Electr EngDOI 10.1007/s00202-013-0291-9

ORIGINAL PAPER

Analysis of influence of imperfect contact between groundingelectrodes and surrounding soil on electrical propertiesof grounding loops

J. Trifunovic · M. Kostic

Received: 13 July 2011 / Accepted: 10 November 2013© Springer-Verlag Berlin Heidelberg 2013

Abstract The measurements of the grounding resistanceof grounding loops installed in soils characterised by thestructure that prevents a good contact between the groundingelectrodes and the surrounding soil (e.g. karst and sandy ter-rains) showed that it is considerably influenced by the effec-tive contact surface. Therefore, in such cases the groundingresistance cannot be predicted using the standard engineeringmethods based on the Laplace solution of the problem, wherethe perfect contact was assumed. The aim of this researchwas the estimation of the influence of imperfect contact onthe loop grounding resistance and potential distribution inthe soil during the earth fault. The research is performedapplying the finite-element method on a real grounding loopburied in a two-layer soil. Imperfect contact is modelled byair gaps placed between the grounding loop electrodes andthe surrounding soil. The analysis of the influence of size,number and position of such air gaps on the loop groundingresistance and potential distribution in the soil showed thedominant effect of the grounding loop surface covered withair gaps.

Keywords Grounding loop · Grounding resistance ·Potential distribution · Imperfect contact ·Contact resistance · Finite-element method

1 Introduction

The safety and reliability of electric power systems dependon the quality of their grounding grids, usually made of steel

J. Trifunovic (B) · M. KosticFaculty of Electrical Engineering, University of Belgrade,Bulevar kralja Aleksandra 73, 11000 Belgrade, Serbiae-mail: jovan.trifunovic@etf.rs

M. Kostice-mail: kostic@etf.rs

strips forming two-dimensional grids. The grounding resis-tance, which represents one of the most important parametersof the grid, considerably affects the earth potential rise dur-ing earth faults. If the grounding resistance is high, person-nel may be killed or injured and equipment damaged. There-fore, the grounding resistance should be estimated in an earlydesign phase to conceive the main geometrical parameters ofthe grid. This justifies the efforts made in the past to developrelatively simple formulas for assessing the grounding resis-tance of typical grounding systems including grids. Simplemethods and the designer-oriented formulas for the calcula-tion of the grid grounding resistance are given in standards[1] and [2]. In addition, many papers proposed simple meth-ods and formulas for the calculation of the grounding resis-tance of complex grounding systems buried in uniform ornon-uniform soil. For example, the calculation of the ground-ing resistance of a rectangular grid installed in uniform soilwas presented in [3]. Grids and rods buried in two-layer soilwere analysed in [4–6] and [7], respectively. The foundationgrounding systems, which represent grounding grids encap-sulated in concrete, were considered assuming uniform soilin [8–10]. More complex geometries were also analysed (e.g.foundation grounding systems surrounded by two-layer soil[11,12], foundation grounding systems with external loopsand rods [13] and foundation grounding systems with exter-nal grids [14]). All of those methods and the derived formulasare based on the Laplace solution of the problem, assumingperfect contact surface between the grounding grid electrodesand the surrounding soil. However, it was noticed in prac-tice [15] that such formulas could not satisfactorily be usedfor the calculation of the grid grounding resistance in soilswhere the contact surface is significantly smaller than the sur-face of the electrodes (e.g. karst and sandy terrains). In suchcases, calculated grounding resistances several times lowerthan the actual ones are frequently obtained. Such deviations

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can cause dangerous situations during earth faults. It was sug-gested in [15] that the big difference between the measuredand computed grounding resistances is caused by a bad con-tact between the grounding electrodes and the surroundingsoil. However, this physical phenomenon was not theoreti-cally investigated in [15], because it was impossible to modela bad contact with mathematical techniques and calculationtools available at that time.

The development of the finite-element method (FEM)and the corresponding software, as well as improvementsof the performance of PCs, enabled the application of three-dimensional (3D) finite-element models based on small sizeelements surrounding the grounding electrodes. FEM is anumerical technique for finding approximate solutions toboundary condition problems. The method is based on thedivision of the problem domain into a set of small sub-domains, named finite elements, to accurately representits complex geometry and dissimilar material properties.Each finite element is represented by a set of equationsrelated to the problem. The element equations are simple(for steady-state problems they represent algebraic equa-tions), locally approximating the original complex equa-tions (often partial differential equations). All sets of ele-ment equations are systematically recombined into an over-all system of equations, which can be solved using standardtechniques. A mathematical basis for the FEM was given in[16], while the explanations for its use in electromagneticsand electrical engineering were presented in [17] and [18],respectively.

During the past decade, FEM has been used for the calcu-lation of the grid grounding resistance in a number of cases[19–22]. The advantages of FEM, compared to the conven-tional methods for the calculation of the grid grounding resis-tance, are a simple representation of the total solution andcapture of local effects. It also possesses an advantage of nothaving any limitations regarding the shape and size of thegrid, as well as the soil structure. For the calculation of theelectrical properties of grounding grids using FEM a reason-able level of segmentation is sufficient for practical purposes,and an increased number of elements is needed only if highlyaccurate results are requested [23]. Consequently, consider-ably smaller computational effort is required for practicalpurposes.

In order to develop a method for precise predictions of thegrounding resistance of loops (grids) laid in soils that pre-vent a good contact between the grounding electrodes andthe surrounding soil, it is essential to theoretically investi-gate and gain understanding of the electrical behaviour ofthe grounding loops installed in such soils. The aim of theresearch presented in this paper was estimation of the influ-ence of imperfect contact between the grounding electrodesand the surrounding soil on the loop grounding resistanceand potential distribution in the soil during earth fault. To the

best of the authors’ knowledge, such an analysis has not beencarried out until now.

This paper deals with the application of FEM to a ground-ing loop embedded in a two-layer soil, the behaviour of whichwas experimentally analysed in [15]. Imperfect contact wasmodelled by a number of air gaps placed between the ground-ing loop electrodes and the surrounding soil. The influenceof size, number and position of such air gaps on the loopgrounding resistance and potential distribution was analysedin detail.

2 Application of the finite-element method on theconsidered loop

In order to obtain the necessary understanding of the elec-trical behaviour of grounding loops buried in soils charac-terised by a bad contact with the grounding electrodes, theexperimental set-up described in [15] was modelled apply-ing the FEM. All input parameters necessary for modellingthe grounding loop embedded in two-layer soil were takenfrom [15], where the experimental set-up and measurementprocedure were presented in detail.

As reported in [15], the grounding loop was installed ina former stonebed, located 50 km from Belgrade. This sitewas selected because it is distant from the nearest buildingsand installations (there is no influence of let-go currents) andthe soil has almost identical electrical properties (resistivi-ties) through the whole location. Using the Wenner’s four-pinmethod [24] and the ground resistivity measurement interpre-tation techniques [25], the soil structure was represented bya two-layer soil (ρupper = 170 �m, ρlower = 75 �m andH = 8 m). The upper soil layer is made of stone. The loop,made of frequently used zinc-protected steel strips with a rec-tangular cross-section (30 × 4 mm), was installed at a depthof 0.5 m (Fig. 1).

The dimensions of the buried grounding loop (5 × 5 m)

belong to the range of the dimensions of grounding loopsused as parts of a grounding system for 35 kV transmis-sion line towers, as well as of loops used in transformer sta-tions 10/0.4 kV. The backfill material of the loop channel wasthe excavated material. It was reported in [15] that the loopgrounding resistance was measured to be R = 50.2 � (thefall-of-potential method was used [26]), while the calculatedresistance amounted to R = 14.6 � (formula from [6] wasused). It should be mentioned that another identical ground-ing loop was installed at the same site, but backfilled with1,200 L of bentonite suspension (to enhance contact betweenthe loop electrodes and the surrounding soil)—the rest of thechannel was filled with the excavated material. The differencebetween the measured and calculated values of the groundingresistance in that case was very small, which indicates that

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Fig. 1 A grounding loop buried in a two-layer soil

all input parameters used for the calculation of the groundingresistance were correctly measured or determined.

In this research FEM was applied similarly as in Refs. [20,27,28]. The initial model comprised a cubical volume (20 ×20 × 20 m). The grounding loop, located at a depth of 0.5 mand in the middle of the cube cross-section, was modelledas a subdomain with its realistic dimensions and electricalproperties. The properties of each soil layer were definedby means of the electrical conductivity. The finite-elementmesh in this volume was made by four-node solid elements(tetrahedrons). Each side of this volume, except for the upperside representing the boundary between the soil and air, wassurrounded by additional 2 m-thick walls (subdomains) madeof boundary infinite elements [29], also tetrahedrons. Due tothe symmetry, the final model (Fig. 2) comprises only oneeighth of the initial model, with a triangular cross-section(the area determined by α = 45◦ in Fig. 1). Its depth is20 + 2 = 22 m.

The following formulas are valid for each finite element:

∇2ϕ = 0 (1)�E = −∇ϕ (2)�J = �E/ρ (3)

ϕ = N · ϕe, (4)

Fig. 2 The final finite-element model for the grounding loop underconsideration

where

ϕ is the potential of a point within the finite element, includ-ing the points on the lateral faces,

ϕe is the column vector of potentials of finite element rep-resentative nodes,

N is the correlation matrix depending on the type of a finiteelement,

�E is the electrical field vector,�J is the current density vector, andρ is the electrical resistivity within the finite element.

It is assumed that the grounding resistance only dependson the soil structure and the loop geometry. Accordingly,the grid potential can be arbitrary. The following boundaryconditions are adopted for the considered case:

ϕe0 = 200 V (5)

ϕe inf = 0 V (6)

E1t = E2t (7)

E1n/ρ1 = E2n/ρ2 (8)

where

ϕe0 is the potential of the grounding loop,ϕeinf is the potential of the external boundaries of outer

subdomains made of the infinite elements,

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Fig. 3 The finite-element mesh close to the strip of the grounding loop(close-up of a part of the model, containing one eighth of the loop)

E1t, E2t and E1n, E2n are the tangential and perpendicu-lar components of the electrical field vector at theboundary surface between the adjacent finite ele-ments, respectively, and

ρ1 and ρ2 are electrical resistivities of the materialenclosed by the adjacent finite elements.

Using Eqs. (1)–(8), the potentials of all finite-elementnodes, as well as the current density at arbitrary locationof the model volume, can be calculated. This makes it pos-sible to determine the total current, I , dissipating from thegrounding loop:

I =∫

S

�J · d �S (9)

where S is a surface enclosing the loop.The following equation can be used for the determination

of the loop grounding resistance:

R = ϕe0 − ϕe inf

I. (10)

The number of tetrahedral finite elements used in this analysisranged from 105,000 to 220,000 providing high accuracy ofthe results. Figure 2 shows the model and the finite-elementmesh used for the calculation of the resistance and otherelectrical properties of the loop. The close-up of a part ofthe model, containing one eighth of the loop, is presented inFig. 3. It shows that very small elements are used close to thestrip, increasing in size as they get further away (the strip,which cannot be seen in Fig. 3, connects the centres of thedark areas).

All FEM calculations were performed using the COMSOLMultiphysics software package, installed on a PC which wasequipped with a 2.53 GHz dual-core processor and 3.50 GB

Fig. 4 Schematic representation of the two basic concepts of placingair gaps along the grounding strip (C1 and C2)

of RAM. The duration of simulations ranged from 20 to 110 s,depending on the number of tetrahedral finite elements.

3 Modelling of imperfect contact between the groundingloop electrodes and the surrounding soil

Imperfect contact was modelled by air gaps placed betweenthe grounding loop electrodes and the surrounding soil. Thefollowing two basic concepts of placing air gaps along thegrounding loop strip (C1 and C2, shown in Fig. 4) were used:

1. Air gaps are placed sequentially along the groundingloop perimeter, preventing any contact between the stripand the surrounding soil over the whole surface of thesequence which is completely surrounded by the air gap[the cross-section in xz plane of the modelled air gap sur-rounding a strip sequence, as well as a part of the strip inxy plane showing the sequential distribution of air gaps,are presented in Fig. 4—C1 (b represents the length ofthe strip sequence completely surrounded by the air gap,and w the length of the strip sequence with the perfectcontact between its surface and the surrounding soil)],

2. Air gap is placed continuously along the grounding strip,causing a reduced contact between the strip and the sur-rounding soil over its whole length (Fig. 4—C2, where arepresents the width of a part of the strip surface havingthe perfect contact with the surrounding soil).

The first concept simulates the situation where the ground-ing loop channel is backfilled with the excavated material

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Table 1 Grounding resistanceof the loop for variousdistribution of air gaps along theloop

Model Conceptof placingair gaps

Air gaps on theloop corners

d(10−3 m) a(10−3 m) n F(%) R(�)

M0 C1 − 0 − − 0 14.85

M1 C1 Yes 4 − 4 50 21.07

M2 C1 Yes 4 − 8 50 19.96

M3 C1 Yes 4 − 12 50 19.29

M4 C1 Yes 4 − 80 50 16.92

M5 C1 No 4 − 4 50 20.97

M6 C1 No 4 − 8 50 19.48

M7 C1 No 4 − 12 50 18.97

M8 C1 No 8 − 12 50 19.01

M9 C1 No 16 − 12 50 19.06

M10 C1 Yes 16 − 80 50 17.38

M11 C1 Yes 16 − 80 80 23.92

M12 C1 Yes 16 − 80 92 37.25

M13 C1 Yes 16 − 80 95 49.12

M14 C1 Yes 16 − 80 96 56.64

M15 C2 − 16 27.20 − 60 23.68

M16 C2 − 16 13.60 − 80 30.32

M17 C2 − 16 6.80 − 90 42.16

M18 C2 − 16 4.76 − 93 52.06

M19 C2 − 16 3.40 − 95 64.50

containing large pieces which cannot tightly compress thestrip surface. This causes big air gaps which prevent the dis-sipation of current from those parts of the strip.

The second concept simulates the situation where thebackfill material is fragmented into finer pieces. In suchcases, big air gaps along the strip surface are not formed.However, the air gaps exist on the microscopic level, coveringa larger part of the strip surface. As it is practically impossi-ble to model the remaining microscopic surfaces with perfectcontact, they were integrated in a rectangular segment of thestrip surface with the width a (Fig. 4, C2).

The influence of size, number and position of the describedair gaps on the grounding loop resistance (varying the lengthof a, b, d and w shown in Fig. 4, as well as the number ofthe air gaps along the whole loop, n) is analysed using FEM,to better understand the influence of the contact resistanceon the electrical properties of the grounding loops and grids.An important parameter that was also varied during the cal-culations is the fraction of the grounding loop surface whichis covered with air gaps, F . For the concept C1 it can becalculated as

F(%) = b

T× 100 = b

b + w× 100, (11)

where T is determined by

T = P

n(12)

[P is the grounding loop perimeter (20 m)],and for the concept C2 as

F(%) = a

p× 100, (13)

where p is the length of the strip cross-section perimeter(p = 2 × (30 mm + 4 mm) = 68 × 10−3 m).

Table 1 contains the relevant input parameters of 20 differ-ent models (M0–M19), which were analysed using FEM. Itshould be emphasised that the air gaps were placed in a man-ner to keep one eighth symmetry. Besides, two possibilitieswere analysed when the concept C1 was used:

– the loop corners are surrounded by air gaps, and– the loop corners are in contact with the surrounding

soil.

4 Results and discussion

4.1 Grounding resistance

Model M0 represents the basic case without air gaps, i.e. thecase with perfect contact surface. In this case the groundingresistance obtained by FEM amounted to R0 = 14.85 �,which is very close to the value of R = 14.6 �, [15] obtained

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by an analytical expression [6]. Models M1–M19 are used forthe analysis of the influence of the following input parameterson the loop grounding resistance:

– n (M1–M7),– d (M7–M9), and– F (M10–M19).

4.1.1 Influence of the number of the air gaps on the loopgrounding resistance

By examining the values of the grounding resistance calcu-lated for models M1–M4, it can be concluded that the numberof the air gaps along the loop does not have significant influ-ence on its grounding resistance [for n = 80, the increase ofthe grounding resistance equals 14 % compared to the basicvalue, R0, while for n = 4 the increase amounts to 42 % (inall four cases for d = 4 × 10−3 m and F = 50 %)]. In fact,by increasing the number of the air gaps the loop groundingresistance approaches its basic (theoretical) value, and not theactual (experimentally obtained) one. In addition, by com-paring the values of the grounding resistance calculated formodels M1–M3 with those computed for models M5–M7, itcan be noticed that the grounding resistance is always a bithigher if the air gaps are placed on the corners of the ground-ing loop. However, the differences are practically negligible.Therefore, it can be concluded that for d = 4 × 10−3 m andF = 50 % the experimentally obtained value of R = 50.2 �

cannot be achieved by varying the number of air gaps alongthe loop.

4.1.2 Influence of the depth of the air gaps on the loopgrounding resistance

In models M7–M9, the depth of the air gaps, d, was variedfor the fixed values of n = 12 and F = 50 %. By examiningthe values of the grounding resistance shown in Table 1, itcan be noticed that an increase of d for even 300% (from 4 to16 × 10−3m) causes an increase of the grounding resistanceof only 0.5 % (from 18.97 to 19.06 � ). Hence, the depth ofthe air gaps does not practically influence the grounding loopresistance.

4.1.3 Influence of the fraction of the loop surface coveredwith the air gaps on the loop grounding resistance

In models M10–M14 (concept C1) and M15–M19 (conceptC2), F was varied for the fixed value of d = 16 × 10−3 m(and for n = 80 for the concept C1), aiming to approachthe experimentally obtained value of the loop groundingresistance of R = 50.2 �. The results show that F repre-sents a parameter which most significantly influences theloop grounding resistance. By examining the values of the

grounding resistance shown in Table 1, it was noticed thatthe grounding resistance, as a function of F , can be approx-imated by the following expression:

R(F) = R0 − Riv + K P (F) × Rbc, (14)

where

R0 is the basic (theoretical) value of the loop groundingresistance, representing the soil resistance betweenthe whole loop surface and the remote earth,

Riv is the resistance of the soil in an immediate vicin-ity of the loop electrodes (up to a distance d fromthe electrodes), assuming perfect contact between theelectrodes and the surrounding soil; it can be approx-imated as

Riv = ρupper × d

p × P, (15)

Rbc is the resistance of the soil in an immediate vicin-ity of the loop electrodes (up to a distance d fromthe electrodes), assuming a bad contact between theelectrodes and the surrounding soil; it can be approx-imated as

Rbc = ρupper × d

p × P × (100 − F)/100, and (16)

K P (F) is the correction polynomial of the second order

K P (F) = K0 + K1 × F + K2 × F2 (17)

(K0, K1 and K2 are the correction coefficients).The correction polynomial was needed to compensate the

errors made when approximating Riv and Rbc by Eqs. (15)and (16), respectively. Its second order was sufficient forproviding high accuracy of the results.

Incorporating Eqs. (15)–(17) into Eq. (14), the latterbecomes

R(F) = R0 − ρupper × d

p × P

+ (K0 + K1 × F + K2 × F2)

× ρupper × d × 100

p × P × (100 − F). (18)

By using the method of least squares and the iterativecalculation method which started from (K0, K1, K2) =(1, 0, 0), the following values of the correction coefficientsK0, K1 and K2, providing the best compliance of Eq. (18)with the values of the loop grounding resistance given inTable 1, are determined:

• (K0, K1, K2) = (0.857573, 0.017936,−0.000184) forthe concept C1, and

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Fig. 5 Fitted curves R(F) forthe considered case and bothconcepts (C1 and C2)

• (K0, K1, K2) = (1.001041, 0.044629,−0.000438) forthe concept C2.

The curves R(F) related to the considered case, plottedusing Eq. (18), are shown in Fig. 5. They contain the pointsrepresenting the loop grounding resistance for various valuesof F taken from Table 1.

Applying Eq. (18), the experimentally obtained loopgrounding resistance of R = 50.2 � is obtained for F =95.19 % using the concept C1, and for F = 92.60 % using theconcept C2. It was reported in [15] that during 30 months theloop grounding resistance varied in the range of 50.2−216 �.For the grounding resistance of 216 � Eq. (18) gives the val-ues of F = 99.19 % for the concept C1 and F = 98.88 %for the concept C2 (the variations of the soil resistivity areneglected). It appears that in cases where grounding loops(grids) are laid in soils that prevent a good contact with theelectrodes (e.g. karst and sandy terrains) the current is beingdissipated from a very small fraction of the electrode surface.Therefore, the contact resistance becomes the dominant com-ponent of the total grounding resistance. In such cases, thereexists a problem with the prediction of the contact resistance:due to extremely high values of gradient ∂ R/∂ F (see Fig. 5),small variations of the effective contact surface (which areusually caused by the changes of the soil moisture content)cause great variations of the contact resistance and, conse-quently, the total grounding resistance.

The method presented above can successfully be usedfor the analysis and explanation of the measured results.Unfortunately, it cannot be used for precise predictions ofthe grounding resistance of loops (grids) laid in soils thatprevent a good contact. Our present attempts are focused

on the development of a method which will solve this prob-lem. Nevertheless, the presented results show that the contactresistance can have major influence on the loop groundingresistance. In such cases the use of backfill materials, such asbentonite [15], is recommended, because they significantlyreduce the contact resistance in karst and sandy soils.

4.2 Potential distribution in the soil

As stated in Sect. 1, using FEM not only the groundingresistance of complex grounding systems can be calculated,but also the potential at any point of the model volume canbe determined. This offers an opportunity to perform fur-ther analysis to obtain deeper understanding of the electricalbehaviour of grounding loops. Figure 6, serving as an illus-tration, displays the potential distribution in the soil obtainedfor model M10.

Once the potentials at all points of the model volume aredetermined, potential distribution over any plane or alongarbitrary line within the model volume can be obtained. Forthe considered case, the potential distribution over xy planelocated at the depth of 0.5 m gives the best insight into theelectrical behaviour of a grounding loop buried in the soilcharacterised by a bad contact with the electrodes (x and ycoordinates correspond to the coordinate system defined inFig. 1). Figure 7 shows the comparison of the two potentialdistributions over the considered xy plane: the first is relatedto the case of perfect contact (Fig. 7a, model M0), and thesecond to the case of an imperfect contact characterised byF = 50 % (Fig. 7b, model M10).

According to the diagrams shown in Fig. 7, it appearsthat imperfect contact does not significantly influence the

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Fig. 6 Potential distribution in the soil (one eighth of the groundingloop, model M10)

uniformity of the potential distribution over the whole areaof interest. However, although in such cases the potentialdistribution becomes uniform very close to the groundingelectrode (at a distance of around 0.1 m), it seems that thefall of potential in the soil in the vicinity of the groundingelectrodes becomes significant when increasing the fractionof the grounding loop surface covered with air gaps. Thepotential distribution in the soil, over the considered xy planeand in the vicinity of the grounding electrodes, is presentedin Fig. 8.

According to the graphics shown in Fig. 8, it appears thatthe structure of the soil closest to the electrodes can sig-nificantly influence the potential rise in the vicinity of theelectrodes and, consequently, in the whole area of interest.In order to investigate the influence of the parameter F onthe fall of potential in the soil in an immediate vicinity of thegrounding electrodes, the potential distribution along the linewhich is only 20 mm away from one of the loop electrodes is

Fig. 7 Potential distributions over the considered xy plane [one eighthof the grounding loop, models M0 (a) and M10 (b)]

analysed for various values of the parameter F . The poten-tial distributions along the straight line between the points(x, y) = (2.535 m, 0 m) and (x, y) = (2.535 m, 1 m),placed in the considered xy plane, are presented in Fig. 9 formodels M0 and M10–M14 (x and y coordinates correspondto the coordinate system adopted in Fig. 1).

According to the diagram shown in Fig. 9, the parame-ter F significantly influences the fall of potential in thesoil in an immediate vicinity of the grounding electrodes,which affects the potential distribution at the ground sur-face, relevant for the calculation of touch and step voltages.The diagram shown in Fig. 10 contains curves representingthe potential distributions along the line between the points(x, y) = (0 m, 0 m) and (x, y) = (8 m, 0 m) belonging tothe ground surface (z = 0 m), related to models M0 andM10–M14. Figure 11 presents the dependence of the maxi-mum potential along the considered line at the ground surface(ϕmax ) from the parameter F . The maximum potential variesfrom 140.8 V (valid for F = 0 %) to 37.2 V (F = 96 %).

The diagrams shown in Figs. 10 and 11 illustrate howthe effective contact surface between the grounding elec-

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Fig. 8 Potential distributions in the soil over xy plane at a depth of0.5 m and in the vicinity of the grounding electrodes [models M0 (a)and M10 (b)]

trodes and the surrounding soil affects the potential distri-bution on the ground surface during earth fault. It is obvious

that the touch voltage, which represents the potential dif-ference between the ground potential rise and the groundsurface potential at a point where a person is standing whileat the same time having a hand in contact with a groundedstructure, considerably depends on the effective contact sur-face. The step voltages, representing the difference in groundsurface potentials experienced by a person bridging a dis-tance of 1 m, show similar dependence. Consequently, insoils in which the contact resistance represents the dominantcomponent of the total grounding resistance, the touch andstep voltages—the parameters that indicate the quality of thegrounding system—cannot accurately be predicted using thestandard methods (derived assuming a perfect contact sur-face). Therefore, a new method is needed for such cases toenable precise predictions of the grid grounding resistanceand touch and step voltages. The method should provide thedesigner a possibility to take into account the variations ofthe effective contact surface, as well as the effects of the useof backfill materials. The research presented in this paper,along with the research presented in [30], represents a the-oretical basis for the development of such a method, andour present attempts are focused on the achievement of thatgoal.

5 Conclusions

The aim of this research was the estimation of the influenceof imperfect contacts between the grounding loop electrodesand the surrounding soil on the loop grounding resistanceand potential distribution in the soil during the earth fault.The research is performed applying the FEM on an actualgrounding loop embedded in a two-layer soil.

Fig. 9 Potential distributionsalong a line placed in animmediate vicinity of one of theloop electrodes, presented formodels M0 and M10–M14(curves from top to bottom)

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Fig. 10 Potential distributionsalong a line situated at theground surface, presented formodels M0 and M10–M14(curves from top to bottom)

Fig. 11 Dependence of the maximum potential along the consideredline at the ground surface from the parameter F

Imperfect contact is modelled by air gaps placed betweenthe grounding loop electrodes and the surrounding soil. Ana-lyzing the influence of size, number and position of suchair gaps on the loop grounding resistance, it is concludedthat the number of the air gaps along the grounding loopand their depth do not have significant influence. How-ever, the fraction of the loop surface covered with the airgaps has the most significant impact on the loop groundingresistance.

The results showed that in soils in which the contact resis-tance represents the dominant component of the total ground-ing resistance, the loop grounding resistance, as well as touchand step voltages, will vary a lot with the variations of theeffective contact surface (which are usually caused by thechanges of the soil moisture content). Therefore, their values

cannot satisfactorily be predicted using the standard engi-neering methods, based on the Laplace solution of the prob-lem, assuming perfect contact surface.

The method presented in this paper can successfully beused for the analysis and explanation of the deviation of themeasured values of the grounding resistance from those cal-culated using the standard engineering methods. However,it cannot be used for precise predictions of either the loop(grid) grounding resistance or the potential distribution atthe ground surface for soils causing imperfect contact withelectrodes. Our present attempts are focused on the develop-ment of a method intended for the practitioners, which willenable to take into account the influence of imperfect con-tacts, as well as the use of backfill materials. The researchpresented in this paper, along with the research presented in[30], represents a theoretical basis for the development ofsuch a method.

Acknowledgments This research was partially supported by the Min-istry of Education and Science of Serbia (project TR 36018).

References

1. (1986) Guide for safety in AC substation grounding. ANSI/IEEEStd 80

2. (2000) Guide for safety in AC substation grounding. ANSI/IEEEStd 80

3. Nahman J, Skuletic S (1979) Resistances to ground and mesh volt-ages of ground grids. Proc IEE 126:57–61

4. Salama MMA, Elsherbiny MM, Chow YL, Kim KC (1995) Calcu-lation and interpretation of a grounding grid in two-layer earth withthe synthetic-asymptote approach. Electr Power Syst Res 35:157–165

123

Electr Eng

5. Mombello E, Trad O, Rivera J, Andreoni A (1996) Two-layer soilmodel for power station grounding system calculation consideringmultilayer soil stratification. Electr Power Syst Res 37:67–78

6. Nahman J, Salamon D (1984) Analytical expressions for the resis-tance of grounding grids in nonuniform soil. IEEE Trans PowerAppar Syst 103:880–885

7. Chow YL, Elshabiny MM, Salama MMA (1996) A fast and accu-rate analysis of grounding resistance of a driven rodbed in a two-layer soil. IEEE Trans Power Deliv 11:808–814

8. Brandenbursky V, Farber A, Korj V, Braunshtein A (2011) Groundresistance calculation for small concrete foundations. Electr PowerSyst Res 81:408–413

9. Kostic MB, Popovic BD, Jovanovic MS (1990) Numerical analysisof a class of foundation grounding systems. IEE Proc C 137:123–128

10. Thapar B, Ferrer O, Blank DA (1990) Ground resistance of concretefoundations in substations yards. IEEE Trans Power Deliv 5:130–136

11. Kostic MB, Shirkoohi GH (1993) Numerical analysis of a class offoundation grounding systems surrounded by two-layer soil. IEEETrans Power Deliv 8:1080–1087

12. Kostic MB (1994) Parametric analysis of foundation groundingsystems surrounded by two-layer soil. IEEE Trans Power Deliv9:1406–1411

13. Kostic MB (1993) Analysis of foundation grounding systems withexternal loops and rods. IEE Proc C 140:73–76

14. Kostic MB (1998) Analysis of complex grounding systems con-sisting of foundation grounding systems with external grids. IEEETrans Power Deliv 13:752–756

15. Kostic MB, Radakovic ZR, Radovanovic NS, Tomasevic-CanovicMR (1999) Improvement of electrical properties of groundingloops by using bentonite and waste drilling mud. IEE Proc GenerTransm Distrib 146:1–6

16. Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite ele-ment method: its basis and fundamentals. Elsevier Butterworth-Heinemann, Oxford

17. Jin J (2002) The finite element method in electromagnetics. Wiley,New York

18. Silvester PP, Ferrari RL (1996) Finite elements for electrical engi-neers. Cambridge University Press, Cambridge

19. Colominas I, Gomez-Calvino J, Navarrina F, Casteleiro M (2002)A general numerical model for grounding analysis in layered soils.Adv Eng Softw 33:641–649

20. Nahman J, Paunovic I (2006) Resistance to earth of earthing gridsburied in multi-layer soil. Electr Eng 88:281–287

21. Güemes JA, Hernando FE (2004) Method for calculating theground resistance of grounding grids using FEM. IEEE TransPower Deliv 19:595–600

22. Güemes-Alonso JA, Hernando-Fernández FE, Rodríguez-Bona F,Ruiz-Moll JM (2006) A practical approach for determining theground resistance of grounding grids. IEEE Trans Power Deliv21:1261–1266

23. Colominas I, Navarrina F, Casteleiro M (1999) A boundary ele-ment numerical approach for grounding grid computation. ComputMethod Appl M 174:73–90

24. Wenner F (1916) A method of measuring earth resistances. BullNatl Bureau Stand 12:469–482 (Report no. 258)

25. Dawalibi F, Blattner CJ (1984) Earth resistivity measurement inter-pretation techniques. IEEE Trans Power Appl Syst 103:374–382

26. (1983) Guide for measuring earth resistivity, ground impedance,and earth surface potentials of a ground system. ANSI/IEEE Std81

27. Nahman J, Paunovic I (2007) Effects of the local soil nonunifor-mity upon performances of ground grids. IEEE Trans Power Deliv22:2180–2184

28. Nahman J, Paunovic I (2010) Mesh voltages at earthing grids buriedin multi-layer soil. Electr Power Syst Res 80:556–561

29. Zienkiewicz OC, Emson C, Bettess P (1983) A novel boundaryinfinite element. Int J Numer Method Eng 19:393–404

30. Trifunovic J (2012) The algorithm for determination of necessarycharacteristics of backfill materials used for grounding resistancesof grounding loops reduction. J Electr Eng 63:373–379

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