Communications on Hydraulic and Geotechnical Engineering
2014-01
ISSN 0169-6548
Ratio between stone diameter and nominal diameter
———————————— analysis of measured data —————————————
Henk Jan Verhagen*
Laura Jansen**
February 2014
*
**
Associate Professor, Department f Hydraulic Engineering, Faculty of Civil Engineering and Geosciences,
Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands.
Tel. + 31 15 27 85067; Fax: +31 15 27 85124
e-mail: [email protected]
Bachelor student, Department of Hydraulic Engineering
Communications on Hydraulic and Geotechnical Engineering 2014-01
Communications on Hydraulic and Geotechnical Engineering
2014-01
ISSN 0169-6548
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© 2014 TU Delft, Department Hydraulic Engineering,
Henk Jan Verhagen
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Communications on Hydraulic and Geotechnical Engineering 2014-01
1. Introduction
For describing the dimensions of stones both the values d50 and dn50 are used. The value of d50
is determined by sieving a sample and d50 is the “median diameter”, i.e. 50% of the total
weight of the stones are larger than the value d50. It is therefore relevant to know the relation
between d50 and dn50. The ratio between d50 and dn50 is given by:
dn50  Fs*d50
(1)
or
3
M n50  Fs d50
(2)
*
In literature (e.g. ROCK MANUAL [2007]) for Fs a value of 0.84 is given, while for Fs a value
of 0.6 is given, with a range between 0.34 and 0.72. For small stones in laboratory
experiments the range is between 0.66 and 0.70. In terms of Fs* this means a value between
0.70 and 0.90 for armour stone and 0.87 and 0.89 for laboratory stones. However, good
background information on this matter is missing. The only source for these values mentioned
in the Rock Manual is a publication of Laan from 1981.
2. Earlier work
The earliest found reference to Fs by the author is in a publication of VAN BENDEGOM [1967,
p6.4.29]. He mentions that Fs has a value of 0.5, however he does not give any reference or
background. This implies an Fs* of 0.8.
For the commonly used value of Fs* = 0.84 is usually referred to LAAN [1981]. Unfortunately
this publication is lost, so no information is available on the background and accuracy of the
value 0.84. In a follow up publication [LAAN, 1996] is given that the mean value of Fs is 0,6
with a standard deviation of 0,07. This implies a mean value of Fs* of 0,84 and a range from
0.81 to 0.88 (bandwidth of one standard deviation of Fs). In this research experiments are
done to find data in order to determine Fs*.
In an earlier report [LAAN, 1982] states that:
“… the relation between mass and diameter could be described by:
(3)
in which a and b are constants to be determined from experiments. Reference is made to
[LAAN 1979] and [LAAN 1981].
In order to determine the constants tests have been made by sieving many stones with
sieves with mesh sizes varying from 30 to 180 mm. The errors in converting a mass-curve
to a sieve curve were in general smaller than 10%, especially when the batches had only a
limited number of stones with high elongation.
M  a zb
For light and heavy gradings the relation between mass and thickness has been determined [LAAN 1981]. Six batches were investigated varying from 60-300 kg to 6000-10000 kg.
The average value of t/l for these stones varied from 0.57 to 0.53.
As stated above for four batches the relation between mass and sieve-size has been determined. Three of these four batches of smaller stones showed a mean value for t/l of about
0.44 and an average value for t/m of 0.75. The fourth batch consisted of very flat material
with a mean value for t/l of 0.33 and a mean value for t/m of 0.59.
It has been assumed that the ratio t/m = 0.75 is also valid for light and heavy gradings,
which then implies that for all types of investigated rock the relation between mass and
thickness and between mass and sieve size can be determined. This results in the following
equations:
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Communications on Hydraulic and Geotechnical Engineering 2014-01
M  0.6  m3
(4)
M  1.4  t 3
The error in general application of these relations is usually limited to less than 10%.
The influence of the value t/l on the mass is not large. Besides an increase of t/l may imply
as well as an increase or a decrease of the mass. When a decrease of t/l is caused by an
increase of l, the mass is increased. However when the decrease of t/l is caused by a decrease of t, the mass is decreased.”
(the above quote is a translation from the original Dutch text. The symbols have been adapted
to the symbols used in this report:
m = mesh size of sieve where the stone is just passing
l = length of the stone
t = thickness of the stone)
The coefficient 0.6 in equation 4 is equal to Fs. The value of Fs* can be found from the above
numbers in the following way:
Fs 
t
t
l  m  0.33  0.56
l 0.59
m
(5)
Fs*  3 Fs  0.824
From the above one may also conclude that Laan has derived the value of Fs* only from fine
gradings (his maximum sieve size was 180 mm).
3. Definition of M50 and dn50
Because for larger stones sieving is impossible the value of d50 is replaced by dn50, which is
often called the median nominal diameter:
d n50  3 V  3
M 50
(6)

In which  is the stone density in kg/m3 and M50 the “median stone weight”. According to the
ROCK MANUAL [2007], the definition of the M50 (p 108): “M50 is the mass of the theoretical
block for which half of the mass of the sample is lighter”, or more general: “The block mass is
expressed by My, where y per cent of the total (or cumulative) sample mass is lighter than M”.
But in the same document M50 is called the “median mass” (e.g. on page 107).
This is incorrect use of the term “median”. In statistics and probability theory, the median is
the numerical value separating the higher half of a data sample, a population, or a probability
distribution, from the lower half. The median of a finite list of numbers can be found by
arranging all the observations from lowest value to highest value and picking the middle one
(e.g. the median of {3, 5, 9} is 5) [Wikipedia]. On basis of the full distribution, the median
stone mass Mme is defined by:
M me

f ( x)dx 

1
2

 f ( x)dx
(7)


However, because by definition
 f ( x)dx  1 for a normalised distribution, this reduces to:

M me


f ( x)dx 
1
2
(8)
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Communications on Hydraulic and Geotechnical Engineering 2014-01
In which f(x) is the probability density function and Mme is the median stone mass. The
equation for the M50 as given in the rock manual is:
M 50


x  f ( x)dx 
1
2

 x  f ( x)dx
(9)

Example:
Given a set of 11 stones with a mass 1, 2, 2, 4, 5, 6, 7, 8, 9, 11, 15 kg. The total mass of this
sample is 70 kg. The average mass is 70/11 = 6.36 kg. The median mass Mme of the sample is
6 kg, while the M50 is 7 kg.
Figure 1: cumulative distribution of stone mass
Also for d50 often the term ”median grain size” is used. This is also incorrect, for the same
reason as explained above why the term “median stone mass” is incorrect for M50. However,
this usually does not lead to confusion, because it is practically impossible to determine the
value of dme from a sample when the particles are smaller than 5 mm. For values between 5
and 100 mm one could determine the dme by counting the individual number of stones on a
sieve, but that is seldom done.
4. Experiments
In order to get more insight in the distribution of Fs* a sample of stones has been measured in
detail. Also for each stone elongation and blockiness have been determined. For the
experiment a batch of 244 stones (609 kg) of stones from a depot were used. The stones were
approximately in class 90/150 mm. However this was not a batch to be handled according to a
given standard. The stones were provided by Rivierendriesprong in Papendrecht, Netherlands.
All tests were performed on their yard. The stones were Belgium limestone.
All stones were sieved with standard sieves (31.5, 45, 63, 90, 125, 180, 250 and 360 mm)
according to EN13383. Before sieving the stones were washed and before weighing the stones
were dried. All stones were marked and numbered.
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Communications on Hydraulic and Geotechnical Engineering 2014-01
Figure 1: Normal stone (left) and stone with soft, white lime (right
It was conclude that the material was not completely homogeneous. Part of the stones
consisted partly of some grey material. There were two variants of this material, a fast-drying
version and a slow drying version. Sometimes the grey area had a clear white borderline.
Figure1: Sieves used to measure the stones
Also from all stones the weight was determined, as well as elongation and blockiness.
Elongation was determined by determining the quotient of maximum length divided by the
thickness (smallest diameter) of the stone.
Figure 2: Calliper to measure elongation
The blockiness was determined by measuring the smallest rectangular box which could fit the
stone and dividing the volume of the stone by the volume of this box.
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Communications on Hydraulic and Geotechnical Engineering 2014-01
Figure 3: tool to measure the blockiness
From a selected number of stones also the density has been measured. The water content of
the stones varied from 0.11 % to 0.9%. There were a few stones of different composition in
the sample. The average density of the stones was 2660 kg/m3, within a range from 2550 to
2750 (standard deviation 85 kg/m3).
All data are presented in Annex 1.
The results of the sieving are presented in Figure 4:
Sieve size
Weight on sieve
Fraction on sieve
Fraction through
sieve
mm
kg
250
0,000
0,0000
1,0000
180
9,861
0,0162
0,9838
125
220,277
0,3617
0,6221
90
343,270
0,5636
0,0585
63
33,925
0,0557
0,0028
45
1,201
0,0020
0,0008
30
0,417
0,0007
0,0001
rest
0,085
0,0001
0,0000
total
609,034
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Communications on Hydraulic and Geotechnical Engineering 2014-01
100%
percentage througn sieve
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
30
300
grains size (mm)
Figure 4: Results of the sieving
For the analysis one may consider stones smaller than 30 mm as splinters. They were
probably created during handling of the batch and not representative of the stone class.
5. Determination of the d50 and the dn50
By fitting a line through the sieve curve using linear interpolation between the measured point
one finds a d50 of 117.4 mm (see figure 4). By fitting the data to Gauss curve, one finds a d50
of 117.3 mm, see figure 5.
Figure 5: Results of the sieving with Gauss fit
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Communications on Hydraulic and Geotechnical Engineering 2014-01
In summary sieving resulted in the following values:
value (mm)
perc
lineair
Gauss
5%
85,88
83,12
D10
10%
92,58
89,69
D15 (NLL)
15%
95,68
94,42
D25
15%
95,68
94,42
D50
50%
117,42
117,32
D60
60%
123,63
123,72
D85
85%
159,65
145,78
D90 (NUL)
90%
167,26
153,47
D98 (EUL)
98%
179,42
180,42
D60/D10
1,34
1,38
D85/D15
1,67
1,54
D05 (ELL)
From all individual stones also the dimensions were measured. From these dimensions one
may calculate elongation and blockiness. In the appendix the values are given. Elongation is
defined as:
LT  l
(10)
t
Blockiness is defined as:
BLc 
Vs
M 1

xyz  s xyz
(11)
From each stone one may calculate the dn = (M/s)0.33.
After sorting all the stones following their weight one may plot an exceedance graph of dn.
Figure 6 Sieve analysis of d50 and distribution of dn50
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Communications on Hydraulic and Geotechnical Engineering 2014-01
From this graph one can read the value of dn50. For this sample dn50 = 105 mm. From the sieve
analysis (figure 4 or figure 5) followed that the d50 was 117 mm, so the ratio Fs* = dn50/ d50 =
105.0/117.4 = 0,894 for this sample, which is a higher value than suggested by LAAN [1981].
However, the found dn50 is from a different stone than the found d50.
Another disadvantage of this approach is that one can only compare the values from the uses
sizes of the sieves, and interpolate in between. Using more sieves would give a better curve,
however, this is not physically possible. Therefore a virtual sieve can be used.
Figure 7: virtual sieve
From each stone the dimensions were determined. For the blockiness the values x, y and z are
known. The longest value, x, is not relevant for this analysis. The values y and z determine if a
stone may pass through the mesh of a sieve. See figure 7. When the stone is rather round
(light grey stone in figure 7) the value of y  z. In that case the mesh size m equals y. In case
the stone is rather flat (dark grey stone in figure 7) the value of m = y/√2 = y/1.4. The
following equation is an estimate for 0 < z < y:
m
y

z
1  0.45 1  
y

(12)
In this equation the factor 0.45 is a geometrical fit factor. From the above considerations
follow that for z = y the value of this factor is not relevant, and for z = 0 this value has to be
0.4. A factor of 0.45 gives a good fit for the data points.
With the use of this formula, one may determine the virtual mesh size of each individual stone.
As a next step one can sort stones on increasing mesh size and make an exceedance line.
One can plot the values of dn also in the same exceedance graph, see figure 8. One may read
from this graph that d50virtual is 121 mm, and dn50 is 105 mm. This gives an Fs* value of
105/121 = 0.868.
However, the stone which provides the value of d50virtual is a different stone, than the stone
providing the value of dn50 (in fact the d50virtual comes from stone #125-2, while the dn50 comes
from stone #125-26). But because from each individual stone the value of d50virtual and dn50 is
known it is possible to calculate Fs* = d/dn for each individual stone.
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Communications on Hydraulic and Geotechnical Engineering 2014-01
Figure 8 continuous virtual sieve results and individual values of Fs* plotted as function of dn
This value has also been plotted in figure 8 as a function of d. The average value Fs* = 0.845.
The median value Fs*me of is also 0.845, and the Fs* 50 is 0,843 (i.e. the value of Fs*
exceeded by 50% of the total weight of the batch. The difference between these three types of
“average” values is small. However it is clear that Fs* reduces for the bigger stones in the
batch. So it seems that Fs* is decreasing when the stone size is increasing. The average value
of Fs* = 0.85 is very near to the suggested value of LAAN [1981], this in contrary to the value
dn50/ d50 which is 0,868.
However, it is assumed that the value of Laan is based on dn50/ d50. The found value of Fs* =
0.868 falls within the ranges for Fs*as given in LAAN [1996]: 0.81 < Fs*< 0.88.
6. Relation with blockiness and elongation
One may expect a relation between Fs* and the elongation or blockiness. In figure 9 and figure
10 these relations are given.
Figure 9: relation between elongation and Fs*
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Communications on Hydraulic and Geotechnical Engineering 2014-01
Figure 10: Relation between blockiness and Fs*
From these figures it is obvious that in this sample there is no relation between elongation and
Fs*, and that there is a very week (and therefore not really significant) relation between
blockiness and Fs*.
7. Test with very small units
Recently VAN DEN HEUVEL [2013] did some sieve analysis on small scale stones to be used in
a hydraulic model investigation. He determined the distribution both by sieving as well as by
weighing individual stones. This resulted in the following data:
Non-exceeded percentages
5%
15%
50%
90%
98%
Density [kg/m3 ]
Yellow Sun d [mm]
Yellow Sun dn [mm]
0.99
0.99
1.16
1.09
1.50
1.50
2.06
2.13
2.50
2.39
2679
2679
Remarkable is that from this test follows that dn  d. However, when comparing these results
with figure 8 it seems indeed that when the diameter decreases Fs* increases.
8. Conclusions and recommendations
From the test with the stone batch followed that the average value of Fs* is nearly equal to the
value as presented by LAAN [1981]. However, one has to determine the d50 and the dn50
separately, one should not calculate the dn50 from the data of the weight of a stone with size
d50. It seems that for smaller stones Fs* approaches a value of 1. Blockiness and elongations
seems to have no influence on the value of Fs*.
Because of the differences between Fs* and Fs* , one cannot use the value of Fs* to calculate
for example the d15 from the dn15.
It is recommended to repeat this measurement with other batches, especially of a batch with a
larger size, but also see the differences with other types of stones.
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Communications on Hydraulic and Geotechnical Engineering 2014-01
References
LAAN, G. [1979] De relatie tussen de korrelverdeling en de massaverdeling, report RL-KO-79.04
Rijkswaterstaat, Wegbouwkundige Dienst, Delft
LAAN, G. [1981] De relatie tussen vorm en gewicht van breuksteen (the relation between shape and
weight of pieces of rock), report MAW-R-81079, Rijkswaterstaat, Wegbouwkundige Dienst,
Delft (Laan refers in another paper to this report with a slighly different title: “De relatie tussen
de vorm en de massa van stukken breuksteen”
LAAN, G. [1982] Kwaliteit en kwaliteitscontrole van breuksteen in de waterbouw, report MAW-R81054, WKE-R-82002, Rijkswaterstaat, Wegbouwkundige Dienst, Delft
Laan, G [1996] De relatie tussen eisen aan loskorrelige steenmaterialen en ontwerpparameters, report
P-DWW-096.069, Rijkswaterstaat, DWW
ROCK MANUAL [2007] The Rock manual, the use of rock in hydraulic engineering, CIRIA publication
C683, CIRIA-CUR-CETMEF, London
VAN BENDEGOM, L. [1967] Algemene waterbouwkunde, deel IIa, de natuur, Lecture notes TU Delft
VAN DEN HEUVEL, H.P.A. [2013] The effect of multiple storms on the stability of near bed structures,
M.Sc. –thesis TU Delft
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Communications on Hydraulic and Geotechnical Engineering 2014-01
Symbols used
d
dn
l
m
t
Fs
Fs *
M
diameter of the stone, defined as the mesh through which the stone is just passing
nominal diameter of the stone, as defined by eq. 4
longest size of the block (length)
mesh size of a sieve
shortest size of the block (thickness)
ratio between stone diameter and volume
ratio between stone diameter and nominal diameter
mass of the stone
14
Annex 1: Data
20,8
20,0
23,2
22,2
28,5
33,1
19,6
23,9
30,4
18,2
22,5
26,1
22,6
28,3
27,1
30,1
26,5
32,0
23,3
21,3
8,9
8,6
5,9
10,3
9,8
10,7
10,1
9,3
11,4
9,8
7,6
7,1
7,6
8,2
11,2
10,3
8,6
11,1
10,7
9,4
17,8
16,9
20,4
20,2
24,7
32,8
17,1
22,5
29,7
15,3
21,9
26,0
19,4
27,1
26,9
28,9
25,0
30,6
20,6
20,6
14,8
16,1
18,8
17,5
20,1
20,2
15,6
20,7
21,3
14,1
18,6
18,2
19,4
16,8
18,5
17,5
15,2
18,2
15,4
14,7
8,8
9,0
6,0
10,2
10,2
10,7
10,1
9,4
11,4
9,8
8,3
7,0
7,8
8,8
11,2
10,3
8,6
11,2
10,8
9,6
Water/stone
3551,8
3857,5
3116,5
5461,4
5777,1
8649,7
4008,1
5091,1
9193,7
3086,2
4303,9
4627,5
3592,1
4859,0
6989,3
8193,8
4301,8
7947,7
4295,8
3832,6
Water
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
9853,3
Volume (ml)
M,dry
180
M,before
10,8 28,9 26,0 10,9
Remarks
31,4
Z (cm)
9860,7
Y (cm)
1
X (cm)
Length (cm)
250
Thickn (cm)
Mass (g)
mass
Stone nr
Blockiness
Sieve size
Elongation
Communications on Hydraulic and Geotechnical Engineering 2014-01
125
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
5161,9
4466,6
3519,4
3796,5
3260,5
3703,4
4355,5
5492,1
4882,0
3278,1
3579,6
5173,9
4190,8
3623,6
4686,3
3463,6
3317,9
4697,8
3554,9
3438,6
3171,3
5010,9
3591,2
3271,9
3342,5
3936,1
1884,8
3714,6
2019,8
3953,8
23,9
25,1
22,6
23,6
21,5
21,5
22,5
28,1
24,7
22,1
20,7
25,6
20,0
24,3
25,5
18,2
19,3
26,7
18,3
20,1
21,0
22,9
22,0
21,3
19,0
21,2
20,9
20,9
22,6
18,3
8,5
10,6
8,5
7,0
7,4
9,5
9,8
9,2
7,5
8,0
10,1
8,5
10,2
8,5
10,7
11,8
9,6
11,3
11,7
9,1
8,7
9,0
8,1
8,5
11,5
10,1
5,8
8,6
3,4
11,3
22,6
24,4
20,1
21,9
19,2
21,0
21,8
25,3
23,5
18,6
20,3
23,1
17,5
22,3
24,4
16,2
17,2
26,0
17,1
19,1
17,9
20,1
20,1
20,9
16,4
21,1
19,7
18,0
21,6
16,9
22,0
14,1
16,3
20,3
18,8
13,9
17,4
20,0
19,0
18,4
13,8
21,6
17,1
17,3
15,4
14,2
16,6
15,6
14,1
17,2
17,7
18,8
18,6
15,3
13,7
14,2
16,9
17,6
18,9
15,9
8,6
10,8
8,5
7,0
7,5
9,6
9,8
9,2
7,5
8,0
10,8
8,6
10,2
8,5
10,8
12,1
9,6
11,4
11,7
9,2
8,7
9,0
8,1
8,5
11,5
10,0 *
5,8 Flat
8,6
3,4 Flat
11,3
1
1879,1
16,1
10,4 12,7 11,3 10,5
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Communications on Hydraulic and Geotechnical Engineering 2014-01
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
2143,5
1925,9
1663,0
1582,7
2977,1
2403,2
1877,9
2180,4
1938,9
3595,2
3639,1
2480,0
2807,7
1771,5
2125,8
2882,9
2290,5
2699,6
2328,7
2419,5
2533,3
2279,5
2632,8
3009,8
3076,6
1630,0
1607,7
2000,0
2446,4
2058,2
1981,8
2086,8
17,7
16,8
15,8
13,9
19,1
17,4
17,2
21,1
16,0
23,5
21,0
16,9
19,4
19,1
19,3
20,1
19,6
22,2
23,0
18,9
19,1
19,9
19,2
22,6
25,3
15,3
15,8
17,3
21,2
17,5
16,2
21,4
7,9
8,1
8,3
8,0
8,8
8,2
8,7
6,4
9,4
7,3
9,4
9,5
8,2
6,3
6,1
10,0
9,0
9,9
7,4
7,5
9,2
7,8
7,5
8,5
7,4
7,5
8,6
8,5
7,9
10,2
7,9
5,9
17,4
15,4
13,7
12,9
17,8
15,7
17,1
19,6
14,2
23,2
20,7
16,4
17,6
16,2
17,2
19,6
19,0
21,7
21,9
18,9
17,6
17,0
19,2
21,2
25,0
14,3
13,1
14,6
18,5
12,6
15,9
21,0
14,6 7,9
13,6 8,1
13,6 8,3
10,8 8,1
13,8 8,8
15,0 8,2
10,6 8,8
11,8 6,4
13,3 9,6
15,9 7,3
13,1 9,4
12,0 9,5
13,5 8,2
14,9 6,3
15,4 6,1
10,3 10,0
11,4 9,2
10,2 10,1
13,6 7,4
15,1 7,5
12,4 9,3
15,3 7,8
12,3 7,5
13,5 8,5
13,4 7,4
11,1 7,6
12,3 8,6
12,3 8,5
13,2 8,0
11,9 10,2
12,3 8,1
12,3 5,9
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Communications on Hydraulic and Geotechnical Engineering 2014-01
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35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
1696,2
3116,4
1141,2
2113,2
2936,9
3309,7
3664,7
2155,9
1057,8
3728,5
2366,7
3744,6
1626,3
3602,8
3149,7
2407,8
4280,7
4344,4
3948,6
2757,9
2076,0
3305,6
2918,1
3134,2
2520,7
2603,3
1997,7
1629,2
2074,3
3253,0
1582,1
2146,9
13,7
18,1
14,2
17,2
19,8
17,6
25,1
18,0
13,1
22,0
18,7
28,9
15,5
22,0
21,5
19,4
22,2
28,1
28,4
23,2
17,1
19,9
19,3
19,8
20,9
19,2
19,7
18,6
17,3
21,1
15,7
19,5
10,2
10,7
5,8
7,7
9,4
11,1
9,6
8,6
7,5
9,8
9,3
8,6
6,7
10,1
7,8
7,9
10,5
8,7
8,9
7,9
7,2
9,8
9,8
8,8
9,4
10,0
7,4
6,0
7,9
9,7
8,4
7,7
13,5
16,4
13,1
15,1
18,8
15,6
24,7
17,7
12,3
21,9
15,7
28,0
14,2
22,0
21,5
17,9
22,0
27,2
28,4
22,4
16,4
19,9
18,0
19,5
19,2
16,9
18,0
17,0
16,1
18,3
15,7
19,2
10,6
13,3
13,0
13,1
11,8
15,2
13,4
13,1
10,7
14,6
14,7
13,5
12,8
12,4
14,3
12,1
11,5
16,0
12,5
13,1
11,1
14,7
13,1
14,0
12,1
12,8
12,1
12,7
13,6
15,7
10,3
12,4
10,3
10,7
5,8
7,8
9,4
11,1
9,6
8,7 Much soft white
7,7
9,8
9,3
8,6
7,0
10,1
8,0
8,4
10,7 Blocky?
8,7
9,1
7,9
7,2
9,8
9,8
8,8
10,9
10,1
7,4
6,1
8,7
9,7 * Pictures
8,4
8,0
2147,9 2141,3
1720,0
2620
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67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
2434,2
1815,0
2044,1
2273,9
2030,4
1423,2
1389,8
1693,3
1378,6
1703,4
1607,9
2163,8
1203,0
1502,6
1366,4
1479,7
1612,3
1759,0
1944,5
2398,7
2190,7
2183,6
2046,3
1826,5
2101,7
2313,1
2361,6
1988,8
1917,6
1704,3
2808,4
1816,8
18,7
18,8
18,2
23,0
17,1
15,8
15,7
15,5
15,9
14,3
14,0
20,4
15,2
13,6
12,1
15,5
14,7
18,3
19,3
17,9
16,9
17,4
16,0
15,4
17,1
19,2
22,2
16,6
21,0
16,6
22,6
16,6
8,0
6,1
9,0
7,0
8,7
7,1
5,8
8,0
7,6
9,0
9,3
8,4
6,0
7,1
10,2
6,2
8,2
7,0
8,2
9,4
8,6
9,0
10,2
9,0
9,3
8,5
7,9
7,6
7,9
7,8
9,2
8,5
18,5
18,8
18,0
22,4
15,6
15,4
15,1
13,7
15,4
12,5
13,0
19,7
14,4
12,4
11,2
14,1
14,0
16,0
18,1
17,9
15,2
16,6
15,7
14,9
16,7
19,2
20,0
14,9
19,8
13,9
20,3
15,5
14,5 8,3
14,2 6,1
10,0 9,0
12,8 7,0
12,1 8,7
9,2 7,4
12,0 5,9
12,9 8,3 softwhite border
10,2 7,7
12,4 9,0
10,9 9,3
10,2 8,5
10,1 6,2
12,3 7,4
10,9 10,2 large softwhite border
12,4 6,2
12,3 8,2
13,0 7,0
11,3 8,2
12,4 9,4
14,5 8,6
11,9 9,1
11,2 11,2
11,4 9,0
11,4 9,3
13,0 8,6
14,9 7,9
14,5 7,6
11,6 8,0
12,5 8,1
12,6 9,3
12,3 8,5
1687,6 1683,4
1725,0
2390,0
1362,3 1357,8
1715,0
2250,0
19
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98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
1896,2
2881,9
1378,3
2588,6
1424,4
1439,2
2801,2
2016,8
2143,8
2856,7
1768,1
2585,9
1299,5
1115,1
1534,1
2439,5
2316,7
2219,5
2111,5
1019,8
2547,7
3489,2
3281,6
2822,2
2883,9
3109,0
3363,7
1483,7
2077,2
3060,1
1750,4
3088,2
16,2
19,0
16,2
21,8
20,7
16,8
20,2
18,0
17,4
21,3
16,7
21,6
15,4
15,3
15,6
18,6
19,2
19,0
20,9
14,3
17,7
24,0
22,4
23,0
23,0
19,6
22,4
17,1
17,8
21,2
15,7
21,7
7,9
9,6
6,3
8,7
6,7
5,8
9,0
6,1
7,6
8,3
7,3
7,4
6,1
5,8
8,2
8,1
8,6
8,8
6,6
6,0
10,6
8,5
9,8
9,3
8,6
9,0
10,0
6,4
8,2
8,6
8,5
7,6
15,5
16,5
16,0
20,9
20,7
16,0
19,1
16,2
15,6
19,5
13,7
20,9
13,1
13,5
14,0
17,5
18,4
18,4
20,4
14,1
15,5
23,6
22,4
22,3
22,4
18,1
20,3
16,0
15,6
18,2
14,8
21,0
13,7 7,9
13,2 9,9
10,8 6,3
14,4 8,9
11,0 6,7
11,8 5,9
13,3 9,3
14,1 6,1
13,0 7,6
13,7 8,5
13,4 7,3
14,5 7,4
12,8 6,1
12,5 5,9
13,7 8,4
14,1 8,3
13,2 8,6
11,8 9,3
13,4 6,6
12,1 6,0
11,3 10,7
13,1 8,5
14,2 10,0
12,6 9,4
12,5 8,6
15,1 9,1
12,5 10,1
13,3 6,4
15,0 8,2
16,5 8,6
11,2 8,6
14,7 7,6
20
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130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
1537,4
2258,7
2218,7
1834,7
2412,3
1348,8
2436,6
3219,9
3814,9
2651,2
2352,2
2325,6
2693,0
2193,7
1791,2
1811,0
2854,4
2242,7
1774,6
1322,4
1553,1
17,4
19,3
18,8
18,0
18,0
15,0
18,3
20,9
26,0
19,6
21,3
21,5
19,3
20,8
17,3
16,5
23,0
21,4
15,4
14,5
17,5
8,2
7,4
9,3
6,0
9,5
7,5
10,0
8,5
9,1
9,3
6,3
7,5
8,5
6,9
6,4
6,3
9,5
7,7
7,9
7,3
4,4
14,2
17,8
18,0
17,3
16,4
13,1
13,8
17,9
25,0
19,4
20,0
20,5
17,7
19,3
16,6
16,1
20,1
20,8
14,2
13,4
16,2
12,4 8,3
14,1 7,4
10,5 9,5
13,1 6,0
11,5 9,5
12,2 7,5
13,6 10,0
16,4 8,5
17,0 9,1
11,3 9,3
15,5 6,3
14,4 7,5
14,9 8,7
12,0 6,9
13,4 6,4
12,5 6,3
14,4 9,5
11,2 7,7
13,5 7,9
12,2 7,3 much soft lime
14,7 4,4 flat
1
2
3
4
5
6
7
760,1
976,8
1038,6
904,2
1198,4
590,0
884,6
12,4
15,1
14,5
13,6
13,3
12,9
13,9
4,3
6,9
7,5
6,5
7,5
5,5
5,0
11,0
14,6
11,9
12,6
12,8
11,5
13,1
10,7
9,0
11,7
9,9
10,0
9,0
10,2
8
9
920,7
1610,5
17,7
16,6
4,8 17,0 8,1
7,0 15,5 10,2
4,4
6,9
7,5
6,6
7,5
5,6 normal stone
5,1 normal stone with thin border
Normal soft stone with soft white
5,0 border
7,0
1321,6 1314,8
1700
2250
590,0
884,4
589,0
881,3
710,0
1405,0
925,0
1750,0
920,7
918,7
1400,0
1755,0
21
Communications on Hydraulic and Geotechnical Engineering 2014-01
10
11
12
13
14
15
16
17
18
797,4
1321,2
1007,3
1307,8
985,4
1808,8
1065,2
700,0
1036,4
15,1
15,6
17,4
18,6
16,7
23,6
14,1
13,1
18,6
5,5
6,3
5,4
6,8
5,0
7,9
7,7
5,7
4,2
13,9 8,9
14,7 11,3
16,7 9,0
18,2 8,5
16,4 9,2
23,1 9,4
12,0 10,4
10,9 9,0
17,7 10,6
19
839,0
12,7
6,0 11,2 11,2
20
21
22
23
24
25
26
27
28
29
30
31
886,4
1002,1
1617,9
634,7
915,2
1292,4
1199,3
1823,0
1276,0
1227,3
887,9
1410,6
18,4
14,1
17,9
17,0
13,1
17,1
15,5
23,0
20,4
18,1
13,0
19,1
4,8
6,4
7,5
4,3
7,6
5,7
8,0
6,0
5,5
6,9
5,5
6,3
18,3
12,6
17,2
17,0
11,4
16,0
15,1
22,3
19,8
17,7
11,5
18,4
8,0
11,1
10,4
9,0
7,9
9,2
7,8
10,3
10,1
7,2
10,2
9,7
63
1
2
3
319,0
432,5
449,0
11,3
11,3
13,0
3,9 10,2
6,0 10,4
3,6 12,4
6,7
7,0
7,5
4,1
6,0
3,6
45
1
2
3
103,7
122,3
101,6
8,5
6,9
6,2
1,9
3,9
3,0
5,0
5,5
4,7
1,9
4,1
3,1
7,9
6,0
5,6
5,7 Normal stone
6,5
5,4
6,9
5,1
7,9
7,7 soft normal stone
5,7 normal stone
4,3
Normal soft stone with soft white
6,3 border
Normal soft stone with soft white
4,8 border
6,4 soft stone
7,8 soft stone with hard white
4,3 soft stone
7,6 normal stone
5,7
8,3
6,0
5,8
7,1
5,7 mainly hard stone
6,3
797,4
797,1
710,0
1005,0
1064,9 1058,7
700,1 699,0
1400,0
700,0
1805,0
960,0
838,2
1400
1705
886,4 884,8
1002,1 999,5
1617,9 1608,6
634,7
634
913,8 906,9
2000
2000
1995
1990
1990
2330
2370
2620
2220
2345
1975
2300
839,1
887,8
886,7
22
Communications on Hydraulic and Geotechnical Engineering 2014-01
4
5
6
7
8
9
88,9
30,7
25,2
10,5
8,9
9,2
23