Active anchors¶

Active anchors (pre-stressed tie-rods) apply a pre-load on the wedge as soon as they are installed, regardless of any movement. They follow NTC 2018 §6.6 with the classical 3-limit + ξ + γ_Ra,t chain.

Capacity of the single anchor¶

Three limits, R_min = min of the three:

Limit	Symbol	Formula
Steel resistance	R_steel	A_s · f_yd · η
Bar ↔ grout bond (bond zone only)	R_bond	π · D_bar · L_bond · τ_b
Bulb pull-out	R_pullout	π · D_bulb · L_bond · τ_ult

In rock: τ_ult ≈ 0.1 · σ_c (Bustamante-Doix 1985).

Reduction chain¶

\[R_k = \frac{R_{min}}{\xi}, \quad R_d = \frac{R_k}{\gamma_{Ra,t}}, \quad \text{Capacity} = \frac{R_d}{FS_{local}}\]

Coefficient	Source	Notes
ξ	NTC Tab. 6.6.III	conservative fallback ξ=1.4 with 0 pull-out tests; decreases with the number of preliminary pull-out tests (1.4 → 1.3 → 1.2 → 1.1 with ≥4 tests)
γ_Ra,t	NTC §6.6	1.10 for temporary anchors, 1.20 for permanent anchors
FS_local	designer	extra local safety factor, default 1.0

ξ table¶

no. preliminary pull-out tests	ξ
0 (no test — conservative fallback)	1.40
1	1.40
2	1.30
3	1.20
≥4	1.10

Pull-out tests, not boreholes

The number of "preliminary pull-out tests" refers to dedicated anchor pull-out tests prior to construction (NTC Tab. 6.6.III). It is not the count of geotechnical boreholes (that one applies to piles, Tab. 6.4.IV).

Input fields¶

Field	Notes
φ bar [mm]	strand or bar diameter
L total [m]	total length (free + bond)
L free [m]	free length (no bond), in the wedge
L bond [m]	bond length in the intact rock mass
φ hole [mm]	borehole diameter
z avg [m]	average bulb depth
f_yd [MPa]	design steel resistance
η work [%]	steel work rate (typical 60–90% for anchors)
τ_b [N/mm²]	bar↔grout bond stress (typical 1.5–3 N/mm²)
no. pull-out tests	for ξ from Tab. 6.6.III
γ_Ra,t	automatically updated when temporary/permanent is changed

In the right panel "Design resistances · nails / anchors" the full ξ / γ_Ra,t / FS chain is shown step by step.

Active vs passive¶

Active anchor: pre-load F applied immediately as an action on the wedge. Reduces both the driving shear S and the normal N (via the angle Δ).
Passive nail: no pre-load. Mobilises force only when the wedge tries to move. Adds resistance via the τ resisting term (see passive nails →).

For the same single capacity F, active anchors are slightly more effective (they reduce S directly), but passive nails are simpler to install and don't require tensioning equipment.