Prediction of the resilient modulus of two tropical subgrade soils considering unsaturated conditions

Journal Pre-proof Prediction of the resilient modulus of two tropical subgrade soils considering unsaturated conditions

Jeferson Barbosa de Freitas, Lilian Ribeiro de Rezende, Gilson de F.N. Gitirana PII:

S0013-7952(19)31006-3

DOI:

https://doi.org/10.1016/j.enggeo.2020.105580

Reference:

ENGEO 105580

To appear in:

Engineering Geology

Received date:

27 May 2019

Revised date:

30 September 2019

Accepted date:

5 March 2020

Please cite this article as: J.B. de Freitas, L.R. de Rezende and G.d.F.N. Gitirana, Prediction of the resilient modulus of two tropical subgrade soils considering unsaturated conditions, Engineering Geology (2020), https://doi.org/10.1016/j.enggeo.2020.105580

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© 2020 Published by Elsevier.

Journal Pre-proof

Prediction of the resilient modulus of two tropical subgrade soils considering unsaturated conditions Jeferson Barbosa de Freitasa, Lilian Ribeiro de Rezendea* & Gilson de F. N. Gitirana Jr.a a

School of Civil and Environmental Engineering, Federal University of Goias, Goiania, GO, Brazil.

*Corresponding author

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E-mail adresses: [email protected] (J. B. Freitas), [email protected] (L. R. Rezende), [email protected] (G. F. N. Gitirana Jr.)

ABSTRACT

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The resilient modulus (MR) is essential for the understanding of pavement response to climate effects, and to seasonal fluctuations of water content and matric suction. Unfortunately, only few studies have been directed towards the unsaturated resilient behavior of tropical soils and the influence of weathering and degree of laterization. This paper presents a study of the unsaturated resilient behavior of two tropical soils with distinct degrees of laterization, used as subgrades of highways in Brazil. The experimental program involved the measurement of the soil-water characteristic curve (SWCC), and the MR at different water contents and matric suctions. Eight models for MR, taken from the literature, were evaluated, and a new family of equations is proposed. The obtained SWCCs of the lateritic soil presented bimodal behavior, while the non-lateritic soil is unimodal. The bimodal behavior was attributed to clay aggregates produced by the laterization process. The observed relationship between MR and the stress-state variables depended on the degree of laterization. The lateritic subgrade soil showed significantly higher values of MR, but the resilient behavior was more sensitive to the water content when compared to the non-lateritic soil. The analysis of the literature models for MR indicated limitations in the manner how the unsaturated behavior was incorporated, producing adjusted coefficients of determination (Adj. R2) between 0.48 and 0.77. The newly proposed MR model was based on the statistical analyses of seven equations. The final proposed model includes two independent stress-state variable and a third state variable, that accounts for the water content deviation from optimum conditions. Finally, the proposed model was validated using MR data from the literature. The proposed model produced superior results when comparing to the previously proposed equations, resulting in values of Adj. R² varying between 0.93 and 0.99. The newly proposed model proved to be flexible, being capable of modeling both the lateritic and non-lateritic soils in an accurate manner. These results are expected to offer significant improvements to the Brazilian mechanistic-empirical pavement design guide, and for similar guides in other countries where tropical soils are found.

Keywords: Pavement design; Resilient modulus; Matric suction; Unsaturated Soils; Tropical soils.

1 Introduction

Journal Pre-proof The pavement base, subbase, and subgrade materials are generally compacted in unsaturated conditions that correspond to their optimum water content. However, seasonal fluctuations of degree of saturation are expected during the pavement service life. The occurrence of excessive moisture produces undesirable reduction in the structural capacity, and affects the onset of pavement degradation (Croney, 1952; Mahalinga-iyer and William, 1995; Saevarsdottir and Erlingsson, 2013; Yan et al., 2018, Mustaque et al., 2019). The soil resilient modulus (MR) is an essential property for the understanding of pavement behavior (Hveem, 1955; Hicks and Monismith, 1971). The resilient behavior is

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directly related to fatigue cracking and permanent deformation, which are the two main

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criteria for pavement design (Seed et al., 1962; Brown, 1996;). The soil resilient behavior is affected by soil density, fines content, maximum aggregate diameter, and particle shape

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(George, 2004). The stress state, stress state history, and water content also play significant

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roles. A decrease of the MR is observed with the decrease in confining stresses, most notably under high degrees of saturation (Lekarp et al., 2000). Because of the complex relationship

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between MR, material type, stress state, stress state history, and water content, the assessment of the expected changes of MR, under traffic and weather conditions, becomes necessary

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within the framework of modern mechanistic design approaches. Fredlund et al. (1977), in a pioneering work, sought the development of a theory that

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univocally correlates the stress state variables with the MR, considering unsaturated conditions. The authors have shown, through stress analysis, that MR is a function of three

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independent stress state variables, namely the net confining pressure,  3  ua  ; the matric suction,  m   ua  uw  ; and the deviator stress,  1   3  . Since then, numerous models have been proposed to represent the effect of the unsaturated state on MR. For example, the mechanistic-empirical pavement design guide (MEPDG), presented by ARA Inc. (2004), recommended an analysis of MR subgrade soil behavior considering the variation of degree of saturation under different seasonal conditions. The matric suction was shown to be a key parameter to predict and interpret the mechanical behavior of unsaturated soils submitted to moisture variation (Han and Vanapalli, 2016a). Several authors have observed substantial decrease in the value of MR with the increase in water content (Edil and Motan., 1979; Ksaibati et al., 2000; Khoury and

Journal Pre-proof Zaman, 2004; Ekblad and Isacsson, 2006; Liang et al., 2007; Gupta et al., 2007; Kim and Kim, 2007; Yang et al., 2008; Thom et al., 2008; Khoury et al., 2009; Khoury et al., 2009b; Khoury et al., 2011; Ng et al., 2013; Sivakumar et al., 2013; Han and Vanapalli, 2015; Han and Vanapalli, 2016b; El-Ashwah et al., 2019). Despite the numerous studies regarding the effect of unsaturated conditions on the MR, the resilient behavior of tropical soils has received limited attention. The tropical soils are predominant in many regions and countries, such as Brazil, India, Indonesia, Indo-china, Australia, and Central Africa. These materials have specific characteristics and behavior that

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differ from those of the soils in temperate climates. The geotechnical properties of tropical

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soils depend on factors, such as weathering conditions, parent rock, and degree of laterisation, varying sigficantly between and even within the same region and country

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(Winterkorn and Chandrasekharan, 1951; Gidigasu, 1972; Mahalinga-Iyer and Williams,

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1991; Mahalinga-Iyer and Williams, 1997; Sunil and Krishnappa, 2012). The use of tropical soils in paving has gained significant momentum since the 1970s (Medina and Motta, 1988;

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Nogami and Villibor, 1991; Mahalinga-Iyer and Williams, 1994; Camapum de Carvalho et al., 2015). Some of the few recent studies that present the analysis of the influence of

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unsaturated conditions on the MR of tropical soils are Motta (1991), Parreira and Gonçalves (2000), Ceratti et al. (2004), Pérez-García et al. (2015), and Kumar and George (2018).

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Studies in tropical regions of Brazil indicate that pavements with efficient drainage systems reach a state of water content equilibrium with the surrounding environment a few

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months after construction. The range of equilibrium water contents under these conditions is typically below the optimum condition (Souza et al., 1977; Ricci et al., 1983; Medina and Motta, 1988; Nogami and Villibor, 1995; Bernucci, 1995; Núñez, 1997; Gonçalves, 1999; Camacho, 2002; Takeda, 2006; Silva, 2009). Therefore, it is generally believed that the moisture content conditions of pavements in tropical regions of Brazil are more favorable than in cold or temperate climates subjected to freeze-thaw cycles. Unfortunately, recurrent cost savings in construction often lead to unsatisfactory drainage conditions, resulting in increased degrees of saturation and often in pavement failure (Jayakumar and Soon, 2015). For these reasons, the consideration of higher water content ranges benefits the analysis of pavement behavior.

Journal Pre-proof This paper presents a study of the influence of moisture and matric suction conditions on the resilient behavior of two tropical soils, used as subgrades of highways, in the Midwest region of Brazil. Two materials with significantly different degrees of laterization were investigated, so that a wide range of typical regional subgrade behavior is evaluated. This paper also evaluates the use of numerous existing models for the effect of unsaturated conditions on MR, and proposes new models for both lateritic and non-lateritic tropical soils, to be used in a mechanistic pavement design method in tropical regions.

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2 Materials and Methods

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2.1 Subgrade Materials

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Two tropical subgrade soils are considered herein. These materials correspond to two test tracks located in the GO 070 highway, state of Goias, Brazil. Table 1 shows the basic

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properties and the classification of these materials.

Lateritic soil: Subgrade 1 (SUB1)

Particle size

without dispersant

with dispersant

without dispersant

with dispersant

Gravel (%)

4.1

4.1

8.9

8.9

Sand (%)

57.8

60.9

69.9

60.4

38.0

8.8

21.2

30.7

0.0

26.2

0.0

0.0

Index properties Specific gravity

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Clay (%)

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Silt (%)

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Properties

Non-lateritic soil: Subgrade 2 (SUB2)

2.700

2.660

34

not determined

Plastic limit (%)

18

not determined

Plasticity index (%)

16

non-plastic

TRB

CL

SM

USCS

A6

A4

MCT

LG'

NS'

Classification

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Liquid limit (%)

Compaction and CBR (standard Proctor energy) wopt (%)

17.5

13.4

d max (g/cm³)

1.720

1.800

18

5

CBR (%)

Swelling (%) 0.08 2.30 Notation: TRB = Transportation Research Board, USCS = Unified Soil Classification System, MCT = Tropical Soil Classification, LG’ = clayey lateritic, NS’ = non-lateritic sandy silt, wopt = optimum water content, d max = maximum dry density, CBR = California Bearing Ratio.

Journal Pre-proof Table 1. Basic properties for the subgrade soils.

The property values presented in Table 1 are commonly observed for Brazilian tropical soils (Camapum de Carvalho et al., 2015). Soil SUB1 is lateritic, while soil SUB2 is non-lateritic. The distinction between the two subgrade soils, in terms of laterization process, may impact its resilient behavior. One of the main differences between lateritic and non-lateritic soils is the stability of clay aggregates when the water content changes. The lateritic soil (SUB1) presents a greater percentage of clay particles if an adequate chemical

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dispersant is used during the specimen preparation. The presence of clay aggregates, that are stable when wetted, is typical of fine-grained lateritic soils. The lateritic soils also have

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particles with greater specific surfaces and can store more water, which leads to a higher

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optimum water content, wopt. For the same compaction energy, the lateritic soil presents California Bearing Ratio (CBR) values higher than those of non-lateritic subgrades. Finally,

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swelling characteristics are also significantly affected by the degree of laterization. The non-lateritic soils, such as SUB2, are generally expansive and this characteristic is related to

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the predominant presence of primary clay minerals, that were not subjected to significant

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weathering. 2.2 Methods

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The resilient behavior of subgrade materials was analyzed considering moisture variations above and below the optimum water content. All specimens were compacted at

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wopt and maximum specific dry mass, d max, and later subjected to water content changes. The details of the extensive experimental program and modeling exercises will be discussed in the next sections.

2.2.1 Soil-Water Characteristic Curve Testing and Modeling The MR of the subgrade materials and their behavior under varying unsaturated conditions have been analyzed considering the water content, the degree of saturation, and matric suction. The matric suction values are particularly important, because most empirical models, proposed for the study of moisture influence on the resilient behavior of subgrades, considered this stress state variable (Ceratti et al., 2004; Parreira and Gonçalves, 2000; Khoury et al., 2009a; Han and Vanapalli, 2015a).

Journal Pre-proof The soil-water characteristic curve (SWCC) was determined by using the filter paper technique, as described by Marinho and Oliveira (2006). The specimens were molded using static compaction at wopt, inside polymerizing vinyl chloride (PVC) rings, with internal diameters of 39.92  0.08 mm and heights of 9.95  0.19 mm. The wetting curve was measured by taking 15 specimens of each subgrade material and air-drying for 7 days before wetting. After wetting to the desired degrees of saturation, the soil-filter paper set was packed in foil paper, followed by aluminum paper, and inserted in a sealed container during the sample’s equilibration period (15 days). The filter paper was placed in contact with the

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specimens, so that only the matric suctions were measured. The Whatman No. 42 filter paper, and the corresponding calibration curve proposed by Chandler et al. (1992) were

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used.

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The curve fitting was accomplished using the models of Gitirana Jr. and Fredlund

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(2004). Equation (1) and Equation (2) were used for unimodal and bimodal curves, respectively. Equation (3), proposed by Fredlund and Xing (1994), was also considered.  S2

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S1  S2

S=

  

d

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  1     b res  where

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 a  tan i 1  ri  ln   i  i  Si =   1 2 2 1  ri tan i 



1  tan  

1  r

i

where,

i=1,2;

ri = tan  i 1  i  / 2 =



2

2

i

tan i  2

(1)

2

2 2   a  a 1  ri tan 2i  ri ln   Sia  2  1  t an    i  i 2

i =   i 1  i  / 2 = aperture

angles

hyperbolas tangents;

rotation

0 = 0

angles; ;



i = arc tan  Sia  Sia1  / ln  ia1 /  ia  = desaturation slopes; S1a = 1; S2a = Sres ; S3a = 0 ;  1a =  b ;  2a =  res ;  3a = 106 and d = 2 exp 1/ ln  res /  b  = weight factor for S 1 and S 2. .

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S=

S1  S2 d1

   1      b1 res1   S3  S 4    1     b3 res 3 



  

S 2  S3   1     b2 res 2 

d3

  

d2

(2)

 S4

where S i ,  i , r i , and i were defined in Equation (1); i=1,2,3,4; S1a = 1 ;



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S2a = Sres1 ; S3a = Sb ; S4a = Sres 2 ; S5a = 0 ;  1a =  b1 ;  2a =  res1 ;  3a =  b 2 ;  4a =  res 2 ;



1



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

n ln e   / a    

m

(3)

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S=

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a a  5a = 106 ; d j = 2 exp 1/ ln  j  1/  j  = weight factors. J=1 ,2, 3.

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where a = parameter related to the inflection point; n = controls the slope of the desaturation zone; m = affects the asymmetry of the curve above the inflection point.

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2.2.2 Resilient Behavior Analyzes

The influence of the water content on the resilient behavior was evaluated according

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to the methodology proposed by Pérez-García et al. (2015), allowing the use of a reduced

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number of samples. The specimens were compacted at optimum conditions, and following the procedures presented by the Brazilian standard (DNIT, 2013). The specimens were later subjected to moisture changes above and below the optimum water content, in a range of -5% to + 2%. Some specimens were air-dried towards various target water contents. Drying was undertaken in a slow manner to avoid cracking (Pérez-García et al., 2015). Other specimens were wetted by the capillary rise. The various target water contents were obtained by monitoring the specimen weight. Drying and wetting was imposed by offering or removing moisture from the specimen surface. To produce homogeneous conditions, specimens were protected using plastic film and aluminum foil, placed in hermetically sealed containers, and stored for 15 days for equilibrium. The dynamic triaxial tests were performed using a Servo-Hydraulic Universal

Journal Pre-proof Testing Machine UTM, with 30 kN of loading capacity. The adopted testing procedures are presented by the Brazilian standard (DNIT, 2018), in which a conditioning step is applied with three sequences of 500 cycles over a frequency of 1 Hz to eliminate the permanent deformations, that may occur in the first deviator stress deviation. The test itself is carried out with the application of 18 pairs of stresses with 10 cycles each, varying the confining stress between 0.020 and 0.140 MPa, and the deviator stress between 0.020 and 0.420 MPa. The correlation between the state variables and the resilient modulus was evaluated using the Pearson correlation coefficient, which provides a measurement of the direction and

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intensity, by which the variables and MR are linearly associated. In addition, the Spearman

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post correlation, which can be used for non-linear data, was also computed.

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2.2.3 Evaluation of Literature Models

Table 2. Reference

Variables

MR1

HICKS (1970)

b

MR2

HICKS (1970)

3

MR3

SVENSON (1980)

d

MR4

MACÊDO (1996)

Equation

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ID

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The experimental results were modeled considering the eight equations presented in

3 ; d

M R = k1b

k2

(4)

M R = k1 3 2

(5)

M R = k1 d

(6)

k

k2

M R = k1 3 2 d k

k3

(7) k

 b  2   oct  M R = k1 pa     1  pa   pa 

(8) (9)

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 b ;  oct

ARA-ERES (2004)

MR6

PARREIRA and GONÇALVES (2000)

d ; m

M R = k1 d 2 m 3

MR7

KHOURY et al. (2009a)

 b ;  oct ; m

  2   3  M R = k1 pa  b   k4  oct   1 m 1 (10) pa   pa  

MR8

PEREZ-GARCIA et al. (2015)

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MR5

3 ; d ; w

k

k

k

MR = e

k1  k2 ( w wopt )

k

k

 d  3    3 

(11)

Notation: ID = identification, b = bulk stress, 3 = confining stress, d = deviator stress, oct = octahedral shear stress, m = matric suction, w-wop t = deviation from the optimum water content. Table 2. Resilient modulus models from the literature.

The MR1 to MR5 models take into consideration some basic aspects of resilient behavior that are associated with soil type, but do not consider the effect of changes in water content and matric suction. For example, the MR1 and MR2 equations account for the

Journal Pre-proof resilient properties of untreated granular materials that are mainly affected by bulk or confining stresses. The MR3 model considers soils with resilient behavior primarily governed by the deviator stresses, which is often the case of clayey materials. The MR4 model incorporates both previous behavior aspects, being applicable to both granular and fine-grained soils, and officially adopted in Brazil by the National Department of Transportation Infrastructure (DNIT). It is also important to emphasize that superior performance should be expected if the previous models are employed to represent the soil under constant water contents. This fact is recognized by the Mechanistic-Empirical

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Pavement Design Guide (MEPDG), which applies the MR5 equation to the resilient behavior under optimum water content, but extends the formulation using an additional

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equation to account for the effect of water content changes (ARA-ERES, 2004).

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Since Fredlund et al. (1977), new equations have incorporated the effect of the water

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content and matric suction into the modeling of the resilient modulus. The MR6 equation was developed based on the measured effect of suction on the behavior of a lateritic soil

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from a highway subgrade in Brazil. It was found that higher suctions produced higher resilient moduli regardless of the deviator stress value. The MR7 model considered the

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influence of matric suction on the resilient modulus of subgrade materials from Oklahoma, USA. This model correlated MR with bulk stress, octahedral stress, and matric suction.

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Finally, the MR8 model was based on the behavior of sands and fine-grained soils from Mexico and introduces the water content in the MR equation. While the usefulness of models

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MR1 to MR5 has been proven in the past, particularly when used in pavements with low water content fluctuations, the introduction of water content and matric suction variables in the modeling of the resilient modulus represents important advances to the design of pavements under more general conditions. The validity of models such as MR1 to MR5 under constant water contents conditions is not disputed herein. Their use under variable water contents in the next sections serves the purpose of demonstrating that such equations should not be extended beyond their capabilities and intended purposes. Some models could not be considered in this study, because of the unavailability of required input parameters. Among them, Ng et al. (2013) equation involves the MR values at a reference stress state, and Han and Vanapalli (2015b) model requires MR values in the saturated condition.

Journal Pre-proof Statistical analyses were carried out to consolidate results, and provide an unbiased comparison between the models. The Adjusted coefficient of determination (Adj. R2) was used, because it compensates for the number of predictors used in the equations. The Akaike information criterion (AIC) was also employed, because it estimates the comparative quality of each model and shows the relative amount of information lost by a given equation. Finally, the Schwarz Bayesian criterion (BIC) was also considered, because it is widely used for model selection among a finite set. Both the AIC and BIC criteria introduce penalty

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terms to consider the number of parameters. 2.4 Validation of New Models

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New equations for MR are proposed and evaluated herein. These new equations were

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developed taking into consideration the characteristics and performances of the existing models shown in Table 2. The new models will be verified using the results of the

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experimental program described in section 2.2. Further details of the proposed equations will

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be discussed in section 3.4.

Regression analyses were carried out to define the best fit parameters. The proposed

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models were statistically compared using the same criteria described in the previous section. The proposed models were evaluated considering the MR behavior of the tropical soils

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presented herein, and of soils from previously published studies by Han and Vanapalli (2016b) and Rahman and Tarefder (2015). Table 3 shows a summary of the physical

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properties of the materials collected from the literature. These materials are not tropical soils, and were selected to allow the evaluation of the proposed equations for a wider range of material types.

It is important to highlight some aspects of these studies. Han and Vanapalli (2016b) studied the unsaturated resilient behavior of four Canadian soils: a silty clay from Toronto (TSC), a lean clay from Kincardine (KLC), a glacial till from Indian Head (IHT), and a marine clay from Ottawa (OLC). For the TSC, KLC, and OLC soils, the matric suction changes were imposed by moisture changes after compaction, and for the IHT material, its water content and matric suction were imposed employing the axis translation technique. Han and Vanapalli (2016b) verified the application of the equation proposed by Han and Vanapalli (2015b), and found that the proposed method results in optimal predictions and

Journal Pre-proof requires less experimental data. Han and Vanapalli (2016b) KLC IHT

Properties TSC

OLC

Rahman and Tarefder (2015) NM (CL) NM (CH)

Gravel (%)

0.0

0.0

0.0

0.0

0.0

5.0

Sand (%)

3.0

15.0

28.0

20.0

50.4

25.8

Silt (%)

81.0

60.0

42.0

48.0

49.6

60.2

Clay (%)

16.0

25.0

30.0

32.0

Nd

nd

Specific gravity

2.680

2.710

2.720

2.750

Nd

nd

Liquid limit (%)

19

31

35

48

29

69

10

19

26

13

42

13.5

20.3

15.5

23.0

15.1

14.7

d max (g/cm3)

1.915

1.631

1.846

1.616

1.970

2.040

CL-ML

CL

CL

CL

CL

CH

USCS

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6

wopt (%)

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Plasticity index (%)

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TRB A-4 A-4 A-6 A-6 A-6 A-7-6 Notation: nd = not determined, wopt = optimum water content, d max = maximum dry density, USCS = Unified Soil Classification System, TRB = Transportation Research Board.

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Table 3. Summary of the physical properties from Rahman and Tarefder (2015) and Han and Vanapalli (2016b).

Rahman and Tarefder (2015) studied the unsaturated resilient behavior of two subgrade soils of the US 491 highway in New Mexico (NM), treated with lime stabilization.

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For both studies, the MR test was conducted according to the 15 loading sequences outlined in T 307 (AASHTO, 2003). The wetting process was carried out by dipping samples in a

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water tank. Rahman and Tarefder (2015) found that the resilient modulus reduced

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considerably when the water content increased, and attributed that reduction to the high moisture sensitivity of clayey soils. The authors also found that relatively high deviator stresses produced a softening effect and a decrease in the resilient modulus.

3 Results and Discussion 3.1 Specimen Compaction and Soil-Water Characteristic Curve Table 4 shows the after-compaction volume-mass parameters, their dispersion, and deviation with respect to the target values, considering fifteen specimens for each soil. The conformity to specified compaction conditions and repeatability of specimen preparation was considered satisfactory. Figure 1 presents the SWCCs obtained using the filter paper

Journal Pre-proof technique and the corresponding best-fit curves, and the parameters using the Gitirana Jr. and Fredlund (2004) and Fredlund and Xing (1994) models. Properties

Lateritic soil (SUB1)

Non-lateritic soil (SUB2)

Target

Mean

CV (%)

Target

Mean

CV (%)

w (%)

17.5

16.9

1.10

13.4

12.8

1.57

d (g/cm³)

1.720

1.700

0.13

1.800

1.770

0.12

e (-)

0.570

0.585

0.35

0.500

0.523

0.35

S (%)

82.9

78.0

1.24

72.1

58.9

1.60

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Notation: w = water content, d = dry density, CV = coefficient of variation, e = void ratio, S= degree of saturation. Table 4. Summary of compaction parameters for filter paper test specimens.

Figure 1. SWCC and best-fit curves using: (a) Gitirana Jr. and Fredlund (2004) model and (b) Fredlund and Xing (1994).

Journal Pre-proof There are several factors that affect the shape of the SWCC, such as soil type, grain-size distribution, fabric, void ratio, and initial state. The SWCC obtained for the lateritic soil (SUB1) presented a significantly different shape, when compared to the curve obtained for the ono-lateritic soil; the first has a bimodal behavior and the latter is unimodal. These differences may be attributed mainly to the type of soil and its genesis. The lateritic soils from this region often present macropores and micropores with two distinct air-entry values. The soil SUB2 has a slightly higher air-entry values than SUB1. However, the slope of the SWCC for the two soils was similar.

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The best-fit SWCCs obtained for both soils will be required for the modeling of MR,

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requiring adequate fits. The Fredlund and Xing (1994) equation is generally considered capable of providing an adequate fit for unimodal materials (Leong and Rahardjo, 2002).

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However, the bimodal SWCC cannot be described using a unimodal SWCC equation. Thus,

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the presence of two air-entry values is represented by the model of Gitirana Jr. and Fredlund (2004), that incorporates the bimodal behavior in its equation. Other equations have been

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proposed for bimodal soils, and may also be used for tropical soils (Pham and Fredlund, 2008; Gould et al., 2012; Satyanaga et al., 2013; Li et al. 2014; Wijaya and Leong, 2016).

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3.2 Experimental Study of the Unsaturated Resilient Behavior

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Table 5 shows the obtained results for the specimen preparation and dynamic triaxial tests; nine specimens were analyzed for subgrade 1 and eight specimens for subgrade 2.

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During the water content changes, negligible volume change was observed for all specimen. Therefore, a constant void ratio was assumed in the computation of the degree of saturation. The values of MR, presented in Table 5, are the average for the last eight load test stages. The complete MR dataset will be used later, and is comprised of 198 determinations for the multiple loading stage conditions. Table 5 shows that uniform specimen conditions were obtained during compaction. As shown in Table 5, MR increased with the decrease of the degree of saturation, as expected. Several researchers observed similar behavior, and indicated that MR could be predicted by taking the moisture deviations with respect to the wopt (Edil and Motan, 1979; Phillip and Cameron, 1995; Parreira and Gonçalves, 2000; Khoury and Zaman, 2004; Khoury et al., 2009a; Khoury et al., 2011; Pérez-García et al., 2015). The MR of several

Journal Pre-proof specimens prepared in the wet condition could not be determined, because they failed at the beginning of the test, before the end of the second 500-cycle confinement phase. These results indicate that both soils are moisture-sensitive materials that do not perform satisfactorily in excessively wet conditions.

Compaction

Triaxial tests

Specimen

d (g/cm3)

e (-)

DC (%)

wi (%)

Si (%)

w (%)

w-wopt (%)

S (%)

MR (MPa)

Lateritic (SUB1)

1 2 3 4 5 6 7 8 9

1.700 1.700 1.690 1.710 1.700 1.700 1.710 1.730 1.740

0.590 0.588 0.596 0.583 0.592 0.588 0.575 0.557 0.554

98.7 98.8 98.3 99.2 98.6 98.8 99.6 100.8 100.9

19.0 18.5 18.9 18.0 18.7 18.9 18.8 18.8 18.5

87.0 85.1 85.7 83.4 85.5 86.9 88.3 90.9 90.1

12.9 13.7 14.3 15.6 16.1 16.9 19.7 19.7 19.8

-4.5 -3.8 -3.2 -1.9 -1.4 -0.6 2.2 2.2 2.3

59.4 62.7 64.7 72.1 73.4 77.5 92.5 95.4 96.2

768 725 836 430 356 279 nd nd nd

Non-lateritic (SUB2)

10 11 12 13 14 15 16 17

1.700 1.700 1.700 1.700 1.710 1.700 1.710 1.700

0.566 0.567 0.564 0.568 0.557 0.567 0.559 0.57

94.4 94.3 94.4 94.2 94.9 94.3 94.7 94.1

13.8 13.8 13.8 13.8 13.5 13.6 13.8 14.1

64.8 64.7 65.0 64.4 64.2 63.6 65.8 65.8

9.9 10.2 10.8 11.1 11.6 15.7 16.2 16.4

-3.5 -3.2 -2.5 -2.3 -1.7 2.3 2.9 3.0

46.5 47.7 51.1 51.9 55.6 73.6 77.2 76.5

160 138 156 140 135 nd nd nd

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Material

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Notation: nd = not determined, d = dry density, DC = degree of compaction, w = water content, e = void ratio, w-wopt = deviation from the optimum water content, S = degree of saturation, MR = resilient modulus. Table 5. Summary of specimens’ parameters and MR results.

The lateritic SUB1 specimens have degrees of saturation ranging from 59.4 to 77.5%, which correspond to matric suction values from 5.9 to 71 kPa, approximately. The non-lateritic SUB2 specimens presented degrees of saturation ranging from 46.5 to 55.6%, which correspond to matric suction values from 69 to 120 kPa, approximately. Relatively similar matric suction ranges of 65 and 51 kPa were obtained for both materials. Yet, these comparable matric suction changes produced significantly different effects in terms of MR, which ranged from 279 to 768 MPa for the lateritic material, and from 135 MPa to 160 MPa for the non-lateritic subbase soil.

Journal Pre-proof The MR of lateritic soils is commonly found to be highly sensitive to changes in water content and matric suction (Kim and Kim, 2007; George et al., 2009; Kumar and George, 2018). The difference between the SWCC’s of the lateritic and non-lateritic soils may explain the observed behavior. For the lateritic soil, water content changes, imposed around and near the optimum water content, result in significant changes in terms of the first desaturation branch, which corresponds to the macropores. The mechanical behavior of the bimodal lateritic soils is largely controlled by variations in the state of macropores, which are formed between clay aggregates and silt-sized particles held together by clay bridges.

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These clay bridges are in a meta-stable condition, that is highly sensitive to water content

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changes (Pereira et al., 2005).

It is important to note that an experimental program with different soil types and

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degrees of laterization is necessary to further extend these findings. In addition to the

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influence of matric suction, the initial water content of the sample and the wetting or drying trajectories imposed also affect the MR values of tropical soils (Khoury et al., 2009b; Ceratti

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et al., 2004). The current experimental program was purposely designed to avoid drying-wetting cycles or multiple compaction conditions, that would produce an excessive

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number of behavioral features.

Correlation analyses were carried out between MR and the testing state variables,

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using the Pearson correlation coefficient and the Spearman’s rank-order correlation. The identification criteria for significant correlations vary among different fields, with 0.5 or

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higher and 0.6 or higher being considered moderate correlation factors in the areas of Psychology (Dancey and Reidy, 2007) and Medicine (Chan, 2003), respectively. The interpretation of correlation coefficients that fall in the interval between 0.1 and 0.9 require careful interpretation. However, the values below 0.1 and above 0.9 are generally considered to indicate the absence of correlation and strong correlation, respectively (Schober et al., 2018). In certain fields, like Soil Science, the analysis of correlation factors is associated with the analysis of the expected behavior for each variable. In this case, if the expected standard behavior is observed, then strong correlations may be recognized even when the correlation coefficient is relatively low (Kozak et al., 2012). Table 6 shows that the MR values of both soils presented high correlation coefficients

Journal Pre-proof with the variable associated with the water content: matric suction (m), degree of saturation (S), and moisture deviation (w – wopt). Therefore, the SWCC must be of paramount importance for the modeling of MR. It is also important to note that the effects of the variables associated with the water content are generally more significant than the effects of the confining and deviator stresses.

d (MPa)

0.17

0.33

d/3 (-)

0.12

0.00

(MPa)

0.21

0.61

(MPa)

0.17

0.33

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3 (MPa)

Spearman Lateritic Non-lateritic (SUB1) (SUB2) 0.79 0.21

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Pearson Lateritic Non-lateritic (SUB1) (SUB2) 0.19 0.76

Variables

m-GF (kPa)

0.77

m-FX (kPa)

0.89

e (-)

0.56

S (%)

-0.87

w-wopt (%)

-0.88

0.27

0.18

0.00

0.24

1.00

0.21

0.62

0.61

0.86

0.27

0.61

0.86

0.39

-0.02

0.54

0.37

-0.69

-0.86

0.35

-0.86

0.37

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0.21

-0.70

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Notation: 3 = confining stress, d = deviator stress, bulk stress, octahedral shear stress, m-GF = matric suction from the Gitirana and Fredlund (2004) model, m-FX = matric suctions from the Fredlund and Xing (1994) model, e = void ratio, S = degree of saturation, w-wopt = deviation from optimum water content. Table 6. Summary of correlations analysis

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In terms of total stress variables, the non-lateritic soil has a better correlation with the confining and deviator stresses than the lateritic soil. Such high correlations are typical for coarse materials (Hicks and Monismith, 1971). Although the lateritic soil presents a better correlation with the same stress variables, the correlation values are also similar for the other stress variables. This fact may indicate the transition state between the sandy (SUB-2) and the clayey soil (SUB-1), that is more dependent on the deviator and octahedral shear stress variables. 3.3 Evaluation of Literature Models The performance of the eight models, presented in Table 2, have been evaluated for the lateritic and non-lateritic subgrade materials. The three first models (MR1, MR2, and

Journal Pre-proof MR3) have been analyzed for historical reasons, as they only consider one stress state variable and have limited capabilities. The models MR4 and MR5 combine the effects of the compression and shearing stress states, but disregard the effect of matric suction or water content. The model MR5, proposed by Ara-Eres (2004), is particularly relevant, because it has been widely used. Finally, models MR6, MR7, and MR8 introduce the effect of matric suction or water content. The model MR7, presented by Khoury et al. (2009a), is somewhat comparable to the model presented by Ng et al. (2013). Figure 2 shows best-fit results for the first three models. Upon first inspection, the

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experimental data presents significant dispersion, when related to each of the stress

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variables, indicating that none of these stress variables can, by itself, fully describe the resilient behavior of the materials. The dispersion observed is significantly lower for the

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non-lateritic soil (SUB2), when considering its correlation with bulk and confining stress.

resilient behavior of the SUB2 material.

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This reduced dispersion indicates that, bulk and confining stresses play a greater role in the

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Figure 3 presents best-fit results for the models MR5, MR6, and MR8. The MR5 model produced a poor fit to the MR data for the SUB1 material, and a deficient but relatively

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superior fit for the non-lateritic soil, SUB2. This indicates that the effect of matric suction or water content on the MR of the lateritic soil could be considerable. The modeling exercises,

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using equations MR6 and MR8, confirm that finding. The water content and matric suction

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effects are predominant over the other stress state variable. Table 7 shows the statistical results for the regression exercises using the eight models from Table 2. Despite the differences between the methods of analysis, all of the adopted criteria presented agreement regarding the best models for each subgrade material. The residual sum of squares (RSS) offers a measurement of the discrepancy between the model and the observed data. For the lateritic subgrade, the smallest error was found for model 8, 7, and 6. The “classic” models (MR1 to MR5) do not consider the influence of water content or related variables on MR and as a result, perform poorly. However, for the non-lateritic subgrade, most of the classic models presented superior performance. This finding can be explained by the correlation analyses presented in the previous section, which has shown that the non-lateritic soil is more affected by the confining and bulk stresses. The

Journal Pre-proof poor performance of the MR3 model is corroborated by the lowest correlation between M R

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and deviator stress. All these findings are confirmed by the coefficient of determination, R2.

Figure 2. Best fit-analyses using models: (a) MR1 for SUB1; (b) MR1 for SUB2; (c) MR2 for SUB1; (d) MR2 for SUB2; (e) MR3 for SUB1; (f) MR3 for SUB2.

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Figure 3. Best fit-analyses using: (a) model MR5 for SUB1; (b) model MR5 for SUB2; (c) model MR6 for SUB1; (d) model MR6 for SUB2; (e) model MR8 for SUB1; (f) model MR8 for SUB2.

Journal Pre-proof R²

Adj. R²

AIC

BIC

Diff BIC

2.72×10

6

0.05

0.04

561.68

566.96

70.69

MR2

2.77×10

6

0.04

0.02

562.49

567.78

71.51

MR3

2.74×106

0.05

0.03

562.07

567.36

71.08

MR4

2.72×10

6

0.06

0.02

563.92

570.78

74.50

2.72×10

6

0.06

0.02

563.97

570.83

74.56

1.20×10

6

0.58

0.57

522.10

528.95

32.68

MR7

1.21×10

6

0.58

0.53

530.55

541.47

45.19

MR8

6.31×105

0.78

0.77

489.41

496.27

-

MR1

3.88×10

4

0.42

0.41

299.22

303.89

17.76

MR2

2.75×104

0.59

0.58

284.40

289.07

2.93

MR3

5.52×10

4

0.18

0.16

314.35

319.02

32.89

2.75×10

4

0.59

0.57

286.82

292.81

6.68

2.35×10

4

0.65

0.63

280.14

286.14

-

3.27×10

4

0.51

0.49

294.27

300.26

14.13

MR1

Lateritic (SUB1)

MR5 MR6

Non-lateriti c (SUB2)

MR4 MR5 MR6 MR7

Did not converge

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RSS

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Model ID (Table 2)

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Soil

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MR8 3.31×104 0.51 0.48 294.85 300.85 14.71 Note: RSS= residual sum of squares; R²= coefficient of determination; Adj. R²= Adjusted coefficient of determination; AIC= Akaike Information Criterion; BIC= Schwarz Bayesian Criterion; Diff. BIC= Difference between Schwarz Bayesian Criterion with best fit.

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Table 7. Summary of the statistical analysis of literature models.

The values of Adj. R2 include a penalty proportional to the number of fitting

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parameters. For the lateritic soil, the superior performance of model MR8 is augmented when compared to MR7, because the later model contains six fitting parameters. These

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findings are largely confirmed by AIC and BIC. Table 8 also presents the difference between BIC indices for each model and for the best model (i.e., Diff BIC). Diff BIC values less than 2.00 result in a non-conclusive test response; values between 2.00 and 10.00 indicate an inconclusive possibility that the smaller BIC model is correct; and values greater than 10.00 indicate a decisive conclusion. As a result, the statistical analyses confirm that MR8 is the best model for the lateritic soil. Regarding the non-lateritic soil, it is interesting to note that the model MR5 did not converge, which may be attributed to the high number of fitting parameters. The models MR6 and MR8 presented an insufficient performance, with Adj. R2 of 0.49 and 0.48, respectively. These models were affected by the deviator stress term, that bears low

Journal Pre-proof correlation with MR of coarse materials. Finally, according to the AIC and BIC criteria, the best model for the non-lateritic soil was the model MR5, followed by models MR2 and MR4. However, this finding is inconclusive, because Diff BIC for MR2 and MR4 varied from 2.00 to 10.00. 3.4 Development of New Models for the Resilient Modulus Sauer and Monismith (1968), Edris and Lytton (1976), Fredlund et al. (1977), Edil and Motan. (1979), and Han and Vanapalli (2016a) discussed the importance of

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incorporating water content in the constitutive models, allowing a rational prediction of the

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relationship between MR and matric suction. The analysis of the literature models presented in the previous section showed that, the models that incorporate the water content as an

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independent variable, produce the best results. Besides, it was observed that the presence of a total stress variable is required, but the deviator stress may impair the model depending on

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the soil type. Based on the results obtained in the previous section, the model MR8, proposed

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by Pérez-García et al. (2015), was established as the basis for a series of new equations, that are presented in Table 8. These equations offer a series of combinations of confining and

Variables

Fitting Parameters

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ID

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deviator stresses, matric suction, water content, and degree of saturation.

Equation

FRG1

3 ; d ; m

k1 ; k 2 ; k3 ; k 4

MR = e

FRG2

3 ; w

k1 ; k 2 ; k3

MR = e 1

FRG3

3 ; d ; w

k1 ; k 2 ; k3 ; k 4

MR = e 1

FRG4

3 ; m ; w

k1 ; k 2 ; k3 ; k 4

MR = e 1

FRG5

3 ; S

k1 ; k 2 ; k3

MR = e 1

FRG6

3 ; m

k1 ; k 2 ; k3

MR = e 1

FRG7

3 ; d ; m ; w

k1 ; k 2 ; k3 ; k 4

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



k1  k2 w wopt



k  k2 w wopt



k3



(13)

3

3

k  k2 w wopt

k4

  k3 k4 m 3

k

(15) (16)

3 3 k

 w wopt k1  k2    d 

(14)

d

3 3

k  k2 m

MR = e

m

 d  4   (12)  3  

  k3 



k  k2 w wopt

k  k2 S

k

k3

   

(17)

 m 3 3 4 k

k

(18)

Note: ID = identification, 3 = confining stress, d = deviator stress, m = matric suction, w-wopt = deviation from the optimum water content. Table 8. Proposed models for the resilient modulus.

Journal Pre-proof The FRG1 model incorporates matric suction to the equation proposed by Perez-Garcia et al. (2015), as a new independent stress state variable. The other models introduce more significant changes to the stress state and moisture variables. For the FRG2 to FRG7 equations, the confining stress was maintained as a primary variable, because of the good correlation with the non-lateritic soil. For models FRG1 to FRG4, the water content deviation from wopt was used as the primary variable related to the soil moisture. Finaly, the FRG5 and FRG7 models proposed new approaches, such as the use of degree of saturation, matric suction, and the rate of change of water content deviation from wopt with respect to the

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deviator stress. The models FRG2, FRG3, FRG5, and FRG6 have only one parameter related

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to the soil moisture state, while the others have two parameters.

Table 9 shows the statistical regression results for the seven equations proposed

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herein. Superior performance is observed, when compared to the base model, MR8,

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presented by Perez-Garcia et al. (2015), with an Adj. R² of 0.77 and 0.48. This represents an improvement of 20.8% and 75.0% with respect to the FRG4 model, for the lateritic (SUB1)

Soil

Model ID

RSS

3.57×10

5

n

AIC

BIC

Diff BIC

0.87

4

462.88 471.21

1.44

6.17×10

0.79

0.78

3

488.35 495.2

25.44

6.13×10

5

0.79

0.77

4

490.41 498.74

28.97

3.47×10

5

0.88

0.87

4

461.44 469.77

-

FRG5

5.53×10

5

0.81

0.80

3

482.7 489.56

19.79

FRG6

1.43×105 0.50

0.48

3

531.32 538.18

68.42

FRG3

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FRG4

FRG7 FRG1 FRG2 FRG3

Non-lateritic (SUB2)

Adj. R²

0.88

FRG2 Lateritic (SUB1)

R²

5

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FRG1

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and non-lateritic (SUB2) soils, respectively.

FRG4 FRG5 FRG6

1.17×10

5

0.59

0.57

4

523.58 531.9

62.14

2.63×10

4

0.61

0.58

4

287.46 294.64

42.63

1.46×10

4

0.78

0.77

3

259.57 265.57

13.55

1.34×10

4

0.80

0.79

4

258.37 265.55

13.54

1.08×10

4

0.84

0.83

4

249.23 256.41

4.40

1.51×10

4

0.77

0.76

3

261.19 267.18

15.17

1.44×10

4

0.78

0.77

3

259.15 265.15

13.13

4

FRG7 9.75×10 0.85 0.84 4 244.83 252.01 Notation: RSS = residual sum of squares; R² = coefficient of variation; Adj. R² = Adjusted coefficient of variation; n = number of parameters; AIC = Akaike Information Criterion; BIC = Schwarz Bayesian Criterion; Diff. BIC = Difference between Schwarz Bayesian Criterion with best fit. Table 9. Summary of statistical analysis for proposed models.

Journal Pre-proof Figure 4 shows the best-fit parameters and the resulting fit for materials SUB1 and SUB2, for the best performing models. For the lateritic soil, the best performing equations were FRG1 and FRG4, with an Adj. R² of 0.87. Both models use matric suction as an independent stress state variable. According to the BIC values obtained, the comparison between the FRG1 and FRG4 models’ performances was inconclusive, because the difference was smaller than 2.00. The non-lateritic material presented two equations with similarly good performances, FRG7 and FRG4, with Adj. R² of 0.85 and 0.84, respectively. However, the FRG7 model presented better results according to the AIC and BIC values.

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The three best models, FRG1, FRG4, and FRG7 bear some similarities, such as four fitting parameters, two variables related to the moisture state, and a total stress variable. The

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moisture variation was introduced using an exponential relationship, while the matric

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suction follows a power law.

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Most of the equations for the non-lateritic material presented Adj. R² values above 0.75; the exception was FRG1, with a relatively low value of 0.58. The results show that the

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inclusion of two variables associated with the moisture state improves the model and produce Diff BIC values that are greater than 10. The models FRG3 and FRG7 also include

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the deviator stress as a variable associated, but the corresponding fitting parameter tends to zero and neutralize the influence of this variable.

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In summary, the results obtained for the set of MR models presented herein indicate

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that the best-performing equation has the following general format:



k  k2 w wopt

MR = e 1



k3 m

4 k

(19)

where w-wopt = the deviation from the optimum water content, m = matric suction, and  = the total stress state variable that has the highest correlation with MR. While the FRG4 model performed adequately for the lateritic and non-lateritic materials, Equation (19) provides a more general modeling procedure, which must be based on a preliminary correlation analysis, followed by the selection of the ideal total stress state variable, such as the confining stress (3), the deviator stress (d), the bulk stress (b), or the octahedral shear stress ().

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Figure 4. Best fit-analyses using models: (a) FRG1 for SUB1; (b) FRG1 for SUB2; (c) FRG4 forSUB1; (d) FRG4 for SUB2; (e) FRG7 for SUB1; (f) FRG7 for SUB2.

3.5 Model Validation To validate the proposed model, the MR data published by Rahman and Tarefder

Journal Pre-proof (2015) and Han and Vanapalli (2016), was analyzed. First, a correlation analysis was performed to select the total stress variables to be used in Eq. 19. Table 10 presents the correlation results and the selected total stress state variable. The octahedral shear stress was selected for the Rahman and Tarefder (2015) soils, and the bulk stress was selected for the Han and Vanapalli (2016) materials.

Rahman and Tarefder (2015)

TSC

KLC

IHT

OLC

NM (CL)

NM (CH)

0.65

0.22

0.09

0.12

0.00

0.00

0.21

0.16

0.12

0.05

0.68

0.27

0.12

0.13

0.21

0.16

0.12

0.05

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3  d  

Han and Vanapalli (2016)

0.22

0.23

0.12

0.11

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Stress state variable (MPa)

0.22

0.23

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 (Eq. 19)       Note:  = bulk stress;  = octahedral shear stress; TSC= silty clay from Toronto; KLC = lean clay from Kincardine, IHT = glacial till from Indian Head; OLC = marine clay from Ottawa; NM(CL) = New Mexico lean clay; NM(CH) = New Mexico fat clay. Table 10. MR-Stress correlation analysis for Rahman and Tarefder (2015) and Han and Vanapali (2016)

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soils.

Figure 5 presents some of the modeling results, obtained for the TSC and CH soils.

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Table 11 summarizes the results obtained using the FRG4 (Eq. 15) model and, the general

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model presented by Eq. 19.

Figure 5. Correlation for: (a) TSC soil; (b) CH soil.

Journal Pre-proof Reference

Han and Vanapalli (2016b) FRG4 (Eq. 15) Rahman and Tarefder (2015)

Adj. FRG4 Han and Vanapalli (2016b) (Eq. 19) Rahman and Tarefder (2015)

ID

k1

k2

k3

k4

Adj. R²

TSC KLC

2.99 2.98

0.11 0.34

0.02 0.01

0.24 0.2

0.88 0.91

IHT

35.41

0.45

0.06

-9.5

0.98

OLC

3.82

0.63

0.03

0.12

0.92

CL CH TSC KLC

9.85 4.50 1.93 1.77

0.34 0.19 0.11 0.34

-0.31 0.24 0.02 0.01

-0.15 0 0.38 0.39

0.99 0.94 0.93 0.94

IHT

5.69

0.44

0.06

-0.38

0.98

OLC

3.10

0.63

0.03

0.23

0.93

CL

9.85

0.34

-0.31

-0.15

0.99

of

Model

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CH 4.99 0.19 0.23 -0.13 0.99 Notation: ID = soil identification; k1, k2, k3, k4 = model parameters; Adj. R² = adjusted coefficient of determination.

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Table 11. Parameters and summary of statistical analysis for model validation.

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The FRG4 (Eq. 15) model provided excellent results for all soils. The obtained Adj. R² values ranged from 0.88 to 0.92 for the Han and Vanapalli (2016) soils, and from 0.94 to

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0.99 for the Rahman and Tarefder (2015) soils. However, the general formulation from Eq. 19 resulted in significant improvements, with Adj. R² values ranging between 0.93 and 0.98

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and Tarefder (2015).

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for the Han and Vanapalli (2016) soils, and with 0.99 for the two soils presented by Rahman

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4 Summary and Conclusions This paper presented a study of the resilient behavior of two tropical subgrade soils from Brazil and introduced a new MR model that considers the influence of unsaturated parameters. The study was based on laboratory tests, the evaluation of models from the literature, and statistical analyses. The laboratory tests showed that water content deviations from the optimum water content strongly influenced the MR values. The effect was more significant for the fine lateritic soil than for the non-lateritic soil. Yet, the lateritic soil presented minimum MR values that were higher than the minimum values from the saprolitic soil, showing that even under the imposed water content variations the lateritic soil presented better resilient

Journal Pre-proof behavior. The correlation analysis by Spearman and Pearson confirmed this behavior, and indicated that MR is highly dependent on variables related to the moisture regime, such as matric suction, degree of saturation, and water content variation around the optimum condition. The classic models from Hicks (1970), Svenson (1980), Macêdo (1996), and ARA Inc. (2004), that do not incorporate the parameters related to water content, presented relatively poor performance under variable water content conditions. The models from Parreira and Gonçalves (2000), Khoury et al. (2009a), and Pérez-García et al. (2015), that incorporate water content or matric suction variables, also presented some limitations.

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A family of new resilient modulus equations was proposed, based on two types of

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modifications to the Pérez-García et al. (2015) model: (a) replacement of the variable related to unsaturated behavior or incorporation of a second variable, such as matric suction or

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degree of saturation, and (b) replacement of total stress variable. Regression analyses

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indicated that the proposed modifications produced superior fitting capabilities. The three best models presented four fitting parameters, two unsaturated state variables, and one total

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stress variable. Based on these findings, a model was presented (Eq. 19) to account for the main behavior aspects of the lateritic and non-lateritic soils studied. This model was further

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evaluated using data from two other studies, with results that indicate superior fitting capabilities when compared to other models from the literature.

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The practical impact of the proposed MR models should be further evaluated, by assessing the variation of pavement water content under different construction standards and

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drainage conditions. It is also desirable to assess the performance of the proposed model considering more soils, with varying degrees of laterization. Such additional studies should aid in the introduction of the model in a mechanist method for pavement design.

Acknowledgements The authors are thankful for the funds provided by the Brazilian Petroleum Corporation (Petrobras) and Brazilian Funding Agency for Studies and Projects (FINEP).

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Journal Pre-proof Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Journal Pre-proof Highlights

Tropical soils as subgrade of pavements;

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Moisture and matric suction influence on the resilient behavior;



Laboratory tests, model’s evaluation, and statistical analyses;



The results can be applied for many types of soils.

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