Stochastic analysis of seepage under water-retaining structures

This paper investigated the problem of confined flow under dams and water retaining structuresusing stochastic modelling. The approach advocated in the study combined a finite elementsmethod based on the equation governing the dynamics of incompressible fluid flow through aporous medium with a random field generator that generates random hydraulic conductivity basedon lognormal probability distribution. The resulting model was then used to analyse confined flowunder a hydraulic structure. Cases for a structure provided with cutoff wall and when the wall didnot exist were both tested. Various statistical parameters that reflected different degrees ofheterogeneity were examined and the changes in the mean seepage flow, the mean uplift forceand the mean exit gradient observed under the structure were analysed. Results reveal that underheterogeneous conditions, the reduction made by the sheetpile in the uplift force and exit hydraulicgradient may be underestimated when deterministic solutions are used.

Modelling attribute non-attendance in choice experiments for rural landscape valuation

Non-market effects of agriculture are often estimated using discrete choice models from stated preference surveys. In this context we propose two ways of modelling attribute non-attendance. The first involves constraining coefficients to zero in a latent class framework, whereas the second is based on stochastic attribute selection and grounded in Bayesian estimation. Their implications are explored in the context of a stated preference survey designed to value landscapes in Ireland. Taking account of attribute non-attendance with these data improves fit and tends to involve two attributes one of which is likely to be cost, thereby leading to substantive changes in derived welfare estimates.

Using simulation to assess cardiac first-responder schemes exhibiting stochastic and spatial complexities

A Monte-Carlo simulation-based model has been constructed to assess a public health scheme involving mobile-volunteer cardiac First-Responders. The scheme being assessed aims to improve survival of Sudden-Cardiac-Arrest (SCA) patients, through reducing the time until administration of life-saving defibrillation treatment, with volunteers being paged to respond to possible SCA incidents alongside the Emergency Medical Services. The need for a model, for example, to assess the impact of the scheme in different geographical regions, was apparent upon collection of observational trial data (given it exhibited stochastic and spatial complexities). The simulation-based model developed has been validated and then used to assess the scheme's benefits in an alternative rural region (not a part of the original trial). These illustrative results conclude that the scheme may not be the most efficient use of National Health Service resources in this geographical region, thus demonstrating the importance and usefulness of simulation modelling in aiding decision making.

A probabilistic modelling scheme for analysis of long-term failure of cemented femoral joint replacements

Reliable prediction of long-term medical device performance using computer simulation requires consideration of variability in surgical procedure, as well as patient-specific factors. However, even deterministic simulation of long-term failure processes for such devices is time and resource consuming so that including variability can lead to excessive time to achieve useful predictions. This study investigates the use of an accelerated probabilistic framework for predicting the likely performance envelope of a device and applies it to femoral prosthesis loosening in cemented hip arthroplasty.
A creep and fatigue damage failure model for bone cement, in conjunction with an interfacial fatigue model for the implant–cement interface, was used to simulate loosening of a prosthesis within a cement mantle. A deterministic set of trial simulations was used to account for variability of a set of surgical and patient factors, and a response surface method was used to perform and accelerate a Monte Carlo simulation to achieve an estimate of the likely range of prosthesis loosening. The proposed framework was used to conceptually investigate the influence of prosthesis selection and surgical placement on prosthesis migration.
Results demonstrate that the response surface method is capable of dramatically reducing the time to achieve convergence in mean and variance of predicted response variables. A critical requirement for realistic predictions is the size and quality of the initial training dataset used to generate the response surface and further work is required to determine the recommendations for a minimum number of initial trials. Results of this conceptual application predicted that loosening was sensitive to the implant size and femoral width. Furthermore, different rankings of implant performance were predicted when only individual simulations (e.g. an average condition) were used to rank implants, compared with when stochastic simulations were used. In conclusion, the proposed framework provides a viable approach to predicting realistic ranges of loosening behaviour for orthopaedic implants in reduced timeframes compared with conventional Monte Carlo simulations.

Integrating geophysical data and upscaling techniques to support regional groundwater flow modelling: A practical example of the Lagan Valley, Northern Ireland

When studying heterogeneous aquifer systems, especially at regional scale, a degree of generalization is anticipated. This can be due to sparse sampling regimes, complex depositional environments or lack of accessibility to measure the subsurface. This can lead to an inaccurate conceptualization which can be detrimental when applied to groundwater flow models. It is important that numerical models are based on observed and accurate geological information and do not rely on the distribution of artificial aquifer properties. This can still be problematic as data will be modelled at a different scale to which it was collected. It is proposed here that integrating geophysics and upscaling techniques can assist in a more realistic and deterministic groundwater flow model. In this study, the sedimentary aquifer of the Lagan Valley in Northern Ireland is chosen due to intruding sub-vertical dolerite dykes. These dykes are of a lower permeability than the sandstone aquifer. The use of airborne magnetics allows the delineation of heterogeneities, confirmed by field analysis. Permeability measured at the field scale is then upscaled to different levels using a correlation with the geophysical data, creating equivalent parameters that can be directly imported into numerical groundwater flow models. These parameters include directional equivalent permeabilities and anisotropy. Several stages of upscaling are modelled in finite element. Initial modelling is providing promising results, especially at the intermediate scale, suggesting an accurate distribution of aquifer properties. This deterministic based methodology is being expanded to include stochastic methods of obtaining heterogeneity location based on airborne geophysical data. This is through the Direct Sample method of Multiple-Point Statistics (MPS). This method uses the magnetics as a training image to computationally determine a probabilistic occurrence of heterogeneity. There is also a need to apply the method to alternate geological contexts where the heterogeneity is of a higher permeability than the host rock.

Stochastic Analysis of Saltwater Intrusion in Heterogeneous Aquifers using Local Average Subdivision

This study investigates the effects of ground heterogeneity, considering permeability as a random variable, on an intruding SW wedge using Monte Carlo simulations. Random permeability fields were generated, using the method of Local Average Subdivision (LAS), based on a lognormal probability density function. The LAS method allows the creation of spatially correlated random fields, generated using coefficients of variation (COV) and horizontal and vertical scales of fluctuation (SOF). The numerical modelling code SUTRA was employed to solve the coupled flow and transport problem. The well-defined 2D dispersive Henry problem was used as the test case for the method. The intruding SW wedge is defined by two key parameters, the toe penetration length (TL) and the width of mixing zone (WMZ). These parameters were compared to the results of a homogeneous case simulated using effective permeability values. The simulation results revealed: (1) an increase in COV resulted in a seaward movement of TL; (2) the WMZ extended with increasing COV; (3) a general increase in horizontal and vertical SOF produced a seaward movement of TL, with the WMZ increasing slightly; (4) as the anisotropic ratio increased the TL intruded further inland and the WMZ reduced in size. The results show that for large values of COV, effective permeability parameters are inadequate at reproducing the effects of heterogeneity on SW intrusion.