grounding resistance

IEEE Transactions on Power Delivery, Vol. 10, No. 2, April 1995

EQUIVALENT RESISTIVITY OF NON-UNIFORM SOIL FOR GROUNDING GRID DESIGN

Baldev Thapar Victor Gerez Senior Member Senior Member

Montana State University, Bozeman, Montana

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Abstract - This paper develops a method to determine equivalent resistivity of heterogeneous soils to be used in the available expressions for uniform soils employed to calculate the ground resistance, mesh and step voltages. The results obtained with the proposed equivalent resistivity are compared with the results obtained from the two layer and the multilayer models of the soil and with the results from a computer program, developed by the authors, directly based on the potential produced by a point source in heterogeneous soil.

Keywords: Grounding Grids, Ground Resistivity, Substations.

I. INTRODUCTION

Important parameters in the design of grounding grids for ac substations are ground resistance, mesh and step voltages. If the soil is assumed uniform, simple formulas to determine these parameters are available.[ 1 1. However, the ground under the surface of the earth is by no means homogeneous. Techniques and computer programs have been developed to calculate the design parameters of the grounding grids in non-uniform soil by considering the soil as a two or a multilayered media with horizontal or spherical stratifications.[2,3,4], These techniques require the use of complex mathematics and time consuming computations but they give accurate results only when the actual ground conditions are close to the model of the ground used. A typical cross section of the underground indicates complex heterogeneity and does not show regular and distinct stratification. Therefore, the refined techniques for grounding calculations in multilayered media are good only for particular cases and may not give good results in practical situations. It has also been suggested to use the expressions for uniform soil employing an equivalent resistivity for the heterogeneous soi1.[5,6,7]. However, this equivalent resistivity is based on the horizontally stratified ground and is not convenient to determine.

Changes caused by weather and season, by rain and frost and by temperature variations influence the resistivity of the soil and greatly affect the grounding parameters. Because of the random nature of these changes a high degree of accuracy in the calculations of the grounding parameters is not required. A method that is simple, reasonably accurate and applicable to heterogeneous soils without requiring the modelling of the soil is needed for the grounding calculations and to ascertain that the electric system shall not experience technical trouble or cause accidents. This paper presents two such methods.

In both the methods a knowledge of the underground soil structure is not required and only a point source apparent resiTtivity graph for the site is needed. (1) The first is the direct method. The potential produced by a point

94 SM 387-1 FWRD A paper recommended and approved by the IEEE Substations Committee of the IEEE Power Engineering Society for presentation at the IEEE/PES 1994 Summer Meeting, San Francisco, CA, July 24 - 28, 1994. Manuscript submitted July 19, 1993; made available for printing May 9, 1994.

source is used directly to calculate the ground resistance, mesh and step potentials. (2) The second is the equivalent resistivity method. The present available expressions to calculate the ground resistance, the mesh and the step voltages, are used. The value of the resistivity to be used in these expressions is determined from the point source apparent resistivity graph.

The results obtained with these two methods are compared with the results from scale model studies and with the results from the refined methods for the multilayered grounds.

11. POINT SOURCE APPARENT RESISTIVITY

In a uniform soil, the voltage produced by a point current source S near the surface of the ground at a point P also near the surface of the ground is given by[X]:

Where I = current discharged by S. p = resistivity of the soil. x = distance between S and P.

At a site direct measurement of V and 1 for a spacing x between S and P are made. For these measurements a vertical linear electrode of length less than 1/5th of the spacing x may be considered as a point electrode. To obtain reasonable accurate results the remote current and potential probes C, and Pz respectively, should be located at a distance of about 10 times the value of "x", from the point current source S. To avoid mutual coupling between the leads the angle between S-C, and S-P, should be about 90'. Using measured data for various values of x, the resistivity of the soil is determined from equation (1 ). This is the apparent resistivity of the soil, pa, between the points S and P. When the soil is heterogeneous pa will change with x.

The relation between pa and x is independent of the location of the source and the direction of x if the soil is horizontally stratified. In practice this is not true; but as the variation of the resistivity in the vertical direction is generally more than the variation in the horizontal direction, the relation between pa and x does not vary much with the location of S and directions of x within the switchyard area. A mean graph of pd vs x over the area of the switchyard for a number of point source locations and directions of x is obtained.

Because of the large distance between the probes the method of measurement outlined above may not be convenient to use in all situations. For such cases the source point apparent resistivity can be indirectly determined from the data obtained with the Wenner Four Probe Method, which is commonly used to measure the resistivity of the soil. Let paw(x) be the resistivity obtained with the Wenner Four Probe Method for a spacing of "x" between the adjacent probes. The following equation gives the relation between the point source apparent resistivity, pa , and the Wenner resistivity, paw @I:

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A convenient procedure to estimate p,(x) from the Wenner resistivity paw(x), is given below:

(a) paw(x) versus x graph is obtained for various values of x upto a value of x large enough so that p,,(x) does not change appreciably with further increase in x. (b) From this graph note paw for x equal to 1,2,4,8,16,32,64 ...... m. (c) Start at a high value of x beyond which paw(x) does not change appreciably. Suppose this value of x is 128m. At this point consider paw( 128)=p,( 128) (d) pa for the next lower value of x, i.e. 64m, is then calculated from equation (2). (e) pa at the next lower value of x, i.e. 32m, is then calculated and this procedure is continued until the pa for the lowest value of x is determined.

An illustration of getting pa(x) from paw(x) will be found in Table 3.

111. DIRECT METHOD

To calculate the ground resistance of a horizontal grid, the point source apparent resistivity graph obtained with both the source and the observation point at the depth of the grid is required. Whereas to calculate the mesh and step voltges, the point source apparent resistivity graph obtained with the source point at the depth of the grid and the observation point at the surface of the ground is needed.

A grounding grid is usually buried at a depth of 0.5 m. For this depth there is only a little difference between the two apparent resistivity graphs mentioned above. Therefore, as an approximation the apparent resistivity, pa, obtained with both source and the observation point near the surface of the soil may be used to calculate the ground resistance, the mesh and the step voltages.

A computer program "NUGL" has been developed by the authors, to determine the ground resistance, the mesh and step voltages. This program is based on the modified form of the commonly used method of analysis in which the grid is divided in small linear segments. The following modifications are adopted.

(a) To determine the self ground resistance of a small linear segment, the apparent resistivity, pa, for x=r is used. Where r is the equivalent radius of the linear segment given by:

Where I, = length of the segment

a = radius of the segment.

(b) To determine the mutual ground resistance between the two small segments p and q the apparent resistivity, pa. for x=pq is used. Where pq is the distance between the centers of the two segments.

(c) To determine the potential at a point m on the surface of the ground because of the current discharged by a segment p, the apparent resistivity p, for x=pm is used. Where pm is the distance between m and the center of the segment p.

results appreciably. However, the computer program can be extended to include the vertical rods of large lengths. To do this, additional measurements of the resistivity are needed to determine the apparent resistivity of the soil with the source and the observation points at various depths.

The computer program NUGL should give good results as it is based directly on the potential measurements made at the site and does not require the modelling of the soil. The validity of the computer program was tested with the scale model tests described in the next section.

IV. MODEL TESTS

Analog model studies were conducted in a cylindrical tank of about 2 m diameter, filled with tap water to a depth of about 10 cm. The inside cylindrical surface of the tank was lined with aluminum foil to act as the collecting electrode for the current. Tests were conducted in two widely different cases of heterogeneous soil. The lower layer of the soil had infinite resistivity in one case and zero resistivity in the other case. These cases were simulated by lining the bottom of the tank (a) with a non conducting plastic sheet and (b) with an aluminum foil connected to the aluminum foil on the cylindrical surface, respectively.

The apparent resistivity was obtained by discharging a current of about 30 mA through a 12 AWG probe placed vertically at the center of the tank with a length of about 1 cm dipping in the water. Voltage between the collecting electrode and points on the surface of the water at various distances from the probe was measured. From these measurements the graph of apparent resistivity, pa , versus the distance x from the probe was obtained. The graphs for the two cases, AR1 (lower layer of infinite resistivity) and AR2 (lower layer of zero resistivity) are shown in Figure 1 .

The following models of the square grids made of 12 AWG bare copper wire were tested in the tank.

1. 20 cm x 20 cm, 4 meshes. 2. 20 cm x 20 cm, 16 meshes. 3. 30 cm x 30 cm, 4 meshes. 4. 30 cm x 30 cm, 16 meshes.

The model was suspended horizontally at a depth of about 1 cm and a current of 0.1A to 1.0A was discharged through it. The ground resistance and the mesh potential at the center of the corner mesh were measured in each case. These experimental values were

P. ohm-m

The program is good for grounding grids without vertical Presence of a few short vertical rods does not change the rods.

x. cm. Figure I - Apparent resistivity of the two models of the soil.


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compared with the calculated values using the computer program "NUGL". Both sets of values are shown in Table 1.

A comparison of the values in Table 1 shows that the results obtained from the computer program NUGL both for the ground resistance and the mesh voltage are close to the model test results. The data given in Table 1 also shows that for the two widely different models, AR1 and AR2, of the ground, the ground resistance of a grid is very different whereas the mesh voltage is not. This clearly shows that the equivalent resistivity of the medium to be used for ground resistance calculations is different from the one to used for the mesh voltage.

U Figure 2 - Model of a grid for ground resistance calculations.

V. EQUIVALENT RESISTIVITY

A . Ground Kesisturtce

The ground resistance, R, of a grid in uniform soil is given by [1J: Where I, = current that flows from the plate to ground.

p,(x) = the point source apparent resistivity at distance x.

The total potential at the center of the plate is given by: R = p a (4)

(5) ( 7 )

Where p = resistivity of the soil, ohm-m. L = the length of the buried conductor, m. A = the area occupied by the grid, sq.m. h = the depth of the grid, m.

Consider Vfl, to be the ground resistance, R.

The ground resistance of a grid in heterogeneous soil can be calculated conveniently with the use of equation (4) if the equivalent resistivity of the soil to be used in the equation can be estimated.

Let per, (independent of x) be the equivalent resistivity of the soil that gives the same ground resistance, R.

Practical grounding grids are buried near the surface of the earth and have usually more than 30 meshes. Their ground resistance is close to that of a circular plate whose area is equal to the area occupied by the grid. Consider a circular plate of diameter 6 buried horizontally near the surface of the earth. Assume that the current dissipation over the surface of the plate is uniform. The potential at the center of the plate due to an elemental ring of radius x and thickness Ax, as shown in Figure 2 is given by [ 5 ] :

From equations (8) and (9)

Table I - Ground Resistance and Mesh Voltage.

Apparent Test Results Computer Results

Graph Resistance Voltage Resistance Voltage Gridr Resistivity Ground Mesh Ground Mesh

Therefore, per is the average value of the point source apparent resistivity of the soil from x=0 to x=6/2. 20x20~4 AR1 163

20x20~4 AR2 47.7 16.4 174 15.8 49.6

14.3 14.2

20x20~16 ARl 158 20x20~16 AR2 43.8

5.7 17 1 5.1 48.3

6.4 4.6

B. Mesh Voltage

In a uniform soil the mesh voltage is given by [11:

Em = P I, P (1 1)

P = K , Y / L (12)

K, = 0.656 + 0.172 n (13)

30x30~4 AR1 129 30x30~4 AR2 30.9

10.3 135 11.2 28.8

10.5 13.9

30x30~16 AR1 125 30x30~16 AR2 24.2

5.8 133 4.1 26.5

6.7 4.1

The ground resistance is in ohms. The mesh voltage is in volts per ampere current discharged by the grid.

* Length, cm x Width, cm x Number of meshes.


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ohm-m P. 4ooo- ,":

Figure 3 - Model of a grid for mesh voltage calculations.

[

K,, = 1424'" for grids with no rods or grids with only a few rods, none located in the corners or on the perimeter.

K,, = 1 for grids with ground rods along the perimeter or for grids with ground rods along the perimeter and throughout the grid area.

K, = I/(l+hj

Where D = spacing between the parallel conductors, m. h= depth of the grid conductor, m. n = number of the parallel conductors. d = diameter of the grid conductor, m. I, = grid current that flows from the grid to the ground, A.

To estimate the equivalent resistivity, pem, of the heterogeneous soil that can be used in equation ( 1 I ) , consider the grid as a circular plate of diameter 6. A mesh with a conductor spacing of D may be represented by a circular hole of diameter D at the center of the plate as shown in Figure 3. When this plate is buried horizontally near the surface of the ground, the potential, V,, of the ground surface at the center of the mesh (hole in the plate), for Di<6, is given by:

From equation (7) and (15) the mesh potential is obtained as

If pen, (independent of xj is the equivalent resistivity of the soil that gives the same mesh voltage, E , , then

From equation (16) and (17)

(18)

Therefore, p., is the average value of the point source apparent resistivity of the soil from x=O to x=D/2.

C. Step Voltage

The major contribution to the step voltage comes from the conductors of the grid which are near to the location where the step voltage is calculated as the conductors located farther away produce about the same voltage at the location of the two feet. The step voltage is normally calculated with one foot above the corner the grid. The equivalent resistivity p,, for calculating the step voltage can be taken as approximately equal to the point source equivalent resistivity at x=h. In practical cases the step voltage is not as critical as the mesh voltage. Therefore, any refined estimation of the equivalent resistivity for the step voltage was not attempted.

VI. VERIFICATION

To verify the equivalent resistivities given in the previous section, five point source apparent resistivity graphs shown in Figures 4 and 5 were considered. These graphs represent approximately the point source apparent resistivity of the heterogeneous soils at the following five locations:

a. Reston Substation, Bonneville Power Administration.[Y]. b. E. Omak Substation, Bonneville Power Administration.[ IO]. c. W. Davenport Substation, Florida Power Corp.[ll]. d. Bayridge Substation, Florida Power Corp.[ 111. e. Texas Valley Substation, Georgia Power Company.[ 121.

x, meters Figure 4 - Apparent resistivity (a).

3000 ! .

:,, 1

x, meters Figure 5 - Apparent resistivity (b, c, d , e)


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Following four square grids made of 4/0(1.2cm dia.) conductor, at a depth of 0.5 m were considered:

1. 30m x 30m, 16 meshes. 2. 30m x 30m, 25 meshes. 3. 32m x 32m, 64 meshes. 4. 80m x 80m, 64 meshes.

Table 2 - Verification of the Equivalent Resistivities.

Equivalent Resistivity, ohm-m

Soil Grid per (Grd. Resist.) pem (Mesh Voltage) # #

From From From From NUGL pa graph NUGL pa graph

a a a a

b b b b

C C

C

C

d d d d

e e e e

1 3216 2 3242 3 3350 4 4327

1 1883 2 1892 3 1900 4 1800

1 1823 2 1794 3 1697 4 1057

1 1175 2 1090 3 999.8 4 803.8

1 294.4 2 288.1 3 271.4 4 211.0

3016 3016 3083 4394

1961 1961 1965 1905

1958 1958 1882 912.7

927.4* 927.4* 905.6 633.2*

277.6 277.6 268.0 173.2

1996 2021 208 I 2548

1639 1674 1731 1655

3037 2984 2853 2364

3320 2913 2357 2678

587.2 555.0 505.9 506.3

2227 2182 2124 230 1

1709 1688 1660 1745

2845 2895 2961 2761

1912* 2126* 2407 1555*

486.5 508.8 538.2 449.3

* q > l

Table 3 - Soil Resistivity

Soil Resistivitv. ohm-m x, m S y n d g e W.Davenport Texas ‘3) Valley

T-x- Paw@ P a P a w P a

1 4000 3089 3200 3048 630 555 2 3500 2179 3200 2896 600 480 4 1000 857 3000 2593 480 360 8 800 715 3500 2186 340 240

16 800 630 1500 872 170 140 32 700 460 400 244 110 110 64 280 220 90 88 110 110 128 160 160 86 86 110 110

( 1 ) and ( 2 ) - The data is from the graphs in reference [ l l ] (3) - The data is from the graph for winter in reference 1121

The ground resistance and the mesh voltage for all the 20 combinations of the soils and the grids were determined with the computer program NUGL. The parameters a and p for all the grids were calculated and the current I, was taken as unity. From equations (4) and (1 1) the equivalent resistivities for the ground resistance and the mesh voltage were calculated. The results of the calculations are given in Table 2. This Table also gives the equivalent resistivities determined from the point source apparent resistivity graphs with the use of equations (10) and (18).

Since equation (10) and (18) have been developed considering the grid as a plate, the values given by these equations are good if the variation of the apparent resistivity with respect to the spacing between the conductors is not large. Study of a number of cases shows that these equations give good results if the following unitless ratio, q, is less than 1.

Where U = slope of the point source apparent resistivity graph at

p =Maximum value of the point source apparent resistivity, x=O, ohm-m/m.

ohm-m.

In most practical situations q < 1. Table 2 shows a close agreement between the equivalent resistivities obtained from the detailed calculations done by the computer program NUGL and from the point source apparent resistivity graphs. For q < 1, the difference is less than 20%.

The method of equivalent resistivity is compared with the two layer and multilayer methods for the following three stations:

1. Bayridge Substation, Florida Power Corp. 2. W. Davenport Substation, Florida Power Corp. 3. Texas Valley Substation, Georgia Power Company.

The Wenner soil resistivity,p,,, data for these stations is given in Table 3. From this data the point source apparent resistivity, pa, is calculated and is tabulated in Table 3. The grid data is given in Table 4. The ground resistance and the mesh voltage calculated with the equivalent resistivity method and with two layer and multilayer models are given in Table 5. The results show that the values obtained from the equivalent resistivity method are close to those obtained from the two layer and multilayer models.

Table 4 - Grid Data

Items Bayridge“’ W.Davenport‘” Texas Vall@’

Area of grid, sq.m 3969 1951 3561 Length of buried cond, m 2772 530 1289 Depth of grid, m 0.5 0.5 0.5

Spacing between cond, m 3 9 5.7 Dia. of grid cond, cm 1.2 1.2 1.2 Number of parallel cond. 22 6 12

( 1 ) and ( 2 ) - The data is from reference / I 1 1 (Bayridge 4 and West Davenport 2). (3) - The data is from reference [I21


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Table 5 - Comparison of Results ~

Items Bayridge* W.Davenport* Texas Vallep*

Equiv. resistivity for 703.8 1465 194.8 ground resistance, perQ-m

Equiv. resistivity for 2545 2794 513.2 mesh voltage, p,,Q-m

Equation (10)

Equation( 18)

Ground resistance, ohm Equiv. restvty method 5.16 17.2 1.56

Multilayer model 5.25 20.3 2 layer model 5.77 11.7 1.1

Mesh voltage, V per Amp Equiv. restvty method 2.14 8.97 0.80 2 layer model 1.8 7.6 0.66 Multilayer model 1.9 6.1

*Data for 2-layer and multilayer models is from reference [ I l l **Data for 2-layer and multilayer models is from reference [I21

VII. CONCLUSIONS

1. The two methods for calculating the grounding parameters presented in this paper do not require a knowledge of the underground soil structure that is usually complex. Only the point source apparent resistivity of the soil at the site is needed. This can be either measured directly at the site or obtained from the Wenner Four Probe resistivity measurements.

2. A computer program, based on the direct method has been developed. This program does not require to model the heterogeneity of the earth as it is based directly on the potential measurements made at the site. Model testing has shown that it gives good results.

3. The method to determine the equivalent resistivity of the soil given in the paper is simple. The use of the equivalent resistivity in the expressions for uniform soil gives reasonably accurate results.

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5.

VIII. REFERENCES

"IEEE Guide for Safety in AC Substation Grounding", ANSI/IEEE Std. 80, 1986.

F. Dawalibi and Dinkar Mukhedkar, "Optimum Design of Substation Grounding in a Two Layer Earth Structure, Part I - Analytical Study", IEEE Transactions on Power apparatus and Systems, vol. PAS - 94, pp. 252-261, 1975.

R.J. Heppe, "Step Potential and Body Currents Near Grounds in Two-layer Earth," IEEE Transactions on Power Apparatus and Systems, vol. PAS - 98, pp. 45-59, 1979.

A.P. Meliopoulos, R.P. Webb and E.B. Joy, "Analysis of Grounding Systems," IEEE Transactions on Power Apparatus and Systems, vol. PAS - 101, pp. 1039-1048, 1981.

J. Zaborszky, "Efficiency of Grounding Grids with Nonuniform Soil," AIEE Transactions, pt. I11 (Power Apparatus and Systems), vol. 74, pp. 1230-1233, 1955.

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12.

B. Thapar and E.T.B. Gross, "Grounding Grids for High Voltage Stations. IV - Resistance of Grounding Grids in Non- unform Soil," IEEE Transactions on Power Apparatus and Systems, vol. 82, pp. 782-788, 1963.

B. Thapar and J.K. Arora, "Step and Mesh Potentials at High Voltage Stations in Non-uniform Soil," Proceedings, 43rd Annual Research Session, Central Board of Inigation and Power, India, vol. IV (Power), 1973.

E.D. Sunde, "Earth Conduction Effects in Transmission Systems," (book), Dover Publications, Inc., New York, 1968.

A.L. Kin yon, "Earth Resistivity Measurements for Grounding Grids," AIEE Transactions, Pt.111 (Power Apparatus and Systems), vol. 80, pp. 795-800, 1961.

"Soil Resistivity Analysis at East Omak Substation Site", Department of Energy - Bonneville Power Administration, Laboratory Report No. ERGJ-8 1-4, 198 1.

F. Dawalibi and N. Barbeito, "Measurements and Computations of the Performance of Grounding Systems Buyried in Multilayer Soils", IEEE Transactions on Power Delivery, vol. 6 PWRD, pp. 1483-1490, 1991.

"Seasonal Variations of Grounding Parameters by Field Tests", Electric Power Research Institute, EPRI TR - 100863, 1992.

Baldev Thauar (M'60, SM'62)was bom in India on Sept. 1, 1930. He received the B.Sc.(Honours) degree from Banaras Hindu University, M.S. and Ph.D. degrees from Illinois Institute of Technology, in 1953, 1960 and 1963 respectively, all in electrical engineering.

From 1953 to 1955 he was with Punjab Public Works Department, India, working in Power System Operation. In 1955 he joined the

faculty of Punjab Engineering College, Chandigarh, India, where he was Professor, Electrical Engineering from 1966 to 1985. In 1985-86 he was a visiting Professor at Louisiana State University. At present he is a Professor in the faculty of Electrical Engineering Department, Montana State University, Bozeman.

Dr. Thapar is a Fellow of Institution of Engineers (India). He is a member of Eta Kappa Nu, Tau Beta Pi and Sigma Xi. His research interests are in electric power system analysis, protection and grounding.

Victor G e m (SM) was bom in Santander, Spain, on April 11, 1934. He received his Engineering degree from National University of Mexico and his M.S. and Ph.D. degrees from the University of California at Berkeley in 1958, 1969 and 1972 respectively, all in electrical engineering.

From 1958 to 1965 he was an electrical design engineer in several Mexican companies. From 1966 to 1973 he was a member of the

technical staff of Mexico's National Utility. In 1973 he became chairman of the Mechanical-Electrical Engineering Department at the National University of Mexico. In 1977 he was named director of the power system division in Mexico's Electric Research Institute. He joined the Electrical Engineering Department at Montana State University in 1983 and became chairman in 1984.

Dr. Gerez is the author of several articles on system and power engineering and co-author of six electrical and system engineering textbooks widely used in Spanish speaking countries.


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D I S C U S S ION

Hans R . Seedher and J. K. Arora (Punjab Engineering College, Chandigarh, India) : The authors are to be complemented for presenting two methods for obtaining performance of grounding grids using measured soil resistivity data !:stead ' o f a soil model based on the measured data. The designer is thus not constrained to use a simplified soil model for a complex variation in measured Wenner resistivity. The equivalent resistivity concept is useful in extending the well known formulae applicable to uniform earth to the case of non-homogeneous soil.

The discussers would appreciate authors' comments about the following: i)

ii)

Point source apparent resistivity p is to be obtained from the measured values of Wenner apparent reistivity paw. In order to use (2) for obtaining pa, Wenner apparent resistivity measurement must be made for electrode spacing large enough so that paw does not change appreciably with further increase in electrode spacing. For a relatively large resistivity of the lower stratum, required maximum electrode spacing would be impracticably large. For example, for a two layer earth structure with a ratio of lower to upper soil resistivities equal to 50 and depth of upper layer equal to 5 m, the required electrode spacing would be about 500 m. Unless the measured apparent resistivity curve is available upto this spacing, extrapolation might be needed, and determination of pa by (2) might lead to large error. From measured paw, values of p can be obtained only for discrete values of x . How are the values of pa for other values of x required for computing self and mutual resistances and for earth surface potentials computed in NUGL.

iii) The expressions for equivalent resistivity developed in the paper may not be justified for configuration of a grid differing considerably from that of a square grid with square meshes; and it is rare that a practical grid is square shaped with square meshes.

Manuscript received August 9, 1994.

F. P. Dawalibi, Safe Engineering Services & technologies ltd, Montreal, Quebec, Canada, H3M 1G4.: My first reaction when 1 read this paper was that it introduced a novel and interesting method. However, afier carefully reviewing all aspects of the engineeiing process which takes place during a realistic grounding design, it became very clear to 11ic that one should avoid using the approach described in this paper for the reasons outlined hereafter.

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1.

2.

3.

No proof, or upper-bound error analysis is provided to demonstrate that the response of a point source electrode at the surface of the soil will be a good approximation to that of a conductor segment buried at a depth of 0.5m or more in various soil structure models. It is incorrect to state that the apparent soil resistivity between a current source and an observation point is dependent only on the separation between them. The buiial depths in hoiizontally layered soils and relative locations of the source and observation point in vertically hyered soils as well as sphcricully layered soils inay have a significant eflcct on the response. Our expericnce reveals that the response of a conductor scgment close to rhc interl'aoe of two horizontal layers with a high resistivity contrast may be quite different froin the response of a point source at the surface of the soil. The use of complex mathematics in modern engineeiing software is transparcnt to the user and should not be a dctencnt or a justification for using or not using a specific method, Many time-consuming computations are based on simple mathematical approaches while very coinplex analytical method inay very well be computationally inexpensive. A typical example of this is illustrated by hemispherically laycred soils. What should matter is the fitness of a particular approach for coinplcring a specific: design task. It appears t o me that rhc paper is trying to address a non-cxistcnt problcin. A carchil investigation of the situations in which the novel approach of the paper can be used inay reveal other types of problems to which it could be applied successfully. Grounding does not appear to be one of them at this time. Ironically, exactly the same reasons given by the authors to justify the use of their new approach can be invoked to strongly oppose their suggestion. "Changes caused by weather and season, by rain and frost and by temperature variations ..." affect only top soil resistivities up to a depth which rarely exceed one or two meters. Because of this, a sound engineering design of any grounding system may take into account the resistivity


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variations of the top layers and the worst case scenario should constitute the basis for the final design. This is easily done when one has determined a suitable model for the soil stmcture. Moreover, "what if" types of questions can be easily answered during the design stage when a soil structure model is available. For example, questions such as "what if a thin layer of water is above the soil surface ..." or "what if the surface layer is frozen or thawed...", etc. There is a fundamental difference between inability to obtain accurate data and normal variations of data for which upper and lower bounds are easily obtainable. Soil resistivity measurements should be used to develop approximate soil models, not only to calculate grounding system perfoiniance but also to determine the most appropriate design €or the kind of soil model encountered ( use of short versus long ground rods, use of equal or unequal conductor spacing, etc.). Last but not least, since the method, as admitted by the authors themselves, is restricted to cases in which the soil model has horizontal layers only and the grounding system is only in the top layer with no conductors penetrating the other layers, the designer is confronted with the contradictory requirement of determining the soil structure to insure that he is not violating the preceding require men t s.

The authors' reply to our comments would be greatly appreciated.

Manuscript received August 15, 1994.

BALDEV THAPAR, VICTOR GEREZ: The authors thank the discussers for their comments and the interest shown by them. Since most of the questions raised by the discussers relate to the layered soil models, first of all we would like to comment on the application of these models. Layered soil models are useful for the analysis of the grounding systems in heterogeneous soils. However a misconception has developed in recent times that these models are good for the analysis of the grounding electrodes located anywhere in the soil. This needs to be corrected.

Two layer or multilayer soil models are developed from the test data obtained either from the Wenner Four Probe Method or Driven Rod Method. The Wenner test is

conducted with the source and the observation points both on or near the surface of the soil. Therefore, in general, a model developed from Wenner test data is good only for the conductor segments that are at or near the surface of the soil. If the conductor segments are not near the surface of the soil then the two layer model may give erroneous results unless the soil is actually made of the two distinct layers as determined in the model. This is apparent from the following simple example.

In most of the soils the resistivity gradually changes with the depth. Consider a soil where the resistivity,p, changes with the depth,z, according to the following equation:

p = 100+9900 Ohm-m

Applying the method given by Sunde [Cl], the Wenner Four Probe Test data for this soil is calculated and is given in Table C1. For this data the computer program "SOMIP" gives the following best estimte of the two layer soil model.

= 3293 ohm-m = 101 ohm-m = 3 m

Resistivity of the top layer Resistivity of the bottom layer Depth of the top layer

I

TABLE Cl - WENNER FOUR PROBE DATA

1 2 4 8 16 32 64

6640 4485 2075 533 126 100 100

Figure C 1 gives the variation of the resistivity with the depth of the actual soil and of its two layer model.

Now consider a sphere of radius 10 cm at a depth of 4 m. The ground resistance of the sphere is primarily determined by the resistivity of the soil around it up to a distance of about 10 times the radius of the sphere (1 m in this case). The resistivity of the actual soil up to a distance of 1 m


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around the sphere varies from 600 to 2000 ohm-m (an average value of 1300 ohm-m). In the two layer model the resistivity up to a distance of 1 m around the sphere is 100 ohm-m. Therefore the two layer model will give the pound resistance of the sphere approximately 80 ohms [ lOO/(4XO.1)], whereas the actual ground resistance is approximately 1035 ohms [1300/(47d).l)]. There is a difference of order in the two values. Hence, the error in using a two layer soil model in this case is enormous and is not acceptable even in grounding practice.

A similar situation will occur with the practical linear electrodes when they are not near the surface of the soil. Vertical rods which are near the interface of the two layers will not have the same response in a two layer model as in an actual soil where the resistivity varies gradually.

The soil model obtained from the driven rod test data is also not unique. It can be shown that this model is good only for driven rods which are of approximately same length as those used to determine the test data. This model may give erroneous results for other configurations of the grounding electrodes unless the model matches the actual soil conditions.

An ideal two layer stratification is seldom encountered. A two layer model of the soil obtained from the Wenner test data is good to be used for the conductor segments which are near the surface of the soil. For the segments which are deep in the soil, this model is not applicable and may give erroneous results for most of the soils where the resistivity changes gradually with the depth.

Now we shall answer the specific questions raised by the discussers:

F.P. Dawalibi

1. When conducting Wenner Four Probe resistivity test, in most of the soils it is necessary to drive the probes to a depth os 15 cm or more. Electric field strength because of these probes at a distance of more than 1 m becomes identical with that for a point source. As mentioned in the paper the source and the observation points are near the surface of the soil. Through a number of field measurements we have experienced that no significant difference is noticed in the apparent resistivity if the source and the observation points are at a depth of 0.5 m or 0.15 m. However this will not be true in a very rare case when a distinct stratification of the soil with large variation of the resistivity occurs very near to the surface of the soil. In that case the measurements can be made with the source a a depth of 0.5 m and the observation points near the surface

and at a depth of 0.5 m. Because of the nature of the problem the upper bound error analySis is considered needless.

2. The layered soil models using complex mathematics do not give good grounding design in every case. As shown above these models have limitations. Unless the actual soil conditions are known, the layered soil models, horizontal or spherical, cannot be claimed to give good design. The method presented in the paper uses the actual response of the electrodes directly without resorting to any model. It gives reliable results.

3. The practical worst case scenario for any particular case can be determined through measurements and for that the assumptions and the modelling are not necessary. What is needed is to make the resistivity measurements at a suitable time. Cold dry season will give the highest resistivity measurements.

4. The layered soil models have some applications but the analysis of the vertical ground rods is not one of these unless the actual soil conditions match the model. We are working on extending the method given in the paper to include the vertical ground rods. This will be reported soon.

5. In the methods given in the paper we do not assume any distinct horizontal stratifkauon of the soil.

Hans R. Seedher and J.K. Arora

i) If the Wenner method is used and the resistivity measurements cannot be made for large spacing, it would be necessary to make extrapolation. That may introduce some judgement errors. In such cases it would be better to make the point source apparent resistivity measurements directly as described in the paper.

ii) Using the method of least squares a polynomial function to fit the known points of pa versus x is obtained. This function can then be used to determine the value of pa for any value of x.

iii) The equivalent resistivities developed in the paper can be used for the grounding grids which are nearly square. Model studies have been conducted to check the validity of the equivalent resistivities for rectangular grids having width to length ratio up to 1:3. This covers most of the grids encountered in practice.

[Cl]. E.D. Sunde, "Earth Conduction Effects in Transmission Systems;' (book), Dover Publications, Inc., New York, 1968.

Manuscript received October 26, 1994.


grounding resistance

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