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1.
In-situ Rock Spalling Strength near Excavation Boundaries   总被引：2，自引：0，他引：2  
It is widely accepted that the in-situ strength of massive rocks is approximately 0.4 ± 0.1 UCS, where UCS is the uniaxial compressive strength obtained from unconfined tests using diamond drilling core samples with a diameter around 50 mm. In addition, it has been suggested that the in-situ rock spalling strength, i.e., the strength of the wall of an excavation when spalling initiates, can be set to the crack initiation stress determined from laboratory tests or field microseismic monitoring. These findings were supported by back-analysis of case histories where failure had been carefully documented, using either Kirsch’s solution (with approximated circular tunnel geometry and hence σ max = 3σ 1 ?σ 3) or simplified numerical stress modeling (with a smooth tunnel wall boundary) to approximate the maximum tangential stress σ max at the excavation boundary. The ratio of σ max /UCS is related to the observed depth of failure and failure initiation occurs when σ max is roughly equal to 0.4 ± 0.1 UCS. In this article, it is suggested that these approaches ignore one of the most important factors, the irregularity of the excavation boundary, when interpreting the in-situ rock strength. It is demonstrated that the “actual” in-situ spalling strength of massive rocks is not equal to 0.4 ± 0.1 UCS, but can be as high as 0.8 ± 0.05 UCS when surface irregularities are considered. It is demonstrated using the Mine-by tunnel notch breakout example that when the realistic “as-built” excavation boundary condition is honored, the “actual” in-situ rock strength, given by 0.8 UCS, can be applied to simulate progressive brittle rock failure process satisfactorily. The interpreted, reduced in-situ rock strength of 0.4 ± 0.1 UCS without considering geometry irregularity is therefore only an “apparent” rock strength.  相似文献   

2.
True triaxial shear tests have been performed to determine the peak shear strengths of tension-induced fractures in three Thai sandstones. A polyaxial load frame is used to apply mutually perpendicular lateral stresses (σp and σo) to the 76 × 76 × 126 mm rectangular block specimens. The normal to the fracture plane makes an angle of 59.1° with the axial (major principal) stress. Results indicate that the lateral stress that is parallel to the fracture plane (σp) can significantly reduce the peak shear strength of the fractures. Under the same normal stress (σn) the fractures under high σp dilate more than those under low σp. According to the Coulomb criterion, the friction angle decreases exponentially with increasing σp/σo ratio and the cohesion decreases with increasing σp. The lateral stress σp has insignificant effect on the basic friction angle of the smooth saw-cut surfaces. The fracture shear strengths under σp = 0 correlate well with those obtained from the direct shear tests. It is postulated that when the fractures are confined laterally by σp, their asperities are strained into the aperture, and are sheared off more easily compared to those under unconfined condition.  相似文献   

3.
As technologies for deep underground development such as tunneling underneath mountains or mass mining at great depths (>1,000 m) are implemented, more difficult ground conditions in highly stressed environments are encountered. Moreover, the anticipated stress level at these depths easily exceeds the loading capacity of laboratory testing, so it is difficult to properly characterize what the rock behavior would be under high confinement stress conditions. If rock is expected to fail in a brittle manner, behavior changes associated with the relatively low tensile strength, such as transition from splitting to the shear failure, have to be considered and reflected in the adopted failure criteria. Rock failure in tension takes place at low confinement around excavations due to tensile or extensional failure in heterogeneous rocks. The prospect of tensile-dominant brittle failure diminishes as the confinement increases away from the excavation boundary. Therefore, it must be expected that the transition in the failure mechanism, from tensile to shear, occurs as the confinement level increases and conditions for extensional failure are prevented or strongly diminished. However, conventional failure criteria implicitly consider only the shear failure mechanism (i.e., failure envelopes touching Mohr stress circles), and thus, do not explicitly capture the transition of failure modes from tensile to shear associated with confinement change. This paper examines the methodologies for intact rock strength determination as the basic input data for engineering design of deep excavations. It is demonstrated that published laboratory test data can be reinterpreted and better characterized using an s-shaped failure criterion highlighting the transition of failure modes in brittle failing rock. As a consequence of the bi-modal nature of the failure envelope, intact rock strength data are often misinterpreted. If the intact rock strength is estimated by standard procedures from unconfined compression tests (UCS) alone, the confined strength may be underestimated by as much as 50 % (on average). If triaxial data with a limited confinement range (e.g., σ3 ? 0.5 UCS due to cell pressure limitations) are used, the confined strength may be overestimated. Therefore, the application of standard data fitting procedures, without consideration of confinement-dependent failure mechanisms, may lead to erroneous intact rock strength parameters when applied to brittle rocks, and consequently, by extrapolation, to correspondingly erroneous rock mass strength parameters. It follows that the strength characteristics of massive rock differ significantly in the direct vicinity of excavation from that which is remote with higher confinement. Therefore, it is recommended to adopt a differentiated approach to obtain intact rock strength parameters for engineering problems at lower confinement (near excavation; e.g., excavation stability assessment or support design), and at elevated confinement (typically, when the confinement exceeds about 10 % of the UCS) as might be encountered in wide pillar cores.  相似文献   

4.
Summary. Most currently used techniques for analysing the stability of near surface structures, such as rock slopes, are based on the application of the effective Coulomb shear strength parameters cohesion c′, and the angle of friction φ′ on some known or anticipated shear surface subjected to an effective normal stress σ′n. The most widely used of these techniques are the variants of the method of slices and related upper bound techniques. If the Hoek-Brown criterion is to be used to model the strength of near surface fractured rocks, it is necessary to determine equivalent Coulomb shear strength parameters for the specified level of effective normal stress. Calculation of the equivalent Coulomb parameters for the Hoek-Brown criterion for cases when a ≠ 0.5 is not a straightforward matter. A simple procedure for calculating instantaneous values of c′i and φ′i has been developed based on spreadsheet calculations and the application of a numerical optimisation routine. This procedure can also be applied to calculating the Hoek-Brown envelope plotted in shear stress/normal stress space. A simple closed form solution for c′i and tan φ′i has also been developed for the special case when a = 1. A three-dimensional version of the Hoek-Brown criterion has been developed by combining it with the Drucker-Prager criterion. This new yield criterion has been implemented by numerical solution of the governing equations. A simplification of this three-dimensional yield criterion has been developed by introducing an intermediate principal stress weighting factor. Comparison with published results demonstrates that this simplified criterion has the capacity to model the results of true triaxial tests for a range of different rock types over a wide range of stress levels. The new three-dimensional yield criterion has the advantage that its input parameters can be determined from routine uniaxial compression tests and mineralogical examination.  相似文献   

5.
A particle-based distinct element method and its grain-based method are used to generate and simulate a synthetic specimen calibrated to the rupture characteristics of an intact (non-jointed) low-porosity brittle rock deformed in direct shear. The simulations are compared to the laboratory-generated ruptures and used to investigate rupture at various normal stress magnitudes. The fracturing processes leading to shear rupture zone creation and the rupture mechanism are found to be normal stress dependent (progressing from tensile splitting to shear rupture) and show partial confirmation of rupture zone creation in nature and in experiments from other materials. The normal stress dependent change is found to be due to the orientation of the major principal stress and local stress concentrations internal to the synthetic specimens being deformed. The normal stress dependent rupture creation process results in a change to the rupture zone’s geometry, shear stress versus horizontal displacement response, and thus ultimate strength.  相似文献   

6.
This paper presents a new analytical criterion for brittle failure of rocks and heavily over-consolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as half of the critical distance. This fracture criterion is known as the point method, and is part of the theory of critical distances, which is utilised in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, σ 0, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, σ c and σ t. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (σ c/σ t = 3–50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low-confining stresses.  相似文献   

7.
A new constitutive model to describe the shear behavior of rock joints under constant normal stiffness (CNS) and constant normal load (CNL) conditions is proposed. The model was developed using an empirical approach based on the results of a total of 362 direct shear tests on tensile fractured rock joints and replicas of tensile joints and on a new quantitative roughness parameter. This parameter, the active roughness coefficient C r, is derived from the features of the effective roughness mobilized at the contact areas during shearing. The model involves a shear strength criterion and the relations between stresses and displacements in the normal and shear directions, where the effects of the boundary conditions and joint properties are considered by the shape indices C d and C f. The model can be used to predict the shear behavior under CNS as well as CNL conditions. The shear behavior obtained from the experimental results is generally in good agreement with that estimated by the proposed model, and the effects of joint roughness, initial normal stress, and normal stiffness are reasonably reflected in the model.  相似文献   

8.
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9.
When rock samples are loaded until macroscopic fractures develop, the failure process can be divided into several stages based on axial and lateral strain responses or the acoustic emission sequence during uniaxial compression tests. Several stress thresholds may be identified: the crack closure stress σ cc, crack initiation stress σ ci, crack damage stress σ cd, and uniaxial compressive strength σ ucs; these may be used as a warning indicator for rock rupture. We investigated the crack damage stress σ cd, its threshold, and a possible relationship between σ cd and the uniaxial compressive strength. The σ cd of different rock types were compiled from previous studies based on uniaxial compression tests. The results showed that the overall averages and standard deviations of σ cd /σ ucs for igneous, metamorphic, and sedimentary rocks were ~0.78 (±0.11), ~0.85 (±0.11), and ~0.73 (±0.18), respectively. There were no significant differences in σ cd /σ ucs between the different rock types, except that the sedimentary rock had a slightly larger standard deviation attributed to the variation of porosity in the samples, while the metamorphic rock had higher average σ cd /σ ucs resulting from the small statistical sample size. By excluding the higher-porosity (>10 %) rock samples, the averages and standard deviations of σ cd /σ ucs for igneous, metamorphic, and sedimentary rocks were ~0.78 (±0.09), ~0.85 (±0.09), and ~0.78 (±0.11), respectively. The results imply that the rock origin process (i.e., igneous, metamorphic, and sedimentary) has a minimal effect on σ cd /σ ucs. The ratio σ cd/σ ucs could be an essential intrinsic property for low-porosity rocks, which could be used in rock engineering for predicting the failure process.  相似文献   

10.
Estimation of uniaxial compressive strength (UCS) by P-wave velocity (VP) is of great interest to geotechnical engineers in various design projects. The specimen diameter size is one of the main factors that influence rock parameters such as UCS and VP. In this study, the diameter size of specimens that effect UCS and VP is investigated. Moreover, the correlation between UCS and VP are examined via empirical analysis. For this purpose, 15 travertine samples were collected and core specimens with a diameters size of 38, 44, 54, 64 and 74 mm were prepared. Then, uniaxial compressive strength and P-wave velocity tests were conducted according to the procedure suggested by ISRM (1981). It is concluded that the diameter size of the specimen has a significant effect on UCS and VP. Moreover, it was found that the best correlation between relevant parameters obtained for the specimen diameter of 38 mm.  相似文献   

11.
The uniaxial compressive strength (UCS) of rocks is a critical parameter required for most geotechnical projects. However, it is not always possible for direct determination of the parameter. Since determination of such a parameter in the lab is not always cost and time effective, the aim of this study is to assess and estimate the general correlation trend between the UCS and indirect tests or indexes used to estimate the value of UCS for some granitoid rocks in KwaZulu-Natal. These tests include the point load index test, Schmidt hammer rebound, P-wave velocity (Vp) and Brazilian tensile strength (σt). Furthermore, it aims to assess the reliability of empirical equations developed towards estimating the value of UCS and propose useful empirical equations to estimate the value of UCS for granitoid rocks. According to the current study, the variations in mineralogy, as well as the textural characteristics of granitoid rocks play an important role in influencing the strength of the rock. Simple regression analyses exhibit good results, with all regression coefficients R2 being greater than 0.80, the highest R2 of 0.92 being obtained from UCS versus σt. Comparison of equations produced in the current study as well as empirical equations derived by several researchers serves as a validation. Also illustrate that the reliability of such empirical equations are dependent on the rock type as well as the type of index tests employed, where variation in rock type and index tests produces different values of UCS. These equations provide a practical tool for estimating the value of UCS, and also gives further insight into the controlling factors of the strength of the granitoid rocks, where the strength of a rock is a multidimensional parameter.  相似文献   

12.
Shear strain γ in brittle fault zones is related to final and initial grain size parameters, df and di, respectively, by an expression of the form: where μk the coefficient of kinetic friction of crushed rock and σn the normal stress across the zone at the time of faulting.Technological literature suggests that ƒ(df, di) may be given by 10 , where Wi is a material constant. The resulting relationship between shear strain and grain size seems to be compatible with existing experimental data.  相似文献   

13.
The experimental determination of anelastic strain recovery (ASR) compliances for three types of rocks (granite, marble, and sandstone) was performed in the laboratory. Preloading of specimens for uniaxial compression creep tests was at 50 % of the uniaxial compressive strength (UCS) for each rock type. We obtained the shear mode Jas(t) and volumetric mode Jav(t) ASR compliances and calculated the ratio of Jas(t) to Jav(t). The Kelvin model for rock rheology was then applied in numerical simulations and the results were in good agreement with the measured data for Jas(t) and Jav(t). These results showed that both the magnitude and rate of increase of the ASR compliances are strongly dependent on the rock type, and the values of the Jas(t)/Jav(t) ratio for a loading of 50 % of the UCS showed a trend leading to different constants for each of the three rock types. Further experimental and numerical analyses showed approximate power-law relationships between the ASR compliances at 50 % of UCS, and both the UCS and the tangential Young’s modulus at 50 % of UCS (E t50). These relationships may be useful for the preliminary estimation of ASR compliances.  相似文献   

14.
The estimated undrained shear strength (su) is often not a unique value because it can be evaluated by various test types and/or procedures, such as different failure modes, shear strain rates, and boundary conditions. This study explores (1) the relationship between reference undrained shear strength and in situ shear wave velocity in terms of the effective overburden stress, and (2) the independent relationships to evaluate the undrained shear strength with special consideration of different directional and polarization modes (VH, HV, HH shear waves), which has not been reported. This evaluation is done via a worldwide database compiled from 43 well-documented geotechnical test sites associated with soft ground. Finally, new correlation models are proposed to estimate the undrained shear strength based on the in situ shear wave velocity as well as the plasticity index or the overconsolidation ratio. The application of the shear wave velocity–undrained shear strength relation is illustrated through two independent case studies. The proposed relationships are expected to contribute to reasonable estimates of undrained shear strength as well as offer practical guidance on even extrapolation beyond the data that is available to geotechnical engineers.  相似文献   

15.
Binary-medium contact interfaces widely exist in rock engineering. They have significant impacts on the safety of rock engineering due to their poor shear behavior. A material of different strength is produced by pouring mortar of a different sand-to-cement ratio on the top of a rock-like mortar material (with the ratio of 1:1), thereby forming a binary-medium structural plane. Then, direct shear test is performed on the structural plane by applying different normal stresses. The shear strength parameters of the structural plane (cohesion \(c\) and friction angle \(\varphi\)) are obtained from the Mohr–Coulomb criterion. Moreover, the mechanical behaviors of the structural plane are compared with the unitary-medium specimen in the shearing process. A similar shear stress–shear displacement rule is observed in the shearing process. However, the peak and residual shear strengths of the binary structural plane are far lower than those of the unitary ones. The difference between the unitary and binary planes at cohesion \(c\) decreases with the increasing sand–cement ratio, whereas a up-down trend is observed in the friction angle \(\varphi\) with the increasing sand-to-cement ratio. When the upper and lower parts of the structural plane are different in sand-to-cement ratio, the cohesion \(c\) of the structural plane slightly increases with the increasing ratio of the upper specimen. However, when the two parts are identical in ratio, the cohesion of the structural plane reaches the peak, and its friction angle \(\varphi\) substantially increases with the increasing ratio of the upper part.  相似文献   

16.
Grain growth experiments have been performed at 1 atm on fine grain size (<10 μm) synthetic olivine (Fo91) aggregates at various temperatures (1200° to 1400° C), oxygen fugacities (10-4 to 10-11 atm) and total anneal times (10, 30, 60, 100 and 200 h). The rate of grain growth increased with increasing temperature and with increasing oxygen fugacity. The presence of a second phase (residual porosity), introduced during sample fabrication, has a significant effect on grain growth, with evolution in grain size paralleled by changes in the size and frequency of the pores. When the grain growth data were fit to a growth law G n ?G O n =κ0 tf 0 m 2e?Q/RT, the growth exponents fall in the range of n=4 to 5, suggesting that grain growth may be controlled by the coalescence of the second phase. The evolution in pore size and frequency may occur either by the transport of the ionic species constituting olivine between the pores or by the movement of the pores themselves along the grain boundaries and edges. Thus, the rate of growth of the pores and grains is probably limited by diffusion of the slowest ionic species constituting olivine (magnesium, iron, silicon, or oxygen) moving along the fastest path for that species (through the lattice, along the grain boundaries, around the surface of the moving pores, or through the vapor phase in the pores). Activation energies for grain growth of Q=290 ± 20 kJ/mol and 345 ± 25 kJ/mol were calculated from our results for n=4 and 5, respectively. These activation energies preclude vapor-phase transport and iron diffusion along grain boundaries but do not otherwise permit a discrimination between the rate limiting species or path. The oxygen fugacity exponent of m ≈0.12 suggests that lattice diffusion does not control the grain growth. However, the lack of data for magnesium, iron, silicon and oxygen surface and grain boundary diffusion in olivine makes definitive determination of the mechanism controlling grain growth difficult.  相似文献   

17.
Different failure modes during fracture shearing have been introduced including normal dilation or sliding, asperity cut-off and degradation. Attempts have been made to study these mechanisms using analytical, experimental and numerical methods. However, the majority of the existing models simplify the problem, which leads to unrealistic results. With this in mind, the aim of this paper is to simulate the mechanical behaviour of synthetic and rock fracture profiles during direct shear tests by using the two-dimensional particle flow computer code PFC2D. Correlations between the simulated peak shear strength and the fracture roughness parameter D R1 recently proposed by Rasouli and Harrison (2010) are developed. Shear test simulations are carried out with PFC2D and the effects of the geometrical features as well as the model micro-properties on the fracture shear behaviour are studied. The shear strength and asperity degradation processes of synthetic profiles including triangular, sinusoidal and randomly generated profiles are analysed. Different failure modes including asperity sliding, cut-off, and asperity degradation are explicitly observed and compared with the available models. The D R1 parameter is applied to the analysis of synthetic and rock fracture profiles. Accordingly, correlations are developed between D R1 and the peak shear strength obtained from simulations and by using analytical solutions. The results are shown to be in good agreement with the basic understanding of rock fracture shear behaviour and asperity contact degradation.  相似文献   

18.
Since cross-anisotropic sand behaves differently when the loading direction or the stress state changes, the influences of the loading direction and the intermediate principal stress ratio (b = (σ 2 ? σ 3)/(σ 1 ? σ 3)) on the initiation of strain localization need study. According to the loading angle (angle between the major principal stress direction and the normal of bedding plane), a 3D non-coaxial non-associated elasto-plasticity hardening model was proposed by modifying Lode angle formulation of the Mohr–Coulomb yield function and the stress–dilatancy function. By using bifurcation analysis, the model was used to predict the initiation of strain localization under plane strain and true triaxial conditions. The predictions of the plane strain tests show that the major principal strain at the bifurcation points increases with the loading angle, while the stress ratio decreases with the loading angle. According to the loading angle and the intermediate principal stress ratio, the true triaxial tests were analyzed in three sectors. The stress–strain behavior and the volumetric strain in each sector can be well captured by the proposed model. Strain localization occurs in most b value conditions in all three sectors except for those which are close to triaxial compression condition (b = 0). The difference between the peak shear strength corresponding to the strain localization and the ultimate shear strength corresponding to plastic limit becomes obvious when the b value is near 0.4. The influence of bifurcation on the shear strength becomes weak when the loading direction changes from perpendicular to the bedding plane to parallel. The bifurcation analysis based on the proposed model gives out major principal strain and peak shear strength at the initiation of strain localization; the given results are consistent with experiments.  相似文献   

19.
Particle flow code (PFC2D) software was adopted to investigate the anchorage behaviour and the characteristics of crack initiation, propagation and coalescence of reinforced specimens containing a single fissure (RSCSF). The microscopic parameters of the specimens in the numerical simulation were first validated by experimental outcomes of intact specimens, while the microscopic parameters of the rock bolts were validated based on the results of the RSCSF tests. Then, the mechanical parameters as well as the failure modes in the physical experiments were compared with those derived by the numerical simulation; the results showed good agreement between the simulated macroscopic mechanical properties and failure modes and those obtained in the laboratory experiments. The peak strength, number of cracks and the failure mode varied considerably as the anchorage angle α and fissure angle β increased. Three types of stress–strain curves, types I to III, were obtained from the RSCSF. Shear cracks were observed for all three categories of curves, but the tensile cracks were dominant. The number of cracks and the rate of bond failures decreased as the curve changed from type II to type I to type III. RSCSF failure can be classified into three failure modes: (1) tip crack propagation mode, (2) midpoint crack propagation mode and (3) rock bolt crack propagation mode. These failure modes are primarily differentiated by relations between α and β, and the ratio UCSS/UCSI between the uniaxial compressive strength (UCS, σ max) of the RSCSF (UCSS) and the uniaxial compressive strength of the intact specimen (UCSI).  相似文献   

20.
The stress [crack damage stress (σ cd) and uniaxial compressive strength (σ c)] and strain characteristics [maximum total volumetric strain (ε cd), axial failure strain (ε af)], porosity (n) and elastic constants [elastic modulus (E) and Poisson’s ratio (ν)] and their ratios were coordinated with the existence of two different types (type 1 and type 2) of volumetric strain curve. Type 1 volumetric strain curve has a reversal point and, therefore, σ cd is less than the uniaxial compressive strength (σ c). Type 2 has no reversal point, and the bulk volume of rock decreases until its failure occurs (i.e., σ cd = σ c). It is confirmed that the ratio between the elastic modulus (E) and the parameter λ = n/ε cd strongly affects the crack damage stress (σ cd) for both type 1 and type 2 volumetric strain curves. It is revealed that heterogeneous carbonate rock samples exhibit different types of the volumetric strain curve even within the same rock formation, and the range of σ cd/σ c = 0.54–1 for carbonate rocks is wider than the range (0.71 < σ cd/σ c < 0.84) obtained by other researchers for granites, sandstones and quartzite. It is established that there is no connection between the type of the volumetric strain curve and values of n, E, σ cd, ν, E/(1 ? 2ν), M R = E/σ c and E/λ. On the other hand, the type of volumetric strain curve is connected with the values of λ and the ratio between the axial failure strain (ε af) and the maximum total volumetric strain (ε cd). It is argued that in case of small ε af/ε cd–small λ, volumetric strain curve follows the type 2.  相似文献   

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