Maintenance problem for infrastructures such as bridge, road, airport, etc., attracts keen interest in modern Japan. We have to cope with repair and maintenance for infrastructures with limited financial resources. In airport pavements, repair works are restricted by daily flight operation, so that efficient maintenance planning is required. In this paper, we try to model deterioration of an existing airport runway, which is composed of 100 units. PRI (Pavement Rehabilitation Index) for each unit is obtained by 3 to 8 times of inspection during around 28 years. PRI is an index to provide an objective evaluation of pavement surface condition, with criteria determined for judging the need for rehabilitation work on runway, taxiway, and apron pavements. Many researches and practitioners use PRI for airport pavement maintenance in Japan. The spatial distribution of deterioration in airfield pavement is not discussed in many previous studies. This study discusses deterioration curve for each unit and feature of spatial distribution. The distribution of deterioration based on PRI and the probability of exceedance of each PRI criteria in future are estimated by the proposed method.

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Kriging, which uses theory of conditional Gaussian random field, has been widely used in geotechnical problems. Least square method and L2 norm plays an important role in the method. The concept of sparse modeling attracts much attention from various fields. It is reported that it is successfully applied to many problems in various fields such as signal processing, image processing, machine learning and so on. The representative formulation LASSO uses L1 norm instead of L2 norm in the formulation. After illustrating the concept and formulation of sparse modeling, application to evaluation of soil property from limited number of boring data is discussed. One dimensional and two dimensional cases are indicated with assumption of sparsity in first-order and second-order differentiation space. In one dimensional case, both assumptions, which are sparsity in first-order and second-order differentiation, give reasonable distribution. In two-dimensional case, however, the assumption of sparsity in first-order differentiation gives unnatural distribution in the numerical examples. In the evaluation of spatial distribution of geotechnical problems, assumption of sparsity in second-order differentiation space seems reasonable.