Prego, è stato utile riprendere questo argomento generalmente ignorato. Dopo varie, forse troppe iterazioni con GPT5, tanto che adesso mi fermo, siamo arrivati a un punto credo sufficientemente plausibile. GPT5 propone 3 soluzioni, con vari livelli di conservativismo.

Synthesis: Simple Envelope-Fitting Bounds for a Flat Rock Surface

When fitting a straight Mohr–Coulomb line to the curved Hoek–Brown envelope over
0 ≤ σ′₃ ≤ σ′₃₋ₘₐₓ, you need a practical choice for
σ′₃₋ₘₐₓ that doesn’t rely on knowing the ultimate capacity or running
finite-element models. Three widely used, flat-surface bounds are:

1. 
   Constant-Fraction of Intact Strength
   
   
   
   • 
     Formula:
     σ′₃₋ₘₐₓ = 0.25 · σci
     
   
   
   • 
     Rationale:
     Hoek & Brown (1980) observed that, for shallow loads, the minor principal
     stress range in jointed rock lies between 0.1·σci and 0.4·σci. A midpoint of
     0.25·σci gives a representative upper bound without further data.
     
   
   
   
   



2. 
   At-Rest Horizontal Stress (K₀) Approach
   
   
   
   • 
     Formula:
     σ′₃₋ₘₐₓ = K0 · γ · Df, K0 ≈ 1 − sin φ′
     
   
   
   • 
     Rationale:
     Prior to loading, a rock mass at depth Df supports a vertical
     stress γ·Df. Taking its natural horizontal stress
     σh′ = K₀·γ·Df as σ′₃₋ₘₐₓ ties the
     envelope limit to the actual in-situ confinement.
     
   
   
   
   



3. 
   Mid-Envelope Point via Rock Mass Parameters
   
   
   
   • 
     Formula:
     
σ′₃₋ₘₐₓ = (s / mb) · σci

mb = mi · exp((GSI − 100) / (28 − 14D))

s = exp((GSI − 100) / (9 − 3D))

     
   
   
   • 
     Rationale:
     The term (mb·σ₃′/σci + s)a shifts the
     Hoek–Brown curve from intact rock (s = 1) toward jointed mass (s < 1). Setting
     mb·σ₃′/σci = s locates the stress where intact-rock
     and joint-mass contributions are equal—an intuitive “mid-curve” bound.
     
   
   
   
   

Conservatism Comparison

Method	Typical Value*	Conservatism (Lower σ′₃₋ₘₐₓ)
0.25 · σci	12.5 MPa	Moderate
K₀·γ·Df (K₀≈0.5, γ=25 kN/m³, Df=2 m)	25 kPa	High
(s / mb) · σci (e.g. s=0.01, mb=5, σci=50 MPa)	0.1 MPa	Very High

*Example assumes σci = 50 MPa, φ′≈30° ⇒ K₀≈0.5,
γ=25 kN/m³, Df=2 m, GSI=50,
D=0.5.