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Reinforced concrete (RC) deep beams are commonly used in structural design to transfer vertical loads when there is a vertical discontinuity in the load path. Much experimental research has been conducted on simply supported deep beams, but little research has been carried out using monotonic loads. In our study, an experimental investigation was conducted to study fixed-ended reinforced concrete deep beams under cyclic and monotonic loads. Five specimens were experimentally tested. The specimens had similar geometry but different reinforcement details. Four specimens were tested under cyclic loads and one specimen under a monotonic load to observe the deflection of the mid-span where the load was applied, as well as the crack patterns, failure modes, and shear strengths. The results show that web reinforcements are more effective than longitudinal bars at increasing shear capacity in fixed-ended RC deep beams.

We document measurable, lasting gains in student achievement caused by a change in teachers' evaluation incentives. A short-lived rule created a discontinuity in teachers' incentives when allocating effort across their assigned students: students who failed an initial end-of-year test were retested a few weeks later, and then only the higher of the two scores was used when calculating the teacher's evaluation score. One year later, long after the discontinuity in incentives had ended, retested students scored 0.03σ higher than nonretested students. Otherwise identical students were treated differently by teachers because of evaluation incentives, despite arguably equal returns to teacher effort.

Rock quality designation (RQD) has been considered as a one-dimensional jointing degree property since it should be determined by measuring the core lengths obtained from drilling. Anisotropy index of jointing degree (AIjd) was formulated by Zheng et al. (2018) by considering maximum and minimum values of RQD for a jointed rock medium in three-dimensional space. In accordance with spacing terminology by ISRM (1981) , defining the jointing degree for the rock masses composed of extremely closely spaced joints as well as for the rock masses including widely to extremely widely spaced joints is practically impossible because of the use of 10 cm as a threshold value in the conventional form of RQD. To overcome this limitation, theoretical RQD (TRQDt) introduced by Priest and Hudson (1976) can be taken into consideration only when the statistical distribution of discontinuity spacing has a negative exponential distribution. Anisotropy index of the jointing degree was improved using TRQDt which was adjusted to wider joint spacing by considering Priest (1993) 's recommendation on the use of variable threshold value (t) in TRQDt formulation. After applications of the improved anisotropy index of a jointing degree ( A I jd ′ ) to hypothetical jointed rock mass cases, the effect of persistency of joints on structural anisotropy of rock mass was introduced to the improved A I jd ′ formulation by considering the ratings of persistency of joints as proposed by Bieniawski (1989) 's rock mass rating (RMR) classification. Two real cases were assessed in the stratified marl and the columnar basalt using the weighted anisotropy index of jointing degree (W_ A I jd ′ ). A structural anisotropy classification was developed using the RQD classification proposed by Deere (1963) . The proposed methodology is capable of defining the structural anisotropy of a rock mass including joint pattern from extremely closely to extremely widely spaced joints.

This paper deals with a well known open problem raised by Kannan (Bull. Calcutta Math. Soc., 60: 71–76, 1968) and B. E. Rhoades (Contemp. Math., 72: 233–245, 1988) on the existence of general contractions which have fixed points, but do not force the continuity at the fixed point. We propose some new affirmative solutions to this question using two new contractions called $ (\psi, \varphi) $-$ \mathcal{A} $-contraction and $ (\psi, \varphi) $-$ \mathcal{A^{\prime}} $-contraction inspired by the results of H. Garai et al. (Applicable Analysis and Discrete Mathematics, 14(1): 33–54, 2020) and P. D. Proinov (J. Fixed Point Theory Appl. (2020) 22: 21). Some new fixed point and common fixed point results in compact metric spaces and also in complete metric spaces are proved in which the corresponding contractive mappings are not necessarily continuous at their fixed points. Moreover, we show that new solutions to characterize the completeness of metric spaces. Several examples are provided to verify the validity of our main results.

Discontinuity in cross-section depth may exist in RC columns. If present in a non-seismically detailed frame, such a discontinuity (termed herein setback in columns, SBC) may trigger unexpected seismic damage. However, this typology of irregularity within connections has long been overlooked. This paper offers initial experimental evidence showing how vulnerable these irregular, non-conforming RC connections would be under earthquake-like loading. Four full-scale exterior beam-column subassemblies with SBC were constructed and cyclically tested, including three “as-built” units and a control one improved with seismic detailing. Results indicated that all the units succumbed to joint shear failure, and exhibited distinctly asymmetric responses in different loading directions. Particularly, when subjected to a positive (sagging) beam moment, the “as-built” units displayed a very steep joint cracking pattern and, hence, remarkably lower peak loads as compared to the case where a negative (hogging) beam moment was applied. Possible causes inducing such a salient failure mode are discussed, and a detailed account of the cyclic behaviors of the four units presented. Moreover, based on the concept of wide and narrow joint panels, existing major code provisions and analytical procedures for regular connections were adapted to evaluate the joint shear capacity of the current irregular subassemblies. A practical modeling approach was also developed through ABAQUS user-defined subroutine for capturing the observed global hysteretic responses. Overall, the outcomes of this study highlight the vulnerability of non-seismically detailed exterior connections with SBC, and provide a reference for future related research.

Failure angle, also called maximum safe slope angle, is an important design parameter for rock slope stability analysis and slope excavation. This study aims to scientifically acquire the failure angle of the jointed rock slope, and a method incorporating the kinematic analysis, Bayesian estimation and Monte Carlo simulation is proposed. The probabilistic kinematic analysis could consider the variety of discontinuity properties. The Bayesian estimation and Monte Carlo simulation could consider the varieties and uncertainties of the failure angle data. The proposed method is applied to a discontinuity-controlled rock slope located in the Fusong County, Jilin Province, China. Numerous widely scattered failure angle data is firstly obtained using the probabilistic kinematic analysis. Then the Bayesian estimation and Monte Carlo simulation are applied to determine the failure angle scientifically. The suggested failure angle of west, middle and east section of the studied slope are 65.67°, 65.79° and 64.76°, respectively. The probabilities of kinematic instabilities are also obtained based on the failure angle data. In general, the studied slope is stable and suitable to develop projects.

Joints that represent locations of discontinuity were the prominent factors affecting the overall behavior of precast segmental bridges. In this study, the steel shear key was designed, which was used to transmit the shear stress of the joints. To study the mechanical characteristics of the steel shear keyed joints in the construction and finished states, direct shear experiments and numerical analysis were carried out. The experimental results showed that the steel shear keyed joints had a high bearing capacity and good ductility. Under the action of confining stress, the joints relied on the mechanical occlusion between the steel keys to transmit the shear forces. When the load-displacement curve entered the horizontal stage, it can still bore large relative deformation, and the bearing capacity did not decrease. In the construction state, the inelastic deformation of the steel shear key should be used to control the design value of the temporary load. In the finished state, the bearing capacity of joints should be controlled by the direct shear strength of the steel shear key, which can be calculated according to the shear formula. The shear strength of the material and size of the steel shear key are the main factors affecting the bearing capacity of steel shear keyed joints.

The Boundary Element Method (BEM) associated with the Continuum Strong Discontinuity Approach (CSDA) can be used as a non-geometric alternative for the modelling of crack growth in physically non-linear three-dimensional problems of solid mechanics. This work makes use of the refereed approach through the implementation of volumetric hexahedral cells with embedded discontinuity that enables the evaluation of discontinuous jumps in the displacement field along a crack discontinuity surface. This is made with an internal equilibrium verification, using a regularized isotropic damage constitutive model. Although this formulation has been extensively studied for two-dimensional problems over the past few years, this is the first time that a three-dimensional extension is presented. The strong discontinuity regime in the cells were imposed directly after the end of the elastic regime, as a typical behaviour of the fracture process of brittle materials. These cells are needed only at the specific region of the solid domain where the cracks propagation is supposed to occur, while the remaining non-discretized regions of domains are considered to work in elastic regime. Some simple numerical examples shows the feasibility of such methodology.

Rock masses with remarked rock structure are likely to be highly anisotropic; thus, the relative orientation of the tunnel with respect to the rock structure will affect the tunnel behavior. Displacements measured at the walls of tunnels in highly anisotropic rock masses often reveal an asymmetric deformation pattern around the tunnel perimeter, which is often interpreted as the result of rock heterogeneity or changing geology. However, numerical and analytical investigation of tunnels in anisotropic rock masses show that the tunnel axis misalignment with the principal directions of stress and material anisotropy induce anti-symmetric axial displacements (i.e., axial distortion of the tunnel cross section) far behind the tunnel face. Near the face, the axial distortion is partially constrained, causing asymmetric radial displacements. In this study, tunnels excavated with and against dip of the major rock mass discontinuity are explored using 3D FEM modeling. A detailed analysis on the mechanisms associated with the direction of excavation is provided. It is shown that the asymmetric displacements near the face may strongly affect the displacements measured at the tunnel walls, which may explain the asymmetric displacements commonly observed on tunnels in anisotropic rock.

In order to study the instantaneous mechanical properties of rock mass discontinuities with different 3D morphologies during the shear process, the Brazilian splitting method is used to prepare natural rock mass discontinuities, and the high-precision 3D scanning test of discontinuities is carried out. The Z 2 is selected as the evaluation parameter of the discontinuities. Based on the graded cyclic shear test results of discontinuities, the influence of the morphology characteristics on the strength and deformation characteristics is analyzed. With the increase of shear times, the 3D morphology characteristic parameters of the structural plane decrease steadily after the graded cyclic shear. Based on the test curve, the graded cyclic shear characteristics of rock mass discontinuities are analyzed from the shear deformation, and the shear process of the discontinuities is finely divided by combining with the variation characteristics of shear stiffness. Combined with the 3D morphology parameters, an empirical formula for the shear strength of discontinuities is proposed. Through verification, the effect of the new model is better than that of the classical JRC-JCS model.

Построение в физическом пространстве решения задачи о распаде специального разрыва, т.е. трехмерных изэнтропических течений политропного газа, возникающих после мгновенного разрушения в начальный момент времени непроницаемой стенки, отделяющей неоднородный движущийся газ от вакуума. В задаче учитывается действие силы тяжести и силы Кориолиса. В систему уравнений газовой динамики введена автомодельная особенность в переменную, которая выводит с поверхности раздела. Для полученной системы поставлена задача Коши с данными на звуковой характеристике. Решение задачи строилось в виде степенных рядов. Часть коэффициентов рядов определялась при решении алгебраических уравнений, а часть из решений - обыкновенных дифференциальных уравнений. Методом мажорант доказана сходимость построенных рядов. Построенное решение позволяет задавать начальные условия для разностной схемы при численном моделировании решений данной характеристической задачи Коши The aim of this study is to construct a solution to the problem of the decay of a special discontinuity in physical space. The problem reduces to finding of three-dimensional isentropic flows of a polytropic gas that occur after the instantaneous destruction of an impermeable wall separating an inhomogeneous moving gas from a vacuum at the initial moment of time. The problem takes into account the forces of gravity and Coriolis. Research methods. In the system of gas dynamics equations, a self-similar feature is introduced in a variable that outputs from the initial interface. For the resulting system, the Cauchy problem is formulated using conditions on the sound characteristic. The solution to this problem is constructed in the form of power series. The coefficients of the series are partly determined by solving algebraic equations, another part can be found as solutions of ordinary differential equations. The convergence of the constructed series is proved by the Majorant method The results obtained in the work. In the form of a convergent power series, solutions to the problem of the decay of a special discontinuity in physical space are constructed. Conclusions. The solution constructed in physical space allows setting the initial conditions for the numerical simulation of this characteristic Cauchy problem using a difference scheme.

In this study, a data analysis method for the relaxation test was proposed under step loading by conducting creep and stress relaxation tests of dentate discontinuity poured by cement mortar using biaxial creep machine under step loading and single-stage loading. First, a superposition method for the stress relaxation curve was deduced based on the data processing method of creep test by considering the effect of loading history on the relaxation curve and the characteristic of relaxation was analyzed. Second, this superposition method was verified by testing data under step loading and single-stage loading. Finally, this paper indicate the accurate way for the processing of relaxation test data under step loading. The results show that under the same stress level, the values of relaxation curve after the superposition are different from that under the single-stage loading test. Furthermore, the relaxation curves in the step loading test under different stress levels are similar to those in single-stage loading under the same stress level. Furthermore, creep deformation increase monotonically during the creep, but stress do not exhibit such a trend during relaxation, which is inconsistent with the Boltzmann superposition principle. The relaxation curve in the step loading test under different shear stress could reflect the relaxation properties of the single-stage loading test under the same shear stress, and unlike the data processing method of step loading creep test, superimposition is not needed.

A novel approach for mapping induced fractures and associated lineaments has been introduced based on microseismic data, and thus their contribution towards identification, and prediction of the risk zones which may lead to a collapse or rockburst in a coal mine. By taking Tashan Coal Mine (TCM) in Datong coalfield of China as an example, the real-time microseismic data was acquired for a period of 7 months. The microseismic data was processed using standard processing schemes followed by source location and parameters estimation. The proposed approach utilizes microseismic events, trace them to map the induced fractures, and based on their network to interpret associated lineaments. Based on the configuration, geometry, and network, thousands of fractures were identified which vary in length. Regional lineaments have been interpreted based on the orientation of these fractures. The fractures and lineaments distribution were further correlated with computed microseismic energy distribution. The spatial distribution of microseismic energy helped in identification of a geological discontinuity (fault) that clearly separates the study area into northern and southern parts. The reactivation of this fault may pose significant threats to mass stability, life, and property. The northern half is characterized by more and short length fractures while southern by prolonged and fewer fractures. The upper northern half is dominated by high energy ( ≥ 50, 000 J), while the lower part is characterized by variable energy pattern (22,000 to 40, 000 J). It is inferred from the energy-lineaments correlation figure, the northern half describes relatively stronger rock type in comparison to the southern part suggesting different rock deformational behavior. The fractures and lineaments converging towards a single point define risk zones where future collapse or rockburst can be expected. This identification of risk zones provides a strong basis for the real-time prediction of future catastrophic hazards in the coal mines. This study may benefit global underground engineering researchers for hazards prediction and establishing of the early warning systems.

A large amount of high-quality teleseismic data is used for common conversion point (CCP) stacking of receiver functions in the Longmenshan area. The results show that a large-scale high-velocity anomaly or lithospheric delamination can completely destroy upper mantle discontinuities or erase the phase boundary of olivine, which is a very important finding and can be used to assess stagnant slabs in the mantle transition zone globally. The deepening region of the 660 km discontinuity beneath the Songpan-Ganzi terrane might indicate that the large-scale high-velocity anomaly in the mantle transition zone is a cold domain and can affect the topography of upper mantle discontinuities.

Any Structure that is designed in today’s world has to be designed not only for aesthetics but also for stability. These days high rise multi storied structures are quiet prominent. These types of structures, should not only be designed for aesthetic point of view but also must be designed to resist earthquake forces which are subjected on these structures. These earthquake forces acting on the structures are also known as seismic forces. Due to architectural purposes, some buildings, have openings, provided in them, this creates structural discontinuities in the building. These openings or discontinuities can change the load transfer path of the structures which may cause significant change in the building behavior, under the application of the seismic forces. In this paper pushover analysis is carried out to study the behavior of the building in case of architectural opening for staircase or cut outs etc which results in discontinuity in the structure. Keywords: Diaphragm, Discontinuity, ETABS, Pushover Analysis, Seismic

Most previous studies exploit the discontinuity in children’s school entry age around the enrolment cut-off to identify the effect of delayed school entry on child learning. However, the effect so ...

In this paper, we study a penny-shaped crack model with electrically and thermally semi-permeable boundary conditions in a three-dimensional transversely isotropic piezoelectric semiconductor. An extended displacement discontinuity boundary element method together with an iterative process is proposed to analyze the penny-shaped crack model. The extended displacement discontinuities across crack face, electric displacement and heat flux along an inner crack cavity, as well as extended stress intensity factors near crack front are obtained via the proposed method. The effects on extended intensity factors near crack front are discussed, including boundary conditions across crack face, applied loads and initial electron concentration. It is shown that boundary conditions across crack face significantly affect extended stress intensity factors near crack front. This implies that a larger initial electron concentration can lead to electrical failure.

Since the failure modes of fully grouted bolts subject to displacements of rock joints are difficult to predict, the joint displacements in this study are categorised into two types: opening displacement and shear displacement. At first, a closed-form solution incorporating the nonlinear constitutive model of interfaces between bolts and grout is developed, which is able to formulate the full-range behaviour of bolts subject to the opening displacements of rock joints. Then, a novel numerical approach considering the nonlinear rock reaction force is proposed, which can analyse stress and displacement conditions on each point along a bolt. The results of the proposed numerical approach are validated by existing test results. Combining the proposed numerical approach with the improved closed-form solution, a comprehensive model for predicting yield and failure patterns of rock bolts is proposed. In this way, decoupling between the bolt and grout, the yield and failure patterns of two potential points along the bolt are also highlighted and discussed. Further discussions about the influences of bolt inclined angles to the discontinuity and the dilatancy effect of the joint face are carried out at last. This work provides a useful tool to evaluate the behaviours and estimate the load-bearing capacity of fully grouted bolts in jointed rock masses.

Transparent ceramics are typically used as the strike-face layer owing to their superior mechanical properties, such as high strength and high hardness. For typical transparent ceramic armor, the ceramic layer is usually divided into small ceramic tiles because of the size limitations. However, the tiled structure is restricted in application due to the discontinuity between ceramic tiles, which can be solved by covering the outer surface with a glass plate. In this study, the effect of the glass cover layer on the ballistic performance of transparent ceramic armor is investigated through a combination of experimental testing and finite element (FE) simulation. The results exhibited that under the impact of 7.62 mm armor-piercing incendiaries, the ceramic tiles were prematurely damaged when the glass cover was added. Besides, the reduction of the ceramic energy dissipation was greater than the energy dissipation of the glass cover itself, thus reducing the ballistic performance of the transparent ceramic armor. The results also revealed that the pre-damage area increased as the thickness of the glass cover increased from 1 mm to 4 mm.

This article examines the continuities and discontinuities in the historical trajectory of the commercialisation of places. It outlines a performative approach to understanding how the process of t...

Inherent microcrack populations have a significant effect on the fracture behaviour of natural rocks. The present study addresses this topic in numerical simulations of uniaxial tension and three-point bending tests. For this end, a rock fracture model based on multiple intersecting embedded discontinuity finite elements is developed. The inherent (pre-existing) microcrack populations are represented by pre-embedded randomly oriented discontinuity populations. Crack shielding (through spurious locking) is prevented by allowing a new crack to be introduced, upon violation of the Rankine criterion, in an element with an initial crack unfavourably oriented to the loading direction. Rock heterogeneity is accounted for by random clusters of triangular finite elements representing different minerals of granitic numerical rock. Numerical simulations demonstrate the strength lowering effect of initial microcrack populations. This effect is substantially stronger under uniaxial tension, due to the uniform stress state, than in semicircular three-point bending having a non-uniform stress state with a clear local maximum of tensile stress.

The importance of discontinuity geomechanical properties is increasing as the use of numerical models with explicit or discrete rock mass structure becomes the state of practice. Joint normal stiffness and joint shear stiffness are two parameters that characterize the deformation behaviour of discontinuities. This paper presents practical guidelines to correct direct shear testing data for machine influences with regard to normal and shear joint stiffness using a method originally employed by Goodman (Methods of geological engineering in discontinuous rocks. West Publishing Company, St. Paul, 1976) to correct the normal deformation of a direct shear test. This method of correcting the normal deformation has been extended to the shear deformation to account for machine influence during the shear loading stage. The normal stiffness of 23 rough fracture specimens and 10 smooth ground specimens were measured on discontinuities in granitic specimens from NQ and NQ3 sized core using a power law (Swan in Rock Mech Rock Eng 16:19–38, 1983), a hyperbolic law (Bandis et al. in Int J Rock Mech Min Sci Geomech Abstr 20:249–268, 1983), and two semi-logarithmic laws (Bandis et al. 1983; Evans et al. in Geotherm Resour Counc Davis Calif USA 16:449–456, 1992). Measurements from direct shear tests completed at varying maximum applied normal stress show a positive correlation between normal stiffness and normal stress. In addition, the shear stiffness was measured on 19 rough fracture specimens and 4 smooth ground specimens. The compilation of results from these measurements has a range of measured shear stiffness due to varying joint topology and roughness showed a positive correlation between shear stiffness and maximum applied normal stress. As the majority of the joints exhibited non-linear behaviour under normal loading conditions and linear behaviour under shear loading conditions, it is recommended that a stress-dependent normal stiffness model and a linear shear stiffness model be used for numerical modelling purposes.

Wave velocity as a nondestructive test is widely used in various fields such as mining, civil, rock mechanics and rock engineering, and dynamic elastic properties of rocks are also determined by wave velocity. Rock mass contains discontinuities with different orientation angles, numbers of sets and frequencies and the impacts of such discontinuity properties on the wave velocity have not yet been systematically investigated. In this study, 20 groups of jointed cylindrical specimens with a wide range of discontinuity orientation angles (0°, 30°, 45°, 60° and 90°), numbers of sets and frequencies were prepared, and their P-wave velocities were measured. P-wave velocity (VP) significantly increased with increasing orientation angle (θ) and decreasing the discontinuity frequency (F). Several relations were applied to analyze the results. Finally, a new empirical relation was developed to predict VP as a function of θ angle using two parameters of P-wave velocity perpendicular to the discontinuity plane (VP0°) and P-wave velocity along the discontinuity direction (VP90°) or anisotropy degree (e = (VP90° − VP0°)/VP0°) with a good correlation of determination (R2 = 0.933), low RMSE (RMSE = 200.0 m/s) and low CV (CV = 6.7%). A good correlation between VP and F was also achieved for the test results. The intact rock elements in the complex nature of a rock mass are surrounded by discontinuities like a three dimensional puzzle. Treatment of such a rock mass system using cement grouting is an attractive method to improve its quality for various purposes. All 20 groups of jointed cylindrical specimens were grouted by cement. Wave velocities of the grouted specimens were measured after 2 months. VP significantly increased after grouting for all models of jointed specimens, as wave velocity of jointed specimens improved and approached to the wave velocity of the intact rock for most cases. The discontinuity orientation of the specimens had no significant effect on the wave velocities after grouting. But the results showed that VP and VS increased little with increasing orientation angle for jointed specimens consisting only of one set of discontinuity. After grouting the jointed specimens, orientation angle and frequency of discontinuities had also similar effects on the dynamic Young's modulus (E), Poisson's ratio (ν), shear modulus (μ), bulk modulus (K) and Lame’s constant (λ). These results also showed that the dynamic elastic properties of jointed specimens significantly improved using cement grouting.

SUMMARYThe detailed structure near the 410-km discontinuity provides key constraints of the dynamic interactions between the upper mantle and the lower mantle through the mantle transition zone (MTZ) via mass and heat exchange. Meanwhile, the temperature of the subducting slab, which can be derived from its fast wave speed perturbation, is critical for understanding the mantle dynamics in subduction zones where the slab enters the MTZ. Multipathing, i.e. triplicated, body waves that bottom near the MTZ carry rich information of the 410-km discontinuity structure and can be used to constrain the discontinuity depth and radial variations of wave speeds across it. In this study, we systematically analysed the trade-off between model parameters in triplication studies using synthetic examples. Specifically, we illustrated the necessity of using array-normalized amplitude. Two 1-D depth profiles of the wave speed below the Tatar Strait of Russia in the Kuril subduction zone are obtained. We have observed triplications due to both the 410-km discontinuity and the slab upper surface. And, seismic structures for these two interfaces are simultaneously inverted. Our derived 410-km discontinuity depths for the northern and southern regions are at 420$\pm $15 and 425$\pm $15 km, respectively, with no observable uplift. The slab upper surface is inverted to be located about 50–70 km below the 410-km discontinuity. This location is between the depths of the 1 and 2 per cent P-wave speed perturbation contours of a regional 3-D full-waveform inversion (FWI) model, but we found twice the wave speed perturbation amplitude. A wave speed increase of 3.9–4.6 per cent within the slab, compared to 2.0–2.4 per cent from the 3-D FWI model, is necessary to fit the waveforms with the shortest period of 2 s, indicating that high-frequency waves are required to accurately resolve the detailed structures near the MTZ.

The sliding of rock blocks along rock discontinuities is caused by accumulated deformation and can result in disasters such as rock bursts and earthquakes. Creep along rock discontinuities leads to the accumulation of sliding deformation and random instability over time. The initial stress and deformation are important factors that strongly influence creep behavior. To investigate the influence of the initial state on the creep behavior of rock discontinuities, shear creep tests with loading–unloading shear pre-stress paths and shear creep tests with different initial stress and deformation states were conducted on artificial rock discontinuity samples prepared according to Barton’s standard roughness profiles. The creep behavior characteristics were investigated in detail according to the initial stress and deformation conditions. The results show that the initial stress and deformation states, which are related to crack development and plastic deformation accumulation, strongly influence creep behavior. Larger initial stress and deformation produce lower creep deformation, creep rates, and accelerated velocities. Samples with higher joint roughness coefficients produce more noticeable creep because more asperities provide additional space for creep to occur. A limit curve is also proven to exist, which allows the stress–deformation coordinate system to be divided into stable and unstable regions. When the current stress state of a sample is insufficient to drive the formation of further cracks or deformation in the rock discontinuity, the deformation and stress remain stable and no further creep is observed.

© 2021 The Author(s). Published by Oxford University Press on behalf of The Royal Astronomical Society.Flat slab subduction has been ascribed to a variety of causes, including subduction of buoyant ridges/plateaus and forced trench retreat. The former, however, has irregular spatial correlations with flat slabs, while the latter has required external forcing in geodynamic subduction models, which might be insufficient or absent in nature. In this paper, we present buoyancy-driven numerical geodynamic models and aim to investigate flat slab subduction in the absence of external forcing as well as test the influence of overriding plate strength, subducting plate thickness, inclusion/exclusion of an oceanic plateau and lower mantle viscosity on flat slab formation and its evolution. Flat slab subduction is reproduced during normal oceanic subduction in the absence of ridge/plateau subduction and without externally forced plate motion. Subduction of a plateau-like feature, in this buoyancy-driven setting, enhances slab steepening. In models that produce flat slab subduction, it only commences after a prolonged period of slab dip angle reduction during lower mantle slab penetration. The flat slab is supported by mantle wedge suction, vertical compressive stresses at the base of the slab and upper mantle slab buckling stresses. Our models demonstrate three modes of flat slab subduction, namely short-lived (transient) flat slab subduction, long-lived flat slab subduction and periodic flat slab subduction, which occur for different model parameter combinations. Most models demonstrate slab folding at the 660 km discontinuity, which produces periodic changes in the upper mantle slab dip angle. With relatively high overriding plate strength or large subducting plate thickness, such folding results in periodic changes in the dip angle of the flat slab segment, which can lead to periodic flat slab subduction, providing a potential explanation for periodic arc migration. Flat slab subduction ends due to the local overriding plate shortening and thickening it produces, which forces mantle wedge opening and a reduction in mantle wedge suction. As overriding plate strength controls the shortening rate, it has a strong control on the duration of flat slab subduction, which increases with increasing strength. For the weakest overriding plate, flat slab subduction is short-lived and lasts only 6 Myr, while for the strongest overriding plate flat slab subduction is long-lived and exceeds 75 Myr. Progressive overriding plate shortening during flat slab subduction might explain why flat slab subduction terminated in the Eocene in western North America and in the Jurassic in South China.

A flat strong discontinuity in a polymer fluid is investigated in the rheological Vinogradov−Pokrovsky model. Relationships for a strong discontinuity are given. The existence of discontinuous stationary solutions of the problem without rotation of the velocity vector at the discontinuity and with rotation (rotational discontinuity) is substantiated. Examples of numerical stationary solutions are given.

—Numerical modeling of induced seismicity resulting from fluid injection into the subsurface is considered. One of important factors determining the slip dynamics of a tectonic fault during fluid injection loading is the form of the law of friction acting on the fault sides. The numerical analysis in the context of a slider model compared to the results of laboratory experiments has shown that a two-parameter rate-and-state friction law describes the widest spectrum of the observed sliding modes. A double porosity model and a slider model for fracture are used to simulate the induced seismicity in ​​the region of Basel, Switzerland, caused by geothermal stimulation. A physically complete model of embedded fractures which allows for calculating fluid flow in a rock with fractures or faults taking into account changes in the hydraulic properties of the latter is presented. Fault deformation process is described based on the displacement discontinuity method. Based on the model, the results of the field experiment on water injection into a fault in the southern France are analyzed. The development of fault slips is studied as a function of a number of parameters characterizing a fault, filtration properties of a rock, and injection pattern. The conditions for the emergence of seismic slip in the context of the proposed model are established.

In order to obtain the accurate mechanical parameters of deep-buried coal goaf rock mass, the limitation of geological strength index (GSI) in concealed rock mass is analyzed. Based on the test result and analysis of the current normative standards, the classification indexes of rock mass structural are optimized based on discontinuity distance d and rock mass integrity index K v . The ratio of rock mass saturated strength to dry strength, η, is introduced, quantization formula of structural surface conditions is proposed, and the influence of groundwater and rock types is included in structural surface condition classification. The GSI system is improved to better suit all types of deep-buried and water-rich rock masses. Furthermore, the rock mass disturbance factor D’s quantitative formula is listed according to the Hoek–Brown (HB) criterion. Taking the goaf roof under railway as an example, the parameters of deep-buried rock mass are obtained based on the improved quantitative GSI system and HB criterion. This research provides a scientific reference for achieving geological parameters and engineering designing in goaf areas.

The solution for the buckling problems of fibre metal laminates is usually based on the assumptions that the plates are subjected to uniform edges loads without any discontinuity or damages. Nevertheless, in practice the plates are subjected to various kinds of nonlinear/nonuniform edge loads along with various sized and positioned openings. The present work mainly focused on the vibration and buckling performance of inter laminar hybrid fiber metal laminates (HFMLs) with and without cutouts subjected to different kinds of nonlinear loading conditions by utilizing finite element approach. Towards this a 9-noded heterosis plate element has been used to discretize the plate by taking into account the effect of shear deformation and rotary inertia. Since the stress distribution within the plate is highly non-uniform in nature, the dynamic approach has been used to solve the buckling problems. The present study consists of aluminum metal face sheets bonded with four layered symmetric hybrid cross-ply laminates, in which six different hybrid configurations have been considered. The performance of each hybrid configuration along with different sized and positioned cutouts is well investigated under various nonlinear loading conditions.

O presente trabalho visa discutir o uso de métodos de aquisição de dados geotécnicos de maciços rochosos. A área de estudo é uma pedreira de brita desativada, localizada na cidade de Belo Horizonte (Minas Gerais, Brasil), onde afloram gnaisses migmatizados, com constante queda de blocos. Os métodos de aquisição empregados foram o tradicional mapeamento de talude e o levantamento remoto por fotogrametria digital terrestre. A classificação de maciços Slope Mass Rating (SMR) foi aplicada. Os resultados evidenciaram diferenças nos ranges de detecção de estruturas e a fotogrametria se mostrou mais completa, com mais dados de descontinuidades do que o mapeamento tradicional, com exceção das estruturas oblíquas ao talude. Esta deficiência se explica pelo fato do talude estudado ser subvertical, sem reentrâncias e saliências, que permitem muitas vezes a detecção dos traços de descontinuidades e não dos planos. Contudo, mesmo nestes casos, a fotogrametria mostrou-se importante, por permitir a caracterização de todo talude, impossível pelo método tradicional. A classificação SMR mostrou baixos valores, indicando instabilidade por rupturas planares e em cunha do maciço em alguns pontos, o que coincide com as frequentes quedas de blocos.

The article discusses the types of dangerous defects in welded joints. The main methods of non-destructive testing are described, their advantages and disadvantages are briefly reflected. The comparison of the automated ultrasonic testing methods with radiographic ones is given on the example of testing the welded joints of ASME DN350 Py250 pipe fittings with a thickness of the welded edges of 53.9 ÷ 61.3 mm. The comparison results of the methods by the criterion of the accuracy of determining the coordinates of defects are presented, which show the expediency of replacing the automated ultrasonic method with the radiographic one, provided that the thickness of the welded edges is shallow.

In addition to the discontinuity of the rail profile of a normal turnout, the unique S-shaped curve of a crossover significantly affects the negotiation performance of a train. For heavy-haul freig...

The effect of the bedding structure on the mechanical properties of layered shale was studied by means of experiment and numerical simulation. Based on continuum damage theory and discrete fracture network modeling method (D-DFN), a finite element model describing structural discontinuity and mechanical anisotropy of shale is established. In this model, the degradation process of stiffness and strength of shale after failure is described based on the stress-displacement relationship of elements. In order to distinguish the mechanical properties between the bedding and the matrix, a nonzero initial damage variable is set in bedding elements to show initial lower elastic modulus and strength of bedding elements compared with initially nondamaged matrix elements. The calibration of model parameters is discussed, and the simulation results are compared with the experimental results. The results show that the D-DFN method can effectively simulate the anisotropic characteristics of shale deformation and strength, which verifies the effectiveness of the method.

This article is presented to investigate the influence of several discontinuity like interfacial-crack, void and inclusion in the bimaterial plate, to analyze the normalized mixed-mode stress inten...

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

In this article I explore the confluence of Gustav Mahler’s affiliation with a Jewish minority and his approach to musical form and expression. To this end, I devise a theoretical framework that combines Gilles Deleuze and Félix Guattari’s theory of Minor literature with current theories of musical form and analyse selected excerpts from ‘Der Abschied’, the Finale of Mahler’s Das Lied von der Erde (1909). While ‘Der Abschied’ aspires towards monumental expression, it rejects its own realization as a musical monument through musical and textual ambiguities. By means of musical analysis I illustrate how discontinuous and fragmented motion in the musical realm undermines the materialization of apotheotic culminations and negates the interpretative framework of monumentality. Against that background, I then compare Mahler’s formal approach to Kafka’s poetics—the prototype of ‘Minor literature’—and discuss how their ‘Minor works’ concurrently appropriate and subvert the Romantic concept of monumentality and related constructs.

By convention, carbon isotope ratios are expressed relative to VPDB defined by the calcite standard NBS19 in the 1980s. [See T. Coplen, Pure Appl. Chem. 1994, 66, 273–276.] To improve the realization of the VPDB scale, a second fixed point (lithium carbonate, LSVEC) was introduced in 2006 [T. Coplen et al. Anal. Chem. 2006, 78, 2439–2441], which is now known to be isotopically unstable. [Assonov, S. Rapid Commun. Mass Spectrom., 2018, 32, 827–830.] With the high-quality reference materials made available in 2020, it is now possible to realize the VPDB scale with high confidence. [Assonov, S. et al. Rapid Commun. Mass Spectrom., 2020, 34, e8867; Assonov, S. Rapid Commun. Mass Spectrom. 2021, 35, e9014; Qi, H. et al. Rapid Commun. Mass Spectrosc. 2021, 35, e9006.] Here, we report the analysis of 25 reference materials using isotope ratio combustion mass spectrometry, show the discontinuity between the values measured against the new IAEA reference materials and the values currently assigned to these reference materials on the VPDB2006, and provide a link bringing these materials onto the new VPDB2020.

The main purpose of this study is to explore the intensity of the scattered wave energy and the total intensity scattered around a discontinuity in a slab, considering strain and kinetic energy in ...

The climatological state and the seasonal variability of the Arabian Heat Low (AHL) and the Intertropical Discontinuity (ITD) are investigated over the Arabian Peninsula using the 1979-2019 ERA-5 reanalysis data. The AHL is a summertime feature, mostly at 15º-35ºN and 40º-60ºE, exhibiting a clear strengthening over the last four decades in line with the observed increase in surface temperature. However, no clear shift in its position is detected. The AHL has a center over the Arabian Gulf and eastern Arabian Peninsula, co-located with the highest surface temperatures, and another over central Saudi Arabia, driven by low-level wind convergence and subsequent increase in atmospheric thickness. The ITD is the boundary between the hot and dry desert air and the cooler and more moist air from the Arabian Sea. It lies along the Arabian Peninsula’s southern coastline in the cold season but reaches up to 28º N between 50º - 60º E in the summer months. While the former has a rather small diurnal variability, the latter shows daily fluctuations of up to 10º. The ITD exhibited a weak northward migration in the 41-year ERA-5 period, likely driven by the increased sea surface temperatures in the Arabian Sea. On interannual timescales, the El Niño-Southern Oscillation, the Indian Ocean Dipole, and solar-geomagnetic effects play an important role in the AHL’s and ITD’s variability.

Origami-based sheet metal, a novel emerging technique, is explored in this paper. The process is similar to traditional process of making the Origami art from paper. Sheet metal forming is also con...

Out of numerous available methods to reduce the lateral earth pressure on the retaining structures, a retaining wall with relief shelves, though known for more than a few decades, is one of the least practiced approaches to minimize the earth pressure on a wall due to the complex behavior of such walls as well as the lack of design recommendations or the codal provisions. Moreover, the previous studies were silent on explaining the mechanics behind the working of these walls. This study focuses on static force analysis of a wall with multiple relief shelves retaining a dry cohesionless backfill using principles of mechanics and theory of bending to develop a novel closed-form solution to handle the discontinuity at the joint of the relief shelf and wall stem for the evaluation of the distribution of shear force, bending moment, and deflection of the wall at any wall section and furnish design recommendations on the optimum width of the relief shelves. The outcomes of the present work establish the fact that the relief shelves reduce shear force, bending moment, and deflection of the wall and increase the overall stability of the structure. Furthermore, it is concluded that the bending moment at any section of the wall with relief shelves is governed by the position as well as the width of the relief shelves, though, the shear force depends only on the positioning of the relief shelves along the height of the wall. A comparison of the structural design of the walls demonstrated that the use of relief shelves to walls substantially reduces the volume of excavation, concrete, and reinforcing steel compared to the wall having no relief shelf.

A four-way enhanced numerical manifold method (NMM) is proposed in order to simulate crack propagation in rock media and progressive failure of jointed rock slopes. Specifically, the original NMM is improved in the following four aspects: (1) An “enriched local approximation” is employed to characterize singularity and discontinuity of the displacement/stress fields near the crack tip. (2) A “modified generalized Duffy transformation” is proposed to improve the accuracy of numerical integration associated with the 1/r and 1 / r singularities. (3) A “critical length cracking criterion” is introduced to determine propagation length and direction for both tensile-shear and compressive-shear cracks in rock mass. (4) A “cone-complementary-based contact formulation” is incorporated to resolve the cohesive/frictional contact phenomena between discontinuous interfaces more accurately. Some examples demonstrate the performance and application prospect of the presented NMM in stability and failure analysis of the jointed rock slopes.

The present study is to assess the slope stability of road cuts along the National Highway 150 (202 present). Rock mass classification enables preliminary assessment of rock slope failure and guide the planners to choose suitable alignment for road construction and engineering structures. This technique includes collection of data from the intact rock and discontinuity parameters. Seven locations have been selected for slope stability analysis using RMR, SMR and CoSMR techniques. These empirical methods are used to determine the mode of failures and characterise the slope as well. Kinematic analysis deciphers the causes of instability and the mode of discontinuous rock failures. Results shows majority of road section between Ukhrul and Jessami falls under partial stable to unstable zone.

Public transportation is a basic everyday activity. Costs imposed by violence might have far-reaching consequences. We conduct a survey and exploit the discontinuity in the hours of operati...

The apparent monolithic behaviour of multi-leaf walls is compromised by the discontinuity planes that the load transfer mechanisms generate for the following reasons: i) difference between mechanical characteristics of layers; ii) lack or weakness of the structural interaction between core and external layers. The goal of this paper is to evaluate through parametric analysis the dimensional ratios by reference to core confinement effects of multileaf masonry walls with several interface and mechanical characteristics of layers. The study was carried out through the finite element analysis performed in non-linear field on two-dimensional plain strain models calibrated on experimental basis and numerical results are presented and discussed. The horizontal interfaces hand the load transfer and structural performances of multi-leaf walls. The behaviour of short specimens is controlled by confinement of external layers while for slender masonry walls the out of plane mechanisms affect the confinement effect.

Reservoir discontinuity is a practical representation of reservoir heterogeneity, which leads to the nonuniform flow of hydrocarbons during production and increases the difficulties of producing the remaining oil in clastic reservoirs. For offshore oilfields, reservoir discontinuity analysis will have to rely on seismic data due to their sparse well distribution. However, traditional discontinuity detection methods are restricted to large-scale discontinuities (such as faults). It is difficult to detect small-scale discontinuities in seismic data such as interfaces of sands. To interpret small-scale discontinuities below the seismic resolution, we have adopted a direction-adaptive mathematical morphology gradient algorithm that can detect the boundaries of reservoir architectures in different directions on horizon-based seismic attributes. We elaborated a hierarchy of fluvial reservoir architectures and classified compound sandstones as different architectural elements according to the deposition period. Forward models were designed to analyze the seismic responses of the architectures. The results demonstrate that amplitude-related seismic attributes could be sensitive to different reservoir architectures below the seismic resolution. The amplitude-related seismic attributes can be extracted through a time window guided by the horizons. The horizon-based attributes can be treated as digital images, which may contain the information of compound sandstones with hidden discontinuity boundaries. Then, our algorithm is applied to detect discontinuity boundaries based on this extracted attribute. The application to field data in the Bohai Bay demonstrates that our algorithm can detect the discontinuity boundaries inside the compound sandstone, which is less than the seismic resolution. This method could enhance our capability to visualize and understand the complexity of reservoir heterogeneity.