Report Estimating Dry Density From Soil Stiffness ...€¦ · Report Estimating Dry Density ... moisture content and stiffness is a potential alternative method for determining dry

Scott Fiedler, Product Manager Melvin Main, MarketingHumboldt Mfg. Co. Main Associates

7300 West Agatite Ave., Norridge, 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)

Report

Estimating Dry Density

From

Soil Stiffness & Moisture Content

29 June, 1999

Humboldt Mfg. Co.

7300 West Agatite

Norridge, IL 60656-4704

1

PPPPrrrroooobbbblllleeeemmmmIf any new method of evaluating soil compaction is to be widely accepted, a firmrelationship must be established between this method and the most accepted currentmethods, measurements of dry density.

OOOObbbbjjjjeeeeccccttttiiiivvvveeeeDevelop an analytical-empirical relationship between soil stiffness and density. Validatethe relationship with data from Humboldt GeoGauge™ measurements and acceptedmethods of measuring density.

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

ρD =ρ0

1 + 1.2 [ - .3].5CK

.5

where

C =(C1 σ1

P)4a

(1-υ)

C1 = is a function of moisture and soil type

σ1 = is the overburden stress

P = is typically between 1/2 and 1/4a = is the foot radiusυ = is Poisson’s ratio

ρD = is the dry density

ρ0 = is the ideal, void free density

K = is stiffness

Define C for a geographical region or group of soil classes, independent of everything butmoisture. Do this based on companion stiffness, moisture content and densitymeasurements. Then use C, measured stiffness and measured moisture content toestimate dry density. Compare the estimates to density measurements made with anuclear gauge and sand cone.

1 Roman D. Hryciw & Thomas G. Thomann, “Stress-History-Based Model for Cohesionless Soils”,Journal of Geotechnical Engineering, Vol. 119, No, 7, July, 1993

1)

2

RRRReeeessssuuuullllttttssss

Analytical-Empirical RelationshipEarly attempts at following this approach revealed two things.

• A more precise estimation was possible when moisture content was broken out ofthe constant C and

• More precision was possible when the values of C were calculated from a linearrelationship 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 drydensity. It also allows the values of C determined from the companion measurements tobe fitted to a linear equation with our two independent variables, K and m.

wheren is the slopeandb is the intercept.

This linear relationship between C, K and m allows a more appropriate value of C to usedin the estimate of each dry density as opposed to selecting a limited number of Cs to usedover several moisture ranges. Breaking m out of C and using this linear relationshipprovided closer agreement between measured and estimated dry density in 23% of thecases compared to not doing either.

Numerous other modifications of equation 1) were numerically analyzed relative toactual companion measurement data. The analytical-empirical relationship representedby equations 3 and 4 fit the data the best. Figure 1 is a 3D surface plot of K, M and ρD 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 theabove approach.

C = K{[(ρ0/ρD-1)/1.2] + 0.3}2

C = (K/m){[(ρ0/ρD-1)/1.2] + 0.3}2

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

2)

3)

4)

3

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 a

correlation coefficient of > .3 (typically > .5).

Validation of the RelationshipFive hundred and seventy seven (577) companion measurements were made inCalifornia, Ohio, Florida, Missouri, New York, North Carolina and Virginia by theFHWA, California Polytechnic Institute, the H. C. Nutting Co., the City of San Jose, theFDOT, the MODOT, the NYSDOT and the NCDOT. These measurements were madelargely independent of Humboldt. The data, the estimates of dry density and thecomparisons of the estimates to direct measurements are presented in Appendices 1through 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 & moisture

segregated 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 afunction of K and m, the presence of more than one linear relationship was apparent. Inother cases, there was a clustering of values of C that were calculated from companionmeasurements. When one or both of these conditions coincided with test sites orlocations, the data was correspondingly segregated and analyzed independently. Thisgreatly improved the results of the analysis in meeting the criteria stated earlier. Sinceonly 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 providesatisfactory estimates of density for every soil. Soils due to stabilization additives,construction methods, site conditions or just their nature are apparently atypical. Thedata from the FDOT is a good example. As can be seen from the raw data in Appendices5 and 6, that sandy, limestone stabilized soil are not typical of the soil behavior illustratedin 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 2is a 3D surface plot of K, M and ρD 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 ofthis information is available upon request.

4

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 inthe MODOT data.

CCCCoooonnnncccclllluuuussssiiiioooonnnnssssAn analytical-empirical relationship has been developed that allows the estimation of drydensity from soil stiffness and moisture content within tolerances that are typical in theuse current field measurements. The successful application of this relationship requiresthat it be adjusted for groups of similarly performing soils and atypical soils. Thisrelationship firmly connects soil stiffness, as measured by the Humboldt GeoGauge™,with dry density. This relationship in conjunction with companion measurements ofmoisture content and stiffness is a potential alternative method for determining drydensity.

5

FFFFiiiigggguuuurrrreeee 1111::::SSSSuuuurrrrffffaaaacccceeee PPPPllllooootttt ooooffff KKKK,,,, MMMM aaaannnndddd ρDDDD

aaaassss DDDDeeeessssccccrrrriiiibbbbeeeedddd bbbbyyyy EEEEqqqquuuuaaaattttiiiioooonnnnssss 3333)))) &&&& 4444))))

ρD =ρ0

1 + 1.2 [ - .3]mCK

.5

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

6

FFFFiiiigggguuuurrrreeee 2222::::SSSSuuuurrrrffffaaaacccceeee PPPPllllooootttt ooooffff KKKK,,,, MMMM aaaannnndddd ρDDDD

aaaassss DDDDeeeessssccccrrrriiiibbbbeeeedddd bbbbyyyy EEEEqqqquuuuaaaattttiiiioooonnnnssss 1111)))) &&&& 4444))))

ρD =ρ0

1 + 1.2 [ - .3]CK

.5

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

7

TTTTaaaabbbblllleeee 1111:::: SSSSuuuummmmmmmmaaaarrrryyyy ooooffff RRRReeeessssuuuullllttttssss

∆%, ρD (GeoGauge) re ρD (Nuc)(percentage of estimates within 5, 10and 15 % of the direct measurements)

DataSource

Number ofCompanion

Measurements

RelationshipUsed

5% 10% 15%

Density SpanGeoGauge/Nuc

(pcf)

R2

(correlation coefficient)ρD (Nuc) vs.

ρD (GeoGauge)

Cal. Poly. 80 Eq. 3 & 4 82% 100% - 32/35 0.83H.C.Nutting

66 Eq. 3 & 4 95% 5% - 34/33 0.86

San Jose 120 Eq. 3 & 4 70% 99% 100% 33/27 0.33FDOT(field)

112 Eq. 1 & 4 88% 100% - 23/18 0.43

FDOT(lab)

34 Eq. 1 & 4 97% 100% - 10/9 0.39

MODOT 30 Eq. 3 & 4 60% 100% - 39/36 0.77NYSDOT 50 Eq. 3 & 4 90% 100% - 0.31/0.34

Mg/m30.51

NCDOT 17 Eq. 3 & 4 100% - - 17/16 0.90FHWA 60 Eq. 3 & 4 88% 100% - 66/62 0.94

8

Appendix 1

Analysis of NCDOT Data

9

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10

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∆%: ρD (HSG) re ρ

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

ρD =ρ0

1 + 1.2 [ - .3]mCK

.5

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

DDDD eeeetttteeee rrrrmmmmiiiinnnnaaaa ttttiiiioooonnnn ooooffff CCCC

Soil Group #1:C = 3.7095(K/m.25) + 8.2414R2 = 0.8987

Soil Group #2:C = 5.6425(K/m.25) + 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

ρD, (HSG), pcf

Data

Linear Fit

∆%, ρD (GeoGauge) re ρD (Nuc)

ρD (GeoGauge), pcf

Measured vs. Estimated Density

11

Appendix 2

Analysis of Cal. Poly. Data

12

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13

CCCCaaaalllliiiiffffoooorrrrnnnniiiiaaaa PPPPoooollllyyyytttteeeecccchhhhnnnniiiicccc IIIInnnnssssttttiiiittttuuuutttteeee,,,, SSSSaaaannnn LLLLuuuuiiiissss OOOObbbbiiiissssppppoooo,,,, CCCCAAAADDDDaaaattttaaaa AAAAnnnnaaaallllyyyyssssiiiissss SSSSuuuummmmmmmmaaaarrrryyyy

∆%: ρD (HSG) re ρD (Nuc)

-10 -5 0 5 10

1

6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

%. Percent


Site #1, AASHTO A-2-6(U):C = 4.4561(K/m.25) + 12.704R2 = 0.8943

Site #2, AASHTO A-6(6):C = 3.765(K/m.25) + 19.165R2 = 0.8378

Site #3, AASHTO A-6(7):C = 4.2431(K/m.25) – 4.8947R2 = 0.8199

ρD =ρ0

1 + 1.2 [ - .3]mCK

.5

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

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

y = 0.9708x + 3.9808

R2

= 0.8292

90

100

110

120

130

90 100 110 120 130

ρD (HSG), pcf

Data

Linear Fit

s


ρD (GeoGauge), pcf


14

Appendix 3

Analysis of H. C. Nutting Data

15

HHHH.... CCCC.... NNNNuuuuttttttttiiiinnnngggg RRRRaaaawwww DDDDaaaattttaaaa

16

HHHH.... CCCC.... NNNNuuuuttttttttiiiinnnngggg CCCCoooo....,,,, CCCCiiiinnnncccciiiinnnnnnnnaaaattttiiii,,,, OOOOHHHHDDDDaaaattttaaaa AAAAnnnnaaaallllyyyyssssiiiissss SSSSuuuummmmmmmmaaaarrrryyyy

- 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

∆%, ρD (HSG) re ρD (Nuc)

Data Not Used for C

Data Used for C

%, Percent


Soil Group #1:C = 2.8335(K/m.25) + 11.465R2 = 0.7417

Soil Group #2:C = 3.1484(K/m.... 22225555) + 2.6727R2 = 0.9693

Soil Group #3:C = 2.8146(K/m.... 22225555) + 10.44R2 = 0.9414

Measured vs. Predicted Density(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

ρD (HSG), pcf

Data

Linear Fit


ρD (GeoGauge), pcf


17

Appendix 4

Analysis of San Jose Data

18

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19

CCCCiiiittttyyyy ooooffff SSSSaaaannnn JJJJoooosssseeee,,,, CCCCAAAADDDDaaaattttaaaa AAAAnnnnaaaallllyyyyssssiiiissss SSSSuuuummmmmmmmaaaarrrryyyy

- 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

∆%: ρD(HSG) re ρ

D (Nuc)

%, Percent

ρD =ρ0

1 + 1.2 [ - .3]mCK

.5

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

Determination of C

y = 3.421x + 12.423R2

= 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

0 32919 0

9 5

100

105

110

115

120

125

130

9 0 100 110 120 130

ρD (HSG), pcf


ρD (GeoGauge), pcf


20

Appendix 5

Analysis of FDOT Field Data

21

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22

FFFFDDDDOOOOTTTTFFFFiiiieeeelllldddd DDDDaaaattttaaaa AAAAnnnnaaaallllyyyyssssiiiissss SSSSuuuummmmmmmmaaaarrrryyyy

ρD =ρ0

1 + 1.2 [ - .3]CK

.5

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

∆%: ρD (HSG) re ρD (Nuc)

- 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 6

4 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

R2

= 0.4305

9 5

100

105

110

115

120

125

ρD (HSG), pcf

Data

Linear Fit


Soil Group #1:C = 0.3536(K/m.25) + 1.8587R2 = 0.9439

Soil Group #1a:C = 0.4613(K/m.25) + 1.0223R2 = 0.97

Soil Group #2:C = 0.5391(K/m.... 22225555) + 0.1964R2 = 0.9568

Soil Group #3:C = 0.4126(K/m.... 22225555) + 0.8955R2 = 0.9828

Soil Group #4:C = 0.1288(K/m.25) + 6.48R2 = 1


ρD (GeoGauge), pcf


23

Appendix 6

Analysis of FDOT Lab Data

24

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25

FFFFDDDDOOOOTTTTLLLLaaaabbbb DDDDaaaattttaaaa AAAAnnnnaaaallllyyyyssssiiiissss SSSSuuuummmmmmmmaaaarrrryyyy

ρD =ρ0

1 + 1.2 [ - .3]CK

.5

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

∆%: ρD (HSG) re ρ

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

Measured vs. Predicted Density(FDOT Data)

y = 0.5861x + 44.97

R2

= 0.3865

104

106

108

110

112

114

116

104 106 108 110 112 114 116

ρD(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)

DataLinear Fit


ρD (GeoGauge), pcf


26

Appendix 7

Analysis of MODOT Data

27

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28

MMMMOOOODDDDOOOOTTTTDDDDaaaattttaaaa AAAAnnnnaaaallllyyyyssssiiiissss SSSSuuuummmmmmmmaaaarrrryyyy

∆%: ρD (HSG) re ρD

(Nuc)

- 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

ρD =ρ0

1 + 1.2 [ - .3]mCK

.5

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


Soil Group #1:C = 4.5241(K/m.25) – 2.0602R2 = 0.9239

Soil Group #2:C = 5.9674(K/m.25) – 16.752R2 = 0.9834

Measured vs. Predicted Density(MODOT Data)

y = 0.7527x + 26.806R

2

= 0.7717

8 5

9 5

105

115

125

135

145

8 5 9 5 105 115 125 135ρ

D (HSG), pcf

Data

Linear Fit


ρD (GeoGauge), pcf


29

Appendix 8

Analysis of NYSDOT Data

30

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31

NNNNYYYYSSSSDDDDOOOOTTTTDDDDaaaattttaaaa AAAAnnnnaaaallllyyyyssssiiiissss SSSSuuuummmmmmmmaaaarrrryyyy

∆%, ρ(HSG) re ρ( 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

ρD =ρ0

1 + 1.2 [ - .3]mCK

.5

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

Measured vs. Predisted Density(NYSDOT Data)

y = 0.7879x + 0.4068

R2

0 5073

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 2.10ρD (HSG), Mg/m

3

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


ρD (GeoGauge), pcf


32

Appendix 9

Analysis of FDOT Lab Data

33

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34

FFFFHHHHWWWWAAAA TTTTuuuurrrrnnnneeeerrrr---- FFFFaaaaiiiirrrrbbbbaaaannnnkkkkssssDDDDaaaattttaaaa AAAAnnnnaaaallllyyyyssssiiiissss SSSSuuuummmmmmmmaaaarrrryyyy

ρD =ρ0

1 + 1.2 [ - .3]mCK

.5

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

∆%: ρD (HSG) re ρD

(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 + 4.5858R

2

= 0.9383

80

90

100

110

120

130

140

150

160

ρD (HSG), pcf

Data

Linear Fit


Soil Group #1 (Bridge):C = 7.7675(K/m.25) – 12.337R2 = 0.5699

Soil Group #2 (Agg. Pit):C = 5.8177(K/m.... 22225555) – 25.173R2 = 0.9839

Soil Group #3 (Sand Pit):C = 3.1862(K/m.... 22225555) + 2.5947R2 = 0.932

Soil Group #4 (Clay Pit):C = 33.626(K/m.25) – 69.423R2 = 0.9556


ρD (GeoGauge), pcf


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Report Estimating Dry Density From Soil Stiffness ...€¦ · Report Estimating Dry Density ... moisture content and stiffness is a potential alternative method for determining dry