Geomechanics & Ground Control

In-situ Stress Measurement & Instrumentation

Overcoring, flatjack and hydraulic fracturing — how virgin ground stresses are measured, plus the convergence/load instruments that watch openings.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Underground openings respond to the in-situ (virgin) stress field, which must be measured, not guessed. The vertical stress is usually gravitational:

σ_{v} = γ H

(unit weight × depth). The horizontal stress is expressed through the lateral stress ratio

k = σ_{h} / σ_{v}

. Field techniques: overcoring (a strain cell is set in a borehole, then stress-relieved by coring around it — the recovered strain gives stress), flatjack (slot cut in a wall, jack pressurised to cancel the relaxation), and hydraulic fracturing (a sealed borehole interval is pressurised until the wall cracks; the breakdown and shut-in pressures give the horizontal stresses). Monitoring instruments — convergence stations, extensometers, load cells and stress meters — track how the opening deforms over time.

The Core Formula Matrix

Vertical stress:

σ_{v} = γ H

(unit weight

γ

× depth

H

); rule of thumb

\approx 0.025 MPa/m = 1 MPa per 40 m

.

Lateral stress ratio:

k = \frac{σ _{h}}{σ _{v}}

Hydrofrac (impermeable rock): breakdown

P_{b} = 3 σ_{h, min} - σ_{h, ma x} - P_{0} + T

(

P_{0}

= pore pressure,

T

= tensile strength)

Shut-in pressure:

P_{s} = σ_{h, min}

(closes the fracture, giving the minimum horizontal stress directly).

The ‘IIT Traps’

⚠
Vertical stress depends on depth, not opening size. $σ_{v} = γ H$ uses overburden depth; the drive dimensions don't enter.
⚠
**Use unit weight $γ$ (kN/m³), not density** in $σ_{v} = γ H$ ; if given $ρ$ , multiply by $g$ .
⚠
Shut-in pressure gives the *minimum* horizontal stress directly; breakdown pressure needs the full formula with $T$ and $P_{0}$ .
⚠
** $k$ can exceed 1.** Near the surface and in tectonic regions horizontal stress often exceeds vertical.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

Which in-situ stress measurement technique relies on stress-relieving a strain cell by drilling a larger-diameter core around it?

Q2MEDIUM2 Marks · NAT

Rock of unit weight

25 kN/m^{3}

overlies a drive at a depth of

600 m

. The vertical in-situ stress is ______ MPa. (Round off to one decimal place.)

MPa

Q3HARD2 Marks · NAT

In a hydraulic fracturing test in impermeable rock with negligible pore pressure, the breakdown pressure is

18 MPa

and the shut-in pressure is

7 MPa

. If the rock tensile strength is

3 MPa

, the maximum horizontal stress is ______ MPa. (Round off to one decimal place.)

MPa