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Theoretical model

RockPlane NX follows the Hoek-Bray planar wedge scheme (1981, RocPlane). The wedge is a 2D rigid body; the analysis is per metre of development along the crest. The Limit Equilibrium Method (LEM) is applied directly — no iteration, no slice subdivision, closed-form solution.

Reference frame

[ O = (0, 0) \text{ — toe of the slope (origin)} ] [ +X \text{ — toward the mountain (intact rock)} ] [ +Y \text{ — vertical, upward} ] [ \hat{t} = (-\cos\alpha, -\sin\alpha) \text{ — sliding direction (toward valley-down)} ]

  • O = (0, 0) — toe of the slope
  • B = (H·cot β, H) — crest of the slope face
  • C = top of the failure plane (on the upper bench)
  • D = top of the tension crack (if present)

Geometry — Case A (no tension crack)

Equations (1)–(9) of the theoretical manual:

[ N = \frac{H}{\sin\beta} ] [ B_x = H \cdot \cot\beta, \quad B_y = H ] [ L = H \cdot \frac{1 - \cot\beta \cdot \tan\psi}{\sin\alpha - \cos\alpha \cdot \tan\psi} ] [ M = \frac{L \cdot \cos\alpha - H \cdot \cot\beta}{\cos\psi} ] [ C_x = L \cdot \cos\alpha, \quad C_y = L \cdot \sin\alpha ] [ A = \frac{1}{2} \cdot |B_x \cdot C_y - B_y \cdot C_x| ] [ W = \gamma \cdot A ]

Geometry — Case B (with tension crack)

The TC adds a vertex D between B and C. The failure plane goes O → D (instead of O → C), and the wedge is the quadrilateral OBCD.

Limit equilibrium (eq. 26–30 of the manual)

Sum the actions in the global frame:

[ F_x = E_x + S_x + J_x + V_x + U_{p,x} + R1_x ] [ F_y = W_y + E_y + S_y + J_y + V_y + U_{p,y} + R1_y ]

where:

  • W: wedge weight (always negative Y)
  • E: external load
  • S: seismic
  • J: active anchor pre-load
  • V: water in the tension crack
  • Up: ponded water at the toe
  • R1: drape mesh normal pressure
  • K: passive nail forces (enter separately into N and τ)

Project onto the failure plane:

[ N = -(F_y + K_y) \cdot \cos\alpha + (F_x + K_x) \cdot \sin\alpha - U \quad \text{(eq. 28)} ] [ S = -F_y \cdot \sin\alpha - F_x \cdot \cos\alpha \quad \text{(eq. 29)} ]

Resisting τ:

\[ \tau = \frac{c \cdot L}{\gamma_c} + N \cdot \frac{\tan\varphi}{\gamma_\varphi} + K_x \cdot \cos\alpha + K_y \cdot \sin\alpha + \tau_{R2} \quad \text{(eq. 30)} \]

Factor of safety:

\[ FS = \frac{\tau}{|S|} \quad \text{verified: } FS \ge FS_{required} (\gamma_R) \]

Barton-Bandis variant

When the Barton-Bandis criterion is active, the friction term is replaced with:

\[ \tau = \sigma_n \cdot \tan(\varphi_b + i_{eff}) \cdot N/\gamma_\varphi + K \cdot \cos\alpha + ... \]

with ieff = JRC · log₁₀(JCS / σn) and σn = N / L. The dependency on σn makes the formula non-linear in N, so the software solves it directly using the computed N.

Reinforcement

  • Active anchors (J): axial pre-load applied as an action. Reduces S and N.
  • Passive nails (K): mobilised force. Enters τ directly via cos α + sin α components, and also increases N (and hence friction).
  • R1 meshes: normal pressure q on the slope face, enters R1x, R1y.
  • R2 meshes: τ added directly to the resisting term.

Overturning verification

The software also computes an overturning safety factor Fr as ratio of stabilising to overturning moments about the toe O. This is a structural overall check (typical of the GeoStru SRS desktop), separate from sliding.

See verification page →