Report,_Density_vs._K

8/7/2019 Report,_Density_vs._K

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Scott Fied ler, Prod uct Man ager Melvin Main , Marketin gHumbold t Mfg. Co. Main Associates

7300 West Agatite Ave., Nor ridge, IL 60656, U.S.A. 16 Vegas Dr., Hanover, PA 17331, U,S,A.800-544-7220 extension 231 (Voice) 717-637-8246 (Voice & Fax)

708-456-0137 (Fax) [email protected] (Email)

[email protected] (Email)

Repo r t

Est ima t in g Dr y Den sit y

Fr o m

So il St if f n ess & Mo ist u r e Co n t en t

29 Ju n e, 1999

Hu mbol d t Mf g . Co .

7300 West Aga t it e

No r r id ge, IL 60656-4704


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PPPPrrrr oooo bbbb llll eeeemmmmIf any new method of evaluating soil compaction is to be widely accepted, a firmrelationship must be established between this method and the most accepted current

methods, measurements of dry density.

OOOO bbbb jjjj eeeecccc tttt iiii vvvv eeeeDevelop an analytical-empirical relationship between soil stiffness and density. Validatethe relationship with data from Humboldt GeoGauge measurements and accepted

methods of measuring density.

AAAApppppppprrrr oooo aaaacccc hhhhBegan with the analytical-empirical relationship that was developed by BBNTechnologies of Cambridge, MA some 4 years ago from the work of Hryciw & Thomann1.

D =0

1 + 1.2 [ - .3].5C

K

.5

where

C =(C11P)4a

(1-)

C1 = is a function of moisture and soil type

1 = is the overburden stressP = is typically between 1/2 and 1/4

a = is the foot radius

= is Poissons ratio

D = is the dry density

0 = is the ideal, void free densityK = is stiffness

Define C for a geographical region or group of soil classes, independent of everything but

moisture. Do this based on companion stiffness, moisture content and density

measurements. Then use C, measured stiffness and measured moisture content to

estimate dry density. Compare the estimates to density measurements made with anuclear gauge and sand cone.

1Roman D. Hryciw & Thomas G. Thomann, Stress-History-Based Model for Cohesionless Soils,

Journal of Geotechnical Engineering, Vol. 119, No, 7, July, 1993

1)


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RRRReeeessss uuuu llll tttt ssss

Analytical-Empirical Relationship

Early attempts at following this approach revealed two things.

A more precise estimation was possible when moisture content was broken out of

the constant C and More precision was possible when the values of C were calculated from a linear

relationship with stiffness and moisture content.

Solving equation 1) for C yields

If we let C = Cm, where m = (% moisture content by weight)/100), then C can berepresented as

This representation allows for moisture content to be included in each estimate of dry

density. It also allows the values of C determined from the companion measurements to

be fitted to a linear equation with our two independent variables, K and m.

where

n is the slope

and

b is the intercept.

This linear relationship between C, K and m allows a more appropriate value of C to used

in the estimate of each dry density as opposed to selecting a limited number of Cs to used

over several moisture ranges. Breaking m out of C and using this linear relationshipprovided closer agreement between measured and estimated dry density in 23% of the

cases compared to not doing either.

Numerous other modifications of equation 1) were numerically analyzed relative toactual companion measurement data. The analytical-empirical relationship represented

by equations 3 and 4 fit the data the best. Figure 1 is a 3D surface plot of K, M and D asdescribed by this relationship. The relationship appears to be well behaved in the rangesof density, stiffness and moisture content that most applications will encounter.

Based on the usage of current methods for evaluating compaction and a consensus ofGeoGauge customers, the following criteria were established for the evaluation of the

above approach.

C = K{[(0/D-1)/1.2] + 0.3}2

C = (K/m){[(0/D-1)/1.2] + 0.3}2

C = n(K/m.25) + b

2)

3)

4)


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a) Estimates of dry density should be within 5% of the measured values about 70% ofthe time & within 10% > 90% of the time.

b) The span of measured & estimated densities should be almost the same.

c) A one-to-one correspondence of measured to estimated densities should yield acorrelation coefficient of > .3 (typically > .5).

Validation of the Relationship

Five hundred and seventy seven (577) companion measurements were made inCalifornia, Ohio, Florida, Missouri, New York, North Carolina and Virginia by the

FHWA, California Polytechnic Institute, the H. C. Nutting Co., the City of San Jose, the

FDOT, the MODOT, the NYSDOT and the NCDOT. These measurements were madelargely independent of Humboldt. The data, the estimates of dry density and the

comparisons of the estimates to direct measurements are presented in Appendices 1

through 9.

Each appendix contains the following information.

Multiple plots of raw data; density vs. stiffness vs. moisture content

Summaries of how well C was determined form a function of stiffness & moisturesegregated by groups of similarly performing soils

Plots of estimated vs. measured density in terms of percentage difference and one-

to-one correspondence All the data used to determine C and numerical data for all density estimates,

segregated by data that was used to determine C and data that was not2

It was evident that several classes or groups of similarly performing soils wererepresented by the data from each source. In some cases, when C was plotted against a

function of K and m, the presence of more than one linear relationship was apparent. In

other cases, there was a clustering of values of C that were calculated from companion

measurements. When one or both of these conditions coincided with test sites orlocations, the data was correspondingly segregated and analyzed independently. This

greatly improved the results of the analysis in meeting the criteria stated earlier. Since

only the California Polytechnic Institute provided soil classifications with its data, thevalidity of this operation will need to be confirmed with the sources of the data.

It is also evident that the relationship represented by equations 3 and 4 will not provide

satisfactory estimates of density for every soil. Soils due to stabilization additives,construction methods, site conditions or just their nature are apparently atypical. The

data from the FDOT is a good example. As can be seen from the raw data in Appendices

5 and 6, that sandy, limestone stabilized soil are not typical of the soil behavior illustrated

in the other appendices. For such soils, it was found that by using the relationshiprepresented by equations 1 and 4 satisfactory estimates of density were possible. Figure 2

is a 3D surface plot of K, M and D as described by equations 1 and 4.

2 Due to the volume of data, this information is omitted from the pdf version of the report. A hard copy of

this information is available upon request.


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Table 1 summaries the results presented in the appendices. The 3 evaluation criteriaapplied across the 10 data sources are met 96% of the time. Only criteria a) is missed in

the MODOT data.

CCCC oooo nnnn cccc llll uuuu ssss iiiioooo nnnn ssss

An analytical-empirical relationship has been developed that allows the estimation of drydensity from soil stiffness and moisture content within tolerances that are typical in the

use current field measurements. The successful application of this relationship requires

that it be adjusted for groups of similarly performing soils and atypical soils. This

relationship firmly connects soil stiffness, as measured by the Humboldt GeoGauge,with dry density. This relationship in conjunction with companion measurements of

moisture content and stiffness is a potential alternative method for determining dry

density.


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FFFFiiiigggg uuuurrrr eeee 1111 ::::

SSSSuuuurrrr ffff aaaacccc eeee PPPPllll oooo tttt oooo ffff KKKK,,,, MMMM aaaannnn dddd DDDDaaaassss DDDDeeeesssscccc rrrr iiiibbbbeeeedddd bbbbyyyy EEEEqqqq uuuuaaaatttt iiiioooo nnnn ssss 3333 )))) &&&& 4444 ))))

D =0

1 + 1.2 [ - .3]mCK.5

C = n(K/m.25) + b


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FFFFiiiigggg uuuurrrr eeee 2222 ::::

SSSSuuuurrrr ffff aaaacccc eeee PPPPllll oooo tttt oooo ffff KKKK,,,, MMMM aaaannnn dddd DDDDaaaassss DDDDeeeesssscccc rrrr iiiibbbbeeeedddd bbbbyyyy EEEEqqqq uuuuaaaatttt iiiioooo nnnn ssss 1111 )))) &&&& 4444 ))))

D = 0

1 + 1.2 [ - .3]CK.5

C = n(K/m.25) + b


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TTTTaaaabbbb llll eeee 1111 :::: SSSSuuuummmmmmmmaaaarrrr yyyy oooo ffff RRRReeeessssuuuu llll tttt ssss

%, D (GeoGauge) re D (Nuc)(percentage of estimates within 5, 10

and 15 % of the direct measurements)

Data

Source

Number of

Companion

Measurements

Relationship

Used

5% 10% 15%

Density Span

GeoGauge/Nu

(pcf)

Cal. Poly. 80 Eq. 3 & 4 82% 100% - 32/35

H.C.Nutting

66 Eq. 3 & 4 95% 5% - 34/33

San Jose 120 Eq. 3 & 4 70% 99% 100% 33/27 FDOT

(field)

112 Eq. 1 & 4 88% 100% - 23/18

FDOT(lab)

34 Eq. 1 & 4 97% 100% - 10/9

MODOT 30 Eq. 3 & 4 60% 100% - 39/36

NYSDOT 50 Eq. 3 & 4 90% 100% - 0.31/0.34

Mg/m3

NCDOT 17 Eq. 3 & 4 100% - - 17/16

FHWA 60 Eq. 3 & 4 88% 100% - 66/62


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Appen d ix 1

An a l ysis o f NCDOT Da t a


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NNNNCCCCDDDDOOOOTTTT RRRRaaaawwww DDDDaaaatttt aaaa


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NNNNCCCCDDDDOOOOTTTTDDDDaaaatttt aaaa AAAAnnnn aaaallll yyyyssss iiiissss SSSSuuuummmmmmmmaaaarrrr yyyy

%: D (HSG) re D (Nuc)

-4.0 -2 .0 0.0 2.0 4.0 6.0

1

3

5

7

9

1 1

1 3

1 5

1 7

%. Percent

D =0

1 + 1.2 [ - .3]mCK

.5

C = n(K/m.25) + b

DDDD eeeetttt eeee rrrr mmmmiiii nnnn aaaa tttt iiii oooo nnnn oooo ffff CCCC

Soi l Gr ou p # 1:C = 3 .7095(K/ m.2 5) + 8 .2414R2 = 0 . 8987

Soi l Gr ou p # 2:C = 5 .6425(K/ m.2 5) + 3 .4313R2 = 0 . 8331

Measured vs. Predicted Density

(NCDOT Data)

y = 0.8154x + 15.339

R

2

= 0.9029

75.0

80.0

85.0

90.0

95.0

75.0 80.0 85.0 90.0 95.0

D

, (HSG), pcf

Data

Linear Fit

%, GeoGau e re Nuc

GeoGau e , cf

Measured vs. Estimated Density


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Appen d ix 2

An a l ysis o f Ca l . Po l y. Da t a


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CCCCaaaallll .... PPPPoooo llll yyyy.... RRRRaaaawwww DDDDaaaatttt aaaa


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CCCCaaaallll iiiiffff oooo rrrr nnnn iiiiaaaa PPPPoooo llll yyyytttt eeeecccc hhhhnnnn iiiicccc IIIInnnn ssss tttt iiiitttt uuuu tttt eeee,,,, SSSSaaaannnn LLLLuuuu iiiissss OOOObbbbiiiissssppppoooo ,,,, CCCCAAAADDDDaaaatttt aaaa AAAAnnnn aaaallll yyyyssss iiiissss SSSSuuuummmmmmmmaaaarrrr yyyy

%: D (HSG) re D

(Nuc)

-10 -5 0 5 10

1

6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

%. Percent


Sit e # 1 , AA SHTO A -2 -6 (U):C = 4 .45 61 (K/ m.2 5 ) + 12 .704R2 = 0 . 8943

Sit e # 2, A ASHTO A -6(6):C = 3 .765 (K/ m.2 5 ) + 19 .165R2 = 0 . 8378

Sit e # 3, A ASHTO A -6(7):C = 4 .24 31 (K/ m.2 5 ) 4 .8947R2 = 0 . 8199

D =0

1 + 1.2 [ - .3]mCK

.5

C = n(K/m.25) + b

Measured vs. Predicted Density(Cal. Poly. Data)

y = 0.9708x + 3.9808

R

2

= 0.8292

90

10 0

11 0

12 0

13 0

90 100 110 120 130

D

(HSG), pcf

Data

Linear Fit

s

%, GeoGau e re Nuc

GeoGau e , cf



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Appen d ix 3

An a l ysis o f H. C. Nu t t in g Da t a


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HHHH.... CCCC .... NNNNuuuu tttt tttt iiiinnnn gggg RRRRaaaawwww DDDDaaaatttt aaaa


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HHHH.... CCCC .... NNNNuuuutttt tttt iiiinnnn gggg CCCCoooo ....,,,, CCCC iiiinnnn cccc iiiinnnn nnnn aaaatttt iiii,,,, OOOOHHHHDDDDaaaatttt aaaa AAAAnnnn aaaallll yyyyssss iiiissss SSSSuuuummmmmmmmaaaarrrr yyyy

- 1 5 - 1 0 - 5 0 5 1 0 1 5

1

3

5

7

9

1 1

1 3

1 5

1 7

1 9

2 1

2 3

2 5

2 7

2 9

3 1

3 3

%, D (HSG) re D (Nuc)

Data Not Used for C

Data Used for C

%, Percent


Soi l Gr ou p # 1:

C = 2 .8335(K/ m.2 5) + 1 1 .465R2 = 0 .7417

Soi l Gr ou p # 2:C = 3 .1484(K/ m.... 2222 5555 ) + 2 .6727R2 = 0 .9693

Soi l Gr ou p # 3:C = 2 .8146(K/ m.... 2222 5555 ) + 1 0.44R2 = 0 .9414


(H.C. Nutting Data)

y = 0.9174x + 9.489

R2

= 0.8638

9 0

100

110

120

130

140

9 0 100 110 120 130 140

D(HSG), pcf

Data

Linear Fit

%, GeoGau e re Nuc

GeoGau e , cf



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Appen d ix 4

An a l ysis o f Sa n Jo se Da t a


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SSSSaaaannnn JJJJoooo sssseeee RRRRaaaawwww DDDDaaaatttt aaaa


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CCCC iiiitttt yyyy oooo ffff SSSSaaaannnn JJJJoooo sssseeee,,,, CCCCAAAADDDDaaaatttt aaaa AAAAnnnn aaaallll yyyyssss iiiissss SSSSuuuummmmmmmmaaaarrrr yyyy

- 2 0 - 1 5 - 1 0 - 5 0 5 1 0 1 5

1

4

7

1 0

1 3

1 6

1 9

2 2

2 5

2 8

3 1

3 4

3 7

4 0

4 3

4 6

4 9

5 2

5 5

5 8

Data Not used for C

Data Used for C

%: D(HSG) re

D(Nuc)

%, Percent

D =0

1 + 1.2 [ - .3]mCK

.5

C = n(K/m.25) + b

Determination of C

y = 3.421x + 12.423

R2 = 0.8517

0

2 0

4 0

6 0

8 0

100

120

140

160

180

200

0 1 0 2 0 3 0 4 0 5 0

K/(m0.25

), MN/m

Measured vs, Predicted Density(San Jose Data)

y = 0.5763x + 49.73

R2

9 0

9 5

100

105

110

115

120

125

130

9 0 100 110 120 130

D (HSG), pcf

%, GeoGau e re Nuc

GeoGau e , cf



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Appen d ix 5

An a l ysis of FDOT Fiel d Da t a


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FFFFDDDDOOOOTTTT RRRRaaaawwww FFFF iiiieeeellll dddd DDDDaaaatttt aaaa


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FFFFDDDDOOOOTTTTFFFF iiiieeeellll dddd DDDDaaaatttt aaaa AAAAnnnnaaaallll yyyyssss iiiissss SSSSuuuummmmmmmmaaaarrrr yyyy

D =0

1 + 1.2 [ - .3]CK

.5

C = n(K/m.25) + b


- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8

1

4

7

1 0

1 3

1 6

1 9

2 2

2 5

2 8

3 1

3 4

3 7

4 0

4 3

4 64 9

5 2

5 5

5 8

6 1

6 4

6 7

7 0

7 3

7 6

7 9

8 2

8 5

8 8

9 1

9 4

9 7

100

103

106

109

112

115

%, Percent

Measured vs, Predicted Density(FDOT Data)

y = 0.589x + 44.563

R

2

= 0.4305

9 5

100

105

110

115

120

125

D (HSG), pcf

Data

Linear Fit


Soi l Gr oup #1 :C = 0 .353 6(K/ m.2 5 ) + 1 .85 87R2 = 0 . 9439

Soi l Gr oup # 1a :C = 0 .461 3(K/ m.2 5 ) + 1 .02 23R2 = 0 .97

Soi l Gr oup #2 :C = 0 .539 1(K/ m.... 2222 5555 ) + 0 .1964R2 = 0 . 9568

Soi l Gr oup #3 :C = 0 .412 6(K/ m.... 2222 5555 ) + 0 .8955R2 = 0 . 9828

Soi l Gr oup #4 :C = 0 .128 8(K/ m.2 5 ) + 6 .48R2 = 1

%, D GeoGau e re D Nuc

GeoGau e , cf



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Appen d ix 6

An a l ysis o f FDOT La b Da t a


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FFFFDDDDOOOOTTTT RRRRaaaawwww LLLLaaaabbbb DDDDaaaatttt aaaa


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FFFFDDDDOOOOTTTTLLLLaaaabbbb DDDDaaaatttt aaaa AAAAnnnn aaaallll yyyyssss iiiissss SSSSuuuummmmmmmmaaaarrrr yyyy

D =0

1 + 1.2 [ - .3]CK

.5

C = n(K/m.25) + b

%: D (HSG) re D

(Lab.)

- 4 - 3 - 2 - 1 0 1 2 3 4 5

1

2

3

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

1 5

1 6

1 7

%, Percent

Data Not Used for C

Data Used for C


(FDOT Data)

y = 0.5861x + 44.97

R

2

= 0.3865

104

106

108

110

112

114

116

104 106 108 110 112 114 116

D(HSG), (pcf)

Data

Linear Fit

Determination of C

y = 0.3947x + 1.8007

R2

= 0.9397

4

5

6

7

8

9

1 0

1 1

1 2

1 3

1 4

0 1 0 2 0 3 0

K/m, (MN/M)

Data

Linear Fit

%, D GeoGau e re D Nuc

GeoGau e , cf



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Appen d ix 7

An a l ysis o f MODOT Da t a


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MMMMOOOODDDDOOOOTTTT RRRRaaaawwww DDDDaaaatttt aaaa


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MMMMOOOODDDDOOOOTTTTDDDDaaaatttt aaaa AAAAnnnn aaaallll yyyyssss iiiissss SSSSuuuummmmmmmmaaaarrrr yyyy


- 1 0 - 5 0 5 1 0

1

4

7

1 0

1 3

1 6

1 9

2 2

2 5

2 8

%. Percent

D =0

1 + 1.2 [ - .3]mCK

.5

C = n(K/m.25) + b


Soi l Gr ou p # 1:C = 4 .524 1(K/ m.2 5) 2 .0602R2 = 0 .9239

Soi l Gr ou p # 2:C = 5 .967 4(K/ m.2 5) 16 .752R2 = 0 .9834


(MODOT Data)

y = 0.7527x + 26.806

R

2

= 0.7717

8 5

9 5

105

115

125

135

145

8 5 9 5 105 115 125 135

D

(HSG), pcf

Data

Linear Fit

%, GeoGau e re Nuc

GeoGau e , cf



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Appen d ix 8

An a l ysis o f NYSDOT Da t a


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NNNNYYYYSSSSDDDDOOOOTTTT RRRRaaaawwww DDDDaaaatttt aaaa


32/35

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NNNNYYYYSSSSDDDDOOOOTTTTDDDDaaaatttt aaaa AAAAnnnn aaaallll yyyyssss iiiissss SSSSuuuummmmmmmmaaaarrrr yyyy

%, (HSG) re ( N u c )

-10 -5 0 5 10

1

3

5

7

9

11

13

15

17

19

21

23

25

27

29

%, Percent

Not Used for C

Used for C

D =0

1 + 1.2 [ - .3]mCK

.5

C = n(K/m.25) + b

Measured vs. Predisted Density

(NYSDOT Data)

y = 0.7879x + 0.4068

R2

1.70

1.75

1.80

1.85

1.90

1.95

2.00

2.05

2.10

1.70 1.80 1.90 2.00 2.10

D (HSG), Mg/m

Data

Linear Fit

Deterimination of C

y = 4.1333x + 11.744

R

2

= 0.887

6

5 6

106

156

206

256

1 0 2 0 3 0 4 0 5 0

K / m , MN/m

Data

Linear Fit

%, GeoGau e re Nuc

GeoGau e , cf



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Appen d ix 9

An a l ysis o f FDOT La b Da t a


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FFFFHHHHWWWWAAAA RRRRaaaawwww DDDDaaaatttt aaaa


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FFFFHHHHWWWWAAAA TTTTuuuurrrr nnnneeeerrrr ---- FFFFaaaaiiiirrrr bbbbaaaannnn kkkkssssDDDDaaaatttt aaaa AAAAnnnn aaaallll yyyyssss iiiissss SSSSuuuummmmmmmmaaaarrrr yyyy

D =0

1 + 1.2 [ - .3]mCK

.5

C = n(K/m.25) + b

%: D

(HSG) re D(Nuc)

- 1 5 - 1 0 - 5 0 5 1 0 1 5

1

3

5

7

9

1 1

1 3

1 5

1 7

1 9

2 1

2 3

2 5

2 7

2 9

%, Percent

Data Not Used for C

Data Used for C

Measured vs, Predicted Density

(FHWA Data)

y = 0.9686x + 4.5858

R2

= 0.9383

80

90

10 0

11 0

12 0

13 0

14 0

15 0

16 0

Data

Linear Fit


Soi l Gr ou p # 1 (Br idg e):C = 7 .7675(K/ m.2 5) 12 .337R2 = 0 . 5699

Soil Gr oup # 2 (A gg . Pit ):C = 5 .8177(K/ m.... 2222 5555 ) 25 .173R2 = 0 . 9839

Soi l Gr oup # 3 (San d Pi t ):C = 3 .1862(K/ m.... 2222 5555 ) + 2 .59 47R2 = 0 .932

Soil Gr ou p # 4 (Cl ay Pit ):C = 33 .626(K/ m.2 5) 69 .423R2 = 0 . 9556

%, GeoGau e re Nuc


Report,_Density_vs._K

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