Squeezing of seams intersecting tunnels and shafts in rock is treated as elasto-plastic deformation of the material. Approximate analytical solutions are given for elastic, rigid-plastic and elastic/rigid-plastic material models. Numerical methods are applied for non-dilatant, cohesive and dilatant, frictional material models. The parameters for the models were determined in standard laboratory tests. Results of the numerical analyses are compared to the measurements done in laboratory model tests.


La pression des filons intersectant tunnels et puits en roche est traitee comme deformation elastoplastique du materiau. Des solutions analytiques approchees sont donnees pour des materiaux elastiques, plastiques rigides et elastiques/ plastiques rigides. Des methodes numeriques sont appliquees à des modèles en materiaux non-dilatants, cohesifs et dilatants. Les paramètres pour les modèles ont ete determines par des essais en laboratoire normaux. Les resultats des analyses numeriques sont compares avec les mesures faites dans des essays de modèle en laboratoire.


Die Quetschung einzelner Schichtlagen, die von Tunneln oder Schachten durchschnitten werden, wird als elastisch-plastische Deformation des Gesteins behandelt. Fuer elastische, starr-plastische und elastische/starr-plastische Stoffgesetze werden analytische Naherungslösungen gegeben. Fuer bindige, nichtdilatierende und rollige, dilatierende Materialien, deren Stoffparameter mittels Laboruntersuchungen bestimmt wurden, sind numerische Methoden entwickelt worden. Die Resultate der numerischen Lösungen werden mit Meßergebnissen von Modellversuchen verglichen.


Terzaghi's soft ground classification for tunneling purposes (Terzaghi 1950) defines squeezing ground as a ground which advances into the tunnel from all sides without any signs of fracturing. All materials may squeeze because an opening made in a stressed medium tends to shrink. Squeezing is notable in soft or medium clays and argillaceous rocks. The development of deformations is called squeezing in underground construction when the displacements of the opening perimeter are large. Although no definitive values are agreed upon to call the ground behavior squeezing, a tunnel closure of more than one percent can be considered squeezing deformation. Laboratory tests on squeezing materials show that plastic yielding must take place to produce the strain observed in squeezing ground because a large part of the deformations is permanent. In the present paper squeezing is treated as elastic-plastic deformation of rock or soil around underground openings. Analytical solutions exist which take into account the viscous properties of geologic materials in tunnel design. Most of the presented solutions are based on visco-elastic models (Goodman, 1980). Recently, analytical (Nonaka, 1978 and 1980; Zhu, 1981) and numerical, solutions have been presented for visco-plastic material models. All analytical visco-elastic and visco-plastic solutions known at this point are for plane strain conditions and hydrostatic stress fields, which assumptions make the problem geometrically one dimensional.


Approximate elastic and rigid-plastic solutions are developed for a layer with a circular opening, figure 1, Saari (1982). The material of the layer is assumed isotropic and loading is symmetric. Internal pressure inside the opening is denoted by Pi. The lining of the tunnel or shaft can be represented by an elastic spring with spring constant S. The boundary tractions at the parallel faces-of the layer are the axial stress σn and shear stress τn both of which are functions of radius as are the other two stress components σnand σ 00. The stresses in the layer also depend on the axial dimension z. If the layer is thin compared to the radius of the opening an approximate. solution can be found when the average values of stresses in the axial direction are used.

2.1. Elastic Solutions

The' axial' displacement of the parallel boundaries in re1ation'to the center plane of the layer is Δw.

2.1.1. Cohesive Interface

In an exact solution ρ would be infinitely far from the opening. In the approximate case ρ is the distance where no slip at the-interface takes place. The constants A1 and A2 are determined from equations (4) - (6) and an equation for ρ is obtained and thus radial displacement and stresses become known, figure 2.

2.1.2. Frictional Interface

A transcendental equation for ρ is obtained from which ρ can be solved iteratively. Once ρ is known the radial displacement and stress distribution are known, figure 3.

2.2. Rigid-Plastic Solution

An analytical solution can be found for the circular hole with a thin, layer confined between two rigid surfaces for a material with von Mises-type yield function and plastic potential.

2.3. Elastic/Rigid-Plastic Solution

A refinement to-elastic and rigid-plastic solutions is found in the form of an elastic/rigidplastic solution where elastic deformations are assumed negligble in the plastic region.

3.1. Model tests

In the theoretical treatment of the problem it was found that plastic yielding of a layer is observed as squeezing type displacement of the opening perimeter. It was found necessary to verify the analytical and numerical results in laboratory tests. The behavior of squeezing layers was studied in the laboratory using sand-bentonite-water and sand-wax mixtures as model materials.

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