Bak Kong Low

Reliability analysis using object-oriented constrained optimization

A practical procedure is presented for reliability analysis involving correlated nonnormals. Equivalent normal transformation is performed as in the first order reliability method; the correlation matrix is used as it is without orthogonal transformation. Performance functions appear as simple spreadsheet cell objects but may embody substantial user-created program codes. The multidimensional equivalent dispersion ellipsoid is likewise a single cell object that contains various spreadsheet routines for equivalent normal transformation and matrix operations. The procedure can be viewed as the constrained optimization of the equivalent hyperellipsoid (yielding the reliability index) in the original space, and is automatic and efficient in the ubiquitous spreadsheet platform. Different probability distributions can be selected at ease and conveniently transformed to equivalent normals using a short program code given in the paper. Illustrations are presented using a three-variate simple performance function and various combinations of ten common distributions. This is followed by two relatively complicated examples, namely an asymmetrically loaded beam on Winkler medium, and a complex strut with implicit performance function. The probabilities of failure inferred from reliability indices are compared with Monte Carlo simulations. The simplicity, transparency and flexibilities of the object-oriented constrained optimization approach are demonstrated.

Reliability analysis of laterally loaded piles using response surface methods

Abstract Response surface methods have been applied to the reliability analysis of laterally loaded piles. Beam elements and a series of discrete springs are used to model the pile–soil system. The pile head displacement and the maximum bending moment in the piles are used as the performance criteria in this study. It is shown in the illustrative example that the CDF and PDF curves of the pile head displacement and the maximum bending moment in the pile obtained from the proposed methods are in good agreement with Monte Carlo simulation. The failure probabilities of the pile under specified performance criteria, the probabilistic responses of the pile-soil system, and the effect of pile-soil parameters to the failure probability of the pile are also studied.

Stratified Response Surfaces for System Probabilistic Evaluation of Slopes

AbstractThe need for probabilistic slope analysis that takes into account the uncertainty of soil properties has been acknowledged by the geotechnical profession. Traditionally, probabilistic slope analysis involves only single-mode failure that is considered based on the critical slip surface. This may result in underestimating the failure probability. In contrast, system reliability analysis for slopes is deemed more rational. This study aims at improving the existing methods of slope reliability analysis by considering system reliability. A stratified response surface method (stratified RSM) is proposed to describe the performance functions of possible failure modes. The proposed method differs from conventional response-surface–based slope reliability analysis (which constructs a single approximate performance function) by generating a group of (stratified) response surfaces. Based on these stratified response surfaces, system reliability analysis can be efficiently carried out by means of either a fi...

Slope reliability analysis accounting for spatial variation

A practical and transparent procedure is described for implementing a generalized limit equilibrium method via cell-object-oriented constrained optimization in the spreadsheet platform. The formulation allows switching among the Spencer, Bishop simplified and wedge methods on the same template by specifying different side-force inclination and different constraints of optimization. Search for the critical circular or non-circular slip surface is possible. The deterministic procedure is extended probabilistically by implementing the first-order reliability method via constrained optimization of the equivalent dispersion ellipsoid in the original space of the random variables. This procedure is illustrated for an embankment on soft ground, and for a clay slope in southern Norway, both involving spatially correlated soil properties. The effects of autocorrelation distance on the results of reliability analysis are studied. Shear strength anisotropy is modelled via user-created simple function codes in the programming environment of the spreadsheet. The meaning of probability of failure is discussed.

Probabilistic slope analysis using Janbu's generalized procedure of slices

Abstract Practical spreadsheet techniques are proposed for the deterministic slope stability analysis based on Janbus generalized procedure of slices (GPS) and a probabilistic analysis that obtains the same reliability index as the first order reliability method (FORM). The equilibrium equations of slices are solved automatically. An intuitive ellipsoid perspective greatly simplifies the reliability analysis. A search for the deterministic critical slip surface and the reliability-based critical slip surface is automatic, despite the fact that the factor-of-safety expressions and the performance function are non-explicit. The conceptual simplicity, ease of implementation, and practical versatility of the proposed perspectives and methods are emphasized.

Slip circle analysis of reinforced embankments on soft ground

Abstract Simple equations and a chart are proposed for computing the factor of safety of embankments constructed on soft ground and reinforced with geotextiles. The analysis considers only rotational failures based on the limit equilibrium method. The reinforcement is assumed to be horizontal and located at the base of the embankment. Different orientation of the force in the reinforcement can be considered, as well as different unit weight, slope, cohesion, and angle of friction of the soil in the embankment. The foundation soil has been assumed to be undrained. The proposed chart and the equations have been compared with two computer programs and four existing chart solutions. Examples illustrate the difference between the charts and the programs. The limitations of the limit equilibrium methods are stressed. Other failure modes should also be considered since these may prove more critical.

System Reliability Assessment for a Rock Tunnel with Multiple Failure Modes

This paper presents a practical procedure for assessing the system reliability of a rock tunnel. Three failure modes, namely, inadequate support capacity, excessive tunnel convergence, and insufficient rockbolt length, are considered and investigated using a deterministic model of ground-support interaction analysis based on the convergence–confinement method (CCM). The failure probability of each failure mode is evaluated from the first-order reliability method (FORM) and the response surface method (RSM) via an iterative procedure. The system failure probability bounds are estimated using the bimodal bounds approach suggested by Ditlevsen (1979), based on the reliability index and design point inferred from the FORM. The proposed approach is illustrated with an example of a circular rock tunnel. The computed system failure probability bounds compare favorably with those generated from Monte Carlo simulations. The results show that the relative importance of different failure modes to the system reliability of the tunnel mainly depends on the timing of support installation relative to the advancing tunnel face. It is also shown that reliability indices based on the second-order reliability method (SORM) can be used to achieve more accurate bounds on the system failure probability for nonlinear limit state surfaces. The system reliability-based design for shotcrete thickness is also demonstrated.

Effect of reinforcement force distribution on stability of embankments

Abstract The effect of reinforcement force distribution on the stability of reinforced embankments is studied. The stability of reinforced embankments is analyzed using the extended generalized method of slices by incorporating the effect of reinforcement. The proposed method is capable of handling features such as a tension crack in the embankment, a varying soil strength profile in the foundation soil and a general slip surface. The method allows the tensile force distribution along the reinforcement to be varied. The stability analysis of reinforced embankments is solved using a spreadsheet optimization tool. The versatility of the proposed method is demonstrated through several cases of reinforced embankments. The results obtained from the proposed method are in good agreement with those obtained from other analytical or numerical methods. The assumed force distribution along the reinforcement appears not to affect the embankment stability in undrained condition. In drained condition, it has some effect on the location of the critical slip surface, but small effect on the factor of safety.

Testing bias and parametric uncertainty in analyses of a slope failure in San Francisco Bay mud

An underwater slope in San Francisco Bay Mud that failed during excavation will be analyzed, first deterministically using data from field vane shear and laboratory triaxial tests, then probabilistically, accounting for parametric uncertainty and correlation of the undrained shear strength and soil unit weight. In the deterministic analysis, the factors of safety will be compared based on field vane shear test data, and triaxial tests on 35 mm test specimens and 70 mm Shelby tube specimens. The principal factors influencing these measures of undrained strength are shown to be sample disturbance and testing rate. Computed factors of safety are also affected by extrapolation of measured strengths to depths greater than the actual depths of sampling and vane shear testing. The deterministic analysis is extended into reliability analysis to account for parametric uncertainty and correlation among input parameters. The results from the first-order reliability method (FORM) and Monte Carlo simulation method are compared and discussed. The effects of different input probability distributions on the probability of slope failure are investigated.

Experimental nailed soil walls

Normal gravity model tests were carried out in a trench to study the influence of several design parameters on the behavior of nailed soil-retaining walls. Six nailed walls were built by varying the nail length, nail inclination, and the method of nail installation. The construction of each wall involved gradual placement of 36m(3) of sand using a clamshell attached to an overhead traveling crane, followed by excavation (in front of the facing) and installation of model soil nails. Each completed nailed soil wall and its retained sand measured 3.0 by 3.0 m in plan and was 2.4 m high before placement of surcharge fill. This paper describes the method adopted for reducing side wall friction, the sand placement procedure, the checks on uniformity and reproducibility of the relative density of the sand, the instrumentation, and the stage-by-stage excavation and nailing process. A summary of monitored results of all the tests is presented, and the results of Test 1 are discussed.