strength estimation of cement-treated marine clay with

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Soils and Foundations 60 (2020) 1065–1083

Technical Paper

Strength estimation of cement-treated marine clay with wide rangesof sand and initial water contents

Erika Yamashita a, Arlyn Aristo Cikmit b, Takashi Tsuchida c,⇑, Ryota Hashimoto d

aNippon Koei Co. Ltd. 5-4 Kojimachi, Chiyoda-ku, Tokyo 102-8539, JapanbDepartment of Civil Engineering, Faculty of Engineering, Sriwijaya University, Jl. Raya Palembang-Prabumulih Km. 32, Ogan Ilir, South Sumatra,

30662, IndonesiacResilience Research Center, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japan

dGraduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima, Hiroshima, 739-8527, Japan

Received 18 November 2019; received in revised form 4 May 2020; accepted 14 May 2020Available online 4 September 2020

Abstract

A new strength estimation equation for cement-treated clay is proposed for marine clay with wide ranges of sand and initial watercontents. The proposed equation can determine the strength of cement-treated soil by using two parameters, the ratio of the cement con-tent to the mass of fine particles in the soil and the volumetric solid ratio excluding sand, where sand is defined as particles greater than0.075 mm. A series of strength tests was performed on cement-treated soil with various sand, cement, and initial water contents. From thetest results, it was found that the strength of cement-treated clay is primarily determined by the ratio of the water and cement contents tothe fine-grained soil and was not related to the sand particles. The applicability of the proposed equation was compared to that of theexisting three strength estimation equations. The proposed equation demonstrated the best fitness between the measured and the esti-mated strengths of marine clays with the wide ranges of sand and initial water contents.� 2020 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Cement-treated soil; Marine clay; Water content; Sand content; Unconfined compressive strength; Strength estimation equation

1. Introduction

In coastal areas, sediment dredging is regularly per-formed to maintain navigable channels and harbors; thisannually generates a significant amount of dredged soil.Generally, the dredged soil will be landfilled in a disposalfacility close to the dredging site. However, most disposalfacilities are currently lacking sufficient capacity owing tothe difficulties of constructing new disposal facilities.Hence, the recycling of dredged soil is necessary.

https://doi.org/10.1016/j.sandf.2020.05.002

0038-0806/� 2020 Production and hosting by Elsevier B.V. on behalf of The

This is an open access article under the CC BY-NC-ND license (http://creativec

Peer review under responsibility of The Japanese Geotechnical Society.⇑ Corresponding author.E-mail address: [email protected] (T. Tsuchida).

A promising method for recycling dredged soil is to sta-bilize it with a binder (e.g., cement) and then employ thetreated dredged soil as a geomaterial for coastal develop-ment. Nowadays, massive sand mining, that was per-formed in the past for various purposes such asembankment fill, is no longer legal due to environmentalissues. Consequently, the stabilizaton of dredged soil usingcement, creating cement-treated soil, is being conducted atvarious construction sites to replace sand as a fill material.For example, according to Sato (2003), 8.6 million m3 ofcement-stabilized dredged soil was used as embankmentmaterial for the construction of the Chubu InternationalAirport in 2000. Moreover, Watabe and Noguchi (2011)and Noguchi et al. (2012) reported that 620,000 m3 ofcement-treated soil, dredged soil that was taken from the

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Nomenclature

A:N:D average normalized differenceAi, calculated strengthbi measured strengtha; b; x; y;A;B;E; F experimental constants that vary

according to soil and binder typesqu unconfined compressive strength (kN/m2)wc mass of clay-water (kg)C mass of cement (kg)D days of curing (days)LI liquid indexKc strength increment coefficient determined by

each curing timec ratio of cement mass to solid soilc0 ratio of minimum cement mass to the mass of

solid soilc* ratio of mass of cement to total mass of solid of

soil mixturec0* ratio of minimum cement mass to total mass of

soil mixture to gain strength

cf � ratio of cement mass to masses of clay and siltc�f 0 ratio of minimum mass of cement to mass of dry

clay and silt to gain strength developmenty volumetric solid ratio, ratio of volume of soil

and cement to total volume of soil mixtureN coefficient of space-gap structure in cement-

treated soilmcement mass of cement (kg)mfine masses of clay and silt (kg)msand mass of sand (kg)V fine volumes of clay and silt (m3)V sand volume of sand (m3)V cement volume of cement (m3)V water volume of water (m3)S ratio of sand mass to total mass of soil (%)y�F ratio of volumes of clay, silt, and cement to vol-

ume of soil mixture excluding sand

1066 E. Yamashita et al. / Soils and Foundations 60 (2020) 1065–1083

navigation channel of Tokyo Port and stabilized, wasadopted for the construction of the D-Runway at HanedaAirport in 2010. Ueno et al. (2012) demonstrated the con-struction of an artificial tidal flat using dredged soil as amethod of recycling dredged soil. In addition, cement-treated soil has several other uses, for instance, as soilwater-shielding material for waste disposal sites(Kawasaki et al., 2009; Tsuchida et al., 2017), as embank-ment material in offshores (Tan et al., 2002; Lu et al.,2012), and as light-weight backfilling material (Watabeet al., 2009).

As described above, cement-treated soil has beenthought of as a well-established option for the improve-ment of soft soil; however, an adequate estimation of thestrength development is still significantly dependent on ahuge number of laboratory tests. To define the optimumamount of cement addition, in practice, numerous testsmust be performed for each project. This causes a wasteof time and labor. The situation could be bypassed by pro-viding a new and more general equation applicable to sim-ilar projects at different sites.

The physico-chemical and engineering characteristics ofcement-treated soil have progressively been studied (Uddinet al., 1997; Das, 2000; Sivapullaiah et al., 2000; Tan et al.,2002; Chew et al., 2004; Kamruzzaman et al., 2006, 2009;Pakbaz and Alipour, 2012; Sarkar et al., 2012) to scientif-ically clarify the strength development of the soil. Manystudies on strength estimation equations have also beenconducted in various regions, and several equations havebeen proposed, as listed in Table 1 (Japan CementAssociation, 2007; Horpibulsuk et al., 2011; Chian et al.,2016; Mitchell et al., 1974; Tang et al., 2001; Lorenzo

and Bergado, 2004; Kida et al., 1977; Omine et al., 1998;Liu et al., 2008; Consoli et al., 2016; Tsuchida and Tang,2015). However, the utility of these equations seems to belimited by the various ground conditions. In the presentstudy, four proposed equations were targeted for reviewin terms of estimating the strength of cement-treated claywith wide ranges of sand and initial water contents.

The purpose of this study is to investigate the contribu-tion of sand content and initial water content of clay to thestrength of cement-treated soil. A series of strength tests oncement-treated soil was performed with various sand,cement, and initial water contents. From the results, amodified equation capable of estimating the strength ofcement-treated marine soil with wide ranges of sand andinitial water contents was proposed.

2. Review of previous studies

In Japan, the most prominent equation for estimatingthe strength development of cement-treated clay is oneadopted from concrete engineering, shown as follows(Japan Cement Association, 2007):

qu ¼awcC

� �x þ b ð1Þ

where qu (kN/m2) is the unconfined compressive strength ofthe cement-treated soil, wc/C is the ratio of the clay-watermass to the cement mass, and a, b, and x are the experi-mental constants. It is well known that the strength of con-crete is determined by the water-cement ratio of the cementpaste and not related to the aggregate. In the case ofcement-treated soil, unlike concrete, the pore distribution

Table 1Examples of proposed strength estimation equations for cement-treated clay.

No. Strength estimation equation Proposer

(1) qu¼ awccð Þx þb Japan Cement Association (2007)

(2) qu wc=cð Þ1;Dqu wc=cð Þ0;28

� �¼ wc=cð Þ0;28

wc=cð Þ1;D

h ibðEþF lnDÞ Horpibulsuk et al. (2011)

(3) qu¼ xy wc=cð Þ ln Dð Þ¼ aþb s=cð Þ

y wc=cð Þ ln Dð Þ Chian et al. (2016)

(4) qD¼qD0þKlog D=D0ð Þ Mitchell et al. (1974)(5) qu¼ K c-c0ð Þ

Gsw=100þ1ð Þ2Tang et al. (2001)

(6) qu¼ApaexpbeotAw

� �Lorenzo and Bergado (2004)

(7) qu¼ aCwx þb Kida et al. (1977)

(8) quðF Þ¼ ðb�1ÞF sþ1

bf 2s =quðLÞþð1�F sÞ=quð�Þ

Omine et al. (1998)

(9) qu¼Kr1R � 1

R0

� �Liu et al. (2008)

(10) qu¼a bivð Þxh i-a Consoli et al. (2016)

(11) qu¼Kc c� � c�0� �

yN Tsuchida and Tang (2015)

E. Yamashita et al. / Soils and Foundations 60 (2020) 1065–1083 1067

in the soil greatly varies with the soil conditions. And thepore distribution greatly affects the strength of cement-treated soil (Consoli et al., 2011). However, Eq. (1) doesnot include any parameters for the pore distribution ofthe soil.

Horpibulsuk et al. (2003, 2011) suggested an equationfor determining the strength of cement-treated soil usingAbrams’ law, as shown below:

qu wc=Cð Þ1;Dqu wc=Cð Þ0;28

( )¼ wc=Cð Þ0;28

wc=Cð Þ1;D

" #B

E þ F lnDð Þ; ð2Þ

where qu(wc/C)1,D (kN/m2) is the unconfined compressivestrength of the cement-treated soil at a clay-water/cementratio of the studied soil (wc/C)1,D after D days of curing,qu(wc/C)0,28 (kN/m2) is the unconfined compressive strengthof the cement-treated soil at a clay-water/cement ratio ofthe reference soil (wc/C)0 after 28 days of curing, and B,

E, and F are the experimental constants. Eq. (2) is applica-ble when the clay-water content is in the range of the liquidindex, (LI) = 1–2, and the wc/C = 2.5–15. Eqs. (1) and (2)determine the strength of the cement-treated soil using thewc/C ratio without any parameters related to the pore dis-tribution of the soil.

Tsuchida and Tang (2015) and Chian et al. (2016) pro-posed equations that consider parameters for the pore dis-tribution of cement-treated soil. The equation by Chianet al. (2016) determines the strength of the cement-treatedsoil using the two basic parameters and Abrams’ law, asfollows:

qu ¼x

y wc=Cð Þ ln Dð Þ ¼ aþ b s=Cð Þy wc=Cð Þ ln Dð Þ; ð3Þ

where s/C is the ratio of the soil mass to the cementmass, x, y, a, and b are the experimental constants, andD (days) is the curing time. By using parameters wc/Cand s/C, the ratio of water (pore) to soil, wc/s, is consideredin this equation. Chian et al. (2017) studied the influence of

the sand content using the proposed equation and con-cluded that the conventional wc/C and s/C ratios wereinsufficient for presenting a holistic strength prediction ofcement-treated clayey soil containing sand. The equationby Tsuchida and Tang (2015) has a form similar to thatof the well-known gel-space ratio theory expressing thestrength of cement paste (Powers, 1958). The proposedequation was further discussed by Kang et al. (2015,2016) and Kang et al., 2017a, 2017b. In the estimationequation, the strength is given by the cement content andthe volumetric solid ratio, as shown below:

qu ¼ kc c� � c�0� �

Y N ; ð4Þwhere kc is the strength increment coefficient determined

by each curing time. The cement ratio c* (%) is the ratio ofthe mass of the cement to the total mass of the solid in thesoil mixture, and c0*(%) is the ratio of the minimum massof the cement to the total mass of the cement-treated soilneeded to gain strength development. Volumetric solidratio Y is the volume ratios of the soil and the cement tothe total volume of the soil mixture, and N is an experimen-tal coefficient related to the gap structure in the treated soilspecified in the data regression. Tsuchida and Tang (2015)defined the N parameter as the dependence of the compres-sive strength on the porosity of the hardened bulk ofcement-treated soil. The N value was determined as thevalue for which the linear relationship of the equation exhi-bits the highest coefficient of correlation (R2). As the focushere is placed on the effect of the sand content on thestrength of cement-treated soil, the definitions of cementcontent c* and volumetric solid ratio Y are given as fol-lows, separating the mass and the volume of the fine grainsand the sand in the soil:

c� ¼ mcement

mfine þ msand þ mcement� 100 ð5Þ

Y ¼ V fine þ V sand þ V cement

V fine þ V sand þ V cement þ V waterð6Þ

Table 3Physical properties of Toyoura sand (Wu et al.,2013).

Mean grain size (mm) 0.20

Coefficient of uniformity 1.21Specific gravity 2.656Minimum dry density (g/cm3) 1.332Maximum dry density (g/cm3) 1.646Internal friction angle (�) 44.0

Table 4Physical composition of Ordinary Portlandcement.

Chemical compound Mass percentage (%)

CaO 67.7SiO2 23.3Ai2O3 5.8Fe2O3 2.6SO3 0.3MgO 0.1


where mfine, msand, and mcement (kg), are the masses of finesoil (clay and silt), sand, and cement, respectively. Vfine,Vsand, Vcement, and Vwater (m

3) are the volumes of fine soil(clay and silt), sand, cement, and water, respectively. Eqs.(3) and (4) include the parameters for the pore distributionof the soil. However, the proposed equations do not con-sider the effect of the sand content on the strength develop-ment of the cement-treated soil.

The sand content of dredged soil usually exhibits a largevariation, depending on the dredged location (i.e., distancefrom the estuary), even if the soil is dredged at the sameport. Although cement-treated dredged soil with signifi-cantly different sand contents generally shows differentstrength characteristics, it has not been clarified how thesand content is to be considered in the estimation of thestrength development of cement-treated soil. For example,in concrete engineering, sand and gravel are treated asaggregates and the concrete strength is determined onlyby the strength of the cement paste which is dependenton the so-called water-cement ratio. Coarse aggregatesare considered as constituents with no contribution to thestrength development of the concrete. The question thenarises as to whether the sand contributes to the strengthof the cement-treated soil or not.

3. Outline of experiment

In this study, two types of strength tests, laboratoryvane shear tests and unconfined compression tests, wereperformed with various sand, cement, and initial watercontents.

3.1. Materials

In this study, Tokuyama Port clay, Toyoura sand, andordinary Portland cement were used as the main materials.The Tokuyama Port clay, drawn from a large area of adredging-disposal facility, originated from the dredged sed-iment of Tokuyama Port. The soft soil was relativelyhomogenous in particle distribution and similar in consis-tency and initial water content. The Toyoura sand was typ-ically clean sand; it is commercially available in Japan andused for various experiments (Zhang et al., 2010; Wu et al.,2013). The physical properties of Tokuyama Port clay,Toyoura sand, and ordinary Portland cement are summa-rized in Tables 2, 3, and 4, respectively.

Table 2Physical properties of Tokuyama Port clay.

Sand content, S(%)

Liquid limitwL

Plastic limitwP

Plasticity indexIP

0 108.9% 44.5% 64.430 73.3% 31.5% 41.750 53.5% 24.9% 28.770 35.1% 18.9% 16.1

3.2. Preparation of samples

Tokuyama Port clay was filtered using a 75-lm sieve toremove the coarse particles, sand, shell pieces, and coralfragments. The clay and the added distilled water were pre-viously cooled to 2 �C in a refrigerator to delay the cement–water hydration during the clay–cement mixing process.The cement and the added distilled water were carefullymixed into cement milk before being added to the clay-sand mixture. The soil and cement mixture was then stirredfor 2 min with a hand mixer, and then further mixed with avacuum mixer for 30 min to produce a uniform mixture.After mixing, the soil mixture was poured into containersfor the laboratory vane shear tests and unconfined com-pression tests. Cylindrical containers, 60 mm in diameterand 60 mm in height, were used as the molds for the labo-ratory vane shear tests, while cylindrical containers, 50 mmin diameter and 100 mm in height, were used as the moldsfor the unconfined compression tests. During the process ofpouring, the containers were lightly tapped to expel airbubbles from the soil mixture. The bottom of the cylindri-cal containers used for the unconfined compression testswas drilled to create holes for allowing the water to pene-trate the specimens. Immediately after pouring, the topends of the poured samples were wrapped with polyethy-lene, and the holes beneath them were covered with tapeto avoid moisture loss. The tape and the polyethylene wrapwere then removed, and the specimens were cured in 20 �Cdistilled water. Holes were not drilled in the cylindricalcontainers used for the laboratory vane shear tests. Afterpouring, the samples for the laboratory vane shear testswere wrapped with polyethylene and cured in a room at20 �C. Nader and Chang (1993) discovered that the curingmethod, whether the specimen was soaked or unsoaked,did not affect the strength development of the cement-


treated soil in the shorter curing times of up to seven days.The laboratory vane shear tests were conducted at shortercuring times (0.5, 2, 5, 7, 10, and 15 h); therefore, the curingmethod in the room was chosen for the samples of the lab-oratory vane shear tests. In addition, the laboratory vaneshear tests were conducted using different specimens foreach curing time. The curing was started 30 min after themixing process.

3.3. Method and cases of strength tests

The samples that were cured in the room or in water at20 �C were tested at the designated curing times of 0.5, 2, 5,7, 10, and 15 h and 1, 2, 3, 7, 28, and 90 days. The labora-tory vane shear tests were performed for the shorter curingtimes of 0.5, 2, 5, and 7 h because the specimens were extre-mely soft and could not stand on their own, whereas theunconfined compression tests were performed for thelonger curing times of 15 h and 1, 2, 3, 7, 28, and 90 days.

Table 5Experiment cases.

Case Initial water content c* (%)

1 1.5wL (%) 102 103 104 105 206 207 208 209 3010 3011 3012 3013 4514 60

15 0.9wL (%) 2016 2017 2018 20

19 1.0wL (%) 2020 2021 2022 20

23 1.25wL (%) 2024 2025 2026 20

27 2.0wL (%) 2028 2029 2030 20

31 2.5wL (%) 2032 2033 2034 20

Table 5 shows the experimental cases. Here, c* is thecement content of the dry mass of clay, silt, and sand, Sis the sand content, and cf* is the cement content of thedry mass of clay and silt. The equations for S and cf* areshown below:

S ¼ msand

mfine þ msand� 100 ð7Þ

cf � ¼ mcement

mfine þ mcement� 100 ð8Þ

As shown in Table 5, the c* values for Cases 8 and 13are 20% and 45%, respectively. Even though the c* valuesfor these cases are different, their cf* is almost the same(45%) owing to the different sand contents. The c* valuesfor Cases 12 and 14 are 30% and 60%, respectively, buttheir cf* is almost the same (60%) owing to the differentsand contents. These cases were deliberately prepared tofurther study the effect of sand in the strength developmentof cement-treated clay.

S (%) cf* (%) Curing time

0 10.0

0.5, 2, 5, 7, 10, 15 (hours)1, 2, 3, 7, 28, 90 (days)

30 13.750 18.270 27.00 20.030 26.350 33.370 45.50 30.030 38.050 46.270 58.80 45.00 60.0

0 20.0

1, 2, 3, 7, 28, 90 (days)

30 26.350 33.370 45.5

0 20.030 26.350 33.370 45.5

0 20.030 26.350 33.370 45.5

0 20.030 26.350 33.370 45.5

0 20.030 26.350 33.370 45.5

(a) cf* = 20%-45.5%

(b) cf* ≈ 45%

1

10

100

1,000

10,000

0 1 10 100 1,000 10,000

Str

ength

qu

(kP

a)

Curing time (hour)

c*20S0, cf*=20.0

c*20S30, cf*=26.3

c*20S50, cf*=33.3

c*20S70, cf*=45.5

Tokuyama Port Clay

cf* 20-45%

1

10

100

1,000

10,000

0 1 10 100 1,000 10,000

Str

ength

qu

(kP

a)

Curing time (hour)

c*20s70 c*45s0c*20S70, cf

*=45.5

c*45S0, cf*=45.0

Tokuyama Port Clay

cf* 45%

(c) cf*≈ 60%

(d) cf*=27%-33.3%

1

10

100

1,000

10,000

100,000

0 1 10 100 1,000 10,000

Str

ength

qu

(kP

a)

Curing time (hour)

c*30s70 c*60s0c*30S70, cf

*=58.8

c*60S0, cf*=60.0

Tokuyama Port Clay

cf* 60%

1

10

100

1,000

10,000

0 1 10 100 1,000 10,000

Str

ength

qu

(kP

a)

Curing time (hour)

c*10S70, cf*=27.0

c*30S0, cf*=30.0

c*20S50, cf*=33.3

Tokuyama Port Clay

cf* 27-33%

Fig. 1. Relationship between unconfined compressive strength qu and curing time.


4. Results

4.1. Treatment of sand content in strength calculation

Cases 8 and 13, and Cases 12 and 14, shown in Table 5exhibit the same cf* values of 45% and 60% (excluding thesand content), respectively, at the same initial water con-tent, despite different c* (including the sand content) andS values. Fig. 1(a) shows the relationship between theunconfined compressive strength and the curing time underthe same c*, but with different cf* and S. Fig. 1(b) and (c)show the relationship between the unconfined compressivestrength and the curing time with the same cf* values of45% and 60%, respectively, despite different c* and S.From Fig. 1(a), it is found that different levels of strengthdevelopment are exhibited when the c* values are the same,but the cf* and S values are different. From Fig. 1(b), it isfound that the specimens in Cases 8 and 13 exhibit thesame levels of strength development despite the differentratios of cement contents to the dry mass of clay, silt,and c*, and sand content S. The same trend is seen inFig. 1(c). Fig. 1(d) shows the relationship between theunconfined compressive strength and the curing time whenthe cf* values are from 27 to 33.3%. From Fig. 1(d), it isfound that the strength increases as the cf* value increases,regardless of the c* value. These results imply that the sandcontent does not affect the parameters of the strength esti-mation equation for cement-treated soil nor the concrete

aggregates, and that cement content c* and volumetricsolid ratio Y must be defined only by the fine-grained clayand the silt particles. The parameters for the mass of onlydry clay and silt, cf* and Yf*, should be used in Eq. (4).Furthermore, the modified equation using parameters cf*and Yf*, and the definition of the volumetric solid ratioexcluding the sand content, Yf*, are shown in Eqs. (9)and (10).

qu ¼ k�c c�f � c�f 0� �

Y �Nf ð9Þ

Y �f ¼

V fine þ V cement

V fine þ V cement þ V waterð10Þ

where kc* is a strength increment coefficient derivedfrom a set of soil mixture strength tests. The added cementratio, cf* (%), is the ratio of the mass of the cement to onlythe mass of dry clay and silt, cf0* (%) is the ratio of the min-imum mass of the cement to the mass of dry clay and siltrequired to increase the strength development, volumetricsolid ratio Yf*is the ratio of the volumes of clay, silt, andcement to the volume of the soil mixture excluding the sandcontent, and N is a coefficient related to the space gapstructure in treated soil that is specified in the dataregression.

However, Eq. (9) does not include a parameter for thecuring time. Therefore, a new formula, including a param-eter for the curing time, is proposed. By taking cf0* and N

as the average value for each curing time, the linear rela-

(a) Relationship between clay-water/cement ratio wc/Cand unconfined compressive strength qu b (S=0%, w0/wL=0.9-2.5)

(b) Comparison of measured strength and estimated strength by

(14) (w0/wL=0.9-2.5)

qu= 9890(wc/C)-1.48+b (b=0 at maximum R2)

R² = 0.88


R² = 0.92


R² = 0.92

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

0 5 10 15 20

q u -b

(kP

a)

wc/C

Tokuyama Port Clay sand mixture

7days

28days

90days

Sand content=0(%)

w0/wL=0.9, 1.0,1.25,1.5, 2.0, 2.5

Curing time=7, 28, 90days

100

1000

10000

100 1000 10000

Cal

cula

ted

qu

(kP

a)

Measured qu (kPa)

Tokuyama Port Clay sand mixture Sand content=0~70(%)

w0/wL=0.9,1.0,1.25,1.5,2.0,2.5

Curing time=7,28, 90days

Equation of

clay-water/cement ratio

Average of normalized

difference A.N.D =32.9%

w0=0.9wLw0=1.0wLw0=1.25wLw0=1.5wLw0=2.0wLw0=2.5wL

Eq.

Fig. 2. Analysis of Tokuyama Port clay using Eq. (1) (w0/wL = 0.9–2.5).

(a) Relationship between clay-water/cement ratio wc/C and unconfined compressive strength qu (S=0%, w0/wL=0.9-2.5)

(b) Relationship between curing time and

(q(wc/C)1,D/q(wc/C)0,28)/((wc/C)0,28/(wc/C)1,D)B (w0/wL=0.9-2.5)

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

0 5 10 15 20

q u(k

Pa)

wc/C


7days

28days

90days

Sand content=0%w0/wL=0.9,1.0,1.25,1.5,2.0,2.5B in Eq.(2) = -1.43

qu= 8970(wc/C)-1.43

R² = 0.88

qu= 15800(wc/C)-1.43

R² = 0.92

qu= 20500(wc/C)-1.43

R² = 0.91

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

011 100

(q(w

c/C

) 1,D/q

(wc/

C) 0,

28)/

((w c

/C) 0

,28/

(wc/

C)1,

D)B

Curing time (day)


0.9

1

1.25

1.5

2

2.5

Sand content=0%w0/wL=0.9,1.0,1.25,1.5,2.0,2.5, B=-1.43

(q(wc/C)1,D/q(wc/C)0,28

)/((wc/C)0,28/(wc/C)1,D)B

= 0.273ln(D) + 0.107, R² = 0.74


(c) Comparison of measured strength and estimated strength by

Eq. (2) (w0/wL=0.9-2.5)

100

1,000

10,000

100,000

100 1,000 10,000 100,000

Cal

cula

te q

u(k

Pa)

Measured qu (kPa)


Sand content = 0~70%w0/wL=0.9,1.0,1.25,1.5,2.0,2.5

Curing time=7,28,90daysEq.(2) by Horpibulsuk et al.

Average of normalizeddefference=35.9%




tionship between kc* and the curing time can be obtained,as shown in Eq. (11). The new formula obtained by the lin-ear relationship (Eq. (11)) and Eq. (9) is shown below.

k�c¼E�þF �lnD ð11Þ

qu ¼ E�þF �lnDð Þ c�f � c�f 0� �

Y �f

� �Nð12Þ

where E*and F* are the experimental constants, and Dis the curing time. N is the average of the coefficientsrelated to the gap structure in treated soil that is specifiedin the data regression for each curing time.

4.2. Applicability of strength estimation equations

The difference between the measured and the calculatedstrengths, using each strength estimation equation, wascompared for the cement-treated soil with various sandand initial water contents. The difference between the mea-

sured and the calculated values, using the proposedstrength estimation equation, was evaluated using Eq. (13).

A:N:D¼ 1

n

Xn

i¼1

Ai-Bið Þ=Bij j; ð13Þ

where A.N.D is the average normalized difference, n isthe number of data values, Ai is the calculated strength,and Bi is the measured strength.

qu = 4990/1.334(wc/C)

R² = 0.67

qu = 8150/1.324(wc/C)

R² = 0.73

qu = 10400/1.316(wc/C)

R² = 0.78

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

0 5 10 15 20

q u(k

Pa)

wc/C


7day

28day

90day

Sand content=0~70%w0/wL=0.9,1.0,1.25,1.5,2.0,2.5Curing time=7, 28, 90 dayss/C=all data

Fig. 4. Relationship between clay-water/cement ratio wc/C and uncon-fined compressive strength qu (S = 0–70%, w0/wL = 0.9–2.5).

(a) s/C=2.3

(b) s/C=4.0

(c) s/C=9.0

qu = 4020ln(D)/y(wc/C)

R² = 0.68


R² = 0.54


R² = 0.54

0

5,000

10,000

15,000

20,000

0 1 2 3 4

q u(k

Pa)

ln(D)/y(wc/C)


7day

28day

90day

Sand content=0~70%

w0/wL=0.9,1.0,1.25,1.5,2.0,2.5


s/C=2.3, y=1.325


R² = 0.68


R² = 0.68


R² = 0.83

0

5,000

10,000

15,000

0 1 2 3 4

q u(k

Pa)

ln(D)/y(wc/C)


7day28day90day

Sand content=0~70%

w0/wL=0.9,1.0,1.25,1.5,2.0,2.5


s/C=4.0, y=1.325


R² = -0.50


R² = 0.03


R² = 0.09

0

500

1,000

1,500

2,000

2,500

0 0.5 1 1.5

q u(k

Pa)

ln(D)/y(wc/C)


7day28day90day

Sand content=0~70%

w0/wL=0.9,1.0,1.25,1.5,2.0,2.5


s/C=9.0, y=1.325

Fig. 5. Relationship between unconfined compressive strength qu and ln(D)/y(wc/C) (s/C = 2.3–9.0, w0/wL = 0.9–2.5).

x = -247(s/C) + 4380R² = 0.82

0

1,000

2,000

3,000

4,000

5,000

0 2 4 6 8 10

x

s/C


Sand content=0~70%w0/wL=0.9,1.0,1.25,1.5,2.0,2.5Curing time=7,28,90dayss/C=2.3, 4.0, 9.0, y=1.325

Fig. 6. Relationship between parameter x of Eq. (3) and soil cement ratios/C (w0/wL = 0.9–2.5).

10

100

1,000

10,000

10 100 1,000 10,000

Cal

cula

ted

qu

(kP

a)

Measured qu (kPa)

Tokuyama Port Clay sand mixtureSand content=0~70%w0/wL=0.9,1.0,1.25,1.5,2.0,2.5Curing time=7, 28, 90days

Eq.(3) using Abrams' law

and soil-cement ratio

Average of normalizeddifference A.N.D =75.1%


Fig. 7. Comparison of measured strength and estimated strength by Eq.(3) (w0/wL = 0.9–2.5).


4.3. Applicability of strength estimation equations with wide

ranges of clay initial water contents and various sand

contents

The applicability of the strength estimation equationswith initial water contents ranging from 0.9 to 2.5 timesthe liquid limit of each clay and sand mixture was analyzedthoroughly.

As for Eq. (1) (equation by clay-water/cement ratio),Fig. 2(a) shows the relationship between clay-water/cement ratio wc/C and unconfined compressive strengthqu–b at 7, 28, and 90 days of curing time with the datafor the sand content equal to 0%. Assuming that parame-ters a, b, and x were determined using the power regressionline of each curing time in Fig. 2(a), the parameter set atthe highest coefficient of determination was finally selected,as follows:

qu¼ 9890 wc=cð Þ�1:48 ð7 daysÞqu¼15500 wc=cð Þ�1:42 ð28 daysÞqu¼19000 wc=cð Þ�1:39 ð90 daysÞ

9>=>; ð14Þ

(a) Relationship between cf* and qu(Yf

*)-N

(S =0%, w0/wL=0.9-2.5)

(c) Relationship between cf* and qu(Yf

*)-N

(S =0%, w0/wL=0.9-2.5, N=2.7, cf0*=2.5)

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

0 10 20 30 40 50 60 70

q uY f

*-N

(k

Pa)

cf* (%)


0.9wL

1.0wL

1.25wL

1.5wL

2.0wL

2.5wL

Sand content=0(%)

w0/wL=0.9,1.0,1.25,1.5,2.0,2.5

Curing time=7,28,90days

7days, N=2.7

quYf*-N = 2780cf

*-17700

R² = 0.91


90days, N=2.5

quYf*-N = 3300cf

*

R² = 0.90

28days, N=2.9

quYf*-N = 4590cf

*

R² = 0.96

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

0 10 20 30 40 50 60 70

q uY f

*-N

(k

Pa)

cf* (%)


0.9wL1.0wL1.25wL1.5wL2.0wL2.5wL

Sand content=0(%)

w0/wL=0.9,1.0,1.25,1.5,2.0,2.5


N=2.7, cf0*=2.5

7days

quYf*-N = 2460(cf

*-2.5)

R² = 0.90


28days

quYf*-N = 3260(cf

*-2.5)

R² = 0.95

90days

quYf*-N = 4640(cf

*-2.5)

R² = 0.85

(d) Relationship between kc*

and curing time (Tokuyama Port clay)

(e) Comparison of measured strength and estimated strength by

Eq. (12) (Tokuyama Port clay)

kc* = 846ln(D) + 699

R² = 0.96

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

011 100

k c*

Curing time (day)

Tokuyama Port Clay sand mixtureSand content=0%

w0/wL=0.9,1.0,1.25,1.5,2.0,2.5

100

1,000

10,000

100 1,000 10,000

Cal

cula

ted q

u(k

Pa)

Measured qu (kPa)


0.9wL1.0wL1.25wL1.5wL2.0wL2.5wL

Sand content=0~70(%)

w0/wL=0.9,1.0,1.25,1.5,2.0,2.5


Equation of revised

volumetric solid ratio

E=699, F=846,

cf0*=2.5, N=2.7




(b) Relationship between cf* and qu(Yf

*)-N

(S =0%, w0/wL=0.9-2.5, N=2.7)

0

50,000

100,000

150,000

200,000

250,000

300,000

0 10 20 30 40 50 60 70

q uY f

*-N

(k

Pa)

cf* (%)


0.9wL1.0wL1.25wL1.5wL2.0wL2.5wL

Sand content=0(%)

w0/wL=0.9,1.0,1.25,1.5,2.0,2.5


N=2.7

7days

quYf*-N = 2800(cf

*-6.3)

R² = 0.91


28days

quYf*-N = 3640(cf

*-1.2)

R² = 0.96

90days

quYf*-N = 4300cf

*

R² = 0.87



6,000

8,000

10,000

12,000

14,000

16,000

q u(k

Pa)


7days

Sand content=0%w0/wL=1.0,1.25,1.5B in Eq.(2) = -1.20

qu= 7940(wc/C)-1.20

R² = 0.96

qu= 12900(wc/C)-1.20

R² = 0.98

qu= 16200(wc/C)-1.20

R² = 0.98

Table 6Parameters N, cf0*, kc*, E*, and F* of Tokuyama Port clay.

Type of clay Curing time N Average Nave cf0* Average cf0* kc* E* F*

TokuyamaPort clay

7 days 2.7 2.7 6.3 2.5 2460 699 84628 days 2.9 1.2 326090 days 2.5 0 4640


Fig. 2(b) shows a comparison of the measured and thecalculated strengths using Eq. (14), where the average nor-malized difference was 32.9%.

As for Eq. (2) by Horpibulsuk, the parameters for theequation were determined using the data for the sand con-tent equal to 0%. Parameter B in Eq. (2) is the same asparameter x in Eq. (1), but in Eq. (2), parameter B isassumed to be constant and independent of the curingtimes. From the average of �1.48, �1.42, and �1.39 inEq. (14), which is parameter x in Eq. (1) for 7-day, 28-day, and 90-day curing times, respectively, parameter B

in Eq. (2) was determined to be �1.43. The power regres-

(a) Relationship between clay-water/cement ratio wc/C and unconfined compressive strength qu–b (S=0%, w0/wL=1.0-1.5)

(b) Comparison of measured strength and estimated strength by

Eq.(16) (w0/wL=1.0-1.5)

qu= 8980(wc/C)-1.45+177

R² = 0.98


R² = 0.98


R² = 0.99

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

0 5 10 15 20

q u -b

(kP

a)

wc/C


7days

28days

90days

Sand content=0(%)

w0/wL=1.0,1.25,1.5


100

1000

10000

100 1000 10000

Cal

cula

ted

qu

(kP

a)

Measured qu (kPa)

Tokuyama Port Clay sand mixture Sand content=0~70(%)

w0/wL=1.0,1.25,1.5


Equation of




w0=1.0wLw0=1.25wLw0=1.5wL


sion line with B = �1.43 is shown in Fig. 3(a). The coeffi-cient of determination of the equation from the collecteddata was 0.88–0.92. Fig. 3(b) shows the relationship

(a) Relationship between clay-water/cement ratio wc/C and unconfined compressive strength qu (S=0, w0/wL=1.0-1.5)

(b) Relationship between curing time and (q(wc/C)1,D/q(wc/C)0,28)/((wc/C)0,28/(wc/C)1,D)B

(w0/wL=1.0-1.5)

0

2,000

4,000

0 5 10 15 20

wc/C

28days

90days

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

011 100

(q(w

c/C

) 1,D/q

(wc/

C) 0,

28)/

((w c

/C) 0

,28/

(wc/

C)1,

D)B

Curing time (day)


11.251.5

Sand content = 0%w0/wL=1.0,1.25,1.5, B=-1.20

(q(wc/C)1,D/q(wc/C)0,28

)/((wc/C)0,28/(wc/C)1,D)B

= 0.312ln(D) + 0.176, R² = 0.90

w0=1.0wLw0=1.25wLw0=1.5wL

(c) Comparison of measured strength and estimated strength by Eq. (2) (w0/wL=1.0-1.5)

100

1,000

10,000

100,000

100 1,000 10,000 100,000

Cal

cula

te q

u(k

Pa)

Measured qu (kPa)


Sand content = 0~70%w0/wL=1.0,1.25,1.5

Curing time=7,28,90daysEq.(2) by Horpibulsuk et al.

Average of normalizeddefference=13.3%

w0=1.0wLw0=1.25wLw0=1.5wL


(a) s/C=2.3


R² = 0.71


R² = 0.84


R² = -12.9

0

1,000

2,000

3,000

4,000

5,000

0 0.5 1 1.5 2 2.5 3

q u(k

Pa)

ln(D)/y(wc/C)

Tokuyama Port Clay sand mixrure

7day28day90day

Sand content=0~30%

w0/wL=1.5,2.0,2.5


s/C=2.3, y=1.277


R² = 0.64


R² = 0.74


R² = 0.78

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

q u(k

Pa)


7day28day90day

Sand content=0~30%

w0/wL=1.5,2.0,2.5


s/C=4.0, y=1.277


between the curing time and (q(wc/C)1,D/q(wc/C)0,28)/((wc/C)0,28/(wc/C)1,D)

B. In this study, the strength at 28 days,(wc/C)0,28 = 6.5, was taken as the reference strength,q(wc/C)0,28 in Eq. (2), and it is assumed that clay-watercement ratio wc/C remains unchanged during the curing.q(wc/C)1,D/q(wc/C)0,28 is the strength after D days of curingnormalized by q(wc/C)0,28.

Parameters E and F were determined from Fig. 3(b)using a regression line. From Fig. 3(a) and (b), parametersB, E, and F were obtained as 1.43, 0.107, and 0.273, respec-tively. Fig. 3(c) shows a comparison of the measured andthe calculated strengths using parameters B, E, and F, withthe data for the various sand contents. From Fig. 3(c), theaverage normalized difference was 35.9%.

As for Eq. (3), Chian et al. (2017) conducted experi-ments and analyses with sand contents from 0 to 40%.The parameters in Eq. (3) were determined in the sameway as Chian et al. determined theirs, namely, the sandwas treated as a part of the clay-sand mixtures. Fig. 4shows the relationship between clay-water/cement ratiowc/C and unconfined compressive strength qu at 7, 28,and 90 days of curing time, where the sand contents werein the range of 0 to 70%. From this figure, parameter y

in Eq. (3) was determined using a power regression line.Parameter x is different for each s/C, and it was obtainedfrom the relationship between ln(D)/ywc/C), calculated withparameter y (obtained previously) and qu in each s/C(Fig. 5). Subsequently, parameters a and b in Eq. (3) wereobtained from the relationship between s/C and x , shownin Fig. 6, with a high coefficient of determination, 0.82.From Figs. 4 and 6, parameters y, a, and b were determinedas 1.325, 4380, and �247, respectively. Consequently, fromFig. 7, the A.N.D. between the measured and the calculateddata using Eq. (3) was 75.1%.

As for Eq. (12), Fig. 8(a) shows the relationship betweencf* and qu(Yf*)

�N by the curing time with the data for thesand content equal to 0%. For each curing time, the valueof N was selected to maximize the coefficient of determina-tion R2. From Fig. 8(a), the average value of N = 2.7among the curing times of 7 days, 28 days, and 90 days,

qu = 3920/1.280(wc/C)

R² = 0.62

qu = 6483/1.275(wc/C)

R² = 0.72

qu = 8680/1.275(wc/C)

R² = 0.80

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

0 5 10 15 20

q u(k

Pa)

wc/C


7day

28day

90day

Sand content=0~30%w0/wL=1.5,2.0,2.5Curing time=7, 28, 90dayss/C=all data

Fig. 11. Relationship between clay-water/cement ratio wc/C and uncon-fined compressive strength qu (w0/wL = 1.5–2.5, Sand content = 0–30%).

was taken as the parameter in Eq. (12). Using N = 2.7,the relationship between cf* and qu(Yf*)

�N at the three cur-ing times with the data for the sand content equal to 0% isshown in Fig. 8(b). From this figure, the average cf0* value,determined by averaging the value of cf0* for each curingtime, cf0*=2.5, was obtained. Using N = 2.7 andcf0*=2.5, the relationship between cf* and qu(Yf*)

-N atthe three curing times with the data for the sand contentequal to 0% is shown in Fig. 8(c). From this figure, thekc* of each curing time was obtained. Fig. 8(d) shows therelationship between kc* and the curing time. From this fig-ure, parameters E* and F* were obtained as follows:

K�c¼ 699þ846lnD ð15ÞAll these parameters, N, cf0*, kc*, E*, and F*, are shown

in Table 6. Fig. 8(e) shows a comparison of the measuredand the calculated strengths using the parameters deter-mined with the data for various sand contents. From thisfigure, the average normalized difference was 22.1%.

(b) s/C=4.0

(c) s/C=9.0

0

0 0.5 1 1.5 2

ln(D)/y(wc/C)


R² = 0.63


R² = 0.56


R² = 0.88

0

200

400

600

800

1,000

1,200

1,400

0 0.1 0.2 0.3 0.4 0.5

q u(k

Pa)

ln(D)/y(wc/C)


7day28day90day

Sand content=0~30%

w0/wL=1.5,2.0,2.5


s/C=9.0, y=1.277

Fig. 12. Relationship between unconfined compressive strength qu and ln(D)/y(wc/C) (w0/wL = 1.5–2.5, Sand content = 0–30%).

Table 7Physical properties of dredged clays

Dredged clay Liquidlimit wL

Plasticlimit wP

Initial clay water content/Liquid limit w/wL

Yokohama Port 61.8% 29.8% 1.2–1.9Amagasaki Port 100.2% 32.0% 1.2–1.8Tokushima

KomatsushimaPort

35.5% 22.7% 1.5–2.5

2,000Yokohama Port Clay


From Figs. 2(b), 3(c), 7, and 8(e), it is found that thecorrelation between the calculated value from Eq. (12)and the measured value was the highest for the cement-treated soil using Japanese clay. When the parameters weredetermined using the data for sand contents of 0–70% inEqs. (1), (2), and (12), the average normalized differenceswere 31.5, 33.0, and 23.4%, respectively. From the results,it can be concluded that Eqs. (1), (2), and (3) did notdemonstrate good agreements between the measured andthe calculated strengths for the Tokuyama Port clay withvarious ranges of sand and water contents. Eq. (12) mostlytakes the same factors into account as Eq. (3), such as thecuring time, the soil structure, and the cement content.However, the A.N.D value between the measured strengthand the calculated strength in Eq. (12) was higher than thatin Eq. (3) for cement-treated soil using Tokuyama Portclay. The improvement was mainly because Eq. (12)focused only on the fine particle content of the cement-treated soil which is more adequate for clay with a highsand content. Eqs. (1), (2), and (3) can be utilized with cer-tain conditions for the soil, water, and cement contents.Therefore, in the next section, the applicability of Eqs.(1), (2), and (3) is further analyzed within the limited con-ditions associated with each equation.

10

100

1,000

10,000

10 100 1,000 10,000

Cal

cula

ted q

u(k

Pa)

Measured qu (kPa)


Sand content=0~30%w0/wL=1.5,2.0,2.5Curing time=7, 28, 90daysEq.(3) using Abrams' law

and soil-cement ratio



w0=1.5wL

w0=2.0wL

w0=2.5wL

Fig. 14. Comparison of measured strength and estimated strength by Eq.(3) (w0/wL = 1.5–2.5, Sand content = 0–30%).

x = 263(s/C) + 1060R² = 0.83

0

1,000

2,000

3,000

4,000

5,000

0 2 4 6 8 10

s/C


Sand content=0~30%w0/wL=1.5,2.0,2.5Curing time=7,28,90dayss/C=2.3, 4.0, 9.0

Fig. 13. Relationship between parameter x of Eq. (3) and soil cement ratios/C (w0/wL = 1.5–2.5, Sand content = 0–30%).

4.4. Applicability of Eqs. (1), (2), and (3) with a limited

range of clay initial water contents

The applicability of the strength estimation equationwas analyzed with a narrow range of initial water contents,namely, from 1.0 to 1.5 times the liquid limit. According toHorpibulsuk et al. (2011), Eq. (2) is effective for estimatingthe strength of cement-treated soil with a limited range ofinitial water contents; the liquidity index = 1–2. A liquidity

(a) Relationship between clay-water/cement ratio wc/Cand unconfined compressive strength qu–b (Yokohama Port clay)

(b) Comparison of measured strength and estimated strength by Eq.(17) (Yokohama Port clay)

qu = 158000(wc/C)-3.07+b(b=0 at maximum R2)

R² = 0.97


R² = 0.87

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

0 2 4 6 8 10

q u-b

(kP

a)

wc/C

7days

28days

w0/wL=1.2~1.9

Curing time=7, 28days

100

1,000

000,1001

Cal

cula

ted

qu

(kP

a)

Measured qu (kPa)

Yokohama Port Clay

1.2wL1.3wL1.6wL1.9wL

w0/wL=1.2~1.9

Curing time=7, 28,days

Equation using



difference X=9.7%

w0=1.2wLw0=1.3wLw0=1.6wLw0=1.9wL

Fig. 15. Analysis of Yokohama Port clay using Eq. (1).


index from 1 to 2 is approximately equal to an initial watercontent from 1.0 to 1.5 times the liquid limit. Using thislimited range of the data in the present study, the parame-ters in Eqs. (1), (2), and (3) were determined and a compar-ison of the measured and the calculated strengths wasmade. As for Eq. (1), Fig. 9(a) shows the relationshipbetween clay-water/cement ratio wc/C and unconfinedcompressive strength qu–b at 7, 28, and 90 days of curingtime with the data for the sand content equal to 0%. Theparameter set at the highest coefficient of determinationwas selected as follows:

qu ¼ 8980 wc=Cð Þ�1:45 þ 177 ð7 daysÞqu ¼ 12900 wc=Cð Þ�1:20 ð28 daysÞqu ¼ 15600 wc=Cð Þ�1:18 ð90 daysÞ

9>=>; ð16Þ

Fig. 9(b) shows a comparison of the measured and thecalculated strengths using Eq. (16) with the data for vari-ous sand contents. The average normalized difference was12.5%, which was much improved from the 32.9% shownin Fig. 2(b).

As for Eq. (2), Fig. 10(a) shows the relationship betweenthe clay-water/cement ratio and the unconfined compres-

(a) Relationship between clay-water/cement ratio wc/C and unconfined compressive strength qu–b (Amagasaki Port clay)

(b) Comparison of measured strength and estimated strength by Eq. (17)

(Amagasaki Port clay)


R² = 0.97


R² = 0.98

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 2 4 6 8 10 12

q u-b

(kP

a)

wc/C

Amagasaki Port Clay

7days

28days

w0/wL=1.2~1.8


100

1,000

000,1001

Cal

cula

ted q

u(k

Pa)

Measured qu (kPa)

Amagasaki Port Clay

1.2wL1.3wL1.4wL1.5wL1.6wL1.7wL1.8wL

w0/wL=1.2~1.8


Equation using



difference X=11.1%

w0=1.2wLw0=1.3wLw0=1.4wLw0=1.5wLw0=1.6wLw0=1.7wLw0=1.8wL

Fig. 16. Analysis of Amagasaki Port clay using Eq. (1).

sive strength at 7, 28, and 90 days of curing time with thedata for the sand content equal to 0%, where parameterB was determined to be �1.20. Fig. 10(b) shows the rela-tionship between the curing time and (q(wc/C)1,D/q(wc/C)0,28)/((wc/C)0,28/(wc/C)1,D)

B with the data for thesand content equal to 0%. The strength at 28 days, (wc/C)0,28 = 6.5, was taken as the standard as before. FromFig. 10(a) and (b), parameters B, E, and F were obtainedas 1.20, 0.176, and 0.312, respectively. Fig. 10(c) shows acomparison between the measured and the calculatedstrengths using the parameters determined with the datafor various sand contents. The average normalized differ-ence was 13.3%, which was much improved from the35.9% shown in Fig. 3(c).

The range of initial water contents used by Chian et al.(2016) was 1.38 to 2.50 times the liquid limit of the soil andthe range of sand contents was 0 to 40%. The applicabilityof Eq. (3) was examined with the data for initial water con-tents of 1.5wL, 2.0wL, and 2.5wL and sand contents of 0 to30%. Fig. 11 shows the relationship between the clay-water/cement ratio and the unconfined compressivestrength at 7, 28, and 90 days of curing time for the deter-mination of parameter y in Eq. (3). Fig. 12 shows the

(a) Relationship between clay-water/cement ratio wc/C and unconfined compressive strength qu–b (Tokushima Komatsushima Port clay)

(b) Comparison of measured strength and estimated strength by Eq. (17)

(Tokushima Komatsushima Port clay)

qu = 10100(wc/C)-1.90+31

R² = 0.85

qu = 11100(wc/C)-1.66+17

R² = 0.83

qu = 10700(wc/C)-1.53+36

R² = 0.82

0

200

400

600

800

1,000

1,200

1,400

1,600

0 5 10 15 20

q u-b

(kP

a)

wc/C

TK Port Clay

7days

14days

28days

w0/wL=1.5~2.5


100

1,000

000,1001

Cal

cula

ted

qu

(kP

a)

Measured qu (kPa)

TK Port Clay

1.5wL 1.6wL1.7wL 1.8wL1.9wL 2.0wL2.3wL 2.4wL2.5wL

w0/wL=1.5~2.5


Equation using



defference=21.3%

w0=1.5wLw0=1.7wLw0=1.9wLw0=2.3wLw0=2.5wL

w0=1.6wLw0=1.8wLw0=2.0wLw0=2.4wL

Fig. 17. Analysis of Tokushima Komatsushima Port clay using Eq. (1).


relationship between ln(D)/ywc/C) and qu for each s/C.Fig. 13 shows the relationship between parameter x ands/C. From Figs. 11, 12, and 13, parameters y, a, and b weredetermined as 1.277, 1060, and 263, respectively. Fig. 14shows a comparison of the measured and the calculatedstrengths using the determined parameters with the datafor various sand contents. The average normalizeddifference was 58.9%, which was a slight improvement


from the 75.1% shown in Fig. 7, but was still a largedifference.

From Fig. 9(b) and 10(c), it is seen that, when the initialwater content was in the limited range, the fitness betweenthe measured and the calculated strengths in Eqs. (1) and(2) indicated good results even if the sand content varies.From Fig. 14, it is seen that, although the correlationwas improved in Eq. (3), it was much lower than that inEqs. (1) and (2). This is in agreement with the strength of

(a) Relationship between clay-water/cement ratio wc/C and unconfined compressive strength qu (Amagasaki Port clay)

(b) Relationship between curing time and

(q(wc/C)1,D/q(wc/C)0,28)/((wc/C)0,28/(wc/C)1,D)B(Amagasaki Port clay)

(c) Comparison of measured strength and estimated strength by Eq. (2) (Amagasaki Port clay)

qu = 74200(wc/C)-2.59

R² = 0.97

qu = 166000(wc/C)-2.75

R² = 0.98

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 2 4 6 8 10 12q u

(kP

a)

wc/C

Amagasaki Port Clay

7days

28days

w0/wL=1.2~1.8


(q(wc/C)1,D/q(wc/C)0,28

)/((wc/C)0,28/(wc/C)1,D)B

= 0.259ln(D) + 0.106

R² = 0.76

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

011 100

(q(w

c/C )

1,D/q

(wc/

C)0,

28)/

((w c

/C) 0

,28/

(wc/

C) 1

,D)B

Curing time (day)

Amagasaki Port Clay

w0/wL=1.2~1.8


100

1000

0001001

Cal

cula

ted

qu

(kP

a)

Measured qu (kPa)

Amagasaki Port Clay

1.2wL


1.7wL

1.8wL

w0/wL=1.2~1.8


Eq.(2) by Horpibulsuk et al.


difference X=11.5%

w0=1.2wLw0=1.3wLw0=1.4wLw0=1.5wLw0=1.6wLw0=1.7wLw0=1.8wL




cement-treated clay with sand contents reported by Chianet al. (2017). Chian et al. suggested replacing clay-waterto cement ratio wc/C in Eq. (3) with the free water tocement ratio to improve the assessment of the strength.

Table 8Parameters B, E, and F in Eq.(2) for 3 clays.

Type of clay B E (kN/m2) F (kN/m2/ln(days))

Yokohama Port 2.82 �0.129 0.263Amagasaki Port 2.67 0.106 0.259TK port 1.51 �0.190 0.344

5. Applicability of Eqs. (1), (2), and (12) using data for othermarine clays

Tsuchida and Tang (2015) showed the strength ofcement-treated clays for various marine clays with a negli-gible amount of sand particles (Yokohama Port clay, Ama-gasaki Port clay, and Tokushima Komatsushima Port clay(TK Port Clay)). For these three clays, as there was aninsufficient amount of data to determine the parametersin Eq. (3), the applicability of Eqs. (1), (2), and (12) wereinvestigated. The physical data for these clays are shown

in Table 7. As for Eq. (1), from Figs. 15(a), 16(a), and 17(a), parameters a, b, and x for each variety of clay wereselected as follows:

qu¼158000 wc=cð Þ�3:07 ð7 days; Yokohama Port clayÞ

qu¼122000 wc=cð Þ�2:58 ð28 days; Yokohama Port clayÞ

qu¼74200 wc=cð Þ�2:59 ð7 days; Amagasaki Port clayÞ

qu¼166000 wc=cð Þ�2:75 ð28 days; Amagasaki Port clayÞ

qu¼10100 wc=cð Þ-1:90þ31 ð7 days; Tokushima Komatsushima Port clayÞ



9>>>>>>>>>>>>>>>>>>>>>>>=>>>>>>>>>>>>>>>>>>>>>>>;

ð17Þ

Figs. 15(b), 16(b), and 17(b) show comparisons of themeasured and the calculated strengths using Eq. (17) foreach clay. As for Eq. (2), from Figs. 18(a), 19(a), and 20(a), parameter B was determined for each clay. FromFigs. 18(b), 19(b), and 20(b), parameters E and F weredetermined. The parameters, B, E, and F of Eq.(2), aresummarized in Table 8. Figs. 18(c), 19(c), and 20(c) showcomparisons of the measured and the calculated strengthsusing the determined parameters for clay. As for Eq.(12), from Fig. 21(a), (b), and (c), 22(a), (b), and (c), and23(a), (b), and (c), parameters N, cf0*, kc*, E*, and F* weredetermined as shown in Table 9. Figs. 21(d), 22(d), and 23(d) show the relationship between the measured and thecalculated strengths of each clay. The average normalizeddifferences between the various clays using Eqs. (1), (2),and (12) are shown in Table 10.

From Table 10, in the cases of clay with a narrow rangeof initial water contents (Yokohama Port clay and Ama-gasaki Port clay), the correlation between the measuredand the calculated strengths using Eq. (1) or (2) is seen tobe as high as when using Eq. (12). However, in the caseof clay with a wide range of initial water contents (Tokush-ima Komatsushima Port Clay), the correlation between themeasured and the calculated strengths using Eq. (1) or (2)is seen to be lower than when using Eq. (12). Consequently,when the initial water content is in a limited range, thestrength of cement-treated soil with a different type ofJapanese marine clay can be estimated by using Eqs. (1)and (2). When the clays have wide range of initial watercontents, Eq. (12) can estimate the strength of cement-treated soil more accurately.

Table 9Parameters N, cf0*, kc*, E*, and F* in Eq. (12) for 3 clays.

Type of clay Curing time N Average N cf0*(%) Average cf0*(%) kc* (kN/m2) E* (kN/m2) F*(kN/m2/ln(days))

YokohamaPort clay

7 days 2.4 2.3 4.5 4.3 2950 �722 189028 days 2.1 4.1 5560

AmagasakiPort clay

7 days 2.4 2.5 3.9 4.0 5300 364 254028 days 2.6 4.2 8820

TokushimaKomatsushimaPort clay

7 days 4.3 4.2 2.4 2.3 4510 �1350 308028 days 4.2 2.5 705090 days 4.0 1.9 8790

(a) Relationship between cf* and qu(Yf

*)-N

(Yokohama Port clay, N=2.3)

(b) Relationship between cf* and qu(Yf

*)-N

(Yokohama Port clay, N=2.3, cf0*=4.3)

0

5,000

10,000

15,000

20,000

25,000

30,000

0 1 2 3 4 5 6 7 8 9 10

q u(Y

f* )-N

(kP

a)

cf* (%)

Yokohama Port Clay


w0/wL=1.2~1.9

Curing time=7,28days

N=2.3

w0=1.2wLw0=1.3wLw0=1.6wLw0=1.9wL

7days

qu(Yf*)-N =3180(cf

*-4.5)

R2=0.99

28days

qu(Yf*)-N =5190(cf

*-4.1)

R2=0.84

0

5,000

10,000

15,000

20,000

25,000

30,000

0 1 2 3 4 5 6 7 8 9 10

q u(Y

f* )-N

(kP

a)

cf* (%)

Yokohama Port Clay


w0/wL=1.2~1.9


N=2.3, cf0*=4.3

w0=1.2wLw0=1.3wLw0=1.6wLw0=1.9wL

7days

qu(Yf*)-N =2950(cf

*-4.3)

R2=0.98

28days

qu(Yf*)-N =5560(cf

*-4.3)

R2=0.83

(c) Relationship between kc* and curing time

(Yokohama Port clay)

(d) Comparison of measured strength and estimated strength by

Eq. (12) (Yokohama Port clay)

kc*= 1890ln(D) - 722

0

1,000

2,000

3,000

4,000

5,000

6,000

011 100

k c*

Curing time (day)

Yokohama Port Clay

w0/wL=1.2~1.9


N=2.3

100

1,000

000,1001

Cal

cula

ted

qu

(kP

a)

Measured qu (kPa)

Yokohama Port Clay

1.2wL

1.3wL

1.6wL

1.9wL

w0/wL=1.2~1.9


Equation of revised

volumetric solid ratio

E*=-722, F*=1890,

cf0*=4.3, N=2.3


difference X=9.4%

w0=1.2wLw0=1.3wLw0=1.6wLw0=1.9wL





6. Conclusions

In this paper, a series of strength tests on cement-treatedmarine soil was performed with wide ranges of sand,cement, and initial water contents.

1 The role of the sand content on the strength of cement-treated soil was investigated. It was found that thestrength of cement-treated clay is primarily determinedby the ratio of the water and cement contents to thefine-grained soil and is not related to the sand particles.

2 A new strength estimation equation for cement-treatedclay was proposed for marine clay with wide ranges ofsand and initial water contents, as follows:

qu ¼ E� þ F �lnDð Þ c�f � c�f 0� �

Y �f

� �Nð18Þ

where the ratio of the cement content to the mass of thefine particles of the soil, cf* (%), and the volumetric solidratio excluding the sand particles, Yf *, are defined usingthe masses of the cement and the fine particles of the soil,

mcement and mfine, respectively, and the volumes of thecement, the fine particles of the soil, and the water, Vcement,Vfine, and Vwater, respectively, as follows:

cf � ¼ mcement

mfine þ mcement� 100 ð19Þ

Y �f ¼

V fine þ V cement

V fine þ V cement þ V waterð20Þ

D is the curing time. The minimum cement content cf0*,the void parameter, N, strength increment parameters E*and F*are determined by mixing proportion tests.

3 The applicability of the proposed equation was com-pared to that of the three existing strength estimationequations, namely, the equation by the clay water-cement ratio (Japan Cement Association, 2007), theequation by Horpibulsuk et al. (2003, 2011), and theequation by Chian et al. (2016). In the comparison,the parameters for the equations were determined usingthe soil data with no sand content (S = 0%), and thestrengths of cement-treated soils with different sand


Table 10Average normalized difference of various clays using Eqs. (1), (2), and (12).

Type of clay w0/wL Eq. (1) Eq. (2) Eq. (12)

Tokuyama Port clay 0.9–2.5 32.9% 35.9% 22.1%1.0–1.5 12.5% 13.3% –

Yokohama Port clay 1.2–1.9 9.7% 10.3% 9.4%Amagasaki Port clay 1.2–1.8 11.1% 11.5% 9.6%Tokushima Komatsushima Port clay 1.5–2.5 21.3% 23.0% 9.9%


contents (S = 0–70%) were compared. The proposedequation has demonstrated the best fitness between themeasured and the estimated strengths of marine clayswith the wide range of initial water and sand contents.

4 The proposed equation was found to be applicable tocement-treated soil with wide ranges of sand (0–70%)and initial water contents (0.9–2.5wL). However, thisconclusion was made under the limitation of the typeof clay used in this study (Japanese dredged marine soil).

Further study on the applicability of the equation tocement-treated soil in different regions is necessary.

Acknowledgments

This work was financially supported by the ScientificResearch Fund of the Ministry of Education, Culture,Sports, Science, and Technology Research (No. 25289146).


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