Chapter 8 — Rock Slopes in Civil & Open Pit Mining Engineering¶

8.1 The Scale Spectrum of Mining Slopes¶

Open pit rock slopes operate across three distinct geometric scales:

Bench Scale (\(10 - 30\text{ m}\) height): Stability controlled by kinematic planar, wedge, and toppling failures along individual joint surfaces. The primary function is to provide catch-berm retention width (\(b \ge 0.2 H + 4.5\text{ m}\)) catching ravelling rocks.
Inter-Ramp Scale (\(50 - 200\text{ m}\) height): Governed by fault persistence, groundwater pressures behind the face, and haulage road integrity.
Overall Slope Scale (\(300 - 1,000\text{ m}\) depth): Massive global stability governed by non-linear rock mass shear failure (Hoek-Brown criterion), regional fault zones, and regional aquifer recharge.

8.2 Primary Failure Mechanisms in Rock Slopes¶

A. PLANAR SLIDING           B. WEDGE SLIDING            C. TOPPLING FAILURE
    |  /                       |   / \                     | ||||
    | / (Dip psi_p)            |  /   \ (Intersec)         | |||| (Steep joints
    |/                         | /     \                   |/////  dipping in)

1. Planar Failure¶

Occurs along a single persistent joint striking parallel (\(\pm 20^\circ\)) to the slope face with daylighting dip (\(\phi < \psi_p < \psi_f\)):

\[FS = \frac{c A + (W \cos\psi_p - U - V \sin\psi_p) \tan\phi}{W \sin\psi_p + V \cos\psi_p}\]

Where: - \(W\) = weight of the sliding rock block - \(A\) = base sliding area - \(U\) = uplift pore water force on the sliding plane: \(U = \frac{1}{2} \gamma_w z_w A\) - \(V\) = horizontal hydrostatic cleft water force acting in tension cracks behind the crest: \(V = \frac{1}{2} \gamma_w z_w^2\)

2. Wedge Failure¶

Occurs along the line of intersection of two dipping joint planes dipping flatter than the slope face but steeper than their combined friction angle.

3. Toppling Failure¶

Occurs where joint sets dip steeply into the slope face (\(\psi_d + \psi_f \ge 90^\circ + \phi\)). Gravitational moment causes tall rock columns to tilt outward, opening basal cross-joints and toppling downhill.

4. Circular / Composite Rock Mass Failure¶

Occurs in heavily fractured, highly weathered, or altered rock masses (\(GSI < 40\)) where structural fabric does not dictate a preferred planar slide path. Analyzed via Bishop, Morgenstern-Price, or shear strength reduction (SSR) numerical modeling.

8.3 The Catastrophic Role of Groundwater¶

Groundwater is the single greatest driving factor in open pit slope collapses: 1. Reduces Effective Stress: Fluid pore pressure (\(u\)) directly subtracts from normal clamping stress: \(\sigma' = \sigma - u\). 2. Hydrostatic Cleft Force (\(V\)): Rain filling tension cracks behind the pit crest introduces huge driving lateral forces with zero friction resistance. 3. Accelerates Chemical Alteration: Weathering of clay gouge infill reduces residual friction angles from \(25^\circ\) down to \(8^\circ\).

Depressurization Drainage Design¶

Sub-horizontal drain holes (\(75 - 100\text{ mm}\) diameter, perforated PVC casing) drilled \(50 - 150\text{ m}\) into highwalls drop the phreatic line, increasing the slope Factor of Safety by \(20 - 40\%\) without moving rock.

8.4 Monitoring Open Pit Slopes¶

Instrument System	Measured Parameter	Role in Early Warning
Ground-Based Radar (SSR)	Displacement along Line of Sight (LOS)	Scans entire pit 24/7; provides real-time heat maps of accelerating velocity (\(mm/hr\))
Robotic Total Stations (RTS)	3D coordinate vector \((x,y,z)\)	High-precision monitoring of prisms installed on haul roads and crests
Vibrating Wire Piezometers (VWP)	Deep pore water pressure (\(u\))	Verifies effectiveness of horizontal drainage drilling and pumping dewatering wells
In-Place Inclinometers (IPI)	Deep shear displacement vs depth	Identifies exact depth of basal shear surface beneath pit floor

8.5 Canonical Terminology¶

English Term	Canonical Vietnamese Translation	Definition
Catch berm	Cơ tầng lưu giữ đá rơi	Horizontal bench left between steep slopes to catch fallen rock
Planar failure	Phá hoại trượt phẳng	Sliding of a rock block along a single continuous plane
Toppling failure	Phá hoại trượt lật	Rotational overturning of steep rock columns dipping into slope
Tension crack	Vết nứt tách đỉnh	Tensile rupture opening behind the crest prior to sliding
Depressurization drain	Lỗ khoan tháo khô hạ áp	Sub-horizontal borehole drilled into rock to lower water table