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The purpose of this paper is to propose a fast, accurate and efficient algorithm for assessment of transient behavior of grounding grids buried in horizontal multilayered earth model considering soil ionization effect.

The purpose of this paper is to develop a numerical simulation method to calculate the lightning impulse response of the grounding grid buried in a horizontal multilayered earth model. The mathematical model about the hybrid method based on PI basic function belonging to time domain is proposed in the paper; the mode can precisely calculate the lightning current distribution and lightning impulse response to grounding grids buried in horizontal multilayered soil model considering soil ionization effect. To increase computing efficiency, quasi-static complex image method (QSCIM) and its time-domain Green’s function closed form are introduced in the model.

The hybrid model is rather stable, with the respect to the number of elements used and with excellent convergence rate. In addition, because this mathematical model belongs to the time domain algorithm, it is very powerful for the simulation of soil ionization caused by high amplitude lightning current.

To increase computing efficiency, QSCIM and its time domain Green's function closed form are introduced in the model.

The mathematical model about the hybrid method based on PI basic function can precisely calculate the lightning current distribution and lightning impulse response to grounding grids buried in horizontal multilayered soil model considering the soil ionization effect.

Considering the soil ionization effect, the simulation calculation of lightning impulse response of substation grounding grid buried in the actual horizontal multilayered earth can effectively support the scientific and efficient design of lightning protection performance of substation grounding grid.

The hybrid model in time domain is originally developed by the authors and used to precisely calculate the lightning current distribution and lightning impulse response to grounding grids buried in horizontal multilayered soil model considering soil ionization effect. It is simple and very efficient and can easily be extended to arbitrary grounding configurations.

This paper aims to describe a numerical procedure for approximating the potential distribution for a harmonic current point source, which is either buried in horizontally stratified multilayer earth, or positioned in the air. The procedure is very efficient and general. The total number of layers and the source position in relation to the medium model layers are completely arbitrary.

The efficiency of the computation procedure is based on the successful application of the numerical approximation of two kernel functions of the integral expression for the potential distribution within an arbitrarily chosen layer of the medium model. Each kernel function of the observed layer is approximated using a linear combination of 15 real exponential functions. Using these approximations and the analytical integration based on the Weber integral, a simple expression for numerical approximation of potential distribution within boundaries of the observed medium layer is given. Potential retardation is taken into account approximately.

The numerical procedure developed for the approximation of potential distribution for a harmonic current point source, which is positioned arbitrarily in air or in horizontally stratified multilayer earth, is efficient, numerically stable and generally applicable.

Numerical model developed for the harmonic current point source is the basis of a wider numerical models for computation of the harmonic and transient fields of earthing system, which consists of earthing grids buried in horizontally stratified multilayer earth and metallic structures in the air.

This is efficient and numerically stable frequency dependent harmonic current point source model. Potential retardation, which has been neglected at the first step of the approximation, is subsequently added to the potential expression in such a way that the Helmholtz differential equation has been approximately solved without introducing the Sommerfeld integrals.

This paper aims to focus on the inclusion of the frequency behavior of grounding system effect on surge arrester (SA) model parameters’ estimation.

The grounding system impedance and its frequency behavior are the factors that have influence on the SA performance. Up to now, the grounding system impedance effect and the frequency behavior of the soil parameters have not been studied for the estimation of the parameters of the SA frequency-dependent model. In this paper, the grounding system’s influence on the SA dynamic model has been simulated for rod- and counterpoise-shaped electrodes. Particle swarm optimization with a grey wolf optimization algorithm has been implemented as an optimization algorithm to adjust the parameters of the SA dynamic model.

The results show that the frequency behavior of the grounding impedance and soil electrical parameters can impress the optimum parameters of the SA frequency-dependent model and should be considered for more reliable results. Also, the results evidence that the proposed optimization method provides more accurate results compared to other optimization methods.

To the best of the authors’ knowledge, this work is one of the first attempts to investigate the effect of frequency grounding system on SA frequency-dependent model parameters.

The per-unit-length earth return mutual impedance of the overhead conductors plays an important role for analyzing electromagnetic transients or couplings of multi-conductor systems. It is impossible to have a closed-form expression to evaluate this kind of impedance. The purpose of this paper is to propose an efficient numerical approach to evaluate the earth return mutual impedance of the overhead conductors above horizontally multi-layered soils.

The expression of the earth return mutual impedance, which contains a complex highly oscillatory semi-infinite integral, is divided into two parts intentionally, i.e. the definite and the tail integral, respectively. The definite integral is calculated using the proposed moment functions after fitting the integrand into the piecewise cubic spline functions, and the tail integral is replaced by exponential integrals with newly developed asymptotic integrands.

The numerical examples show the proposed approach has a satisfactory accuracy for different parameter combinations. Compared to the direct quadrature approach, the computational time of the proposed approach is very competitive, especially, for the large horizontal distance and the low height of the conductors.

The advantage of the proposed approach is that the calculation of the highly oscillatory integral is completely avoided due to the fact that the moment function can be evaluated analytically. The contribution of the tail integral is well included by means of the exponential integral, though in an asymptotic way. The proposed approach is completely general, and can be applied to calculate the earth return mutual impedance of overhead conductors above a soil structure with an arbitrary number of horizontal layers.

This paper aims to develop a quantitative model for predicting the productivity of excavators using artificial neural networks (ANN), which is then compared with the multiple regression model developed by Edwards & Holt (2000). A neural network using the architecture of multilayer feedforward (MLFF) is used to model the productivity of excavators. Finally, the modelling methods, predictive behaviours and the advantages of each model are discussed. The results show that the ANN model is suitable for mapping the non‐linear relationship between excavation activities and the performance of excavators. It concludes that the ANN model is an ideal alternative for estimating the productivity of excavators.

Solutions for the earth return mutual impedance play an important role in analyzing couplings of multi-conductor systems. Generally, the mutual impedance is approximated by Pollaczek integrals. The purpose of this paper is devising fast algorithms for calculation of this kind of improper integrals and its applications.

According to singular points, the Pollaczek integral is divided into two parts: the finite integral and the infinite integral. The finite part is computed by combining an efficient Levin method, which is implemented with a Chebyshev differential matrix. By transforming the integration path, the tail integral is calculated with help of a transformed Clenshaw–Curtis quadrature rule.

Numerical tests show that this new method is robust to high oscillation and nearly singularities. Thus, it is suitable for evaluating Pollaczek integrals. Furthermore, compared with existing method, the presented algorithm gives high-order approaches for the earth return mutual impedance between conductors over a multilayered soil with wide ranges of parameters.

An efficient truncation strategy is proposed to accelerate numerical calculation of Pollaczek integral. Compared with existing algorithms, this method is easier to be applied to computation of similar improper integrals, such as Sommerfeld integral.

The finite element method (FEM) is used to calculate the two-dimensional anti-plane dynamic response of structure embedded in D’Alembert viscoelastic multilayered soil on the rigid bedrock. This paper aims to research a time-domain absorbing boundary condition (ABC), which should be imposed on the truncation boundary of the finite domain to represent the dynamic interaction between the truncated infinite domain and the finite domain.

A high-order ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. A new operator separation method and the mode reduction are adopted to construct the time-domain ABC.

The derivation of the ABC is accurate for the single layer but less accurate for the multilayer. To achieve high accuracy, therefore, the distance from the truncation boundary to the region of interest can be zero for the single layer but need to be about 0.5 times of the total layer height of the infinite domain for the multilayer. Both single-layered and multilayered numerical examples verify that the accuracy of the ABC is almost the same for both cases of only using the modal number excited by dynamic load and using the full modal number of infinite domain. Using the ABC with reduced modes can not only reduce the computation cost but also be more friendly to the stability. Numerical examples demonstrate the superior properties of the proposed ABC with stability, high accuracy and remarkable coupling with the FEM.

A high-order time-domain ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. The proposed ABC is suitable for both linear elastic and D’Alembert viscoelastic media, and it can be coupled seamlessly with the FEM. A new operator separation method combining mode reduction is presented with better stability than the existing methods.

The purpose of this paper is to develop a numerical (finite-difference) model exploring phase and group velocities of SH-wave propagation in initially stressed transversely isotropic poroelastic multi-layered composite structures and initially stressed viscoelastic-dry-sandy multi-layered composite structures in two distinct cases.

With the aid of relevant constitutive relations, the non-vanishing equations of motions for the propagation SH-wave in the considered composite structures have been derived. Haskell matrix method and finite-difference scheme are adopted to deduce velocity equation for both the cases. Stability analysis for the adopted finite-difference scheme has been carried out and the expressions for phase as well as group velocity in terms of dispersion-parameter and stability-ratio have been deduced.

Velocity equations are derived for the propagation of SH-wave in both the composite structures. The obtained results are matched with the classical results for the case of double and triple-layered composite structure along with comparative analysis. Stability analysis have been carried out to develop expressions of phase as well as group velocity in terms of dispersion-parameter and stability-ratio. The effect of wavenumber, dispersion parameter along with initial-stress, porosity, sandiness, viscoelasticity, stability ratio, associated with the said composite structures on phase, damped and group velocities of SH-wave has been unveiled.

To the best of authors’ knowledge, numerical modelling and analysis of propagation characteristics of SH-wave in multi-layered initially stressed composite structures composed of transversely isotropic poroelastic materials and viscoelastic-dry-sandy materials remain unattempted inspite of its importance and relevance in many branches of science and engineering.

The purpose of this paper is to present a new numerical model for shallow water flows over heterogeneous sedimentary layers. It is already several years since the single-layered models have been used to model shallow water flows over erodible beds. Although such models present a real opportunity for shallow water flows over movable beds, this paper is the first to propose a multilayered solver for this class of flow problems.

Multilayered beds formed with different erodible soils are considered in this study. The governing equations consist of the well-established shallow water equations for the flow, a transport equation for the suspended sediments, an Exner-type equation for the bed load and a set of empirical equations for erosion and deposition terms. For the numerical solution of the coupled system, the authors consider a non-homogeneous Riemann solver equipped with interface-tracking tools to resolve discontinuous soil properties in the multilayered bed. The solver consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms.

This paper reveals that modeling shallow water flows over multilayered sedimentary topography can be achieved by using a coupled system of partial differential equations governing sediment transport. The obtained results demonstrate that the proposed numerical model preserves the conservation property, and it provides accurate results, avoiding numerical oscillations and numerical dissipation in the approximated solutions.

A novel implementation of sediment handling is presented where both averaged and separate values for sediment species are used to ensure speed and precision in the simulations.

This study aims to analyse the deep resource mining that causes high in situ stress, and the disturbance of tunnelling and mining which may induce large stress concentration, plastic deformation and rock strata compression deformation. The depth of deep resources, excavation rate and multilayered heterogeneity are critical factors of excavation disturbance in deep rock. However, at present, there are few engineering practices used in deep resource mining, and it is difficult to analyse the high in situ stress and dynamic three-dimensional (3D) excavation process in laboratory experiments. As a result, an understanding of the behaviours and mechanisms of the dynamic evolution of the stress field and plastic zone in deep tunnelling and mining surrounding rock is still lacking.

This study introduced a 3D engineering-scale finite element model and analysed the scheme involved the elastoplastic constitutive and element deletion techniques, while considering the influence of the deep rock mass of the roadway excavation, coal seam mining-induced stress, plastic zone in the process of mining disturbance of the in situ stress state, excavation rate and layered rock mass properties at the depths of 500 m, 1,500 m and 2,500 m of several typical coal seams, and the tunnelling and excavation rates of 0.5 m/step, 1 m/step and 2 m/step. An engineering-scale numerical model of the layered rock and soil body in an actual mining area were also established.

The simulation results of the surrounding rock stress field, dynamic evolution and maximum value change of the plastic zone, large deformation and settlement of the layered rock mass are obtained. The numerical results indicate that the process of mining can be accelerated with the increase in the tunnelling and excavation rate, but the vertical concentrated stress induced by the surrounding rock intensifies with the increase in the excavation rate, which becomes a crucial factor affecting the instability of the surrounding rock. The deep rock mass is in the high in situ stress state, and the stress and plastic strain maxima of the surrounding rock induced by the tunnelling and mining processes increase sharply with the excavation depth. In ultra-deep conditions (depth of 2,500 m), the maximum vertical stress is quickly reached by the conventional tunnelling and mining process. Compared with the deep homogeneous rock mass model, the multilayered heterogeneous rock mass produces higher mining-induced stress and plastic strain in each layer during the entire process of tunnelling and mining, and each layer presents a squeeze and dislocation deformation.

The results of this study can provide a valuable reference for the dynamic evolution of stress and plastic deformation in roadway tunnelling and coal seam mining to investigate the mechanisms of in situ stress at typical depths, excavation rates, stress concentrations, plastic deformations and compression behaviours of multilayered heterogeneity.