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Given the critical role of true triaxial strength assessment in underground rock and soil engineering design and construction, this study explores sandstone true triaxial strength using data-driven machine learning approaches. Fourteen distinct sandstone true triaxial test datasets were collected from the existing literature and randomly divided into training (70%) and testing (30%) sets. A Multilayer Perceptron (MLP) model was developed with uniaxial compressive strength (UCS, σ c ), intermediate principal stress ( σ 2 ), and minimum principal stress ( σ 3 ) as inputs and maximum principal stress ( σ 1 ) at failure as the output. The model was optimized using the Harris hawks optimization (HHO) algorithm to fine-tune hyperparameters. By adjusting the model structure and activation function characteristics, the final model was made continuously differentiable, enhancing its potential for numerical analysis applications. Four HHO-MLP models with different activation functions were trained and validated on the training set. Based on the comparison of prediction accuracy and meridian plane analysis, an HHO-MLP model with high predictive accuracy and meridional behavior consistent with theoretical trends was selected. Compared to five traditional strength criteria (Drucker–Prager, Hoek–Brown, Mogi–Coulomb, modified Lade, and modified Weibols–Cook), the optimized HHO-MLP model demonstrated superior predictive performance on both training and testing datasets. It successfully captured the complete strength variation in principal stress space, showing smooth and continuous failure envelopes on the meridian and deviatoric planes. These results underscore the model's ability to generalize across different stress conditions, highlighting its potential as a powerful tool for predicting the true triaxial strength of sandstone in geotechnical engineering applications. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The synergetic effects of alkaline red mud (RM) and sulfate-based phosphogypsum (PG) on the undrained triaxial behavior of cement-admixed clay were explored in this study. A series of isotropically consolidated undrained triaxial tests were performed on stabilized clay with respect to different admixed RM/PG proportions. The triaxial behavior of stabilized clay is presented in terms of a stress–pore pressure–strain relationship, failure mode, undrained deformation modulus, stress path, and failure envelope. Scanning electron microscopy (SEM) tests were conducted to survey microscopic evolution. The results showed that the brittleness of the specimen intensified with a high RM content, which was manifested by a predominant postpeak strength reduction. As the PG content increased, the strain-softening behavior weakened and gradually evolved into strain-hardening. The failure mode changed from local shear failure to the single cone failure and bulging failure correspondingly. The RM played a role in increasing soil cohesion, whereas PG contributed to a larger frictional angle at the postyield stage. Microscopic observations indicated that the alkali source from RM significantly promoted pozzolanic reactions and strengthened cementation bonds, which increased the peak strength, deformation modulus, and cohesion. In addition, the sulfate in PG contributed to ettringite generation among clay particles and clusters, resulting in a more ductile behavior and a larger frictional angle due to large clusters formed. [ABSTRACT FROM AUTHOR]

The current design of member foundation only considers horizontal forces (H) and ignores the effect of torque (T), which may lead to torsional failure of the foundation. To analyze the bearing characteristics of rigid rectangular foundation subjected to horizontal force and torque (H-T), according to the stress characteristics of the foundation, the corresponding simplified calculation model is established, and the theoretical solutions of the stress and deformation analysis of the foundation under the two bearing modes of torque (T), horizontal force (H) - eccentric bending moment (M) are derived; numerical simulation analysis is carried out to obtain the failure envelope of rigid rectangular foundations under push torsion H-T load. And then the rationality of the theoretical calculation method is verified by the indoor model test. Finally, the influences of torsion ratio and foundation resistance ratio coefficient m on the stress and deformation of foundation are analyzed. The results show that the failure envelope of rigid rectangular foundation under push torsion H-T load is approximately parabolic. With the increase of torsion-thrust ratio, the horizontal bearing capacity of the foundation decreases, and its failure mode changes from horizontal deformation failure to torsional deformation failure. The increase of the proportional coefficient m can reduce the horizontal displacement and rotation angle at the foundation ground effectively. To ensure the safety and stability of the rigid rectangular foundation, the nature and compaction of the overlying backfill should satisfy the design requirements. This study can provide basic information for the design of multi-rod unified rod foundations.

In the present work, the response and first-ply failure of composite tubes subjected to axial and torsional loadings are studied. Both uniform-diameter and tapered composite tubes are considered. The random spatial variations of in-situ material properties that are caused during the manufacturing of the ply material and the laminated tube are considered. The in-situ stiffness and strength properties of the composite ply are represented as random variables. The first-ply failure envelopes of the tubes are determined based on the finite element modeling and the Tsai-Wu failure criterion. Existing works are used to validate the finite element models. In addition, a new analytical solution for the response of the tapered composite tube is developed and is used for validation. The reliability of the composite tube is quantified based on the probability density functions of the response and failure parameters. The reliability-based failure envelopes are developed based on the Monte Carlo simulation and the variabilities in the failure envelopes are characterized. It is shown that the change in the first-ply failure loading with the reliability is not linear and that when conventional design methodology is used in conjunction with the mean values of the material properties, only 50% reliability is achieved. Considering these aspects and limitations, a new reliability-based design methodology for the composite tubes is developed. Using this new methodology, composite tubes can be designed for the reliability desired in the specific application, considering the uncertainties in the in-situ material properties that are induced during the manufacturing of the tube. [ABSTRACT FROM AUTHOR]

MECH-Gcomp was developed as web-based free software to aid in learning and to help researchers and industry professionals in failure analysis of composite materials. The software is already well-established for the study of micromechanics and has extended to other fields. This work focuses on one of its newest modules, related to the failure analysis of composite laminae, for which thirteen different failure criteria were implemented, along with an important tool for the construction of failure envelopes. The programming and characteristics of this module are presented and discussed. In addition, jute/polyester composites were manufactured and tested under different stress states to verify the software predictions. The root-mean-square error ranged from 0.096 to a maximum of 0.545, and most of the analyzed criteria yielded reasonable agreement compared to the experimental data. A significant variation in predictions among the criteria could be clearly observed, especially based on the produced failure envelopes for the different stress states. [ABSTRACT FROM AUTHOR]

Copyright of Hydrogeology & Engineering Geology / Shuiwendizhi Gongchengdizhi is the property of Hydrogeology & Engineering Geology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To study the failure (strength) regularities of rocks under complex stress states, we propose a novel three-parameter deviatoric function that includes the shape of the failure envelope on the Mohr–Coulomb (MC), Ottosen, Bigoni–Piccolroaz, and Wu–Zhang deviatoric planes. This function realizes the deviatoric plane shape of numerous classic criteria, including the Rankine, Tresca, von Mises, generalized Tresca, MC, Drucker–Prager (DP), Matsuoka–Nakai (MN), Lade–Duncan (LD), and Ottosen. On this basis, taking the nonlinear characteristics of the power function, we establish a novel 3D NUF criterion, namely MCNUF and LDNUF criteria, where the novel parameter γ is based on the basic parameters of two classical criteria, MC and LD, respectively. Based on the triaxial test data of different rocks, the proposed MCNUF and LDNUF criteria are compared with the previous criteria (the generalized nonlinear failure criterion (MNGNF), the DP and MN unified (DPMNu) criterion). Results show that: (1) the internal friction angles predicted by each criterion are equal under the same meridian plane parameters. (2) For four kinds of rock materials, the prediction performance of the proposed criteria is generally better than that of the MNGNF and DPMNu criteria. (3) The proposed criteria describe the hydrostatic stress and IPS and their coupled effect on various rock materials. (4) The 3D graphical visualization of the proposed criteria is carried out systematically, which plays a positive guiding role in enriching and perfecting the strength theory. [ABSTRACT FROM AUTHOR]

The long-term periodicity and uncontrollable interface properties during the preparation process for silicon carbide fiber reinforced silicon carbide-based composites (SiCf/SiC CMC) make it difficult to thoroughly investigate their mechanical damage behavior under complex loading conditions. To delve deeper into the influence of the interface strength and toughness on the mechanical response of microscopic representative volume element (RVE) models under complex loading conditions, in this work, based on numerical simulation methods, a microscale representative volume element (RVE) with periodic symmetric boundary conditions for the material is constructed. The phase-field fracture theory and cohesive zone model are coupled to capture the brittle cracking of the matrix and the debonding behavior at the fiber/matrix interface. Simulation analysis is conducted for tensile, compressive, and shear loading as well as combined loading, and the validity of the model is verified based on the Chamis theory. Further investigation is conducted into the mechanical response behavior of the microscale RVE model under complex loading conditions in relation to the interface strength and interface toughness. The results indicate that under uniaxial loading, increasing the interface strength leads to a tighter bond between the fiber and matrix, suppressing crack initiation and propagation, and significantly increasing the material's fracture strength. However, compared to the transverse compressive strength, increasing the interface strength does not continuously enhance the strength under other loading conditions. Meanwhile, under the condition of strong interface strength of 400 MPa, an increase in the interface toughness significantly increases the transverse compressive strength of the material. When it increases from 2 J/m2 to 20 J/m2, the transverse compressive strength increases by 28.49%. Under biaxial combined loading, increasing the interface strength significantly widens the failure envelope space under σ2-τ23 combined loading; with the transition from transverse compressive stress to tensile stress, the transverse shear strength shows a trend of first increasing and then decreasing, and when the ratio of transverse shear displacement to transverse tensile/compressive displacement is −1, it reaches the maximum. This study provides strong numerical support for the investigation of the interface properties and mechanical behavior of SiCf/SiC composites under complex loading conditions, offering important references for engineering design and material performance optimization. [ABSTRACT FROM AUTHOR]

The existing research on anchor foundations has predominantly focused on their axial load-carrying capacity, disregarding their resistance to the combined uplift and lateral forces during operation. To address this gap, the present study employs a three-dimensional finite-difference analysis to examine the behavior of horizontal anchor foundations buried in sand under the influence of uplift and lateral loads. The novelty of this work lies in the application of combined loading on the shaft head and the subsequent evaluation of both vertical and horizontal displacements of the foundation. The results reveal that the displacements are notably more significant in the horizontal direction. Furthermore, the paper presents a detailed analysis of the foundation's failure mechanisms under various combinations of vertical and horizontal forces. It is observed that pure vertical forces induce an uplift shear failure, whereas pure horizontal forces lead to a rotational failure. Based on the results, a failure envelope in the V:H loading plane is proposed for the horizontal anchor foundation subjected to oblique loads. [ABSTRACT FROM AUTHOR]

Rock strength is an essential parameter in the design of any underground excavation, and it has become even more relevant as the focus increasingly shifts to sustainable excavations. The heterogeneous nature of rock material makes characterising the strength of rocks a difficult and challenging task. The research results presented in this article compare the impact on the strength when the classic stress paths in laboratory experiments are applied versus when in situ stress paths would be applied. In most laboratory experiments, the rock specimens are free of stress at the beginning of the tests, and the load is increased systematically until failure occurs. Opposite paths occur around an underground excavation; that is, the rock is in equilibrium under a triaxial stress state and at least one stress component decreases while another component may increase. Based on discrete element simulations, the research shows that different stress paths result in different failure envelopes. The impact of this finding is evaluated in the application of wellbore stability (e.g., the minimum or maximum mud weight), whereby it is concluded that failure envelopes, based on stress paths closer to the in situ stress paths, result in a more accurate design. Although the most critical location along the circumference is not different, the required density of the mud is significantly different if the rock strength criteria are based on the more realistic in situ stress paths. This means that a change in the way the strength of rocks is characterised improves the sustainable design of all underground excavations. [ABSTRACT FROM AUTHOR]

Soil spatial variability is a common situation in marine geotechnical engineering, while most studies have primarily focused on evaluating the uniaxial vertical (V), horizontal (H), or moment (M) bearing capacity of foundations in spatially variable clay. Whereas the process of combined bearing capacity analysis by probe method is complex, resulting in low efficiency. As a result, the simplified modified swipe (SMS) method is proposed in this paper, which can represent the capacity in any direction of the load space accurately and takes just 6.5 times the duration of a single probe loading for a half-failure envelope. Based on the established three-dimensional random finite element models, the effectiveness of this method is demonstrated by analyzing the combined bearing capacity of five kinds of foundations in spatially variable clay. Furthermore, Monte Carlo simulations revealed that the spatial variability of the soil cause various failure envelopes, and the response of the combined bearing capacity is not identical in all directions. The VHM failure envelopes with different probabilities are given and could be found that the safety factors recommended by the guidelines are insufficiently conservative for structures susceptible to soil spatial variability. Finally, a strategy for applying different safety factors to both load directions is proposed, which could be helpful for the design of foundations in spatially variable clay. [ABSTRACT FROM AUTHOR]

This paper reports numerical investigations on the bearing performance of a novel finned suction caisson foundation under combined vertical, horizontal, moment, and torsional loading in clay. From comprehensive comparison analyses between finned and nonfinned suction foundations, improvements in uniaxial and combined loading capacities due to the assembled fins are examined and interpreted by insights into the failure mechanisms. Effects of non-coplanar torsional loading on the combined loading capacity surfaces are investigated and evaluated with the aid of the failure envelope method. A set of closed-form expressions accommodated to three different loading scenarios (zero-, low- and high-torsion conditions) are proposed based on a detailed design chart to estimate the bearing performance under combined vertical (V), horizontal (H), moment (M), and torsional (T) loading (denoted as VHMT loading) in clay. The critical considerations in design including effects of loading direction and foundation–soil interface are also discussed. [ABSTRACT FROM AUTHOR]

Deep rocks are typically under a true-triaxial stress state. The strength of deep rock is thus dictated by both the direction and magnitude of principal stresses. The formulation of three-dimensional strength criterion for rocks is thus essential for evaluating the stability of deep-buried rock structures. With advancements in true-triaxial experimental instrumentation, several three-dimensional strength criteria have been proposed, necessitating a systematic review and consolidation of these criteria. This review first introduces the concept of three-dimensional stress state. Subsequently, classical strength criteria such as the Mohr-Coulomb Criterion, the Hoek-Brown criterion, and the Drucker-Prager criterion are reiterated. However, these traditional strength criteria inadequately describe rock strength under true-triaxial stress conditions. To better capture the influence of intermediate principal stress, hydrostatic pressure, and Lode angle on rock strength, researchers have revised classical strength criteria. Modified strength criteria and unified strength criteria based on classical formulations are also introduced. Notably, the unified strength criterion incorporates multiple single criteria and demonstrates wider applicability. Furthermore, beyond macroscopic strength criteria, this review also discusses micromechanical strength criteria, where the stress state and crack propagation govern rock mechanical behaviors. This comprehensive review may serve as a valuable source for addressing the problem of deep rock strength in energy extraction and other rock engineering applications.

Failure of trees in high winds is of interest to a broad array of stakeholders: foresters, meteorologists, homeowners, insurance industry, parks and recreation management. Equally broad is the array of disciplines that contribute to understanding windthrow failure of trees: aerodynamics, forest management sciences, biomechanics, tree biology, and geotechnical engineering. This paper proposes a mechanistic model for assessing the windthrow failure of trees from a geotechnical engineering perspective. The model assumes a homogenized tree root–soil structure enclosed within a cylindrical volume characterizing the root spread and depth. The model predicts the anchorage resistance of a soil–root system by estimating the uprooting resistance of an equivalent circular footing using a 3D load failure envelope with a rotated parabolic ellipsoid shape. The proposed model was validated using the UK Forest Research Tree Pulling Database (UTPD) with 1239 conifer trees of six common species. The results show that the model successfully predicts the windthrow resistance of various tree species and sizes for different soil states. The soil type and state significantly affected the uprooting resistance, with the effective soil unit weight and water table depth being key soil parameters controlling tree anchorage. Conversely, soil friction angle and soil cohesion have only a modest influence on tree anchorage. The influence of desaturation due to negative pore water pressures was also investigated and found to have a significant effect on the uprooting resistance. Although the model shows promise, the paper concludes that further improvements could be made in form and calibration, as discussed in the paper. [ABSTRACT FROM AUTHOR]

The strength behavior of rocks is a question of complex determination. The Hoek–Brown failure criterion for rock masses is the currently accepted solution to this problem and has been applied to a large number of projects worldwide. However, the estimation of Hoek–Brown parameters is directly dependent on complex and time-consuming tests (e.g., triaxial tests), demanding excessive investments, and complicated analysis. This paper proposes a method to calculate the Hoek–Brown parameters and derive the nonlinear failure envelope of distinct types of artificially cemented materials (where the integrity of the samples is ensured), comparing these results with real laboratory data. The method utilizes basic tests, such as unconfined compression tests and Brazilian tests, to estimate the maximum shear strength of materials in triaxial tests with effective confining pressures up to 400 kPa. The proposed methodology presents an accurate and conservative fit for the experimental strength results, indicating the applicability of the approach to a wide range of artificially cemented materials without the need to perform triaxial tests or any other elaborate and time-consuming procedures. [ABSTRACT FROM AUTHOR]

Given the critical role of true triaxial strength assessment in underground rock and soil engineering design and construction, this study explores sandstone true triaxial strength using data-driven machine learning approaches. Fourteen distinct sandstone true triaxial test datasets were collected from the existing literature and randomly divided into training (70%) and testing (30%) sets. A Multilayer Perceptron (MLP) model was developed with uniaxial compressive strength (UCS, σc), intermediate principal stress (σ2), and minimum principal stress (σ3) as inputs and maximum principal stress (σ1) at failure as the output. The model was optimized using the Harris hawks optimization (HHO) algorithm to fine-tune hyperparameters. By adjusting the model structure and activation function characteristics, the final model was made continuously differentiable, enhancing its potential for numerical analysis applications. Four HHO-MLP models with different activation functions were trained and validated on the training set. Based on the comparison of prediction accuracy and meridian plane analysis, an HHO-MLP model with high predictive accuracy and meridional behavior consistent with theoretical trends was selected. Compared to five traditional strength criteria (Drucker–Prager, Hoek–Brown, Mogi–Coulomb, modified Lade, and modified Weibols–Cook), the optimized HHO-MLP model demonstrated superior predictive performance on both training and testing datasets. It successfully captured the complete strength variation in principal stress space, showing smooth and continuous failure envelopes on the meridian and deviatoric planes. These results underscore the model’s ability to generalize across different stress conditions, highlighting its potential as a powerful tool for predicting the true triaxial strength of sandstone in geotechnical engineering applications.

Skirted foundation is widely applied in the design of offshore structures. A large number of studies have been carried out to examine the failure envelope of the skirted foundation, but most of them focused on the static loading conditions without considering the effect of cyclic load and providing cyclic failure envelopes. Therefore, this paper proposes a numerical framework to predict the cyclic bearing capacity of the skirted foundation based on the dynamic strength curves and the probe loading method, which is modified so that it can be applied to the cyclic failure envelope calculation. It was found that the cyclic uniaxial capacity is affected by initial average load, number of cycles, and cyclic load amplitude. Cyclic load has a limited impact on the shapes of the failure envelope under combined loading and the degree of its scaling is related to the cyclic degradation ratio controlled by the dynamic strength curves. [ABSTRACT FROM AUTHOR]

AbstractThe traditional foundation design does not consider the bearing capacity under multi-directional coupling load. However, the foundation is usually subjected to vertical (V), horizontal (H) and moment (M) loading simultaneously on the seabed. The present study examines the undrained multi-directional bearing capacity of hybrid subsea foundation in saturated soft clay using finite element analysis. The contribution of the mudmat and the suction bucket to the bearing capacity of the hybrid subsea foundation was evaluated. The results show that the suction bucket can effectively make up for the lack of horizontal anti-slip and anti-overturning ability of the mudmat. It has a significant contribution to the horizontal and moment bearing capacity. In addition, the failure envelope of bearing capacity in horizontal-moment (H-M), vertical-horizontal (V-H), and vertical-moment (V-M) load space is obtained by using prescribed displacement ratio loading method. Based on the simulation results, the expression of approximate envelope of foundation bearing capacity under combined load of horizontal and moment is proposed. The study also found that a certain value of vertical load can increase the horizontal and moment bearing capacity of the hybrid subsea foundation, while excessive vertical load will lead to a decrease in bearing capacity. [ABSTRACT FROM AUTHOR]

The estimation of passive thrust, which causes toe failure when the mass above the toe of a slope experiences compression due to downslope movement, is necessary for both physical models and geotechnical works. Slope models lying on a bedding plane were prepared with lateral confinement and a toe support to investigate the development of passive thrust. The overburden on the slope crest of the physical models was modelled by surcharge weights. The lateral resistance developing on the side walls and the passive earth resistance developing near the slope toe were considered in three-dimensional slope stability analyses. The results showed that the development of passive thrust, associated with the shear strength reduction ratio and Rankine’s passive earth pressure theory, can be used to reasonably evaluate the total resistance of a slope. The shear strength reduction method was adapted to determine the lateral pressure acting on the side walls and the toe from the normal pressure acting on the bedding plane. The application of the proposed approach was demonstrated by the back-analysis of the unknown water pressure head under the slab floor of the low wall of Mae Moh open-pit mine where failure occurred in the rainy season of 2020 and could not be correctly predicted by a two-dimensional stability analysis. Therefore, the back-analysis of low wall instability requires a three-dimensional stability analysis and the use of the shear strength reduction ratio of 1.0 to explain how the rock mass at the yield stage is appropriate and convenient for slope engineering. [ABSTRACT FROM AUTHOR]

Helical anchor is a kind of novel foundation for floating offshore wind turbines, which should be subjected to combined tensile loading caused by wind, wave and current. However, the research about the capacity of helical anchor was mainly examined under uniaxial loading and scarcely explored under combined loading. In this study, three-dimensional finite element limit analysis is adopted to assess the bearing capacities of single-plate rigid helical anchors with different ratios of helix to shaft diameter, DH/DS and embedment ratios L/DS. Result shows that the vertical, horizontal and moment bearing capacities increase with increasing DH/DS and L/DS. The normalized V-H failure envelopes expands with increasing L/DS, while the normalized V–M failure envelopes tend to contract with the increase of DH/DS. With increasing DH/DS or decreasing L/DS, the normalized H-M failure envelopes expand when the horizontal and moment loading act in the same direction and contract when they act in the opposite direction. The effect of DH/DS and L/DS on the shape of H–M failure envelope become insignificant when L/DS ≽ 4. A series of failure mechanisms under different loading conditions were observed and can be used to explain the trend. Besides, a series of approximate expressions were proposed to fit the uniaxial bearing capacities and the failure envelopes. [ABSTRACT FROM AUTHOR]

With the shift of the offshore wind energy sector to deeper waters, demand for the development of more complex foundation solutions, particularly suction bucket – supported tripod/tetrapod and jacket foundations, has increased. This paper is divided into two main sections. The first part comprises a comprehensive review of the performance of circular surface and shallow foundations under combined loading (VHM), and how it can principally be understood in a theoretical framework of plasticity theory. Examination of the considered data suggested that the general assumption of over‐estimated non‐association degree with constant failure surface parameters and increasing vertical load may require further investigation. This may be attributed to the complex interplay of multiple properties such as stress level, soil strength profile and foundation geometry. The existing data in the literature were also used to provide practical guidance for a successful implementation of the elasto‐plastic constitutive relationships in offshore foundation design. In second part of the paper, the suitability of the non‐associated plasticity formulation for a baseline multi‐pod system in H‐M load space was investigated using three‐dimensional (3D) finite element (FE) analyses and not verified. Furthermore, the failure envelopes and hardening law for caissons with different embedment ratios differed from those recommended in the literature were established. Parametric studies of multi‐caisson foundations revealed that the failure mechanism of multi‐bucket foundations under horizontal loading depended greatly on the bucket spacing. The horizontal bearing capacities increased with the bucket spacing until they reached a threshold. Meanwhile, analyses of the multi‐bucket foundation under moment loading confirmed the occurrence of a push‐pull failure mechanism. [ABSTRACT FROM AUTHOR]

Tracked vehicles are widely deployed for heavy lifting and transportation on inaccessible terrains such as swamps, bogs, and peatlands. The stability of a tracked vehicle is traditionally assessed only under uniaxial loading conditions and the impact of combined loading from different directions is ignored. This makes the conventional design framework somewhat unreliable. The failure envelope approach has been widely employed to assess the load-carrying capacity of shallow foundations. However, the failure envelopes available in public domain mainly focused on single isolated foundations, ignoring the interference effect between the tracks due to the rigid connection of the vehicle. This paper aims to develop an integrated framework to assess the stability of a tracked vehicle on a soft soil under fully three-dimensional loading conditions. The finite element method is adopted to simulate the soil–vehicle interactions, with the tracks idealised as two shallow foundations in parallel. The stability of the foundation system is described in terms of failure envelopes considering various track configurations and load combinations. Failure envelopes are represented by expressions and ultimately integrated into a multiple-nested function to determine the overall stability factor. The framework is demonstrated by a case study of designing a tracked vehicle under combined loading conditions. [ABSTRACT FROM AUTHOR]

The article examines and assesses the phenomenological strength theory of composite materials. A comparative analysis of the theoretical envelopes was conducted for each criterion. A unified form of the phenomenological strength criterion was established. The study specifically examined the effects of altering the interaction parameter on the Tsai-Wu criterion’s theoretical envelope. Based on the available experimental data, the study plotted the failure envelopes of each strength criterion under planar composite stress states. The variation of these envelopes across various stress quadrants was highlighted. As a result of the examinations, four typical phenomenological strength criteria were chosen. The composites’ off-axis tensile and biaxial loading test data were used to evaluate the predictive power objectively. The results showed that not all stress states’ test results agreed with the predictions of the phenomenological strength theory. The criterion proposed by Norris and Tsai-Hill performed better at accounting for the material’s different compressive and tensile characteristics. The other criteria tended to be conservative under particular circumstances. Simultaneously, the Hoffman criterion matched the test data more closely over a broader range of stress states. Overall, this study clarified the limitations and applicability of various strength criteria in composite material strength prediction.

The long-term periodicity and uncontrollable interface properties during the preparation process for silicon carbide fiber reinforced silicon carbide-based composites (SiCf/SiC CMC) make it difficult to thoroughly investigate their mechanical damage behavior under complex loading conditions. To delve deeper into the influence of the interface strength and toughness on the mechanical response of microscopic representative volume element (RVE) models under complex loading conditions, in this work, based on numerical simulation methods, a microscale representative volume element (RVE) with periodic symmetric boundary conditions for the material is constructed. The phase-field fracture theory and cohesive zone model are coupled to capture the brittle cracking of the matrix and the debonding behavior at the fiber/matrix interface. Simulation analysis is conducted for tensile, compressive, and shear loading as well as combined loading, and the validity of the model is verified based on the Chamis theory. Further investigation is conducted into the mechanical response behavior of the microscale RVE model under complex loading conditions in relation to the interface strength and interface toughness. The results indicate that under uniaxial loading, increasing the interface strength leads to a tighter bond between the fiber and matrix, suppressing crack initiation and propagation, and significantly increasing the material’s fracture strength. However, compared to the transverse compressive strength, increasing the interface strength does not continuously enhance the strength under other loading conditions. Meanwhile, under the condition of strong interface strength of 400 MPa, an increase in the interface toughness significantly increases the transverse compressive strength of the material. When it increases from 2 J/m2 to 20 J/m2, the transverse compressive strength increases by 28.49%. Under biaxial combined loading, increasing the interface strength significantly widens the failure envelope space under σ2-τ23 combined loading; with the transition from transverse compressive stress to tensile stress, the transverse shear strength shows a trend of first increasing and then decreasing, and when the ratio of transverse shear displacement to transverse tensile/compressive displacement is −1, it reaches the maximum. This study provides strong numerical support for the investigation of the interface properties and mechanical behavior of SiCf/SiC composites under complex loading conditions, offering important references for engineering design and material performance optimization.

A novel virtual experimental testing methodology that utilizes virtual microstructures representative of genuine fiber distribution, is devised to micromechanically simulate and scrutinize the inter-fiber failure of unidirectional (UD) carbon fiber reinforced polymer (CFRP) composites. The experimentally identified nonlinear behavior of the matrix is incorporated by utilizing the Drucker-Prager plasticity model. The interaction behavior between fiber-matrix interfaces, including delamination and friction, is represented by means of a cohesive interaction approach. The results of virtual testing demonstrate that interfacial parameters and the epoxy properties exert considerable influences on the predicted macroscopic responses under individual loading cases. Additionally, the interface and epoxy material properties are inversely determined through virtual testing analysis assisted by experimental results. Furthermore, the validated virtual testing method is utilized to obtain the inter-fiber failure envelope of the composites. The predictions are then compared with those theoretically derived from classical failure criteria. The current comparative studies indicate that the existing classical failure criterion exhibits limited predictive ability with computational data.

Featured Application: This article describes, based on a discrete element model of a representative volume element, the importance of applying a stress path close to the in situ stress path during rock characterisation. The strength of rock is a non-intrinsic property, and this means that numerous parameters influence the strength values. In most laboratory experiments, specimens are free of stress at the start of the tests, and the load is increased systematically until failure occurs. Around excavations, the opposite path occurs, i.e., the rock is in equilibrium under a triaxial stress state and at least one stress component decreases while another component may increase. Hence, the stress paths in classic laboratory experiments are different from the in situ stress paths. In the research presented, a first step was made to evaluate with an open mind the effect of these different stress paths on the failure process and failure envelope. The research was based on distinct element models, allowing the simulation of micro-fracturing of the rock, which is essential to correctly model rock failure. The micro-fracturing when loading rock (from zero or low stress state) until failure was different from the micro-fracturing when unloading rock (from the in situ stress state) until failure. And, hence, by this difference in weakening processes, the failure envelopes were significantly different. The conventional loading resulted in the largest strength and, thus, overestimated the rock strength in comparison to the real in situ behaviour. This finding, after being confirmed by further lab experiments, will have a direct effect on how one characterises rock material and on the design of rock excavations. [ABSTRACT FROM AUTHOR]

Helical piles are one promising foundation option in offshore industries to support wind turbines and floating structures. During service, the helical piles are subjected to combined loading originating from the superstructure and environmental factors. For the inclined pullout capacity of helical piles, several studies focused on the influence of helical plate configurations and soil properties. In contrast, this paper aims to assess the effect of the random distribution of soil strength. This is undertaken through the use of a large deformation random finite element analysis combing the random field theory, coupled Eulerian-Lagrangian method and Monte Carlo approach. Spatial variability and linearly increasing with depth of soil strength are modeled as a three-dimensional random field and a mean trend term. The probabilistic failure envelope as well as the failure mechanism can be then determined from each random realization. It is found that soil randomness has an insignificant influence on the failure mechanism. For different spatial soil configurations, the probabilistic failure envelopes vary widely from one another. An equation is established to fit the envelopes with different occurrence probabilities and probabilistic analyses are conducted. The present findings might help to improve the helical pile design practices to achieve better reliability. [ABSTRACT FROM AUTHOR]

The stress-strain response under progressive damage and the ultimate failure of solid propellants are two key issues affecting the integrity of solid rocket motors. Previous research primarily focused on the progressive damage in solid propellants during production and storage. However, they failed to take the temperature/strain-rate-dependent ultimate failures into consideration. The failure strains of solid propellants are experimentally observed to show strong temperature/strain-rate dependence and exhibit an abnormal evolution at low and high temperatures, respectively. With increasing loading strain rate, the failure strains decrease at low temperatures near the glass transition temperature (Tg) but increase at high temperatures far above Tg. In this study, we introduce the glassy and rubbery failure criteria based on strain energy densities at ultralow and ultrahigh temperatures, respectively, into a viscoelastic constitutive model and build a unified model for the progressive damage and the ultimate failure of solid propellants. With the introduction of these two additional criterion parameters, the developed model can effectively predict the yield-type stress-strain responses, microscopic damage-induced volume dilatations, and temperature/strain-rate-dependent ultimate failures of the solid propellants by comparing the model predictions with the experimental results. The competition between the glassy failure and the rubbery failure results in the propellants exhibiting a maximum break strain near the glass transition temperature. Consequently, when the strain rate is increased, the propellants exhibit a predominantly glassy response, which shifts the failure envelope toward a higher temperature. This induces an abnormal evolution of failure strains by making the propellants stretchable at high temperatures and brittle at low temperatures. [ABSTRACT FROM AUTHOR]

This article emphasizes the significance of investigating the nonlinear behavior and strength characteristics of polymer composite materials under various strain rates. The study utilizes test results of a unidirectional (UD) composite material subjected to compression at different angles relative to the reinforcement direction, using quasi-static, static, and dynamic strain rates. The analysis focused on a UD layer experiencing compressive stresses perpendicular to the fiber reinforcement and in-plane shear stresses. A novel model is presented, enabling the calculation and prediction of the strength of a UD composite under uniaxial loading at different angles to the fiber direction, considering various strain rates. The developed model facilitates the derivation of equations for the failure envelopes of UD Carbon Fiber-Reinforced Polymers (CFRPs) under quasi-static, static, and dynamic loading conditions. To construct the failure envelopes of CFRPs, it is necessary to acquire experimentally determined values of tensile and compressive strength in the direction perpendicular to the reinforcement, as well as the ultimate strength in uniaxial compression of a specimen with reinforcement at a 45° angle to the loading axis. The failure envelopes generated using the proposed model exhibit excellent agreement with experimental data, with coefficients of determination ranging from 0.864 to 0.957, depending on the deformation rate. Consequently, the developed model holds promise for predicting the strength of other UD polymer composite materials. [ABSTRACT FROM AUTHOR]

One of the important issues for suction caissons is to demonstrate the effect of the contact between the base and the soil on the ultimate capacities of vertical (V), lateral (H), and moment (M) loads. It has not yet been analytically revealed how the ultimate capacities of suction caissons are dependent on the contact conditions of tension and no-tension interfaces under combined loads including vertical compressive and tensile loads. In this article, an analytical investigation into the effect of interfaces on the ultimate vertical, lateral, and moment capacities of suction caissons in nonhomogeneous clay is made using a traditional bearing capacity theory with tension and no-tension interfaces. For failure envelopes of suction caissons in clay subjected to lateral and moment loads under vertical compressive and tensile loads, the results predicted by the present method are compared with those obtained from the finite element analysis. In order to compare failure envelopes obtained from a tension interface and those obtained from a no-tension interface under general loading, failure envelopes in the H-V, M-V, and H-M planes and in H-M-V space for suction caissons in clay are investigated. [ABSTRACT FROM AUTHOR]

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

Deeply embedded caissons with a significantly large diameter, widely used as bridge foundation elements, are generally subjected to the complex combinations of several environmental and operational forces. The undrained capacities of rigid caisson foundations embedded in soils with increasing strength with depth and under combined loading are investigated using finite-element analyses. Estimation of uniaxial capacities followed by biaxial failure envelopes is carried out to capture the effect of vertical load on ultimate transverse capacities. Two-dimensional failure envelope in H-M loading space is presented to define the combined ultimate loading state of the circular caissons where the shape of the envelope is illustrated by a series of closed form expressions. The trajectory of the V-H-M failure envelope obtained from numerical analysis is validated by the mechanisms of upper bound limit analysis. Finally an example problem is provided to showcase the applicability of the expressions proposed to execute the design approach. [ABSTRACT FROM AUTHOR]

Torsional load arising from horizontal load eccentricity has a significant effect on the ultimate horizontal load carrying capacity of tripod bucket foundations in clay. In this paper, the effect of torsional load on the failure mechanism and ultimate horizontal capacity of tripod bucket foundations in undrained clay was studied using 3D finite-element analyses. Three single buckets were connected to form a rigid tripod bucket foundation system. Two different shear strength profiles, that is, uniform and linearly increasing with depth were considered. A detailed parametric study was conducted by varying the bucket spacing and embedment depth to explore the effects of different governing parameters. All the analyses were carried out for smooth and rough interface conditions. The influence of torsion on horizontal capacity is presented in the form of combined horizontal-torsional (H-T) failure envelopes. Reductions in ultimate horizontal capacity with increasing load eccentricity were quantified for the ease of practice. Finally, an expression for estimating combined H-T capacity is provided as a function of normalized spacing and embedment. Additional analyses were also performed to evaluate the effect of moment arising from vertical eccentricity on the combined H-T capacity. [ABSTRACT FROM AUTHOR]

Helical piles are utilized worldwide as foundations for onshore infrastructure, providing fast installation and high capacity. Their unique advantages have led to their potential as an alternative to monopile foundations for offshore wind turbines. One challenge in their service life is dealing with combined loading caused by wind, waves, current, and the weight of the structure itself. While research has focused on helical piles' capacity for uniaxial tensile loads, there is limited knowledge regarding their performance under combined loads. This study used FEM analysis to investigate the impact of aspects such as helix-to-shaft diameter ratios and helix position on the capacity and failure mechanisms of hollow shaft single-plate helical piles in clay. With 561 analysis cases under both uniaxial and combined loading, failure envelopes were evaluated for various helix-to-shaft diameter ratios and positions. The study revealed a linear positive correlation between helix-to-shaft diameter aspect ratios and load-bearing ability, while the effect of helix positioning on failure envelopes was more complex and nonlinear. The outcomes from this comprehensive analysis enabled the development of a formula to predict the bearing capacity of helical anchors under combined loading. [ABSTRACT FROM AUTHOR]

Monopiles, which have been most extensively used in the offshore wind industries, are usually subject to threats from local scour. The effects of local scour on the bearing capacity of monopiles have been studied based on deterministic soil properties and local scour dimensions. However, the properties of the seabed soil and the dimensions of the local scour both have uncertainty. In this study, a new nonstationary random field model, which can better simulate the nonstationary characteristics of the seabed clayey soil and result in a safer probabilistic design of foundations, is proposed to characterize the spatial variability of the seabed clayey soil. Then, the effects of the spatial variability of the seabed clayey soil and the uncertainty of the local scour depth on the bearing capacity of monopiles are investigated under both uniaxial loading and vertical-horizontal-moment (VHM) combined loading using the random finite-element method combined with kriging metamodeling technique and Monte Carlo simulation. The undrained shear strength of the seabed clayey soil was simulated with a lognormally distributed nonstationary random field, and the local scour depth was treated as a uniform random variable. The negative correlation between them was also considered. The results show that the factor of safety required for the local scoured seabed decreased from 3.3 to 2.6 as the negative correlation was enhanced, greater than or equal to that [factor of safety (FS)=2.6 ] for the intact seabed. The procedure of analyzing the design failure envelop of a monopile in spatially variable clayey soil with a local scour proposed in this study can provide a reference for geotechnical engineers. [ABSTRACT FROM AUTHOR]

Wind turbines are typically designed based on fatigue and serviceability limit states, but still require an accurate assessment of bearing capacity. Overconsolidated clay deposits in Canada often have a thin layer of crust with a relatively high undrained shear strength. However, existing bearing capacity design methods do not consider surficial crusts. This paper studies the undrained VHMT (vertical, horizontal, moment, and torsional) failure envelope of circular foundations founded on a surficial crust underlain by a uniform soil using finite element analysis. Crust correction factors have been introduced to account for the effects of the stiff layer on the vertical and moment capacities. The same forms of equation that are used for uniform soils, but with different parameters provide satisfactory fits for the failure envelopes for a soil with a crustal layer. An analytical expression for the 4-D VHMT failure envelope is derived, and an application of this method is provided. [ABSTRACT FROM AUTHOR]

The foundations of many large onshore and offshore structures are designed to be symmetrical polygons (e.g. octagons). However, the available analytical approaches for the ultimate limit state design of shallow foundations under combined loadings focus predominately on strip, rectangular and circular foundations. Although equivalent inscribed circular foundations have been recommended for foundation design by some guidelines, this simple approximation for octagonal foundations needs to be rigorously assessed due to the high dependence of the failure envelope on foundation shapes. The present study has investigated the general VHM (vertical, horizontal and moment) failure envelope of octagonal foundations under a zero-tension interface for undrained soil conditions using finite element analysis. The effects of soil strength heterogeneity and foundation embedment on the VHM failure envelope have been investigated. Analytical expressions have also been proposed to characterize the failure envelopes for use in design. The results show that octagonal foundations have larger bearing capacity than the corresponding circular foundations, and the difference (around 10%) between them is not negligible. A full 3-D analytical expression for the VHM failure envelope has also been proposed based on the calculated failure envelopes. [ABSTRACT FROM AUTHOR]

The performance of the novel fish anchor has been assessed through field tests. The tests were carried out at three different locations in the Swan River, Perth. The water depths were 2.91–4.73 m. The riverbed soils consisted of clay (Location 1), silty clay (Location 2) and silt (Location 3). The anchor was installed in the riverbed by dropping first through an air column followed by a water column, and finally striking the riverbed at an impact velocity of 10.4 (Location 1), 11.43 (Location 2), 11.72 (Location 3) m/s. The anchor tip embedment depth in the riverbed was measured at 1–2.5 times the anchor length. For similar impact velocity, the tip embedment depth in clay was 1.56–1.68 and 2–2.1 times of that in silty clay and silt, respectively. The capacity was found to reduce with loading angle at the padeye to the horizontal. The ultimate capacity was 1.5–2.6 times the weight of the anchor submerged in water for loading angle 90°, which increased to 8.2–15.6 times the weight for θ0=∼16°. The fish anchor dove, as opposed to pull out of the riverbed, for loading angles ≤37–47° , resulting in nonelliptical failure envelopes, which have been expressed mathematically. [ABSTRACT FROM AUTHOR]

Little analytical work has been done to elucidate the ultimate capacity of suction caissons under vertical tensile (V), lateral (H), and moment (M) loads in soils. In this paper, in order to reveal the effect of vertical tensile, lateral, and moment loads on the ultimate capacity of suction caissons in sand, an analytical investigation was made using a traditional bearing capacity theory. Taking account of the vertical equilibrium of an annular element of a skirt, through the vertical tractions inside and outside the skirt of a suction caisson when a vertical tensile load is applied, the vertical displacement of the soils adjacent to the skirt of the suction caisson was presented. The most appropriate bearing capacity equation for predicting the experimental results was shown for suction caissons having an embedment larger than a diameter in sand. For the deformation-load responses of suction caissons with various embedment ratios in sand, subjected to inclined tensile loads, there was a good agreement between the results obtained from laboratory tests and those predicted by the present method. The failure surfaces, considering the ultimate tensile capacity in the H-M, H-V, and M−V planes, and in the H-M−V space, for suction caissons in sand, were presented.

Piles are widely used to transfer the horizontal load of high-rise buildings, transmission towers, and bridges, especially for superstructures constructed near slopes. This study investigated bearing capacities of single piles under the combined horizontal force (H) and bending moment (M) for the pile in sloping ground. A 3D finite element model was proposed to simulate the non-linear pile–soil interaction and was verified by a model test. A series of numerical tests were conducted to obtain the failure envelope of bearing capacities of single piles under various combinations of H and M. The existence of slopes significantly reduced the bearing capacity of piles, especially when the horizontal and rotational displacements moved to the dip direction of the slope. An oblique ellipse was able to describe the failure envelope of bearing capacities of single piles near slopes in the HM plane. As the pile was installed away from the crest of the slope, both the width and height of the ellipse increased and the center of the ellipse was approaching the origin. The results of this article can provide useful references for designing horizontally loaded piles near slopes.