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Chapter 9 — Tunnels in Weak Rock & Squeezing Ground

9.1 Squeezing Ground Mechanics

When deep tunnels are excavated through weak rock masses (shales, phyllites, schists, mudstones, or heavily sheared fault gouge), induced boundary tangential stresses (\(\sigma_\theta\)) exceed the rock mass compressive strength (\(\sigma_{cm}\)).

Under these conditions, the rock does not fail by brittle spalling. Instead, it undergoes time-dependent ductile squeezing—large plastic shear strains yielding inward into the opening, resulting in severe convergence (\(> 5\% - 20\%\) of tunnel diameter), buckling of steel sets, and shear rupture of rigid concrete liners.

Hoek's Squeezing Index:

Hoek and Marinos (2000) correlated the ratio of rock mass compressive strength to in-situ overburden stress (\(\sigma_{cm} / \gamma H\)) with expected tunnel diametral strain (\(\epsilon = \Delta D / D\)):

\[\frac{\sigma_{cm}}{\gamma H} = \frac{\sigma_{ci} \cdot s^a}{\gamma H}\]
Ratio \(\sigma_{cm} / \gamma H\) Tunnel Strain \(\Delta D / D\) Severity Category & Operational Impact
\(> 1.0\) \(< 1\%\) Few support problems; standard rockbolts and mesh
\(0.5 - 1.0\) \(1\% - 2.5\%\) Minor squeezing; light steel sets or pattern bolts with shotcrete
\(0.3 - 0.5\) \(2.5\% - 5\%\) Moderate squeezing; heavy support installed close to face
\(0.15 - 0.3\) \(5\% - 10\%\) Severe squeezing; yielding steel arches, forepoling umbrellas
\(< 0.15\) \(> 10\%\) Very severe squeezing; face collapse, yielding slots in shotcrete

9.2 The Convergence-Confinement Method (CCM)

The Convergence-Confinement Method is the standard analytical design framework coupling three fundamental curves:

Internal Support Pressure pi
      ^
  p_0 |  \ Ground Reaction Curve (GRC)
      |    \
      |      \        Support Characteristic Curve (SCC)
 p_eq |------- \-----/
      |         \   /
      |          \ / (Equilibrium Point: u_eq, p_eq)
      |           v
      +-------------------------> Radial Convergence u_r
                 u_0  u_eq
  1. Ground Reaction Curve (GRC): Shows the decrease in internal support pressure \(p_i\) required to maintain equilibrium as radial wall convergence \(u_r\) increases from initial state (\(p_i = p_0, u_r = 0\)) to unconfined state (\(p_i = 0, u_r = u_{\max}\)).
  2. Longitudinal Deformation Profile (LDP): Relates radial convergence \(u_r(x)\) to distance from the advancing tunnel face \(x\). Approximately \(25 - 35\%\) of total convergence occurs ahead of the face before support can be installed.
  3. Support Characteristic Curve (SCC): Represents the elastic-plastic load-deformation response of the installed ground support (rockbolts, shotcrete, steel arches). Support must be installed at initial convergence \(u_0\) corresponding to face setback distance.

9.3 Rigid vs. Yielding Ground Support Philosophy

Attempting to halt squeezing in severe ground with ultra-stiff, rigid liners is impossible; the immense rock mass thrust (\(p_0 = \gamma H\)) will crush any economically feasible concrete shell.

The Modern Yielding Support Strategy:

  1. Ductile yielding elements: Steel sets equipped with frictional sliding connections (TH-arches) or yielding steel canisters (LSC cylinders) that deform plastically under a controlled resistance force (\(200 - 400\text{ kN}\)).
  2. Longitudinal slots in shotcrete: Gaps left in shotcrete lining parallel to the tunnel axis allow radial closure without inducing compressive crushing in the shotcrete shell. Once convergence stabilizes, the slots are concreted closed.
  3. Yielding rockbolts (Swellex, D-Bolts): Deform up to \(15 - 20\%\) strain without tensile rupture, maintaining continuous confinement on the fractured plastic annulus.

9.4 Canonical Terminology

English Term Canonical Vietnamese Translation Definition
Squeezing ground Đất đá ép lún Time-dependent plastic inward deformation of rock under high overstress
Convergence-Confinement Method (CCM) Phương pháp đường cong phản ứng nền (CCM) Analytical framework balancing rock convergence with support reaction
Ground Reaction Curve (GRC) Đường cong phản ứng nền (GRC) Relationship between internal support pressure and radial wall displacement
Longitudinal Deformation Profile (LDP) Biểu đồ biến dạng theo trục dọc hầm (LDP) Radial wall convergence as a function of distance from advancing face
Yielding support Kết cấu chống giữ dẻo hấp thu biến dạng Ductile ground support designed to deform plastically without failing