2017 International Conference on Transportation Infrastructure and Materials (ICTIM 2017) ISBN: 978-1-60595-442-4

Study on Light Dynamic Penetration to Test Coarse Sand

Relative Density in Bridge Culvert Back Sand Filling

J.B. Lv, Y.M. Yin, Z.T. Yu, Z.C. Xu, G. F. Chen, F. Yang

Guangdong University of Technology, Guangdong Guangzhou, China, 510006

With the rapid development of highway construction in China, vehicle

bouncing at bridge approach has become a very important influencing factor

and has been paid much attention in domestic and overseas transportation study.

Strict quality control in bridge-culvert back sand filling and construction

process is of vital importance to prevent the differential settlement of bridge

approach. However, the objective and effective test of sand relative density in

bridge-culvert backfilling has been a hot yet difficult problem. In this study,

based on model and on-site test under a scientific research program of the

Guangdong Transportation Group － Sand Relative Density Test on

Bridge-Culvert Backfilling (2008-13), the mechanism and the feasibility of light

penetration test have been systematically studied. Through model and field test,

the feasibility of light penetration to test relative density of coarse sand in

bridge-culvert back-wall filling is testified. And through static penetration test

contrast, the reliability of this test is further confirmed. Based on the above, the

empirical relationship between the light penetration blow-counts N10 and the

relative density Dr is established after simple calculation. Thus the light

penetration method is proposed to test the relative density of medium and

coarse sand in bridge-culvert back-wall filling. This study lays a foundation for

the spread-use of the light dynamic penetration to count the technical

index—the relative density of sand in bridge-culvert back-wall filling.

Keywords: highway bridge-culvert back-wall filling; light penetration,

blow-counts, relative density, test method

1. Introduction

Light dynamic penetrating test is a kind of commonly used in-situ soil test

method. The method utilizes hammer force to hit the drill into soil and judges

the soil nature according to the strength of penetrating force, which reflexes the

different nature of soil mechanism. The light dynamic penetrating test apparatus

is light, portable and convenient for control, and many countries have launched

researches in this field and reached great achievements ever since the 1950s. At

the same time, the application of the light dynamic penetrating test method in

the sand soil has been improved. However, due to the light hammer and the

weak hitting force and the possible elastic bending of the pile, this method was

considered applicable only in dividing the soil mechanism layers and in

evaluating the equi-distribution degree of soil layers in fine sand soil. However,

construction practice manifests that light penetration is also applicable to test

the relative density of medium, coarse and gravelly sand in bridge-culvert

back-wall filling.

In bridge-culvert back-wall filling, sand soil and material of good

permeability are suitable. The medium coarse sand is widely used in highway

bridge-culvert backfilling for its good permeability, availability, convenience

and low price. However, the appropriate evaluating method is still unavailable

to measure the technical index—the “relative density” of backfill sand, which

causes a problem for quality control of bridge-culvert back-fill that is widely

and dispersedly used in highway construction. Based on the model test and field

test, the study systematically analyzed the feasibility, the test and evaluation of

light penetration to test the sand relative density in bridge-culvert back-wall fill.

The symbols and notation used in the paper analysis are defined in table l.

Table 1. Symbols and notation.

Cu coefficient of uniformity, uniformity coefficient

Cc coefficient of curvature

Dr sand relative density

emax maximum void ratio

emin minimum void ratio

F coefficient of compressibility

Gs specific gravity

h drill penetrating depth

hcr critical depth

Mx Fineness modulus

N10 the light penetration 30cm blow-counts above

critical depth

N10L blow-counts right at the critical depth

N10＇ revised light penetration blow-counts above critical

depth

N10L＇ revised light penetration blow-counts right at

critical depth

ρ the Correlation Coefficient

Qc the static penetration cone point resistance

2. Model test

2.1 Brief introduction of model test

Figure 1. The testing model tank.

φ45

40

φ25

drill

drill pole

hammer base

heavy hammer

Leading bar

Figure 2. The light dynamic penetrating apparatus.

16

φ40

60°

34.64

8

φ25

Figure 3. Size of the driller (unit mm).

In this study, sand of four sizes are chosen in bridge and culvert backfill,

and the model test is proceeded in a model tank (2m×2m×2m). 23 effective tests

are accomplished and 72 groups of data are collected. The model sink is shown

in figure 1, the light dynamic penetrating equipment and its index is shown in

table 2. The drawing of the light dynamic penetrating equipment is shown in

figure 2, the driller structure in figure 3, the constituents of test sand in table 3

and the substantial index of sand in table 4.

Table 2. The dynamic penetrating equipment and its index in model test.

The hitting hammer The driller Diameter of

the

penetrating

pile

(mm)

Penetrating

index

(Blow/30cm)

Weight of

the hammer

(kg)

Hitting

distance

(cm)

Diameter

(mm)

Cone-shaped

angle

(°)

10±0.2 50±2 40 60 25 N10

Table 3. Constituents of test sand（%）.

Sand Sieve grain diameter(mm)

10 5 2 1 0.5 0.25 0.074

No.1 97.2 86.8 32.9 14.8 6.3 0.0 0.0

No.2 100.0 99.8 92.6 66.8 42.6 17.5 4.0

No.3 100.0 94.1 73.4 57.5 41.2 13.9 2.9

No.4 100 95.3 66.8 38.1 20.8 3.2 1.2

Table 4. Substantial index of the test sand.

Sand

Fineness

modulus

Mx

Gs emax emin F d50

/mm Soil

No.1 4.17 2.65 0.9410 0.3862 1.4358 1.285 Super-coarse sand

No.2 2.47 2.63 1.0293 0.4611 1.2323 0.565 Fine sand

No.3 2.66 2.65 0.7980 0.4096 0.9478 0.600 Medium sand

No.4 3.36 2.66 0.9710 0.4409 1.2014 1.450 Coarse sand

Note 1： Mx is counted out after sieving analysis, compressibility factor

F=(emax-emin)/emin；

Note 2: The test sand is called quartz sand because of its quartz

component.

2.2 Model Test Work

0

30

60

90

120

150

180

210

0 20 40 60 80100120140160

enetrating depth h(cm)

blow counts N10(blow/30cm)

Dr=

0.5

4Dr=

0.7

0

0

30

60

90

120

150

180

210

0 20 40 60 80100120140160

enetrating depth h(cm)

blow counts N10(blow/30cm)

D

r

=

0…

Figure 4. Sand No.1 result. Figure 5. Sand No.2 result.

0

30

60

90

120

150

180

210

0 20 40 60 80 100 120 140

enetrating depth h(cm)

blow counts N10(blow/30cm)

Dr=0.49

Dr=0.59

Dr=0.74

Dr=0.90

0

30

60

90

120

150

180

210

0 20 40 60 80 100 120 140 160 180

enetrating depth h(cm)

blow counts N10(blow/30cm)

Dr=0.49Dr=0.62Dr=0.7

6

Figure 6. Sand No.3 result. Figure 7. Sand No.4 result.

Based on the features of material commonly-used in highway

bridge-culvert backfill, four different sizes of medium and coarse sand are

chosen for model test in the model tank (2m×2m×2m) and Figure 4~7 is a

curve graph that shows the relation between Dr and N10 and h. as shown in the

figures, from the very beginning of the driller penetrating into the earth surface,

N10 increases gradually with the reaching of penetrating depth; when certain

depth is reached, N10 reaches its utmost and increases little downward. The

certain depth is called critical depth and marked as hcr.

2.2.1 Analysis of model test results

1. Critical depth hcr

When the light penetration is applied to test the sand relative density in

bridge-culvert backfill, the sand surface is also a part of vital importance.

However, because of the influence from the surface effect and sand self-weight

stress, the light penetration blow-counts N10 increases with the reach of

penetrating depth. In order to figure out change rule of the blow-counts in such

a depth range so as to control the construction quality of bridge-culvert backfill

and to effectively measure the backfill-sand relative density, it is necessary to

make sure of the critical depth in light penetration and make the critical depth as

a boundary. When the drill is above the critical depth, right at it or under it, the

rules of blow-counts change with the depth are studied separately.

Through analysis of the model test results, hcr～Dr relation (shown in

Figure 8) of the four sand types is revealed. And as shown in Figure 8, hcr in

light penetration test really exists and increases with Dr.

2. Light penetration blow-counts N10

From model test results, N10 increases with penetrating depth h and sand

relative density Dr. when above critical depth; when critical depth is reached and

downward, N10 keeps stable. Test results shows that Dr is the most sensitive

factor to influence the blow-counts right at critical depth N10L, which is well

related to the sand relative density Figure 9). From Figure 9, N10L evidently

increases with Dr.

0

30

60

90

120

150

180

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

relative density Dr

critical depth h

cr(cm)

sand No.1 Mx=4.17 sand No.2 Mx=2.47

sand No.3 Mx=2.66 sand No4 Mx=3.36

Figure 8. hcr-Dr relation in model.

In addition, N10L also has relation with the sand fineness modulus Mx. from

Figure 9, when Dr＜0.80 and N10L is stable, the bigger the Mx, the greater the

relative density. The size order of Dr is: fine sand＜medium sand＜coarse sand

＜super coarse sand.

0

30

60

90

120

150

180

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

blow counts N10L

relative density Dr

sand No.1 Mx=4.17sand No.2 Mx=2.47sand No.3 Mx=2.66

Figure 9. N10L-Dr relation in model test.

3. Contrastive analysis of light penetration to test sand relative density in

bridge-culvert back-wall fill

There have already been a great deal of static penetration study and its

theory and test study are relatively mature. Therefore, the static penetration is

accepted and testified in the engineering field. In order to test the feasibility of

light penetration to test the sand relative density in bridge-culvert back-wall fill,

the contrastive analysis between light penetration and static penetration occurs

at the same time. After comprehensive study on the test results from static

penetration and light penetration, close linear relationship are found existing in

the two penetration methods to test coarse sand relative density, as shown in

Table 5.

Table 5. Relationship between light penetration blow-count above critical

depth N10 and the static penetration cone point resistance Qc.

Sand Formula concerned ρ

No.1 N10=5.6916Qc＋3.1361 0.9852

No.2 N10=4.5820Qc＋7.4610 0.9800

No.3 N10=4.4725Qc＋7.3006 0.9881

No.4 N10=4.0083Qc＋2.3670 0.9791

In the above table, N10 in the formula refer to 30cm blow-counts, Qc is the

weighted average of cone point resistances at the correspondent 30cm depth.

2.2.2 Dr～N10 empirical formula regression of the model test

According to the features of light penetration test curve-line and the analysis on

the Dr～N10 relation, application of critical depth as the boundary leads into two

cases:

When above the critical depth, statistical analysis and linear regression of

test data of the four sands show multi-linear relation between Dr and Mx and h

and N10 (blow-counts/30cm). Non-linear regression analysis results in formula

(1).

When at critical depth and below, based on the non-linear regression

analysis, the N10L ~ Dr relation satisfies the log function relation (in formula 2).

Dr=0.3237+0.1090Mx-0.0037h+0.0070N10 （ρ＝0.9175） （1）

Dr=-0.1057+0.2080ln(N10L) （ρ＝0.9368） （2）

Where h is drill penetrating depth below critical depth（cm），h＜hcr.

It can be seen from formula (2) that, when above the critical depth, except

N10, sand fineness Mx has the biggest influence on Dr; when other parameters

are the same, the bigger the Mx, the greater the sand relative density; next is the

influence of N10, when other parameter are the same, the bigger the N10, the

greater the relative density.

3. Field test

3.1 Field test work

Model test result of this paper has been put into field test practice in

several super-highways. Two abutments (real shape shown in Figure 10) of

K124+820 culverts in 22nd

contracted section of Yue-Gan super-highway are

taken as an example to proceed field test so that the influence of the

model-tank-size to the test result is known. And in this way, the interrelationship

between the light penetration model test and the field test is testified, and the

application of model test result to constructions is displayed.

Figure 10. Exploration of abutment in field test.

The effective size of the field-test back-wall ＞ 3m × 3m × 5m;

Composition and physical index of backfill sand are shown in Table 6;

penetration result in Figure 11.

0

30

60

90

120

150

180

210

240

270

0 20 40 60 80 100

blow counts N10 (blow/30cm)

penetrating depth h(cm)

1#-3Mx=3.01

0#-1Mx=2.93

0#-2Mx=2.90

Figure 11. N10-h relation in field test.

Table 6. Composition and physical index of backfill sand.

Mx Sand composition /%

Gs emin emax F Cu Cc 9.5 4.75 2.36 1.18 0.60 0.3 0.15 0.075 <0.075

3.00 98.4 93.7 74.2 55.1 28.6 6.6 1.5 0.2 0 2.65 0.4171 0.9065 1.1730 4.2 0.7

Note: the filter-hole size unit mm

3.2 Analysis of field test data

From Figure 11 and Figure 12, field test light penetration curve and its

deformation are the same as model test the correction coefficient of N10 in

model test is 3

2 , Figure 12 shows the contrast between the field-test

blow-counts and the N10L～Dr relationship which is the result when N10L of the

No.4 sand is divided by the similar coefficient 3

2 . From Figure 12, after

correction, when N10L in model test is the same as N10L in field test, sand

relative density basically shows no difference. It can be deduced from the above

that, formula (3) and (4) are the revision of formula (1) and (2).

0

30

60

90

120

150

180

210

0 0.2 0.4 0.6 0.8 1

relative density Dr

blow-counts N

10L（

blow/30cm）

No.4 sand of in-door test

field test

Figure 12. N10L comparison between sand No.4 and in field test.

Dr=0.3237+0.1090Mx-0.0037h+0.0070N10＇ （3）

Dr=-0.1057+0.2080ln(N10L＇) （4）

Where N10＇ is revised light penetration blow-counts above critical depth,

/10

'

10 NN ， =3

2 ；N10L＇ is revised light penetration blow-counts right at critical

depth, /10

'

10 LL NN ; h is penetrating depth in light penetration (cm), h＜hcr.

Table 7. Contrast between Dr value of backfill sand at 1#－2 test points and

the field surveying value.

MX h N10 Computation

value

Real-survey

value

difference/ratio notes

3.00 30 28 0.73 0.76 -0.03/-3.9%

3.00 60 44 0.73 0.76 -0.03/-3.9%

3.00 90 59 0.72 0.76 -0.04/-5.3%

3.00 120 80 0.81 0.76 0.05/6.6%*

3.00 150 75 0.79 0.76 0.03/3.9%

*Critical depth site in field test.

Put the test data from 1#－2 testing points into empirical formula （1） and

（2） respectively; counted out is the contrast between Dr value of backfill sand

at 1#－2 test points and the field surveying value (shown in table 7). from table

7, during field test, when penetrating depth h＜hcr, error tolerance is less than

10% between relative density Dr computed out by formula (1) and the field

survey value; when h≥hcr, corresponding error tolerance is less than 10% when

Dr is computed out by formula (2), which has proved the feasibility and

correctness of model empirical formula (1) and (2).

Put the No.4 sand test data into revised formula (3) and (4); counted out is

the contrast between relative density in field light penetration test and field

survey value (shown in table 8). from table 8, when penetrating depth h＜hcr

(above the critical depth), error tolerance is less than 5% between the Dr value

computed out by formula (3) and field survey value; when h≥hcr (below critical

depth), error tolerance is less than 10% when value computed by formula (4),

which shows the correctness of revised in-door model test result and that it can

be put into field test use.

Table 8. Contrast between computed No.4 sand Dr value and field

surveyed Dr value.

MX h N10 Computed

value

Value in Field

survey

difference/

ratio

notes

3.36 30 17 0.73 0.76 -0.03/-3.9%

3.36 60 34 0.76 0.76 0.00/0.0%

3.36 90 43 0.73 0.76 -0.03/-3.9%

3.36 120 45 0.73 0.76 -0.03/-3.9%*

3.36 150 44 0.72 0.76 -0.04/-5.3%

* Critical depth site in mode test

4. Light penetration method to test bridge-culvert sand backfill

Based on test research achievements and the author’s experience

accumulated in long period of construction practice, when to test the relative

density of bridge-culvert sand backfill by light penetration method, the key

points are as follows:

Fetch the representative backfill sand sample from the construction site

to do the in-door test according to current regulations and to fix the sand

fineness modules Mx;

Depth should be controlled within 2m (3m the utmost) each time when

light penetration is used to test relative density of backfill sand.

According to the actual shape and size of the bridge-culvert back-wall,

disperse 3~5 test points at random in each back-wall. Distance between

two test-points is more than 1.2m; the effective distance between the test

points and the back-wall border should be more than 0.6m, so that

influences of test point to test point and back-wall border to test point

can be avoided.

Applied is the light-penetration test equipment (shown in table.2) to

penetrate from the sand surface. Keep the pole upright, the utmost

inclining angle is less than 2%; lift the 10kg hammer to the effective

drop-height and let it fall freely with the blow frequency 15~30 hits/min.

Record the blow-counts N10 in each 30cm penetration. When the

blow-counts is over 100, or when the penetrating depth reaches 3m, stop

working;

Take N10 as the x-axis and penetrating depth h as Y-axis, draw a N10-~h

curve, according to field backfill material features to rectify penetrating

abnormal points so as to eliminate the influence of huge-sized sand to

the penetrating result.

Based on N10～h curve, confirmed is the critical depth hcr at single test

point in light penetration test. (N10 increases with the reaching of

penetrating depth; when certain depth is reached, blow-counts N10

reaches its utmost, and increases little downwardly. This depth is named

critical depth in this paper.). Above the critical depth, put the surveyed

N10 into the empirical formula (3) to compute the sand relative density

Dr; blow the critical depth, put N10 into the empirical formula (4) to

compute Dr;

． Take 0.6m as one layer and respectively compute the representative

value of relative density according to formula as follows.

Sn

tDD rrk

(5)

In the formula:

rD refers to the average value of all relative density of sand at each test

point in back-wall;

t refers to the modulus that changes with the layer and the guaranteed

efficiency (or confidence degree ); as shown in documents in attached table

B, the guaranteed efficiency of t is 95%

S refers to standard deviation of each single point value;

n refers to single value.

5. Conclusion

1) In the light penetration test, the sand relative density is the most

sensitive factor that influences the blow-counts N10. Sand fineness modulus Mx

also exerts influence on the blow-counts N10.

2) According to the analysis of model test result, above the critical depth,

the sand relative density has linear relationship with the light penetration

blow-counts N10. Regression formula (1) is obtained based on the Crammer

Rule; below critical depth, the blow-counts N10L ~ Dr relation satisfies the log

function relation.(seen in formula 2).

3) After revision of the model similar modulus in empirical formula （1）

and （2）, revised formula (3) and (4) are obtained. When the penetrating depth

is h＜hcr, formula (3) can be applied to compute the sand relative density based

on the parameters in field test; when h≥hcr, formula (4) can be used to count

the relative density of field filling sand based on the surveyed N10.

4) According to the contrastive analysis between test study and static

penetration study, the feasibility of light penetration is testified in its use to test

relative density of medium and coarse sand in bridge-culvert back-wall filling.

Based on the above, a set of convenient and applicable test method is put

forward to test the “relative density” of medium and coarse sand in

bridge-culvert back-wall filling.

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