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To verify the novel method of achieving a true-triaxial stress path with the pseudo-triaxial apparatus, a series of drained and undrained tests were carried out for the identical scheme with pseudo-triaxial apparatus and true-triaxial apparatus respectively. The differences between the two types of tests were quantified. The results show that the novel method effectively achieved the true-triaxial stress path by controlling the loading ratio of the pseudo-triaxial apparatus. The relationships of q  −  ε 1 and η  −  ε s measured by the two apparatuses had a higher similarity which decreases slightly with the b increase. When 0 ≤  b  < 0.5, the slope of the critical state line measured by both apparatuses was almost identical. When 0.5 ≤  b  ≤ 1, the slope of the critical state line measured by the novel method was slightly lower, but the biggest change was within 10% compared with the two Mohr–Coulomb criteria, the peak strength measured by the two apparatuses was distributed near the criteria, indicating the feasibility and rationality of the novel method. The tests show that the novel method greatly enriches the test range of pseudo-triaxial apparatus, which not only simplifies the process of soil 3D testing but also reduces the test cost.

To clarify the stress–strain behaviour, strength on the deviatoric plane, shear band formation, and dilatancy characteristics of aeolian sand under three-dimensional loading conditions, a series of true-triaxial tests with various intermediate principal stress coefficients b  ∈ [0.0, 1.0] at constant effective mean principal stress p ' were conducted under drained and undrained conditions. The results presented that the variations of the stress–strain, strength, and effective internal friction angle show its significant dependence on the relative magnitude of the intermediate principal stress expressed in terms of the b value. Because a clear penetrating shear band was produced in the prismatic specimen at b  = 0.2 and b  = 0.4, the stress–strain response exhibits softening, and its peak shear stress and effective internal friction angle are reduced. Besides, shear bands often appear in the hardening regime. Moreover, the dilatancy was the weakest at b  = 0.0 and the strongest at b  = 0.4, which depended on the stress path in terms of the b value. The peak shear stress on the deviatoric plane decreased in a transverse “S” shape with the b value varying from 0.0 to 1.0, correspondingly, the effective internal friction angle increased first and then decreased. But in the case of increasing p ' value, aeolian sand has a unified critical state line and phase transformation line at constant b value.

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil, hydraulic, mechanical, aerospace, military, and other engineering disciplines. Therefore, the comprehensive study of the generalized nonlinear strength theory (GNST) of geomaterials has significance for the construction of engineering rock strength. This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths. First, it systematically summarizes the research progress of GNST (classical and empirical criteria). Then, the latest research the authors conducted over the past five years on the GNST is introduced, and a generalized three-dimensional (3D) nonlinear Hoek–Brown (HB) criterion (NGHB criterion) is proposed for practical applications. This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance. The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%–3.5091% and 1.0144%–3.2321%, respectively. Finally, the development and outlook of the GNST are expounded, and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed. The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.

Aeolian sand is a special roadbed filler, but its three-dimensional mechanical properties are rarely studied. To obtain the characteristic of its deformation, strength on the deviatoric plane, and failure in three dimensions, a series of triaxial drained tests on aeolian sand in the Tengger Desert, under the condition of the constant average principal stress, p, were conducted by an equivalent alternative method to achieve a true triaxial stress path by a pseudo-triaxial apparatus. The results show that the method can better determine the strength. The peak shear stress decreases gradually with the increase of the intermediate principal stress coefficient, b, at the same p. Compared with the SMP and Mohr–Coulomb criteria, the peak shear stress is near the strength lines predicted by both criteria. At a lower p, the specimen exhibited strain-softening behaviours, but at a higher p, it showed hardening behaviours. Under the conditions of a higher p and lower b, the specimen exhibited contraction first and then dilatancy. The specimen deformation is greatly affected by anisotropy, and as the p-value increases, the effect of the initial anisotropy on the specimen begins to weaken. The εs (generalized shear strain)/η (stress ratio)-εs curves, can be expressed by a linear equation, of which the slope is affected by the b-value. The experiment verifies the feasibility and rationality of the equivalent method. The test data provide support for the maintenance of desert roadbeds and the sustainable development of the economy and society in ecologically fragile areas.

Rock strength criteria are the theoretical grounding of geotechnical design and stability estimation, the Mohr–Coulomb (MC) and Hoek–Brown (HB) criteria are the widely accepted criteria at present, due to their reasonability and unambiguous concept, however they overlook the effect of intermediate principal stress, and contain six singular corners in π plane. Aimed at overcoming those limitations, the MC and normal parabolic criterion (NPC) were improved to their 3D versions that lead to smooth and convex for a wide range of strength parameters. The extended 3D strength criteria coincide with corresponding original forms in the triaxial compression and triaxial extension states, which not only take intermediate principal stress into account, but also provide great convenient in numerical calculation. Multigroup of poly-axial strength datasets gathered from the references are used to check the prediction accuracy of the proposed 3D criteria by the least absolute deviation method. Research proved that the 3D NPC criterion has a relatively larger deviation on poly-axial strength data prediction, but the proposed 3D MC criterion can describe peak strength with low misfit for soft or hard rocks. Peak strength σ 1 increases first and then decreases with the increase of σ 2 , whether increasing or decreasing σ 2 , both will result in rock failure. Moreover, the 3D MC can fit the poly-axial strength data well for lower or higher values of σ 3 , which strongly suggests the proposed 3D MC criterion is adequate. Applicability of the proposed strength criterion will be discussed in further research. Article Highlights The normal parabolic criterion and Mohr-Coulomb criterion are modified to their 3D versions. The established criteria are checked for poly-axial data using the least absolute deviation method. The 3D MC can provide reliable predictions on poly-axial strength for various rock types. The 3D MC can provide reliable predictions on poly-axial strength for various rock types.

Triaxial loading tests were carried out on the gangue-based haydite concrete cube specimens (100 × 100 × 100 mm 3 ) and plate specimens (100 × 100 × 50 mm 3 ) to investigate the mechanical behavior of this kind of lightweight aggregate concrete (LWAC) under multi-axial stress state, and accordingly to develop the failure criterion for the finite element analysis of LWAC structures. Experimental results revealed that, under triaxial compression loading, most of the haydites within the specimen were crushed when the stress ratios σ 1/ σ 3  ≥ 0.3 and σ 2/ σ 3  ≥ 0.5. The gangue haydite concrete exhibited “plastic flow plateau” at this stage, which was conservatively regarded as the ultimate strength of the LWAC under triaxial compressive stress state. As a result, the tensile and compressive meridians on failure envelope surface are intersected with hydrostatic axial at two points, completely different from the characteristics of normal weight concrete for which the failure surface is unclosed and open-ended under compression. In terms of the test data, a four-parameter triaxial failure criterion for LWAC was developed. The strength envelope in the deviatoric plane adopted elliptic curve similar to that of Willam–Warnke model, and the tensile and compressive meridians were represented by quadratic functions with four parameters. Two alternative methods, i.e. the characteristic strength points method and the least square regression method, were used to determine the model parameters. After compared with the failure criterion recommended by fib Model Code 2010, methods proposed in this study are preferred especially when the plastic flow property is taken into account.

The Unified Strength Theory (UST) provides the fundamentals for the systematic study of various strength hypotheses and yields criteria for isotropic materials. It shows relationship between known models (M ohr -C oulomb , P isarenko -L ebedev , Twin-Shear Theory of Y u ), and apart from these known models, this model contains also classical models like the normal stress hypothesis, von  M ises , T resca and S chmidt -I shlinsky . The UST can be adapted for different types of materials. Thus, it is a suitable tool for the analysis of experimental data. For the UST, the inelastic Poisson’s ratio and the maximum hydrostatic tension stress will be computed as a function of model parameters which simplifies the comparison with another model. The correlations between uniaxial, biaxial and hydrostatic stress will be illustrated and compared with classical models. For all classical models and for the UST, the uniaxial and biaxial tension failure stress and also the uniaxial and biaxial compression failure stress are equal. In this sense, the UST can be classified as a classical model. The failure behavior of new materials like some polymers and alloys differs from the classical one. The UST can be extended to such failure behavior. For this purpose, the Unified Yield Criterion (UYC) as part of the UST will be modified so that all known criteria of incompressible material behavior can be approximated. With the help of a simple substitution, the UYC can be further developed for compressible material behavior. Different convex lines can be adjust for the form of the meridian. With this substitution, the hydrostatic tension stress will be restricted with one of the parameters. Furthermore, the model can be applied for the description of failure behavior of ceramics, hard foams and sintered materials. For this application, both the hydrostatic tension and compression stress will be restricted too. Some reference values for hydrostatic loading are established. For the visual comparison of different parameter setting of the models, graphical methods can be used. The UST will be represented in the principal stress space. Further considerations will be carried out in the B urzyński -plane and in the π -plane. For engineering applications, the Burzyński-plane is preferred to the meridional cut. For better analysis and a direct comparison of fitted models to the experimental values, the line of the plane stress state will be shown in the B urzyński -plane and in the π -plane.

Constitutive models of particulate materials often rely on distances between the current stress state in stress space and various surfaces. Examples of these surfaces include the bounding surface and the dilatancy surface. This paper proposes a rigorous method for determination of distance to a surface in stress space. It starts by examining operations on stress variables defined in the π plane. Algorithms for determination of an image point on a surface are then presented as a function of the location of the current stress state with respect to the surface. For points within the surface, the bisection method is used; otherwise, the secant method is used. The paper shows that implementation of the proposed algorithm locates the image point on a surface in stress space with accuracy and rigor, providing an accurate measure of the distance to the surface that can be used in hardening or flow rules.

Flat punch hole expansion tests are valuable for anisotropic plasticity model evaluation sine they activate a spectrum of tensile stress states across all in-plane material orientations. Pressure-independent yield functions with an associated flow rule typically overlook the state of plane strain tension (PST) during their calibration. Studies have shown that PST occurs near a principal stress ratio of 1:2 for materials that approximately follow deviatoric plasticity but this plane strain constraint (PSC) has been largely overlooked in anisotropic yield function calibration. This study proposes an efficient methodology to characterize and calibrate associated deviatoric plasticity models for materials with a broad range of anisotropy and hardening characteristics including AA5182-O and AA7075-T6 aluminum, and DC04 and 980GEN3 steels. The PST response was evaluated from notch tests using an inverse finite-element analysis approach with correlations provided when cruciform or notch test data is unavailable. The isotropic hardening assumption was evaluated to large strains by determining the stress response from analysis of area of the neck in tensile tests. The anisotropic Yld2000 and Yld2004 yield functions were calibrated to enforce the PSC, ensuring a zero plastic strain increment in directions without a deviatoric stress. The isotropic Hosford and quadratic Hill-48 functions, which universally satisfy and violate the PSC respectively, were also considered. Yield functions that enforced the PSC accurately predicted the global forces, strains, and PST locations in flat punch hole expansion simulations. In contrast, the Hill-48 model failed to accurately predict the radial distance from the hole in PST where the minor strain vanished, highlighting the importance of considering plane strain data for yield function calibration.

On 5 April 2017, an Mw6.1 earthquake occurred about 50 km NE of the city of Fariman, northeast Iran. Several hundreds of aftershocks including two M > 5 events followed the main shock. The quake struck numerous towns and villages across the region, killed one person, and injured tens of people. Many schools and universities were evacuated around the epicentral area, and a lot of people left their residences for a few days. The northeastward motion of the central Iran toward Eurasia influences the epicentral region. Regional movements occur by shortening on the northwest-trending reverse faults. We studied teleseismic source parameters of this earthquake by applying different moment tensor decomposition methods including grid search for the nodal planes of the best double couple; linear inversion for a deviatoric moment tensor; grid search for the best double-couple moment tensor; grid search for the best deviatoric moment tensor; and grid search for the best full moment. Based on the moment tensors, the event occurred on a reverse fault following the regional compressional motion. The results of this study will provide useful information for future regional seismotectonic investigations and are of significant use for applications such as regional seismic hazard evaluations.