High performance interior point methods for three-dimensional finite element limit analysis

The ability to obtain rigorous upper and lower bounds on collapse loads of various structures makes finite element limit analysis an attractive design tool. The increasingly high cost of computing those bounds, however, has limited its application on problems in three dimensions. This work reports on a high-performance homogeneous self-dual primal-dual interior point method developed for three-dimensional finite element limit analysis. This implementation achieves convergence times over 4.5× faster than the leading commercial solver across a set of three-dimensional finite element limit analysis test problems, making investigation of three dimensional limit loads viable. A comparison between a range of iterative linear solvers and direct methods used to determine the search direction is also provided, demonstrating the superiority of direct methods for this application. The components of the interior point solver considered include the elimination of and options for handling remaining free variables, multifrontal and supernodal Cholesky comparison for computing the search direction, differences between approximate minimum degree [1] and nested dissection [13] orderings, dealing with dense columns and fixed variables, and accelerating the linear system solver through parallelization. Each of these areas resulted in an improvement on at least one of the problems in the test set, with many achieving gains across the whole set. The serial implementation achieved runtime performance 1.7× faster than the commercial solver Mosek [5]. Compared with the parallel version of Mosek, the use of parallel BLAS routines in the supernodal solver saw a 1.9× speedup, and with a modified version of the GPU-enabled CHOLMOD [11] and a single NVIDIA Tesla K20c this speedup increased to 4.65×

Three dimensional lower bound solutions for the stability of plate anchors in sand

Soil anchors are commonly used as foundation systems for structures that require uplift or lateral resistance. These types of structures include transmission towers, sheet pile walls and buried pipelines. Although anchors are typically complex in shape (e.g. drag or helical anchors), many previous analyses idealise the anchor as a continuous strip under plane strain conditions. This assumption provides numerical advantages and the problem can solved in two dimensions. In contrast to recent numerical studies, this paper applies three dimensional numerical limit analysis and axi-symetrical displacement finite element analysis to evaluate the effect of anchor shape on the pullout capacity of horizontal anchors in sand. The anchor is idealised as either square or circular in shape. Results are presented in the familiar form of breakout factors based on various anchor shapes and embedment depths, and are also compared with existing numerical and empirical solutions

Computation of bounds for anchor problems in limit analysis and decomposition techniques

Numerical techniques for the computation of strict bounds in limit analyses have been developed for more than thirty years. The efficiency of these techniques have been substantially improved in the last ten years, and have been successfully applied to academic problems, foundations and excavations. We here extend the theoretical background to problems with anchors, interface conditions, and joints. Those extensions are relevant for the analysis of retaining and anchored walls, which we study in this work. The analysis of three-dimensional domains remains as yet very scarce. From the computational standpoint, the memory requirements and CPU time are exceedingly prohibitive when mesh adaptivity is employed. For this reason, we also present here the application of decomposition techniques to the optimisation problem of limit analysis. We discuss the performance of different methodologies adopted in the literature for general optimisation problems, such as primal and dual decomposition, and suggest some strategies that are suitable for the parallelisation of large three-dimensional problems. The propo sed decomposition techniques are tested against representative problems.Peer ReviewedPreprin

Foundation Failure Case Histories Reexamined Using Modern Geomechanics

Case histories have played an important role in guiding development of geotechnical engineering during a time when theory was not sophisticated enough to model even simple problems with an acceptable level of rigor. As the discipline transitions from overwhelming reliance on empiricism to a greater reliance on science, it is useful to reexamine the best known case histories as a general check on modern methods of analysis. In the engineering of foundations in clay, three case histories the collapses of the Transcona and Fargo grain elevators and the near collapse of the leaning tower of Pisa stand out. We will see that limit analysis, which is a method of analysis based on two theorems from plasticity theory that allow bounding the collapse load from above and below, produces collapse load estimates that match closely the estimated collapse loads for the two failed grain elevators. It does so without giving the analyst much latitude in selection of input parameters, not requiring the elaborate assumptions needed when attempts are made to use an excessively simplified theory to analyze a real problem. We will also show, using the problem of a leaning tower, how resort to a complete analysis of a boundary-value problem, using a method like the finite element method, is sometimes required in determining the critical ultimate limit state

Stability of anchored sheet wall in cohesive-frictional soils by FE limit analysis

Preprin

Computational limit analysis for anchors and retaining walls

The computation of the bearing capacity of engineering structures commonly relays on results obtained for simple academic examples. Recent developments in computational limit analysis have allowed engineers to compute bounds of the bearing capacity of arbitrary geometries. We here extend these formulations to problems with practical interest such as retaining walls, anchors, or excavations with particular interface conditions. These situations require the special treatment of the contact conditions between different materials, or the modelling of joints and anchors. We demonstrate the potential of the resulting tool with some practical examples

The stability of inclined plate anchors in purely cohesive soil

Soil anchors are commonly used as foundation systems for structures requiring uplift resistance such as transmission towers, or for structures requiring lateral resistance, such as sheet pile walls. To date the design of these anchors has been largely based on empiricism. This paper applies numerical limit analysis and displacement finite element analysis to evaluate the stability of inclined strip anchors in undrained clay. Results are presented in the familiar form of break-out factors based on various anchor geometries. By obtaining both upper and lower bound limit analysis estimates of the pullout capacity, the true pullout resistance can be bracketed from above and below. In addition, the displacement finite element solutions provide an opportunity to validate these findings thus providing a rigorous evaluation of anchor capacity

Mesh generation for lower bound limit analysis

This paper describes a general strategy for generating lower bound meshes in D-dimensions. The procedure is based on a parametric mapping technique, coupled with midpoint splitting of subdomains, and permits the user to control the distribution of the discontinuities and elements precisely. Although it is not fully automatic, the algorithm is fast and automatically generates extension zones for problems with semi-infinite domains