Strength Criterion For Rock Masses Research Articles

Plastic zone characteristics and rapid stability evaluation indexes of circular tunnels subjected to non-hydrostatic stress: A novel complex variable solution incorporating 3D rock mass strength

The morphological characteristics and distribution range of the plastic zone around tunnels, influenced by the true three-dimensional high geostress environment in deep engineering, constitute fundamental reference data for both tunnel design and the control of surrounding rock stability. Based on the GZZ three-dimensional rock mass strength criteria and the complex variable method, a novel semi-analytical method for solving the plastic zone of a circular tunnel subjected to non-hydrostatic stress is presented. The conformal mapping is employed to intricately transform the complex boundaries of plastic zones characterized by diverse shapes onto the unit circle boundary within the image plane. This framework proves invaluable for the precise analytical process of the complex plastic zone morphology and the plastic influence range within the surrounding rock under complex stress conditions. In contrast to traditional analytical methods, the efficacy and versatility of our proposed approach are substantiated. Notably, it demonstrates unique advantages, particularly in the context of non-hydrostatic stress fields and varied rock mass parameters, with respect to predicting both surrounding rock stability and plastic zone morphology. Through the analysis of numerous cases, the study reveals the systematic patterns of influence that in-situ stress and surrounding rock characteristic parameters have on the shape and maximum depth of the plastic zone. The results indicate that (1) there are notable disparities in the morphology and extent of the plastic zone between the GZZ and GHB criteria; (2) the transition of the plastic zone in surrounding rock from U-shaped to V-shaped is significantly influenced by the geostress-to-strength ratio Kσ; (3) there is a notable linear correlation observed between the maximum plastic zone thickness rmax and both Kσ and the stress concentration factor KSCF, importantly, this correlation is independent of far-field stress and the brittleness characteristics of the surrounding rock. These findings provide a novel discriminative method for the rapid analysis of surrounding rock stability in deep circular tunnels.

An exact solution of three-dimensional rock mass strength criterion

An exact solution of three-dimensional rock mass strength criterion

Strength criterion of rock mass considering the damage and effect of joint dip angle

It is highly significant to theoretically assess the effect, under load, of initial stress and structure on the mass damage of rock mass. In this reported study, first a multi-factor coupling damage constitutive model under the action of joint-load was established by fully considering the non-uniformity, anisotropy and initial structure of a rock mass based on the Weibull distribution and D-P criterion. The relationship between the damage evolution and joint angle in the rock mass was elaborated. Then, a jointed rock mass strength criterion was built in line with the D–P criterion and the limit state of rock mass failure by the method of multivariate function total differential as based on the constitutive model. The results showed that the established constitutive model was in good agreement with the test results, which accurately reflected the damage characteristics of jointed rock mass during the entire loading process. The initial damage value of the rock mass increased with increasing joint dip angles, and the damage evolution of the jointed rock mass could be divided into the initial, stable, accelerated and failure damage stages. Comparing the results of this approach with other methods it was found that the strength criterion better reflected the effects of minimum principal stress σ3, volume stress σm, shear stress J21/2 and joint dip angle β on rock mass strength than other existing strength criteria, which showed that the proposed method offered important guiding principles for the engineering practice.

3-D Rock Mass Strength Criteria—A Review of the Current Status

The presence of complex discontinuity patterns, the inherent statistical nature of their geometrical parameters, the uncertainties involved in the estimation of the discontinuity geometrical and geo-mechanical properties and complex three dimensional (3-D) in-situ stress make the accurate prediction of rock mass strength a difficult task. It has been a great challenge for the rock mechanics and rock engineering professions to develop a rock mass strength criterion in three dimensions that incorporates the effect of the minor and intermediate principal stresses and captures the scale dependent and anisotropic properties resulting from the discontinuity geometry parameters, such as the number of discontinuity sets, 3-D discontinuity intensity, and the distributions of the discontinuity orientation and size. Rock mechanics and rock engineering researchers have dealt with this topic for more than 55 years. The paper provides a critical review of the current state of the art regarding 3-D jointed rock mass strength criteria. The shortcomings of several rock mass strength criteria are discussed. The historic development of rock mass strength criteria that incorporate the effect of the minor and intermediate principal stresses and capture the scale dependent and anisotropic properties is presented. The most advanced 3-D rock mass strength criteria currently available in the literature are presented, including suggested future improvements.

Failure mechanism and control technology of large deformation for Muzhailing Tunnel in stratified rock masses

Deep tunnels in soft rock with high in situ stresses always exhibit large deformations. A case study in the Muzhailing Tunnel was carried out to explore the failure mechanism and investigate the control technology of the tunnel. The numerical simulation software Universal Discrete Element Code (UDEC) was used to establish a model, the results of which were analyzed. Combined with the rock mass strength criteria of the Geological Strength Index (GSI), the parameters of the rock mass around the tunnel were evaluated, and the microparameters of the rock mass from the UDEC were calibrated. Considering the results of the original support scheme to those calculated without support, failure first occurred in the roof and floor surfaces and then developed deeper into the surrounding rock. In the end, the tunnel suffered from a large asymmetric deformation with roof subsidence, rib shrinkage, and steel arch frame bending and twisting, which could be clearly observed from the stress, displacement, and crack evolution. Considering the failure of the original support with insufficient strength and stiffness, a new support scheme with high constant resistance anchor cables was proposed to control the large deformation of the tunnel. The anchor cables have been proved to be effective with high constant resistance and large deformation by the laboratory test, numerical simulation and field test. The results showed that the new support could effectively control the deformation of the tunnel. The new support scheme transforms the large deformation and nonuniform stress distribution of the tunnel into a small deformation and uniform stress distribution, which could provide useful references for support design in deep underground engineering.

A New Shear Strength Criterion for Rock Masses with Non-Persistent Discontinuities Considering the Nonlinear Progressive Failure Process.

The shear strength characteristics of rock masses containing non-persistent discontinuities are strongly affected by discontinuities and rock bridges. The linear Jennings criterion cannot reflect the nonlinear mechanical behavior during progressive failure of rock masses with non-persistent discontinuities. In this study, a new nonlinear shear strength criterion was developed. First of all, a series of shear test data about artificial rock mass samples were collected on the basis of the published literatures, and five types of samples were differentiated according to the positions of discontinuities. After that, a new nonlinear shear strength criterion was proposed by introducing two correction coefficients A and B into the basic form of the Jennings criterion, which could correct the weight of the cohesion and the internal friction coefficient of rock bridges respectively. Then, the new criterion was determined by fitting the basic form of the Jennings criterion with the laboratory data. It was found that the parameters A and B had a nonlinear exponential and negative exponential relation with the connectivity rate respectively. It indicated that both the cohesion and the internal friction coefficient estimated by the new criterion were superior to those estimated by the Jennings criterion. Compared with the linear Jennings criterion, the new nonlinear shear strength criterion had a better applicability.

Development of New Three-Dimensional Rock Mass Strength Criteria

Two new three-dimensional rock mass strength criteria are developed in this paper by extending an existing rock mass strength criterion. These criteria incorporate the effects of the intermediate principal stress, minimum principal stress and the anisotropy resulting from these stresses acting on the fracture system. In addition, these criteria have the capability of capturing the anisotropic and scale dependent behavior of the jointed rock mass strength by incorporating the effect of fracture geometry through the fracture tensor components. The new criteria are proposed after analyzing 284 numerical modeling results of the polyaxial, triaxial and biaxial compression tests conducted on the jointed rock blocks having one or two joint sets by the PFC3D software. Some of these simulation results were compared with experimental results to validate the developed PFC3D model that was used for numerical modeling of jointed blocks. In this research to have several samples with the same properties a synthetic rock material that is made out of a mixture of gypsum, sand and water was used. Altogether, 12 joint systems were chosen; some of them had one joint set and the rest had two joint sets. Joint sets have different dip angles varying from 15° to 45° at an interval of 15° with dip directions of 30° and 75° for the two joint sets. Each joint set also has three persistent joints with the joint spacing of 42 mm in a cubic sample of size 160 mm. The minimum and intermediate principal stress combination values were chosen based on the uniaxial compressive strength (UCS) value of the modeled intact synthetic rock. The minimum principal stress values were chosen as 0, 0.2, 0.4 and 0.6 of the UCS. For each minimum principal stress value, the intermediate principal stress value varies starting at the minimum principal stress value and increasing at an interval of 0.2 of the UCS until it is slightly lower than the strength of the sample under the biaxial loading condition with the same minimum principal stress value. To express the new rock mass strength criteria, it was also necessary to determine the intact rock strengths under the same confining stress combinations mentioned earlier. Therefore, the intact rock was also modeled for all three compression tests and the intact rock strengths were found for 33 different minimum and intermediate principal stress combinations.

Supporting Technology Research in Deep Well Based on Modified Terzaghi Formula

In order to solve the difficult problem of supporting roadway with large cross section and broken surrounding rock, the large‐section inclined shaft of Pingdingshan Coal Mine is taken as the research instance. In this paper, a modified formula for the Terzaghi ultimate bearing capacity of a foundation is established based on rock mass strength criteria. As per the engineering practice, the maximum roof pressure of the inclined shaft is calculated to be 2.7 MPa, and the minimum pressure value from the modified formula is only 0.3 MPa. In order to control the floor heave of the roadway, a U‐type steel inverted arch and bolts support scheme was designed. After calculating through the mechanical model of the inverted arch, its bearing capacity is 0.56 Mpa. Through comparison and analysis of various supporting schemes, finally, the “U‐type steel + inverted arch + pouring concrete + backwall grouting” technology is selected, and the engineering practice shows that the supporting scheme can effectively improve surrounding rock stability.

Fault dislocation modeled structure of lobate scarps from Lunar Reconnaissance Orbiter Camera digital terrain models

Before the launch of the Lunar Reconnaissance Orbiter, known characteristics of lobate scarps on the Moon were limited to studies of only a few dozen scarps revealed in Apollo‐era photographs within ~20° of the equator. The Lunar Reconnaissance Orbiter Camera now provides meter‐scale images of more than 100 lobate scarps, as well as stereo‐derived topography of about a dozen scarps. High‐resolution digital terrain models (DTMs) provide unprecedented insight into scarp morphology and dimensions. Here, we analyze images and DTMs of the Slipher, Racah X‐1, Mandel'shtam‐1, Feoktistov, Simpelius‐1, and Oppenheimer F lobate scarps. Parameters in fault dislocation models are iteratively varied to provide best fits to DTM topographic profiles to test previous interpretations that the observed landforms are the result of shallow, low‐angle thrust faults. Results suggest that these faults occur from the surface down to depths of hundreds of meters, have dip angles of 35–40°, and have typical maximum slips of tens of meters. These lunar scarp models are comparable to modeled geometries of lobate scarps on Mercury, Mars, and asteroid 433 Eros, but are shallower and ~10° steeper than geometries determined in studies with limited Apollo‐era data. Frictional and rock mass strength criteria constrain the state of global differential stress between 3.5 and 18.6 MPa at the modeled maximum depths of faulting. Our results are consistent with thermal history models that predict relatively small compressional stresses that likely arise from cooling of a magma ocean.

The Influence of Rock Properties and Size into Strength Criteria: A Proposed Criterion for Soft Rock Masses

A new modified strength criterion for soft rock masses is proposed in this paper in order to provide a suitable estimation for soft rock mass strength. The new criterion is based upon the current compression test data of soft materials of over 150 samples, and available published data of soft rock strength. It is shown that the proposed criterion estimates reasonable values of soft rock mass strength. Rock properties and size contribute significantly into the strength, represented by friction angle and unconfined compressive strength. Examples exercised reveal that the structure of soft rock masses takes a dominant part in controlling the strength, which then determines the modelled strength of soft rock masses. The results also show that the strength of the proposed equation could relatively be higher three times than the strength of the Hoek-Brown criterion for a massive soft rock mass.

Thrust faults and the near-surface strength of asteroid 433 Eros

[1] NEAR Shoemaker images reveal widespread occurrence of tectonic landforms on asteroid 433 Eros. Hinks Dorsum is a ridge that extends for about 18 km around the asteroid and strongly resembles thrust fault structures on the terrestrial planets. Tectonic landforms can provide information on the mechanical properties of asteroids, a subject of much controversy. Modeling constrained by topographic data shows that Hinks Dorsum can be accounted for by a shallow rooted thrust fault no greater than 250 m in depth with ∼90 m of cumulative slip. Strength envelopes based on frictional and rock mass strength criteria suggest the near-surface shear strength of Eros is from ∼1 to 6 MPa. A spatial correlation is found between Shoemaker crater, a transition from low to high crater density, and Hinks Dorsum. This spatial relation along with the estimated strength of the asteroid suggests the thrust fault was formed by impact induced compression.

Rock mechanical investigations of seismic events in a deep longwall coal mine

Seismic events, i.e., fractures in rock that radiate detectable seismic waves, are a worldwide phenomena associated with mining and reservoir exploitation. Longwall mining in German coal mines often causes seismic events, which can be felt at surface where they can lead to a considerable annoyance of residents and sometimes even lead to minor damages of buildings and infrastructure. Strong seismic events are in a large part responsible for a more and more decreasing community acceptance of mining. The mines therefore have to investigate the local conditions, which cause the generation of seismic events, to find ways of avoiding strong mining induced seismic events. This paper describes the research on mining-induced seismicity around a specific active longwall at 1100 m depth under several previously mined longwall panels. Seismic events are recorded by a local network featuring 15 surface and six subsurface stations. Location and fault plane solutions show the occurrence of at least three different event types, which are characterized by distinct modes of failure. Underground core drilling and an extensive rock testing program are used to build up a rock mechanical model featuring a multi-layer strata for use with numerical analyses. The numerical model is able to explain the different failure mechanisms as fault activation, remnant pillar punching and beam failure. The use of rock mass classification, rock mass strength criteria and in situ stresses together with 2D and 3D numerical analyses facilitates the evaluation of the results from seismology approaches, and makes future analysis of longwall-related seismic events possible.

Finite Element Analysis of Dongjusi Railway Tunnel within Hard Rock Mass Based on the Unified Rock Mass Strength Criterion

The twin shear strength criterion has been proposed to consider the intermediate principal stress effect on the rock mass strength. The unified rock mass strength criterion could consider the intermediate principal stress effect on the rock mass strength. The unified rock mass elasto-plastic material model is implemented in ABAQUS user interface. As a case for study, the stability analysis of Dongjusi railway tunnel within hard rock mass is studied using the unified rock mass strength material. For comparison, the Hoek-Brown empirical strength criterion is also chosen for the rock mass material modeling. The computation results show that the plastic zone calculated using the unified rock mass strength criterion is smaller than that using the Hoek-Brown empirical strength criterion. The railway tunnel lining structure is designed according to the unified rock mass strength criterion and greatly makes use of the rock mass potential strength, which decreases engineering cost.

An anisotropic strength criterion for jointed rock masses and its application in wellbore stability analyses

AbstractIn this paper, an anisotropic strength criterion is established for jointed rock masses. An orientation distribution function (ODF) of joint connectivity, is introduced to characterize the anisotropic strength of jointed rock masses related to directional distributed joint sets. Coulomb failure condition is formulated for each plane of jointed rock masses by joint connectivity, where the friction coefficient and cohesion of the jointed rock mass are related to those of the intact rock and joint and become orientation dependent. When approximating joint connectivity by its second‐order fabric tensor, an anisotropic strength criterion is derived through an approximate analytical solution to the critical plane problem. To demonstrate the effects of joint distribution on the anisotropic strength of jointed rock masses, the failure envelopes are worked out for different relative orientations of material anisotropy and principal stress axes. The anisotropic strength criterion is also applied to wellbore stability analyses. It is shown that a borehole drilled in the direction of the maximum principal in situ stress is not always the safest due to the anisotropic strength of the jointed rock mass. Copyright © 2007 John Wiley & Sons, Ltd.

Tensile resistance of rock anchors

Abstract Using the Euler's variational method and assuming a rock mass failure criterion of Hoek and Brown type (Hoek E, Brown ET. Empirical strength criterion for rock masses. J Geotech Eng Division, American Society of Civil Engineers 1980;106(GT9)1013–35. Hoek E, Wood D, Shah S. A modified Hoek-Brown criterion for jointed rock masses. In: Hudson JA, editor. Proc., Rock Characterization Symp. of ISRM: Eurock 92. London: British Geotechnical Society, 1992. p. 209–14), the tensile resistance of rock anchors is obtained. The rupture surface shape through the rock mass is also obtained and checked against some published data. Depending on the slenderness ratio ( L / D ; L =anchor length, D =anchor diameter) two types of failure surfaces are obtained; short and long ones. This second type of surface is a complex one and it is composed by a cylinder and a surface of revolution with an hyperbolic type shape. The values of the ultimate pullout strength, depending on the rock type and its Bieniawski indexes, are obtained and compared with the values published in technical literature. A reasonable agreement is obtained.

A study of the mechanical behaviour of coal for pillar design

Abstract A series of triaxial compression tests was carried out on 61, 101, 146 and 300 mm diameter samples to investigate the effects of scale on the mechanical behaviour of coal. The “inherent variability” of laboratory coal strength data was found to be related to the degree of cleating or brightness of the coal samples. Using this observed relationship, a method was developed for estimating in situ coal seam strength based upon the “intact” properties of dull coal samples and seam brightness profiles. The peak strength criterion for in situ coal uses the parameters σ c , m and s of the Hoek–Brown empirical strength criterion for rock masses. Unloading cycles were used to investigate the yield behaviour of the coal samples. The results show that, depending on the magnitude of the confining stress, the failure mechanism of coal alters significantly with a change from an axial splitting to a shearing mechanism. Measurements of the volumetric strain response also indicate an absence of scale dependence in the deformation behaviour of the three larger sample sizes. Unloading cycles were used as a means of investigating the development of recoverable (elastic) and irrecoverable (plastic) components of strain. The irrecoverable strain loci, for the larger sizes, were taken to be representative of the in situ deformation response of coal.

A physical model study of jointed rock mass strength under uniaxial compressive loading

Abstract Jointed rock mass strength is investigated through physical modeling using model material blocks subjected to only uniaxial compressive loading. Jointed model material blocks exhibited different failure modes depending on the joint configurations. Orientation of the joint sets played a significant role related to the modes of failure. It was possible to obtain a strong non-linear relation between the jointed model mass strength and the fracture tensor component to cover the strengths resulting from all the different failure modes observed in the investigation. The fracture tensor component was used to obtain the combined effect of number of joint sets, joint density, and distributions of size and orientation of the joint sets in a chosen direction. Needed future research are suggested to generalize the promising rock mass strength criterion obtained in the performed research.

Probabilistic slope stability analysis using a microcomputer

Summary A probabilistic slope stability analysis has been adapted for use on a microcomputer. The analysis uses the Janbu method of slices with geological input provided in the form of the Hoek-Brown rock mass strength criteria. A Monte Carlo simulation allows the results of this analysis to be presented as a probability that the factor of safety for the slope will fall below a critical level. The demonstration program is described for a slope in a Carboniferous limestone quarry at Chipping Sodbury.

Probabilistic stability analysis of variable rock slopes : Priest, S D; Brown, E T Trans Inst Min Metall (Sect A Min Ind), V92, Jan 1983, PA1–A12

A new probabilistic method for analyzing the stability of slopes excavated in fractured, variable rock masses is described. The method is based on a Monte Carlo simulation routine with use of the Janku method of slices for which strength parameters are derived by the Hoek-Brown rock mass strength criterion. The input values for the strength criterion are derived empirically by use of existing rock mass classification schemes applied to data obtained from borehole core and the examination of surface exposures. The results of the analyses, presented as cumulative probability distributions of the factor of safety for each slope, can be used to find the probability that the factor of safety will fall below a given critical level. Results obtained for open pit slopes to be excavated in a variable fractured limestone rock mass showed that, in certain cases, slopes that would have been acceptable on the basis of the mean factor of safety alone were unsatisfactory when considered on the basis of the probabilistic criteria.

Ground Response Curves for Rock Tunnels

Calculations of support pressure—tunnel convergence relationships, or ground response curves are used to improve understanding or rocksupport interaction and to aid in the dimensioning of tunnel support elements. Methods of response curve calculation are presented for a tunnel of circular cross‐section excavated in a rock mass initially subjected to a hydrostatic in situ stress field. Plane strain conditions are assumed. The two solutions presented use nonlinear peak and residual rock mass strength criteria. Particular consideration is given to the influence of plastic volumetric strains in the rock mass surrounding the tunnel. A closed‐form solution is presented for an elastic‐brittle‐plastic material behavior model in which post‐peak dilatancy occurs at a constant rate with major principal strain. A second solution is presented as a stepwise sequence of calculations for an elastic‐strain, softening‐plastic model in which post‐peak dilatancy occurs at a lower rate with major principal strain in the const...