Failure Plane Research Articles

Understanding progressive rock failure and associated seismicity using ultrasonic tomography and numerical simulation

Monitoring the stability of underground rock excavation zones, such as tunnels and underground mines, is critical to their operational safety. The stability of these structures is related to the stress redistribution introduced by the excavation process and disturbance during the operation. Therefore, the characteristics of progressive rock failure behaviour at different stress conditions must be investigated. In this study, we address this problem using a laboratory experiment, coupled with ultrasonic tomography (UT) and numerical simulation. A time-lapse two-dimensional (2D) UT observation was conducted on a granite slab under uniaxial compression. This test was then reproduced numerically by the combined finite-discrete element method (FDEM). This innovative combination of technologies depicted the entire deformation and failure processes at macroscopic and microscopic scales. Quantitative assessments of the results suggested six precursory behaviours indicating the catastrophic failure of the rock: (1) decrease of the average wave velocity perpendicular to the loading direction, (2) increase of the heterogeneity and anisotropy of wave velocity, (3) exponential increase of seismic rate, (4) spatial localization of damage onto the failure plane, (5) increase of the dominance of shear failure, and (6) slight recovery of b-value, followed by a significant drop. An integrated monitoring and analysis of these indicators, accompanied by carefully calibrated numerical simulations, may provide vital information regarding the stability of underground structures.

Analytical expressions for determining the stability of cohesionless soil slope under generalized seismic conditions

In recent major earthquakes, the researchers have found the need for consideration of vertical seismic acceleration for the stability analysis of the man-made and natural slopes. However, in most past studies, the performance of slopes has been assessed by accounting only the horizontal seismic component of the ground motion, without giving due weightage to the effect of vertical component. In the present study, analytical expressions are derived to determine the factor of safety, yield seismic coefficient and consequently the seismic displacement of cohesionless soil slope under combined horizontal and vertical components of the ground motion. The derivation uses the Newmark’s sliding block approach, in which the soil slope with a planar failure surface within the framework of conventional pseudo-static analysis is assumed to follow the Mohr-Coulomb failure criterion. The effects of vertical seismic coefficient on the stability of cohesionless slope have been studied through a set of graphical presentations for a specific range of soil parameters. It is observed that overlooking the effect of the vertical component of the ground motion on factor of safety and the displacement while designing the slope may be detrimental, resulting in the slope failure. The general expressions presented in this paper may be highly useful in the field of earthquake geotechnical engineering practice for designing the cohesionless soil slopes under combined horizontal and vertical seismic loads.

The Ideal Plasticity Theory Usage Peculiarities to Concrete and Reinforced Concrete

The usage aspects of ideal plasticity theory for concrete and reinforced concrete are investigated. The plastic deformation is considered to be localized n thin layers on the failure plane which divides the element into rigid parts. The variation method is used and the solutions in discontinuous functions are received. The functional of virtual velocities principle is investigated to stationary condition, the minimal capability of plastic deformation is found with which the solid changes into the mechanism. The limit and realization criterion of concrete failure under shear are set. The reinforcement influence on the element load-carrying capacity is taken into account.

Dynamics of the Askja caldera July 2014 landslide, Iceland, from seismic signal analysis: precursor, motion and aftermath

Abstract. Landslide hazard motivates the need for a deeper understanding of the events that occur before, during, and after catastrophic slope failures. Due to the destructive nature of such events, in situ observation is often difficult or impossible. Here, we use data from a network of 58 seismic stations to characterise a large landslide at the Askja caldera, Iceland, on 21 July 2014. High data quality and extensive network coverage allow us to analyse both long- and short-period signals associated with the landslide, and thereby obtain information about its triggering, initiation, timing, and propagation. At long periods, a landslide force history inversion shows that the Askja landslide was a single, large event starting at the SE corner of the caldera lake at 23:24:05 UTC and propagating to the NW in the following 2 min. The bulk sliding mass was 7–16 × 1010 kg, equivalent to a collapsed volume of 35–80 × 106 m3. The sliding mass was displaced downslope by 1260 ± 250 m. At short periods, a seismic tremor was observed for 30 min before the landslide. The tremor is approximately harmonic with a fundamental frequency of 2.3 Hz and shows time-dependent changes of its frequency content. We attribute the seismic tremor to stick-slip motion along the landslide failure plane. Accelerating motion leading up to the catastrophic slope failure culminated in an aseismic quiescent period for 2 min before the landslide. We propose that precursory seismic signals may be useful in landslide early-warning systems. The 8 h after the main landslide failure are characterised by smaller slope failures originating from the destabilised caldera wall decaying in frequency and magnitude. We introduce the term “afterslides” for this subsequent, declining slope activity after a large landslide.

Inter-fibre failure of through-thickness reinforced laminates in combined transverse compression and shear load

Extensive studies have been reported on the improvement of through-thickness reinforcement to inter-laminar performance of composite laminates; current understanding on the in-plane performance is relatively limited, although it is also concerned in industrial application. The influence of through-thickness reinforcement (Z-pinning) on the inter-fibre failure in compression of unidirectional laminates was investigated. Both unpinned and Z-pinned laminates were tested at four different off-axis angles, representing different combinations of transverse compression and in-plane shear stress. It was found that the stiffness of Z-pinned laminates decreased significantly in all off-axis angles. The failure strain and strength were reduced in shear dominated failure modes, while improved in the compression dominated failure modes by the presence of the Z-pins. A further investigation on the angle of failure plane was carried out and a comparison with analytical failure models is presented.

Prediction of earthquake-induced slope displacements considering 2D topographic amplification and flexible sliding mass

The Newmark approach is commonly used in predicting earthquake-induced displacements as an index of slope stability under seismic loading. However, this method is limited to a rigid block assumption in which the incident wave fails to interact with either the slope geometry or the sliding mass. In reality, ground motions are amplified near the slope crest due to the topographic effect or de-amplified at deep failure planes that consider the overlying deformable sliding mass. Therefore, a series of 2-dimensional (2D) dynamic analyses are performed to characterize this interaction behavior in this study. A general prediction model for slope response that considers both the topographic effect and flexible sliding mass is developed based on peak ground acceleration and mean period of incident ground motions conditioned on the natural period of sliding mass and the slope angle. Consequently, the predicted displacement of the 2D slope under seismic loading is achieved using the proposed prediction model of slope response in conjunction with the previously developed rigid displacement prediction model.

Experimental study and failure criterion analysis of plain concrete under combined compression-shear stress

To study the mechanical properties of plain concrete (with a standard compressive strength of 30 MPa) under combined compression-shear stress, the concrete was tested using material compression-shear hydraulic servo machine under various axial compression conditions. In the experimental study, the shear failure modes and shear load-displacement curves of concrete are obtained. The peak shear strength and residual strength of concrete are then extracted from the load-displacement curves. A total of three development stages of shear load-displacement curves are identified and mechanical characteristics at each stage are analyzed. The results show that the shear failure behavior of concrete under different axial compression is quite different, and as the increase of axial compression ratio, the traces of friction on shear plane get more evident and the concrete failure slag also increases. Based on the experiment data and regression analysis, it is observed that both the peak shear strength and residual strength of concrete increase linearly as the increase of axial compression ratio. From the residual strength analysis, the shear failure plane of plain concrete has a relatively stable friction coefficient of 1.46. According to octahedral stress space analysis and unified strength theory, the failure criterion curves of concrete under compression-shear stress are obtained and the results fit the test data well. The proposed two types of failure criterion theories can effectively model the strength law of plain concrete under combined compression-shear stress.

Acoustic emission and kinetic fracture theory for time-dependent breakage of granite

Earthquakes, mine failures, and initiation of hydraulic fractures have all been associated with time-delayed breakage of rocks subjected to loads insufficient to incur instantaneous failure. To better model and identify failure precursors for rocks under these so-called static fatigue conditions, Acoustic Emission (AE) was monitored in beams of Coldspring Charcoal Granite subjected to constant three point loading. As a result of varying the magnitude of the loading, the times to failure range from O(101)toO(105) seconds. The experiments show a number of consistencies in the AE data. In all cases the event rate exponentially declines for a period that is about 0.4–0.6 of the total time to failure. This period is followed by a period in which the event rate exponentially increases. The total number of events generated during these two periods is also consistent among the experiments. Motivated by these observations, we propose a modified kinetic fracture theory that captures both the period of event rate decline and the period of event rate increase. It does this by firstly accounting for early time depletion of available bonds for breakage, similar to previous models. The model also accounts for generation of critically stressed bonds in the vicinity of previous bond breakages due to stress redistribution, thereby also predicting the event rate increase and further providing consistency with the observed tendency of the events to become increasingly concentrated around the eventual plane of failure as time progresses.

The role of the intermediate principal stress on the direction of damage zone during hydraulic stimulation

The Mohr–Coulomb criterion is widely used to describe rock failure and the orientation of failure planes with respect to the stress field. However, in many cases, the seismic clouds created during hydraulic stimulations do not follow the orientations predicted by the Mohr–Coulomb criterion. In this paper we model rock deformation using continuum damage mechanics and calibrate the parameters using the stress-strains curve and failure of laboratory rock samples (KTB amphibolite and Westerly granite) under true-triaxial loading. We then present results of numerical simulations of the evolving fault structure associated with fluid injection. We simulate the effects of σ2 on failure conditions and failure plane orientation initiated and driven by fluid injected in the center of the simulated rock volume. A pore pressure rise at the injection point decreases the volumetric strain while keeping the deviatoric strain unchanged. Therefore the failure process starts close to the injection well, where the pore pressure is the highest, and propagates away from the well as more fluid reaches the tip of the damage zone. The final geometry of the damage zone demonstrates that the orientation of faulting is strongly affected by σ2. The angle between σ1 and the damage zone changes from 35° at σ2= σ3 to almost 0° at σ2= σ1. At σ2= σ3 (σx=σy), cylindrical symmetry allows many possible conjugate directions and poly-modal fault patterns with orthorhombic symmetry comprising clusters of four sets of shear failure planes. The Mohr–Coulomb criterion is shown to be valid only at σ2= σ3. Although not exactly following the Mohr–Coulomb criterion, when σ2 is less than halfway between σ1 and σ3, it can still be considered as a good approximation. When σ2 is more than halfway between σ1 and σ3, deformation is more similar to mode-I type failure geometry. Yet, the direction of the damage zone meanders and is not always parallel to σ2. The curvature of the meanders decreases with increasing σ2. The mechanism that creates the geometry related σ2 is related to the effect σ2 has on the proximity to failure.

New methodology for estimating the shear strength of layering in slate by using the Brazilian test

A new method is proposed in order to estimate the shear strength of schistosity planes in slate in terms of Mohr–Coulomb cohesion and internal friction angle. The procedure consists in carrying out the Brazilian method under different loading-foliation angles, for which experimental tests were achieved in slates from the northwest of the Iberian Peninsula (Spain). The experimental fracture patterns were analytically studied and justified by simulating the stress field in the discontinuity planes contained in the whole sample, taking into account the first failure registered in the tests. By combining experimental and analytical studies and a procedure based on the representation of the threshold state of stresses—in the elastic regime—in the failure plane, it is possible to estimate the foliation’s strength envelope through a lineal adjustment according to the Mohr–Coulomb criterion and, thus, to characterize the layering. Finally, the proposed procedure was validated by the direct shear test. The cohesion and the internal friction angle obtained with this convenctional test were very close to that calculated by the proposed method, verifying the methodology developed by the authors. This procedure may be interesting in various engineering applications, either in the study of the properties of cleavage in slate, which is commonly used as an industrial rock, or in dam foundations, underground excavations and slope engineering, since one of the main failures in civil engineering is due to sliding along weak planes.

Weathering and Excavation Effects on the Stability of Various Cut Slopes in Flysch-Like Deposits

Cut slopes are very sensitive to weathering because of disturbed rock mass and topographical condition by excavation. During and right after an excavation process of a cut slope, weathering and erosion may act on this newly exposed rock material and mass. These acting on the rock may degrade and change its engineering properties and the stability of the cut slope in its engineering lifetime. In this study, weathering and excavation effects on stability of sixteen cut slopes in flysch-like deposits at North West Black Sea region of Turkey were investigated. The properties of the weathered and fresh rock materials including unit weight, uniaxial compressive strength, direct shear, slake durability and methylene blue tests were determined in the laboratory. Kinematic, limit equilibrium and rockfall analyses were performed for each stop. It was found that two testing cycles are insufficient to assess the degradation of the rocks based on the slake durability test results. Based on the limit equilibrium analyses, plane failure is expected with low factor of safety in one of the cut slopes. Factor of safeties of the cut slopes for mass failure are generally high except two slopes also evidenced with the field observations. No significant rockfall problems are expected according to the analyses. The effects of weathering and excavation were found to be changing between 10 and 50 cm in average within 5 years lifespan of the cut slopes. According to the results these disturbed zones would only create surficial degradation for the current thicknesses.

The Effect of Joint Dip Angle on the Mechanical Behavior of Infilled Jointed Rock Masses under Uniaxial and Biaxial Compressions

Due to the complex formation process of a rock mass, a large number of fissures, joints, faults, other defects exist and the defects commonly contain infilled materials. The jointed rock masses are in a complex geological environment, in which the geometric distribution and the boundary condition can greatly affect the mechanical behavior of the infilled jointed rock mass. In this study, the infilled jointed rock mass specimens with different dip angles are prepared using similar materials, and the uniaxial and biaxial compression tests on the specimens are conducted. The effect of the joint dip angle on the mechanical behavior of the infilled jointed rock mass under uniaxial and biaxial compressions is investigated. The results show that the uniaxial compressive strength shows a W-shaped variation, and the biaxial compressive strength shows a V-shaped variation with an increase in the dip angle. Most of the cracks appear in pairs around the joint and occur symmetrically in a bilateral distribution, and the existence of the infilled joints induces a nonlinear mechanical behavior in the specimen. In addition, the specimens exhibit three failure modes under uniaxial compression: splitting failure, step-path failure and planar failure. The specimens present two failure modes under biaxial compression: splitting failure and planar failure.

Influence of hydraulic characteristics on stability of unsaturated slope under transient seepage conditions

This paper examines the current procedure for determining the soil-water characteristic curve (SWCC) model with a particular focus on its application to slope stability analysis under transient unsaturated seepage conditions. A series of laboratory experiments was performed to determine the SWCC of different soils, ranging from high plasticity clay to silty sand, found across the Korean Peninsula. The experimental results were utilized to identify the suitable SWCC model for each soil type based on the fitting criterion. Also, this paper developed a numerical framework for infinite slope stability analysis under transient unsaturated seepage conditions. The significant advantage of the proposed framework, from the practical viewpoint, is to directly predict the timing of failure and potential failure plane based on rainfall recording. The effect of choice of SWCC models on predictability in stability analysis was evaluated by adopting the present framework along with the identified SWCC models. Furthermore, a case study of landslides after a 3-month rainfall in Pohang, Korea, was revisited to assess the performance of the proposed framework. The obtained results demonstrate the significant role of SWCC model on the results of slope stability analysis. The analysis using the SWCC model satisfying the fitting criterion could still not capture the real behavior of unsaturated soil. The comprehensive transient analysis is strongly suggested as a complementary means to the current fitting criterion for determining the suitable SWCC model for stability analysis under transient seepage conditions.

Modelling of R/C members accounting for shear failure localisation: Hysteretic shear model

SummaryReinforced concrete (R/C) frame buildings designed according to older seismic codes represent a large part of the existing building stock worldwide. Their structural elements are often vulnerable to shear or flexure‐shear failure, which can eventually lead to loss of axial load resistance of vertical elements and initiate vertical progressive collapse of a building. In this study, a hysteretic model capturing the local shear response of shear‐deficient R/C elements is described in detail, with emphasis on post‐peak behaviour; it differs from existing models in that it considers the localisation of shear strains after the onset of shear failure in a critical length defined by the diagonal failure planes. Additionally, an effort is made to improve the state of the art in post‐peak shear response modelling, by compiling the largest database of experimental results for shear and flexure‐shear critical R/C columns cycled well beyond the onset of shear failure and/or up to the onset of axial failure, and developing empirical relationships for the key parameters defining the local backbone post‐peak shear response of such elements. The implementation of the derived local hysteretic shear model in a computationally efficient beam‐column finite element model with distributed shear flexibility, which accounts for all deformation types, will be presented in a companion paper.

Extension of Puck's inter fibre fracture (IFF) criteria for UD composites

Puck's action plane failure criteria have already proven their capability in the first and second world-wide failure exercises (WWFE-I and WWFE-II). However, Puck and his co-workers have only recommended inclination parameters for GFRP/Epoxy and CFRP/Epoxy. These UD composites generally have high transverse compressive-to-tensile strength ratios YC/YT, and are regarded by them as intrinsically brittle materials. Therefore, Puck's inter fibre fracture (IFF) criteria might not be directly applied to other types of UD composites with low YC/YT ratios. In particular, Puck's original IFF criteria will result in unrealistic predictions if YC/YT is extremely low. In the present study, Puck's original IFF criteria are extended to all types of UD composite materials to solve the problem. Composites are divided into three categories, namely semi-brittle materials, brittle materials, and intrinsically brittle materials. Depending on the material category, three different algorithms are proposed for determination of the two parameters in Puck's IFF criteria, namely the resistance of the action plane against transverse tensile stressing, R⊥At, as well as the inclination parameter of contour lines of the fracture body, p⊥⊥. The present criteria are theoretically evaluated for composites with low YC/YT ratios, while the predictions of the present criteria are compared with the test results of composites with high YC/YT ratios such as thermoset GFRP and CFRP. Theoretical and experimental assessment demonstrates the reasonableness of the extension of Puck's IFF criteria.

Simple three-dimensional Mohr-Coulomb criteria for intact rocks

A major component of the Mohr-Coulomb (M-C) criterion is that the failure of the material is independent of the intermediate principal stress σ2 along the potential planes of sliding. To account for the effect of σ2, a linear relationship between the octahedral shear stress τoct and the mean stress σm,2 on the plane of failure (called the Mogi-Coulomb criterion) is widely used to represent rock failure in polyaxial compression (PXC) in practice. In this research, a linear relationship between the equivalent stress σe (or τoct) and major principal stress σ1 (or minor principal stress σ3) is proposed, which has a similar expression as the Mogi-Coulomb criterion. The relationship between the proposed failure criteria and M-C criterion is like the relationship between the Tresca and Von-Mises criteria. The material parameters can be related to the M-C strength parameters, and can be easily obtained from conventional triaxial tests. The proposed criteria are numerically calibrated against triaxial compression (TXC) and PXC data sets using three different methods. Sensitivity of the range of TXC stress data employed for fitting on the prediction results in PXC are further discussed. Comparisons of two proposed criteria with the Mogi-Coulomb criterion for rocks in PXC demonstrate that one new criterion with convex failure envelope gives the best performance for seven rock types and provides an acceptable modelling for the rest of rock types. Another new criterion and the Mogi-Coulomb criterion result in large prediction error for three (or two) rock types though they can give best performance for some rock types.

Response of RC panels accounting for crack development and its interaction with rebars

The response of reinforced concrete (RC) elements subjected to in-plane shear and axial stresses is governed by various potential failure mechanisms. For structural panels subjected to uniform stress states, their ultimate strength can be governed by yielding of the reinforcement, crushing of the concrete struts, sliding along a failure plane or spalling of the concrete cover. Although some expressions have been proposed in the literature to address this issue, they normally are empirical or semi-empirical in nature and do not distinguish among the failure mechanisms and their interaction. The purpose of this paper is to derive a mechanically-based efficiency factor for concrete in compression that is able to predict the actual behaviour of structural cracked concrete. This approach is shown to suitably predict the various potential failure modes and the development of the secondary shear cracks as well as the interaction between the reinforcement and the concrete.

Probability of Failure and Slope Safety Factors Based on Geological Structure of Plane failure on Open Pit Batu Hijau Nusa Tenggara Barat

Batu Hijau is a gold mine which is now run and managed by PT Amman Mineral Nusa Tenggara (PT AMNT) with open mining method. The located in Sekongkang District, West Sumbawa Regency - West Nusa Tenggara Province. The geological structure aspects are interesting as objects in this study, due to the condition is very tight and become to trigger for the slope failure. Slope stability is one of the important terms for supporting in open pit mining activities. One of the slope failure indication is the failure caused by the structure. Geological structure analysis performed with kinematic analysis which takes into account the probability of failure and type of failure. The probability of Failure can count by structure orientation, the orientation of the mine slope design, and friction angle with using dips 6 software. The percentage of slide obtained from the ratio between the critical point from the critical zone with the total critical point in stereographic projection. The count applied in all geotechnics domain with inputting of parameter structure orientation, the orientation of the mine slope design, and friction angle. The result shows between 0% to 2.63% of planar failure. The percentages show probability of failure but still in the safe category with 10% safety limit. Slope safety factor counts manually based on the mathematical formula applied to all domains in Batu Hijau Open Pit Mining. The result shows the value between 1.04 to 1.905 on planar failure. This value shows the condition of slope in the research site is stable.

Failure potential of infinite slopes in bonded soils with tensile strength cut-off

Infinite slope analyses are used in practice to assess the safety of slopes against shallow slides, with much of the soil mass moving parallel to a plane failure surface. Stability calculations typically involve the Mohr–Coulomb yield function, but the limitation on tensile strength is discussed and applied in stability considerations for bonded soils. Once the strength envelope is truncated in the tensile regime, the envelope becomes nonlinear and the normality flow rule admits deformation with large volumetric strains. For gentle slopes and in the absence of seepage, the difference in factors of safety calculated with and without tensile strength cut-off is small. However, in the presence of seepage and with increasing inclination of slopes, the difference becomes significant. As the deformation regime moves into the nonlinear portion of the yield envelope, application of the traditional definition of the factor of safety is not straightforward. If the strength envelope is truncated with a circular arc, then the envelope reduced by the factor of safety assumes an elliptical shape. The novelty in this paper is in presenting an analysis for bonded geomaterials with tensile strength cut-off, and indicating that tension cut-off can have a significant impact on the outcome of stability analysis for steep slopes subjected to seepage.

Modelling of R/C members accounting for shear failure localisation: Finite element model and verification

SummaryReinforced concrete (R/C) frame buildings designed according to older seismic codes represent a large part of the existing building stock worldwide. Their structural elements are often vulnerable to shear or flexure‐shear failure, which can eventually lead to loss of axial load resistance of vertical elements and initiate vertical progressive collapse of a building. In this study, a computationally efficient member‐type finite element model for the hysteretic response of shear critical R/C frame elements up to the onset of axial failure is presented; it accounts for shear‐flexure interaction and considers, for the first time, the localisation of shear strains, after the onset of shear failure, in a critical length defined by the diagonal failure plane. Its predictive capabilities are verified against experimental results of column and frame specimens and are shown to be accurate not only in terms of total response, but also with regard to individual deformation components. The accuracy, versatility, and simplicity of this finite element model make it a valuable tool in seismic analysis of complex R/C buildings with shear deficient structural elements.