How are the maximum allowable thrusts calculated as a function of pipe material and terrain?

Q: How are the maximum allowable thrusts calculated as a function of pipe material and terrain?

In pipe ramming (microtunneling), the maximum allowable thrust is obtained by comparing the required thrust (design thrust) with the limiting thrust of the pipe/joints, the thrust system, and the attack shaft. As a guide, the design thrust is estimated as Ed ≈ F_face (excavation pressure × area) + F_friction (perimeter friction τ × perimeter × length) + losses (bending, joints and local friction). Soil influences mainly τ and F_face (especially with high water table), while the pipe material conditions the structural limit (axial compression and joint capacity). The final allowable thrust is the minimum between: pipe/joint limit, capacity of cylinders/frame and intermediate stations, and resistance of the well reaction wall. Feasibility requires Ed ≤ E_adm; if not met, adjust interwell length, lubrication, geometry, method/equipment or incorporate intermediate thrusts.

In a pipe jacking (microtunneling), The “maximum allowable thrust” is obtained by comparing two things:

the necessary work thrust (what is “requested” by the terrain and the layout), and
the limit thrust that can safely withstand the pipe + gaskets, the pusher system and the attack shaft.

1) Design thrust (what you need to move forward)

As a rule of thumb, the design thrust is estimated as:
Ed ≈ F_front + F_friction + losses. (curvature, joints, local friction). This is explained in How to dimension the attack and reception shafts: admissible thrust, hoisting and logistics.

F_front: resistance/“excavation pressure” at the face × excavated area (and, if applicable, hydraulic component due to water table and water pressure).
F_friction: pipe-ground friction along the driven section. A practical way is:
F_friction ≈ τ × (π × D_ext × L)
where τ is the unit perimeter friction (very sensitive to terrain and lubrication), D_ext the outer diameter and L the driven length.
Losses: increase with curvature, The following are the most common types of wear, deviations, seals, starts/stops and local friction.

Practical key: friction is usually the dominant term, and it is reduced with lubrication (bentonite/polymers), see What tools and machines are key in pipe driving, and with a strategy of geometry control and operation (otherwise, the risk of blockage increases), see Geotechnical risks in microtunnelling and their mitigation..

2) Maximum allowable thrust (what you must NOT exceed)

The maximum admissible thrust is taken as the minimum of these limits:

Structural limit of the pipe and, above all, of its joints. (usually the most “delicate” criterion).
Axial compression and crushing/joint damage are verified with a type approach: N_adm, tube ≈ σ_adm × A (allowable material stress × resistant area), applying joint coefficients and verifications according to the piping system.
As a reminder of typologies, the following are frequently used in ramming reinforced concrete, steel, polycrete/polyester resin and ceramic/gres, see Pipe jacking.
Capacity of the thrust system (cylinders, frame) and possible intermediate stations.
In long stretches, the intermediate stations allow stress distribution and maintain the thrust below the pipe/gasket limit, as mentioned in Pipe jacking and in Geotechnical risks....
Capacity of the attack shaft and its reaction wall (structure that “closes” the thrust).
This is designed/validated in How to size attack and reception wells and in What are the requirements for civil works and manholes for a pile-driving project?.

3) How the terrain “enters” in the allowable thrust.

Soil does not change the strength of the pipe material, but does change the thrust required (Ed) mainly by:

Friction τ (increases in abrasive, heterogeneous soils, with poor lubrication or demanding geometries; decreases with good lubrication).
Water table and water pressure (F_front rises and complicates stability if not controlled).
Curvature and deviations (they generate additional lateral loads and can penalize seals and friction).

4) Outcome: how to decide feasibility

The safety condition is: Ed ≤ E_adm, being E_adm the minimum of the limits (pipe/gasket, equipment, well).
If not met, typical levers are: reduce inter-well length, improve lubrication, adjust geometry/tolerances, rethink method/equipment (see Choice of tunnel boring machine) or incorporate intermediate stations.

If you need us to leave it “closed” for sheet or RFQ (values, hypothesis and margin), the most direct way is to do it from Technical assistance and engineering.