Practical exercises

2021 ◽  
pp. 223-251
Author(s):  
Jean-Luc Bouchez ◽  
Adolphe Nicolas
Keyword(s):  
Principal Stress ◽  
Structural Data ◽  
The State ◽  
Mohr Circle ◽  
State Of Stress ◽  
Seismological Data ◽  
Stress Directions ◽  
Geodynamic Processes

Some structural geological exercises performed by geologists are presented in this chapter. Many of the practical problems are related to the orientation of planes, lines or principal stress directions. We have chosen to pay particular attention to the Mohr circle, used for analysing stress as well as strain, and to the use of orientation diagrams that allow the geologist to visualize structural data in 3D. Fractured outcrops and seismological data are presented under the form of exercises that help the geologist to document the state of stress associated with past or present geodynamic processes. The chapter ends with a very classic exercise based on the principle of Archimedes.

Stresses Around Wellbores in Nonlinear Rock

1968 ◽  
Vol 8 (03) ◽  
pp. 304-312 ◽  
Author(s):  
M.A. Mahtab ◽  
R.E. Goodman
Keyword(s):  
Finite Element Analysis ◽  
Principal Stress ◽  
Intermediate Principal Stress ◽  
The State ◽  
Initial Stresses ◽  
Stress Strain ◽  
Element Analysis ◽  
Deviator Stress ◽  
State Of Stress ◽  
Strain Data

ABSTRACT The state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore is considered an axisymmetric body with axisymmetric loading. The initial vertical and horizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-wise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses are now reintroduced along with the changed moduli and original boundary constraints. This procedure is repeated until convergent stresses are reached. The effect of nonlinearity on stresses is examined for a 6,000-ft wellbore in a schistose gneiss and Berea sandstone using results of laboratory triaxial compression tests. The results show that the effect is restricted to one well radius from the bottom periphery of the hole. Beyond a distance of one-quarter radius, the effect of nonlinearity on stresses is almost always less than 5 percent for the cases considered. The consideration of a static pressure inside the well does not magnify the effect of nonlinearity on borehole stresses. INTRODUCTION The terms "wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding the behavior of the lined or unlined hole, hydraulic fracture response, and the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Topping1 and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (s1-s3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for the gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (?) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of ? with deviator stress application, but the rate of increase diminishes with confinement. The ET and ? curves for the two rock types are tabulated in Tables 1A and 1B for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation.

scholarly journals State of stress from focal mechanisms before and after the 1992 landers earthquake sequence

1994 ◽  
Vol 84 (3) ◽  
pp. 917-934 ◽  
Author(s):  
Egill Hauksson
Keyword(s):  
Shear Stress ◽  
Stress State ◽  
Principal Stress ◽  
Central Zone ◽  
Focal Mechanisms ◽  
The State ◽  
Rupture Zone ◽  
State Of Stress ◽  
Background Seismicity ◽  
Before And After

Abstract The state of stress in the Eastern California Shear Zone (ECSZ) changed significantly because of the occurrence of the 1992 Mw 6.1 Joshua Tree and the MW 7.3 Landers earthquakes. To quantify this change, focal mechanisms from the 1975 Galway Lake sequence, the 1979 Homestead Valley sequence, background seismicity from 1981 to 1991, and the 1992 Landers sequence are inverted for the state of stress. In all cases, the intermediate principal stress axis (S2) remained vertical, and changes in the state of stress consisted of variations in the trend of maximum and minimum principal stress axes (S1 and S3) and small variations in the value of the relative stress magnitudes (ϕ). In general, the stress state in the ECSZ has S1 trending east of north and ϕ = 0.43 to 0.65, suggesting that the ECSZ is a moderate stress refractor and the style of faulting is transtensional. South of the Pinto Mountain fault, in the region of the 1992 Joshua Tree earthquake, the stress state determined from the 1981 to 1991 background seismicity changed on 23 April and again on 28 June 1992. In the central zone, S1 rotated from N14° ± 5°E to N28° ± 5°E on 23 April and back again to N16° ± 5°E on 28 June. Thus, the Landers mainshock in effect recharged some of the shear stress in the region of the Mw 6.1 Joshua Tree earthquke. Comparison of the state of stress before and after 28 June 1992, along the Landers mainshock rupture zone, showed that the mainshock changed the stress orientation. The S1 trend rotated 7° to 20° clockwise and became progressively more fault normal from south to north. Along the Emerson-Camp Rock faults, the variation was so prominent that the focal mechanisms of aftershocks could not be fit by a single deviatoric stress tensor. The complex distribution of P and T axes suggests that most of the uniform component of the applied shear stress along the northern part of the rupture zone was released in the mainshock. The San Bernardino Mountains region of the Mw 6.2 Big Bear earthquake has a distinctively different state of stress, as compared to the Landers region, with S1 trending N3° ± 5°W. This region did not show any significant change in the state of stress following the 1992 Mw 6.2 Big Bear sequence.

scholarly journals Half-plane contacts subject to remote tension

2021 ◽  
pp. 030932472098844
Author(s):  
Nils Cwiekala ◽  
David A Hills
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Asymptotic Form ◽  
Fretting Fatigue ◽  
The State ◽  
Partial Slip ◽  
Practical Relevance ◽  
Plane Contact ◽  
State Of Stress ◽  
Plane Contact Problem

The state of stress present in an elastic half-plane contact problem, where one or both bodies is subject to remote tension has been investigated, both for conditions of full stick and partial slip. The state of stress present near the contact edges is studied for different loading scenarios in an asymptotic form. This is of practical relevance to the study of contacts experiencing fretting fatigue, and enables the environment in which cracks nucleate to be specified.

scholarly journals Effect of the Rock Stress on the Water Jet Cutting Performance

2021 ◽  
Author(s):  
Battista Grosso ◽  
Valentina Dentoni ◽  
Augusto Bortolussi
Keyword(s):  
Numerical Models ◽  
Step Function ◽  
Water Jet ◽  
The State ◽  
Cutting Performance ◽  
Lagrangian Analysis ◽  
State Of Stress ◽  
Water Jet Cutting ◽  
Cutting Rate ◽  
Available Technology

AbstractUnderground quarrying is rarely adopted for granite extraction due to the difficulties in the implementation of traditional technologies (drilling and explosive). As alternative to drilling and explosive, the combination of diamond wire and water jet seems to be the most promising available technology. The cutting performance achievable with the water jet technology depends on the operative parameters, the material characteristics and the state of stress within the rock massif. To assess the effect of the state of stress on the cutting rate, laboratory tests have been performed with an oscillating water jet machine on granite samples subjected to a static load. The stress distribution in the layer of rock to be removed has been evaluated by numerical simulation with the FLAC code (Fast Lagrangian Analysis of Continua). The correlation between the results of the cutting tests and the numerical models of the rock samples has been inferred. Starting from a conceptual model, which theoretically describes the relationship between the cutting rate and the stress, a step function was defined that indicates the ranges of stress where predefined values of the cutting rate are workable.

scholarly journals Sub-Level Stoping in an Underground Limestone Quarry: An Analysis of the State of Stress in an Evolutionary Scenario

2016 ◽  
Vol 61 (1) ◽  
pp. 199-216 ◽  
Author(s):  
Marilena Cardu ◽  
Sergio Dipietromaria ◽  
Pierpaolo Oreste
Keyword(s):  
Numerical Models ◽  
The State ◽  
In Situ Tests ◽  
Future Scenario ◽  
Limestone Quarry ◽  
Geomechanical Properties ◽  
State Of Stress ◽  
Upper Level ◽  
Pillar Structure

Abstract The aim of this study was to evaluate the state of stress of a „voids-pillar“ structure excavated by means of the sub-level stoping method in an underground limestone quarry near Bergamo (Italy). Both the current structure of the quarry (i.e. the rooms exploited till now) and a possible future scenario were analysed using the (FDM) FLAC 2D code. The quarry has been in operation since 1927; at present, exploitation is carried out underground via the sub-level stoping method. Exploitation involves two levels, with 5 rooms on the upper level and 9 rooms on the lower level. After analysing data obtained from laboratory and in situ tests carried out on rock samples and natural discontinuities, the geomechanical properties of the medium, knowledge of which is essential in order to establish the parameters that must be included in the numerical model, were evaluated. The implementation of three numerical models made it possible to study both the present conditions of quarry exploitation and the evolution of the exploited rooms, as well as a possible expansion involving a third level of rooms. Using the results obtained regarding the stress-strain present in the pillars, a potential change in room geometry was proposed aimed at reducing the stress state inside the pillars, decreasing plasticity and increasing overall quarry safety.

Experimental Determination of the Two-Dimensional State of Stress and the Orthotropic Elasticity Coefficients for Coatings

1990 ◽  
Vol 203 ◽  
Author(s):  
Richard J. Farris ◽  
M. A. Maden ◽  
K. Tong
Keyword(s):  
Elastic Constants ◽  
Physical Property ◽  
The State ◽  
Normal Stresses ◽  
Free Standing ◽  
Vibrationally Excited ◽  
Plane Shear ◽  
Plane Normal ◽  
State Of Stress ◽  
The One

ABSTRACTThe state of stress for a uniform coating away from the edges reduces to that of plane stress, two in-plane normal stresses, and an in-plane shear stress. For this state, the interface between the coating and the substrate is totally stress free. Since the substrate and the coating are not interacting mechanically, an internal section of the substrate can be removed creating a tensioned drum-like membrane without altering the stress state. Holographic interferometry of vibrationally excited membranes is used to evaluate the stress. Using this technique, up to thirty vibrational modes can be obtained. This high degree of redundancy enables one to determine the one shear and two normal stresses that act in the plane of the coating. The only physical property requires is the coating density. The density is obtained from commonly reported literature values. Simple variations on the membrane vibration scheme, e.g., cutting the membrane to create a uniaxially tensioned ribbon, enables one to determine the in-plane Poisson's ratio and shearmodulus.In separate but related experiments on commercially made free-standing films with residual orientation, the above techniques, combined with special free and axially constrainedcompressibility experiments should enable all of the Poisson's ratios and elasticmoduli for an orthotropic material (nine elastic constants) to be determined. Methods for measuring the state of stress and the elastic constants are required to predict the state of stress in complex coating geometries.

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