Failure Envelope Research Articles

Influence of sample preparation method on static liquefaction behaviour of geotextile reinforced sandy soil

This paper aims to evaluate the influence of soil deposition methods on the shear strength of reinforced sand using a triaxial test. Non-woven geotextile layers were used as reinforcement in the experiment to reconstitute specimens of natural sand prepared at loose relative density (Dr = 30%). Arrangements of reinforcement layers (0, 1 and 2 layers) on soil samples were prepared using two different deposition methods [dry funnel pluviation (DFP) and wet deposition (WD)] and consolidated under three levels of confining pressures. Result shows that geotextile inclusion improves the mechanical behavior of sand; a significant increase in the shear strength is obtained by adding up layers of reinforcement. However, it reveals also that the soil-geotextile reinforcement interface efficiency is directly related to the number of layers and the soil dispositional method as well as their initial state. Since, the DFP method exhibits samples strain hardening compared to the WD samples which is very sensitive to static liquefaction. It is important to note that the difference in behavior of test on reinforced WD samples was attributed to the strain at failure, where unreinforced soil tested at ({text{p}}_{{text{c}}}^{{prime }} = {50},{text{kPa}}) has attained complete liquefaction at small stain (εfa = 1.6% for sample tested at 50 kPa of confining pressure) compared to reinforced samples tests in which failure envelope be found for more axial strain.

Numerical study on the combined bearing performance of tripod-bucket foundation for floating and fixed wind turbines

The tripod-bucket foundation has been proposed as an alternative foundation type for floating and fixed wind turbines. Its combined bearing capacities are necessary for describing the ultimate load combinations of the foundation. In this paper, three-dimensional finite element models of tripod-bucket foundations are constructed based on the structure-soil-interaction. Considering the foundation being used for floating and fixed wind turbines, the vertical upward and downward load conditions are involved and the calculation results were compared in detail. The uniaxial ultimate bearing capacities Vult, Hult, and Mult, as well as the V-H, V-M, H-M, and V-H-M failure envelopes of the tripod-bucket foundation in homogeneous clay are calculated. The failure mechanisms of soil surrounding the tripod-bucket foundation under different uniaxial loads are compared. Results show that the bearing capacities are much lower when the tripod-bucket foundation is subjected to upward loads than the downward load. The modes of the H- M envelope changing with the vertical load are quite different, comparing the vertical upward and downward load conditions.

A Review of Techniques for Measuring the Biot Coefficient and Other Effective Stress Parameters for Fluid-Saturated Rocks

Abstract Predicting the behavior of a saturated rock with variations in pore fluid pressure during geo-energy production and storage, deep geological disposal of nuclear wastes, etc. with skeletal mechanical behavior in the linear elastic range is carried out using the isothermal theory of poroelasticity that incorporates Biot's effective stress principle. For conditions that are not within linear elasticity, other effective stress coefficients are used. Several experimental methods for determining Biot's and other effective stress coefficients have been documented in the literature. The objective of this study is to review the fundamentals of these techniques, their advantages and disadvantages, and to include several case studies. Current techniques for Biot's coefficient are based on different premises: jacketed and unjacketed bulk moduli or compressibility values; volume changes of the bulk and pore fluid from a drained triaxial test on a saturated sample; isotropic-isochoric compression tests on a saturated sample; matching volumetric strains for dry and saturated samples; estimation of the Biot coefficient from other poroelastic parameters; and approximation of the jacketed bulk modulus from ultrasonic wave velocities and/or unjacketed bulk modulus from the mineralogical compositions. Other effective stress coefficients are based on matching failure envelopes for dry and saturated samples and variations of rock properties (such as volumetric strain, permeability, and ultrasonic wave velocities) with respect to confining stress and pore pressure. This article discusses variations in Biot's and other effective stress coefficients produced using the different techniques and how factors such as pore geometry, test conditions, stress path, and test temperature affect the coefficients.

Failure Envelopes for Ring Foundations Resting on Tresca Soil under Combined Loading

Failure Envelopes for Ring Foundations Resting on Tresca Soil under Combined Loading

Griffith-based analysis of crack initiation location in a Brazilian test

The Brazilian test has been extremely popular while prompting significant debate. The main source of controversy is rooted in its indirect nature; the material tensile strength is inferred upon assuming that cracking initiates at the centre of the sample. Here, we use the Griffith criterion and finite element analysis to map the conditions (jaws geometry and material properties) that result in the nucleation of a centre crack. Unlike previous studies, we do not restrict ourselves to evaluating the stress state at the disk centre; the failure envelope of the generalised Griffith criterion is used to establish the crack nucleation location. We find that the range of conditions where the Brazilian test is valid is much narrower than previously assumed, with current practices and standards being inappropriate for a wide range of rock-like materials. The results obtained are used to develop a protocol that experimentalists can follow to obtain a valid estimate of the material tensile strength. This is showcased with specific case studies and examples of valid and invalid tests from the literature. Furthermore, the uptake of this protocol is facilitated by providing a MATLAB App that determines the validity of the experiment for arbitrary test conditions.

Drained Axial Pipe-Soil Resistance at Low Confinement Using Tilt Table and Direct Shear Tests

Establishing a reliable value for the axial pipe–soil interface resistance is critical for the design of offshore pipelines. Over the last few years, several independent research groups have modified existing methodologies or devised new testing setups to further develop our understanding of the behavior of the pipe–soil interface at low contact stresses. The most common laboratory experimental methods adopted have been based on either tilt table tests or interface direct shear tests. However, a direct comparison between the results of these two testing methodologies has not been established. This paper aims at designing and fabricating a tilt table and interface direct shear setup capable of accurately estimating the drained interface resistance at low normal stresses, in addition to comparing their results under identical testing conditions. Both setups tested the drained clay–solid interface response by varying the soil composition (high and low plasticity clay), the interface roughness (smooth and rough), and the normal stress range. Results showed that the drained residual failure envelopes for the clays and clay–solid interfaces were nonlinear and could be modeled by a simple power model. The interface response was clearly dependent on the interface roughness, particularly when the roughness was normalized with the mean grain size. In the case of smooth interfaces, identical friction angles were obtained from the tilt table and the interface direct shear, whereas in the case of rough interfaces, the interface direct shear yielded lower friction angle values.

An experimental study of the transition from tensile failure to shear failure in Carrara marble and Solnhofen limestone: Does “hybrid failure” exist?

Failure of brittle rocks under axisymmetric extensional loading, when the minimum principal stress is tensile, results in the formation of one or more opening-mode cracks that are oriented normal to the extension axis. When all the principal stresses are compressive, failure occurs through the formation of numerous grain-scale tensile cracks, which coalesce into a shear-mode fault that is inclined at >20° to the maximum principal stress. There have been few attempts to study the transition between these failure modes, particularly those that incorporate microstructural analyses. A transitional mode of failure, termed “hybrid failure”, is often proposed to describe the orientation of faults between these end-member loading conditions, but this concept has traditionally been based on a parabolic, “Griffith-type” failure envelope that describes the growth of the single most critically-oriented crack. By integrating axisymmetric rock deformation experiments with microstructural analyses, it can be shown that failure under these transitional conditions involves the formation of several transgranular tensile cracks, which coalesce into a shear-mode fault that is inclined at <10° to the maximum principal stress. The stress intensity at the tip of each crack interacts with adjacent cracks to produce a stair-step geometry along the failure surface. These are what may be appropriately considered “hybrid faults”, the angle of which systematically increase as the maximum principal stress, and thus the differential stress increases. There is, however, no evidence of a distinct “hybrid failure” mode, which involves the in-plane propagation of a single crack that is subject to a combined shear stress and tensile normal stress. The results of this experimental study provide novel insights into the mechanical behaviour of carbonate rocks and into the interpretation of meso-scale natural examples of failure under mixed stress-states.

Multi-Criteria Evaluation of the Failure of CFRP Laminates for Frames in the Automotive Industry.

Methods to predict the fracture of thin carbon fibre-reinforced polymers (CFRPs) under load are of great interest in the automotive industry. The manufacturing of composites involves a high risk of defect occurrence, and the identification of those that lead to failure increases the functional reliability and decreases costs. The performance of CFRPs can be significantly reduced in assembled structures containing stress concentrators. This paper presents a hybrid experimental-numerical method based on the Tsai-Hill criterion for behavior of thin CFRPs at complex loadings that can emphasize the threshold of stress by tracing the σ-τ envelope. Modified butterfly samples were made for shearing, traction, or shearing-with-traction tests in the weakened section by changing the angle of force application α. ANSYS simulations were used to determine the zones of maximum stress concentration. For thin CFRP samples tested with stacking sequences [0]8 and [(45/0)2]s, the main mechanical characteristics have been determined using a Dynamic Mechanical Analyzer (DMA) and ultrasound tests. A modified Arcan device (AD) was used to generate data in a biaxial stress state, leading to the characterization of the material as a whole. The generated failure envelope allows for the prediction of failure for other combinations of normal and shear stress, depending on the thickness of the laminations, the stacking order, the pretension of the fasteners, and the method used to produce the laminations. The experimental data using AD and the application of the Tsai-Hill criterion serve to the increase the safety of CFRP components.

Capacity of a multi-compartment single-bucket breakwater structure in silt-over-clay under combined V-H-M loading

Foundations are subjected to combined vertical-horizontal-moment (V-H-M) loadings during operation, and no investigations have been carried out for multicompartment single-bucket structures under combined loadings. Based on the actual stratum distribution of Xu Wei port in Lianyungang, a series of finite element analyses were performed through the finite element software ABAQUS to explore the influence of silt layer thickness, silt strength non-homogeneity and foundation embedment depth on the structural bearing capacity, and the bearing capacity of the structure under combined loading was systematically analyzed. The results suggested that the uniaxial capacity of the structure showed an evident trend with the above parameters. The normalized failure envelopes were not affected by the silt strength non-homogeneity index and were influenced to some extent by the silt layer thickness for a given embedment depth. The normalized V-H and V-M failure envelopes shrank inward, while the normalized H-M failure envelopes tended from negative eccentricity to positive eccentricity with an increasing embedment depth. On this basis, formulas for predicting the uniaxial capacity and the failure envelopes as a function of the overlying silt layer thickness, silt strength non-homogeneity and embedment depth were proposed to provide a reference for its design.

Failure of short carbon-fiber-reinforced PEEK composites under high strain rate biaxial loading

The dynamic failure of short carbon fiber reinforced polyether-ether-ketone (SCFR-PEEK) composites under biaxial stresses was investigated in this paper. Cruciform specimens were loaded with a biaxial split Hopkinson tensile bar system, and a high-speed camera was utilized to record the deformation and failure processes. A nonlinear numerical model calibrated with dynamic uniaxial tests was used to estimate the stress in the cruciform specimen, in conjunction with strain fields from digital image correlation (DIC) of high-speed camera images. The failure of the cruciform specimen initiated inside the gauge section under all dynamic loading cases, and the numerical strain fields are in good agreement with the experimental ones. The dynamic failure envelope under biaxial stresses was successfully obtained, the failure strain decreased and failure stress increased with strain rate noticeably. The testing method developed here is also applicable for dynamic biaxial testing of many other composites.

FRP Stay-in-Place Formworks for High Performance of Concrete Slabs

Stay-in-Place (SiP) formworks obviate the transportation, placement, removal and storage requirements of conventional formworks. Fibre Reinforced Polymer SiPs (FRP-SiP) have additional advantages, such as corrosion resistance, high specific strength and durability. This paper discusses an experimental instigation consisting of two sets of slabs having varying span-to-depth ratios cast on an FRP-SiP. Control specimens with conventional steel bar reinforcements were also cast. Several treatments for improving interfacial bonds at the interface between concrete and FRP-SiP have been investigated. Cyclic flexural tests were performed to evaluate their structural performance. Load-displacement relationship and load capacity are presented. Failure envelopes and energy absorption capacity were evaluated. It was found that the load capacity of FRP-SiP was around 107% greater than the conventional steel rebar specimens. Bond treatment on the FRP-SiP specimens increased the load capacity by around 215% over the untreated specimens. The load-deflection behaviour and the failure modes of the FRP-SiP specimens were distinctly different from those of the conventional specimens. The flexure and shear provisions in American Concrete Institute Standards (ACI 440) were found to be conservative in comparison to the present results. This study demonstrates that FRP-SiPs improve both the structural performance and construction efficiency of concrete slabs, however, new standards would be necessary to be able to utilize their improved capacity.

Inversions of landslide strength as a proxy for subsurface weathering

Distributions of landslide size are hypothesized to reflect hillslope strength, and consequently weathering patterns. However, the association of weathering and critical zone architecture with mechanical strength properties of parent rock and soil are poorly-constrained. Here we use three-dimensional stability to analyze 7330 landslides in western Oregon to infer combinations of strength - friction angles and cohesion - through analysis of both failed and reconstructed landslide terrain. Under a range of conditions, our results demonstrate that the failure envelope that relates shear strength and normal stress in landslide terrain is nonlinear owing to an exchange in strength with landslide thickness. Despite the variability in material strength at large scales, the observed gradient in proportional cohesive strength with landslide thickness may serve as a proxy for subsurface weathering. We posit that the observed relationships between strength and landslide thickness are associated with the coalescence of zones of low shear strength driven by fractures and weathering, which constitutes a first-order control on the mechanical behavior of underlying soil and rock mass.

Investigation of Biaxial Properties of CFRP with the Novel-Designed Cruciform Specimens.

The biaxial loading properties of carbon-fiber-reinforced polymer (CFRP) are critical for evaluating the performance of composite structures under the complex stress state. There are currently no standardized specimens for the CFRP biaxial experiments. This work developed a new design criterion for the cruciform specimen coupled with the Hashin criterion. The finite element analysis was conducted to investigate the effect of geometric parameters on the stress distribution in the test area. The embedded continuous laying method (ECLM) was proposed to achieve the thinning of the center of the test region without introducing defects. The manufacturing quality of the cruciform specimens was verified by the ultrasonic C-scanning test. The biaxial test platform consisting of the biaxial loading system, digital image correlation (DIC) system, strain electrical measurement system, and acoustic emission detection system was constructed. The biaxial tensile tests under different biaxial loading ratios were conducted. The results showed that the biaxial failure efficiently occurred in the test area of the cruciform specimens designed and manufactured in this paper. The failure modes and morphology were characterized using macro/microscopic experimental techniques. The biaxial failure envelope was obtained. The results can be used to guide the design of composite structures under biaxial stress.

Effect of nearby strip loading on lateral capacity of offshore large-diameter monopiles in clay slope

This study is devoted to investigating the effect of nearby strip loading on the lateral bearing capacity of offshore large-diameter monopiles at the crest of marine clay slope by the finite element limit analysis (FELA) method. After the successive validations by cases of rigid piles and strip footings at the clay slope crest, the safe domains for the laterally loaded large-diameter monopiles are defined by the failure envelopes relating the dimensionless lateral bearing capacity H u/(c u D 2) to dimensionless strip loading q/c u. Particularly, all failure envelopes are depicted by closed-form expressions and design charts can then be given for a quick and straightforward assessment of dimensionless lateral bearing capacity for a wide range of frequently-encountered cases. In addition, the interaction between the pile bearing capacity and nearby strip loading is characterized by introducing the relationship of normalized parameters H u/(c u D 2) and q/c u, then graphically explained by plastic multiplier contour plots. Several kinds of representative curves are given successively to further clarify the effects of dimensionless factors on the interaction.

Sensitivity analysis applied to SiC failure probability in TRISO modeled with BISON

A sensitivity analysis on the failure probability of the Silicon Carbide (SiC) layer in tristructural isotropic (TRISO) nuclear fuel during transient conditions predicted by the BISON fuel performance code is performed. The principal goal of the analysis is to understand the most important parameters dictating SiC failure behavior in BISON during Reactivity Initiated Accidents (RIAs). SiC brittle fracture probability is modeled using Weibull statistics. A total of seven inputs related to SiC failure has been selected for the analysis, including the Weibull statistics parameters, elastic moduli for SiC and Pyrolitic Carbon (PyC) and SiC stress-free temperature. A 1D TRISO BISON model has been established for various reactivity insertions performed at the Nuclear Safety Research Reactor (NSRR). The principal advantage associated with the 1D TRISO model developed in this work is its computational efficiency. The Sobol variance decomposition method is used, and the sensitivity indices are presented for eight different values of the energy deposition. The results show that the two most important parameters impacting the predicted SiC failure probability are the Weibull modulus and the characteristic stress, and a co-variance amongst these parameters is obtained for low reactivity insertions. An additional new finding of this work is that the relative importance of Weibull parameters depends on the energy deposition, and thus reactivity, regime. For low energy depositions, two parameters are of influence on SiC failure probability, while for high energy depositions only one parameter impacts failure probability results. Moreover, optimization of the Weibull modulus and characteristic stress is performed by minimizing the RMSE between BISON failure probability predictions and experimental failure fractions for each energy deposition. This work also demonstrates the validity of the NSRR tests BISON simulations and of the respective sensitivity analysis results as conservative, yet indicative for slower transients characterized by lower deposited energies. Such verification is achieved through the partial extension of the analysis to a group Control Rod Withdrawal reproduced from a previous study. Another novel result of this analysis is that no single set of Weibull parameters can reproduce all reactivity insertion experimental failure results, which is related to the intrinsic nature of SiC failure properties, and a new range for the parameters is proposed to produce a failure probability envelope that encompasses the experimental fractions. Additionaly, this work proposes a new approach for future failure analysis with BISON, consisting in the use of Weibull parameters ranges, rather than fixed sets, along with failure envelopes generation.

Unified fatigue characterization of asphalt mixture under multi-field coupling condition: Stress state, frequency, and temperature

For a scientific and reliable design of asphalt mixture subjected to fatigue damage, a comprehensive understanding and realistic prediction of asphalt mixture fatigue life under complex loading conditions with variable loading rates or temperature were a major concern. In this study, direct tensile test, uniaxial compression test, indirect tensile test, and four-point bending test were used to study the fatigue behavior of asphalt mixtures with a particular focus on the action of temperature and frequency. Strength and fatigue were investigated separately under varied loading rates at several temperatures. A new idea for determining the stress ratio based on the strength failure envelope line considering temperature and loading rate was proposed. The connection between strength and fatigue was established by the stress ratio. The test conditions for strength and fatigue tests were set to be the same leading to the fatigue data distributed regularly. Experimental data were analyzed and normalized by studying the evolution of the number of cycles with the stress ratio. A new analytical approach was introduced to simulate the fatigue performance. The fatigue performance under multi-field coupling conditions was uniformly characterized. The dispersion of fatigue equation caused by the test method and conditions is eliminated. Engineering application showed that the design deviation of the pavement fatigue resistance was reduced to less than 6%.

Data-driven analysis on compressive behavior of unconfined and confined recycled aggregate concretes

It is widely accepted that the inferior characteristics of recycled concrete aggregates (RCAs) reduce the mechanical properties of structural concrete and the available prediction models receive undesirable accuracies in estimating the compressive behavior of recycled aggregate concrete (RAC). To this end, this paper presents a series of data-driven analysis on unified modeling of the compressive behavior of unconfined and confined RACs. First, four reliable experimental databases containing the results of natural aggregate concrete (NAC) and RAC under uniaxial compression, RAC under triaxial compression, and fiber reinforced polymer (FRP)-confined RAC under axial compression were assembled through an extensive literature review, respectively. Based on the collected data, Mohr-Coulomb failure criterion was then employed to construct a model for estimation of the failure envelope of RAC under axial compression and different lateral active confinement stresses. Finally, unified models for predicting the compressive properties (i.e., compressive strength/peak stress and strain at peak stress) of unconfined and confined concretes incorporating natural aggregates (NAs) and/or RCAs were developed so as to provide a design-oriented procedure for material and structural assessments of both NAC and RAC. The results demonstrate that the proposed models exhibit acceptable predictions, thereby making various stakeholders gain sufficient confidence in use of RAC products.

Crater-rim collapse at Stromboli volcano: understanding the mechanisms leading from the failure of hot rocks to the development of glowing avalanches

The failures of volcanic crater-rims frequently lead to the development of avalanches of glowing rocks, a hybrid phenomenon between rock avalanches and pyroclastic density currents, reaching considerable distances from the eruptive centres and therefore be a serious threat for inhabited areas. The collapse conditions have been here taken in to account by means of slope stability analysis using a Limit Equilibrium Method analysis on the crater-rim of Stromboli volcano (Italy). A Stromboli, crater-rim collapses occurred frequently (at least seven events in the last two decades) and were always associated with high-level of magma within the conduits, testified by the increased eruptive activity and ground-deformation. The more frequent/intense eruptive activity produced a greater accumulation of volcaniclastic material, whereas the high level of magma increased magmastatic thrust on the deposits. Volcaniclastic material was modelled by combining the nonlinear failure envelopes as the Generalized Hoek and Brown criterion, with the addition of the failure's envelope of the rockfill-like material described by the Barton-Kjaernsli criterion, taking into consideration the presence of discontinuities within proximal, partially welded, volcaniclastic masses. In addition to the lithological and morphological characteristics of the crater terrace rim and the magmatic thrust, the effects of the explosions in terms of seismic ground acceleration and disturbance factor (D) of the volcaniclastic material were also considered here. While the ground acceleration compatible with the explosive activity of Stromboli has little influence on the stability of the crater terrace rims, the increase in D increases the proneness for failure.

A New Discrete Form of Hoek–Brown Criterion and Its Application to Limit Equilibrium Analysis of Rock Slope Stability

The generalized Hoek–Brown criterion (GHB) is recognized as one of the standard failure criteria in rock engineering and its validity extends to a wide range of rock mass quality. A drawback of this criterion is the difficulty of transforming it into an explicit form defining the Mohr failure envelope when its strength parameter a is not equal to 0.5. The information on the functional form of the Mohr envelope for the full range of rock mass conditions enables the implementation of classical engineering approaches, such as the limit equilibrium method and limit analysis, in the framework of the GHB criterion. Knowing that for a≠0.5 the exact closed-form representation of the Mohr envelope is not feasible, an alternative is to express it in an approximate analytical form. The main purpose of this study is to propose a new improved method to define an approximate Mohr envelope of the GHB criterion that is much more accurate compared with the recently published approximations. The idea behind the formulation is to expand the Balmer’s equation, which defines the relationship between the normal stress and minor principal stress at failure, by invoking the finite Taylor series centered at the known solution for a=0.5. The formulation is then completed by substituting this solution into another Balmer’s equation, defining the relationship between the shear strength and the minor principal stress. The Taylor polynomial approximations of up to third degree are considered in the formulation. The accuracy of the shear strength prediction is shown to be much better than that of the approximate formula of Lee and Pietruszczak proposed in 2021. An illustrative example of limit equilibrium analysis of rock slope stability, incorporating the new approximate expression for the Mohr envelope, is provided. The analysis incorporates a modified version of the Bishop approach, which is simpler and more rigorous than the original nonlinear expression. The study confirms that the new approximate representation of the Mohr failure envelope can facilitate the application of the GHB criterion to a range of practical rock engineering calculations.

Combined loading of RC pile groups in clay accounting for N–M interaction

Motivated by the need for retrofit of existing bridges, this paper explores the nonlinear response of pile groups in clay under combined loading. The problem is analysed numerically, employing a kinematic hardening model for soil, and the Concrete Damaged Plasticity (CDP) model for the reinforced concrete (RC) piles. Using a reference 2 × 1 pile group, it is shown that three resistance mechanisms are mobilized: axial pile loading (Max), pile bending (Mb), and pilecap resistance (Mcap). While current design practice typically considers only the first mechanism, it is shown that allowing for strongly nonlinear soil response and full mobilization of all three mechanisms may lead to a significant increase of pile group moment capacity. The analysis also reveals the need to account for axial force–bending moment (N−M) interaction of the RC piles, which is feasible through the CDP model. Especially for existing pile groups, more realistic estimation of ultimate moment capacity may facilitate the development of rational retrofit strategies. A parametric study is subsequently conducted, exploring the effect of the safety factor against vertical loading (FSv), the moment to shear (M/H) ratio, interface modelling, and pilecap contribution. The results are generalized by analysing more complex 3 × 1 and 4 × 1 pile group typologies and by deriving 3D failure envelopes in the V – H – M space. Thanks to the contribution of the pilecap, the decrease of FSv leads to an expansion of the failure envelope, which can be of relevance for existing pile group assessment after bridge widening. Finally, the interaction diagrams are normalized, leading to a unique non-dimensional 3D failure envelope for all examined pile group typologies.