The asymptotic pseudo-trajectory approach to stochastic approximation of Benaïm, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into the mean field to produce convergence results which remain similar to those of an equivalent synchronous process. In addition, this allows many of the restrictive assumptions previously associated with asynchronous stochastic approximation to be removed. The framework is extended for a coupled asynchronous stochastic approximation process with set-valued mean fields. Two-timescales arguments are used here in a similar manner to the original work in this area by Borkar. The applicability of this approach is demonstrated through learning in a Markov decision process.

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Laboratory-based, large-scale experiments are reported on pavement test sections with aggregate base layers containing a layer of geosynthetic reinforcement. The tests involved comparative reinforced and unreinforced test sections with pavement layer materials and thicknesses commonly encountered in the field. Pavement load was provided by a nontranslating, cyclic load applied to a plate resting on the pavement surface. The test sections contained an extensive array of sensors to measure pavement load, surface deformation, stress in the base and subgrade layers, and strain in the asphalt concrete, base, subgrade, and geosynthetic layers. Test section variables include geosynthetic type, geosynthetic placement position within the base, and base layer thickness. The test results show a significant improvement in the permanent deformation behavior of the pavement system due to geosynthetic reinforcement for the variables examined. Stress and strain measurements illustrate reinforcement mechanisms pertinent to paved roadways, which include a reduction of radial strain developed in the bottom of the base, an improved vertical stress distribution on the top of the subgrade, and a reduction of shear deformation in the top of the subgrade. These mechanisms result in lower vertical strain in the base and subgrade layers. A comparison of benefits due to reinforcement and those realized by the addition of aggregate base shows that geosynthetic reinforcement and additional base aggregate provide similar structural enhancements to the pavement system.

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In recent years, geosynthetics have been proposed and used as reinforcement in the base course layer of flexible pavements for the purpose of improving performance and/or to allow for the reduction of base course thickness. Much of the pioneering work with geosynthetic-reinforced unpaved roads on very soft subgrades has indicated that appreciable deformation of the roadway surface is necessary before the reinforcement qualities of the geosynthetic can be realized. It may be expected that this same condition is necessary in a paved road, thereby obviating the practical use of geosynthetics as reinforcement. It appears that this view has gained acceptance in the research and practice oriented engineering communities. The purpose of this paper is to provide a synthesis and evaluation of the literature focusing on this application. The paper focuses on studies involving laboratory-scale experiments using stationary cyclic loads or moving wheel loads and field studies using controlled vehicle loads or random traffic loads. The majority of the studies reviewed indicate that appreciable improvement can be realized by proper placement of a geosynthetic in the base course of a flexible pavement and that improvement is seen over the entire service life of the pavement and not only for conditions of excessive surface deformation.