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Time-dependent drift degradation due to the progressive failure of rock bridges along discontinuities

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Abstract

An important element of time-dependent drift degradation is the progressive failure of intact segments along discontinuities, referred to as rock bridges. A fracture mechanics model is developed to simulate the time-dependent failure of rock bridges along discontinuities. The time dependence of the rock bridge failure process is modeled utilizing subcritical crack growth. The rock bridges give an effective cohesion to the discontinuities, and this cohesion is time-dependent due to the time-dependent failure of the rock bridges. The resulting first-order differential equation for joint cohesion is implemented into the UDEC distinct element numerical code to model time-dependent drift degradation. The model and its implementation into UDEC are validated using several simple examples, including a direct shear test and a rigid block on a slope. Two time-dependent drift degradation examples are then shown, one with and one without thermal loading. These examples used similar geometry, material parameters and in situ stresses as for the proposed underground drifts for the storage of nuclear waste at Yucca Mountain. Both with and without thermal loading, a large zone develops around the excavation where the joint cohesion and tensile strength drop to zero due to the failure of rock bridges. This in turn results in an excavation that is significantly less stable than if time dependence was not included. The results demonstrate the importance of time-dependence on the stability of underground excavations in hard rock.

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... Na avaliação da estabilidade de estruturas em rochas frágeis, é importante considerar a dependência do tempo para as propriedades destes materiais, principalmente no caso de aberturas que devam permanecer estáveis por longos períodos. De acordo com Kemeny (2005), estas estruturas podem se degradar pelo processo de deformação e ruptura gerada com a propagação e coalescência de microfraturas. ...
... Neste artigo é realizada a avaliação da estabilidade por equilíbrio limite de um bloco triangular, formado no teto de uma escavação, utilizando um modelo apresentado por Kemeny (2005), no qual se assume que a ruptura por cisalhamento de pontes rochosas ocorre devido a propagação subcrítica de fraturas. Além disso, é feita uma comparação do tempo estimado para a estabilidade do bloco por meio da teoria da propagação subcrítica com o tempo de auto suporte empírico proposto pela classificação geomecânica RMR (Rock Mass Rating) de Bieniawsky (2011). ...
... Foi adotado o modelo de mecanismo de fratura para uma simples ponte rochosa de comprimento 2 , em um corpo de extensão 2 diante um campo de tensões normais e cisalhantes (Kemeny, 2005). As medidas do tamanho da descontinuidade e sua ponte variaram de acordo com a geometria do prisma. ...
... Kemeny found that an expression of rock bridge penetration velocity with time and applied load can be established as per subcritical crack propagation. 35 For rock cracks under quasi-static load or creep conditions, there is a power law relationship between rock bridge penetration velocity and the stress intensity factor, ...
... ARTICLE scitation.org/journal/adv Initial total length of the joint, ω 0.100 m Initial length of the rock bridge, a 0.026 m Internal friction angle, ϕ 20 ○ Joint inclination, β 45 ○ Rock parameter, n 35 25 Rock parameter, A 35 10 −5 m/s Shear fracture toughness, K IIC 35 0.5 MPa √ m Maximum principal stress, σ 1 26 MPa Minimum principal stress, σ 3 5 MPa ...
... ARTICLE scitation.org/journal/adv Initial total length of the joint, ω 0.100 m Initial length of the rock bridge, a 0.026 m Internal friction angle, ϕ 20 ○ Joint inclination, β 45 ○ Rock parameter, n 35 25 Rock parameter, A 35 10 −5 m/s Shear fracture toughness, K IIC 35 0.5 MPa √ m Maximum principal stress, σ 1 26 MPa Minimum principal stress, σ 3 5 MPa ...
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There are a large number of non-penetrating collinear cracks in the rock slope of an open-pit mine. The timeliness of cracks in the rock mass is a problem that cannot be ignored in terms of slope engineering safety. Based on the superposition principle and fracture mechanics, the stress intensity factor of the rock mass crack tip with collinear fractures under biaxial compression was calculated in this study. A mechanical model of rock mass crack propagation with collinear fractures under constant load was established according to the Charles equation. The effects of loading time, crack penetration rate, and crack dip angle on crack propagation along the direction of the rock bridge were analyzed theoretically. The variations in crack propagation with time in the rock mass were examined using a LS-DYNA creep numerical model. The results show that the fracture growth rate changes in three stages over time, progressing through a stable stage, a decreasing stage, and an abrupt stage. A higher crack penetration rate and a larger crack inclination angle cause a higher rock bridge penetration rate in the rock mass. When the crack penetration rate exceeds 74% or the fracture inclination angle is about 60°, the crack expansion directly enters the abrupt stage, and the rock bridge is penetrated. The theoretical analysis results are in close agreement with the numerical results of this work, which validates the proposed age expansion mechanical model for rock masses with non-penetrating collinear fractures.
... Researchers have studied the discontinuity behavior more deeply (Bieniawski, 1970;Malan, 2002;Tan and Kang, 1980) while simplifying or ignoring the aging of intact rock strength (Aubertin et al., 2000;Kemeny, 2003;Napier and Malan, 1997). The cohesion of the intact rock or the rock bridge (Lajtai and Schmidtke, 1986) at the junction of the discontinuous surface weakens over time/deformation due to subcritical propagation of the cracks (Atkinson, 1984;Kemeny, 2005) (i.e., the time-dependent deformation is considered a macroscopic consequence of the progressive degradation of the material structure at the microscopic scale (Shao et al., 2003) or environmental factors . In the short term, the stability of the rock mass could be primarily controlled by the discontinuous surface, and in the long term, the stability of the rock mass is determined both by the discontinuous surface and the rock bridge (Chen et al., 2004;Lajtai, 1991). ...
... )is the difference value between the external load and the long-term strength; t is in hours Deng et al. (2016) ⎧ n is the circulation number under immersion-air drying Kemeny (2003Kemeny ( , 2005, Zhou et al. ...
... a. The internal friction is a constant value (Kemeny, 2005(Kemeny, , 2003Zhou, 2005;Zhou et al., 2017); b. The internal friction angle is increasing (typically, the cohesion weakening and frictional strengthening (CWFS) model) (Hajiabdolmajid et al., 2002;Maquaire et al., 2003;Zhou, 2014); c. ...
... On one hand, the duration before failure of samples significantly decreases with increasing shear rate, from 10 3 s (for 1 mm displacement at shear rate of 1 μm/s) to 0.1 s (for 1 mm displacement at shear rate of 10 mm/s). At low shear rates, subcritical crack growth has a long duration to contribute to micro-cracking through physical mechanisms such as stress corrosion (Anderson & Grew, 1977), which accumulates damage in rock bridges and thus weakens the peak shear strength (Kemeny, 2003(Kemeny, , 2005Sano et al., 1981). This explains why rock bridges fail at lower peak strength with decreasing shear rate. ...
... For intact granite rocks, experiments have also documented rate effects on the peak shear strength and stress drop, under dry and room temperature conditions (at strain rates varied from 10 −8 to 10 −4 /s, Masuda et al., 1987; 10 −7 to 10 −5 /s, Lockner, 1998) as well as simulated crustal conditions of temperature and lithostatic pressure (10 −7 to 10 −5 /s, Kato et al., 2003). Explanations for the rate effects in these works were based on subcritical crack growth, consistent with our study and the model of Kemeny (2003Kemeny ( , 2005 on the time-dependent failure of rock bridges. With differences in the state of stress, temperature, and fluid being taken into account, the rate dependence observed in our experiments could be in principle up-scaled to failures on heterogeneous faults, where variations in local loading rate have been argued to exert influences on the slip instability of faults (Kato & Ben-Zion, 2021;McLaskey, 2019). ...
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Natural faults are often heterogeneous with spatially variable cohesion caused by healing processes. Using rock bridges as laboratory analogs, we investigate how cohesion‐healed patches rupture at different shear rates. We performed direct shear experiments on granite rock bridges at shear rates from 1 μm/s to 10 mm/s (low to subseismic shear rates), and quantitatively characterized the failure surface morphology by integrating laser scanning with ArcGIS. The results show a notable dependence of both mechanical and morphological characteristics on shear rate. The failure mode transitions from tensile failure at low shear rates to shear failure at subseismic shear rates. At low shear rates, tensile failure forms curved coalescence patterns and undulating failure surfaces with significant roughness and morphological anisotropy. At subseismic shear rates, straighter shear‐formed coalescence patterns are observed. In addition, the peak shear strength, the roughness and morphological anisotropy increase with increasing shear rate within the subseismic rate regime. We explain the observed rate‐dependent behaviors by the energy and geometric features of micro‐cracking mechanisms. We suggest through the variations in 3D morphological parameters that rate effects should be incorporated into models of fault morphology. In addition, the failure surfaces at all shear rates are asymmetric, with asperities more inclined to the direction of the shear load. We find that this asymmetry results from both the fracture of rock bridges and the further shearing after failure, and it can be used to determine the sense of fault displacement.
... Rock bridges have been the subject of considerable research since the 1970's, with a focus on developing methods to measure rock bridges and quantifying their role with respect to rock mass strength (e.g., Terzaghi 1962;Jennings 1970;Call and Nicholas 1978;Einstein et al. 1983;Read and Lye 1984;Baczynski 2000Baczynski , 2008Kemeny 2005;Dershowitz et al. 2017;Elmo et al. 2009Elmo et al. , 2018Spreafico et al. 2017;Romer and Ferentinou 2019). Note that all those authors have considered rock bridges in the context of natural and engineered slopes; rock bridges in the context of underground excavations are seldom discussed in the literature. ...
... Rights reserved. simplicity, these example demonstrates the importance of considering the time dependency of progressive failure of intact rock bridges (Kemeny 2005) and the impact of weathering on intact rock strength, and tensile strength in particular (Arikan et al. 2007;Alzo'ubi 2009). However, Content courtesy of Springer Nature, terms of use apply. ...
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Rock bridges have been the subject of considerable research since the 1970’s with a focus on developing methods to measure rock bridges and quantifying their role with respect to rock mass strength. In the literature, rock bridges are generally defined as a portion of intact rock separating discontinuity surfaces; however, whether a portion of intact rock resists failure and, therefore, represents a critical rock bridge depends on the failure mechanisms that may develop within the rock mass. The difficulty of defining what constitutes a rock bridge is associated with the challenge of measuring rock bridges in the field. This aspect is often ignored by engineers and practitioners, who fail to recognise that rock bridges could exist even within a rock mass characterised by fully continuous surfaces. Furthermore, field evidence of rock slope failure shows that rock bridges do not fail at the same time, and a simple definition of a rock bridge as the distance between existing discontinuities cannot account for progressive rock mass damage and changes in stresses within a rock mass. The authors suggest that the concept itself of rock bridges may be flawed, and more attention should be given to better understanding damage-related processes, including time-dependent damage in the context of engineered structures.
... Previous research has shown that failure occurs through progressive fracturing of intact rock bridges, in a process termed step-path failure (Kemeny, 2005;Eberhardt et al., 2004;Scavia, 1995;Brideau et al., 2009) that may in some cases be compared to a cascade-effect failure which can cause rock bridges to fail like dominoes along sloping channels (Bonilla-Sierra et al., 2015;Harthong et al., 2012;Zhou et al., 2015). The contribution of rock bridges has been implemented in numerical models of rock slope stability using apparent cohesion (Eberhardt et al., 2004;Fischer et al., 2010;Gischig et al., 2011) or areas of intact rock (Stead et al., 2006;Sturzenegger and Stead, 2009;Agliardi et al., 2013;Paronuzzi et al., 2016). ...
... An example of this is model 3, which considers in particular a higher cohesion value (130 kPa for model 3 compared to 45 kPa for model 1). Moreover, as shown by previous research, the compartment instability occurs through progressive fracturing of intact rock bridges, in a process termed step-path failure (Kemeny, 2005;Eberhardt et al., 2004;Scavia, 1995;Brideau et al., 2009) that may in some cases be compared to a cascadeeffect failure: they can fail like dominoes along sloping channels (Bonilla-Sierra, et al., 2015;Harthong et al., 2012;Zhou et al., 2015). The study presented in this paper corroborates the previously observed cascade-effect failure of rock bridges. ...
Article
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Plane failure along inclined joints is a classical mechanism involved in rock slope movements. It is known that the number, size and position of rock bridges along the potential failure plane are of prime importance when assessing slope stability. However, the rock bridge failure phenomenology itself has not been comprehensively understood up to now. In this study, the propagation cascade effect of rock bridge failure leading to catastrophic block sliding is studied and the influence of rock bridge position in regard to the rockfall failure mode (shear or tension) is highlighted. Numerical modelling using the distinct element method (UDEC, Itasca) is undertaken in order to assess the stability of a 10 m3 rock block lying on an inclined joint with a dip angle of 40 or 80∘. The progressive failure of rock bridges is simulated assuming a Mohr–Coulomb failure criterion and considering stress transfers from a failed bridge to the surrounding ones. Two phases of the failure process are described: (1) a stable propagation of the rock bridge failures along the joint and (2) an unstable propagation (cascade effect) of rock bridge failures until the block slides down. Additionally, the most critical position of rock bridges has been identified. It corresponds to the top of the rock block for a dip angle of 40∘ and to its bottom for an angle of 80∘.
... Shear strength of intact rock is usually greater than the shear strength of pre-existing discontinuities. 1 Consequently, a low content of rock bridges (1%-3%), which is optimally distributed in the rock mass, can dramatically improve the stability of a slope. Rock bridges can be simply defined as the intact rock between two tips of adjacent discontinuities (Fig. 1). 2 Initiation, development, and coalescence of rock bridges between the non-persistent joints are the most challenging issues in the field of rock slopes failure. ...
... The analysis of experiments in this research is based on the factors presented in Tables 1 and 2 According to Tables 1 and 8, in order to analyze the experiments in Taguchi method, the factors of area, number and normal stress on the rock bridges were used (in the experimental analysis, the expected normal stress shown in Table 8 was not used) and according to Tables 2 and 9 to analyze the experiments in CCD method the number of joints, joint length, joint angle and normal stress were used. To facilitate the analysis of the results, a parameter was defined as the surface continuity of the rock bridge (k a ), which can be calculated based on equation (1). This parameter is obtained by dividing the surface of the rock bridge to the total shear surface. ...
Article
Presence of rock bridges (RB) in natural non-persistent discontinuity sets is an effective factor on the stability of rock structures. Investigations show that the bearing capacity of jointed rocks is changed with variation of different joint parameters. Therefore, in order to investigate the effect of parameters such as contact area and number of rock bridges, normal load, angle, length, and number of joints on shear strength of non-persistent rock joints and also to recognize the interaction of these parameters on the mechanical behavior of joints, experimental design methods of Taguchi and central composite design (CCD) were used for the sample generation, testing and numerical modeling. The effective parameters on the shear strength of jointed samples were obtained based on the previous studies. Using the Taguchi method, 16 samples were tested at CNL condition and the effect of parameters such as normal stress, number, and area of rock bridges was investigated. To evaluate other joints parameters, 30 experiments were designed using CCD method and examined using numerical modeling. Using the analysis of variance (ANOVA), it was found that the obtained models are statistically significant. According to the results of ANOVA, the area of rock bridges and the angle of joints showed the highest and the lowest effect on shear strength of coplanar and non-coplanar jointed samples, respectively. The results displayed that the dominant failure for planar non-persistent joints is pure shear and a combination of tensile and shear cracks is created from the both tips of adjacent joints. Moreover, it was found that the dominant failure of non-coplanar joints is the combination of shear and tension. Bonded particle model (BPM) and smooth joint model (SJM) were also applied for numerical modeling. A new method was considered for applying SJ to the models, which solved the interlocking problem during the test.
... They found that in the absence of a through-going failure plane in the dam foundation the presence of rock bridges can play a key role in dam stability. Kemeny (2005) investigated the time dependent degradation of intact rock bridges using a fracture mechanics based model in which the sub-critical crack growth was taken into account. In this method, an intact rock bridge provides cohesion to discontinuities that is a function of mode II fracture toughness, the size of the rock bridge and the size of the adjacent cracks. ...
... The formation of a failure surface is impeded by the presence of intact rock bridges that may exist along shallow-dipping joint sets. A failure surface may be developed either by i) fracturing through the intact rock bridges in shear (Kemeny, 2005) through time dependent degradation of rock bridges or by tensile fracturing of closely spaced coplanar/parallel joints that are separated by a rock bridge, or ii) by by-passing the intact rock bridges if alternative cross joints are present that allow for a stepped failure surface which minimizes the effect of intact rock bridges on the slope stability. ...
... Recognition of the role that this phenomenon may play in preconditioning and triggering rockfalls and sediment production has drawn the attention of researchers for decades (Tricart 1956;Rapp 1960;Tharp 1987;Hallet 2006;Savi et al. 2015;Jia et al. 2017;Krähenbühl et al. 2018). Rock slope failure is mainly dominated by the complex interaction between existing natural mechanical discontinuities (e.g., bedding planes, foliations, joints, fractures, faults) and subcritical fracture propagation through intact rock bridges (Eberhardt et al. 2004;Kemeny 2005;Einstein et al. 1983). Rupturing of cohesive rock bridges is indeed considered one of the most important processes that controls rock mass failure followed by gravitationally driven collapse (Scavia and Castelli 1996;Kemeny 2005). ...
... Rock slope failure is mainly dominated by the complex interaction between existing natural mechanical discontinuities (e.g., bedding planes, foliations, joints, fractures, faults) and subcritical fracture propagation through intact rock bridges (Eberhardt et al. 2004;Kemeny 2005;Einstein et al. 1983). Rupturing of cohesive rock bridges is indeed considered one of the most important processes that controls rock mass failure followed by gravitationally driven collapse (Scavia and Castelli 1996;Kemeny 2005). In case of high-altitude mountainous terrain, the regular occurrence of ice at rock fall backscarps after a collapse of rock walls (e.g., Gruber and Haeberli 2007;Phillips et al. 2017) indicates that ice-driven mechanical weathering may be a critical factor that leads rock bridges to fail. ...
Article
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Ice-driven mechanical weathering in mountainous environment is considered as an efficient process for slow but cyclical mechanical preconditioning of rockfall events. In this study, we simulate subcritical microfracture propagation under frost wedging conditions along pre-existing mechanical weaknesses of intact rock bridges with an innovative experimental approach. Two series of freeze–thaw experiments conducted in an environmental chamber were carried out to investigate and monitor the propagation of artificially induced fractures (AIF) in two twin gneiss samples. A displacement sensor recorded the sample’s in situ deformation in an environmental chamber during the experiments. 3D X-ray CT scans, performed before and after the experiments, as well as thin sections showing the post-experiment state of the deformed samples allowed tracking and quantification of fracture propagation. Our results demonstrate that frost wedging propagated the AIFs 1.25 cm² and 3.5 cm² after 42 and 87 freeze–thaw cycles, respectively. The experiments show that volumetric expansion of water upon freezing, cooperating with volumetric thermal expansion and contraction of the anisotropic rock, plays a key role in fracture widening and propagation. Based on these results, this study proposes that: (1) frost wedging exploits intrinsic pre-existing mechanical anisotropies of the rock; (2) the fracturing process is not continuous but alternates between stages of fast propagation and more quiet stages of stress accumulation; and (3) downward migration of “wedging grains,” stuck between the walls of the fracture, increases the tensile stress at the tip, widening and propagating the fractures with each freeze–thaw cycle. The experimental design developed in this study offers the chance to visualize and quantify the long-term efficiency of frost wedging in near-natural scenarios.
... The shear strength of discontinuities is one to two orders of magnitude less than that of intact rocks. [1][2][3] Thus, the characteristics of discontinuities play an important role in the deformation and destruction of rock masses. Among these characteristics, discontinuity persistence, which is known as the areal extent or size of discontinuities within a rock mass, 4 has been recognized as one of the most important parameters that affect the strength of rock masses and stability in rock engineering. ...
... Among these characteristics, discontinuity persistence, which is known as the areal extent or size of discontinuities within a rock mass, 4 has been recognized as one of the most important parameters that affect the strength of rock masses and stability in rock engineering. 1,2,[5][6][7][8][9] Information on actual discontinuity persistence is minimal because discontinuities are hidden in the subsurface. Many studies have attempted to propose various concepts to estimate the actual discontinuity persistence. ...
... Geological tectonic forces generate structural features such as cracks, bedding planes, voids, and fragile interlayers within rock masses (Shi et al., 2020;Chen Q. Z. et al., 2022;Zaheri and Ranjbarnia, 2022). These varied discontinuities significantly weaken the inherent strength of the rock formations, presenting considerable stability challenges, especially in the field of mining Numerical model of bolted rock joint.. engineering (Jaeger, 1971;Pariseau, 1999;Kemeny, 2005;Cao et al., 2020;Zheng et al., 2024a;Wang et al., 2024). To avoid engineering geological disasters caused by the sliding of jointed rock mass, reinforcement measures must be taken. ...
Article
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Rock masses are formed through long-term, complex geological processes, and the presence of joints significantly reduces their strength and increases their deformation. Rock bolts effectively enhance the strength and stability of rock masses and are extensively utilized for reinforcement. According to field investigations, a significant portion of the damage to bolted rock masses stems from shear deformation at joint surfaces. Moreover, roughness affects friction and surface contact, thus influencing the shear behavior between rock and rock bolts. This study considers two crucial factors affecting the shear characteristics of bolted rock joints: joint surface roughness and normal stress. Using the Particle Flow Code discrete element numerical method, the Barton standard joint profile lines were input to establish numerical models of both unbolted and bolted rock joints for direct shear tests. Results reveal that the peak shear stress and stiffness of both unbolted and bolted rock joints increase with rising normal stress and joint roughness coefficient. The peak shear stress and stiffness of bolted rock joints are notably higher than those of unbolted ones, with a maximum increase of 17.5%. Crack development in bolted rock joints occurs in stages of rapid, slow, and stable development, whereas no distinct slow development stage is observed in unbolted rock joints. Additionally, micro cracks in both unbolted and bolted rock joints are primarily tensile cracks, originating around the joint surface and extending outward with increasing shear displacement. These findings offer valuable insights into the microscopic shear mechanics of bolted rock joints and provide practical references for engineering design and applications in rock reinforcement projects.
... Rock bridges play an anti-shear role in slopes with rock bridge-locked segments, and the stability of slopes is mainly controlled by the rock bridges 21 . There have been many studies on the mechanical properties of rock masses with rock bridge-locked segments [22][23][24] , giving rise to rock bridge failure theory [25][26][27] . Liu et al. 8 (1) � = A� α www.nature.com/scientificreports/ ...
Article
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The locked segment is critical for determining the stability of locked segment-type landslides. Research indicates that the volume expansion point marks the transition from the secondary creep stage to the tertiary creep stage in a landslide’s evolution, and also separates the stable crack growth stage from the unstable crack growth stage in the locked segment. Identifying the volume expansion point is essential for early warning and predicting locked segment-type landslides. A series of instruments (resistance strain gauges, acoustic emission system, piezoelectric acceleration sensors, etc.) were used to conduct physical model tests of the landslide with retaining-wall-like locked segment under external load on the landslide’s trailing edge. The evolution process of this landslide was analyzed through changes in slope shape and stress response characteristics. The experimental results reveal the failure mechanism of the landslide with retaining-wall-like locked segment: the upper part of the landslide thrusts and slides, the middle part squeezes and uplifts, the retaining-wall-like locked segment produces a locking effect, and compression-shear fracture of the retaining-wall-like locked segment leads to landslide failure. Based on the deformation and acoustic emission characteristics of the locked segment, a method for identifying the volume expansion point was established. This point was used as the onset of acceleration point in the inverse velocity method to predict the failure time of the locked segment-type landslides, incorporating the three-stage creep model and Fukumoto’s theory.
... The FLAC3D program is used to simulate the 2D and 3D stability and deformation of landslides (Titti et al., 2020;Zhang et al., 2013;Zhou et al., 2020). To investigate the 3D stability and deformation behaviors of the Tizicao landslide, this study introduced three rock bridge models into the FLAC3D program, namely IRMM (Kemeny, 2005;Zhang et al., 2020), JM (Bonilla-Sierra et al., 2015;Jennings, 1970), and CSM-HSP (Huang et al., 2015;Scholtès and Donze, 2015), as shown in Fig. 9. ...
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Rock bridges, also known as locking masses in landslides, affect the three-dimensional (3D) stability and deformation patterns of landslides. However, it is always difficult to simulate rock bridges with continuous grid models in 3D landslides due to their discontinuous deformations. Tizicao landslide, located in Maoxian County, southwest China, is a typical landslide with a super-large rock mass volume of about 1388.2 × 104 m3 and a locking segment. To explore a better rock bridge model used to simulate 3D stability and deformations of the Tizicao landslide, this study introduced three rock bridge models into the FLAC3D program, including the intact rock mass model (IRMM), the Jennings model (JM), and the contact surface model with high strength parameters (CSM-HSP). The CSM-HSP model was eventually used in the FLAC3D program to obtain the 3D deformation characteristics of the landslide. In addition, the two-dimensional (2D) stability of the Tizicao landslide was analyzed using the GeoStudio program. The simulation results indicate that the Tizicao landslide is generally stable under current conditions owing to the existence of the locking segment in its southern front. This inference is consistent with the field deformation and monitoring data. It was found that the general stability and local deformations of the landslide are influenced by the locking segment according to the comparison between the 2D and 3D stability. There was a linear relationship between the locking ratio and the factor of safety (Fos), which applied to the 2D stability analysis of the landslides with a locking segment each, while there existed an approximate quadratic parabola suitable for the 3D stability of the landslides. Finally, this study analyzed the laws of the 3D Fos varying with the locking ratio and strength parameters of the locking masses and the sliding surface. Furthermore, it explored the advantages and disadvantages of the three rock bridge models in the simulation of the 3D stability of landslides with a locking segment.
... The schematic failure propagation sketched in Fig. 16 is in accordance with the polyphase character of the rock fall process and the overhanging post-failure geometry of the failed rock slope observed in nature (Fig. 6). The time lag between the rock fall events in nature, i.e. 112 days between the 1 st and 2 nd rock fall event and 101 days between the 2 nd and 3 rd , may result from progressive failure along discontinuities (Kemeny 2005). This especially highlights the challenge of unravelling the timing and clear trigger factors of slope failures ). ...
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Even after decades of intensive research, assessing rock slope stability remains a challenge. One reason for this is the spatial variability of rock bridges (RBs) related to non-persistent, pre-existing geological structures, especially as the detection of RBs is generally limited to the post-failure period. Thus, the identification and classification of RBs and their inclusion in numerical studies are demanding, yet essential, since even small quantities of RBs can be decisive for rock slope stability. In our study, we demonstrate how brittle RB failure and pre-existing geological structures control the mechanisms of a polyphase rock slope failure. Therefore, we present a case study in the Austrian Alps, where three rock falls with a failure volume of 30,000 m ³ occurred in 2019. Based on detailed process reconstructions, high-resolution terrain models, and comprehensive geological and rock mechanical investigations, we derived high-quality input for our distinct element model (DEM). By applying asymmetric Voronoi tessellation in the DEM, we modelled the coalescence of pre-existing geological structures by brittle RB failure. As a result, we identified toppling as the predominant failure mechanism at the study site. Distinctive geological structures decisively affected the failure mechanism. However, the toppling failure was only reproducible by incorporating RBs in the DEM in their pre-failure position. Finally, we found that joint persistence, and consequently the presence of potential RBs, controls which initial rock fall failure mechanism was developed. In conclusion, we state that the initial toppling failure of the Hüttschlag rock falls is controlled by non-persistent geological structures in interplay with RBs.
... Tang et al. [17] elaborated the landslide causes and failure mechanism by field investigation on the locking highspeed landslide in Jiweishan, southwest China, and established corresponding mechanical equations to simulate the mechanical behavior of the fracture penetration. Kemeny [18] established a fracture mechanics model to simulate the time-varying failure of the fracture penetration along the rock bridge, and used subcritical crack propagation to simulate the time-dependent failure process. In the laboratory test of fractured rocks, Pan et al. [19] compared the influence of the number of fractures and the spacing distance parameters on the macroscopic failure process by constructing a small physical model of slope. ...
... The physical model test is an important means to study the mechanisms and characteristics of an anchor support. The model test can visually and intuitively simulate the whole process of force, deformation, and damage of the engineering structure and can simulate the complex geology more comprehensively and the support structure more realistically [9][10][11]. Although the physical model can simulate the failure process of the anchor, it is unfortunate that the damage process inside the model cannot be seen and captured, and repeating the physical experiment is difficult. ...
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Various diseases and failures inevitably appear on expressway roadways in water-rich strata under the long-term erosion of water. It is very difficult to support the surrounding rock of a water-rich roadway because water will corrode the anchorage bond and weaken the surrounding rock mass. In the process of supporting, damage and fracture of anchor bolt often appear in water-rich roadway. In order to study the stability analysis of a support anchor bolt in the process of surrounding rock fracture evolution and the relationship between the prestressed value and the length of the anchor bolt, this paper studied the fracture evolution law of surrounding rock and the progressive debonding law of the bolt are studied by RFPA3D numerical simulation and used MATLAB software to calculate and draw several graphs to reveal the mechanism by analytical method. The following main conclusions were drawn: (1) the change and attenuation of the surrounding rock stress have a certain influence on the stability of the supporting bolt. The existence of confining pressure (horizontal stress) has a significant impact on the ultimate pullout force of anchor bolts. (2) With the gradual destruction of the surrounding rock, the shear stress, horizontal stress, and vertical stress in the surrounding rock are gradually reduced to zero, and the change speed of the surrounding rock is fast at the shallow surface and slow at the deep. (3) The interface shear stress tends to a low stable value after debonding, which means the value of friction resistance is relatively stable in different positions. (4) The frictional resistance after interface debonding is an important condition to maintain the balance of higher anchorage force. If there is no friction resistance, when the axial force of the anchor bolt reaches the initial critical value, the interface debunking process will develop catastrophically and cannot be stabilized until complete failure, even if the axial force no longer increases.
... Subcritical crack growth is a process by which the brittle propagation of fractures occurs relatively slowly at lower stress magnitudes [104,105]. The effects of subcritical crack growth (in shear) on slopes have been conceptually investigated, using numerical modelling, by Kemeny [106,107]. Later applications include the investigation of time-dependent tensile failure of in-plane rock bridges [108]. Donati et al. [16] proposed that subcritical crack growth was a critical factor in the progressive failure of the 1965 Hope Slide, based on geomorphic and numerical modelling analyses ( Figure 5). ...
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The stability and kinematics of rock slopes are widely considered to be functions of lithological, structural, and environmental features. Conversely, slope damage features are often overlooked and considered as byproducts of slope deformation. This paper analyzes and discusses the potential role of slope damage, its time-dependent nature, and its control on both the stability of rock slopes and their kinematics. The analysis of several major landslides and unstable slopes, combined with a literature survey, shows that slope damage can play an important role in controlling short- and long-term slope stability. Seasonal and continuously active events cause permanent deformation within the slope due to the accumulation of slope damage features, including rock mass dilation and intact rock fracturing. Rock mass quality, lithology, and scale control the characteristics and complexity of slope damage, as well as the failure mechanism. The authors propose that the role of slope damage in slope kinematics should always be considered in slope stability analysis, and that an integrated characterization–monitoring–numerical modelling approach can enhance our understanding of slope damage, its evolution, and the controlling factors. Finally, it is emphasized that there is currently a lack of guidelines or frameworks for the quantitative assessment and classification of slope damage, which requires a multidisciplinary approach combining rock mechanics, geomorphology, engineering geology, remote sensing, and geophysics.
... These frost crack interaction and coalescence are fundamentally important to rock stability. Especially, for alpine rock masses that are rich in joints of different scales (Fig. 24a), the complex interactions and coalescence between joints and cracks propagating through the intact rock bridges control the global failure of rock masses (Eberhardt et al. 2004;Kemeny 2005;Einstein et al. 1983;Sun et al. 2022). For example, in one sample of the D-45° experiment (Fig. 24b), a triangular damage area formed in the center of the specimen after the frost crack coalescence was observed, which potentially lead to accelerated deterioration. ...
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Frost crack evolution induced by cyclic freeze–thaw is responsible for rock deterioration in cold regions and poses major threats to public safety, engineering structures, and alpine slope stability. This paper presents experimental and numerical works aimed at investigating the frost crack evolution in fissured rock masses, as well as the interaction between frost cracks. A series of laboratory freezing experiments are conducted on rock-like specimens with various pre-existing fissures. Experimental results show that frost cracks initiate at the pre-existing fissure tips and propagate under the freeze–thaw treatment. Moreover, the frost crack evolution is significantly influenced by external stress conditions and frost crack interactions, forming several typical propagation patterns (e.g., deflection, coplanar and butterfly shape, etc.). Then, numerical simulations with a low-temperature thermal–mechanical coupled model, where the water/ice phase transition and hence volume expansion are explicitly simulated, are conducted to reproduce the experimental observation. The numerical results are consistent with the experimental observations and help to reveal the underlying mechanisms of the frost crack growth and frost crack interaction. This experimental and numerical investigation helps to improve the understanding of frost cracking mechanisms that can inform engineering design in cold regions with fissured rock masses.
... Time-dependent behavior can be described as a phenomenon caused by the weakening of a rock mass with time, such as creep, consolidation/dilation, swelling, and stress relaxation. A detailed knowledge of the time-dependent behavior of rocks is important to predict the long-term stability of underground structures (Diederichs and Kaiser 1999), surface structures and rock slopes (Kemeny 2005;Yu et al. 2012;Zhang et al. 2020), nuclear waste repositories (Malan 2002;Nara et al. 2010), oil and gas industry, enhanced geothermal systems (EGS), and CO 2 and waste water disposal (Miura et al. 2003;Zhuang et al. 2020) in which a damagecontrolled failure is required. ...
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Time-dependent rock deformation caused by the initiation and growth of fractures leads to the weakening of the rock mass. Understanding the fracturing mechanisms involved in the time-dependent behavior in brittle rocks is very important and to achieve this goal, a systematic series of three types of experiments was performed on double-flawed prismatic Barre granite specimens under unconfined compression. The first series aimed to identify the failure mechanism in the short-term failure mode under monotonic loading, the, second series involved multistage relaxation (constant strain) experiments to analyze the damage at different strain levels, and the third series explored the fracture propagation under multistage creep (constant load) experiments. The spatial and temporal evolution of cracking mechanisms were evaluated using the acoustic emission (AE) and two-dimensional digital image correlation (2D-DIC) techniques to observe the whole crack growth process as well as the accumulated inelastic strain at the specified region of interest. Results suggest that in the case of multistage creep experiments, the time to failure was less compared to the multistage relaxation, when loaded above the crack damage threshold (CD) estimated from the monotonic testing. The frequency magnitude distribution of the AE events generated in the three loading conditions followed the Gutenberg Richter model. A relatively lower b-value was obtained for the creep experiments, indicative of high energy AE events and faster crack growth. In addition, the AE and DIC results also revealed high evolution of tensile cracks at-different stages of creep and relaxation compared to shear and mixed-mode cracks.
... promoting progressive failure mechanisms (Whalley, 1974;Kemeny, 2005;Griffiths et al., 2012;Wolter et al., 2016). The erosive action of glaciers and rivers extended over long periods of time can also cause a progressive oversteepening of the slope, and promote landsliding due to stress concentrations and reduction of kinematic constraints (Larsen and Montgomery, 2012). ...
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The 2020 Elliot Creek landslide-tsunami-flood cascade originated from an 18.3 Mm³ rock slope failure in quartz diorite bedrock in a valley undergoing rapid glacial retreat. We used airborne LiDAR and optical imagery to characterize the slope and its surroundings. Using the LiDAR, we determined that two rockslides (2020 and an older undated one) occurred on this slope and shared a common basal rupture surface. We mapped two main sets of lineaments that represent structures that controlled the orientation of the lateral and rear release surfaces. Analysis of the topographic profile indicates a wedge-shaped failure block and a stepped rupture surface. Further topographic profile analysis indicates the possibility of a structurally controlled geomorphic step in the valley that corresponds with a change in the orientation of the valley. The rapid retreat of the West Grenville Glacier and the positions of the rupture surfaces suggest glacial retreat played a role in the landslides.
... Accordingly, researchers always perform a back analysis to study the mechanical behaviours of rock bridges on a laboratory scale by setting pre-existing intact rock bridges (Dershowitz and Einstein 1988), with a classical method being the direct shear test with a constant normal stress applied to the discontinuous plane because of the consistency of boundary conditions between direct shear tests and engineering practices (e.g., rock slope stability and surface excavation stability) (Lajtai 1969;Muralha et al. 2014). In this context, although a plethora of researchers have investigated the effects of normal stress (Wong et al. 2001;Cundall et al. 2016), joint length (Zhang et al. 2005;Ghazvinian et al. 2007;Asadizadeh et al. 2018), joint orientation (Gehle and Kutter 2003;Zhong et al. 2020) and joint overlap (Kemeny 2004;Sarfarazi et al. 2014) on rock bridges in direct shear, the investigation of the scale effects of rock bridges in a laboratory is still difficult because of the high cost and high failure rate of handcraft specimens with multiple rock bridges (Shang et al. 2018). Thus, it is necessary to introduce numerical simulations into this research. ...
Article
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Due to the challenge of measuring rock bridges in the field and the negligence of progressive damage and changes in stresses within a rock mass when defining rock bridges, it is questionable to evaluate mechanical properties of rock bridges using only geometric parameters. A demonstration is the scale effects of rock bridges, because the same geometric parameter may refer to different sizes and numbers of rock bridges, leading to erroneous equivalent rock mass responses. In this context, in-plane rock bridges in rock slope engineering were equivalent to rock bridges subjected to direct shear by conducting numerical simulations employing the Universal Distinct Element Code (UDEC) and described by constant geometric parameters, i.e., joint persistence, while the sizes and numbers of rock bridges were variant. In this way, the scale effects of rock bridges were investigated from the perspective of load–displacement curves, stress and displacement fields, crack propagations and AE characterizations. The results revealed that the mechanical properties of rock bridges deteriorated with decreasing scales. More specifically, the shear resistance and the area and value of stress concentration decreased with decreasing scale. Furthermore, an uneven distribution of displacement fields in an arc manner moving and degrading away from the load was observed, indicating the sequential failure of multiple rock bridges. It was also found that the propagation of tensile wing cracks was insensitive to scale, while the asperity of macro shear fracture mainly formed by secondary cracks decreased with decreasing scale. In addition, increasing the dispersion of rock bridges would overlap the failure precursors identified by intense AE activities. Based on the abovementioned results, the scale effects of rock bridges were characterized using existing rock bridge potential (RBP) index and degree of persistence (DoP) index. Interestingly, a scale threshold to possibly identify a rock bridge was found.
... For example, Chen et al. [25,26] established a heterogeneous numerical model for lifetime prediction on the basis of subcritical crack growth, and determined the mode I and mode II fracture toughness. Kemeny et al. [27] and Ko et al. [28,29] developed a subcritical crack growth model (LEFM model) based on subcritical crack growth theory, which can predict cohesion degradation. Although the above mentioned research content is helpful to understand the subcritical crack growth of rock, it mainly focuses on subcritical crack growth under quasi-static loading, and rarely considers subcritical crack growth under cyclic loading, while actual subcritical cracks often expand under cyclic loading [22]. ...
Article
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To further investigate the Mode I crack growth and damage mechanism, compression tests were performed on notched semi-circular bending (NSCB) specimens at different cycle amplitudes. The crack propagation gauge and digital image correlation (DIC) recorded the entire process of crack growth. The real-time crack growth rate and evolution of the horizontal strain field during crack growth were obtained. Based on the crack growth rate, the crack growth process can be divided into three stages: the cracking latent period (primary stage), stable crack growth stage (secondary stage), and accelerated crack growth stage (tertiary stage).The cracking latent period accounts for a large proportion of the entire crack growth. The stable crack (i.e., steady subcritical crack growth) expanded slowly to a certain extent after initiation, and then the accelerated crack growth led to failure. With the increase in the cyclic amplitude, the cracking latent period is shortened and the crack growth rate is accelerated. The crack growth rate is positively correlated with the stress intensity factor. Moreover, scanning electron microscopy (SEM) was used to analyse the development of the fracture process zone (FPZ) and the subcritical crack damage mechanism. The SEM images showed two damage phenomena: (1) intergranular cracks caused by grain debonding (primary mechanism) and (2) transgranular cracks (secondary mechanism).
... Today, it is widely recognised that rockslides are accompanied by gravity-induced damage that occurs within the unstable rock mass before the eventual collapse (Stead et al., 2006;Brideau et al., 2009;Paronuzzi and Bolla, 2015a). This precursory phenomenon, which anticipates the slope rupture, is commonly termed "progressive failure mechanism" (Tang, 1997;Szwedzicki, 2003;Eberhardt et al., 2004;Tham et al., 2004;Kemeny, 2005) and results in the development of a continuous, three-dimensional failure surface over time. ...
Article
This work describes field evidence of gravity-induced cracking that has been identified on the failure scar of a small rockslide (volume = 6–7 m³) that occurred in March 2004 in the Rosandra Valley near the town of Trieste (north-eastern Italy). This shallow rock slope failure involved a limestone slope that was re-profiled through blasting about 135 years ago for the construction of an old railway, which has now been reconverted into a cycle path. Field observations ascertained that the slope failure was characterised by a cascading rupture process in which adjacent blocks collapsed in rapid sequence as a result of the progressive breakage of a number of rock bridges (domino-like collapse), thus highlighting a progressive failure mechanism. The rock bridges were localised in eccentric positions on lateral and rear release planes and failed in tension as a result of combined tensile and bending loading conditions (tensile strength of intact rock = 5 ± 2 MPa). The rockslide was triggered by cyclic loading related to freeze-thaw (ice jacking) that occurred over some consecutive days of daily snowmelt and nocturnal frost. The recognition of newly formed fractures also proves the current progressive development of 3D rupture surfaces of some unstable blocks susceptible to failure. This study provides innovative content to detect gravity-induced cracking in the field, which is an important precursory sign relating to the progressive failure of rock slopes. Gravity-induced cracks can be distinguished from pre-existing discontinuities for their more irregular profile (zigzag pattern), rougher surface, lower persistence and potentially different orientation. This study also provides some new insights into the step-path failure process of steep rock slopes. The mechanical process of initiation, growing and coalescence of gravity-induced fractures is strongly time- and stress-dependent. In the absence of external changing factors that profoundly modify the acting stress state (for instance, engineering countermeasures), progressive failure is a dynamic and irreversible process. For excavated slopes, the creation of a new rock face may abruptly provide the kinematic freedom of potentially unstable blocks, thus determining a very quick stress redistribution. If the mechanical system is not able to redistribute the stress on resisting stiff parts without overcoming the intact rock strength, gravity-induced cracking initiates and propagates until reaching slope collapse within times that are much shorter (from hours to 100–200 years) compared to natural rock slopes subjected to long-lasting geological processes (from 1000 to 2000 up to 10,000–20,000 years).
... In a stratified slope, a potential slip surface usually intersects with the layered strata that play the role of the locked segment, such as an antidip stratified landslide (Figure 1(a)) and a dip stratified landslide whose dip angle is larger than the slope angle ( Figure 1(b)) [2]. Currently, there are many researches on rock bridge-type landslide [20][21][22][23][24][25]. Different locked segment type landslides have different evolution mechanism and deformation characteristics [26,27]. ...
Article
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The failure of locked segment-type slopes is often affected by rainfall, earthquake, and other external loads. Rainfall scours the slope and weakens the mechanical properties of rock-soil mass. At the same time, rainfall infiltrates into cracks of slope rock mass. Under the action of in situ stress, hydraulic fracturing leads to the development and expansion of rock cracks, which increases the risk of slope instability. Under seismic force, the slope will be subjected to large horizontal inertial force, resulting in slope instability. In this paper, a self-developed loading device was used to simulate the external loads such as rainfall and earthquake, and the model tests are carried out to study the evolution mechanism of landslide with retaining wall locked segment. Three-dimensional laser scanner, microearth pressure sensors, and high-definition camera are applied for the high-precision monitoring of slope shape, deformation, and stress. Test results show that the retaining wall locked segment has an important control effect on landslide stability. The characteristics of deformation evolution and stress response of landslide with retaining wall locked segment are analyzed and studied by changing the slope shape, earth pressure, and the displacement cloud map. The evolutionary process of landslide with retaining wall locked segment is summarized. Experimental results reveal that as the landslide with retaining wall locked segment is at failure, the upper part of the landslide thrusts and slides and the retaining wall produces a locking effect; the middle part extrudes and uplifts, which is accompanied with shallow sliding; and compression-shear fracture of the locked segment leads to the landslide failure.
... Therefore, it provides a theoretical basis and reference for mines disaster early-warning, prediction and determining reasonable support time. Meanwhile, there are abundant achievements presented in domestic and foreign scholars' corresponding reports (Allison and Lama, 1979;Singh and Digby, 1989;Rao and Ramana, 1992;Kemeny, 2005;Adhikary and Dyskin, 2007;Kim and Kemeny, 2009;Wang et al., 2011;Ls and Fvda, 2012;Tan et al., 2014;Gischig et al., 2016;Shao, 2016a, 2016b;Nguyen et al., 2017;Zhang et al., 2019b;Song and Zhang, 2021). On the other hand, from the (Zhang and Zhao, 2014;Liu and Dai, 2021). ...
Article
The progressive failure process and fracture mechanism of rocks has been a key scientific issue which needs to be solved. Therefore, the progressive failure process and fracture mechanism of rocks under compression are comparatively analyzed based on the perspectives of energy evolution, rock burst starting and mesoscopic characterization. Then, the structural evolution theory to reveal the progressive failure process and fracture mechanism of rocks is proposed. Additionally, the evolution characteristics of four stages and progressive failure mechanism of rocks under compression are better verified according to the results captured by multiple methods. The main conclusions are as follows: (1) The fundamental reason caused the stress changed and transferred is the change of system structure, and the stress is only the external manifestation of system structure changed. (2) The macroscopic instability of rocks occurs in the post-peak sub-instability stage. (3) Critical slowing down theory can provide sufficient evidence for the structural evolution perspective. (4) The driving force of the structure self-adjustment in rocks comes from the activation of its self-organizing and the energy consumption. The conclusions above can provide new ideas and concepts for the fundamental theoretical research of deep rock mechanics, thus provide a certain of theoretical reference for the practice of field engineering.
... A rock block cannot fall or slide from an excavation or slope until the appropriate rock bridges have failed. The rock bridge failure involves the failure of the intact rock, which can be an order of magnitude stronger than the rock mass (Kemeny 2005). The importance of rock bridges or non-persistent joints on the stability of rock slopes has been studied by, among others, Einstein et al. (1983), Sjöberg (1996 and Nichol et al. (2002), and the effect of rock bridges on the strength or deformation properties of rock masses has been discussed by Kemeny & Cook (1986), Shen et al. (1995) and Kemeny (2003), among others. ...
Article
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Most of the models that simulate fractured rock masses assume fully persistent discontinuities, simplifying the fact that, in nature, fractured rock masses are made of non-continuous sets of joints. A rock bridge gives an effective cohesion to the fracture and a block of rock cannot fall or slide until all the rock bridges fail. This failure involves the failure of the intact rock, which can be orders of magnitude stronger than the shear strength of the rock joint. In this study we focus on how the distribution of rock bridges influences the overall rock mass behaviour, to contribute to the understanding of how the presence of rock bridges influences the ‘scale’ effect that is observed between strength values measured on intact rock in the laboratory and those observed at the rock mass scale. To estimate the influence of spatial fracture, parameters of the rock mass strength and deformation were determined, using the orthogonal arrays method, UDEC and variance analysis. The numerical model was first calibrated on shear tests of samples made of continuous joints, and then used to investigate the shear behaviour of a fractured rock mass with non-persistent joints. The 2D approach was successfully extended to 3D models using 3DEC with the aim of providing a better approach for simulating the stability of an underground cavern in a fractured rock mass.
... Moreover, defects in rocks may be created artificially for some engineering purposes. Whether the defects are formed naturally or created artificially, they affect the load-bearing capacity of the rock [1][2][3][4]. Defects in rock masses are stress-raisers and play a key role in the rock fracturing processes. Therefore, understanding the role of different types of defects on the mechanical behavior of rocks under various loading conditions is an essential task for any rock engineering design. ...
Article
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Discontinuities are natural structures that exist in rocks and can affect the stability of rock structures. In this article, the influence of notch presence on the strength and failure evolution around a hole in compressed rock specimens is investigated numerically. Firstly, the uniaxial compressive test on a rock specimen with a circular hole is modeled, and the failure evolution in the specimen is simulated. In a separate model, notches are created at the surface of the hole. Results show that, when the notches are created in the model, a failure zone around the hole is transferred to a distance away from the surface of the hole. In addition, a parametric study is carried out to investigate the influence of the notch length and the confining pressure on the fracturing behavior of the specimen. Numerical results presented in this article indicate that the presence of notches at the surface of the hole and their dimensions can affect the fracturing mechanism of the specimen. In some cases, the failure at the boundary of the hole is prevented when the notches of certain dimensions are added to the hole. The insights gained from this numerical study may be helpful to control the failure around underground excavations.
... Moreover, defects in rock may be created artificially for some engineering purposes. Whether the defects are formed naturally or created artificially, they affect the load-bearing capacity of the rock (Brace 1961;Cai et al. 2004;Howarth and Rowlands 1987;Kemeny 2005). Defects in rock masses are stress raisers and play a key role in the rock fracturing processes. ...
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Discontinuities are natural structures that exist in rocks and can affect the stability of rock structures. In this article, the influence of notch presence on the failure evolution around a hole in compressed rock specimens is investigated numerically. Firstly, the uniaxial compressive test on a rock specimen with a circular hole is modeled and the failure evolution in the specimen is simulated. In a separate model, notches are created at the surface of the hole. Results show that when the notches are created in the model, failure zone around the hole is transferred to a distance away from the surface of the hole. In addition, a parametric study is carried out to investigate the influence of the notch length and the confining pressure on the fracturing behavior of the specimen. Numerical results presented in this article indicate that the presence of notches at the surface of the hole and their dimensions can affect the fracturing mechanism of the specimen. In some cases, the failure at the boundary of the hole is prevented when the notches of certain dimensions are added to the hole. The insights gained from this numerical study may be helpful to control the failure around underground excavations.
... To date, domestic and foreign scholars have conducted many studies on the failure mechanics behaviour of coal and rock and obtained many achievements (Kemeny 2005;Li & Zhou 2013;Li & Tang 2015;Nikolic & Ibrahimbegovic 2015;Bai et al. 2019;Xiong et al. 2019;Liu et al. 2020). Fu et al. (2016Fu et al. ( , 2017Fu et al. ( , 2018 placed cracks with different quantities and spatial locations inside a new material to simulate a jointed rock. ...
Article
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Conventional triaxial loading tests with different confining pressures and stress-seepage coupling tests on sandstone with different confining pressures and seepage pressures were conducted. A permeability model considering strength and strain was established, which better characterized the progressive deformation mechanical behaviour of sandstone under stress-seepage coupling. The results showed the following. (i) The confining pressure not only affects the peak strength of sandstone but also affects the axial deformation under conventional triaxial loading conditions. (ii) Compared with the seepage pressure effect, the degree of the confining pressure effect on the strength of sandstone was weaker, but the degree of that on the axial, radial and volumetric deformations of sandstone was stronger under stress-seepage coupling. (iii) With increasing confining pressure, the axial strain of sandstone decreased, while the corresponding radial and volumetric strains showed progressively increasing evolution characteristics under identical seepage pressures and different confining pressures. With increasing seepage pressure, the axial strain continuously decreased, while the corresponding radial and volumetric strains showed the progressive evolution characteristic of first increasing and then decreasing under identical confining pressures and different seepage pressures. (iv) Compared with the confining pressure effect, the degree of the seepage pressure effect on the permeability progressive evolution law of sandstone was weaker under stress-seepage coupling. The research conclusions could enrich the theories for the prevention and control of water inrush accidents in coal mines.
... Particularly for rockslide debris flow, the joints have profound effects on the rock-slope stability [13]. Joint parameters, that is, joint spacing, joint length, joint roughness, and joint orientation, influence the weathering velocity, the size of blocks, the rock strength, and the fissure-fluid pressure distribution during heavy rainfall events [14][15][16]. Subtle differences in joints can lead to significant differences in the erodibility and rockslope stability, thus leading to the initiation of this type of debris flows [17]. ...
Article
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Our understanding of debris-flow initiation by slope failure is restricted by the challenge of acquiring accurate geomorphic features of debris flows and the structural setting of the rock mass in the remote mountainous terrain. Point cloud data of debris flows in Sabino Canyon, Tucson, Arizona, July 2006, with initiation by joint-controlled rock slope were obtained using multitemporal LiDAR scanning. Topographic changes were detected by comparing historical LiDAR scanning data of this area since 2005 by adopting open-source CloudCompare software. The results showed persistent scour and erosion in the debris flows after 2006. Point cloud data of joint-controlled rock in the initiation zone were generated by the means of photogrammetry using Pix4D software. The joint planes, the dip direction and the dip value of the joint plane, the joint spacing, and the joint roughness were therefore acquired by point cloud processing. Our study contributes a foundation for analyzing the relationship between the rock features, the generation of slope failure, and the initiation of debris flows.
... Previous research has shown that failure occurs through progressive fracturing of intact rock bridges, in a process termed steppath failure (Kemeny 2005;Eberhardt, Stead, and Coggan 2004;Scavia 1995;Brideau, Yan, and Stead 2009) that may in some cases be compared to a cascade-effect failure which can fail like dominoes along sloping channels (Bonilla-Sierra et al. 2015;Harthong, Scholtès, and Donzé 2012; Zhou et al. 2015). The contribution of rock bridges has been implemented in numerical models of rock slope stability using apparent cohesion (Eberhardt, Stead, and Coggan 2004;Fischer et al. 2010; Gischig et al. 55 2011) or areas of intact rock (Stead, Eberhardt, and Coggan 2006;Sturzenegger and Stead 2009;Agliardi et al. 2013;Paronuzzi, Bolla, and Rigo 2016). ...
Preprint
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Plane failure along inclined joints is a classical mechanism involved in rock slopes movements. It is known that the number, size and position of rock bridges along the potential failure plane are of main importance when assessing slope stability. However, the rock bridges failure phenomenology itself has not been comprehensively understood up to now. In this study, the propagation cascade effect of rock bridges failure leading to catastrophic block sliding is studied and the influence of rock bridges position in regard to the rockfall failure mode (shear or tensile) is highlighted. Numerical modelling using the distinct element method (UDEC-ITASCA) is undertaken in order to assess the stability of a 10 m3 rock block lying on an inclined joint with a dip angle of 40° or 80°. The progressive failure of rock bridges is simulated assuming a Mohr–Coulomb failure criterion and considering stress transfers from a failed bridge to the surrounding ones. Two phases of the failure process are described: (1) a stable propagation of the rock bridge failures along the joint and (2) an unstable propagation (cascade effect) of rock bridges failures until the block slides down. Additionally, the most critical position of rock bridges has been identified. It corresponds to the top of the rock block for a dip angle of 40° and to its bottom for an angle of 80°.
... Numerical methodssuch as the finite element method or the distinct element methodhave also gained recent attention to study the creep behaviour of rocks and rock masses (Kemeny 2005;Lisjak and Grasselli 2014). In particular, the DEM approach, in conjunction with the RPT, has been shown to be particularly useful to model soil creep Mitchell 1992, 1993;Kwok and Bolton 2010;Liu et al. 2019). ...
Article
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Rock creep behaviour is crucial in many rock engineering projects. Different approaches have been proposed to model rock creep behaviour; however, many cannot reproduce tertiary creep (i.e., accelerating strain rates leading to rock failure). In this work, the distinct element method (DEM) is employed, in conjunction with the rate process theory (RPT) of M.R. Kuhn and J.K. Mitchell (published in 1992) to simulate rock creep. The DEM numerical sample is built using a mixture of contact models between particles that combines the Flat Joint Contact Model and the Linear Model. Laboratory uniaxial compression creep tests conducted on intact slate samples are used as a benchmark to validate the methodology. Results demonstrate that, when properly calibrated, DEM models combined with the RPT can reproduce all creep stages observed in slate rock samples in the laboratory, including tertiary creep, without using constitutive models that incorporate an explicit dependence of strain rate on time. The DEM results also suggest that creep is associated with damage in the samples during the laboratory tests, due to new microcracks that appear when the load is applied and maintained constant at each loading stage.
... Various numerical simulation methodologies, such as discrete element method (DEM), hybrid finite element-discrete element method (FEM-DEM), damage mechanics methods, and grain-based DEMs (e.g. particle flow code (PFC) (Itasca, 2008), and universal distinct element code (UDEC)-Voronoi code (Itasca, 2014)), have been utilised successfully to simulate the brittle failure mechanisms of rocks (Bruno, 1994;Diederichs, 2000;Potyondy and Cundall, 2004;Kemeny, 2005;Lan et al., 2010;Ivars et al., 2011;Kazerani et al., 2012;Bewick et al., 2014;Farahmand and Diederichs, 2014;Farahmand et al., 2018;Vazaios et al., 2018). The analyses presented in this study focus on simulating the mechanical responses of the rock to account for the role of interaction between the pore fluid and the solid phase of the rock. ...
Article
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Excavation damage zone (EDZ) Grain-based model (GBM) calibration Stress-fracturing of rock Cohesive crack model Stress-dependent permeability a b s t r a c t The objective of this paper is to develop a methodology for calibration of a discrete element grain-based model (GBM) to replicate the hydro-mechanical properties of a brittle rock measured in the laboratory, and to apply the calibrated model to simulating the formation of excavation damage zone (EDZ) around underground excavations. Firstly, a new cohesive crack model is implemented into the universal distinct element code (UDEC) to control the fracturing behaviour of materials under various loading modes. Next, a methodology for calibration of the components of the UDEC-Voronoi model is discussed. The role of connectivity of induced microcracks on increasing the permeability of laboratory-scale samples is investigated. The calibrated samples are used to investigate the influence of pore fluid pressure on weakening the drained strength of the laboratory-scale rock. The validity of the Terzaghi's effective stress law for the drained peak strength of low-porosity rock is tested by performing a series of biaxial compression test simulations. Finally, the evolution of damage and pore pressure around two unsupported circular tunnels in crystalline granitic rock is studied.
... The timing and location of fragment release observed here implies a failure mechanism that evolves progressively, such as the time-dependent growth of microfractures and breakage of rock bridges (Kemeny, 2005). Although here we only capture the spatial and temporal patterns of rockfalls that occur as a consequence of the underlying failure process, our findings concur with forensic studies of rockfall failure mechanisms from these cliffs, whereby a combination of discontinuities and rock bridge breakage are the primary rockfall release mechanisms (de Vilder et al., 2017). ...
Article
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Rockfalls commonly exhibit power law volume‐frequency distributions, where fewer large events are observed relative to more numerous small events. Within most inventories, the smallest rockfalls are the most difficult to detect and so may not be adequately represented. A primary challenge occurs when neighboring events within a single monitoring interval are recorded as one, producing ambiguity in event location, timing, volume, and frequency. Identifying measurement intervals that minimize these uncertainties is therefore essential. To address this, we use an hourly data set comprising 8,987 3‐D point clouds of a cliff that experiences frequent rockfalls. Multiple rockfall inventories are derived from this data set using change detections for the same 10‐month period, but over different monitoring intervals. The power law describing the probability distribution of rockfall volumes is highly sensitive to monitoring interval. The exponent, β , is stable for intervals >12 hr but increases nonlinearly over progressively short timescales. This change is manifested as an increase in observed rockfall numbers, from 1.4 × 10 ³ (30 day intervals) to 1.4 × 10 ⁴ (1 hr intervals), and a threefold reduction in mean rockfall volume. When the monitoring interval exceeds 4 hr, the geometry of detected rockfalls becomes increasingly similar to that of blocks defined by rock mass structure. This behavior change reveals a time‐dependent component to rockfall occurrence, where smaller rockfalls (identifiable from more frequent monitoring) are more sensitive to progressive deformation of the rock mass. Acquiring complete inventories and attributing discrete controls over rockfall occurrence may therefore only be achievable with high‐frequency monitoring, dependent upon local lithology.
Chapter
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In literature, the time-dependent mechanical behaviour of geomaterials is well established and explained in the light of various phenomena, ranging from purely mechanical processes, evolving with time, to those resulting from thermo/hydro/chemo/me-chanical coupling. This chapter provides a concise overview of the most prominent constitutive modelling approaches, developed in recent decades, incorporating time variable and based on rate-dependent elastic-plasticity.
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Shear failure of rock bridges is an important process in geological phenomena, including landslides and earthquakes. However, the progressive failure of natural rock bridges has not yet been fully understood. In this work, we carried out direct shearing experiments on both granite and marble rock bridges, and applied acoustic emission (AE) monitoring throughout the experiments. With the mechanical curves and the evolution of AE activity (including AE energy rate and b value), the failure of rock bridges can be divided into three pre-failure phases and one ultimate failure phases. We analyzed the effects of normal stress and lithology on the pre-failure phases. We noted that with the increasing of normal stress, the length of stable cracking phase decreases and the length of unstable cracking phase slightly increases, except for marble rock bridges at high normal stress, which maintains a great proportion of stable cracking phase that possibly results from the great off-fault damage. Increasing normal stress also suppresses the dilation of granite rock bridges, but has a different effect on marble rock bridges, which also suggests the effect of lithology on failure modes.
Article
Rock bridges are commonly encountered in incipiently jointed rock masses and rock engineering practices, which play a significant role in the stabilization of rock masses. Although the effect of joint length, as a key influence factor on mechanical properties of rock bridges, has been extensively studied, the influence of joint dip angle and aperture on fractured rock properties has rarely been investigated. In this study, we carried out an investigation on a new conceptual model of fractured rock bridges, based on the evaluation of a pre-existing transfixion joint in the middle and two rock bridges of equal length on both sides. The specimens with four different joint dip angles and apertures were investigated using uniaxial compression-shear experiments, in which the surface deformation was monitored by the particle image velocimetry (PIV) method. The experimental results demonstrated that the maximum failure load of rock bridges decreased as the joint aperture and dip angle increased, and can be described using a linear and a first-order exponential decay functions, respectively. The rock bridge failure along the projection line of the pre-existing transfixion joint, a dense displacement contours region, was formed along with the formation of new fractures. It was found that the tensile failure effect increases as the aperture increases, and compression failure effect increases with the fracture dip angle decrease. A new method to test rock cohesive c and internal friction angle φ is also provided based on the new conceptual model of artificial rock bridges. The present study helps improve our knowledge of the effect of rock bridges and will contribute to the development of shear strength criteria and test methods.
Article
In this study, the effect of low normal stress levels on shear behavior of jointed samples was investigated using discrete element method (DEM). Based on the experimental design, 50 jointed samples with different joint persistency (JP) were modeled under low normal loads. The results of numerical modeling showed that the effectiveness of the normal load is greater in the post-peak and enters operation after the failure point. Moreover, increasing the normal stress on the shear surface changes the behavior from brittle to ductile. Standard deviations of shear strengths showed that changes in normal stress at higher JP have less effect on the shear strength of jointed samples. Also, for a constant JP, the shear stiffness of the sample increases with normal stress, and increasing the JP does not have a significant effect on the shear stiffness of the sample. Increase in JP at a constant normal stress level decreases the sample dilation. Considering the crack formation in a constant JP, it was observed that up to the peak shear stress, the number of cracks increases with increasing the normal stress, and this is not continuous after the peak and shows different variations. The results showed that with decreasing the JP, the relative growth of cracks in the vertical direction decreased and more cracks were created in the direction of the shear plane. The propagation and coalescence of cracks and the creation of a failure surface can also cause stress relaxation, and the magnitude of the contact force between the particles depends on this issue.
Article
Slope rock mass containing locked segments is susceptible to freeze–thaw (F-T) weathering. It can result in slope instability and serious geological hazards. This paper conducts mechanical analysis and F-T tests to investigate the failure mechanism of the rock slope with locked segment subjected to F-T cycles. Using theoretical analysis, the cusp catastrophe prediction model for the failure of locked slope in cold regions is established, and the catastrophe eigenvalues are derived. The results show that the stability of the locked slope is related to the stiffness ratio considering the F-T treatment. As the F-T cycles increase, the damage variable increases in the form of a power function. In addition, a threshold of the number of F-T cycles exists for the degradation of locked slope caused by F-T weathering. By substituting the damage variables of the F-T cycles obtained from the experiment into the developed cusp catastrophe model, it can be deduced that the locked slope with 45° creep-slipping segment is the most sensitive to the effects of F-T degradation, and the most prone to landslides. Finally, the frost resistance is the strongest for the locked slope with 15° creep-slipping segment.
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The concept of joint persistence has been widely used to study the mechanics and failure processes of rock masses benefitting from the simplicity of statistical linear weighing of the discontinuity. Nevertheless, this term neglects the scale effects of rock bridges, meaning that the same joint persistence may refer to different numbers and spacings of rock bridges, leading to erroneous equivalent rock mass responses. To fill in this gap, an intact rock bridge was dispersed as multi rock bridges while maintaining a constant joint persistence, subjected to direct shear by conducting numerical simulations employing Universal Distinct Element Code (UDEC). In this way, scale effects of rock bridges were investigated from the perspective of load-displacement curves, stress and displacement fields, crack propagations and AE characterizations. Results revealed that the shear resistance and the area and value of stress-concentration decreased with increasing dispersion. Furthermore, uneven distribution of displacement fields in an arc manner moving and degrading away from the load was first observed, indicating the sequential failure of multi rock bridges. It was also found that the propagation of wing cracks was insensitive to scale, while the asperity of macro shear fracture mainly formed by secondary cracks decreased with increasing dispersion. In addition, increasing dispersion of rock bridges would overlap the failure precursors identified by intense AE activities. Based on the abovementioned results, we evaluated existing methods to characterize the joint persistence, and a threshold was observed to possibly define a rock bridge.
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When a flat steel with double cracks fails, the stress fields between different cracks will interact. The area between the cracks, that is, the steel bridge area, will be penetrated. This paper embeds the strain strength criterion into the discrete element numerical simulation method, and uses the block discrete element software UDEC to simulate the crack propagation and penetration in the steel bridge region of the prefabricated double-crack flat steel sample. Numerical simulation results show that there are four basic penetration modes in the double-crack steel sample during compression: (1) Discontinuous mode, which is characterized by no penetration between cracks, and the two pre-crack tip wing cracks independently expand; (2) Shear penetration mode, which is characterized by shear cracks penetrating the steel bridge. The principal stress field and shear stress field are concentrated in the steel bridge area, but the shear stress plays a leading role in penetration; (3) Tensile penetration mode, its characteristics: In order to penetrate the steel bridge with tensile cracks, the principal stress field is highly concentrated accumulated and nucleated in the area of the steel bridge, and the steel bridge penetration is instantaneous; The process occurs after the peak intensity.
Article
A detailed understanding of the failure characteristics of infilled jointed rock is a key concern in underground engineering and is critical to the design, construction and maintenance of relevant projects. In this paper, uniaxial compression tests were performed to investigate the effect of the joint arrangement (different rock bridge angles) on the strength and crack propagation of red sandstone containing a set of preexisting infilled flaws of the same sizes and angles, while the crack fracturing process was observed by AE and strain monitoring. When the angle between the rock bridge and loading stress was less than 24°, the rock mass failure form was tensile failure with some localized shear failure occurring in the rock bridge damaged by crack penetration, leading to an overall decrease in the carrying capacity. The turning points of the strain and AE signal were clearly observed to be caused by the initiation and propagation of cracks, and the energy consumed by the initiation of shear cracks was greater than that of tensile cracks. The study was further conducted using the fracture mechanics numerical code FRACOD to investigate the crack propagation law and failure mechanism under different loading stress conditions. Simulation results from three 2D similar models showed that the percentage of open fractures decreased, but slipping increased; in addition, the total length of the fractures was greatly reduced with increasing confining stress. These results are important and valuable for understanding the crack mechanism of rock engineering in deep underground mining excavations.
Article
Joints are the boundary that controls slope failure of rock slope. Most of the joints are non-persistent and embedded in the rock slope. The creep mechanism of non-persistent joints is of great significance to reveal the creep deformation behavior of the slope over time. However, the embedded non-persistent joints are difficult to sample and to replicate uniformly in large numbers. In the study, a modeling method for embedded non-persistent joints is proposed, and the shear creep test on embedded non-persistent joints was conducted. Based on uniaxial compression testing and shear creep testing, the phase characteristics of creep testing are analyzed, a nonlinear viscous acceleration element and damage variable suitable for structural surfaces are introduced, and a shear-creep-damage constitutive model for non-persistent joints is established. Three-dimensional shear creep constitutive equation is derived using the Laplace transform. Furthermore, Levenberg-Marquardt (L-M) algorithm and global optimization method are used to identify the creep curves and solve the model parameters. After identification and comparison of experimental results and model fitting results, the new constitutive model can clearly reflect the creep characteristics of the non-persistent joints, which provide reference for deformation characteristics of non-persistent joint rock slopes.
Article
Subcritical crack growth strongly influences the mechanical behavior of rock and the precursory phase of geohazards and catastrophic failure. In earlier studies, indirect measuring methods were used to investigate the subcritical crack growth behavior of rock materials. However, these methods cannot fully reflect the whole process of subcritical crack growth of geomaterials. Therefore, in this study, a new method (DC voltage fluctuation method) was developed which can monitor the whole process of crack growth and measure the crack growth rate in real time. This method is based on the monitoring principle of change in voltage caused by the change in resistance. Then, the whole processes of Mode I and Mode II subcritical crack growth of gypsum specimen were monitored in real time by the self-designed fracture strain gauge, which consists of 10 breakable resistance wires, and a DC voltage signal monitor. Furthermore, using the measured crack growth rates and the stress intensity factors of varying crack path lengths, the parameters of the modified Charles model were fitted. The results show that: (1) the subcritical crack growth process mainly includes three stages: cracking latent period (primary stage), steady-state crack growth stage (secondary stage), and accelerated crack growth stage (tertiary stage). The cracking latent period lasts for the largest proportion of the entire fracture process duration. The duration of each stage decreases gradually with increasing applied load. (2) In the steady-state crack growth stage, both Mode I and Mode II crack growth rates increase with increasing applied load. However, the crack growth rates in the accelerated stage are basically the same with increasing applied load. When a specimen is subjected to a given constant applied load, the subcritical crack growth rate of Mode II is higher than that of Mode I in the secondary and tertiary stages. (3) The parameters A and n of the subcritical crack growth model (modified Charles model) (secondary stage) increase with increasing external applied load. The parameters are closely associated with the size of fracture process zone at the crack tip. The results of this study can provide a deeper insight into the macroscopic failure of rock, and also provide the parameters for the time-dependent damage evolutional process of underground constructions
Article
Shear creep is one of the most important mechanical behaviors of rock discontinuities. The creep mechanism and prediction of starting point of the accelerating creep stage are vital for establishing the creep model and predicting creep failure. In this study, a series of multi-step creep tests are conducted. The three creep stages of shear creep tests are investigated in detail, and a method for predicting the accelerating creep stage is proposed. Distinct nonlinear and local fluctuations caused by cracking are observed in the creep curve. To describe the transition creep stage and steady creep stage, an empirical creep model is established, and the creep characteristics related to the joint roughness coefficient (JRC) and the normal stress are explored in detail using the model’s parameters. The creep process can be described as involving the JRC resistance weakening and frictional resistance compensation, and a model also established to describe this process. The frictional resistance cannot compensate for the loss of JRC resistance; consequently, creep failure occurs. The starting point of the accelerating creep stage can be predicted by combining the JRC weakening and frictional mobilization model and the empirical creep model. A new method for determining long-term strength is also proposed based on the relationships between the starting point creep deformation and the shear creep stress.
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The data base used in developing the Barton-Bandis joint model is reviewed. It is shown how tilt testing to obtain JRC is extrapolated, both in terms of stress-level and block-size. Field measurement of JRC is demonstrated and a relationship with Jr in the Q-system is shown. Constitutive modelling of shear stress-displacement, dilation and shear reversal are also described.
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Rupture in individual earthquakes apparently is limited to regions between bends in faults. This is illustrated for eight events that have occurred since 1966. A model based on geometric concepts describes why this is so and clarifies earlier ideas of ``asperities'' and ``barriers'' used to explain earthquake initiation and termination processes. Because of their importance in the rupture process, bend zones should be monitored for precursory effects.
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The time-dependent properties of ceramic materials such as rocks depend both on preexisting cracks and chemical properties acting at their tips. We have examined the direct effect of chemical processes on the growth of a crack population by carrying out triaxial flow-through compression tests on Locharbriggs sandstone. The tests were carried out at temperatures of 25-80°C and at strain rates ranging from 10-5 to 10-8 s-1 under constant stress rate loading. The exit pore fluid was analyzed after the tests for the concentration of dissolved ions and acoustic emission was monitored in real time throughout the tests. The exit pore fluid silica concentration and microcrack damage derived from the acoustic emission (AE) data both exhibited an exponential increase during the strain hardening phase of deformation. Damage parameters inferred from the AE data predict the stress-strain curves adequately, or at least up to the point of strong microcrack coalescence. The damage parameters and silica signal were strongly correlated by a power law relationship. The observed environment and strain rate dependence of mechanical properties can hence be attributed uniquely to time-dependent crack growth by the stress corrosion mechanism.
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A dilatational step-over between the right-lateral Hayward and Rodgers Creek faults lies beneath San Pablo Bay in the San Francisco Bay area. A key seismic hazard issue is whether an earthquake on one of the faults could rupture through the step-over, enhancing its maximum possible magnitude. If ruptures are terminated at the step-over, then another important issue is how strain transfers through the step. We developed a combined seismic reflection and refraction cross section across south San Pablo Bay and found that the Hayward and Rodgers Creek faults converge to within 4 km of one another near the surface, about 2 km closer than previously thought. Interpretation of potential field data from San Pablo Bay indicated a low likelihood of strike-slip transfer faults connecting the Hayward and Rodgers Creek faults. Numerical simulations suggest that it is possible for a rupture to jump across a 4-km fault gap, although special stressing conditions are probably required (e.g., Harris and Day, 1993, 1999). Slip on the Hayward and Rodgers Creek faults is building an extensional pull-apart basin that could contain hazardous normal faults. We investigated strain in the pull-apart using a finite-element model and calculated a � 0.02-MPa/yr differential stressing rate in the step-over on a least-principal-stress orientation nearly parallel to the strike-slip faults where they overlap. A 1- to 10- MPa stress-drop extensional earthquake is expected on normal faults oriented per- pendicular to the strike-slip faults every 50-500 years. The last such earthquake might have been the 1898 M 6.0-6.5 shock in San Pablo Bay that apparently pro- duced a small tsunami. Historical hydrographic surveys gathered before and after 1898 indicate abnormal subsidence of the bay floor within the step-over, possibly related to the earthquake. We used a hydrodynamic model to show that a dip-slip mechanism in north San Pablo Bay is the most likely 1898 rupture scenario to have caused the tsunami. While we find no strike-slip transfer fault between the Hayward and Rodgers Creek faults, a normal-fault link could enable through-going segmented rupture of both strike-slip faults and may pose an independent hazard of M � 6 earthquakes like the 1898 event.
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A semiempirical constitutive law is presented for the brittle deformation of intact Westerly granite. The law can be extended to larger displacements, dominated by localized deformation, by including a displacement-weakening break-down region terminating in a frictional sliding regime often described by a rate- and state-dependent constitutive law. The intact deformation law, based on an Arrhenius type rate equation, relates inelastic strain rate to confining pressure Pc, differential stress σΔ, inelastic strain εi, and temperature T. The basic form of the law for deformation prior to fault nucleation is In ε̇i = c - (E*/RT) + (σΔ/aσo)sin-α(πε i/2εo) where σo and εo are normalization constants (dependent on confining pressure), a is rate sensitivity of stress, and α is a shape parameter. At room temperature, eight experimentally determined coefficients are needed to fully describe the stress-strain-strain rate response for Westerly granite from initial loading to failure. Temperature dependence requires apparent activation energy (E* ∼ 90 kJ/mol) and one additional experimentally determined coefficient. The similarity between the prefailure constitutive law for intact rock and the rate- and state-dependent friction laws for frictional sliding on fracture surfaces suggests a close connection between these brittle phenomena.
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Discontinuity persistence has a major effect on rock mass resistance (strength) but, as direct mapping of discontinuities internal to a rock mass is not possible, persistence is a difficult parameter to measure. As a result, the conservative approach of assuming full persistence is often taken. In this paper a method is developed for relating rock mass stability and hence persistence to the geometry and spatial variability of discontinuities. The method is applied to slope stability calculations in which the probability of failure is related to discontinuity data, as obtained in joint surveys. The complete method makes use of dynamic programming and simulation, but a closed form expression satisfactory for most purposes is also presented.
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Palaeoseismic studies over the past several years have indicated that segments of certain major faults tend to rupture at fairly regular intervals in characteristic earthquakes of about the same size1. This implies the presence of local structural controls which govern the nucleation and stopping of ruptures. Understanding rupture arrest is important, not only because it governs the size of characteristic earthquakes, but also because deceleration of ruptures results in the radiation of high-frequency energy leading to strong ground motion2. I show here that rapid opening of linking extensional fracture systems to allow passage of earthquake ruptures through dilational fault jogs in fluid-saturated crusts is opposed by transient suctional forces induced near the rupture tips3. Rupture arrest may then be followed by delayed slip transfer as fluid pressures re-equilibrate by diffusion.
Article
This chapter highlights a few aspects of the persistence/connectivity problem and their possible solutions. Specifically, geometric descriptions of discontinuity patterns and of the associated connectivity are discussed first. A part of this discussion involves the representation of connectivity with simple measures. Brief comments are made on the appropriate consideration of persistence and other kinematic aspects in stability analysis. The second major issue discussed is that of interaction between intact rock and discontinuities. -from Author
Article
Effects of the strain rate and pressure on various brittle properties of granite under compressional loading are studied experimentally. Granite specimens were tested to failure under various constant strain rates at confining pressures of 0. 1 to 200 MPa. The strain rates in these tests varied from 10** minus **4 to 10** minus **8 s** minus **1. The results show that the strength of granite decreases linearly as the logarithm of the strain rate decreases, and that the strain-rate dependence on the strength is enhanced at high confining pressures. The dilatant strain and elastic wave velocity variations with stress were found to be independent of the strain rate if the stress is normalized by the strength. Some of the time-dependent properties are explained by a theory based on the concept of subcritical stress-corrosion cracking, but the theory does not provide reasonable explanations of the variation of acoustic emission rate with stress and the variation of strain with stress at the stage immediately before fracture.
Article
A comprehensive survey of the available experimental data on subcritical crack growth in geological materials is presented. The available data are then extrapolated to conditions of interest in the earth's crust. For variables whose influence on subcritical cracking of rocks has not been studied experimentally, schematics of probable trends are presented based upon work with ceramics and upon theoretical perspectives. The vast majority of experimental studies of subcritical cracking in geological materials have been made using the double torsion testing method. Because of this, a discussion of the method is presented in the appendix.
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Fault traces consist of numerous discrete segments, commonly arranged as echelon arrays. In some cases, discontinuities influence the distribution of slip and seismicity along faults. To analyze fault segments, we derive a two-dimensional solution for any number of nonintersecting cracks arbitrarily located in a homogeneous elastic material. The solution includes the elastic interaction between cracks. Crack surfaces are assumed to stick or slip according to a linear friction law. For an array of echelon cracks the ratio of maximum slip to array length significantly underestimates the difference between the driving stress and frictional resistance. The ratio of maximum slip to crack length slightly overestimates this difference. Stress distributions near right- and left-stepping echelon discontinuities differ in two important ways. For right lateral shear and left-stepping cracks, normal tractions on the overlapped crack ends increase and inhibit frictional sliding, whereas for right-stepping cracks, normal tractions decrease and facilitate sliding. The mean compressive stress between right-stepping cracks also decreases and promotes the formation of secondary fractures, which tend to link the cracks and allow slip to be transferred through the discontinuity. For left-stepping cracks the mean stress increases; secondary fracturing is more restricted and tends not to link the cracks. Earthquake swarms and aftershocks cluster near right steps along right lateral faults. Our results suggest that left steps store elastic strain energy and may be sites of large earthquakes. Opposite behavior results if the sense of shear is left lateral.
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The behavioral modes to which a rock slope is susceptible are many and complex. This article discusses a long but not exhaustive list of common failure styles, highlighting observable characteristics that distinguish one from another. Slopes in both strong and weak rock masses are considered. Principles are stated to explain how and why different failure modes develop in different rocks. The discussion is illustrated with examples of diverse failure modes in foliated metamorphic rocks developed in the walls of an eroded spillway runout.
Article
Quasi-state propagation and dilation of macroscopic mode I cracks is considered as a source of elastic strain in crustal rocks undergoing extensional deformations. The approach here is to first characterize the propagation of a single dilating crack and then to consider how a large two-dimensional array of similar, parallel crack accomodates an applied deformation. The driving force for propagation of each crack Gi, is found as a function of the applied strain and the instantaneous crack lengths ci. The rate of crack propagation is taken to be a function of the instantaneous crack extension force ci=c(Gj). A specific propagation rate extension force relation is developed that both fits the available experimental data and has vanishing propagation rate at a finite value of G. From these results a specific internal state variable constitutive law is derived relating uniaxial stress to the instantaneous uniaxial strain and crack density. For strains less than those necessary to cause crack propagation, the rock is predicted to behave like a linear elastic solid. Following the onset of propagation, the average stress may continue to increase if the strain rate accomodated by crack growth is slow in comparison to the applied strain rate. For constant strain rate boundary conditions the solutions exhibit strain softening, leading to peak stress and then a stress decrease. The peak stress increases nearly logarithmically with increasing applied strain rate. The response to unloading depends strongly on whether or not cracks heal. Unloading that follows sealing of the cracks with mineral precipitates causes the rock to undergo a pernmanent nonrecoverable strain.
Article
In this paper, a fracture mechanics model is developed to illustrate the importance of time-dependence for brittle fractured rock. In particular a model is developed for the time-dependent degradation of rock joint cohesion. Degradation of joint cohesion is modeled as the time-dependent breaking of intact patches or rock bridges along the joint surface. A fracture mechanics model is developed utilizing subcritical crack growth, which results in a closed-form solution for joint cohesion as a function of time. As an example, a rock block containing rock bridges subjected to plane sliding is analyzed. The cohesion is found to continually decrease, at first slowly and then more rapidly. At a particular value of time the cohesion reduces to value that results in slope instability. A second example is given where variations in some of the material parameters are assumed. A probabilistic slope analysis is conducted, and the probability of failure as a function of time is predicted. The probability of failure is found to increase with time, from an initial value of 5% to a value at 100 years of over 40%. These examples show the importance of being able to predict the time-dependent behavior of a rock mass containing discontinuities, even for relatively short-term rock structures.
Article
Water vapor corrosion of a simple soda‐lime glass has been studied in regard to its effect on static fatigue of the same glass. A mechanism of dissolution has been proposed in which alkali ion self‐diffusion controls the initial steps of water corrosion and leads to breakdown of the glass network. Since experiments show that an expansion of a glass network enhances corrosion rate, it is postulated that asymmetrical contitions of expansion around a surface flaw, brought about by applied stress, could lead to growth of the flaw in a preferential direction to bring about delayed failure.
Article
Barton, N., 1973. Review of a new shear-strength criterion for rock joints. Eng. Geol., 7: 287–332.The surface roughness of rock joints depends on their mode of origin, and on the mineralogy of the rock. Amongst the roughest joints will be those that formed in intrusive rocks in a tensile brittle manner, and amongst the smoothest the planar cleavage surface in slates. The range of friction angles exhibited by this spectrum will vary from about 75° or 80° down to 20° or 25°, the maximum values being very dependent on the normal stress, due to the strongly curved nature of the peak strength envelopes for rough unfilled joints.Direct shear tests performed on model tension fractures have provided a very realistic picture of the behaviour of unfilled joints at the roughest end of the joint spectrum. The peak shear strength of rough—undulating joints such as tension surfaces can now be predicted with acceptable accuracy from a knowledge of only one parameter, namely the effective joint wall compressive strength or JCS value. For an unweathered joint this will be simply the unconfined compression strength of the unweathered rock. However in most cases joint walls will be weathered to some degree. Methods of estimating the strength of the weathered rock are discussed. The predicted values of shear strength compare favourably with experimental results reported in the literature, both for weathered and unweathered rough joints.The shear strength of unfilled joints of intermediate roughness presents a problem since at present there is insufficient detailed reporting of test results. In an effort to remedy this situation, a simple roughness classification method has been devised which has a sliding scale of roughness. The curvature of the proposed strength envelopes reduces as the roughness coefficient reduces, and also varies with the strength of the weathered joint wall or unweathered rock, whichever is relevant. Values of the Coulomb parameters c and Φ fitted to the curves between the commonly used normal stress range of 5–20 kg/cm2 appear to agree quite closely with experimental results.The presence of water is found in practice to reduce the shear strength of rough unfilled joints but hardly to affect the strength of planar surfaces. This surprising experimental result is also predicted by the proposed criterion for peak strength. The shear strength depends on the compressive strength which is itself reduced by the presence of water. The sliding scale of roughness incorporates a reduced contribution from the compressive strength as the joint roughness reduces. Based on the same model, it is possible to draw an interesting analogy between the effects of weathering, saturation, time to failure, and scale, on the shear strength of non-planar joints. Increasing these parameters causes a reduction in the compressive strength of the rock, and hence a reduction in the peak shear strength. Rough—undulating joints are most affected and smooth—nearly planar joints least of all.
Article
Scanning electron microscope (SEM) observations were made on two suites of ion-thinned samples deformed at 400 MPa, 350°C and 250 MPa, 150°C. The latter suite includes 5 samples retrieved at different stages in the post-failure region. The pre-failure samples in both suites show numerous transgranular cracks at low angles (<15°) to maximum compression direction. We did, however, also observe many high-angle(/lt;15°) transgranular cracks.The deformation in post-failure samples is localized. Typically a localized zone is comprised of a number of almost coplanar cracks inclined at angles of 15°–45° to the maximum compression direction. Elsewhere, axial crack arrays extend over entire grains forming slender columns. In plagioclase, complex crack networks link up with the pores. The crack arrays and networks act as ‘barriers’ to the joining up of the inclined cracks to form a shear zone. A through-going fault is formed by coalescence of arrays and networks with the inclined cracks, accompanied by extensive crushing into fine-grained gouge.Elastic anisotropy and pore, as well as grain scale inhomogeneity, can influence the development of stress-induced cracks. Consequently, the four minerals in Westerly granite behave differently during faulting, the failure mechanisms being dependent on both mineralogy and grain orientation.
Article
Time dependency in rock deformation under compression is modelled by considering an elastic body containing cracks that grow under compressive stresses due to sub-critical crack growth. This is considered the prime mechanism for the time-dependent deformation of brittle rocks at low temperatures. The growth of cracks under compressive stresses is formulated using the “sliding crack” model, which considers extensile crack growth due to stress concentrations around pre-existing flaws. Subcritical crack growt is included into the sliding crack model by utilizing the empirical Charles power law relation between crack velocity and the crack tip stress intensity factor. The model is able to predict the dependence of the stress-strain curve on the applied strain rate, and agrees extremely well with experimental data. Also, the model is able to predict the occurrence of both transient and tertiary creep. The transient creep behavior is derived in closed-form, and is found to give creep that depends on the logarithm of time, which is similar to many empirical formulae for creep in brittle rocks. Tertiary creep in the model is due to crack interaction, and is found to occur at a critical value of crack density. This allows time-to-failure predictions to be made, which could be useful for underground structures required to remain open for long periods of time.
Article
Fracture coalescence, which plays an important role in the behavior of brittle materials, is investigated by loading pre-fractured specimens of gypsum, used as a rock model material, in uniaxial and biaxial compression. Several new phenomena and their dependence on geometry and other conditions are observed. The specimens have two pre-existing fractures or flaws that are arranged in different geometries, and that can be either open or closed. Two different test series are performed with these flaw geometries, one under uniaxial loading and one with biaxial loading in which confining stresses of 2.5, 5.0, 7.5 and 10 MPa are applied. As the vertical (axial) load is increased, new cracks emanate from the flaws and eventually coalesce. Flaw slippage, wing crack initiation, secondary crack initiation, crack coalescence, and failure are observed. Two types of cracks occur: wing cracks, which are tensile cracks, and secondary cracks which initiate as shear cracks in a plane roughly co-planar with the flaw. The secondary cracks usually propagate as shear cracks in the same plane but, depending on the geometry, they also propagate out of plane as either tensile or shear cracks. The wing cracks initiate at the flaw tips for uniaxial or low confinement biaxial conditions but move to the middle of the flaw and disappear completely for higher confining stresses. Three types of coalescence, which depend on the geometry of the flaws and to some extent on stress conditions, occur; they can be distinguished by different combinations of wing cracks and secondary cracks. For closed flaw specimens, at least partial debonding and slippage of the flaws is required prior to initiation of a crack. In uniaxial compression coalescence and failure occur simultaneously, while failure in biaxial compression occurs after coalescence.
Article
A new testing method called punch-through shear test for measurement of Mode II fracture toughness, KIIC, of rock is introduced. Results from a finite element modelling (FEM) and a series of laboratory tests on limestone, marble and granite are presented. Core samples with 50 mm diameter are cut to length equal to diameter. Circular notches are drilled to different depths at both ends leaving an intact portion in the centre of the core. The sample is subjected to different confining pressures up to 70 MPa and an axial load is applied to punch through the central portion of the core. KIIC is calculated from a displacement gradient approach using FEM, assuming linear elasticity to be valid according to the fracture breakdown zone model by Cowie and Scholz. Results from testing show that KIIC increases with increasing confining pressure and in the order of limestone, marble and granite. At confining pressures higher than 30 MPa the Mode II fracture toughness approaches a constant value. Fracture initiation and propagation differ among the three rock types where grain size is found to have a strong influence on the mechanism of microfracturing and failure. It is suggested that data of KIIC should be presented for high confining pressures as large confining pressures enhance the appearance of shear fractures.
Probabilistic key block analysis at Yucca Mountain
  • D C Kicker
  • M Lin
  • J M Kemeny
  • C A Stone
Kicker DC, Lin M, Kemeny JM, Stone CA. Probabilistic key block analysis at Yucca Mountain. Proceedings of the fourth North American rock mechanics symposium, Seattle, WA. Rotterdam: A.A. Balkema. 2000. p.1249–56.
Universal Distinct Element Code (UDEC) Version 3.1. Minneapolis: Itasca Consulting Group
  • Itasca
Itasca. Universal Distinct Element Code (UDEC) Version 3.1. Minneapolis: Itasca Consulting Group, Inc.; 2003.
Large scale slope stability in open pit mining-a review
  • J Sjoberg
Sjoberg J. Large scale slope stability in open pit mining—a review. Technical Report 1996:10T, Lulea University of Technology, Division of Rock Mechanics, Lulea, Sweden; 1996. p. 229.
Shear box testing and modeling of joint bridges
  • T Savilahti
  • E Nordlund
  • O Stephansson
Savilahti T, Nordlund E, Stephansson O. Shear box testing and modeling of joint bridges. In: Proceedings of the International Symposium on Rock Joints, Loen, June 4–6. 1990, pp. 295–300.
UDEC mesh for time-dependent drift degradation with and without thermal loading. Fig. 9. Plot of displacement vectors around the excavation at t=0, no thermal
  • Article In
  • Fig
ARTICLE IN PRESS Fig. 8. UDEC mesh for time-dependent drift degradation with and without thermal loading. Fig. 9. Plot of displacement vectors around the excavation at t=0, no thermal. J. Kemeny / International Journal of Rock Mechanics & Mining Sciences 42 (2005) 35–46 References
Size effect of the mode II fracture toughness of rock Rock mechanics and industry. Balkema
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