Horizontal Multilayer Soil Research Articles

Inversion of one‐dimensional parameters of horizontal multi‐layer soil model based on dynamic state electromagnetic field theory and ant colony optimization algorithm

AbstractBuilding a reliable soil model is a prerequisite for accurately calculating the ground potential distribution of the grounding grid. Research shows that the soil electrical parameters are frequency‐dependent, so frequency domain inversion of soil parameters should consider the soil inhomogeneity and the frequency characteristic of parameters. A method for retrieving parameters of horizontal multilayer soil model is proposed. The theoretical formula of apparent complex resistivity with considering dynamic state electromagnetic field theory is derived from Green's function. Discrete dynamic state complex image method is introduced to solve the infinite integral in Green's function. Ant colony optimization algorithm is applied to optimize the inversion process of soil parameters. In the first stage, applicability of this method is confirmed by interpreting field data under DC field. DC parameters including DC resistivity, thickness and number of layer are determined. The performance of different optimization algorithms in terms of computational efficiency is compared at this stage. In the second stage, soil resistivity and relative dielectric constant are retrieved by inverting frequency domain experimental data. Different representations based on quasi‐static electromagnetic field and dynamic state electromagnetic field theories are taken into account. The frequency characteristic of soil parameters is concluded by discussing the inversion results. In the study of parameter inversion of horizontal multi‐layer soil model, our method has shown strong performance in computational efficiency and accuracy of inversion results.

Kernel Function-Based Inverting Algorithm for Structure Parameters of Horizontal Multilayer Soil

A multilayer soil structure model is fundamental to design grounding systems. A new method is presented to invert the structure parameters of horizontal multilayer soil. The structure parameters of soil are determined by analyzing the kernel function of the integral equation of the apparent resistivity. The essence of the proposed method avoids the difficulties encountered in general optimization methods; namely, the calculation of the apparent resistivity and its derivative.

Parameters estimation of horizontal multilayer soilsusing a heuristic algorithm

The grounding grid is buried in horizontal multilayer soils, so accurate parameters (resistivity , thickness, the number of soil layers) estimation of the soil is the basis for accurately calculating the grounding parameters and design of grounding grids. At present, the parameters estimation is usually solved by non-heuristic algorithms and heuristic algorithms. However, existing non-heuristic algorithms depend too much on the initial value and conventional heuristic algorithms could deviate from the correct solution too far, which would easily fall into local optimal solution, causing calculation errors. To solve the above problem, this paper first studies the relationship between the apparent soil resistivity and soil parameters based on the Wenner's method. Then, an innovative PSO-DE (Particle Swarm Optimization-Differential Evolution) optimization algorithm and its initialization method are proposed. The results of PSO-DE, conventional heuristic intelligent optimization algorithms, CDEGS, and literatures are compared, which verifies the superiority and accuracy of the PSO-DE. Therefore, the contribution of this work can lay a solid theoretical foundation for grounding parameters calculation.

Calculation of Earth Surface Potential and Neutral Current Caused by HVDC Considering Three-Dimensional Complex Soil Structure

In ground return mode of high-voltage direct current (HVDC) transmission, direct current is injected into the soil through a ground electrode, causing ground potential rise in different areas and direct current at the neutral point of transformers. Earth surface potential (ESP) and neutral current are closely related to the 3-D structure of soil, but few studies treat the soil three dimensionally when calculating these two parameters. In this article, a 3-D resistor network (RN) is developed to construct the soil model, and a soil–grid unified circuit model is proposed to simplify the calculation of neutral current. The RN method is verified by calculating ESP of a horizontal multilayer soil model and contrasting the result with that of CDEGS software. The feasibility and accuracy of the soil–grid unified circuit model is demonstrated through comparing neutral currents of two substations with the results calculated by finite-element method (FEM). The influence of resistivity changes in a water-bearing fault on ESP and neutral current is specifically analyzed using RN method and FEM to prove the necessity of considering the 3-D complex soil structure. The results of this article contribute to the simulation of DC distribution of wide-area HVDC transmission in complex soil structures.

Optimization of substation grounding grid design for horizontal and vertical multilayer and uniform soil condition using Simulated Annealing method.

Grounding systems are critical in safeguarding people and equipment from power system failures. A grounding system’s principal goal is to offer the lowest impedance path for undesired fault current. Optimization of the grounding grid designs is important in satisfying the minimum cost of the grounding system and safeguarding those people who work in the surrounding area of the grounded installations. Currently, there is no systematic guidance or standard for grounding grid designs that include two-layer soil and its effects on grounding grid systems, particularly vertically layered soil. Furthermore, while numerous studies have been conducted on optimization, relatively limited study has been done on the problem of optimizing the grounding grid in two-layer soil, particularly in vertical soil structures. This paper presents the results of optimization for substation grounding systems using the Simulated Annealing (SA) algorithm in different soil conditions which conforms to the safety requirements of the grounding system. Practical features of grounding grids in various soil conditions discussed in this paper (uniform soil, two-layer horizontal soil, and two-layer vertical soil) are considered during problem formulation and solution algorithm. The proposed algorithm’s results show that the number of grid conductors in the X and Y directions (Nx and Ny), as well as vertical rods (Nr), can be optimized from initial numbers of 35% for uniform soil, 57% for horizontal two-layer soil for ρ1> ρ2, and 33% for horizontal two-layer soil for ρ1< ρ2, and 29% for vertical two-layer soil structure. In other words, the proposed technique would be able to utilize square and rectangle-shaped grounding grids with a number of grid conductors and vertical rods to be implemented in uniform, two-layer horizontal and vertical soil structure, depending on the resistivity of the soil layer.

Proposing two new metaheuristic algorithms of ALO-MLP and SHO-MLP in predicting bearing capacity of circular footing located on horizontal multilayer soil

In this study, for the issue of shallow circular footing’s bearing capacity (also shown as Fult), we used the merits of artificial neural network (ANN), while optimized it by two metaheuristic algorithms (i.e., ant lion optimization (ALO) and the spotted hyena optimizer (SHO)). Several studies demonstrated that ANNs have significant results in terms of predicting the soil’s bearing capacity. Nevertheless, most models of ANN learning consist of different disadvantages. Accordantly, we focused on the application of two hybrid models of ALO–MLP and SHO–MLP for predicting the Fult placed in layered soils. Moreover, we performed an Extensive Finite Element (FE) modeling on 16 sets of soil layer (soft soil placed onto stronger soil and vice versa) considering a database that consists of 703 testing and 2810 training datasets for preparing the training and testing datasets. The independent variables in terms of ALO and SHO algorithms have been optimized by taking into account a trial and error process. The input data layers consisted of (i) upper layer foundation/thickness width (h/B) ratio, (ii) bottom and topsoil layer properties (for example, six of the most important properties of soil), (iii) vertical settlement (s), (iv) footing width (B), where the main target was taken Fult. According to RMSE and R2, values of (0.996 and 0.034) and (0.994 and 0.044) are obtained for training dataset and values of (0.994 and 0.040) and (0.991 and 0.050) are found for the testing dataset of proposed SHO–MLP and ALO–MLP best-fit prediction network structures, respectively. This proves higher reliability of the proposed hybrid model of SHO–MLP in approximating shallow circular footing bearing capacity.

Horizontal Multilayer Soil Parameter Estimation Through Differential Evolution

This paper presents a methodology to represent an unknown soil through a stratified horizontal multilayer soil model. It uses the experimental electrical apparent resistivity curve, obtained by measurements on the ground, using a 4-wire earth ground resistance tester kit, along with some calculations. This curve is then compared with the theoretical electrical apparent resistivity curve, obtained through calculations over a horizontally stratified soil, whose parameters are known. The horizontal multilayer soil model parameters, such as number of layers, in addition to the resistivity and thickness of each layer, are optimized by the Differential Evolution algorithm. In order for both apparent resistivity curves to get close, the model can be a representation of the unknown soil. We also present methodologies to verify the theoretical apparent resistivity calculations, by extending the characteristic curve approximation, and to improve error peaks between the apparent resistivity curves, by giving opportunities for other more uniform solutions to excel. A case study uses experimental data from other methods for further comparisons.

Multilayer Stratification Earth by Kernel Function and Quasi-Newton Method

Obtaining the resistivity of the soil layers and their thicknesses from measurements constitutes an essential stage of grounding systems projects, since these data provide valuable guidance to the engineer. The literature presents methods that may result in inaccurate stratification. In order to implement a robust quasi-Newton algorithm to calculate the parameters of horizontal multilayer soils using measurement data collected with the Wenner array, this article uses first derivatives of the objective function and two approaches: a kernel function with the Prony's method and the other for the apparent resistivity. The method does not use infinite series neither solves improper integrals, and shows accuracy and robustness. Soil stratifications with two, three, four and five layers are obtained from published data in order to validate the proposed method.

Analysis of Grounding Systems in Horizontal Multilayer Soils Containing Finite Heterogeneities

This paper presents a theoretical model for the analysis of grounding systems located in multilayer soils in which arbitrary heterogeneities (finite volumes) are embedded. The presence of the heterogeneities is handled through a boundary element method, whereas that of the horizontal soil layers is analytically handled using image theory (or any other equivalent technique). Numerical results are presented for several cases and are shown to agree with limiting cases. The results also clearly show that the presence of finite heterogeneities in multilayer soils can have a very strong impact on the safety performance of a grounding system.

Analysis of Grounding Systems Including Freely Oriented Plates of Arbitrary Shape in Multilayer Soils

This paper presents the analysis of grounding systems including freely oriented conductors and metallic plates of arbitrary shapes in horizontal multilayer soils. The analysis method yields not only the scalar potential but also the electric field and current density in the soil in the low frequency limit. Numerical results are provided for various configurations such as a single plate, a plate with rods, parallel plates, a box, or cylinders formed by multiple plates and are verified against available analytical methods.

Analysis of Foundation Grounding System Buried in a Horizontal Multilayer Soil by Means of the Fictitious Conductivity Concept

The theoretical model for the analysis of grounding system encased in the foundation region in a horizontal multilayer soil is presented. By means of fictitious conductivity concept, the effects of foundation are replaced by a set of equivalent current sources. The analysis of grounding system can be carried out by combining the moment method with additional equivalent current sources. The main advantage of the proposed approach is that it can be linked with the existing codes easily. The results are compared with those found in the literature and obtained by other popular software

Analysis of the toroidal HVDC grounding systems in horizontal multilayer soils

A Fredholm integral equation of the first kind has been developed for analyzing the performance of the toroidal high-voltage direct current (HVDC) grounding system buried in the horizontal multilayer soil. The method of moment is used to solve the equations. The formulation of potential in the earth due to a circular current is proposed in closed form by means of conception of the complex resistivity and depth, which leads to the saving of the computational time greatly. The numerical results show the good agreements with those in other papers and the measured data

Numerical Green's Function of a Point Current Source in Horizontal Multilayer Soils by Utilizing the Vector Matrix Pencil Technique

Numerical Green's function approach is proposed to calculate Green's function of a point current source in an arbitrary horizontal multilayer soil. The coefficients of Green's function are straightforwardly sampled in an iterative way in terms of the simultaneous equation system satisfying the pertinent boundary value problem, then the closed-form expression of Green's function for multilayer soil can be given by the vector matrix pencil technology. The approach proposed could be practically applied in grounding problems in an arbitrarily layered soil without needing to derive the analytical expression of Green's function.

Two-Stage Algorithm for Inverting Structure Parameters of the Horizontal Multilayer Soil

The multilayer soil structure model is the fundament to design grounding systems. A fast algorithm is presented to invert the structure parameters of the horizontal multilayer soil. The procedure is divided into two independent stages. First, Fredholm equation of the first kind with respect to the apparent resistivity is solved by using the technology of decay spectrum, which can reduce the computation time greatly. Second, the structure parameter of soil is determined by the generalized Newton-Kantorovich method, which is more robust and less noise sensitive because of using the generalized inverse algorithm to solve the nonlinear equation system. The numerical results show the validities and main features of the proposed approach. The numerical results by using the proposed method are in a good agreement with ones from geophysical exploration.

A general method for numerical Green's function in arbitrarily layered soils *

Abstract A straightforward approach is developed to calculate Green's function of a point current source in horizontal multi-layer soils. The sampling value of the coefficient of Green's function is obtained in an iterative way in terms of the equation group satisfying the pertinent boundary value problem. Further, the closed-form expression of multilayered soil Green's function can be given by the vector matrix pencil technology. The numerical results are in agreement with those by using other softwares. The approach proposed here is applicable to grounding problems with the structure of arbitrarily layered soil without needing the analytical expression of Green's function.

Fast algorithm for inverting structure parameters of the horizontal multi-layer soil*

A fast algorithm is presented to invert the structure parameter of the horizontal multi-layer soil. The procedure is divided into two independent stages. First, Fredholm equation of the first kind with respect to the apparent resistivity is solved by the technology of decay spectrum to reduce computation time greatly. Second, the structure parameter of soil is determined by the generalized Newton-Kantorovich method, which is more robust and less noise sensitive because of using the generalized inverse algorithm to solve the nonlinear equation group. The numerical results show the validities and main features of the proposed approach.

A general method for numerical Green's function in arbitrarily layered soils

A straightforward approach is developed to calculate Green's function of a point current source in horizontal multi-layer soils. The sampling value of the coefficient of Green's function is obtained in an iterative way in terms of the equation group satisfying the pertinent boundary value problem. Further, the closed-form expression of multilayered soil Green's function can be given by the vector matrix pencil technology. The numerical results are in agreement with those by using other softwares. The approach proposed here is applicable to grounding problems with the structure of arbitrarily layered soil without needing the analytical expression of Green's function.

Two-layer soil model for power station grounding system calculation considering multilayer soil stratification

Two-layer soil models are commonly used for the design of power station grounding systems. Calculations based on such models usually give correct values for the gound resistance of grounding electrodes and for the step and touch potentials on the surface of the ground. However, the two-layer model of the actual soil can give absurd results if incorrect values of the layer resistivities and the first layer thickness are used. Conventional methods of fitting the apparent resistivity curve in order to obtain those parameters do not give good results in all cases. This may happen when the soil has a multilayer structure and certain combinations of different layer resistivities exist. In this paper, an analysis of critical cases was carried out, and a novel calculation method for the parameters of the two-layer soil model is presented. The proposed method is valid for an arbitrary number of soil layers with arbitrary values of resistivity, and it is applicable to simple as well as complex grounding systems. The numerical results of this method were compared with electromagnetic field calculations carried out with a computer program based on the finite-element method. The proposed model permits the use of computer programs based on the method of images and a two-layer soil model for the design of station grounding systems buried in horizontal multilayer soil stratifications. Thus, the risk of serious calculation errors that may appear by application of the apparent resistivity fitting method can be avoided.