Three-dimensional Stress State Research Articles

Strength and Deformation Characteristics of Reconstituted Sand under Different Stress Paths in True Triaxial Tests

To improve the geotechnical stress–strain analysis, the stress–strain behavior of geomaterial under general three-dimensional stress conditions prevailing in the field need to be captured. The true triaxial apparatus is an enhanced version of the conventional triaxial apparatus, which allows to simulate stresses by applying loadings independently in 3 orthogonal directions. This study evaluated the strength and deformation behavior of Bangka sand under true triaxial test conditions. The test specimens were prepared by means of the multi-sieve sand pluviation method. Various true triaxial test stress paths were applied under axial compression, lateral extension, axial extension, and lateral compression with the objective of understanding and developing the empirical correlation of coarse-grained soil strength parameters in axial compression stress paths related to other stress paths. The test results showed that an increase in the value of b, the parameter used to quantify the relative magnitude of the intermediate principal stress to the other principal stresses, resulted in an increase of the internal friction angle and a decrease of the peak stress ratio. In addition it was observed that the Lade-Duncan failure criterion fitted the results of this study better than other failure criteria, namely the extended von Mises, Mohr-Coulomb, and Matsuoka-Nakai failure criteria.

EFFECT OF SUBSTRATE PREPARATION ON THE LOAD-BEARING BEHAVIOR OF CFRP-CONFINED RC COLUMNS

The confinement of reinforced concrete (RC) columns with fiber reinforced polymer (FRP) jackets is an effective measure for the strengthening and retrofitting of existing structures. The jacket withstands the increasing lateral strains of the axially loaded column causing a three-dimensional stress state inside the concrete. In the result, a higher concrete compressive strength can be achieved. So far, extensive international research on FRP-confined concrete has been conducted, but there are still some open issues regarding the influence of different parameters on the load-bearing behavior. This paper is focusing on the effect of the substrate preparation on the maximum concrete strength and stress-strain behavior. Therefore, an experimental study of carbon fiber reinforced polymer (CFRP) confined concrete cylinders with various substrate conditions and preparation methods is presented. The results are compared with previous investigations and assessed accordingly. Furthermore, recommendations regarding the substrate preparation by current national codes and guidelines are specified and considered critically.

Study of residual stress and microstructural evolution in as-deposited and inter-pass rolled wire plus arc additively manufactured Inconel 718 alloy after ageing treatment

The manufacture of structural components made from nickel-based super alloys would benefit from the commercial advantages of Wire + Arc Additive Manufacturing (WAAM), as it is commonly expensive to process using other conventional techniques. The two major challenges of WAAM are process residual stress and undesired microstructure. Residual stress causes part distortion and build failures, while the as-deposited microstructure does not allow the common heat-treatment to be effective in achieving the desired mechanical properties. This paper focuses on understanding the microstructural features, phase formation and three-dimensional residual stress state variation in as-deposited and inter-pass rolled conditions and after solutionising, quenching and ageing. The thermal history from successive deposition and cold working were correlated to the phase formation and macro residual stress formation and subsequent evolution. The {311} family of crystallographic planes were used as atomic strain gauge to determine the macrostrain and analysis of three dimensional stress state in different processing conditions. The measured strain were corrected for the compositional variation by measuring EDM machined d0 specimens manufactured under similar processing conditions. While the as-deposited part show significant stress redistribution and distortion after removal from the main fixture, inter-pass rolling was found to reduce part distortion significantly, the residual stress profile after inter-pass rolling showed highest tensile magnitude near the substrate while near the top of the deposit it was compressive as can be expected from the rolling process. The other two beneficial effects of inter-pass rolling on the microstructure are mitigation of the formation of undesired Laves-phase, thereby improving the response to solution treatment and aging together with significantly reduced grain size and texture. The application of inter-pass rolling reduces the potential part complexity, which however does not prevent the manufacture of common candidate parts, which are typically 1-to-1 replacements of forged, cast or machined from solid.

Experimental investigation on influence of loading rate on rockburst in deep circular tunnel under true-triaxial stress condition

To investigate the influence of loading rate on rockburst in a circular tunnel under three-dimensional stress conditions, the true-triaxial tests were conducted on 100 mm×100 mm×100 mm cubic sandstone specimens with d50 mm circular perforated holes, and the failure process of hole sidewall was monitored and recorded in real-time by the microcamera. The loading rates were 0.02, 0.10, and 0.50 MPa/s. The test results show that the rockburst process of hole sidewall experienced calm period, pellet ejection period, rock fragment exfoliation period and finally formed the V-shaped notch. The rockburst has a time lag and vertical stress is high when the rockburst occurs. The vertical stress at the initial failure of the hole sidewall increases with loading rate. During the same period after initial failure, the rockburst severity of hole sidewalls increased significantly with increasing loading rate. When the vertical stress is constant and maintains a high stress level, the rockburst of hole sidewall under low loading rate is more serious than that under high loading rate. With increasing loading rate, the quality of rock fragments produced by the rockburst decreases, and the fractal dimension of rock fragments increases.

Strain evolution of saturated clays under cyclic loadings in three-dimensional stress condition

The strain evolution of saturated clays under cyclic loadings has been studied by means of various laboratory testing methods, aiming for the accurate simulation of engineering conditions such as the consolidation states of clays, cyclic stress paths of external loadings and boundary conditions in situ. Considering that the subgrade clays are usually overconsolidated rather than normally consolidated, the drainage condition is normally partially drained instead of undrained under long-term cyclic loadings, and the cyclic stress paths are in three-dimensional stress state, this study explores the three-dimensional strain characteristics of both normally and overconsolidated clays in partially drained condition based on a true triaxial apparatus. Emphasis are put on the effects of cyclic stress ratio (CSR), overconsolidation ratio (OCR) and coefficient of cyclic intermediate principal stress (bcyc) on the accumulation of permanent strain components including major, intermediate, minor principal strains, and volumetric strain. Test results show that the relative magnitudes of strain components are strongly influenced by both bcyc and OCR, while the accumulated directions of strain paths tend to be identical for various bcyc values. The increase of bcyc leads to a linear growth of permanent volumetric strain for both normally and overconsolidated clays, while the permanent major principal strain shows a firstly increasing and then decreasing trend versus the increase of bcyc. For the normally consolidated and overconsolidated clays, the largest permanent major principal strains are achieved at around bcyc = 0.4 and 0.2, respectively. The accumulation of permanent intermediate principal strain is always promoted by the increase of bcyc. In addition, the development of permanent major principal and volumetric strains with cycle number is analyzed in the double logarithmic plane, which are found to be combined by two linear parts.

An advanced shell model for the analysis of geometrical and material nonlinear shells

In this paper layered shells subjected to static loading are considered. The displacements of the Reissner–Mindlin theory are enriched by a an additional part. These so-called fluctuation displacements include warping displacements and thickness changes. They lead to additional terms for the material deformation gradient and the Green–Lagrangian strain tensor. Within a nonlinear multi-field variational formulation the weak form of the boundary value problem accounts for the equilibrium of stress resultants and couple resultants, the local equilibrium of stresses, the geometrical field equations and the constitutive equations. For the independent shell strains an ansatz with quadratic shape functions is chosen. This leads to a significant improved convergence behaviour especially for distorted meshes. Elimination of a set of parameters on element level by static condensation yields an element stiffness matrix and residual vector of a quadrilateral shell element with the usual 5 or 6 nodal degrees of freedom. The developed model yields the complicated three-dimensional stress state in layered shells for elasticity and elasto-plasticity considering geometrical nonlinearity. In comparison with fully 3D solutions present 2D shell model requires only a fractional amount of computing time.

Material parameter determination for the simulation of hyperelastic bonds in civil engineering considering a novel material model

In the field of structural glass, an increasing number of facade constructions is being manufactured using adhesives due to the possibility to achieve a maximum degree of transparency using circumferential bonds. The basis for the design of such load-bearing silicone bonds is currently the European Technical Approval Guideline 002 (ETAG 002) for Structural Sealant Glazing Kits. However, ETAG provides for a global nominal stress concept, which does not correctly represent the real three-dimensional stress state within the joint. The softening of the material typical of silicones (Mullins-effect) is also not covered. The guideline sets high safety coefficients, which do not consider the actual potential of the bond. In this article, a material model is presented which can realistically simulate the load-deformation behaviour of such bonds under consideration of multi-axial stresses and material softening. The focus here is on determining the necessary material parameters based on different, clearly determinable multi-axial basic tests as well as the validation of the model on small scale test specimens with complex loading analogous to Structural Sealant Glazing systems.

Long-term deformation of railway tracks considering train-track interaction and non-linear resilient behaviour of aggregates – a 3D FEM implementation

Railway track designers and maintenance entities have long been pursuing for a robust and reliable method to predict the track’s long-term behaviour. The complexity of this railway system, in terms of its changing structural and material behaviour throughout its life cycle, have hindered that quest. This paper presents a novel computer implementation focused on the estimation of the ballast and sub-ballast long-term deformation that provides a realistic reproduction of the actual behaviour of the structures because (i) it considers the three-dimensional aspect of the problem, (ii) incorporates accurate non-linear resilient material laws for the granular layers, (iii) uses a robust constitutive high-cycle strain accumulation model specifically devised for railway tracks that accounts for the three-dimensional stress conditions to determine both the volumetric and deviatoric permanent deformations and (iv) explicitly considers the dynamic train-track interaction. After calibration and validation with the results from an experimental case study comprising a physical model, a simulation scenario, considering different train types, is presented to demonstrate the potential of this approach. This implementation allows the construction of sufficiently extensive and elaborate representations of the railway track, allowing the study of geometrically complex cases and of the influence of many other aspects on its long-term behaviour.

Efficient modelling of beam-like structures with general non-prismatic, curved geometry

The analysis of three-dimensional (3D) stress states can be complex and computationally expensive, especially when large deflections cause a nonlinear structural response. Slender structures are conventionally modelled as one-dimensional beams but even these rather simpler analyses can become complicated, e.g. for variable cross-sections and planforms (i.e. non-prismatic curved beams). In this paper, we present an alternative procedure based on the recently developed Unified Formulation in which the kinematic description of a beam builds upon two shape functions, one for the beam’s axis, the other for its cross-section. This approach predicts 3D displacement and stress fields accurately and is computationally efficient in comparison with 3D finite elements. However, current modelling capabilities are limited to the use of prismatic elements. As a means for further applicability, we propose a method to create beam elements with variable planform and variable cross-section, i.e. of general shape. This method employs an additional set of shape functions which describes the geometry of the structure exactly. These functions are different from those used for describing the kinematics and provide local curvilinear basis vectors upon which 3D Jacobian transformation matrices are produced to define non-prismatic elements. The model proposed is benchmarked against 3D finite element analyses, as well as analytical and experimental results available in the literature. Significant computational efficiency gains over 3D finite elements are observed for similar levels of accuracy, for both linear and geometrically nonlinear analyses.

Strength prediction model considering material, ultrasonic and stress of cemented waste rock backfill for recycling gangue

Recycling gangue as the aggregate of cemented waste rock backfill (CWRB) to filling mining is the most economical, environmental and friendly method, which solves the environmental problems caused by gangue discharge and reduces the mining damages. Evaluating the strength property of CWRB is of great significance for maximizing the utilization of gangue recycling and improving the economic benefits of filling mining. In this paper, the triaxial compression and ultrasonic detection tests were carried out on 208 CWRB specimens to determine the relations between its strength parameters and ultrasonic pulse velocity (UPV). The coupling relations between the confining pressure, dosage of cementing material and particle size distribution (PSD) of aggregates and the strength parameters of CWRB under three-dimensional compression were established. Three models were proposed to predict the compressive strength, cohesion and internal friction angle of CWRB, in which Model I was built through the UPV, Model II was established based on the input of influencing parameters, Model III was constructed by combining material properties with on-site UPV and stress tests. The differences among these three models and their accuracies were discussed to obtain an optimal prediction model. The results show that the strength parameters of CWRB are positively correlated with its UPV, a modified exponential function can be used to describe those relationships. The strength parameters of CWRB increase with the confining pressure and dosage of cementing material, while increase firstly and then decrease with the PSD of aggregate particles, these coupling relationships between the multiple influencing factors and the strength parameters are optimized by the constructed genetic algorithm (GA). Compared with Model I using single UPV and Model II with the only input of influencing parameters, Model III combining ultrasonic technology that is conducive to field verification and intelligent technology GA for parameterizing work have higher evaluation accuracy, which eliminates the prediction distortion of the strength parameters of CWRB in three-dimensional stress state. This accurate and timely assessment is a pioneering work for ensuring the backfill stability, reducing the waste of the filling material and the filling costs.

Cement-based piezoelectric composite sensor designed for charactering the three-dimensional stress state in concrete

We reported a sensor, designed based on the specific working modes of piezoelectric, to characterize the three-dimensional (3-D) stress state in concrete. The sensor contains 6 piezoelectric elements: 3 elements working in normal mode to measure the normal stress, and 3 elements working in shear mode to measure the shear stress. Cement-based piezoelectric composite, fabricated by cutting-filling method, was used to fabricate the sensor, as it has better mechanical compatibility with concrete than piezoelectric ceramics. By embedding the sensor into a cement mortar column, we systematically characterized its performance under dynamic uniaxial load from 3.0 MPa to 7.5 MPa with frequency from 1 Hz to 20 Hz. Results demonstrate that the sensor can measure the 3-D stress state in concrete well, and has good linearity, high sensitively, and excellent working bandwidth. The cross sensitivities of the sensor were also calculated and discussed.

A new anisotropic coal permeability model under the influence of stress, gas sorption and temperature: Development and verification

Modeling approach to permeability especially anisotropic permeability of coal in front of working face is of significance for gas extraction in coal mining. Considering three-dimensional stress condition and multi-field influence, in this study, an anisotropic permeability model was suggested for coal in front of working face. The anisotropic permeability was assumed to be controlled by the directional fracture strain under the condition of multi-field influence caused by effective stress, adsorption-desorption and thermal stress. The directional fracture strain induced by effective stress was governed by the generalized Hooke constitutive model. Based on the matrix-fracture interaction, the constitutive model of directional fracture strain induced by adsorption-desorption was established from the improved Langmuir equation. Assuming that the coal matrix was connected by the matrix bridge, the constitutive model of directional fracture strain induced by thermal stress was constructed by proposing the thermal internal swelling coefficient. Consequently, a new anisotropic coal permeability model was developed based on the directional fracture strain under the influence factor of stress, gas sorption and temperature. Moreover, the new permeability model was verified by laboratory tests under different effective stresses, gas pressures, temperatures and their combined influence. The theoretical results of proposed anisotropic permeability model may provide a better understanding of permeability evolution in multi-field coupling geological environment during coal mining.

Hyperelastic constitutive modeling of hydrogels based on primary deformation modes and validation under 3D stress states

In isotropic linear elasticity, a constitutive model calibrated using a single deformation mode (e.g., compression or tension or shear) is sufficient to describe a complex three-dimensional (3D) stress state. Such an approach, however, is likely inadequate for modeling hydrogels, which exhibit a nonlinear stress-strain response that varies significantly between deformation modes and is also sensitive to microstructure via gel concentration. In this study, a combined experimental and constitutive modeling framework is proposed for the development and validation of concentration-dependent 3D hyperelastic models for hydrogels. Agarose hydrogel in a concentration range of 0.4–4% w/v is chosen as the model material. Uniaxial compression, uniaxial tension, and simple shear (three primary deformation modes) experiments are conducted. The small strain elastic modulus-gel concentration relationships obtained from experiments are compared with those predicted by the molecular theory of rigid polymer networks (Jones-Marques theory) to identify the concentration range in which entropic elastic (hyperelastic) response dominates. In this range (1.5–4% w/v), four hyperelastic constitutive models are fit to the combined compression-tension-shear stress-strain data: Mooney-Rivlin, three-parameter generalized Rivlin, Gent, and Gent-Gent models. It is demonstrated that the generalized Rivlin model offers the best overall accuracy, and the variation of its model parameters with gel concentration is consistent with the Jones-Marques theory. The resulting concentration-dependent Extended Generalized Rivlin model is employed in finite element simulations of the non-homogeneous 3D stress state of wedge indentation. Simulated load versus depth and strain field predictions show very good agreement with experimental wedge indentation results. Finally, it is shown that a hyperelastic model calibrated using only a single deformation mode yields poor results for other primary and 3D deformations, and thus multiple primary deformation modes (preferably all three) should be considered.

Analysis on Three-Dimensional Strength Influencing Factors and Control Measures of Asphalt Mixtures.

Strength is an important parameter for the design of asphalt pavement materials and structures. To study the influence of various factors on the three-dimensional strength of asphalt mixtures, three aggregate gradations (dense-graded bituminous mixture AC-13, stone mastic asphalt SMA-13 and bituminous stabilization aggregate paving mixture OGFC-13) and two binders (SBS modified bitumen and 70# base bitumen) were used to prepare the asphalt mixture specimens. Among them, SBS+SMA-13 asphalt mixture has the best performance. On this basis, the uniaxial compressive test, uniaxial tensile test and confining triaxial test were conducted on the SBS+SMA-13 asphalt mixture under six oil-stone ratios conditions (5.5%, 5.7%, 5.9%, 6.1%, 6.3%, and 6.5%), six temperatures conditions (5 °C, 10 °C, 15 °C, 20 °C, 25 °C, and 30 °C), and five loading rates conditions (1 mm/min, 2 mm/min, 3 mm/min, 4 mm/min, and 5 mm/min). In addition, a unified three-dimensional strength calculation model considering the influence of temperature, loading rate, and oil-stone ratio was proposed, and the change law of the three-dimensional strength with these above factors was revealed. Furthermore, two sets of three-factor three-level orthogonal tests were carried out on the SMA-13 asphalt mixture. The sensitivity analysis and strength regulation research between three-dimensional strength and each factor were carried out. The results show that the type of asphalt has the greatest influence on the strength of the mixture, the temperature has the second most influence, the loading rate has less influence, and the oil-stone ratio has the least influence. The strength regulations proposed to improve the strength of the asphalt mixture include the use of modified asphalt, high-temperature stability high-quality asphalt, and the lower oil-stone ratio than the Marshall optimal oil-stone ratio. The strength control measures proposed from the perspective of the three-dimensional stress state, the joint failure of each stress components and real stress states are taken into consideration.

Geotechnical Engineering Design and Visual Research Based on 3D Geological Model

In geotechnical engineering, the geotechnical mass is in a three-dimensional state of stress, and the three principal stresses all play an important role in the stability of the slope. At the same time, with the influence of the excavation, blasting vibration, rock joint crack and fault around the slope, the structure and stress state of rock and soil mass change constantly. Therefore, in order to reflect the actual situation more truly, the influence of the three principal stresses on the stability of geotechnical engineering must be analysed and studied as a three-dimensional problem.

Time Interval Effect in Triaxial Discontinuous Cyclic Compression Tests and Simulations for the Residual Stress in Rock Salt

When rock salt is subjected to discontinuous fatigue, time intervals (periods during which the stress remains constant) can accelerate plastic deformation and reduce the fatigue life due to the internal residual stress generated between various defects and the host material. However, the time interval effect on rock salt in a three-dimensional stress state has rarely been investigated despite its great significance in the use of underground salt caverns as storages. In this research, a series of triaxial discontinuous cyclic compression tests were conducted on salt and the residual stress was reproduced through numerical simulations. Experimental results show that the interval effect decreases with the increase of the confining pressure. The change in plasticity caused by time intervals is small and constant when the stress level (ratio of the maximum stress to strength) is below “60%” but then increases as a linear function of the stress level. During simulations, it was observed that the greater the difference in the elasticity modulus between the host material and impurities, the larger the residual stress. The moderate effect of time interval under confinement is the result of the fact that a higher confining pressure strengthens the host material, reduces the volume of impurities and thus leads to a smaller residual stress. In addition, when the stress level is below a certain threshold (which is shown to be at 0.8–0.85 of the critical yield stress), the residual stress is relatively low in magnitude and area of influence. Above that threshold, the residual stress grows rapidly. This is the reason why the interval effect displays a distinct behavior before and after dilatancy point.

Fracture behaviour of SiCp/Al composites with network architecture

It is found that, for discontinuous metal matrix composites (MMCs) with an inhomogeneous network reinforcement distribution, a thin network layer and large alloy cells are favorable for the toughness.. The network layers contribute to the high modulus and strength, while large alloy cells work in deflecting crack propagation and thus enhancing the toughness. Furthermore, mutually coordinated and restricted deformation behaviors of alloy cells may create a three-dimensional tensile stress state, which induces the anomalous brittle fracture of intrinsically ductile aluminum matrix in some alloy cells. These phenomena have weakened the matrix alloy plastic deformation capacity, constrained the crack propagation and improved the toughness of network composites.

Damage evolution analysis of open-hole tensile laminated composites using a progress damage model verified by AE and DIC

A three-dimensional finite element model of composite laminates for progressive damage analysis has been established based on continuum damage mechanics. The model contains four kinds of damage modes of composite laminates under three-dimensional stress states, which include matrix damage, fiber breakage, delamination and fiber pull-out. Damage initiations adopt the mixed failure criterion composed by Linde criterion and Hashin criterion, which choose strain as parametric description. An improved exponential non-linear evolution model is adopted for damage variables, which take into account the effect of material dissipated energy on the damage variables. The damage variables calculated by material dissipated energy are different from that calculated by fracture dissipation energy employed by Linde, the material dissipated energy is the result of various damage accumulation of composite material, which can reflect the gradual damage evolution process of material. The progressive damage simulations have been performed to investigate damage evolution of unidirectional laminate and bidirectional laminate with a hole under tension, the damage evolutions simulated by FEA have a good agreement with that obtained from real-time acoustic emission (AE), digital image correlation (DIC) monitoring and load–displacement relationship, which validate efficiency of the proposed 3D FEM model.

Strength-weakening effect and shear-tension failure mode transformation mechanism of rockburst for fine-grained granite under triaxial unloading compression

The occurrence of rockburst is closely related to initial high stress state and excavation unloading effects. To investigate the effects of three-dimensional (3D) stress state and unloading rate on the rockburst mechanism, triaxial unloading compression tests were performed on cubic fine-grained granite specimens (50 mm × 50 mm × 50 mm). Two unloading rates (0.08 and 40 MPa/s) were employed in the tests with seven initial 3D confining pressures (5, 10, 20, 30, 40, 50, and 60 MPa). For comparison, triaxial and biaxial compression tests were conducted at the same initial confining pressures. The results show that, under the same confining pressures, the variations in peak strength of granite specimens are in the following order: triaxial compression test > biaxial compression test > triaxial unloading compression test under low unloading rate > triaxial unloading compression test under high unloading rate, which indicating that unloading induces an obvious strength-weakening effect on fine-grained granite. In the triaxial unloading compression test with the same unloading rate, a higher confining pressure results in a greater rock bearing strength and stress drop. More energy will be stored in the rock, and the rockburst intensity will be more serious when the rock is destroyed. When the confining pressure is constant, the lower unloading rate is beneficial for improving the rock bearing strength, and more elastic energy will be accumulated and stored in the rock. Once rockburst occurs, the energy released by rock is larger and the degree of rockburst is stronger. The failure mode of fine-grained granite specimens in triaxial unloading compression tests transforms from shear-tension failure to tension failure with increasing confining pressure, which is the main reason for the weakening of rock strength. Establishing a strength criterion for 3D rock considering the unloading effect is a key for understanding the mechanism of rockburst.

Confining stress effect on the elastoplastic ground reaction considering the Lode angle dependence

The convergence confinement methods are solutions employed to estimate convergence in circular tunnels. They are mostly based on constitutive equations governed by the Mohr-Coulomb and Hoek-Brown yield criteria. However, the solutions based on these criteria neglect the intermediate principal stress confining effect on the ground reaction estimation. Therefore, in this paper, a Drucker-Prager yield criterion governed solution integrated with the Lode angle parameter is employed. It considers the intermediate principal stress influence and the critical effect of the parameter on failure characterization. Subsequently, it is verified with results attained from numerical simulations which consider an elastic-perfectly plastic constitutive law with a non-associative flow rule within FLAC3D. It was drawn from the results that the ground reaction and plastic evolution are influenced by the confining stress. Furthermore, considering a suitable yield criterion leads to realistic convergence and plastic evolution estimation. The circumscribed DP criterion governed solution with Lode angle parameter value (0.8) is considered appropriate for the realistic ground reaction estimation in the three-dimensional (3D) stress state rock mass. It estimates approximately 3.4% of tunnel convergence as compared to the classic solutions (5%) and plastic radius estimated to be approximately 2.45 m compared to 2.84 m.