5 ≤ W ≤ 85 kJ:

v_res = k_p · √W / r^1.3, r = √(L² + x²) (L = toe depth; L = 0 → r = x, conservative)

k_p = 5 (all piles driven to refusal)

k_p = 3 (toe through very stiff cohesive, dense granular, or fill with large obstructions)

k_p = 1.5 (toe through stiff cohesive, medium dense granular, compacted fill)

k_p = 1 (toe through soft cohesive, loose granular, loose fill, organic soils)

k_p is a ground-condition factor, NOT a probability. BS 5228-2 attaches no exceedance probability to the percussive predictor; probabilistic k_p values (50/33/5 %) do not exist in the standard and are not offered. An explicit site-calibrated k_p may be passed instead of the class. In the app the toe depth is the retained height + embedment of the wall design.

Site-calibrated power law (course §9.4, §15.5), with K and n from §8:

v = K · x⁻ⁿ

Receiver framework 1

3. SBR Trillingsrichtlijn A: Schade aan bouwwerken (2017)

The framework used in Belgian monitoring practice (the T26L053 trillingsmonitoring example). The characteristic value V_kar of the building part is reduced by three partial factors; the allowable measured top velocity follows from the SBR-A inequality V_d = V_top·γ_v ≤ V_r = V_kar/(γ_t·γ_s):

V_top,allow = V_kar / (γ_s · γ_v · γ_t)

V_r = V_kar / (γ_t · γ_s) (reported)

Table	Quantity	Values implemented
10.8	V_kar, ground-floor load-bearing structure, f in Hz (linear interpolation)	category 1: 20 mm/s (0–10 Hz) → 40 (50 Hz) → 50 (100 Hz); category 2: 5 → 15 → 20 mm/s; above 100 Hz the 100 Hz value
10.9	V_kar, highest floor and non-load-bearing parts (all frequencies)	category 1: 40 mm/s; category 2: 15 mm/s
10.7	γ_s building condition / monumental status	normal 1.0; sensitive 1.7; monument 1.7
9.2	γ_v type of measurement	extensive 1.0; limited 1.4; indicative 1.6
10.6	γ_t type of vibration — structure and parts	short 1.0; repeated short-term 1.5; continuous 2.5
10.6	γ_t — settlement-sensitive foundation	short 1.0; repeated 1.6; continuous 2.0
§10.3.5	Foundation (settlement) criterion, frequency-independent	V_kar = 10·C_D, C_D = 1 + (8 − H)/7 ≤ 2 (H = thickness of the settlement-sensitive layer, m; unknown → C_D = 1); a_kar = 1 m/s² divided by γ_v only (Table 10.11: γ_t, γ_s, C_D do not apply to the acceleration)
legacy	Category 3 (pre-2017 editions: monuments / poor-condition masonry)	3 → 8 → 10 mm/s (ground floor), 8 mm/s (top floor) — kept as an explicitly labelled legacy line; SBR-A 2017 replaced it by category 2 with γ_s = 1.7 (kader 50), which the note recommends

Example reproduced exactly (T26L053 CN001A, category 2, γ_s = 1.7, γ_v = 1.6, γ_t = 1.5 structure / 1.6 foundation): 1.23 mm/s (≤ 10 Hz), 1.53 (15), 2.45 (30), 3.68 (50), 4.29 (75), 4.90 (100 Hz); top floor / non-load-bearing 3.68; foundation 10/(1.7·1.6·1.6) = 2.30 mm/s. The app's defaults are measurement type “indicative” and vibration type “repeated”.

Receiver framework 2

4. DIN 4150-3:2016-12

Guideline values (Anhaltswerte) for short-term vibration at the foundation (Table 1, frequency-dependent, linear interpolation) and in the plane of the floor of the uppermost storey (Table 1, all frequencies), and for long-term vibration at the uppermost floor (Table 3). The values are unchanged from the 1999 edition; the 2016 text itself is paywalled and was verified through reproductions plus the 2016 foreword.

Line	Foundation 1–10 Hz	10–50 Hz	50–100 Hz	Top floor, short-term	Top floor, long-term (Table 3)
1 — commercial, industrial and similar	20	20–40	40–50	40	10
2 — dwellings and similar	5	5–15	15–20	15	5
3 — particularly sensitive / listed	3	3–8	8–10	8	2.5

Above 100 Hz at least the 100 Hz value applies (Table 1 footnote); below 1 Hz the 1 Hz value is used.
Table 3 (long-term) is defined at the uppermost floor; asking for it at the foundation returns the Table 3 value with a note. DIN “short-term” is about the absence of fatigue and resonance, not calendar duration — vibratory piling may fall under the long-term provisions.
Course check: line 2 at 35 Hz = 11.25 mm/s.

Receiver framework 3

5. BS 7385-2:1993

Table 1 transient guide values for cosmetic damage, as peak component particle velocity at the base of the building, with the course §12.3 linear interpolation of line 2:

line 1 (reinforced / framed, industrial and heavy commercial): 50 mm/s at 4 Hz and above

line 2 (unreinforced / light framed, residential and light commercial): 15 + (5/11)·(f − 4) for 4 ≤ f ≤ 15 Hz

line 2: 20 + (30/25)·(f − 15) for 15 < f < 40 Hz; 50 mm/s at 40 Hz and above

continuous vibration able to excite resonance: guide value × 0.5 (BS 7385-2 allows a reduction of up to 50 % — conditional, not automatic; applied only when the option is set)

Below 4 Hz the standard also limits displacement (line 2: 0.6 mm zero-to-peak); the 4 Hz velocity value is used with a note to consult the standard.
Course check: line 2 at 35 Hz = 44 mm/s (22 mm/s with the continuous-vibration reduction); 15 Hz → 20 → 7.5 mm/s reduced.
The wording and the “up to 50 %” figure are verified; the exact clause number of the continuous-vibration reduction differs between fetched copies (the module cites §7.5) and is treated as unverified.

Occupants

6. Human response — BS 5228-2 Table B.1

Descriptors of the PPV at the point of entry into the recipient; these are not building-damage limits (a formal assessment uses BS 6472-1):

PPV	Effect
0.14 mm/s	Might be just perceptible in the most sensitive situations for most construction vibration frequencies.
0.3 mm/s	Might be just perceptible in residential environments.
1.0 mm/s	Likely to cause complaint in residential environments, but can be tolerated if prior warning and explanation has been given to residents.
10 mm/s	Likely to be intolerable for any more than a very brief exposure in most building environments.

The wrapper reports the band (below perception / perceptible / complaints likely / intolerable) next to the structural verdict, and a utilisation = predicted / limit with the verdict ok, attention (≥ 75 % of the limit by default) or exceeds.

Execution control

7. Trigger-action monitoring plan (monitoring-plan.js)

buildMonitoringPlan assembles the traffic-light plan of course §16 with the levels of the Belgian example (alarm at the SBR-A limit, SMS at 75 %):

Levels

Expected: Median-type prediction (e.g. TRL 429 k_v = 60).
Upper: Conservative prediction (e.g. k_v = 266) — the prediction-review level. If it exceeds the stop level the method must be revised before work starts; if it exceeds the warning level amber events are to be expected.
Stop (alarm): The allowable value of the selected framework at the dominant frequency (SBR-A: V_top,allow; DIN / BS: the guideline value). A project override may only lower it; a higher request is rejected with a note. Missing dominant frequency → the lowest-frequency (most conservative) limit.
Warning (SMS): warning = 0.75 × stop by default (the fraction is an input in (0, 1)).
Structural guide: The unfactored V_kar / guide value at the dominant frequency, or a project-supplied value.
Human objective: 1.0 mm/s (BS 5228-2 Table B.1 “complaints likely”), not a damage limit.

The frequency table follows the SBR-A example (Figuur 2): for f = 0, 5, 10 … 100 Hz it lists V_kar, V_allow = V_kar/(γ_sγ_vγ_t) and the warning level; for DIN 4150-3 and BS 7385-2 the V_kar column holds the guideline value and V_allow equals it (those standards have no partial factors; f is floored at 1 Hz and 4 Hz respectively). The states are:

Green — PPV below the warning level, stable penetration, no abnormal movement: continue, log, review trends.
Amber — warning ≤ PPV < stop, or the upper prediction reached, PPV rising with depth, penetration rate falling, complaint: reduce the eccentric moment / adjust the frequency, pause if needed, verify sensors and alignment.
Red — PPV ≥ stop, abnormal building or ground movement, sensor overload, prolonged refusal: stop immediately, inspect, notify the responsible engineer, revise the method before restart.

suggestSensorLayout proposes the course §15.2 layout: near-field control ≈ 5 m, intermediate ≈ 10 m and ≈ 20 m (only those closer than 0.8 × the receiver distance; an attenuation fit needs ≥ 3 distances) on triaxial geophones rigidly coupled to the ground, plus the receiver sensor on the lowest accessible load-bearing element on the source-facing side, all on a common time reference with depth, frequency and moment setting recorded simultaneously (course §15.3).

Stop level versus framework limit. The stop level must sit below the receiver limit by an allowance for instrument uncertainty, signal delay and run-down vibration (course §16.1); the plan says so in its notes, and the project must choose that allowance.

Instrumented trial

8. Site calibration of the attenuation law (attenuation-calibration.js)

Two-point calibration (course §15.5) — two measurements (x₁, v₁), (x₂, v₂) give the power law directly; no residual estimate is possible:

n = ln(v₁/v₂) / ln(x₂/x₁), K = v₁ · x₁ⁿ

Log-log least squares (course §15.6), N ≥ 3 points, X = ln x, Y = ln v:

n = −Σ(X_i − X̄)(Y_i − Ȳ) / Σ(X_i − X̄)², ln K = Ȳ + n·X̄

s = √[SSE/(N − 2)] (residual standard deviation of ln v), r² = 1 − SSE/S_yy

One-sided 95 % upper prediction (course §15.7):

ln v₉₅(x) = ln K − n·ln x + z·s, z = 1.645

Residuals in ln v are treated as normal with constant variance (homoscedastic in log space).
Small-N caveat: 1.645 is the large-sample one-sided 95 % normal quantile; with fewer than 6 points it underestimates the true prediction bound. The one-sided 95 % Student-t quantile for ν = N − 2 (6.314, 2.920, 2.353, 2.132, 2.015 … for ν = 1 … 5) is returned as tFactor for information and a note recommends a formal small-sample interval or a conservative envelope; the course expression (1.645) is what the upper prediction uses unless z is overridden.
A fitted n ≤ 0 (no attenuation with distance) and s = 0 (two-point or perfect fit — no statistical allowance) are flagged. A best-fit line is not an upper bound; operational variability (start-up, refusal, depth) must be added separately. Separate fits are required for materially different source conditions.
Course example reproduced: (10 m, 5.0 mm/s) and (20 m, 2.0 mm/s) → n = 1.3219, K = 104.93, v(30 m) = 1.17 mm/s.

Assumptions and limitations

9. Documented assumptions

The TRL 429 / BS 5228-2 predictors are screening tools calibrated on a UK database (resultant PPV at the ground surface, 1–100 m); they use neither the vibrator force, the CPT data nor the soil damping, and the 5 % curve is not a maximum.
No acceleration predictor exists for the SBR-A foundation criterion (a_kar = 1 m/s²); it is exposed as a monitoring criterion only.
Settlement and densification of loose saturated sand are not covered by any PPV criterion (course §13) and require a separate cyclic assessment.
SBR-A category 3 is verified only for the pre-2017 editions and is labelled legacy; DIN 4150-3 values were verified through reproductions of the 1999 table and the 2016 foreword; the BS 7385-2 clause number of the continuous-vibration reduction is unverified (the value is not).
Non-Belgian guidance (BS 5228-2, BS 7385-2, DIN 4150-3) is used only when specified or technically justified (course §3.2); none of it is a Eurocode partial-factor rule.
Human exposure is a separate comfort assessment (BS 6472-1); the Table B.1 descriptors are indicative.

References

10. Reference basis

Hiller, D.M. & Crabb, G.I. (2000). Groundborne vibration caused by mechanised construction works. TRL Report 429 — the vibratory-piling predictor k_v·x^−δ.
BS 5228-2:2009+A1:2014. Code of practice for noise and vibration control on construction and open sites — Part 2: Vibration. Annex E Table E.1 (predictors and calibration ranges), Table E.2 (k_p), Annex B Table B.1 (human response) — verified from the full text and cross-checked with NZTA research report 485.
SBR Trillingsrichtlijn A: Schade aan bouwwerken: 2017 (SBRCURnet) — §9.5 Table 9.2, §10.3.2 Tables 10.6–10.7, §10.3.3 Table 10.8, §10.3.4 Table 10.9, §10.3.5 (foundation), Table 10.11, kader 50 — verified from the guideline text and a consultant's worked examples.
DIN 4150-3:2016-12. Erschütterungen im Bauwesen — Einwirkungen auf bauliche Anlagen. Table 1 (short-term), Table 3 (long-term).
BS 7385-2:1993. Evaluation and measurement for vibration in buildings — Part 2: Guide to damage levels from groundborne vibration. Table 1 and the continuous-vibration clause.
BS 6472-1:2008 — human exposure to vibration in buildings (referenced, not implemented). ISO 4866:2010 — measurement and evaluation of vibration effects on structures.
Course text: Manual Design of Vibratory Pile Installation (edition 1.0) — §9–12 quantities, TRL 429 worked example and receiver criteria, §15 instrumented trial and calibration, §16 trigger-action plan.
MADEP. T26L053 CN001A — LL Trillingsmonitoring (2026-08-27) — the Belgian SBR-A limit derivation V_top,allow = V_kar/(γ_s·γ_v·γ_t) and the frequency table the plan reproduces.

Every coefficient on this page is transcribed from ppv-prediction.js, receiver-criteria.js, attenuation-calibration.js and monitoring-plan.js; the per-value verification trail is in worklog/agent-vibration-report.md. The three Node scripts (139 checks) run with npm run verify:vibration.