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Evaluation of Earth Resistivity for Grounding Systems in Non-Uniform Soil Structure M. E. Ghourab

Abstract

The variation in soil resistivity have a considerable influence on the perfortnance of most grounding systems, affecting both the value of ground resistance, the ground potential rise, the step and touch siirface potentials. This paper presents LZ suggested mathematical model to examine the behavior of earthing system in non-uni- form three-layer soil conditions. The study of the appcirent soil resistivity of a driven ground rod as well as the value obtained by the four-point Wenner method has been done and its dependence on the characteristic of each layer is discussed. A comparison between the two methods is emphasized. Finally, the results demonstrute that there is a predicable relationship between the calculated results obtained by these two methods.

1 Introduction

The ground resistance represents an important pa- rameter of the substation grounding system determining the potential level of the system at ground faults and af- fecting the fault current distribution as well as its mag- nitude, at adversegrounding conditions [ I -31. For these reasons, the tools for assessing ground resistance of an earthing system are highly desirable. Whenever doing earth construction work, it is necessary to estimate the number and the depth of electrodes to be implanted in order to obtain the required resistance value. The basic techniques which are universally used for the measure- ment of earth resistivity are the driven rod test method (fall-of-potential method) and the four-point Wenner method. There are some difficulties and inaccuracy when these methods are used to measure the resistance of a large grounding system as usually encountered in power system networks. These difficulties are mainly due to the size and configuration of the grounding system and soil heterogeneity. Homogeneous soil is sel- dom met, practically when large areas are involved. In most cases there are several layers of different soils. For nonhomogeneous soils, an apparent resistivity is de- fined for an equivalent homogeneous soil. An experi- mental and theoretical analysis for two-layer soil was discussed in [4, 51. A mathematical model [ 6 , 7 ] based on the Wenner's measuring method, is used to find the electrical grounding parameters (pi, fi and h) in two layer soil structure. Parameters estimation are carried out in such away as to get an optimum fittings between the set of resistivity values measured in field, and those calculated from the mathematical model using such pa- rameters. Numerical results to study the grounding grid performance in multilayer soil (more than two layer) are presented [8,9]. The effect of soil resistivity on the grid performance (earth resistance, current distribution, grid potential rise, touch and step voltages) are emphasized by the authors. In this paper a theoretical analysis is per- formed for the previously mentioned driven rod test method and the four-point test method in three-layer soil conditions. Equations are derived to calculate the appar-

ent resistivity at the ground surface. The results show that the magnitude and range of the differences in the cal- culated resistivity values are predicable. Finally, i t is shown that this relationship must be considered when it is planned to install ground rods based on resistivity measurements obtained by the four-point test method.

2 Analytical Expression for Resistivity in Three-Layer Soil Structure

For acomplete analysis of the test results in non-uni- form soil conditions, a theoretical analysis based on three-layer soil conditions is given. There is a surface layer of resistivity pI of thickness hi followed by an intermediate layer of resistivity p2 and thickness h2 over- laying a third layer ofresistivity p3. which extends to an infinite distance in the downward direction. The current density at the surface of the rod is primarily adirect func- tion of the resistivity of the surrounding soil and is inde- pendent of where the current flows after leaving the rod. The current penetrating the soil outward from rod fol- lows a laminar flow pattern parallel to the earth surface. Fig. 1 shows the case of a vertical driven rod installed in three-layer soil. Owing to the change in resistivity in the soil surrounding the rod, the assumption that the current flows uniformly from the rod all along its length is no longer valid. It was proved in [ lo], that for a single rod

--c 7-r +-

I I Ground surface

Fig. 1. Driven rod in three-layer soil structure

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in multi-layer soil, the relationship pkik = const always applies except at the rod extremities. Where ik is the cur- rent per unit length of the rod part which is in layer k of soil resistivity symbol pk.

Let il, i2 and i3 be the current per unit length for the three layers respectively, therefore:

i lp , = i2p2 = i3p3 ( 1 )

I = i , h , = i2h2 = i3 ( l - (h l + hz)) . ( 2 ) Starting from the well-known equation for the resis-

tance R of a single ground rod of length 1 and radius r buried in uniform soil of resistivity p I [l I ] as:

and the total current I in the rod is

(3)

If the voltage applied to the rod is U the current f I produced in the rod is given by:

I1 = UIRI

and the current per unit length i I for a rod of length 1 bur- ied in a soil of uniform resistivity p I is:

Similarly, for the rod driven in soils of uniform re- sistivities p~ and p3 the current per unit length, i2 and i3, may be expressed as follows:

and

2x u

Therefore, with the help of eq. (2) the total current is approximately given by:

L ( r j J The resistance of a vertical rod Rd is given by:

(7)

LPI P2 p3 J But the driven rod apparent soil resistance obtained

from the three-point method takes the form [ 1 I]:

From eqs. (7) and (8) the apparent soil resistivity pd as seen by the rod is given by:

Pd I - - [ h , -+;+ h, l - ( h ~ + h , ) ]

PI P2 P3

. (9) - - 1PI PZ P3

4 P Z P , + h 2 P I P 3 + ( ~ - ( h l +h,))PlP?

An equation presented in [ 1 I ] included the effect of image caused by the reflection at the discontinuity of the soils and the rod penetration into the lower level in two- layer soil condition. This equation takes the following form:

I+k, PI R = -

or

R =fp(R1 + R,). Where R I is the resistance of rod in p I ; R, is the ad-

ditional resistance due to second layer resistivity. The penetration factorf, and the reflection coefficient k,, are equal :

fp-= ( I - k,) + 2 k,h,'l' 1+k,

k,=-. P? - PI P2 +PI

When the rod penetrates the second and the third soil layers the effect of image needs to be taken into consid- eration. Following the same procedure and neglecting the interference between the upper and lower layers, the apparent soil resistivity, eq. (9), can take the form:

which is applicable only for 1 > (hl + h2). The p factor accounts for the images caused by the reflection at the discontinuity of the soil and equals:

where m is the number of layers and

Pj+l - Pj Pj+l + Pj

4e.j =

The terms PI and P2 are the approximate values of P with respect to the first and the second and between the second and the third layers respectively. From eq. (1 I), if the top layer thickness hl is reduced to zero, then the equation is reduced to that of two-layer soil as:

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-u"uI 2 3 4 5 6 7 8 m 10 : --c

Fig. 2. Dependence of PI and j?? on electrode depth z (parameter: kre)

If .(hl + hZ) > 1 then

P d = LPlpZ (I+P, + P 2 ) . hl P? + h2 PI

Finally if hl 2 I, the equation reduces to:

P d = PI ( 1 + PI + Pd. Fig. 2 shows the calculated values of PI andp, terms

for a ground rod driven into a three-layer soil condition where the top layer thickness h, = I m and the second layer thickness /z2 = 2 m. The values of k,, varies from -0.82 to 0 between the first and the second layer and from 0 to 0.82 between the second and third layers. This figure shows that the effect of P term will diminish with increasing penetration into the lower soil. It has a signif- icant effect only for smaller rod depths and extreme pos- itive values of krc.

3 Characteristics of the Calculated Results

Fig. 3 shows the dependency of apparent soil resis- tivity on rod depth 2 of a vertical rod driven into soil where the top layer resistivity pI = 200 Rm, an inter- mediate layer pz = 100 Rm and with different values of third layer resistivity p3. It can be seen that the apparent soil resistivity equals to pI till the rod depth is greater than hl. Its value decreases when the rod penetrates the second soil layer of lower resistivity than the first layer. Once the rod started to enter the third layer, the apparent soil resistivity increases again. This is due to the effect of the third layer which is of higher resistivity. It is clear from this figure that the rate of increase depends on the value of p3. but there is no linear relationship between the change of p 3 and the resultant values of P d . Finally

, the relationship between the apparent resistivity and the depth of burial seems to have logarithmic dependence. In Fig. 4 the apparent soil resistivity decreases as the rod penetrates the underlying second and third layers of

z ---c

Fig. 3. Computed rod apparent resistivity pd as a function of 2 : parameter: p3 ( h , = I m, h? = 2 m. pI = 200 Rm, p2 = 100 Rm)

lower resistivity than the first one. The rate of decrease appears to be taken as an exponential shape and dif- ferent in the second and the third layers due to the dif- ference of current density. Fig. 5 shows the dependence of resistivity on the rod depth if the second layer has a higher resistivity. This figure illustrates that the resis- tivity started to increase with increasing of pI and again its value begins to decrease when the rod pene- trates the third layer of lower resistivity. Also, this fig- ure shows that the rate of change of the resistivity de- pends strongly on the layer of higher resistivity value. I t can be seen from the previous results that the apparent resistivity values are greatly dependent on the layer in which the rod is located. When it is located in a low re- sistivity layer, the apparent resistivity is low. These re- sults have an agreement with the previous calculated earth resistance, directly proportional to the apparent re- sistivity, value in [8]. It is stated in [ I21 that in uniform soil the grid resistance decreases with increasing of bu- rial depth but this is not always valid in non-uniform soil structure.

2 -D

Fig. 4. Computed rod apparent resistivity pd as a function of z : parameter: p I ( h , = I m, hl = 2 m, p? = 200 Rm. p3 = 100 Rm)

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z *

Fig. 5. Computed rod apparent resistivity pd as il function of z ; parameter: p- (h i = I m, h2 = 1 m. p , = pz = 100 Rm)

In a non-homogeneous earth structure the equation of the apparent resistivity which mentioned in [ I31 is modified to take the following:

1

* (14)

According to the previous results in Fig. 2 and in most-practical engineering applications involving inter- pretation of soil resistivity measurement the reflection coefficient related to the non-adjacent layers is not sig- nificant. Therefore, this term can be neglected in the above mentioned equation.

5 Discussion of the Calculated Results 4 Four-Point Test Method

The arrangement of four electrodes in a straight line at equal intervals d is shown in Fig. 6. The current I between the current electrodes CI and C2 and the volt- agedifference U between the potential electrodes PI and PL are represented by:

Finally, from the measured resistance RW the appar- ent soil resistivity pw can be expressed by:

p~ = 2 ~ d R w . (13) The analysis is canied out using different values of

electrode spacing d. A good approximation is to assume that when the electrode spacing d is less than h,, the earth may be approximated by a two-layer structure with the second layer of resistivity p2 assumed to extend to infi- nite depth. For electrode spacing greater than h2, the earth may approximated by a three-layer structure. In this case the first two layers can be combined together to a single layer of depth he, = (h l + hz) and equivalent resistivity:

- PI Pt@I + h2 1 P24+ PIh?

Peq -

00 h Fig. 6. Circuit diagram for Wenner measuring method

The calculated results for the apparent soil resistiv- ity by the Wenner method are shown in Fig. 7 and 8.

(1 - c

Fig. 7. Computed Wenner apparent resistivity pw as a function of d; parameter: pz ( h , = 1 m, h2 = 2 m, pI = 100 Rm, p2 = I00 Rm) .

j i i l ' I 2 3 6 7 8 A /O

d ---P

Fig. 8. Computed Wenner apparent resistivity pw as a function of d; parameter: p I . ( h , = 1 m,h2 = 2 m,p2 = 200Rm,p3 = l 0 0 R m )

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f

I’G

I 2 3 4 5 6 7 8 m 1 0 z or d --w

Fig. 9. Ratio pc = p d /pw at rod depth : or probe spacing d (parameter: kre. 2)

Fig. 7 shows the results with different values of third layer resistivity. It can be seen from this figure that the resistivity curves are continuous both for probe spacing less than the first layer depth, h, , and as probe spacing increases to larger than the first layer depth. The appar- ent soil resistivity is approximately equal to pI if the spacing nearly reaches h l . The effect of the third layer resistivity started to appear after 2 m spacing between adjacent electrodes (depth of the second layer). By con- sidering the effect of third layer with increasing the spac- ing between electrodes the increasing rate of resistivity seems to be logarithmic. Fig. 8 shows the effect of the first layer resistivity pi on the calculated results. The curves are continuous in all cases, also the rate of de- crease appears to have exponential dependence on spac- ing between electrodes.

6 Comparison Between the Two Methods

Fig. 9 shows a comparison between the calculated apparent resistivity of rod compared to that obtained by four-point of spacing equals to rod depth. This figure il- lustrates the ratio pc = pd/pw as a function of rod depth z or probe spacing d at h , = I m, hz = 2 m, krc. I = -0.33 and different values of kre. 2. The curves indicate that p d

may be considerably less or somewhat greater than pw depending on the depth of the rod. These curves also demonstrate the degree of variance of p d with respect to p w as the magnitude of k,,,z and the depth of the rod are increased. It is important to recognize these variations when a grounding system design is utilized by ground rods and the soil resistivity test data obtained by the four- point Wenner method.

7 Conclusions

Relatively simple formulae for calculation of the ap- parent soil resistivity of a driven rod and four-point method in three-layer soils are derived. The effects of soil heterogeneities on the calculated apparent resistiv- ity values have been discussed and illustrated in this

paper. The apparent resistivity. is greatly dependent on the layer in which the rod is buried. It is clear from the calculated results that increasing the rod depth or the probe spacing causes a small influence of the top layer resistivity on the calculated apparent resistivity. The confirmation of the results is seen from the agreement with the published results which emphasize the depen- dence of grid resistance on the layer resistivity in multi- layer soil. A relationship between the two test methods has been studied. This relation must be considered dur- ing the design of grounding systems.

8 List of Symbols and Abbreviations

resistivity of upper and lower layers in two-layer soil upper layer thickness in two-layer soil resistivity of upper, intermediate and lower layers i n three-layer soil depth of upper and intermediate layers in three-layer soil driven rod radius length of driven rod in contact with earth current per unit length of the rod parts in pI, p? and p~ respectively total rod current rod voltage driven rod resistance of length 1 additional resistance due to second layer resistivity apparent soil resistivity as seen by the rod reflection coefticient number of layers penetration factor

PI. pz, p3 constants d spacing between electrodes R W

Pw

measured resistance by four-point Wen- ner method measured soil resistivity by four-point Wenner method

values of (driven rod/Wenner) resistivity 7 c rod depth PG

C , , cz current electrodes PI, P2 potential electrodes

(PG = Pd/PW)

References [ I ] Sverek, J. G. etal.: Save substationGrounding-P. I1 (IEEE

80 Guide for Safety in A-C Substations- Rev.). IEEETrans. Power Appar. a. Syst. PAS-I01 (1982) pp. 4006-4023

[ 2 ] Hitoshi. K.: Earth Resistance Estimation Instrument. 2 I . Int. Conf. on Lightning Protection, BedidGermany 1992, Proc. Rep. 3.12, pp. 145- 150 Dawnlibi, E P; Mukhecikas D.: Resistance Measure- ment of Large Grounding Systems. IEEE Trans. Power Appar. a. Syst. PAS-98 ( 1979) pp. 2 348 -2 354

[4] 5luttnes C. J.: Study of Driven Ground Rods and Four Point Soil Resistivity Tests. IEEE Trans. Power Appar. a. Syst. PAS- 10 I ( 1982) pp. 2 873 - 2 850 Blattnec C. J.: Analysis of Soil Resistivity Test Methods in Two-Layer Earth. IEEE Trans. Power Appar. a. Syst.

[3]

[ 5 ]

PAS- 104 (1985) pp. 3603-3 608

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[61 Alamo def, J. L.: A Comparison Among Eight Differ- ent Techniques to Achieve an Optimum Estimation of Electrical Grounding Parameters in Two-Layered Earth. IEEE Trans. Power Delivery PWRD-8 ( I 993)

[7] Seedhe< H. R.; Arora, J. K.: Estimation of Two Layer Soil Parameters Using Finite Wenner Resistivity Ex- pressions. IEEETrans. Power Delivery PWRD-7 ( 1992)

[8] Dawalibi, E k?; Ma. J.: Southhey, R. D.: Behavior of Grounding Systems in Multilayer Soils: A parametric Analysis. IEEE Trans. Power Delivery PWRD-9 (1994)

Ma, J.; Dawalibi, E R ; Daily, U! K.: AnalysisofGround- ing Systems in Soils with Hemispherical Layering. IEEE Trans. Power Delivery PWRD-8 (1993) pp. 1 773 - I 78 I

[lo] Dawalibi, E I?: Mukhedkar: D.: Influence of Ground Rods on Grounding Grids. IEEE Trans. Power Appar. a.

[ 1 I ] Tagg, G. E: Earth Resistance. LondodGB: Pitt. Publ. Corp.. 1964

[ I21 El-Morshedy. A.; Zeitoun, A. G.: Ghourab. M. E.: Mod- elling of Substation Grounding Grids. IEE Proc. C I33 (1986) no. 5, pp. 289-292

pp. I 890- 1 899

pp. 1213-1216

pp. 334-342 [9]

Syst. PAS-98 (1979) pp. 2089-2097

[ 131 Caldecotr. R.: Kczsren, D. C.; Minkara, S.: Investigation of Soil Resistivity Measuring Techniques Using an Electrolytic Tank. IEEE Trans. Power Appar. a. Syst. PAS-I03 (1984) pp. 2983-2988

Manuscript received on April 26, 1994

The Author Mohamed E. Ghourab ( 1955) received the B.Sc. and MSc. degrees in electri- cal engineering from Suez Canal Uni- versitylEgypt in 1981 and 1984, re- spectively. He received the Ph.D. de- gree in electrical engineering from Hungarian Academy of Sciences, Bu- dapest/Hungaria, in 1993. From 1982 to 1988 he was a research associate with the department of electrical engi- neering, Suez Canal University. In

1993 he joined the same department as an Assistant Professor. His present research interests include problems in high volt- age engineering. (Suez Canal University, Faculty of Enginee- ring, Electrical Engineering Department, 42523 Port FouadlEgypt, T i 20571332896, Fax + 2066/400936)

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