Answer Happy

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Supplemental Information:
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Problem 1. Four resistance measurements were conduted at a substation site using the Wenner 4-pin method. The measurements in Table 2 below were recorded: Measurement No. 1 2 3 4 R (92) 1.52 2.40 1.15 0.95 a(m) 30 20 40 b(m) 3 3 3 3 50 Calculate the soil resistivity for each of these measurements and the average measured soil resistivity. Measurements a nd b are in meters.
IEEE Std. 81-1983 describes a number of measuring techniques. The Wenner four-pin method is the most commonly used technique. Figure 4.46 illustrates this method. In this method, four probes (or pins) are driven into the earth along a straight line, at equal distances apart, driven to a depth b. The voltage between the two inner (i.e., potential) electrodes is then measured and divided by the current between the two outer (i.e., current) electrodes to give a value of resistance R. The apparent resistivity of soil is determined from 41aR a Pa (4.124) 1+(20/ Va? +46%) Va’ +b? where P, is the apparent resistivity of the soil, S2-m R is the measured resistivity, 22 a is the distance between adjacent electrodes, m b is the depth of the electrodes, m In the event that b is small in comparison to a, then Pe=2qaR (4.125) The current tends to flow near the surface for the small probe spacing, whereas more of the cur- rent penetrates deeper soils for large spacing. Because of this fact, the previous two equations can be used to determine the apparent resistivity P, at a depth a. The Wenner four-pin method obtains the soil resistivity data for deeper layers without driving the test pins to those layers. No heavy equipment is needed to do the four-pin test. The results are not greatly affected by the resistance of the test pins or the holes created in driving the test pins into the soil. Because of these advantages, the Wenner method is the most popular method.