Stability Charts Research Articles

Chatter Stability Analysis of Milling Processes

AbstractFull utilization of the available machine tool cutting performance is often inhibited by chatter vibrations which can lead to poor surfaces, reduced tool life, increased noise emissions and even damage to the machine tool. In this contribution, a systematic approach for modelling regenerative chatter based on measured, modal models of the machine tool is presented. Furthermore, three different methods for solving the governing equations and generating stability charts are compared.

Stability charts based on the finite element method for underground cavities in soft carbonate rocks: validation through case-study applications

Abstract. The stability of man-made underground cavities in soft rocks interacting with overlying structures and infrastructures represents a challenging problem to be faced. Based upon the results of a large number of parametric two-dimensional (2-D) finite-element analyses of ideal cases of underground cavities, accounting for the variability both cave geometrical features and rock mechanical properties, specific charts have been recently proposed in the literature to assess at a preliminary stage the stability of the cavities. The purpose of the present paper is to validate the efficacy of the stability charts through the application to several case studies of underground cavities, considering both quarries collapsed in the past and quarries still stable. The stability graphs proposed by Perrotti et al. (2018) can be useful to evaluate, in a preliminary way, a safety margin for cavities that have not reached failure and to detect indications of predisposition to local or general instability phenomena. Alternatively, for sinkholes that already occurred, the graphs may be useful in identifying the conditions that led to the collapse, highlighting the importance of some structural elements (as pillars and internal walls) on the overall stability of the quarry system.

A Mathematical Model Based on Artificial Neural Networks to Predict the Stability of Rock Slopes Using the Generalized Hoek–Brown Failure Criterion

Stability of rock slopes is a critical issue in many mining and civil engineering projects. The current state of practice for slope stability analysis is based on obtaining the factor of safety (FOS). Stability charts are widely used by engineers to obtain a FOS for a quick assessment of the initial stability of slopes. The stability of rock slopes with vertical walls in urban areas adjacent to existing structures is another important issue in this regard. However, the stability of earth or rock slopes are usually analyzed ignoring surcharge loads. The effect of adjacent structures (as surcharge load) on slope stability (considering these loads) can be very useful in slope stability analyses in urban or even non-urban areas. In the present study, it is tried to investigate the effect of surcharge load on the stability of rock slopes based on the generalized Hoek–Brown failure criterion using a finite element numerical software and the related charts are presented. Since there is a stability chart for each slope angle, a comprehensive mathematical model utilizing artificial neural networks is proposed to predict the stability factor of rock slopes. The independent variables in this study were slope angles, slope height, the intensity of surcharge load, Geological Strength Index (GSI), and unconfined compressive strength of the intact rock. Sensitivity analysis showed that the changes in GSI, effect of surcharge and unconfined compressive strength of rock have the highest effect on the slope stability assurance coefficient.

Stability test and dominant eigenvalues computation for second-order linear systems with multiple time-delays using receptance method

© 2019 Elsevier Ltd Stability analysis and dominant eigenvalues computation for second-order linear systems with multiple time-delays are addressed by using a reduced characteristic function and the associated characteristic matrix comprised of measured open-loop receptances. This reduced characteristic function is derived from the original characteristic function of the second-order time delayed systems based on a reasonable assumption that eigenvalues of the closed-loop system are distinct from those of the open-loop system. Then a contour integral is used to test the stability and provide the stability chart with respect to different displacement and velocity feedback time-delays, and a Newton-type method to compute the dominant eigenvalues via this characteristic function. The proposed approach also utilizes the spectrum distribution features of the retarded time-delay systems. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.

Stability analysis of 3D geosynthetic–reinforced earth structures composed of nonhomogeneous cohesive backfills

Soils are assumed to be homogeneous in most designs of geosynthetic-reinforced earth structures (GRESs), thus ignoring the influences of the possible cohesion and cohesion nonhomogeneity of backfills. However, the actual stability of GRESs is directly influenced by the presence of cohesion and cohesion nonhomogeneity of backfills along with the three-dimensional (3D) character of GRESs. In the present study, a chart-based stability analysis of a 3D GRES composed of nonhomogeneous cohesive backfills subjected to the seismic excitation/pore water pressure is conducted by means of the limit analysis method. Work rates by seismic forces and pore water pressure are calculated based on the pseudo-static method and the pore water pressure coefficient, respectively; thereafter the energy balance equation is derived by equating the external work rates of the soil weight and seismic forces/pore water pressure to the sum of the work rate of the geosynthetics and internal energy dissipation caused by soil cohesion. The analytical expression of the required unfactored reinforcement strength is derived and the optimized solutions are consequently captured. A comparison is drawn to verify the present study and a parametric analysis is conducted thereafter to investigate the effects of the 3D character, cohesion nonhomogeneity, seismic excitation and pore water pressure on the stability of GRESs. Finally, a set of stability charts considering the 3D effects, cohesion nonhomogeneity, seismic force and pore water pressure on long-term stability is proposed for preliminary design purposes.

Stability Charts for Sustainable Infrastructure: Collapse Loads of Footings on Sandy Soil with Voids

The presence of underground voids in regions suitable for sustainable development can adversely affect the stability of the overlying infrastructures. In this paper, the collapse loads of strip rigid footings resting on sand with single and double continuous voids are determined for a frictional Mohr-Coulomb material following the non-associated flow rule. For use by practitioners, design charts are proposed to evaluate the well-known bearing capacity factor Nγ as a function of the dimensionless parameters related to the vertical and horizontal void distances from the footing, void shape, and spacing between the two voids, as well as the soil friction angle. The computational result compares quite favorably with the available theoretical and numerical solutions. The failure mechanism is broadly discussed based on the pattern of soil displacement around the footing and void.

Stability of dual square tunnels in rock masses subjected to surcharge loading

The stability of dual unlined square tunnels subjected to surcharge loading in rock masses, obeying Generalized Hoek-Brown (GHB) failure criterion, is investigated by adaptive finite element limit analysis (AFELA) under plane strain conditions. Both upper bound (UB) and lower bound (LB) of the dimensionless stability number N are obtained, with the relative errors being found within 7%. Extensive parametric studies are conducted to investigate the effects of the center-to-center distance ratio, cover depth ratio, geological strength index (GSI) and material constant for intact rock (mi). The results are presented in the form of dimensionless stability tables and charts for engineers to use, and typical failure mechanisms are discussed. The results obtained in this study compare reasonably well with the solutions reported in the literature.

Stability analysis of slopes reinforced with anchor cables and optimal design of anchor cable parameters

Pre-stressed anchor cables are widely used in slope engineering for effectively improving slope stability as a reinforcement measure. Based on assumptions of stresses on a slip surface, this work proposes a new limit equilibrium (LE) method to analyse the stability of slopes reinforced with anchor cables. Meanwhile, the nonlinear Mohr–Coulomb (M–C) strength criterion has been adopted to describe the slope sliding for shear failure of the slip surface. Then, after comparison and analysis of several examples, the feasibility of the proposed method is verified. Compared with the traditional LE methods, the proposed method has a simple calculation process without iterative loop calculation of the slope factor of safety, and a reasonable solution can also be obtained. Furthermore, the slope reinforced by anchor cables with more than a row can be simplified into a slope with a row to analyse its stability because the same stability would be obtained for the reinforced slope with different reinforcement patterns under an equivalent reinforcement relation. Thereafter, to facilitate the engineering application and optimize the design of anchor cable parameters, the stability charts of the reinforced slope under the linear M–C strength criterion are drawn.

Bifurcations in basic models of delayed force control

Basic single-degree-of-freedom mechanical models of force control are presented to achieve desired contact forces between actuators and objects. Nonlinear governing equations are constructed for both collocated and non-collocated force sensor configurations. The models take into account large time delays in the feedback loop, which may occur, for example, in case of human or remote force control. The corresponding stability charts are compared for the collocated and non-collocated cases. The bifurcations at the stability boundaries are analyzed in the presence of the relevant nonlinearity that is originated in the saturation of the actuation. The stability properties as well as the nonlinear vibrations for the two sensor locations are compared also from the viewpoint of the achievable maximal proportional gains. The bifurcation calculations are done with the method of multiple scales and normal form calculations. The results on global dynamic properties are supported with numerical simulations, and the two force control strategies are discussed from application viewpoint.

Upper-bound solutions for the face stability of a non-circular NATM tunnel in clays with a linearly increasing undrained shear strength with depth

The face stability of the NATM tunnels (the New Austrian Tunneling Method) in undrained clays with a linearly increasing strength is numerically and analytically investigated by defining two types of the safety factors F in this paper. Based on the kinematic approach of the limit analysis, a continuous velocity field for an open-face tunnel is proposed. Moreover, the calculated solutions are compared with the results obtained from the numerical simulation and other existing literatures to validate its effectivity and superiority. The stability charts for different influence factors are also provided. Finally, an improved velocity field is presented, which provides a closer result to the real situation of the face collapse.

Landslide stability assessment along Panchkula–Morni road, Nahan salient, NW Himalaya, India

We report the slope stability analysis of three vulnerable sites (S1, S2 and S3) within the lower Siwalik along the Panchkula–Morni road section in the Nahan salient, north-western Himalaya. Kinematic analysis of joint data was conducted to understand the different modes of failure. Rock mass classification techniques like rock mass rating, slope mass rating (SMR) and continuous SMR were used for stability classification and the factor of safety was calculated using stability charts. At site S1, the instability is controlled by the orientation of the discontinuity joint J1 which is parallel to the bedding and at site S2, the slope fails due to the wedge. The Umri landslide site S3 is the product of a damage zone by the normal faults which intersect at joint J3; a wedge is formed which falls in the critical zone. The damage zone in the Umri landslide greatly affects the porosity and permeability of the rockmass and acts as a pathway for the percolation of water during rainfall which reduces effective stress. The slope failures are tectonically controlled results due to the high slope angles, structural discontinuities like joints and faults and structural damage zones associated with the faults.

An investigation into the motion and stability behaviour of a RO-RO vessel

Studies on motion response of a vessel is of great interest to researchers, since a long time. But intensive researches on stability of vessel during motion under dynamic conditions are few. A numerical model of vessel is developed and responses are analyzed in head, beam and quartering sea conditions. Variation of response amplitude operator (RAO) of vessel based on Strip Theory for different wave heights is plotted. Validation of results was done experimentally and numerical results was considered to obtain effect of damping on vessel stability. A scale model ratio of 1:125 was used which is suitable for dimensions of wave flume at National Institute of Technology Calicut. Stability chart are developed based on Mathieu\'s equation of stability. Ince-Strutt chart developed can help to capture variations of stability with damping.

Effect of cohesion on internal stability of bilinear geosynthetic-reinforced slopes

This paper presents a limit equilibrium (LE) approach to analyze the internal stability of the bilinear geosynthetic-reinforced slopes comprised of cohesive reinforced fill. This LE analysis uses a top-down log spiral mechanism to formulate the resultant reinforcement force in the lower tier required for internal design of such reinorced slopes. The presented formulation considers both cohesion and depth of crack, and then the required unfactored reinforcement strength is defined and used for subsequent analysis. Results are presented in the form of stability charts, enabling quick assessment of reinforcement strength required for internal stability. In addition, the effect of cohesion and depth of crack on the critical slip surface is discussed, respectively.

Size effect of oscillating columns on mixing: A CFD study

Abstract Computational Fluid Dynamics (CFD) simulations were performed to study the effect of the size of the column on mixing in an oscillating column. Volume of Fluid (VOF) method was employed to track the interface, and tracer simulations were carried out to estimate the mixing time. The fluid was assumed to be water, and the ratio of the height of the water in the column and the diameter of the column was equal to 1. The amplitude of the applied oscillation was kept constant at 0.25 cm, and the frequency was varied from 1 Hz to 20 Hz. Two cylindrical columns were considered in this work: one with a radius twice the benchmark geometry and the other with a radius half of it. The benchmark geometry was the cylindrical column with radius = 0.05 m, which was utilized in our previous work (Bale et al., 2017). It was observed that the mixing within an oscillating column was nonlinear with respect to the applied oscillation. The mixing time per unit volume was much smaller for the larger column, with similar power per unit mass applied to both the columns. The optimal condition to operate the two columns under consideration were reported. The numerical simulation results were corroborated by the stability chart determined theoretically by solving a series of Mathieu equation, contour plots through the column, and the snapshots of the free surface.

Stability analysis of seismic slopes with tensile strength cut-off

In this study, an analytical approach is developed to obtain the upper-bound solutions of the slope stability, for both static and dynamic conditions, based on the limit analysis theory. Stability charts for slopes with tensile strength cut-off under different seismic accelerations are provided. Effects of the tensile strength cut-off on the earthquake-induced displacement are evaluated. Considering the tension cut-off, the stability factor is reduced by 55% for vertical slopes subjected to seismic loads, while the earthquake-induced displacement of slopes is approximately twice that obtained by using the Mohr-Coulomb (M−C) yield criterion.

Incorporating suction in to stability charts for unsaturated soil slopes

Incorporating suction in to stability charts for unsaturated soil slopes

Limit Equilibrium Analysis of Slope Stability with Coupling Nonlinear Strength Criterion and Double-Strength Reduction Technique

Currently, the strength parameters are reduced by a uniform coefficient for the traditional strength-reduction technique in the slope stability analysis. However, observations proved that the contributions of the strength parameters on slope stability are different from each other when the slope reaches the limit equilibrium (LE) state, which means that the strength parameters should be reduced with their own reduction coefficient. Thus, based on the assumptions of stresses on slip surfaces and the overall mechanical equilibrium conditions of the slope sliding body, this work establishes the LE solution for slope stability under the double-strength reduction (DSR) technique. In the LE stress-based analysis, the loop iteration strategy is given to solve the LE stability of slope with the nonlinear strength criterion. Moreover, a new method (i.e., the square root method) is proposed to calculate the slope comprehensive factor of safety (FOS) for evaluating the slope stability with application of the DSR technique. Thus, by comparing and analyzing some slope examples, the accuracy of the present method is verified. Furthermore, from the obtained stability charts of slope under the DSR technique, the study shows that if the characteristic stability number is less than 0.04 for clay soil, then the internal friction angle would have a larger contribution to the slope stability than cohesion; whereas if the characteristic stability number is more than 1.00, then the larger contributor on the slope stability would be the cohesion.

Taylor's slope stability chart for combined effects of horizontal and vertical seismic coefficients

Design standards and codes of practice on earth slope stability often recommend the pseudo-static method of analysis for determining the factor of safety of a slope subjected to seismic forces. In most pseudo-static methods of analysis, the horizontal seismic force is considered without due weightage to vertical seismic force. In the past, Taylor's stability chart for a homogeneous cohesive-frictional soil slope has been extended to consider the effect of horizontal seismic force only. In this paper, an attempt is made to develop an analytical formulation considering both horizontal and vertical seismic forces in order to estimate the factor of safety of the homogeneous, cohesive-frictional soil slopes with simple profiles using Taylor's stability chart. The analytical formulation is based on the friction circle method, which is one of the methods of static slope stability analysis. Several field cases have been analysed considering slope geometry, soil properties and seismic loading conditions so that Taylor's stability chart can be routinely used by practising engineers considering the effects of both horizontal and vertical seismic forces. An illustrative example is included in order to explain how practising engineers can use the graphical presentations developed in this paper as the design charts for stability analysis. This illustrative example has also been solved using Plaxis 2D, a commercially available finite-element software, as a comparison.

Study on roof collapse of deep circular cavities in jointed rock masses using adaptive finite element limit analysis

This paper investigates the roof collapse of deep circular cavities in jointed rock masses using adaptive finite element limit analysis. The rock mass strength is described by the generalized Hoek-Brown failure criterion. The calculated results of the stability number Ns are presented in the form of dimensionless stability charts and are compared to the transformational results of an analytical upper bound solution by former investigators. The transformations are conducted using an algorithm proposed in the appendix of this paper. Parametric studies are performed to investigate the impacts of the Hoek-Brown parameters on the stability number and failure mechanism of underground cavities. In particular, different levels of rock mass disturbance are considered by adopting various rock mass disturbance factors D in the analyses.

Stability assessment of three-dimensional slopes with cracks

The stability of three-dimensional (3D) slopes with cracks is presented based on the kinematic approach of limit analysis. The sequence quadratic program optimization procedure is applied to obtain the least upper bound results. The most critical crack, including the crack depth and crack location in the 3D slope, is discussed. To provide a quick reference of the slope safety factor, stability charts are presented. The geometry of the critical failure surfaces, including the most unfavorable cracks for slopes with different width constraints and inclinations, are analyzed as well. Conclusions can be drawn that the critical height of the slope reduces due to the presence of cracks. A larger reduction in the critical height of slopes is found under plane strain conditions, compared to that under three-dimensional conditions. This reduction drops, however, with decreasing slope inclination angle. In addition, when compared with plane-strain conditions (slope width approaches infinity), the 3D slopes (with limited width) exhibit shallow sliding characteristics.