Static Failure Stress Research Articles

Application of Asaoka’s Method in Multistage Triaxial Compression Testing of Normally Consolidated Soils

Abstract Determination of shear strength parameters becomes a challenge when it is difficult to retrieve a minimum of three identical undisturbed soil specimens. In such a situation, multistage triaxial compression testing can be adopted using a single specimen. Multistage triaxial testing involves stage-wise consolidation and shearing at three confining pressures without the failure of the specimen until the last stage. A critical issue associated with multistage triaxial testing is the estimation of ultimate deviator stress and the corresponding pore pressure as the specimen was not allowed to reach failure in each stage. Conventionally, the failure stress state in each stage is computed by extrapolating the stress–strain and pore pressure–strain data to a finite strain by employing Kondner’s rectangular hyperbola model. However, it is reported in the literature that the aforementioned method often overestimates the deviator stress and pore pressure values. In this context, the present study investigates the suitability of Asaoka’s observational procedure for predicting these values at failure state. The validity of the proposed procedure is verified by comparing the ultimate deviator stress and pore pressure values obtained by analyzing the stress–strain data collected from the literature and by performing multistage triaxial testing on three reconstituted soil samples with that of the rectangular hyperbola method. From the results, it was observed that Asaoka’s method is more suited for predicting the shear strength parameters. It is believed that the proposed methodology would aid in obtaining the shear strength parameters of a soil from a single specimen by conducting multistage triaxial testing.

Holistic estimation and sensitivity-based experiment design method of composite laminate first-ply failure models using statistical approaches

In this paper, a probabilistic approach is presented to simultaneously evaluate all strength and additional fitting parameters of a pre-selected composite first-ply failure model using known uniaxial and multiaxial failure stress states. The method processes all available mechanical test results in terms of failure stress states as one batch of data. For parameter fitting it implements the Maximum Likelihood Method and controlled numerical sampling techniques. The present work introduces the theoretical background as well as investigates the effect of the selection of the underlying strength distribution function type. The biggest benefit of this approach is the simultaneous handling of all available test data as well as the generality in terms of assumed strength distribution function and failure model type. In addition, the automatic evaluation of the uncertainty of all strength parameters enables introduction of a safety factor quantification related to uncertainty in material properties as one of the main contributors to scatter sources. A local sensitivity-based stress-state determination process is also introduced to design a set of input failure stresses that guarantee the identifiability of all parameters thus, ensuring robustness of the fitted constants. The entire methodology is demonstrated through the example of the Tsai-Wu model by processing experimental data and by comparing the results against the literature.

A numerical unit cell model for predicting the failure stress state of vertically perforated clay block masonry under arbitrary in-plane loads

As vertically perforated clay block masonry advances into more demanding building categories, knowledge of the effective masonry strength under different loading states becomes crucial. However, experimentally identifying macroscopic failure surfaces for such masonry requires a massive effort. In this study, we propose a FEM-based simulation concept to predict failure stress states of masonry under arbitrary in-plane loading. The proposed concept is validated using seven experiments from the literature. Subsequently, subjecting the validated model to various load cases allows for deriving a failure surface comparable to the Rankine–Hill surface. Thus, by applying the presented concept, we can effectively generate macroscopic failure surfaces for any perforated clay block design.

Manufacturing and testing of waste PET reinforced with sand bricks

The high and increasing demand for plastic materials has led to a global challenge in the form of plastic pollution, because of the different types of discarded plastic, such as polyethylene terephthalate (PET), polypropylene (PP), and high-density polyethylene (HDPE), etc.; it has become difficult to recycle it. Thus, only a limited percentage of plastic is recycled. Many studies in this field are trying to find alternative solutions such as the introduction of plastic in building materials. This study examines brick particles as reinforcement in polyethylene as a matrix. 30%, 35%, 40%, and 45% of weighted brick sand were combined with PET and prepared by melt compounding and processed through a single-screw extruder at 260°C. Thermal properties were studied by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). The results show that in the presence of brick particles, the thermal degradation temperature of the composites increased. The composite that contains 45% of brick sand weight attempted 314.323°C as the highest degradation temperature, as well as the glass transition temperature. Mechanical tests show that the addition of brick in the matrix leads to a significant reduction in impact resistance. Static failure stress reaches 26.26 (MPa) in a composition of 30% of the brick sand weight. Young’s modulus shows better results in 30% of weighted brick sand equal to 2,771 (MPa). The scanning electron microscope (SEM) reveals a uniform distribution of the reinforcing charge.

A general method for numerical identifiability and sensitivity analysis of failure criteria for continuous fibre-reinforced plastics

Modelling the static failure of fibre-reinforced composite laminates is a challenging problem, as the parameters of the relevant mechanical models might not have a physical interpretation. Failure parameters are usually determined experimentally, where the parameter fitting and experimental design can be non-standard and intricate. In order to improve efficiency in designing mechanical experiments for the fitting of composite failure model parameters, a general method for quantifying the sensitivity of failure criteria parameters to failure stress states has been developed. This method helps selecting the failure stress states with regards to a failure model that result in the most robust fit of the model parameters. The method is demonstrated on the commonly used Tsai–Wu and Puck failure models, but is valid for a wide range of other models as well. The practical application of this method is also demonstrated by evaluating an experimental data set.

Anisotropic damage model for concrete and other quasi-brittle materials

A thermodynamically consistent formulation to model anisotropic damage for quasi-brittle materials is proposed. The model is based on proper expressions for the specific Gibbs free energy and the complementary form of the dissipation potential. Damaging of the material is described by a symmetric positive definite second order damage tensor. Especially, the failure surface is formulated in such a way that it will mimic the behaviour of the well known Ottosen’s four parameter failure surface. While testing the model against the experimental results found in literature, the results were in good agreement in uniaxial tensile and compressive loadings as well as in biaxial compression. Besides the correct failure stress states, the model predicts the correct failure modes of concrete: axial splitting along the direction of uniaxial compression and tensile damaging normal to the direction of tension.

Investigation of Failure Mechanism of Inclined Coal Pillars: Numerical Modelling and Tensorial Statistical Analysis with Field Validations

Analysis of the failure mechanism of inclined coal pillars is one of the complicated issues. The wide variability of dip angles of inclined coal pillars makes it more complex. The asymmetric stress distribution and the tendency of shearing along the bedding planes make the inclined coal pillars to behave differently from the flat coal pillars. There is a need for in-depth investigation of the failure mechanism for addressing the instability problems of the inclined coal pillars. Most of the literature quantifies only the magnitudes of the mean principal stresses by classical statistics. As the stress is a second-order tensor having six independent components, the classical statistics is not appropriate to calculate the mean and variability of the principal stresses at the onset of failure of the pillars. In this paper, a comprehensive analysis is done to understand the complex failure mechanism of the inclined coal pillar using numerical modelling as well as tensorial statistics and validated the results with field measurement data of failure cases. The failure mechanism is analysed by quantification of the characteristics of the inclined coal pillars by the principal-stress magnitude and its orientation, induced at the time of failure. Since the spatial variability of the magnitudes and orientations of the induced principal stresses exist within the inclined coal pillars, the mean induced principal stresses $$\left( {\overline{{\sigma_{1} }} {, }\;\overline{{\sigma_{2} }} {\text{ and }}\overline{{\sigma_{3} }} } \right)$$ are used to quantify the stress states within it. The failure stress states within the coal pillars having different dip angles are generated by the calibrated elasto-plastic numerical modelling with the ubiquitous joint model. Several statistical parameters are calculated to quantify the stress-tensor variability and the correlation among the stress-tensor components. It is found that the correlation coefficients among the shear components increase significantly with the increase of the coal pillar dip angle. Therefore, the inclined coal pillars are highly susceptible to shear failure. The magnitudes, as well as orientations of the mean induced principal stresses within the coal pillars obtained through numerical modelling, are quantified by the tensorial as well as classical statistics. It is found that the magnitude of the mean major induced principal stress $$\left( {\overline{{\sigma_{1} }} } \right)$$ at the time of failure, i.e. the strength of the pillar decreases with the increase of the dip angles. The validation of the results with the actual stress measurement data shows that all the failed pillar cases are correctly predicted by the tensorial statistical approach whereas the classical statistical approach does not effectively predict the actual failed condition of the pillars. The study would help to characterise the behaviour of the inclined pillars and address the instability issues for safe and efficient mining of inclined coal seams.

Biaxial tensile failure of short carbon-fibre-reinforced PEEK composites

The biaxial tensile failure of short carbon fibre reinforced polyether-ether-ketone (SCFR-PEEK) composites is characterized in this paper. An improved cruciform specimen was proposed to apply biaxial stresses, and five different stress ratios were employed in experiments. The stress distribution within the gauge section is not measurable across the varying stress ratios, therefore it is not trivial to obtain stress-strain data in the experiments. In this work, a combined experimental and numerical approach was proposed to deduce the true material behaviour during biaxial tensile tests. A numerical model with consideration of anisotropy and plasticity was proposed, it was further calibrated with uniaxial experiments and then validated with biaxial tests. Through this approach, the failure stress states at different stress ratios were successfully obtained. Compared with the numerical results based on constitutive relations, numerical results with linear elastic simplification overestimate the biaxial tensile strength, and are not suitable for material with an apparent nonlinear segment. The biaxial tensile failure envelope matches the Tsai-Hill criterion, and equal biaxial tensile results can be used for determining interaction coefficient F12 in the Tsai-Wu criterion. This research approach offers an accurate and reliable solution for biaxial tensile testing of materials with consideration of anisotropic and nonlinear behaviour.

Determination of Passive Failure Surface Geometry for Cohesionless Backfills

Correct determination of the passive failure surface geometry is necessary for the design of retaining structures. The conventional theories assume linear passive failure surfaces even though it is known that the actual failure surfaces are non-linear. Many researchers claimed the appropriateness of a hybrid curved-linear method. This approach estimates the curved section by a log-spiral function, which then connects to the backfill surface with the conventional linear assumption. The main drawback here is that the geometric properties of the hybrid mathematical function is not directly related to the mechanical properties of soils. Thus, this study attempts to provide a mechanical description for the assumed geometrical parameters. For this purpose, a series of 1 g small scale retaining wall model tests, simulating passive failure, are conducted on two different backfill soils. The relative density is varied in the model tests and the resultant peak friction angles of the backfills are calculated as functions of failure stress state and relative density using a well-known empirical equation. Transparent sidewalls allow for visualization of the failure surface evolution, which is obtained by capturing images and analysing then through Particle Image Velocimetry (PIV) technique. Subsequently, the quantified slip zones are fitted with the hybrid curved-linear approach. The relationships between the peak friction angle and the geometrical characteristics of the best-fit log-spiral and linear functions are investigated. Obtained results are used to propose a set of equations that allow the estimation of non-linear passive failure surfaces as function of peak friction angle.

A generic computational model for three-dimensional fracture and fragmentation problems of quasi-brittle materials

Fracture and fragmentation in three dimensions are of great importance to understand the mechanical behaviour of quasi-brittle materials in failure stress states. In this paper, a generic computational model has been developed in an in-house C/C++ code using the combined finite-discrete element method, which is capable of modelling the entire three-dimensional fracturing process, including pre-peak hardening deformation, post-peak strain softening, transition from continuum to discontinuum, and explicit interaction between discrete fragments. The computational model is validated by Brazilian tests and polyaxial compression tests, and a realistic multi-layer rock model in an in situ stress condition is presented as an application example. The results show that the computational model can capture both continuum and discontinuum behaviour and therefore it provides an ideal numerical tool for fracture and fragmentation problems.

Yield Parameters for Iron Powder Compaction on Different Particle Size

Shear failure yield line in Drucker-Prager yield surface for iron powder on different particle size and amount of interparticle lubricant has been estimated. Critical stress state and uniaxial failure stress state have been determined by a single shear test and uniaxial failure test for a green compact. Compaction cap parameter has been estimated by the lateral force measurement test by instrumented die compaction system. By those estimations, materials input parameters for the Drucker-Prager Cap (DPC) model have been determined successfully, and differences in particle size and amount of lubricant can be recognized. Finite element method (FEM) analysis of simple closed-die compaction has been conducted. As a result, the materials input parameters for the DPC model on different powder properties have been successfully identified as the FEM analysis fairly predicts compaction pressure and density distribution on uniaxial compaction.

Stress–strain behaviour of bio-desaturated sand under undrained monotonic and cyclic loading

Microbial (or bio-) desaturation is a new method for mitigation of the liquefaction hazard of sand. In this paper, a series of monotonic and cyclic triaxial tests was performed on bio-desaturated sand under undrained conditions to demonstrate that the bio-desaturation method is effective in enhancing the liquefaction resistance of sand under either monotonic or cyclic loading conditions. The test results showed that, under monotonic loading, the undrained shear strength increased by more than two times and the behaviour of soil changed from strain softening to strain hardening when the degree of saturation (Sr) reduced from 100% to 86·4%. The undrained shear strength ratio (su/p′0) has a unique relationship with the peak excess pore water pressure ratio (Δumax/σ′c) regardless of different effective confining stress conditions. Under the applied cyclic load, the liquefaction resistance showed a significant increase when the sample was slightly desaturated. For the same cyclic stress ratio and number of cycles, the accumulated excess pore water pressure (Δu) in the sample with a degree of saturation of 96% was only a quarter of that in the fully saturated sample. The instability behaviour of sand was also studied. The results showed that the slope of the instability line, which is a measurement of the resistance of sand to collapse, also increased with the reduction in degree of saturation under monotonic loading. The failure stresses obtained in cyclic triaxial tests conducted under different cyclic stress ratios coincide with the instability line obtained under monotonic conditions for sand with the same degree of saturation. This provides good support for the use of the instability line to predict the failure stress state of sand for both monotonic and cyclic loading conditions.

Estimation of Yield Surface on Iron Powder Compaction for Finite Element Analysis using Drucker-Prager Cap Model

Shear failure yield line in Drucker-Prager yield surface for conventional atomized iron powder has been estimated with critical stress state and uniaxial failure stress state by single shear test and uniaxial failure test for green compact. Lateral force measurement test was also conducted using newly devised instrumented die compaction system to identify compaction yield characteristics as Cap yield surface. By those estimations, materials input parameters for Drucker-Prager Cap model have been determined successfully. Finite element analysis of simple closed-die compaction has been conducted and good correspondence in variation of compaction pressure with densification has been recognized.

Field and laboratory time-dependent behaviors of geotextiles in reinforced soil walls

Laboratory and field investigation of time-dependent behavior of geotextiles reinforcing a fine-grained soil are evaluated herein. The field assessment consisted of analyses of two instrumented sections of a geotextile reinforced soil wall with identical layouts, including one section with a woven and another with a nonwoven geotextile. In addition, in-soil and in-isolation laboratory creep tests were conducted using the same geosynthetics and soil used in the Geosynthetic-Reinforced Soil (GRS) wall sections to better assess time-dependent behaviors in the field. Construction and time-dependent behavior of the full-scale GRS wall proved to be satisfactory over the 4 years of monitoring of both woven and nonwoven geotextile structures. Soil confinement, due to vertical earth pressure on the reinforcement, was found to greatly affect the deformability of the nonwoven geotextile and to have a minor effect on the woven geotextile. Time-dependent strain rates were higher when the failure stress state of the soil was reached. Under lower vertical stresses, the time-dependent behavior of both geosynthetics was similar. Time-dependent behavior was underestimated from in-soil laboratory creep tests and better estimated using in-isolation laboratory tests. However, the GRS wall data did not account for installation damage and wetting-drying processes, which were found to influence time-dependent strain predictions.

Determination of active failure surface geometry for cohesionless backfills

The extent by which economy and safety concerns can be addressed in earth retaining structure design depends on the accuracy of the assumed failure surface. Accordingly, this study attempts to investigate and quantify mechanical backfill properties that control failure surface geometry of cohesionless backfills at the active state for translational mode of wall movements. For this purpose, a small scale 1 g physical model study was conducted. The experimental setup simulated the conditions of a backfill behind a laterally translating vertical retaining wall in plane strain conditions. To monitor the influence of dilative behavior on failure surface geometry, model tests were conducted on backfills with different densities corresponding to different dilation angles. Failure surface geometries were identified using particle image velocimetry (PIV) method. Friction and dilation angles of the backfill are calculated as functions of failure stress state and relative density of the backfill using a well-known empirical equation, making it possible to quantify the influence of dilation angle on failure surface geometry. As a result, an empirical equation is proposed to predict active failure surface geometry for cohesionless backfills based on peak dilatancy angle. It is shown that the failure surface geometries calculated using the proposed equation are in good agreement with the identified failure surfaces.

The Theoretical Measure of the Ductility of Failure for All Isotropic Materials in All States of Stress1

The ductile/brittle failure theory for homogeneous and isotropic materials is extended to give a rational and mathematically rigorous measure for the ductility of failure. This new failure number methodology is completely developed and proved to be valid and general. It applies to all isotropic materials as subjected to any and all states of stress. Not only does the failure theory predict the safety or failure for any given stress state, it then projects the quantitative ductility level for the failure stress state. Many important examples are given with detailed interpretations of the results and with guides for general usage.

English

The failure mechanisms and failure stress states of 2D and 3D FRP composite is investigated through experimental work, SEM, finite element analysis and failure theories. In this research work, feasibility of ASTM standard D6641 is investigated for testing of 3D FRP composite. A 3D finite element model is developed in ABAQUS with homogeneous orthotropic laminate to investigate the failure stress state in the gage section of the test specimens. Two failure theories are considered for failure investigation that is fully interactive three dimensional Tasi Wu failure criteria and limit criteria (maximum stress criteria). SEM is carried out to investigate the failure mechanisms and failure location in the specimens. Experimental results shows that the compressive strength of 3D FRP composite is less as compared to 2D FRP composite, also standard deviation (SD) and coefficient of variance (COV) of 3D FRP composite is high. This paper highlights the problems associated with the use of ASTM D6641 for 3D FRP composite, and internal failure mechanisms in 3D FRP composite using compression through combine end and shear loading.   Key words: 3D fiber reinforced polymeric (FRP) composites, 2D FRP composite, ASTM D6641, finite element analysis.

Deformation Properties of Untreated and Enzyme-Treated Bottom Ash Waste for Use in Foundations

The use of waste and recycled materials in different construction applications is a widespread approach. In this work, incinerator bottom ash (IBA) waste was mixed with limestone at different levels, namely, 0%, 30%, 50%, and 80%, to produce blends for use as pavement foundation layers. The study focused on evaluating the resistance to permanent deformation of IBA–limestone blends, which is vital to prevent or minimize pavement rutting. An experimental program was undertaken to investigate the influence of plant-based enzyme treatment on the behavior of these blends. Cyclic and static triaxial compression tests were adopted to determine the materials’ mechanical characteristics. Emphasis was on examining the effect of various parameters, such as IBA content, enzyme content, moisture content, curing time, stress level, and number of load applications, on the behavior of the investigated blends. The accumulated permanent strain and strain rate were used to describe the blends’ shakedown stress limits. Results showed that IBA blends gave a favorable performance as foundation layers in comparison with the control limestone blend. Enzyme addition improved the permanent deformation resistance for the control limestone blend; however, it did not have any noticeable effect on the IBA blends. According to the shakedown concept analysis, all blends, at a cyclic stress level of more than 21% of the static failure stress, underwent excessive plastic strain.

Analysis of Three-Dimensional Quadratic Failure Criteria for Thick Composites using the Direct Micromechanics Method

Currently fiber composites are used in thick structures with significant out of plane stresses for which new 3D failure criteria are required. In this article the direct micromechanics method is used to determine the exact failure envelope of a unidirectional graphite/epoxy composite. A hexagonal unit cell of the composite is modeled using finite elements. Assuming that the failure criteria for the fiber and matrix materials and for the fiber-matrix interface are known, the exact failure envelope is constructed from a large number of three-dimensional stress states that correspond to failure initiation in the composite. These 3D failure stress states are then used to develop five three-dimensional phenomenological failure criteria: maximum stress; maximum strain; quadratic stress; quadratic strain; and optimized quadratic failure criteria. It is observed that the 3D quadratic stress and strain failure criteria may not always be closed, that is, they predict infinite strength in some directions. They can be made closed in combination with the maximum stress or the maximum strain failure criterion. It is found that a combination of aforementioned 3D failure criteria make failure prediction in thick composites more accurate and reliable. It is noted that the newly proposed optimized quadratic failure criteria is always closed, and is found to be more reliable than all other 3D failure criteria.

Fatigue performance of metallic beam strengthened with a bonded CFRP plate

This paper gives details of a fatigue test programme of a series of small-scale steel beams bonded with a carbon fibre reinforced polymer (CFRP) plate. Backface-strain technique was used to detect crack initiation and monitor crack growth. Results show that this technique could detect crack initiation and track the deterioration of the adhesive layer. The strains recorded show that crack initiates and grows in Mode I earlier than in Mode II in the bonded joints, and this finding agrees with the observations on double-lap joints published in literature. The strains recorded also show that the adhesive spew fillet at the end of the CFRP plate is beneficial to the fatigue performance, although the improvement is not significant. An S– N curve was developed from the test results. The curve correlates the maximum principal interfacial stress at the plate end to the number of cycles to crack initiation. This maximum stress can be calculated from the authors’ previous analytical work. The fatigue limit of the S– N curve was found to be about 30% of the ultimate static failure stress.