Reply by C. F. Hendriks

Letter to the Editor

Reply by C. F. Hendriks     

Resonator stability subject to dynamic random-tilt aberration

We derive the behavior of the average exit time (i.e., the number of reflections before escape) of a ray path traveling between two perfect mirrors subject to dynamic random-tilt aberrations. Our calculation is performed in the paraxial approximation. When small random tilts are taken into account, we may consider an asymptotic regime that generically reduces the problem to the study of the exit time from an interval for a harmonic, frictionless oscillator driven by Gaussian white noise. Despite its apparent simplicity, the exact solution of this problem remains an open mathematical challenge, and we propose here a simple approximation scheme. For flat mirrors, the natural frequency of the oscillator vanishes, and, in this case, the average exit time is known exactly. It exhibits a 2/3 scaling-law behavior in terms of the variance of the random tilts. This behavior also follows from our approximation scheme, which establishes the consistency of the scaling law. Our mathematical results are confirmed with simulation experiments.     

Non-destructive testing of concrete strength: statistical control

Some problems of statistical control of concrete strength in non-destructive testing are considered. The procedures for rejection of gross errors and accounting for the actual law of concrete strength distribution are given. In the non-destructive control, the reliability and accuracy of a test result, f_i, as well as the probability of a specified concrete strength, f′ _c , should be the same as in testing with the use of a standard method (specimen testing). Proceeding from this concept, known acceptance criteria are analysed and those recommended by the author are described. The use of the latter permits a considerable reduction of the consumer's risk. Procedures for specifying a required average strength, f _cr , are also analysed. In the use of the proposed acceptance criteria, the value of f _cr may be reduced in many cases, and hence the cement content may be decreased.     

Analyzing Dynamic Behavior of Geosynthetic-Reinforced Soil Retaining Walls

An advanced generalized plasticity soil model and bounding surface geosynthetic model, in conjunction with a dynamic finite element procedure, are used to analyze the behavior of geosynthetic-reinforced soil retaining walls. The construction behavior of a full-scale wall is first analyzed followed by a series of five shaking table tests conducted in a centrifuge. The parameters for the sandy backfill soils are calibrated through the results of monotonic and cyclic triaxial tests. The wall facing deformations, strains in the geogrid reinforcement layers, lateral earth pressures acting at the facing blocks, and vertical stresses at the foundation are presented. In the centrifugal shaking table tests, the response of the walls subject to 20 cycles of sinusoidal wave having a frequency of 2 Hz and of acceleration amplitude of 0.2g are compared with the results of analysis. The acceleration in the backfill, strain in the geogrid layers, and facing deformation are computed and compared to the test results. The results of analysis for both static and dynamic tests compared reasonably well with the experimental results.     

A simple drug anchoring microfiber scaffold for chondrocyte seeding and proliferation

The structural properties of microfiber meshes made from poly(2-hydroxyethyl methacrylate) (PHEMA) were found to significantly depend on the chemical composition and subsequent cross-linking and nebulization processes. PHEMA microfibres showed promise as scaffolds for chondrocyte seeding and proliferation. Moreover, the peak liposome adhesion to PHEMA microfiber scaffolds observed in our study resulted in the development of a simple drug anchoring system. Attached foetal bovine serum-loaded liposomes significantly improved both chondrocyte adhesion and proliferation. In conclusion, fibrous scaffolds from PHEMA are promising materials for tissue engineering and, in combination with liposomes, can serve as a simple drug delivery tool.     

Applied bearing pressure beneath a reinforced soil foundation used in a geosynthetic reinforced soil integrated bridge system

Geosynthetic reinforced soil integrated bridge system (GRS-IBS) design guidelines recommend the use of a reinforced soil foundation (RSF) to support the dead loads that are applied by the reinforced soil abutment and bridge superstructure, as well as any live loads that are applied by traffic on the bridge or abutment. The RSF is composed of high-quality granular fill material that is compacted and encapsulated within a geotextile fabric. Current GRS-IBS interim implementation design guidelines recommend the use of design methodologies for bearing capacity that are based around rigid foundation behavior, which yield a trapezoidal applied pressure distribution that is converted to a uniform applied pressure that acts over a reduced footing width for purposes of analysis. Recommended methods for determining the applied pressure distribution beneath the RSF for settlement analyses follow conventional methodologies for assessing the settlement of spread footings, which typically assume uniformly applied pressures beneath the base of the foundation that are distributed to the underlying soil layers in a fashion that can reasonably be modeled with an elastic-theory approach. Field data collected from an instrumented GRS-IBS that was constructed over a fine-grained soil foundation indicates that the RSF actually behaves in a fairly flexible way under load, yielding an applied pressure distribution that is not uniform or trapezoidal, and which is significantly different than what conventional GRS-IBS design methodologies assume. This paper consequently presents an empirical approach to determining the applied pressure distribution beneath the RSF in GRS-IBS construction. This empirical approach is a useful first step for researchers, as it draws important attention to this issue, and provides a framework for collecting meaningful field data on future projects which accurately capture real GRS-IBS foundation behavior.     

Limit state design framework for geosynthetic-reinforced soil structures

Conventional design of geosynthetic-reinforced soil structures is divided into two categories, walls and slopes, based on the batter of its facing system. Internal stability, characterized as sufficient reinforcement anchoring and strength, is performed using earth pressure-based design criteria for reinforced walls while reinforced slopes are founded on limit equilibrium (LE) slope stability analyses. LE analyses are also used to assess the global or compound stability of both types of structures, accounting for the geometry of the reinforced, retained and foundation soils. The application of LE-based methods typically results in determination of a slip surface corresponding to the lowest attained Safety Factor (SF), known as the Factor of Safety (Fs); however, it yields little information about reinforcement loading or connection load. In this study, use of the analyzed spatial distribution of SF known as a Safety Map, is modified to attain a prescribed constant Fs at any location in the reinforced soil mass. This modified framework, implemented through an iterative, top-down procedure of LE slope stability analyses originating from the crest of a reinforced structure and exiting at progressively lower elevations on the facing, enables the determination of a Tension Map that illustrates the required distribution of reinforcement tension to attain a prescribed limit state of equilibrium. This tension map is directly constrained by a pullout capacity envelope at both the rear and front of each reinforcement layer, providing a unified, LE-based approach towards assessing an optimal selection of mutually dependent strength and layout of the reinforcement. To illustrate the utility of the Limit State framework, a series of instructive examples are presented. The results demonstrate the effects of facing elements, closely-spaced reinforcements, secondary reinforcement layers, and is compared to conventional design approaches.     

Microwave pulses compressed in a quasi-optical resonator with corrugated mirror

A microwave pulse compressor, representing a three-mirror resonator supplied with a radiation beam reflected from a corrugated mirror, was constructed and experimentally tested. A fivefold compression of microwave pulses with a 70% efficiency was obtained in a 9-mm wavelength range.     

Entrance radiation doses during paediatric cardiac catheterisations performed for diagnosis or the treatment of congenital heart disease

The purpose of this study was to estimate the radiation exposure of children, during cardiac catheterisations for the diagnosis or treatment of congenital heart disease. Radiation doses were estimated for 45 children aged from 1 d to 13 y old. Thermoluminescent dosemeters (TLDs) were used to estimate the posterior entrance dose (DP), the lateral entrance dose (DLAT), the thyroid dose and the gonads dose. A dose-area product (DAP) meter was also attached externally to the tube of the angiographic system and gave a direct value in mGy cm2 for each procedure. Posterior and lateral entrance dose values during cardiac catheterisations ranged from 1 to 197 mGy and from 1.1 to 250.3 mGy, respectively. Radiation exposure to the thyroid and the gonads ranged from 0.3 to 8.4 mGy to 0.1 and 0.7 mGy, respectively. Finally, the DAP meter values ranged between 360 and 33,200 mGy cm2. Radiation doses measured in this study are comparable with those reported to previous studies. Moreover, strong correlation was found between the DAP values and the entrance radiation dose measured with TLDs.