26
Soil Investigation Employing A New Method of
Layer-Value Determination for Earth
Resistivity Interpretation
H. E . BARNES, Soils Engineer,
Michigan State Highway Department
• IN an effort to improve methods of
making soil investigations of proposed
borrow sites and highway construction
the Michigan State Highway Department
is now employing the "earth resistivity"
method as a means of obtaimng information. The objective m adopting this
method is to eliminate, or at least r e duce, the chances of costly errors in
estimates of earth quantities and quality
of earth borrow due to the lack of adequate information. Until this resistivity
instrument was acquired nearly all investigations were made by hand augering
with the occasional assistance of jet
borings when the importance of the information warranted its cost of operation.
These methods are laborious and in most
cases, give inadequate data. It is i m possible to auger into a granular material
which lies below water table without the
use of power drilling and some form of
casing. Although a soils engineer can
determine the source of good granular
borrow, for example, from a few hand
borings and trained observations, it is
very difficult to estimate the size and
location of the deposit or to detect a
hidden clay stratum even if its presence
is suspected.
With the purchase of the
resistivity instrument it was the intent of
the Department to develop a procedure that
would give more detailed and accurate information of soil conditions.
It has now been about two years since
the instrument was purchased during which
time considerable e:q)enmentation has
been carried on with the result that detailed information on types, quantities,
and locations of certain soil materials can
now be determined with an accuracy which
is considered to be within practical limits.
BACKGROUND AND METHODS O F USE
Instruments for measuring earth r e sistivity have been used for-many years
by geologists and geophysicists in their
attempts to prospect and explore the
earth's crust in search of oil, minerals,
etc. In the course of years much research
has been done to improve the techniques,
instruments, and interpretation of results
to obtain better detail and accuracy. It is
not the writer's intention to go into an explanation of the numerous methods used
by various groups of geophysicists and
engineers other than to give a partial list
of the more common ones as follows:
Porous Pot, direct method; Gish-Rooney*
method; "Megger" method; Single Probe
method.
After considerable study and experimentation to determine the advantages
and disadvantages of various methods
with respect to the type of information
desired from soil investigations,
the
Gish-Rooney method was selected. One
of the main advantages of this method is
the elimination of the effects of ground
and stray currents by the use of an a l ternating, or more correctly, commutated circuit.
Voltages and currents
are read separately from which the apparent average resistivity of the soil is
computed.
The arrangement of four
electrodes in a straight line spaced an
equal distance from each other i s used
almost exclusively. This arrangement
'Gish, O H , 'Improved Equipment for Measuring EarthCurrent Potentials and Earth Resistivity". National Research
Council, Bulletin, Nov 1926, Vol I I , Pt 2, No 56.
27
-A—4
'Weimar's equation lor the average resistivity of soil
Figure 2.
4<AR
I• •
2A
10
When B is small compared to A, the equation simplifies to-
Stollon 44
Tailurol Rongs Volues In Ohm-Cm < lO'^
«S
90
100
f •2irA
*Wenner,U a Bureau of Standards Scientific Paper Na298
Figure 1.
Wenner's configuration in the
spacing of electrodes used in the GishRooney method for measuring earth r e s i s t i v i t y , i l l u s t r a t i n g the equipotential-bowl
theory.
is generally known as Wenner's* configuration. By using this arrangement
the spacing between electrodes is equal
to the depth of soil investigated as shown
in Figure 1. As with any tool being applied to a new field, there is a stage of
development during which different approaches and practices are studied, tried,
revised, discarded or improved, and
finally a definite procedure embracing
the limitations of the tool is adopted
as standard practice.
The procedure
adopted by the Department as standard
practice, at least for the present time,
consists of making depth-profile measurements at selected stations along one
or more lines of traverse. The distance
between stations and the number of traverse lines selected depend upon the size
and depth of the soil body for which information is desired and the time allowed
to make the investigation.
Naturally
there are exceptions made to the stand•Wenner, Frank, "Method of Measuring Earth Resistivity".
U S Bureau of Standards, Scientific Paper No. Z58, Bulletin, Vol 12-No 3, 1915-16
>
<
\
I.J.I.I , •.•
O
so
1
40
60
eo
100
120
140
Loyer-voliM Retlttlvlty (p J In 0hm-Cm> 1 0 ' '
160
Figure 3.
ard practice for those cases requiring
specific and particular information. In
general, traverse lines are made not
more than 100 feet apart and the distance
between stations is held to not more than
100 feet In measuring depth profiles, it
IS considered good practice to use 3foot intervals of layer thickness for depths
up to 15 or 21 feet and 5-foot intervals
for depths of investigation greater than
this 15 or 21 feet. The advantages obtained
by measuring several shallow layers in
preference to fewer layers of greater
thickness will be appreciated when the
interpretation of field results as developed
and used by the Department is understood.
28
Figure 4.
Assembly of equipment for earth-resistance survey.
INTERPRETATIONS OF
FIELD MEASUREMENTS
The interpretation of f i e l d m e a s u r e ments f r o m which r e l i a b l e deductions can
be made presented a most difficult p r o b lem.
A study w a s made of the s e v e r a l
different methods of interpretations as
presented in v a r i o u s published bulletins
and p a p e r s , some of which a r e based on
theoretical and mathematical c o n s i d e r a tions and at least one of which i s based
upon purely e m p i r i c a l considerations.
In general, theoretical and mathematic a l methods r e q u i r e such a great volume
of computations that the amount of time
r e q u i r e d to obtain the d e s i r e d i n f o r m a tion would defeat the purpose of using
the r e s i s t i v i t y instrument inasmuch as
time and costs of obtaining a c c u r a t e i n formation a r e p r i m e considerations. On
the other hand, after many attempts to
apply e m p i r i c a l methods, it w a s found
that even the m o r e recent methods of
e m p i r i c a l interpretation w e r e somewhat
inadequate and not sufficiently r e l i a b l e .
T h e r e f o r e , it w a s felt that a method
of interpretation might be developed which
would give the p a r t i c u l a r type of detailed
and r e l i a b l e information such as r e q u i r e d
by the Department if only on a c o m p a r a tive b a s i s . A s a r e s u l t of much f i e l d work
and calculation of e l e c t r i c a l m e a s u r e ments a method of interpreting f i e l d data
has been developed on the p r e m i s e that
Wenner's f o r m u l a i s a truly fundamental
e x p r e s s i o n f o r determining the average
apparent r e s i s t i v i t y of any thickness of an
earth m a s s .
EQUATION F O R
DETERMINING L A Y E R V A L U E
W e n n e r ' s f o r m u l a f o r the 4- electrode.
equal spacing configuration i s given as:
P = 27rAy
(1)
where P = average s p e c i f i c r e s i s t i v i t y of
depth A in o h m - c m s
A = spacing of electrodes and depth
investigated in c m s
'op cit.
29
E = potential differential a c r o s s the
inner two electrodes through
"A" depth of earth in volts
I = c u r r e n t c a r r i e d through the
m a s s a s introduced through
the outer electrodes i n a m p e r e s
See F i g u r e 1 f o r W e n n e r ' s f o r m u l a and a
sketch i l l u s t r a t i n g the equi-potential bowl
theory.
I n a s m u c h as A i s a v a r i a b l e , then in
order that " r e m a i n constant for different
t h i c k n e s s e s of a homogeneous s o i l , the
ratio of E / I must v a r y i n v e r s e l y with A.
T h e c u r v e i n F i g u r e 2 shows the r e l a t i o n ship of E / I to A.
T h e equation f o r determimng l a y e r
v a l u e s which i s being presented at this
time i s based on the hypothesis that
l a y e r s of earth a r e analogous in behavior to p a r a l l e l e l e c t r i c a l r e s i s t a n c e s .
On the b a s i s of this hypothesis, each
l a y e r of a two or m o r e l a y e r s y s t e m w i l l
have i t s p a r t i c u l a r value of r e s i s t a n c e a s
i l l u s t r a t e d in the following sketch f o r a
three-layer system:
A'
A'
A'
Ri
R2
R3
Layer 1
Layer 2
Layer 3
T h r e e l a y e r s of
non - homogeneous
soil.
A' = thickness of l a y e r i n t e r v a l
R = average r e s i s t a n c e of l a y e r
For
the
above
condition the average
Figure 6.
Commutoter
Potentiometer Circuit
Power Circuit
II
Figure
h
II
I I
5.
Schematic c i r c u i t diagram of
e a r t h - r e s i s t i v i t y equipment.
r e s i s t i v i t y v a l u e s obtained by the earth
r e s i s t i v i t y equipment would be Pi f o r
depth A ' , P2 for depth 2 A ' , and Pa f o r
depth 3 A ' , etc.
It i s r e c o g m z e d that the
P r o f i l e contours, Stations 311 to 333.
30
Figure 7.
Slope stake i n center at top of cut i s 60 f t .
of S t a t i o n 332 (see F i g . 6 ) .
368
369
370
371
372
i7i
374
375
576
377
right
378
379
3«l
100 Rt o1 Survajr C«nltr
g
Cloyojr T
• Snnd
Oapth cil/t Sounding -
423
Figure 8.
424
42S
426
427
428
Cross sections from p r o f i l e contours.
429
382
31
Figure 9.
Cross section from p r o f i l e contour.
E
value of Y in W e n n e r ' s f o r m u l a ( E q . 1)
may give only an approximate value of
r e s i s t a n c e f o r the s o i l because the equipotential bowl theory does not take into
consideration the warping effect caused
by the v a r i e d paths taken by the c u r r e n t
through heterogeneous m a t e r i a l s . N e v e r t h e l e s s , it s e r v e s as a comparative value
with which different types of s o i l may be
differentiated f r o m each other. C o n s i d e r ing now the value of r e s i s t a n c e f o r the
f i r s t l a y e r , in the sketch above, it may
be a s s u m e d that A' r e p r e s e n t s a l a y e r of
homogeneous s o i l and, therefore,
the
value of r e s i s t a n c e i s equal to the quotient obtained by dividing the potential
differential by the c u r r e n t c a r r i e d a s r e a d
S
f r o m the r e s i s t i v i t y instrument.
Thus:
R i = - j ^ , o r the average s p e c i f i c
r e s i s t a n c e f o r L a y e r 1. If E 2 and I2 a r e
the v a l u e s r e a d when investigating the
depth 2A' and the assumption i s made
that L a y e r s 1 and 2 act a s p a r a l l e l r e s i s tance of different v a l u e s through which the
c u r r e n t i s pushed, then this
condition
may be i l l u s t r a t e d by the following analogy:
l2
1010
580
981
Qoy
Figure 10.
Stations
\ ••••••••V^ Cloyey Sands ond Silts
Sand
"
Depth of p Sounding
P r o f i l e contours taken on construction centerline.
32
Figure 11.
593
S94
599
99«
Slope stake at top of cut i s 50 f t .
586 + 50 (see F i g . 10).
l e f t of S t a t i o n
997
60e
Clay«]r Till
MB
| ^
Figure 12.
800
| Sand
601
602
D.plh el p Sounding
80}
£04
,-
609
60T
.
Cross sections from p r o f i l e contours.
609
6L0 6JI
7M
ei ST3
T58
NoH A l l borloflt n o i t « * » ( B « f l
IsrttlstlvltTlDtiprttollaL
ciortrTiii
Figure 13.
Ptmm - Contours hOM not bMO
•^Dtpth flr/»SoimdngJtM
alt«r«tf to conform » l t b borlog data.
Cross sections from p r o f i l e contours.
The unknown value of Ra in the above
analogy i s determined a s follows:
No. 2 w i l l be
Step 1) R i = ^
(known)
4) I2 =
+ I^^
2)1^ = 1
(known)
5) I . = f
.
Using the same analogy and p r i n c i p l e s as
used above f o r R2 the value of Rs f o r the
third l a y e r may be found a s follows where
E3 and I3 a r e the r e s p e c t i v e potential diff e r e n t i a l and c u r r e n t v a l u e s given by the
r e s i s t i v i t y instrument f o r the 3A' depth.
Es-
6) I ?
R2
E2
7) R2 = T T
Ri
|
T
E2
l2 - 5 Ri
p^2
=
ZTTARZ
El
Substituting R2 f o r "j" in W e n n e r ' s equation,
the value of r e s i s t i v i t y , P^2'
Layer
a C k m Till w MarotX
M
•
Figure 14.
, .......
Cross sections from p r o f i l e contours.
(2)
34
Figure 15.
Cut p a r t i a l l y excavated, 60 f t . l e f t of Station 41+50.
However,
8) I j . = - J ' (known)
9) I
Es
d
R2
Es
Rs
10) I
E3
Ra
(known)
13)
14) Ra
E3_
R3
/Es^EsN
\Ri
R2''
Ea
VRi
R2''
A l l of the v a l u e s in Step 14) a r e known
except Ra which, therefore, can be determined. T h i s equation may, of c o u r s e ,
be used f o r any number of l a y e r s and w i l l
take the general f o r m f o r any number of
l a y e r s n as:
E
"n
^ /E
E
I -( n + n +
^
VRi
R2
E
R
\
n \
J
(3)
T h e use of Equation 3 b e c o m e s r a t h e r
laborious when it i s d e s i r e d to determine
the value of r e s i s t i v i t y f o r a l a y e r located
s e v e r a l depth-intervals below the s u r f a c e .
rE
E
' n +
^Ri
E
R2
n +
it can be proven that the t e r m
•ff^ )
%-l^
equals
the
term
T h e substitution of the latter t e r m
R
n-1
in Equation 3 then r e n d e r s ths solution of
the l a y e r values of r e s i s t i v i t y much more
expedient.
Proof of the identity of the above t e r m s
i s given as follows with r e f e r e n c e being
made to the t h r e e - l a y e r case:
Let R
designate the average value of r e s i s t a n c e
f o r an individual l a y e r of m a t e r i a l , and let
R designate the average value of r e s i s t a n c e
f o r any depth of s o i l m e a s u r e d f r o m the
s u r f a c e as given by the ratio of E it i s
evident that f o r the f i r s t l a y e r R i = R i =
but f o r subsequent l a y e r s the equality does
not hold. T h e r e f o r e , R^^
will represent
the average r e s i s t a n c e value f o r the depth
of n number of l a y e r s minus one, o r
35
1Q\
^3l2 ^ E3I2
- 3 ^
Ei"
Equation 3 can now be e x p r e s s e d a s ,
E
I
n
(4)
n
R
n-1
If in the three l a y e r c a s e a l l of the s o i l i s
considered to be homogeneous, then R i =
R2 = R 3 . Now, r e f e r r i n g to F i g u r e 2, the
question a r i s e s a s to whether the l a y e r
Equations 3 and 4 take into consideration
the fact that f o r a homogeneous m a t e r i a l
g
the ratio of |- or R , v a r i e s i n v e r s e l y with
the depth.
If the l a y e r equations do take into consideration this v a r i a t i o n , then it can be
proved, when R i = R 2 = R 3 , that Ra =
or t h a t R
14)
Figure 15.
n-1
E3
E3
or
I3
E3_
R2
E3
Also R 3 = R i
=-
3E3
where R2 = R
_ E2
n-1
I2
E2E1
-
E 2 ,
• Rl
Ri
21) I3
R2
R2
E3
E3
R3
Since R 2 = R i
„ , E3_.
2E3
R^ ^
5
Es
= —
n
Station 45 ^^ .
Kn-11 = ^ n - l
R3
n
E 2 I 1 E 1 I 2 - E 2 I 1 (from
Step 7)
22) R i = ^ =
23)
R3
=y-\
3R3
or
- Ri
If,
R2
Ri R2
E
T h e n substituting =-for r e s p e c t i v e R s and
Rs,
THE
USE O F T H E L A Y E R
PRACTICE
(5)
EQUATION
16) E3l2 _ E3I1 ^ E 3 E 1 I 2 - E s E J i
17)
E3I2 _ E3I1 ^ E 3 E 1 I 2 _ E 3 E 2 I 1
E2E1
EzEi
E2
1
E3I2 _ E3I1 ^ E3I2
E3I1
In o r d e r to c l a s s i f y the types of s o i l s
encountered, a s y s t e m of recognition i s
provided based upon ranges of l a y e r - v a l u e
r e s i s t i v i t i e s determined f r o m experience.
F o r the types of s o i l s existing in the
lower P e n i n s u l a r of Michigan the f o l l o w ing table has been developed:
36
Soil T y p e s
PL
0 -
10,000
10,000 -
25,000
25,000 -
50,000
50,000 - 150,000
150,000 - 500,000
C l a y and Saturated
Silt
Sandy C l a y and Wet
Silty Sand
Clayey Sand and Saturated Sand
Sand
Gravel
When the value of the l a y e r r e s i s t i v i t y
IS g r e a t e r than 500,000 o h m - c m the i n terpretation of s o i l must be augmented with
boring information. T h e r e a s o n for this
IS that a number of conditions c a n exist
which w i l l show high r e s i s t i v i t y v a l u e s ,
and these conditions range f r o m dry loose
sand and g r a v e l to weathered r o c k and
bedrock.
Inasmuch a s the thickness of the l a y e r
i s an a r b i t r a r y selection, the l a y e r - v a l u e
of r e s i s t i v i t y must represent the average
r e s i s t i v i t y of a l l the s o i l types lying w i t h in the boundaries of any p a r t i c u l a r l a y e r .
A f t e r a l l of the l a y e r - v a l u e s have been
calculated they a r e plotted in b a r - g r a p h
fashion agamst their r e s p e c t i v e i n t e r v a l s
of depth a s shown on F i g u r e 3. T h e v a l ues for the l a y e r s a r e then connected to
each other by lines drawn f r o m the middle
of e a c h l a y e r . T h e intersection of the
v a r i o u s range values with the r e s i s t i v i t y
connecting lines w i l l determine the e l e v a tion l i m i t s for the s o i l types. T h e s e i n t e r section points can then be connected f r o m
station to station to f r o m contour bounda r i e s which, in effect, gives a c r o s s -
sectional view of the s o i l p r o f i l e to any
depth investigated showing the type, l o cation, and relative quantity of s o i l m a terials.
CONCLUSION
It IS the w r i t e r ' s opinion that i n v e s t i gations of borrow and proposed c u t sections of considerable s i z e c a n be made
f a s t e r and provide g r e a t e r a c c u r a c y and
detail by the r e s i s t i v i t y method than by
such methods a s hand augering and s o i l
borings.
F o r example, there have been
a number of o c c a s i o n s when the a n a l y s i s
of s o i l deposits by the r e s i s t i v i t y method
h a s indicated the p r e s e n c e of m a t e r i a l s
not apparent f r o m s u r f a c e conditions and
shallow borings usually employed.
Although t h i s method i s s t i l l in the development stage, subsequent borings and pit
excavations proved the a n a l y s e s to be c o r rect.
T h u s the method of interpreting
the f i e l d data by the l a y e r - v a l u e d e t e r mination equation has been s u c c e s s f u l to
date.
It IS felt that the l a y e r - v a l u e d e t e r mination a s outlined here i s not s e r i o u s l y
affected, if at a l l , by the warping of the
equipotential bowl which n e c e s s a r i l y must
take place to conform to the v a r i o u s r e s i s t a n c e s of the heterogeneous l a y e r s
of m a t e r i a l . T h e r e f o r e , it i s the w r i t e r ' s
opinion that a s m o r e experience i s obtained and with f u r t h e r laboratory study,
the method w i l l prove to be sufficiently
accurate and r e l i a b l e to s a t i s f a c t o r i l y
predict the s o i l c h a r a c t e r i s t i c s and c o n ditions a s r e q u i r e d by the Department.