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AbstractSimilar to pile group, the process of designing an anchor group requires the determination of an efficiency factor that describes the overlapping effects of neighboring anchors. This research article introduces an efficiency factor denoted as ξ, which represents the ratio of the ultimate uplift pressure of a single anchor within a group to the ultimate uplift pressure of an isolated anchor. The primary approach employed involves advanced 3D finite element limit analysis with an adaptive meshing technique, which can be utilized to examine the uplift stability problem of 3D anchor groups. Numerical findings are compared with those obtained from previous research, incorporating both experimental and analytical results. This would ensure that our results are validated and provide valuable information into the performance of anchor groups. In addition to these findings, we introduce a MARS machine learning model, which has been trained using a dataset of 875 data points. This model is designed to establish an empirical equation that can be practically used for design purposes. To further enhance our understanding, we present the relative importance index (RII). This index allows us to identify which factors have the most significant impact on the behavior of anchor groups. In conclusion, the results presented in this article are of practical significance for the geotechnical engineering community. [ABSTRACT FROM AUTHOR]

Highlights: •A state of art approach to evaluate the elliptical tunnel stability of Hoek–Brown rock mass.•Rigorous upper bound and lower bound solutions of elliptical tunnel stability are derived using advanced finite element limit analysis.•Comprehensive design tables and equations are proposed for stability evaluation. [ABSTRACT FROM AUTHOR]

Sinkhole occurrences due to underground water mains operations have piqued people's curiosity. Most research works were in relation to geophysical practices to discover the subsurface cavity. Very few works can be found in relation to the investigation of soil stability due to underground cavity shapes. The actual shape of an underground cavity and its transformation is difficult to predict, though the sinkhole failures are mostly circular in shape on the ground surface. This study explores the three-dimensional collapse stability of three distinct idealized cavity geometries, namely the circular, semi-spherical, and spherical cavities. For an active failure, dimensionless parameters are used to investigate the combined impacts of soil cover, surcharge pressure, soil weight, and internal pressure using advanced finite element limit analysis. Numerical results are compared with the two-dimensional axisymmetric results, and design charts presented to cover a wide range of design parameters for practical applications. [ABSTRACT FROM AUTHOR]

Highlights: A state of art approach to evaluate the stability of Hoek–Brown rock mass with a spherical cavity. Rigorous upper bound and lower bound solutions of stability factors are solved using advanced finite element limit analysis. Comprehensive design charts, tables and equations are presented for stability evaluation. [ABSTRACT FROM AUTHOR]

This paper presents rigorous plasticity solutions to the classical active and passive earth pressure problems. The primary method adopted is a conventional equation based on the soil property and three stability factors (F c , F s, and F γ), that are analogous to Terzaghi's bearing capacity factors (N c , N s , and N γ) of strip footings. The proposed method is considered as a practical yet smart approach to the determination of earth pressures and is one of the main novelties in this study. To achieve this, the finite element limit analysis (FELA) of upper and lower bounds solutions, a powerful tool in studying the behaviour of soil stability, is employed to compute the three stability factors for a wide range of soil internal friction angles, wall roughness, and surcharge pressures. In addition, analytical solutions based on statistically admissible stress fields are adopted to validate the proposed FELA solutions. The validation satisfactorily demonstrated the accuracy and reliability of the proposed solutions. It follows that the numerical results are presented in the form of tables, figures, and several examples provided to demonstrate the practical use of the three factors in estimating active and passive earth pressures with various backfill soils, wall roughness, and surcharge pressure. The study should, therefore, be of value to practitioners. [ABSTRACT FROM AUTHOR]

• A state of art approach to study 3D sinkhole stability due to underground cavities. • Advanced 3D finite element limit analysis for circular and square openings. • Rigorous 3D upper bound and lower bound solutions of active and passive trapdoors. • Comprehensive design charts, tables and equations presented. • Stability numbers and factors of safety for a wide range of design parameters. There has been an increasing interest in the study of sinkhole occurrences due to frequent underground activities. Most of the research direction are related to the detection of the underground cavity using geophysics techniques. Very little is done in the area of soil stability. This paper investigates the three-dimensional stability of circular and square trapdoors. The combined effect of surcharge pressure, soil weight and supporting pressure is considered in Broms and Bennermarks' original stability number for a cohesive soil. The study uses the finite element limit analysis to compute upper bound and lower bound minimum supporting pressures for both collapse and blowout scenarios. The obtained critical stability numbers and factor of safety are compared with other published results in both two- and three- dimensions. Design charts, tables and equations are presented to cover a wide range of design parameters and a practical example is introduced to illustrate how to use the them. [ABSTRACT FROM AUTHOR]

This paper investigates the use of stability factors to estimate tunnel heading pressures. The primary method adopted is a conventional equation based on the soil property and stability factors, analogous to the bearing capacity factors (N c , N s and N γ) of strip footings. The finite element limit analysis (FELA) is employed to determine rigorous upper bound (UB) and lower bound (LB) solutions of stability factors (F c , F s and F γ), which are functions of the depth ratio (C/D) and soil internal friction angle (Ø). The obtained results are compared and validated by using the finite difference analysis as well as other available published results in the literature. A number of examples are illustrated on how to use the factors to estimate tunnel heading pressures. [ABSTRACT FROM AUTHOR]

This paper investigates the three-dimensional (3D) stability of a circular tunnel in drained cohesive-frictional soil. Numerical simulations are performed to study the face stability of a circular tunnel for various soil properties and tunnel diameter-to-depth ratios. The finite element limit analysis (FELA) is employed to determine rigorous upper and lower bounds solutions of tunnel stability factors (F c , F s and F γ), which are functions of the depth ratio and soil internal friction angle. These stability factors are used to estimate the critical heading pressures at collapse. The obtained results are compared with existing published solutions in the literature. The study aims to improve the available solutions by using the latest 3D finite element limit analysis technique. A number of examples are provided, which demonstrate the practical use of the three stability factors in estimating tunnel heading pressures. [ABSTRACT FROM AUTHOR]

Pit-in-pit (PIP) excavations in an aquifer-aquitard system likely undergo catastrophic failures under the hydraulic uplift, the associated undrained stability problem, however, has not been well analyzed in the past. To this end, a hypothetical model of PIP braced excavation in typical soil layers of Shanghai, China is developed using the finite element limit analysis (FELA) tool. The FELA solutions of safety factors (FSs) against hydraulic uplift are verified with the results from the finite element analysis with strength reduction technique (SRFEA) and existing design approaches. Subsequently, FELA is employed to identify the triggering and failure mechanisms of PIP braced excavations subjected to hydraulic uplift. A series of parametric studies considering the various geometric configurations of the PIP excavation, undrained shear strengths of aquitard, and artesian pressures are carried out. The sensitivities of relevant design parameters are further assessed using a multivariate adaptive regression splines (MARS) model that is capable of accurately capturing the nonlinear relationships between a set of input variables and output variables in multi-dimensions. A MARS-based design equation used for predicting FS is finally presented using the artificial dataset from FELA for practical design uses. [ABSTRACT FROM AUTHOR]