geomechanics · stress
Maximum Horizontal Stress — Stress Polygon Bound
SHmax_max = (Shmin − Pp) × [√(μ²+1) + μ]² + Pp
click formula to derive ↑
Inputs
psi
psi
—
Description
Bounds the maximum horizontal stress (SHmax) using the stress-polygon method: the assumption that the crust is everywhere at the verge of frictional failure on optimally-oriented, pre-existing faults caps the ratio of any two effective principal stresses. Given Shmin, pore pressure, and an assumed fault friction coefficient, this gives an upper bound on SHmax — not a single value. This is a genuinely different relation from the Mohr-Coulomb Failure Criterion calc: that one governs new shear failure through intact rock; this one governs frictional slip on rock that is already broken (a pre-existing fault).
Variables
| Symbol | Unit | Description |
|---|---|---|
| SHmax_min | psi | SHmax Lower Bound |
| SHmax_max | psi | SHmax Upper Bound |
| f(μ) | — | Frictional Stress Ratio Limit |
| Shmin | psi | Minimum horizontal stress at the depth of interest — typically the Shmin output of the Fracture Gradient (Eaton 1969) calc. |
| Pp | psi | Pore pressure at the depth of interest — typically the output of the Eaton Pore Pressure calc. |
| μ | — | Coefficient of friction on optimally-oriented, pre-existing faults. Byerlee's Law finds 0.6-1.0 typical for most crustal rock; clay-rich gouge or serpentinite-bearing faults can be as low as 0.3-0.4. |
Assumptions
- The crust is everywhere at the verge of frictional failure on optimally-oriented, pre-existing faults (the central assumption of the stress-polygon method)
- Shmin is genuinely the minimum principal effective stress — valid in normal and strike-slip faulting regimes; in a reverse-faulting regime Sv could instead be the minimum, which this bound does not account for
- A single representative friction coefficient μ applies to the relevant fault population in the basin
Limitations
- Produces a RANGE (Shmin to the frictional limit), not a point estimate — narrowing it further requires independent data this calculator does not use, such as wellbore breakout width/orientation from image logs or an extended leak-off test
- Does not use the poroelastic horizontal-strain method (which can in principle give a point estimate) because that method requires independently known horizontal tectonic strains that are almost never directly measurable — it is not built here to avoid asking for inputs that cannot realistically be supplied
- Assumes Shmin is the minimum principal stress; in a reverse-faulting regime this assumption can break down and the bound is not valid as written
- A single basin-wide μ is a simplification — fault gouge mineralogy (especially clay-rich or serpentinite faults) can push the true value well below the 0.6-1.0 Byerlee range
Use Cases
- → SHmax bound when no image-log breakout data exists: Provide a defensible upper bound on SHmax in exploration or early-appraisal wells before any wellbore-breakout or extended-LOT data is available.
- → Critical mud weight input: Feed the upper bound (or an independently known SHmax) into the Critical Mud Weight (Wellbore Breakout) calc as the SH input.
- → Sanity-checking measured or assumed SHmax values: Check whether an SHmax value taken from regional/offset-well data is even consistent with frictional equilibrium, given the well's own Shmin and Pp.
Related Calculations
Region Notes
Permian Basin
The Permian Basin is generally interpreted as a strike-slip to transitional normal/strike-slip stress regime, consistent with this bound's assumption that Shmin is the minimum principal stress; published Wolfcamp/Delaware Basin SHmax estimates commonly use μ≈0.6 as a starting point.
Global
Byerlee's Law (μ≈0.6-1.0) is unusually rock-type-insensitive compared to most rock-mechanical properties, but documented exceptions exist for clay-gouge and serpentinite-bearing faults — calibrate μ to known regional fault behavior where available rather than relying on the default alone.
References
Primary source
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