Reliability-Based Design for Internal Stability of Mechanically Stabilized Earth Walls

A parametric study was conducted using Monte Carlo simulation to assess how uncertainty in design parameters affects the probability of internal failure of mechanically stabilized earth (MSE) walls. Bishop’s simplified method was used to conduct the internal stability analyses. The results of the analyses indicate that the mean and coefficient of variation of the backfill friction angle, mean and coefficient of variation of the tensile strength of reinforcement, mean unit weight of the backfill, mean surcharge, mean reinforcement vertical spacing, and mean reinforcement length have a significant effect on the probability of internal failure of MSE walls. Based on the results of the parametric study, a series of additional simulations were conducted where the significant parameters were varied over a broad range. The results of these simulations were used to develop a set of reliability-based design (RBD) charts for internal stability of MSE walls. A method to adapt these charts to address model bias and model uncertainty is also presented. A MSE wall was designed using the RBD method and two other deterministic design methods. The required tensile strength of the reinforcement obtained from the RBD method fell between the strengths determined from the deterministic methods.     

Fabrication of small size inner spiral ribbed copper tube by fluid mandrel drawing

This paper is concerned with the development of ultra-small inner spiral ribbed copper tubes with high-quality heat transfer. Since the demand for the ultra-small tubes in electrical appliances is currently high and will be greater in the future, the technology employed must enable the production of inner spiral ribbed fine tubes with various features, such as small size, high quality, high functionality, and low processing cost so as to meet the increasing demand. The conventional production method is suitable for large tubes with high drawability but is unsuitable for fabrication of long ultra-small tubes because of the difficulty to manufacture both an ultra-small spiral ribbed mandrel and a floating plug. This research paper has proposed four drawing methods as follows: tube sinking, water, oil, and wax as mandrels and presented the comparison of seven parameters, i.e., drawing stress ratio, wall thickness ratio, ribbed base width ratio, ribbed tip width ratio, ribbed height ratio, ribbed pitch ratio, and ribbed spiral angle ratio. It was found that tube sinking was unfit for making the ultra-small inner spiral ribbed copper tubes due to the resulting high ratio of wall thickness. The results of all the parameters were similar in the cases of oil and wax. Despite less impressive outcomes, water was easily removed from the inner spiral ribbed copper tube compared to oil and wax. Thus, the tube drawing using water as mandrel was most suitable for the production of the inner spiral ribbed copper tube.     

Reliability-Based Design for External Stability of Mechanically Stabilized Earth Walls

A two-phase approach was used to develop a reliability-based design (RBD) method for external stability of mechanically stabilized earth (MSE) walls. In the first phase, a parametric study was conducted using Monte Carlo simulation to identify parameters that affect the probability of external failure of MSE walls. Three modes of failure were considered: sliding, overturning, and bearing capacity. External stability was assessed by treating the reinforced soil as a rigid mass using the same procedures employed for conventional gravity-type wall systems. Results from the parametric study indicate that the mean and coefficient of variation of the backfill friction angle are significant for sliding, the mean and coefficient of variation of the friction angle of the backfill and coefficient of variation of the unit weight of the backfill are significant for overturning, and the mean and coefficient of variation of the friction angle of the foundation soil and the mean of the backfill friction angle are significant for bearing capacity. In the second phase, a series of additional simulations was conducted where the significant parameters identified in the parametric study were varied over a broad range. Results of these simulations were used to develop a set of RBD charts for external stability of MSE walls. A comparison indicates that similar reinforcement lengths are obtained using RBD and conventional methods and that the inherent probability of external failure in conventional deterministic design is ? 0.001. This probability of external failure is similar to inherent probability of failure reported by other investigators for similar geotechnical structures.     

Bounded Real Lemma for Structured Noncommutative Multidimensional Linear Systems and Robust Control

We obtain a standard Bounded Real Lemma and a strict Bounded Real Lemma for the class of input/state/output linear systems with evolution along a free semigroup recently introduced by the authors. As an application we show the equivalence of this result with a recent result from robust control theory: the structured μ-singular value of an operator (taken in a certain uniform sense) is equal to its upper bound computed via diagonal scalings in case the structured singular value is taken with respect to the collection of time-varying perturbations given by a linear-fractional model. Mathematics Subject Classification (2000) Primary: 93D09, Secondary: 13F25, 47A56, 47A60, 93B28 Published online: April 2006 The first author was partially supported by US National Science Foundation under Grant Number DMS-9987636; The second author is supported by the National Research Foundation of South Africa under Grant Number 2053733; The third author was supported by a grant from Naresuan University, Thailand     

Multidimensional Linear Feedback Control Systems and Interpolation Problems for Multivariable Holomorphic Functions

This paper examines the connections between feedback stabilization and H⁸ control, model matching problems and multivariable Nevanlinna-Pick interpolation problems for multidimensional or n-D linear systems.