ABSTRACT:

Experimental results from hollow-cylinder tests on a weak sandstone under isotropic and plane strain conditions show a significantly different behavior in terms of deformation response and external radial stress at initial failure of the inner hole. The test results, theoretical simulations and failure predictions demonstrate the need for advanced constitutive models and proper assessment of loading conditions in connection with appropriate failure criteria to predict successfully the behavior and failure of weak formation sandstones.

RÉSUMÉ:

Les resultats experimentaux d'essais de chargement de cylindres creux d'un grès faible mettent en evidence un comportement different en terme de deformation et de contrainte externe radiale à la rupture suivant qu'on les charge en deformation plane ou en condition isotrope. Les resultats experimentaux, les simulations theorques et les previsions de rupture montrent la necessite de modèles constitutifs elabores et de critères de rupture appropries pour prevoir avec succes Ie comportment et la rupture des formations de grès faibles.

ZUSAMMENFASSUNG:

Die Ergebnisse von Hohlzylinderexperimenten mit weichem Sandstein bei isotroper Belastung und ebener Verzerrung zeigen ein deutlich verschiedenes Verhalten bezueglich der Deformation und del' Radialspannung bei beginnendem Bruch des Lochrandes. Die hier beschriebenen Ergebnisse, sowie theoretische Simulationen und Bruchvoraussagen erforden erweiterte Modelle, die, unter Beruecksichtigung del' Belastungs und Bruchkriterien, welche das Versagen weicher Sandstein Formationen erlauben wird.

I INTRODUCTION

Hollow cylinder (HC) rock specimens are frequently tested in the petroleum industry for the assessment of the stability of boreholes and perforations in the field. For reasons of experimental simplicity, the majority of these tests are performed under isotropic loading conditions, where the externally applied radial stress equals the applied axial stress. On the other hand, in the analysis of HC test results, planestrain loading conditions are often assumed for simplicity, where zero deformation takes place in the direction of the HC inner-hole axis. In several problems in tunneling and borehole stability the validity of such an assumption is questionable. In this paper the impact of this assumption on HC stability is addressed both theoretically and experimentally. Planestrain HC experiments allow the direct comparison of the strength of the HC inner hole with isotropic tests and quantify the errors introduced when a simplified plane-strain analysis is performed on an isotropic problem. Section 2 presents experimental results from HC tests on a weak sandstone under isotropic and plane-strain loading conditions. Section 3 presents theoretical simulations of the HC experiments using a stress-dependent elastic, Mohr- Coulomb elastic-plastic constitutive model. Initial HC failure for the two loading cases is predicted on the basis of the bifurcation theory for HC stability in a Cosserat continuum. Discussion of results and conclusions are drawn in Section 4.

2 EXPERIMENTS ON A WEAK SANDSTONE

Two isotropic and two plane-strain loading tests were performed on hollow-cylinder Red Wildmoor sandstone specimens with external diameter 100 mm, internal diameter 20 mm, and height 75 mm. Red Wildmoor (RW) is a fine-grained, weak Triassic outcrop sandstone with mean grain diameter 107 um, and porosity 25.8 percent. RW is water sensitive due to its high smectite content, and thus the specimens were stored in controlled 100 percent relative humidity environment at 24°C for at least one week prior to testing. The uniaxial compressive strength of this humid RW was measured at 11.4 MPa. The HC tests with zero internal pressure were performed in the pressure cell depicted in Figure I, and described previously by Tronvoll and Fjaer (1994). In the plane-strain loading tests the cell was mounted in a load frame, and axial load was applied through the axial loading piston. The applied axial load was controlled by a servo loop with feedback signal the axial deformation such that no axial deformation of the specimen was allowed during the increase of the external radial (confining) stress.

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