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ORIGINAL PAPER
Experimental Study on Guabirotuba’s Soil StabilizationUsing Extreme Molding Conditions
Jair de Jesus Arrieta Baldovino . Ronaldo Luis dos Santos Izzo .
Fernanda Feltrim . Erico Rafael da Silva
Received: 26 November 2018 / Accepted: 23 December 2019 / Published online: 3 January 2020
� Springer Nature Switzerland AG 2020
Abstract The porosity/cement ratio (g/Civ) was
employed in this research to study the evolution of
unconfined compressive strength (UCS or qu) and split
tensile strength (STS or qt) of a silty soil stabilized
with cement in several molding conditions not shown
in the literature. Five molding moisture contents (x)fixed between 14.67 and 33.34%, three dry unit weight
of molding between 13 and 16 kN/m3, four cement
contents (C) between 3 and 9% (by dry mass of the
natural soil) and a curing time of 28 days were used to
study the influence of g/Civ on qt and qu under
normalized conditions. With the increase in dry
molding unit weight and cement content, as well as
reducing the initial porosity of the samples, qu and qtstrengths increase for all mixtures. On the other hand,
qu and qt also increase potentially depending on the g/Civ ratio, adjusted to an exponent of 0.44, which
remained constant for all molding conditions. The g/Civ ratio was able to establish empirical ratios between
qt/qu, which obtained values between 0.135 and 0.163
and which depended on the moisture content used
during compaction. Regarding molding moisture
content, there was an augment in qu and qt, with an
increased molding moisture content up to 28% (con-
verting into an optimum value) using the g/Civ ratio in
normalized terms. After x = 28%, the strength of the
mixtures was reduced. Finally, two equations to dose
and estimate qt and qu were obtained, set to 96.5%, and
with a 6% error. Thus, all strengths showed the same
normalized potential trend as a function of x,compatible with the value of g/Civ
0.44 = 35.
Keywords Ground improvement � Porosity/cement
ratio � Split tensile � Unconfined compressive �Molding conditions � Empirical relationships
List of Symbols
D50 Mean particle diameter
D10 Effective size
C Cement content (expressed in relation to
mass of dry soil)
Civ Volumetric cement content (expressed in
relation to the total specimen volume)
Biv Volumetric binder content (expressed in
relation to the total specimen volume)
qu Unconfined compressive strength
qt Split tensile strength
J. J. A. Baldovino � R. L. S. Izzo (&) � F. Feltrim �E. R. da Silva
Department of Civil Construction, Federal University of
Technology- Parana, Street Deputado Heitor Alencar
Furtado, 5000, Campus Curitiba, Ecoville,
Parana ZIP: 81280-340, Brazil
e-mail: [email protected]
J. J. A. Baldovino
e-mail: [email protected]
F. Feltrim
e-mail: [email protected]
E. R. da Silva
e-mail: [email protected]
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Geotech Geol Eng (2020) 38:2591–2607
https://doi.org/10.1007/s10706-019-01171-x(0123456789().,-volV)( 0123456789().,-volV)
qu�norm Normalized unconfined compressive
strength
qt�norm Normalized split tensile strength
cd Dry unit weight
g Porosity
x Moisture content
r Value of a given adjusted porosity/cement
css Unit weight of soil
csc Unit weight of cement
n Tensile/compressive strength ratio
R2 Coefficient of determination
1 Introduction
Cement is one of the most widely used binders in the
world, especially in the engineering sector in the
construction of buildings, rigid pavements, founda-
tions, channels, among other infrastructure works.
Besides these applications, cement is also widely used
for soil stabilization (Baldovino et al. 2019a). When
the cement is mixed with soil in the presence of water
and then compressed, it is known as soil–cement. The
soil–cement reaches higher strength than soil under
normal conditions, and, in a short time, cement helps
in workability, reduces expansion, decreases porosity
and increases the durability of the mixture when it is
used (Henzinger et al. 2018; Baldovino 2018). The
cement benefits on the properties mentioned are due to
the substantial amount of cement used or the high
compaction energy used. Therefore, the volume of
cement used and the initial porosity in the soil–cement
are vital variables to stabilize soil with cement, as it
can be observed in recent studies (Festugato et al.
2017; Consoli et al. 2017d; Diambra et al. 2018;
Henzinger et al. 2018; Baldovino and Izzo 2019).
Consoli et al. (2007) used the g/Civ ratio to study
the qu strength of a clayey sandy soil mixed with high
early strength cement. In the study, the same density
(19 kN/m3) and several molding moistures (4 up to
14%) were set, and the molding moisture content
(x) = 10%was the value at which the mixtures had the
highest strengths under non-normalized conditions,
and without considering g/Civ, only evaluating the
cement content used (2–12% regarding the dry soil
mass). For the set value of x = 10%, the molding
density also varied, obtaining strengths close to
5 MPa, after 7 curing days. Consoli et al. (2009a)
concluded that, for a sandy lean clay soil mixed with
lime and cement, using the same dry density (18 kN/
m3), the x molding moisture (between 10 and 16%)
had no significant effects on qu strength of any mixture
(soil–lime or soil–cement) under non-normalized
conditions and without the use of g/Civ. In a study,
Consoli et al. (2011) applied strengths normalization
to study the effects of the dry unit weight of molding,
porosity and molding moisture on the mechanical
behavior of silt mixed with cement, using different
unsaturated molding conditions: and x varying
between 17 and 23%, cement between 3 and 9% and
cd between 14 and 16 kN/m3. With the normalization
of qu strength as a function of g/Civ, it was found that
the strength increased linearly from x = 17 to
x = 23%. Stracke et al. (2012) mixed sandy soil with
cement to verify the effects of molding moisture
(between 6 and 14%) and void ratios (e) on the
compressive and tensile strength of samples after 7
curing days. It was concluded that, for this type of soil,
moisture reduction increased mechanical resistance,
being 6% the value of x in which the samples reached
maximum values of qu and qt as a function of g/Civ.
Finally Consoli et al. (2016a), used the g/Civ ratio to
study the strength of silt mixed with high early
strength cement, using several molding conditions:
moisture between 17 and 23%, molding dry unit
weight between 14 and 16 kN/m3 and using 7 curing
days. In the study, normalized equations were devel-
oped to estimate qu and qt as a function of x and g/Civ,
and potential growth in strength was observed between
17 and 23%.
Under normalized conditions, Consoli et al.
(2011, 2016a) and Stracke et al. (2012) did not
establish the limits in which the molding moisture
content increases or decreases the strength of stabi-
lized soils in terms of g/Civ. Thus, this study
determines these limits, using several molding condi-
tions and expanding the experimental program of the
previously mentioned studies. For this purpose,
molding moistures were studied from 14.67 to
33.34%, and the dry unit weight of molding from 13
to 16 kN/m3, using silt from the Guabirotuba Forma-
tion of Curitiba/Brazil, stabilized with cement con-
tents from 3 to 9%, at 28 curing days. Other aspects
approached in this study were: calculation of equa-
tions that control qu and qt as a function of g/Civ;
calculation of empirical ratios between
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2592 Geotech Geol Eng (2020) 38:2591–2607
tensile/compression (qt/qu) of the mixtures, for each
moisture content used; and determination of dosage
equations to estimate the strength of the mixtures.
2 Background
The porosity/binder (g/Biv) ratio is a relationship
between void and binder volumes in a blend with the
soil. Porosity/binder ratio is a rational criterion to
study the mechanical properties (unconfined compres-
sive-UCS, split tensile, stiffness, and shearing) of
lime–soil, soil–cement, lime–soil–fly ash, soil–ce-
ment–fibers, and crushed reclaimed asphalt pave-
ment–lime mixes, among others (Henzinger et al.
2018). The relationship g/Biv was introduced in the
literature by Consoli et al. (2007) to study the
evolution of UCS for soil–cement mixes. The g/Biv
was extended to study the initial shear modulus and the
effective Mohr–Coulomb strength parameters of an
artificially cemented sand (Consoli et al. 2009c), the
strength parameters of a sandy clay treated with lime
and cement (Consoli et al. 2009a), the compressive
properties of sand–cement blends (Rios et al. 2012),
the study of Jet Grouting mechanicals properties
(Tinoco et al. 2012), the influence of grain size and
mineralogy on the porosity/cement ratio and the
correlation of this ratio with the mechanical behavior
of different soils (Rios et al. 2013), the compressive
strength of residual soil–fly ash–lime blends (da Rocha
et al. 2014), the compressive properties of lime
stabilized sandy clay using distinct molding moisture
content (Consoli et al. 2014; Baldovino et al. 2018b),
the shear behavior of an artificially cemented soil
(Rios et al. 2014), the UCS of zeolite and cement
addition on a sandy soil (Mola-Abasi and Shooshpasha
2016), the UCS and split tensile strength for non-
plastic clayey sand–cement mixes reinforced with
polypropylene fibers (Festugato et al. 2017), the
theoretical derivation of artificially cemented granular
soils strength (Diambra et al. 2017), the effect of water
salinity in lime-fly ash treated sand (Karim et al.
2017), the split tensile/compressive ratio of long-term
lime–soil mixes (Baldovino et al. 2018a), the uncon-
fined compressive strength evolution of sedimentary
silt-roof tiles waste mixes (Moreira et al. 2019a), the
equations controlling split tensile/compressive
indexes for silts-cement compacted blends using
different compaction efforts (Baldovino et al.
2019a, 2019b), the strength of homogeneous and
non-homogeneous mixtures of fine-grained soil with
lignite fly ash (Henzinger et al. 2018) and the strength
of reclaimed asphalt pavement–fly ash–carbide lime
blends (Consoli et al. 2018b). The g/Biv is also a
parameter to study durability properties of soil-binder
mixes: sandy soils stabilized with waste glass and
carbide lime (Consoli et al. 2018c), compacted gold
tailings—cement mixes (Consoli et al. 2018a) and
compacted clay-industrial wastes blends (Consoli
et al. 2017a). In all the above-mentioned studies, g/Biv is a suitable parameter to predict the unconfined
compressive, split tensile, stiffness, and durability of
stabilized soils. The general equation (Eq. 1) for
studying the evolution of these properties (compres-
sive and split tensile, mainly) is given by:
qu _ qt ¼ Ag
Civð ÞC
" #�B
ð1Þ
where A, B, and C are empirical constants, with A
having the same units as qu and qt (in kPa). When the
mixtures are evaluated depending on the cure time,
‘‘A’’ values usually increase (Consoli et al. 2014;
Baldovino et al. 2018a).
Recent studies have addressed B and C values
under normalized conditions for various soil types.
Consoli et al. (2017c) used seven different silty/clayey
soils (London clay, Dispersive clay, Botucatu resid-
ual soil, Organic soft clay, Red silty clay, Silt Gold
tailings, and Coal fly ash) mixed with early strength
Portland cement (1–9% cement content regarding the
dry weight of the soil) and different dry molding unit
weights (5–19 kN/m3) at curing periods ranging from
3 to 28 days. For all silty/clayey soils studied,
B = 3.85 and C = 0.28 were calculated. Then, Consoli
et al. (2017b) studied the UCS for four different fine-
grained soils: Botucatu residual soil, Osorio sand with
10% fines (crushed sand), Osorio sand with 30% fines
(crushed sand), and Osorio sand with 50% fines
(crushed sand), mixed with high early strength Port-
land cement—Type III ? Fibre (6 mm, 12 mm, and
24 mm) using different molding void ratio (0.34–0.66)
at 7 curing days, obtaining values for B = 2.45 and
C = 0.28. Finally, Consoli et al. (2016b) studied the
UCS and the tensile strength of four different sand
types: well-graded granitic sand, poorly graded sand
made from crushed basalt, silica sand obtained as a by-
product of agate polishing, and eolic, uniform Osorio
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Geotech Geol Eng (2020) 38:2591–2607 2593
sand, stabilized with general-purpose cement, early
strength cement, and low heat of hydration cement
(1–12% cement content regarding to the dry weight of
the sands) using curing periods from 2 to 28 days. For
sandy soils, B has taken a value of 1.38 and C of 1.00.
Thus, C value depends on the soil and type of binder
and takes values between 1.00 and 0.01. Values for C
close to 1.00 are most found for granular soils, where
the parameters g and Biv have the same magnitude
over qu and qt, and proportional variations in the
values of g and Civ cause qu and qt values to remain
constant [e.g., Consoli et al. (2007, 2017a)]. Values for
C close to 0.01 mean the influence of porosity (g) andvoids of the soil–binder mixture exerts a more
significant effect on qu and qt than the volumetric
content of binder so that an increase in porosity of a
proportionally higher binder content get bigger to
compensate the increased voids due to lack of
compaction and to maintain a constant mechanical
resistance (e.g., Consoli et al. 2009b, 2014; Baldovino
et al. 2018c). The empirical constant ‘‘B’’ assumes
negative values, which means that increases in
mechanical resistance are potential. Thus, it can be
verified how efficient parameter B has been to study
different types of soil stabilized with different types of
binders under different molding conditions (e.g.,
compaction efforts, water content, cure time, dry unit
weight).
3 Experimental Program
The experimental program was defined over the
previous study by Consoli et al. (2016a, 2017d);
Baldovino et al. (2018a) and according to the Brazilian
experience in cement–soil and soil–lime mixes
(Stracke et al. 2012; da Rocha et al. 2014; Festugato
et al. 2017). Thus, the experimental program was
divided into two stages. The first stage involved soil
and cement characterization tests. The soil granulom-
etry curve was obtained under ASTM D2487 (ASTM
2011a) and by laser analyzer for fine fraction.
Atterberg limits of the soil following ASTM 4318
(ASTM 2010), the specific gravity of the soil accord-
ing to ASTM D854 (ASTM 2014). One-dimensional
consolidation properties of soil using the ASTM
D2435/D2435M-11 (ASTM 2011b). The compaction
properties [Maximum Dry Density (MDD) and Opti-
mum Moisture Content (OMC)] of soil (in the three
efforts: standard, intermediate, and modified) were
conducted in agreement with Brazilian NBR 7182
(ABNT 2016). The direct soil shear parameters
(internal angle and cohesion) in the natural state were
obtained according to ASTM D3080-11 (2011c), and
the specific gravity of the cement according to NBR
16605 (ABNT 2017). The second stage consisted of
molding, curing, and rupture of the specimens sub-
jected to unconfined compressive and split tensile
tests. The unconfined compressive strength and split
tensile strength are the most commonly used mechan-
ical properties to study improved soils (or ground
improvement) according to recent studies (Mola-
Abasi and Shooshpasha 2016; Diambra et al. 2018;
Henzinger et al. 2018). The characteristics of the
materials and the methodology used in this article are
shown below.
3.1 Materials: Soil, Cement, and Water
In the present study, silty sedimentary soil, early
strength Portland cement, and distilled water were the
three materials used.
The soil sample was manually collected, in an
undeformed and deformed state, southeast of Curitiba
(Brazil), in the city of Sao Jose dos Pinhais (metropoli-
tan area of Curitiba), avoiding possible contamination,
and was taken in enough quantity to perform all the
tests. The soil was collected on a road slope and
extracted from a depth of about 2–2.5 m. The soil
belongs to the second layer of the Guabirotuba
Formation. The soils of the Guabirotuba geological
formation are located in Curitiba and its metropolitan
region and are predominantly fine-grained (clays and
silts). The undeformed samples were collected for
unconfined compressive, split tensile, one-dimen-
sional consolidation, and direct shear tests in the
natural state. The soil in its natural state presented
hygroscopic moisture of 40% and a dry unit weight of
11.60 kN/m3.
An early strength Portland cement (Type V in
Brazil) [ASTM C150 (ASTM 2016)] mainly com-
posed of calcium oxide (CaO), Silicon dioxide (SiO2),
and aluminum oxide (Al2O3), produced and sold in
southern Brazil, was used for the study.
To prevent undesired reactions and limit the
number of variables, distilled water at 24 ± 2 �Cwas used to conduct all characterization tests of soil
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2594 Geotech Geol Eng (2020) 38:2591–2607
and soil–cement mixtures as well as to mold the test
specimens.
The 10%, 30%, 50%, 60% and 90% finer particle
diameters of soil were measured as D10 = 0.003 mm,
D30 = 0.01 mm, D50 = 0.025 mm, D60 = 0.038 mm
and D90 = 0.3 mm. Moreover, the uniformity coeffi-
cient (Cu) and coefficient of curvature (Cc) were
measured as Cu = 8.33 and Cc = 1.33, from which the
soil was characterized as elastic silty with sand (MH)
in accordance with the Unified Soil Classification
System (USCS) criterion. The results of the soil and
cement characterization tests, performed as described
in the experimental program, are presented in Tables 1
and 2, respectively. Table 1 shows that the largest soil
size corresponds to 60% silt. The specific gravity is
2.62 and 3.11 to soil sample and cement, respectively.
The predominant color of the soil is yellow due to the
oxidation and important presence of goethite in the
subtropical climate in southern Brazil (Baldovino
et al. 2019a). In addition, the total quantitative
chemical composition of soil was acquired by
energy-dispersive X-ray spectroscopy (EDX) using
Table 1 Properties of the soil sample
Properties Value Standard
Liquid limit (%) 50.82 ASTM 4318 (ASTM 2010)
Plastic limit (%) 35.96
Plastic index (%) 14.86
Specific gravity of soil (Gs) 2.62 ASTM 854 (ASTM 2014)
Coarse sand (0.6 mm\ diameter\ 2 mm) (%) 5 NBR 6502 (ABNT 1995)
Medium sand (0.2 mm\ diameter\ 0.6 mm) (%) 12
Fine sand (0.06 mm\ diameter\ 0.2 mm) (%) 18
Silt (0.002 mm\ diameter\ 0.06 mm) (%) 60
Clay (diameter\ 0.002 mm) (%) 5
Effective size (D10) (mm) 0.003
Mean particle diameter (D50) (mm) 0.038
Uniformity coefficient (Cu) 8.33
Coefficient of curvature (Cc) 1.33
Classification (USCS) MH
UCS-natural state (kPa) 104.58
STS-natural state (kPa) 16.62
STS/UCS ratio-natural state 0.16
Preconsolidation pressure (r0c) (kPa) 300 D2435/D2435M-11 (ASTM 2011b)
Coefficient of consolidation (Cv) (cm2/s) 0.02
Internal friction angle-natural state (/) (degrees) 26 ASTM D3080-11 (ASTM 2011c)
Cohesion-natural state (kPa) 23
Color Yellow
Table 2 Chemical composition and some physical properties
of cement
Property Value
Al2O3 (%) 4.30
SiO2 (%) 18.96
Fe2O3 (%) 2.95
CaO (%) 60.76
MgO (%) 3.26
SO3 (%) 3.18
Insoluble residue (%) 0.77
Strength at 7 days (MPa) 44.7
Strength at 28 days (MPa) 54.2
Fineness (%) 0.04
Specific gravity 3.11
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Geotech Geol Eng (2020) 38:2591–2607 2595
an energy-dispersive X-ray fluorescence spectrometer.
Table 3 exhibits the chemical composition of the soil
sample, mainly SiO2, Al2O3, and Fe2O3, which are
usually found in sedimentary soils and participate
actively in the soil chemical stabilization process
(Moreira et al. 2019b).
3.2 Split Tensile and Unconfined Compressive
Strength Program
To define the molding points, the soil compaction tests
were carried out in three efforts: normal, intermediate
and modified, in accordance with the Brazilian
standard NBR 7182 (ABNT 2016) to find the
compaction properties (optimum moisture content
and maximum dry unit weight) of the soil, and the
results are presented in Fig. 1. The molding points
were established after plotting the compaction soil. In
order to study the influence of the dry molding unit
weight, moisture content, and porosity on the mechan-
ical strength of the cement-improved soil, the molding
points were delimited according to Fig. 1 and Table 4.
Variating the molding conditions gets the voids and
porosity to vary, and then changes in mechanical
properties of compacted soils. These molding points
were strategically defined considering possible field
conditions, without exceeding the modified energy
and optimum moisture content of all efforts. During
the mixing process, it was verified that the lowest
moisture percentage in which the specimens could be
molded was superior to 14%. The first attempts were
made with x = 10%, but the specimens broke effort-
lessly because the soil–cement particles in the pres-
ence of so little water could not adhere enough.
Therefore, the first molding point was chosen at
x = 14.67%, with variations of 4.67% up to
x = 33.34%. To study the effects of these non-optimal
compaction conditions on the mechanical strength of
soil–cement mixes, 28 curing period was chosen.
Figure 2 shows the experimental program chart.
3.3 Molding Specimens for Split Tensile
and Unconfined Compressive Tests
Test specimens, with a 100 mm height and 50 mm
diameter, were molded for unconfined compressive
and split tensile tests. The soil was dried in a heating
chamber at a temperature of 100 ± 5 �C and divided
into evenly distributed portions to be mixed with
different cement contents. The percentages of cement
chosen for this research were: 3, 5, 7, and 9% to the dry
mass of the soil, taking into account current literature
and Brazilian experience (Consoli et al. 2016a). Thus,
a quantity of dry cement was added to achieve the four
different addition contents (Fig. 3a). The mixture of
soil and cement was prepared to be homogenous to the
maximum extent. Subsequently, a percentage of water
was added, determined regarding the water content of
the molding points (i.e., non-optimal conditions of
compaction) shown in Table 4.
The samples for molding the test specimens were
statically compacted with a 50 mm internal diameter,
100 mm height, and 5 mm thick stainless-steel mold.
12.00
12.50
13.00
13.50
14.00
14.50
15.00
15.50
16.00
16.50
17.00
0 3 6 9 12 15 18 21 24 27 30 33 36 39
Dry
Uni
t Wei
ght (
kN/m
3 )
Moisture content, ω (%)
Standard effort
Intermediate effort
Modify effort
S=100%
Molding points
A1
A2
A3 B3C3
B2 C2 D3
D2
B1
C1 D1 E1
E2
Fig. 1 Compaction properties of soil sample and split tensile
and unconfined compressive strength program (molding points).
S degree of saturation of soil
Table 3 Soil sample chemical composition
Compost Concentration by weight (%)
SiO2 48.78
Al2O3 44.51
Fe2O3 0.61
K2O 0.84
TiO2 0.92
SO3 4.12
LOI 0.16
LOI loss on ignition
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2596 Geotech Geol Eng (2020) 38:2591–2607
The specimens were extruded from their molds using a
hydraulic device. An example of compacted specimens
is presented in Fig. 3b. To ensure the maximum dry
density obtained during the compaction tests, the mold
volume and weight of the wet mixture necessary for
each test specimen were calculated. The time taken to
prepare, mix, and compact the specimens were always
lower than 10 min, to avoid the early reactions of
cement in water’s presence. The test specimens were
weighed on a 0.01 g precision scale, and the dimensions
were measured using a caliper with a 0.01 mm error.
Three wet samples of the mixture were taken to check
the mold moisture by oven drying. Thus, the initial
specimen�s porosity was calculated using Eq. (2)
g ¼ 100�100cd
1þ C=100ð Þ
� �� 1
cSSþ C=100
cSC
� �� �ð2Þ
where cSS and cSC are the specific gravity of the soil
and cement grains, respectively. Equation (2) was
previously defined by Baldovino et al. (2019a) and
Fig. 2 Experimental program chart
Table 4 Molding points for soil–cement mixes
Molding point Dry unit weight (kN/m3) Moisture content (%) Degree of saturation/% Specimens (for qt and qu)
A1-Line A 13.00 14.67 0.37 24
A2-Line A 14.50 14.67 0.46 24
A3-Line A 16.00 14.67 0.58 24
B1-Line B 13.00 19.33 0.49 24
B2-Line B 14.50 19.33 0.62 24
B3-Line B 16.00 19.33 0.78 24
C1-Line C 13.00 24.00 0.61 24
C2-Line C 14.50 24.00 0.77 24
C3-Line C 16.00 24.00 0.98 24
D1-Line D 13.00 28.67 0.73 24
D2-Line D 13.75 28.67 0.83 24
D3-Line D 14.50 28.67 0.94 24
E1-Line E 13.00 33.34 0.86 24
E2-Line E 13.75 33.34 0.96 24
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Geotech Geol Eng (2020) 38:2591–2607 2597
Consoli et al. (2018a). The extracted test specimens
were wrapped in a transparent plastic film to maintain
the moisture content. Finally, the test specimens were
stored in a humidity chamber for the curing process for
27 days, at an average temperature of 25 ± 3 �C and
relative humidity above 95%, to prevent significant
changes in the moisture until the testing day. After 27
curing days, the specimens were submerged in a
distilled water tank for 24 h (1 day), expecting to
saturate the samples prior to compression and tensile
tests and trying to minimize the possibility that suction
would influence the final strength value. This proce-
dure has been used in the current literature to reduce
the effect of suction (Consoli et al. 2007; da Rocha
et al. 2014). Additionally, the moisture content in the
soil–cement mixes was cross-checked by oven drying
after the completion of the UCS and STS tests.
The following maximum errors were taken into
account when conducting the unconfined compressive
and split tensile tests for the samples: sample dimen-
sions with a diameter of ± 0.5 mm and height of ±
1 mm, dry unit weight (cd) of ± 1%, and water
content (x) of ± 0.5% (Consoli et al. 2009b, 2018c;
Baldovino et al. 2018a). For each molding point and
cement content, three test specimens were molded.
Three replicate samples were tested for each com-
paction state to verify repeatability in UCS and STS
results. 168 test specimens were molded for each of
the tests (unconfined compressive and split tensile),
making a total of 336 samples.
3.4 Split Tensile and Unconfined Compressive
Tests
To perform the unconfined compressive and split
tensile tests, an automatic press was used along with
rings calibrated for a 30 kN axial load. The tests were
conducted using an automated system at a test speed of
1 mm/min to measure the applied force with a
resolution of 2.5 N and strain with a sensitivity of
0.01 mm. The procedures for the unconfined com-
pressive tests followed ABNT (2007). UCS is the
maximum rupture load of the material or the pressure
corresponding to the load at which a specific defor-
mation to the 20%-soil test specimen occurs when the
axial stress–strain curve does not exhibit a maximum
peak. When the axial stress–strain curve exhibited a
maximum peak in a test, the UCS (qu) was selected by
the following expression:
qu ¼PR
AT
ð3Þ
where PR is the rupture load at the peak of the axial
stress–strain curve, and AT is the corrected cross-
sectional area of the test specimen. Tensile strength is
an essential parameter in predicting the suitability of a
subgrade material in pavement construction. The split
tensile strength tests comply with the Brazilian
standard NBR 7222 (ABNT 2011). Split tensile
strength qt was adopted according to the following
expression:
qt ¼2PRd
pDHð4Þ
Fig. 3 a Raw materials. b Soil–cement specimens for UCS and STS tests
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2598 Geotech Geol Eng (2020) 38:2591–2607
where PRd is the rupture load at the peak of the
diametrical stress–strain curve, and D and H are the
diameter and height of the test specimen, respectively
(Baldovino et al. 2018a). The split tensile test, also
known as the indirect tensile test or Brazilian Test, was
developed independently in Brazil and Japan in 1943.
The test is performed by applying a compression load
in a cylindrical specimen positioned between two
rectangular pieces with dimensions determined as a
function of the specimen diameter and positioned
diametrically opposite from each other. The test
mechanism is carried out as follows: in addition to
causing compression, the conditions imposed by the
load on elastic materials also produce a practically
uniform tensile stress over a significant area of the
diametrical plane containing the applied load.
4 Results and Discussion
4.1 Effects of Porosity/Cement Ratio
on Unconfined Compressive and Split Tensile
Strength
The porosity/volumetric cement content ratio (g/Civ)
was used in this study to verify the evolution of
unconfined compressive strength and split tensile
strength. The g/Civ ratio is defined regarding the
voids of soil–cement and the volume of cement used in
the mixture under the initial molding conditions
previously defined (Fig. 1 and Table 4). Porosity is
calculated as an initial condition of the soil–cement
matrix at a pre-established dry unit weight cd and the
desired moisture content. Therefore, the mechanical
resistance of the soil–cement matrix might happen as a
direct relation of the specimens’ porosity, as well as a
function of the inverse of the volumetric content of
cement (1/Civ), as demonstrated by Consoli et al.
(2009b) and Henzinger et al. (2018). To find a direct
and compatible alignment between g and Civ as a
mathematical ratio and convert the two variables as a
dependency for qu and qt, Civ value should be set as an
exponent C between 0.01 and 1.00 with variations of
0.01, as observed in the current literature (Festugato
et al. 2017; Consoli et al. 2017d; Diambra et al. 2018).
In this way, the C value that best fits the values of quand qt for this experimental program was 0.44. This
value means that the influence of porosity (g) and the
voids in the soil–cement mixture has more significant
impact in UCS and STS than the cement volumetric
content so that an increase in porosity needs a
proportionally more substantial increase in cement
content, in order to compensate the increase in voids
due to lack of compaction and to maintain constant
strength (Leon 2018). Values for C close to 1.00 are
most commonly found for granular soils, where the
parameters g and Civ exert the same magnitude on quand qt, in which proportional variations in g and Civ
values cause constant qu and qt values (Rios et al.
2013). In other words, to ensure high strength to
cement mixtures with granular soils, both the voids
and the volume of cement have the key to reach a
specific value for qu and qt. However, for cement
mixtures with fine-grained soils (silts and clay), the
crucial to achieving high strength is to apply high
compaction energy or significantly increase the
cement amount.
Figures 4, 5, 6, 7 and 8 show the influence of g/Civ
ratio (adjusted to 0.44) on unconfined compressive
strength and split tensile strength for the samples with
molding moisture contents of 14.67, 19.33, 24.00,
28.67, and 33.34%, respectively. The g/Civ0.44 ratio
0
500
1000
1500
2000
2500
3000
3500
20 25 30 35 40 45 50
q tan
d q u
(kPa
)
η/Civ0.44
UCSSTS
: qu= 51×106(η/Civ0.44)-3.30 (R2=0.97)
: qt= 6.9×106 (η/Civ0.44)-3.30 (R2=0.95)
qt/qu =0.135
Fig. 4 Influence of porosity/volumetric cement content (g/Civ)
ratio on split tensile strength (qt) and unconfined compressive
strength (qu) for silty soil–cement mixes, considering all studied
dry unit weights, distinct cement contents, and moisture content
of 14.67% (Line A)
123
Geotech Geol Eng (2020) 38:2591–2607 2599
influences qu and qt directly under all molding
conditions, presenting a potential trend of g/Civ-quand g/Civ-qt. So, when the g/Civ values decrease due
to the voids reduction or the cement volume increase
in the mixture, the strength values of the specimens
increase. As noted in Figs. 4, 5, 6, 7 and 8, to increase
qu by 1000 kPa, g/Civ should be reduced by 5%. As
for qt, this same reduction might generate a significant
increase of 150 kPa.
Figure 4 shows the results for qu and qt in the
molding line A (x = 14.67%), with maximum value
for qu of 2110 kPa and 320 kPa for qt. For molding
line B (x = 19.33%), maximum values of 2560 and
400 kPa were attained for qu and qt, respectively, as
presented in Fig. 5. Ultimately, for line C
(x = 24.00%), maximum strengths for qu and qt of
3000 and 500 kPa were obtained, respectively
(Fig. 6). The maximum values for qu and qt (Line A,
B, and C) were obtained for the same value of g/Civ
0.44 = 21 (or g/Civ = 9.4). That is, there was an
increase in both qu and qt as the amount of water added
in the mixture increased to a set value of g/Civ and the
same variation of cd (Table 4) between 14.67% and
0
500
1000
1500
2000
2500
3000
3500
20 25 30 35 40 45 50
q tan
d q u
(kPa
)
η/Civ0.44
UCS
STS
: qu= 64.6×106(η/Civ0.44)-3.30 (R2=0.97)
: qt= 8.9×106 (η/Civ0.44)-3.30 (R2=0.95)
qt/qu =0.138
Fig. 5 Influence of porosity/volumetric cement content (g/Civ)
ratio on split tensile strength (qt) and unconfined compressive
strength (qu) for silty soil–cement mixes, considering all studied
dry unit weights, distinct cement contents, and moisture content
of 19.33% (Line B)
0
500
1000
1500
2000
2500
3000
3500
20 25 30 35 40 45 50
q tan
d q u
(kPa
)
η/Civ0.44
UCS
STS
: qu= 76×106(η/Civ0.44)-3.30 (R2=0.95)
: qt= 12.4×106 (η/Civ0.44)-3.30 (R2=0.99)
qt/qu =0.163
Fig. 6 Influence of porosity/volumetric cement content (g/Civ)
ratio on split tensile strength (qt) and unconfined compressive
strength (qu) for silty soil–cement mixes, considering all studied
dry unit weights, distinct cement contents, and moisture content
of 24% (Line C)
0
500
1000
1500
2000
2500
3000
3500
20 25 30 35 40 45 50
q tan
d q u
(kPa
)
η/Civ0.44
UCSSTS
: qu= 80×106(η/Civ0.44)-3.30 (R2=0.98)
: qt= 12.7×106 (η/Civ0.44)-3.30 (R2=0.99)
qt/qu =0.159
Fig. 7 Influence of porosity/volumetric cement content (g/Civ)
ratio on split tensile strength (qt) and unconfined compressive
strength (qu) for silty soil–cement mixes, considering all studied
dry unit weights, distinct cement contents, and moisture content
of 28.67% (Line D)
123
2600 Geotech Geol Eng (2020) 38:2591–2607
24.00%. For line D (x = 28.67%), the maximum
values of 1720 and 331 kPa were observed for qu e qt,
respectively (Fig. 7) (for g/Civ = 11.7). Finally, for
line E (x = 33.34%), maximums of 1080 and 175 kPa
were found for qu and qt, respectively, for a defined
value of g/Civ = 13.2 (Fig. 8).
According to the molding points established in
Table 4, the g/Civ0.44 ratio was limited between the
values of 22 and 46.5 for molding moisture contents
between 14.67 and 24% (between lines A and C). As
for Lines D and E, the g/Civ0.44 range of the specimens
was (25–46.5) and (27.2–46.5), respectively. The g/Civ value increased due to the reduction in the dry unit
weight of the samples. Although there was a change in
the g/Civ ratio, its potential growth trend was main-
tained due to the change in moisture and the
water/compaction cement ratio. The potential trend
was excellently set for the experimental points, which
was demonstrated by the elevated determination
coefficient values higher than 0.92 (see Figs. 4, 5, 6,
7, 8).
It was observed that, in Figs. 4, 5, 6, 7 and 8, the
potential equations that describe the growth of qu and
qt follow the form: qu ¼ A� gCciv
h i�B
and
qt ¼ A� gCciv
h i�B
, respectively, where A, B, and C
are constants. The value of A might depend on curing
time, molding moisture as well as cementing or
binding agent (e.g., lime, cement, and fly-ash). For this
study, A value changes depending on the molding
moisture, with moisture contents in the following
order: A (x = 14.67%)\A (x =19.33%)\A
(x =24.00%)\A (x =28.63%)[A (x =33.34%). The equa-
tions presented in Figs. 4, 5, 6, 7 and 8 obtained the
same value for C and B, both for qu and qt. The only
difference between these equations is the value of A
(in the same units if qu and qt - kPa). For compressive
values, A ranges from 51 9 106 and 80 9 106 kPa
(variation of 57%) and, for tensile values, it ranges
from 6.9 9 106 and 12.7 9 106 kPa (variation of
84%). This means that the strength of the soil–cement
mixtures has more considerable additions in terms of
tensile strength than unconfined compression.
Figures 4, 5, 6, 7 and 8 show that, for the same
value of g/Civ, qu gets a different value for each
molding moisture content, and the highest values were
obtained in line D, followed by Line C, Line E, Line B,
and Line A, which demonstrates the superiority of the
28%moisture to provide greater silty soil strength. For
(Rios et al. 2012; Mola-Abasi and Shooshpasha 2016;
Festugato et al. 2017; Diambra et al. 2018), the g/Civ
ratio proved to be an excellent setting parameter to
describe the unconfined compressive behavior of
cement-stabilized soils.
4.2 Empirical Relationships Between Unconfined
Compressive And Split Tensile Strength
An empirical relation between compressive and split
tensile strengths can be calculated in terms of molding
moisture of soil–cement samples. This relation can be
called n ¼ qt
quand is independent of the g
Civð Þ0:44 ratio.
Thus, the equations that describe the growth of qu and
qt as a function ofg
Civð Þ0:44 (see Figs. 4, 5, 6, 7, 8) can be
expressed as a direct ratio of qt/qu for each molding
moisture content outlined in Table 5. The qt/qu ratio
ensures a decimal constant, calculated in Table 5,
which also shows the equations representing the
increase of qu and qt, with a potential trend for each
value ofx. Therefore, n gets values between 0.135 and0.163 (variation of 3%). The calculated values of n
0
500
1000
1500
2000
2500
3000
3500
20 25 30 35 40 45 50
q tan
d q u
(kPa
)
η/Civ0.44
UCSSTS
: qu= 71×106(η/Civ0.44)-3.30 (R2=0.92)
: qt= 9.9×106 (η/Civ0.44)-3.30 (R2=0.96)
qt/qu =0.139
Fig. 8 Influence of porosity/volumetric cement content (g/Civ)
ratio on split tensile strength (qt) and unconfined compressive
strength (qu) for silty soil–cement mixes, considering all studied
dry unit weights, distinct cement contents, and moisture content
of 33.34% (Line E)
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Geotech Geol Eng (2020) 38:2591–2607 2601
grow from x = 14.67 to x = 24.00% and decrease
from x = 28.67 to x = 33.34%, as shown in Fig. 9.
Thus, qt proves to be a percentage of 13.5, 13.8, 16.3,
15.9, and 13.9% of the value of qu for lines A, B, C, D,
and E, respectively.
According to Diambra et al. (2018), in artificially
cemented sandy soils, the existence of a tensile/com-
pressive strength ratio (qt/qu) is independent of the
curing time. The ratio is mainly ruled by the tensile
strengths (or properties of friction) of cement. Authors
such as Consoli et al. (2016a, b) calculated a qt/qu ratio
of 0.13 for compacted fine-grained soil-Portland
cement blends using molding moisture contents of
17, 20, and 23%, and dry unit weights between 14 and
16 kN/m3. Festugato et al. (2017) mixed sandy soil
with cement and monofilament polypropylene fiber;
they calculated a n value of 0.10 for the non-fiber soil
and the fiber-reinforced soil they found a value of
n = 0.15, using a ratio of g
Civð Þ0:28. Other authors such
as Anggraini et al. (2015) determined a direct ratio of
n = 0.16 for soft, coconut-fiber-reinforced, lime-
treated soil. For Correia et al. (2015), there is a
decrease in the qt/qu ratio (from 0.20 to 0.24) with
increasing amounts of cement-slag-fiber in the same
mixture. Finally, Muntohar et al. (2013) studied the qt/
qu ratio for lime-stabilized and fiber-reinforced soil.
The addition of fibers to the stabilized soil slightly
increased the n value from about 0.11 to 0.13,
increasing the fiber content from 0.1 to 1.2%. Thus,
the ratio of strength n for cemented/reinforced soils
varies between 10 and 20% on average. Consequently,
the empirical qt and qu ratios reported in this study are
within these ranges.
4.3 Normalization of qt and qu Strengths to Assess
the Optimum Moisture Content of the Mix
in g/Civ Ratio
The equations shown in Table 5 can be normalized in
terms of g/Civ for equal molding moisture values.
Potential equations describing the growth of qu and qtas a function of g/Civ can be divided by the same value
of 106 � g
Civð Þ0:44� ��3:30
, thus, ensuring a constant
calculated for its corresponding molding moisture
value, both for qu and qt. Therefore, if the moisture
correlates with its respective normalized constant (qu
divided by 106 � g
Civð Þ0:44� ��3:30
or qt divided by
Table 5 Equations controlling split tensile/compressive
strength ratio of silty soil–cement mixes for distinct molding
moisture contents
Moisture content (%) Equations for qt-qu and qt/qu ratio
14.67
n ¼ qt
qu¼
6:9�106g
Civð Þ0:44
" #�3:30
51�106g
Civð Þ0:44
" #�3:30 ¼ 0:135
19.33
n ¼ qt
qu¼
8:9�106g
Civð Þ0:44
" #�3:30
64:6�106g
Civð Þ0:44
" #�3:30 ¼ 0:138
24.00
n ¼ qt
qu¼
12:4�106g
Civð Þ0:44
" #�3:30
76�106g
Civð Þ0:44
" #�3:30 ¼ 0:163
28.67
n ¼ qt
qu¼
12:7�106g
Civð Þ0:44
" #�3:30
80�106g
Civð Þ0:44
" #�3:30 ¼ 0:159
33.34
n ¼ qt
qu¼
9:9�106g
Civð Þ0:44
" #�3:30
71�106g
Civð Þ0:44
" #�3:30 ¼ 0:139
0
0.05
0.1
0.15
0.2
0 5 10 15 20 25 30 35 40
ξ=q t
/qu
ω ω (%)
Fig. 9 Variation of unconfined compressive strength (qu)-split
tensile strength (qt) ratio (n = qt/qu) with distinct molding
moisture content (x)
123
2602 Geotech Geol Eng (2020) 38:2591–2607
106 � g
Civð Þ0:44� ��3:30
), a point is found on the Carte-
sian plane. Thus, the variation of qu and qt normalized
depends on the moisture content (Fig. 10). This
variation follows a polynomial trend represented by
the form:
qu _ qt ¼ �aix3 þ aiix
2 � aiiixþ aiv� �
kg
Civð ÞC
" #�B
ð5Þ
where ai, aii, aiii and aiv are constants that depend on
the polynomial trend, x is the molding moisture
content, and k is a normalization-dependent constant,
which, in this case, is equal to 106. Thus, the equations
that allow calculating qu and qt strengths for any
molding condition limited by the variables of this
study are defined as:
qu ¼ � 0:0088x3 þ 0:46x2 � 5:11xþ 54:37� �� 106
g
Civð Þ0:44
" #�3:30
R2 ¼ 0:96� �
ð6Þ
qt ¼ � 0:0041x3 þ 0:25x2 � 4:43xþ 30:90� �� 106
g
Civð Þ0:44
" #�3:30
R2 ¼ 0:97� �
ð7Þ
Equations (6) and (7), which estimated the
strengths of the mixtures for any value of x, g, andCiv, have excellent coefficients of determination
R2 = 0.96 and R2 = 0.97, for qu and qt, respectively,
when validated to the real values of the 336 specimens
(real 9 calculated). Statistical analysis was per-
formed with real values and the estimated equations.
Themean absolute percentage error (MAPE, in%) and
the normalized root-mean-square error (NRMSE, in
%) were analyzed to validate the equations and the
coefficient of determination. For the 118 unconfined
compression data, percentages of 2.68% and 1.64%
were calculated for MAPE and NRMSE, respectively.
For the 118 tensile samples, percentages of 3.18% and
1.60% were calculated for MAPE and NRMSE,
respectively. Overall, the statistical analysis shows
excellent fits and high quality of the normalized model
used in this study. TheMAPE and NRMSE parameters
indicate an error close to 3% of the model. The (g) andvolumetric content of cement (cement volume in terms
of the sample volume) are optimal predictor variables
of the mechanical resistance for cement-compacted
silt. Parameter R2 had average results of 96.5% in all
developed equations and, simultaneously with other
statistical parameters, indicates that the molding
values and the soil–cement mixtures conditions [dry
unit weight, binder content, curing time, moisture, and
curing temperature] are excellent to estimate qu and qtin any of these molding situations.
Conversely, in Fig. 10, there is an ‘‘optimum’’
normalized maximum of qt and qu divided by
106 9 (g/Civ0.44)-3.30, where the maximum strengths
of the soil–cement mixtures are obtained. Thus, from
the first partial found from Eqs. (6) to (7), the
‘‘normalized optimal moisture content’’ can be calcu-
lated as a function of g/Civ0.44. The normalized
optimum value for any molding condition for qu isx�28% and x � 28% for qt; therefore, an empirical ratio
of n = 0.16 was also achieved (See Fig. 9). Although a
higher value for the equation qu _ qt ¼ A� gCciv
h i�B
is
found at point x = 28% (A achieves a value of 81�106
qu = [-0.0088ω3+0.46ω2 -5.11ω +54.37]×106[η/Civ
0.44]-3.30
qt = [-0.0041ω3 +0.25ω2 -4.43ω +30.97]×106[η/Civ
0.44]-3.30
0
10
20
30
40
50
60
70
80
90
10 15 20 25 30 35
q tan
d q u
divi
ded
by 1
06 (η/C
iv0.
44)-3
.30
Moisture content, ω (%)
Opt
imum
moi
stur
e co
nten
t to
mix
at
η/(C
iv0.
44)0.
33in
dex
→ω
=28%
Fig. 10 Variation in normalized unconfined compressive
strength (qu) and split tensile strength (qt) with distinct molding
moisture content (x)
123
Geotech Geol Eng (2020) 38:2591–2607 2603
for qu and of 13�106 for qt), there is a limitation
regarding the degree of saturation reaching real
strengths. Even though a theoretical 28% humidity
molding line could get higher strengths, they would be
limited by the reduction of gCciv
with a maximum of
cd = 15.25 kN/m3. Therefore, in theory [applying
Eqs. (6) and (7)], the maximum value reached in this
point would be of 2474 kPa and 415 kPa for qu and qt,
respectively, at 28 curing days and with 9% cement
added. As for point x = 23% (maximum of cd-= 16 kN/m3), the strengths of 3112 kPa (increase of
25% regarding x = 28%) and 492 kPa (increase of
18% regarding x = 28%) for qu and qt could be
achieved under the same conditions since they would
not be limited by the dry molding unit weight provided
in this study. Nevertheless, it should be mentioned that
changes in real field molding conditions could lead to a
higher/lower construction cost, such as pavement
layers, foundation supports, reinforcement of slopes
and dams.
4.4 Normalization of qt and qu Strengths to Assess
the Single Mixing Trend at g/Civ0.44 Ratio
The normalization (division) of the strengths is used to
find an equation able to estimate qu and qt as a function
of normalized g/Civ in a single potential trend.
According to Consoli et al. (2016b), to find an
equation to estimate cement-stabilized silty/argilla-
ceous soil using the g/Civ ratio, firstly, all normaliza-
tion strengths must be determined using a particular
value of g/Civ0.44 = r for each variable on which the
strengths depend (in this case, the molding moisture).
The particular value of r to normalize the strengths
can be chosen within the range reported in this
research, between 20 and 50, for each molding
moisture value of the soil–cement, both for split
tensile (qt-norm) and unconfined compression (qu-norm).
So, for this study, the value ofg/Civ0.44 = r = 35 was
chosen. The number r = 35 was replaced in the
equations that control qu and qt (shown in Table 5 and
in Figs. 4, 5, 6, 7, 8) to calculate normalization
strengths for each value of molding moisture (x). Thenormalization strengths for qu-norm with x values of
14.67 (Line A), 19.33 (Line B), 24.00 (Line C), 28.67
(Line D), and 33.34% (Line E), are 409.4, 518.6,
610.1, 642.2 and 569.9 kPa, respectively. The nor-
malization strengths for qt-norm with x values of 14.67
(Line A), 19.33 (Line B), 24.00 (Line C), 28.67 (Line
D), e 33.34% (Line E), are 55.4, 71.4, 99.5, 101.9 and
79.5 kPa, respectively. After calculating normaliza-
tion strengths, the strengths should be normalized over
the reported unconfined compressive and indirect
tensile values, which result in dividing the value of
unconfined compressive and tensile strength of each
specimen by the value of normalization strength of its
corresponding molding moisture (both for qu and qt).
Thus, normalization is obtained dividing Eq. (1) by
specific and arbitrary values of unconfined compres-
sive and tensile strengths, corresponding to a defined
porosity value g/CivC = r, which leads to:
qu
qu�normg
CC
iv
¼ r� _ qt
qt�normg
CC
iv
¼ r�
¼A g=CC
iv
� ��B
A rð Þ�B¼ rð ÞB g=CC
iv
� ��B ð8Þ
Therefore, with the value of r = 35, Eq. (8) is
converted into:
qu
qu�normg
C0:44
iv
¼ 35
� _ qt
qt�normg
C0:44
iv
¼ 35
� ¼ 124:5� 103 g=C0:44
iv
� ��3:30 ð9Þ
Normalized values of qu/qu norm e qt/qt-norm of all
specimens tested for unconfined compressive and
tensile strength of the type V PC in different moisture
contents acquire the same potential trend described in
Eq. (9). Values corresponding to normalized qu/qu-
norm e qt/qt-norm are shown in Fig. 11 with the
respective trend. The normalized values for the
mechanical resistance obtain a coefficient of determi-
nation of 0.95, being a single trend for all experimental
and normalized points, and for all moisture contents in
which the specimens were molded. Thus, if the sample
values of B and C are applied in Eq. (9), the expression
to estimate the mechanical behavior through tensile
and compressive tests for the studied silty soil and the
cement type used is converted into the form described
by Eq. (10)
qu
qu�normg
C0:44
iv
¼ r� _ qt
qt�normg
C0:44
iv
¼ r�
¼ rð Þ3:30 g=C0:44iv
� ��3:30 ð10Þ
123
2604 Geotech Geol Eng (2020) 38:2591–2607
with ther value of a soil specimen studied and mixed
with cement and its respective result of qu e qt in a
determined curing time and moisture value, qu e qtbehavior can be estimated for any value of g/Civ, and
this equation may be used to conduct soil–cement
mixtures projects without the need for broad testing
programs, which demand time and money.
5 Concluding Remarks
According to the type of soil, cement, the methodol-
ogy, the presentation, and analyses of results used in
this study, the following conclusions can be drawn:
1. For all studied soil–cement mixtures, the reduc-
tion in initial molding porosity and the increase in
the quantity of cement caused an increase in split
tensile and unconfined compression strengths after
28 curing days.
2. In normalized terms of porosity/volumetric
cement content, the compressive and tensile
strengths of all soil–cement mixtures increased
up to 28%moldingmoisture (between Lines C and
D). Afterward, they decreased until 33.34% of
moisture (Line E).
3. It was possible to calculate the equations that
control qu and qt as a function of g/Civ (to the
power of 0.44) and the empirical ratios between
qu/qt. Empirical ratios varied depending on the
molding moisture used, from 0.135 to 0.163
(Table 5).
4. There is a single normalized potential trend of quand qt as a function of molding moisture and
apparent dry unit weights used. The single trend
(Eq. 9) can be extended to any high early strength
cement stabilized silty soil molding condition in
this study.
Acknowledgements The authors are thankful to the Federal
University of TechnologyParana and to the financial support
given by Coordination for the Improvement of Higher
Education Personnel (CAPES), Fundacao Araucaria do Parana
and National Council for Scientific and Technological
Development (CNPq) in Brazil. Finally, authors would like to
thank the anonymous reviewers for their in-depth comments,
suggestions, and corrections, which have greatly improved the
manuscript.
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0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
20 25 30 35 40 45 50
q tan
d q u
divi
ded
by q
tor
qu
norm
aliz
ed a
t η/C
iv0.
44=3
5
η/Civ0.44
UCS (Line A) STS (Line A)UCS (Line B) STS (Line B)UCS (Line C) STS (Line C)UCS (Line D) STS (Line D)UCS (Line E) STS (Line E)
qt or qu divided by qt-norm or qu-norm at [η/Civ
0.44=35] = 124.5×103(η/Civ0.44)-3.30
(R2=0.95)
95% Upper Prediction Band
95% Lower Prediction Band
Line of Equality
Fig. 11 Normalization of unconfined compressive strength (qu)
and split tensile strength (qt) (for the whole range ofg/Civ0.44) by
dividing for qu and qt at g/Civ0.44 = 35 considering strength of
cement-treated silty soil using 28 curing days and molding
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