A simple failure criterion for rough joints and compound shear surfaces

The subject under investigation is the strength of a single shear plane which exhibits a regular, asymmetric roughness pattern. In the shear direction the asperities are so steeply inclined that the joint becomes mechanically non-effective with the result that the asperities are sheared off. Against the shear direction the asperities are only gently inclined. It is shown that this particular roughness pattern is of some general importance in geomechanics (examples: unconfined compression test; shear plane with secondary fractures).

Simple analytical considerations allow the formulation of a shear criterion, which is dependent on friction angle ø_m and cohesionc_m of the intact rock and on the inclination γ of the gently inclined parts of the asperities which are dipping against the shear direction. In the Mohr-diagram the criterion results in envelopes which converge at high normal stresses against the envelope of intact rock. Furthermore, the criterion expresses that both the slope of the envelopes and the dilation angle continuously decrease with increasing normal stress. Therefore the criterion adequately describes features which are regarded as most important when shearing rough joints or compound shear surfaces.     

Friction and degradation of rock joint surfaces under shear loads

The morpho‐mechanical behaviour of one artificial granite joint with hammered surfaces, one artificial regularly undulated joint and one natural schist joint was studied. The hammered granite joints underwent 5 cycles of direct shear under 3 normal stress levels ranging between 0.3 and 4 MPa. The regularly undulated joint underwent 10 cycles of shear under 6 normal stress levels ranging between 0.5 and 5 MPa and the natural schist replicas underwent a monotonics shear under 5 normal stress levels ranging between 0.4 and 2.4 MPa. These direct shear tests were performed using a new computer‐controlled 3D‐shear apparatus. To characterize the morphology evolution of the sheared joints, a laser sensor profilometer was used to perform surface data measurements prior to and after each shear test. Based on a new characterization of joint surface roughness viewed as a combination of primary and secondary roughness and termed by the joint surface roughness, SR_s, one parameter termed ‘joint surface degradation’, D_w, has been defined to quantify the degradation of the sheared joints. Examinations of SR_s and D_w prior to and after shearing indicate that the hammered surfaces are more damaged than the two other surfaces. The peak strength of hammered joint with zero‐dilatancy, therefore, significantly differs from the classical formulation of dilatant joint strength. An attempt has been made to model the peak strength of hammered joint surfaces and dilatant joints with regard to their surface degradation in the course of shearing and two peak strength criteria are proposed. Input parameters are initial morphology and initial surface roughness. For the hammered surfaces, the degradation mechanism is dominant over the phenomenon of dilatancy, whereas for a dilatant joint both mechanisms are present. A comparison between the proposed models and the experimental results indicates a relatively good agreement. In particular, compared to the well‐known shear strength criteria of Ladanyi and Archambault or Saeb, these classical criteria significantly underestimate and overestimate the observed peak strength, respectively, under low and high normal stress levels. In addition and based on our experimental investigations, we put forward a model to predict the evolution of joint morphology and the degree of degradation during the course of shearing. Degradations of the artificial undulated joint and the natural schist joint enable us to verify the proposed model with a relatively good agreement. Finally, the model of Ladanyi and Archambault dealing with the proportion of total joint area sheared through asperities, a_s, once again, tends to underestimate the observed degradation. Copyright © 2001 John Wiley & Sons, Ltd.     

Effects of Cyclic Loading on the Shear Behaviour of Infilled Rock Joints Under Constant Normal Stiffness Conditions

The variation of the shear strength of infilled rock joints under cyclic loading and constant normal stiffness conditions is studied. To simulate the joints, triangular asperities inclined at angles of 9.5° and 18.5° to the shear movement were cast using high-strength gypsum plaster and infilled with clayey sand. These joints were sheared cyclically under constant normal stiffness conditions. It was found that, for a particular normal stiffness, the shear strength is a function of the initial normal stress, initial asperity angle, joint surface friction angle, infill thickness, infill friction angle, loading direction and number of loading cycles. Based on the experimental results, a mathematical model is proposed to evaluate the shear strength of infilled rock joints in cyclic loading conditions. The proposed model takes into consideration different initial asperity angles, initial normal stresses and ratios of infill thickness to asperity height.     

The Influence of Shearing Velocity on Shear Behavior of Artificial Joints

In this paper, the effects of shear velocity on the shearing behavior of artificial joints have been studied at different normal stress levels. Here, artificial joints with planar and rough surfaces were prepared with the plaster (simulating soft rock joints) and concrete (medium-hard rock joints) materials. The rough joints had triangular shaped asperities with 10° and 20° inclination angles. Direct shear tests were performed on these joints under various shear velocities in the range of 0.3–30 mm/min. The planar plaster–plaster and planer concrete–concrete joints were sheared at three levels of normal stress under constant normal load boundary condition. Also, the rough plaster–plaster and concrete–concrete joints were sheared at one level of normal stress under constant normal stiffness boundary condition. The results of the shear tests show that the shearing parameters of joints, such as shear strength, shear stiffness and friction angle, are related to the shear velocity. Shear strength of planar and rough plaster–plaster joints were decreased when the shear velocity was increased. Shear strength of concrete joints, except for rough joints with 10° inclination, increased with increasing shear velocity. Regardless of the normal stress level, shear stiffness of both planar plaster–plaster and concrete–concrete joints were decreased when the shear velocity was increased.     

Analytical modelling of the shear behaviour of rock joints with progressive degradation of two-order roughness

We present an analytical model for the shear behaviour of rock joints with progressive degradation of two-order asperities including waviness and unevenness. Critical waviness and critical unevenness are used to respectively represent the mechanical involvements of waviness and unevenness during shear. The degradation process of two-order asperities are predicted by considering the stepwise relationship among dilation angle, sheared and unsheared asperity areas, and plastic tangential work. The dilation angle of each asperity decreases as plastic tangential work accumulates. The progressive degradation transiting from critical unevenness to critical waviness is realised through examining the dilation angle and the unsheared area of critical unevenness. The model's predictions are compared with the experimental data from direct shear tests on both regular- and irregular-shaped joints. Good agreement between analytical and experimental curves demonstrate the credence of the proposed model. Therefore, the model, after implemented in finite and discrete element codes, is practicable for the stability assessment of rock-engineering structures.     

Contact mechanism of a rock fracture subjected to normal loading and its impact on fast closure behavior during initial stage of fluid flow experiment

Fast closure of rock fractures has been commonly observed in the initial stage of fluid flow experiments at environmental temperatures under low or moderate normal stresses. To fully understand the mechanisms that drive this fast closure, the evolution of local stresses acting on contacting asperities on the fracture surfaces prior to fluid flow tests needs to be evaluated. In this study, we modeled numerically the asperity deformation and failure processes during initial normal loading, by adopting both elastic and elastic–plastic deformation models for the asperities on a real rock fracture with measured surface topography data, and estimated their impact on initial conditions for fluid flow test performed under laboratory conditions. Compared with the previous models that simulate the normal contact of a fracture as the approach of two rigid surfaces without deformations, our models of deformable asperities yielded smaller contact areas and higher stresses on contacting asperities at a given normal stress or normal displacement. The results show that the calculated local stresses were concentrated on the contacts of a few major asperities, resulting in crushing of asperity tips. With these higher contact stresses, however, the predicted closure rates by pressure solution are still several orders of magnitude lower than that of the experimental measurements at the initial stage of fluid flow test. This indicates that single pressure solution may not likely to be the principal compaction mechanism for this fast closure, and that the damages on contacting asperities that occur during the initial normal loading stage may play an important role. Copyright © 2015 John Wiley & Sons, Ltd.     

Shear behaviour of fractured rock as a function of size and shear displacement

This paper presents laboratory results regarding the shear behaviour of an artificial tensile fracture generated in granite. We used a direct shear rig to test fractures of different sizes (from 100 mm to 200 mm) under various shear displacements up to 20 mm and cyclic shear stresses with constant normal stress of 10 MPa. To determine the evolution of surface damage and aperture during shear, cyclic loading was performed at designated shear displacements. These changes in the surfaces topography were measured with a laser profilometer ‘non-contact surface profile measurement system’. In addition, changes were also measured directly by using pressure-sensitive film.

The results showed that the standard deviation (SD) of the initial aperture of the sheared fracture significantly increases with both shear displacement and size, which result in an increase in the non-linearity of the closure curve (since the matedness of the fracture surfaces decreases with shear displacement). Therefore, we concluded that shear dilation is not only governed by the surfaces sliding over each other, but is also strongly influenced by the non-linearity of closure with shear displacement. Furthermore, while the shear stiffness of the fracture during the initial stage decreases with fracture size, it increases with fracture size in the residual stage. This can be attributed to the fact that only small asperities with short wavelengths were mainly damaged by shearing. Moreover the result showed that the damaged zones enlarge and localise with shear displacement, and eventually tend to form perpendicular to the shear displacement.     

Analysis of a deformable fracture in permeable material

The response of deformable fractures to changes in fluid pressure controls phenomena ranging from the flow of fluids near wells to the propagation of hydraulic fractures. We developed an analysis designed to simulate fluid flows in the vicinity of asperity‐supported fractures at rest, or fully open fractures that might be propagating. Transitions between at‐rest and propagating fractures can also be simulated. This is accomplished by defining contact aperture as the aperture when asperities on a closing fracture first make contact. Locations on a fracture where the aperture is less than the contact aperture are loaded by both fluid pressure and effective stress, whereas locations where the aperture exceeds the contact aperture are loaded only by fluid pressure. Fluid pressure and effective stress on the fracture are determined as functions of time by solving equations of continuity in the fracture and matrix, and by matching the global displacements of the fracture walls to the local deformation of asperities. The resulting analysis is implemented in a numerical code that can simulate well tests or hydraulic fracturing operations. Aperture changes during hydraulic well tests can be measured in the field, and the results predicted using this analysis are similar to field observations. The hydraulic fracturing process can be simulated from the inflation of a pre‐existing crack, to the propagation of a fracture, and the closure of the fracture to rest on asperities or proppant. Two‐dimensional, multi‐phase fluid flow in the matrix is included to provide details that are obscured by simplifications of the leakoff process (Carter‐type assumptions) used in many hydraulic fracture models. Execution times are relatively short, so it is practical to implement this code with parameter estimation algorithms to facilitate interpretation of field data. Copyright © 2006 John Wiley & Sons, Ltd.     

天然水镁石纤维的化学松解技术

研究了不同表面活性剂对不同等级水镁石纤维的松解效果，通过对纤维悬浮液叩解度、粘度、纤维表面Zeta电位、纤维混凝土强度等的研究，并经扫描电镜分析，证明了化学松解工艺对水镁石纤维具有较好地劈分作用。表面活性剂种类及用量对纤维的叩解度、纤维的表面电位、悬浮液粘度均有影响，对不同等级纤维的影响有差异。随表面活性剂用量增加，纤维的叩解度、纤维表面的负电荷量、悬浮液的粘度一般均呈增加趋势。经过化学分散试验，水镁石纤维得到了较好松解，纤维直径由微米级下降至纳米级。将水镁石纤维应用于混凝土，抗折强度随纤维叩解度的增加而提高，说明纤维的化学分散有利于纤维对混凝土增强作用的发挥。     

Microscopic characteristics of orthoquartzite from sliding friction experiments. I. Sliding surface

Optical and TEM observations were made on the active surfaces of the sliding blocks from orthoquartzite subjected to sliding friction experiments (Hayes, 1975; Dunn and Hayes, 1975) at a constant effective confining pressure of 500 bars and a shortening rate of 2.5 · 10⁻⁵ s⁻¹, dry and in the presence of pore fluids. Surface-wear features show that the sequence in the destruction of the sliding surface is: (a) penetration, ploughing, and immediate shearing off of brittle asperities to produce gouge, (b) formation of cracks at grain boundaries and intragranular cracks, facilitating shearing of asperities, and forming pluckouts and a rough or smooth sliding surface. Microcracks occurring and terminating in dislocation-free regions indicate that crack growth through dislocation coalescence of pre-existing dislocations is invalid for orthoquartzite at room temperature.     

Strain localization in soft rock—a typical rate‐dependent solid: experimental and numerical studies

Strain localization developing inside soft rock specimens is examined through experimental observation and numerical simulation. In the experimental study, soft rock specimens are sheared at different strain rates under plane strain conditions and deformation and strain localization characteristics are analysed. Transition of localization mode from highly localized mode for higher strain rate to distributed and diffused mode of strain localization for lower strain rates was observed. In the numerical study, simulations of plane strain compression tests are carried out at different strain rates by using an overstressed‐type elasto‐viscoplastic model in finite element computations. The role of strain rates on setting gradients of strain fields across shear band is clarified. The probable mechanism for transition of localization mode is discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

High Temperature Strain Structures and Quartz C-Axis Fabrics from Mylonitic Rocks in the Ailaoshan-Red River Shear Zone, Yunnan, and Their Tectonic Implication

<正>The Ailaoshan-Red River(ASRR) shear zone is one of the major Southeast Asian tectonic discontinuities that have figured the present tectonic framework of the eastern Tibet.Several metamorphic massifs are distributed linearly along the shear zone,e.g.Xuelongshan,Diancangshan, Ailaoshan and Day Nui Con Voi from north to south.They bear a lot of lines of evidence for the tectonic evolution of the eastern Tibetan at different crustal levels in different tectonic stages.Controversy still exists on the deformation structures,microstructures and their relationship with metamorphisms along the ASRR.In this paper detailed microstructural and EBSD(Electron Backscattered Diffraction) fabric analysis of some highly sheared granitic rocks from different massifs along the ASRR are conducted.High temperature structures and microstructures are preserved in unsheared gneisses,in weakly sheared xenoliths or in some parts of the highly sheared rocks(mylonites).Several types of high temperature quartz c-axis fabrics show symmetrical patterns or transitions from symmetrical to asymmetrical patterns.The former are attributed to coaxial deformation during regional shortening in an early stage of the Indian-Eurasian tectonic interaction and the latter are related to the transitions from coaxial compression to noncoaxial shearing during the post-collisional ASRR left lateral shearing.     

Numerical studies of shear banding in interface shear tests using a new strain calculation method

Strain localization is closely associated with the stress–strain behaviour of an interphase system subject to quasi‐static direct interface shear, especially after peak stress state is reached. This behaviour is important because it is closely related to deformations experienced by geotechnical composite structures. This paper presents a study using two‐dimensional discrete element method (DEM) simulations on the strain localization of an idealized interphase system composed of densely packed spherical particles in contact with rough manufactured surfaces. The manufactured surface is made up of regular or irregular triangular asperities with varying slopes. A new simple method of strain calculation is used in this study to generate strain field inside a simulated direct interface shear box. This method accounts for particle rotation and captures strain localization features at high resolution. Results show that strain localization begins with the onset of non‐linear stress–strain behaviour. A distinct but discontinuous shear band emerges above the rough surface just before the peak stress state, which becomes more expansive and coherent with post‐peak strain softening. It is found that the shear bands developed by surfaces with smaller roughness are much thinner than those developed by surfaces with greater roughness. The maximum thickness of the intense shear zone is observed to be about 8–10 median particle diameters. The shear band orientations, which are mainly dominated by the rough boundary surface, are parallel with the zero extension direction, which are horizontally oriented. Published in 2007 by John Wiley & Sons, Ltd.     

A dislocation model of aseismic fault slip under nonuniform friction

A model is proposed for studying the mechanical behaviour of faults during their interseismic periods. The model considers a plane fault surface in an elastic medium, subject to a uniform shear stress which increases slowly with time. A1-D friction distribution is assumed on the fault, characterized by asperities and a weaker zone. The traction vector on the fault plane has an arbitrary orientation: in particular, it can be nonperpendicular to the asperity borders. Aseismic fault slip takes place when the applied stress exceeds the frictional resistance: slip starts in weak zones and is confined by asperities, where it propagates at increasing velocity. Propagation into asperities is characterized by a dislocation front, advancing perpendicularly to the asperity border. Fault slip does not take prate in the direction of traction, except when traction is perpendicular or parallel to the asperity border. The propagation of such aseismic dislocations produces a stress redistribution along the fault and can play a key role in determining the conditions which give rise to earthquakes.     

Evolution of a fold-thrust belt deforming a unit with pre-existing linear asperities: Insights from analog models

Heterogeneity, whether geometric or rheologic, in crustal material undergoing compression affects the geometry of the structures produced. This study documents the thrust fault geometries produced when discrete linear asperities are introduced into an analog model, scaled to represent bulk upper crustal properties, and compressed. Varying obliquities of the asperities are used, relative to the imposed compression, and the resultant development of thrust fault traces and branch lines in map view is tracked. Once the model runs are completed, cross-sections are created and analyzed. The models show that asperities confined to the base layer promote the clustering of branch lines in the surface thrusts. Strong clustering in branch lines is also noted where several asperities are in close proximity or cross. Slight reverse-sense reactivation of asperities cut through the sedimentary sequence is noted in cross-section, where the asperity and the subsequent thrust belt interact. The model results are comparable to the situation in the Dinaric Alps, where pre-existing faults to the SW of the NE Adriatic Fault Zone contribute to the clustering of branch lines developed in the surface fold-thrust belt. These results can therefore be used to evaluate the evolution of other basement-involved fold-thrust belts worldwide.     

Physical Modelling of Stress-dependent Permeability in Fractured Rocks

This paper presents the results of laboratory experiments conducted to study the impact of stress on fracture deformation and permeability of fractured rocks. The physical models (laboratory specimens) consisted of steel cubes simulating a rock mass containing three sets of orthogonal fractures. The laboratory specimens were subjected to two or three cycles of hydrostatic loading/unloading followed by the measurement of displacement and permeability. The results show a considerable difference in both deformation and permeability trends between the first loading and the subsequent loading/unloading cycles. However, the micrographs of the contact surfaces taken before and after the tests show that the standard deviation of asperity heights of measured surfaces are affected very little by the loadings. This implies that both deformation and permeability are rather controlled by the highest surface asperities which cannot be picked up by the conventional roughness characterization technique. We found that the dependence of flow rate on mechanical aperture follows a power law with the exponent n smaller or larger than three depending upon the loading stage. Initially, when the maximum height of the asperities is high, the exponent is slightly smaller than 3. The first loading, however, flattens these asperities. After that, the third loading and unloading yielded the exponent of around 4. Due to the roughness of contact surfaces, the flow route is no longer straight but tortuous resulting in flow length increase.     

Influence of interaction between small asperities on various types of slow earthquakes in a 3-D simulation for a subduction plate boundary

Recently, the occurrence of slow earthquakes such as low-frequency earthquakes and very low-frequency earthquakes have been recognized at depths of about 30 km in southwest Japan and Cascadia. These slow earthquakes occur sometimes in isolation and sometimes break into chain-reaction, producing tremor that migrates at a speed of about 5–15 km/day and suggesting a strong interaction among nearby small asperities. In this study, we formulate a 3-D subduction plate boundary model with two types of small asperities chained along the trench at the depth of 30 km. Our simulation succeeds in representing various types of slow earthquakes including low-frequency earthquakes and rapid slip velocity in the same asperity, and indicates that interaction between asperities may cause the very low-frequency earthquakes. Our simulation also shows chain reaction along trench with propagation speed that can be made consistent with observations by adjusting model parameters, which suggests that the interactions also explain the observed migration of slow earthquakes.     

A new approach to modeling the surface magnetic fields of chemically peculiar stars

A reconstruction of the line-of-sight component and modulus of the surface-magnetic-field vector is proposed, using a model with artificial point sources of the magnetic field with “virtual” magnetic charges in the body of a star. This approach for the direct calculation of the field from the superposition of the potentials of individual magnetic charges enables the reconstruction of most possible configurations of the surface magnetic field of a star. Proper choice of the axis orientations for the three coordinate systems used makes it possible to obtain a simple representation for the vector components of the surface magnetic field. In a dipole approximation, the expression for the line-of-sight component of the magnetic field averaged over the visible disk of the star reduces to the form obtained in other studies.     

A direction-dependent shear strength criterion for rock joints with two new roughness parameters

The surface morphology of a rock joint is closely related to its mechanical properties. To reasonably characterize a rock surface, two new roughness parameters were proposed in this paper. One is related to the average slope angle of asperities that contribute to the shear strength, and the other reflects the frictional behavior of asperities that is defined as the maximum possible contact area in the shear direction. Taking the standard joint roughness coefficient profiles as example, these two roughness parameters can be applied to describe the directional characteristics of shear strength. Based on their relationships with initial dilation angles, the proposed roughness parameters were incorporated into a peak shear strength criterion. It is shown that the predicted peak shear strength is consistent with experimental data, and there is a power–law relationship. The application range of new roughness parameters was determined, which may facilitate a measurement process.