1 · Purpose and scope
BuriedPipeCalc assesses the effect of temporary surface patch loads (plant, outriggers, stockpiles, propping) on an existing buried pipe or service. It computes the surcharge-induced vertical stress at pipe level by elastic theory, adds it to the in-situ overburden, and runs an optional structural check to BS 9295:2020+A1:2025.
It is a screening and serviceability tool for an existing pipe of known diameter, depth and material family. It is not a full pipe design. It does not size new pipe, and it does not cover ring-bending strain / wall fracture (which require wall-section data), longitudinal effects, joint performance, fatigue, or thermal effects. The acceptance decision rests with the engineer; this tab states exactly what the program computes, what is assumed, and what the checker must independently confirm.
2 · Notation
| Symbol | Meaning | Units |
|---|
| P | total vertical load on a patch | kN |
| q | patch contact pressure = P / (Bx·By) | kPa |
| Δσz | Boussinesq vertical stress increase at the pipe | kPa |
| z, R | depth below surface; slant distance element→point | m |
| γ, z_c, D | soil bulk unit weight; depth to crown; pipe diameter | kN/m³, m, m |
| p_v | total vertical pressure at crown = γ·z_c + Δσz | kPa |
| SN | nominal ring stiffness (BS EN ISO 9969) = EI/D³ | kN/m² |
| E′ | modulus of soil reaction (entered in MPa) | kPa |
| D_L, K | deflection lag factor; bedding constant | – |
| Δ/D | predicted diametral deflection ratio | – |
| q_cr, B′, R_w | buckling allowable pressure; elastic-support coeff.; buoyancy factor | kPa, –, – |
| W | vertical line load on pipe = p_v·D_o | kN/m |
| F_c, F_m, F_se | works crushing strength; bedding factor; factor of safety | kN/m, –, – |
| K₀ | at-rest earth-pressure coefficient = 1 − sin φ′ | – |
3 · Geometry and conventions
The setting-out axis runs parallel to the pipe. X is the perpendicular offset from the axis to the pipe centreline; Y is the chainage along the pipe. Each patch is a rectangle defined by its centre (X,Y), side lengths Bx (along the patch axis) and By (perpendicular), and an angle θ measured anti-clockwise from the X datum.
Patch load is entered as a total vertical load P (kN) and converted to a uniform contact pressure q = P / (Bx·By). Loads are taken to act at the ground surface (z = 0). Depths are measured from that surface to crown, centre (z_c + D/2) and invert (z_c + D).
The pipe is evaluated on its vertical centreline (x = offset) and the program reports the worst section, i.e. the chainage giving the maximum crown stress.
4 · Surcharge stress — Boussinesq elastic half-space
Vertical stress increase under a surface point load Q at depth z and slant distance R (Boussinesq, 1885):
Δσz = 3·Q·z³ / (2π·R⁵) , with R = √(rₓ² + r_y² + z²)
Each patch is integrated over its rotated plan area, dQ = q·dA, and contributions from all active patches are superposed (linear elasticity). The integral is evaluated numerically by an 18 × 18 grid of sub-cells with 2 × 2 Gauss–Legendre quadrature per cell (nodes ±1/√3).
Verification: the numerical integration reproduces the closed-form Newmark/Fadum solution for a uniformly loaded rectangle, and the point-load limit Δσz → 3Q/(2πz²) directly beneath a small patch, in both cases to five significant figures. Convergence is achieved well below the 18-cell density used. Boussinesq is the conventional, conservative basis for surcharge stress on buried apparatus (it gives higher near-load stresses than Westergaard).
5 · In-situ and total stress
Existing crown overburden (total vertical stress): σ_v,exist = γ·z_c
Total crown pressure used in the structural check: p_v = γ·z_c + Δσz,crown
Percentage increase = Δσz,crown / (γ·z_c) × 100.
A single bulk unit weight is used and no pore-water pressure is modelled; σ and Δσ are therefore consistent total stresses. The percentage increase, and the ring / ovalisation pressure indices on the results panel, are relative indicators for judging how far the loading regime has changed — they are not limit states and are not pipe-wall stresses.
6 · BS 9295 check — flexible pipe (plastic, steel, ductile iron)
Soil-supported pipes are checked for ring deflection (serviceability) and constrained buckling (stability). Diametral deflection by the modified Iowa / Spangler equation, expressed in nominal ring stiffness:
Δ/D = D_L·K·p_v / (8·SN + 0.061·E′)
Derived from Spangler Δx = D_L·K·W·r³/(EI + 0.061·E′·r³) with W = p_v·D and EI/r³ = 8·EI/D³ = 8·SN. Because SN = EI/D³ is a class property, diameter cancels from the ratio — wall thickness is not required.
Constrained (in-soil) buckling allowable pressure (AWWA M45 form):
q_cr = (1/F_b)·√(32·R_w·B′·E′·SN) , B′ = 1 / (1 + 4·e^(−0.213·H_ft)) , H = z_c + D/2
Utilisations: deflection = (Δ/D) / (Δ/D)_allow ; buckling = p_v / q_cr. The governing (larger) utilisation drives the verdict.
Ring-bending strain / wall fracture is not evaluated (needs wall thickness and material strain limit). For thermoplastics the deflection limit normally governs serviceability; buckling matters more at depth, under vacuum, or below the water table.
7 · BS 9295 check — rigid pipe (concrete, vitrified clay)
Rigid pipes fail by wall fracture and are checked on crushing strength × bedding factor against the field line load:
Field vertical line load: W = p_v · D_o (D_o taken as the pipe diameter)
Allowable line load: W_allow = F_c · F_m / F_se → utilisation = W / W_allow
If the crushing strength is not entered, the program instead reports the required works (three-edge-bearing) strength: F_c,req = W · F_se / F_m
F_c is a manufacturer/class property (e.g. BS 5911 concrete, BS EN 295 clay) and must be taken from the pipe specification. The required-strength output lets a rigid pipe be screened even when its class is unknown.
8 · Acceptance criteria
The limit-state criterion is demand ≤ allowable, i.e. utilisation ≤ 1.00. The program reports a banded verdict:
| Verdict | Condition | Interpretation |
|---|
| PASS | utilisation ≤ 0.85 | demand comfortably within allowable |
| REVIEW | 0.85 < utilisation ≤ 1.00 | within allowable but close — confirm inputs and factors |
| REVIEW | capacity not defined | rigid pipe, no F_c entered; required F_c shown |
| FAIL | utilisation > 1.00 | demand exceeds allowable |
The limit boundary is utilisation = 1.00 (demand = allowable). The 0.85 PASS/REVIEW split is a conservative, non-codified margin flag chosen for this program — it is not a BS 9295 requirement. A result of 0.85–1.00 is still within the stated allowable.
The flexible deflection limit is a serviceability criterion (protecting cleaning, CCTV, lining and lateral connections), not a structural collapse limit — flexible pipes do not reverse curvature until ~20–30% deflection. The allowable Δ/D must be taken from the project specification, the pipe manufacturer's data, or the asset owner's requirement. Commonly specified long-term limits are ~5–8% (≈6% is common UK practice); the program default of 5% is at the conservative end and must be confirmed for the actual pipe.
9 · Assumed values and program defaults
All values below are editable. Defaults are conservative starting points, not recommendations for a specific pipe. The checker should confirm each against the pipe specification and BS 9295:2020+A1:2025.
9.1 Analysis / integration
| Parameter | Value | Note |
|---|
| Sub-cell grid per patch | 18 × 18 | fixed; Gauss-converged |
| Quadrature per cell | 2 × 2 Gauss–Legendre | nodes ±1/√3 |
| Sample points along pipe | 151–401 | auto = ⌈L×30⌉+1 |
| Chainage range | auto | min(0, y_min−2.0) to y_max+2.0 m |
9.2 Flexible check
| Parameter | Default | Options / basis |
|---|
| Ring stiffness SN | 4 kN/m² | SN2 / SN4 / SN8 / SN16 / custom (BS EN ISO 9969) |
| Soil modulus E′ | 3 MPa | 1.5 / 3 / 7 / 14 MPa / custom (Howard, modulus of soil reaction) |
| Deflection lag D_L | 1.0 | 1.0 immediate; up to ~1.5 long-term granular |
| Bedding constant K | 0.10 | 0.083–0.110 (Spangler), per bedding angle |
| Allowable Δ/D | 5 % | serviceability limit — set from spec/manufacturer/owner |
| Buckling FoS (F_b) | 2.5 | AWWA M45 |
| Water buoyancy R_w | 1.00 / 0.84 | dry / below water table (toggle) |
9.3 Soil modulus E′ guidance (Howard)
| Embedment condition | E′ (MPa) |
|---|
| Poor — dumped / low compaction fines | ≈ 1.5 |
| Moderate — slight compaction granular | ≈ 3 |
| Good — well-compacted granular | ≈ 7 |
| High — heavily compacted granular | ≈ 14 |
9.4 Rigid check — bedding factor F_m
| Bedding class | F_m (default set) |
|---|
| Class N — natural / as-dug | 1.1 (default) |
| Class F — granular bed | 1.5 |
| Class B — granular bed + cover | 1.9 |
| Class S — full granular surround | 2.2 |
| Class A — concrete bed / cradle | 2.6 |
Factor of safety F_se default = 1.25; works crushing strength F_c blank by default. Bedding factors above are typical values for screening — confirm against BS 9295 and the actual bedding detail.
10 · Validity, limitations and checker's verification list
Key modelling assumptions a checker should be aware of:
• Free-field stress: the pipe's own stiffness is ignored in the Boussinesq stage. This is reasonable (slightly conservative) for flexible pipe — soil-structure interaction re-enters through E′ in the deflection check — but rigid pipes attract load relative to the ground, so the crushing check relies on the bedding factor to represent support.
• Loads act at the ground surface; depths are from that surface. If plant bears at a formation level below ground, enter the depth from the load plane.
• Loads are characteristic / unfactored. Apply partial and dynamic factors externally as required (BS 9295 aligns traffic loading to BS EN 1991-2).
• Single bulk unit weight; no groundwater pore pressure in the overburden term.
Before accepting a result, confirm:
| Item | Source to confirm against |
|---|
| Pipe type (flexible / rigid) — steel and DI are flexible | pipe records / material standard |
| Diameter, depth to crown, soil unit weight | site records / trial holes |
| SN (flexible) or F_c crushing class (rigid) | pipe specification / manufacturer |
| E′ and bedding factor F_m | backfill / bedding detail, BS 9295 |
| Allowable Δ/D and factors of safety | project spec / owner / BS 9295 |
| Load magnitudes and partial factors | temporary-works design / BS EN 1991-2 |
With these inputs confirmed, the computed demand (validated Boussinesq) and the BS 9295 capacity checks are traceable and reproducible: every equation, factor and assumed value used is listed on this tab and echoed numerically in the Calc tab for the actual run.
11 · References
• BS 9295:2020+A1:2025 — Guide to the structural design of buried pipes (UK established method; complementary to BS EN 1295-1:2019).
• BS EN 1295-1:2019 — Structural design of buried pipelines, general requirements (defers structural methodology to national standards).
• BS EN ISO 9969 — Thermoplastics pipes: determination of ring stiffness (SN).
• BS EN 1991-2 — Eurocode 1: traffic loads (referenced by BS 9295 for surface loading).
• Boussinesq, J. (1885) — vertical stress in an elastic half-space under a point load.
• Newmark, N.M. (1942) / Fadum, R.E. (1948) — influence factors for rectangular loaded areas (used for verification).
• Spangler, M.G. & Watkins, R.K. — Iowa / modified Iowa deflection formula for flexible buried pipe.
• Howard, A.K. — modulus of soil reaction E′ and coefficient of elastic support; AWWA M45 — Fiberglass Pipe Design (constrained buckling).