An iterative algorithm for random upper bound kinematical analysis

A new approach for stochastic upper bound kinematical analyses is described. The study proposes an iterative algorithm that uses the Vanmarcke spatial averaging and kinematical failure mechanisms. The iterative procedure ensures the consistency between failure geometry and covariance matrix, which influences the quality of the results. The proposed algorithm can be applied to bearing capacity evaluation or slope stability problems. The iterative algorithm is used in the study to analyse the three-dimensional undrained bearing capacity of shallow foundations and the bearing capacity of the foundation for two-layered soil, in both cases, the soil strength spatial variability is included. Moreover, the obtained results are compared with those provided by the algorithm, based on the constant covariance matrix. The study shows that both approaches provide similar results for a variety of foundation shapes and scale of fluctuation values. Therefore, the simplified algorithm can be used for purposes that require high computational efficiency and for practical applications. The achieved efficiency using a constant covariance matrix for one realisation of a three-dimensional bearing capacity problem that includes the soil strength spatial variability results in about 0.5 seconds for a standard notebook. The numerical example presented in the study indicates the importance of the iterative algorithm for further development of the failure mechanism application in probabilistic analyses. Moreover, because the iterative algorithm is based on the upper bound theorem, it could be utilised as a reference for other methods for spatially variable soil.

An Upper Bound Solution for the Compression of an Orthotropic Cylinder

The upper bound theorem is used in conjunction with Hill’s quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity field in the vicinity of the friction surface if the maximum friction law is adopted. The regime of sticking is also taken into consideration. The effect of this regime on the upper bound limit load is revealed. In particular, the kinematically admissible velocity field that includes the regime of sticking may result in a lower upper bound than that with no sticking. The boundary value problem is classified by a great number of geometric and material parameters. Therefore, a systematic parametric analysis of the effect of these parameters on the compression force is practically impossible. An advantage of the solution found is that it provides a quick estimate of this force for any given set of parameters.

Simulation Upper Bound Theorem to Prediction Extrusion Load

A metal extrusion was process that extrusion puncture perforate surface of material to throw and flow across outlet of die. This operation was a complex process in extrusion while penetration occurred at same time. This process can be seen in many production operations, like in forming of making portion of metal strip, and forming of extruded portion in a complex fineblanking with extrusion operation. Also exhibit the operation properties and give the method of numerical solution. So increasing load to 610KN with increased friction factor to 0.7 and increased with increasing the reduction ratio and stroke of operation. For the results and mesh distortion, with allocations of strains may be predicted. Analyzing results was submitted of metal extruded may be classified into two zones for the different lineaments deformation. moreover, energy in the zones of deformation may be classified into two parts for their different lineaments of internal zone and contact zone with the die . Fracture location has been found from simulations. Keyword Load, Extrusion, upper bound, numerical solution

Limit Analysis of Collapse Mechanisms for Tunnel Roofs Subjected to Pore Water Pressure: A Numerical Approach

The collapse mechanism of a circular unlined tunnel roof subjected to the pore water pressure under plane strain conditions is investigated in this article. First, the model of calculating the function expression of the detaching surface for the collapsing block is formed in the framework of the upper bound theorem of limit analysis and the extremum principle. The analytical solution of the pore water pressure around the tunnel in a two-dimensional steady seepage field is employed in the equations of the model. Then, the numerical approach based on the Runge–Kutta algorithm and traversal search method is proposed to solve the complex equations. The obtained expression of the detaching surface for the collapsing block provides the shape of the collapsing block and a theoretical basis for designing the support force for tunnels. The proposed limit analysis method and numerical approach are verified by comparing with existing theoretical solutions and the numerical simulation result, and they are suitable for deep, shallow tunnels and layered strata. Moreover, the effects of different parameters on the collapse mechanism are investigated, and qualitative results are provided.

A bubble-enhanced quadrilateral finite element for estimation bearing capacity factors of strip footing

In this paper, a computational approach using a combination of the upper bound theorem and the bubble-enhanced quadrilateral finite element (FEM-Qi6) is proposed to evaluate bearing capacity factors of strip footing in cohesive-frictional soil. The new element is built based on the quadrilateral element (Q4) by adding a pair of internal nodes to solve the volumetric locking phenomenon. In the upper bound finite element limit analysis, the soil behaviour is described as a perfectly plastic material and obeys associated plastic flow rule following the Mohr-Coulomb failure criterion. The discrete limit analysis problem can be formulated in the form of the well-known second-order cone programming to utilize the interior-point method efficiently. The bearing capacity factors of strip footing and failure mechanisms in both rough and smooth interfaces are obtained directly from solving the optimization problems and presented in design tables and charts for engineers to use. To demonstrate the accuracy of the proposed method, the results of bearing capacity factors using FEM-Qi6 were compared with those available in the literature. Keywords: limit analysis; bearing capacity factors; strip footing; SOCP; FEM-Qi6.

Investigation on the Stability of Fissured Slopes Reinforced with Anchor Cables under Seismic Action

Based on the upper bound theorem of limit analysis (UBLA) combined with the pseudostatic methods, this paper elaborates on a calculated procedure for evaluating fissured slope stability under seismic conditions reinforced with prestressed anchor cables. An existing simple slope case is presented as a case study in this work. The comparison is given to verify that the solution derived from this study is correct and feasible. By means of a numerical optimization procedure, the critical location of the crack is determined from the best upper bound solutions. The results demonstrate a significant influence of the depth of crack and seismic acceleration coefficient on the critical location distribution of the cracks. Meanwhile, the axial force of anchor cables is investigated via parametric studies. It is shown that the variation of the crack depth has little effect on the axial force of anchor cables. Moreover, this paper also illustrates the variation in the axial force of anchor cables under the impact of five marked factors (crack depth, anchor arrangement, anchor inclination angle, slope angle, and seismic conditions). Finally, the required critical length of the free section of anchor cables is determined to ensure the stability of fissured slopes subjected to seismic action.

Seismic Behavior of Flexible Geogrid Wrap-Reinforced Soil Slope

In this study, the failure mode of flexible reinforced soil slopes under earthquake action was investigated by shaking table tests. The distribution law of a potential failure surface of a flexible no-faceplate reinforced soil slope under earthquake action was obtained based on the analysis results. A simplified trilinear failure surface suitable for flexible reinforced soil slopes without faceplate was proposed. Subsequently, based on the upper-bound theorem of limit analysis, we derived the formula for calculating the yield seismic acceleration coefficient of a flexible no-faceplate reinforced soil slope under a seismic load. The main parameters that affect its seismic performance were determined. The flexible geogrid reverse-packed reinforced earth structure can effectively limit the fracture of a slope body and improve the stability of the slope. This provides a theoretical basis for facilitating the engineering of flexible reinforced soil slopes.

The Upper Bound Theorem in Forging Processes: Model of Triangular Rigid Zones on Parts with Horizontal Symmetry

This paper presents the analytical method capacity of the upper bound theorem, under modular approach, to extend its application possibilities. Traditionally, this method has been applied in forging processes, considering plane strain condition and parts with double symmetry configuration. However, in this study, the double symmetry is eliminated by means of a fluency plane whose position comes from the center of mass calculated. The study of the load required to ensure the plastic deformation will be focus on the profile of the part, independently on both sides of the fluence plane, modifying the number and the shape of the modules that form the two halves in which the part is defined. This way, it is possible to calculate the necessary load to cause the plastic deformation, whatever its geometric profile.