Proposed Strength Criterion Research Articles

A new three-dimensional rock strength criterion based on shape function in deviatoric plane

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 σ1 increases first and then decreases with the increase of σ2, whether increasing or decreasing σ2, both will result in rock failure. Moreover, the 3D MC can fit the poly-axial strength data well for lower or higher values of σ3, which strongly suggests the proposed 3D MC criterion is adequate. Applicability of the proposed strength criterion will be discussed in further research.

Nonlinear unified strength criterion for frozen soil based on homogenization theory

To establish a strength criterion that can consider the composite properties and internal non-homogeneity of frozen soil, a load sharing model is first defined based on homogenization theory and the binary-medium structure model, and then the strength functions of frozen soil on the p-q plane and the π plane are established, respectively. Finally, a three-dimensional nonlinear unified strength criterion for frozen soil is proposed. The applicability of the proposed strength criterion is verified based on the multi-group triaxial compression test results and the directional shear test results at different stress Lode angles.

Strength criterion for frozen silty clay considering the effect of initial water content

The initial water content and confining pressure significantly affect the deformation and strength behaviors of frozen soils. To investigate the influence of the initial state of water on the mechanical properties of frozen silty clay (FSC), triaxial compression tests are conducted on artificial FSC with five initial water contents (12.5%, 14.0%, 16.0%, 18.0%, and 20.0%) at the temperature of −6 °C. The results show that when the initial water content is 12.5%, the frozen soil samples present strain softening and strain hardening successively with increasing confining pressure. As the initial water content increases, the degree of strain hardening under the same confining pressure gradually weakens. The frozen soil samples mainly present strain softening when the initial water content is more than or equal to 18%. According to the test results, when the initial water contents ranging from 12.5% to 20%, the relationship between the strength and mean stress has three forms: increases nonlinearly, increases first and then decreases, and maintains an approximately constant value. Linear and nonlinear strength envelope equations based on different types of strength envelopes are proposed. Additionally, the relationship between the initial water content and internal friction angle is analyzed. In the p-q plane, based on the nonlinear strength characteristics of FSC with initial water contents of 12.5%, 14.0%, and 16.0%, a modified mean stress expression p* is derived to represent the nonlinear strength criterion equation according to the modified Cam-Clay model. Furthermore, a shape function in the deviatoric plane is proposed by modifying the Lade–Duncan model, and a strength criterion is established by integrating the strength functions in the p-q and deviatoric planes. The proposed strength criterion can effectively represent the nonlinear strength behaviors of FSC, including the effects of the initial water content, ice melting, and crushing.

Mechanical properties of thermal aged HTPB composite solid propellant under confining pressure

With the purpose of investigating the effects of confining pressure and aging on the mechanical properties of Hydroxyl-terminated polybutadiene (HTPB) based composite solid propellant, tensile tests of thermal accelerated aged propellant samples under room temperature and different confining pressure conditions were performed through the use of a self-made confining pressure device and conventional testing machine. Afterwards, the maximum tensile stress σm and the corresponding strain εm for the propellant under different test conditions were obtained and analyzed. The results indicate that confining pressure and aging can significantly affect the mechanical properties of HTPB propellant, and the coupled effects are very complex. On the one hand, the stress σm increases as a whole when confining pressure becomes higher or thermal aging time rises. Besides, this stress is more sensitive to aging with increasing confining pressure. There are almost three regions in the stress increments σmP−σm0/σm0 and thermal aging time curves for HTPB propellant. The maximum value of the stress increment σmP−σm0/σm0 for the propellant is about 98% at 7.0 MPa and 170 d. On the other hand, the strain εm decreases with increasing thermal aging time under the whole confining pressure conditions. However, the variation of this strain with confining pressure is more complex at various thermal aging time, which is different from that of unaged solid propellant in previous researches. In addition, this strain is slightly less sensitive to aging as the confining pressure increases. Furthermore, there is also a critical confining pressure in this investigation, whose value is between 0.15 MPa and 4.0 MPa. Beyond this critical pressure, the trends of the stress σm and the corresponding strain εm all change. Moreover, there are some critical thermal aging time for the stress increment (σmP−σm0)/σm0 and strain increment (εmP−εm0)/εm0 of HTPB propellant in this investigation, which are about at 35, 50 and 170 d. Finally, based on the twin-shear strength theory, a new modified nonlinear strength criterion of thermal aged HTPB propellant under confining pressure was proposed. And the whole errors of fitted results are lower than 6%. Therefore, the proposed strength criterion can be selected as a failure criterion for the analysis the failure properties of aged HTPB propellant under different confining pressures, the structural integrity of solid propellant grain and the safety of solid rocket motor during ignition operation after long periods of storage.

A novel dynamic cavity expansion model to predict the resistance of reactive powder concrete (RPC) against projectile impact

The dynamic cavity expansion (DCE) model is a commonly used analytical model to predict the resistance of concrete materials subjected to projectile impact. In this paper, a modified Griffith strength criterion was proposed for reactive powder concrete (RPC), which has a form easy to solve and can well capture the tensile, compressive and triaxial strength of RPC. Combined with the Murnaghan equation of state, the proposed strength criterion was used as the material model for RPC. The cavity expansion resistance was calculated numerically and analytically. It indicates that the numerical and analytical solutions are almost consistent under the same material response. Then, the strain softening behavior that cannot be resolved analytically was further introduced into the material model, and the numerical solution of the DCE model was obtained using LS-DYNA. To verify the present method, the 122.6 MPa RPC targets were tested using 14.5 mm diameter ogival nose projectiles at impact velocities of from 286 to 942 m/s. Combined with previous penetration model, the penetration depth of the present test was predicted. In addition, numerical simulation of this penetration test adopting the HJC model was also performed. It shows predictions of the present model are in good agreement with test and simulation results. Furthermore, the present model was used to predict the existing test date of RPCs with compressive strength of between 67.5 and 140 MPa, and the effectiveness of the present method was verified by comparing with predictions of previous empirical formulas.

A strength criterion for rocks

A simple strength criterion J2=α+βσ3 is investigated to describe the ultimate stress capacity of rocks. This criterion takes the intermediate principal stress σ2 into consideration. The nonlinear parabolic form on the meridian plane makes the present criterion is more suitable in rock mechanics than the linear Mohr–Coulomb failure criterion. The present criterion has only 3 corners on the π plane, resulting in higher efficiency and reliability in solving the corner problems in numerical analysis than Mohr-Coulomb and Hoek-Brown criteria. Comparison by the experimental results indicates that the proposed strength criterion gives a better agreement with experimental data than Mohr-Coulomb, Hoek-Brown, Drucker-Prager and modified Lade-Duncan criteria.

Analytical Solution for a Loess Tunnel Based on a Bilinear Strength Criterion

The design load of a loessal tunnel is usually calculated using the conventional Mohr-Coulomb strength criterion, which ignores the structural strength of loess and provides inaccurate calculation results. The present paper therefore proposes a bilinear strength criterion considering the structural strength characteristics of loess determined in a triaxial shear experiment. Then, using the new strength criterion, a new theoretical solution is derived for the stress and displacement of loess in each region separately; the solution is validated by numerical simulation. Lastly, the ground reaction curve and the design load of a tunnel are obtained using the proposed method considering the structural strength of loess. The results obtained using the new method are more reasonable and accurate than the results calculated using the conventional method. The proposed strength criterion and theoretical solution expand the knowledge base of loess engineering and provide guidelines for the design and construction of underground structures in loess ground.

A general failure criterion for soil considering three-dimensional anisotropy

Abstract This paper proposes a generalized three-dimensional (3D) failure criterion for cross-anisotropic soils based on the spatially mobilized plane (SMP) criterion. In the proposed criterion, the anisotropic property of soil is considered by introducing a novel modification stress tensor, in which the angle between the principal stress and the soil depositional direction serves as a basic variable. Taking advantage of the SMP criterion, the proposed anisotropic criterion is subtly extended into a 3D version. The proposed criterion only involves two friction angles, φ v and φ h , which are determined by triaxial compression test along and perpendicular to the depositional direction, respectively. To account for the effects of the depositional direction, two special modification stress tensors regarding different depositional conditions (vertical and inclined) are discussed in this study. Comparisons between the predictions from the proposed strength criterion and the observations of the true triaxial tests on four cross-anisotropic soil samples show that the proposed generalized failure criterion can well capture both the cross-anisotropic behaviors and the 3D strength of cross-anisotropic soils.

A long-term strength criterion for frozen clay under complex stress states

To study long-term strength characteristics under complex stress states, a series of hollow cylinder creep tests were conducted on frozen clay under different stress levels at a temperature of −6 °C. Experimental results showed that the creep characteristics of frozen clay were significantly affected by the mean principal stress and the intermediate principal stress coefficient. Most generalized shear creep curves of frozen clay presented typical non-attenuation creep under axial load and torque. A long-term strength criterion for frozen soil, exhibiting the strength characteristics of multiple stress components under complex stress states, was obtained based on activation energy theory. In addition, a modified elliptical function and a generalized nonlinear strength theory (GNST) were introduced to describe the evolution of the strength envelope with time. Finally, a new strength criterion for frozen clay in three-dimensional principal stress space, considering the effect of time, was established by combining the modified elliptical equation and the GNST shape function. The proposed strength criterion has great significance for predicting the strength characteristics of frozen clay under complex stress states.

Evaluation of Chloride Resistance of Early-Strength Concrete Using Blended Binder and Polycarboxylate-Based Chemical Admixture

The mixing proportions of concrete were examined with regard to the durability performance and early strength in coastal areas. Research was conducted to improve the C24 mix (characteristic strength of 24 MPa). C35 concrete (characteristic strength of 35 MPa) was selected as a comparison group, as it exhibits the minimum proposed strength criterion for concrete in the marine environment. To secure the early strength of the C24 concrete, 50% of the total ordinary Portland cement (OPC) binder was replaced with early Portland cement (EPC); and to provide durability, 20% was substituted with ground granulated blast-furnace slag (GGBS). In addition, a polycarboxylate (PC)-based superplasticizer was used to reduce the unit water content. The compressive strength, chloride ion diffusion coefficient, chloride penetration depth, and pore structure were evaluated. After one day, the compressive strength improved by 40% when using EPC and GGBS, and an average increase of 20% was observed over 91 days. EPC and GGBS also reduced the overall porosity, which may increase the watertightness of concrete. The salt resistance performance was improved because the rapid early development of strength increased the watertightness of the surface and immobilization of chloride ions, decreasing the chloride diffusion coefficient by 50%.

Simulation of fracture of elastoplastic materials in mode III: from brittle to ductile

The initiation of a longitudinal shear crack (mode III fracture) in elastoplastic materials with the limiting strain is considered. The crack propagation criterion is formulated using a modified Leonov–Panasyuk–Dugdale model using an additional parameter—the width of the plasticity zone (the width of the pre-fracture zone). Conditions of a small-scale yielding in the presence of a stress field singularity in the vicinity of the crack tip are considered. A two-parameter criterion for quasi-brittle fracture of an elastoplastic material is formulated for mode III cracks. The proposed fracture criterion includes the deformation-based criterion, which is formulated at the crack tip, as well as the force-based criterion, formulated at the tip of a model crack. The lengths of the initial and model cracks differ by the length of the pre-fracture zone. The application of the proposed strength criterion to the determination of fracture loads for bodies containing longitudinal shear cracks is demonstrated. The diagrams of quasi-brittle fracture are constructed for a strip of finite width with an edge crack in case of the out-of-plane deformation. It is proposed to determine the model parameters using an idealized simple shear diagram and the critical stress intensity factor. For quasi-ductile and ductile types of fracture, the limiting loads are determined numerically. The propagation of plastic zones in the vicinity of the crack tip under quasistatic loading is successively described by the nonlinear finite element method. It is shown that the shapes of the numerically simulated plastic zones differ significantly from the known classical concepts.

A strength criterion for frozen clay considering the influence of stress Lode angle

To investigate the influence of stress Lode angle on frozen soil, a series of directional shear tests was conducted on artificial frozen clay at three temperatures (–6, –10, and –15 °C) and five stress Lode angles (θσ= –30°, –16.1°, 0°, 16.1°, and 30°) using a hollow cylindrical apparatus. An elliptical function was proposed according to the strength envelope evaluation with the mean principal stress (p) in the p–q plane. In addition, generalized nonlinear strength theory (GNST) was introduced in the π plane to describe the evolution of the strength envelope with increasing mean principal stress. Then a strength criterion for frozen clay in three-dimensional principal stress space was proposed by combining strength functions in the p–q and π planes. The temperature effect was also introduced into the strength criterion. The proposed strength criterion can predict the multi-axial strength characteristics of frozen clay and reveal the influence of the stress Lode angle.

Application of new twin-shear unified strength criterion to frozen soil

A new twin-shear unified strength criterion is proposed in this study. This criterion reveals the relationship among single-shear, twin-shear, and triple-shear strength criteria. All known linear and nonlinear strength criteria—such as Huber–von Mises, Drucker–Prager, Mohr–Coulomb, Tresca, and twin-shear series—are special cases of the new twin-shear unified strength criterion. The proposed unified strength criterion was employed to study the strength characteristics in the compressed meridional plane (where the stress Lode angle,θσ = − 30°) of frozen soil, based on the soil's nonlinear and asymmetric properties. In the criterion, β and C, which denote the relationship between the shear stress τ and normal stress σ on the twin-shear stress acting plane, are deemed variable; they vary with the change in normal stress σ or mean stress p. Through a comparison of results, we found that the results obtained with the proposed strength criterion were in good agreement with the results of tests on frozen soil. On this basis, expressions for the cohesive force and the internal friction angle of frozen soil were derived and discussed.

A strength criterion for frozen moraine soils

The strength behavior of frozen soils has been extensively investigated in frozen soils mechanics for many years. In order to study the strength properties of frozen moraine soils, a series of cryogenic tri-axial compression tests are carried out under confining pressures ranging from 0.5 MPa to 16 MPa at the temperatures of −0.5 °C, −2.0 °C and −6.0 °C, respectively. The test results show that when the mean stress is less than the consolidation yield pressure defined as a boundary stress of the strength envelope, the strength envelope is nonlinear, while when the mean stress is greater than the consolidation yield pressure, the strength envelope becomes linear approximately and can be described by the Mohr-Coulomb strength criterion. According to the test results, a new strength criterion is proposed based on the concept of binary medium model to describe the nonlinear strength behavior of frozen moraine soils. The proposed strength criterion has taken the heterogeneous characteristics of frozen moraine soils into account and can describe the nonlinear strength behavior on the hypothesis of that a representative volume element (RVE) of frozen moraine soils is a binary medium consisting of some bonded elements and frictional elements, and the bonded elements will be gradually broken and transformed into frictional elements under certain stress conditions. Finally, compared with test results, it is demonstrated that the proposed new strength criterion could well reflect the strength behavior of frozen moraine soils at the temperatures of −0.5 °C, −2.0 °C and −6.0 °C, respectively.

Rock strength criterion considering the effect of hydrostatic stress on lode angle effect

AbstractRock strength criterion is a basic subject in mining engineering and petroleum engineering. It has important guiding significances to the process of underground energy exploitation. Different rocks have different strength envelopes. Most strength criteria have only one type of envelope in π plan. Thus, these criteria cannot predict different rock strengths accurately. Most criteria consider only the hydrostatic stress and the Lode angle effects and neglect their interaction. However, based on the experimental results in this study, there is an evident interaction between the two effects. In this study, a new strength criterion is proposed considering the hydrostatic stress and Lode angle effects, as well as the effect of hydrostatic stress on the Lode angle effect. Applicable results of previous experimental data showed that the proposed strength criterion has good applicability for different rocks. Compared with other strength criteria, this criterion has the advantage of being able to adjust the strength of the Lode angle effect based on the hydrostatic stress. This advantage allows the strength criterion to show different types of strength envelopes in the π plan and to accommodate different rocks under different stress states. The effect of hydrostatic stress on the Lode angle effect of rock may be caused by the proportion of particles destroyed in the rock.

Strength criterion and temperature dependent strength model of metallic glasses

In this paper, the different fracture mechanisms of bulk metallic glasses in tension and compression are investigated through combining its macroscopic fracture behaviors and unique atomic structure. It is found that the compressive fracture process of metallic glasses should be mainly controlled by the shear progress. In addition, both local shear process and local quasi-cleavage will happen under tensile loading due to the normal stress. Based on the analysis, a new strength criterion is proposed for metallic glasses from the viewpoint of energy, which is suitable for the whole range of stress states. The proposed criterion can give a good description of the experiment data of Zr-based metallic glasses in a wide normal stress range. Moreover, a temperature dependent compressive strength model is established based on the temperature dependent shear modulus model and the proposed strength criterion. The temperature dependence of tensile fracture angle can also be explained reasonably by the new criterion.

Simulation of fracture of elasto-platic solids with cracks under conditions of out-of plane deformation

The paper considers a tearing mode crack (mode III fracture) propagation in elasto-plastic materials having ultimate strain. The fracture process of such material has been described in the modified Leonov-Panasyuk-Dugdale model with using an extra parameter such as the plastic zone width (the pre-fracture zone width. The two-parameter criterion of quasi-brittle fracture for mode III cracks in elasto-plastic material has been derived for conditions of the low-scale yielding in the presence of a stress field singularity of the field in the vicinity of a crack. The deformation fracture criterion has been deduced for the initial crack tip, whereas the force criterion has been deduced for tangential stresses with account for their averaging at the tip of a model crack. The lengths of initial and model cracks differ by the length of the pre-fracture zone. The sequential analysis of application possibility of the proposed strength criterion has been performed when determining fracture loads for solids with tearing mode cracks. Fracture diagrams of quasi-brittle fracture under conditions of antiplane deformation have been plotted for a band with an edge crack.

Consolidated Undrained Triaxial Compression Tests and Strength Criterion of Solidified Dredged Materials

Consolidated undrained triaxial compression tests were performed to investigate the shear strength behavior of the solidified dredged materials (SDM). The variation law of deviator stress and excess pore water pressure with the increase of the applied confining pressure was investigated. It is found that the shear strength envelope is consisted of two lines, and there exists a transitional stress on the intersection point. The undrained shear strength develops slightly with the increase of applied normal stress in the preyield state. However, the undrained shear strength increases significantly in the postyield state, and the strength envelope is nearly a straight line with the extension through the origin. Based on the triaxial test data and the binary medium model, a strength criterion considering strength evolution mechanism is proposed and the relevant parameters of the strength criterion were discussed. Comparisons of the predicted results and experimental data demonstrate that the proposed strength criterion can properly describe the strength evolution rules of the SDM.

A new strength criterion for frozen soils considering the influence of temperature and coarse-grained contents

Strength of frozen soils is a hot topic, which has been being extensively investigated in frozen soil mechanics. In order to describe the effects of temperature and coarse-grained contents on the strength properties of frozen soils, a series of cryogenic triaxial compression tests for frozen soils are analyzed at different temperatures, and different coarse-grained contents at −6°C. A new strength criterion is proposed based upon the modified slope method of downward CSL (critical state line) curve in the meridian plane, in which the various parameters as well as their physical meanings are analyzed and discussed in detail, with their variations expressed by temperature and coarse-grained contents. In addition, on the basis of envelope theorem, the internal frictional angle is investigated and introduced to Lade-Duncan model in the deviatoric plane. Compared with test results, it is demonstrated that the proposed new strength criterion could well reflect the strength varying rules at different confining pressures ranging from lower to higher pressures for frozen soils. For frozen mixed soils with different coarse-grained contents, the strength decreases first and then increases with increasing coarse-grained content, which can also be predicted by the proposed strength criterion well.

A strength criterion for frozen sodium sulfate saline soil

Salt content has been proven to be an important influencing factor on the mechanical properties of frozen saline soils, whose strength criterion is different from that of unfrozen saline soils or frozen soils without salts. In this paper, a series of conventional triaxial tests are carried out for frozen saline soils with sodium sulfate at a temperature of –6 °C. A strength criterion of the frozen saline soils, including the influence of salt content, is established by using the generalized nonlinear strength theory. Based on conventional triaxial test results, a modified hydrostatic pressure expression is proposed according to the critical strength function of the modified Cam clay model in the meridian plane. The influence of salt content on the shear strength of the frozen saline soils is investigated according to their freezing temperature curves as well as the formation of salt and ice crystals. The relationship between salt content and friction angle is analyzed. The proposed strength criterion of frozen saline soil is proved to be reliable by extrusion elongation triaxial tests. This criterion can reasonably reflect the major nonlinear strength characteristics of frozen saline soils, including the influences of change in salt content, pressure melting, and ice crushing.