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A meshless method namely, discrete least square method (DLSM), is presented in the paper for the solution of free surface seepage problem. In this method computational domain is discredited by some nodes and then the set of simultaneous equations are built using moving least square (MLS) shape functions and least square technique. The proposed method does not need any background mesh therefore it is a truly meshless method. Several numerical two dimensional examples of Poisson partial differential equations (PDEs) are presented to illustrate the performance of the present DLSM. And finally a free surface seepage problem in a porous media is solved and results are presented.

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A meshless approach, collocation discrete least square (CDLS) method, is extended in this paper, for solving

elasticity problems. In the present CDLS method, the problem domain is discretized by distributed field nodes. The field

nodes are used to construct the trial functions. The moving least-squares interpolant is employed to construct the trial

functions. Some collocation points that are independent of the field nodes are used to form the total residuals of the

problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of the

residuals for the collocation points. The final stiffness matrix is symmetric and therefore can be solved via efficient

solvers. The boundary conditions are easily enforced by the penalty method. The present method does not require any

mesh so it is a truly meshless method. Numerical examples are studied in detail, which show that the present method

is stable and possesses good accuracy, high convergence rate and high efficiency.

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The concept of Geosynthetic Cellular Systems (GCS) has recently emerged as a new method in construction of breakwaters and coastal protective structures. The method potentially has significant advantages compared to conventional systems from the standpoint of constructability, cost effectiveness, and environmental considerations. This paper presents the results of physical model testing on the hydraulic responses of GCS structures under wave action. A series of model tests were carried out in a wave flume on GCS models with different shapes and soil types, subjected to various wave characteristics. Horizontal wave forces acting on the models were measured at different elevations. The maximum horizontal force in each test was calculated and compared with conventional formula of predicting wave pressure on breakwaters. The results show that Goda’s equation overestimates the hydrodynamic water pressure on these structures. This can be attributed to the influence of seeping water through the GCS models because of relative permeability of the GCS.

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In this paper, different aspects of the behavior of 2×2 pile groups under liquefaction-induced lateral spreading in a 3-layer soil profile is investigated using large scale 1-g shake table test. Different parameters of the response of soil and piles including time-histories of accelerations, pore water pressures, displacements and bending moments are presented and discussed in the paper. In addition, distribution of lateral forces due to lateral spreading on individual piles of the groups is investigated in detail. The results show that total lateral forces on the piles are influenced by the shadow effect as well as the superstructure mass attached to the pile cap. It was also found that lateral forces exerted on the piles in the lower half of the liquefied layer are significantly larger than those recommended by the design code. Based on the numerical analyses performed, it is shown that the displacement based method is more capable of predicting the pile group behavior in this experiment comparing to the force based method provided that the model parameters are tuned.

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A numerical meshless method is proposed to investigate shallow water equations. Because of The numerical solution of the pure convection equations represents a very important issue in many problems, an Element Free Galerkin (EFG) method is used for solving these equations, and its implementation is described. In this method there is no need to nodal connectivity and just uses nodal data which may be the same as those used in the Finite Element Methods (FEMs) and a description of the domain boundary geometry are necessary. The essential boundary condition is enforced by the penalty method, and the Moving Least Squares (MLS) approximation is used for the interpolation scheme. The numerical efficiency of the proposed method is demonstrated by solving several benchmark examples. Sensitivity analysis on parameters of the EFG method is carried out and results are presented.