New equations for predicting the field penetration index of tunnel boring machines in fractured rock mass

The Queens Water Tunnel No. 3, stage 2 having 7.5-km length and 7-m diameter, is excavated by a high-power tunnel boring machine (TBM) underneath Brooklyn and Queens area for distributing freshwater throughout the New York City, USA. This paper offers a review of the project by considering the TBM performance and rock mass interaction. Using the individual cutter force, intact, and mass rock properties, TBM performance by means of field penetration index (FPI) was predicted and compared with actual results obtained in the field. Further, the study involves statistical analysis of the laboratory and field data including machine, intact, and mass rock properties to develop new empirical equations to estimate FPI. It is stated that the FPI, also converted to the rate of penetration, could be estimated utilizing intact and mass rock properties together with cutter force for similar type of rocks with correlation coefficient of 0.88.     

Artificial neural networks and nonlinear regression techniques to assess the influence of slake durability cycles on the prediction of uniaxial compressive strength and modulus of elasticity for carbonate rocks

Understanding rock material characterizations and solving relevant problems are quite difficult tasks because of their complex behavior, which sometimes cannot be identified without intelligent, numerical, and analytical approaches. Because of that, some prediction techniques, like artificial neural networks (ANN) and nonlinear regression techniques, can be utilized to solve those problems. The purpose of this study is to examine the effects of the cycling integer of slake durability index test on intact rock behavior and estimate some rock properties, such as uniaxial compressive strength (UCS) and modulus of elasticity (E) from known rock index parameters using ANN and various regression techniques. Further, new performance index (PI) and degree of consistency (Cd) are introduced to examine the accuracy of generated models. For these purposes, intact rock dataset is established by performing rock tests including uniaxial compressive strength, modulus of elasticity, Schmidt hammer, effective porosity, dry unit weight, p‐wave velocity, and slake durability index tests on selected carbonate rocks. Afterward, the models are developed using ANN and nonlinear regression techniques. The concluding remark given is that four‐cycle slake durability index (I_d4) provides more accurate results to evaluate material characterization of carbonate rocks, and it is one of the reliable input variables to estimate UCS and E of carbonate rocks; introduced performance indices, both PI and Cd, may be accepted as good indicators to assess the accuracy of the complex models, and further, the ANN models have more prediction capability than the regression techniques to estimate relevant rock properties. Copyright © 2011 John Wiley & Sons, Ltd.     

A comparision of interpolation methods for producing digital elevation models at the field scale

Digital elevation models have been used in many applications since they came into use in the late 1950s. It is an essential tool for applications that are concerned with the Earth's surface such as hydrology, geology, cartography, geomorphology, engineering applications, landscape architecture and so on. However, there are some differences in assessing the accuracy of digital elevation models for specific applications. Different applications require different levels of accuracy from digital elevation models. In this study, the magnitudes and spatial patterning of elevation errors were therefore examined, using different interpolation methods. Measurements were performed with theodolite and levelling. Previous research has demonstrated the effects of interpolation methods and the nature of errors in digital elevation models obtained with indirect survey methods for small‐scale areas. The purpose of this study was therefore to investigate the size and spatial patterning of errors in digital elevation models obtained with direct survey methods for large‐scale areas, comparing Inverse Distance Weighting, Radial Basis Functions and Kriging interpolation methods to generate digital elevation models. The study is important because it shows how the accuracy of the digital elevation model is related to data density and the interpolation algorithm used. Cross validation, split‐sample and jack‐knifing validation methods were used to evaluate the errors. Global and local spatial auto‐correlation indices were then used to examine the error clustering. Finally, slope and curvature parameters of the area were modelled depending on the error residuals using ordinary least regression analyses. In this case, the best results were obtained using the thin plate spline algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Accurate pressure gradient calculations in hydrostatic atmospheric models

Most models of atmospheric flow which use the primitive equations require a diagnostic equation to determine local total pressure. In hydrostatic models, this equation is the vertically integrated hydrostatic equation. A frequently used approximation to this integration is to hold the temperature constant within model layers yielding a linear proportionality between p or (Exner's function) and z. This procedure yields static pressures with errors on the order of 10^–3mb.If terrain following coordinates are used, terms arise in the horizontal momentum equations involving the gradient of total pressure along the coordinate surface, less a correction for the variation of the hydrostatic pressure along a sloped surface. Erroneous horizontal accelerations are common in these models which result from spurious pressure gradients that are due to inaccurate computation of the static pressure. This error may be amplified if the computation of the slope correction term of the horizontal pressure gradient is not consistent with the method of calculating the total pressure.We derive a methodology to be used in the vertical pressure integrations that is exact if the potential temperature lapse rate is constant between integration limits. The method is applied to both the integration of the hydrostatic equation and the computation of the slope correction term in the horizontal pressure gradient. The method employs a fixed vertical grid and a dynamic one defined by the significant levels in the vertical temperature distribution. With this methodology, the error in calculation of the horizontal pressure gradient acceleration is greatly reduced, especially in situations where the isothermal surfaces are not parallel to the vertical coordinate surfaces. The problem of aliasing and the treatment of significant temperature levels is described.