Failure Plane Research Articles

Spalling Criterion of Hard Brittle Rock Mass Based on Dilatation Lateral Strain.

Spalling failure is a typical failure phenomenon after excavation and unloading of a deep, hard brittle rock mass, which seriously threatens the safe construction of deep roadways (tunnels) and other projects. From the engineering viewpoint, it is essential to accurately evaluate the range and depth of surrounding rock spalling failure. From the perspective of the laboratory and engineering site, the strength and formation mechanism of hard rock spalling failure were statistically summarized and analyzed. Under uniaxial and low confining pressure conditions, when the load reached the rock damage stress, cracks in the rock penetrated to form a failure plane approximately parallel to the axial loading direction, and the strength of rock mass spalling was much smaller than that of intact rock spalling. A triaxial compression test was conducted to analyze the dilatation axial strain and dilatation lateral strain characteristics of gneiss. The results showed that dilatation axial strain gradually increased with the increase of confining pressure, whereas dilatation lateral strain was almost unchanged. Therefore, a safety factor (FS) based on dilatation lateral strain was developed. Through comparison with other strain-based spalling criteria, the establishment and physical meaning of the method were described in detail. In addition, FS was applied to analyze the deep roadway of the Hongtoushan Copper Mine in China and the Rm415 test tunnel in Canada. The results showed that the spalling criterion could accurately indicate the range and depth of the surrounding rock spalling failure, which verified the rationality and applicability of the new spalling criterion. Thus, FS can be utilized as a new theory and analysis tool for the assessment and prevention of spalling failure in deep hard rock roadways.

Investigation on damage evolution mechanism of various FRP strengthened concrete subjected to chemical-freeze-thaw coupling erosion.

The corrosion resistance of FRP-reinforced ordinary concrete members under the combined action of harsh environments (i.e., alkaline or acidic solutions, salt solutions) and freeze-thaw cycles is still unclear. To study the mechanical and apparent deterioration of carbon/basalt/glass/aramid fiber cloth reinforced concrete under chemical and freeze-thaw coupling. Plain concrete blocks and FRP-bonded concrete blocks were fabricated. The tensile properties of the FRP sheet and epoxy resin sheet before and after chemical freezing, the compressive strength of the FRP reinforced test block, and the bending capacity of the prismatic test block pasted with FRP on the prefabricated crack side were tested. The deterioration mechanism of the test block was analyzed through the change of surface photos. Based on the experimental data, the Lam-Teng constitutive model of concrete reinforced by alkali-freeze coupling FRP is modified. The results indicate that, in terms of apparent properties, with the increase in the duration of chemical freeze-thaw erosion, the surface of epoxy resin sheets exhibits an increase in pores, along with the emergence of small cracks and wrinkles. The texture of FRP sheets becomes blurred, and cracks and wrinkles appear on the surface. In terms of failure modes, as the number of chemical coupling erosion cycles increases, the location of failure in epoxy resin sheets becomes uncertain, and the failure plane tilts towards the direction of the applied load. The failure mode of FRP sheets remains unchanged. However, the bonding strength between FRP sheets and concrete decreases, resulting in a weakened reinforcement effect. In terms of mechanical properties, FRP sheets undergo the most severe degradation in the coupled environment of acid freeze-thaw cycles. Among them, GFRP experiences the largest degradation in tensile strength, reaching up to 30.17%. In terms of tensile performance, the sheets rank from highest to lowest as follows: CFRP, BFRP, AFRP, and GFRP.As the duration of chemical freeze-coupled erosion increases, the loss rate of compressive strength for specimens bonded with CFRP is the smallest (9.62% in salt freeze-thaw environment), while the loss rate of bearing capacity is higher for specimens reinforced with GFRP (33.8% in acid freeze-thaw environment). In contrast, the loss rate of bearing capacity is lower for specimens reinforced with CFRP (13.6% in salt freeze-thaw environment), but still higher for specimens reinforced with GFRP (25.8% in acid freeze-thaw environment).

Challenges in the measurement of cross-shore geotechnical characteristics of sandy beach surface sediments

Geotechnical properties of surficial beach sediments affect beach erosion and shoreline changes. This study sets out to measure relative density, moisture content, friction angle, and shear strength of sandy beach surface sediments from dune to swash zone towards the goal of assessing their importance in sandy beach morphodynamics. Methods of sediment sampling, a conductivity based moisture probe, field penetrometers, and a field vane shear were deployed to collect data at the sandy Atlantic-side beach in Duck, North Carolina. The tools used were assessed based on their operability in the beach environment and data quality, and results are discussed in the context of beach morphodynamics. A digital field vane shear provided an efficient and direct method of measuring shear strength, but the difficulty of computing stresses on the failure plane, which is necessary to validate the results, ultimately reduced the usability of this instrument. The results from three penetrometers were compared to a partially-saturated bearing capacity model, where a portable free-fall penetrometer yielded the best fit. However, a modified velocity-dependent strain rate correction factor (K=0.31vi) was required to convert dynamic sediment resistance to a quasi-static resistance for the partially saturated sands. A small-scale digital push in penetrometer also achieved a positive correlation when compared to moisture content, but the small tip diameter (5 mm) coupled with the grain size at the beach (0.35 mm) raised concerns about the ability to derive an accurate measure of strength. It was determined that estimating strength parameter using a partially saturated bearing capacity model was appropriate for water contents less than 25% by volume, or anywhere in the crosshore above the swash to the dune. Relative density and moisture content were found to be closely linked, with partial saturation resulting in samples that featured negative relative densities up to −40%.

Plowing mechanism of rapid flow-like loess landslides: Insights from MPM modeling

Plowing refers to the phenomenon by which a landslide displaces and pushes the path material forward. Despite its importance in shaping the dynamics of many rapid flow-like loess landslides, the mechanism of plowing is not fully understood. Therefore, this paper presents an improved numerical model based on the material point method (MPM). This model takes into account the interactions between the landslide mass and the path material. The reliability of this model was validated by simulating two granular column collapse experiments involving interaction with an erodible mass. The model was then applied to analyze the plowing dynamics of the Ximiaodian loess landslide in Jingyang County, Shaanxi Province, China. A series of well-designed simulations were conducted to investigate this specific landslide event, contributing to a deeper understanding of the plowing phenomenon in loess landslides. The simulation results show that our model can satisfactorily simulate the plowing process of the Ximiaodian landslide. The plowing process of a rapid-flow loess landslide is proposed to consist of four distinct stages: 1) the collision stage, when the landslide strikes the terrace, resulting in the bending of its strata; 2) the shear failure stage, characterized by significant plastic shear deformation within the bent strata, resulting in the formation of multiple shear failure planes; 3) the steady plowing stage, during which the deformation structure in the affected terrace stabilizes and plowing continues in a steady pattern; and 4) the stopping stage, when the propagation of the disturbed terrace gradually stops. Furthermore, the disturbed terrace zone exhibits three distinct deformation structures. In the rear part, a stable zone develops where the terrace layers are compressed. However, due to the compressive forces exerted by the overlying loess, no significant shear deformation is observed. The middle part is the shear failure zone, characterized by the formation of multiple shear failure planes. The front part is the upheaval zone, where the terrace layers are slightly bent and tilted.

Study on progressive failure mode of surrounding rock of shallow buried bias tunnel considering strain-softening characteristics

Mountain tunnels portal often have to pass through slope terrain unavoidably, thus forming a shallow buried bias tunnel. During the construction of shallow buried bias tunnel, disasters such as slope sliding and tunnel collapse frequently occur. The failure mode of surrounding rock obtained by current research is based on the limit equilibrium theory, which cannot reflect the progressive failure characteristics of the surrounding rock of shallow buried bias tunnel. In order to reveal the failure mechanism of the gradual instability of surrounding rock of shallow buried bias tunnel, the problem of gradual failure of the surrounding rock is reduced to an elastic–plastic analysis problem for surrounding rock considering the strain-softening characteristics. Based on the elastic–plastic analysis of the failure process of shallow buried bias tunnel, MATLAB was used to compile a program to read the finite-difference calculation result file, extract the effective information such as shear strain and tensile strain at the center point of each unit, and establish the analysis method of the progressive failure mode of shallow buried bias tunnel. The reliability of the method proposed was verified by comparing the failure process of the model test with the development process of shear strain increment. Under the condition of no support, the formation mechanism of failure plane of surrounding rock on both sides of shallow buried bias tunnel is different. The shallow buried side is the shear failure plane formed by the collapse of surrounding rock, while the deep buried side of the tunnel is the shear failure plane formed by the collapse of surrounding rock and slope sliding. Under the conditions of excavation and support, the failure plane of the shallow buried bias tunnel can be divided into three parts according to the formation sequence and reasons. The part I is the failure plane, which is formed by active shear under the influence of tunnel excavation. The part II is the failure plane formed by tensile crack of slope top. The part III is the failure plane formed by passive shear under the push of the soil in the upper part of the slope.

Failure strength of glacier ice inferred from Greenland crevasses

Abstract. Ice fractures when subject to stress that exceeds the material failure strength. Previous studies have found that a von Mises failure criterion, which places a bound on the second invariant of the deviatoric stress tensor, is consistent with empirical data. Other studies have suggested that a scaling effect exists, such that larger sample specimens have a substantially lower failure strength, implying that estimating material strength from laboratory-scale experiments may be insufficient for glacier-scale modeling. In this paper, we analyze the stress conditions in crevasse onset regions to better understand the failure criterion and strength relevant for large-scale modeling. The local deviatoric stress is inferred using surface velocities and reanalysis temperatures, and crevasse onset regions are extracted from a remotely sensed crevasse density map. We project the stress state onto the failure plane spanned by Haigh–Westergaard coordinates, showing how failure depends on mode of stress. We find that existing crevasse data are consistent with a Schmidt–Ishlinsky failure criterion that places a bound on the absolute value of the maximal principal deviatoric stress, estimated to be 158±44 kPa. Although the traditional von Mises failure criterion also provides an adequate fit to the data with a von Mises strength of 265±73 kPa, it depends only on stress magnitude and is indifferent to the specific stress state, unlike Schmidt–Ishlinsky failure which has a larger shear failure strength compared to tensile strength. Implications for large-scale ice flow and fracture modeling are discussed.

Shear rate and roughness effect on clay-steel interface strength properties in CU and CPD drainage conditions

Based on the concept of the preformed failure plane, this paper conducted a series of clay-interface tests using a modified triaxial apparatus that can directly measure the interface pore pressure, to investigate the shear rate and interface roughness effect on the deviator stress, interface excess pore pressure, interface stress path, and interface friction angle in both consolidated undrained (CU) and consolidated partially drained (CPD) interface drainage conditions. In general, the specimen with the clay-steel interface had a lower shear strength than the pure clay specimen under the same testing conditions. In CU tests, the total and effective interface friction angles increase approximately linearly with the shear rate in the semi-logarithmic scale, while in CPD tests, both the total and effective interface friction angles decrease with increasing shear rate. Moreover, the increased surface roughness is found to enhance the interface shear strength and the maximum interface pore pressure at a given shear rate and confining pressure. In CU tests, both the normalized efficiency parameter E and the corresponding interface friction angle increase with the average roughness (Ra) in a logarithmic relationship, but it is difficult to describe the positive correlation perfectly in CPD tests.

Proportioning optimization of transparent rock-like specimens with different fracture structures

Clarifying the principles of proportioning optimization for brittle transparent rock-like specimens with differential fracture structures is crucial for the visualization study of the internal fracture and seepage evolution mechanisms in rock masses. This study, utilizing orthogonal experimental methods, uncovers the influence mechanisms, extents, and patterns by which the ratios of resin, hardener, and accelerator, along with the freezing duration, impact the mechanical characteristics of transparent rock-like specimens. Notably, it was observed that as the accelerator ratio and freezing time are increased, there’s a general decline in the uniaxial compressive strength, tensile strength, and elastic modulus of the specimens. In contrast, an increase in the hardener ratio initially leads to an enhancement in these mechanical properties, followed by a subsequent decrease. Under uniaxial compressive loading, the specimens exhibit four typical modes of failure: bursting failure, splitting failure, single inclined plane failure, and bulging failure. As the hardener and accelerator ratios increase, the mode of failure gradually shifts from bulging to bursting, with freezing time having a minor overall impact on the evolution of failure modes. The study proposes a method for inducing random three-dimensional closed fractures within the specimens and further clarifies the principles for optimizing the proportions of specimens with different fracture structures, such as intact, embedded regular, and random three-dimensional fractures. This research facilitates the in-depth application of transparent rock-like materials in various scenarios and provides theoretical guidance and technical support for visualizing the evolution of fracture and seepage characteristics within the fractured rock mass.

ANALYSIS OF ROCK QUALITY AND LANDSLIDE POTENTIAL IN NORTH JERING HILLS, SLEMAN, YOGYAKARTA

The study was to identify the direction and type of potential landslides, as well as assess the rock quality on the slopes of North Jering Hills. The scanline method, consisting of stretching the meter, was employed to collect data on the plane of failure. The information gathered encompassed the direction, slope level, and condition of the unsuccessful plane, aligned with the parameters in the RMR table of Bieniawski from 1989. Following the collation of data, kinematic and rock mass quality analysis was undertaken using stereographic projection and RMR parameter weighting respectively. The kinematic analysis revealed a planar avalanche type on the slope. The RMR value of the research location's slope was 80, classifying it as good rock.

Slope Design in Surface Mining with a Total Probability Methodology [Diseño de Taludes en Minería Superficial con una Metodología de Probabilidad Total

The main goal of this research is to propose a methodology for the design of optimal slopes in surface mining, by applying the probability of total failure in the process of determining the geometry of the berm-bench of rock slopes. The rock mass is characterized by being a discontinuous, anisotropic and random medium. Therefore, to design slopes, a deterministic value or Safety Factor that represents the reliability of the design is not sufficient, and the inherent uncertainty of the geotechnical properties must be considered. The stability of slopes at bench level is a function of the quality of the rock mass and is controlled by the strength of the intact rock, the structural rocks, or a combination of both. When the slope has a defined structural control, planar, wedge or toppling failure modes are formed; These, depending on the stability conditions and generates rockfall events. Therefore, it is necessary to apply an effective method to establish the optimal geometry of the bench. The purpose of the berm-bench is to retain and mitigate the risk of rockfall and contain spill from upper slopes due to inherent instabilities, to provide a safe environment for personnel and equipment working near the slopes. The proposed methodology considers the variability of the dip, dip direction, persistence, and friction of the discontinuities. The procedure begins with the collection and analysis of the geotechnical information of the rock mass, which defines geotechnical domains, design sectors and main families of discontinuities; then, statistical analysis and kinematic evaluation are carried out and the conceptual berm width is determined; finally, the kinetic and probability of total failure analysis is carried out, validating the design geometry. The research focused on a domain with 04 sectors of geotechnical design. The results show that the applicable design bench face angle is between 53° and 71°, which corresponds to a berm width of 9.3m to 8.6m and a geometric interramp angle between 36° and 48° respectively. Likewise, probabilities of total planar failure of up to 31% and total wedge of 41% were obtained according to the geotechnical peculiarities of each sector. It was proven that, in the sectors with a greater probability of failure, a lower bench face angle and a greater catch bench of the design berm are considered acceptable designs, due to a greater probability of crest loss. Finally, in the sectors with a lower probability of failure, a greater interramp angle is considered an acceptable design. In conclusion, through the applied methodology it has been demonstrated that the results of the berm-bench design process meet the acceptability criteria of the Probability of Failure. Therefore, the developed method, which considers the variability of the parameters of the rock mass discontinuities, allows designing safe and reliable slopes validated through an acceptable level of probability.

Direction-dependent failure envelopes of sand-structure interfaces with snakeskin-inspired surfaces

Snakeskin-inspired surfaces generate direction-dependent interface strengths, with shearing in the cranial direction (i.e.; against the scales) generating greater strength than in the caudal one (i.e.; along the scales). This directionality is enabled by the transfer of load in friction and passive resistances. It is unclear if failure of these interfaces can be captured by models used for purely frictional interfaces. Interface shear tests complemented with particle image velocimetry (PIV) analyses were performed on snakeskin-inspired surfaces with different asperity geometries and on reference rough and smooth surfaces. The results of experiments performed at different initial effective stresses under constant normal stiffness boundary conditions show significant dilation-induced increases in effective stress. These increases were greater during cranial than caudal shearing, producing greater cranial strengths. These surfaces yielded nonlinear failure envelopes, with greater shear to effective stress ratios at smaller effective stresses, while the rough and smooth surfaces mobilized linear failure envelopes. The PIV analyses indicate that the snakeskin-inspired surfaces induce localized strains in the vicinity of the asperities, leading to wavy failure planes. The average shear strains are correlated with the mobilized shear strengths, with increases in effective stress leading to decreases in both strains and stress ratio.

Modelling the brittle rock failure by the quaternion-based bonded-particle model in DEM

This paper presents an investigation of brittle rock failure by the quaternion-based bonded-particle model in discrete element method (DEM). Unlike traditional approaches that utilize Euler angles or rotation matrices, this model employs unit quaternions to represent the spatial rotations of particles. This method simplifies the representation of 3D rotations, providing a more intuitive framework for modelling complex interactions in granular materials. The numerical model was validated by the uniaxial compression tests on rock, with good agreement with well-documented experimental data in terms of the rock uniaxial compression strength (UCS) and failure mode. During loading, the rock sample demonstrated a linear-elastic response at an axial strain of smaller than 0.45%. However, as internal bond breakage accumulated, this linear relationship weakened, and the stress-strain curve began to deviate from its initial linear trajectory. The bond breakage and the overall deformation of the rock were primarily controlled by the shear bonding force. The UCS was achieved at an axial strain of 0.625%, at which point the internal shear bonding force chains were predominantly aligned vertically. The brittle failure occurred when the internal damage of solids nucleated to form an interconnected failure plane, accompanied by a sharp rise in the internal damage ratio. The area of failure plane increased with the loading strain rate, gradually transforming the failure pattern from the local damage to a complete fragmentation.

Behavior of back-to-back mechanically stabilized earth walls as railway embankments

Twelve physical model tests were carried out to investigate the role of the type and arrangement of reinforcements on the behavior of back-to-back mechanically stabilized earth walls (BBMSEWs) supporting railway tracks. Six metal-strip reinforced BBMSEW models and six geogrid reinforced models were prepared with different reinforcement arrangements and then were vertically loaded to failure using wooden railway sleepers. The findings indicated that the reinforcement stiffness played a more prominent role in improving the bearing capacity than the pull-out capacity. The connection of two opposing walls with continuous reinforcements and the complete separation of them from each other were found to be the best and worst reinforcement arrangements, respectively, for improving the bearing capacity and reducing wall deformation in BBMSEWs. The respective use of these two arrangements mobilized the maximum and minimum forces in the reinforcements. Moreover, the creation of a proper connection between the opposing walls using continuous inextensible reinforcements or those with a sufficient overlap length were found to be efficient solutions to preventing the propagation of a failure plane across the back-to-back MSE walls.

Dip effect on the orientation of rock failure plane under combined compression–shear loading

Shear failure often occurs in engineering rock mass (such as inclined pillar) in gently inclined strata. Prediction and characterization the orientation of shear failure plane is the foundation of rock mass engineering reinforcement. In this paper, sandstone samples are used to perform uniaxial and shear tests to obtain the basic mechanical parameters. Then, by employing the numerical method, the combined compression–shear loading tests were carried out for inclined specimens varied from 0° to 25° at an interval of 5°, to obtain the dip effect on the orientation of rock failure plane. The results show that the failure plane of rock changes with the change of dip angle of rock sample. Based on the Mohr–Coulomb criterion, the ultimate stress state of rock was characterized under combined compression–shear loading. The ultimate strength of rock is equal to the ratio of the stress circle radius of rock under combined compression–shear condition to the stress circle radius of rock under uniaxial compression condition, multiplied by the uniaxial compressive strength. The fracture angle of rock was defined under combined compression–shear loading. A theoretical model was developed for predicting the fracture angle. The developed model could be characterized by internal friction angle, dip angle of rock sample and Poisson's ratio. Finally, the numerical results of the fracture angle were analyzed, which are consistent with the predicted results of the model. The investigation shows that the rock fracture angle has a dip effect, which decreases with the increase of the inclination angle of the sample. The research results provide a new means to identify the potential failure plane of engineering rock mass, and lay a theoretical foundation for calculating the orientation of rock fracture plane.

Investigation of constitutive properties of high plasticity clay soils mixed with crushed rubber tire waste

Addressing the enormous waste resulting from discarded worn rubber tires is an environmental challenge. Recycling and using crushed rubber tire waste (CRTW) in construction materials can help in addressing this challenge. This study investigates the effect of addition of CRTW on the engineering properties of high plasticity clay soils (HPCS). There is a paucity of research in the application of CRTW in HPCS. This research tries to fill this research gap. Specifically, this study seeks to investigate the effect of mixing CRTW on the constitutive properties of HPCS. After identifying a locally available HPCS, mixtures of the clay and several percentages (0%, 6%, 12%, 18%, and 24%) by weight of CRTW were prepared. A range of CRTW shapes and sizes were investigated. Three different particle shapes of CRTW (granular rubber, rubber chips, and rubber fiber), and two particle sizes (fine and coarse) were studied. The parameters studied included unconfined compressive strength (UCS), strain at failure, post-peak strength loss (PPSL), modulus of elasticity, failure modes/mechanisms, repeatability of tests results, and examination of CRTW particles and mixtures via binocular and SEM microscope. Our findings unveiled that the highest level of repeatability was observed in granular CRTW, with a maximum variability of only 5%. Moreover, the mixtures containing granular CRTW exhibited, on average, 10% and 15% higher strength and modulus of elasticity, respectively, in comparison to mixtures incorporating other shapes of CRTW. In general, the HPCS-CRTW mixtures displayed higher shear strains, averaging 25% greater than pure HPCS. Furthermore, the addition of CRTW to HPCS resulted in a reduction of its PPSL and a transition in behavior from brittle to slightly ductile. Examination of failed specimens revealed the existence of two primary failure modes: shear plane failure and shear plane failure accompanied by multiple vertical cracks within the mixtures. These results suggest that the utilization of granular CRTW in HPCS can improve certain properties of HPCS. However, it is advisable to limit the rubber content in this mixture to 6% to mitigate significant adverse effects on its strength.

Influence of Hydraulic Distribution Pattern on the Rock Slope Stability under Block Toppling Failure

In this paper, an analytical model for the stability analysis of rock slope subjected to block toppling pertaining to different hydraulic forms has been developed. In the traditional analytical model, ground water pressure is considered to be varied hydrostatically. To better reflect the physical situation, three different hydraulics forms have been considered in developing a stability model for a rock slope susceptible to block toppling. It is well known fact that presence of ground water causes the instability in a rock slope. The present study observes that hydraulic distribution forms also significantly influence the stability of the rock slope. Ground water pressure markedly increases the toppling forces on the blocks and reduces the normal and shear force at the base of block along failure plane, thereby causing instability. The increase in toppling force and reduction in the factor of safety on the blocks are more prominent when the flow slit is blocked, indicating a condition of permanent or seasonal frozen strata. The study highlights that adopting the traditional hydraulic form to analyse block toppling stability, considering presence of ground water would not be suitable for all field conditions. This necessitates the selection of an appropriate hydraulic distribution form based on the encountered field conditions.

Forensic Analysis of a Distressed Railroad Embankment

Land subsidence is becoming a prevalent worldwide occurrence, perhaps with a devastating impact on civilian lives. Moreover, natural and man-made slopes formed are susceptible to damage unless there is adequate stability. The bulk of the slope failures is due to intensive rains. Examination of slope stability due to massive rains is an important issue to inspect in the area with high precipitation. This study is aimed at exploring the effects of severe flooding on the stability of the slope. A 30 m long railroad embankment failure that happened on May 25, 2011, in the city of Ann Arbor, Michigan, is introduced. The collapse happened due to the rainy season that brought about ponding water against the embankment and sufficiently high-water pressures that brought about the instability of the railroad embankment. The back investigation is a much more dependable and predictable strategy to evaluate the shear parameters in situ. The back investigation of a slope is solved using the Resistance Envelope method wherein the embankment is divided through a certain number of slices. Forces on each slice are estimated and the potential failure surface is identified. The shear parameters are extracted employing the resistance envelope method for the actual failure plane and are verified with the initial condition. This study aims to find the impact of precipitation on slope stability using Geostudio 2012 software.

Experimental Study on the Effect of High Temperature on the Physical and Mechanical Properties of Sandstone with Different Bedding Angles

As a typical sedimentary rock, the number of beddings in the horizontal direction of sandstone is far greater than that in the vertical direction, leading to its physical and mechanical properties showing obvious anisotropy with changes in bedding angle. After high temperature exposure, bedding damage further transforms the change rule of the physical and mechanical properties of sandstone with the bedding angle. This study tested the appearance, wave velocity, uniaxial compression, and conventional triaxial compression properties of sandstone with five bedding angles before and after high temperature exposure. The results show that (1) the longitudinal wave velocity, shear wave velocity, elastic modulus, and cohesion decreased, while the internal friction angle increased slightly. At the same temperature, when the dip angle of sandstone was 30° or 60°, the mechanical properties were optimal, and when the dip angle was 45°, the mechanical properties were the worst. (2) High temperature increases the development degree of micropores and microfractures in the sandstone bedding plane and matrix, thus increasing the anisotropy degree of the physical and mechanical properties of sandstone with different bedding angles. (3) With increasing temperature, the rock samples gradually transitioned from brittle failure to ductile failure. Sandstone with a bedding angle of 0° presented splitting failure that vertically penetrated the bedding plane at different temperatures. Sandstone with dip angles of 30° and 40° presented shear failure that penetrated the matrix and bedding plane. A failure plane along the bedding plane appeared at the end. Sandstone with dip angles of 60° and 90° was more prone to failure along the bedding plane, showing shear failure along the bedding plane and tensile failure along the bedding plane, respectively.

Formula omitted]-TFA based multiscale analysis of failure in elasto-plastic composites

This paper describes a novel homogenization methodology for analyzing the failure of elastoplastic composite materials based on elastic and eigen influence tensors-driven transformation field analysis (E2-TFA). The proposed technique considers the microscopic eigenstrain field accounting for intra-phase damage and inelastic strains. This results in realistic computations by alleviating the post-damage stiffness response, which is a drawback of TFA-based methods. We attain computational efficiency by identifying the preprocessing data solely from the elastic and eigen transformation functions and adopting a reduced order modeling technique with a piecewise constant eigenstrain field throughout the subdomains. The performance of the model is assessed by simulating the response for (a) the representative volume element (RVE) as a homogenized continuum and (b) the various composites under complex load histories with intricate macroscale morphologies. Furthermore, the nonlinear shear stress–strain response of a glass fiber composite is calculated and compared to experimentally measured fracture initiation parameters, failure plane orientation, and strain histories. Finally, we show that E2-TFA can accurately and efficiently capture damage and inelastic deformations in order to estimate the mechanical response of composite materials in a better way.

Earthquake design loads for retaining walls

Free-standing retaining walls are usually designed for earthquake loads assuming cohesionless backfill soil and using the Mononobe-Okabe method. This simple design approach has led to satisfactory performance and is supported by laboratory testing and analytical studies. For major wall structures there are a number of refinements to the method that should be considered. In the paper methods of assessing the influence on the earthquake loads of the flexibility of the wall, soil cohesion and ground water in the backfill are presented. Equations for predicting failure plane angles to allow a better assessment of the soil properties within the failure wedge are included. Procedures for estimating the outward displacement and the influence of passive resistance and wall geometry on the sliding resistance are discussed. Design charts are presented which allow the magnitude of these refinements to be rapidly assessed.