Mohr circles
This spreadsheet calculates and visualizes Mohr circles for subsurface stress conditions using linearized Mohr‑Coulomb faulting theory. It evaluates fault stability by plotting shear stress against effective normal stress derived from user-input stress gradients, depth, pore pressure, cohesion, and friction. The tool orders the principal stresses to identify the faulting regime and provides a simple visual comparison between the stress state and the failure envelope. The app also calculates the minimum ΔP to failure, and determines the optimal dip and strike associated with that minimum ΔP.
Input data:
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Sv, Shmax, Shmin: Vertical, maximum horizontal, and minimum horizontal stress gradients.
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Sv > others --> normal faulting; Shmax > others --> strike slip faulting; Shmin > others --> reverse faulting.
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Depth: Target depth for stress calculations.
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Pore Pressure: Fluid pressure at depth, used to compute effective stress.
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Cohesion (So): Shear strength at zero normal stress.. Default value is 0, which is appropriate for faults.
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Mu (μ): Friction coefficient; controls the slope of the failure envelope.
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Max σₑ: Maximum effective normal stress shown on the plot (axis scaling).
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Sigma (σ) refers to the three principal stresses, always ordered from largest to smallest:
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σ₁ = largest; σ₂ = intermediate, σ₃ = smallest.
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This ordering also determines the stress anisotropy (σ₁/σ₃).
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σₑ, refers to the effective normal stress after subtracting the pore pressure (σₑ = σ - Pp)
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SHmax Orientation (optional): Strike of the maximum horizontal stress (0–180°), used to calculate the optimal strike orientation under the given stress state. 0 degrees is North.
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Units: you can use any pressure or pressure gradient units, as long as you use the same for all parameters (use our Units Converter if needed), All units in the example are psi/ft.
Assumptions:
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Linear Mohr-Coulomb failure criterion, All inputs and outputs assume consistent units (e.g., psi, MPa); no unit conversion is performed internally.
Output
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Mohr Circles: Represent the stress state at depth.
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Failure Envelope: τ = So + μ·σₑ, showing the shear failure threshold.
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Minimum Delta P to failure: Minimum pore-pressure increase required for the Mohr circle to reach the frictional failure envelope. Assumes an optimally oriented plane is present.
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Optimal Dip and Strike: Orientation of the plane that results in the minimum ΔP to failure under the specified stress state and friction coefficient. In strike-slip regimes, two conjugate optimal strikes are possible; only one is reported.
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Position of the optimal dip and strike on the Mohr circle (black dot). A 90-degree dip is vertical.
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Aphi: A continuous parameter that describes the stress state from normal faulting (Aphi = 0.5), to strike slip faulting (Aphi = 1.5) to reverse faulting (Aphi = 2.5) (Zoback & Kohli, 2019).
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Stress anisotropy calculated as σ₁/σ₃.
