IEEE Transactions on Power Apparatus and Systems, Vol. PAS-99, No. 5 Sept/Oct 1980

PREDICTION OF SOIL RESISTIVITY AND GROUNDROD RESISTANCE FOR DEEP GROUND ELECTRODES

C. J. Blattner, Senior Member IEEENiagara Mohawk Power Corporation

Syracuse, New York

ABSTRACT - A technique for the prediction of soilresistivity and ground rod resistance for deep groundelectrodes has been developed. The methodextrapolates limited test ground rod data to a factorof up to ten times the known depth values. Thetechnique has been shown to accurately predict theeffectiveness of installing deep ground electrodesand the predicted results are compared to actualfield test results.

INTRODUCTION

Initial substation ground system designs arequite often based on a limited number of preliminaryground rod test measurements. On occasions, we havefound that the test ground rods were driven to adepth of only two (2) meters or less before a layerof rock had been encountered. Generally, in thissituation, the top layer of soil has a relativelyhigh value of resistivity. As a result, the designermust consider the options of installing an extensiveground system utilizing the known soil conditions ofthe top layer of soil or he can consider the probableeffectiveness of installing deep ground electrodes.To accurately assess the probable effectiveness ofdeep ground electrodes, additional information on thelower soil layers is required. This data is notusually available except by additional tests such asthe Wenner four pin method [1] [2] [6] [7] or a trialinstallation of a deep ground electrode. This paperdescribes a new technique for the extrapolation ofthe known original test data as a basis forpredicting the probable soil resistivities and groundrod resistances for deep ground electrodes at thissite. The predicted values can then be used toassess the probable effectiveness of the deep groundelectrodes in the evaluation of alternate groundsystems.

The problem of trying to predict soil resistivityis not unlike trying to predict the weather. Theearth resistivity is a very variable quantity and theonly safe way to know the value at given time of yearis to measure it. [2] As was stated in a recentpaper [3] there should not be any "illusions" thatstrict accuracy is to be expected. However, thetechnique presented herein should produce results ofsufficient accuracy for the purposes intended in thispaper.

The term soil resistivity in this paper is definedas the effective soil resistivity for calculating theresistance of a rod electrode driven to a given depth.

F 80 174-3 A paper recommended and approved by theIEEE Substations Committee of the IEEE PowerEngineering Society for presentation at the IEEE PESWinter Meeting, New York, NY, February 3-8, 1980.Manuscript submitted August 6, 1979; made availablefor printing October 30, 1979.

ANALYSIS OF THE METHOD

The objective of this study was to develop amethod to extrapolate known test rod data to tentimes the known test rod depth and within reasonableaccuracy. The initial effort was to formulateequations which would approximate the behavior ofknown resistance values for actual deep test groundrods for depths up to 20 meters. It soon becameapparent that it was easier to formulate equationswhich duplicated the soil resistivity values ratherthan the rod resistance values. The rod resistancevalues could then be calculated easily by use ofpublished formulas. [4] [5] As might be expected, alogarithmic type curve best approximated the actualvariation of soil resistivity with increasing depth.A general equation was developed which closelyduplicated the actual soil resistivity curves forindividual known ground rod test results:

P= PO - A ln Bx

Where px soil resistivity value depending ondepth

po = known soil resistivity value at or nearthe surface

x = distance between Px and poA&B are constants peculiar to each rod and

determined from the known data

An empirical relationship was eventuallyestablished between the known values of soilresistivity and rod resistance within the first fewmeters of depth which closely approximated the "B"constant value. This reduced the problem to thesimple "one equation and one unknown" situation sothat the constant "A" value could be determined fromthe known values of soil resistivity at the samedepths. With the resolution of the "A" and "B"constants problem, the basis was established for thedevelopment of a more generalized equation whichcould be used for the extrapolation of known soilresistivity values. This equation can be expressedas follows:

Px = PO - kp (b + ln x) (1)

Where px = soil resistivity to be determined at adepth Lx

po = known value of soil resistivity at adepth Lo

(Note: depth Lx is always greater than Lo)kp = soil resistivity constantx = distance in meters between Lo and Lx

= Lx - Lo2 x Ro x 1.6] a (2)b =

Po X RpO = known value of soil resistivity at a

depth Lo= known value of soil resistivity at a

depth greater than LoRo = known value of rod resistance at a

depth LoR2 = known value of rod resistance at same

depth as P2a±=±l

= + 1 if P2 is less than po (P2<po)- - 1 if P2 is greater than pO (P2>Po)

0018-9510/80/0900-1758$00.75( 1980 IEEE

1758

1759

To verify the accuracy of equation (1),extrapolation of known ground rod test results wasmade by selecting known values within the first fewmeters of depth and then projecting the soilresistivity values to the actual depths obtained.Figures 1 through 4 show a comparison of actualvalues and projected values for four different typesof soil conditions. The arrows indicate the valuesselected for the basis of the projection. Afavorable comparison has been obtained for themajority of the known test rod results used.

- Actual

Projected

SOILC-IaN

"II

0Mi

(D

N.

a

I

~0

mu

I I I I I I I I I I

O 1 2 3 4 5 6 7 8 9 10DEPTH (meters)FIGURE 1

Iom

I

:0UaUam

a .

ED-

No .

,4

a0

:~~~~~gA\ SAND

a. l-. i i i I a i 1

o 1 2 3 4 5 6 7 8 9 10111213141516DEPH ( )

FIGURE 4

SAMPLE CALCULATION

Table No. 1 gives the values of soil resistivityand ground rod resistances obtained from an actualground test.

Depth R p

OhmMeters Feet Ohms Meters

0.6 2 1200* 975*1.2 4 1200 16981.8 6 1150 22712.14 8 1150 28863.1 10 1100* 3328*

*values used for projection

Ground Test Data

Table No. 1

First determine b from equation (2), then settingPx=P2, solve for kp from equation (1) using Lo = 0.6meters and Lx = 3.1 meters.

0 2 4 6 8 10 12 14 16 18 20 22 24

DEPTH (meters)FIGURE 2

where p0 = 975 Om and Ro = 1200QP2 = 3328 Om and R2 = llOOQx = 3.1 - 0.6 = 2.5 metersa = -1P2>Pl

then b = 3328 x 1200 x 1.61 -1 0.168L9714 x 1100o

and kp = Po Px - 975 3328 -2353 - -2179b -n 0.168 + ln 2.5 1.08b + lnlx

The general equation for this test ground rod can beexpressed as:

Px = 975 - (-2179)[0.168 + ln x]= 975 + 2179 [0.168 + in xJ

1,1 1 :1I111 1

(3)

DEPTH (meters)FIGURE 3

8 0

E y'4 R-

0 NX oa0

0 .8101241612022 42O 2 4 6 8 10 12 14 16 18 20 22 24 2Z; 28 30

-d

I

1760

Calculation for Px at Lx = 214.14 meters (80 feet)using equation (3)

x = Lx - Lo = 24.14 - 0.6 = 23.8 metersPx = 975 + 2179 [0.168 + ln 23.8]

= 8248 Qm

Calculation for Rx at Lx = 24.4 meters using equationdeveloped by A. B. Purdy [5]

Rx 2Px [(Ln ) _l]

where d = .016 meters

Rx - 82482ir(214.14)

L(Ln 8(24.4) ) - 1_ .016_

= 4520

The actual field test at this depth = 14500

APPLICATION

The technique was used to predict the soilresistivity and ground rod resistance values at a new345 kV substation site. The preliminary test groundrods were limited to two meters or less in depth dueto an underlying layer of rock. The top soil layerhad a high soil resistivity value and the preliminaryground system designs indicated a very extensive gridarrangement would be required unless deep ground rodscould be used to lower the resistance of the groundsystem.

Using the preliminary ground test data from tentest rods, the soil resistivities and rod resistancesup to 20 meters were projected. Four actual testborings were made up to 10.7 meters (35 feet) and oneboring was extended to 12.2 meters (140 feet). Atabulation of the projected values and the actualvalues is shown in Table No. 2. A favorablecomparison was obtained between the average predictedvalues and the average actual values.

An analysis has also been made at anothersubstation site where the test ground rods werelimited to two meters in depth. The results from thethree test rods were projected to a depth of 21.3meters. Twelve test borings were made to a depth of7.3 meters with one boring extended to 21.3 meters.The available test data for the deep rods waslimited; however the average predicted valuescompared favorably with the average of the actualvalues. Table 3 shows a comparison of the minimumprojected values with the test values obtained withthe one 21.3 meter deep rod. The values obtained forthis ground rod were the minimum values of all therods tested. Note that in this table the soilresistivity increased with depth whereas in table no.2 the resistivity decreased with depth.

Calculation~~~~~~~~~~~foIxa x=2.4mtr et

Comparison - MinimValues

Table No. 3

Predicted Values Actual ValuesRange Avg

R P Value

Min Max Min Max R P

30 123 122 491 68 272

15 88 81 485 46 252

7 69 52 481 34 238

4 57 30 477 27 228

1 149 13 4714 23 219

143 4172 21 212

38 470 19 207

RangeR p

Min Max Min Max

AvgValue

R p.-45 80 183 325 66 269

35 55 196 308 46 273

30 50 212 354 39 274

20 60 170 510 31 266

16 35 168 346 22 215

14 24 157 269

12 - 151 -

17 194

Table No. 2

De th Predicted Actual(in)_R P R P

14.6 24 136 20 131

6.1 22 157 14 101

7.6 20 173 15 130

9.1 19 185 14 141

10.7 17 196 14 160

12.2 16 205 14 178

13.7 15 213 14 197

15.2 15 220 13 200

16.8 14 226 13 216

18.3 13 232 13 233

19.8 13 237 13 249

21.3 12 242 13 265

Depth

(m) (FT)

3 10

4.6 15

6.1 20

7.6 25

9.1 30

10.7 35

12.2 40

Depth

R P

1.5 3000 5097

2.4 150* 376*

3.3 80 262

m

5246

127

4.3 70 282 -20

5.2 42* 199* 92

Depth

(m) R P

1.5 3120 5301

1.8 1620 3199

2.1 1470 3300

2.4 957* 2401*

2.7 735 2036

3.1 528* 1598*

* - values for projections

Typical Test Ground Rod DataTable No. 4

PRACTICAL LIMITATIONS

For purposes of this technique, the individualtest ground rod projections should be averaged to beused as a guide for assessing the probableeffectiveness of installing deep ground electrodes.

Sufficient test rod measurements must be made toinsure a representative sample is obtained of thehorizontal variation in soil resistivity. Mr. B.Husock in his recent paper [3] provided a mostvaluable example of the possible variations in soilresistivity at one location.

An analysis of known test ground rod data hasdemonstrated that the accuracy of the predictions isgreatly effected by the rate of change of the soilresistivity over the readings obtained with thepreliminary test ground rods. If the rate of changeper meter is relatively constant, the more likely theprojection will be accurate. Consider the examplesin Table No. 4.

For rod no. 1, the rate of change of the soilresistivity is relatively constant and a projectionof the values shown will yield a good approximationof the actual ground rod test results. For rod no. 2the rate of change between 1.5 meters and 2.4 metersis a factor of several times greater than the rate ofchange below 2.4 meters. For this rod, the values at2.4 meters and 5.2 meters will yield a reasonablyaccurate projection. If the values at 1.5 meterswere used (R = 3000, p = 5097) the predicted soilresistivity would indicate negative values at depthsgreater than 6 meters. For rod no. 3 the rate ofchange does not become relatively constant until adepth of 2.4 meters is reached.

In a few instances, due to lack of sufficientfield data or variations in soil conditions, the rateof change of soil resistivity did not yield adiscernible trend and accurate projections have notbeen obtainable. Additional work is required toresolve this problem area.

CONCLUSIONS

A technique for the prediction of soilresistivity and ground rod resistance for deep groundelectrodes by extrapolation of known data has beendeveloped. The method has been shown to accuratelypredict the effectiveness of installing deep groundelectrodes and the predicted results compared toactual field test results. The limitations of thetechnique have also been reviewed.

ACKNOWLEDGEMENT

The author desires to thank William G. Weichertfor his help in the preparation of this paper.

REFERENCES

(1) IEEE Recommended Guide for Measuring GroundResistance and Potential Gradients in the Earth.IEEE Std 81-1962

(2) Manual on Earth - Resistance Testing, James G.Biddle Co.

(3) Husock, Bernard. A Statistical ProbabilityMethod for Soil Resistivity Determination. IEEEPaper A79 077-9

(4) IEEE Guide for Safety in A.C. SubstationGrounding. IEEE Std 80-1976

(5) Purdy, A.B. Accurate Equations for theCharacteristics of Rod Electrodes in a

Homogeneous Medium. IEEE Paper A79 027-4

(6) Kinyon, A.L. Earth Resistivity Measurements forGrounding Grids. IEEE Transactions PAS Dec 1961,page 795

(7) Thapar, B and Gross, E.T.B. Grounding Grids forHigh-Voltage Stations. IEEE Transactions PAS Oct1963, page 782

Rod #1 Rod #2 I Rod #3

Depth

(m).6

1.2

1.8

2.4

3.0

1761

R P

1200* 975*

1200 1698

1150 2271

1150 2886

1100* 3328*

m

-1207

-955

-1025

-737

APm

7007

-337

2997

1217

1460

1762

Discussion

F. Dawalibi (SF5, LTD. Montreal, Quebec, Canada): I would like tocongratulate Mr. Blattner for his novel technique for predicting soilresistivity.

The measurement methodology is similar to the "variation ofdepth" method described in guide IEEE 81 [ 1 but the analytical for-mulae and interpretation technique are different. This method lookspromising. Further work, however, is still required to better tune thetechnique and remove the major limitation of the method which asmentioned by the author, is related to the rate of change of soil resistiv-ity. I would like to discuss further this practical limitation.

I believe that the method willfail to give accurate predictions ifthe following conditions exist.

1. The next layer of soil is at a depth significantly larger than themaximum length of the rod; sayS times or more; (negligiblerate of change).

2. The next layer of soil is close to the surface layer and has aresistivity significantly different from the top soil (Abruptvariations of the rate of change per meter). For example, if thetop layer of soil has a much higher resistivity than the nextlayer, the resistance of the rod will decrease sharply as soon asit penetrates the deep layer. In contrast, if the top soil is sig-nificantly more conductive than the deeper soil, no noticeablechange of the rod resistance will be measured when the rodpenetrates the next high resistivity soil.

In order to improve this new technique, I suggest that an addi-tional parameter, namely, "effective top layer thickness" be used inequation (1). This new parameter should improve the method sincemost soil measurements indicated that soil could be simulated by anequivalent two-layer earth structure (Figures1 to 4).

I will appreciate the author's comments on the above discussion.Also, could the author comment on the merits of his method comparedto the classical Wenner resistivity measurement.

Manuscript received January 9, 1980.

Warren R. Jones (Rochester Gas & Electric, Rochester, NY): The authoris to be congratulated for developing his technique for predicting theresistance for Deep Ground Rods. It will greatly enhance groundingdesign in rocky soil where obtaining a low resistance to remote groundcan be a very expensive proposition.

I would like the author to respond to the following questions:1. Please define "Sufficient Accuracy" as used in the second para-

graph of the Introduction. Can we expect the results to alwaysbe within, let's say10% of predicted?

2. Please define the term "Effective Soil Resistivity" as used inthe third paragraph of the Introduction. I assume the actualtest borings you made were involved in obtaining the soil re-sistivity values. Please explain how these values were obtained.Was the Wenner 4 Pin method of obtaining soil resistivity usedin addition to your method? If so, how do they compare?

3. In your calculation of Rod Resistance you used a formulawhich was developed by A. B. Purdy in his paper entitled"Accurate Equations for the Characteristics of Rod Electrodesin a Homogeneous Medium."

Mr. Purdy's equation is for a vertical rod "in a homogeneousinfinite medium." Your application is most definitely a multi-layer soil.

Have you studied the problem using the 2 layer soil model?If so, how do the results using a single resistivity value torepresent a multi-layer soil compare to the 2 layer soil modelsolution? Can a 2 layer soil model be used to obtain resultswhere you found your method unable to make accurateprojections?

4. You report that "the preliminary test ground rods were limitedto two (2) meters or less in depth due to an underlying layerof rock," yet as part of the final design you report deep groundrods of up to twenty (20) meters being installed.How was the installation of these deep ground rods accom-

plished?

Manuscript received February 7, 1980.

Richard P. Keil (Dayton Power and Light Company, Dayton, Ohio): Iwould like to congratulate the author for his efforts in developing a newtechnique to predict the resistance of deep driven ground rods. The ad-vantages and use of deep rods have been advocated over the years bymany authors. This new technique can be used to predict the practicallimits for driving deep rods, and thus eliminate the many extra rods andvaluable construction time spent installing deep rods.

Using the author's method to predict rod resistances, I comparedthe average measured resistance for a group of ground rods to the cal-culated resistances. The reference points,po and P2, were 10 and 20feet. The predicted resistance value at 30 feet was 6.5% higher than theaverage test results. The resistance values of the tested rods varied by asmuch as a factor of two, indicating different lower soil layers at 30 feet.At 40 feet, the predicted resistance value was 2.2% lower than theaverage test values. In this case the resistance values of the tested rodsvaried by only 10%, indicating a more uniform layer at 40 feet. I feelthat in either case, the predicted resistance is well within an acceptablelimit for designing a grid system.

There are some questions I would like the author to comment on.Has this method been compared to the Wenner 4 pin method? If so, isthere good correlation? Since a relatively constant ratio of change ofthe soil resistivity is important for an accurate prediction, could the 4pin method be used to determine the rate of change at a particular site?Can the author place limitation on the rate of change before this methodstarts to give misleading results? Finally, has the author experiencedany problems in predicting deep rod resistance if the initial readingswere taken in soil affected by seasonal changes, such as moisture ortemperature? This may happen when the initial readings are taken infrozen strata and the deep soil is unaffected by the top layer condition.

Manuscript received February 29,1980.

Eldon J. Rogers (Bonneville Power Administration, Vancouver, WA):The author has developed a method of predicting from test ground rodsthe effective resistivity to use to calculate the resistance of deep groundrods. BPA has recently completed installation of two wells to be usedfor grounding at our 230-5OOkV Ashe Substation located in the HanfordArea. With an ultimate fault magnitude of 42kA and a grid resistance ofapproximately 0.5 ohm, it was necessary for BPA Designers to resort togrounding wells to reduce grid resistance to between 0.1 and 0.2 ohms.From Wenner earth resistivity measurements, it was estimated that theAshe Site could be modeled by three layer earth: A top layer of 700-1000 ohm-meters, 1.9m deep. A second layer of 1700-2500 ohm-metersto 22.5m. A third layer of 20-40 ohm-meters. Thus, sufficient wellpenetration into the third layer would be useful for grid resistancereduction.

Table 1. Well Resistance Versus Depth

Depthm

4.3623. 8130.6332.00*39. 22#S-72. 465**79.5592.0896.10

101. 3a104.14

Resistanceohm

71.625.77.697.13.490.510.390.300.250.230. 22

Resistivityiohm-meters509

667246235137332724212019

8.12-61.7-8.03-13.57-3.13-0.85-0. 24-0.50-0.30-0.36

Table 1 summarizes resistance measured at various depths for Well#1. Resistivity at each depth is calculated using the ground rod formula.With varying degrees of success, I have used the author's technique toestimate final deep well resistance from well resistance measured atsmall depths. Table 2 summarizes resistivity extrapolation for the finalwell depth using resistivity and resistance data (marked by asterisks)from Table 1. Extrapolation with data from the first two depths wasvery inaccurate, but as resistivity change per meter becomes more con-stant there is better agreement between the predicted values and themeasured resistance. I would conclude that the authors method is not

applicable as the test rod penetrates earth layers of larger differing re-sistivity and is only useful when the rod penetrates a more constantstrata. In the ground rod resistance formula, resistivity varies directlywith rod length and inversely as a function of the log of length. Yet inthe author's formula, resistivity change varies directly with the log ofchange in length. Has the author developed any theoretical basis for hisformula?

Determination of effective earth resistivity for use in deep groundrod or grid resistance calculations is an important contribution togrounding design.

Table 2. Predicting Well Resistance

Dn ta* to *** tc ***

*t to ***

a

+1+1+1

_b kp1.397 25.353.075 30.02.593 17.18

Lx

104 .14104.14104 . 14;

0.D.

0.16840. 16840.1684

RX

0.91st0. 17 -c

0.24 -t.

Manuscript received March 4, 1980.

C. J. Blattner: The author expresses his appreciation for the interestshown and valuable comments made by the discussors. The most con-sistent question has been for a comparison of the results of this techniqueas compared to the Wenner 4 pin method. No comparison tests weremade during the development of this technique. However, arrangementshave been made to perform dual tests at several selected locations whichwill enable direct comparisons to be made of the two methods.

The application of the technique to known ground rod measure-ments by Messrs. Keil and Rogers is very much appreciated. Such com-parisons help to demonstrate both the practical application and thelimitations of the method. In reply to Mr. Jones' questions, the term"sufficient accuracy" can be defmed as a "good approximation of theactual conditions." As stated in the paper, there should be no "illusions"that strict accuracy is to be expected. The term "effective soil resistivity"means the apparent soil resistivity as seen by the ground rod over theentire length of the ground rod. Mr. Jones questions the use of homoge-neous soil equations in multi-layer soil conditions. Actually, the applica-tion has been in two-layer soil conditions, rather than multi-layer soilconditions. Nevertheless, it is apparent that application of the methodmay be limited to more or less homogeneous soil conditions. The actual

1763

installation of the deep ground electrodes was accomplished by drillinga four-inch hole, backfilling with Bentonite, and then installing theground rods. The method is similar to that described in Mr. Jones' paper,F79 628-9, "Bentonite rods assure ground rod installation in problemsoils," presented at the 1979 PES Summer Meeting.

Mr. Keils' results obtained by use of the technique is most en-couraging. Concerning his question on rate of change, no specific limita-tion has been determined. However, small rates of change (lOAp/M)yield more consistently accurate results than very large rates of change(10OAp/M). No problem has been encountered in predicting deep rodresistances due to seasonable variations. The projections shown in Table 2of the paper were based on test rod readings taken in the autumn whereasthe deep electrodes were installed six months later in the spring.

Mr. Dawalibi indicates several conditions where the technique mayfail to give accurate projections. For the first condition, the next layeris significantly beyond the known test rod readings. This is similar tothe problem encountered by Mr. Rogers in trying to predict the lowerlayer resistivity values based only on the test values obtained in the toplayer. This is a limitation of the method. The remaining conditionsdescribed by Mr. Dawalibi are well taken. However, it has been deter-mined that when the test rod penetrates the lower layer sufficiently toobtain consistent rate of change readings, then accurate projections havebeen possible regardless of the top layer soil resistivity value. His sug-gestion to add an "effective top layer thickness" parameter is greatlyappreciated as a means to improve the equation for two-layer conditions.

Mr. Rogers noted that the resistivity change varies directly as afunction of the log of the length. This resulted from a review of knowneffective soil resistivity values plotted versus the driven length of thetest rod. It was found that a logarithmic type curve best approximatedthe soil resistivity readings. In a paper by B. Thapar and E. T. B. Gross[I ], the resistivity change varied directly as a function of the exponentof the natural logarithm factor e:

P = P2 - (P2 -p, )e-bS (2 - eTb)Where S = probe spacing

b = constant.

REFERENCE

[1 ] Thapar, B., and Gross, E. T. B., Grounding Grids for High-VoltageStations. IEEE Transactions PAS Oct. 1963, page 782.

Manuscript received March 27, 1980.