Element Method For Stability Analysis Research Articles

A new combined finite-discrete element method for stability analysis of soil-rock mixture slopes

PurposeThe purpose of this paper is to propose a new combined finite-discrete element method (FDEM) to analyze the mechanical properties, failure behavior and slope stability of soil rock mixtures (SRM), in which the rocks within the SRM model have shape randomness, size randomness and spatial distribution randomness.Design/methodology/approachBased on the modeling method of heterogeneous rocks, the SRM numerical model can be built and by adjusting the boundary between soil and rock, an SRM numerical model with any rock content can be obtained. The reliability and robustness of the new modeling method can be verified by uniaxial compression simulation. In addition, this paper investigates the effects of rock topology, rock content, slope height and slope inclination on the stability of SRM slopes.FindingsInvestigations of the influences of rock content, slope height and slope inclination of SRM slopes showed that the slope height had little effect on the failure mode. The influences of rock content and slope inclination on the slope failure mode were significant. With increasing rock content and slope dip angle, SRM slopes gradually transitioned from a single shear failure mode to a multi-shear fracture failure mode, and shear fractures showed irregular and bifurcated characteristics in which the cut-off values of rock content and slope inclination were 20% and 80°, respectively.Originality/valueThis paper proposed a new modeling method for SRMs based on FDEM, with rocks having random shapes, sizes and spatial distributions.

A Limit Equilibrium Method Based on Geostress Calculated by Implicit Stabilized Node-Based Smoothed Finite Element Method for Stability Analysis of Soil Slopes

A Limit Equilibrium Method Based on Geostress Calculated by Implicit Stabilized Node-Based Smoothed Finite Element Method for Stability Analysis of Soil Slopes

Three-dimensional Distinct Element Method for stability analysis of marble quarries in the Apuan Alps (Italy)

The present article analyses and proposes an innovative dynamic planning methodology, supported by computer tools and in-situ measurements, for the optimization of the planning techniques of underground marble quarries. The abovementioned planning methodology has been implemented in ‘Cava Piastreta’, an underground marble quarry located in the Apuan Alps, Italy. The entire excavation area has been characterized with tridimensional topographic surveys, geotechnical traditional surveys, and radar surveys, as well as stress-level measurement campaigns through a CSIRO cell. When an underground excavation project concerning stone material is designed, it is mandatory to have an instrument allowing a forecast of the stress-strain behavior of the rock mass. To this end, the rocky outcrop can also be represented by different mathematical models to schematize the geomechanical behavior. The accuracy and reliability of the simulation of the mechanical response of the fractured mass depend on the exactness with which the rocky outcrop is defined. Therefore, the geometric modeling phase acquires prominent importance. To better address the discontinuous nature of the studied rocky mass, the distinct element method has been used in modeling the mechanical behavior of the mass itself. Given the peculiar geometrical characteristics of the excavation site in question, the deterministic approach has been chosen to simulate as closely as possible the position of the major discontinuities identified in-situ. The present article thus aims to briefly describe a study that has been developed over the last years intended to deepen the analysis of the geostructural characterization of the excavation site, as well as to compare the obtained results through the geometrical tridimensional modeling with the values measured in-situ.

A stable node-based smoothed finite element method for stability analysis of two circular tunnels at different depths in cohesive-frictional soils

This paper investigates the stability of two circular tunnels at different depths in cohesive-frictional soils subjected to surcharge loading using a stable node-based smoothed finite element method (SNS-FEM). In the present method, the numerical integration domains are approximately circular regions of the node-based smoothing domain by the node-based smoothed finite element method (NS-FEM). Four additional integration points are employed for each node to form the stabilization items associated with the variance of the smoothed shape function gradient. The tunnels are modelled under plane strain conditions, and the soil is described as a uniform Mohr-Coulomb material, and it obeys an associated flow rule. The stability numbers of two circular tunnels are obtained directly by solving the optimization problems. In this study, the effects of soil properties (γD/c), the ratio of tunnel diameter to its depth (H/D), the horizontal and vertical spacing ratio (S/D, L/D) and soil internal friction angle (ϕ) on the stability numbers (σs/c) are investigated. Several numerical results of two circular tunnels have been carried out showing that the proposed approach can demonstrate the efficiency and reliability solutions. Based on upper bound limit analysis using SNS-FEM, the results are presented in the form of design tables and charts for engineers to use.

A node-based Smoothed Finite Element Method for Stability Analysis of Dual Square Tunnels in Cohesive-frictional Soils

This paper presents an upper bound limit analysis procedure using the node-based smoothed finite element method (NS-FEM) and second order cone programming (SOCP) to evaluate the stability of dual square tunnels in cohesive-frictional soils subjected to surcharge loading. The displacement field of the tunnel problems is approximated by using NS-FEM triangular elements (NS-FEM-T3). Next, commercial software Mosek is employed to deal with optimization problems, which are formulated as second order cone. Collapse loads and failure mechanisms of dual square tunnels were performed by solving the optimization problems with a series of size-to-depth ratios and soil properties. For dual square tunnels, the distance between centers of two parallel tunnels is the major parameter used to determine the stability. In this study, surcharge loading is applied to the ground surface and drained conditions are considered. Numerical results are verified with those available to demonstrate the accuracy of the proposed method.

NURBS-augmented finite element method for stability analysis of arbitrary thin plates

In the analysis of a plate, the geometry plays a very important role. The non-uniform rational B-spline (NURBS) basis functions are employed for the representation of the geometry and field variables in the isogeometric analysis. These basis functions are able to represent the geometry accurately. They are non-interpolating in nature, and hence do not satisfy the Kronecker-Delta property. Hence, it becomes difficult to enforce the essential boundary conditions at the control variables. A new method called NURBS-augmented finite element method (NAFEM) was proposed (Mishra and Barik, Comput Struct, https://doi.org/10.1016/j.compstruc.2017.10.011 , 2017) and arbitrary shaped plates were successfully dealt for bending analysis. In the NAFEM, the authors adopted the finite element basis functions for the field variables as they satisfy the Kronecker-Delta property so that the boundary conditions were enforced with ease and the NURBS basis functions were employed for the geometry, thereby representing the shape of the plate accurately. In the present work, the same is extended for stability analysis of plates having different geometries and boundary conditions and the results are found to be in excellent agreement with the existing ones. Some new shapes have also been considered, and the new results are presented.

Spectral element method for stability analysis of milling processes with discontinuous time-periodicity

This paper presents an application of the spectral element method for the stability analysis of regenerative machine tool chatter models in milling operations. An extension of the spectral element method is introduced in order to handle the discontinuities in the cutting force in an efficient way. The efficiency of the method is demonstrated on some well-known machine tool chatter models taken from the literature. Efficiency is characterized by the computational time, the convergence of the stability boundaries, and the convergence of critical characteristic multipliers. Results show that compared to the most widespread methods in machining literature, the spectral element method provides significant improvements in computational time while maintaining high accuracy levels.

Extension of the spectral element method for stability analysis of time-periodic delay-differential equations with multiple and distributed delays

The spectral element method was introduced by Khasawneh and Mann (2013) for the stability analysis of time-periodic delay-differential equations (DDEs) with multiple delays. In this paper, this method is generalized for time-periodic DDEs with multiple delays and distributed delay. For this general case, an explicit formula is given for the construction of the matrix approximation of the monodromy operator. The derived formula enables the algorithmic application of the method to DDEs with general combinations of delays for arbitrary point sets and test functions. Stability analysis is demonstrated for specific case studies, and the computation code is provided for a complex example.

A least-square spectral element method for stability analysis of time delay systems

This paper presents a numerical method for the stability analysis of retarded functional differential equations with time-periodic coeficients. The method approximates the solution segments, corresponding to the end points of the principal period, by their piecewise Lagrange interpolants. Then a mapping between these solution segments is obtained by the minimization of the least-square integral of the residual error. Finally, stability properties are determined using the matrix approximation of the monodromy operator, obtained by this mapping, according to the Floquet theorem. The formulation of the method is presented for an equation of general type while results are shown for the delayed oscillator.

Stability chart for the delayed Mathieu equation

In the space of system parameters, the closedform stability chart is determined for the delayed Mathieu equation defined as (t)(cost)x(t) bx(t2). This stability chart makes the connection between t...