Intact Rock Failure Research Articles

Numerical simulations of failure behavior around a circular opening in a non-persistently jointed rock mass under biaxial compression

Pre-existing discontinuities change the mechanical properties of rock masses, and further influence failure behavior around an underground opening. In present study, the failure behavior in both Inner and Outer zones around a circular opening in a non-persistently jointed rock mass under biaxial compression was investigated through numerical simulations. First, the micro parameters of the PFC3D model were carefully calibrated using the macro mechanical properties determined in physical experiments implemented on jointed rock models. Then, a parametrical study was undertaken of the effect of stress condition, joint dip angle and joint persistency. Under low initial stress, the confining stress improves the mechanical behavior of the surrounding rock masses; while under high initial stress, the surrounding rock mass failed immediately following excavation. At small dip angles the cracks around the circular opening developed generally outwards in a step-path failure pattern; whereas, at high dip angles the surrounding rock mass failed in an instantaneous intact rock failure pattern. Moreover, the stability of the rock mass around the circular opening deteriorated significantly with increasing joint persistency.

Numerical simulation of a jointed rock block mechanical behavior adjacent to an underground excavation and comparison with physical model test results

Mechanical behavior of a jointed rock mass with non-persistent joints located adjacent to a free surface on the wall of an excavation was simulated under without and with support stress on the free surface using approximately 0.5m cubical synthetic jointed rock blocks having 9 non-persistent joints of length 0.5m, width 0.1m and a certain orientation arranged in an en echelon and a symmetrical pattern using PFC3D software package. The joint orientation was changed from one block to another to study the effect of joint orientation on strength, deformability and failure modes of the jointed blocks. First the micro-mechanical parameters of the PFC3D model were calibrated using the macro mechanical properties of the synthetic intact standard cylindrical specimens and macro mechanical properties of a limited number of physical experiments performed on synthetic jointed rock blocks of approximately 0.5m cubes. Under no support stress, the synthetic jointed rock blocks exhibited the same three failure modes: (a) intact rock failure, (b) step-path failure and (c) planar failure under both physical experiments and numerical simulations for different orientations. The jointed blocks which failed under intact rock failure mode and planar or step-path failure mode produced high and low jointed block strengths, respectively. Three phases of convergence of free surface were discovered. The joint orientation and support stress played important roles on convergence magnitude. The average increment of jointed block strength turned out to be about 10, 7.9 and 6.6 times the support stress when support stresses of 0.06MPa, 0.20MPa and 0.40MPa were applied, respectively. The modeling results offer some guideline in support design for underground excavations.

Uncertainty analysis of impact indicators for the integrity of combined caprock during CO2 geosequestration

CO2 capture and geologic sequestration represent one of the most promising options for reducing atmospheric emissions of CO2. Operator choices and subsurface uncertainties each have significant effects on avoiding the risk of triggering fault failure or intact rock failure that could lead to CO2 leakage. With the application of response surface methodology, a Box–Behnken design of experiments was utilized to evaluate the statistical significance of impact indicators, and uncertainty analysis was performed using a robust model to forecast the optimal combination of impact indicators for maintaining caprock integrity during CO2 injection in saline aquifers of the Ordos Basin, China. The Coulomb failure stress and vertical deformation of 130 statistically designed combinations were experimentally determined using numerical simulation. Then, according to the analysis of variance conducted for the response surface quadratic model, the burying depth, friction angle, Young's modulus, Poisson's ratio, and stress field, as well as quadratic terms such as burying depth∗friction angle and Poisson's ratio∗Poisson's ratio, were found to be highly significant with respect to the level of Coulomb failure stress. Among the variables, only burying depth was highly significant with respect to the level of vertical deformation. Furthermore, the results were analyzed and an optimal combination of impact indicators for Coulomb failure stress was determined according to the minimum Coulomb failure stress. The optimum combination had a desirability value of 1.000, which demonstrated the fitness of the selected statistical model in analyzing the experimental data.

Re-Estimated Effects of Deep Episodic Slip on the Occurrence and Probability of Great Earthquakes in Cascadia

Research Article| November 26, 2013 Re‐Estimated Effects of Deep Episodic Slip on the Occurrence and Probability of Great Earthquakes in Cascadia N. M. Beeler; N. M. Beeler U.S. Geological Survey, Cascades Observatory, 1300 Cardinal Court, Bldg. 10 Suite 100, Vancouver, Washington 98683 Search for other works by this author on: GSW Google Scholar Evelyn Roeloffs; Evelyn Roeloffs U.S. Geological Survey, Cascades Observatory, 1300 Cardinal Court, Bldg. 10 Suite 100, Vancouver, Washington 98683 Search for other works by this author on: GSW Google Scholar Wendy McCausland Wendy McCausland U.S. Geological Survey, Cascades Observatory, 1300 Cardinal Court, Bldg. 10 Suite 100, Vancouver, Washington 98683 Search for other works by this author on: GSW Google Scholar Author and Article Information N. M. Beeler U.S. Geological Survey, Cascades Observatory, 1300 Cardinal Court, Bldg. 10 Suite 100, Vancouver, Washington 98683 Evelyn Roeloffs U.S. Geological Survey, Cascades Observatory, 1300 Cardinal Court, Bldg. 10 Suite 100, Vancouver, Washington 98683 Wendy McCausland U.S. Geological Survey, Cascades Observatory, 1300 Cardinal Court, Bldg. 10 Suite 100, Vancouver, Washington 98683 Publisher: Seismological Society of America First Online: 14 Jul 2017 Online ISSN: 1943-3573 Print ISSN: 0037-1106 Bulletin of the Seismological Society of America (2014) 104 (1): 128–144. https://doi.org/10.1785/0120120022 Article history First Online: 14 Jul 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation N. M. Beeler, Evelyn Roeloffs, Wendy McCausland; Re‐Estimated Effects of Deep Episodic Slip on the Occurrence and Probability of Great Earthquakes in Cascadia. Bulletin of the Seismological Society of America 2013;; 104 (1): 128–144. doi: https://doi.org/10.1785/0120120022 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyBulletin of the Seismological Society of America Search Advanced Search Abstract Mazzotti and Adams (2004) estimated that rapid deep slip during typically two week long episodes beneath northern Washington and southern British Columbia increases the probability of a great Cascadia earthquake by 30–100 times relative to the probability during the ∼58 weeks between slip events. Because the corresponding absolute probability remains very low at ∼0.03% per week, their conclusion is that though it is more likely that a great earthquake will occur during a rapid slip event than during other times, a great earthquake is unlikely to occur during any particular rapid slip event. This previous estimate used a failure model in which great earthquakes initiate instantaneously at a stress threshold. We refine the estimate, assuming a delayed failure model that is based on laboratory‐observed earthquake initiation. Laboratory tests show that failure of intact rock in shear and the onset of rapid slip on pre‐existing faults do not occur at a threshold stress. Instead, slip onset is gradual and shows a damped response to stress and loading rate changes. The characteristic time of failure depends on loading rate and effective normal stress. Using this model, the probability enhancement during the period of rapid slip in Cascadia is negligible (<10%) for effective normal stresses of 10 MPa or more and only increases by 1.5 times for an effective normal stress of 1 MPa. We present arguments that the hypocentral effective normal stress exceeds 1 MPa. In addition, the probability enhancement due to rapid slip extends into the interevent period. With this delayed failure model for effective normal stresses greater than or equal to 50 kPa, it is more likely that a great earthquake will occur between the periods of rapid deep slip than during them. Our conclusion is that great earthquake occurrence is not significantly enhanced by episodic deep slip events. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

New empirical polyaxial criterion for rock strength

A new criterion is presented for prediction of intact rock and rock mass failure under polyaxial state of stresses. A comprehensive database of the results of uniaxial, triaxial, and polyaxial tests on intact rock was utilized for evaluation of the new criterion and comparison of its accuracy with the most accurate and frequently used criteria. Analysis of 195 individual data groups of brittle failure in the form of ( σ 3, σ 1) for twelve different rock types showed that the proposed criterion lead to determination coefficients higher than 0.99 in most cases. It also gave the lower values of root mean squared errors relative to Mohr–Coulomb and Hoek–Brown criteria in fitting the normalized strength data for each rock type. The criteria were used to fit a typical series of triaxial strength data including brittle and ductile behavior. It showed that the new criterion can maintain its accuracy over a wider range of stresses. In the absence of rock mass strength data, applicability of the new criterion for rock mass was verified by fitting it to typical Hoek–Brown failure envelopes. Regression analysis of the polyaxial strength data in the form of ( σ 3, σ 2, σ 1) for six rock types showed that the new criterion predict the strength more accurately than the Modified Wiebols–Cook and You criteria in all cases.

Comparison of intact rock failure criteria using various statistical methods

This paper compares four different rock failure criteria based on triaxial test data of ten different rock strength data using various statistical methods. Least square, least median square and re-weighted least square techniques are used to determine the best fit parameters utilizing the experimental data that describes the failure state for each criterion. The least median square method could identify the scattered data and these scattered data points are observed at higher confining stress. It was observed that the fitting of failure criteria to different rock strength data depends upon the statistical methods used. The prediction of unconfined compressive strength and failure strength for different rocks estimated using various statistical methods are discussed in terms of different statistical performances of the prediction.

True-triaxial strength criteria for rock

This paper reviews some strength criteria which include the role of the intermediate principal stress, and proposes a new criterion. Strength criteria of the form σ oct= f N( σ oct), such as Drucker–Prager, represent a rotation surface in the principal stress space, symmetric to the line σ 1= σ 2= σ 3 in the meridian plane. Because σ oct= f N( σ oct) must fit the pseudo-triaxial compressive strength, it will have a non-physical outcome for triaxial extension. Mogi's criteria, σ oct= g 1( σ m,2) and σ max= g 2( σ β ) are able to fit experimental data reasonably well, but the prediction of strength is not good and sometimes problematic. Strength criterion with the form λ( σ 1, σ 2, σ 3)= F[ η( σ 1, σ 2, σ 3)], or a curve of two variables which can be decided by fitting pseudo-triaxial experimental data, is not expected to describe the strength under various stress states, no matter how high the correlation coefficient of λ and η is, or how low the misfit of the equation λ= F( η) is, as these seemingly good correlations usually result from the dominant influence of the maximum principal stress in the metrics of λ and η. The intermediate principal stress may improve the strength of rock specimen, but its influence will be restricted by σ 3. Also when σ 2 is high enough to cause failure in the σ 2– σ 3 direction, the strength will decrease with the increasing σ 2. The new strength criterion with exponent form has just such a character, and gives much lower misfits than do all seven criteria discussed by Colmenares and Zoback [Colmenares LB, Zoback MD. A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks. Int J Rock Mech Min Sci 2002;39:695–729].

Apparent stress scaling for tectonic and induced seismicity: Model and observations

A macroscopic model of seismic sources provides a scaling relationship for the apparent stress, treated as a function of three independent parameters: seismic moment, rupture area size, and average slip acceleration. These parameters represent three different factors: kinematic, geometric and material. This relationship allows us to distinguish and explain the following statistical characteristics of the log apparent stress versus log seismic moment plot. The regional trends, represented by a series of 1/2 slope lines, are related to the averaged shape of slip velocity pulses, so they reflect kinematic characteristics of the rupture process. The global trend, represented by the 1/6 slope line, is expected to characterize sets of events of wide range of rupture area sizes and assumes dependence of rupture area size on total slip, so it is related to the rupture initiation, propagation and arrest conditions; therefore, it reflects earthquake rupture dynamics. Additional shiftings among the trend lines obtained for the smallest induced tremors, larger tectonic earthquakes, and slow tsunami earthquakes, reflect differences between the intact rock failure and the frictional slip failure, that is, between fracture energies of these different earthquake classes.

Numerical modelling of uniaxial compressive failure of granite with and without saline porewater

It is important for rock engineering design to be able to validate numerical simulations, i.e. to check that they adequately represent the rock reality. In this paper, the capability and validity of four numerical models is assessed through the simulation of an apparently simple case: the complete process of microstructural breakdown during the uniaxial compressive failure of intact crystalline rock. In addition to comparing the capabilities of the four models, the results generated by each model were compared with the experimentally determined complete stress–strain curves for the Swedish Ävrö granite for different porewater conditions. In this way, it has been possible to audit the models’ adequacy for this particular simulation task. It was found that although the models had common features, they were each idiosyncratically different and required considerable expertise to match the actual stress–strain curves (which did not monotonically increase in axial strain)—indicating that, for more complex simulations, both adequate modelling and appropriate validation are not going to be an easy task. The work was conducted within the framework of the international 2004–2007 DEmonstration of COupled models and their VALidation against EXperiments with emphasis on Thermo Hydro Mechanic and Chemical aspects (DECOVALEX-THMC) phase on coupled modelling extended to include chemical effects and with application to the excavation damaged zone (EDZ) in crystalline rock.

The instantaneous rate dependence in low temperature laboratory rock friction and rock deformation experiments

Earthquake occurrence probabilities that account for stress transfer and time‐dependent failure depend on the product of the effective normal stress and a lab‐derived dimensionless coefficient a. This coefficient describes the instantaneous dependence of fault strength on deformation rate, and determines the duration of precursory slip. Although an instantaneous rate dependence is observed for fracture, friction, crack growth, and low temperature plasticity in laboratory experiments, the physical origin of this effect during earthquake faulting is obscure. We examine this rate dependence in laboratory experiments on different rock types using a normalization scheme modified from one proposed by Tullis and Weeks [1987]. We compare the instantaneous rate dependence in rock friction with rate dependence measurements from higher temperature dislocation glide experiments. The same normalization scheme is used to compare rate dependence in friction to rock fracture and to low‐temperature crack growth tests. For particular weak phyllosilicate minerals, the instantaneous friction rate dependence is consistent with dislocation glide. In intact rock failure tests, for each rock type considered, the instantaneous rate dependence is the same size as for friction, suggesting a common physical origin. During subcritical crack growth in strong quartzofeldspathic and carbonate rock where glide is not possible, the instantaneous rate dependence measured during failure or creep tests at high stress has long been thought to be due to crack growth; however, direct comparison between crack growth and friction tests shows poor agreement. The crack growth rate dependence appears to be higher than the rate dependence of friction and fracture by a factor of two to three for all rock types considered.

A new rock mass failure criterion for biaxial loading conditions

To simulate brittle rocks, a mixture of glastone, sand and water was used as a model material. Thin galvanized sheets of thickness 0.254 mm were used to create joints in blocks made out of the model material. To investigate the failure modes and strength, both the intact material blocks as well as jointed model material blocks of size 35.6 × 17.8 × 2.5 cm having different joint geometry configurations were subjected to uniaxial and biaxial compressive loadings. A new intact rock failure criterion is proposed at the 3-D level. This criterion is validated for biaxial loading through laboratory experimental results obtained on intact model material blocks. Results obtained from both the intact and jointed model material blocks are used to develop a strongly non-linear new rock mass failure criterion for biaxial loading. In this failure criterion, the fracture tensor component is used to incorporate the directional effect of fracture geometry system on jointed block strength. The failure criterion shows the important role, the intermediate principal stress plays on rock mass strength.

Imaging Unstable Wellbores While Drilling

Summary This paper presents a case study of borehole instability from four wellbores on the Gulf of Mexico (GOM) shelf, offshore Louisiana. Logging-while-drilling (LWD) borehole images are combined with observations of cavings and modeling of borehole shear failure to diagnose the mechanisms of instability and, thus, select the appropriate remedial action. It is observed that instability caused by shear failure of intact rock (borehole breakout) can be suppressed by increasing the MW. However, where pre-existing planes of weakness (such as bedding planes and fractures) dominate the mechanism of instability, mudweight increases do not necessarily lead to a more stable hole and can, in fact, further destabilize the wellbore.

Effect of strain rate on constitutive properties for the shear failure of intact granite in seismogenic environments

To investigate how the constitutive parameters prescribing the slip‐dependent law for the shear failure of intact rock are affected by strain rate, we conducted a series of triaxial fracture experiments at a strain rate in the range from 10−5 to 10−7/s in seismogenic environments using Tsukuba granite samples. The experimental results showed that the peak shear strength decreases modestly with a reduction in strain rate, according to a logarithmic law. The reduction rate tested at wet conditions was larger than at dry conditions. It was found that the maximum slip‐weakening rate slightly increases with an increase in strain rate at wet conditions. This indicates that the mechanical instability of the shear failure process is slightly enhanced by an increase in strain rate.

A constitutive scaling law and a unified comprehension for frictional slip failure, shear fracture of intact rock, and earthquake rupture

It is widely recognized that some of the physical quantities inherent in a rupture are scale‐dependent, and the scale dependence is one of the most no facts and features of rupture phenomena. The paper addresses how such scale‐dependent shear rupture of a broad range from laboratory‐scale frictional slip failure and shear fracture of intact rock to field‐scale rupture as an earthquake source can be unified by a single constitutive law. Noting that the earthquake rupture is a mixed process between frictional slip failure and the shear fracture of intact rock, it is concluded that the constitutive law for the earthquake rupture be formulated as a unifying law that governs both frictional slip failure and shear fracture of intact rock. It is demonstrated that the slip‐dependent constitutive law is such a unifying law, and a constitutive scaling law is derived from laboratory data on both frictional slip failure and shear fracture of intact rock. This constitutive scaling law enables one to provide a consistent and unified comprehension for scale‐dependent physical quantities inherent in the rupture, over a broad range from small‐scale frictional slip failure and shear fracture in the laboratory to large‐scale earthquake rupture in the field.

A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks

Abstract In this study we examine seven different failure criteria by comparing them to published polyaxial test data (σ1>σ2>σ3) for five different rock types at a variety of stress states. We employed a grid search algorithm to find the best set of parameters that describe failure for each criterion and the associated misfits. Overall, we found that the polyaxial criteria Modified Wiebols and Cook and Modified Lade achieved a good fit to most of the test data. This is especially true for rocks with a highly σ2-dependent failure behavior (e.g. Dunham dolomite, Solenhofen limestone). However, for some rock types (e.g. Shirahama Sandstone, Yuubari shale), the intermediate stress hardly affects failure and the Mohr–Coulomb and Hoek and Brown criteria fit these test data equally well, or even better, than the more complicated polyaxial criteria. The values of C0 yielded by the Inscribed and the Circumscribed Drucker–Prager criteria bounded the C0 value obtained using the Mohr–Coulomb criterion as expected. In general, the Drucker–Prager failure criterion did not accurately indicate the value of σ1 at failure. The value of the misfits achieved with the empirical 1967 and 1971 Mogi criteria were generally in between those obtained using the triaxial and the polyaxial criteria. The disadvantage of these failure criteria is that they cannot be related to strength parameters such as C0. We also found that if only data from triaxial tests are available, it is possible to incorporate the influence of σ2 on failure by using a polyaxial failure criterion. The results for two out of three rocks that could be analyzed in this way were encouraging.

Rate‐ and state‐dependent friction of intact rock and gouge

The shear traction during frictional sliding depends on the instantaneous sliding strain rate and on a state variable ψ which represents the previous history of the sample. A formulation of rate and state friction covers the continuum between gouge and intact rock, as well as the behavior at high and low normal tractions. A traditional formula for the instantaneous coefficient of friction is retained, , where μ0 is the steady state coefficient of friction at the reference strain rate , and a and b are small constants. The normalizing ψ0 for isothermal conditions is ΔPN/ΔPN0, where ΔP is the effective normal traction, ΔP0 is a reference normal traction, and N is an exponent. The coefficient of friction of intact rock is approximately μclose−bN ln(ΔP/ΔPclose), where the coefficient of friction is μclose, at the normal traction ΔPclose where essentially all the pore space is closed during steady state sliding. The formulation provides an acceptable fit to the observed coefficient of friction of Westerly Granite at normal tractions up to 1500 MPa including steady sliding and intact rock failure.

A constitutive law for the shear failure of rock under lithospheric conditions

This paper first reviews recent studies on constitutive formulations for shear failure, which leads to the conclusion that revealing the constitutive property for not only frictional slip failure, but also shear failure of intact rock in the brittle to brittle-plastic transition regimes is critical to establish the constitutive law which governs earthquake shear failure that proceeds in the lithosphere. To this end, a unique, high stiffness testing apparatus capable of applying polyaxial stress fields to rectangular rock specimens, has been constructed, for which a brief description is given. The paper then presents new results of laboratory experiments on constitutive properties of shear fracture of intact granite at lithospheric conditions. In view of the physical principles and constraints to be imposed on the constitutive law for shear failure, the slip-dependency is a more fundamental property than the time- or rate-dependency, and hence the constitutive law for shear failure should primarily be slip-dependent. This slip-dependent constitutive law, which itself is self-consistent, can unifyingly and quantitatively treat the entire phases from stable, quasistatic ruture growth to unstable, dynamic fast-speed rupture propagation for shear failure of any type, whether it is frictional slip failure along a preexisting fault or shear fracture of intact materials. The slip-dependent constitutive law includes a scaling parameter D c (critical slip displacement) explicitly, which in turn is scaled by a characteristic length λ c representing geometrical irregularities of the fault surfaces. Incorporation of D c (or λ c) enables this constitutive law to provide a common interpretation for shear failure of any size scale as an earthquake source, from small scale in the laboratory to large scale in the Earth. The present experiments corroborate the slip-dependent constitutive relation and other constitutive properties over the entire process from slip-strengthening to slip-weakening of intact granite, under the conditions that confining pressure is in the range 440 to 500 MPa, pore pressure is in the range 30 to 300 MPa, temperature is in the range from room temperature to 456°C, and strain rate is in the range 10 −4 to 10 −7/s. It is found that some constitutive law parameters are not independent, but mutually related. The constitutive relation for shear failure and the parameters such as Δτ p (breakdown stress drop) and D c prescribing its relation, are affected by ambient conditions such as temperature and strain rate.

Anisotropic Nature of Jointed Rock Mass Strength

Analytical models that describe the strength of jointed rock under a wide variety of multiaxial states of stress with one or two components being tensile are presented. The intact rock is. isotropic and its strength is described by a Hoek and Brown criterion. The joints have zero tensile strength and a shear strength defined by a Coulomb criterion. The strength of jointed rock is represented by superposition of the intact rock and joint failure surfaces and the joint nonnegative normal stress condition in a coordinate system having two stress ratios as a measure of distance along the coordinate axes. The symmetry of the intact rock failure surface in this coordinate system is lost because of the directional nature of joint strength. The anisotropic strength reduction associated with the joints and the influence of the intermediate stress on the strength of regularly jointed rock are analyzed. The effect of water pressure on jointed rock strength is also addressed.

Potash mining and seismicity: A time-dependent finite element model

This paper attempts to answer questions associated with induced seismicity over underground excavations with special reference to potash mines in Saskatchewan, Canada. These seismic disturbances are widely understood to be generated in the competent, carbonate Dawson Bay Formation and are induced by potash mining activity. The earthquake initiation process, subsequent development and the associated failure mechanism(s) must be better understood to minimize the potential consequences. In this regard, a realistic finite element model based on viscoelasticlviscoplastic material behaviour has been developed. This model is specifically designed to include those capabilities required to model the complex fabric of stratified and jointed rock associated with potash mining and includes the ability to model time-dependent closure of excavations. Possible modes of failure are investigated with the aid of this numerical model. From the results of various models, it is suggested that the seismicity is caused by the brittle failure of intact carbonate rock. Slip along existing discontinuities is a second possible mode responsible for seismic activity.