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For gravity dams built on foundations with directional joint sets, the seepage in the foundation possesses anisotropic characteristics and may have adverse effects on the foundation stability. A methodology for system reliability analysis of gravity dam foundations considering anisotropic seepage and multiple sliding surfaces is proposed in this paper.

Anisotropic seepages in dam foundations are simulated using finite element method (FEM) with the equivalent continuum model (ECM), and their effect on dam foundation stability is involved by uplift pressures acting on the potential sliding surfaces. The system failure probability of the dam foundation is efficiently estimated using Monte Carlo method (MCM) combined with response surface method (RSM).

The case study shows that it is necessary to consider the possibly adverse effect of anisotropic seepage on foundation stability of gravity dams and the deterministic analysis of the foundation stability may be misleading. The system reliability analysis of the dam foundation is justified, as the uncertainties in shear strength parameters of the foundation rocks and joint sets as well as aperture, connectivity and spacing of the joint sets are quantified and the system effect of the multiple potential sliding surfaces on the foundation reliability is reasonably considered.

(1) A methodology is proposed for efficient system reliability analysis of foundation stability of gravity dams considering anisotropic seepage and multiple sliding surfaces (2) The influence of anisotropic seepage on the stability of gravity dam foundation  is revealed (3) The influence of estimation errors of RSMs on the system reliability assessment of dam foundation is investigated.

The main purpose of this paper is presenting Thin Plates Spline-based Differential Quadrature (TPS-DQM) as a meshless numerical method to solve the steady and transient groundwater equation in complex geometry.

The computational nodes are randomly distributed in domain, and the governing equations of groundwater flow are solved, relying on the capability of present model for solving the partial differential equations (PDEs) in irregular domains. To show the accuracy of the proposed model, several seepage problems in both homogenous and non-homogenous soils are solved, and the results are compared with those existing analytical solution and well-known finite element-based software SEEP/W.

The results indicate that the present meshless method is capable of simulating steady-state and unsteady seepage problems, especially in complex geometry and it provides sufficient accuracy and reliability, despite the low computational effort and no need for additional parameters like shape factor.

The main advantage of the method is its meshless characteristic, which does not require structured grid generation and able to solve governing equation in arbitrary geometry.

The purpose of this paper is to extend the scaled boundary radial point interpolation method (SBRPIM), as a novel semi-analytical scheme, to the analysis of the steady state confined seepage flows.

This method combines the advantages of the scaled boundary finite element method and the BRPIM. In this method, only boundary nodes are used, no fundamental solution of the problem is required, and as the shape functions constructed based on the RPIM satisfy the Kronecker delta function property, the boundary conditions of problems can be imposed accurately and easily.

Three numerical examples, including seepage flow through homogeneous and non-homogeneous soils, are analyzed in this paper. Comparing the flow net obtained by SBRPIM and other numerical methods confirms the ability of the proposed method in analyzing seepage flows. In addition, in these examples, the accuracy of the SBRPIM in modeling the velocity singularity at a sharp corner is illustrated. SBRPIM accurately models the singularity point in non-homogeneous and anisotropic soil.

SBRPIM method is a simple effective tool for analyzing various kinds of engineering problems. It is easy to implement for modeling the velocity singularity at a sharp corner. The proposed method accurately models the singularity point in non-homogeneous and anisotropic soil.

A numerical solution to the free boundary problem of three‐dimensional transient seepage through an earth dam with accretion is presented. The numerical model uses a Baiocchi type transformation to extend the unknown solution region to a fixed known region. The initial value problem is then solved by an iterative method of successive over‐relaxation type. A seepage situation of sudden rise of water level on one side of a dam is presented as an example problem. The effects of variation of accretion, effective porosity and hydraulic conductivity are studied.

This study aims to present a new numerical model for the simulation of water flow through porous media of anisotropic character, based on the network simulation method and with the use of the free code Ngspice.

For its design, it starts directly from the flow conservation equation, which presents several advantages in relation to the numerical simulation of the governing equation in terms of the potential head. The model provides very precise solutions of streamlines and potential patterns in all cases, with relatively small meshes and acceptable calculation times, both essential characteristics when developing a computational tool for engineering purposes. The model has been successfully verified with analytical results for non-penetrating dams in isotropic media.

Applications of the model are presented for the construction of the flow nets, calculation of uplift pressures, infiltrated flow and average exit gradient in anisotropic scenarios with penetrating dams with and without sheet piles, being all this output information part of the decision process in ground engineering problems involving these retaining structures.

This study presents, for the first time, a numerical network model for seepage problems that is not obtained from the Laplace's governing equation, but from the water flow conservation continuity equation.

This paper aims at the problem of surrounding rock excavation damage zone of tunneling in the rich water region, this paper aims to propose a new seepage-stress-damage coupling model and studied the numerical algorithm. This reflects the characteristics of rock damage evolution, accompanied by plastic flow deformation and multi-field interaction.

First of all, rock elastoplastic damage constitutive model based on the Drucker–Prager criterion is established, the fully implicit return mapping algorithm is adopted to realize the numerical solution. Second, based on the relation between damage variation and permeability coefficient, the rock stress-seepage-damage model and multi-field coupling solving iterative method are presented. Finally, using the C++ language compiled the corresponding programs and simulated tunnel engineering in the rich water region.

Results show that difference evolution-based back analysis inversed damage parameters well, at the same time the established coupling model and calculating program have more advantages than general conventional methods. Multiple field coupling effects should be more considered for the design of tunnel support.

The proposed method provides an effective numerical simulation method for the construction of the tunnel and other geotechnical engineering involved underground water problems.

The purpose of this study is to understand the basics of interactions of groundwater and surface water, which is needed for effective management of water resources.

The experimental setup was framed using curved flume and the straight flume, which simulates the model of river and groundwater storage, respectively. The model set up further consists, downstream, central and upstream sections where 14 observation wells, which are arranged at a measured distance from the canal side.

Exit gradient is higher at downstream when the average head differences between canal and river are 31.9 cm and 35.7 cm. Free seepage height is more in the downstream wells than upstream and central wells. At the downstream section, there is a greater chance of instability of the riverbank.

Results will be used for better planning of hydraulic structural design.

Results will help in storing the large water and better irrigation planning for the water acute states and locations.

The originality is own developed physical model and its own first type to understand the basic of interaction and effects.

Understanding the fluid flow through rock masses, which commonly consist of rock matrix and fractures, is a fundamental issue in many application areas of rock engineering. As the equivalent porous medium approach is the dominant approach for engineering applications, it is of great significance to estimate the equivalent permeability tensor of rock masses. This study aims to develop a novel numerical approach to estimate the equivalent permeability tensor for fractured porous rock masses.

The radial point interpolation method (RPIM) and finite element method (FEM) are coupled to simulate the seepage flow in fractured porous rock masses. The rock matrix is modeled by the RPIM, and the fractures are modeled explicitly by the FEM. A procedure for numerical experiments is then designed to determinate the equivalent permeability tensor directly on the basis of Darcy’s law.

The coupled RPIM-FEM method is a reliable numerical method to analyze the seepage flow in fractured porous rock masses, which can consider simultaneously the influences of fractures and rock matrix. As the meshes of rock matrix and fracture network are generated separately without considering the topology relationship between them, the mesh generation process can be greatly facilitated. Using the proposed procedure for numerical experiments, which is designed directly on the basis of Darcy’s law, the representative elementary volume and equivalent permeability tensor of fractured porous rock masses can be identified conveniently.

A novel numerical approach to estimate the equivalent permeability tensor for fractured porous rock masses is proposed. In the approach, the RPIM and FEM are coupled to simulate the seepage flow in fractured porous rock masses, and then a numerical experiment procedure directly based on Darcy’s law is introduced to estimate the equivalent permeability tensor.

The paper aims to clarify the relationship between the micro-structures of porous media and the coefficient of permeability. Most materials involve different types of defects like caves, pores and cracks, which are important characters of porous media and have a great influence on the physical properties of materials. To study the seepage mechanical characteristics of damaged porous media, the constitutive model of porous media dealing with coupled modeling of pores damage and its impact on permeability property of a deforming media was studied in this paper.

The paper opted for an exploratory study using the approach of continuum damage mechanics (CDM).

The paper provides some new insights on the fluid dynamics of porous media. The dynamic evolution model of permeability coefficient established in this paper can be used to model the fluid flow problems in damaged porous media. Moreover, the modified Darcy's law developed in this paper is considered to be an extension of the Darcy's law for fluid flow and seepage in a porous medium.

Owing to the limitations of time, conditions, funds, etc., the research results should be subject to multifaceted experiments before their innovative significance can be fully verified.

The paper includes implications for the development of fluid dynamics of porous media.

This paper fulfils an identified need to study the relationship between the micro-structures of porous media and the coefficient of permeability.

In petroleum industry, hydraulic fracturing is essential to enhance oil productivity. The hydraulic fractures are usually generated in the process of hydraulic fracturing. Although some mathematical models were proposed to analyze the well-flow behavior of conventional fracture, there are few models to depict unconventional fracture like reorientation fracture. To figure out the effect of reorientation fracture on production enhancement and guide the further on-site operating, this paper aims to investigate the well-flow behavior of vertical reorientation fracture in horizontal permeability anisotropic reservoir.

Based on the governing equation considering horizontal permeability anisotropy, the mathematical models for reorientation fractures in infinite reservoir are developed by using the principle of superposition. Furthermore, a rectangular closed drainage area is also considered to investigate the well-flow behavior of reorientation fracture, and the mathematical models are developed by using Green’s and source functions.

Computational results indicate that the flux distribution of infinite conductivity fracture is uniform at very early times. After a period, it will stabilize eventually. High permeability anisotropy and small inclination angle of reorientation will cause significant end point effect in the infinite conductivity fracture. The reorientation fractures with small inclination angle in high anisotropic reservoir are capable of improving 1-1.5 times more oil productivity in total.

This paper develops the mathematical methods to study the well-flow behavior for unconventional fracture, especially for reorientation fracture. The results validate the production enhancement effect of reorientation fracture and identify the sensitive parameters of productivity.