ap-3-11.dvi

Acta Polytechnica Vol. 51 No. 3/2011

Surface Roughness and Porosity of Hydrated Cement Pastes

T. Ficker, D. Martǐsek, H. M. Jennings

Abstract

3Dprofile and roughness parameters were used to perform an extensive study of the fracture surfaces of hydrated cement
pastes. One hundred and eight specimens were prepared with six different water-to-cement ratios. The surfaces of the
fractured specimens are the subject of a study analysing the height irregularities and the roughness. The values of
the 3D surface profile parameters and the roughness parameters of the fractured specimens were computed from digital
replicas of surface reliefs assembled bymeans of confocal microscopy in three differentmagnifications: 5×, 20× and 50×.
Seventy-eight graphs were plotted to describe and analyze the dependences of the height and roughness irregularities
on the water-to-cement ratio and on the porosity of the cement hydrates. The results showed unambiguously that the
water-to-cement ratio or equivalently the porosity of the specimens has a decisive influence on the irregularities of the
fracture surfaces of this material. The experimental results indicated the possibility that the porosity or the value of
the water-to-cement ratio might be inferred from the height irregularities of the fracture surfaces. It was hypothesized
that there may be a similarly strong correlation between porosity and surface irregularity, on the one hand, and some
other highly porous solids, on the other, and thus the same possibility to infer porosity from the surfaces of their fracture
remnants.

Keywords: roughness analysis, fracture surfaces, cement-based materials, confocal microscopy.

1 Introduction
The surface features of fractured materials are valu-
able sources of information on the topological, struc-
tural and mechanical properties of the materials.
However, in the research field of cementitious ma-
terials there have only been a restricted number of
studies dealing with the surface features of frac-
tured specimens. Some early surface studies of hy-
drated cement materials focused on fractal proper-
ties [1, 2], whereas others [3–5] investigated rough-
ness numbers (RN) or similar surface characteris-
tics [6–8].
In the RN studies [3–5] dealing with fracture

surfaces, the authors used as a research tool the
so-called roughness numbers RN, which proved to
be correlated to energy-based mechanical quantities
e.g. toughness but, unfortunately, they did not
show a correlation with porosity-dependent quanti-
ties, e.g. compressive strength. In our preliminary
study [9], it was illustrated that, in addition to the
roughness numbers RN, there are very promising
surface parameters of another kind called the sur-
face profile (SP) and surface roughness (SR) pa-
rameters derived from three-dimensional (3D) dig-
ital replicas of fracture surfaces. It has been in-
dicated [9] that these SP and SR parameters, in
contrast to RN, might show a correlation with
porosity and with porosity-based quantities such as
compressive strength and, as such, they could be-
come an important complement to RN characteris-
tics.

As has been highlighted previously [9], the strik-
ing difference between RN and SP/SR characteris-
tics consists in their definitions. RN numbers quan-
tify the increase in the area of fracture surfaces, i.e.
they are overall area characteristics, whereas SP/SR
parameters evaluate surface irregularities, i.e. they
quantify height differences on fracture reliefs.
In our preliminary report [9], only three types of

SP/SR parameters were tested, though there is a
larger series of these 3D parameters. In addition, in
the preliminary report [9] the tested specimens cov-
ered only four values of the water-to-cement ratio r,
namely 0.4, 0.6, 0.8, and 1.0, though the reliability of
the experimental conclusion is increasedby including
more values of r. Last but not least, some vagueness
may be added to the results by the porosity of speci-
mens inferred from the r-values that are used, rather
than fromdirectmeasurements. All thesepointshave
been improved in the present communication, which
is basedona larger series of SP/SR parameters, on a
more numerous spectrum of r-values, on direct mea-
surements of porosity and, in addition, on a larger
number of specimens. Thismakes the present results
more reliable and more precise than the preliminary
results [9].
The goal of the present communication is to pro-

vide clear experimental evidence showing porosity as
a main factor controlling the irregularity of the frac-
ture surfaces of porous materials. For this purpose,
the behavior of the profile parameters SP and rough-
ness parameters SR has been analyzed in terms of
various porosity values.

Acta Polytechnica Vol. 51 No. 3/2011

Fig. 1: Scheme of surface irregularities

2 Surface profile and
roughness parameters

In this study, six different profile parameters (SPp,
SPv, SPz, SPc, SPa, SPq,) andsevendifferent rough-
ness parameters (SRp, SRv, SRz, SRc, SRa, SRq,
SRzjis) are employed. This means that thirteen in-
dependent parameters are used as a measure of the
irregularity of fracture surfaces. All these parame-
ters are derived from 3D digital replicas (maps) of
the surfaces. In our case, the digital maps have been
created by means of confocal microscopy (for more
details, see [9]). The map may be viewed as a three-
dimensionalmatrix [xi, yi, zi]where thediscrete func-
tion zi = f(xi, yi) approximates the fracture surface,
which is in realitymore or less a smoothwavy surface
z = f(x, y).

SP parameters are derived from the measured
map f(xi, yi), whereas SR parameters are associ-
ated with a different function fR(xi, yi) formed from
f(xi, yi) by filtering out the wavy components pos-
sessing wave lengths longer than a critical value λc
(for more details see [9]). Briefly, SP parameters
characterize surfaces on all measured length scales,
but SR chracterizes those length scales that are
shorter than λc. The algorithms for the computa-
tion of SP and SR parameters are very similar; only
their source functions differ. To determine SP the
starting function is given by f(xi, yi), whereas for
SR it is the filtered function fR(xi, yi). The compu-
tationalalgorithmsarebrieflyexplained inthe follow-
ing paragraphs with the aid of Figure 1, which has
been drawn for simplicity in two dimensions rather
than in three dimensions.
Parameters SPp/SRp — these parameters repre-

sent the total maxima on the graphs of the source
functions f(xi, yi)/fR(xi, yi) (Figure 1), i.e.

SPp/SRp → total max{zpi} (1)

Parameters SPv/SRv — inform us about the to-
tal minima on the graphs of the source functions
f(xi, yi)/fR(xi, yi) (Figure 1), i.e.

SPv/SRv → total min{zvi} (2)
Parameters SPz /SRz — are determined by the

sumof the totalmaximumand the totalminimumon
the graphs of the source functions f(xi, yi)/fR(xi, yi)
(Figure 1), i.e.

SPz /SRz → total max{zpi}+total min{zvi} (3)
Parameters SPc/SRc —represent the arithmetic

averagesof the sumsof the localmaximaandminima
on the graphs of the source functions (Figure 1), i.e.

SPc/SRc →
1
m

m∑
i=1

(local max{zpi}+local min{zvi})
(4)

where m is an overall number of local extremes (local
maxima and local minima).
Parameters SPa/SRa — are given as mean

heights of the graphs of the source functions
f(xi, yi)/fR(xi, yi) (Figure 1), i.e.

SPa =
1

L · M

∫ ∫
(LM)

|f(x, y)|dxdy (5)

SRa =
1

L · M

∫ ∫
(LM)

|fR(x, y)|dxdy (6)

where L × M is the area of vertical projection of
f(x, y)/fR(x, y) into the plane xy.
Parameters SPq/SRq — provide us with the

square roots of the mean of the squares of the
source functions f(xi, yi)/fR(xi, yi) — rms values
(Figure 1), i.e.

SPq =

√
1

L · M

∫ ∫
(LM)

[f(x, y)]2dxdy (7)

SRq =

√
1

L · M

∫ ∫
(LM)

[fR(x, y)]2dxdy (8)

Acta Polytechnica Vol. 51 No. 3/2011

Parameter SRzjis — represents the ten-point
arithmetic average of the five highest peaks and the
five deepest valleys of the source function fR(x, y)
(Figure 1), i.e.

SRzjis →
1
5

5∑
i=1

(zmax5pi + z
min5
vi ) (9)

Analyzing the functionality and the capability of
parameters SP/SR defined above, we can recog-
nize their characteristic properties, whichmake them
unique and distinguishable. For example, the first
three parameters of both kinds, i.e. SPp, SPv, SPz,
and SRp, SRv, SRz haveonly a local character, since
each of them determines a value belonging to a sin-
gle point of the surface (i.e. the local extreme) with-
out taking into account the influence of other surface
points. In other words, they select from the very nu-
merous set of peaks, valleys and z-widths only one
value, i.e. the extreme value. From the viewpoint
of statistics, the representativeness of such values is
very limited and may suffer from essential variabil-
ity. In addition, the z-modifications of the SP or SR
parameters may be expected partly to resemble the
behavior of p- or v-modifications of these parameters,
since the z-modification is actually a combination of
p- and v-modifications. For all these reasons, the
groups of parameters SPp, SPv, SPz, and SRp, SRv,
SRz shouldbe consideredas statistically less relevant
than the remaining parameters SPc, SPa, SPq, or
SRc, SRa, SRq, SRzjis, since these two groups rep-
resent averaged quantities. Nevertheless, a certain
specificity may be observed with parameter SRzjis.
Although defined as an averaged quantity, it is not a
complete average since the averagingdoesnot goover
all the surface features but only over the five highest
peaks and the five deepest valleys. Due to this cir-
cumstance, SRzjis also ranks among the statistically
less reliable characteristics.
The parameters SPc, SPa, SPq, and SRc, SRa,

SRq represent true averages. Their c-components are
the results of averaging over all the local z-widths,
which consist of the p- and v-components of the given
surface relief, and as such the c-components include
properties of both the ‘upper’ and the ‘lower’ sides of
the relief. This makes them rather prone to imitate
the behavior of the p- and v-components.
During the computation of the a- and q-

components the entire ‘lower halves’ of the surface
reliefs are ‘rotated’ up, and in this way they are
unified with the ‘upper’ parts of the reliefs. To-
gether they create a statistically indistinguishable
unit which does not suffer so much from the ‘two-
side effect’. The a- and q-components seem to be
statistically the most reliable components among all
those employed in this study. However, there is a cer-
tain difference between SPa/SPq and SRa/SRq pa-

rameters. The R-parameters are extracted from the
roughness function fR(xi, yi), which lacks the larger
wave lengths of thewavyprofiles, and this helps SPa
and SPq to be better representatives of the overall
surface irregularity of fracture specimens.
Finally, it should be mentioned that there are

some differences between the surface parameters
measured at different magnifications. In the case of
smaller magnifications, priority is given to the larger
surface features of reliefs but the details are sup-
pressed. This means that the values of all param-
eters will be shifted to larger quantities — they are
set on scales of greater length. At greater magnifi-
cations the situation is opposite: the details are ac-
cented but the larger relief features are missing, so
that the values of all parameters will be shifted to
smaller quantities— they are set on scales of shorter
length. These propertiesmake all the surface param-
eters scale-dependent quantities. The surface places
(sites) on which measurements were performed are
specified in Section 3.
All thementionedproperties of the profile param-

eters (SP) and roughness parameters (SR) can be
observed with the graphs presented in Section 4.

3 Experimental arrangement

One hundred eight specimens (2 cm×2 cm×16 cm)
of hydrated ordinary Portland cement paste of six
water-to-cement ratios r (0.3, 0.4, 0.5, 0.6, 0.7, 0.8)
were prepared (eighteen samples per r-value). The
specimens were rotated during hydration to achieve
better homogeneity. All specimens were stored for
the whole hydration time at 100 % RH and 20◦C.
After 60 days of hydration, the specimens were frac-
tured in three-point bending and the fracture sur-
faceswere immediately used formicroscopic analysis.
Other parts of the specimens were used for porosity
measurements and for further mechanical tests.
Porosity was determined by the common weight-

volume method. The wet specimens were weighed
and their volumewasmeasured. Then theywere sub-
jected to a temperature of 105◦C for one week until
theirweight stoppedchanging, andthedryspecimens
were weighed again.
The microscopic analysis was performed using

an Olympus Lext 3100 confocal microscope. Ap-
proximately 150 image sections were taken for each
measured surface site, from the very bottom of the
surface depressions (valleys) to the very top of the
surface protrusions (peaks). The investigated area
L × M = 1280 μm × 1280 μm (1024 pixels×1024
pixels)was chosen infivedifferent places of each frac-
ture surface (in the center, and in four positions near
the corners of the rectangular area), i.e. each plotted
point in the graphs of the profile and roughness pa-
rameters corresponds to an average value composed

Acta Polytechnica Vol. 51 No. 3/2011

Fig. 2: The dependence of porosity P (measured by evaporable water content) on the original water-to-cement ratio r

of 90measurements (18 samples×5 surfacemeasure-
ments). Each measurement was performed for three
different magnifications, namely 5×, 20× and 50×,
giving 270 measurements performed for the particu-
lar r-value. Each site measurement amounts about
150optical sections (digital files), i.e. 40 500files had
to be processed to create 270 digital maps per one
r-value. This resulted in 1620 digital maps for all
r-values altogether (6 r-values×270 maps for each
r-value). These 1620 digital fracture surfaces were
then subjected to 3D profile and roughness surface
analyses using Olympus Lext 3100 software, ver-
sion 6. The critical wavelength λc for filtering out
wavycomponents of longerwavelengthwas set to 100
pixels, which is about 10 % of the reference length
L =1024 pixels.
In this way an extensive statistical ensemble was

created, providing a sufficiently reliable basis for
making relevant conclusions.

4 Results and discussion
Prior to a discussion of the graphs of profile and
roughness parameters, it is necessary to recall some
basic facts about theprocess of formingporositywith
hydrated cement pastes.
When cement is mixed with water, the hydration

process combines some water into the C–S–H1 gel,
a main hydration product, and the remaining water
is either physically adsorbed in tiny gel pores or re-
mains as free water in the capillary pores. When the
water-to-cement ratio r = w/c is increased, the cap-
illarywater increases, and alongwith it the capillary
space extendswithin thehydratedcementpaste. The

higher the ratio r, the larger the capillary space. Nat-
urally, this scheme holds onlywhen all the freewater
is integrated into the paste. At extremely high ratios
(r > 0.6), this is a problem because of sedimentation
and segregation of cement grains. Nevertheless, ro-
tation of specimens and adding admixtures preserves
sufficient homogeneity of the hydrated specimens.
It follows from the foregoing paragraph that the

main factor controlling the capillary porosity of ce-
ment paste is the water-to-cement ratio, r, which is
primarily reflected in the total porosity P . There-
fore, strong dependence of porosity on the r-ratio,
i.e. a strong correlation P(r), is expected. This well-
knownrelationship isnot surprising, and it alsoworks
with our specimens — see Figure 2. At first sight,
graph P(r) in Figure 2 seems to be linear. However,
some caution is necessarywhen inspecting functional
behavior within a narrow interval. Many graphs of
non-linear functions seem to be almost linear in very
narrow intervals. It is necessary to observe the be-
havior in a wider interval. In our case, the porosity
cannot exceed a value of 1, but it can approach this
value for large r-ratios, i.e.

lim
r→∞

P(r)= 1 (10)

This requirement cannot be guaranteed by any com-
mon linear function, but canbe guaranteedbya non-
linear function, e.g. by the exponentially growing
function P(r) = 1 − exp(−r/ro) or by some type of
a hyperbolically growing function, to mention only
some of the possible candidates. Regardless of the
type of P(r) function, one fact is clear: P(r) in the
interval r ∈ (0.3,0.8) with our specimens is only

1C–S–H gel in cement notation: C=CaO, S=SiO2, H=H2O.

Acta Polytechnica Vol. 51 No. 3/2011

slightly non-linear, which qualifies the linear approx-
imation as a possible tentative candidate for P(r) in
this interval. As we shall see later, this will have a
special impact on the investigated graphical depen-
dences.
Let us briefly summarize the facts that have

been formulated in the foregoing lines. The ini-
tial value of the water-to-cement ratio r determines
the value of the porosity P of hydrated cement
paste, which leads to a strongly correlated depen-
dence P(r). This inevitably leads to the conclusion
that all the quantities dependent on the water-to-
cement ratio, r, must also be dependent on porosity
P , and vice versa. In our case these consequences are
perfectly fulfilledwithin the seriesof 78graphs inFig-
ures 3–15. The series of graphs contains six graphs
SPp(r), SPv(r), SPz(r), SPc(r), SPa(r), SPq(r),
seven graphs SRp(r), SRv(r), SRz(r), SRc(r),
SRa(r), SRq(r), SRzjis(r), six graphs SPp(P),
SPv(P), SPz(P), SPc(P), SPa(P), SPq(P), and
seven graphs SRp(P), SRv(P), SRz(P), SRc(P),
SRa(P), SRq(P), SRzjis(P). All the graphs are re-
peated in threedifferentmagnifications: 5×, 20×and
50×. The graphs document in a very straightforward
manner the strongdependence of both the profile pa-
rameters and the roughness parameters on thewater-
to-cement ratio r, and also on porosity P . In addi-
tion, these dependences on r and P are very similar
in shape within the investigated intervals, which is
also a consequence of the almost linear behavior of
P(r).
All the graphs contain error bars that seem to

be rather large. This is because they represent lim-
iting statistical errors, i.e. intervals with 99.73 %
confidence. In normal laboratory practice, statisti-
cal intervals with 50 % confidence are usually used
and as such they would be 4.5× shorter. However,
the limiting intervals are more instructive since they
allowus to recognize other possible positions ofmea-
suredpoints, and enable us to consider other possible
shapes of the graphs.
The next Section discusses the plotted graphs in

greater detail.

4.1 Dependences on the
water-to-cement ratio

Graphs of the dependences SPp(r), SPv(r), SPz(r),
SPc(r), SPa(r), SPq(r) and SRp(r), SRv(r),
SRz(r), SRc(r), SRa(r), SRq(r), SRzjis(r) are
shown in the upper halves of Figures 3–14 and in
Figure 15. When comparing these graphical results
for different magnifications (5×, 20×, 50×), it is ob-
vious that both the SP profile parameters and the
SR roughness parameters change their numerical ex-
tent according to the magnification. For example, in
Figure 3 (magnification 5×) the numerical extent of

the SPp parameter is 280 μm, inFigure 4 (magnifica-
tion 20×) the value is 110 μm, and in Figure 5 (mag-
nification 50×) the value is only 62 μm. This is in
full agreementwithwhatwasmentioned in Section 2
about the scale-dependent properties of SP/SR pa-
rameters.
An inspection of all the SP/SR graphswithin the

framework of all the magnifications used here, 5×,
20×, 50×, results in the conclusion that the smallest
statistical scatter of the measured values (not the er-
ror bars) can be found in the graphs associated with
magnification20×. It is likely that thismagnification
is set at the most favorable length scales character-
istic for the studied fracture surfaces. At magnifi-
cation 5x, the fine length scales are not included in
the measurements. Thus a larger statistical scatter
can be observed at the side of the small water-to-
cement ratios, where finer fracture surfaces, i.e. finer
length scales, are localized (see Figures 3, 6, 9, 12
or 15). On the other hand, at magnification 50× the
coarser length scales of the fracture surfaces are ex-
cluded. Thus a larger scatter appears at the side of
the higher water-to-cement ratios, since coarser sur-
faces (with larger length scales) are localized there
(see Figures 5, 11 or 15). Intermediate magnifica-
tion 20× is optimum for covering the characteristic
length scales of the studied surfaces. Thus it shows
the smallest statistical scatter of the SP/SR parame-
ter values. Similarly,we candetermine someparame-
terswhosebehavior is almostunaffectedby statistical
scatter. Parameters SPa and SPq measured at mag-
nification20× showalmost smoothbehavior,with no
major scatter of their values. Parameters SRa and
SRq are less representative thanparameters SPa and
SPq due to their filtered large length scales.
Analyzing the mutual differences between p-, v-,

z-componentsand c-, a-, q-componentswithboth the
SP and SR parameters, it is obvious that the larger
statistical scatter ismost pronouncedwith the p-, v-,
z-components (compare, e.g., Figures 3 and 6). As
was highlighted in Section 2, this is because the p-,
v-, z-components are not averaged over the fracture
surface, while the c-, a-, q-components are true aver-
ages.
It is interesting to compare the behavior of

the z-components with the behavior of the p-, v-
components. For example, Figures 5 shows that the
SPv parameter records the reduction in surface irreg-
ularity (the depth reduction of the deepest valley) at
high water-to-cement ratios 0.8, while the SPp pa-
rameter shows no reduction, and SPz — as a com-
bination of the former two parameters — reports a
clear reduction in surface irregularity at this point.
Naturally, this is a consequence of the definition of
the SPz parameter, which consists in the sumof SPp
and SPv. Moreover, SPz partly influences SPc for
similar reasons. In Figures 5 and 8, the drop in sur-

Acta Polytechnica Vol. 51 No. 3/2011

Fig. 3: 3D profile parameters SPp, SPv, SPz as dependents on the water-to-cement ratio r and porosity P – magnifica-
tion 5×

Fig. 4: 3D profile parameters SPp, SPv, SPz as dependents on the water-to-cement ratio r and porosity P – magnifica-
tion 20×

Acta Polytechnica Vol. 51 No. 3/2011

Fig. 5: 3D profile parameters SPp, SPv, SPz as dependents on the water-to-cement ratio r and porosity P – magnifica-
tion 50×

Fig. 6: 3D profile parameters SPc, SPa, SPq as dependents on the water-to-cement ratio r and porosity P – magnifica-
tion 5×

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Fig. 7: 3D profile parameters SPc, SPa, SPq as dependents on the water-to-cement ratio r and porosity P – magnifica-
tion 20×

Fig. 8: 3D profile parameters SPc, SPa, SPq as dependents on the water-to-cement ratio r and porosity P – magnifica-
tion 50×

Acta Polytechnica Vol. 51 No. 3/2011

Fig. 9: 3D roughness parameters SRp, SRv, SRz as dependents on the water-to-cement ratio r and porosity
P – magnification 5×

face irregularities is clearly visible, not onlywith SPz
but also with SPc. Parameter SPc actually repre-
sents SPz averaged over the whole fracture surface,
and in this sense they are mutually related.
Finally, noting that the shapes of the SP and SR

graphs are similar (compare, e.g. Figures 6 and 12),
it is also noted that their characteristic length scales
do not differ enough tomodify their vertical arrange-
ments.

4.2 Dependences on porosity

The lower halves of Figures 3–15 show the graphs of
the dependences of the profile parameters SPp(P),
SPv(P), SPz(P), SPc(P), SPa(P), SPq(P) and the
roughness parameters SRp(P), SRv(P), SRz(P),
SRc(P), SRa(P), SRq(P), SRzjis(P) onporosity P .
All of theabovediscussiononthewater-to-cementra-
tio r in Section 4.1 canbe applied to the dependences
on porosity P . This is because there is a strong cor-
relation between these two quantities, as is also il-
lustrated in Figure 2. The unambiguous and almost
linear correspondence between P and r of the stud-
ied specimens in the interval r ∈ (0.3,0.8) ensures an
unambiguous, almost linear transition between the
r-axes and the P-axes of the graphs in Figures 3–15.
This in turn guarantees almost identical shapes of
the graphs, regardless whether they are based on r-
variables or on P-variables.

The same strongdependences of the surface irreg-
ularity parameters SP/SR on r- or P-quantities to-
gether with their identical graphical shapes are con-
vincing evidence of the governing roles of r and P
related to the irregularity of the fracture surfaces of
highly porous hydrated cement pastes. The influence
of porosity on surface irregularity is not necessarily
only a specific feature of porous cement pastes, but
may be an inherent feature of other porous solidma-
terials.
Thefinding that surface irregularity is prevalently

determined by porosity is in accordancewith the ob-
servation of Ponson and others [10,11]. They stud-
ied the roughness of the fracture surfaces of glass ce-
ramics made of small glass beads sintered in bulk
with porosity that could be varied within a certain
interval up to ∼ 30 %. They observed that the two-
dimensional profile parameter [10] increased in value
with increasing porosity.
Porosity seems to be amajor factor governing the

height irregularities of the fracture surfaces of porous
solids. The roughness of the fracture remnants may
be inferred from the porosity values, and conversely
the porositymay be assessed from the surface rough-
ness of the fracture remnants. Unfortunately, there is
no exact theory to support this close relationbetween
porosity and surface irregularity. This task remains
as a challenge for future research.

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Fig. 10: 3D roughness parameters SRp, SRv, SRz as dependents on the water-to-cement ratio r and porosity
P – magnification 20×

Fig. 11: 3D roughness parameters SRp, SRv, SRz as dependents on the water-to-cement ratio r and porosity
P – magnification 50×

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Fig. 12: 3D roughness parameters SRc, SRa, SRq as dependents on the water-to-cement ratio r and porosity
P – magnification 5×

Fig. 13: 3D roughness parameters SRc, SRa, SRq as dependents on the water-to-cement ratio r and porosity
P – magnification 20×

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Fig. 14: 3D roughness parameters SRc, SRa, SRq as dependents on the water-to-cement ratio r and porosity
P – magnification 50×

Fig. 15: 3D roughness parameter SRzjis as dependent on the water-to-cement ratio r and porosity P – magnifications
5×, 20× and 50×

Acta Polytechnica Vol. 51 No. 3/2011

5 Conclusion
An extensive study of the fracture surfaces of hy-
drated cement pastes has been performed using 3D
SP profileparametersand SR roughnessparameters.
Thirteen 3D parameters of different kinds have been
employed to describe and analyze surface irregulari-
ties on 106 specimens of cement pastes preparedwith
6 differentwater-to-cement ratios. Each fracture sur-
face has been tested on 5 different sites, so that each
value of the 3D surface parameters belonging to the
particular ratio r has been averaged over 80 mea-
sured values. This essential statistical relevancy has
been associatedwith each experimental point on the
plotted graphs. This has enabled us to specify some
of our preliminary results [9] more precisely and reli-
ably.
Themicroscopicmeasurementswereperformed in

triplicate in three different magnifications 5×, 20×
and50×, resulting in 78graphsdescribing thebehav-
ior of the surface irregularities of fractured specimens
in dependence on variouswater-to-cement ratios and
porosities.
The 3D SP profile parameters and SR rough-

ness parameters have proved to be capable of ana-
lyzing the geometric irregularities of the surfaces of
hydrated cement pastes and of providing information
on height differences, on morphological singularities
andon somemissing surface features, e.g. suppressed
protrusions (peaks) or depressions (valleys).
The results achieved in different magnifications

have shown that the values of 3D surface parame-
ters SP/SR are dependent on the length scales, and
for this reason their values are reduced when using
a largermagnification and their values are expanded
at small magnifications.
It has been shown that SPa, SPq are the most

reliable of all the studied parameters as regards the
minimum statistical scatter of the processed values.
The specific distribution of the length scales of the
studied fracture surfaces of cement pastes has proved
to be well treated in magnification 20×, at which
the 3D profile parameters SP and roughness param-
eters SR provide the most stable values. Naturally,
this does not mean at all that the fracture surfaces
of other materials with differently distributed length
scales of surface irregularities will also prefer magni-
fication 20×.
The present study has shown a close relation be-

tween surface irregularities and the porosity of hy-
drated cement pastes. Since porosity is influenced by
the water-to-cement ratio, a close relation has also
been found between the surface irregularities and the
water-to-cement ratio. For this reason, the surface ir-
regularities, quantified by parameters SP/SR, show
very similar analytical dependences both on porosity
P and on water-to-cement ratio r.

The initial valueof thewater-to-cementratioused
for mixing cement paste is one of the main factors
that decides about the future porosity of cement hy-
drates, and is also influential for the surface irregu-
larities of the fracture remnants of this material.

Acknowledgement

This work was supported by the Ministry of the
CzechRepublic under Contract no. ME09046 (Kon-
takt).

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Prof. RNDr. Tomáš Ficker, DrSc.
Phone: +420 541 147 661
E-mail: ficker.t@fce.vutbr.cz
Department of Physics
Faculty of Civil Engineering
Brno University of Technology
Veveř́ı 95, 662 37 Brno, Czech Republic

Assoc. Prof. PaedDr. Dalibor Martǐsek, Ph.D.
Department of Mathematics
Faculty of Mechanical Engineering
Brno University of Technology
Technická 2896/2, 616 00 Brno, Czech Republic

Adjunct Professor Hamlin M. Jennings, Ph.D.
Department of Civil and Environmental Engineering
Massachusetts Institute of Technology
77 Massachusetts Avenue, Cambridge, MA, 02139,
U.S.A.