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ABSTRACT, and (2) adding computational routines for suction-dependent strain and net stress (i.e., total stress minus gas pressure) for unsaturated soils. We implemented a thermo-elasto-plastic version of the BBM wherein the soil strength depends on both suction and temperature. The implementation of the BBM into TOUGH-FLAC was verified and tested against several published numerical model simulations and laboratory experiments involving the coupled thermal-hydrologicalmechanical (THM) behavior of unsaturated soils. The simulation tests included modeling the mechanical behavior of bentonite-sand mixtures, which are being considered as back-fill and buffer materials for geological disposal of spent nuclear fuel. We also tested and demonstrated the use of the BBM and TOUGH-FLAC for a problem involving the coupled THM processes within a bentonitebackfilled nuclear waste emplacement tunnel. The simulation results indicated complex geomechanical behavior of the bentonite backfill, including a nonuniform distribution of buffer porosity and density that could not be captured in an alternative, simplified, linear-elastic swelling model. As a result of the work presented in this paper, TOUGH-FLAC with BBM is now fully operational and ready to be applied to problems associated with nuclear waste disposal in bentonitebackfilled tunnels, as well as other scientific and engineering problems related to the mechanical behavior of unsaturated soils.2

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This paper examines a stochastic process for Bose-Einstein statistics that is based on Gibrat's Law (roughly: the probability of a new occurrence of an event is proportional to the number of times it has occurred previously). From the necessary conditions for the steady state of the process are derived, under two slightly different sets of boundary conditions, the geometric distribution and the Yule distribution, respectively. The latter derivation provides a simpler method than the one earlier proposed by Hill [J. Amer. Statist. Ass. (1974) 69, 1017-10261 for obtaining the Pareto Law (a limiting case of the Yule distribution) from Bose-Einstein statistics. The stochastic process is applied to the phenomena of city sizes and growth.

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