Reply by the authors to G. H. F. Gardner

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 1016-1017
Author(s):  
N. I. Christensen ◽  
H. F. Wang
Keyword(s):  
Shear Velocity ◽  
Confining Pressure ◽  
Differential Pressure ◽  
High Porosity ◽  
Inelastic Behavior ◽  
Velocity Measurements ◽  
Pressure Cycle ◽  
Confining Pressures ◽  
Cyclic Variations ◽  
Pressure Changes

Gardner suggests that velocity data in which confining pressure changes are not canceled by equal pore pressure changes may be due to hysteresis effects that prevent velocity from being a unique function of the differential pressure. This is supported by shear velocity measurements in dry Berea sandstone as a function of cyclic variations of differential pressure (Gardner et al., 1965). High porosity and clayey sandstones indeed can demonstrate this behavior. Cyclic pressure variations can lead to work hardening and other inelastic behavior. For our measurements, however, we believe that the effects of hysteresis were minimal because of (1) the pressure cycle followed to obtain velocity as a function of pore and confining pressures, and (2) the large elapsed time between our measurements.

On: “The influence of pore pressure and confining pressure on dynamic elastic properties of Berea sandstone,” by N. I. Christensen and H. F. Wang (GEOPHYSICS, 50, 207–213, February 1985).

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 1016-1016
Author(s):  
G. H. F. Gardner
Keyword(s):  
Pore Pressure ◽  
Confining Pressure ◽  
Hysteresis Curve ◽  
Hysteresis Cycle ◽  
Berea Sandstone ◽  
Experimental Accuracy ◽  
Confining Pressures ◽  
History Of ◽  
Pressure Changes ◽  
Dynamic Elastic Properties

The authors present their results as if Berea sandstone were an elastic material; that is, velocities are given as functions of confining and pore pressure. In fact, most rocks are inelastic and velocities depend on the history of the confining and pore pressure, and not just on the present values. Some measurements of hysteresis were reported by Gardner et al. (1965). The confining pressure was cycled between two pressures [Formula: see text] and [Formula: see text] for a fixed pore pressure [Formula: see text], following a fixed schedule of pressure changes, until repeatable values of velocity were obtained. (At any intermediate pressure the velocity measured for increasing pressure was different from the value for decreasing pressure, giving rise to a hysteresis cycle). When the same schedule of pressure changes for the differential pressure [Formula: see text] was followed by holding [Formula: see text] fixed and varying [Formula: see text], the measured velocities followed the same hysteresis curve within the limits of experimental accuracy. In brief, when hysteresis was taken into account, changes in pore and confining pressures were equally effective in changing velocity. In their article, Christensen and Wang do not refer to hysteresis; perhaps they would like to comment on its relevance.

scholarly journals Effects of Displacement Velocity on Rock Fracture Shear Strengths under Large Confinements

2016 ◽  
Vol 5 (2) ◽  
pp. 32 ◽  
Author(s):  
Matsee Kleepmek ◽  
Supattra K Hamrat ◽  
Kittitep Fuenkajorn
Keyword(s):  
Rock Fracture ◽  
Shear Velocity ◽  
Confining Pressure ◽  
Displacement Velocity ◽  
Test Results ◽  
Shear Tests ◽  
Confining Pressures ◽  
Strong Rock ◽  
Load Frame ◽  
Induced Fractures

Triaxial shear tests are performed to assess the effects of displacement velocity and confining pressure on shear strengths and dilations of tension-induced fractures and smooth saw-cut surfaces prepared in granite, sandstone and marl specimens. A polyaxial load frame is used to apply confining pressures between 1 and 18 MPa with displacement velocities ranging from 1.15×10-5 to 1.15×10-2 mm/s. The results indicate that the shearing resistances of smooth saw-cut surfaces tend to be independent of the displacement velocity and confining pressure. Under each confinement the peak and residual shear strengths and dilation rates of rough fractures increase with displacement velocities. The sheared-off areas increase when the confining pressure increases, and the displacement rate decreases. The velocity-dependent shear strengths tend to act more under high confining pressures for the rough fractures in strong rock (granite) than for the smoother fractures in weaker rocks (sandstone and marl). An empirical criterion that explicitly incorporates the effects of shear velocity is proposed to describe the peak and residual shear strengths. The criterion fits well to the test results for the three tested rocks.

Mechanical behaviour of powders using a medium pressure flexible boundary cubical triaxial tester

2003 ◽  
Vol 217 (3) ◽  
pp. 233-241 ◽  
Author(s):  
F Li ◽  
V M Puri
Keyword(s):  
Shear Modulus ◽  
Mechanical Behaviour ◽  
Triaxial Compression ◽  
Three Dimensional ◽  
Volumetric Strain ◽  
Confining Pressure ◽  
Alumina Powder ◽  
Medium Pressure ◽  
Mean Pressure ◽  
Confining Pressures

A medium pressure (<21 MPa) flexible boundary cubical triaxial tester was designed to measure the true three-dimensional response of powders. In this study, compression behaviour and strength of a microcrystalline cellulose powder (Avicel® PH102), a spray-dried alumina powder (A16SG), and a fluid-bed-granulated silicon nitride based powder (KY3500) were measured. To characterize the mechanical behaviour, three types of triaxial stress paths, that is, the hydrostatic triaxial compression (HTC), the conventional triaxial compression (CTC), and the constant mean pressure triaxial compression (CMPTC) tests were performed. The HTC test measured the volumetric response of the test powders under isostatic pressure from 0 to 13.79MPa, during which the three powders underwent a maximum volumetric strain of 40.8 per cent for Avicel® PH102, 30.5 per cent for A16SG, and 33.0 per cent for KY3500. The bulk modulus values increased 6.4-fold from 57 to 367MPa for Avicel® PH102, 3.7-fold from 174 to 637 MPa for A16SG, and 8.1-fold from 74 to 597MPa for KY3500, when the isotropic stress increased from 0.69 to 13.79 MPa. The CTC and CMPTC tests measured the shear response of the three powders. From 0.035 to 3.45MPa confining pressure, the shear modulus increased 28.7-fold from 1.6 to 45.9MPa for Avicel® PH102, 35-fold from 1.7 to 60.5MPa for A16SG, and 28.5-fold from 1.5 to 42.8MPa for KY3500. In addition, the failure stresses of the three powders increased from 0.129 to 4.41 MPa for Avicel® PH102, 0.082 to 3.62 MPa for A16SG, and 0.090 to 4.66MPa for KY3500, respectively, when consolidation pressure increased from 0.035 to 3.45MPa. In addition, the shear modulus and failure stress values determined from the CTC test at 2.07, 2.76, and 3.45MPa confining pressures are consistently greater than those from the CMPTC test at the same constant mean pressures. This observation demonstrates the influence of stress paths on material properties. The CTT is a useful tool for characterizing the three-dimensional response of powders and powder mixtures.

scholarly journals Experimental Study on the Effects of Stress Variations on the Permeability of Feldspar-Quartz Sandstone

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Fugang Wang ◽  
Zhaoxu Mi ◽  
Zhaojun Sun ◽  
Xufeng Li ◽  
Tianshan Lan ◽  
...  
Keyword(s):  
Injection Pressure ◽  
Confining Pressure ◽  
Repeated Loading ◽  
Micropore Structure ◽  
Injection Process ◽  
Reservoir Permeability ◽  
Stress Changes ◽  
Cyclic Variations ◽  
Loading And Unloading ◽  
Stress Variations

The multistage and discontinuous nature of the injection process used in the geological storage of CO2 causes reservoirs to experience repeated loading and unloading. The reservoir permeability changes caused by this phenomenon directly impact the CO2 injection process and the process of CO2 migration in the reservoirs. Through laboratory experiments, variations in the permeability of sandstone in the Liujiagou formation of the Ordos CO2 capture and storage (CCS) demonstration project were analyzed using cyclic variations in injection pressure and confining pressure and multistage loading and unloading. The variation in the micropore structure and its influence on the permeability were analyzed based on micropore structure tests. In addition, the effects of multiple stress changes on the permeability of the same type of rock with different clay minerals content were also analyzed. More attention should be devoted to the influence of pressure variations on permeability in evaluations of storage potential and studies of CO2 migration in reservoirs in CCS engineering.

Experimental investigation of the effect of compliant pores on reservoir rocks under hydrostatic and triaxial compression stress states

2019 ◽  
Vol 56 (7) ◽  
pp. 983-991
Author(s):  
Hua Yu ◽  
Kam Ng ◽  
Dario Grana ◽  
John Kaszuba ◽  
Vladimir Alvarado ◽  
...  
Keyword(s):  
Pore Pressure ◽  
Triaxial Compression ◽  
Matrix Material ◽  
Volumetric Strain ◽  
Confining Pressure ◽  
Differential Pressure ◽  
Sandstone Sample ◽  
Stress States ◽  
Rock Springs ◽  
Stage 1

The presence of compliant pores in rocks is important for understanding the stress–strain behaviors under different stress conditions. This paper describes findings on the effect of compliant pores on the mechanical behavior of a reservoir sandstone under hydrostatic and triaxial compression. Laboratory experiments were conducted at reservoir temperature on Weber Sandstone samples from the Rock Springs Uplift, Wyoming. Each experiment was conducted at three sequential stages: (stage 1) increase in the confining pressure while maintaining the pore pressure, (stage 2) increase in the pore pressure while maintaining the confining pressure, and (stage 3) application of the deviatoric load to failure. The nonlinear pore pressure – volumetric strain relationship governed by compliant pores under low confining pressure changes to a linear behavior governed by stiff pores under higher confining pressure. The estimated compressibilities of the matrix material in sandstone samples are close to the typical compressibility of quartz. Because of the change in pore structures during stage 1 and stage 2 loadings, the estimated bulk compressibilities of the sandstone sample under the lowest confining pressure decrease with increasing differential pressure. The increase in crack initiation stress is limited with increasing differential pressure because of similar total crack length governed by initial compliant porosity in sandstone samples.

scholarly journals Research on Microscopic Evolution Laws of Sandstone Deformation and Failure Based on the Particle Discrete Element Method

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhiwei Cai ◽  
Tongqing Wu ◽  
Jian Lu ◽  
Yue Wu ◽  
Nianchun Xu
Keyword(s):  
Shear Crack ◽  
Rock Fracture ◽  
Confining Pressure ◽  
Particle Flow Code ◽  
Shear Cracks ◽  
Deformation And Failure ◽  
Fracture Development ◽  
Confining Pressures ◽  
The Law ◽  
Microcrack Growth

The fracture of sandstone is closely related to the condition of internal microcracks and the fabric of micrograin. The macroscopic mechanical property depends on its microscopic structures. However, it is difficult to obtain the law of the microcrack growth under loading by experiments. A series of microscopic sandstone models were established with particle flow code 3D (PFC3D) and based on the triaxial experiment results on sandstones. The experimental and numerical simulations of natural and saturated sandstones under different confining pressures were implemented. We analyzed the evolution of rock deformation and the rock fracture development from a microscopic view. Results show that although the sandstones are under different confining pressures, the law of microcrack growth is the same. That is, the number of the microcracks increases slowly in the initial stage and then increases exponentially. The number of shear cracks is more than the tensile cracks, and the proportion of the shear cracks increases with the increase of confining pressure. The cracking strength of natural and saturated sandstones is 26% and 27% of the peak strength, respectively. Under low confining pressure, the total number of cracks in the saturated sample is 20% more than that of the natural sample and the strongly scattered chain is barely seen. With the increase of the confining pressure, the effect of water on the total number of cracks is reduced and the distribution of the strong chain is even more uniform. In other words, it is the confining pressure that mainly affects the distribution of the force chain, irrespective of the state of the rock, natural or saturated. The research results reveal that the control mechanism of shear crack friction under the different stress states of a rock slope in the reservoir area provides a basis for evaluating the stability of rock mass and predicting the occurrence of geological disasters.

Uplift behaviour of tapered piles established from model tests

2000 ◽  
Vol 37 (1) ◽  
pp. 56-74 ◽  
Author(s):  
M Hesham El Naggar ◽  
Jin Qi Wei
Keyword(s):  
Load Transfer ◽  
Compressive Loading ◽  
Compressive Load ◽  
Tensile Load ◽  
Confining Pressure ◽  
Cohesionless Soil ◽  
Uplift Capacity ◽  
Experimental Modelling ◽  
Confining Pressures ◽  
Load Tests

Tapered piles have a substantial advantage with regard to their load-carrying capacity in the downward frictional mode. The uplift performance of tapered piles, however, has not been fully understood. This paper describes the results of an experimental investigation into the characteristics of the uplift performance of tapered piles. Three instrumented steel piles with different degrees of taper were installed in cohesionless soil and subjected to compressive and tensile load tests. The soil was contained in a steel soil chamber and pressurized using an air bladder to facilitate modelling the confining pressures pertinent to larger embedment depths. The results of this study indicated that the pile axial uplift capacity increased with an increase in the confining pressure for all piles examined in this study. The ratios of uplift to compressive load for tapered piles were less than those for straight piles of the same length and average embedded diameter. The uplift capacity of tapered piles was found to be comparable to that of straight-sided wall piles at higher confining pressure values, suggesting that the performance of actual tapered piles (with greater length) would be comparable to that of straight-sided wall piles. Also, the results indicated that residual stresses developed during the compressive loading phase and their effect were more significant on the initial uplift capacity of piles, and this effect was more pronounced for tapered piles in medium-dense sand.Key words: tapered piles, uplift, axial response, load transfer, experimental modelling.

A Theoretical Description of Rotary Drilling for Idealized Down-Hole Bit/Rock Conditions

1969 ◽  
Vol 9 (04) ◽  
pp. 443-450 ◽  
Author(s):  
Paul F. Gnirk ◽  
J.B. Cheatham
Keyword(s):  
Mechanical Properties ◽  
Rate Equation ◽  
Chip Formation ◽  
Confining Pressure ◽  
Drill Hole ◽  
Differential Pressure ◽  
Drilling Rate ◽  
Rotary Drilling ◽  
Rock Interaction ◽  
Rock Bit

Abstract The results of combined analytical and experimental studies involving simulated multiple bit-tooth penetration into rock are incorporated into a drilling rate equation for roller-cone bits assuming rather idealized downhole conditions. In particular, it is assumed That the rock behaves statically in a ductile fashion during bit-tooth penetration and that the rock chips are instantaneously removed from the bottom of the drill hole. The general analysis demonstrates an application of plasticity theory for the rock/bit-tooth interaction to The formulation of an upper limit on rotary drilling rate. Introduction Extensive experimentation involving single and indexed bit-tooth penetration into rock in a confining pressure environment has demonstrated that the pressure environment has demonstrated that the chip formation process is of a ductile, or pseudoplastic, nature at sufficiently low differential pseudoplastic, nature at sufficiently low differential pressures so as to be of interest in rotary drilling. pressures so as to be of interest in rotary drilling. Coincident with the experimentation, analytical consideration has been given to the theoretical problems of single and indexed bit-tooth penetration problems of single and indexed bit-tooth penetration into rock. In general, the analyses have assumed that the rock behaves statically in a rigid-plastic fashion and obeys the Mohr-Coulomb yield criterion. The quantitative comparison between experimental and calculated values of bit-tooth load required for chip formation has been remarkably good for a variety of rocks commonly encountered in drilling and at simulated differential pressures as low as 500 to 1,000 psi. Results obtained recently for indexed bit-tooth penetration indicate that the work (or energy) penetration indicate that the work (or energy) required to produce a unit volume of rock chip can be minimized by a proper combination of bit-tooth spacing and bit-tooth load for a given rock type and differential pressure. By utilizing this information, it is possible co formulate a drilling rate equation, at least in a preliminary fashion, for a roller-cone bit performing under rather idealized downhole conditions. In particular, through the use of characteristic dimensionless quantities pertinent to a roller-cone bit and to indexed bit-tooth penetration, interrelationships among bit weight, rotary speed, rotary power, bit diameter, rock strength and bit-tooth shape and spacing can be explicitly expressed. In the formulation of the equations, however, it is assumed that the rock chips are instantaneously removed from the bottom of the drill hole and that the rock behaves in a ductile manner during bit-tooth penetration. In addition, the effects of bit-tooth load application And penetration by a yawed tooth at an oblique angle are neglected. Although the analysis is presented in the light of some rather restrictive conditions, it does demonstrate a method of applying fundamental rock/bit-tooth interaction data, obtained by combining the results of analysis and experiment to the formulation of a drilling rate equation for rotary drilling. INDEXED BIT-TOOTH/ROCK INTERACTION PREVIOUS RESULTS PREVIOUS RESULTS The mechanics of bit-tooth/rock interaction under simulated conditions of borehole environment have been extensively described in a number of papers. In particular, the effects of differential papers. In particular, the effects of differential pressure, mechanical properties of rock, pore fluid, pressure, mechanical properties of rock, pore fluid, bit-tooth shape and spacing, rate of bit-tooth load application and dynamic filtration below the bit-tooth have been investigated experimentally. From a sequence of experiments, it was demonstrated that, for dry rock at atmospheric pore pressure, the mode of chip formation exhibits a transition, with increasing confining pressure, from predominantly brittle to predominantly ductile. SPEJ P. 443

scholarly journals The meso-fracturing mechanism of marble under unloading confining pressure paths and constant axial stress

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Linna Sun ◽  
Liming Zhang ◽  
Yu Cong ◽  
Yaduo Song ◽  
Keqiang He
Keyword(s):  
Shear Failure ◽  
Axial Stress ◽  
Confining Pressure ◽  
Particle Flow Code ◽  
Shear Cracks ◽  
Confining Pressures ◽  
Tension Cracks ◽  
Trial And Error Method ◽  
Unloading Confining Pressure ◽  
Fracturing Mechanism

AbstractFailure tests on marble during unloading confining-pressure under constant axial stress and simulations with the particle flow code were performed. The influence mechanism of the unloading rate of the confining pressure, initial unloading stress, and confining pressure on the failure characteristics of, and crack propagation in, marble was studied. By using the trial-and-error method, the conversion relationship between the unloading rates of confining pressures in laboratory tests and numerical simulations was ascertained. Micro-cracks formed in the unloading process of confining pressure are dominated by tension cracks, accompanied by shear cracks. The propagation of shear cracks lags that of tension cracks. As the confining pressure is increased, more cracks occur upon failure of the samples. The proportion of shear cracks increases while that of tension cracks decreases. The failure mode of samples undergoes a transition from shear-dominated failure to conjugated shear failure.

scholarly journals Intragranular deformation mechanisms in calcite deformed by high-pressure torsion at room temperature

2020 ◽  
Vol 114 (2) ◽  
pp. 105-118
Author(s):  
Roman Schuster ◽  
Gerlinde Habler ◽  
Erhard Schafler ◽  
Rainer Abart
Keyword(s):  
High Pressure ◽  
Twin Boundary ◽  
Brittle Failure ◽  
Room Temperature ◽  
High Pressure Torsion ◽  
Confining Pressure ◽  
Temperature Deformation ◽  
Orientation Relationships ◽  
High Confining Pressure ◽  
Confining Pressures

AbstractPolycrystalline calcite was deformed to high strain at room-temperature and confining pressures of 1–4 GPa using high-pressure torsion. The high confining pressure suppresses brittle failure and allows for shear strains >100. The post-deformation microstructures show inter- and intragranular cataclastic deformation and a high density of mechanical e$$ \left\{01\overline{1}8\right\} $$011¯8 twins and deformation lamellae in highly strained porphyroclasts. The morphologies of the twins resemble twin morphologies that are typically associated with substantially higher deformation temperatures. Porphyroclasts oriented unfavorably for twinning frequently exhibit two types of deformation lamellae with characteristic crystallographic orientation relationships associated with calcite twins. The misorientation of the first deformation lamella type with respect to the host corresponds to the combination of one r$$ \left\{10\overline{1}4\right\} $$101¯4 twin operation and one specific f$$ \left\{01\overline{1}2\right\} $$011¯2 or e$$ \left\{01\overline{1}8\right\} $$011¯8 twin operation. Boundary sections of this lamella type often split into two separated segments, where one segment corresponds to an incoherent r$$ \left\{10\overline{1}4\right\} $$101¯4 twin boundary and the other to an f$$ \left\{01\overline{1}2\right\} $$011¯2 or e$$ \left\{01\overline{1}8\right\} $$011¯8 twin boundary. The misorientation of the second type of deformation lamellae corresponds to the combination of specific r$$ \left\{10\overline{1}4\right\} $$101¯4 and f$$ \left\{01\overline{1}2\right\} $$011¯2 twin operations. The boundary segments of this lamella type may also split into the constituent twin boundaries. Our results show that brittle failure can effectively be suppressed during room-temperature deformation of calcite to high strains if confining pressures in the GPa range are applied. At these conditions, the combination of successive twin operations produces hitherto unknown deformation lamellae.

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