TECHNICAL SPESIFICATION FOR WENNER ELECTROD ARRANGEMENT IN RESISTIVITY 1-D DAN 2-D

ABSTRACT

Currently, the geoelectric survey is developed so rapidly. It is caused development of electronic and computer so fast with high precision and accurate  performance. The development of resistivity meter for multy channels has been created for resistivity 2-D. Those equipments are so expensive, however handy to use in the field. The explanation and using the one channel resistivity meter could be use for the resistivity 1-D and 2-D. The sample will be taken with for the Wenner electrode arrangement only and it will be applied to other array.

1. INTRODUCTION

The meaning of resistivity one channel is the equipment has been existed before appeared the resistivity 2-D. Those equipments are OYO OHM Type 2115, Yokogawa Resistivity meter type 3244, ABEM SAS 300, and NANIURA NRD 300 HF. The equipment for survey geoelictlric 2 D (2 Dimensi)  had been development such us ABEM SAS 4000, GEORES, OYO PROFILER 4 in 10 years ago.

The resistivity meter could be used for resistivity 1-D and 2-D. The sample of the survey will be applied to Wenner Electrode Arrangement.  The procedure for exc cution is explain in the following items.

2. THE BASIC THEORY OF ELECTRICITY

The principle of resistivity survey is to inject electric current trough 2 ( two ) electrode current ( ∆ I ) , so there is influence the differences of a pair inner potensial electrode ( ∆ V).  If we knows the diferences current and potensial , so we can get the resistance ( R ) from OHM LAW  :

  R =  (∆ V)/(∆ I) in ohm.                                             ( 1 )

If the electric current trought the homogeneus sylinder of bar , so the value R depend on the lenght of bar ( L ) and the sylinder area ( A ).

R ­­= L / A (ohm-m)                                                                 ( 2 )

The equation above has the fixed value  in unit of ohm-m. To know the resistivity of material the equation became :

r = AV/ L I ( ohm-m)  or r = K R                                         ( 3 )

where K= A./L is  the geometric factor, which is depend on the position of the current electrode and potential elctrode.  The geometric factor are different from the each of electrodes arrangement as shown in Figure 1.

Figure 1. The geometric factor from various electrode arrangements.

The geometric factor for electrode arrangement Of WENNER is K =  2pa and r = 2pa R in unit ohm-m, where  a or  L is the distance of electrode WENNER.

In electrode arrangement of SCHLUMBERGER m the geometric factor as follows :

K = 2 p/(1/AM – 1/AN) – (1/BM – 1/BN)  or

K = p{(AB)² – (MN)² } , where  AB=current electrode and MN=electrode  pot.

                    4 MN

  ρ =     KR = p{(AB)² – (MN)² }  R                                                   ( 4  )

                               4 MN

Figure 2. The electrode arranggement of SCHLUMBERGER     

In the SCHLUMBERGER methode the electrode potensial is fixed and will be change at certained distances. The maximum distance of AB/2 is not more than  5 x  MN/2.

  

3.     RESISTIVITY 1 D FOR WENNER ELECTRODE ARRANGEMENT

The first attempt to measure electrical resistivity of soils was made at the end nineteenth century with the two-electrode technique. Whitney et.al.(1887), Gardner (1898), and Briggs (1899 ) developed relationships between soil method measures the sum of both electrical resistivity and soil water content, temperature, and salt content, The two-electrode  method measures the sum of both soil resistivity and the contact resistivity between the electrode and soil. The latter is very eratic and unpredicted.

Wenner  (1915 ) based on the work of Schlumberger suggested that a linear array of four equally spaced electrode would minimize are separated contact problems if potential measuring and current – induced electrodes are separated in space. Since then all electrical resistivity methods applied in geophysics and soil are based on the standards four electrodes principles. The Wenner Electrode Arrangement devided into Wenner α , Wenner β  , and Wenner γ shown on Figure 1. The procedure for theWenner Electrode Arrangement is as follows :

1.     Determine the point O on the ground surface.

2.     The four electrode arrangement set on the ground and measure the deferent of current ( ∆ I ) and different of potential ( ∆ V ). The data is write  on the field data sheet

3.     The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 1.0 meter.

4.     The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 1.5 meter.

5.     The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 2 meter

6.     The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 3 meter.

7.     The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 5 meter

8.     The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 7 meter.

9.     The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 10 meter.

10.  The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 12 meter.

11.  The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 15 meter.

12.  The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 20 meter.

13.  The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 25 meter.

14.  The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 30 meter.

15.  The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 40 meter.

16.  The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 50 meter

17.  The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 60 meter

18.  The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 75 meter

19.  The first Wenner  Electrode Arrangement set on C₁ P₁ = P₁ P₂ =C₂ P₂ = a = 100 meter

20.  In the field plotted data on double log paper.

21.  The resistivity curve could be intrepreted using RES 1D, VESPC, RESINT 53, IP2Win and GRIVEL.

                                               

                                               Figure 3. Three Types Wenner Electrod Arrangement

  

Figure 4. The equipotential lines , current line and datum points on the four electrod array ( Wenner and Schlumberger ).

Figure 5. Field Data Sheet For Wenner Array Resistivity 1-D

Figure 6. Interpretation resistivity curve with software IP2Win

Figure 7. The Geological Profile based on Resistivity Values

3.     RESISTIVITY 2 D FOR WENNER ELECTRODE ARRANGEMENT

An example of the electrodes arrangement and measurement sequence that can be used for a 2-D electrical imaging survey shown in Figure 6 . The procedures to get data resistivity 2-D with Wenner α electrode arrangement with 20 electrodes and electrode spacing a with level 6. Firstly, mark the peg on the ground with numbering from 1 to 20.

The first step is to make all the possible measurement with the Wenner array with electrode spacing “1a”.  For the first measurement electrodes number 1,2,3. and 4 are used. Notice the electrode 1 is used as the first current electrode C₁ , electrode 2 as the first potential electrode P₁ , electrode 3 as the second potential electrode P₂ and electrode 4 as the second current electrode C_2. for the second measurement, electrode number 2, 3, 4 and 5 are used for C₁ , P₁ , P₂ , C₂  respectively. This repeated down the line of electrodes until electrodes 17, 18, 19 and 20 are used for the last measurement with “1a” spacing. For a system with 20 electrodes , note that there are 17 ( 20-3) possible measurements with “1a” spacing for the Wenner array.

After completing the sequence of measurements with “1a” spacing, the next sequence of measurement with “2a” electrode spacing is made. First electrodes 1.3.5 and 7 are used for the first measurement. The electrodes are chosen so that the spacing between adjacent electrodes is “2a”. For a system with 20 electrodes , note that there are 14 ( 20-2x3) possible measurement with “2a” spacing.

The same process is repeated for measurements with “3a”, “4a”, “5a” and “6a” spacings. To get the best results with the equipment one channel, the measurement in the field survey should be measurements one step by one step and record data on the field sheet. The field sheet is shown on Appendix 2 and the program resistivity 2-D as shown on Fig   .The sample of Wenner Electrode Arrangement is shown on the RES2DINVx32  program on the folder of LANDFILL.DAT. The LANDFILL.DAT is an example field data for the Wenner array obtained by survey with 50 electrode.

Figure 8. Multy – Channel Digital Resistivity Meter

Figure 9. Program RES2DINV for LANDFILL SURVEY

Figure 10. Sequence of measurement to build up a pseudosection in resistivity 2-D

3.     CONCLUSSION AND RECOMMENDATION

1.        The resistivity meter one channel can be used for measuring survey on resistivity 1-D and      resistivity 2-D.

2.        The measurement of resistivity 1-D is very fast and for 1 (one) day works could be finish 5 or 6 sounding points.

3.        The measurement of resistivity 2-D is take time then the equipment 1 (one ) channels. It is caused to many datum points ( 334 datums ) and required  1 (one ) or 2 (two days ) measure

REFERENCES :

1.     Geoelectrical Imaging 2-D 3-D GEOTOMO SOFTWARE, Agust 2004, RES2DINV ver.3.54 for Windows 98/Me/2000/NT/XP. Rapid 2-D Resistivity & IP inversion using the least – squares method.

2.      Loke, M.H. Dr. Electrical imaging surveys for environment and engineering studies. A practical guide 2 D and 3-D surveys. Copyright (1997,1999,2000) email:mhloke@pc.jaring.my.

3.     University of Moscow. 2000 IP2Win. A program for resistivity interpretation.

4.     Wenner F. 1955. A method of measuring earth resistivity. US Dept. Com.Bur. Standard Sci.Paper 258.

5.     Briggs,L.J. 1899. Electrical instrument for determining the moisture , temperature, and soluble salt content of soils. U.S. Dept, Agr. Bul,15,

6.     Gadners, F.D., 1898 The electrical metod of moisture determination in soils: results and modifications in 1897, U.S. Dept. Agr. Bul,12,

7.     Whitney, M,F.F.D. Garned. And L,J. Briggs, 1897., An Electrical Methodof determining the moisture content of arable soil.U.S. Depth. Agr.Bul.6.

Appendix 1

Single Channel Resistivity Meter

Naniura NRD 300 HF

Appendix 2

Field Data Sheet For Resistivity 2D

DOWN HOLE SEISMIC FOR ENGINEERING STRUCTURES

I. INTRODUCTION

1.1. General  Statement

Applied seismic on engineering structure divided into 2 (two) advantages, that are:

Firstly, refraction seismic exploration is to get lateral distribution of velocity layers underneath ground level. The velocity layers related to bearing capacity of soil or rocks. Beside that, the velocity layers could be known unconsolidated material and solid rock, depth of soil or base rock. Others, usefully of seismic exploration are to reduce core drilling in feasibility stage engineering study.

Secondly, down hole seismic is to get bearing capacity parameter in relation to engineering structure when the earthquake happened. The method to do down hole seismic is to install geophones on the bore hole, than making artificial trigger on the surface. The impulse or artificial trigger can be rise compression wave and shear wave. The result of preliminary wave and the secondary wave can be use to get the dynamic characteristic of the soil or rocks.

The result of the applied seismic given to engineer for designing the resistance of earthquake on engineering structure.

1.2. Basic Theory

In the seismic refraction method an explosive charge, weight drop or hammer blow is used to generate an elastic pulse (shot) at the earth’s surface. Some of the radiating energy which travels by several paths in the medium is refracted along subsurface boundaries and returns to surface to be recorded by a line of detectors (seismometer or geophone). The time lapse between the shot and the first arrival of the refracted energy at each of geophone is plotted on the time-distance curve (Fig.1) and this provides information on the depths to the refracting horizons and the seismic velocities of underlying layer. Fortunately, refracting horizon normally corresponds to distinct geological horizons and thus the depths to the geological interfaces may be computed. Modern interpretation techniques permit the measurement of depth to an irregular refracting interface at each seismometer position along the profiles.

1.3. The Down Hole Seismic

The purpose of down hole seismic is to be able to predict with accuracy behavior earthquakes of structure and the ground on which its rest, and used for effective a seismic design. It is necessary to know the dynamic characteristics of the ground.

The dynamic characteristics of soil that must be known in order to analyze deformation and stress resulting from dynamic loads are the Poison’s ratio (α), shear modulus (G), Young’s modulus (E) and kinetic bulk density (K).  

Those parameters can be calculated using the formula as shown bellows:

Kinetic Poisson ratio’s                      α = {1 – 2 (Vs/Vp) ²} / {2-2(Vs/Vp) ²}

Kinetic Rigidity Modulus                 G = 1/g.r.Vs² (in kg/cm²)

Kinetic Deformation Coefficient      E = 2(1+r) G (in kg/cm²)

Kinetic Bulk Modulus                       K = E/3(1-2r) (in kg/cm²)

Where             g = acceleration from gravitation (9.75 m/sec²)

                        r = bulk density of the ground (tonf/m³)

                        Vs and Vp = seismic velocity (m/sec)

The primary wave (Vp) and shear wave (Vs) is known from the down hole seismic record.

CHAPTER 2. PROCEDURE OF DOWN HOLE SEISMIC

The three of geophones is inserting to the bore hole as shown in Fig.2. The length of prove is 1.00 m, where on the tip of prove contained three geophones perpendicular each others.

The P wave and S wave propagation determine by using 3 geophones, 1 geophone placed vertical and two geophones horizontal. The two geophones placed on the right angles to each others. The shot point is toward the hole about 1.50 m – 2.00 from the hole. The wooden plate hammering is method to generate shear wave referred to every depth of hole. 

The wooden plate is 1.50 m – 2.00 m long, 50 cm wide and 10 cm thickness is firmly fixed on the ground. The data will be checked for be sure measurement of S waves. The record will be every 1 m interval and the record similar up to the depth of hole. The V wave and S wave determined from the record and plotted on the paper to determine of velocity layers.

Figure 2. Schematic Down Hole Seismic using the Oyo Mc Seis 160. 

2.1. Calculation of Dynamic Parameter

The down hole seismic method is applied to find the velocity distribution of P wave and S wave in bore hole. The first step of finding velocity distribution is to read the first arrival time on the seismic record. Afterward, data is plotted on the millimeter paper and drawing the time - travel curve. On the curve find the best fit of velocity distribution (Vp or Vs= distance / time = m/sec.)

The velocity distribution of P wave and S wave are used to calculate the dynamic elastic constant as shown on the flow chart on Table 1.

Table 1. Processing to produce dynamic elastic constants from S wave and P wave (OYO, 1978, TN 18).

P wave velocity is chiefly a function of volume elasticity and rigidity of the layer, become smaller in rigidity in proportion as the layer is soft with result that volume elasticity comes to have a larger influence.

S wave velocity, which is function of only rigidity, is a volume which serves s direct standard of hardness of layers. The values of material density (r) is obtained from Table 2.

Table 2. Density values (r), angle of friction (φ⁰), compaction (C) according to JIS Manual.

Material types	Rock types	Unit Weight (r) (tf/m3)	Angle of friction (φ0)	Compaction ( C ) =kgf/cm2	Soil Classification
Banking Material		1,4 – 2,0	150 - 400	0,1 – 0,5	GW,GP SW,SP SM,SC ML,CL VH
	Gravel	2,0 1,8	40o 35	0	GW,GP
	Sand with gravel	2,1 1,9	40 35	0	GW,GP
	Sand	2,0 1,9	35 30	0	SW,SP
Natural	Sandy soil	1,9 1,7	30 25	0	SM,SC
Material	Clayey soil	1,5 1,6	25 20	0	ML.CL
	Clay and silt	1,6 – 1,7 1,4 – 1,5	20 15	0	ML.CL MH
	Volcanic ash	1,4	5	0,3	VH

CHAPTER 3. THE RESULTS OF DOWN HOLE SEISMIC

The time travel curves and elastic modulus shown on Table 4 and Table 5. The elastic modulus related to the depth of ground bed design and the weight of proposed engineering structure. The summary result of down hole seismic shown on Table 3.

CHAPTER 4. CONCLUSIONS

Elastic modulus taken from the data of AR 1 on the depth of 15 m is as follows :  

α    = 0.33 – 0. 50

G   = (0.2 x 10³ – 189.9 x 10³) kg/cm²

E   = (1.34 x 10³ – 1025.34 x 10³) kg/cm²

K   = (41.22 x 10³ – 483.50 x 10³) kg/cm²

r    = 1, 7 – 1, 8    

REFERENCES

1.    Masuda, H., 1975, Seismic Refraction Analysis for Engineering Study. OYO Technical Note TN 10.

2.    Imai, T., 1975, An Introduction to the geophysical prospecting for civil engineering purposes. OYO Technical Note TN 11.

3.    Hawkins, L.V., 1961. The reciprocal method of routine shallow seismic refractions lines. Geophysical Prospecting, 6, 285 -182.

4.    Hawkins, L.V., 1961. Seismic Refraction Surveys for Civil Engineering. Geophysical Memorandum 2/69, ABEM Printed Matter No.90091.

5.    Angela M. Davis, 1977, A Technique for Insitu Measurement of Shear Wave Velocity, Marine Science Laboratories, University Collage of North Wales U.K,, Abem  Case History, ABEM Printed Matter – No.90180

6.    Takeshi Okubo, Akhiro Satake, Masaki Ishoguro, Minuro Nakagawa and Ken Ito, 1978, Seismic Survey for Civic Engineering by Handy Seismograph, OYO Technical Note TN – 18, OYO Corporation. 

 7.Satoru Ohya, Tsuneaki Takeuchi, Tsuneo Imai and Ken Ito, 1978, Geophysical Investigation for Civil Engineering purposes in Japan. OYO Technical Note TN – 33 OYO Corporations.