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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.

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.

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

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.

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.

© 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.

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.

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 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.

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 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.

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.

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.

It is well known that baby Mandelbrot sets are homeomorphic to the original one. We study baby Tricorns appearing in the Tricorn, which is the connectedness locus of quadratic anti-holomorphic polynomials, and show that the dynamically natural straightening map from a baby Tricorn to the original Tricorn is discontinuous at infinitely many explicit parameters. This is the first known example of discontinuity of straightening maps on a real two-dimensional slice of an analytic family of holomorphic polynomials. The proof of discontinuity is carried out by showing that all non-real umbilical cords of the Tricorn wiggle, which settles a conjecture made by various people including Hubbard, Milnor, and Schleicher., Same as published version. The original undivided version is available at: arXiv:1605.08061v3, and Part II is available at: arXiv:2010.01129. arXiv admin note: text overlap with arXiv:1209.1753 by other authors

A numerical investigation utilizing the 3D displacement discontinuity method is performed to examine the stress perturbations and induced displacements near a weak fault with arbitrary orientations and dip, assuming zero shear stress and normal displacement. The in-situ stress field near the fault is taken as known and varied with depth. The modelling is constructed based on indirect boundary integral equations. In this work, the fault plane is first modelled as a rectangular plane with negligible thickness between the adjacent surfaces. The fault plane is then divided into numerous rectangular boundary elements with imposed shear singularities on the surface, which is normal to the fault plane to simulate a traction-free scenario. The numerical results of the total induced stresses and displacements are then compared to the existing solutions of a penny-shaped crack for validation purpose. With validated results, the paper moves on to the discussion of various factors that have impacts on the induced stress and displacements, including: aspect ratio which is defined by strike over dip; orientation of the strike on the horizontal ground surface; as well as dip. The boundary integration method with modification is also used to model an elliptical distribution of singularities with inner, corner, and edge elements to accommodate more complex shape of a discontinuity; small differences are observed. Cited as: Chai, Y., Yin, S. 3D displacement discontinuity analysis of in-situ stress perturbation near a weak fault. Advances in Geo-Energy Research, 2021, 5(3): 286-296, doi: 10.46690/ager.2021.03.05

Background Patients with schizophrenia need continuous integrated healthcare, but many discontinue their treatment, often experiencing adverse outcomes. The first objective of this study is to assess whether patient characteristics or treatment history are associated with discontinuity of psychiatric elective care. The second objective is to assess whether practice variation between providers of psychiatric care contributes to discontinuity of elective care. Methods A large registry-based retrospective cohort of 9194 schizophrenia patients, who were included if they received elective psychiatric care in December 2014–January 2015. Logistic regression models were used to identify predictive factors of discontinuity of care. The dependent variable was the binary variable discontinuity of care in 2016. Potential independent predictive variables were: age, sex, urbanization, and treatment history in 2013–2014. Practice variation between providers was assessed, adjusting for the case mix of patients regarding their demographic and care utilization characteristics. Results 12.9% of the patients showed discontinuity of elective psychiatric care in the follow-up year 2016. The risk of discontinuity of care in 2016 was higher in younger patients (between age 18 and 26), patients with a history of receiving less elective psychiatric care, more acute psychiatric care, more quarters with elective psychiatric care without antipsychotic medication, or receiving no elective treatment at all. No evidence for practice variation between providers was found. Conclusions Our findings show that the pattern of previous care consumption is an important prognostic factor of future discontinuity of elective care. We propose that previous care consumption can be used to design strategies to improve treatment retention and focus resources on those most at risk of dropping out.

Background: Proximal full-thickness free hamstring tendon injury (ie, tendon avulsion or rupture) is a severe injury. Treatment decision making relies on clinical factors and magnetic resonance imaging (MRI) variables; it specifically relies on which tendons are injured as well as the extent of tendon retraction. According to a worldwide evaluation of current practice, discontinuity of both proximal tendons and retraction of >2 cm are used as surgical indications. However, both the diagnosis and the use of MRI variables in decision making may be fraught with uncertainty in clinical practice. A reliable standardized MRI assessment is required. Purpose: To propose an MRI assessment for acute proximal full-thickness free hamstring tendon injury and to evaluate its interater reliability. Study Design: Cohort study (diagnosis); Level of evidence, 2. Methods: We included 40 MRI scans of patients with acute (≤4 weeks of injury) proximal full-thickness free hamstring tendon injury. Three musculoskeletal radiologists assessed proximal full-thickness free hamstring tendon discontinuity using the novel “dropped ice cream sign” and tendon retraction (in mm). Quantification of tendon retraction (in mm) was performed using 2 different methods: (1) a direct (ie, shortest distance between the center of the hamstring origin and the tendon stump) method and (2) a combined craniocaudal/mediolateral measurement method. Absolute and relative interrater reliability were calculated. Results: We found an almost perfect interrater agreement (kappa = 0.87) for assessment of full-thickness tendon discontinuity using the dropped ice cream sign. Interrater agreement for the direct and craniocaudal retraction measurements was good for both the conjoint (intraclass correlation coefficient [ICC], 0.88 and 0.83) and the semimembranosus tendons (ICC, 0.81 and 0.79). The mediolateral retraction measurement yielded only moderate to poor reliability for the conjoint (ICC, 0.53) and semimembranosus tendons (ICC, 0.41). Conclusion: The standardized MRI assessment to identify proximal hamstring tendon discontinuity and quantify tendon retraction is reliable. We recommend using the novel dropped ice cream sign and the direct retraction measurement in clinical practice and research.

The assumed enhanced strain (AES) method has been successfully used to deal with the strain localization or shear band problems. With AES treating the localization deformation as strong discontinuity in displacement field, the structural phenomenon and the associated strength loss manifested in strain localization could be reflected in a way independent of mesh density and alignment. On the other hand, the numerical manifold method (NMM) excels at dealing with non-homogeneity and discontinuity problems because of the two sets of covers. By combining the NMM with the AES method, this paper could investigate the influence of soil non-homogeneity on shear band evolution naturally and mesh independently. The Gauss Seidel projection contraction (GSPC) method is invoked because it is simple and efficient in tackling the integration difficulties induced by cutting the tensile part of the Drucker Prager (DP) model. Finally, this paper studies the influences of erratic boulders and weak soil layer on the evolution of shear band in the slope.

Rock blocks sliding along discontinuities can cause serious disasters, such as landslides, earthquakes, or rock bursts. The shear rate-dependent behavior is a typical time-dependent behavior of a rock discontinuity, and it is closely related to the stability of a rock block. To further study the shear rate-dependent behavior of rock discontinuities, shear tests with alternating shear rates (SASRs) were conducted on rock discontinuities with various surface morphologies. The dynamic evolution of the shear rate dependency was studied in detail based on the shear test results, and three stages were identified with respect to the shear stress and shear deformation states. The test results revealed that dynamic changes in shear stiffness and the energy storage abilities of the rock discontinuities occurred in relation to the shear rate-dependent behavior of crack growth, which increased with an increase in normal stress and/or the joint roughness coefficient. The stage of decreasing shear stiffness corresponded to a stage of noticeable shear rate-dependency, and the shear rate was found to have no influence on the initial crack stress.

A recent reform in the Italian labour market has modified the permanent contract by reducing firing costs. Using a discontinuity in the application of the reform, we evaluate its effect on the probability of being still employed about three and a half years later. In contrast with theoretical predictions, we find that the job survival probability is not smaller for the treated and even significantly larger in some cases. We investigate the composition of permanent workers hired after the reform and we find evidence of treated firms changing their recruitment strategy in favour of potentially more productive workers.

Galaxy clusters are known to harbour magnetic fields. The nature of the intra-cluster magnetic fields remains an unresolved question. Intra-cluster magnetic field can be observed at the density contact discontinuity formed by cool and dense plasma running into hot ambient plasma, and the discontinuity exists near the 2nd BCG MRC 0600-399 of a merging galaxy cluster Abell 3376 (z=0.0461, hereafter as A3376). Elongated X-ray image in the east-west direction with a comet-like structure reaches a Mpc-scale (Fig1.(a)). Previous radio observations detected the bent jets from MRC 0600-399, moving in same direction as the sub-cluster's motion against ram pressure.Here we report a new radio observation of a radio galaxy MRC 0600-399 which is 3.4 times and 11 times higher resolution and sensitivity than the previous results. Contrary to typical jets, the MRC 0600-399 shows a 90deg bend at the contact discontinuity and the collimated jets further extend over 100 kpc from the bend point. Diffuse, elongated emission named "double-scythe" structures were detected for the first time. The spectral index flattens downstream of the bend point, indicating cosmic-ray re-acceleration. High-resolution numerical simulations reveal that the ordered magnetic field along the discontinuity plays a significant role in the change in the jet direction. The morphology of the "double-scythe" bear remarkable similarities with the simulations, which strengthens our understanding of the interaction between relativistic electrons and intra-cluster magnetic field., Comment: 4 figures

Based on the data of cores, thin sections, well logs, and test experiments, the characteristics and main controlling factors of lamellation fractures in continental shales of the third and fourth members of the Paleogene Qianjiang Formation in the Qianjiang Depression, Jianghan Basin, are studied. Lamellation fractures mainly develop along laminas in shales. They have various morphological characteristics such as straightness, bending, discontinuity, bifurcation, pinching out, and merging. Lamellation fractures with high density show poor horizontal continuity and connectivity characteristics. The average linear density of the lamellation fractures is mainly between 20 m-1 and 110 m-1, and the aperture is usually less than 160 μm. The density of lamellation fractures is related to their apertures. The smaller the apertures of lamellation fractures are, the higher the density is. The development degree of lamellation fractures is mainly controlled by mineral composition, type, thickness, density of lamination, contents of organic matter and pyrite, lithofacies, structural position, etc. Lamellation fractures develop well, especially under the conditions of medium dolomite content, large lamination density, small lamination thickness, and high total organic carbon (TOC) and pyrite contents. The influences of lithofacies on the lamellation fractures are complex. The lamellation fractures are most developed in carbonaceous layered limestone dolomite and carbonaceous layered dolomite mudstone, followed by stromatolite dolomite filled with carbonaceous pyroxene. The fractures in the massive argillaceous dolomites and carbonaceous massive mudstones are poorly developed. No fractures can be found in the carbonaceous dolomitic, argillaceous glauberites or salt rocks with high glauberite content. Structure is also an important factor controlling lamination fractures. Tectonic uplifts are beneficial to the expansion and extension of lamellation fractures, which increases fracture density. Therefore, when other influence factors are similar, lamellation fractures develop better in the high part of the structure than in the low part.

In order to get the law of rainwater infiltration and the law of progressive water damage, the slope of Tianshang bridge foundation in Yunnan Province is taken as the engineering basis. The site investigation of the damaged slope is carried out, The traditional Green-Ampt model is improved by considering the ponding effect of dynamic water flow on the slope surface. Based on the variation characteristics of wetting front obtained by the improved infiltration model, the progressive failure process of slope with continuous infiltration is simulated by FLAC3D software. The results show that: the water damage of Tianshang bridge slope is mainly caused by the slope absorbing a lot of rainwater in a short time, which has obvious time discontinuity characteristics in time, and shows obvious multi-layer progressive failure characteristics in failure space. The wetting front characteristics obtained by the improved Green-Ampt infiltration model are more consistent with the engineering practice, the water accumulation effect of surface water gradually weakens with the increase of the wet front depth. the slope failure develops gradually from the toe to the top and from shallow to deep, and the intermittent failure characteristics provide surplus time for the engineering treatment, the gravel soil slope should be treated after a small-scale water damage occurs.

The earth’s crustal stress determination is a crucial item in civil, petroleum, and mining engineering and also in energy development fields. The hydraulic fracturing (HF) is one of the standard methods for estimating in situ stress, which is often analyzed with classical approach for stress estimations. The classical approach neglects the presence of pre-existing cracks in rock mass; however, the hydraulic fracturing is a phenomenon of fracture propagation in which the fracture mechanics approach is more appropriate to consider more complex items in stress estimations. In this study, the in situ stress tests are conducted in Azad Pumped Storage Power Plant (Azad PSPP) in the west of Iran and then the classical approach and four available analytical fracture mechanics methods are applied to determine the in situ stresses. Moreover, numerical modeling based on the displacement discontinuity method (DDM) is used to model hydraulic fracturing process and the results are compared with analytical methods. A comprehensive analysis on the length of pre-existing crack is done as an influential parameter on stress magnitudes. The results indicate that the magnitudes of in situ stresses calculated by the fracture mechanics approach are often greater than the stress magnitudes calculated by the classical approach. Also, the effect of crack inclination angle and pre-existing crack length on the magnitudes of σH is studied. In addition, the distribution of fluid pressure along the cracks and its influence on the stress intensity factor in the crack tip are analyzed, and consequently, the estimation of in situ stress is investigated.

Analyzing the shear resistance of a potential sliding surface based on discontinuity persistence usually does not consider the number of coplanar rock bridges. To examine the effect of the dispersion/number of rock bridges on the shear strength and rock slope stability, direct shear tests and large-scale rockslide simulations were conducted employing the 2D particle flow code (PFC2D). The shear strength of rock bridges under different configurations and the same discontinuity persistence was analyzed based on both the shear behavior controlled by the stress response and crack propagation. The results at both the laboratory and slope scales indicate that the shear resistance decreases with increasing dispersion/number of rock bridges due to multiple rock bridges breaking separately, the mechanism of which is that the rock bridge system more easily experiences initial failure with increasing dispersion/number of rock bridges. On this basis, a function of the strength reduction coefficient with the number of rock bridges was established considering the laboratory-scale numerical simulation results. A feasible stability analysis method, i.e., the improved limit equilibrium method based on the strength reduction coefficient, was proposed to consider the effect of the dispersion/number of rock bridges on the slope stability, which is a useful innovation to ensure that the stability analysis method of potential rockslides, including coplanar rock bridges, is more realistic and accurate.

Binocular disparity signals are highly informative about the three-dimensional structure of visual scenes, including aiding the detection of depth discontinuities between surfaces. Here, we examine factors affecting sensitivity to such surface discontinuities. Participants were presented with random dot stereograms depicting two planar surfaces slanted in opposite directions and were asked to judge the sign of the depth discontinuity created where those surfaces met. Although the judgement was focussed on the adjacent edges, the precision of depth discontinuity discrimination depended upon the slant of the two surfaces: increasing surface slants to ±60° increased discontinuity discrimination thresholds by, on average, a factor of 5. Control experiments examining discontinuity discrimination across surfaces with identical slants showed either biases in discontinuity judgements or reduced threshold elevation. These results suggest that sensitivity to depth discontinuities is affected by processing limitations in both local absolute disparity measurement mechanisms and mechanisms selective for disparity differences. As further evidence in support of this conclusion, we show that our results are well-described by a model of discontinuity discrimination based on the encoding of local differences in relative disparity.

PURPOSE: This study examines whether parental marijuana use that occurs during the life of a child impacts patterns of continuity and discontinuity in adolescent substance use among father-child dyads. METHODS: The study uses data from 263 father-child-mother triads involved in the Rochester Youth Development Study (RYDS) and the Rochester Intergenerational Study (RIGS). We use a dual trajectory model is used to examine the research questions. RESULTS: Results suggest that both paternal and maternal marijuana use during the child’s life increase the probability that a child will follow a moderate or high substance use trajectory during adolescence, beyond the risk incurred from paternal adolescent history of substance use. Some nuances related to the timing of concurrent parental marijuana use emerge across parent sex. CONCLUSION: Concurrent parental marijuana use predicts child’s substance use beyond a parent’s prior substance use history. The results highlight the important role of both caregivers in the explanation of patterns of discontinuity across generations, as well as the relevance of considering when the use occurred.

Some spousal carers experience their current relationship with the person with dementia as a continuation of the loving relationship they shared prior to the onset of dementia. For others, the experience is one of discontinuity; the prior relationship is lost and replaced with a different kind of relationship. The aim of this study was to investigate whether these differences are associated with particular symptoms of dementia. Thirty-five spousal carers completed the Birmingham Relationship Continuity Measure, the Revised Memory and Behavior Checklist (providing scores relating to cognitive decline, depression and challenging interpersonal behaviour), the Communicative Effectiveness Index and the Bristol Activities of Daily Living Scale. Experiencing discontinuity in the relationship was significantly correlated with communication difficulties, challenging interpersonal behaviour and the need for assistance in activities of daily living, but not with cognitive decline or depression. In a multiple regression, only the measures of challenging interpersonal behaviour and activities of daily living made significant unique contributions to the variance in continuity/discontinuity scores. Discontinuity is associated with reduced psychological well-being for the spousal carer and the provision of less person-centred care. Understanding which symptoms are more likely to lead to discontinuity allows the identification of those at risk of these experiences. Those at risk may require support to enable them to make sense of, and adjust to, certain symptoms of dementia in a way that has a less negative impact on their relationship.

The rock slope instability along the Khalifan-Bekhal-Rawanduz main road has been studied in the southwestern limb of the Bradost anticline (Mountain) and both northeastern and southwestern limb of the Korek anticline (Mountain) in the northeast of the Erbil city, Kurdistan Region, Iraq. The major factors of the instability of the rock slopes in the study area are types of discontinuous and the degree of erosion. Ten stations have been chosen for fieldwork. The expected failure types that may occur along the road are plane sliding and wedge sliding. This research is mainly focused on the type of failure along the rock slope and the factor that affect the instability of the studied slopes and have found that they are slope orientation and geometry of the discontinuity. Different remediation methods are proposed for the studied rock slopes base on rock slope analysis. The rock slopes along the road require continuous monitoring because of their hazard conditions.

China experienced a 47% expansion in higher education enrolment between 1998 and 1999 and a sixfold expansion in the decade to 2008. Using a fuzzy discontinuity in the months of births, we show tha...

The fractal geometry method has been employed to quantitatively characterize the roughness of a rock discontinuity, which is one of the key factors affecting its shear strength and the seepage characteristics of a rock mass. However, the current fractal methods involving the three-dimensional discontinuity morphology suffer from one or more problems, such as a complicated calculation procedure, an inaccurate calculation result and an inability to characterize the undulation and anisotropy of a discontinuity. To cope with these problems, the discontinuities in artificial granite samples with irregular and undulating surfaces were taken as examples, and a quantitative study on the discontinuity morphology was conducted based on the method of three-dimensional laser scanning in combination with ArcGIS data processing, geographical research, theoretical calculations and regression analysis. After performing systematic research, we proposed an extensive 3D fractal dimension including three discontinuity morphological parameters, i.e. the fractal dimension of discontinuity morphology, the ratio between the maximal undulating amplitude and the discontinuity length, and the average value of all the apparent dip angles of the discontinuity surfaces dipping opposite the shear direction. The extensive 3D fractal dimension can comprehensively characterize the roughness, undulation and anisotropy of the discontinuity morphology. A set of theoretical calculation methods were then developed to determine the three discontinuity morphological parameters of the extensive 3D fractal dimension based on ArcGIS. We finally established a mathematical expression of the extensive 3D fractal dimension. Compared with the current fractal methods, the extensive 3D fractal dimension can effectively compensate for the inability to characterize the undulation and anisotropy of the discontinuity morphology. Its calculation methods have the advantages of simplification, low-time consumption and high precision.

Rencana Pembangunan Bendungan Bener terletak Kecamatan Bener Kabupaten Purworejo mempunyai Terowongan Pengelak. Penentuan metode ekskavasi yang tepat sangat penting dan dibutuhkan untuk menjaga efektifitas dan efisiensi dalam proses pelaksanaan konstruksi terowongan pengelak. Penentuan metode ekskavasi juga penting untuk perhitungan biaya pelaksanaan pekerjaan. Tujuan Penelitian ini adalah mendukung perencanaan penentuan metode ekskavasi bukaan Terowongan Pengelak Bendungan Bener yang tepat dan apa saja yang perlu dilakukan untuk mengetahui kondisi geologi teknik batuan disekitar terowongan baik permukaan dan bawah permukaan sehingga dapat dilakukan analisis untuk menentukan metode ekskavasi tersebut. Penentuan metode ekskavasi dilakukan dengan metode empirik berdasarkan parameter masukan kondisi batuan baik itu kualitas massa batuan, densitas bidang diskontinyuitas dalam batuan dan nilai kuat tekan batuan. Kondisi lintasan terowongan didominasi oleh breksi andesit dengan kualitas baik (good rock). Analisis empirik metode ekskvasi menunjukan bahwa bukaan lintasan Terowongan Pengelak Bendungan Bener membutuhkan tipe ekskavasi peledakan (blasting) dan very hard ripping, namun sebagian besar memerlukan tipe ekskavasi peledakan (blasting).

Background: Though ossicular discontinuity is more common in cases of cholesteatoma, it may happen in non-cholesteatoma COM. The long process of incus is more frequently involved ossicle. Peroperative assessment of ossicular integrity is the gold standard way. But the discontinuity of the ossicular chain can be assumed before surgery by analyzing perforation edge adherent to medial wall and wide air-bone gap The purpose of the study was to find out the preoperative findings which can predict the ossicular discontinuity in non-cholesteatoma cases. Methods: This cross-sectional study was conducted in the department of Otolaryngology-Head & Neck Surgery, Bangabandhu Sheikh Mujib Medical University from January 2013 to June 2014. 81 patients of COM without cholesteatoma were selected as per inclusion and exclusion criteria. Relevant data were collected in a predesigned data collection sheet and analyzed with standard statistical method. Statistically significant inferred for P value 40 dB was found in 60% cases of ossicular discontinuity, followed by air bone gap 31-40 dB(20%), 21-30 dB(13.33%) and 11-20 dB( 6.67%) respectively. So ossicular discontinuity was more in higher air-bone gap group and it was statistically highly significant (p 40 dB. Ossicular discontinuity was also found more in cases where there is attachment of perforation edge to medial wall, and presence of granulation tissue. If preoperative information can be gathered to determine whether or not the ossicular chain is intact, the patient can be better informed, counseled for ossiculoplasty before surgery. J Dhaka Medical College, Vol. 29, No.1, April, 2020, Page 47-52

The accurate analysis of cracking phenomena in the concrete structures has been a research topic of growing interest over the past few decades, with notable developments in the modeling techniques based on either smeared or discrete fracture approaches. The well-known cohesive zone models, belonging to discrete fracture approaches, are commonly judged as very effective for accurately representing the real crack pattern in quasi-brittle materials. The present work deals with comparing two different finite element-based cohesive fracture models: (i) a novel diffuse interface model, and (ii) an existing embedded crack model, based on an inter- and intra- element fracture approach, respectively. The first one relies on an intrinsic cohesive formulation by which the damage process inside the material is represented as a collection of imperfect interfaces randomly placed at the internal boundaries of a finite element mesh. The second one is based on a strong discontinuity approach according to which the crack is modeled as a discontinuity embedded into the displacement field of a standard continuum, allowing concrete cracking along nonprescribed paths to be correctly simulated. Cracking behavior in concrete specimens subjected to general loading conditions has been simulated by these two models and a detailed comparison between the numerical results is provided. Finally, a critical discussion regarding of computational efficiency and numerical accuracy highlights the efficacy of the newly proposed diffuse interface model.