JPH0829464A - Method for estimating ground resistance corresponding to burial depth of bar-shaped ground electrode - Google Patents

Abstract

PURPOSE:To determine the burial depth of a bar-shaped ground electrode by calculating a potential difference/current ratio at each point using Wenner's our-electrode method while varying in steps the interval between electrodes, and obtaining an estimated resistance value through the multiplication of each value by a constant determined by the diameter of the bar-shaped ground electrode, and estimating this value to be the ground resistance of the ground electrode buried to a depth matching the electrode-to-electrode interval. CONSTITUTION:Four point electrodes C1, P1, P2, C2 are arranged on a straight line on the surface of the ground at intervals a, and a direct current l is passed between the electrodes C1, C2 to measure a potential difference V between the electrodes P1, P2. When the diameter and length of a bar-shaped ground electrode are D and L, respectively, the distance between the upper end of the ground electrode and the surface of the ground is t and the length of the ground electrode corresponding to a hemispherical electrode having a diameter of 1m is L1, then a=l+t so that the ground resistance R of the ground electrode is R = (1/1.41) (L1+t) (V/I)=C(V/I), the constant C determined by the diameter D. Therefore, the interval a is varied in steps to calculate V/I at each point, and the value of V/I is multiplied by the constant C to obtain an estimated resistance value, and this value can be estimated to be ground resistance when the ground electrode is buried to a depth matching the interval a.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for estimating a grounding resistance corresponding to a buried depth of a rod-shaped ground electrode when a rod-shaped ground electrode is buried vertically in the ground for grounding.

[0002]

2. Description of the Related Art According to "Technical Standards for Electrical Equipment", the ground resistance is defined as 10 Ω or less for the first and special third types and 100 Ω or less for the third type. The ground resistance varies greatly depending on the geology of the land, and it is often very difficult to obtain a ground resistance of 10Ω or less in a poor geological location.

In the grounding work, a hole having a diameter of several tens of mm is usually drilled vertically by boring, and a conductive metal rod having a diameter of 10 to several tens mm is inserted into the hole over substantially the entire length, and the metal rod and the inner periphery of the hole are inserted. The method is performed by pouring a conductive curable resin into a gap between the surface and the resin and curing the resin. In this case, the metal rod and the cured conductive resin are integrated to form a rod-shaped ground electrode. In some cases, a conductive metal rod having the same diameter as the hole drilled by boring is driven into a rod-shaped ground electrode. In any case, in order to obtain the target grounding resistance in a poor geological location, the length of the rod-shaped grounding electrode should be increased and the embedding depth of the rod-shaped grounding electrode (depth of the tip of the rod-shaped grounding electrode) should be deepened. There must be.

[0004] The construction cost of the grounding work is generally determined based on the burial depth of the rod-shaped ground electrode (corresponding to the excavation depth of boring). However, since the ground resistance varies greatly depending on the geology of the land, it is extremely difficult to predict the burial depth of the bar-shaped ground electrode to obtain a target ground resistance. For this reason, the grounding work is performed until the target grounding resistance is obtained on site at all times, and there is a problem that it is difficult to schedule the construction cost and the construction period.

SUMMARY OF THE INVENTION In view of the above problems, it is an object of the present invention to provide a method of knowing how much the burial depth of a rod-like ground electrode should be laid in order to obtain a target ground resistance when performing grounding work. Another object of the present invention is to provide a method of estimating a ground resistance corresponding to a buried depth of a rod-shaped ground electrode.

[0006]

[Means for Solving the Problem and Its Action] The ground resistance in the case where the rod-shaped ground electrode is vertically buried in the ground for grounding is
The rod-shaped ground electrode largely depends on the specific resistance of the ground in which it is embedded. Wen is a means of measuring the resistivity of the earth
The ner four-electrode method is known. This method uses four point electrodes C ₁ along a straight line on the ground surface as shown in FIG.
P ₁ , P ₂ , C ₂ are arranged at equal intervals, and electrodes C ₁ , C
_A direct current I is passed between the _two electrodes, and the potential difference V between the intermediate electrodes P ₁ and P ₂ is measured with a potentiometer.

Assuming that the specific resistance of the ground is uniform, the specific resistance ρ _X [Ω-m] is (V / I) measured by Wenner's four-electrode method and the electrode spacing a at that time. From
It can be calculated by the following formula.

[0008]

[Equation 1]

This formula is called Wenner's formula, and is satisfied when the resistivity of the ground is uniform.

In Wenner's four-electrode method, the electrode spacing a
When is small, the flow at the top most part close to the ground surface of the current returning to C ₂ from C ₁ through the ground, less susceptible to ground of the lower layer portion. However, when the electrode interval a becomes large, the current path is widened and the current also flows to the lower part in the ground, so that when the upper part and the lower part have different specific resistances,
The measured value of ρ _X differs depending on the electrode interval a. We
Nner's four-electrode method is applied to geological exploration and the like by applying this principle.

However, even when the resistivity of the ground is not uniform in the depth direction, the electrode spacing a
It can be considered that the larger the value is, the correspondingly measured “average resistivity” deep into the ground.

On the other hand, as shown in FIG. 2 (a), when the rod-shaped ground electrode 1 is buried vertically in the ground for grounding, the burying depth L + t (t is When the depth becomes 0.75 [m], the ground resistance decreases accordingly, but the ground resistance of the rod-shaped ground electrode at a certain burial depth is the "average" of the earth up to the burial depth. It can be considered that it is almost determined by "specific resistivity".

The present inventor pays attention to this point, and
As a result of investigating the relationship between (V / I) and the ground resistance when the electrode spacing a of the four-electrode method of r and the embedding depth of the rod-shaped ground electrode have a one-to-one correspondence, they have a proportional relationship. The present invention has been completed and the present invention has been completed.

That is, according to the present invention, the V / I at each electrode interval a is changed stepwise by the Wenner's four-electrode method.
The value of (potential difference / current) is measured, and each V / I value is multiplied by a constant C determined by the diameter of the rod-shaped ground electrode to obtain an estimated resistance value. It is estimated as the ground resistance when the electrodes are buried at a depth corresponding to each electrode interval a.

The reason why the ground resistance of the rod-shaped ground electrode can be estimated by this method will be described below.

The ground resistance is defined as follows. Assuming that there is one ground electrode 1 as shown in FIG. 2A and a ground current I [A] flows into this electrode, FIG.
The potential of the ground electrode 1 is higher than the surrounding ground by V
It becomes higher by [V]. At this time, V / I [Ω] is called the ground resistance of the ground electrode. That is, the ground resistance is defined as the resistance between the ground electrode and the auxiliary electrode at an infinite distance (the point where the potential does not change due to the ground current) from the ground electrode.

Now, as shown in FIG. 3, the depth a from the surface of the earth
Assuming a two-layered earth where the average resistivity of the formation up to [m] is ρ ₁ and the average resistivity of the formation that continues infinitely deeper than a [m] is ρ ₂ , according to Hummel's electric image theory, When the current I [A] flows through the point current source C on the ground surface, the potential V _P at the point P distant by a [m] from C can be expressed as follows.

[0018]

[Equation 2]

Here, K is a reflection coefficient, and n is the number of boundaries. The reflection coefficient K is represented by the following equation.

[0020]

(Equation 3)

Also, as shown in FIG.
Assuming a two-layer structure ground having an average resistivity ρ ₁ up to [m] and an average resistivity deeper than ρ ₂ , the Wenner four-electrode method sets the electrode interval to a [m], C ₁ , The potential difference V between P ₁ and P ₂ when the current I is passed between C ₂ can be expressed as follows.

[0022]

[Equation 4]

Ρ _X [Ω when the resistivity of the ground is uniform
−m] is expressed by the following equation (1), and the following equation is obtained by substituting the equation (4) into the equation (1).

[0024]

(Equation 5)

This equation shows that ρ _X / ρ ₁ is a function of K, n. If the right side of Equation 5 is set to S, Equation 5 can be expressed as follows.

[0026]

(Equation 6)

This equation shows the relationship between the specific resistance ρ ₁ of the upper layer of the two-layer structure ground assumed under the point current source and the specific resistance ρ _X of the ground when the specific resistance is assumed to be uniform. I have.

To clarify this relationship, the value of S will be determined. The reflection coefficient K in the equation ( ₂ ) changes in the range of -1 <K <1 depending on the values of ρ ₁ and ρ ₂ . K from -1 to +
The value of S in the case of dividing into 0.2 at intervals of 0.2 and changing n for each K is calculated and shown in a graph as shown in FIG. According to FIG. 5, Equation 6 is supposed to calculate n up to infinity, but if n = 10 or more, it can be considered that the value of S is almost constant.

This shows that in the ground of the two-layer structure assumed by Hummel's electric image theory, it is sufficient to consider n = 10. The ground resistance is defined as the resistance between the ground electrode and the auxiliary electrode at infinity therefrom. FIG. 5 shows that a value equivalent to infinity is obtained even in the range up to n = 10. Is shown.

S ₁ in {｛} of Equation 2, and {｛} in Equation 4
When the inner and S (the same as equation (5) on the right side), the relationship of S ₁ and S, the following conditions are required in order to satisfy the definition of ground resistance.

[0031]

(Equation 7)

Equation 7 can be modified as follows.

[0033]

(Equation 8)

In order to obtain a value of K that satisfies Equation 8, K is divided from −1 to +1 at intervals of 0.2, and the values of S ₁ , S, and (S ₁ −S) for each K are calculated. FIG. 6 shows a graph. According to FIG. 6, K is ρ
_Although it is a function of ₁ and ρ ₂ (Equation 2), it can be seen that there is only “one point” K that satisfies the condition of Equation 7. When the values of K and S at this time are calculated, K = 0.869
, S = 1.41.

The value of S is determined by the potential V related to the ground resistance.
_P (Equation 2) is a factor that links the potential difference V (Equation 4) measured by the Wenner four-electrode method. That is, by substituting S = 1.41 into the formula 6, the following formula is obtained.

[0036]

[Equation 9]

This equation is expressed as ρ _{X by the} Wenner's four-electrode method.
It shows that ρ ₁ can be obtained by measuring. That is, in FIG. 3, since the potential V _P of the point P generated when the flow of infinity two points current from the point C can be obtained by the four-electrode method of Wenner, knowing the potential V _P of the point P, it The resulting ground resistivity ρ ₁ is determined. Since ρ ₁ is the specific resistance up to the depth a [m], if this is known, the ground resistance of the ground electrode embedded at the depth a [m] can be estimated.

Since Hummel's electroimaging is based on the concept of point current, the constant (1 / 1.41) in Equation 9 can be used only under point current conditions. In order to estimate the ground resistance when the rod-shaped ground electrode is used, it is necessary to consider the equivalent radius when the rod-shaped ground electrode is converted into a hemispherical electrode. The above (1 / 1.41) is a constant when the rod-shaped ground electrode is embedded at a depth corresponding to the equivalent radius r = 1 [m].

The ground resistance R of the rod-shaped ground electrode 1 shown in FIG. 2A can be expressed by the following equation, assuming that the ground resistivity is uniform and ρ _X [Ω-m] (Nippon Denki Kogyo Co., Ltd.) JECA "Research on Safety Grounding of Construction Electrical Equipment").

[0040]

[Equation 10]

However, L: length of the rod-shaped ground electrode D: diameter of the rod-shaped ground electrode t: depth from the ground surface to the upper end of the rod-shaped ground electrode

On the other hand, the ground resistance R of the hemispherical electrode having the radius r is calculated by the following equation.

[0043]

[Equation 11]

From equations (10) and (11), length L and diameter D
The equivalent radius r corresponding to the hemispherical electrode of the rod-shaped ground electrode can be expressed by the following equation.

[0045]

(Equation 12)

The shape factor f of the rod-shaped ground electrode is expressed by the following equation, where ρ _x = 1 in equation (10).

[0047]

(Equation 13)

From Equations (12) and (13), the shape factor f of the rod-shaped ground electrode is expressed by the following equation, where the equivalent radius is r [m].

[0049]

[Equation 14]

The ground resistance R of the rod-shaped ground electrode when the specific resistance of the ground is ρ ₁ can be expressed by the following expression when the idea of the shape factor of the expression (13) is entered.

[0051]

(Equation 15)

Since Equation 9 is established between ρ ₁ and ρ _X , the ground resistance when the rod-shaped ground electrode is buried in the formation having the specific resistance ρ ₁ is equivalent to the equivalent radius r [m]. By introducing the concept, it can be expressed by the following equation.

[0053]

[Equation 16]

However, A and B are as follows. A = r / (L + t): Ratio of the embedded depth L + t [m] of the rod-shaped ground electrode having an arbitrary length L to the equivalent radius r [m] of the rod-shaped ground electrode B = 1 / (L ₁ + t ): Buried depth L ₁ + t [m] of a rod-shaped ground electrode having a length L ₁ corresponding to an equivalent radius of 1 [m]
And the equivalent radius 1 [m]

Equation 16 to Equation 1 and Equation 14 and A and B
Substituting the relationship of and rearranging as a = L + t, the following equation is obtained.

[0056]

[Equation 17]

Here, L ₁ is the length of the rod-shaped ground electrode corresponding to a hemispherical electrode having a radius of 1 [m], and thus is uniquely determined if the diameter of the rod-shaped ground electrode is determined. Specifically, L ₁ can be obtained by the following equation obtained by substituting r = 1 [m] and t = 0.75 [m] (values determined by the technical standard of electrical equipment) into the equation 12 it can.

[0058]

(Equation 18)

According to the equation (18), L ₁ is a constant determined by the diameter D of the rod-shaped ground electrode.
1.41) · (L ₁ + t) is also a constant determined by the diameter D (because t is defined as 0.75 [m] in the technical standard of electrical equipment).

If (1 / 1.41)  (L ₁ + t) = C is set here, this constant C is as shown in the equation (17).
This is a proportionality constant that associates the value of V / I measured by Wenner's four-electrode method with the electrode interval being a and the ground resistance R when the bar-shaped ground electrode is buried at the depth a.
For example, assuming that the diameter D of the rod-shaped ground electrode is 0.056 [m],
From equation (18), L ₁ = 6.58 [m], so C = 5.20 is obtained. Thus, when the rod-shaped ground electrode is buried at a depth corresponding to the electrode interval a, the ground resistance is R = 5.20 (V / I).
It can be estimated that

Therefore, according to Wenner's four-electrode method, the electrode spacing a is changed stepwise to obtain V / I at each electrode spacing a.
(Electric potential difference / current) is measured, and each V / I value is multiplied by a constant C determined by the diameter of the rod-shaped ground electrode to obtain an estimated resistance value. This means that it can be estimated as a ground resistance when the ground electrode is buried at a depth corresponding to the electrode interval a.

The diameter of the rod-shaped grounding electrode is determined by drilling a hole by boring, inserting a conductive metal rod into the hole, pouring a conductive curable resin into a gap in the hole and curing the resin. Is the same as the inner diameter of the hole.

[0063]

DESCRIPTION OF THE PREFERRED EMBODIMENTS In order to confirm the accuracy of the estimation method of the present invention, ground resistance is estimated by the estimation method of the present invention.
A test was conducted in which a rod-like ground electrode was actually buried to measure the ground resistance. The results are shown in Examples 1 to 4.

Example 1 Measurement location: Okura Village, Yamagata Prefecture Diameter of rod-shaped ground electrode D = 0.056 [m] (C = 5.20)

[0065]

[Table 1]

According to this result, it can be predicted that the buried depth of the rod-shaped ground electrode should be approximately 70 m in order to obtain the ground resistance of 10 Ω or less.

Example 2 Measurement location: Nagai City, Yamagata Prefecture Diameter of rod-shaped ground electrode D = 0.056 [m] (C = 5.20)

[0068]

[Table 2]

According to these results, it can be predicted that the buried depth of the rod-shaped ground electrode should be about 90 m in order to obtain the ground resistance of 10 Ω or less.

[Example 3] Measurement location: Nasu Town, Tochigi Prefecture Diameter of rod-shaped ground electrode D = 0.0405 [m] (C = 5.50)

[0071]

[Table 3]

According to the result, it can be understood that it is expected that the ground depth of the rod-shaped ground electrode should be approximately 40 m in order to obtain the ground resistance of 10Ω or less.

Example 4 Measurement location: Chitose City, Hokkaido Diameter of rod-shaped ground electrode D = 0.0405 [m] (C = 5.50)

[0074]

[Table 4]

According to the result, it can be understood that it is expected that the ground depth of the rod-shaped ground electrode should be set to approximately 40 m in order to obtain the ground resistance of 10 Ω or less.

In each of the above embodiments, the electrode spacing a is changed stepwise by the Wenner four-electrode method to obtain V / I at each electrode spacing a.
Value is calculated, and each V / I value is multiplied by a constant C determined by the diameter of the rod-shaped ground electrode to obtain an estimated resistance value. The estimated resistance value at each electrode interval a is calculated by using the rod-shaped ground electrode for each electrode. A method of estimating the ground resistance when buried at a depth corresponding to the distance a was adopted.

However, in a normal case, the target ground resistance (for example, 10Ω or less) is known before starting the measurement.
According to the present invention, a target ground resistance is divided by a constant C determined by the diameter of a rod-shaped ground electrode to obtain a reference value, and the electrode spacing a is changed stepwise by the Wenner four-electrode method to obtain each electrode spacing a. V / I
When the value of V / I measured at a certain electrode interval a is substantially equal to the reference value, the rod-shaped ground electrode is buried vertically at a depth corresponding to the electrode interval a. It is also possible to carry out the method of estimating that a ground resistance similar to the target ground resistance can be obtained.

Although the method is similar to that of each of the above-described embodiments, the present invention sets a target ground resistance and changes the electrode spacing a stepwise by the Wenner's four-electrode method to obtain each electrode spacing a. V / I
Value is measured, and the estimated resistance value is obtained by multiplying each V / I value by a constant C determined by the diameter of the rod-shaped ground electrode, and the estimated resistance value obtained at a certain electrode interval a is equal to the target ground resistance. It is presumed that if the rod-shaped ground electrodes are vertically embedded at a depth corresponding to the electrode spacing a when the same level is reached, a ground resistance equivalent to the target ground resistance is obtained. It is also possible.

[0079]

As described above, according to the present invention, it is possible to estimate the ground resistance corresponding to the burial depth of the rod-shaped ground electrode on the land. It is possible to estimate the burial depth of the bar-shaped ground electrode for obtaining the ground resistance. Therefore, it is possible to plan the construction cost and the construction period for the grounding work, and there is an advantage that the grounding work can be carried out systematically.

[Brief description of drawings]

FIG. 1 is an explanatory diagram showing a Wenner four-electrode method in the case where the resistivity of the ground is uniform.

FIGS. 2A and 2B are explanatory diagrams illustrating a buried state of a rod-shaped ground electrode, and FIG. 2B is an explanatory diagram illustrating a definition of a ground resistance.

FIG. 3 is an explanatory diagram showing a potential at a point P when a current is supplied from a point current source C on the ground surface in a ground having a two-layer structure.

FIG. 4 shows Wenne assuming a two-layered ground.
FIG. 4 is an explanatory view showing a four-electrode method of r.

FIG. 5 is a graph showing the relationship between n and S at various K values.

FIG. 6 is a graph showing the relationship between K and S ₁ , S, (S ₁ −S).

[Explanation of symbols]

 1: Rod-shaped ground electrode L: Length of rod-shaped ground electrode D: Diameter of rod-shaped ground electrode t: Depth from ground surface to upper end of rod-shaped ground electrode

Claims (4)

[Claims] 1. The Wenner four-electrode method is used to measure the value of V / I (potential difference / current) at each electrode interval a by gradually changing the electrode interval a and measuring the respective V / I values. Is multiplied by a constant C determined by the diameter of the rod-shaped ground electrode to obtain an estimated resistance value, and the estimated resistance value at each electrode interval a is grounded when the rod-shaped ground electrode is buried at a depth corresponding to each electrode interval a. A method for estimating the ground resistance corresponding to the burial depth of the rod-shaped ground electrode, characterized in that the resistance is estimated. 2. A reference value is obtained by dividing a target ground resistance by a constant C determined by the diameter of a rod-shaped ground electrode. The electrode distance a is changed stepwise by a Wenner's four-electrode method. V / I at a
Is measured, and when the V / I value measured at a certain electrode spacing a becomes approximately the same as the reference value, if the rod-shaped ground electrode is vertically embedded at a depth corresponding to the electrode spacing a, A method of estimating the ground resistance corresponding to the burial depth of the rod-shaped ground electrode, characterized in that it is estimated that a ground resistance equivalent to the target ground resistance can be obtained. 3. A target grounding resistance is set, and the electrode spacing a is changed stepwise by the Wenner four-electrode method to obtain V / I at each electrode spacing a.
Value is measured, and the estimated resistance value is obtained by multiplying each V / I value by a constant C determined by the diameter of the rod-shaped ground electrode, and the estimated resistance value obtained at a certain electrode interval a is equal to the target ground resistance. It is presumed that if the rod-shaped ground electrodes are vertically embedded at a depth corresponding to the electrode spacing a when the same level is reached, a ground resistance equivalent to the target ground resistance can be obtained. A method for estimating the ground resistance corresponding to the buried depth of the rod-shaped ground electrode. 4. The value of a constant C determined by the diameter of the rod-shaped ground electrode is C = (L ₁ + t) /1.41 (where L ₁ is a radius of 1).
3. The length of a rod-shaped ground electrode having a diameter D which provides the same ground resistance as the [m] hemispherical electrode, and t is the depth from the ground surface to the upper end of the rod-shaped ground electrode. 3
Method of estimating the earth resistance described.