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Proceedings Papers

Paper presented at the ISRM 2nd International Conference on Rock Dynamics, May 18–19, 2016

Paper Number: ISRM-ROCDYN-2016-30

... strength are obtained by the difference of the longitudinal stress and lateral stress. Results suggest that rock materials are deforming in the inelastic manner and Hugoniot

**Elastic****Limit**(HEL) is deduced. Experimental results are compared and contrasted to the existing data for other geological materials...
Abstract

ABSTRACT: Plate impact experiments have been conducted on one fine-grained metamorphic rock, Carrara marble and one coarse-grained igneous rock, South Africa Gabbro. Embedded manganin stress gauges (i.e. longitudinal and lateral gauges) are used for the measurements of shock stresses. Shear strength are obtained by the difference of the longitudinal stress and lateral stress. Results suggest that rock materials are deforming in the inelastic manner and Hugoniot Elastic Limit (HEL) is deduced. Experimental results are compared and contrasted to the existing data for other geological materials. The detailed experimental procedures used to make measurements are to great extent standard methods when determining mechanical properties and deformation fields at high pressure.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 18–20, 1971

Paper Number: OTC-1355-MS

... the principle of least Work for the cylindrical tube under pure bending when part of the tube is beyond the

**elastic****limit**. The tube is allowed to assume that elliptical cross-section which minimizes the strain energy. Ades' analysis has been successfully employed to predict results which were obtained...
Abstract

INTRODUCTION The question of pipe ovalization and its effect on moment-curvature relationships in the elastic case have been treated by Brazier1 and others. 2-4 The effect of ovalization in the nonlinear (strain hardening) case has been treated numerically by Ades. 5 Ades' analysis employs the principle of least Work for the cylindrical tube under pure bending when part of the tube is beyond the elastic limit. The tube is allowed to assume that elliptical cross-section which minimizes the strain energy. Ades' analysis has been successfully employed to predict results which were obtained experimentally in pipe bending tests at Rice U. Since tension is generally employed in offshore pipeline laying operations, the importance of this effect on Ades' analysis is worth investigating. The relationship between the reduction in, maximum moment carrying capacity as the axial tension is increased is desired. The pipe is allowed to deform beyond the elastic limit and the effect of pipe ovalization is included. Review of Ades' Analysis Consider the cylindrical pipe loaded as shown in Fig. 1. A hollow tube subjected to pure bending is known to flatten and take on an ovalled shape. The ovalled shape is assumed to be elliptical (Fig. 2), and it is assumed that the circumferential deformation is in extentional insofar as relating the elliptical cross-section to the initial circular cross-section. Other assumptions made by Ades are that the tube is subjected to pure bending, it is long enough that end effects may be ignored, and the material is isotropic with the same stress strain curve in tension and compression. Referring to Fig. 2, the work per unit length in the elastic range is (Mathematical equation available in full paper) elastic and plastic 'ranges. It should be noted that the conventional stress-strain curve in a uniaxial tension test is the stress intensity strain intensity curve for that case. Thus, the standard stress-strain curve from a simple tension test is used in both elastic and plastic ranges. Ades implies the use of the principle of least work, but the procedure he follows is to first bend the tube and then let it oval to that elliptical cross-section for which the strain energy is a minimum. Since the externally applied moment does no work during the ovalization, this procedure actually finds that value of a/r (a being the semi major axis of the ellipse and r the original average radius of the unreformed tube) which minimizes the strain energy. Where E(k) is the complete elliptic integral of the second kind. Thus, for a given value of air, the eccentricity, k, of the ellipse can be found. Fig. 3 shows how one-half of the ellipse is broken up into equal arc lengths and points numbered. It is noted that the y axis is an axis of symmetry. At each division point along the arc length, the wall is divided into four equal parts. The work per unit volume is computed at each point, and the integration across the wall carried out using Simpson's rule.

Images

in Pulse Fracturing in Shale Reservoirs: Geomechanical Aspects, Ductile/Brittle Transition, and Field Implications
> SPE Journal

**Published:**18 December 2015

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the IADC/SPE Asia Pacific Drilling Technology Conference, August 25–27, 2014

Paper Number: SPE-170524-MS

.... The constitutive relations were constructed simulating the

**elastic**and plastic deformations up to the failure. The radial compression tests showed stability of casings was maintained until the stresses at four cross-points of the stress concentration areas exceeded the yield strength. The higher grade...
Abstract

Most companies producing from high compaction reservoirs continue using casings even if they find that these casings have been elongated or compressed exceeding the yield stress ( Furui, et al., 2011 ). The magnitude of elongation and compression of these casings are often 3 to 5% while the strains at the yield strength are supposed to be 0.3–0.5%. Since casings are actually used beyond casing yield strength, field engineers should take into account the casing properties during plastic deformation. In this study, extension, compression and radial loading tests were conducted from H-40 to V-150 casings up to failure. The tests gave the following results: Under extension tests, the casings were uniformly deformed beyond the yield strength. The uniform deformation continued while the casings were stretched by 4 to 25% until non-uniform deformation was induced. The constitutive relations were constructed simulating the elastic and plastic deformations up to the failure. The radial compression tests showed stability of casings was maintained until the stresses at four cross-points of the stress concentration areas exceeded the yield strength. The higher grade casings did not significantly increase the maximum strength after yielding while lower grade casings significantly increased the strength while being stretched or compressed uniformly after yielding. The analyses show that the casings were uniformly deformed until the maximum strength so that they were usable. The peak load of the uniform deformation is the limit load since they rupture after the uniform deformation. When casings are compressed or extended by geo-technical loadings, thicker casings with a lower grade prevent rupture and kinks while higher grade casings tend to rupture with a large formation deformation. When casings are compressed by directional geo-technical load, the casings start losing the load-support capability after the stresses at four cross-points of the casings exceed the yield stress. Selecting a proper grade and thickness of casings are the key for mitigating casing failure where the data of casing deformation beyond the yield strength are essential information for casing designing using geomechanical models.

Images

**Published:**24 October 2016

Images

**Published:**16 April 2012

Figure 2

**Elastic**stress**limit**(τ oe ) and plastic stress**limit**(τ op ) as a function of temperature for the Louann Salt in the Gulf of Mexico ( Infante, et al., 1989 ). Data re-plotted after Infante & Chenevert. More
Proceedings Papers

Publisher: Society of Exploration Geophysicists

Paper presented at the 1996 SEG Annual Meeting, November 10–15, 1996

Paper Number: SEG-1996-0723

... reservoir characterization reflection response synthetic upstream oil & gas seismic data MOD 3.5 Building a detailed

**elastic**depth model with**limited**information J. C. Dunne* and G. Beresford, University of Melbourne, Australia; B. L. N. Kennett, Australian National University, Australia S u m m...Images

**Published:**03 June 2019

Figure 9 Force

**limited**by formation shear strength (t f ) compared with**elastically**calculated force from formation to well. Left: Case A with 100 m overburden thickness. Right: Case B with 1000 m overburden thickness. t 1 :**elastic**force from reservoir. t 2 :**elastic**force from overburden. MoreImages

**Published:**24 October 2016

Figure 7 Experimental values of

**elastic**strength**limits**for rock samples with different lithology and corresponding to the initial**limiting**surface MoreImages

**Published:**24 October 2016

Figure 8 Experimental values of

**elastic**strength**limits**for rock samples with different lithology and corresponding to the finite**limiting**surface MoreImages

**Published:**24 October 2016

Figure 9 Experimental values of

**elastic**strength**limits**for rock samples with different lithology and correspondentto the finit and initial**limiting**surface More
Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Russian Petroleum Technology Conference and Exhibition, October 24–26, 2016

Paper Number: SPE-182028-MS

... after testing up to rupture) A last point on a straight section – this is the

**limit**of**elasticity**. With further strain increasing an interrelation "stress–strain" is nonlinear, the internal stress in the sample reaches a maximum, after which the sample is collapses (we can observe a rupture...
Abstract

The purpose of our work – is to show our version of determining the strength properties, elastic modules and compressibility factors at reservoir conditions on the example of rock fields OOO "LUKOIL–Western Siberia". This paper briefly shows a method of measurement and processing of the results. The paper also shows some results of the determination of dynamic and static elastic moduli of rocks (Poisson's ratio, Young's modulus, shear modulus, compressibility, ultimate strength, elastic limits). This article also shows some results of a comparison of dynamic and elastic Young's modulus. Static deformation and strength characteristics of the rock were determined by direct measurements of the longitudinal and transverse strains. All measurements were made at reservoir conditions by increasing the axial load until destruction of the sample. The rate of deformation changes was no more than 1.5 • 10 -6 s -1 , reservoir pressure and temperature were maintained automatically with a high degree of accuracy. Static deformation and strength characteristics are the most reliable, and reflect real properties of both homogeneous and heterogeneous anisotropic rocks. In our laboratory, on by our optimized measurement method were performed investigations of dynamic and static strength properties of more than 500 rock samples from different oilfields of OOO "LUKOIL–Western Siberia". Our Company has received a very valuable information about the rocks in the form of diagrams "Stress–Strain," of Mohr's circles, elastic limits, ultimate strengths, elastic modulus, graphs of compressibility factor and Biot's coefficients depending on the pressures. It should also be noted that we have not been able to find any general and uniform dependence (laws) in all studied formations and fields, between dynamic and static elastic moduli. For solving of some specific tasks (for example, a field development, design of hydraulic fracturing) and for obtaining high–quality and reliable results on the rock mechanics we need use only static strength characteristics of rocks identified at true reservoir conditions. Our methodology is based on the American Standard ASTM D 3148–93, and the results of our experimental work and the measurement procedure (Owner's Manual) for our equipment, taking into account the specific properties of sedimentary rocks of OOO "LUKOIL–Western Siberia". For concrete oil formations studied fields of OOO "LUKOIL–Western Siberia" we had found quite close links between the dynamic and static Young's modulus. Such petrophysical links is possible to use for obtaining more important information from the results of rocks research by dynamic method.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Vail Rocks 1999, The 37th U.S. Symposium on Rock Mechanics (USRMS), June 7–9, 1999

Paper Number: ARMA-99-0927

... ABSTRACT: Design of safe, stable mine excavations requires consideration of time-dependent phenomena, a rather neglected area outside salt and potash mines. In this regard, viscoplasticity is the simplest extension of the standard

**elastic**model,**limited**by rock mass strength, into the time...
Abstract

ABSTRACT: Design of safe, stable mine excavations requires consideration of time-dependent phenomena, a rather neglected area outside salt and potash mines. In this regard, viscoplasticity is the simplest extension of the standard elastic model, limited by rock mass strength, into the time domain. The main consequence ofviscoplasticity is time- dependent displacement, above the elastic limit, that grows with ever increasing strain, although at a diminishing rate. Rounded stair-step displacement versus time curves are similar to those often observed in the field. Such a process INTRODUCTION Rock falls, pillar spaIls and floor heave in underground mine openings are very often time-dependent (e.g, Merrill 1952, Obert and Duvall 1967, Pariseau et al. 1984). Time-dependent closure is especially noticeable in salt and potash formations. Slope motion in surface mines is also quite often time-dependent (Zavodni and Broadbent 1980). In some instances the motion develops into catastrophic failure. However, despite much observational evidence for time-dependent behavior of rock masses, surprisingly little has been done to quantify the effects and to improve forecasting of potential instabilities and unsafe conditions. In response, a critical review of viscoplasticity was recently undertaken (Pariseau, 1998). This contribution is a condensed version of that report. Viscoplastic effects are synonymous with strain-rate effects. Such effects range over orders of magnitude in time from fractions of a second in blast wave dynamics to hundreds of years in creep of geologic media, especially salt. The latter are often described as fluid-like viscoelastic media that have no well-defined elastic limit. Interestingly enough, the original viscoplastic model, proposed by Bingham (1922) and subsequently elaborated upon in continuum mechanics, was motivated by fluid mechanics observations. However, concern here is with extension of what may be called the standard model in rock mechanics, a material limited by strength or possibly stability criteria. Guidance for the validity and limitations of the model is found in laboratory test data for intact rock and mine measurements for rock masses. The objective is to achieve greater realism in engineering design by accounting for time-dependent rock mass behavior and eventually anticipating the development of fast, catastrophic failures. Here, a brief outline of theory is presented first; several test problems are then examined for the consequences of viscoplasticity.

Journal Articles

Journal:
SPE Journal

Publisher: Society of Petroleum Engineers (SPE)

*SPE J.*5 (02): 148–157.

Paper Number: SPE-57959-PA

Published: 01 June 2000

... model is used to describe the yielding of the samples at low temperatures. The

**elastic**-**limit**, static, and dynamic yield stresses as a result of different static cooling processes were determined from controlled stress and oscillatory rheological measurements. The types of histories examined include...
Abstract

Summary The effect of the thermal history on the waxy structure of two statically cooled waxy crude oils is examined using a controlled stress rheometer for rheological measurements and a microscope to observe microstructure of wax crystals. A three-yield-stress model is used to describe the yielding of the samples at low temperatures. The elastic-limit, static, and dynamic yield stresses as a result of different static cooling processes were determined from controlled stress and oscillatory rheological measurements. The types of histories examined include the temperature, cooling rate (0.5 to 4°C/min), and isothermal holding time before testing (up to 15 hours). In addition, the reversibility over time of the waxy structure after yielding was investigated. The results from both yield stress measurements and microscopic observations show that the waxy structure strongly depends on both the temperature and the cooling rate. The isothermal holding time both before and after yielding was found to have no observable influence on the structure over the time period studied in these experiments. Introduction Pipelines transporting waxy crude oils may be shut down regularly for normal operational reasons and occasionally for emergency reasons, such as power failure, line damage, or even earthquake, etc. 1 In these cases, the warm crude oil in the pipeline may be cooled statically below its pour point, leading to a strong waxy crystal interlocking network forming in the oil. The strength of this waxy structure is influenced by many factors found in the cooling process, such as the starting and final temperatures, the cooling rate, the isothermal holding time before restart, and the temperature cycling. To restart the pipeline filled with the gelled oil, a sufficient pressure must be applied to make the oil yield. The yielding process of the gelled oils has been shown to occur sequentially by an elastic response, creep, and a final fracture. 2,3 Three yield stresses, an elastic-limit, a static, and a dynamic yield stress, are required to describe the yielding process and the sheared state after yielding. The elastic-limit yield stress is the stress limit for an oil sample to retain a reversible waxy crystal structure. The static yield stress is the minimum shear stress required to produce an unbounded deformation. Both the elastic-limit and static yield stress are dependent on the strength of the waxy structure before yielding, and thus can be used as an indication of the strength of the waxy structure. The dynamic yield stress is useful in describing the oil properties at the final sheared state after the waxy structure has been destroyed. It is a parameter used in the constitutive equation of state for the liquid-state oil after yielding. The three yield stresses may be determined using three direct measurements—a controlled stress test, a creep-recovery test, and a dynamic oscillation test—in a controlled stress rheometer. Both the static and dynamic yield stresses were found to depend on the time scale of the measurement, such as the stress loading rate in the controlled stress test, the stress time in the creep-recovery test, and the frequency in the dynamic oscillation test. Therefore, the determined static and dynamic yield stresses can only be compared with those obtained with the same time scale and with the same technique under other thermal conditions. The elastic-limit yield stress, however, was found to be independent of the time scale of the test from both the creep-recovery and dynamic oscillatory tests. 3,4 It has been known for a very long time that the thermal history or heat treatment to which the oils have been subjected influences the fluidity of some residual oils. 5 Many studies have been carried out for the effect of thermal conditions on the equilibrium viscosity, which is the viscosity after yielding, for waxy crude oils. 6–9 The pour point was often taken as the index of the pumpability in the earlier stage. 5,10,11 A systematic investigation of the variables affecting the yield strength of waxy crude oils was started in the 1970's after it was gradually realized that the yield value was a better measure of the pumpability. 7,9,11-17 A phase contrast microscope was used in some work to determine the effect of thermal conditions on the size and morphology of waxy crystals, and was then used to explain the viscosity or yield stress variation with the thermal conditions. 7,14,18 The factors that have been investigated involved temperature history (testing temperature, temperature cycling, and cooling rate), shear history, aging, and composition; but some conflicting conclusions have been found. The reproducibility of the yield stress measurements has been found to be poor in many earlier studies. This poor reproducibility may be caused by many reasons, among which are the confused definition of the yield stress, limitation of the instruments and the techniques, and poor control of the thermal conditions of the experiments. Recently, a controlled stress rheometer with cone-and-plate geometry was introduced with which the true yield values of waxy crude oils can be directly determined. 17–19 The small volume of the sample used in the cone-and-plate geometry and the improved temperature control function of the rheometer make it possible to effectively control the temperature and thermal history, which was difficult to do with the instruments using a large volume of the sample, such as the pipeline or vane.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 54th U.S. Rock Mechanics/Geomechanics Symposium, June 28–July 1, 2020

Paper Number: ARMA-2020-1185

... with its loading history. Behavior of the samples above the

**elasticity****limit**was of special interest. It was shown that while the samples show**elastic**behavior, permeability tends to decrease with increase in effective compressive stress. Nevertheless, with inelastic strain is being accumulated...
Abstract

The paper presents the results obtained from a series of triaxial loading tests performed for rock samples from a Russian oil field. The tests were performed in order to obtain a valid relationship between fluid permeability of the samples and their actual stress-strain state alongside with its loading history. Behavior of the samples above the elasticity limit was of special interest. It was shown that while the samples show elastic behavior, permeability tends to decrease with increase in effective compressive stress. Nevertheless, with inelastic strain is being accumulated, this accumulation provides an increase in permeability of the samples with increase in compressive stress. This nonlinear and non-monotonic relationship was studied for liquid-saturated samples. The obtained dependencies may be used for coupling geomechanical and hydrodynamic modeling of hydrocarbon reservoir development. The observed nonlinear and non-monotonic behavior of permeability vs. stress state dependency shows the need of using complicated functions for coupling. It is important to consider permeability growth with increase of compressive stresses if their changes are large enough for inelastic strains accumulation in hydrocarbon reservoir. 1. INTRODUCTION The interrelation between mechanical and hydrodynamic processes occurring in hydrocarbon reservoirs is a wellknown issue in reservoir geomechanics. There are different problems of reservoir exploration and development characterized by an utter need to couple geomechanical and hydrodynamic modeling including compaction, subsidence and depletion taking place during the evolution of effective stresses' and fluid fields in the reservoir due to its development. One of the major factors standing for the importance of solving coupled geomechanical and hydrodynamic problems is the deep connection between void space of the fluid-saturated rock mass and its current stress state. This connection leads to considerable changes in reservoir filtration properties which are needed to be taken into account for optimizing reservoir development strategy. Generally, the fully coupled system of equations of poroelasticity and filtration (Coussy, 2004) should be solved to understand the hydrodynamic and geomechanical processes in a saturated rock mass. Kim, 2010 has given an overview of existing methods of solving this system of equations. The main difference between the published research papers on this topic is the method of solving the system of equations: so, Osorio et al., 1999 and others used the finite difference scheme; Settari and Mourits, 1998, Schutjens et al. 2001, and others used finite element method and so on. The problem of coupling geomechanical and hydrodynamic modelling is usually particularly considered: Inoue and Fontoura, 2009 and Samier et al., 2007 have shown that stress fields and pore pressure fields can be modeled separately with coupling performed through relationships between filtration properties and effective stresses.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 4–7, 1975

Paper Number: OTC-2209-MS

... of longitudinal bending moment and external pressure. These areas are the sag region and in the overbend region, often toward the lower tip of the stinger. The stresses that develop during the pipeline laying operation may be significantly above the

**elastic****limit**of the material. Buckling formulations based...
Abstract

ABSTRACT Investigation of the buckling characteristics of offshore pipelines produced solutions to nonlinear equilibrium and compatibility equations that demonstrate the pre- and postbuckling configurations of pipelines under combined loads. In general, this study enhances our understanding and insight into the nature of pre- and postbuckling behavior of pipelines having low diameter-to-thickness (D/t) ratios - i.e., in the range from 20 to 100. INTRODUCTION When laying a pipeline with a typical lay barge operation (Figure 1), most buckling occurs in regions of combined loadings of longitudinal bending moment and external pressure. These areas are the sag region and in the overbend region, often toward the lower tip of the stinger. The stresses that develop during the pipeline laying operation may be significantly above the elastic limit of the material. Buckling formulations based on elastic deformations are therefore incapable of properly describing prebuckling and postbuckling behavior. During the past 6 years analytical and experimental research has been conducted at Battelle's Columbus Laboratories to investigate the elastoplastic pre- and postbuckling characteristics of offshore pipelines. The goal of this research was to develop an experimentally verified analytical method that would predict the buckling strength of undersea pipelines and to provide a comprehensive understanding and insight into the nature of pre- and postbuckling behavior of cylinders having low diameter to thickness (D/t) ratios, i.e., D/t's in the range from 20 to 100. Although this work was directed toward pipelines, the general concepts are applicable to any cylindrical shells under such loads. ANALYTICAL FORMULATION The stresses developed during the laying of pipelines are for the most part the result of bending and hydrostatic pressure. Generally speaking, stability solutions to problems involving combined loading - one of which is bending - are quite difficult. However, it has been shown by Vol'mir(l) and again by Kemper, et ale (2), that in the case of elastic buckling the problem may be simplified since the critical longitudinal buckling stress caused by bending is equal to the critical longitudinal buckling stress caused by pure axial load.. Based on these works, a simplifying assumption that appears justifiable, at least from the standpoint of providing a lower bound to the buckling load, is that the longitudinal buckling strain calculated according to hydrostatic pressure and axial load is equal to or less than the longitudinal buckling strain that results from the combined loads of hydrostatic pressure and pure bending. When stresses are in excess of the elastic limit, the material behavior is termed nonlinear, plastic, 'or inelastic. The concern for this behavior dates back nearly a century. Historically, while studying the inelastic behavi0J:" of column buckling, two theories evolved: the tangent modulus theory and the double modulus theory. If a structure is loaded to a stress below the elastic limit, the material essentially follows the same stress-strain path when unloaded. The tangent modulus theory assumes that this stress-strain behavior is also true above the elastic limit.

Proceedings Papers

Paper presented at the ISRM European Rock Mechanics Symposium - EUROCK 2017, June 20–22, 2017

Paper Number: ISRM-EUROCK-2017-018

... (I) pores compressibility. Micro- and macro-dilatancy

**limits**can help in the second**limit**selection. They provide the most important information about rocks in geological databases, because they**limit**the**elastic**state of the rock. They are also referred to as crack damage stresses [2, 6...
Abstract

Abstract Young modulus is one of a basic geo-mechanical parameters used for the defining of the phenomena in rock mass. It is determined based on a uni-axial compressive test. According to the International Society of Rock Mechanics one may calculate it in three different ways as the tangent, secant and average modulus. This discretion causes, as the result that one can obtain results, which differ from each other significantly, even threefold or more. The laboratory tests for Carboniferous rocks: claystones, mudstones, sandstones and coals are presented in the paper. The modulus value distributions for the recommended methodology were compared using statistical analysis. The typical range of the elastic linear deformability for the chosen rock types was determined. Thus the evaluation of the best Young modulus determination method was performed. Tangent Young modulus was recommended as the guiding one, studied with the range of 25–75% of ultimate stress. 503 rock samples have been investigated for this analysis. The elastic behaviour of rocks and the range of their elasticity are of crucial importance in rock engineering. In solving problems in mining engineering or tunnelling, the change of stress fields forced by an excavation drivage first depends on the elastic and then the post-failure properties of rock. Hence, determining the rock mass properties appropriately is of crucial importance for a roadway stability evaluation and support design. Among elastic rock properties one may mention: Young's modulus, shear modulus, bulk modulus and Poisson's ratio. As the shear modulus and bulk modulus are functions of Young's modulus and Poisson ratio the last two parameters are the most important in solving geo-mechanical problems. Some authors even emphasise, that elastic modulus becomes a critical parameter to describe the rocks' behaviour under load because of their brittleness [1, 10]. All numerical models for stress and deformation analyses such as FLAC, PHASE or UDEC use Young's modulus for solving rock engineering problems [11]. Young's modulus is also a base to derive a deformation modulus of blocky and jointed rock masses, which are non-elastic.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 2–5, 2011

Paper Number: OTC-21668-MS

... in a lateral buckle are high and usually involve straining beyond the

**elastic****limit**of the pipe; these strains can be high enough to induce local buckling of the pipe wall. Within this paper, and in most design codes, the buckling capacity is defined by the**limit**point - the position of maximum moment...
Abstract

Abstract The SAFEBUCK JIP was initiated to develop methodologies to deliver a safe and effective pipeline design that admits lateral buckling. A key limit state for designing to accommodate lateral buckling is local buckling. Local buckling is driven by the high imposed bending in combination with internal and external pressure. Relatively little work has addressed the effect of these combined loads for the D/t (diameter/thickness) range of interest to submarine pipelines (between 10 and 45). Further, little attention has been paid to the importance of Lüder banding. This type of behaviour is normal in seamless linepipe, which is used for most in-field flowlines, and can be extremely detrimental to the local buckling capacity of a pipe. To address this, the SAFEBUCK JIP performed a combination of full-scale testing and numerical modelling to investigate the local buckling behaviour of seamless linepipe. The work showed that the local buckling response is fundamentally influenced by the Lüder plateau. Pipes with a low D/t ratio buckle at strains far above the Lüder strain and have a high buckling capacity. However, pipes with a high D/t ratio may buckle below the Lüder strain, in which case there is essentially no beneficial effect of strain hardening and the pipe has a very low buckling capacity. This work looked at buckling capacity across a wide D/t range, including the D/t transition zone where the behaviour changes from one response to the other. Current design equations do not capture the influence of the Lüder plateau, and the design margin implied by the equation varies considerably over the range of parameters considered. Introduction The SAFEBUCK JIP was initiated to develop methodologies to deliver a safe and effective pipeline design that admits lateral buckling. The bending loads in a lateral buckle are high and usually involve straining beyond the elastic limit of the pipe; these strains can be high enough to induce local buckling of the pipe wall. Within this paper, and in most design codes, the buckling capacity is defined by the limit point - the position of maximum moment in the moment-curvature response. Although this is not the point at which the pipe loses all structural resistance, beyond this point softening and severe strain localisation occurs; accurate calculation of the structural response is extremely involved and influenced by parameters which are not well controlled or known. Consequently, the curvature associated with the limit point is taken to represent the buckling capacity of the section. The local buckling response within the buckled pipeline can either be assessed using a moment limit or a curvature limit. The two extremes of imposed loading are generally termed load controlled or displacement controlled. For bending dominated deformations this implies moment controlled bending or curvature controlled bending. For curvature control, the curvature developed in the pipe does not depend upon its bending resistance, because the bending process will always result in the same curvature, irrespective of the pipe moment-curvature relationship. A typical example of this is the bending of a pipe to fit the radius of a former. However, real structures are rarely truly displacement controlled or load controlled - they tend to exhibit elements of both. The application of these approaches to a typical pipeline response is illustrated in Figure 1. Once yielding of the cross-section becomes established, the moment-curvature response is very flat; so that there is significant increase in curvature with little increase in moment. As a result of the flat response, any moment limit must be defined before significant plasticity has developed. This is appropriate if the imposed moment is not self limiting - since failure can quickly result if the design value is exceeded. During lateral buckling, the bending will exceed the elastic limit of the pipeline; this is an inevitable consequence of the buckling behaviour in all but the most benignly loaded systems. This means that a moment limit may well be too onerous to apply to this condition.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Symposium: Petrophysics XXI. Core, Well Logging, and Well Testing, June 9–10, 2021

Paper Number: SPE-208427-MS

... № oбp 609-130-7 A= 36 MM B= 23 MM P эфф =σ 3 = 43,93 MПa P пp пp = 145,3 MПa β=ATaHг(A/B)= 57,4 o (гpaд) φ=2 β-90= 24,9 o (гpaд) CцеплеHие C= 27 MПa Sample Confining pressure (MPa) Pore pressure (MPa)

**Elastic****limit**(MPa...
Abstract

The strength properties of the rock determine many physical processes occurring in the formation and at the bottom of the well. Deformation and destruction of rocks under the influence of external forces can be both a positive and a negative factor for working with formations at all stages of development. To create the optimal design of the well drilling trajectory, select the optimal development project, the fluids extraction rate from the formations, efficient planning and implementation of hydraulic fracturing procedures, prevention of emergencies during drilling and operation and reduction of oil recovery due to irreversible loss of reservoir properties and solving many other problems, it is necessary to consider possible destruction of the rock. The Mohr-Coulomb envelope (rock strength passport) can be used as a strength criterion for such tasks, it characterizes the boundary values of stresses in the rock, at which its destruction occurs according to the Mohr-Coulomb theory. At article discusses three methods for determinate strength passports based on the results of laboratory studies of rock samples: multistage loading of the sample, assessment of the sample fracture after triaxial compression strength test, the use of "twin" samples for testing. The features of each method, its advantages and limitations are disclosed, examples of construction of strength passports for rocks from fields in Western Siberia are shown. According to the research results, the most preferable is the use of "twin" samples. However, this method is associated with technical difficulties.

Proceedings Papers

Paper presented at the ISRM International Symposium, September 21–24, 1981

Paper Number: ISRM-IS-1981-117

... INTRODUCTION Observations on deep underground caverns show two major phenomena: – the

**elastic****limit**can be exceeded (high Convergencies development of a fracture zone around the cavity, slabbing …), without necessarily endangering the whole stability of the structure; – the non**elastic**...
Abstract

INTRODUCTION Observations on deep underground caverns show two major phenomena: – the elastic limit can be exceeded (high Convergencies development of a fracture zone around the cavity, slabbing …), without necessarily endangering the whole stability of the structure; – the non elastic phenomena are often time dependant (stabilisation of convergencies need some weeks, months or years …). The classical elastic-perfect plastic theory is generally not sufficient to describe the above phenomena. Moreover it seems too optimistic as it predicts that any tunnel in a cohesive material need no support. Progress in laboratory devices, as servo Controlled machines, have led to a more comprehensive analysis of rock behaviour, and consequently, many authors have proposed theories including a softening behaviour: [Egger, 1973, Nguyen Q.S. & Bui,1974, Panet, 1976, Nguyen Minh, Berest 1977, Mroz, 1980]. But these theories stay in the framework of Continuum mechanics. Considering an equivalent continuous material may rise criticisms as extended cracking in the post failure phase may develop into a major shear crack. Some authors [Habib, 1979], asked themselves whether the softening concept could exist if major shear cracks were to multiply, and whether, in this case the Perfect plasticity was not more convenient. A Special attention has been paid for these problems in this paper: comparison between laboratory experiments, in situ observations and theory have been carried on with a view to provide a simple rheological model accounting for the time-dependant strain Softening behaviour of rocks. - SOME GENERAL LAWS FROM EXPERIMENTAL OBSERVATIONS IN LABORATORY Rocks appear in nature with existing discontinuities at different scales. Their non elastic behaviour are strongly dependent on these discontinuities and of their growth. When performing an uniaxial test on such a material, globally considered as homogeneous, the force-displacement curve will be considered as intrinsic for an equivalent continuous model, if no localized major discontinuity will appear and change the geometry of the sample. This is the case with shear cracks (fig. 1.a); similar phenomena happen with other geometries, e.g. for thick follow rock cylinders (fig. I.b), which will be considered later. With these reserves, we can admit the following laws from classical triaxial strain-controlled tests we have performed in our laboratory and from datas reported by other authors [ wawersik & Fairdhurst, 1970, Peng & Podnieks, 1972, Houpert, 1974]. (Figure in full paper) Softening behavior This phenomenon is now classically known for rocks: in a uniaxial test at constant strain rate, the load F increases to a maximum value and then decreases (post failure phase, or "softening"). This phenomena is typically plastic-like as it is shown by some unloading-reloading cycles, (fig. 2). The points B 1 , B 2 …are the elastic limits which will be precised later. It can be remarked that the elastic modulous E 1 , E 2 , E 3 … decrease with softening of the rock, which testify of the weakening of the material due to extended development of cracks.

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