A methodology for estimation of spatial distribution known as Geostatistics or Kriging has been used widely in various fields. The formulation to estimate trend component is one of important topics in Geostatistics. This study proposes a method that estimates trend component based on concept of sparse modelling, and random component based on Kriging, namely conventional least square method. Through application of the proposed method to simple hypothetical one dimensional data, we point out a problem that conventional LASSO type formulation produces bias to the estimated trend. A method to correct the bias is also proposed and demonstrated. Applying the proposed method to actual data obtained by cone penetration test in river dike, we estimate trend and random component of two dimensional spatial distribution of SPT value.

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 The practical three-dimensional multiple shear mechanism model requires huge memory to store so many parameters of each spring. Thus, this model is not suitable for large-scale analyses under current ordinary computational systems. This study proposes contraction of three-dimensional multiple shear mechanism model which retains the basic concept of the original model, focusing on reduction of the amount of memory consumption in the finite element method. The original model uses many virtual planes which contain many springs in order to consider many mechanical directions in the three-dimensional space. Hence, the original model could have redundancy of springs in some numerical conditions. The main purpose of the contracted model is to solve the disadvantage of the original model and the contracted model is mathematically designed in order to make each mechanical direction be expressed by one spring. The contracted model accomplishes to reduce drastically both the amount of memory consumption and execution time in numerical experiments, which examine verification of the contracted model in comparison with the original model.

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 Linearized Inverse Scattering Methods based on Kirchhoff approximation can be applicable to visualize flaw shapes with scattering waves from the flaw. Scattering waves from the flaws are measured by pseudo UT pulse-echo mode that two probes are operated simultaneously. In order to visualize the flaws inside the concrete, Parasitic Discrete Wavelet Transform (P-DWT) is applied to extract the frequency characteristic components in the scattered waves. The basis waveform of real-signal mother wavelet (RMW) is acquired by Finite Element Method (FEM) analysis. Scattered waves are filtered by P-DWT; then, they are processed with Kirchhoff Inverse Scattering Method. The imaging process includes to select the optimum Mother Wavelet with AIC and a suitable decomposition level in the wavelet analysis. It is possible to make it highly accurate to visualize the flaws by P-DWT with RMW created from FEM analysis.

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 We need to consider a velocity dependent contact angle (dynamic contact angle) in the analysis of the liquid penetration in a capillary tube. In this study, a velocity dependent capillary pressure (dynamic capillary pressure), which assumed that a linear relationship between the dynamic capillary pressure and the penetration velocity of liquid, was defined. Next, the analytical solution using the governing equation, which is formulated on the basis of dynamic balance of the force regarding the liquid penetration in a vertical capillary tube, was derived. Furthermore, the accuracy of the proposed dynamic mechanism and the adequacy of the approximation of the proposed analytical solution were confirmed by the result that good agreement between the proposed analytical result and the experimental result is obtained.

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 A new damage model for the simulation of crack growth in mutiphase composite materials is presented. The characteristic of the proposed model is a formulation based on the theoretical solution of 1D elastic bar problem, which allows us to evaluate the damage of matrix phase in multiphase composites using finite element meshes generated independently of material interfaces. Our study begins with the formulation of the damage model in 1D problem, and extends it to the formulation for 2D and 3D problems by using an equivalent strain and stress. Fracture problems of two-phase composites in 1D and 2D are solved to verify the validity of the proposed damage model, and the results are compared to reference solutions. The model is then applied to the simulation of 3D crack growth in heterogeneous material with a large number of spherical inclusions.

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 The necessity of taking measures against fault displacement hazards has recently been strongly pointed out. A numerical simulation based on a fundamental mechanism of fault rapture process is essential for more reliable estimations of surface fault displacement. In this paper, we discussed the mechanism in terms of friction on fault plane and confinement of rock ground, and organized requirements for simulations. Then, we constructed a simple fault model based on the mechanism and analyzed mathematical characteristics of fault displacement. It is shown that complicated propagation and jump of slip on fault planes can occur in a simulation bused on the mechanism.

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 Recent development of Additive Manufacturing technology made it possible to manufacture the complex-shaped porous structures: this leads to further development and research for porous structures with special functions and characteristics. In particular, the so-called infill structure is paid attention for its high strength and robustness, and also the optimal design methods for infill structures have been reported. However, few studies has examined to extend to the practical design with stress constraint. With this reason, the present study addresses a topology optimization method for infill structures to avoid stress concentration by adding the local volume constraint and p-norm type stress constraint concept. In addition, we propose a new method, namely variable influence radius, to solve a specific problem which arises in infill optimization. Finally we discuss the setting of optimization problem and demonstrate the accuracy and performance of the proposed method by a series of numerical examples.

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