infrastructures

Article Effects of the Ratio of to Volumetric Cement Content on the Unconfined Compressive Strength of Cement Bound Fine Grained

Teresa Santana 1 , João Gonçalves 1, Fernando Pinho 2 and Rui Micaelo 2,*

1 UNIC—Research Center in Structures and Construction, Department, NOVA School of Science and Technology, Lisbon, Campus da Caparica, 2829-516 Caparica, Portugal; [email protected] (T.S.); [email protected] (J.G.) 2 CERIS—Civil Engineering Research and Innovation for Sustainability, NOVA School of Science and Technology, Lisbon, 2829-516 Caparica, Portugal; [email protected] * Correspondence: [email protected]

Abstract: This paper presents an experimental investigation into the effects of porosity, dry density and cement content on the unconfined compressive strength and modulus of elasticity of cement- bound mixtures. A clayey was used with two different proportions of type IV Portland cement, 10% and 14% of the dry mass of the soil. Specimens were moulded with the same but using four different compaction efforts, corresponding to four different dry densities. Unconfined compression testing was conducted at seven days of curing time on unsoaked samples. The results showed that the compressive strength increased with the increase in cement content   and with the decrease in porosity. From the experimental data, a unique relationship was found between the unconfined compressive strength and the ratio of porosity to volumetric cement content Citation: Santana, T.; Gonçalves, J.; for all the mixtures and compaction efforts tested. The equation developed demonstrates that it is Pinho, F.; Micaelo, R. Effects of the Ratio of Porosity to Volumetric possible to estimate the amount of cement and the dry density to achieve a certain level of unconfined Cement Content on the Unconfined compressive strength. A normalized general equation was also found to fit other authors’ results Compressive Strength of Cement for similar soils mixed with cement. From this, a cement-bound soil model was proposed for the Bound Fine Grained Soils. development of a mixing design procedure for different soils. Infrastructures 2021, 6, 96. https:// doi.org/10.3390/infrastructures6070096 Keywords: cement-bound soil; clayey sand; cement-treated soil; porosity; unconfined compressive strength; modulus of elasticity Academic Editor: Maria do Rosário Veiga

Received: 16 May 2021 1. Introduction Accepted: 23 June 2021 Published: 26 June 2021 One of the most common soil improvement techniques for fine-grained soils is to compact the in situ soil with cement, as adequate strength can be achieved quickly. Thus,

Publisher’s Note: MDPI stays neutral the beneficial effects of cement treatment, or other binding agents, on the engineering with regard to jurisdictional claims in properties of a broad range of soils have been widely documented [1–11]. Clayey published maps and institutional affil- are fine-graded soils that are rich in and particles, whose physical state is highly iations. affected by the water content and therefore are expected to provide fair to poor . The addition of a small amount of cement to the soil has proved to be effective in decreasing moisture sensitivity and expansion/shrinkage, which allows better control of workability during compaction and, ultimately, results in significant cost savings compared to removal and replacement of fill material in some projects. Furthermore, the Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. environmental impacts of soil replacement are incompatible with the globally accepted This article is an open access article sustainable development goals. distributed under the terms and The treatment process begins by mixing the soil with cement while relatively dry conditions of the Creative Commons and then adding the water specified for compaction. Compaction is needed to make soil Attribution (CC BY) license (https:// particles slip over each other and move into a densely packed state becoming suitable creativecommons.org/licenses/by/ earthwork material [12]. The mechanisms by which the cement improves the fine-graded 4.0/). soil properties are the cation exchange between clay and cement (water sensitivity), the

Infrastructures 2021, 6, 96. https://doi.org/10.3390/infrastructures6070096 https://www.mdpi.com/journal/infrastructures Infrastructures 2021, 6, 96 2 of 19

flocculation and agglomeration of particles (workability and compactability) and the cement hydration and pozzolanic reactions that create cement–soil particle bonds (bearing capacity) [13,14]. However, the engineering properties of the soil treated by cement may vary widely because of differences in the microstructure formed, which will depend on the soil properties, the cement and water added and the compaction energy applied [15]. A similar trend has also been identified with different binders [16,17]. In Europe, soils treated by cement are divided in two groups [18]—cement stabilized soil (CSS) and cement-bound soil (CBS)—depending on the amount of cement added to the soil. For CSS, the cement is just enough to improve the engineering properties of fine-graded soils to a level similar to that of good natural soil or untreated aggregate base. In contrast, in CBS, when more cement is added to the soil, the soil–cement mixture attains a level of structural integrity that can be directly measured by the unconfined compressive strength, tensile strength and elastic modulus tests. CBS is a technical solution used to improve the bearing capacity of subgrade of the overlaying structure (embankments, and railway structures and building foundations). Typical 7-day unconfined compressive strengths (Rc) for CBS range from 0.7 to 2.1 MPa [19]. The placement process of this material usually includes compaction, as in an embank- ment, and the soil–cement mixture needs to have a water content close to the optimum of a Proctor compaction test for a given energy level. Recent literature indicates that the struc- tural performance of CBS is essentially influenced by the cement type and content, porosity, type of soil, age and degree of compaction [20]. A reliable evaluation of strength and defor- mation characteristics of a CBS must take into account the characteristics of compaction in order to seek the minimum amount of cement that can guarantee the required mechanical performance. Although cyclic loading/dynamic tests are more suitable for evaluating the mechanical properties of these materials when used in transport infrastructures [20], monotonic tests are most often used in practice [18] and for research purposes [1,15,16]. The water content close to the optimum of CBS mixtures means that these mixtures are cured in a non-saturated condition and the water content does not reflect the amount of voids. Thus, in CBS mixtures, the water/cement ratio (defined as the water mass divided by the cement mass) is inadequate for analysis, whereas in cement concrete, most of voids are filled with water, so the water content reflects more accurately the volume of voids and the concrete stress–strain behavior is related to the initial water content. In addition, in deep soil mixing, with columnar inclusions in soils with a high natural water content, close to the liquid limit, the water/cement ratio plays a fundamental role in the assessment of target strength, like in concrete technology [21]. According to Consoli [22], the porosity affects the strength by modifying the number of contact points between particles, i.e., the soil microstructure. The influence of the volumetric properties on unconfined compressive strength of soil– cement mixtures was established by Larnach in the 1960s [8]. More recently, in [2], the ratio of porosity to cement volumetric content (n/Civ) has been proposed for evaluation, with n being the porosity and Civ the cement volumetric content (unhydrated cement, immediately after compacting the specimen). Thus, it was reported that a relationship between Rc and n/Civ could be found for the soil–cement mixture. Some studies that investigated other cementitious materials have also found similar relationships, even with different soils [8]. Hence, the relationship Rc-(n/Civ) can play a fundamental role in the determination of the cement content for a CBS design mixture to meet a target unconfined strength. Cement is an effective chemical stabilizer for improving both the index and strength properties of soils, but the optimum percentage of cement varies from one soil type to another [23]. Therefore, further research must be carried out in order to verify if similar relationships Rc-(n/Civ) can be used with other soils, from different regions, and with variable percentages of cement and porosity values. In this study, a natural clayey sand treated with Portland cement, collected in Almada, Portugal, is investigated. The soil– cement mixtures were fabricated with two different cement contents (10% and 14% of dry mass of the soil) and compacted with four different compaction efforts to evaluate the effect Infrastructures 2021, 6, x FOR PEER REVIEW 3 of 19

variable percentages of cement and porosity values. In this study, a natural clayey sand treated with Portland cement, collected in Almada, Portugal, is investigated. The soil– cement mixtures were fabricated with two different cement contents (10% and 14% of dry Infrastructures 2021, 6, 96 mass of the soil) and compacted with four different compaction efforts to3 ofevaluate 19 the effect of the cement content and the volumetric properties on compressive strength and stiffness of the CBS mixtures, tested after the specimens had been cured for 7 days at 23 ± 2 °C ofand the cementrelative content humidity and theof 55%. volumetric The relationship properties on found compressive between strength Rc and and (n/C stiffnessiv) enabled the ◦ ofdetermination the CBS mixtures, of the tested conditions after the required specimens in hadthe beenfield curedto attain for a 7 target days at R23c value± 2 forC the type andof relativesoil studied, humidity and of its 55%. normalized The relationship form was found found between to beRc andin good (n/Civ agreement) enabled the with other determinationauthors’ results. of the Furthermore, conditions required a simple in the labo fieldratory to attain testing a target procedureRc value foris proposed the type for CBS ofwith soil studied,different and soils. its normalized form was found to be in good agreement with other authors’ results. Furthermore, a simple laboratory testing procedure is proposed for CBS with different soils. 2. Materials and Experiments 2.2.1. Materials Experimental and Experiments Plan 2.1. Experimental Plan The experimental plan is summarized in the diagram presented in Figure 1. A fine- gradedThe experimental cohesive soil plan was is summarizedselected for inthis the study diagram to presentedinvestigate in Figurethe effect1. A fine-of the ratio of graded cohesive soil was selected for this study to investigate the effect of the ratio of porosity to volumetric cement content on the unconfined compressive strength of cement- porosity to volumetric cement content on the unconfined compressive strength of cement- boundbound soil soil mixtures. mixtures. The The soil soil was was first first characterized characterized in termsin terms of theof the most most important important phys- physicalical properties, properties, followed followed by by a compaction test test with with an an adequate adequate compaction compaction effort effort to to sup- supportport the the definition definition of the characteristicscharacteristics of of the the moulding moulding points points of the of CBSthe CBS specimens. specimens. The TheCBS CBS mixtures mixtures were were fabricated fabricated with with a asingle single water water content content and and compacted atat fourfour different differentcompaction compaction levels levelsto obtain to obtain different different volumetr volumetricic properties, properties, as as explained explained in in the the following followingsections. sections. Two different Two different cement cement contents contents were were used. used. The The unconfined unconfined compressive compressive testing testingmethod method was wasused used to evaluate to evaluate the the mechanic mechanicalal properties properties ofof differentdifferent CBS CBS mixtures. mixtures.

Fine-graded soil collection

Soil characterisation tests - Particle density - Particle gradation - Organic matter content - .

Definition of moulding points - Soil Proctor curve at modified compaction effort - Dry density of the soil with

compaction effort (4 levels) at wopt

Cement bound soil mixtures - Fabrication of CBS with 10 % and

14 % cement, and wopt (soil) - Compaction (4 levels) - Dry density of CBS specimens; - Unconfined compressive testing at 7-days curing

FigureFigure 1. Diagram1. Diagram of the of experimentalthe experimental plan. plan.

Infrastructures 2021InfrastructuresInfrastructures, 6, x FOR PEER 2021, REVIEW6, x 96 FOR PEER REVIEW 4 of 19 4 4of of 19

2.2. Materials2.2. 2.2. Materials Materials For this study,ForFor a thissample this study, study, of aa a clayeysample sample sand of of aa wasclayey clayey taken sand sand from was was a taken taken slope from from running a acut cut slope slopealong runningrunning a along along a local road in localaAlmada, local road road south in inAlmada, Almada,of Lisbon south south (see of Figu Lisbon of Lisbonre 2). (see The (see Figu area Figurere comprises2). 2The). The area areaan comprises upland comprises on an the anupland upland on the on smooth south-facingsmooththe smooth south-facingslope south-facing of the Almadaslope slopeof hillsthe of Almada, where the Almada clayeyhills, where hills,soils ar whereclayeye abundant. clayeysoils ar In soilse abundant. the are col- abundant. In the col- In lection site arelectionthe “Xabregas collection site are blue site “Xabregas areclays” “Xabregas [24], blue a clays” geological blue clays”[24], unita [geological24 ],from a geological the unit Miocene from unit theabout from Miocene the15 Miocenem about about15 m thick in the westernmostthick15 m in thick the inwesternmost part the of westernmost the region part of[25]. part the region of the region[25]. [25].

Figure 2. IdentificationFigure 2. Identification of theFigure collection 2. Identificationof the site collection on different of thesite scalescollectionon differen (world; sitet scales country;on differen (world; localt scalescountry; site on(world; anlocal extract country;site on of an the local ex- Geological site on an ex- tract of the Geological Map of Portugal, 34-D sheet [24]). Map of Portugal,tract 34-D of the sheet Geological [24]). Map of Portugal, 34-D sheet [24]).

The soil sampleTheThe was soil soil collectedsample sample was was in its collected collected natural in instate its its natural naturalby state state with by by digging digginga hand toolwith with to a a handcarry hand tool tool to to carry carry out all characterizationoutout all characterization and mechanical and stremechanical ngth tests. stre strength Oncength obtained, tests. Once Once the obtained, obtained, sample wasthe the sample was stored and storedtransportedstored andand transported transportedin suitably in suitablyinsealed suitably pl sealedastic sealed plasticboxes. pl boxes.asticDuring boxes. During the Duringcollection the collection the and collection and transport, and transport, alltransport,all care care was was alltaken taken care to towas avoid avoid taken any any to kindkind avoid of of contamination.any contamination. kind of contamination. Although there Although areare nono homogenousthere are no homogenoushomogenoussoils soils in in nature, nature, soils the the soilin soil nature, sample sample the was wassoil divided sampledivided into was into smaller divided smaller samples intosamples withsmaller with the samples quarter the technique with the quarter techniquequarterto ensure to techniqueensure homogeneity homo to ensuregeneity of the homo of samples thegeneity samples tested. of tested.the samples tested. The particle TheThesize particle particledistribution size size distributionof the soil was of of the determined soil was bydetermined sieving, followingby sieving, the following the protocol definedprotocolprotocol in the defined defined European in the standard European (EN standard ISO 17892-4 (EN ISO 2016 17892-4 [26]). The 2016 particle [[26]).26]). The size particle size distribution isdistributiondistribution shown in Figure is shown 3. The in Figure Atterberg3 3.. The The limits Atterberg Atterberg of the limitssoil limits followed ofof thethe soil soilEN followedfollowedISO 17892-12 EN ISO 17892-12 2016 [27]. The20162016 studied [27]. [27]. Thesoil The containedstudied studied soil soil 40% contained contained fine particles 40% 40% fine fine(<# particles200 particles sieve). (<# 200 200 sieve). sieve).

100 100 90 90 80 80 70 70 60 60 50 50 % passing % % passing % 40 40 30 30 20 20 10 10 0 0 0.010.01 0.1 0.1 1 1 10 10 Sieve size (mm)Sieve size (mm)

Figure 3. ParticleFigureFigure size 3. 3.distribution ParticleParticle size size of distribution distributionsoil. of of soil. soil. Infrastructures 2021, 6, 96 5 of 19

The physical properties of the soil are summarized in Table1. The soil is classified as a clayey sand (SC) in the unified soil classification system [28], and as an A-6 (14) clayey soil with a group index equal to 14 according to the AASHTO classification system [29]. This soil category comprises granular soils with high contents of clay and silt, and provides fair to poor subgrade conditions for infrastructures. When clayey particles are predominant, the soil is sensitive to expansion and shrinkage with the variation in water content. Mixing cement in this type of soil contributes to the reduction of the plasticity index and the potential for expansion/shrinkage, to attain higher compaction in the field, and increases the bearing capacity [30].

Table 1. Physical properties of the soil.

Properties Values Liquid limit (EN ISO 17892-12 2016) 32% Plastic Limit (EN ISO 17892-12 2016) 21% Plastic index (EN ISO 17892-12 2016) 11% 3 Particle density (ρss) (EN ISO 17892-3 2016) 2.64 Mg/m Coarse sand (2.0–4.75 mm) (EN ISO 17892-4 2016) - Medium sand (0.42–2.0 mm) (EN ISO 17892-4 2016) 34.5% Fine sand (0.074–0.42 mm) (EN ISO 17892-4 2016) 25.9% Fines content (<0.074 mm) (EN ISO 17892-4 2016) 39.6% Mean particle diameter (D50) (EN ISO 17892-4 2016) 0.2 mm Unified soil classification (ASTM D 2487) SC ASHTO soil classification (AASHTO M145-42) A-6 (14)

In this research, a commercial Portland cement type CEM IV/A(V) 32.5R-SR (SECIL, Outao plant) was used, which, according to [31], is a pozzolanic cement, containing 64–79% clinker (K) and 21–35% fly ash (FA), is greyish (due to the ferrous component) and has high chemical resistance. An equivalent cement type could be also obtained by mixing cement types I and II with additives type II (pozzolana/fly ash). This cement type is suitable for the manufacture of concretes and mortars with specific durability requirements, namely those used on road pavements, soil–cement mixtures and structures located in aggressive environments, such as the marine environment. As opposed to natural soils, Portland cement is an industrial product which is manufactured under strict standards, ensuring uniformity of quality and performance and has advantages that make it economical and easy to use. The cement properties are listed in Table2. This cement is very fine, with 100% of its particles passing through the 0.074 mm sieve, and has a particle density of 3.15 Mg/m3.

Table 2. Properties of Portland cement [32].

Properties Values >69% K Constituents >26% FA Ignition loss 2.3% Insoluble residue 26.3% Specific surface area (Blaine) (cm2/g) (EN 196-6) 4292 Compression strength 28d (MPa) (EN 196-1) 44.3 Setting time (min) (EN 196-3) >75

In the soil characterization tests, distilled water was used, but in soil–cement mixture specimens, tap water was used.

2.3. Definition of the Moulding Points The moulding points of the CBS test specimens are established by the water content and compaction effort used in the laboratory. To investigate possible variations in field Infrastructures 2021, 6, x FOR PEER REVIEW 6 of 19

construction operations, the moulding points used in this study were defined by varying

Infrastructures 2021, 6, 96 the compaction effort at the parent soil’s optimum water content. For6 this of 19 purpose, a test was performed. The soil was compacted in a Proctor stainless steel mould measuring 102 mm in di- constructionameter and operations, 117 mm the high, moulding using points a modified used in this compaction study were definedeffort with by varying a heavy hammer of the45.4 compaction N, in 5 layers, effort at thewith parent 25 blows soil’s optimum per layer, water from content. a height For this of purpose, 475 mm. a soil This compaction compactioneffort is representative test was performed. of the compaction process adopted in road construction, and is The soil was compacted in a Proctor stainless steel mould measuring 102 mm in diameterdetermined and 117 as: mm high, using a modified compaction effort with a heavy hammer of 45.4 N, in 5 layers, with 25 blows per layer, from a𝐵∙𝑁∙𝑊∙ℎ height of 475 mm. This compaction effort is representative of the compaction process𝐸= adopted in road , construction, and is (1) 𝑉 determined as: B·N·W·h where E is the compaction effortE = (MN.m/m,3); B is the number of blows (1)per layer; N is the V number of layers; W is the weight of the hammer (N); h is the height of fall of the hammer 3 where(m); VE isis the compactionvolume of effortthe mould (MN.m/m (m3);). BForis thethe numberabove conditions, of blows per layer;E is 2.5N MN.m/m3. The is the number of layers; W is the weight of the hammer (N); h is the height of fall of thewaterhammer content (m); wasV is themeasured volume ofimmediately the mould (m after3). Foreach the compaction above conditions, test, andE is determined by 2.5the MN.m/m oven drying3. The waterto constant content wasmass measured (105 °C immediately for 24 h). after each compaction test, ◦ and determinedIn Figure by 4, the the oven effect drying of the to constant water content mass (105 (wC) on for the 24 h). dry density of soil (ρd) is demon- stratedIn Figure with4, the effectcompaction of the water curve content fitted ( w) onto the dryplotted density compaction of soil (ρd) is demon-results. The optimum strated with the compaction curve fitted to the plotted compaction results. The optimum water content (wopt) of the parent soil (without cement) is 13%, and the corresponding water content (wopt) of the parent soil (without cement) is 13%, and the corresponding 3 3 maximummaximum value value of dry of densitydry density (ρd,max) ( isρd,max 1.74) Mg/m is 1.74. Mg/m .

1.80 ρ 1.75 d,max ) 3 1.70

(Mg/m 1.65 d ρ 1.60

1.55

Dry density, Dry 1.50

1.45 wopt Soil - modified effort 1.40 6 8 10 12 14 16 18 20 Water content, w (%) FigureFigure 4. Proctor4. Proctor test resultstest results of soil withof soil modified with modified compaction compaction effort. effort. The moulding points, with less or equal compaction energy than the modified Proctor energy,The were moulding chosen at the points, previously with determined less or equal optimum compaction water content energy level ofthan the soil.the modified Proc- Thesetor energy, moulding were points chosen consisted at the of applying previously an increasing determined number optimum of blows per water layer: content 10 level of the (E1),soil. 15 These (E2), 20 moulding (E3) and 25 points (E4) blows consisted on CBS mixturesof applying with a an water increasing content of 13%,number as of blows per explained in detail in Section 2.4. layer: 10 (E1), 15 (E2), 20 (E3) and 25 (E4) blows on CBS mixtures with a water content of 2.4.13%, Moulding as explained the Specimens in detail for the in Unconfined Section Compression 2.4. Tests The amount of cement mixed with soil varies with the characteristics of the soil and the2.4. modification Moulding goal,the Specimens and can be asfor low the as Unconfined 2% or as high Compression as 16% of the dryTests mass of soil [33]. For the soil used in this study, A-6 (14) soil type, 3–6% of cement should be enough to provideThe long amount time material of cement modification mixed [ 30with], such soil as varies a decrease with in the shrink/swell characteristics potential of the soil and the andmodification an improved/stable goal, and bearing can capacity,be as low whereas as 2% the or recommendedas high as 16% percentage of the dry of cement mass of soil [33]. For the soil used in this study, A-6 (14) soil type, 3–6% of cement should be enough to provide long time material modification [30], such as a decrease in shrink/swell potential and an improved/stable bearing capacity, whereas the recommended percentage of cement is be- tween 9% and 15% to obtain cement-bound soil characteristics [33]. In this study, two dif- ferent cement contents were used, 10% and 14%, to obtain CBS-like characteristics. Infrastructures 2021, 6, 96 7 of 19

Infrastructures 2021, 6, x FOR PEER REVIEW 7 of 19

is between 9% and 15% to obtain cement-bound soil characteristics [33]. In this study, two different cement contents were used, 10% and 14%, to obtain CBS-like characteristics. BeforeBefore the the addition addition of water of water and theand following the following cement cement hydration hydration reaction, reaction, prepared prepared soil–cementsoil–cement mixtures mixtures are are finer finer than than the initial the initial soils because soils because of the increase of the increase in fines induced in fines induced byby the the addition addition of theof cementthe cement [34]. As[34]. mentioned As mentioned earlier, the earlier, cement the used cement in this used study in has this study 100%has 100% of particles of particles smaller thansmaller 0.065 than mm, 0.065 which mm, gives which the CBS gives theoretical the CBS gradations theoretical of soil gradations cementof soil mixturescement mixtures presented presented in Figure5. in Figure 5.

FigureFigure 5. 5.Particle Particle size size distribution distribution of CBS of mixtures.CBS mixtures.

The laboratory program was conducted for CBS with the optimum water content of The laboratory program was conducted for CBS with the optimum water content of the parent soil determined earlier by the modified Proctor compaction test. This allowed the researchthe parent of the soil effect determined of the compaction earlier by effort the on mo thedified volumetric Proctor and compaction mechanical propertiestest. This allowed ofthe CBS research to be carried of the out effect under of thethe samecompaction moisture effort content on conditions. the volumetric and mechanical prop- ertiesTo of prepare CBS to the be CBS, carried the soil out was under oven-dried the same and moisture sieved using content a 2 mm conditions. aperture sieve to eliminateTo prepare coarser the material. CBS, the Afterwards, soil was theoven-dried amount of and cement, sieved by using dry mass a 2 ofmm soil, aperture was sieve addedto eliminate to achieve coarser the percentages material. required:Afterwards, soil withthe amount 10% cement of cement, (C10), and by soildry with mass 14% of soil, was cementadded (C14). to achieve The dry the soil percentages and the cement required: were mixedsoil with and 10% then cement the water (C10), was and added soil to with 14% obtaincement the (C14). 13% water The content.dry soil All and components the cement were were thoroughly mixed and mixed then until the a homogenous water was added to pasteobtain was the obtained. 13% water Then, content. the mixture All components was compacted, were in thoroughly the same way mixed as in until the soil a homoge- compaction tests in the Proctor mould, in 5 layers, but varying the number of blows per nous paste was obtained. Then, the mixture was compacted, in the same way as in the soil layer, in order to create the different compaction efforts corresponding to the four moulding pointscompaction (E1, E2, tests E3 and in E4). the Proctor mould, in 5 layers, but varying the number of blows per layer,Table in 3order summarizes to create the the fabrication different conditions compaction of the efforts eight corresponding CBS mixtures tested. to the The four mould- CBSing arepoints referred (E1, E2, to inE3 the and paper E4). by their cement content and compaction effort (e.g., “C14-E2”Table refers 3 summarizes to a CBS mixture the withfabrication 14% cement conditio compactedns of the at E2eight (15 CBS blows mixtures per layer)). tested. The CBSThe are time referred it took to to in prepare the paper (mixing by their and cement compaction) content was and always compaction less than effort an hour, (e.g., “C14- whichE2” refers is much to a shorter CBS mixture that the with initial 14% setting cement time compacted (75 min, see at Table E2 2(15) of blows the Portland per layer)). cement used. After compaction, the specimen was immediately extracted from the mould using a hydraulic device. Then, the specimens were weighed on scales accurate to the Table 3. Compaction of cement-bound soils. nearest 0.01 g and their diameter and height were measured using a 0.1 mm error calliper. FigureCBS6 shows twoC specimens (%) afterwopt extraction (%) from Blows the mould. Per Layer E (MN.m/m3) C10-E1 10 0.98 C10-E2 15 1.47 10 C10-E3 20 1.97 C10-E4 25 2.50 13 C14-E1 10 0.98 C14-E2 15 1.47 14 C14-E3 20 1.97 C14-E4 25 2.50 Infrastructures 2021, 6, 96 8 of 19

Infrastructures 2021, 6, x FOR PEER TableREVIEW 3. Compaction of cement-bound soils. 8 of 19

3 CBS C (%) wopt (%) Blows Per Layer E (MN.m/m ) C10-E1 10 0.98 C10-E2 15 1.47 The time it took10 to prepare (mixing and compaction) was always less than an hour, C10-E3 20 1.97 whichC10-E4 is much shorter that the initial setting time 25 (75 min, see 2.50Table 2) of the Portland 13 cementC14-E1 used. After compaction, the specimen was10 immediately extracted 0.98 from the mould usingC14-E2 a hydraulic device. Then, the specimens were 15 weighed 1.47on scales accurate to the 14 nearestC14-E3 0.01 g and their diameter and height were measured 20 using 1.97 a 0.1 mm error calliper. C14-E4 25 2.50 Figure 6 shows two specimens after extraction from the mould.

FigureFigure 6. Cement-bound 6. Cement-bound soil specimens. soil specimens.

Then,Then, the specimensthe specimens were wrapped were wrapped with transparent with tran plasticsparent film and plastic were curedfilm and for were cured for 7 days in a humidity and temperature control room at 23 ± 2 ◦C and relative humidity of7 55%.days The in samplesa humidity were and considered temperature suitable forcontrol testing room when at they 23 met± 2 °C the and following relative humidity of tolerances:55%. The (1) samples required were optimum considered water content, suitablewopt for(within testing±1% when of the they target met value the following toler- definedances: for (1) soil required only); (2) optimum dimensions: water diameter content, 102 ± 1 w mmopt and(within height ±1% 117 ±of1 the mm. target value defined forThe soil 24 only); specimens (2) dimensions: prepared (3 specimens diameter for 102 each ± mixture) 1 mm metand the height specimen 117 prepara-± 1 mm. tion andThe dimensions 24 specimens requirements prepared of [35 ].(3 specimens for each mixture) met the specimen prepa- In order to calculate the porosity of specimens, the particle density of each mixture, ρsmration, must and be calculated dimensions from therequirements particle density of of[35]. the soil, ρss, and the particle density of the cement,In orderρsc: to calculate the porosity of specimens, the particle density of each mixture, + sm C 1 ss ρ , must be calculated from theρsm particle= density, of the soil, ρ , and the (2)particle density of C + 1 the cement, ρsc: ρsc ρss where C is the cement content of CBS mixtures (0.10 and𝐶+1 0.14 for 10% and 14% cement, respectively). Using Equation (2), the particle density𝜌 = is 2.68 Mg/m , 3 and 2.69 Mg/m3 for 𝑠𝑚 𝐶 1 (2) the CBS mixtures with 10% and 14% cement, respectively. + 𝜌 𝜌 The porosity is the ratio of the volume of voids (Vv)𝑠𝑐 to that𝑠𝑠 of the sample (V), where thewhere volume C ofis voidsthe cement can be calculated content asof theCBS difference mixtures between (0.10 theand total 0.14 volume for 10% of the and 14% cement, sample and the volume of soil solids (Vs) and the volume of cement (Vc). From this, the 3 3 porosityrespectively). (n) is given Using by: Equation (2), the particle density is 2.68 Mg/m and 2.69 Mg/m for ρ the CBS mixtures with 10% andn =14%1 − cement,d , respectively. (3) ρ The porosity is the ratio of the volumesm of voids (Vv) to that of the sample (V), where 3 wherethe volumeρd and ρsm ofare voids the dry can density be calculated and particle as density, the difference respectively, between of CBS in (Mg/mthe total). volume of the sample and the volume of soil solids (Vs) and the volume of cement (Vc). From this, the 2.5. Unconfined Compression Tests porosity (n) is given by: The unconfined compressive strength Rc is the index used in the European specifica- tions [18] to quantify the improvement given to the soil by𝜌 the𝑑 cement in CBS mixtures. 𝑛=1− , (3) 𝜌𝑠𝑚

where ρd and ρsm are the dry density and particle density, respectively, of CBS in (Mg/m3).

2.5. Unconfined Compression Tests

The unconfined compressive strength Rc is the index used in the European specifica- tions [18] to quantify the improvement given to the soil by the cement in CBS mixtures. Unconfined compression tests (UCT) were conducted on soil specimens (only E4) and ce- ment-treated specimens in accordance with the procedure defined in [36]. All tests were conducted on unsoaked specimens, which had been cured for 7 days. The tests were carried out on a universal testing machine (Zwick) [37], with a maximum load capacity of 50 kN, and under constant displacement control (load plate speed of 1 mm/min). The vertical Infrastructures 2021, 6, 96 9 of 19

Unconfined compression tests (UCT) were conducted on soil specimens (only E4) and cement-treated specimens in accordance with the procedure defined in [36]. All tests were conducted on unsoaked specimens, which had been cured for 7 days. The tests were carried out on a universal testing machine (Zwick) [37], with a maximum load capacity of 50 kN, and under constant displacement control (load plate speed of 1 mm/min). The vertical deformation of the specimen was monitored with a displacement transducer installed on the top plate. The axial strain (ε) was determined from the vertical deformation and the initial height of the specimen, and the average stress (σ) from the load measured during

Infrastructures 2021, 6, x FOR PEER REVIEWthe test and the average initial cross section of the specimen. Based9 of on 19 the requirements defined in [18], the individual strength of the three specimens, moulded with the same characteristics, should not deviate by more than 20% from the mean strength. These deformationrequirements of the were specimen met was with monitored all tested with materials. a displacement transducer installed on the top plate. The axial strain (ε) was determined from the vertical deformation and the initial3. Results height of the specimen, and the average stress (σ) from the load measured during the3.1. test Physical and the Propertiesaverage initial of CBScross Specimenssection of the specimen. Based on the requirements defined in [18], the individual strength of the three specimens, moulded with the same characteristics,Table4 presentsshould not thedeviate average by more values than 20% and from coefficient the mean ofstrength. variation These (CV)re- of the physical quirementsproperties were of fabricatedmet with all tested specimens. materials.

3.Table Results 4. Properties of specimens. 3.1. Physical Properties of CBS Specimens Table 4 presents the average valuesw and coefficient of variation (CV)ρ ofd the physical n properties of fabricated specimens. Material Mean Mean (%) CV (%) 3 CV (%) (%) Table 4. Properties of specimens. (Mg/m ) C10-E1 12.2 3.9 1.61 0.5 39.8 w ρd n Material C10-E2Mean (%) 12.4 CV (%) 6.5Mean (Mg/m3) 1.68CV (%) (%) 0.7 37.4 C10-E1C10-E3 12.2 12.13.9 2.71.61 1.720.5 39.81.5 35.8 C10-E2C10-E4 12.4 12.66.5 1.71.68 1.740.7 37.40.1 35.1 C10-E3C14-E1 12.1 11.92.7 2.21.72 1.601.5 35.80.5 40.7 C10-E4C14-E2 12.6 11.51.7 3.41.74 1.670.1 35.10.4 38.2 C14-E1C14-E3 11.9 12.42.2 2.71.60 1.710.5 40.70.7 36.6 C14-E2C14-E4 11.5 12.43.4 4.11.67 1.740.4 38.20.5 35.3 C14-E3 12.4 2.7 1.71 0.7 36.6 C14-E4 12.4 4.1 1.74 0.5 35.3 3.2. Unconfined Compression Tests 3.2. UnconfinedFigures Compression7 and8 show Tests the stress–strain curves of unconfined compressive tests for the specimensFigures 7 ofand cement-bound 8 show the stress–strain soil with curves 10% of unconfined and 14% compressive cement by tests dry for mass the of soil. specimens of cement-bound soil with 10% and 14% cement by dry mass of soil.

4.5 E4 4.0 E3 3.5 E2 E1

(MPa) 3.0

σ 2.5 2.0

Axial Axial stress, 1.5 1.0 0.5 0.0 0.00.51.01.52.02.53.0 Axial strain, ε (%) FigureFigure 7. 7.UCTUCT stress–strain stress–strain curves for curves CBS specimens for CBS with specimens 10% cement. with 10% cement. InfrastructuresInfrastructures2021 2021, 6, ,6 96, x FOR PEER REVIEW 10 ofof 1919

4.5 E4 4.0 E3 3.5 E2 3.0 E1 (MPa) σ 2.5 2.0 1.5

Axial Axial stress, 1.0 0.5 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 ε Axial strain, (%) FigureFigure 8.8.UCT UCT stress–strainstress–strain curvescurves forfor CBSCBS specimensspecimens with with 14% 14% cement. cement.

The modulus of elasticity (E ) was obtained from the stress–strain curves according The modulus of elasticity (E3030) was obtained from the stress–strain curves according to [38], with E being the secant modulus for the stress range from 0% to 30% of R . The to [38], with E3030 being the secant modulus for the stress range from 0% to 30% of Rc c. The values of E , R and axial strain at R value are summarized in Table5 for the soil (E4) and values of E3030, Rcc and axial strain at Rcc value are summarized in Table 5 for the soil (E4) and thethe CBSCBS mixtures.mixtures. Table 5. Results of unconfined compression tests. Table 5. Results of unconfined compression tests.

Rc ε at Rc E30 Rc ε at Rc E30 Specimen Mean Mean Mean (MPa) CVCV (%) (%) Mean Mean (%) (%) CV CV (%) (%) Mean (MPa) CVCV (%) (%) (MPa) (MPa) Soil-E4 0.22 11 1.62 7.7 2 14 Soil-E4 0.22 11 1.62 7.7 2 14 C10-E1 1.80 11 1.62 4 111.4 14 C10-E1C10-E2 1.802.35 1114 1.96 1.62 7 4102.0 111.4 2 14 C10-E2 2.35 14 1.96 7 102.0 2 C10-E3 2.52 1 1.84 6 137.4 13 C10-E3 2.52 1 1.84 6 137.4 13 C10-E4 3.373.37 11 1.91 1.91 2 2196.5 196.5 14 14 C14-E1 2.352.35 55 1.73 1.73 3 3136.4 136.4 16 16 C14-E2 2.652.65 11 1.82 1.82 3 3147.0 147.0 8 8 C14-E3 3.213.21 22 2.01 2.01 1 1172.4 172.4 12 12 C14-E4 3.863.86 1010 1.91 1.91 4 4215.8 215.8 5 5

4.4. DiscussionDiscussion 4.1.4.1. CBSCBS SpecimensSpecimens The dry density of specimens, listed in Table4, increased significantly with the appli- The dry density of specimens, listed in Table 4, increased significantly with the ap- cation of a higher compaction energy, and this was more important for the lower levels. plication of a higher compaction energy, and this was more important for the lower levels. For instance, the increase was on average 4.1% from 10 to 15 blows while only 1.7% from For instance, the increase was on average 4.1% from 10 to 15 blows while only 1.7% from 20 to 25 blows. The porosity of compacted specimens varied between approximately 35% 20 to 25 blows. The porosity of compacted specimens varied between approximately 35% and 40%. Good compaction of CBS layers is important to ensure in service higher stiffness and 40%. Good compaction of CBS layers is important to ensure in service higher stiffness and less accumulation of permanent deformation with static and cyclic loadings in the and less accumulation of permanent deformation with static and cyclic loadings in the field. Considering the highest dry density (obtained for E4) as the reference, the degree of field. Considering the highest dry density (obtained for E4) as the reference, the degree of compaction obtained for E1 was about 92%, which is not sufficient to guarantee adequate compaction obtained for E1 was about 92%, which is not sufficient to guarantee adequate in-service behavior. The lowest compaction effort applied in the laboratory to comply with in-service behavior. The lowest compaction effort applied in the laboratory to comply normal field requirements, which is a minimum of 95% maximum dry density [30], is E2 with normal field requirements, which is a minimum of 95% maximum dry density [30], (15 blows per layer). is E2Preparation (15 blows per and layer). compaction of different CBS mixtures at the soil optimum water contentPreparation influenced and the compaction obtained results. of different Water isCBS required mixtures in CBS at the to aid soil in optimum the dispersion water ofcontent cement influenced particles the in the obtained soil and results. to achieve Water a is high required dry density in CBS(low to aid porosity), in the dispersion and for Infrastructures 2021, 6, 96 11 of 19

the hydration of the cement to create the bonds with natural soil particles. The optimum water content varies with the material (soil or CBS) and the compaction effort applied. It is expected to decrease with increased compaction effort and with decreased cement content [2,39]. In this situation, the water content used was likely lower (dry side) than the optimum value for the CBS mixtures. However, it was significantly higher than required for full hydration of cement [40]. Moreover, the average water content of all fabricated specimens (see Table4) was below the target of 13% because the water lost to evaporation was higher than initially predicted.

4.2. Unconfined Compressive Strength From Figures7 and8, it can be seen that, as the compaction effort increases, the peak axial stress increases, as expected. The maximum unconfined compressive strength ranges from 1.80 MPa to 3.37 MPa (mean values) for 10% cement, and from 2.35 MPa to 3.86 MPa (mean values) for 14% cement. These values (see Table5) are much higher than the strength (0.22 MPa) obtained for the natural soil, compacted in E4 conditions. According to the European standard [18], with the exception of C10-E1, the CBS specimens are classified in C1.5/2 (minimum Rc in MPa for cylinders of slenderness ratio 2 and 1, respectively). The class of compressive strength is higher than the typical values suggested in the literature for CBS specimens (0.7 to 2.1 MPa [19]). Hence, this demonstrates the potential of the technique to improve the bearing capacity of subgrades with (poor) fine-graded soils. The axial strain sustained by the specimen at peak stress was, in general, similar in all CBS specimens despite the different cement contents and being compacted in different conditions. The only exception was for CBS mixtures compacted with E1, which broke at a lower deformation level. Higher porosity in similar specimen sizes means larger pores and a weaker particle structure. Thus, the cement bonds between soil particles should also have been less effective in spreading the load in the bulk specimen. In the literature, similar conclusions have been reported with different soils [3,5,8]. The values of E30 summarized in Table5 show that compaction has the highest impact on specimen stiffness. For C10 specimens, E30 rose by 76% when the compaction effort increases from E1 to E4, whereas the effect of adding more cement (from 10% to 14%) varied between 10% and 44%. The increase in compaction effort from E3 to E4 was the most significant. In addition, Figure9 demonstrates the importance of both the cement bonding and applied compaction effort to the mechanical properties of CBS, and that Rc and E30 pro- vide the same information for assessing these materials. It can be observed that above a certain porosity level (approximately 38%), the mechanical properties of CBS specimens are affected by the cement content but not by the porosity. This demonstrates the impor- tance of applying a high compaction effort to maximize the cement-bonding benefit in CBS mixtures.

4.3. CBS Volumetric Normalisation To assess the effect of the porosity and cement content on the mechanical properties of CBS mixtures, the analysis of the voids to cement ratio has been proposed, as mentioned earlier. Note that the two quantities have opposite effects on mechanical properties, i.e., the cement–soil mixture is improved (increase in strength) with the decrease in porosity and the increase in cement content. Thus, in [2], the ratio of the porosity to volumetric cement content (n/Civ) was proposed as:

n Vv V = V = v , (4) C Vc V iv V c

where Vv is the volume of voids, Vc is the volume of (unhydrated) cement and V is the total volume. Infrastructures 2021, 6, x FOR PEER REVIEW 12 of 19

5.0 250

(MPa) 4.0 200 c (MPa) R 30 E 3.0 150

2.0 100 C10 - Rc C14 - Rc C10 - E30

Compressive strength, strength, Compressive 1.0 50 C14 - E30 Modulus of elasticicty, elasticicty, of Modulus

0.0 0 34 35 36 37 38 39 40 41 42 Infrastructures 2021, 6, 96 12 of 19 Infrastructures 2021, 6, x FOR PEER REVIEW Porosity (%) 12 of 19

Figure 9. Effect of porosity on unconfined compressive strength and modulus of elasticity.

5.0 250 4.3. CBS Volumetric Normalisation

(MPa) 4.0To assess the effect of the porosity and cement content200 on the mechanical properties c (MPa) R

of CBS mixtures, the analysis of the voids to cement ratio has been30 proposed, as mentioned E earlier.3.0 Note that the two quantities have opposite effects150 on mechanical properties, i.e., the cement–soil mixture is improved (increase in strength) with the decrease in porosity and the increase in cement content. Thus, in [2], the ratio of the porosity to volumetric 2.0 100 C10 - Rc cement content (n/Civ) was proposed as: C14 - Rc C10 - E30 𝑉 Compressive strength, strength, Compressive 1.0 50 C14 - E30 𝑛 𝑉 𝑉 = = , elasticicty, of Modulus (4) 𝐶 𝑉 𝑉 0.0 𝑉 0 34 35 36 37 38 39 40 41 42 where Vv is the volume of voids, Vc is the volume of (unhydrated) cement and V is the total Porosity (%) volume. FigureFigure 9.9. Effect of porosity onon unconfinedunconfined compressivecompressive strengthstrength andand modulusmodulus ofof elasticity.elasticity. The influence of the ratio of porosity to volumetric cement content on the unconfined 4.3.compressive CBSThe Volumetric influence strength of Normalisation the ratio is shown of porosity in Figure to volumetric 10. The cement ratio content n/Civ onvaries the unconfined between 5.1 and 8.6 for compressive strength is shown in Figure 10. The ratio n/C varies between 5.1 and 8.6 for the differentTo assess the CBS effect specimens, of the porosity and andtheir cement strength content variesiv on the in mechanical opposition properties to the n/C iv value. The the different CBS specimens, and their strength varies in opposition to the n/C value. The of CBS mixtures, the analysis of the voids to cement ratio has been proposed, asiv mentioned relationshipsrelationships between betweenR and Rc n/Cand aren/C differentiv are different for the CBS for specimens the CBS fabricated specimens with fabricated with earlier. Note that the twoc quantitiesiv have opposite effects on mechanical properties, i.e., differentdifferent cement cement contents contents but the but agreement the agreement with the experimentalwith the experimental results is good. results By is good. By the cement–soil mixture is improved (increase in strength) with the decrease in porosity dividing the porosity by the volumetric cement content, it was assumed that an increase in anddividing the increase the porosity in cement by content. the volumetric Thus, in [2], cement the ratio content, of the porosity it was to assumed volumetric that an increase porosity could be counteracted by a proportional increase in the volumetric cement content, cementin porosity content could (n/Civ) bewas counteracted proposed as: by a proportional increase in the volumetric cement keeping the unconfined compressive strength unchanged. content, keeping the unconfined compressive strength unchanged. 𝑉 𝑛 𝑉 𝑉 = = , (4) 𝐶 𝑉 𝑉 5.0 𝑉 C14

where Vv is the volume of voids, Vc is the volume of (unhydrated)C10 cement and V is the total (MPa) c

volume.R 4.0 The influence of the ratio of porosity to volumetric cement content on the unconfined compressive strength is shown in Figure 10. The ratio n/Civ varies between 5.1 and 8.6 for 3.0 the different CBS specimens, and their strength varies in opposition to the n/Civ value. The relationships between Rc and n/Civ are different for the CBS specimens fabricated with different2.0 cement contents but the agreement with the experimental results is good. By dividing the porosity by the volumetric cement content, it was assumed that an increase in porosity could be counteracted by a proportional increase in the volumetric cement Compressive strength, strength, Compressive content,1.0 keeping the unconfined compressive strength unchanged.

5.00.0 C14 345678910C10 (MPa) c R 4.0 n/Civ

Figure3.0 10. Effect of the ratio of porosity to volumetric cement content on unconfined compressive strength.

2.0 In fact, in order to keep the same value of Rc, an exponent might be applied to one of the two variables, n or Civ, to make the effects of their variation on Rc [2] compatible. Compressive strength, strength, Compressive It was1.0 found that by applying a power of 0.2 to the parameter Civ, a good adjustment is reached, as shown in Figure 11. 0.0 345678910 n/Civ Infrastructures 2021, 6, x FOR PEER REVIEW 13 of 19

Figure 10. Effect of the ratio of porosity to volumetric cement content on unconfined compressive strength.

In fact, in order to keep the same value of Rc, an exponent might be applied to one of Infrastructures 2021, 6, 96 the two variables, n or Civ, to make the effects of their variation on Rc [2] compatible.13 It ofwas 19 found that by applying a power of 0.2 to the parameter Civ, a good adjustment is reached, as shown in Figure 11.

5.0 C14-E4 C14-E3 C14-E2 (MPa)

c 4.0 R C14-E1 C10-E4 3.0 C10-E3 C10-E2 C10-E1 2.0

Compressive strength, strength, Compressive 1.0

0.0 22 23 24 25 26 27 28 29 30 31 0.2 n/Civ FigureFigure 11. Effect of modified modified ratio of porosity to volumetric cement content on unconfined unconfined compres- sivesive strength.strength.

InIn [[2],2], the the authors authors reported reported an an exponent exponent va valuelue of of0.28 0.28 for for fine-graded fine-graded soils. soils. The Theem- empiricalpirical exponent exponent applied applied to C toiv definesCiv defines the relative the relative contributions contributions of volumetric of volumetric cement cement con- contenttent and and porosity porosity to tothe the unconfined unconfined compressive compressive strength. strength. In In addition, addition, previous previous research withwith differentdifferent soilssoils [[41]41] suggestssuggests thatthat thisthis exponentexponent isis notnot greatergreater thanthan one,one, whichwhich meansmeans thatthat porosityporosity isis moremore importantimportant thanthan cementcement bondingbonding forfor thethe mechanicalmechanical propertiesproperties ofof cement–soilcement–soil mixtures. mixtures. Thus, Thus, for for the the soil soil analyzed analyzed in this in thisstudy, study, a clayey a clayey soil A-6(14), soil A-6(14), mod- modifiedified with with10% to 10% 14% to Portland 14% Portland cement, cement, the un theconfined unconfined compressive compressive strength strength after 7 afterdays 7of days cure ofcan cure be canestimated be estimated from the from porosity the porosity and the and volumetric the volumetric cement cement content content as: as:

!−−3.5853.585 5 𝑛 𝑅𝑐(MPa) = 3.4 × 105 ×n . (5) Rc(MPa) = 3.4 × 10 × 0.2 . (5) 𝐶0.2𝑖𝑣 Civ In addition, to compare the results of cement–soil mixtures with different native soils In addition, to compare the results of cement–soil mixtures with different native soils and binding agents, in [4], the authors proposed the normalization of the Rc-(n/𝐶) as: and binding agents, in [4], the authors proposed the normalization of the Rc-(n/Cα ) as: −𝐵 iv 𝑅𝑐 𝑛 =A× −B , (6) Rc 𝑟𝑒𝑓 n𝐶𝛼 𝑅𝑐 = A × 𝑖𝑣 , (6) re f Cα Rc iv 𝑟𝑒𝑓 where 𝑅𝑐 is the Rc value obtained at the reference (n/𝐶) value, and A and B are model re f α wherefitting Rconstants.c is the RThus,c value considering obtained at the the reference reference (n/(n/C𝐶iv) value,value andof 30 A chosen and B are in model[3] for α fittingsilty/clayey constants. soils, the Thus, results considering obtained in the this reference study were(n/C comparediv) value of in 30Figure chosen 12 with in [3 those] for silty/clayeyof fine-graded soils, cohesive the results soils obtained found in in the this literature study were [2,3,8,34], compared and in listed Figure in 12 Table with those6. All ofstudies fine-graded employed cohesive unconfined soils foundcompressive in the testing literature of CBS [2,3, 8specimens,34], and listedcured inforTable 7 days.6 . The All studiesresults obtained employed for unconfined different fine compressive grained soils, testing with of CBSdifferent specimens cement cured contents for 7 compacted days. The resultsto different obtained effort for levels different align fine in a grained single curve. soils, withAn excellent different fit cement of a power contents law compactedmodel was toobtained different for effort these levelsresults. align Hence, in a the single normal curve.ized Anequation excellent empirica fit oflly a power supports law the model esti- wasmation obtained of the forcompressive these results. strength Hence, of theCBS normalized mixtures with equation different empirically soils with supports similar thege- estimationotechnical characteristics of the compressive (i.e., strengthgranulometry, of CBS limits mixtures of consistency, with different drysoils density with and similar geo- geotechnicallogical origin). characteristics (i.e., granulometry, limits of consistency, dry density and geological origin). Infrastructures 2021, 6, 96 14 of 19 Infrastructures 2021, 6, x FOR PEER REVIEW 14 of 19

10

8

Present study =30) iv 6 [2] [42] (n/C c [3] /R c 4 R [8]

2

0 10 15 20 25 30 35 40 n/Civ0.2 0.2. FigureFigure 12. 12.Normalized NormalizedRc–n/C Rc–n/𝐶iv of of different different studies. studies.

Table 6. CBS research studies foundTable in the 6. literature.CBS research studies found in the literature.

ref 𝑟𝑒𝑓 𝜶 Type of Soil Empirical Correlation α 𝑅 (n/𝑪𝒊𝒗) = 30 Reference Type of Soil Empirical Correlation Rc (n/Civ)=30𝑐 Reference −3.32  −3.32 𝑛 Clayey Sand SC ClayeyR ( Sand) = SC × 4𝑅×(MPa)n = 5 × 104 × 0.62 0.62 [2] [2] c MPa 5 10 𝑐 C0.28 0.28 iv 𝐶𝑖𝑣  −4.266 −4.266 Clayey Sand SC 6 n 𝑛 2.00 [42] Rc(MPa) = 4 × 10 × 0.21 6 Clayey Sand SC 𝑅 (MPa)Civ = 4 × 10 × 2.00 [42] 𝑐 𝐶0.21  −3.85 𝑖𝑣 R ( ) = × 5 × n −3.85 c MPa 4.29 10 C0.28 Paraguay Clay iv 5 𝑛 0.80 Paraguay Clay 𝑅𝑐(MPa) = 4.29−3.85 × 10 × 0.28 0.80 Red Silty Clay R ( ) = × 5 × n 𝐶 1.19 [3] c MPa 4.86 10 C0.28 𝑖𝑣 Silt iv −3.853.02  −3.85 6 n 5 𝑛 RedRc( SiltyMPa) Clay= 1.47 ×𝑅10𝑐(MPa)× 0.28 = 4.86 × 10 × 1.19 [3] Civ 0.28 𝐶𝑖𝑣  −2.64 −3.85 Silty Soil R (MPa) = 9.3 × 103 × n 𝑛 1.17 [8] c C0.4 6 Silt 𝑅𝑐(MPa)iv = 1.47 × 10 × 0.28 3.02  −3.585 𝐶𝑖𝑣 Cohesive Soil CL R ( ) = × 5 × n −2.641.74 Present study c MPa 3.4 10 C0.2 iv 3 𝑛 Silty Soil 𝑅𝑐(MPa) = 9.3 × 10 × 0.4 1.17 [8] 𝐶𝑖𝑣 𝑛 −3.585 5. CBS Design Procedure 5 Cohesive Soil CL 𝑅𝑐(MPa) = 3.4 × 10 × 0.2 1.74 Present study 5.1. Description 𝐶𝑖𝑣 The results obtained in this study support, firstly, the CBS design of the clayey sand 5. CBS Design Procedure soil tested, and furthermore, enable the development of a CBS design method for different soils.5.1. Description From a practical design point of view, the CBS design comprises the definition of the cementThe results content, obtained the water in this content study and support, the target firstly, dry the density CBS design in the of field the toclayey ensure sand a definedsoil tested, mechanical and furthermore, performance, enable which the development is often evaluated of a CBS with design unconfined method compression for different testingsoils. From at seven a practical days of curing.design point The design of view mixture, the CBS procedure design reliescomprises on the the evidence definition that, of asthe observed cement incontent, Figure the11, thewater same content value and of R thec can target be obtained dry density either in by the using field less to ensure cement a contentdefined and mechanical increasing performance, the compaction which effort, is often or it canevaluated be reached with byunconfined increasing compression the cement contenttesting andat seven applying days lessof curing. compaction The design energy. mi Hence,xture procedure this means relies that on using the evidence Equation that, (5), oras a observed similar relationship in Figure 11, if the a different same value soil isof used,Rc can the be cementobtained content either andby using dry density less cement can becontent chosen and to reachincreasing the target the compaction compressive effort, strength or it can value be forreached a given by project.increasing the cement contentThus, and for applying a different less soil compaction to the one energy. investigated Hence, in this means study, Equationthat using (5) Equation is general- (5), izedor a tosimilar [3]: relationship if a different soil is used, the cement content and dry density can  −B be chosen to reach the target compressive strengthn value for a given project. Rc = A × α , (7) Thus, for a different soil to the one investigatedCiv in this study, Equation (5) is gener- wherealizedA to, B [3]:and α are the model constants that vary with the soil and cement used. The method to develop this model with less experimental effort than was used in this study is described in the following section. To establish different combinations that can be Infrastructures 2021, 6, 96 15 of 19

used to reach a target compressive strength value, the porosity/cement ratio (n/Civ) must be calculated. Combining Equations (2) and (3), the porosity is:

ρ  1 C  n = 1 − d + . (8) (C + 1) ρss ρsc

For the calculation of Civ, the total dry mass of the CBS specimen (msm) is the sum of the dry mass of soil (mss) and dry mass of cement:

msm = mss + C.mss = mss(1 + C), (9)

and m m = sm , (10) ss 1 + C

The dry mass of the CBS specimen (msm) is the product of the dry density of specimen (ρsm) by the volume (V) of the specimen, so the dry mass of soil becomes:

ρ ·V m = d (11) ss 1 + C

and the volume of cement Vc is:

mc C.V.ρd Vc = = , (12) ρsc ρsc(C + 1)

Finally, Civ is: Vc C.ρd Civ = = . (13) V ρsc(C + 1) From Equations (8) and (13), the porosity and volumetric cement content in CBS are a function of the dry density of mixture, of the cement content and of the densities of cement and soil particles. For a certain soil and cement, their particle densities are fixed. Hence, n the dry density of the CBS is a function of the cement content for a defined α . However, Civ n  n  due to the exponent α in α , there is not an explicit solution to ρd = f α , C, ρss, ρsc . Civ Civ To solve this, it is assumed that ρd and C can be modelled with a 2nd order polynomial function: 2 ρd = a1·C + a2·C + a3 (14)

where a1, a2 and a3 are the model constants. Introducing Equation (14) in Equations (8) and (13), ∗  the estimated values of the porosity (n*) and Civ Civ are obtained as:

a ·C2 + a ·C + a  1 C  n∗ = 1 − 1 2 3 + , (15) (C + 1) ρss ρsc

2  ∗ C· a1·C + a2·C + a3 Civ = . (16) ρsc(C + 1) In addition, combining Equation (15) with Equation (6), the porosity can be estimated as:

 − 1 2  !α R B C· a1·C + a2·C + a3 n∗∗ = c · . (17) A ρsc(C + 1)

Finally, considering various values of C in a defined range (Cmin–Cmax) and the target Rc, the constants a1, a2 and a3 can be determined using the Solver function in Microsoft Excel to minimize the error: Cmax error = ∑ (n∗ − n∗∗)2. (18) Cmin Infrastructures 2021, 6, x FOR PEER REVIEW 16 of 19

1 𝛼 𝑅 − 𝐵 𝐶∙(𝑎 ∙𝐶2 +𝑎 ∙𝐶+𝑎 ) 𝑛∗∗ = 𝑐 ∙ 1 2 3 . (17) 𝐴 𝜌𝑠𝑐 (𝐶+1)

Finally, considering various values of C in a defined range (Cmin–Cmax) and the target Rc, the constants a1, a2 and a3 can be determined using the Solver function in Microsoft Excel to minimize the error: 𝐶𝑚𝑎𝑥 ∗ ∗∗ 2 Infrastructures 2021, 6, 96 𝑒𝑟𝑟𝑜𝑟 = (𝑛 −𝑛 ) . 16 of(18) 19 𝐶𝑚𝑖𝑛 𝑛 𝑅𝑐 − 𝛼 For the clayey soil investigated, considering the 𝐶𝑖𝑣 model described in n EquationFor the (5) clayey the constants soil investigated, a1, a2 and considering a3 are 0.01, the −0.35Rc − andα model 19.09, describedrespectively. in Equation Figure (5)13 Civ showsthe constants the ρd-Ca1 models, a2 and fora3 arevarious 0.01, R−c0.35 values. and From 19.09, this, respectively. project managers Figure 13 and shows contractors the ρd-C havemodels a range for various of optionsRc values. to expl Fromore. The this, decision project managers on selected and ρd contractors and C depends have on a range project of requirementsoptions to explore. and specific The decision conditions, on selected namelyρd theand constructionC depends on time project constraints, requirements the avail- and abilityspecific of conditions, adequate namelyequipment the constructionto apply the timedesired constraints, compaction the availabilityenergy and ofthe adequate cost of cement.equipment to apply the desired compaction energy and the cost of cement.

2.0 Rc=4.5 MPa Rc=3.5 MPa 1.9 RC=2.5 MPa

3 Rc=1.5 MPa 1.8 1.79 Mg/m

(Mg/m3) 1.72 Mg/m3 d ρ 1.7

1.6 Dry density, density, Dry 1.5

1.4 4 6 8 10121416 Cement content, C (%)

FigureFigure 13. PracticalPractical examples examples of of mix mix design. design.

Finally,Finally, this methodology can also be useful to control compacted cement-bound soil layerslayers in in the the field. field. If If poor poor compaction compaction is is dete detected,cted, this this can can be be readily readily taken taken into into account account in thein the design, design, identifying identifying through through Equation Equation (5 (5)) the the expected expected compressive compressive strength, strength, and adoptingadopting corrective corrective measures measures accordingly, accordingly, su suchch as the reinforcement of the treated layer oror the reduction of the maximum vertical stre stressss admitted in the structural design of the overlaying structure [43]. For example, if Rc = 3.5 MPa is required in the project, the overlaying structure [43]. For example, if Rc = 3.5 MPa is required in the project, the mini- minimum dry density is 1.79 Mg/m3 for 8% cement, and 1.72 Mg/m3 for 14% cement. mum dry density is 1.79 Mg/m3 for 8% cement, and 1.72 Mg/m3 for 14% cement. 5.2. Determination of CBS Model 5.2. Determination of CBS Model The CBS design procedure described considers that a fixed water content is used regardlessThe CBS of design the cement procedure content described and compaction considers effortthat a adopted.fixed water Thus, content in thisis used study, re- gardlessthe compaction of the cement of CBS content materials and at compaction the optimum effort water adopted. content Thus, determined in this forstudy, the soilthe compactionwas investigated of CBS and materials it was observed at the optimum that the unconfinedwater content compression determined strength for the obtainedsoil was investigatedvaries with the and cement it was observed content and that compaction the unconfined effort. compression The authors strength acknowledge obtained that var- by iesprescribing with the thiscement water content content, and the compaction maximum effort. dry density The authors of CBS acknowledge is hard to achieve that becauseby pre- scribingthe optimum this water water content, content the varies maximum slightly dry with density the content of CBS of cement.is hard to Nevertheless, achieve because this themethod optimum allows water considerable content varies savings slightly in the with laboratory the content to designof cement. a CBS Nevertheless, that meets this the project requirements. To build the CBS model, Equation (7), the following procedure is recommended: 1. Build the soil Proctor curve for the determination of the maximum dry density and the optimum water content of the soil; 2. Establish the adequate limits of cement content for the soil type (minimum range 4%), using, for example, recommendations in [33]; 3. Establish the limits of laboratory compaction, for example, E4 and E2; 4. Produce CBS specimens with minimum and maximum values of cement content at the soil optimum water content, compacted at E4 and E2; 5. Test CBS specimens cured for 7 days for unconfined compression strength; 6. Determine n and Civ; Infrastructures 2021, 6, 96 17 of 19

n 7. Fit Equation (6) to α versus Rc results to obtain A, B and α; in the literature, the best Civ fit model is obtained for an α between 0.18 and 0.4.

6. Conclusions This paper describes a study investigating the effects of porosity, dry density and cement content on the mechanical properties of fine-graded soils treated with cement. A clayey sand (A-8 class) extracted in the Almada Municipality, Portugal, was mixed with 10% and 14% of Portland cement type IV of the dry mass of the soil, and compacted at the soil optimum water content. To obtain different volumetric properties in cement-bound soil specimens, the compaction effort used in the laboratory varied from 1.0 to 2.5 MN.m/m3. The mechanical properties were evaluated on unsoaked specimens, cured for 7 days, using unconfined compression testing. From the experiments and discussion of results, and within the limits of test conditions, the following conclusions can be drawn: • The unconfined compressive stress–strain behavior of CBS is affected by the cement content and compaction effort used in the production of the specimens. Increasing ce- ment content and compaction effort leads to higher peak stress (compression strength, Rc) and less deformation at peak, which results in higher modulus of elasticity, E30, values. For a certain cement content, the Rc and E30 had the same variation trend as the specimen porosity. • The compressive strength is strongly affected by the modified porosity to volumetric 0.2 cement content ratio (n/Civ ). The exponent value of 0.2 is in agreement with other studies found in literature for different fine-graded soils. It was also found that by 0.2 normalizing the compressive strength of CBS to a certain n/Civ value, the results of CBS with different parent soils and cements fit a single model. 0.2 • The Rc–n/Civ model allows the determination of the cement content and the dry density required in the field to obtain a certain Rc value. In addition, supported by these conclusions, a practical CBS design approach was proposed for different soils. This approach allows the CBS conditions to be defined (cement content, target dry density, water content) to obtain a minimum unconfined compressive a strength. A protocol was proposed to obtain the Rc–n/Civ model for the soil with fewer tests than usually required. Finally, further studies are required (expanding tests to other cement contents and water contents) in order to check the possibility of generalization of the present findings to different soils and binding agents.

Author Contributions: Conceptualization, T.S.; methodology, T.S.; validation, T.S., J.G. and R.M.; formal analysis, J.G.; investigation, J.G.; resources, F.P.; writing–original draft preparation, T.S.; writing–review and editing, T.S., R.M. and F.P.; supervision, T.S. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. Acknowledgments: The authors would like to express their gratitude to Jorge Silvério and Vítor Silva for helping during the laboratory tests performed at Civil Engineering Department of NOVA School of Science and Technology. Conflicts of Interest: The authors declare no conflict of interest.

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