E. Papamichos

Plane-strain compression of rock-like materials

Abstract A new apparatus for determining the constitutive response of rock and concrete, named the University of Minnesota Plane-Strain Apparatus, was designed and built on a passive stiff-frame concept. The biaxial device, with U.S. Patent number 5,063,785, is unique, because it allows the failure plane to develop and propagate in an unrestricted manner, as opposed to conventional systems where the material is constrained by the testing apparatus. By placing the upper platen on a low friction linear bearing, the prismatic specimen, subjected to confining pressure and compressed axially, has the freedom to translate in the lateral direction once the deformation has localized across the entire specimen. In addition, homogeneous deformation is prompted by the use of a stearic-acid based lubricant, which is placed on the four surfaces of the specimen contacting hardened-steel platens. Thus, the apparatus combines the positive features of a conventional triaxial compression test and a direct shear test. Some 30 experiments on sandstone and mortar indicated that even though localization of deformation was detected by locations of acoustic emission prior to peak load, the failure plane was not fully formed at the peak. For the mortar, one more or less planar shear band, the orientation of which is well predicted by plasticity theories, was observed. A kinked rupture zone with two main portions, one steep and one less inclined, appeared in the sandstone; the steep portion may be a result of fracture phenomena. The dilatancy characteristics of rock-like materials may dictate the type of failure mode, either shear banding for ductile behavior or crack propagation for brittle behavior.

Conductive heat flow and thermally induced fluid flow around a well bore in a poroelastic medium

Transient analytical solutions for temperature and pore pressure changes near a circular borehole under instantaneous temperature and fluid pressure changes inside the borehole are presented. The solutions couple conductive heat transfer with Darcy fluid flow, and a borehole under a nonhydrostatic far-field stress state is simulated. The heat conduction equation is decoupled from the coupled system of isothermal governing equations, and the complete solution is obtained by superimposing this decoupled solution on the isothermal one. The solution is therefore applicable to low-permeability media, where heat transfer is dominated by conduction only. Both cold and warm injection processes are studied, and the applications to hydraulic fracture initiation and thermally induced fluid flow are discussed. Taking Westerly granite as an example, it is concluded that the maximum thermally induced pore pressure inside the rock formation can be 30% higher than the isothermal pore pressure, with a borehole temperature and fluid pressure change ratio (ΔT/Δp) = 1°C/MPa. It is emphasized that the thermally induced pore pressure change can be significant inside a low-permeability porous medium, and a coupled solution must be obtained to address the mechanical, hydraulic, and thermal responses appropriately.

Elasto-plastic modelling of Red Wildmoor sandstone

On the basis of an extensive experimental program of axisymmetric triaxial compression and extension tests, the mechanical behaviour of a weak sandstone (Red Wildmoor sandstone) is analysed and modelled within the frame of the theory of elastoplasticity. Stress-dependent elasticity and damage are incorporated into the model. Pressure sensitivity of the plastic behaviour is described through a non-linear Mohr–Coulomb model with friction hardening and cohesion softening. Emphasis is given on the calibration procedure. Validation of the model is done through back analysis of the experimental tests. Shear-band analysis is performed on the basis of the extension of the constitutive model to non-coaxial plasticity. Copyright

Continuum fracture mechanics of uniaxial compression on brittle materials

Abstract A review of the uniaxial compression test on brittle solids is presented. The discussion focuses on the description of the post-peak behavior, where strength softening and fractures propagating mainly in the axial direction are observed. Based on experimental evidence and dimensional analysis, the post-peak axial stress is seen as a function of the axial displacement normalized by the radius of the specimen, and not of its height. Accordingly, a continuum theory of stress diffusion is developed that is able to account for size effect. As a practical application of the theory, the bearing capacity of a pillar in a deep mine is considered.

THERMAL EFFECTS ON FLUID FLOW AND HYDRAULIC FRACTURING FROM WELLBORES AND CAVITIES IN LOW?PERMEABILITY FORMATIONS

The coupled heat-fluid-stress problem of circular wellbore or spherical cavity subjected to a constant temperature change and a constant fluid flow rate is considered. Transient analytical solutions for temperature, pore pressure and stress are developed by coupling conductive heat transfer with Darcy fluid flow in a poroelastic medium. They are applicable to low permeability porous media suitable for liquid-waste disposal and also simulating reservoir for enhanced oil recovery, where conduction dominates the heat transfer process. A full range of solutions is presented showing separately the effects of temperature and fluid flow on pore pressure and stress development. It is shown that injection of warm fluid can be used to restrict fracture development around wellbores and cavities and generally to optimize a fluid injection operation. Both the limitations of the solutions and the convective flow effect are addressed. Copyright

Permeability reduction due to grain crushing around a perforation

Abstract The permeability reduction around a perforation cavity is analyzed as the result of grain crushing due to the perforation process. The poroelastic solution of a plane wave emanating from a cylindrical cavity is used to derive expressions for the intergranular stresses responsible for grain-crushing phenomena. These phenomena are examined on the basis of Hertzian contact theory of fracture and micromechanical descriptions of granular assemblies assisted by discrete element simulations. Results are presented for hydrostatic loading conditions for comparison with existing experimental results, and for uniaxial strain conditions as an approximation to the stress field around the perforation. The analysis can be applied to the prediction of the extent of the permeability-reduced zone and used for estimating the permeability reduction around the perforation.

Constitutive testing of Red Wildmoor sandstone

The first objective of this research was to improve the experimental measurements for the constitutive behaviour of Red Wildmoor sandstone by optimizing the boundary conditions and specimen geometry, and improving the triaxial test instrumentation. The uniformity of deformation of the rock specimen was improved by minimizing specimen bulging due to specimen slenderness and end-surface frictional constraints. The improvements in the instrumentation were aimed at improving the monitoring of the applied forces, axial and radial deformations, and macroscopic rock failure through use of high precision LVDTs and cantilever gauges, acoustic emission measurements and acoustic pulse transmission velocities. The second objective was to obtain test data for the constitutive modelling and calibration of Red Wildmoor sandstone under various saturating conditions and saturation fluids. An additional task was an experi mental study for the improvement of the uniaxial compression test as an index text for rock mechanics applications. The performed modifications allowed the reliable collection of post-peak stress test data of material softening behaviour, and the identification of the point of macroscopic failure of the specimen beyond which the test data cannot be used directly for continuum modelling of material behaviour.

Surface instability detection apparatus

SummaryA surface instability detection apparatus for investigating axial splitting and spalling phenomena in rocks and rock-like materials is described. The apparatus simulates the conditions under which these phenomena occur and allows one to accurately measure them. Experimental results from tests on Berea sandstone are presented where the successive formation of spalling fractures was monitored with an acoustic emission system and the location of the seismic events was mapped. The test results show the potential for benchmark tests in determining the spalling tendency and characteristics of different rocks.

Overburden modeling above a compacting reservoir using a trap door apparatus

Abstract The consequences of large reservoir compaction on the surface subsidence and the stress path of the overburden formations were investigated with physical modeling experiments where the compacting reservoir was modeled with a circular retracting trap door (TD) under a deformable overburden of sand. Tests with various overburden heights showed the formation of shear bands starting almost vertically at the TD edges and converging successively to the symmetry axis. A shallow and a deep formation mechanism were identified. In the shallow mechanism, the shear bands reach immediately the upper surface and thus the TD displacement is felt immediately at the surface as subsidence. In the deep mechanism, at low TD displacements the shear bands meet initially each other forming an arch and thus only part of the TD displacement is felt at the surface. At higher TD displacements, additional shear bands form above the initial shear band and eventually reach the surface. After that, the TD displacement is directly felt at the surface as subsidence. The TD stress drops rapidly to a minimum value, which appears to be independent of the overburden height.

Rayleigh wave propagation in intact and damaged geomaterials

Abstract An analytical model of an elastically deforming geomaterial with microstructure and damage is assumed to be a material where the second spatial gradients of strain are included in the constitutive equations. Based on this assumption, a linear second gradient (or grade-2) elasticity theory is employed, to investigate the propagation of surface waves in either intact or weathered—–although homogeneous and isotropic at the macroscale—materials with microstructure such as soils, rocks and rock-like materials. First, it is illustrated that in contrast to classical (grade-1) elasticity theory, the proposed higher-order elasticity theory yields dispersive Rayleigh waves, as it is also predicted by the atomic theory of lattices (discrete particle theory), as well as by viscoleasticity theory. Most importantly, it is demonstrated that the theory: (a) is in agreement with in situ non-destructive measurements pertaining to velocity dispersion of Rayleigh waves in monumental stones, and (b) it may be used for back analysis of the test data for the quantitative characterization of degree of surface cohesion or damage of Pendelikon marble of the Parthenon monument of Athens.